Subgroups — C₅₃×#62748 #27270260

Order 13568.

7280 conjugacy classes of subgroups.

The subgroup lattice has 1684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3562	C₂	1	4	yes	maximal, complemented
2	C₅₃×#3561	C₂	1	2	yes	maximal, complemented
3	C₅₃×#3560	C₂	1	4	yes	maximal, complemented
4	C₅₃×#3559	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3558	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3558	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3554	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3552	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3546	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3543	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3537	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3536	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3534	C₂	1	4	yes	maximal, complemented
14	C₅₃×#3529	C₂	1	4	yes	maximal, complemented
15	C₅₃×#3481	C₂	1	4	yes	maximal, complemented
16	C₅₃×#3480	C₂	1	2	yes	maximal, complemented
17	D₄×#41×C₅₃	C₂	1	4	yes	maximal, complemented
18	D₄×#41×C₅₃	C₂	1	2	yes	maximal, complemented
19	C₅₃×#3460	C₂	1	4	yes	maximal, complemented
20	C₅₃×#3459	C₂	1	4	yes	maximal, complemented
21	C₅₃×#3455	C₂	1	2	yes	maximal, complemented
22	C₅₃×#3449	C₂	1	2	yes	maximal, complemented
23	C₅₃×#3444	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₅₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂×C₅₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂²×#41×C₅₃	C₂²	1	4	yes	complemented
27	C₂²×#41×C₅₃	C₂²	1	2	yes	complemented
28	C₅₃×#563	C₂²	1	8	yes	complemented
29	C₅₃×#563	C₂²	1	4	yes	complemented
30	C₅₃×#562	C₂²	1	8	yes	complemented
31	C₅₃×#562	C₂²	1	8	yes	complemented
32	C₅₃×#562	C₂²	1	4	yes	complemented
33	C₅₃×#562	C₂²	1	4	yes	complemented
34	C₅₃×H(3,𝔽₄)	C₂²	1	4	yes	complemented
35	C₅₃×#560	C₂²	1	8	yes	complemented
36	C₅₃×#560	C₂²	1	8	yes	complemented
37	C₅₃×#560	C₂²	1	8	yes	complemented
38	C₅₃×#559	C₂²	1	2	yes	complemented
39	C₅₃×#559	C₂²	1	4	yes	complemented
40	C₅₃×#559	C₂²	1	4	yes	complemented
41	C₅₃×#557	C₂²	1	2	yes	complemented
42	C₅₃×#556	C₂²	1	2	yes	complemented
43	C₅₃×#556	C₂²	1	4	yes	complemented
44	C₅₃×#554	C₂²	1	4	yes	complemented
45	C₅₃×#554	C₂²	1	4	yes	complemented
46	C₅₃×#553	C₂²	1	8	yes	complemented
47	C₅₃×#553	C₂²	1	4	yes	complemented
48	C₅₃×#553	C₂²	1	4	yes	complemented
49	C₅₃×#553	C₂²	1	4	yes	complemented
50	C₅₃×#553	C₂²	1	8	yes	complemented
51	C₅₃×#551	C₂²	1	8	yes	complemented
52	C₅₃×#551	C₂²	1	8	yes	complemented
53	C₅₃×#550	C₂²	1	2	yes	complemented
54	C₅₃×#550	C₂²	1	4	yes	complemented
55	C₅₃×#550	C₂²	1	2	yes	complemented
56	D₄×Q₈×C₅₃	C₂²	1	2	yes	complemented
57	D₄×Q₈×C₅₃	C₂²	1	4	yes	complemented
58	C₅₃×#548	C₂²	1	4	yes	complemented
59	C₅₃×#548	C₂²	1	4	yes	complemented
60	C₅₃×#548	C₂²	1	4	yes	complemented
61	C₅₃×#548	C₂²	1	4	yes	complemented
62	C₅₃×#547	C₂²	1	4	yes	complemented
63	C₅₃×#547	C₂²	1	2	yes	complemented
64	C₅₃×#547	C₂²	1	4	yes	complemented
65	C₅₃×#547	C₂²	1	8	yes	complemented
66	C₅₃×#546	C₂²	1	8	yes	complemented
67	C₅₃×#546	C₂²	1	8	yes	complemented
68	C₅₃×#546	C₂²	1	4	yes	complemented
69	C₅₃×#546	C₂²	1	4	yes	complemented
70	C₅₃×#546	C₂²	1	8	yes	complemented
71	C₅₃×#546	C₂²	1	4	yes	complemented
72	C₅₃×#546	C₂²	1	8	yes	complemented
73	C₅₃×#546	C₂²	1	4	yes	complemented
74	C₅₃×#546	C₂²	1	4	yes	complemented
75	D₄²×C₅₃	C₂²	1	8	yes	complemented
76	D₄²×C₅₃	C₂²	1	4	yes	complemented
77	D₄²×C₅₃	C₂²	1	2	yes	complemented
78	D₄²×C₅₃	C₂²	1	4	yes	complemented
79	D₄²×C₅₃	C₂²	1	4	yes	complemented
80	C₅₃×#544	C₂²	1	4	yes	complemented
81	C₅₃×#543	C₂²	1	4	yes	complemented
82	C₅₃×#542	C₂²	1	4	yes	complemented
83	C₅₃×#542	C₂²	1	4	yes	complemented
84	C₅₃×#542	C₂²	1	4	yes	complemented
85	C₅₃×#542	C₂²	1	4	yes	complemented
86	C₅₃×#542	C₂²	1	8	yes	complemented
87	C₅₃×#541	C₂²	1	4	yes	complemented
88	C₅₃×#540	C₂²	1	4	yes	complemented
89	C₅₃×#540	C₂²	1	8	yes	complemented
90	C₅₃×#540	C₂²	1	4	yes	complemented
91	C₅₃×#540	C₂²	1	4	yes	complemented
92	C₅₃×#539	C₂²	1	4	yes	complemented
93	C₅₃×#539	C₂²	1	4	yes	complemented
94	C₅₃×#539	C₂²	1	8	yes	complemented
95	C₅₃×#539	C₂²	1	8	yes	complemented
96	C₅₃×#539	C₂²	1	8	yes	complemented
97	C₅₃×#538	C₂²	1	4	yes	complemented
98	C₅₃×#538	C₂²	1	4	yes	complemented
99	C₅₃×#538	C₂²	1	4	yes	complemented
100	C₅₃×#538	C₂²	1	4	yes	complemented
101	C₅₃×#538	C₂²	1	8	yes	complemented
102	C₅₃×#538	C₂²	1	8	yes	complemented
103	C₅₃×#538	C₂²	1	8	yes	complemented
104	C₅₃×#538	C₂²	1	8	yes	complemented
105	C₅₃×#537	C₂²	1	4	yes	complemented
106	C₅₃×#537	C₂²	1	4	yes	complemented
107	C₅₃×#537	C₂²	1	4	yes	complemented
108	C₅₃×#536	C₂²	1	4	yes	complemented
109	C₅₃×#536	C₂²	1	4	yes	complemented
110	C₅₃×#535	C₂²	1	4	yes	complemented
111	C₅₃×#535	C₂²	1	4	yes	complemented
112	C₅₃×#535	C₂²	1	4	yes	complemented
113	C₅₃×#535	C₂²	1	4	yes	complemented
114	C₅₃×#534	C₂²	1	4	yes	complemented
115	C₅₃×#534	C₂²	1	4	yes	complemented
116	C₅₃×#534	C₂²	1	8	yes	complemented
117	C₅₃×#534	C₂²	1	4	yes	complemented
118	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
119	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#532	C₂²	1	2	yes	complemented
123	C₅₃×#532	C₂²	1	4	yes	complemented
124	C₅₃×#532	C₂²	1	2	yes	complemented
125	C₅₃×#532	C₂²	1	4	yes	complemented
126	C₅₃×#532	C₂²	1	8	yes	complemented
127	C₅₃×#532	C₂²	1	2	yes	complemented
128	C₅₃×#532	C₂²	1	2	yes	complemented
129	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#532	C₂²	1	2	yes	complemented
131	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#532	C₂²	1	2	yes	complemented
133	C₅₃×#532	C₂²	1	2	yes	complemented
134	C₅₃×#532	C₂²	1	2	yes	complemented
135	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
136	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic, complemented
137	C₅₃×#529	C₂²	1	8	yes	complemented
138	C₅₃×#529	C₂²	1	8	yes	complemented
139	C₅₃×#529	C₂²	1	2	yes	complemented
140	C₅₃×#529	C₂²	1	2	yes	complemented
141	C₅₃×#529	C₂²	1	8	yes	complemented
142	C₅₃×#529	C₂²	1	2	yes	complemented
143	C₅₃×#529	C₂²	1	4	yes	complemented
144	C₅₃×#529	C₂²	1	2	yes	complemented
145	C₅₃×#529	C₂²	1	2	yes	complemented
146	C₅₃×#529	C₂²	1	2	yes	complemented
147	C₅₃×#529	C₂²	1	2	yes	complemented
148	C₅₃×#529	C₂²	1	2	yes	complemented
149	C₅₃×#529	C₂²	1	2	yes	complemented
150	C₅₃×#529	C₂²	1	2	yes	complemented
151	C₅₃×#529	C₂²	1	2	yes	complemented
152	C₅₃×#529	C₂²	1	2	yes	complemented
153	C₅₃×#529	C₂²	1	2	yes	complemented
154	C₅₃×#529	C₂²	1	2	yes	complemented
155	C₂×#126×C₅₃	C₂²	1	2	yes	complemented
156	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
157	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
158	C₂×#124×C₅₃	C₂²	1	2	yes	complemented
159	C₅₃×#525	C₂²	1	8	yes	complemented
160	C₅₃×#525	C₂²	1	8	yes	complemented
161	C₅₃×#525	C₂²	1	4	yes	complemented
162	C₅₃×#525	C₂²	1	8	yes	complemented
163	C₅₃×#525	C₂²	1	8	yes	complemented
164	C₅₃×#525	C₂²	1	8	yes	complemented
165	C₅₃×#525	C₂²	1	2	yes	complemented
166	C₅₃×#525	C₂²	1	2	yes	complemented
167	C₅₃×#525	C₂²	1	2	yes	complemented
168	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
169	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
170	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
171	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
172	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
173	C₄×#41×C₅₃	C₂²	1	4	yes	complemented
174	C₄×#41×C₅₃	C₂²	1	2	yes	complemented
175	C₄×#41×C₅₃	C₂²	1	4	yes	complemented
176	C₄×#41×C₅₃	C₂²	1	2	yes	complemented
177	C₄×#41×C₅₃	C₂²	1	2	yes	complemented
178	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
179	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
180	C₂×C₄×D₄×C₅₃	C₂²	1	8	yes	complemented
181	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	complemented
182	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
183	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
184	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
185	C₂×#117×C₅₃	C₂²	1	2	yes	complemented
186	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
187	C₂×#41×C₅₃	—	4	16	no	—
188	C₂×#41×C₅₃	—	4	8	no	—
189	C₂×#41×C₅₃	C₂³	1	4	yes	—
190	C₂×#41×C₅₃	C₂³	1	2	yes	—
191	C₂×#41×C₅₃	C₂³	1	2	yes	—
192	C₂×#41×C₅₃	C₂³	1	2	yes	—
193	C₂×#41×C₅₃	C₂³	1	4	yes	—
194	C₂×#41×C₅₃	C₂³	1	8	yes	—
195	C₂×#41×C₅₃	C₂³	1	4	yes	—
196	C₂×#41×C₅₃	C₂³	1	4	yes	—
197	C₂×#41×C₅₃	C₂³	1	4	yes	—
198	C₂×#41×C₅₃	C₂³	1	4	yes	—
199	C₂×#41×C₅₃	C₂³	1	4	yes	—
200	C₂×#41×C₅₃	C₂³	1	8	yes	—
201	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
202	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
203	C₂²×Q₈×C₅₃	C₂³	1	4	yes	—
204	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
205	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
206	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
207	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
208	C₂²×D₄×C₅₃	C₂³	1	8	yes	—
209	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
210	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
211	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
212	C₂²×D₄×C₅₃	C₂³	1	8	yes	—
213	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
214	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
215	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
216	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
217	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
218	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
219	C₂³×C₄×C₅₃	C₂³	1	8	yes	—
220	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
221	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
222	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
223	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
224	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
225	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
226	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
227	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	—
228	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	—
229	C₄⋊Q₈×C₅₃	C₂³	1	8	yes	—
230	#127×C₅₃	C₂³	1	2	yes	—
231	#127×C₅₃	C₂³	1	2	yes	—
232	#127×C₅₃	C₂³	1	2	yes	—
233	#127×C₅₃	C₂³	1	2	yes	—
234	#127×C₅₃	C₂³	1	1	yes	characteristic
