Subgroups — C₅₃×#62729 #27270241

Order 13568.

7346 conjugacy classes of subgroups.

The subgroup lattice has 1530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3542	C₂	1	4	yes	maximal, complemented
2	C₅₃×#3541	C₂	1	4	yes	maximal, complemented
3	C₅₃×#3540	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3539	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3538	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3537	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3536	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3535	C₂	1	4	yes	maximal, complemented
9	C₅₃×#3534	C₂	1	4	yes	maximal, complemented
10	C₅₃×#3533	C₂	1	4	yes	maximal, complemented
11	C₅₃×#3532	C₂	1	4	yes	maximal, complemented
12	C₅₃×#3529	C₂	1	4	yes	maximal, complemented
13	C₅₃×#3481	C₂	1	4	yes	maximal, complemented
14	C₅₃×#3475	C₂	1	4	yes	maximal, complemented
15	D₄×#41×C₅₃	C₂	1	4	yes	maximal, complemented
16	C₅₃×#3460	C₂	1	4	yes	maximal, complemented
17	C₅₃×#3459	C₂	1	4	yes	maximal, complemented
18	C₅₃×#3455	C₂	1	2	yes	maximal, complemented
19	C₅₃×#3449	C₂	1	2	yes	maximal, complemented
20	C₂×C₅₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₅₃×#525	C₂	1	2	yes	maximal, complemented
22	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
23	C₂²×#41×C₅₃	C₂²	1	2	yes	complemented
24	C₂²×#41×C₅₃	C₂²	1	2	yes	complemented
25	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
26	C₅₃×#563	C₂²	1	4	yes	complemented
27	C₅₃×#563	C₂²	1	8	yes	complemented
28	C₅₃×#562	C₂²	1	8	yes	complemented
29	C₅₃×#562	C₂²	1	8	yes	complemented
30	C₅₃×#562	C₂²	1	8	yes	complemented
31	C₅₃×H(3,𝔽₄)	C₂²	1	4	yes	complemented
32	C₅₃×#560	C₂²	1	8	yes	complemented
33	C₅₃×#560	C₂²	1	4	yes	complemented
34	C₅₃×#560	C₂²	1	4	yes	complemented
35	C₅₃×#560	C₂²	1	8	yes	complemented
36	C₅₃×#559	C₂²	1	4	yes	complemented
37	C₅₃×#556	C₂²	1	4	yes	complemented
38	C₅₃×#555	C₂²	1	4	yes	complemented
39	C₅₃×#554	C₂²	1	4	yes	complemented
40	C₅₃×#554	C₂²	1	8	yes	complemented
41	C₅₃×#553	C₂²	1	4	yes	complemented
42	C₅₃×#553	C₂²	1	8	yes	complemented
43	C₅₃×#553	C₂²	1	4	yes	complemented
44	C₅₃×#553	C₂²	1	8	yes	complemented
45	C₅₃×#552	C₂²	1	8	yes	complemented
46	C₅₃×#552	C₂²	1	4	yes	complemented
47	C₅₃×#552	C₂²	1	4	yes	complemented
48	C₅₃×#551	C₂²	1	8	yes	complemented
49	C₅₃×#551	C₂²	1	4	yes	complemented
50	C₅₃×#551	C₂²	1	8	yes	complemented
51	C₅₃×#551	C₂²	1	8	yes	complemented
52	C₅₃×#551	C₂²	1	4	yes	complemented
53	C₅₃×#550	C₂²	1	4	yes	complemented
54	D₄×Q₈×C₅₃	C₂²	1	4	yes	complemented
55	C₅₃×#548	C₂²	1	4	yes	complemented
56	C₅₃×#548	C₂²	1	4	yes	complemented
57	C₅₃×#547	C₂²	1	8	yes	complemented
58	C₅₃×#547	C₂²	1	4	yes	complemented
59	C₅₃×#547	C₂²	1	4	yes	complemented
60	C₅₃×#546	C₂²	1	8	yes	complemented
61	C₅₃×#546	C₂²	1	8	yes	complemented
62	C₅₃×#546	C₂²	1	8	yes	complemented
63	C₅₃×#546	C₂²	1	4	yes	complemented
64	C₅₃×#546	C₂²	1	8	yes	complemented
65	C₅₃×#546	C₂²	1	8	yes	complemented
66	C₅₃×#546	C₂²	1	4	yes	complemented
67	D₄²×C₅₃	C₂²	1	8	yes	complemented
68	D₄²×C₅₃	C₂²	1	4	yes	complemented
69	D₄²×C₅₃	C₂²	1	4	yes	complemented
70	C₅₃×#544	C₂²	1	4	yes	complemented
71	C₅₃×#543	C₂²	1	4	yes	complemented
72	C₅₃×#542	C₂²	1	4	yes	complemented
73	C₅₃×#542	C₂²	1	4	yes	complemented
74	C₅₃×#542	C₂²	1	8	yes	complemented
75	C₅₃×#542	C₂²	1	8	yes	complemented
76	C₅₃×#541	C₂²	1	2	yes	complemented
77	C₅₃×#541	C₂²	1	2	yes	complemented
78	C₅₃×#540	C₂²	1	2	yes	complemented
79	C₅₃×#540	C₂²	1	2	yes	complemented
80	C₅₃×#540	C₂²	1	8	yes	complemented
81	C₅₃×#540	C₂²	1	8	yes	complemented
82	C₅₃×#539	C₂²	1	8	yes	complemented
83	C₅₃×#539	C₂²	1	4	yes	complemented
84	C₅₃×#539	C₂²	1	4	yes	complemented
85	C₅₃×#539	C₂²	1	8	yes	complemented
86	C₅₃×#539	C₂²	1	8	yes	complemented
87	C₅₃×#538	C₂²	1	8	yes	complemented
88	C₅₃×#538	C₂²	1	8	yes	complemented
89	C₅₃×#538	C₂²	1	8	yes	complemented
90	C₅₃×#538	C₂²	1	4	yes	complemented
91	C₅₃×#538	C₂²	1	4	yes	complemented
92	C₅₃×#538	C₂²	1	8	yes	complemented
93	C₅₃×#538	C₂²	1	8	yes	complemented
94	C₅₃×#537	C₂²	1	4	yes	complemented
95	C₅₃×#537	C₂²	1	4	yes	complemented
96	C₅₃×#537	C₂²	1	4	yes	complemented
97	C₅₃×#536	C₂²	1	4	yes	complemented
98	C₅₃×#536	C₂²	1	2	yes	complemented
99	C₅₃×#536	C₂²	1	2	yes	complemented
100	C₅₃×#535	C₂²	1	4	yes	complemented
101	C₅₃×#535	C₂²	1	8	yes	complemented
102	C₅₃×#535	C₂²	1	2	yes	complemented
103	C₅₃×#535	C₂²	1	2	yes	complemented
104	C₅₃×#534	C₂²	1	4	yes	complemented
105	C₅₃×#534	C₂²	1	8	yes	complemented
106	C₅₃×#534	C₂²	1	4	yes	complemented
107	C₅₃×#534	C₂²	1	4	yes	complemented
108	C₅₃×#533	C₂²	1	2	yes	complemented
109	C₅₃×#532	C₂²	1	2	yes	complemented
110	C₅₃×#532	C₂²	1	4	yes	complemented
111	C₅₃×#532	C₂²	1	4	yes	complemented
112	C₅₃×#532	C₂²	1	8	yes	complemented
113	C₅₃×#529	C₂²	1	8	yes	complemented
114	C₅₃×#529	C₂²	1	8	yes	complemented
115	C₅₃×#529	C₂²	1	8	yes	complemented
116	C₅₃×#529	C₂²	1	8	yes	complemented
117	C₅₃×#529	C₂²	1	8	yes	complemented
118	C₅₃×#525	C₂²	1	1	yes	characteristic
119	C₅₃×#525	C₂²	1	4	yes	complemented
120	C₅₃×#525	C₂²	1	2	yes	complemented
121	C₅₃×#525	C₂²	1	4	yes	complemented
122	C₅₃×#525	C₂²	1	2	yes	complemented
123	C₅₃×#525	C₂²	1	4	yes	complemented
124	C₅₃×#525	C₂²	1	2	yes	complemented
125	C₅₃×#525	C₂²	1	2	yes	complemented
126	C₅₃×#525	C₂²	1	4	yes	complemented
127	C₅₃×#525	C₂²	1	4	yes	complemented
128	C₅₃×#525	C₂²	1	4	yes	complemented
129	C₅₃×#525	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#525	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#525	C₂²	1	4	yes	complemented
132	C₅₃×#525	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#525	C₂²	1	4	yes	complemented
134	C₅₃×#525	C₂²	1	4	yes	complemented
135	C₅₃×#525	C₂²	1	4	yes	complemented
136	C₅₃×#525	C₂²	1	8	yes	complemented
137	C₅₃×#525	C₂²	1	4	yes	complemented
138	C₅₃×#525	C₂²	1	4	yes	complemented
139	C₅₃×#525	C₂²	1	8	yes	complemented
140	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
141	C₂×#123×C₅₃	C₂²	1	4	yes	complemented
142	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
143	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
144	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
145	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
146	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
147	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
148	C₂×#120×C₅₃	C₂²	1	2	yes	complemented
149	C₂×#120×C₅₃	C₂²	1	4	yes	complemented
150	C₄×#41×C₅₃	C₂²	1	4	yes	complemented
151	C₄×#41×C₅₃	C₂²	1	8	yes	complemented
152	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	complemented
153	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	complemented
154	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	complemented
155	C₂×C₄×D₄×C₅₃	C₂²	1	8	yes	complemented
156	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
157	C₂×#117×C₅₃	C₂²	1	2	yes	complemented
158	C₂×#117×C₅₃	C₂²	1	2	yes	complemented
159	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
160	C₂×#41×C₅₃	—	4	4	no	—
161	C₂×#41×C₅₃	—	4	8	no	—
162	C₂×#41×C₅₃	—	4	8	no	—
163	C₂×#41×C₅₃	C₂³	1	4	yes	—
164	C₂×#41×C₅₃	C₂³	1	8	yes	—
165	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
166	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
167	C₂×#41×C₅₃	C₂³	1	2	yes	—
168	C₂×#41×C₅₃	C₂³	1	4	yes	—
169	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
170	C₂×#41×C₅₃	C₂³	1	2	yes	—
171	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
172	C₂×#41×C₅₃	C₂³	1	4	yes	—
173	C₂×#41×C₅₃	C₂³	1	4	yes	—
174	C₂×#41×C₅₃	C₂³	1	4	yes	—
175	C₂×#41×C₅₃	C₂³	1	4	yes	complemented
176	C₂×#41×C₅₃	C₂³	1	4	yes	complemented
177	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
178	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
179	C₂²×Q₈×C₅₃	C₂³	1	2	yes	complemented
180	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
181	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
182	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
183	C₂²×D₄×C₅₃	C₂³	1	8	yes	—
184	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
185	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
186	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
187	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
188	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
189	C₂²×D₄×C₅₃	C₂³	1	2	yes	complemented
190	C₂³×C₄×C₅₃	—	4	4	no	—
191	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
192	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
193	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
194	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
195	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
196	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
197	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
198	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
199	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
200	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
201	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
202	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
203	C₂³×C₄×C₅₃	C₂³	1	4	yes	complemented
204	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
205	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
206	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
207	C₄⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
208	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
209	#127×C₅₃	C₂³	1	4	yes	—
210	#127×C₅₃	C₂³	1	4	yes	—
211	#127×C₅₃	C₂³	1	8	yes	—
212	#127×C₅₃	C₂³	1	2	yes	complemented
213	#126×C₅₃	C₂³	1	8	yes	—
214	#126×C₅₃	C₂³	1	8	yes	—
215	#126×C₅₃	C₂³	1	8	yes	—
216	#126×C₅₃	C₂³	1	8	yes	—
217	#126×C₅₃	C₂³	1	8	yes	complemented
218	#126×C₅₃	C₂³	1	8	yes	complemented
