Subgroups — C₅₃×#63031 #27270543

Order 13568.

6616 conjugacy classes of subgroups.

The subgroup lattice has 1702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3566	C₂	1	8	yes	maximal, complemented
2	C₅₃×#3562	C₂	1	4	yes	maximal, complemented
3	C₅₃×#3555	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3551	C₂	1	4	yes	maximal, complemented
5	C₅₃×#3548	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3547	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3546	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3539	C₂	1	4	yes	maximal, complemented
9	C₅₃×#3524	C₂	1	4	yes	maximal, complemented
10	C₅₃×#3517	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3515	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3515	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3512	C₂	1	4	yes	maximal, complemented
14	C₅₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3507	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3506	C₂	1	2	yes	maximal, complemented
19	C₅₃×#3506	C₂	1	2	yes	maximal, complemented
20	C₅₃×#3493	C₂	1	4	yes	maximal, complemented
21	C₅₃×#3483	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3482	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3481	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#3480	C₂	1	2	yes	maximal, complemented
25	C₅₃×#3475	C₂	1	2	yes	maximal, complemented
26	C₅₃×#3475	C₂	1	2	yes	maximal, complemented
27	C₅₃×#563	C₂²	1	8	yes	complemented
28	C₅₃×#562	C₂²	1	8	yes	complemented
29	C₅₃×#562	C₂²	1	4	yes	complemented
30	C₅₃×#560	C₂²	1	8	yes	—
31	C₅₃×#560	C₂²	1	8	yes	complemented
32	C₅₃×#559	C₂²	1	1	yes	characteristic
33	C₅₃×#559	C₂²	1	4	yes	—
34	C₅₃×#559	C₂²	1	4	yes	complemented
35	C₅₃×#559	C₂²	1	8	yes	complemented
36	Q₈²×C₅₃	C₂²	1	1	yes	characteristic, complemented
37	C₅₃×#557	C₂²	1	2	yes	complemented
38	C₅₃×#557	C₂²	1	1	yes	characteristic, complemented
39	C₅₃×#557	C₂²	1	4	yes	complemented
40	C₅₃×#557	C₂²	1	2	yes	complemented
41	C₅₃×#556	C₂²	1	1	yes	characteristic
42	C₅₃×#556	C₂²	1	2	yes	—
43	C₅₃×#556	C₂²	1	2	yes	—
44	C₅₃×#556	C₂²	1	2	yes	complemented
45	C₅₃×#556	C₂²	1	4	yes	complemented
46	C₅₃×#556	C₂²	1	2	yes	complemented
47	C₅₃×#556	C₂²	1	4	yes	complemented
48	C₅₃×#556	C₂²	1	8	yes	complemented
49	C₅₃×#556	C₂²	1	2	yes	complemented
50	C₅₃×#555	C₂²	1	1	yes	characteristic
51	C₅₃×#555	C₂²	1	2	yes	—
52	C₅₃×#555	C₂²	1	2	yes	complemented
53	C₅₃×#555	C₂²	1	2	yes	complemented
54	C₅₃×#555	C₂²	1	4	yes	complemented
55	C₅₃×#555	C₂²	1	4	yes	complemented
56	C₅₃×#555	C₂²	1	8	yes	complemented
57	C₅₃×#555	C₂²	1	2	yes	complemented
58	C₅₃×#554	C₂²	1	1	yes	characteristic
59	C₅₃×#554	C₂²	1	1	yes	characteristic
60	C₅₃×#554	C₂²	1	2	yes	complemented
61	C₅₃×#554	C₂²	1	2	yes	complemented
62	C₅₃×#554	C₂²	1	2	yes	complemented
63	C₅₃×#554	C₂²	1	2	yes	complemented
64	C₅₃×#553	C₂²	1	2	yes	—
65	C₅₃×#553	C₂²	1	2	yes	—
66	C₅₃×#553	C₂²	1	4	yes	—
67	C₅₃×#553	C₂²	1	4	yes	—
68	C₅₃×#553	C₂²	1	4	yes	complemented
69	C₅₃×#553	C₂²	1	4	yes	complemented
70	C₅₃×#553	C₂²	1	4	yes	complemented
71	C₅₃×#553	C₂²	1	8	yes	complemented
72	C₅₃×#553	C₂²	1	4	yes	complemented
73	C₅₃×#553	C₂²	1	8	yes	complemented
74	C₅₃×#553	C₂²	1	8	yes	complemented
75	C₅₃×#553	C₂²	1	4	yes	complemented
76	C₅₃×#553	C₂²	1	8	yes	complemented
77	C₅₃×#553	C₂²	1	8	yes	complemented
78	C₅₃×#552	C₂²	1	4	yes	complemented
79	C₅₃×#552	C₂²	1	4	yes	complemented
80	C₅₃×#552	C₂²	1	4	yes	complemented
81	C₅₃×#552	C₂²	1	4	yes	complemented
82	C₅₃×#552	C₂²	1	2	yes	complemented
83	C₅₃×#552	C₂²	1	4	yes	complemented
84	C₅₃×#552	C₂²	1	4	yes	complemented
85	C₅₃×#552	C₂²	1	8	yes	complemented
86	C₅₃×#552	C₂²	1	4	yes	complemented
87	C₅₃×#552	C₂²	1	4	yes	complemented
88	C₅₃×#552	C₂²	1	4	yes	complemented
89	C₅₃×#552	C₂²	1	8	yes	complemented
90	C₅₃×#551	C₂²	1	4	yes	—
91	C₅₃×#551	C₂²	1	8	yes	complemented
92	C₅₃×#551	C₂²	1	8	yes	complemented
93	C₅₃×#550	C₂²	1	2	yes	—
94	C₅₃×#550	C₂²	1	1	yes	characteristic
95	C₅₃×#550	C₂²	1	2	yes	—
96	C₅₃×#550	C₂²	1	4	yes	—
97	C₅₃×#550	C₂²	1	1	yes	characteristic, complemented
98	C₅₃×#550	C₂²	1	2	yes	complemented
99	C₅₃×#550	C₂²	1	4	yes	complemented
100	C₅₃×#550	C₂²	1	2	yes	complemented
101	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#548	C₂²	1	2	yes	—
103	C₅₃×#548	C₂²	1	4	yes	complemented
104	C₅₃×#548	C₂²	1	4	yes	complemented
105	C₅₃×#548	C₂²	1	4	yes	complemented
106	C₅₃×#547	C₂²	1	1	yes	characteristic
107	C₅₃×#547	C₂²	1	2	yes	—
108	C₅₃×#547	C₂²	1	2	yes	complemented
109	C₅₃×#547	C₂²	1	2	yes	complemented
110	C₅₃×#547	C₂²	1	2	yes	complemented
111	C₅₃×#547	C₂²	1	4	yes	complemented
112	C₅₃×#547	C₂²	1	2	yes	complemented
113	C₅₃×#547	C₂²	1	4	yes	complemented
114	C₅₃×#546	C₂²	1	4	yes	—
115	C₅₃×#546	C₂²	1	4	yes	—
116	C₅₃×#546	C₂²	1	2	yes	—
117	C₅₃×#546	C₂²	1	2	yes	—
118	D₄²×C₅₃	C₂²	1	1	yes	characteristic
119	C₅₃×#544	C₂²	1	4	yes	complemented
120	C₅₃×#542	C₂²	1	4	yes	—
121	C₅₃×#542	C₂²	1	4	yes	complemented
122	C₅₃×#542	C₂²	1	4	yes	complemented
123	C₅₃×#542	C₂²	1	8	yes	complemented
124	C₅₃×#541	C₂²	1	4	yes	complemented
125	C₅₃×#541	C₂²	1	8	yes	complemented
126	C₅₃×#541	C₂²	1	4	yes	complemented
127	C₅₃×#541	C₂²	1	4	yes	complemented
128	C₅₃×#540	C₂²	1	8	yes	complemented
129	C₅₃×#540	C₂²	1	4	yes	complemented
130	C₅₃×#540	C₂²	1	8	yes	complemented
131	C₅₃×#540	C₂²	1	8	yes	complemented
132	C₅₃×#540	C₂²	1	4	yes	complemented
133	C₅₃×#539	C₂²	1	8	yes	complemented
134	C₅₃×#539	C₂²	1	8	yes	complemented
135	C₅₃×#539	C₂²	1	8	yes	complemented
136	C₅₃×#538	C₂²	1	8	yes	—
137	C₅₃×#538	C₂²	1	8	yes	complemented
138	C₅₃×#538	C₂²	1	8	yes	complemented
139	C₅₃×#538	C₂²	1	8	yes	complemented
140	C₅₃×#537	C₂²	1	2	yes	—
141	C₅₃×#537	C₂²	1	4	yes	—
142	C₅₃×#537	C₂²	1	4	yes	complemented
143	C₅₃×#537	C₂²	1	2	yes	complemented
144	C₅₃×#537	C₂²	1	4	yes	complemented
145	C₅₃×#536	C₂²	1	2	yes	—
146	C₅₃×#536	C₂²	1	4	yes	complemented
147	C₅₃×#535	C₂²	1	4	yes	—
148	C₅₃×#535	C₂²	1	4	yes	—
149	C₅₃×#533	C₂²	1	2	yes	complemented
150	C₅₃×#533	C₂²	1	2	yes	complemented
151	C₅₃×#533	C₂²	1	2	yes	complemented
152	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
153	C₅₃×#533	C₂²	1	2	yes	complemented
154	C₅₃×#533	C₂²	1	2	yes	complemented
155	C₅₃×#532	C₂²	1	2	yes	—
156	C₅₃×#532	C₂²	1	1	yes	characteristic
157	C₅₃×#532	C₂²	1	2	yes	—
158	C₅₃×#532	C₂²	1	4	yes	complemented
159	C₅₃×#532	C₂²	1	2	yes	complemented
160	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
161	C₅₃×#532	C₂²	1	4	yes	complemented
162	C₅₃×#532	C₂²	1	2	yes	complemented
163	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
164	C₅₃×#529	C₂²	1	4	yes	—
165	C₅₃×#529	C₂²	1	4	yes	—
166	C₅₃×#529	C₂²	1	2	yes	—
167	C₅₃×#529	C₂²	1	2	yes	—
168	C₅₃×#529	C₂²	1	2	yes	—
169	C₅₃×#529	C₂²	1	8	yes	complemented
170	C₅₃×#529	C₂²	1	8	yes	complemented
171	C₅₃×#529	C₂²	1	8	yes	complemented
172	C₅₃×#529	C₂²	1	4	yes	complemented
173	C₅₃×#529	C₂²	1	4	yes	complemented
174	C₅₃×#529	C₂²	1	8	yes	complemented
175	C₅₃×#529	C₂²	1	4	yes	complemented
176	C₂×#125×C₅₃	C₂²	1	4	yes	complemented
177	C₅₃×#525	C₂²	1	4	yes	—
178	C₅₃×#525	C₂²	1	4	yes	complemented
179	C₅₃×#525	C₂²	1	4	yes	complemented
180	C₅₃×#525	C₂²	1	4	yes	complemented
181	C₅₃×#520	C₂²	1	2	yes	complemented
182	C₅₃×#520	C₂²	1	4	yes	complemented
183	C₅₃×#520	C₂²	1	4	yes	complemented
184	C₅₃×#520	C₂²	1	4	yes	complemented
185	C₅₃×#520	C₂²	1	2	yes	complemented
186	C₅₃×#519	C₂²	1	2	yes	complemented
187	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
188	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
189	C₄×#41×C₅₃	C₂²	1	4	yes	complemented
190	C₄×#41×C₅₃	C₂²	1	4	yes	complemented
191	C₄×#41×C₅₃	C₂²	1	2	yes	complemented
192	C₄×#41×C₅₃	C₂²	1	2	yes	complemented
193	C₄×#41×C₅₃	C₂²	1	2	yes	complemented
194	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
195	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	complemented
196	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
197	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
198	C₂×#117×C₅₃	C₂²	1	4	yes	complemented
199	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
200	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
201	C₂×#41×C₅₃	C₂³	1	2	yes	—
202	C₂×#41×C₅₃	C₂³	1	2	yes	—
203	C₂×#41×C₅₃	C₂³	1	4	yes	—
204	C₂×#41×C₅₃	C₂³	1	2	yes	—
205	C₂×#41×C₅₃	C₂³	1	4	yes	—
206	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
207	C₂×#41×C₅₃	C₂³	1	2	yes	—
208	C₂×#41×C₅₃	C₂³	1	4	yes	—
209	C₂×#41×C₅₃	C₂³	1	4	yes	—
210	C₂×#41×C₅₃	C₂³	1	2	yes	—
211	C₂×#41×C₅₃	C₂³	1	4	yes	—
212	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
213	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
214	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
215	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
216	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
217	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
218	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
219	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
220	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
221	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
222	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
223	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
224	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	—
225	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	—
226	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
227	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
228	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
229	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
230	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
231	C₄⋊Q₈×C₅₃	C₂³	1	8	yes	—
232	#127×C₅₃	C₂³	1	1	yes	characteristic
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	2	yes	—
238	#127×C₅₃	C₂³	1	8	yes	—