235	#127×C₅₃	C₂³	1	4	yes	—
236	#127×C₅₃	C₂³	1	4	yes	—
237	#127×C₅₃	C₂³	1	8	yes	—
238	#126×C₅₃	C₂³	1	4	yes	—
239	#126×C₅₃	C₂³	1	4	yes	—
240	#126×C₅₃	C₂³	1	4	yes	—
241	#126×C₅₃	C₂³	1	4	yes	—
242	#126×C₅₃	C₂³	1	4	yes	—
243	#126×C₅₃	C₂³	1	4	yes	—
244	#126×C₅₃	C₂³	1	8	yes	—
245	#126×C₅₃	C₂³	1	8	yes	—
246	#126×C₅₃	C₂³	1	8	yes	—
247	#126×C₅₃	C₂³	1	8	yes	—
248	#126×C₅₃	C₂³	1	8	yes	—
249	#126×C₅₃	C₂³	1	8	yes	—
250	#126×C₅₃	C₂³	1	8	yes	—
251	#125×C₅₃	C₂³	1	2	yes	—
252	#125×C₅₃	C₂³	1	2	yes	—
253	#125×C₅₃	C₂³	1	2	yes	—
254	#125×C₅₃	C₂³	1	2	yes	—
255	#125×C₅₃	C₂³	1	2	yes	—
256	#125×C₅₃	C₂³	1	2	yes	—
257	#125×C₅₃	C₂³	1	2	yes	—
258	#125×C₅₃	C₂³	1	8	yes	—
259	#125×C₅₃	C₂³	1	8	yes	—
260	#125×C₅₃	C₂³	1	8	yes	—
261	#125×C₅₃	C₂³	1	4	yes	—
262	#124×C₅₃	C₂³	1	2	yes	—
263	#124×C₅₃	C₂³	1	2	yes	—
264	#124×C₅₃	C₂³	1	2	yes	—
265	#124×C₅₃	C₂³	1	2	yes	—
266	#124×C₅₃	C₂³	1	4	yes	—
267	#124×C₅₃	C₂³	1	4	yes	—
268	#124×C₅₃	C₂³	1	4	yes	—
269	#124×C₅₃	C₂³	1	4	yes	—
270	#124×C₅₃	C₂³	1	2	yes	—
271	#124×C₅₃	C₂³	1	2	yes	—
272	#124×C₅₃	C₂³	1	2	yes	—
273	#124×C₅₃	C₂³	1	8	yes	—
274	#124×C₅₃	C₂³	1	4	yes	—
275	#124×C₅₃	C₂³	1	8	yes	—
276	#124×C₅₃	C₂³	1	8	yes	—
277	#124×C₅₃	C₂³	1	4	yes	—
278	#124×C₅₃	C₂³	1	4	yes	—
279	#124×C₅₃	C₂³	1	8	yes	—
280	#124×C₅₃	C₂³	1	8	yes	—
281	#124×C₅₃	C₂³	1	8	yes	—
282	#123×C₅₃	C₂³	1	4	yes	—
283	#123×C₅₃	C₂³	1	4	yes	—
284	#123×C₅₃	C₂³	1	4	yes	—
285	#123×C₅₃	C₂³	1	4	yes	—
286	#123×C₅₃	C₂³	1	4	yes	—
287	#123×C₅₃	C₂³	1	4	yes	—
288	#123×C₅₃	C₂³	1	4	yes	—
289	#123×C₅₃	C₂³	1	8	yes	—
290	#123×C₅₃	C₂³	1	8	yes	—
291	#123×C₅₃	C₂³	1	8	yes	—
292	#123×C₅₃	C₂³	1	8	yes	—
293	#123×C₅₃	C₂³	1	8	yes	—
294	#123×C₅₃	C₂³	1	8	yes	—
295	#123×C₅₃	C₂³	1	8	yes	—
296	#123×C₅₃	C₂³	1	8	yes	—
297	#123×C₅₃	C₂³	1	8	yes	—
298	#123×C₅₃	C₂³	1	8	yes	—
299	#123×C₅₃	C₂³	1	8	yes	—
300	#123×C₅₃	C₂³	1	8	yes	—
301	#123×C₅₃	C₂³	1	8	yes	—
302	#123×C₅₃	C₂³	1	8	yes	—
303	#123×C₅₃	C₂³	1	8	yes	—
304	#123×C₅₃	C₂³	1	8	yes	—
305	#123×C₅₃	C₂³	1	8	yes	—
306	#123×C₅₃	C₂³	1	8	yes	—
307	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
308	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
309	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
310	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
311	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
312	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
313	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
314	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
315	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
316	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
317	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
318	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
319	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
320	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
321	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
322	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
323	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
324	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
325	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
326	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
327	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
328	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
329	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
330	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
331	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
332	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
333	#121×C₅₃	C₂³	1	2	yes	—
334	#121×C₅₃	C₂³	1	2	yes	—
335	#121×C₅₃	C₂³	1	2	yes	—
336	#121×C₅₃	C₂³	1	2	yes	—
337	#121×C₅₃	C₂³	1	4	yes	—
338	#121×C₅₃	C₂³	1	4	yes	—
339	#121×C₅₃	C₂³	1	4	yes	—
340	#121×C₅₃	C₂³	1	4	yes	—
341	#121×C₅₃	C₂³	1	4	yes	—
342	#121×C₅₃	C₂³	1	4	yes	—
343	#121×C₅₃	C₂³	1	4	yes	—
344	#121×C₅₃	C₂³	1	4	yes	—
345	#121×C₅₃	C₂³	1	2	yes	—
346	#121×C₅₃	C₂³	1	2	yes	—
347	#121×C₅₃	C₂³	1	2	yes	—
348	#121×C₅₃	C₂³	1	2	yes	—
349	#121×C₅₃	C₂³	1	2	yes	—
350	#121×C₅₃	C₂³	1	2	yes	—
351	#121×C₅₃	C₂³	1	8	yes	—
352	#121×C₅₃	C₂³	1	8	yes	—
353	#121×C₅₃	C₂³	1	8	yes	—
354	#121×C₅₃	C₂³	1	8	yes	—
355	#121×C₅₃	C₂³	1	8	yes	—
356	#121×C₅₃	C₂³	1	8	yes	—
357	#121×C₅₃	C₂³	1	8	yes	—
358	#121×C₅₃	C₂³	1	8	yes	—
359	#121×C₅₃	C₂³	1	8	yes	—
360	#121×C₅₃	C₂³	1	8	yes	—
361	#121×C₅₃	C₂³	1	4	yes	—
362	#121×C₅₃	C₂³	1	4	yes	—
363	#121×C₅₃	C₂³	1	8	yes	—
364	#121×C₅₃	C₂³	1	8	yes	—
365	#121×C₅₃	C₂³	1	4	yes	—
366	#121×C₅₃	C₂³	1	8	yes	—
367	#121×C₅₃	C₂³	1	8	yes	—
368	#121×C₅₃	C₂³	1	8	yes	—
369	#121×C₅₃	C₂³	1	4	yes	—
370	#121×C₅₃	C₂³	1	8	yes	—
371	#121×C₅₃	C₂³	1	4	yes	—
372	#121×C₅₃	C₂³	1	8	yes	—
373	#121×C₅₃	C₂³	1	8	yes	—
374	#121×C₅₃	C₂³	1	8	yes	—
375	#121×C₅₃	C₂³	1	8	yes	—
376	#120×C₅₃	C₂³	1	4	yes	—
377	#120×C₅₃	C₂³	1	8	yes	—
378	#120×C₅₃	C₂³	1	8	yes	—
379	#120×C₅₃	C₂³	1	8	yes	—
380	#120×C₅₃	C₂³	1	8	yes	—
381	#120×C₅₃	C₂³	1	8	yes	—
382	#120×C₅₃	C₂³	1	8	yes	—
383	#120×C₅₃	C₂³	1	8	yes	—
384	#120×C₅₃	C₂³	1	8	yes	—
385	#120×C₅₃	C₂³	1	8	yes	—
386	#120×C₅₃	C₂³	1	8	yes	—
387	#120×C₅₃	C₂³	1	8	yes	—
388	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
389	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
390	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
391	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
392	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
393	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
394	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
395	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
396	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
397	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
398	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
399	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
400	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
401	C₄×D₄×C₅₃	C₂³	1	4	yes	—
402	C₄×D₄×C₅₃	C₂³	1	2	yes	—
403	C₄×D₄×C₅₃	C₂³	1	4	yes	—
404	C₄×D₄×C₅₃	C₂³	1	4	yes	—
405	C₄×D₄×C₅₃	C₂³	1	2	yes	—
406	C₄×D₄×C₅₃	C₂³	1	8	yes	—
407	C₄×D₄×C₅₃	C₂³	1	8	yes	—
408	C₄×D₄×C₅₃	C₂³	1	4	yes	—
409	C₄×D₄×C₅₃	C₂³	1	4	yes	—
410	C₄×D₄×C₅₃	C₂³	1	4	yes	—
411	C₄×D₄×C₅₃	C₂³	1	8	yes	—
412	C₄×D₄×C₅₃	C₂³	1	4	yes	—
413	C₄×D₄×C₅₃	C₂³	1	4	yes	—
414	C₄×D₄×C₅₃	C₂³	1	2	yes	—
415	C₄×D₄×C₅₃	C₂³	1	2	yes	—
416	C₄×D₄×C₅₃	C₂³	1	4	yes	—
417	C₄×D₄×C₅₃	C₂³	1	4	yes	—
418	C₄×D₄×C₅₃	C₂³	1	4	yes	—
419	C₄×D₄×C₅₃	C₂³	1	4	yes	—
420	C₄×D₄×C₅₃	C₂³	1	4	yes	—
421	C₄×D₄×C₅₃	C₂³	1	8	yes	—
422	C₄×D₄×C₅₃	C₂³	1	8	yes	—
423	C₄×D₄×C₅₃	C₂³	1	8	yes	—
424	C₄×D₄×C₅₃	C₂³	1	8	yes	—
425	C₄×D₄×C₅₃	C₂³	1	4	yes	—
426	C₄×D₄×C₅₃	C₂³	1	4	yes	—
427	C₄×D₄×C₅₃	C₂³	1	8	yes	—
428	C₄×D₄×C₅₃	C₂³	1	2	yes	—
429	C₄×D₄×C₅₃	C₂³	1	8	yes	—
430	C₄×D₄×C₅₃	C₂³	1	2	yes	—
431	C₄×D₄×C₅₃	C₂³	1	4	yes	—
432	C₄×D₄×C₅₃	C₂³	1	4	yes	—
433	C₄×D₄×C₅₃	C₂³	1	4	yes	—
434	C₄×D₄×C₅₃	C₂³	1	4	yes	—
435	C₄×D₄×C₅₃	C₂³	1	4	yes	—
436	C₄×D₄×C₅₃	C₂³	1	2	yes	—
437	C₄×D₄×C₅₃	C₂³	1	2	yes	—
438	C₄×D₄×C₅₃	C₂³	1	2	yes	—
439	C₄×D₄×C₅₃	C₂³	1	2	yes	—
440	C₄×D₄×C₅₃	C₂³	1	8	yes	—
441	C₄×D₄×C₅₃	C₂³	1	8	yes	—
442	C₄×D₄×C₅₃	C₂³	1	8	yes	—
443	C₄×D₄×C₅₃	C₂³	1	4	yes	—
444	C₄×D₄×C₅₃	C₂³	1	4	yes	—
445	C₄×D₄×C₅₃	C₂³	1	4	yes	—
446	#117×C₅₃	C₂³	1	4	yes	—
447	#117×C₅₃	C₂³	1	4	yes	—
448	#117×C₅₃	C₂³	1	4	yes	—
449	#117×C₅₃	C₂³	1	4	yes	—
450	#117×C₅₃	C₂³	1	2	yes	—
451	#117×C₅₃	C₂³	1	8	yes	—
452	#117×C₅₃	C₂³	1	4	yes	—
453	#117×C₅₃	C₂³	1	2	yes	—
454	#117×C₅₃	C₂³	1	2	yes	—
455	#117×C₅₃	C₂³	1	4	yes	—
456	#117×C₅₃	C₂³	1	4	yes	—
457	#117×C₅₃	C₂³	1	4	yes	—
458	#117×C₅₃	C₂³	1	8	yes	—
459	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
460	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
461	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
462	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
463	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
464	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
465	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
466	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	—
467	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
468	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
469	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
470	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
471	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
472	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
473	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
474	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
475	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
476	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
477	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
478	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
479	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
480	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
481	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
482	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
483	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
484	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
485	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
486	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
487	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
488	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
489	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
490	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
491	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
492	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
493	C₂×C₄²×C₅₃	C₂³	1	8	yes	—
494	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
495	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
496	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
497	C₂⁴×C₅₃	C₂⁴	1	8	yes	—
498	#41×C₅₃	—	2	8	no	—
499	#41×C₅₃	—	2	16	no	—
500	#41×C₅₃	—	4	16	no	—
501	#41×C₅₃	—	4	8	no	—
502	#41×C₅₃	—	4	4	no	—
503	#41×C₅₃	—	4	8	no	—
504	#41×C₅₃	—	4	16	no	—
505	#41×C₅₃	—	4	4	no	—
506	#41×C₅₃	—	4	8	no	—
507	#41×C₅₃	—	4	8	no	—
508	#41×C₅₃	—	4	8	no	—
509	#41×C₅₃	—	4	8	no	—
510	C₂×Q₈×C₅₃	—	4	2	no	—
511	C₂×Q₈×C₅₃	—	4	4	no	—
512	C₂×Q₈×C₅₃	—	4	8	no	—
513	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