219	#126×C₅₃	C₂³	1	8	yes	complemented
220	#126×C₅₃	C₂³	1	8	yes	complemented
221	#126×C₅₃	C₂³	1	8	yes	complemented
222	#126×C₅₃	C₂³	1	8	yes	complemented
223	#125×C₅₃	C₂³	1	8	yes	complemented
224	#125×C₅₃	C₂³	1	8	yes	complemented
225	#125×C₅₃	C₂³	1	8	yes	complemented
226	#125×C₅₃	C₂³	1	8	yes	complemented
227	#125×C₅₃	C₂³	1	8	yes	complemented
228	#125×C₅₃	C₂³	1	2	yes	complemented
229	#125×C₅₃	C₂³	1	2	yes	complemented
230	#124×C₅₃	C₂³	1	8	yes	—
231	#124×C₅₃	C₂³	1	8	yes	—
232	#124×C₅₃	C₂³	1	8	yes	—
233	#124×C₅₃	C₂³	1	8	yes	—
234	#124×C₅₃	C₂³	1	4	yes	—
235	#124×C₅₃	C₂³	1	4	yes	—
236	#124×C₅₃	C₂³	1	8	yes	—
237	#124×C₅₃	C₂³	1	8	yes	complemented
238	#124×C₅₃	C₂³	1	4	yes	complemented
239	#124×C₅₃	C₂³	1	4	yes	complemented
240	#124×C₅₃	C₂³	1	8	yes	complemented
241	#124×C₅₃	C₂³	1	4	yes	complemented
242	#123×C₅₃	C₂³	1	2	yes	—
243	#123×C₅₃	C₂³	1	8	yes	—
244	#123×C₅₃	C₂³	1	4	yes	—
245	#123×C₅₃	C₂³	1	8	yes	—
246	#123×C₅₃	C₂³	1	4	yes	—
247	#123×C₅₃	C₂³	1	8	yes	—
248	#123×C₅₃	C₂³	1	2	yes	—
249	#123×C₅₃	C₂³	1	2	yes	—
250	#123×C₅₃	C₂³	1	8	yes	—
251	#123×C₅₃	C₂³	1	2	yes	—
252	#123×C₅₃	C₂³	1	4	yes	—
253	#123×C₅₃	C₂³	1	8	yes	—
254	#123×C₅₃	C₂³	1	4	yes	—
255	#123×C₅₃	C₂³	1	8	yes	—
256	#123×C₅₃	C₂³	1	8	yes	—
257	#123×C₅₃	C₂³	1	8	yes	—
258	#123×C₅₃	C₂³	1	8	yes	—
259	#123×C₅₃	C₂³	1	8	yes	—
260	#123×C₅₃	C₂³	1	8	yes	—
261	#123×C₅₃	C₂³	1	8	yes	—
262	#123×C₅₃	C₂³	1	4	yes	complemented
263	#123×C₅₃	C₂³	1	4	yes	complemented
264	#123×C₅₃	C₂³	1	8	yes	complemented
265	#123×C₅₃	C₂³	1	8	yes	complemented
266	#123×C₅₃	C₂³	1	8	yes	complemented
267	#123×C₅₃	C₂³	1	8	yes	complemented
268	#123×C₅₃	C₂³	1	8	yes	complemented
269	#123×C₅₃	C₂³	1	8	yes	complemented
270	#123×C₅₃	C₂³	1	8	yes	complemented
271	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
272	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
273	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
274	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
275	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
276	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
277	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
278	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
279	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
280	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
281	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
282	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
283	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
284	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
285	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
286	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
287	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
288	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
289	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
290	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
291	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
292	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
293	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
294	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
295	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
296	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
297	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
298	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
299	#121×C₅₃	C₂³	1	2	yes	—
300	#121×C₅₃	C₂³	1	4	yes	—
301	#121×C₅₃	C₂³	1	4	yes	—
302	#121×C₅₃	C₂³	1	4	yes	—
303	#121×C₅₃	C₂³	1	2	yes	—
304	#121×C₅₃	C₂³	1	2	yes	—
305	#121×C₅₃	C₂³	1	4	yes	—
306	#121×C₅₃	C₂³	1	2	yes	—
307	#121×C₅₃	C₂³	1	4	yes	—
308	#121×C₅₃	C₂³	1	4	yes	—
309	#121×C₅₃	C₂³	1	4	yes	—
310	#121×C₅₃	C₂³	1	4	yes	—
311	#121×C₅₃	C₂³	1	4	yes	—
312	#121×C₅₃	C₂³	1	4	yes	—
313	#121×C₅₃	C₂³	1	8	yes	—
314	#121×C₅₃	C₂³	1	8	yes	—
315	#121×C₅₃	C₂³	1	8	yes	—
316	#121×C₅₃	C₂³	1	8	yes	—
317	#121×C₅₃	C₂³	1	8	yes	—
318	#121×C₅₃	C₂³	1	8	yes	—
319	#121×C₅₃	C₂³	1	8	yes	—
320	#121×C₅₃	C₂³	1	8	yes	—
321	#121×C₅₃	C₂³	1	8	yes	—
322	#121×C₅₃	C₂³	1	8	yes	—
323	#121×C₅₃	C₂³	1	8	yes	—
324	#121×C₅₃	C₂³	1	8	yes	—
325	#121×C₅₃	C₂³	1	8	yes	—
326	#121×C₅₃	C₂³	1	8	yes	—
327	#121×C₅₃	C₂³	1	8	yes	—
328	#121×C₅₃	C₂³	1	4	yes	complemented
329	#121×C₅₃	C₂³	1	4	yes	complemented
330	#121×C₅₃	C₂³	1	8	yes	complemented
331	#121×C₅₃	C₂³	1	8	yes	complemented
332	#121×C₅₃	C₂³	1	8	yes	complemented
333	#121×C₅₃	C₂³	1	8	yes	complemented
334	#121×C₅₃	C₂³	1	8	yes	complemented
335	#120×C₅₃	C₂³	1	2	yes	—
336	#120×C₅₃	C₂³	1	4	yes	—
337	#120×C₅₃	C₂³	1	8	yes	—
338	#120×C₅₃	C₂³	1	8	yes	—
339	#120×C₅₃	C₂³	1	4	yes	—
340	#120×C₅₃	C₂³	1	8	yes	—
341	#120×C₅₃	C₂³	1	2	yes	—
342	#120×C₅₃	C₂³	1	2	yes	—
343	#120×C₅₃	C₂³	1	8	yes	—
344	#120×C₅₃	C₂³	1	2	yes	—
345	#120×C₅₃	C₂³	1	4	yes	—
346	#120×C₅₃	C₂³	1	8	yes	—
347	#120×C₅₃	C₂³	1	4	yes	—
348	#120×C₅₃	C₂³	1	8	yes	—
349	#120×C₅₃	C₂³	1	8	yes	—
350	#120×C₅₃	C₂³	1	8	yes	—
351	#120×C₅₃	C₂³	1	4	yes	complemented
352	#120×C₅₃	C₂³	1	4	yes	complemented
353	#120×C₅₃	C₂³	1	8	yes	complemented
354	C₄×Q₈×C₅₃	C₂³	1	8	yes	complemented
355	C₄×Q₈×C₅₃	C₂³	1	4	yes	complemented
356	C₄×Q₈×C₅₃	C₂³	1	4	yes	complemented
357	C₄×Q₈×C₅₃	C₂³	1	8	yes	complemented
358	C₄×D₄×C₅₃	C₂³	1	4	yes	—
359	C₄×D₄×C₅₃	C₂³	1	8	yes	—
360	C₄×D₄×C₅₃	C₂³	1	4	yes	—
361	C₄×D₄×C₅₃	C₂³	1	4	yes	—
362	C₄×D₄×C₅₃	C₂³	1	4	yes	—
363	C₄×D₄×C₅₃	C₂³	1	8	yes	—
364	C₄×D₄×C₅₃	C₂³	1	8	yes	—
365	C₄×D₄×C₅₃	C₂³	1	8	yes	—
366	C₄×D₄×C₅₃	C₂³	1	4	yes	—
367	C₄×D₄×C₅₃	C₂³	1	8	yes	—
368	C₄×D₄×C₅₃	C₂³	1	8	yes	—
369	C₄×D₄×C₅₃	C₂³	1	4	yes	—
370	C₄×D₄×C₅₃	C₂³	1	4	yes	—
371	C₄×D₄×C₅₃	C₂³	1	8	yes	—
372	C₄×D₄×C₅₃	C₂³	1	4	yes	—
373	C₄×D₄×C₅₃	C₂³	1	8	yes	—
374	C₄×D₄×C₅₃	C₂³	1	8	yes	—
375	C₄×D₄×C₅₃	C₂³	1	8	yes	—
376	C₄×D₄×C₅₃	C₂³	1	8	yes	—
377	C₄×D₄×C₅₃	C₂³	1	8	yes	—
378	C₄×D₄×C₅₃	C₂³	1	8	yes	—
379	C₄×D₄×C₅₃	C₂³	1	8	yes	—
380	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
381	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
382	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
383	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
384	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
385	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
386	C₄×D₄×C₅₃	C₂³	1	4	yes	complemented
387	C₄×D₄×C₅₃	C₂³	1	4	yes	complemented
388	#117×C₅₃	C₂³	1	4	yes	—
389	#117×C₅₃	C₂³	1	1	yes	characteristic
390	#117×C₅₃	C₂³	1	2	yes	—
391	#117×C₅₃	C₂³	1	2	yes	—
392	#117×C₅₃	C₂³	1	4	yes	—
393	#117×C₅₃	C₂³	1	2	yes	—
394	#117×C₅₃	C₂³	1	1	yes	characteristic
395	#117×C₅₃	C₂³	1	4	yes	—
396	#117×C₅₃	C₂³	1	4	yes	—
397	#117×C₅₃	C₂³	1	4	yes	—
398	#117×C₅₃	C₂³	1	8	yes	—
399	#117×C₅₃	C₂³	1	4	yes	complemented
400	#117×C₅₃	C₂³	1	2	yes	complemented
401	#117×C₅₃	C₂³	1	2	yes	complemented
402	#117×C₅₃	C₂³	1	8	yes	complemented
403	#117×C₅₃	C₂³	1	8	yes	complemented
404	#117×C₅₃	C₂³	1	8	yes	complemented
405	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
406	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
407	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
408	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
409	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
410	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
411	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	complemented
412	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	complemented
413	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
414	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
415	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
416	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
417	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
418	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
419	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
420	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
421	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
422	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
423	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	complemented
424	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
425	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
426	C₂×C₄²×C₅₃	C₂³	1	4	yes	complemented
427	C₂×C₄²×C₅₃	C₂³	1	8	yes	complemented
428	C₂⁴×C₅₃	—	4	2	no	—
429	C₂⁴×C₅₃	—	4	4	no	—
430	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
431	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
432	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
433	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
434	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
435	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
436	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
437	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
438	#41×C₅₃	—	2	16	no	—
439	#41×C₅₃	—	4	2	no	—
440	#41×C₅₃	—	4	4	no	—
441	#41×C₅₃	—	4	2	no	—
442	#41×C₅₃	—	4	4	no	—
443	#41×C₅₃	—	4	2	no	—
444	#41×C₅₃	—	4	2	no	—
445	#41×C₅₃	—	4	8	no	—
446	#41×C₅₃	—	4	8	no	—
447	#41×C₅₃	—	4	8	no	—
448	#41×C₅₃	—	4	8	no	—
449	#41×C₅₃	—	4	16	no	—
450	#41×C₅₃	—	4	8	no	—
451	#41×C₅₃	—	4	8	no	—
452	C₂×Q₈×C₅₃	—	4	2	no	—
453	C₂×Q₈×C₅₃	—	4	4	no	—
454	C₂×Q₈×C₅₃	—	4	4	no	—
455	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
456	C₂×Q₈×C₅₃	C₂⁴	1	8	yes	—
457	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
458	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
459	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
460	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
461	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
462	C₂×D₄×C₅₃	—	4	4	no	—
463	C₂×D₄×C₅₃	—	4	4	no	—
464	C₂×D₄×C₅₃	—	4	8	no	—
465	C₂×D₄×C₅₃	—	4	2	no	—
466	C₂×D₄×C₅₃	—	4	4	no	—
467	C₂×D₄×C₅₃	—	4	16	no	—