239	#126×C₅₃	C₂³	1	4	yes	—
240	#126×C₅₃	C₂³	1	8	yes	—
241	#126×C₅₃	C₂³	1	8	yes	—
242	#126×C₅₃	C₂³	1	4	yes	—
243	#126×C₅₃	C₂³	1	4	yes	—
244	#126×C₅₃	C₂³	1	4	yes	—
245	#126×C₅₃	C₂³	1	8	yes	—
246	#126×C₅₃	C₂³	1	4	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	#126×C₅₃	C₂³	1	8	yes	—
252	#126×C₅₃	C₂³	1	8	yes	—
253	#126×C₅₃	C₂³	1	8	yes	—
254	#126×C₅₃	C₂³	1	8	yes	—
255	#126×C₅₃	C₂³	1	8	yes	—
256	#125×C₅₃	C₂³	1	2	yes	—
257	#125×C₅₃	C₂³	1	2	yes	—
258	#125×C₅₃	C₂³	1	4	yes	—
259	#125×C₅₃	C₂³	1	8	yes	—
260	#125×C₅₃	C₂³	1	4	yes	—
261	#125×C₅₃	C₂³	1	8	yes	—
262	#125×C₅₃	C₂³	1	2	yes	—
263	#125×C₅₃	C₂³	1	4	yes	—
264	#125×C₅₃	C₂³	1	4	yes	—
265	#125×C₅₃	C₂³	1	8	yes	—
266	#125×C₅₃	C₂³	1	8	yes	—
267	#125×C₅₃	C₂³	1	4	yes	—
268	#125×C₅₃	C₂³	1	4	yes	—
269	#125×C₅₃	C₂³	1	2	yes	—
270	#125×C₅₃	C₂³	1	4	yes	—
271	#125×C₅₃	C₂³	1	8	yes	—
272	#125×C₅₃	C₂³	1	8	yes	—
273	#125×C₅₃	C₂³	1	8	yes	—
274	#124×C₅₃	C₂³	1	2	yes	—
275	#124×C₅₃	C₂³	1	2	yes	—
276	#124×C₅₃	C₂³	1	2	yes	—
277	#124×C₅₃	C₂³	1	4	yes	—
278	#124×C₅₃	C₂³	1	4	yes	—
279	#124×C₅₃	C₂³	1	4	yes	—
280	#124×C₅₃	C₂³	1	4	yes	—
281	#124×C₅₃	C₂³	1	4	yes	—
282	#124×C₅₃	C₂³	1	8	yes	—
283	#124×C₅₃	C₂³	1	8	yes	—
284	#124×C₅₃	C₂³	1	4	yes	—
285	#124×C₅₃	C₂³	1	4	yes	—
286	#124×C₅₃	C₂³	1	2	yes	—
287	#124×C₅₃	C₂³	1	4	yes	—
288	#124×C₅₃	C₂³	1	2	yes	—
289	#124×C₅₃	C₂³	1	8	yes	—
290	#124×C₅₃	C₂³	1	8	yes	—
291	#124×C₅₃	C₂³	1	8	yes	—
292	#123×C₅₃	C₂³	1	4	yes	—
293	#123×C₅₃	C₂³	1	4	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	4	yes	—
300	#123×C₅₃	C₂³	1	4	yes	—
301	#123×C₅₃	C₂³	1	4	yes	—
302	#123×C₅₃	C₂³	1	8	yes	—
303	#123×C₅₃	C₂³	1	8	yes	—
304	#123×C₅₃	C₂³	1	4	yes	—
305	#123×C₅₃	C₂³	1	8	yes	—
306	#123×C₅₃	C₂³	1	4	yes	—
307	#123×C₅₃	C₂³	1	8	yes	—
308	#123×C₅₃	C₂³	1	8	yes	—
309	#123×C₅₃	C₂³	1	8	yes	—
310	#123×C₅₃	C₂³	1	8	yes	—
311	#123×C₅₃	C₂³	1	8	yes	—
312	#123×C₅₃	C₂³	1	8	yes	—
313	#123×C₅₃	C₂³	1	8	yes	—
314	#123×C₅₃	C₂³	1	8	yes	—
315	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
316	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
317	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
318	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
319	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
320	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
321	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
322	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
323	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
324	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
325	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
326	C₂²⋊Q₈×C₅₃	C₂³	1	2	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	8	yes	—
331	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
332	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
333	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
334	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
335	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
336	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
337	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
338	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
339	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
340	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
341	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
342	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
343	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
344	#121×C₅₃	C₂³	1	4	yes	—
345	#121×C₅₃	C₂³	1	4	yes	—
346	#121×C₅₃	C₂³	1	2	yes	—
347	#121×C₅₃	C₂³	1	2	yes	—
348	#121×C₅₃	C₂³	1	4	yes	—
349	#121×C₅₃	C₂³	1	4	yes	—
350	#121×C₅₃	C₂³	1	4	yes	—
351	#121×C₅₃	C₂³	1	2	yes	—
352	#121×C₅₃	C₂³	1	2	yes	—
353	#121×C₅₃	C₂³	1	4	yes	—
354	#121×C₅₃	C₂³	1	2	yes	—
355	#121×C₅₃	C₂³	1	2	yes	—
356	#121×C₅₃	C₂³	1	2	yes	—
357	#121×C₅₃	C₂³	1	4	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	8	yes	—
362	#121×C₅₃	C₂³	1	4	yes	—
363	#121×C₅₃	C₂³	1	4	yes	—
364	#121×C₅₃	C₂³	1	2	yes	—
365	#121×C₅₃	C₂³	1	4	yes	—
366	#121×C₅₃	C₂³	1	4	yes	—
367	#121×C₅₃	C₂³	1	2	yes	—
368	#121×C₅₃	C₂³	1	4	yes	—
369	#121×C₅₃	C₂³	1	2	yes	—
370	#121×C₅₃	C₂³	1	4	yes	—
371	#121×C₅₃	C₂³	1	4	yes	—
372	#121×C₅₃	C₂³	1	4	yes	—
373	#121×C₅₃	C₂³	1	8	yes	—
374	#121×C₅₃	C₂³	1	2	yes	—
375	#121×C₅₃	C₂³	1	8	yes	—
376	#121×C₅₃	C₂³	1	4	yes	—
377	#121×C₅₃	C₂³	1	4	yes	—
378	#121×C₅₃	C₂³	1	8	yes	—
379	#121×C₅₃	C₂³	1	8	yes	—
380	#121×C₅₃	C₂³	1	8	yes	—
381	#121×C₅₃	C₂³	1	8	yes	—
382	#121×C₅₃	C₂³	1	8	yes	—
383	#121×C₅₃	C₂³	1	8	yes	—
384	#121×C₅₃	C₂³	1	8	yes	—
385	#121×C₅₃	C₂³	1	8	yes	—
386	#120×C₅₃	C₂³	1	4	yes	—
387	#120×C₅₃	C₂³	1	4	yes	—
388	#120×C₅₃	C₂³	1	8	yes	—
389	#120×C₅₃	C₂³	1	8	yes	—
390	#120×C₅₃	C₂³	1	8	yes	—
391	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
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	4	yes	—
396	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
397	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
398	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
399	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
400	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
401	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
402	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
403	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
404	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
405	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
406	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
407	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
408	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
409	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
410	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
411	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
412	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
413	C₄×Q₈×C₅₃	C₂³	1	8	yes	—
414	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
415	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
416	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
417	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
418	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
419	C₄×D₄×C₅₃	C₂³	1	2	yes	—
420	C₄×D₄×C₅₃	C₂³	1	2	yes	—
421	C₄×D₄×C₅₃	C₂³	1	4	yes	—
422	C₄×D₄×C₅₃	C₂³	1	4	yes	—
423	C₄×D₄×C₅₃	C₂³	1	2	yes	—
424	C₄×D₄×C₅₃	C₂³	1	2	yes	—
425	C₄×D₄×C₅₃	C₂³	1	2	yes	—
426	C₄×D₄×C₅₃	C₂³	1	2	yes	—
427	C₄×D₄×C₅₃	C₂³	1	4	yes	—
428	C₄×D₄×C₅₃	C₂³	1	4	yes	—
429	C₄×D₄×C₅₃	C₂³	1	2	yes	—
430	C₄×D₄×C₅₃	C₂³	1	2	yes	—
431	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
432	C₄×D₄×C₅₃	C₂³	1	2	yes	—
433	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
434	C₄×D₄×C₅₃	C₂³	1	2	yes	—
435	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
436	C₄×D₄×C₅₃	C₂³	1	2	yes	—
437	C₄×D₄×C₅₃	C₂³	1	2	yes	—
438	C₄×D₄×C₅₃	C₂³	1	8	yes	—
439	C₄×D₄×C₅₃	C₂³	1	8	yes	—
440	C₄×D₄×C₅₃	C₂³	1	4	yes	—
441	C₄×D₄×C₅₃	C₂³	1	2	yes	—
442	C₄×D₄×C₅₃	C₂³	1	4	yes	—
443	C₄×D₄×C₅₃	C₂³	1	8	yes	—
444	C₄×D₄×C₅₃	C₂³	1	4	yes	—
445	C₄×D₄×C₅₃	C₂³	1	2	yes	—
446	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
447	C₄×D₄×C₅₃	C₂³	1	2	yes	—
448	C₄×D₄×C₅₃	C₂³	1	2	yes	—
449	C₄×D₄×C₅₃	C₂³	1	4	yes	—
450	C₄×D₄×C₅₃	C₂³	1	4	yes	—
451	C₄×D₄×C₅₃	C₂³	1	4	yes	—
452	C₄×D₄×C₅₃	C₂³	1	2	yes	—
453	C₄×D₄×C₅₃	C₂³	1	4	yes	—
454	C₄×D₄×C₅₃	C₂³	1	4	yes	—
455	C₄×D₄×C₅₃	C₂³	1	8	yes	—
456	C₄×D₄×C₅₃	C₂³	1	8	yes	—
457	C₄×D₄×C₅₃	C₂³	1	8	yes	—
458	C₄×D₄×C₅₃	C₂³	1	8	yes	—
459	C₄×D₄×C₅₃	C₂³	1	8	yes	—
460	C₄×D₄×C₅₃	C₂³	1	4	yes	—
461	C₄×D₄×C₅₃	C₂³	1	8	yes	—
462	C₄×D₄×C₅₃	C₂³	1	8	yes	—
463	C₄×D₄×C₅₃	C₂³	1	8	yes	—
464	C₄×D₄×C₅₃	C₂³	1	8	yes	—
465	C₄×D₄×C₅₃	C₂³	1	4	yes	—
466	C₄×D₄×C₅₃	C₂³	1	8	yes	—
467	C₄×D₄×C₅₃	C₂³	1	4	yes	—
468	C₄×D₄×C₅₃	C₂³	1	4	yes	—
469	#117×C₅₃	C₂³	1	2	yes	—
470	#117×C₅₃	C₂³	1	2	yes	—
471	#117×C₅₃	C₂³	1	4	yes	—
472	#117×C₅₃	C₂³	1	4	yes	—
473	#117×C₅₃	C₂³	1	8	yes	—
474	#117×C₅₃	C₂³	1	8	yes	—
475	#117×C₅₃	C₂³	1	1	yes	characteristic
476	#117×C₅₃	C₂³	1	1	yes	characteristic
477	#117×C₅₃	C₂³	1	2	yes	—
478	#117×C₅₃	C₂³	1	2	yes	—
479	#117×C₅₃	C₂³	1	2	yes	—
480	#117×C₅₃	C₂³	1	4	yes	—
481	#117×C₅₃	C₂³	1	1	yes	characteristic
482	#117×C₅₃	C₂³	1	8	yes	—
483	#117×C₅₃	C₂³	1	4	yes	—
484	#117×C₅₃	C₂³	1	4	yes	—
485	#117×C₅₃	C₂³	1	4	yes	—
486	#117×C₅₃	C₂³	1	8	yes	—
487	#117×C₅₃	C₂³	1	2	yes	—
488	#117×C₅₃	C₂³	1	2	yes	—
489	#117×C₅₃	C₂³	1	8	yes	—
490	#117×C₅₃	C₂³	1	4	yes	—
491	#117×C₅₃	C₂³	1	4	yes	—
492	#117×C₅₃	C₂³	1	4	yes	—
493	#117×C₅₃	C₂³	1	8	yes	—
494	#117×C₅₃	C₂³	1	8	yes	—
495	#117×C₅₃	C₂³	1	4	yes	—
496	#117×C₅₃	C₂³	1	4	yes	—
497	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
498	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
499	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
500	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
501	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
502	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
503	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
504	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
505	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	—
506	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	—
507	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
508	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
509	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
510	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
511	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
512	C₂×C₄²×C₅₃	C₂³	1	8	yes	—
513	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
514	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
515	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
516	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
517	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
