Subgroups — #27549328

Order 13568.

2068 conjugacy classes of subgroups.

The subgroup lattice has 1388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20277901	C₂	1	1	yes	maximal, characteristic, complemented
2	#20277896	C₂	1	1	yes	maximal, characteristic, complemented
3	#20277881	C₂	1	1	yes	maximal, characteristic, complemented
4	#20277881	C₂	1	1	yes	maximal, characteristic, complemented
5	#20277821	C₂	1	1	yes	maximal, characteristic, complemented
6	#20277800	C₂	1	1	yes	maximal, characteristic, complemented
7	#20277800	C₂	1	1	yes	maximal, characteristic, complemented
8	#20277746	C₂	1	1	yes	maximal, characteristic, complemented
9	#20277724	C₂	1	1	yes	maximal, characteristic, complemented
10	#20277680	C₂	1	1	yes	maximal, characteristic, complemented
11	#20277655	C₂	1	1	yes	maximal, characteristic
12	#20277655	C₂	1	1	yes	maximal, characteristic
13	#20277644	C₂	1	1	yes	maximal, characteristic
14	#20277592	C₂	1	1	yes	maximal, characteristic, complemented
15	#20277584	C₂	1	1	yes	maximal, characteristic, complemented
16	#20277521	C₂	1	1	yes	maximal, characteristic, complemented
17	#20277521	C₂	1	1	yes	maximal, characteristic, complemented
18	#20277473	C₂	1	1	yes	maximal, characteristic, complemented
19	#20277473	C₂	1	1	yes	maximal, characteristic, complemented
20	#20277450	C₂	1	1	yes	maximal, characteristic, complemented
21	#20277450	C₂	1	1	yes	maximal, characteristic, complemented
22	#20277435	C₂	1	1	yes	maximal, characteristic, complemented
23	#20277399	C₂	1	1	yes	maximal, characteristic, complemented
24	#20277366	C₂	1	1	yes	maximal, characteristic, complemented
25	#20277348	C₂	1	1	yes	maximal, characteristic
26	#20277348	C₂	1	1	yes	maximal, characteristic
27	#20277318	C₂	1	1	yes	maximal, characteristic, complemented
28	C₂²⋊Q₈×Dic₅₃	C₂	1	1	yes	maximal, characteristic, complemented
29	#20277160	C₂	1	1	yes	maximal, characteristic
30	C₂×#16810509	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×C₅₃×#554	C₂	1	1	yes	maximal, characteristic
32	C₂×Q₈×Dic₅₃	C₂²	1	1	yes	characteristic
33	C₂×Q₈×Dic₅₃	C₂²	1	1	yes	characteristic
34	C₂×#13133176	C₂²	1	1	yes	characteristic
35	C₂×#13133176	C₂²	1	1	yes	characteristic
36	C₂²×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
37	C₂²×C₄×Dic₅₃	C₂²	1	1	yes	characteristic
38	#16810530	C₂²	1	1	yes	characteristic
39	#16810530	C₂²	1	1	yes	characteristic
40	#16810530	C₂²	1	1	yes	characteristic
41	#16810530	C₂²	1	1	yes	characteristic
42	#16810530	C₂²	1	1	yes	characteristic
43	#16810530	C₂²	1	1	yes	characteristic
44	#16810530	C₂²	1	1	yes	characteristic
45	#16810530	C₂²	1	1	yes	characteristic
46	#16810530	C₂²	1	1	yes	characteristic
47	#16810530	C₂²	1	1	yes	characteristic
48	#16810522	C₂²	1	1	yes	characteristic
49	#16810522	C₂²	1	1	yes	characteristic
50	#16810522	C₂²	1	1	yes	characteristic
51	#16810522	C₂²	1	1	yes	characteristic
52	#16810522	C₂²	1	1	yes	characteristic
53	#16810522	C₂²	1	1	yes	characteristic
54	#16810522	C₂²	1	1	yes	characteristic
55	#16810522	C₂²	1	1	yes	characteristic
56	#16810522	C₂²	1	1	yes	characteristic
57	#16810522	C₂²	1	1	yes	characteristic
58	#16810516	C₂²	1	1	yes	characteristic
59	#16810516	C₂²	1	1	yes	characteristic
60	#16810516	C₂²	1	1	yes	characteristic
61	#16810516	C₂²	1	1	yes	characteristic
62	#16810516	C₂²	1	1	yes	characteristic
63	#16810516	C₂²	1	1	yes	characteristic
64	#16810516	C₂²	1	1	yes	characteristic
65	#16810516	C₂²	1	1	yes	characteristic
66	#16810516	C₂²	1	1	yes	characteristic
67	#16810516	C₂²	1	1	yes	characteristic
68	#16810516	C₂²	1	1	yes	characteristic
69	#16810516	C₂²	1	1	yes	characteristic
70	#16810509	C₂²	1	1	yes	characteristic
71	#16810509	C₂²	1	1	yes	characteristic
72	#16810509	C₂²	1	1	yes	characteristic
73	#16810509	C₂²	1	1	yes	characteristic
74	#16810509	C₂²	1	1	yes	characteristic
75	#16810509	C₂²	1	1	yes	characteristic
76	#16810509	C₂²	1	1	yes	characteristic
77	#16810509	C₂²	1	1	yes	characteristic
78	#16810509	C₂²	1	1	yes	characteristic
79	#16810509	C₂²	1	1	yes	characteristic
80	#16810509	C₂²	1	1	yes	characteristic
81	#16810509	C₂²	1	1	yes	characteristic
82	#16810509	C₂²	1	1	yes	characteristic
83	#16810509	C₂²	1	1	yes	characteristic
84	#16810509	C₂²	1	1	yes	characteristic
85	#16810509	C₂²	1	1	yes	characteristic
86	#16810509	C₂²	1	1	yes	characteristic
87	#16810509	C₂²	1	1	yes	characteristic
88	#16810509	C₂²	1	1	yes	characteristic
89	#16810509	C₂²	1	1	yes	characteristic
90	#16810509	C₂²	1	1	yes	characteristic
91	#16810509	C₂²	1	1	yes	characteristic
92	#16810509	C₂²	1	1	yes	characteristic
93	#16810509	C₂²	1	1	yes	characteristic
94	#16810509	C₂²	1	1	yes	characteristic