468	C₂×D₄×C₅₃	—	4	8	no	—
469	C₂×D₄×C₅₃	—	4	8	no	—
470	C₂×D₄×C₅₃	—	4	8	no	—
471	C₂×D₄×C₅₃	—	4	8	no	—
472	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
473	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
474	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
475	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
476	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
477	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
478	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
479	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
480	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
481	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
482	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
483	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
484	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
485	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
486	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
487	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
488	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
489	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
490	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
491	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
492	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
493	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
494	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
495	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
496	C₂²×C₄×C₅₃	—	2	4	no	—
497	C₂²×C₄×C₅₃	—	2	8	no	—
498	C₂²×C₄×C₅₃	—	2	8	no	—
499	C₂²×C₄×C₅₃	—	4	2	no	—
500	C₂²×C₄×C₅₃	—	4	4	no	—
501	C₂²×C₄×C₅₃	—	4	2	no	—
502	C₂²×C₄×C₅₃	—	4	4	no	—
503	C₂²×C₄×C₅₃	—	4	2	no	—
504	C₂²×C₄×C₅₃	—	4	2	no	—
505	C₂²×C₄×C₅₃	—	4	8	no	—
506	C₂²×C₄×C₅₃	—	4	8	no	—
507	C₂²×C₄×C₅₃	—	4	4	no	—
508	C₂²×C₄×C₅₃	—	4	2	no	—
509	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
510	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
511	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
512	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
513	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
514	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
515	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
516	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
517	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
518	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
519	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
520	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
521	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
522	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
523	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
524	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
525	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
526	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
527	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
528	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
529	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
530	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
531	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
532	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
533	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
534	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
535	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
536	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
537	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
538	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
539	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
540	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
541	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
542	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
543	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
544	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
545	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
546	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
547	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
548	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
549	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
550	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
551	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
552	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
553	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
554	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
555	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
556	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
557	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
558	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
559	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
560	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
561	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
562	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
563	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
564	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
565	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
566	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
567	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
568	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
569	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
570	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
571	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
572	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
573	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
574	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
575	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
576	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
577	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
578	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
579	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
580	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
581	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
582	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
583	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
584	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
585	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
586	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
587	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
588	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
589	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
590	C₂²⋊C₄×C₅₃	C₂⁴	1	8	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	8	yes	—
596	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
597	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
598	C₄²×C₅₃	C₂⁴	1	8	yes	—
599	C₄²×C₅₃	C₂⁴	1	2	yes	—
600	C₄²×C₅₃	C₂⁴	1	2	yes	—
601	C₄²×C₅₃	C₂⁴	1	4	yes	—
602	C₄²×C₅₃	C₂⁴	1	8	yes	—
603	C₄²×C₅₃	C₂⁴	1	4	yes	—
604	C₄²×C₅₃	C₂⁴	1	8	yes	—
605	C₄²×C₅₃	C₂⁴	1	4	yes	—
606	C₄²×C₅₃	C₂⁴	1	8	yes	—
607	C₂³×C₅₃	—	2	4	no	—
608	C₂³×C₅₃	—	2	2	no	—
609	C₂³×C₅₃	—	2	4	no	—
610	C₂³×C₅₃	—	2	4	no	—
611	C₂³×C₅₃	—	2	4	no	—
612	C₂³×C₅₃	—	2	4	no	—
613	C₂³×C₅₃	—	2	8	no	—
614	C₂³×C₅₃	—	4	1	no	—
615	C₂³×C₅₃	—	4	2	no	—
616	C₂³×C₅₃	—	4	1	no	—
617	C₂³×C₅₃	—	4	2	no	—
618	C₂³×C₅₃	—	4	2	no	—
619	C₂³×C₅₃	—	4	2	no	—
620	C₂³×C₅₃	—	4	2	no	—
621	C₂³×C₅₃	—	4	4	no	—
622	C₂³×C₅₃	—	4	4	no	—
623	C₂³×C₅₃	—	4	4	no	—
624	C₂³×C₅₃	—	4	4	no	—
625	C₂³×C₅₃	—	4	8	no	—
626	C₂³×C₅₃	—	4	16	no	—
627	C₂³×C₅₃	C₂⁵	1	2	yes	—
628	C₂³×C₅₃	C₂⁵	1	8	yes	—
629	C₂³×C₅₃	C₂⁵	1	2	yes	—
630	C₂³×C₅₃	C₂⁵	1	2	yes	—
631	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
632	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
633	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
634	C₂³×C₅₃	C₂⁵	1	2	yes	—
635	Q₈×C₅₃	—	2	8	no	—
636	Q₈×C₅₃	—	4	1	no	—
637	Q₈×C₅₃	—	4	2	no	—
638	Q₈×C₅₃	—	4	1	no	—
639	Q₈×C₅₃	—	4	4	no	—
640	Q₈×C₅₃	—	4	4	no	—
641	Q₈×C₅₃	—	4	8	no	—
642	D₄×C₅₃	—	2	16	no	—
643	D₄×C₅₃	—	2	8	no	—
644	D₄×C₅₃	—	2	16	no	—
645	D₄×C₅₃	—	2	8	no	—
646	D₄×C₅₃	—	2	8	no	—
647	D₄×C₅₃	—	4	8	no	—
648	D₄×C₅₃	—	4	8	no	—
649	D₄×C₅₃	—	4	4	no	—
650	D₄×C₅₃	—	4	8	no	—
651	D₄×C₅₃	—	4	8	no	—
652	D₄×C₅₃	—	4	8	no	—
653	D₄×C₅₃	—	4	4	no	—
654	D₄×C₅₃	—	4	2	no	—
655	D₄×C₅₃	—	4	1	no	—
656	D₄×C₅₃	—	4	2	no	—
657	D₄×C₅₃	—	4	2	no	—
658	D₄×C₅₃	—	4	1	no	—
659	D₄×C₅₃	—	4	4	no	—
660	D₄×C₅₃	—	4	2	no	—
661	D₄×C₅₃	—	4	2	no	—
662	D₄×C₅₃	—	4	4	no	—
663	D₄×C₅₃	—	4	8	no	—
664	D₄×C₅₃	—	4	8	no	—
665	D₄×C₅₃	—	4	8	no	—
666	C₂×C₄×C₅₃	—	2	2	no	—
667	C₂×C₄×C₅₃	—	2	4	no	—
668	C₂×C₄×C₅₃	—	2	4	no	—
669	C₂×C₄×C₅₃	—	2	8	no	—
670	C₂×C₄×C₅₃	—	2	4	no	—
671	C₂×C₄×C₅₃	—	2	4	no	—
672	C₂×C₄×C₅₃	—	2	4	no	—
673	C₂×C₄×C₅₃	—	2	2	no	—
674	C₂×C₄×C₅₃	—	2	2	no	—
675	C₂×C₄×C₅₃	—	2	4	no	—
676	C₂×C₄×C₅₃	—	2	4	no	—
677	C₂×C₄×C₅₃	—	2	2	no	—
678	C₂×C₄×C₅₃	—	2	2	no	—
679	C₂×C₄×C₅₃	—	2	4	no	—
680	C₂×C₄×C₅₃	—	2	4	no	—
681	C₂×C₄×C₅₃	—	2	4	no	—
682	C₂×C₄×C₅₃	—	2	16	no	—
683	C₂×C₄×C₅₃	—	4	1	no	—
684	C₂×C₄×C₅₃	—	4	2	no	—
685	C₂×C₄×C₅₃	—	4	2	no	—
686	C₂×C₄×C₅₃	—	4	2	no	—
687	C₂×C₄×C₅₃	—	4	2	no	—
688	C₂×C₄×C₅₃	—	4	2	no	—
689	C₂×C₄×C₅₃	—	4	1	no	—
690	C₂×C₄×C₅₃	—	4	4	no	—
691	C₂×C₄×C₅₃	—	4	4	no	—
692	C₂×C₄×C₅₃	—	4	8	no	—
693	C₂×C₄×C₅₃	—	4	8	no	—
694	C₂×C₄×C₅₃	—	4	8	no	—
695	C₂×C₄×C₅₃	—	4	4	no	—
696	C₂×C₄×C₅₃	—	4	4	no	—
697	C₂×C₄×C₅₃	—	4	8	no	—
698	C₂×C₄×C₅₃	—	4	8	no	—
699	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
700	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
701	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