518	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
519	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
520	#41×C₅₃	—	4	4	no	—
521	#41×C₅₃	—	4	8	no	—
522	#41×C₅₃	—	4	4	no	—
523	#41×C₅₃	—	4	4	no	—
524	#41×C₅₃	—	4	4	no	—
525	#41×C₅₃	—	4	8	no	—
526	#41×C₅₃	—	4	8	no	—
527	#41×C₅₃	—	4	2	no	—
528	#41×C₅₃	—	4	2	no	—
529	#41×C₅₃	—	4	8	no	—
530	#41×C₅₃	—	4	8	no	—
531	#41×C₅₃	—	4	4	no	—
532	#41×C₅₃	—	4	2	no	—
533	C₂×Q₈×C₅₃	—	4	4	no	—
534	C₂×Q₈×C₅₃	—	4	4	no	—
535	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
536	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
537	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
538	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
539	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
540	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
541	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
542	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
543	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
544	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
545	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
546	C₂×D₄×C₅₃	—	4	4	no	—
547	C₂×D₄×C₅₃	—	4	4	no	—
548	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
549	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
550	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
551	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
552	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
553	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
554	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
555	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
556	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
557	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
558	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
559	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
560	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
561	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
562	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
563	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
564	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
565	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
566	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
567	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
568	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
569	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
570	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
571	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
572	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
573	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
574	C₂²×C₄×C₅₃	—	4	8	no	—
575	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
576	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
577	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
578	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
579	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
580	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
581	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
582	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
583	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
584	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
585	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
586	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
587	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
588	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
589	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
590	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
591	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
592	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
593	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
594	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
595	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
596	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
597	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
598	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
599	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
600	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
601	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
602	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
603	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
604	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
605	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
606	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
607	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
608	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
609	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
610	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
611	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
612	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
613	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
614	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
615	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
616	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
617	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
618	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
619	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
620	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
621	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
622	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
623	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
624	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
625	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
626	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
627	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
628	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
629	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
630	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
631	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
632	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
633	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
634	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
635	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
636	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
637	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
638	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
639	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
640	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
641	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
642	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
643	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
644	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
645	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
646	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
647	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
648	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
649	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
650	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
651	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
652	C₂²⋊C₄×C₅₃	C₂⁴	1	2	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	4	yes	—
660	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
661	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
662	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
663	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
664	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
665	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
666	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
667	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
668	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
669	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
670	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
671	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
672	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
673	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
674	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
675	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
676	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
677	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
678	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
679	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
680	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
681	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
682	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
683	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
684	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
685	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
686	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
687	C₄²×C₅₃	C₂⁴	1	4	yes	—
688	C₄²×C₅₃	C₂⁴	1	4	yes	—
689	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
690	C₄²×C₅₃	C₂⁴	1	2	yes	—
691	C₄²×C₅₃	C₂⁴	1	2	yes	—
692	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
693	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
694	C₄²×C₅₃	C₂⁴	1	2	yes	—
695	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
696	C₄²×C₅₃	C₂⁴	1	2	yes	—
697	C₄²×C₅₃	C₂⁴	1	4	yes	—
698	C₄²×C₅₃	C₂⁴	1	8	yes	—
699	C₄²×C₅₃	C₂⁴	1	8	yes	—
700	C₄²×C₅₃	C₂⁴	1	2	yes	—
701	C₄²×C₅₃	C₂⁴	1	2	yes	—
702	C₄²×C₅₃	C₂⁴	1	2	yes	—
703	C₄²×C₅₃	C₂⁴	1	2	yes	—
704	C₄²×C₅₃	C₂⁴	1	4	yes	—
705	C₄²×C₅₃	C₂⁴	1	2	yes	—
706	C₄²×C₅₃	C₂⁴	1	4	yes	—
707	C₄²×C₅₃	C₂⁴	1	8	yes	—