95	#16810509	C₂²	1	1	yes	characteristic
96	#16810509	C₂²	1	1	yes	characteristic
97	#16810509	C₂²	1	1	yes	characteristic
98	#16810509	C₂²	1	1	yes	characteristic
99	#16810509	C₂²	1	1	yes	characteristic
100	#16810509	C₂²	1	1	yes	characteristic
101	#16810509	C₂²	1	1	yes	characteristic
102	#16810509	C₂²	1	1	yes	characteristic
103	#16810509	C₂²	1	1	yes	characteristic
104	#16810509	C₂²	1	1	yes	characteristic
105	#16810509	C₂²	1	1	yes	characteristic
106	#16810509	C₂²	1	1	yes	characteristic
107	#16810509	C₂²	1	1	yes	characteristic
108	#16810509	C₂²	1	1	yes	characteristic
109	#16810509	C₂²	1	1	yes	characteristic
110	#16810509	C₂²	1	1	yes	characteristic
111	#16810509	C₂²	1	1	yes	characteristic
112	#16810509	C₂²	1	1	yes	characteristic
113	#16810509	C₂²	1	1	yes	characteristic
114	#16810503	C₂²	1	1	yes	characteristic
115	#16810503	C₂²	1	1	yes	characteristic
116	#16810503	C₂²	1	1	yes	characteristic
117	#16810503	C₂²	1	1	yes	characteristic
118	#16810498	C₂²	1	1	yes	characteristic
119	#16810498	C₂²	1	1	yes	characteristic
120	#16810498	C₂²	1	1	yes	characteristic
121	#16810498	C₂²	1	1	yes	characteristic
122	#16810498	C₂²	1	1	yes	characteristic
123	#16810498	C₂²	1	1	yes	characteristic
124	#16810491	C₂²	1	1	yes	characteristic
125	#16810491	C₂²	1	1	yes	characteristic
126	#16810491	C₂²	1	1	yes	characteristic
127	#16810491	C₂²	1	1	yes	characteristic
128	#16810489	C₂²	1	1	yes	characteristic
129	#16810489	C₂²	1	1	yes	characteristic
130	#16810489	C₂²	1	1	yes	characteristic
131	#16810486	C₂²	1	1	yes	characteristic
132	#16810486	C₂²	1	1	yes	characteristic
133	#16810486	C₂²	1	1	yes	characteristic
134	#16810486	C₂²	1	1	yes	characteristic
135	#16810483	C₂²	1	1	yes	characteristic
136	#16810483	C₂²	1	1	yes	characteristic
137	#16810483	C₂²	1	1	yes	characteristic
138	#16810483	C₂²	1	1	yes	characteristic
139	#16810483	C₂²	1	1	yes	characteristic
140	#16810483	C₂²	1	1	yes	characteristic
141	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
142	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
143	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
144	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
145	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
146	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
147	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
148	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
149	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
150	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
151	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
152	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
153	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
154	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
155	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
156	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
157	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
158	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
159	C₄×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
160	C₄×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
161	C₄×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
162	C₄×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
163	C₄×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
164	C₄×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
165	#16810469	C₂²	1	1	yes	characteristic
166	#16810469	C₂²	1	1	yes	characteristic
167	#16810469	C₂²	1	1	yes	characteristic
168	C₂×#13133124	C₂²	1	1	yes	characteristic
169	C₂×#13133124	C₂²	1	1	yes	characteristic
170	C₂×#13133124	C₂²	1	1	yes	characteristic
171	C₂×#13133124	C₂²	1	1	yes	characteristic
172	C₅₃×#554	C₄	1	16	yes	complemented
173	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
174	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
175	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
176	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
177	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
178	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
179	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
180	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
181	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
182	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
183	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
184	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
185	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
186	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
187	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