514	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
515	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
516	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
517	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
518	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
519	C₂×Q₈×C₅₃	C₂⁴	1	8	yes	—
520	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
521	C₂×D₄×C₅₃	—	4	4	no	—
522	C₂×D₄×C₅₃	—	4	2	no	—
523	C₂×D₄×C₅₃	—	4	8	no	—
524	C₂×D₄×C₅₃	—	4	4	no	—
525	C₂×D₄×C₅₃	—	4	8	no	—
526	C₂×D₄×C₅₃	—	4	4	no	—
527	C₂×D₄×C₅₃	—	4	4	no	—
528	C₂×D₄×C₅₃	—	4	16	no	—
529	C₂×D₄×C₅₃	—	4	8	no	—
530	C₂×D₄×C₅₃	—	4	16	no	—
531	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
532	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
533	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
534	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
535	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
536	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
537	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
538	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
539	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
540	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
541	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
542	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
543	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
544	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
545	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
546	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
547	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
548	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
549	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
550	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
551	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
552	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
553	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
554	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
555	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
556	C₂²×C₄×C₅₃	—	2	4	no	—
557	C₂²×C₄×C₅₃	—	2	8	no	—
558	C₂²×C₄×C₅₃	—	4	2	no	—
559	C₂²×C₄×C₅₃	—	4	8	no	—
560	C₂²×C₄×C₅₃	—	4	16	no	—
561	C₂²×C₄×C₅₃	—	4	2	no	—
562	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
563	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
564	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
565	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
566	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
567	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
568	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
569	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
570	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
571	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
572	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
573	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
574	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
575	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
576	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
577	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
578	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
579	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
580	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
581	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
582	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
583	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
584	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
585	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
586	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
587	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
588	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
589	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
590	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
591	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
592	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
593	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
594	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
595	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
596	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
597	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
598	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
599	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
600	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
601	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
602	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
603	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
604	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
605	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
606	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
607	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
608	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
609	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
610	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
611	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
612	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
613	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
614	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
615	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
616	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
617	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
618	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
619	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
620	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
621	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
622	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
623	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
624	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
625	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
626	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
627	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
628	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
629	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
630	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
631	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
632	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
633	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
634	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
635	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
636	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
637	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
638	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
639	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
640	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
641	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
642	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
643	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
644	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
645	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
646	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
647	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
648	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
649	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
650	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
651	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
652	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
653	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
654	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
655	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
656	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
657	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
658	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
659	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
660	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
661	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
662	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
663	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
664	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
665	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
666	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
667	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
668	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
669	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
670	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
671	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
672	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
673	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
674	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
675	C₄²×C₅₃	C₂⁴	1	4	yes	—
676	C₄²×C₅₃	C₂⁴	1	4	yes	—
677	C₄²×C₅₃	C₂⁴	1	4	yes	—
678	C₄²×C₅₃	C₂⁴	1	8	yes	—
679	C₄²×C₅₃	C₂⁴	1	8	yes	—
680	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
681	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
682	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
683	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
684	C₄²×C₅₃	C₂⁴	1	4	yes	—
685	C₄²×C₅₃	C₂⁴	1	4	yes	—
686	C₂³×C₅₃	—	2	2	no	—
687	C₂³×C₅₃	—	2	2	no	—
688	C₂³×C₅₃	—	2	4	no	—
689	C₂³×C₅₃	—	2	8	no	—
690	C₂³×C₅₃	—	4	1	no	—
691	C₂³×C₅₃	—	4	4	no	—
692	C₂³×C₅₃	—	4	8	no	—
693	C₂³×C₅₃	—	4	2	no	—
694	C₂³×C₅₃	—	4	4	no	—
695	C₂³×C₅₃	—	4	2	no	—
696	C₂³×C₅₃	—	4	8	no	—
697	C₂³×C₅₃	—	4	8	no	—
698	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
699	C₂³×C₅₃	C₂⁵	1	4	yes	—
700	C₂³×C₅₃	C₂⁵	1	8	yes	—
701	C₂³×C₅₃	C₂⁵	1	4	yes	—
702	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
703	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
704	Q₈×C₅₃	—	2	8	no	—
705	Q₈×C₅₃	—	2	4	no	—
706	Q₈×C₅₃	—	2	4	no	—
707	Q₈×C₅₃	—	4	2	no	—
708	Q₈×C₅₃	—	4	8	no	—
709	Q₈×C₅₃	—	4	4	no	—
710	Q₈×C₅₃	—	4	2	no	—
711	Q₈×C₅₃	—	4	2	no	—
712	D₄×C₅₃	—	2	16	no	—
713	D₄×C₅₃	—	2	8	no	—
714	D₄×C₅₃	—	2	8	no	—