708	C₄²×C₅₃	C₂⁴	1	8	yes	—
709	C₂³×C₅₃	—	4	4	no	—
710	C₂³×C₅₃	—	4	4	no	—
711	C₂³×C₅₃	—	4	4	no	—
712	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
713	C₂³×C₅₃	C₂⁵	1	2	yes	—
714	C₂³×C₅₃	C₂⁵	1	4	yes	—
715	C₂³×C₅₃	C₂⁵	1	4	yes	—
716	C₂³×C₅₃	C₂⁵	1	2	yes	—
717	C₂³×C₅₃	C₂⁵	1	2	yes	—
718	Q₈×C₅₃	—	2	2	no	—
719	Q₈×C₅₃	—	2	4	no	—
720	Q₈×C₅₃	—	2	8	no	—
721	Q₈×C₅₃	—	2	2	no	—
722	Q₈×C₅₃	—	2	4	no	—
723	Q₈×C₅₃	—	2	2	no	—
724	Q₈×C₅₃	—	4	4	no	—
725	Q₈×C₅₃	—	4	4	no	—
726	Q₈×C₅₃	—	4	2	no	—
727	Q₈×C₅₃	—	4	2	no	—
728	Q₈×C₅₃	—	4	4	no	—
729	D₄×C₅₃	—	2	2	no	—
730	D₄×C₅₃	—	2	2	no	—
731	D₄×C₅₃	—	2	4	no	—
732	D₄×C₅₃	—	2	4	no	—
733	D₄×C₅₃	—	2	2	no	—
734	D₄×C₅₃	—	2	4	no	—
735	D₄×C₅₃	—	2	4	no	—
736	D₄×C₅₃	—	4	4	no	—
737	D₄×C₅₃	—	4	4	no	—
738	D₄×C₅₃	—	4	4	no	—
739	D₄×C₅₃	—	4	4	no	—
740	D₄×C₅₃	—	4	2	no	—
741	D₄×C₅₃	—	4	4	no	—
742	D₄×C₅₃	—	4	2	no	—
743	D₄×C₅₃	—	4	4	no	—
744	D₄×C₅₃	—	4	4	no	—
745	D₄×C₅₃	—	4	2	no	—
746	D₄×C₅₃	—	4	4	no	—
747	D₄×C₅₃	—	4	4	no	—
748	D₄×C₅₃	—	4	8	no	—
749	D₄×C₅₃	—	4	2	no	—
750	D₄×C₅₃	—	4	4	no	—
751	D₄×C₅₃	—	4	8	no	—
752	D₄×C₅₃	—	4	8	no	—
753	D₄×C₅₃	—	4	8	no	—
754	D₄×C₅₃	—	4	2	no	—
755	C₂×C₄×C₅₃	—	2	4	no	—
756	C₂×C₄×C₅₃	—	2	4	no	—
757	C₂×C₄×C₅₃	—	2	8	no	—
758	C₂×C₄×C₅₃	—	2	4	no	—
759	C₂×C₄×C₅₃	—	2	4	no	—
760	C₂×C₄×C₅₃	—	2	2	no	—
761	C₂×C₄×C₅₃	—	2	4	no	—
762	C₂×C₄×C₅₃	—	2	4	no	—
763	C₂×C₄×C₅₃	—	2	2	no	—
764	C₂×C₄×C₅₃	—	2	2	no	—
765	C₂×C₄×C₅₃	—	2	8	no	—
766	C₂×C₄×C₅₃	—	4	4	no	—
767	C₂×C₄×C₅₃	—	4	4	no	—
768	C₂×C₄×C₅₃	—	4	4	no	—
769	C₂×C₄×C₅₃	—	4	4	no	—
770	C₂×C₄×C₅₃	—	4	4	no	—
771	C₂×C₄×C₅₃	—	4	4	no	—
772	C₂×C₄×C₅₃	—	4	4	no	—
773	C₂×C₄×C₅₃	—	4	4	no	—
774	C₂×C₄×C₅₃	—	4	8	no	—
775	C₂×C₄×C₅₃	—	4	8	no	—
776	C₂×C₄×C₅₃	—	4	8	no	—
777	C₂×C₄×C₅₃	—	4	2	no	—
778	C₂×C₄×C₅₃	—	4	8	no	—
779	C₂×C₄×C₅₃	—	4	2	no	—
780	C₂×C₄×C₅₃	—	4	2	no	—
781	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
782	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
783	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
784	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
785	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
786	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
787	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
788	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
789	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
790	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
791	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
792	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
793	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
794	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
795	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
796	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
797	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
798	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
799	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
800	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
801	#63031	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
802	C₂²×C₅₃	—	2	1	no	—
803	C₂²×C₅₃	—	2	2	no	—
804	C₂²×C₅₃	—	2	2	no	—
805	C₂²×C₅₃	—	2	2	no	—
806	C₂²×C₅₃	—	2	4	no	—
807	C₂²×C₅₃	—	2	1	no	—
808	C₂²×C₅₃	—	2	1	no	—
809	C₂²×C₅₃	—	2	2	no	—
810	C₂²×C₅₃	—	2	4	no	—
811	C₂²×C₅₃	—	2	2	no	—
812	C₂²×C₅₃	—	2	2	no	—
813	C₂²×C₅₃	—	2	2	no	—
814	C₂²×C₅₃	—	2	4	no	—
815	C₂²×C₅₃	—	2	4	no	—
816	C₂²×C₅₃	—	2	4	no	—
817	C₂²×C₅₃	—	2	4	no	—
818	C₂²×C₅₃	—	2	2	no	—
819	C₂²×C₅₃	—	2	2	no	—
820	C₂²×C₅₃	—	8	8	no	—
821	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
822	C₄×C₅₃	—	2	2	no	—
823	C₄×C₅₃	—	2	2	no	—
824	C₄×C₅₃	—	2	2	no	—
825	C₄×C₅₃	—	2	2	no	—
826	C₄×C₅₃	—	2	4	no	—
827	C₄×C₅₃	—	2	1	no	—
828	C₄×C₅₃	—	2	4	no	—
829	C₄×C₅₃	—	2	1	no	—
830	C₄×C₅₃	—	2	1	no	—
831	C₄×C₅₃	—	2	2	no	—
832	C₄×C₅₃	—	2	2	no	—
833	C₄×C₅₃	—	2	2	no	—
834	C₄×C₅₃	—	2	4	no	—
835	C₄×C₅₃	—	2	2	no	—
836	C₄×C₅₃	—	2	8	no	—
837	C₄×C₅₃	—	2	4	no	—
838	C₄×C₅₃	—	2	2	no	—
839	C₄×C₅₃	#585	1	2	yes	—
840	C₄×C₅₃	#585	1	2	yes	—
841	C₄×C₅₃	#585	1	2	yes	—
842	#3566	C₂×C₅₃	1	8	yes	complemented
843	#3562	C₂×C₅₃	1	4	yes	complemented
844	#3555	C₂×C₅₃	1	2	yes	complemented
845	#3551	C₂×C₅₃	1	4	yes	complemented
846	#3548	C₂×C₅₃	1	1	yes	characteristic, complemented
847	#3547	C₂×C₅₃	1	2	yes	complemented
848	#3546	C₂×C₅₃	1	2	yes	complemented
849	#3539	C₂×C₅₃	1	4	yes	complemented
850	#3524	C₂×C₅₃	1	4	yes	complemented
851	#3517	C₂×C₅₃	1	2	yes	complemented
852	#3515	C₂×C₅₃	1	2	yes	complemented
853	#3515	C₂×C₅₃	1	2	yes	complemented
854	#3512	C₂×C₅₃	1	4	yes	complemented
855	#3511	C₂×C₅₃	1	1	yes	characteristic, complemented
856	#3511	C₂×C₅₃	1	1	yes	characteristic, complemented
857	#3509	C₂×C₅₃	1	1	yes	characteristic, complemented
858	#3507	C₂×C₅₃	1	2	yes	complemented
859	#3506	C₂×C₅₃	1	2	yes	complemented
860	#3506	C₂×C₅₃	1	2	yes	complemented
861	#3493	C₂×C₅₃	1	4	yes	complemented
862	#3483	C₂×C₅₃	1	1	yes	characteristic, complemented
863	#3482	C₂×C₅₃	1	1	yes	characteristic, complemented
864	#3481	C₂×C₅₃	1	1	yes	characteristic, complemented
865	#3480	C₂×C₅₃	1	2	yes	complemented
866	#3475	C₂×C₅₃	1	2	yes	complemented
867	#3475	C₂×C₅₃	1	2	yes	complemented
868	C₂×C₅₃	—	4	1	no	—
869	C₂×C₅₃	—	4	2	no	—
870	C₂×C₅₃	—	4	4	no	—
871	C₂×C₅₃	—	4	4	no	—
872	C₂×C₅₃	—	4	2	no	—
873	C₂×C₅₃	—	4	2	no	—
874	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
875	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
876	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
877	#563	C₂²×C₅₃	1	8	yes	complemented
878	#562	C₂²×C₅₃	1	8	yes	complemented
879	#562	C₂²×C₅₃	1	4	yes	complemented
880	#560	C₂²×C₅₃	1	8	yes	—
881	#560	C₂²×C₅₃	1	8	yes	complemented
882	#559	C₂²×C₅₃	1	1	yes	characteristic
883	#559	C₂²×C₅₃	1	4	yes	—
884	#559	C₂²×C₅₃	1	4	yes	complemented
885	#559	C₂²×C₅₃	1	8	yes	complemented
886	Q₈²	C₂²×C₅₃	1	1	yes	characteristic, complemented
887	#557	C₂²×C₅₃	1	2	yes	complemented
888	#557	C₂²×C₅₃	1	1	yes	characteristic, complemented
889	#557	C₂²×C₅₃	1	4	yes	complemented
890	#557	C₂²×C₅₃	1	2	yes	complemented
891	#556	C₂²×C₅₃	1	1	yes	characteristic
892	#556	C₂²×C₅₃	1	2	yes	—
893	#556	C₂²×C₅₃	1	2	yes	—
894	#556	C₂²×C₅₃	1	2	yes	complemented
895	#556	C₂²×C₅₃	1	4	yes	complemented
896	#556	C₂²×C₅₃	1	2	yes	complemented
897	#556	C₂²×C₅₃	1	4	yes	complemented
898	#556	C₂²×C₅₃	1	8	yes	complemented
899	#556	C₂²×C₅₃	1	2	yes	complemented
900	#555	C₂²×C₅₃	1	1	yes	characteristic
901	#555	C₂²×C₅₃	1	2	yes	—
902	#555	C₂²×C₅₃	1	2	yes	complemented
903	#555	C₂²×C₅₃	1	2	yes	complemented
904	#555	C₂²×C₅₃	1	4	yes	complemented
905	#555	C₂²×C₅₃	1	4	yes	complemented
906	#555	C₂²×C₅₃	1	8	yes	complemented
907	#555	C₂²×C₅₃	1	2	yes	complemented
908	#554	C₂²×C₅₃	1	1	yes	characteristic
909	#554	C₂²×C₅₃	1	1	yes	characteristic
910	#554	C₂²×C₅₃	1	2	yes	complemented
911	#554	C₂²×C₅₃	1	2	yes	complemented
912	#554	C₂²×C₅₃	1	2	yes	complemented
913	#554	C₂²×C₅₃	1	2	yes	complemented
914	#553	C₂²×C₅₃	1	2	yes	—
915	#553	C₂²×C₅₃	1	2	yes	—
916	#553	C₂²×C₅₃	1	4	yes	—
917	#553	C₂²×C₅₃	1	4	yes	—
918	#553	C₂²×C₅₃	1	4	yes	complemented
919	#553	C₂²×C₅₃	1	4	yes	complemented
920	#553	C₂²×C₅₃	1	4	yes	complemented
921	#553	C₂²×C₅₃	1	8	yes	complemented
922	#553	C₂²×C₅₃	1	4	yes	complemented
923	#553	C₂²×C₅₃	1	8	yes	complemented
924	#553	C₂²×C₅₃	1	8	yes	complemented
925	#553	C₂²×C₅₃	1	4	yes	complemented
926	#553	C₂²×C₅₃	1	8	yes	complemented
927	#553	C₂²×C₅₃	1	8	yes	complemented
928	#552	C₂²×C₅₃	1	4	yes	complemented
929	#552	C₂²×C₅₃	1	4	yes	complemented
930	#552	C₂²×C₅₃	1	4	yes	complemented
931	#552	C₂²×C₅₃	1	4	yes	complemented
932	#552	C₂²×C₅₃	1	2	yes	complemented
933	#552	C₂²×C₅₃	1	4	yes	complemented
934	#552	C₂²×C₅₃	1	4	yes	complemented
935	#552	C₂²×C₅₃	1	8	yes	complemented
936	#552	C₂²×C₅₃	1	4	yes	complemented
937	#552	C₂²×C₅₃	1	4	yes	complemented
938	#552	C₂²×C₅₃	1	4	yes	complemented
939	#552	C₂²×C₅₃	1	8	yes	complemented
940	#551	C₂²×C₅₃	1	4	yes	—
941	#551	C₂²×C₅₃	1	8	yes	complemented
942	#551	C₂²×C₅₃	1	8	yes	complemented
943	#550	C₂²×C₅₃	1	2	yes	—
944	#550	C₂²×C₅₃	1	1	yes	characteristic
945	#550	C₂²×C₅₃	1	2	yes	—
946	#550	C₂²×C₅₃	1	4	yes	—
947	#550	C₂²×C₅₃	1	1	yes	characteristic, complemented
948	#550	C₂²×C₅₃	1	2	yes	complemented
949	#550	C₂²×C₅₃	1	4	yes	complemented
950	#550	C₂²×C₅₃	1	2	yes	complemented
951	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
952	#548	C₂²×C₅₃	1	2	yes	—
953	#548	C₂²×C₅₃	1	4	yes	complemented
954	#548	C₂²×C₅₃	1	4	yes	complemented
955	#548	C₂²×C₅₃	1	4	yes	complemented
956	#547	C₂²×C₅₃	1	1	yes	characteristic
957	#547	C₂²×C₅₃	1	2	yes	—
958	#547	C₂²×C₅₃	1	2	yes	complemented
959	#547	C₂²×C₅₃	1	2	yes	complemented
960	#547	C₂²×C₅₃	1	2	yes	complemented
961	#547	C₂²×C₅₃	1	4	yes	complemented
962	#547	C₂²×C₅₃	1	2	yes	complemented
963	#547	C₂²×C₅₃	1	4	yes	complemented
964	#546	C₂²×C₅₃	1	4	yes	—
965	#546	C₂²×C₅₃	1	4	yes	—
966	#546	C₂²×C₅₃	1	2	yes	—
967	#546	C₂²×C₅₃	1	2	yes	—
968	D₄²	C₂²×C₅₃	1	1	yes	characteristic
969	#544	C₂²×C₅₃	1	4	yes	complemented
970	#542	C₂²×C₅₃	1	4	yes	—
971	#542	C₂²×C₅₃	1	4	yes	complemented
972	#542	C₂²×C₅₃	1	4	yes	complemented
973	#542	C₂²×C₅₃	1	8	yes	complemented
974	#541	C₂²×C₅₃	1	4	yes	complemented
975	#541	C₂²×C₅₃	1	8	yes	complemented
976	#541	C₂²×C₅₃	1	4	yes	complemented
977	#541	C₂²×C₅₃	1	4	yes	complemented
978	#540	C₂²×C₅₃	1	8	yes	complemented
979	#540	C₂²×C₅₃	1	4	yes	complemented
980	#540	C₂²×C₅₃	1	8	yes	complemented
981	#540	C₂²×C₅₃	1	8	yes	complemented
982	#540	C₂²×C₅₃	1	4	yes	complemented
983	#539	C₂²×C₅₃	1	8	yes	complemented
984	#539	C₂²×C₅₃	1	8	yes	complemented
985	#539	C₂²×C₅₃	1	8	yes	complemented
986	#538	C₂²×C₅₃	1	8	yes	—
987	#538	C₂²×C₅₃	1	8	yes	complemented
988	#538	C₂²×C₅₃	1	8	yes	complemented
989	#538	C₂²×C₅₃	1	8	yes	complemented
990	#537	C₂²×C₅₃	1	2	yes	—