702	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
703	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
704	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
705	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
706	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
707	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
708	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
709	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
710	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
711	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
712	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
713	#62729	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
714	C₂²×C₅₃	—	2	2	no	—
715	C₂²×C₅₃	—	2	2	no	—
716	C₂²×C₅₃	—	2	2	no	—
717	C₂²×C₅₃	—	2	2	no	—
718	C₂²×C₅₃	—	2	1	no	—
719	C₂²×C₅₃	—	2	1	no	—
720	C₂²×C₅₃	—	2	2	no	—
721	C₂²×C₅₃	—	2	2	no	—
722	C₂²×C₅₃	—	2	8	no	—
723	C₂²×C₅₃	—	2	4	no	—
724	C₂²×C₅₃	—	2	8	no	—
725	C₂²×C₅₃	—	2	8	no	—
726	C₂²×C₅₃	—	2	4	no	—
727	C₂²×C₅₃	—	2	2	no	—
728	C₂²×C₅₃	—	2	2	no	—
729	C₂²×C₅₃	—	2	2	no	—
730	C₂²×C₅₃	—	2	2	no	—
731	C₂²×C₅₃	—	4	8	no	—
732	C₂²×C₅₃	—	4	4	no	—
733	C₂²×C₅₃	—	4	4	no	—
734	C₂²×C₅₃	—	4	8	no	—
735	C₂²×C₅₃	—	4	4	no	—
736	C₂²×C₅₃	—	8	4	no	—
737	C₂²×C₅₃	—	8	8	no	—
738	C₂²×C₅₃	—	8	8	no	—
739	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
740	C₂²×C₅₃	#585	1	4	yes	—
741	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
742	C₄×C₅₃	—	2	2	no	—
743	C₄×C₅₃	—	2	1	no	—
744	C₄×C₅₃	—	2	1	no	—
745	C₄×C₅₃	—	2	2	no	—
746	C₄×C₅₃	—	2	2	no	—
747	C₄×C₅₃	—	2	2	no	—
748	C₄×C₅₃	—	2	8	no	—
749	C₄×C₅₃	—	2	8	no	—
750	C₄×C₅₃	—	2	4	no	—
751	C₄×C₅₃	—	2	8	no	—
752	C₄×C₅₃	—	2	4	no	—
753	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
754	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
755	#3542	C₂×C₅₃	1	4	yes	complemented
756	#3541	C₂×C₅₃	1	4	yes	complemented
757	#3540	C₂×C₅₃	1	2	yes	complemented
758	#3539	C₂×C₅₃	1	2	yes	complemented
759	#3538	C₂×C₅₃	1	1	yes	characteristic, complemented
760	#3537	C₂×C₅₃	1	1	yes	characteristic, complemented
761	#3536	C₂×C₅₃	1	2	yes	complemented
762	#3535	C₂×C₅₃	1	4	yes	complemented
763	#3534	C₂×C₅₃	1	4	yes	complemented
764	#3533	C₂×C₅₃	1	4	yes	complemented
765	#3532	C₂×C₅₃	1	4	yes	complemented
766	#3529	C₂×C₅₃	1	4	yes	complemented
767	#3481	C₂×C₅₃	1	4	yes	complemented
768	#3475	C₂×C₅₃	1	4	yes	complemented
769	D₄×#41	C₂×C₅₃	1	4	yes	complemented
770	#3460	C₂×C₅₃	1	4	yes	complemented
771	#3459	C₂×C₅₃	1	4	yes	complemented
772	#3455	C₂×C₅₃	1	2	yes	complemented
773	#3449	C₂×C₅₃	1	2	yes	complemented
774	C₂×#525	C₂×C₅₃	1	1	yes	characteristic, complemented
775	C₂×#525	C₂×C₅₃	1	2	yes	complemented
776	C₂×C₅₃	—	2	2	no	—
777	C₂×C₅₃	—	2	4	no	—
778	C₂×C₅₃	—	4	2	no	—
779	C₂×C₅₃	—	4	1	no	—
780	C₂×C₅₃	—	4	1	no	—
781	C₂×C₅₃	—	4	2	no	—
782	C₂×C₅₃	—	4	8	no	—
783	C₂×C₅₃	—	4	2	no	—
784	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
785	C₂×C₅₃	C₂×#585	1	2	yes	—
786	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
787	C₂²×#41	C₂²×C₅₃	1	2	yes	complemented
788	C₂²×#41	C₂²×C₅₃	1	2	yes	complemented
789	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
790	#563	C₂²×C₅₃	1	4	yes	complemented
791	#563	C₂²×C₅₃	1	8	yes	complemented
792	#562	C₂²×C₅₃	1	8	yes	complemented
793	#562	C₂²×C₅₃	1	8	yes	complemented
794	#562	C₂²×C₅₃	1	8	yes	complemented
795	H(3,𝔽₄)	C₂²×C₅₃	1	4	yes	complemented
796	#560	C₂²×C₅₃	1	8	yes	complemented
797	#560	C₂²×C₅₃	1	4	yes	complemented
798	#560	C₂²×C₅₃	1	4	yes	complemented
799	#560	C₂²×C₅₃	1	8	yes	complemented
800	#559	C₂²×C₅₃	1	4	yes	complemented
801	#556	C₂²×C₅₃	1	4	yes	complemented
802	#555	C₂²×C₅₃	1	4	yes	complemented
803	#554	C₂²×C₅₃	1	4	yes	complemented
804	#554	C₂²×C₅₃	1	8	yes	complemented
805	#553	C₂²×C₅₃	1	4	yes	complemented
806	#553	C₂²×C₅₃	1	8	yes	complemented
807	#553	C₂²×C₅₃	1	4	yes	complemented
808	#553	C₂²×C₅₃	1	8	yes	complemented
809	#552	C₂²×C₅₃	1	8	yes	complemented
810	#552	C₂²×C₅₃	1	4	yes	complemented
811	#552	C₂²×C₅₃	1	4	yes	complemented
812	#551	C₂²×C₅₃	1	8	yes	complemented
813	#551	C₂²×C₅₃	1	4	yes	complemented
814	#551	C₂²×C₅₃	1	8	yes	complemented
815	#551	C₂²×C₅₃	1	8	yes	complemented
816	#551	C₂²×C₅₃	1	4	yes	complemented
817	#550	C₂²×C₅₃	1	4	yes	complemented
818	D₄×Q₈	C₂²×C₅₃	1	4	yes	complemented
819	#548	C₂²×C₅₃	1	4	yes	complemented
820	#548	C₂²×C₅₃	1	4	yes	complemented
821	#547	C₂²×C₅₃	1	8	yes	complemented
822	#547	C₂²×C₅₃	1	4	yes	complemented
823	#547	C₂²×C₅₃	1	4	yes	complemented
824	#546	C₂²×C₅₃	1	8	yes	complemented
825	#546	C₂²×C₅₃	1	8	yes	complemented
826	#546	C₂²×C₅₃	1	8	yes	complemented
827	#546	C₂²×C₅₃	1	4	yes	complemented
828	#546	C₂²×C₅₃	1	8	yes	complemented
829	#546	C₂²×C₅₃	1	8	yes	complemented
830	#546	C₂²×C₅₃	1	4	yes	complemented
831	D₄²	C₂²×C₅₃	1	8	yes	complemented
832	D₄²	C₂²×C₅₃	1	4	yes	complemented
833	D₄²	C₂²×C₅₃	1	4	yes	complemented
834	#544	C₂²×C₅₃	1	4	yes	complemented
835	#543	C₂²×C₅₃	1	4	yes	complemented
836	#542	C₂²×C₅₃	1	4	yes	complemented
837	#542	C₂²×C₅₃	1	4	yes	complemented
838	#542	C₂²×C₅₃	1	8	yes	complemented
839	#542	C₂²×C₅₃	1	8	yes	complemented
840	#541	C₂²×C₅₃	1	2	yes	complemented
841	#541	C₂²×C₅₃	1	2	yes	complemented
842	#540	C₂²×C₅₃	1	2	yes	complemented
843	#540	C₂²×C₅₃	1	2	yes	complemented
844	#540	C₂²×C₅₃	1	8	yes	complemented
845	#540	C₂²×C₅₃	1	8	yes	complemented
846	#539	C₂²×C₅₃	1	8	yes	complemented
847	#539	C₂²×C₅₃	1	4	yes	complemented
848	#539	C₂²×C₅₃	1	4	yes	complemented
849	#539	C₂²×C₅₃	1	8	yes	complemented
850	#539	C₂²×C₅₃	1	8	yes	complemented
851	#538	C₂²×C₅₃	1	8	yes	complemented
852	#538	C₂²×C₅₃	1	8	yes	complemented
853	#538	C₂²×C₅₃	1	8	yes	complemented
854	#538	C₂²×C₅₃	1	4	yes	complemented
855	#538	C₂²×C₅₃	1	4	yes	complemented
856	#538	C₂²×C₅₃	1	8	yes	complemented
857	#538	C₂²×C₅₃	1	8	yes	complemented
858	#537	C₂²×C₅₃	1	4	yes	complemented
859	#537	C₂²×C₅₃	1	4	yes	complemented
860	#537	C₂²×C₅₃	1	4	yes	complemented
861	#536	C₂²×C₅₃	1	4	yes	complemented
862	#536	C₂²×C₅₃	1	2	yes	complemented
863	#536	C₂²×C₅₃	1	2	yes	complemented
864	#535	C₂²×C₅₃	1	4	yes	complemented
865	#535	C₂²×C₅₃	1	8	yes	complemented
866	#535	C₂²×C₅₃	1	2	yes	complemented
867	#535	C₂²×C₅₃	1	2	yes	complemented
868	#534	C₂²×C₅₃	1	4	yes	complemented
869	#534	C₂²×C₅₃	1	8	yes	complemented
870	#534	C₂²×C₅₃	1	4	yes	complemented
871	#534	C₂²×C₅₃	1	4	yes	complemented
872	#533	C₂²×C₅₃	1	2	yes	complemented
873	#532	C₂²×C₅₃	1	2	yes	complemented
874	#532	C₂²×C₅₃	1	4	yes	complemented
875	#532	C₂²×C₅₃	1	4	yes	complemented
876	#532	C₂²×C₅₃	1	8	yes	complemented
877	#529	C₂²×C₅₃	1	8	yes	complemented
878	#529	C₂²×C₅₃	1	8	yes	complemented
879	#529	C₂²×C₅₃	1	8	yes	complemented
880	#529	C₂²×C₅₃	1	8	yes	complemented
881	#529	C₂²×C₅₃	1	8	yes	complemented
882	#525	C₂²×C₅₃	1	1	yes	characteristic
883	#525	C₂²×C₅₃	1	4	yes	complemented
884	#525	C₂²×C₅₃	1	2	yes	complemented
885	#525	C₂²×C₅₃	1	4	yes	complemented
886	#525	C₂²×C₅₃	1	2	yes	complemented
887	#525	C₂²×C₅₃	1	4	yes	complemented
888	#525	C₂²×C₅₃	1	2	yes	complemented
889	#525	C₂²×C₅₃	1	2	yes	complemented
890	#525	C₂²×C₅₃	1	4	yes	complemented
891	#525	C₂²×C₅₃	1	4	yes	complemented
892	#525	C₂²×C₅₃	1	4	yes	complemented
893	#525	C₂²×C₅₃	1	1	yes	characteristic, complemented
894	#525	C₂²×C₅₃	1	1	yes	characteristic, complemented
895	#525	C₂²×C₅₃	1	4	yes	complemented
896	#525	C₂²×C₅₃	1	1	yes	characteristic, complemented
897	#525	C₂²×C₅₃	1	4	yes	complemented
898	#525	C₂²×C₅₃	1	4	yes	complemented
899	#525	C₂²×C₅₃	1	4	yes	complemented
900	#525	C₂²×C₅₃	1	8	yes	complemented
901	#525	C₂²×C₅₃	1	4	yes	complemented
902	#525	C₂²×C₅₃	1	4	yes	complemented
903	#525	C₂²×C₅₃	1	8	yes	complemented
904	C₂×#123	C₂²×C₅₃	1	2	yes	complemented
905	C₂×#123	C₂²×C₅₃	1	4	yes	complemented
906	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
907	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
908	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
909	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
910	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
911	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
912	C₂×#120	C₂²×C₅₃	1	2	yes	complemented
913	C₂×#120	C₂²×C₅₃	1	4	yes	complemented
914	C₄×#41	C₂²×C₅₃	1	4	yes	complemented
915	C₄×#41	C₂²×C₅₃	1	8	yes	complemented
916	C₂×C₄×D₄	C₂²×C₅₃	1	4	yes	complemented
917	C₂×C₄×D₄	C₂²×C₅₃	1	4	yes	complemented
918	C₂×C₄×D₄	C₂²×C₅₃	1	4	yes	complemented
919	C₂×C₄×D₄	C₂²×C₅₃	1	8	yes	complemented
920	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
921	C₂×#117	C₂²×C₅₃	1	2	yes	complemented
922	C₂×#117	C₂²×C₅₃	1	2	yes	complemented
923	C₅₃	#62729	1	1	yes	characteristic, direct product factor, Sylow
924	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
925	C₂×#41	—	4	4	no	—
926	C₂×#41	—	4	8	no	—
927	C₂×#41	—	4	8	no	—
928	C₂×#41	C₂³×C₅₃	1	4	yes	—
929	C₂×#41	C₂³×C₅₃	1	8	yes	—
930	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
931	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
932	C₂×#41	C₂³×C₅₃	1	2	yes	—
933	C₂×#41	C₂³×C₅₃	1	4	yes	—
934	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
935	C₂×#41	C₂³×C₅₃	1	2	yes	—
936	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
937	C₂×#41	C₂³×C₅₃	1	4	yes	—
938	C₂×#41	C₂³×C₅₃	1	4	yes	—
939	C₂×#41	C₂³×C₅₃	1	4	yes	—
940	C₂×#41	C₂³×C₅₃	1	4	yes	complemented
941	C₂×#41	C₂³×C₅₃	1	4	yes	complemented
942	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
943	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
944	C₂²×Q₈	C₂³×C₅₃	1	2	yes	complemented
945	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
946	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
947	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