188	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
189	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
190	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
191	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
192	Q₈×Dic₅₃	—	4	2	no	—
193	Q₈×Dic₅₃	—	4	2	no	—
194	#13133176	—	4	2	no	—
195	#13133176	—	4	2	no	—
196	C₂×C₄⋊Dic₅₃	—	4	2	no	—
197	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
198	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
199	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
200	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
201	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
204	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
205	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
206	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
207	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
208	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
209	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
210	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
211	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
212	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
213	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
214	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
215	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
216	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
218	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
219	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
220	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
221	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
222	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
223	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
224	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
225	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
226	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
227	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
228	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
229	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
230	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
231	C₂×C₄×Dic₅₃	—	4	2	no	—
232	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
233	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
234	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
235	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
236	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
237	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
238	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
239	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
240	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
241	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
242	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
243	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
244	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
245	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
246	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
247	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
248	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
249	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
250	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
251	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
252	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
253	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
254	#13133124	C₂³	1	1	yes	characteristic
255	#13133124	C₂³	1	1	yes	characteristic
256	#13133124	C₂³	1	1	yes	characteristic
257	#13133124	C₂³	1	1	yes	characteristic
258	#13133124	C₂³	1	1	yes	characteristic
259	#13133124	C₂³	1	1	yes	characteristic
260	#13133124	C₂³	1	1	yes	characteristic
261	#13133124	C₂³	1	1	yes	characteristic
262	#13133124	C₂³	1	1	yes	characteristic
263	#13133124	C₂³	1	1	yes	characteristic
264	#13133124	C₂³	1	1	yes	characteristic
265	#13133124	C₂³	1	1	yes	characteristic
266	#13133124	C₂³	1	1	yes	characteristic
267	#13133124	C₂³	1	1	yes	characteristic
268	#13133124	C₂³	1	1	yes	characteristic
269	#13133124	C₂³	1	1	yes	characteristic
270	#13133124	C₂³	1	1	yes	characteristic
271	#13133124	C₂³	1	1	yes	characteristic
272	#13133124	C₂³	1	1	yes	characteristic
273	#13133124	C₂³	1	1	yes	characteristic
274	#13133124	C₂³	1	1	yes	characteristic
275	#13133124	C₂³	1	1	yes	characteristic
276	#13133124	C₂³	1	1	yes	characteristic
277	#13133124	C₂³	1	1	yes	characteristic
278	#13133124	C₂³	1	1	yes	characteristic
279	#13133124	C₂³	1	1	yes	characteristic