991	#537	C₂²×C₅₃	1	4	yes	—
992	#537	C₂²×C₅₃	1	4	yes	complemented
993	#537	C₂²×C₅₃	1	2	yes	complemented
994	#537	C₂²×C₅₃	1	4	yes	complemented
995	#536	C₂²×C₅₃	1	2	yes	—
996	#536	C₂²×C₅₃	1	4	yes	complemented
997	#535	C₂²×C₅₃	1	4	yes	—
998	#535	C₂²×C₅₃	1	4	yes	—
999	#533	C₂²×C₅₃	1	2	yes	complemented
1000	#533	C₂²×C₅₃	1	2	yes	complemented
1001	#533	C₂²×C₅₃	1	2	yes	complemented
1002	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
1003	#533	C₂²×C₅₃	1	2	yes	complemented
1004	#533	C₂²×C₅₃	1	2	yes	complemented
1005	#532	C₂²×C₅₃	1	2	yes	—
1006	#532	C₂²×C₅₃	1	1	yes	characteristic
1007	#532	C₂²×C₅₃	1	2	yes	—
1008	#532	C₂²×C₅₃	1	4	yes	complemented
1009	#532	C₂²×C₅₃	1	2	yes	complemented
1010	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
1011	#532	C₂²×C₅₃	1	4	yes	complemented
1012	#532	C₂²×C₅₃	1	2	yes	complemented
1013	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1014	#529	C₂²×C₅₃	1	4	yes	—
1015	#529	C₂²×C₅₃	1	4	yes	—
1016	#529	C₂²×C₅₃	1	2	yes	—
1017	#529	C₂²×C₅₃	1	2	yes	—
1018	#529	C₂²×C₅₃	1	2	yes	—
1019	#529	C₂²×C₅₃	1	8	yes	complemented
1020	#529	C₂²×C₅₃	1	8	yes	complemented
1021	#529	C₂²×C₅₃	1	8	yes	complemented
1022	#529	C₂²×C₅₃	1	4	yes	complemented
1023	#529	C₂²×C₅₃	1	4	yes	complemented
1024	#529	C₂²×C₅₃	1	8	yes	complemented
1025	#529	C₂²×C₅₃	1	4	yes	complemented
1026	C₂×#125	C₂²×C₅₃	1	4	yes	complemented
1027	#525	C₂²×C₅₃	1	4	yes	—
1028	#525	C₂²×C₅₃	1	4	yes	complemented
1029	#525	C₂²×C₅₃	1	4	yes	complemented
1030	#525	C₂²×C₅₃	1	4	yes	complemented
1031	#520	C₂²×C₅₃	1	2	yes	complemented
1032	#520	C₂²×C₅₃	1	4	yes	complemented
1033	#520	C₂²×C₅₃	1	4	yes	complemented
1034	#520	C₂²×C₅₃	1	4	yes	complemented
1035	#520	C₂²×C₅₃	1	2	yes	complemented
1036	#519	C₂²×C₅₃	1	2	yes	complemented
1037	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
1038	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
1039	C₄×#41	C₂²×C₅₃	1	4	yes	complemented
1040	C₄×#41	C₂²×C₅₃	1	4	yes	complemented
1041	C₄×#41	C₂²×C₅₃	1	2	yes	complemented
1042	C₄×#41	C₂²×C₅₃	1	2	yes	complemented
1043	C₄×#41	C₂²×C₅₃	1	2	yes	complemented
1044	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
1045	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	complemented
1046	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
1047	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
1048	C₂×#117	C₂²×C₅₃	1	4	yes	complemented
1049	C₅₃	#63031	1	1	yes	characteristic, direct product factor, Sylow
1050	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1051	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1052	C₂×#41	C₂³×C₅₃	1	2	yes	—
1053	C₂×#41	C₂³×C₅₃	1	2	yes	—
1054	C₂×#41	C₂³×C₅₃	1	4	yes	—
1055	C₂×#41	C₂³×C₅₃	1	2	yes	—
1056	C₂×#41	C₂³×C₅₃	1	4	yes	—
1057	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1058	C₂×#41	C₂³×C₅₃	1	2	yes	—
1059	C₂×#41	C₂³×C₅₃	1	4	yes	—
1060	C₂×#41	C₂³×C₅₃	1	4	yes	—
1061	C₂×#41	C₂³×C₅₃	1	2	yes	—
1062	C₂×#41	C₂³×C₅₃	1	4	yes	—
1063	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
1064	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
1065	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
1066	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
1067	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
1068	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
1069	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
1070	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
1071	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
1072	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1073	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
1074	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1075	C₄⋊Q₈	C₂³×C₅₃	1	4	yes	—
1076	C₄⋊Q₈	C₂³×C₅₃	1	4	yes	—
1077	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
1078	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1079	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1080	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
1081	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
1082	C₄⋊Q₈	C₂³×C₅₃	1	8	yes	—
1083	#127	C₂³×C₅₃	1	1	yes	characteristic
1084	#127	C₂³×C₅₃	1	2	yes	—
1085	#127	C₂³×C₅₃	1	1	yes	characteristic
1086	#127	C₂³×C₅₃	1	4	yes	—
1087	#127	C₂³×C₅₃	1	4	yes	—
1088	#127	C₂³×C₅₃	1	2	yes	—
1089	#127	C₂³×C₅₃	1	8	yes	—
1090	#126	C₂³×C₅₃	1	4	yes	—
1091	#126	C₂³×C₅₃	1	8	yes	—
1092	#126	C₂³×C₅₃	1	8	yes	—
1093	#126	C₂³×C₅₃	1	4	yes	—
1094	#126	C₂³×C₅₃	1	4	yes	—
1095	#126	C₂³×C₅₃	1	4	yes	—
1096	#126	C₂³×C₅₃	1	8	yes	—
1097	#126	C₂³×C₅₃	1	4	yes	—
1098	#126	C₂³×C₅₃	1	8	yes	—
1099	#126	C₂³×C₅₃	1	8	yes	—
1100	#126	C₂³×C₅₃	1	8	yes	—
1101	#126	C₂³×C₅₃	1	8	yes	—
1102	#126	C₂³×C₅₃	1	8	yes	—
1103	#126	C₂³×C₅₃	1	8	yes	—
1104	#126	C₂³×C₅₃	1	8	yes	—
1105	#126	C₂³×C₅₃	1	8	yes	—
1106	#126	C₂³×C₅₃	1	8	yes	—
1107	#125	C₂³×C₅₃	1	2	yes	—
1108	#125	C₂³×C₅₃	1	2	yes	—
1109	#125	C₂³×C₅₃	1	4	yes	—
1110	#125	C₂³×C₅₃	1	8	yes	—
1111	#125	C₂³×C₅₃	1	4	yes	—
1112	#125	C₂³×C₅₃	1	8	yes	—
1113	#125	C₂³×C₅₃	1	2	yes	—
1114	#125	C₂³×C₅₃	1	4	yes	—
1115	#125	C₂³×C₅₃	1	4	yes	—
1116	#125	C₂³×C₅₃	1	8	yes	—
1117	#125	C₂³×C₅₃	1	8	yes	—
1118	#125	C₂³×C₅₃	1	4	yes	—
1119	#125	C₂³×C₅₃	1	4	yes	—
1120	#125	C₂³×C₅₃	1	2	yes	—
1121	#125	C₂³×C₅₃	1	4	yes	—
1122	#125	C₂³×C₅₃	1	8	yes	—
1123	#125	C₂³×C₅₃	1	8	yes	—
1124	#125	C₂³×C₅₃	1	8	yes	—
1125	#124	C₂³×C₅₃	1	2	yes	—
1126	#124	C₂³×C₅₃	1	2	yes	—
1127	#124	C₂³×C₅₃	1	2	yes	—
1128	#124	C₂³×C₅₃	1	4	yes	—
1129	#124	C₂³×C₅₃	1	4	yes	—
1130	#124	C₂³×C₅₃	1	4	yes	—
1131	#124	C₂³×C₅₃	1	4	yes	—
1132	#124	C₂³×C₅₃	1	4	yes	—
1133	#124	C₂³×C₅₃	1	8	yes	—
1134	#124	C₂³×C₅₃	1	8	yes	—
1135	#124	C₂³×C₅₃	1	4	yes	—
1136	#124	C₂³×C₅₃	1	4	yes	—
1137	#124	C₂³×C₅₃	1	2	yes	—
1138	#124	C₂³×C₅₃	1	4	yes	—
1139	#124	C₂³×C₅₃	1	2	yes	—
1140	#124	C₂³×C₅₃	1	8	yes	—
1141	#124	C₂³×C₅₃	1	8	yes	—
1142	#124	C₂³×C₅₃	1	8	yes	—
1143	#123	C₂³×C₅₃	1	4	yes	—
1144	#123	C₂³×C₅₃	1	4	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	#123	C₂³×C₅₃	1	8	yes	—
1150	#123	C₂³×C₅₃	1	4	yes	—
1151	#123	C₂³×C₅₃	1	4	yes	—
1152	#123	C₂³×C₅₃	1	4	yes	—
1153	#123	C₂³×C₅₃	1	8	yes	—
1154	#123	C₂³×C₅₃	1	8	yes	—
1155	#123	C₂³×C₅₃	1	4	yes	—
1156	#123	C₂³×C₅₃	1	8	yes	—
1157	#123	C₂³×C₅₃	1	4	yes	—
1158	#123	C₂³×C₅₃	1	8	yes	—
1159	#123	C₂³×C₅₃	1	8	yes	—
1160	#123	C₂³×C₅₃	1	8	yes	—
1161	#123	C₂³×C₅₃	1	8	yes	—
1162	#123	C₂³×C₅₃	1	8	yes	—
1163	#123	C₂³×C₅₃	1	8	yes	—
1164	#123	C₂³×C₅₃	1	8	yes	—
1165	#123	C₂³×C₅₃	1	8	yes	—
1166	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
1167	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
1168	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
1169	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
1170	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
1171	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
1172	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
1173	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
1174	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
1175	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
1176	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
1177	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
1178	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
1179	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
1180	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
1181	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
1182	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
1183	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
1184	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
1185	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
1186	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
1187	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
1188	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
1189	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
1190	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
1191	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
1192	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
1193	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
1194	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
1195	#121	C₂³×C₅₃	1	4	yes	—
1196	#121	C₂³×C₅₃	1	4	yes	—
1197	#121	C₂³×C₅₃	1	2	yes	—
1198	#121	C₂³×C₅₃	1	2	yes	—
1199	#121	C₂³×C₅₃	1	4	yes	—
1200	#121	C₂³×C₅₃	1	4	yes	—
1201	#121	C₂³×C₅₃	1	4	yes	—
1202	#121	C₂³×C₅₃	1	2	yes	—
1203	#121	C₂³×C₅₃	1	2	yes	—
1204	#121	C₂³×C₅₃	1	4	yes	—
1205	#121	C₂³×C₅₃	1	2	yes	—
1206	#121	C₂³×C₅₃	1	2	yes	—
1207	#121	C₂³×C₅₃	1	2	yes	—
1208	#121	C₂³×C₅₃	1	4	yes	—
1209	#121	C₂³×C₅₃	1	8	yes	—
1210	#121	C₂³×C₅₃	1	8	yes	—
1211	#121	C₂³×C₅₃	1	8	yes	—
1212	#121	C₂³×C₅₃	1	8	yes	—
1213	#121	C₂³×C₅₃	1	4	yes	—
1214	#121	C₂³×C₅₃	1	4	yes	—
1215	#121	C₂³×C₅₃	1	2	yes	—
1216	#121	C₂³×C₅₃	1	4	yes	—
1217	#121	C₂³×C₅₃	1	4	yes	—
1218	#121	C₂³×C₅₃	1	2	yes	—
1219	#121	C₂³×C₅₃	1	4	yes	—
1220	#121	C₂³×C₅₃	1	2	yes	—
1221	#121	C₂³×C₅₃	1	4	yes	—
1222	#121	C₂³×C₅₃	1	4	yes	—
1223	#121	C₂³×C₅₃	1	4	yes	—
1224	#121	C₂³×C₅₃	1	8	yes	—
1225	#121	C₂³×C₅₃	1	2	yes	—
1226	#121	C₂³×C₅₃	1	8	yes	—
1227	#121	C₂³×C₅₃	1	4	yes	—
1228	#121	C₂³×C₅₃	1	4	yes	—
1229	#121	C₂³×C₅₃	1	8	yes	—
1230	#121	C₂³×C₅₃	1	8	yes	—
1231	#121	C₂³×C₅₃	1	8	yes	—
1232	#121	C₂³×C₅₃	1	8	yes	—
1233	#121	C₂³×C₅₃	1	8	yes	—
1234	#121	C₂³×C₅₃	1	8	yes	—
1235	#121	C₂³×C₅₃	1	8	yes	—
1236	#121	C₂³×C₅₃	1	8	yes	—
1237	#120	C₂³×C₅₃	1	4	yes	—
1238	#120	C₂³×C₅₃	1	4	yes	—
1239	#120	C₂³×C₅₃	1	8	yes	—
1240	#120	C₂³×C₅₃	1	8	yes	—
1241	#120	C₂³×C₅₃	1	8	yes	—
1242	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1243	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
1244	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
1245	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