948	C₂²×D₄	C₂³×C₅₃	1	8	yes	—
949	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
950	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
951	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
952	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
953	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
954	C₂²×D₄	C₂³×C₅₃	1	2	yes	complemented
955	C₂³×C₄	—	4	4	no	—
956	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
957	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
958	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
959	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
960	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
961	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
962	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
963	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
964	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
965	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
966	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
967	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
968	C₂³×C₄	C₂³×C₅₃	1	4	yes	complemented
969	C₄⋊Q₈	C₂³×C₅₃	1	4	yes	complemented
970	C₄⋊Q₈	C₂³×C₅₃	1	4	yes	complemented
971	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	complemented
972	C₄⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
973	C₄⋊Q₈	C₂³×C₅₃	1	4	yes	complemented
974	#127	C₂³×C₅₃	1	4	yes	—
975	#127	C₂³×C₅₃	1	4	yes	—
976	#127	C₂³×C₅₃	1	8	yes	—
977	#127	C₂³×C₅₃	1	2	yes	complemented
978	#126	C₂³×C₅₃	1	8	yes	—
979	#126	C₂³×C₅₃	1	8	yes	—
980	#126	C₂³×C₅₃	1	8	yes	—
981	#126	C₂³×C₅₃	1	8	yes	—
982	#126	C₂³×C₅₃	1	8	yes	complemented
983	#126	C₂³×C₅₃	1	8	yes	complemented
984	#126	C₂³×C₅₃	1	8	yes	complemented
985	#126	C₂³×C₅₃	1	8	yes	complemented
986	#126	C₂³×C₅₃	1	8	yes	complemented
987	#126	C₂³×C₅₃	1	8	yes	complemented
988	#125	C₂³×C₅₃	1	8	yes	complemented
989	#125	C₂³×C₅₃	1	8	yes	complemented
990	#125	C₂³×C₅₃	1	8	yes	complemented
991	#125	C₂³×C₅₃	1	8	yes	complemented
992	#125	C₂³×C₅₃	1	8	yes	complemented
993	#125	C₂³×C₅₃	1	2	yes	complemented
994	#125	C₂³×C₅₃	1	2	yes	complemented
995	#124	C₂³×C₅₃	1	8	yes	—
996	#124	C₂³×C₅₃	1	8	yes	—
997	#124	C₂³×C₅₃	1	8	yes	—
998	#124	C₂³×C₅₃	1	8	yes	—
999	#124	C₂³×C₅₃	1	4	yes	—
1000	#124	C₂³×C₅₃	1	4	yes	—
1001	#124	C₂³×C₅₃	1	8	yes	—
1002	#124	C₂³×C₅₃	1	8	yes	complemented
1003	#124	C₂³×C₅₃	1	4	yes	complemented
1004	#124	C₂³×C₅₃	1	4	yes	complemented
1005	#124	C₂³×C₅₃	1	8	yes	complemented
1006	#124	C₂³×C₅₃	1	4	yes	complemented
1007	#123	C₂³×C₅₃	1	2	yes	—
1008	#123	C₂³×C₅₃	1	8	yes	—
1009	#123	C₂³×C₅₃	1	4	yes	—
1010	#123	C₂³×C₅₃	1	8	yes	—
1011	#123	C₂³×C₅₃	1	4	yes	—
1012	#123	C₂³×C₅₃	1	8	yes	—
1013	#123	C₂³×C₅₃	1	2	yes	—
1014	#123	C₂³×C₅₃	1	2	yes	—
1015	#123	C₂³×C₅₃	1	8	yes	—
1016	#123	C₂³×C₅₃	1	2	yes	—
1017	#123	C₂³×C₅₃	1	4	yes	—
1018	#123	C₂³×C₅₃	1	8	yes	—
1019	#123	C₂³×C₅₃	1	4	yes	—
1020	#123	C₂³×C₅₃	1	8	yes	—
1021	#123	C₂³×C₅₃	1	8	yes	—
1022	#123	C₂³×C₅₃	1	8	yes	—
1023	#123	C₂³×C₅₃	1	8	yes	—
1024	#123	C₂³×C₅₃	1	8	yes	—
1025	#123	C₂³×C₅₃	1	8	yes	—
1026	#123	C₂³×C₅₃	1	8	yes	—
1027	#123	C₂³×C₅₃	1	4	yes	complemented
1028	#123	C₂³×C₅₃	1	4	yes	complemented
1029	#123	C₂³×C₅₃	1	8	yes	complemented
1030	#123	C₂³×C₅₃	1	8	yes	complemented
1031	#123	C₂³×C₅₃	1	8	yes	complemented
1032	#123	C₂³×C₅₃	1	8	yes	complemented
1033	#123	C₂³×C₅₃	1	8	yes	complemented
1034	#123	C₂³×C₅₃	1	8	yes	complemented
1035	#123	C₂³×C₅₃	1	8	yes	complemented
1036	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
1037	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
1038	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
1039	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
1040	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
1041	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
1042	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
1043	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
1044	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
1045	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
1046	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
1047	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
1048	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
1049	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
1050	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
1051	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
1052	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
1053	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
1054	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	complemented
1055	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	complemented
1056	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
1057	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
1058	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
1059	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
1060	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
1061	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
1062	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
1063	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
1064	#121	C₂³×C₅₃	1	2	yes	—
1065	#121	C₂³×C₅₃	1	4	yes	—
1066	#121	C₂³×C₅₃	1	4	yes	—
1067	#121	C₂³×C₅₃	1	4	yes	—
1068	#121	C₂³×C₅₃	1	2	yes	—
1069	#121	C₂³×C₅₃	1	2	yes	—
1070	#121	C₂³×C₅₃	1	4	yes	—
1071	#121	C₂³×C₅₃	1	2	yes	—
1072	#121	C₂³×C₅₃	1	4	yes	—
1073	#121	C₂³×C₅₃	1	4	yes	—
1074	#121	C₂³×C₅₃	1	4	yes	—
1075	#121	C₂³×C₅₃	1	4	yes	—
1076	#121	C₂³×C₅₃	1	4	yes	—
1077	#121	C₂³×C₅₃	1	4	yes	—
1078	#121	C₂³×C₅₃	1	8	yes	—
1079	#121	C₂³×C₅₃	1	8	yes	—
1080	#121	C₂³×C₅₃	1	8	yes	—
1081	#121	C₂³×C₅₃	1	8	yes	—
1082	#121	C₂³×C₅₃	1	8	yes	—
1083	#121	C₂³×C₅₃	1	8	yes	—
1084	#121	C₂³×C₅₃	1	8	yes	—
1085	#121	C₂³×C₅₃	1	8	yes	—
1086	#121	C₂³×C₅₃	1	8	yes	—
1087	#121	C₂³×C₅₃	1	8	yes	—
1088	#121	C₂³×C₅₃	1	8	yes	—
1089	#121	C₂³×C₅₃	1	8	yes	—
1090	#121	C₂³×C₅₃	1	8	yes	—
1091	#121	C₂³×C₅₃	1	8	yes	—
1092	#121	C₂³×C₅₃	1	8	yes	—
1093	#121	C₂³×C₅₃	1	4	yes	complemented
1094	#121	C₂³×C₅₃	1	4	yes	complemented
1095	#121	C₂³×C₅₃	1	8	yes	complemented
1096	#121	C₂³×C₅₃	1	8	yes	complemented
1097	#121	C₂³×C₅₃	1	8	yes	complemented
1098	#121	C₂³×C₅₃	1	8	yes	complemented
1099	#121	C₂³×C₅₃	1	8	yes	complemented
1100	#120	C₂³×C₅₃	1	2	yes	—
1101	#120	C₂³×C₅₃	1	4	yes	—
1102	#120	C₂³×C₅₃	1	8	yes	—
1103	#120	C₂³×C₅₃	1	8	yes	—
1104	#120	C₂³×C₅₃	1	4	yes	—
1105	#120	C₂³×C₅₃	1	8	yes	—
1106	#120	C₂³×C₅₃	1	2	yes	—
1107	#120	C₂³×C₅₃	1	2	yes	—
1108	#120	C₂³×C₅₃	1	8	yes	—
1109	#120	C₂³×C₅₃	1	2	yes	—
1110	#120	C₂³×C₅₃	1	4	yes	—
1111	#120	C₂³×C₅₃	1	8	yes	—
1112	#120	C₂³×C₅₃	1	4	yes	—
1113	#120	C₂³×C₅₃	1	8	yes	—
1114	#120	C₂³×C₅₃	1	8	yes	—
1115	#120	C₂³×C₅₃	1	8	yes	—
1116	#120	C₂³×C₅₃	1	4	yes	complemented
1117	#120	C₂³×C₅₃	1	4	yes	complemented
1118	#120	C₂³×C₅₃	1	8	yes	complemented
1119	C₄×Q₈	C₂³×C₅₃	1	8	yes	complemented
1120	C₄×Q₈	C₂³×C₅₃	1	4	yes	complemented
1121	C₄×Q₈	C₂³×C₅₃	1	4	yes	complemented
1122	C₄×Q₈	C₂³×C₅₃	1	8	yes	complemented
1123	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1124	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1125	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1126	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1127	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1128	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1129	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1130	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1131	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1132	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1133	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1134	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1135	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1136	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1137	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1138	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1139	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1140	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1141	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1142	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1143	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1144	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1145	C₄×D₄	C₂³×C₅₃	1	8	yes	complemented
1146	C₄×D₄	C₂³×C₅₃	1	8	yes	complemented
1147	C₄×D₄	C₂³×C₅₃	1	8	yes	complemented
1148	C₄×D₄	C₂³×C₅₃	1	8	yes	complemented
1149	C₄×D₄	C₂³×C₅₃	1	8	yes	complemented
1150	C₄×D₄	C₂³×C₅₃	1	8	yes	complemented
1151	C₄×D₄	C₂³×C₅₃	1	4	yes	complemented
1152	C₄×D₄	C₂³×C₅₃	1	4	yes	complemented
1153	#117	C₂³×C₅₃	1	4	yes	—
1154	#117	C₂³×C₅₃	1	1	yes	characteristic
1155	#117	C₂³×C₅₃	1	2	yes	—
1156	#117	C₂³×C₅₃	1	2	yes	—
1157	#117	C₂³×C₅₃	1	4	yes	—
1158	#117	C₂³×C₅₃	1	2	yes	—
1159	#117	C₂³×C₅₃	1	1	yes	characteristic
1160	#117	C₂³×C₅₃	1	4	yes	—
1161	#117	C₂³×C₅₃	1	4	yes	—
1162	#117	C₂³×C₅₃	1	4	yes	—
1163	#117	C₂³×C₅₃	1	8	yes	—
1164	#117	C₂³×C₅₃	1	4	yes	complemented
1165	#117	C₂³×C₅₃	1	2	yes	complemented
1166	#117	C₂³×C₅₃	1	2	yes	complemented
1167	#117	C₂³×C₅₃	1	8	yes	complemented
1168	#117	C₂³×C₅₃	1	8	yes	complemented
1169	#117	C₂³×C₅₃	1	8	yes	complemented
1170	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
1171	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
1172	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
1173	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
1174	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
1175	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