715	D₄×C₅₃	—	2	8	no	—
716	D₄×C₅₃	—	2	8	no	—
717	D₄×C₅₃	—	2	4	no	—
718	D₄×C₅₃	—	2	4	no	—
719	D₄×C₅₃	—	2	8	no	—
720	D₄×C₅₃	—	4	4	no	—
721	D₄×C₅₃	—	4	4	no	—
722	D₄×C₅₃	—	4	4	no	—
723	D₄×C₅₃	—	4	8	no	—
724	D₄×C₅₃	—	4	2	no	—
725	D₄×C₅₃	—	4	4	no	—
726	D₄×C₅₃	—	4	8	no	—
727	D₄×C₅₃	—	4	8	no	—
728	D₄×C₅₃	—	4	8	no	—
729	D₄×C₅₃	—	4	4	no	—
730	D₄×C₅₃	—	4	8	no	—
731	D₄×C₅₃	—	4	8	no	—
732	D₄×C₅₃	—	4	8	no	—
733	D₄×C₅₃	—	4	4	no	—
734	D₄×C₅₃	—	4	2	no	—
735	D₄×C₅₃	—	4	2	no	—
736	D₄×C₅₃	—	4	8	no	—
737	C₂×C₄×C₅₃	—	2	2	no	—
738	C₂×C₄×C₅₃	—	2	4	no	—
739	C₂×C₄×C₅₃	—	2	2	no	—
740	C₂×C₄×C₅₃	—	2	2	no	—
741	C₂×C₄×C₅₃	—	2	2	no	—
742	C₂×C₄×C₅₃	—	2	8	no	—
743	C₂×C₄×C₅₃	—	2	2	no	—
744	C₂×C₄×C₅₃	—	2	8	no	—
745	C₂×C₄×C₅₃	—	2	2	no	—
746	C₂×C₄×C₅₃	—	2	2	no	—
747	C₂×C₄×C₅₃	—	2	16	no	—
748	C₂×C₄×C₅₃	—	2	8	no	—
749	C₂×C₄×C₅₃	—	2	2	no	—
750	C₂×C₄×C₅₃	—	2	2	no	—
751	C₂×C₄×C₅₃	—	2	2	no	—
752	C₂×C₄×C₅₃	—	2	8	no	—
753	C₂×C₄×C₅₃	—	4	1	no	—
754	C₂×C₄×C₅₃	—	4	1	no	—
755	C₂×C₄×C₅₃	—	4	1	no	—
756	C₂×C₄×C₅₃	—	4	1	no	—
757	C₂×C₄×C₅₃	—	4	1	no	—
758	C₂×C₄×C₅₃	—	4	1	no	—
759	C₂×C₄×C₅₃	—	4	1	no	—
760	C₂×C₄×C₅₃	—	4	4	no	—
761	C₂×C₄×C₅₃	—	4	8	no	—
762	C₂×C₄×C₅₃	—	4	8	no	—
763	C₂×C₄×C₅₃	—	4	8	no	—
764	C₂×C₄×C₅₃	—	4	8	no	—
765	C₂×C₄×C₅₃	—	4	2	no	—
766	C₂×C₄×C₅₃	—	4	8	no	—
767	C₂×C₄×C₅₃	—	4	2	no	—
768	C₂×C₄×C₅₃	—	4	4	no	—
769	C₂×C₄×C₅₃	—	4	8	no	—
770	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
771	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
772	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
773	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
774	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
775	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
776	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
777	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
778	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
779	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
780	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
781	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
782	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
783	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
784	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
785	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
786	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
787	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
788	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
789	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
790	#62748	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
791	C₂²×C₅₃	—	2	1	no	—
792	C₂²×C₅₃	—	2	1	no	—
793	C₂²×C₅₃	—	2	1	no	—
794	C₂²×C₅₃	—	2	1	no	—
795	C₂²×C₅₃	—	2	4	no	—
796	C₂²×C₅₃	—	2	1	no	—
797	C₂²×C₅₃	—	2	4	no	—
798	C₂²×C₅₃	—	2	8	no	—
799	C₂²×C₅₃	—	2	1	no	—
800	C₂²×C₅₃	—	2	4	no	—
801	C₂²×C₅₃	—	2	1	no	—
802	C₂²×C₅₃	—	2	4	no	—
803	C₂²×C₅₃	—	2	8	no	—
804	C₂²×C₅₃	—	2	8	no	—
805	C₂²×C₅₃	—	2	4	no	—
806	C₂²×C₅₃	—	2	4	no	—
807	C₂²×C₅₃	—	4	4	no	—
808	C₂²×C₅₃	—	8	8	no	—
809	C₂²×C₅₃	—	8	4	no	—
810	C₂²×C₅₃	—	8	16	no	—
811	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
812	C₂²×C₅₃	#585	1	2	yes	—
813	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
814	C₄×C₅₃	—	2	1	no	—
815	C₄×C₅₃	—	2	4	no	—
816	C₄×C₅₃	—	2	1	no	—
817	C₄×C₅₃	—	2	8	no	—
818	C₄×C₅₃	—	2	4	no	—
819	C₄×C₅₃	—	2	1	no	—
820	C₄×C₅₃	—	2	1	no	—
821	C₄×C₅₃	—	2	1	no	—
822	C₄×C₅₃	—	2	1	no	—
823	C₄×C₅₃	—	2	4	no	—
824	C₄×C₅₃	—	2	1	no	—
825	C₄×C₅₃	—	2	1	no	—
826	C₄×C₅₃	—	2	1	no	—
827	C₄×C₅₃	—	2	4	no	—
828	C₄×C₅₃	—	2	4	no	—
829	C₄×C₅₃	—	2	4	no	—
830	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
831	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
832	C₄×C₅₃	#585	1	2	yes	—
833	#3562	C₂×C₅₃	1	4	yes	complemented
834	#3561	C₂×C₅₃	1	2	yes	complemented
835	#3560	C₂×C₅₃	1	4	yes	complemented
836	#3559	C₂×C₅₃	1	2	yes	complemented
837	#3558	C₂×C₅₃	1	2	yes	complemented
838	#3558	C₂×C₅₃	1	2	yes	complemented
839	#3554	C₂×C₅₃	1	2	yes	complemented
840	#3552	C₂×C₅₃	1	2	yes	complemented
841	#3546	C₂×C₅₃	1	2	yes	complemented
842	#3543	C₂×C₅₃	1	2	yes	complemented
843	#3537	C₂×C₅₃	1	2	yes	complemented
844	#3536	C₂×C₅₃	1	2	yes	complemented
845	#3534	C₂×C₅₃	1	4	yes	complemented
846	#3529	C₂×C₅₃	1	4	yes	complemented
847	#3481	C₂×C₅₃	1	4	yes	complemented
848	#3480	C₂×C₅₃	1	2	yes	complemented
849	D₄×#41	C₂×C₅₃	1	4	yes	complemented
850	D₄×#41	C₂×C₅₃	1	2	yes	complemented
851	#3460	C₂×C₅₃	1	4	yes	complemented
852	#3459	C₂×C₅₃	1	4	yes	complemented
853	#3455	C₂×C₅₃	1	2	yes	complemented
854	#3449	C₂×C₅₃	1	2	yes	complemented
855	#3444	C₂×C₅₃	1	1	yes	characteristic, complemented
856	C₂×#532	C₂×C₅₃	1	1	yes	characteristic, complemented
857	C₂×#529	C₂×C₅₃	1	1	yes	characteristic, complemented
858	C₂×C₅₃	—	2	2	no	—
859	C₂×C₅₃	—	2	2	no	—
860	C₂×C₅₃	—	4	1	no	—
861	C₂×C₅₃	—	4	4	no	—
862	C₂×C₅₃	—	4	8	no	—
863	C₂×C₅₃	—	4	4	no	—
864	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
865	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
866	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
867	C₂²×#41	C₂²×C₅₃	1	2	yes	complemented
868	C₂²×#41	C₂²×C₅₃	1	4	yes	complemented
869	#563	C₂²×C₅₃	1	8	yes	complemented
870	#563	C₂²×C₅₃	1	4	yes	complemented
871	#562	C₂²×C₅₃	1	8	yes	complemented
872	#562	C₂²×C₅₃	1	8	yes	complemented
873	#562	C₂²×C₅₃	1	4	yes	complemented
874	#562	C₂²×C₅₃	1	4	yes	complemented
875	H(3,𝔽₄)	C₂²×C₅₃	1	4	yes	complemented
876	#560	C₂²×C₅₃	1	8	yes	complemented
877	#560	C₂²×C₅₃	1	8	yes	complemented
878	#560	C₂²×C₅₃	1	8	yes	complemented
879	#559	C₂²×C₅₃	1	2	yes	complemented
880	#559	C₂²×C₅₃	1	4	yes	complemented
881	#559	C₂²×C₅₃	1	4	yes	complemented
882	#557	C₂²×C₅₃	1	2	yes	complemented
883	#556	C₂²×C₅₃	1	2	yes	complemented
884	#556	C₂²×C₅₃	1	4	yes	complemented
885	#554	C₂²×C₅₃	1	4	yes	complemented
886	#554	C₂²×C₅₃	1	4	yes	complemented
887	#553	C₂²×C₅₃	1	8	yes	complemented
888	#553	C₂²×C₅₃	1	4	yes	complemented
889	#553	C₂²×C₅₃	1	4	yes	complemented
890	#553	C₂²×C₅₃	1	4	yes	complemented
891	#553	C₂²×C₅₃	1	8	yes	complemented
892	#551	C₂²×C₅₃	1	8	yes	complemented
893	#551	C₂²×C₅₃	1	8	yes	complemented
894	#550	C₂²×C₅₃	1	2	yes	complemented
895	#550	C₂²×C₅₃	1	4	yes	complemented
896	#550	C₂²×C₅₃	1	2	yes	complemented
897	D₄×Q₈	C₂²×C₅₃	1	2	yes	complemented
898	D₄×Q₈	C₂²×C₅₃	1	4	yes	complemented
899	#548	C₂²×C₅₃	1	4	yes	complemented
900	#548	C₂²×C₅₃	1	4	yes	complemented
901	#548	C₂²×C₅₃	1	4	yes	complemented
902	#548	C₂²×C₅₃	1	4	yes	complemented
903	#547	C₂²×C₅₃	1	4	yes	complemented
904	#547	C₂²×C₅₃	1	2	yes	complemented
905	#547	C₂²×C₅₃	1	4	yes	complemented
906	#547	C₂²×C₅₃	1	8	yes	complemented
907	#546	C₂²×C₅₃	1	8	yes	complemented
908	#546	C₂²×C₅₃	1	8	yes	complemented
909	#546	C₂²×C₅₃	1	4	yes	complemented
910	#546	C₂²×C₅₃	1	4	yes	complemented
911	#546	C₂²×C₅₃	1	8	yes	complemented
912	#546	C₂²×C₅₃	1	4	yes	complemented
913	#546	C₂²×C₅₃	1	8	yes	complemented
914	#546	C₂²×C₅₃	1	4	yes	complemented
915	#546	C₂²×C₅₃	1	4	yes	complemented
916	D₄²	C₂²×C₅₃	1	8	yes	complemented
917	D₄²	C₂²×C₅₃	1	4	yes	complemented
918	D₄²	C₂²×C₅₃	1	2	yes	complemented
919	D₄²	C₂²×C₅₃	1	4	yes	complemented
920	D₄²	C₂²×C₅₃	1	4	yes	complemented
921	#544	C₂²×C₅₃	1	4	yes	complemented
922	#543	C₂²×C₅₃	1	4	yes	complemented
923	#542	C₂²×C₅₃	1	4	yes	complemented
924	#542	C₂²×C₅₃	1	4	yes	complemented
925	#542	C₂²×C₅₃	1	4	yes	complemented
926	#542	C₂²×C₅₃	1	4	yes	complemented
927	#542	C₂²×C₅₃	1	8	yes	complemented
928	#541	C₂²×C₅₃	1	4	yes	complemented
929	#540	C₂²×C₅₃	1	4	yes	complemented
930	#540	C₂²×C₅₃	1	8	yes	complemented
931	#540	C₂²×C₅₃	1	4	yes	complemented
932	#540	C₂²×C₅₃	1	4	yes	complemented
933	#539	C₂²×C₅₃	1	4	yes	complemented
934	#539	C₂²×C₅₃	1	4	yes	complemented
935	#539	C₂²×C₅₃	1	8	yes	complemented
936	#539	C₂²×C₅₃	1	8	yes	complemented
937	#539	C₂²×C₅₃	1	8	yes	complemented
938	#538	C₂²×C₅₃	1	4	yes	complemented
939	#538	C₂²×C₅₃	1	4	yes	complemented
940	#538	C₂²×C₅₃	1	4	yes	complemented
941	#538	C₂²×C₅₃	1	4	yes	complemented
942	#538	C₂²×C₅₃	1	8	yes	complemented
943	#538	C₂²×C₅₃	1	8	yes	complemented
944	#538	C₂²×C₅₃	1	8	yes	complemented
945	#538	C₂²×C₅₃	1	8	yes	complemented
946	#537	C₂²×C₅₃	1	4	yes	complemented
947	#537	C₂²×C₅₃	1	4	yes	complemented
948	#537	C₂²×C₅₃	1	4	yes	complemented
949	#536	C₂²×C₅₃	1	4	yes	complemented
950	#536	C₂²×C₅₃	1	4	yes	complemented
951	#535	C₂²×C₅₃	1	4	yes	complemented
952	#535	C₂²×C₅₃	1	4	yes	complemented
953	#535	C₂²×C₅₃	1	4	yes	complemented
954	#535	C₂²×C₅₃	1	4	yes	complemented
955	#534	C₂²×C₅₃	1	4	yes	complemented
956	#534	C₂²×C₅₃	1	4	yes	complemented
957	#534	C₂²×C₅₃	1	8	yes	complemented
958	#534	C₂²×C₅₃	1	4	yes	complemented
959	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
960	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
961	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
962	#532	C₂²×C₅₃	1	2	yes	complemented
963	#532	C₂²×C₅₃	1	2	yes	complemented
964	#532	C₂²×C₅₃	1	2	yes	complemented
965	#532	C₂²×C₅₃	1	2	yes	complemented
966	#532	C₂²×C₅₃	1	2	yes	complemented
967	#532	C₂²×C₅₃	1	2	yes	complemented
968	#532	C₂²×C₅₃	1	2	yes	complemented
969	#532	C₂²×C₅₃	1	2	yes	complemented
970	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
971	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
972	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
973	#532	C₂²×C₅₃	1	4	yes	complemented
974	#532	C₂²×C₅₃	1	4	yes	complemented
975	#532	C₂²×C₅₃	1	8	yes	complemented
976	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
977	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic, complemented
978	#529	C₂²×C₅₃	1	2	yes	complemented
979	#529	C₂²×C₅₃	1	2	yes	complemented
980	#529	C₂²×C₅₃	1	2	yes	complemented
981	#529	C₂²×C₅₃	1	2	yes	complemented
982	#529	C₂²×C₅₃	1	2	yes	complemented
983	#529	C₂²×C₅₃	1	2	yes	complemented
984	#529	C₂²×C₅₃	1	2	yes	complemented
985	#529	C₂²×C₅₃	1	2	yes	complemented
986	#529	C₂²×C₅₃	1	2	yes	complemented
987	#529	C₂²×C₅₃	1	2	yes	complemented
988	#529	C₂²×C₅₃	1	2	yes	complemented
989	#529	C₂²×C₅₃	1	2	yes	complemented
990	#529	C₂²×C₅₃	1	2	yes	complemented
991	#529	C₂²×C₅₃	1	2	yes	complemented
992	#529	C₂²×C₅₃	1	8	yes	complemented
993	#529	C₂²×C₅₃	1	8	yes	complemented