1246	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
1247	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
1248	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1249	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1250	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1251	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1252	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
1253	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
1254	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
1255	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
1256	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1257	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
1258	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
1259	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
1260	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
1261	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
1262	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
1263	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
1264	C₄×Q₈	C₂³×C₅₃	1	8	yes	—
1265	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
1266	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
1267	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
1268	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1269	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1270	C₄×D₄	C₂³×C₅₃	1	2	yes	—
1271	C₄×D₄	C₂³×C₅₃	1	2	yes	—
1272	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1273	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1274	C₄×D₄	C₂³×C₅₃	1	2	yes	—
1275	C₄×D₄	C₂³×C₅₃	1	2	yes	—
1276	C₄×D₄	C₂³×C₅₃	1	2	yes	—
1277	C₄×D₄	C₂³×C₅₃	1	2	yes	—
1278	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1279	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1280	C₄×D₄	C₂³×C₅₃	1	2	yes	—
1281	C₄×D₄	C₂³×C₅₃	1	2	yes	—
1282	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1283	C₄×D₄	C₂³×C₅₃	1	2	yes	—
1284	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1285	C₄×D₄	C₂³×C₅₃	1	2	yes	—
1286	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1287	C₄×D₄	C₂³×C₅₃	1	2	yes	—
1288	C₄×D₄	C₂³×C₅₃	1	2	yes	—
1289	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1290	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1291	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1292	C₄×D₄	C₂³×C₅₃	1	2	yes	—
1293	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1294	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1295	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1296	C₄×D₄	C₂³×C₅₃	1	2	yes	—
1297	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1298	C₄×D₄	C₂³×C₅₃	1	2	yes	—
1299	C₄×D₄	C₂³×C₅₃	1	2	yes	—
1300	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1301	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1302	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1303	C₄×D₄	C₂³×C₅₃	1	2	yes	—
1304	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1305	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1306	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1307	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1308	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1309	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1310	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1311	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1312	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1313	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1314	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1315	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1316	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1317	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1318	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1319	C₄×D₄	C₂³×C₅₃	1	4	yes	—
1320	#117	C₂³×C₅₃	1	2	yes	—
1321	#117	C₂³×C₅₃	1	2	yes	—
1322	#117	C₂³×C₅₃	1	4	yes	—
1323	#117	C₂³×C₅₃	1	4	yes	—
1324	#117	C₂³×C₅₃	1	8	yes	—
1325	#117	C₂³×C₅₃	1	8	yes	—
1326	#117	C₂³×C₅₃	1	1	yes	characteristic
1327	#117	C₂³×C₅₃	1	1	yes	characteristic
1328	#117	C₂³×C₅₃	1	2	yes	—
1329	#117	C₂³×C₅₃	1	2	yes	—
1330	#117	C₂³×C₅₃	1	2	yes	—
1331	#117	C₂³×C₅₃	1	4	yes	—
1332	#117	C₂³×C₅₃	1	1	yes	characteristic
1333	#117	C₂³×C₅₃	1	8	yes	—
1334	#117	C₂³×C₅₃	1	4	yes	—
1335	#117	C₂³×C₅₃	1	4	yes	—
1336	#117	C₂³×C₅₃	1	4	yes	—
1337	#117	C₂³×C₅₃	1	8	yes	—
1338	#117	C₂³×C₅₃	1	2	yes	—
1339	#117	C₂³×C₅₃	1	2	yes	—
1340	#117	C₂³×C₅₃	1	8	yes	—
1341	#117	C₂³×C₅₃	1	4	yes	—
1342	#117	C₂³×C₅₃	1	4	yes	—
1343	#117	C₂³×C₅₃	1	4	yes	—
1344	#117	C₂³×C₅₃	1	8	yes	—
1345	#117	C₂³×C₅₃	1	8	yes	—
1346	#117	C₂³×C₅₃	1	4	yes	—
1347	#117	C₂³×C₅₃	1	4	yes	—
1348	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
1349	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
1350	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
1351	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
1352	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
1353	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
1354	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
1355	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
1356	C₂×C₄⋊C₄	C₂³×C₅₃	1	8	yes	—
1357	C₂×C₄⋊C₄	C₂³×C₅₃	1	8	yes	—
1358	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
1359	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
1360	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	—
1361	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
1362	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
1363	C₂×C₄²	C₂³×C₅₃	1	8	yes	—
1364	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
1365	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
1366	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
1367	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
1368	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1369	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
1370	C₂⁴	C₂⁴×C₅₃	1	4	yes	—
1371	#41	—	4	4	no	—
1372	#41	—	4	8	no	—
1373	#41	—	4	4	no	—
1374	#41	—	4	4	no	—
1375	#41	—	4	4	no	—
1376	#41	—	4	8	no	—
1377	#41	—	4	8	no	—
1378	#41	—	4	2	no	—
1379	#41	—	4	2	no	—
1380	#41	—	4	8	no	—
1381	#41	—	4	8	no	—
1382	#41	—	4	4	no	—
1383	#41	—	4	2	no	—
1384	C₂×Q₈	—	4	4	no	—
1385	C₂×Q₈	—	4	4	no	—
1386	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1387	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
1388	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1389	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
1390	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
1391	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1392	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
1393	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
1394	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
1395	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
1396	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
1397	C₂×D₄	—	4	4	no	—
1398	C₂×D₄	—	4	4	no	—
1399	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1400	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1401	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1402	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1403	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1404	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1405	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1406	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1407	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1408	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1409	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1410	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1411	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1412	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1413	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1414	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1415	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1416	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1417	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1418	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1419	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1420	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1421	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1422	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1423	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1424	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1425	C₂²×C₄	—	4	8	no	—
1426	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1427	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1428	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1429	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1430	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1431	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1432	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1433	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1434	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1435	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1436	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1437	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1438	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1439	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1440	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
1441	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