1176	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	complemented
1177	C₂×C₄⋊C₄	C₂³×C₅₃	1	8	yes	complemented
1178	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
1179	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
1180	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
1181	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
1182	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
1183	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
1184	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
1185	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
1186	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
1187	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	—
1188	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	complemented
1189	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
1190	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
1191	C₂×C₄²	C₂³×C₅₃	1	4	yes	complemented
1192	C₂×C₄²	C₂³×C₅₃	1	8	yes	complemented
1193	C₂⁴	—	4	2	no	—
1194	C₂⁴	—	4	4	no	—
1195	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
1196	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1197	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
1198	C₂⁴	C₂⁴×C₅₃	1	4	yes	—
1199	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1200	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
1201	C₂⁴	C₂⁴×C₅₃	1	4	yes	—
1202	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1203	#41	—	2	16	no	—
1204	#41	—	4	2	no	—
1205	#41	—	4	4	no	—
1206	#41	—	4	2	no	—
1207	#41	—	4	4	no	—
1208	#41	—	4	2	no	—
1209	#41	—	4	2	no	—
1210	#41	—	4	8	no	—
1211	#41	—	4	8	no	—
1212	#41	—	4	8	no	—
1213	#41	—	4	8	no	—
1214	#41	—	4	16	no	—
1215	#41	—	4	8	no	—
1216	#41	—	4	8	no	—
1217	C₂×Q₈	—	4	2	no	—
1218	C₂×Q₈	—	4	4	no	—
1219	C₂×Q₈	—	4	4	no	—
1220	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
1221	C₂×Q₈	C₂⁴×C₅₃	1	8	yes	—
1222	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1223	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
1224	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
1225	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1226	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
1227	C₂×D₄	—	4	4	no	—
1228	C₂×D₄	—	4	4	no	—
1229	C₂×D₄	—	4	8	no	—
1230	C₂×D₄	—	4	2	no	—
1231	C₂×D₄	—	4	4	no	—
1232	C₂×D₄	—	4	16	no	—
1233	C₂×D₄	—	4	8	no	—
1234	C₂×D₄	—	4	8	no	—
1235	C₂×D₄	—	4	8	no	—
1236	C₂×D₄	—	4	8	no	—
1237	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1238	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1239	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1240	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1241	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1242	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1243	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1244	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1245	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1246	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1247	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1248	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1249	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1250	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1251	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1252	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1253	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1254	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1255	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1256	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1257	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1258	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1259	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1260	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1261	C₂²×C₄	—	2	4	no	—
1262	C₂²×C₄	—	2	8	no	—
1263	C₂²×C₄	—	2	8	no	—
1264	C₂²×C₄	—	4	2	no	—
1265	C₂²×C₄	—	4	4	no	—
1266	C₂²×C₄	—	4	2	no	—
1267	C₂²×C₄	—	4	4	no	—
1268	C₂²×C₄	—	4	2	no	—
1269	C₂²×C₄	—	4	2	no	—
1270	C₂²×C₄	—	4	8	no	—
1271	C₂²×C₄	—	4	8	no	—
1272	C₂²×C₄	—	4	4	no	—
1273	C₂²×C₄	—	4	2	no	—
1274	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1275	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1276	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1277	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
1278	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1279	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1280	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1281	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1282	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1283	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1284	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1285	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1286	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1287	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1288	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1289	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1290	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1291	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1292	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1293	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
1294	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
1295	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
1296	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1297	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1298	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1299	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
1300	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
1301	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1302	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1303	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1304	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1305	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1306	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1307	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1308	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1309	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1310	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1311	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1312	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1313	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1314	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1315	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1316	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1317	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1318	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1319	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1320	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1321	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1322	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1323	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1324	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1325	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1326	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1327	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1328	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1329	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1330	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1331	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1332	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1333	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1334	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1335	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1336	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1337	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1338	C₂²⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1339	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1340	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1341	C₂²⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1342	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1343	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1344	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1345	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1346	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1347	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1348	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1349	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1350	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1351	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1352	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1353	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1354	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1355	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1356	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1357	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1358	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1359	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1360	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1361	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1362	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1363	C₄²	C₂⁴×C₅₃	1	4	yes	—
1364	C₄²	C₂⁴×C₅₃	1	8	yes	—
1365	C₄²	C₂⁴×C₅₃	1	8	yes	—
1366	C₄²	C₂⁴×C₅₃	1	2	yes	—
1367	C₄²	C₂⁴×C₅₃	1	2	yes	—
1368	C₄²	C₂⁴×C₅₃	1	4	yes	—
1369	C₄²	C₂⁴×C₅₃	1	8	yes	—
1370	C₄²	C₂⁴×C₅₃	1	4	yes	—