994	#529	C₂²×C₅₃	1	8	yes	complemented
995	#529	C₂²×C₅₃	1	4	yes	complemented
996	C₂×#126	C₂²×C₅₃	1	2	yes	complemented
997	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
998	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic, complemented
999	C₂×#124	C₂²×C₅₃	1	2	yes	complemented
1000	#525	C₂²×C₅₃	1	2	yes	complemented
1001	#525	C₂²×C₅₃	1	2	yes	complemented
1002	#525	C₂²×C₅₃	1	2	yes	complemented
1003	#525	C₂²×C₅₃	1	8	yes	complemented
1004	#525	C₂²×C₅₃	1	8	yes	complemented
1005	#525	C₂²×C₅₃	1	4	yes	complemented
1006	#525	C₂²×C₅₃	1	8	yes	complemented
1007	#525	C₂²×C₅₃	1	8	yes	complemented
1008	#525	C₂²×C₅₃	1	8	yes	complemented
1009	C₂×#123	C₂²×C₅₃	1	2	yes	complemented
1010	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1011	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
1012	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
1013	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
1014	C₄×#41	C₂²×C₅₃	1	2	yes	complemented
1015	C₄×#41	C₂²×C₅₃	1	2	yes	complemented
1016	C₄×#41	C₂²×C₅₃	1	2	yes	complemented
1017	C₄×#41	C₂²×C₅₃	1	4	yes	complemented
1018	C₄×#41	C₂²×C₅₃	1	4	yes	complemented
1019	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1020	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
1021	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1022	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
1023	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
1024	C₂×C₄×D₄	C₂²×C₅₃	1	8	yes	complemented
1025	C₂×C₄×D₄	C₂²×C₅₃	1	4	yes	complemented
1026	C₂×#117	C₂²×C₅₃	1	2	yes	complemented
1027	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
1028	C₅₃	#62748	1	1	yes	characteristic, direct product factor, Sylow
1029	C₂×#41	—	4	8	no	—
1030	C₂×#41	—	4	16	no	—
1031	C₂×#41	C₂³×C₅₃	1	2	yes	—
1032	C₂×#41	C₂³×C₅₃	1	4	yes	—
1033	C₂×#41	C₂³×C₅₃	1	2	yes	—
1034	C₂×#41	C₂³×C₅₃	1	2	yes	—
1035	C₂×#41	C₂³×C₅₃	1	4	yes	—
1036	C₂×#41	C₂³×C₅₃	1	8	yes	—
1037	C₂×#41	C₂³×C₅₃	1	4	yes	—
1038	C₂×#41	C₂³×C₅₃	1	4	yes	—
1039	C₂×#41	C₂³×C₅₃	1	4	yes	—
1040	C₂×#41	C₂³×C₅₃	1	4	yes	—
1041	C₂×#41	C₂³×C₅₃	1	4	yes	—
1042	C₂×#41	C₂³×C₅₃	1	8	yes	—
1043	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1044	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
1045	C₂²×Q₈	C₂³×C₅₃	1	4	yes	—
1046	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
1047	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1048	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
1049	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
1050	C₂²×D₄	C₂³×C₅₃	1	8	yes	—
1051	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
1052	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
1053	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
1054	C₂²×D₄	C₂³×C₅₃	1	8	yes	—
1055	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
1056	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
1057	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1058	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
1059	C₂³×C₄	C₂³×C₅₃	1	8	yes	—
1060	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1061	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1062	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
1063	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
1064	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
1065	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
1066	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1067	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1068	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1069	C₄⋊Q₈	C₂³×C₅₃	1	4	yes	—
1070	C₄⋊Q₈	C₂³×C₅₃	1	4	yes	—
1071	C₄⋊Q₈	C₂³×C₅₃	1	8	yes	—
1072	#127	C₂³×C₅₃	1	2	yes	—
1073	#127	C₂³×C₅₃	1	2	yes	—
1074	#127	C₂³×C₅₃	1	2	yes	—
1075	#127	C₂³×C₅₃	1	2	yes	—
1076	#127	C₂³×C₅₃	1	1	yes	characteristic
1077	#127	C₂³×C₅₃	1	4	yes	—
1078	#127	C₂³×C₅₃	1	4	yes	—
1079	#127	C₂³×C₅₃	1	8	yes	—
1080	#126	C₂³×C₅₃	1	4	yes	—
1081	#126	C₂³×C₅₃	1	4	yes	—
1082	#126	C₂³×C₅₃	1	4	yes	—
1083	#126	C₂³×C₅₃	1	4	yes	—
1084	#126	C₂³×C₅₃	1	4	yes	—
1085	#126	C₂³×C₅₃	1	4	yes	—
1086	#126	C₂³×C₅₃	1	8	yes	—
1087	#126	C₂³×C₅₃	1	8	yes	—
1088	#126	C₂³×C₅₃	1	8	yes	—
1089	#126	C₂³×C₅₃	1	8	yes	—
1090	#126	C₂³×C₅₃	1	8	yes	—
1091	#126	C₂³×C₅₃	1	8	yes	—
1092	#126	C₂³×C₅₃	1	8	yes	—
1093	#125	C₂³×C₅₃	1	2	yes	—
1094	#125	C₂³×C₅₃	1	2	yes	—
1095	#125	C₂³×C₅₃	1	2	yes	—
1096	#125	C₂³×C₅₃	1	2	yes	—
1097	#125	C₂³×C₅₃	1	2	yes	—
1098	#125	C₂³×C₅₃	1	2	yes	—
1099	#125	C₂³×C₅₃	1	2	yes	—
1100	#125	C₂³×C₅₃	1	8	yes	—
1101	#125	C₂³×C₅₃	1	8	yes	—
1102	#125	C₂³×C₅₃	1	8	yes	—
1103	#125	C₂³×C₅₃	1	4	yes	—
1104	#124	C₂³×C₅₃	1	2	yes	—
1105	#124	C₂³×C₅₃	1	2	yes	—
1106	#124	C₂³×C₅₃	1	2	yes	—
1107	#124	C₂³×C₅₃	1	2	yes	—
1108	#124	C₂³×C₅₃	1	4	yes	—
1109	#124	C₂³×C₅₃	1	4	yes	—
1110	#124	C₂³×C₅₃	1	4	yes	—
1111	#124	C₂³×C₅₃	1	4	yes	—
1112	#124	C₂³×C₅₃	1	2	yes	—
1113	#124	C₂³×C₅₃	1	2	yes	—
1114	#124	C₂³×C₅₃	1	2	yes	—
1115	#124	C₂³×C₅₃	1	8	yes	—
1116	#124	C₂³×C₅₃	1	4	yes	—
1117	#124	C₂³×C₅₃	1	8	yes	—
1118	#124	C₂³×C₅₃	1	8	yes	—
1119	#124	C₂³×C₅₃	1	4	yes	—
1120	#124	C₂³×C₅₃	1	4	yes	—
1121	#124	C₂³×C₅₃	1	8	yes	—
1122	#124	C₂³×C₅₃	1	8	yes	—
1123	#124	C₂³×C₅₃	1	8	yes	—
1124	#123	C₂³×C₅₃	1	4	yes	—
1125	#123	C₂³×C₅₃	1	4	yes	—
1126	#123	C₂³×C₅₃	1	4	yes	—
1127	#123	C₂³×C₅₃	1	4	yes	—
1128	#123	C₂³×C₅₃	1	4	yes	—
1129	#123	C₂³×C₅₃	1	4	yes	—
1130	#123	C₂³×C₅₃	1	4	yes	—
1131	#123	C₂³×C₅₃	1	8	yes	—
1132	#123	C₂³×C₅₃	1	8	yes	—
1133	#123	C₂³×C₅₃	1	8	yes	—
1134	#123	C₂³×C₅₃	1	8	yes	—
1135	#123	C₂³×C₅₃	1	8	yes	—
1136	#123	C₂³×C₅₃	1	8	yes	—
1137	#123	C₂³×C₅₃	1	8	yes	—
1138	#123	C₂³×C₅₃	1	8	yes	—
1139	#123	C₂³×C₅₃	1	8	yes	—
1140	#123	C₂³×C₅₃	1	8	yes	—
1141	#123	C₂³×C₅₃	1	8	yes	—
1142	#123	C₂³×C₅₃	1	8	yes	—
1143	#123	C₂³×C₅₃	1	8	yes	—
1144	#123	C₂³×C₅₃	1	8	yes	—
1145	#123	C₂³×C₅₃	1	8	yes	—
1146	#123	C₂³×C₅₃	1	8	yes	—
1147	#123	C₂³×C₅₃	1	8	yes	—
1148	#123	C₂³×C₅₃	1	8	yes	—
1149	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
1150	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
1151	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
1152	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
1153	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
1154	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
1155	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
1156	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
1157	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
1158	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
1159	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
1160	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
1161	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
1162	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
1163	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
1164	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
1165	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
1166	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
1167	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
1168	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
1169	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
1170	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
1171	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
1172	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
1173	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
1174	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
1175	#121	C₂³×C₅₃	1	2	yes	—
1176	#121	C₂³×C₅₃	1	2	yes	—
1177	#121	C₂³×C₅₃	1	2	yes	—
1178	#121	C₂³×C₅₃	1	2	yes	—
1179	#121	C₂³×C₅₃	1	4	yes	—
1180	#121	C₂³×C₅₃	1	4	yes	—
1181	#121	C₂³×C₅₃	1	4	yes	—
1182	#121	C₂³×C₅₃	1	4	yes	—
1183	#121	C₂³×C₅₃	1	4	yes	—
1184	#121	C₂³×C₅₃	1	4	yes	—
1185	#121	C₂³×C₅₃	1	4	yes	—
1186	#121	C₂³×C₅₃	1	4	yes	—
1187	#121	C₂³×C₅₃	1	2	yes	—
1188	#121	C₂³×C₅₃	1	2	yes	—
1189	#121	C₂³×C₅₃	1	2	yes	—
1190	#121	C₂³×C₅₃	1	2	yes	—
1191	#121	C₂³×C₅₃	1	2	yes	—
1192	#121	C₂³×C₅₃	1	2	yes	—
1193	#121	C₂³×C₅₃	1	8	yes	—
1194	#121	C₂³×C₅₃	1	8	yes	—
1195	#121	C₂³×C₅₃	1	8	yes	—
1196	#121	C₂³×C₅₃	1	8	yes	—
1197	#121	C₂³×C₅₃	1	8	yes	—
1198	#121	C₂³×C₅₃	1	8	yes	—
1199	#121	C₂³×C₅₃	1	8	yes	—
1200	#121	C₂³×C₅₃	1	8	yes	—
1201	#121	C₂³×C₅₃	1	8	yes	—
1202	#121	C₂³×C₅₃	1	8	yes	—
1203	#121	C₂³×C₅₃	1	4	yes	—
1204	#121	C₂³×C₅₃	1	4	yes	—
1205	#121	C₂³×C₅₃	1	8	yes	—
1206	#121	C₂³×C₅₃	1	8	yes	—
1207	#121	C₂³×C₅₃	1	4	yes	—
1208	#121	C₂³×C₅₃	1	8	yes	—
1209	#121	C₂³×C₅₃	1	8	yes	—
1210	#121	C₂³×C₅₃	1	8	yes	—
1211	#121	C₂³×C₅₃	1	4	yes	—
1212	#121	C₂³×C₅₃	1	8	yes	—
1213	#121	C₂³×C₅₃	1	4	yes	—
1214	#121	C₂³×C₅₃	1	8	yes	—
1215	#121	C₂³×C₅₃	1	8	yes	—
1216	#121	C₂³×C₅₃	1	8	yes	—
1217	#121	C₂³×C₅₃	1	8	yes	—
1218	#120	C₂³×C₅₃	1	4	yes	—
1219	#120	C₂³×C₅₃	1	8	yes	—
1220	#120	C₂³×C₅₃	1	8	yes	—
1221	#120	C₂³×C₅₃	1	8	yes	—
1222	#120	C₂³×C₅₃	1	8	yes	—
1223	#120	C₂³×C₅₃	1	8	yes	—
1224	#120	C₂³×C₅₃	1	8	yes	—
1225	#120	C₂³×C₅₃	1	8	yes	—
1226	#120	C₂³×C₅₃	1	8	yes	—
1227	#120	C₂³×C₅₃	1	8	yes	—
1228	#120	C₂³×C₅₃	1	8	yes	—
1229	#120	C₂³×C₅₃	1	8	yes	—
1230	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
1231	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
1232	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
1233	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
1234	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
1235	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
1236	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
1237	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
1238	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
1239	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
1240	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
1241	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
1242	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
1243	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1244	C₄×D₄	C₂³×C₅₃	1	2	yes	—
1245	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1246	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1247	C₄×D₄	C₂³×C₅₃	1	2	yes	—