1442	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1443	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1444	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1445	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1446	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1447	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1448	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1449	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
1450	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
1451	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1452	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1453	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1454	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1455	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1456	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1457	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1458	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1459	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1460	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1461	C₄⋊C₄	C₂⁴×C₅₃	1	2	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	2	yes	—
1466	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1467	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1468	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1469	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1470	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1471	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1472	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1473	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1474	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1475	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1476	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1477	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1478	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1479	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1480	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1481	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1482	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1483	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1484	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1485	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1486	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1487	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1488	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1489	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1490	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1491	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1492	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1493	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1494	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1495	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1496	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1497	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1498	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1499	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1500	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1501	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1502	C₂²⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1503	C₂²⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1504	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1505	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1506	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1507	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1508	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1509	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1510	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1511	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1512	C₂²⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1513	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1514	C₂²⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1515	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1516	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1517	C₂²⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1518	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1519	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1520	C₂²⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1521	C₂²⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1522	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1523	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1524	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1525	C₂²⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1526	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1527	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1528	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1529	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1530	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1531	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1532	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1533	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1534	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1535	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1536	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1537	C₂²⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1538	C₄²	C₂⁴×C₅₃	1	4	yes	—
1539	C₄²	C₂⁴×C₅₃	1	4	yes	—
1540	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1541	C₄²	C₂⁴×C₅₃	1	2	yes	—
1542	C₄²	C₂⁴×C₅₃	1	2	yes	—
1543	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1544	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1545	C₄²	C₂⁴×C₅₃	1	2	yes	—
1546	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1547	C₄²	C₂⁴×C₅₃	1	2	yes	—
1548	C₄²	C₂⁴×C₅₃	1	4	yes	—
1549	C₄²	C₂⁴×C₅₃	1	8	yes	—
1550	C₄²	C₂⁴×C₅₃	1	8	yes	—
1551	C₄²	C₂⁴×C₅₃	1	2	yes	—
1552	C₄²	C₂⁴×C₅₃	1	2	yes	—
1553	C₄²	C₂⁴×C₅₃	1	2	yes	—
1554	C₄²	C₂⁴×C₅₃	1	2	yes	—
1555	C₄²	C₂⁴×C₅₃	1	4	yes	—
1556	C₄²	C₂⁴×C₅₃	1	2	yes	—
1557	C₄²	C₂⁴×C₅₃	1	4	yes	—
1558	C₄²	C₂⁴×C₅₃	1	8	yes	—
1559	C₄²	C₂⁴×C₅₃	1	8	yes	—
1560	C₂³	—	4	4	no	—
1561	C₂³	—	4	4	no	—
1562	C₂³	—	4	4	no	—
1563	C₂³	C₂⁵×C₅₃	1	2	yes	—
1564	C₂³	C₂⁵×C₅₃	1	2	yes	—
1565	C₂³	C₂⁵×C₅₃	1	4	yes	—
1566	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
1567	C₂³	C₂⁵×C₅₃	1	2	yes	—
1568	C₂³	C₂⁵×C₅₃	1	4	yes	—
1569	Q₈	—	2	2	no	—
1570	Q₈	—	2	4	no	—
1571	Q₈	—	2	8	no	—
1572	Q₈	—	2	2	no	—
1573	Q₈	—	2	4	no	—
1574	Q₈	—	2	2	no	—
1575	Q₈	—	4	4	no	—
1576	Q₈	—	4	4	no	—
1577	Q₈	—	4	2	no	—
1578	Q₈	—	4	2	no	—
1579	Q₈	—	4	4	no	—
1580	D₄	—	2	2	no	—
1581	D₄	—	2	2	no	—
1582	D₄	—	2	4	no	—
1583	D₄	—	2	4	no	—
1584	D₄	—	2	2	no	—
1585	D₄	—	2	4	no	—
1586	D₄	—	2	4	no	—
1587	D₄	—	4	4	no	—
1588	D₄	—	4	4	no	—
1589	D₄	—	4	4	no	—
1590	D₄	—	4	4	no	—
1591	D₄	—	4	2	no	—
1592	D₄	—	4	4	no	—
1593	D₄	—	4	2	no	—
1594	D₄	—	4	4	no	—
1595	D₄	—	4	4	no	—
1596	D₄	—	4	2	no	—
1597	D₄	—	4	4	no	—
1598	D₄	—	4	4	no	—
1599	D₄	—	4	8	no	—
1600	D₄	—	4	2	no	—
1601	D₄	—	4	4	no	—
1602	D₄	—	4	8	no	—
1603	D₄	—	4	8	no	—
1604	D₄	—	4	8	no	—
1605	D₄	—	4	2	no	—
1606	C₂×C₄	—	2	4	no	—
1607	C₂×C₄	—	2	4	no	—
1608	C₂×C₄	—	2	8	no	—
1609	C₂×C₄	—	2	4	no	—
1610	C₂×C₄	—	2	4	no	—
1611	C₂×C₄	—	2	2	no	—
1612	C₂×C₄	—	2	4	no	—
1613	C₂×C₄	—	2	4	no	—
1614	C₂×C₄	—	2	2	no	—
1615	C₂×C₄	—	2	2	no	—
1616	C₂×C₄	—	2	8	no	—
1617	C₂×C₄	—	4	4	no	—
1618	C₂×C₄	—	4	4	no	—
1619	C₂×C₄	—	4	4	no	—
1620	C₂×C₄	—	4	4	no	—
1621	C₂×C₄	—	4	4	no	—
1622	C₂×C₄	—	4	4	no	—
1623	C₂×C₄	—	4	4	no	—
1624	C₂×C₄	—	4	4	no	—
1625	C₂×C₄	—	4	8	no	—
1626	C₂×C₄	—	4	8	no	—
1627	C₂×C₄	—	4	8	no	—
1628	C₂×C₄	—	4	2	no	—
1629	C₂×C₄	—	4	8	no	—
1630	C₂×C₄	—	4	2	no	—
1631	C₂×C₄	—	4	2	no	—
1632	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1633	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1634	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1635	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1636	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1637	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1638	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1639	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1640	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1641	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1642	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1643	C₂×C₄	C₂⁵×C₅₃	1	8	yes	—
1644	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1645	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1646	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1647	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1648	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1649	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1650	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1651	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1652	C₂²	—	2	1	no	—
1653	C₂²	—	2	2	no	—
1654	C₂²	—	2	2	no	—
1655	C₂²	—	2	2	no	—
1656	C₂²	—	2	4	no	—
1657	C₂²	—	2	1	no	—
1658	C₂²	—	2	1	no	—
1659	C₂²	—	2	2	no	—
1660	C₂²	—	2	4	no	—
1661	C₂²	—	2	2	no	—
1662	C₂²	—	2	2	no	—
1663	C₂²	—	2	2	no	—
1664	C₂²	—	2	4	no	—
1665	C₂²	—	2	4	no	—
1666	C₂²	—	2	4	no	—
1667	C₂²	—	2	4	no	—
1668	C₂²	—	2	2	no	—
1669	C₂²	—	2	2	no	—
1670	C₂²	—	8	8	no	—
1671	C₂²	C₂⁶×C₅₃	1	1	yes	characteristic
1672	C₄	—	2	2	no	—
1673	C₄	—	2	2	no	—
1674	C₄	—	2	2	no	—
1675	C₄	—	2	2	no	—
1676	C₄	—	2	4	no	—
1677	C₄	—	2	1	no	—
1678	C₄	—	2	4	no	—
1679	C₄	—	2	1	no	—
1680	C₄	—	2	1	no	—
1681	C₄	—	2	2	no	—
1682	C₄	—	2	2	no	—
1683	C₄	—	2	2	no	—
1684	C₄	—	2	4	no	—
1685	C₄	—	2	2	no	—
1686	C₄	—	2	8	no	—
1687	C₄	—	2	4	no	—
1688	C₄	—	2	2	no	—
1689	C₄	C₅₃×#585	1	2	yes	—
1690	C₄	C₅₃×#585	1	2	yes	—
1691	C₄	C₅₃×#585	1	2	yes	—
1692	C₂	—	4	2	no	—
1693	C₂	—	4	2	no	—
1694	C₂	—	4	4	no	—
1695	C₂	—	4	1	no	—
1696	C₂	—	4	2	no	—