1371	C₄²	C₂⁴×C₅₃	1	8	yes	—
1372	C₂³	—	2	4	no	—
1373	C₂³	—	2	2	no	—
1374	C₂³	—	2	4	no	—
1375	C₂³	—	2	4	no	—
1376	C₂³	—	2	4	no	—
1377	C₂³	—	2	4	no	—
1378	C₂³	—	2	8	no	—
1379	C₂³	—	4	1	no	—
1380	C₂³	—	4	2	no	—
1381	C₂³	—	4	1	no	—
1382	C₂³	—	4	2	no	—
1383	C₂³	—	4	2	no	—
1384	C₂³	—	4	2	no	—
1385	C₂³	—	4	2	no	—
1386	C₂³	—	4	4	no	—
1387	C₂³	—	4	4	no	—
1388	C₂³	—	4	4	no	—
1389	C₂³	—	4	4	no	—
1390	C₂³	—	4	8	no	—
1391	C₂³	—	4	16	no	—
1392	C₂³	C₂⁵×C₅₃	1	2	yes	—
1393	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
1394	C₂³	C₂⁵×C₅₃	1	2	yes	—
1395	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
1396	C₂³	C₂⁵×C₅₃	1	8	yes	—
1397	C₂³	C₂⁵×C₅₃	1	2	yes	—
1398	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
1399	C₂³	C₂⁵×C₅₃	1	2	yes	—
1400	Q₈	—	2	8	no	—
1401	Q₈	—	4	1	no	—
1402	Q₈	—	4	2	no	—
1403	Q₈	—	4	1	no	—
1404	Q₈	—	4	4	no	—
1405	Q₈	—	4	4	no	—
1406	Q₈	—	4	8	no	—
1407	D₄	—	2	16	no	—
1408	D₄	—	2	8	no	—
1409	D₄	—	2	16	no	—
1410	D₄	—	2	8	no	—
1411	D₄	—	2	8	no	—
1412	D₄	—	4	8	no	—
1413	D₄	—	4	8	no	—
1414	D₄	—	4	4	no	—
1415	D₄	—	4	8	no	—
1416	D₄	—	4	8	no	—
1417	D₄	—	4	8	no	—
1418	D₄	—	4	4	no	—
1419	D₄	—	4	2	no	—
1420	D₄	—	4	1	no	—
1421	D₄	—	4	2	no	—
1422	D₄	—	4	2	no	—
1423	D₄	—	4	1	no	—
1424	D₄	—	4	4	no	—
1425	D₄	—	4	2	no	—
1426	D₄	—	4	2	no	—
1427	D₄	—	4	4	no	—
1428	D₄	—	4	8	no	—
1429	D₄	—	4	8	no	—
1430	D₄	—	4	8	no	—
1431	C₂×C₄	—	2	2	no	—
1432	C₂×C₄	—	2	4	no	—
1433	C₂×C₄	—	2	4	no	—
1434	C₂×C₄	—	2	8	no	—
1435	C₂×C₄	—	2	4	no	—
1436	C₂×C₄	—	2	4	no	—
1437	C₂×C₄	—	2	4	no	—
1438	C₂×C₄	—	2	2	no	—
1439	C₂×C₄	—	2	2	no	—
1440	C₂×C₄	—	2	4	no	—
1441	C₂×C₄	—	2	4	no	—
1442	C₂×C₄	—	2	2	no	—
1443	C₂×C₄	—	2	2	no	—
1444	C₂×C₄	—	2	4	no	—
1445	C₂×C₄	—	2	4	no	—
1446	C₂×C₄	—	2	4	no	—
1447	C₂×C₄	—	2	16	no	—
1448	C₂×C₄	—	4	1	no	—
1449	C₂×C₄	—	4	2	no	—
1450	C₂×C₄	—	4	2	no	—
1451	C₂×C₄	—	4	2	no	—
1452	C₂×C₄	—	4	2	no	—
1453	C₂×C₄	—	4	2	no	—
1454	C₂×C₄	—	4	1	no	—
1455	C₂×C₄	—	4	4	no	—
1456	C₂×C₄	—	4	4	no	—
1457	C₂×C₄	—	4	8	no	—
1458	C₂×C₄	—	4	8	no	—
1459	C₂×C₄	—	4	8	no	—
1460	C₂×C₄	—	4	4	no	—
1461	C₂×C₄	—	4	4	no	—
1462	C₂×C₄	—	4	8	no	—
1463	C₂×C₄	—	4	8	no	—
1464	C₂×C₄	H(5,𝔽₂)×C₅₃	1	4	yes	—
1465	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1466	C₂×C₄	C₂⁵×C₅₃	1	8	yes	—
1467	C₂×C₄	C₂⁵×C₅₃	1	8	yes	—
1468	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1469	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1470	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1471	C₂×C₄	C₂⁵×C₅₃	1	8	yes	—
1472	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1473	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1474	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1475	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1476	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1477	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1478	C₂²	—	2	2	no	—
1479	C₂²	—	2	2	no	—
1480	C₂²	—	2	2	no	—
1481	C₂²	—	2	2	no	—
1482	C₂²	—	2	1	no	—
1483	C₂²	—	2	1	no	—
1484	C₂²	—	2	2	no	—
1485	C₂²	—	2	2	no	—
1486	C₂²	—	2	8	no	—
1487	C₂²	—	2	4	no	—
1488	C₂²	—	2	8	no	—
1489	C₂²	—	2	8	no	—
1490	C₂²	—	2	4	no	—
1491	C₂²	—	2	2	no	—
1492	C₂²	—	2	2	no	—
1493	C₂²	—	2	2	no	—
1494	C₂²	—	2	2	no	—
1495	C₂²	—	4	8	no	—
1496	C₂²	—	4	4	no	—
1497	C₂²	—	4	4	no	—
1498	C₂²	—	4	8	no	—
1499	C₂²	—	4	4	no	—
1500	C₂²	—	8	4	no	—
1501	C₂²	—	8	8	no	—
1502	C₂²	—	8	8	no	—
1503	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
1504	C₂²	C₅₃×#585	1	4	yes	—
1505	C₂²	C₂⁶×C₅₃	1	1	yes	characteristic
1506	C₄	—	2	2	no	—
1507	C₄	—	2	1	no	—
1508	C₄	—	2	1	no	—
1509	C₄	—	2	2	no	—
1510	C₄	—	2	2	no	—
1511	C₄	—	2	2	no	—
1512	C₄	—	2	8	no	—
1513	C₄	—	2	8	no	—
1514	C₄	—	2	4	no	—
1515	C₄	—	2	8	no	—
1516	C₄	—	2	4	no	—
1517	C₄	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
1518	C₄	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
1519	C₂	—	2	2	no	—
1520	C₂	—	2	4	no	—
1521	C₂	—	4	2	no	—
1522	C₂	—	4	1	no	—
1523	C₂	—	4	1	no	—
1524	C₂	—	4	2	no	—
1525	C₂	—	4	8	no	—
1526	C₂	—	4	2	no	—
1527	C₂	C₂²×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1528	C₂	C₂×C₅₃×#585	1	2	yes	—

	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×#3542	C₂	semidirect
2. C₅₃×#3541	C₂	semidirect
3. C₅₃×#3540	C₂	semidirect
4. C₅₃×#3539	C₂	semidirect
5. C₅₃×#3538	C₂	semidirect
6. C₅₃×#3537	C₂	semidirect
7. C₅₃×#3536	C₂	semidirect
8. C₅₃×#3535	C₂	semidirect
9. C₅₃×#3534	C₂	semidirect
10. C₅₃×#3533	C₂	semidirect
11. C₅₃×#3532	C₂	semidirect
12. C₅₃×#3529	C₂	semidirect
13. C₅₃×#3481	C₂	semidirect
14. C₅₃×#3475	C₂	semidirect
15. D₄×#41×C₅₃	C₂	semidirect
16. C₅₃×#3460	C₂	semidirect
17. C₅₃×#3459	C₂	semidirect
18. C₅₃×#3455	C₂	semidirect
19. C₅₃×#3449	C₂	semidirect
20. C₂×C₅₃×#525	C₂	semidirect
21. C₂×C₅₃×#525	C₂	semidirect
22. C₂²×#41×C₅₃	C₂²	semidirect
23. C₂²×#41×C₅₃	C₂²	semidirect
24. C₂²×#41×C₅₃	C₂²	semidirect
25. C₂⁴×C₄×C₅₃	C₂²	semidirect
26. C₅₃×#563	C₂²	semidirect
27. C₅₃×#563	C₂²	semidirect
28. C₅₃×#562	C₂²	semidirect
29. C₅₃×#562	C₂²	semidirect
30. C₅₃×#562	C₂²	semidirect
31. C₅₃×H(3,𝔽₄)	C₂²	semidirect
32. C₅₃×#560	C₂²	semidirect
33. C₅₃×#560	C₂²	semidirect
34. C₅₃×#560	C₂²	semidirect
35. C₅₃×#560	C₂²	semidirect
36. C₅₃×#559	C₂²	semidirect
37. C₅₃×#556	C₂²	semidirect
38. C₅₃×#555	C₂²	semidirect
39. C₅₃×#554	C₂²	semidirect
40. C₅₃×#554	C₂²	semidirect
41. C₅₃×#553	C₂²	semidirect
42. C₅₃×#553	C₂²	semidirect
43. C₅₃×#553	C₂²	semidirect
44. C₅₃×#553	C₂²	semidirect
45. C₅₃×#552	C₂²	semidirect
46. C₅₃×#552	C₂²	semidirect
47. C₅₃×#552	C₂²	semidirect
48. C₅₃×#551	C₂²	semidirect
49. C₅₃×#551	C₂²	semidirect
50. C₅₃×#551	C₂²	semidirect
51. C₅₃×#551	C₂²	semidirect
52. C₅₃×#551	C₂²	semidirect
53. C₅₃×#550	C₂²	semidirect
54. D₄×Q₈×C₅₃	C₂²	semidirect
55. C₅₃×#548	C₂²	semidirect
56. C₅₃×#548	C₂²	semidirect
57. C₅₃×#547	C₂²	semidirect
58. C₅₃×#547	C₂²	semidirect
59. C₅₃×#547	C₂²	semidirect
60. C₅₃×#546	C₂²	semidirect
61. C₅₃×#546	C₂²	semidirect
62. C₅₃×#546	C₂²	semidirect
63. C₅₃×#546	C₂²	semidirect
64. C₅₃×#546	C₂²	semidirect
65. C₅₃×#546	C₂²	semidirect
66. C₅₃×#546	C₂²	semidirect
67. D₄²×C₅₃	C₂²	semidirect
68. D₄²×C₅₃	C₂²	semidirect
69. D₄²×C₅₃	C₂²	semidirect
70. C₅₃×#544	C₂²	semidirect
71. C₅₃×#543	C₂²	semidirect
72. C₅₃×#542	C₂²	semidirect
73. C₅₃×#542	C₂²	semidirect
74. C₅₃×#542	C₂²	semidirect
75. C₅₃×#542	C₂²	semidirect
76. C₅₃×#541	C₂²	semidirect
77. C₅₃×#541	C₂²	semidirect
78. C₅₃×#540	C₂²	semidirect
79. C₅₃×#540	C₂²	semidirect
80. C₅₃×#540	C₂²	semidirect
81. C₅₃×#540	C₂²	semidirect
82. C₅₃×#539	C₂²	semidirect
83. C₅₃×#539	C₂²	semidirect
84. C₅₃×#539	C₂²	semidirect
85. C₅₃×#539	C₂²	semidirect
86. C₅₃×#539	C₂²	semidirect
87. C₅₃×#538	C₂²	semidirect
88. C₅₃×#538	C₂²	semidirect
89. C₅₃×#538	C₂²	semidirect
90. C₅₃×#538	C₂²	semidirect
91. C₅₃×#538	C₂²	semidirect
92. C₅₃×#538	C₂²	semidirect
93. C₅₃×#538	C₂²	semidirect
94. C₅₃×#537	C₂²	semidirect
95. C₅₃×#537	C₂²	semidirect
96. C₅₃×#537	C₂²	semidirect
97. C₅₃×#536	C₂²	semidirect
98. C₅₃×#536	C₂²	semidirect
99. C₅₃×#536	C₂²	semidirect
100. C₅₃×#535	C₂²	semidirect
101. C₅₃×#535	C₂²	semidirect
102. C₅₃×#535	C₂²	semidirect
103. C₅₃×#535	C₂²	semidirect
104. C₅₃×#534	C₂²	semidirect
105. C₅₃×#534	C₂²	semidirect
106. C₅₃×#534	C₂²	semidirect
107. C₅₃×#534	C₂²	semidirect
108. C₅₃×#533	C₂²	semidirect
109. C₅₃×#532	C₂²	semidirect
110. C₅₃×#532	C₂²	semidirect
111. C₅₃×#532	C₂²	semidirect
112. C₅₃×#532	C₂²	semidirect
113. C₅₃×#529	C₂²	semidirect
114. C₅₃×#529	C₂²	semidirect
115. C₅₃×#529	C₂²	semidirect
116. C₅₃×#529	C₂²	semidirect
117. C₅₃×#529	C₂²	semidirect
119. C₅₃×#525	C₂²	semidirect
120. C₅₃×#525	C₂²	semidirect
121. C₅₃×#525	C₂²	semidirect
122. C₅₃×#525	C₂²	semidirect
123. C₅₃×#525	C₂²	semidirect
124. C₅₃×#525	C₂²	semidirect
125. C₅₃×#525	C₂²	semidirect
126. C₅₃×#525	C₂²	semidirect
127. C₅₃×#525	C₂²	semidirect
128. C₅₃×#525	C₂²	semidirect
129. C₅₃×#525	C₂²	semidirect
130. C₅₃×#525	C₂²	semidirect
131. C₅₃×#525	C₂²	semidirect
132. C₅₃×#525	C₂²	semidirect
133. C₅₃×#525	C₂²	semidirect
134. C₅₃×#525	C₂²	semidirect
135. C₅₃×#525	C₂²	semidirect
136. C₅₃×#525	C₂²	semidirect
137. C₅₃×#525	C₂²	semidirect
138. C₅₃×#525	C₂²	semidirect
139. C₅₃×#525	C₂²	semidirect
140. C₂×#123×C₅₃	C₂²	semidirect
141. C₂×#123×C₅₃	C₂²	semidirect
142. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
143. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
144. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
145. C₂×#121×C₅₃	C₂²	semidirect
146. C₂×#121×C₅₃	C₂²	semidirect
147. C₂×#121×C₅₃	C₂²	semidirect
148. C₂×#120×C₅₃	C₂²	semidirect
149. C₂×#120×C₅₃	C₂²	semidirect
150. C₄×#41×C₅₃	C₂²	semidirect
151. C₄×#41×C₅₃	C₂²	semidirect
152. C₂×C₄×D₄×C₅₃	C₂²	semidirect
153. C₂×C₄×D₄×C₅₃	C₂²	semidirect
154. C₂×C₄×D₄×C₅₃	C₂²	semidirect
155. C₂×C₄×D₄×C₅₃	C₂²	semidirect
156. C₂×#117×C₅₃	C₂²	semidirect
157. C₂×#117×C₅₃	C₂²	semidirect
158. C₂×#117×C₅₃	C₂²	semidirect
175. C₂×#41×C₅₃	C₂³	semidirect
176. C₂×#41×C₅₃	C₂³	semidirect
179. C₂²×Q₈×C₅₃	C₂³	semidirect
189. C₂²×D₄×C₅₃	C₂³	semidirect
203. C₂³×C₄×C₅₃	C₂³	semidirect
204. C₄⋊Q₈×C₅₃	C₂³	semidirect
205. C₄⋊Q₈×C₅₃	C₂³	semidirect
206. C₄⋊Q₈×C₅₃	C₂³	semidirect
207. C₄⋊Q₈×C₅₃	C₂³	semidirect
208. C₄⋊Q₈×C₅₃	C₂³	semidirect
212. #127×C₅₃	C₂³	semidirect
217. #126×C₅₃	C₂³	semidirect
218. #126×C₅₃	C₂³	semidirect
219. #126×C₅₃	C₂³	semidirect
220. #126×C₅₃	C₂³	semidirect
221. #126×C₅₃	C₂³	semidirect
222. #126×C₅₃	C₂³	semidirect
223. #125×C₅₃	C₂³	semidirect
224. #125×C₅₃	C₂³	semidirect
225. #125×C₅₃	C₂³	semidirect
226. #125×C₅₃	C₂³	semidirect
227. #125×C₅₃	C₂³	semidirect
228. #125×C₅₃	C₂³	semidirect
229. #125×C₅₃	C₂³	semidirect
237. #124×C₅₃	C₂³	semidirect
238. #124×C₅₃	C₂³	semidirect
239. #124×C₅₃	C₂³	semidirect