1248	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1249	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1250	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1251	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1252	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1253	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1254	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1255	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1256	C₄×D₄	C₂³×C₅₃	1	2	yes	—
1257	C₄×D₄	C₂³×C₅₃	1	2	yes	—
1258	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1259	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1260	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1261	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1262	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1263	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1264	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1265	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1266	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1267	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1268	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1269	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1270	C₄×D₄	C₂³×C₅₃	1	2	yes	—
1271	C₄×D₄	C₂³×C₅₃	1	2	yes	—
1272	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1273	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1274	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1275	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1276	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1277	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1278	C₄×D₄	C₂³×C₅₃	1	2	yes	—
1279	C₄×D₄	C₂³×C₅₃	1	2	yes	—
1280	C₄×D₄	C₂³×C₅₃	1	2	yes	—
1281	C₄×D₄	C₂³×C₅₃	1	2	yes	—
1282	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1283	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1284	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1285	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1286	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1287	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1288	#117	C₂³×C₅₃	1	4	yes	—
1289	#117	C₂³×C₅₃	1	4	yes	—
1290	#117	C₂³×C₅₃	1	4	yes	—
1291	#117	C₂³×C₅₃	1	4	yes	—
1292	#117	C₂³×C₅₃	1	2	yes	—
1293	#117	C₂³×C₅₃	1	4	yes	—
1294	#117	C₂³×C₅₃	1	8	yes	—
1295	#117	C₂³×C₅₃	1	2	yes	—
1296	#117	C₂³×C₅₃	1	2	yes	—
1297	#117	C₂³×C₅₃	1	4	yes	—
1298	#117	C₂³×C₅₃	1	4	yes	—
1299	#117	C₂³×C₅₃	1	4	yes	—
1300	#117	C₂³×C₅₃	1	8	yes	—
1301	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
1302	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
1303	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
1304	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
1305	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1306	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
1307	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
1308	C₂×C₄⋊C₄	C₂³×C₅₃	1	8	yes	—
1309	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1310	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
1311	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
1312	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
1313	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
1314	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
1315	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
1316	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
1317	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
1318	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	—
1319	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	—
1320	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	—
1321	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1322	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
1323	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1324	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1325	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1326	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
1327	C₂×C₄²	C₂³×C₅₃	1	8	yes	—
1328	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1329	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1330	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1331	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1332	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1333	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1334	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1335	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1336	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1337	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
1338	C₂⁴	C₂⁴×C₅₃	1	4	yes	—
1339	C₂⁴	C₂⁴×C₅₃	1	8	yes	—
1340	#41	—	2	16	no	—
1341	#41	—	2	8	no	—
1342	#41	—	4	16	no	—
1343	#41	—	4	8	no	—
1344	#41	—	4	4	no	—
1345	#41	—	4	8	no	—
1346	#41	—	4	16	no	—
1347	#41	—	4	4	no	—
1348	#41	—	4	8	no	—
1349	#41	—	4	8	no	—
1350	#41	—	4	8	no	—
1351	#41	—	4	8	no	—
1352	C₂×Q₈	—	4	2	no	—
1353	C₂×Q₈	—	4	4	no	—
1354	C₂×Q₈	—	4	8	no	—
1355	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
1356	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
1357	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
1358	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
1359	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
1360	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
1361	C₂×Q₈	C₂⁴×C₅₃	1	8	yes	—
1362	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
1363	C₂×D₄	—	4	4	no	—
1364	C₂×D₄	—	4	2	no	—
1365	C₂×D₄	—	4	8	no	—
1366	C₂×D₄	—	4	4	no	—
1367	C₂×D₄	—	4	8	no	—
1368	C₂×D₄	—	4	4	no	—
1369	C₂×D₄	—	4	4	no	—
1370	C₂×D₄	—	4	16	no	—
1371	C₂×D₄	—	4	8	no	—
1372	C₂×D₄	—	4	16	no	—
1373	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1374	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1375	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1376	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1377	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1378	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1379	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1380	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1381	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1382	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1383	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1384	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1385	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1386	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1387	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1388	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1389	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1390	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1391	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1392	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1393	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1394	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1395	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1396	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1397	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1398	C₂²×C₄	—	2	4	no	—
1399	C₂²×C₄	—	2	8	no	—
1400	C₂²×C₄	—	4	2	no	—
1401	C₂²×C₄	—	4	8	no	—
1402	C₂²×C₄	—	4	16	no	—
1403	C₂²×C₄	—	4	2	no	—
1404	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1405	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1406	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1407	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1408	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1409	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1410	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1411	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1412	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1413	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1414	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1415	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1416	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
1417	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1418	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1419	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1420	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1421	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1422	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1423	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1424	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1425	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1426	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1427	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1428	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1429	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
1430	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1431	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
1432	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1433	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
1434	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
1435	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
1436	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