1697	C₂	—	4	4	no	—
1698	C₂	C₂×C₅₃×#585	1	1	yes	characteristic
1699	C₂	C₂×C₅₃×#585	1	1	yes	characteristic
1700	C₂	C₂×C₅₃×#585	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3566	C₂	semidirect
2. C₅₃×#3562	C₂	semidirect
3. C₅₃×#3555	C₂	semidirect
4. C₅₃×#3551	C₂	semidirect
5. C₅₃×#3548	C₂	semidirect
6. C₅₃×#3547	C₂	semidirect
7. C₅₃×#3546	C₂	semidirect
8. C₅₃×#3539	C₂	semidirect
9. C₅₃×#3524	C₂	semidirect
10. C₅₃×#3517	C₂	semidirect
11. C₅₃×#3515	C₂	semidirect
12. C₅₃×#3515	C₂	semidirect
13. C₅₃×#3512	C₂	semidirect
14. C₅₃×#3511	C₂	semidirect
15. C₅₃×#3511	C₂	semidirect
16. C₅₃×#3509	C₂	semidirect
17. C₅₃×#3507	C₂	semidirect
18. C₅₃×#3506	C₂	semidirect
19. C₅₃×#3506	C₂	semidirect
20. C₅₃×#3493	C₂	semidirect
21. C₅₃×#3483	C₂	semidirect
22. C₅₃×#3482	C₂	semidirect
23. C₅₃×#3481	C₂	semidirect
24. C₅₃×#3480	C₂	semidirect
25. C₅₃×#3475	C₂	semidirect
26. C₅₃×#3475	C₂	semidirect
27. C₅₃×#563	C₂²	semidirect
28. C₅₃×#562	C₂²	semidirect
29. C₅₃×#562	C₂²	semidirect
31. C₅₃×#560	C₂²	semidirect
34. C₅₃×#559	C₂²	semidirect
35. C₅₃×#559	C₂²	semidirect
36. Q₈²×C₅₃	C₂²	semidirect
37. C₅₃×#557	C₂²	semidirect
38. C₅₃×#557	C₂²	semidirect
39. C₅₃×#557	C₂²	semidirect
40. C₅₃×#557	C₂²	semidirect
44. C₅₃×#556	C₂²	semidirect
45. C₅₃×#556	C₂²	semidirect
46. C₅₃×#556	C₂²	semidirect
47. C₅₃×#556	C₂²	semidirect
48. C₅₃×#556	C₂²	semidirect
49. C₅₃×#556	C₂²	semidirect
52. C₅₃×#555	C₂²	semidirect
53. C₅₃×#555	C₂²	semidirect
54. C₅₃×#555	C₂²	semidirect
55. C₅₃×#555	C₂²	semidirect
56. C₅₃×#555	C₂²	semidirect
57. C₅₃×#555	C₂²	semidirect
60. C₅₃×#554	C₂²	semidirect
61. C₅₃×#554	C₂²	semidirect
62. C₅₃×#554	C₂²	semidirect
63. C₅₃×#554	C₂²	semidirect
68. C₅₃×#553	C₂²	semidirect
69. C₅₃×#553	C₂²	semidirect
70. C₅₃×#553	C₂²	semidirect
71. C₅₃×#553	C₂²	semidirect
72. C₅₃×#553	C₂²	semidirect
73. C₅₃×#553	C₂²	semidirect
74. C₅₃×#553	C₂²	semidirect
75. C₅₃×#553	C₂²	semidirect
76. C₅₃×#553	C₂²	semidirect
77. C₅₃×#553	C₂²	semidirect
78. C₅₃×#552	C₂²	semidirect
79. C₅₃×#552	C₂²	semidirect
80. C₅₃×#552	C₂²	semidirect
81. C₅₃×#552	C₂²	semidirect
82. C₅₃×#552	C₂²	semidirect
83. C₅₃×#552	C₂²	semidirect
84. C₅₃×#552	C₂²	semidirect
85. C₅₃×#552	C₂²	semidirect
86. C₅₃×#552	C₂²	semidirect
87. C₅₃×#552	C₂²	semidirect
88. C₅₃×#552	C₂²	semidirect
89. C₅₃×#552	C₂²	semidirect
91. C₅₃×#551	C₂²	semidirect
92. C₅₃×#551	C₂²	semidirect
97. C₅₃×#550	C₂²	semidirect
98. C₅₃×#550	C₂²	semidirect
99. C₅₃×#550	C₂²	semidirect
100. C₅₃×#550	C₂²	semidirect
101. D₄×Q₈×C₅₃	C₂²	semidirect
103. C₅₃×#548	C₂²	semidirect
104. C₅₃×#548	C₂²	semidirect
105. C₅₃×#548	C₂²	semidirect
108. C₅₃×#547	C₂²	semidirect
109. C₅₃×#547	C₂²	semidirect
110. C₅₃×#547	C₂²	semidirect
111. C₅₃×#547	C₂²	semidirect
112. C₅₃×#547	C₂²	semidirect
113. C₅₃×#547	C₂²	semidirect
119. C₅₃×#544	C₂²	semidirect
121. C₅₃×#542	C₂²	semidirect
122. C₅₃×#542	C₂²	semidirect
123. C₅₃×#542	C₂²	semidirect
124. C₅₃×#541	C₂²	semidirect
125. C₅₃×#541	C₂²	semidirect
126. C₅₃×#541	C₂²	semidirect
127. C₅₃×#541	C₂²	semidirect
128. C₅₃×#540	C₂²	semidirect
129. C₅₃×#540	C₂²	semidirect
130. C₅₃×#540	C₂²	semidirect
131. C₅₃×#540	C₂²	semidirect
132. C₅₃×#540	C₂²	semidirect
133. C₅₃×#539	C₂²	semidirect
134. C₅₃×#539	C₂²	semidirect
135. C₅₃×#539	C₂²	semidirect
137. C₅₃×#538	C₂²	semidirect
138. C₅₃×#538	C₂²	semidirect
139. C₅₃×#538	C₂²	semidirect
142. C₅₃×#537	C₂²	semidirect
143. C₅₃×#537	C₂²	semidirect
144. C₅₃×#537	C₂²	semidirect
146. C₅₃×#536	C₂²	semidirect
149. C₅₃×#533	C₂²	semidirect
150. C₅₃×#533	C₂²	semidirect
151. C₅₃×#533	C₂²	semidirect
152. C₅₃×#533	C₂²	semidirect
153. C₅₃×#533	C₂²	semidirect
154. C₅₃×#533	C₂²	semidirect
158. C₅₃×#532	C₂²	semidirect
159. C₅₃×#532	C₂²	semidirect
160. C₅₃×#532	C₂²	semidirect
161. C₅₃×#532	C₂²	semidirect
162. C₅₃×#532	C₂²	semidirect
163. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
169. C₅₃×#529	C₂²	semidirect
170. C₅₃×#529	C₂²	semidirect
171. C₅₃×#529	C₂²	semidirect
172. C₅₃×#529	C₂²	semidirect
173. C₅₃×#529	C₂²	semidirect
174. C₅₃×#529	C₂²	semidirect
175. C₅₃×#529	C₂²	semidirect
176. C₂×#125×C₅₃	C₂²	semidirect
178. C₅₃×#525	C₂²	semidirect
179. C₅₃×#525	C₂²	semidirect
180. C₅₃×#525	C₂²	semidirect
181. C₅₃×#520	C₂²	semidirect
182. C₅₃×#520	C₂²	semidirect
183. C₅₃×#520	C₂²	semidirect
184. C₅₃×#520	C₂²	semidirect
185. C₅₃×#520	C₂²	semidirect
186. C₅₃×#519	C₂²	semidirect
189. C₄×#41×C₅₃	C₂²	semidirect
190. C₄×#41×C₅₃	C₂²	semidirect
191. C₄×#41×C₅₃	C₂²	semidirect
192. C₄×#41×C₅₃	C₂²	semidirect
193. C₄×#41×C₅₃	C₂²	semidirect
194. C₄×#41×C₅₃	C₂²	semidirect
195. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
198. C₂×#117×C₅₃	C₂²	semidirect
801. #63031	C₅₃	direct (N × H)
842. #3566	C₂×C₅₃	semidirect
843. #3562	C₂×C₅₃	semidirect
844. #3555	C₂×C₅₃	semidirect
845. #3551	C₂×C₅₃	semidirect
846. #3548	C₂×C₅₃	semidirect
847. #3547	C₂×C₅₃	semidirect
848. #3546	C₂×C₅₃	semidirect
849. #3539	C₂×C₅₃	semidirect
850. #3524	C₂×C₅₃	semidirect
851. #3517	C₂×C₅₃	semidirect
852. #3515	C₂×C₅₃	semidirect
853. #3515	C₂×C₅₃	semidirect
854. #3512	C₂×C₅₃	semidirect
855. #3511	C₂×C₅₃	semidirect
856. #3511	C₂×C₅₃	semidirect
857. #3509	C₂×C₅₃	semidirect
858. #3507	C₂×C₅₃	semidirect
859. #3506	C₂×C₅₃	semidirect
860. #3506	C₂×C₅₃	semidirect
861. #3493	C₂×C₅₃	semidirect
862. #3483	C₂×C₅₃	semidirect
863. #3482	C₂×C₅₃	semidirect
864. #3481	C₂×C₅₃	semidirect
865. #3480	C₂×C₅₃	semidirect
866. #3475	C₂×C₅₃	semidirect
867. #3475	C₂×C₅₃	semidirect
877. #563	C₂²×C₅₃	semidirect
878. #562	C₂²×C₅₃	semidirect
879. #562	C₂²×C₅₃	semidirect
881. #560	C₂²×C₅₃	semidirect
884. #559	C₂²×C₅₃	semidirect
885. #559	C₂²×C₅₃	semidirect
886. Q₈²	C₂²×C₅₃	semidirect
887. #557	C₂²×C₅₃	semidirect
888. #557	C₂²×C₅₃	semidirect
889. #557	C₂²×C₅₃	semidirect
890. #557	C₂²×C₅₃	semidirect
894. #556	C₂²×C₅₃	semidirect
895. #556	C₂²×C₅₃	semidirect
896. #556	C₂²×C₅₃	semidirect
897. #556	C₂²×C₅₃	semidirect
898. #556	C₂²×C₅₃	semidirect
899. #556	C₂²×C₅₃	semidirect
902. #555	C₂²×C₅₃	semidirect
903. #555	C₂²×C₅₃	semidirect
904. #555	C₂²×C₅₃	semidirect
905. #555	C₂²×C₅₃	semidirect
906. #555	C₂²×C₅₃	semidirect
907. #555	C₂²×C₅₃	semidirect
910. #554	C₂²×C₅₃	semidirect
911. #554	C₂²×C₅₃	semidirect
912. #554	C₂²×C₅₃	semidirect
913. #554	C₂²×C₅₃	semidirect
918. #553	C₂²×C₅₃	semidirect
919. #553	C₂²×C₅₃	semidirect
920. #553	C₂²×C₅₃	semidirect
921. #553	C₂²×C₅₃	semidirect
922. #553	C₂²×C₅₃	semidirect
923. #553	C₂²×C₅₃	semidirect
924. #553	C₂²×C₅₃	semidirect
925. #553	C₂²×C₅₃	semidirect
926. #553	C₂²×C₅₃	semidirect
927. #553	C₂²×C₅₃	semidirect
928. #552	C₂²×C₅₃	semidirect
929. #552	C₂²×C₅₃	semidirect
930. #552	C₂²×C₅₃	semidirect
931. #552	C₂²×C₅₃	semidirect
932. #552	C₂²×C₅₃	semidirect
933. #552	C₂²×C₅₃	semidirect
934. #552	C₂²×C₅₃	semidirect
935. #552	C₂²×C₅₃	semidirect
936. #552	C₂²×C₅₃	semidirect
937. #552	C₂²×C₅₃	semidirect
938. #552	C₂²×C₅₃	semidirect
939. #552	C₂²×C₅₃	semidirect
941. #551	C₂²×C₅₃	semidirect
942. #551	C₂²×C₅₃	semidirect
947. #550	C₂²×C₅₃	semidirect
948. #550	C₂²×C₅₃	semidirect
949. #550	C₂²×C₅₃	semidirect
950. #550	C₂²×C₅₃	semidirect
951. D₄×Q₈	C₂²×C₅₃	semidirect
953. #548	C₂²×C₅₃	semidirect
954. #548	C₂²×C₅₃	semidirect
955. #548	C₂²×C₅₃	semidirect
958. #547	C₂²×C₅₃	semidirect
959. #547	C₂²×C₅₃	semidirect
960. #547	C₂²×C₅₃	semidirect
961. #547	C₂²×C₅₃	semidirect
962. #547	C₂²×C₅₃	semidirect
963. #547	C₂²×C₅₃	semidirect
969. #544	C₂²×C₅₃	semidirect
971. #542	C₂²×C₅₃	semidirect
972. #542	C₂²×C₅₃	semidirect
973. #542	C₂²×C₅₃	semidirect
974. #541	C₂²×C₅₃	semidirect
975. #541	C₂²×C₅₃	semidirect
976. #541	C₂²×C₅₃	semidirect
977. #541	C₂²×C₅₃	semidirect
978. #540	C₂²×C₅₃	semidirect
979. #540	C₂²×C₅₃	semidirect
980. #540	C₂²×C₅₃	semidirect
981. #540	C₂²×C₅₃	semidirect
982. #540	C₂²×C₅₃	semidirect
983. #539	C₂²×C₅₃	semidirect
984. #539	C₂²×C₅₃	semidirect
985. #539	C₂²×C₅₃	semidirect
987. #538	C₂²×C₅₃	semidirect
988. #538	C₂²×C₅₃	semidirect
989. #538	C₂²×C₅₃	semidirect
992. #537	C₂²×C₅₃	semidirect
993. #537	C₂²×C₅₃	semidirect
994. #537	C₂²×C₅₃	semidirect
996. #536	C₂²×C₅₃	semidirect
999. #533	C₂²×C₅₃	semidirect
1000. #533	C₂²×C₅₃	semidirect
1001. #533	C₂²×C₅₃	semidirect
1002. #533	C₂²×C₅₃	semidirect
1003. #533	C₂²×C₅₃	semidirect
1004. #533	C₂²×C₅₃	semidirect
1008. #532	C₂²×C₅₃	semidirect
1009. #532	C₂²×C₅₃	semidirect
1010. #532	C₂²×C₅₃	semidirect
1011. #532	C₂²×C₅₃	semidirect
1012. #532	C₂²×C₅₃	semidirect
1013. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
1019. #529	C₂²×C₅₃	semidirect
1020. #529	C₂²×C₅₃	semidirect
1021. #529	C₂²×C₅₃	semidirect
1022. #529	C₂²×C₅₃	semidirect
1023. #529	C₂²×C₅₃	semidirect
1024. #529	C₂²×C₅₃	semidirect
1025. #529	C₂²×C₅₃	semidirect
1026. C₂×#125	C₂²×C₅₃	semidirect
1028. #525	C₂²×C₅₃	semidirect
1029. #525	C₂²×C₅₃	semidirect
1030. #525	C₂²×C₅₃	semidirect
1031. #520	C₂²×C₅₃	semidirect
1032. #520	C₂²×C₅₃	semidirect
1033. #520	C₂²×C₅₃	semidirect
1034. #520	C₂²×C₅₃	semidirect
1035. #520	C₂²×C₅₃	semidirect
1036. #519	C₂²×C₅₃	semidirect
1039. C₄×#41	C₂²×C₅₃	semidirect
1040. C₄×#41	C₂²×C₅₃	semidirect
1041. C₄×#41	C₂²×C₅₃	semidirect
1042. C₄×#41	C₂²×C₅₃	semidirect
1043. C₄×#41	C₂²×C₅₃	semidirect
1044. C₄×#41	C₂²×C₅₃	semidirect
1045. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
1048. C₂×#117	C₂²×C₅₃	semidirect
1049. C₅₃	#63031	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×#3566	2
C₅₃×#3562	2
C₅₃×#3555	2
C₅₃×#3551	2
C₅₃×#3548	2
C₅₃×#3547	2
C₅₃×#3546	2
C₅₃×#3539	2
C₅₃×#3524	2
C₅₃×#3517	2
C₅₃×#3515	2
C₅₃×#3512	2
C₅₃×#3511	2
C₅₃×#3509	2
C₅₃×#3507	2
C₅₃×#3506	2
C₅₃×#3493	2
C₅₃×#3483	2
C₅₃×#3482	2
C₅₃×#3481	2
C₅₃×#3480	2
C₅₃×#3475	2
#63031	53

Subgroups — C53×#63031 #27270543

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#63031 #27270543