240. #124×C₅₃	C₂³	semidirect
241. #124×C₅₃	C₂³	semidirect
262. #123×C₅₃	C₂³	semidirect
263. #123×C₅₃	C₂³	semidirect
264. #123×C₅₃	C₂³	semidirect
265. #123×C₅₃	C₂³	semidirect
266. #123×C₅₃	C₂³	semidirect
267. #123×C₅₃	C₂³	semidirect
268. #123×C₅₃	C₂³	semidirect
269. #123×C₅₃	C₂³	semidirect
270. #123×C₅₃	C₂³	semidirect
288. C₂²⋊Q₈×C₅₃	C₂³	semidirect
289. C₂²⋊Q₈×C₅₃	C₂³	semidirect
290. C₂²⋊Q₈×C₅₃	C₂³	semidirect
291. C₂²⋊Q₈×C₅₃	C₂³	semidirect
292. C₂²⋊Q₈×C₅₃	C₂³	semidirect
293. C₂²⋊Q₈×C₅₃	C₂³	semidirect
294. C₂²⋊Q₈×C₅₃	C₂³	semidirect
295. C₂²⋊Q₈×C₅₃	C₂³	semidirect
296. C₂²⋊Q₈×C₅₃	C₂³	semidirect
297. C₂²⋊Q₈×C₅₃	C₂³	semidirect
298. C₂²⋊Q₈×C₅₃	C₂³	semidirect
328. #121×C₅₃	C₂³	semidirect
329. #121×C₅₃	C₂³	semidirect
330. #121×C₅₃	C₂³	semidirect
331. #121×C₅₃	C₂³	semidirect
332. #121×C₅₃	C₂³	semidirect
333. #121×C₅₃	C₂³	semidirect
334. #121×C₅₃	C₂³	semidirect
351. #120×C₅₃	C₂³	semidirect
352. #120×C₅₃	C₂³	semidirect
353. #120×C₅₃	C₂³	semidirect
354. C₄×Q₈×C₅₃	C₂³	semidirect
355. C₄×Q₈×C₅₃	C₂³	semidirect
356. C₄×Q₈×C₅₃	C₂³	semidirect
357. C₄×Q₈×C₅₃	C₂³	semidirect
380. C₄×D₄×C₅₃	C₂³	semidirect
381. C₄×D₄×C₅₃	C₂³	semidirect
382. C₄×D₄×C₅₃	C₂³	semidirect
383. C₄×D₄×C₅₃	C₂³	semidirect
384. C₄×D₄×C₅₃	C₂³	semidirect
385. C₄×D₄×C₅₃	C₂³	semidirect
386. C₄×D₄×C₅₃	C₂³	semidirect
387. C₄×D₄×C₅₃	C₂³	semidirect
399. #117×C₅₃	C₂³	semidirect
400. #117×C₅₃	C₂³	semidirect
401. #117×C₅₃	C₂³	semidirect
402. #117×C₅₃	C₂³	semidirect
403. #117×C₅₃	C₂³	semidirect
404. #117×C₅₃	C₂³	semidirect
411. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
412. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
423. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
426. C₂×C₄²×C₅₃	C₂³	semidirect
427. C₂×C₄²×C₅₃	C₂³	semidirect
713. #62729	C₅₃	direct (N × H)
755. #3542	C₂×C₅₃	semidirect
756. #3541	C₂×C₅₃	semidirect
757. #3540	C₂×C₅₃	semidirect
758. #3539	C₂×C₅₃	semidirect
759. #3538	C₂×C₅₃	semidirect
760. #3537	C₂×C₅₃	semidirect
761. #3536	C₂×C₅₃	semidirect
762. #3535	C₂×C₅₃	semidirect
763. #3534	C₂×C₅₃	semidirect
764. #3533	C₂×C₅₃	semidirect
765. #3532	C₂×C₅₃	semidirect
766. #3529	C₂×C₅₃	semidirect
767. #3481	C₂×C₅₃	semidirect
768. #3475	C₂×C₅₃	semidirect
769. D₄×#41	C₂×C₅₃	semidirect
770. #3460	C₂×C₅₃	semidirect
771. #3459	C₂×C₅₃	semidirect
772. #3455	C₂×C₅₃	semidirect
773. #3449	C₂×C₅₃	semidirect
774. C₂×#525	C₂×C₅₃	semidirect
775. C₂×#525	C₂×C₅₃	semidirect
786. C₂²×#41	C₂²×C₅₃	semidirect
787. C₂²×#41	C₂²×C₅₃	semidirect
788. C₂²×#41	C₂²×C₅₃	semidirect
789. C₂⁴×C₄	C₂²×C₅₃	semidirect
790. #563	C₂²×C₅₃	semidirect
791. #563	C₂²×C₅₃	semidirect
792. #562	C₂²×C₅₃	semidirect
793. #562	C₂²×C₅₃	semidirect
794. #562	C₂²×C₅₃	semidirect
795. H(3,𝔽₄)	C₂²×C₅₃	semidirect
796. #560	C₂²×C₅₃	semidirect
797. #560	C₂²×C₅₃	semidirect
798. #560	C₂²×C₅₃	semidirect
799. #560	C₂²×C₅₃	semidirect
800. #559	C₂²×C₅₃	semidirect
801. #556	C₂²×C₅₃	semidirect
802. #555	C₂²×C₅₃	semidirect
803. #554	C₂²×C₅₃	semidirect
804. #554	C₂²×C₅₃	semidirect
805. #553	C₂²×C₅₃	semidirect
806. #553	C₂²×C₅₃	semidirect
807. #553	C₂²×C₅₃	semidirect
808. #553	C₂²×C₅₃	semidirect
809. #552	C₂²×C₅₃	semidirect
810. #552	C₂²×C₅₃	semidirect
811. #552	C₂²×C₅₃	semidirect
812. #551	C₂²×C₅₃	semidirect
813. #551	C₂²×C₅₃	semidirect
814. #551	C₂²×C₅₃	semidirect
815. #551	C₂²×C₅₃	semidirect
816. #551	C₂²×C₅₃	semidirect
817. #550	C₂²×C₅₃	semidirect
818. D₄×Q₈	C₂²×C₅₃	semidirect
819. #548	C₂²×C₅₃	semidirect
820. #548	C₂²×C₅₃	semidirect
821. #547	C₂²×C₅₃	semidirect
822. #547	C₂²×C₅₃	semidirect
823. #547	C₂²×C₅₃	semidirect
824. #546	C₂²×C₅₃	semidirect
825. #546	C₂²×C₅₃	semidirect
826. #546	C₂²×C₅₃	semidirect
827. #546	C₂²×C₅₃	semidirect
828. #546	C₂²×C₅₃	semidirect
829. #546	C₂²×C₅₃	semidirect
830. #546	C₂²×C₅₃	semidirect
831. D₄²	C₂²×C₅₃	semidirect
832. D₄²	C₂²×C₅₃	semidirect
833. D₄²	C₂²×C₅₃	semidirect
834. #544	C₂²×C₅₃	semidirect
835. #543	C₂²×C₅₃	semidirect
836. #542	C₂²×C₅₃	semidirect
837. #542	C₂²×C₅₃	semidirect
838. #542	C₂²×C₅₃	semidirect
839. #542	C₂²×C₅₃	semidirect
840. #541	C₂²×C₅₃	semidirect
841. #541	C₂²×C₅₃	semidirect
842. #540	C₂²×C₅₃	semidirect
843. #540	C₂²×C₅₃	semidirect
844. #540	C₂²×C₅₃	semidirect
845. #540	C₂²×C₅₃	semidirect
846. #539	C₂²×C₅₃	semidirect
847. #539	C₂²×C₅₃	semidirect
848. #539	C₂²×C₅₃	semidirect
849. #539	C₂²×C₅₃	semidirect
850. #539	C₂²×C₅₃	semidirect
851. #538	C₂²×C₅₃	semidirect
852. #538	C₂²×C₅₃	semidirect
853. #538	C₂²×C₅₃	semidirect
854. #538	C₂²×C₅₃	semidirect
855. #538	C₂²×C₅₃	semidirect
856. #538	C₂²×C₅₃	semidirect
857. #538	C₂²×C₅₃	semidirect
858. #537	C₂²×C₅₃	semidirect
859. #537	C₂²×C₅₃	semidirect
860. #537	C₂²×C₅₃	semidirect
861. #536	C₂²×C₅₃	semidirect
862. #536	C₂²×C₅₃	semidirect
863. #536	C₂²×C₅₃	semidirect
864. #535	C₂²×C₅₃	semidirect
865. #535	C₂²×C₅₃	semidirect
866. #535	C₂²×C₅₃	semidirect
867. #535	C₂²×C₅₃	semidirect
868. #534	C₂²×C₅₃	semidirect
869. #534	C₂²×C₅₃	semidirect
870. #534	C₂²×C₅₃	semidirect
871. #534	C₂²×C₅₃	semidirect
872. #533	C₂²×C₅₃	semidirect
873. #532	C₂²×C₅₃	semidirect
874. #532	C₂²×C₅₃	semidirect
875. #532	C₂²×C₅₃	semidirect
876. #532	C₂²×C₅₃	semidirect
877. #529	C₂²×C₅₃	semidirect
878. #529	C₂²×C₅₃	semidirect
879. #529	C₂²×C₅₃	semidirect
880. #529	C₂²×C₅₃	semidirect
881. #529	C₂²×C₅₃	semidirect
883. #525	C₂²×C₅₃	semidirect
884. #525	C₂²×C₅₃	semidirect
885. #525	C₂²×C₅₃	semidirect
886. #525	C₂²×C₅₃	semidirect
887. #525	C₂²×C₅₃	semidirect
888. #525	C₂²×C₅₃	semidirect
889. #525	C₂²×C₅₃	semidirect
890. #525	C₂²×C₅₃	semidirect
891. #525	C₂²×C₅₃	semidirect
892. #525	C₂²×C₅₃	semidirect
893. #525	C₂²×C₅₃	semidirect
894. #525	C₂²×C₅₃	semidirect
895. #525	C₂²×C₅₃	semidirect
896. #525	C₂²×C₅₃	semidirect
897. #525	C₂²×C₅₃	semidirect
898. #525	C₂²×C₅₃	semidirect
899. #525	C₂²×C₅₃	semidirect
900. #525	C₂²×C₅₃	semidirect
901. #525	C₂²×C₅₃	semidirect
902. #525	C₂²×C₅₃	semidirect
903. #525	C₂²×C₅₃	semidirect
904. C₂×#123	C₂²×C₅₃	semidirect
905. C₂×#123	C₂²×C₅₃	semidirect
906. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
907. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
908. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
909. C₂×#121	C₂²×C₅₃	semidirect
910. C₂×#121	C₂²×C₅₃	semidirect
911. C₂×#121	C₂²×C₅₃	semidirect
912. C₂×#120	C₂²×C₅₃	semidirect
913. C₂×#120	C₂²×C₅₃	semidirect
914. C₄×#41	C₂²×C₅₃	semidirect
915. C₄×#41	C₂²×C₅₃	semidirect
916. C₂×C₄×D₄	C₂²×C₅₃	semidirect
917. C₂×C₄×D₄	C₂²×C₅₃	semidirect
918. C₂×C₄×D₄	C₂²×C₅₃	semidirect
919. C₂×C₄×D₄	C₂²×C₅₃	semidirect
920. C₂×#117	C₂²×C₅₃	semidirect
921. C₂×#117	C₂²×C₅₃	semidirect
922. C₂×#117	C₂²×C₅₃	semidirect
923. C₅₃	#62729	direct (N × H)
940. C₂×#41	C₂³×C₅₃	semidirect
941. C₂×#41	C₂³×C₅₃	semidirect
944. C₂²×Q₈	C₂³×C₅₃	semidirect
954. C₂²×D₄	C₂³×C₅₃	semidirect
968. C₂³×C₄	C₂³×C₅₃	semidirect
969. C₄⋊Q₈	C₂³×C₅₃	semidirect
970. C₄⋊Q₈	C₂³×C₅₃	semidirect
971. C₄⋊Q₈	C₂³×C₅₃	semidirect
972. C₄⋊Q₈	C₂³×C₅₃	semidirect
973. C₄⋊Q₈	C₂³×C₅₃	semidirect
977. #127	C₂³×C₅₃	semidirect
982. #126	C₂³×C₅₃	semidirect
983. #126	C₂³×C₅₃	semidirect
984. #126	C₂³×C₅₃	semidirect
985. #126	C₂³×C₅₃	semidirect
986. #126	C₂³×C₅₃	semidirect
987. #126	C₂³×C₅₃	semidirect
988. #125	C₂³×C₅₃	semidirect
989. #125	C₂³×C₅₃	semidirect
990. #125	C₂³×C₅₃	semidirect
991. #125	C₂³×C₅₃	semidirect
992. #125	C₂³×C₅₃	semidirect
993. #125	C₂³×C₅₃	semidirect
994. #125	C₂³×C₅₃	semidirect
1002. #124	C₂³×C₅₃	semidirect
1003. #124	C₂³×C₅₃	semidirect
1004. #124	C₂³×C₅₃	semidirect
1005. #124	C₂³×C₅₃	semidirect
1006. #124	C₂³×C₅₃	semidirect
1027. #123	C₂³×C₅₃	semidirect
1028. #123	C₂³×C₅₃	semidirect
1029. #123	C₂³×C₅₃	semidirect
1030. #123	C₂³×C₅₃	semidirect
1031. #123	C₂³×C₅₃	semidirect
1032. #123	C₂³×C₅₃	semidirect
1033. #123	C₂³×C₅₃	semidirect
1034. #123	C₂³×C₅₃	semidirect
1035. #123	C₂³×C₅₃	semidirect
1053. C₂²⋊Q₈	C₂³×C₅₃	semidirect
1054. C₂²⋊Q₈	C₂³×C₅₃	semidirect
1055. C₂²⋊Q₈	C₂³×C₅₃	semidirect
1056. C₂²⋊Q₈	C₂³×C₅₃	semidirect
1057. C₂²⋊Q₈	C₂³×C₅₃	semidirect
1058. C₂²⋊Q₈	C₂³×C₅₃	semidirect
1059. C₂²⋊Q₈	C₂³×C₅₃	semidirect
1060. C₂²⋊Q₈	C₂³×C₅₃	semidirect
1061. C₂²⋊Q₈	C₂³×C₅₃	semidirect
1062. C₂²⋊Q₈	C₂³×C₅₃	semidirect
1063. C₂²⋊Q₈	C₂³×C₅₃	semidirect
1093. #121	C₂³×C₅₃	semidirect
1094. #121	C₂³×C₅₃	semidirect
1095. #121	C₂³×C₅₃	semidirect
1096. #121	C₂³×C₅₃	semidirect
1097. #121	C₂³×C₅₃	semidirect
1098. #121	C₂³×C₅₃	semidirect
1099. #121	C₂³×C₅₃	semidirect
1116. #120	C₂³×C₅₃	semidirect
1117. #120	C₂³×C₅₃	semidirect
1118. #120	C₂³×C₅₃	semidirect
1119. C₄×Q₈	C₂³×C₅₃	semidirect
1120. C₄×Q₈	C₂³×C₅₃	semidirect
1121. C₄×Q₈	C₂³×C₅₃	semidirect
1122. C₄×Q₈	C₂³×C₅₃	semidirect
1145. C₄×D₄	C₂³×C₅₃	semidirect
1146. C₄×D₄	C₂³×C₅₃	semidirect
1147. C₄×D₄	C₂³×C₅₃	semidirect
1148. C₄×D₄	C₂³×C₅₃	semidirect
1149. C₄×D₄	C₂³×C₅₃	semidirect
1150. C₄×D₄	C₂³×C₅₃	semidirect
1151. C₄×D₄	C₂³×C₅₃	semidirect
1152. C₄×D₄	C₂³×C₅₃	semidirect
1164. #117	C₂³×C₅₃	semidirect
1165. #117	C₂³×C₅₃	semidirect
1166. #117	C₂³×C₅₃	semidirect
1167. #117	C₂³×C₅₃	semidirect
1168. #117	C₂³×C₅₃	semidirect
1169. #117	C₂³×C₅₃	semidirect
1176. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
1177. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
1188. C₂×C₂²⋊C₄	C₂³×C₅₃	semidirect
1191. C₂×C₄²	C₂³×C₅₃	semidirect
1192. C₂×C₄²	C₂³×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#3542	2
C₅₃×#3541	2
C₅₃×#3540	2
C₅₃×#3539	2
C₅₃×#3538	2
C₅₃×#3537	2
C₅₃×#3536	2
C₅₃×#3535	2
C₅₃×#3534	2
C₅₃×#3533	2
C₅₃×#3532	2
C₅₃×#3529	2
C₅₃×#3481	2
C₅₃×#3475	2
D₄×#41×C₅₃	2
C₅₃×#3460	2
C₅₃×#3459	2
C₅₃×#3455	2
C₅₃×#3449	2
C₂×C₅₃×#525	2
#62729	53

Subgroups — C53×#62729 #27270241

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62729 #27270241