1437	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1438	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1439	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1440	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1441	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1442	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1443	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1444	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1445	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1446	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1447	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1448	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1449	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1450	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1451	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1452	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1453	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1454	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1455	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1456	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1457	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1458	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1459	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1460	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1461	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1462	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1463	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1464	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1465	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1466	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1467	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1468	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1469	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1470	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1471	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1472	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1473	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1474	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1475	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1476	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1477	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1478	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1479	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1480	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1481	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1482	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1483	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1484	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1485	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1486	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1487	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1488	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1489	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1490	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1491	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1492	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1493	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1494	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1495	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1496	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1497	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1498	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1499	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1500	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1501	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1502	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1503	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1504	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1505	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1506	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1507	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1508	C₄²	C₂⁴×C₅₃	1	4	yes	—
1509	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1510	C₄²	C₂⁴×C₅₃	1	4	yes	—
1511	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1512	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1513	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1514	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1515	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1516	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1517	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1518	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1519	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1520	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1521	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1522	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1523	C₄²	C₂⁴×C₅₃	1	4	yes	—
1524	C₄²	C₂⁴×C₅₃	1	4	yes	—
1525	C₄²	C₂⁴×C₅₃	1	4	yes	—
1526	C₄²	C₂⁴×C₅₃	1	8	yes	—
1527	C₄²	C₂⁴×C₅₃	1	8	yes	—
1528	C₂³	—	2	2	no	—
1529	C₂³	—	2	2	no	—
1530	C₂³	—	2	4	no	—
1531	C₂³	—	2	8	no	—
1532	C₂³	—	4	1	no	—
1533	C₂³	—	4	4	no	—
1534	C₂³	—	4	8	no	—
1535	C₂³	—	4	2	no	—
1536	C₂³	—	4	4	no	—
1537	C₂³	—	4	2	no	—
1538	C₂³	—	4	8	no	—
1539	C₂³	—	4	8	no	—
1540	C₂³	C₂⁵×C₅₃	1	4	yes	—
1541	C₂³	C₂⁵×C₅₃	1	4	yes	—
1542	C₂³	C₂⁵×C₅₃	1	8	yes	—
1543	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
1544	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
1545	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
1546	Q₈	—	2	8	no	—
1547	Q₈	—	2	4	no	—
1548	Q₈	—	2	4	no	—
1549	Q₈	—	4	2	no	—
1550	Q₈	—	4	8	no	—
1551	Q₈	—	4	4	no	—
1552	Q₈	—	4	2	no	—
1553	Q₈	—	4	2	no	—
1554	D₄	—	2	16	no	—
1555	D₄	—	2	8	no	—
1556	D₄	—	2	8	no	—
1557	D₄	—	2	8	no	—
1558	D₄	—	2	8	no	—
1559	D₄	—	2	4	no	—
1560	D₄	—	2	4	no	—
1561	D₄	—	2	8	no	—
1562	D₄	—	4	4	no	—
1563	D₄	—	4	4	no	—
1564	D₄	—	4	4	no	—
1565	D₄	—	4	8	no	—
1566	D₄	—	4	2	no	—
1567	D₄	—	4	4	no	—
1568	D₄	—	4	8	no	—
1569	D₄	—	4	8	no	—
1570	D₄	—	4	8	no	—
1571	D₄	—	4	4	no	—
1572	D₄	—	4	8	no	—
1573	D₄	—	4	8	no	—
1574	D₄	—	4	8	no	—
1575	D₄	—	4	4	no	—
1576	D₄	—	4	2	no	—
1577	D₄	—	4	2	no	—
1578	D₄	—	4	8	no	—
1579	C₂×C₄	—	2	2	no	—
1580	C₂×C₄	—	2	4	no	—
1581	C₂×C₄	—	2	2	no	—
1582	C₂×C₄	—	2	2	no	—
1583	C₂×C₄	—	2	2	no	—
1584	C₂×C₄	—	2	8	no	—
1585	C₂×C₄	—	2	2	no	—
1586	C₂×C₄	—	2	8	no	—
1587	C₂×C₄	—	2	2	no	—
1588	C₂×C₄	—	2	2	no	—
1589	C₂×C₄	—	2	16	no	—
1590	C₂×C₄	—	2	8	no	—
1591	C₂×C₄	—	2	2	no	—
1592	C₂×C₄	—	2	2	no	—
1593	C₂×C₄	—	2	2	no	—
1594	C₂×C₄	—	2	8	no	—
1595	C₂×C₄	—	4	1	no	—
1596	C₂×C₄	—	4	1	no	—
1597	C₂×C₄	—	4	1	no	—
1598	C₂×C₄	—	4	1	no	—
1599	C₂×C₄	—	4	1	no	—
1600	C₂×C₄	—	4	1	no	—
1601	C₂×C₄	—	4	1	no	—
1602	C₂×C₄	—	4	4	no	—
1603	C₂×C₄	—	4	8	no	—
1604	C₂×C₄	—	4	8	no	—
1605	C₂×C₄	—	4	8	no	—
1606	C₂×C₄	—	4	8	no	—
1607	C₂×C₄	—	4	2	no	—
1608	C₂×C₄	—	4	8	no	—
1609	C₂×C₄	—	4	2	no	—
1610	C₂×C₄	—	4	4	no	—
1611	C₂×C₄	—	4	8	no	—
1612	C₂×C₄	H(5,𝔽₂)×C₅₃	1	4	yes	—
1613	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1614	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1615	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1616	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1617	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1618	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1619	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1620	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1621	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1622	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1623	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1624	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1625	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1626	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1627	C₂×C₄	C₂⁵×C₅₃	1	8	yes	—
1628	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1629	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1630	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1631	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1632	C₂²	—	2	1	no	—
1633	C₂²	—	2	1	no	—
1634	C₂²	—	2	1	no	—
1635	C₂²	—	2	1	no	—
1636	C₂²	—	2	4	no	—
1637	C₂²	—	2	1	no	—
1638	C₂²	—	2	4	no	—
1639	C₂²	—	2	8	no	—
1640	C₂²	—	2	1	no	—
1641	C₂²	—	2	4	no	—
1642	C₂²	—	2	1	no	—
1643	C₂²	—	2	4	no	—
1644	C₂²	—	2	8	no	—
1645	C₂²	—	2	8	no	—
1646	C₂²	—	2	4	no	—
1647	C₂²	—	2	4	no	—
1648	C₂²	—	4	4	no	—
1649	C₂²	—	8	8	no	—
1650	C₂²	—	8	4	no	—
1651	C₂²	—	8	16	no	—
1652	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
1653	C₂²	C₅₃×#585	1	2	yes	—
1654	C₂²	C₂⁶×C₅₃	1	1	yes	characteristic
1655	C₄	—	2	1	no	—
1656	C₄	—	2	4	no	—
1657	C₄	—	2	1	no	—
1658	C₄	—	2	8	no	—
1659	C₄	—	2	4	no	—
1660	C₄	—	2	1	no	—
1661	C₄	—	2	1	no	—
1662	C₄	—	2	1	no	—
1663	C₄	—	2	1	no	—
1664	C₄	—	2	4	no	—
1665	C₄	—	2	1	no	—
1666	C₄	—	2	1	no	—
1667	C₄	—	2	1	no	—
1668	C₄	—	2	4	no	—
1669	C₄	—	2	4	no	—
1670	C₄	—	2	4	no	—
1671	C₄	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
1672	C₄	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
1673	C₄	C₅₃×#585	1	2	yes	—
1674	C₂	—	2	2	no	—
1675	C₂	—	2	2	no	—
1676	C₂	—	4	1	no	—
1677	C₂	—	4	4	no	—
1678	C₂	—	4	4	no	—
1679	C₂	—	4	8	no	—
1680	C₂	C₂²×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1681	C₂	C₂×C₅₃×#585	1	1	yes	characteristic
1682	C₂	C₂×C₅₃×#585	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₅₃
socle	C₂²×C₅₃	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₅₃×#3562	C₂	semidirect
2. C₅₃×#3561	C₂	semidirect
3. C₅₃×#3560	C₂	semidirect
4. C₅₃×#3559	C₂	semidirect
5. C₅₃×#3558	C₂	semidirect
6. C₅₃×#3558	C₂	semidirect
7. C₅₃×#3554	C₂	semidirect
8. C₅₃×#3552	C₂	semidirect
9. C₅₃×#3546	C₂	semidirect
10. C₅₃×#3543	C₂	semidirect
11. C₅₃×#3537	C₂	semidirect
12. C₅₃×#3536	C₂	semidirect
13. C₅₃×#3534	C₂	semidirect
14. C₅₃×#3529	C₂	semidirect
15. C₅₃×#3481	C₂	semidirect
16. C₅₃×#3480	C₂	semidirect
17. D₄×#41×C₅₃	C₂	semidirect
18. D₄×#41×C₅₃	C₂	semidirect
19. C₅₃×#3460	C₂	semidirect
20. C₅₃×#3459	C₂	semidirect
21. C₅₃×#3455	C₂	semidirect
22. C₅₃×#3449	C₂	semidirect
23. C₅₃×#3444	C₂	semidirect
24. C₂×C₅₃×#532	C₂	semidirect
25. C₂×C₅₃×#529	C₂	semidirect
26. C₂²×#41×C₅₃	C₂²	semidirect
27. C₂²×#41×C₅₃	C₂²	semidirect
28. C₅₃×#563	C₂²	semidirect
29. C₅₃×#563	C₂²	semidirect
30. C₅₃×#562	C₂²	semidirect
31. C₅₃×#562	C₂²	semidirect
32. C₅₃×#562	C₂²	semidirect
33. C₅₃×#562	C₂²	semidirect
34. C₅₃×H(3,𝔽₄)	C₂²	semidirect
35. C₅₃×#560	C₂²	semidirect
36. C₅₃×#560	C₂²	semidirect
37. C₅₃×#560	C₂²	semidirect
38. C₅₃×#559	C₂²	semidirect
39. C₅₃×#559	C₂²	semidirect
40. C₅₃×#559	C₂²	semidirect
41. C₅₃×#557	C₂²	semidirect
42. C₅₃×#556	C₂²	semidirect
43. C₅₃×#556	C₂²	semidirect
44. C₅₃×#554	C₂²	semidirect
45. C₅₃×#554	C₂²	semidirect
46. C₅₃×#553	C₂²	semidirect
47. C₅₃×#553	C₂²	semidirect
48. C₅₃×#553	C₂²	semidirect
49. C₅₃×#553	C₂²	semidirect
50. C₅₃×#553	C₂²	semidirect
51. C₅₃×#551	C₂²	semidirect
52. C₅₃×#551	C₂²	semidirect
53. C₅₃×#550	C₂²	semidirect
54. C₅₃×#550	C₂²	semidirect
55. C₅₃×#550	C₂²	semidirect
56. D₄×Q₈×C₅₃	C₂²	semidirect
57. D₄×Q₈×C₅₃	C₂²	semidirect
58. C₅₃×#548	C₂²	semidirect
59. C₅₃×#548	C₂²	semidirect
60. C₅₃×#548	C₂²	semidirect
61. C₅₃×#548	C₂²	semidirect
62. C₅₃×#547	C₂²	semidirect
63. C₅₃×#547	C₂²	semidirect
64. C₅₃×#547	C₂²	semidirect
65. C₅₃×#547	C₂²	semidirect
66. C₅₃×#546	C₂²	semidirect
67. C₅₃×#546	C₂²	semidirect
68. C₅₃×#546	C₂²	semidirect
69. C₅₃×#546	C₂²	semidirect
70. C₅₃×#546	C₂²	semidirect
71. C₅₃×#546	C₂²	semidirect
72. C₅₃×#546	C₂²	semidirect
73. C₅₃×#546	C₂²	semidirect
74. C₅₃×#546	C₂²	semidirect
75. D₄²×C₅₃	C₂²	semidirect
76. D₄²×C₅₃	C₂²	semidirect
77. D₄²×C₅₃	C₂²	semidirect
78. D₄²×C₅₃	C₂²	semidirect
79. D₄²×C₅₃	C₂²	semidirect
80. C₅₃×#544	C₂²	semidirect
81. C₅₃×#543	C₂²	semidirect
82. C₅₃×#542	C₂²	semidirect
83. C₅₃×#542	C₂²	semidirect
84. C₅₃×#542	C₂²	semidirect
85. C₅₃×#542	C₂²	semidirect
86. C₅₃×#542	C₂²	semidirect
87. C₅₃×#541	C₂²	semidirect
88. C₅₃×#540	C₂²	semidirect
89. C₅₃×#540	C₂²	semidirect
90. C₅₃×#540	C₂²	semidirect
91. C₅₃×#540	C₂²	semidirect
92. C₅₃×#539	C₂²	semidirect
93. C₅₃×#539	C₂²	semidirect
94. C₅₃×#539	C₂²	semidirect
95. C₅₃×#539	C₂²	semidirect
96. C₅₃×#539	C₂²	semidirect
97. C₅₃×#538	C₂²	semidirect
98. C₅₃×#538	C₂²	semidirect
99. C₅₃×#538	C₂²	semidirect
100. C₅₃×#538	C₂²	semidirect
101. C₅₃×#538	C₂²	semidirect
102. C₅₃×#538	C₂²	semidirect
103. C₅₃×#538	C₂²	semidirect
104. C₅₃×#538	C₂²	semidirect
105. C₅₃×#537	C₂²	semidirect
106. C₅₃×#537	C₂²	semidirect
107. C₅₃×#537	C₂²	semidirect
108. C₅₃×#536	C₂²	semidirect
109. C₅₃×#536	C₂²	semidirect
110. C₅₃×#535	C₂²	semidirect
111. C₅₃×#535	C₂²	semidirect
112. C₅₃×#535	C₂²	semidirect
113. C₅₃×#535	C₂²	semidirect
114. C₅₃×#534	C₂²	semidirect
115. C₅₃×#534	C₂²	semidirect
116. C₅₃×#534	C₂²	semidirect
117. C₅₃×#534	C₂²	semidirect
118. C₅₃×#533	C₂²	semidirect
119. C₅₃×#533	C₂²	semidirect
120. C₅₃×#533	C₂²	semidirect
121. C₅₃×#532	C₂²	semidirect
122. C₅₃×#532	C₂²	semidirect
123. C₅₃×#532	C₂²	semidirect
124. C₅₃×#532	C₂²	semidirect
125. C₅₃×#532	C₂²	semidirect
126. C₅₃×#532	C₂²	semidirect
127. C₅₃×#532	C₂²	semidirect
128. C₅₃×#532	C₂²	semidirect
129. C₅₃×#532	C₂²	semidirect
130. C₅₃×#532	C₂²	semidirect
131. C₅₃×#532	C₂²	semidirect
132. C₅₃×#532	C₂²	semidirect
133. C₅₃×#532	C₂²	semidirect
134. C₅₃×#532	C₂²	semidirect
135. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
136. C₂×#127×C₅₃	C₂²	semidirect
137. C₅₃×#529	C₂²	semidirect
138. C₅₃×#529	C₂²	semidirect
139. C₅₃×#529	C₂²	semidirect
140. C₅₃×#529	C₂²	semidirect
141. C₅₃×#529	C₂²	semidirect
142. C₅₃×#529	C₂²	semidirect
143. C₅₃×#529	C₂²	semidirect
144. C₅₃×#529	C₂²	semidirect
145. C₅₃×#529	C₂²	semidirect
146. C₅₃×#529	C₂²	semidirect
147. C₅₃×#529	C₂²	semidirect
148. C₅₃×#529	C₂²	semidirect
149. C₅₃×#529	C₂²	semidirect
150. C₅₃×#529	C₂²	semidirect
151. C₅₃×#529	C₂²	semidirect
152. C₅₃×#529	C₂²	semidirect
153. C₅₃×#529	C₂²	semidirect
154. C₅₃×#529	C₂²	semidirect
155. C₂×#126×C₅₃	C₂²	semidirect
156. C₂×#125×C₅₃	C₂²	semidirect
157. C₂×#124×C₅₃	C₂²	semidirect
158. C₂×#124×C₅₃	C₂²	semidirect
159. C₅₃×#525	C₂²	semidirect
160. C₅₃×#525	C₂²	semidirect
161. C₅₃×#525	C₂²	semidirect
162. C₅₃×#525	C₂²	semidirect
163. C₅₃×#525	C₂²	semidirect
164. C₅₃×#525	C₂²	semidirect
165. C₅₃×#525	C₂²	semidirect
166. C₅₃×#525	C₂²	semidirect
167. C₅₃×#525	C₂²	semidirect
168. C₂×#123×C₅₃	C₂²	semidirect
169. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
171. C₂×#121×C₅₃	C₂²	semidirect
172. C₂×#121×C₅₃	C₂²	semidirect
173. C₄×#41×C₅₃	C₂²	semidirect
174. C₄×#41×C₅₃	C₂²	semidirect
175. C₄×#41×C₅₃	C₂²	semidirect
176. C₄×#41×C₅₃	C₂²	semidirect
177. C₄×#41×C₅₃	C₂²	semidirect
178. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
179. C₂×C₄×D₄×C₅₃	C₂²	semidirect
180. C₂×C₄×D₄×C₅₃	C₂²	semidirect
181. C₂×C₄×D₄×C₅₃	C₂²	semidirect
182. C₂×C₄×D₄×C₅₃	C₂²	semidirect
183. C₂×C₄×D₄×C₅₃	C₂²	semidirect
184. C₂×C₄×D₄×C₅₃	C₂²	semidirect
185. C₂×#117×C₅₃	C₂²	semidirect
186. C₂²×C₄²×C₅₃	C₂²	semidirect
790. #62748	C₅₃	direct (N × H)
833. #3562	C₂×C₅₃	semidirect
834. #3561	C₂×C₅₃	semidirect
835. #3560	C₂×C₅₃	semidirect
836. #3559	C₂×C₅₃	semidirect
837. #3558	C₂×C₅₃	semidirect
838. #3558	C₂×C₅₃	semidirect
839. #3554	C₂×C₅₃	semidirect
840. #3552	C₂×C₅₃	semidirect
841. #3546	C₂×C₅₃	semidirect
842. #3543	C₂×C₅₃	semidirect
843. #3537	C₂×C₅₃	semidirect
844. #3536	C₂×C₅₃	semidirect
845. #3534	C₂×C₅₃	semidirect
846. #3529	C₂×C₅₃	semidirect
847. #3481	C₂×C₅₃	semidirect
848. #3480	C₂×C₅₃	semidirect
849. D₄×#41	C₂×C₅₃	semidirect
850. D₄×#41	C₂×C₅₃	semidirect
851. #3460	C₂×C₅₃	semidirect
852. #3459	C₂×C₅₃	semidirect
853. #3455	C₂×C₅₃	semidirect
854. #3449	C₂×C₅₃	semidirect
855. #3444	C₂×C₅₃	semidirect
856. C₂×#532	C₂×C₅₃	semidirect
857. C₂×#529	C₂×C₅₃	semidirect
867. C₂²×#41	C₂²×C₅₃	semidirect
868. C₂²×#41	C₂²×C₅₃	semidirect
869. #563	C₂²×C₅₃	semidirect
870. #563	C₂²×C₅₃	semidirect
871. #562	C₂²×C₅₃	semidirect
872. #562	C₂²×C₅₃	semidirect
873. #562	C₂²×C₅₃	semidirect
874. #562	C₂²×C₅₃	semidirect
875. H(3,𝔽₄)	C₂²×C₅₃	semidirect
876. #560	C₂²×C₅₃	semidirect
877. #560	C₂²×C₅₃	semidirect
878. #560	C₂²×C₅₃	semidirect
879. #559	C₂²×C₅₃	semidirect
880. #559	C₂²×C₅₃	semidirect
881. #559	C₂²×C₅₃	semidirect
882. #557	C₂²×C₅₃	semidirect
883. #556	C₂²×C₅₃	semidirect
884. #556	C₂²×C₅₃	semidirect
885. #554	C₂²×C₅₃	semidirect
886. #554	C₂²×C₅₃	semidirect
887. #553	C₂²×C₅₃	semidirect
888. #553	C₂²×C₅₃	semidirect
889. #553	C₂²×C₅₃	semidirect
890. #553	C₂²×C₅₃	semidirect
891. #553	C₂²×C₅₃	semidirect
892. #551	C₂²×C₅₃	semidirect
893. #551	C₂²×C₅₃	semidirect
894. #550	C₂²×C₅₃	semidirect
895. #550	C₂²×C₅₃	semidirect
896. #550	C₂²×C₅₃	semidirect
897. D₄×Q₈	C₂²×C₅₃	semidirect
898. D₄×Q₈	C₂²×C₅₃	semidirect
899. #548	C₂²×C₅₃	semidirect
900. #548	C₂²×C₅₃	semidirect
901. #548	C₂²×C₅₃	semidirect
902. #548	C₂²×C₅₃	semidirect
903. #547	C₂²×C₅₃	semidirect
904. #547	C₂²×C₅₃	semidirect
905. #547	C₂²×C₅₃	semidirect
906. #547	C₂²×C₅₃	semidirect
907. #546	C₂²×C₅₃	semidirect
908. #546	C₂²×C₅₃	semidirect
909. #546	C₂²×C₅₃	semidirect
910. #546	C₂²×C₅₃	semidirect
911. #546	C₂²×C₅₃	semidirect
912. #546	C₂²×C₅₃	semidirect
913. #546	C₂²×C₅₃	semidirect
914. #546	C₂²×C₅₃	semidirect
915. #546	C₂²×C₅₃	semidirect
916. D₄²	C₂²×C₅₃	semidirect
917. D₄²	C₂²×C₅₃	semidirect
918. D₄²	C₂²×C₅₃	semidirect
919. D₄²	C₂²×C₅₃	semidirect
920. D₄²	C₂²×C₅₃	semidirect
921. #544	C₂²×C₅₃	semidirect
922. #543	C₂²×C₅₃	semidirect
923. #542	C₂²×C₅₃	semidirect
924. #542	C₂²×C₅₃	semidirect
925. #542	C₂²×C₅₃	semidirect
926. #542	C₂²×C₅₃	semidirect
927. #542	C₂²×C₅₃	semidirect
928. #541	C₂²×C₅₃	semidirect
929. #540	C₂²×C₅₃	semidirect
930. #540	C₂²×C₅₃	semidirect
931. #540	C₂²×C₅₃	semidirect
932. #540	C₂²×C₅₃	semidirect
933. #539	C₂²×C₅₃	semidirect
934. #539	C₂²×C₅₃	semidirect
935. #539	C₂²×C₅₃	semidirect
936. #539	C₂²×C₅₃	semidirect
937. #539	C₂²×C₅₃	semidirect
938. #538	C₂²×C₅₃	semidirect
939. #538	C₂²×C₅₃	semidirect
940. #538	C₂²×C₅₃	semidirect
941. #538	C₂²×C₅₃	semidirect
942. #538	C₂²×C₅₃	semidirect
943. #538	C₂²×C₅₃	semidirect
944. #538	C₂²×C₅₃	semidirect
945. #538	C₂²×C₅₃	semidirect
946. #537	C₂²×C₅₃	semidirect
947. #537	C₂²×C₅₃	semidirect
948. #537	C₂²×C₅₃	semidirect
949. #536	C₂²×C₅₃	semidirect
950. #536	C₂²×C₅₃	semidirect
951. #535	C₂²×C₅₃	semidirect
952. #535	C₂²×C₅₃	semidirect
953. #535	C₂²×C₅₃	semidirect
954. #535	C₂²×C₅₃	semidirect
955. #534	C₂²×C₅₃	semidirect
956. #534	C₂²×C₅₃	semidirect
957. #534	C₂²×C₅₃	semidirect
958. #534	C₂²×C₅₃	semidirect
959. #533	C₂²×C₅₃	semidirect
960. #533	C₂²×C₅₃	semidirect
961. #533	C₂²×C₅₃	semidirect
962. #532	C₂²×C₅₃	semidirect
963. #532	C₂²×C₅₃	semidirect
964. #532	C₂²×C₅₃	semidirect
965. #532	C₂²×C₅₃	semidirect
966. #532	C₂²×C₅₃	semidirect
967. #532	C₂²×C₅₃	semidirect
968. #532	C₂²×C₅₃	semidirect
969. #532	C₂²×C₅₃	semidirect
970. #532	C₂²×C₅₃	semidirect
971. #532	C₂²×C₅₃	semidirect
972. #532	C₂²×C₅₃	semidirect
973. #532	C₂²×C₅₃	semidirect
974. #532	C₂²×C₅₃	semidirect
975. #532	C₂²×C₅₃	semidirect
976. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
977. C₂×#127	C₂²×C₅₃	semidirect
978. #529	C₂²×C₅₃	semidirect
979. #529	C₂²×C₅₃	semidirect
980. #529	C₂²×C₅₃	semidirect
981. #529	C₂²×C₅₃	semidirect
982. #529	C₂²×C₅₃	semidirect
983. #529	C₂²×C₅₃	semidirect
984. #529	C₂²×C₅₃	semidirect
985. #529	C₂²×C₅₃	semidirect
986. #529	C₂²×C₅₃	semidirect
987. #529	C₂²×C₅₃	semidirect
988. #529	C₂²×C₅₃	semidirect
989. #529	C₂²×C₅₃	semidirect
990. #529	C₂²×C₅₃	semidirect
991. #529	C₂²×C₅₃	semidirect
992. #529	C₂²×C₅₃	semidirect
993. #529	C₂²×C₅₃	semidirect
994. #529	C₂²×C₅₃	semidirect
995. #529	C₂²×C₅₃	semidirect
996. C₂×#126	C₂²×C₅₃	semidirect
997. C₂×#125	C₂²×C₅₃	semidirect
998. C₂×#124	C₂²×C₅₃	semidirect
999. C₂×#124	C₂²×C₅₃	semidirect
1000. #525	C₂²×C₅₃	semidirect
1001. #525	C₂²×C₅₃	semidirect
1002. #525	C₂²×C₅₃	semidirect
1003. #525	C₂²×C₅₃	semidirect
1004. #525	C₂²×C₅₃	semidirect
1005. #525	C₂²×C₅₃	semidirect
1006. #525	C₂²×C₅₃	semidirect
1007. #525	C₂²×C₅₃	semidirect
1008. #525	C₂²×C₅₃	semidirect
1009. C₂×#123	C₂²×C₅₃	semidirect
1010. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
1012. C₂×#121	C₂²×C₅₃	semidirect
1013. C₂×#121	C₂²×C₅₃	semidirect
1014. C₄×#41	C₂²×C₅₃	semidirect
1015. C₄×#41	C₂²×C₅₃	semidirect
1016. C₄×#41	C₂²×C₅₃	semidirect
1017. C₄×#41	C₂²×C₅₃	semidirect
1018. C₄×#41	C₂²×C₅₃	semidirect
1019. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
1020. C₂×C₄×D₄	C₂²×C₅₃	semidirect
1021. C₂×C₄×D₄	C₂²×C₅₃	semidirect
1022. C₂×C₄×D₄	C₂²×C₅₃	semidirect
1023. C₂×C₄×D₄	C₂²×C₅₃	semidirect
1024. C₂×C₄×D₄	C₂²×C₅₃	semidirect
1025. C₂×C₄×D₄	C₂²×C₅₃	semidirect
1026. C₂×#117	C₂²×C₅₃	semidirect
1027. C₂²×C₄²	C₂²×C₅₃	semidirect
1028. C₅₃	#62748	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅₃×#3562	2
C₅₃×#3561	2
C₅₃×#3560	2
C₅₃×#3559	2
C₅₃×#3558	2
C₅₃×#3554	2
C₅₃×#3552	2
C₅₃×#3546	2
C₅₃×#3543	2
C₅₃×#3537	2
C₅₃×#3536	2
C₅₃×#3534	2
C₅₃×#3529	2
C₅₃×#3481	2
C₅₃×#3480	2
D₄×#41×C₅₃	2
C₅₃×#3460	2
C₅₃×#3459	2
C₅₃×#3455	2
C₅₃×#3449	2
C₅₃×#3444	2
C₂×C₅₃×#532	2
C₂×C₅₃×#529	2
#62748	53

Subgroups — C53×#62748 #27270260

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62748 #27270260