280	#13133124	C₂³	1	1	yes	characteristic
281	#13133124	C₂³	1	1	yes	characteristic
282	#13133124	C₂³	1	1	yes	characteristic
283	#13133124	C₂³	1	1	yes	characteristic
284	#13133124	C₂³	1	1	yes	characteristic
285	#13133124	C₂³	1	1	yes	characteristic
286	#13133124	C₂³	1	1	yes	characteristic
287	#13133124	C₂³	1	1	yes	characteristic
288	#13133124	C₂³	1	1	yes	characteristic
289	#13133124	C₂³	1	1	yes	characteristic
290	#13133124	C₂³	1	1	yes	characteristic
291	#13133124	C₂³	1	1	yes	characteristic
292	#13133124	C₂³	1	1	yes	characteristic
293	#13133124	C₂³	1	1	yes	characteristic
294	#13133124	C₂³	1	1	yes	characteristic
295	#13133124	C₂³	1	1	yes	characteristic
296	#13133124	C₂³	1	1	yes	characteristic
297	#13133124	C₂³	1	1	yes	characteristic
298	#13133124	C₂³	1	1	yes	characteristic
299	#13133124	C₂³	1	1	yes	characteristic
300	#13133124	C₂³	1	1	yes	characteristic
301	#13133124	C₂³	1	1	yes	characteristic
302	#13133124	C₂³	1	1	yes	characteristic
303	#13133124	C₂³	1	1	yes	characteristic
304	#13133124	C₂³	1	1	yes	characteristic
305	#13133124	C₂³	1	1	yes	characteristic
306	#13133124	C₂³	1	1	yes	characteristic
307	#13133124	C₂³	1	1	yes	characteristic
308	#13133124	C₂³	1	1	yes	characteristic
309	#13133124	C₂³	1	1	yes	characteristic
310	#13133124	C₂³	1	1	yes	characteristic
311	#13133124	C₂³	1	1	yes	characteristic
312	#13133124	C₂³	1	1	yes	characteristic
313	#13133124	C₂³	1	1	yes	characteristic
314	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
315	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
316	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
317	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
318	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
319	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
320	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
321	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
322	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
323	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
324	C₄⋊Q₈×C₅₃	C₂×C₄	1	8	yes	complemented
325	#125×C₅₃	C₂×C₄	1	8	yes	complemented
326	#125×C₅₃	C₂×C₄	1	8	yes	complemented
327	C₂²⋊Q₈×C₅₃	C₂×C₄	1	8	yes	—
328	C₂²⋊Q₈×C₅₃	C₂×C₄	1	8	yes	—
329	C₂²⋊Q₈×C₅₃	C₂×C₄	1	8	yes	—
330	C₂²⋊Q₈×C₅₃	C₂×C₄	1	8	yes	complemented
331	C₂²⋊Q₈×C₅₃	C₂×C₄	1	8	yes	complemented
332	C₂²⋊Q₈×C₅₃	C₂×C₄	1	8	yes	complemented
333	C₄×Q₈×C₅₃	C₂×C₄	1	8	yes	complemented
334	C₄×D₄×C₅₃	C₂×C₄	1	8	yes	—
335	C₄×D₄×C₅₃	C₂×C₄	1	8	yes	—
336	C₄×D₄×C₅₃	C₂×C₄	1	8	yes	—
337	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	8	yes	—
338	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	8	yes	complemented
339	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
340	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
341	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
342	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
343	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
344	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
345	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
346	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
347	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
348	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
349	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
350	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
351	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
352	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
353	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
354	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
355	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
356	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
357	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
358	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
359	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
360	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
361	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
362	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
363	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
364	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
365	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
366	C₂×Q₈×C₅₃	—	4	1	no	—
367	C₂×Q₈×C₅₃	—	4	1	no	—
368	C₂×Q₈×C₅₃	—	4	1	no	—
369	C₂×Q₈×C₅₃	—	4	1	no	—
370	C₂×Q₈×C₅₃	—	4	1	no	—
371	C₂×Q₈×C₅₃	—	4	1	no	—
372	C₂×Q₈×C₅₃	C₂²×C₄	1	4	yes	—
373	C₂×Q₈×C₅₃	C₂²×C₄	1	4	yes	—
374	C₂×Q₈×C₅₃	C₂²×C₄	1	4	yes	—
375	C₂×D₄×C₅₃	—	2	2	no	—
376	C₂×D₄×C₅₃	—	2	2	no	—
377	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
378	C₂²×C₄×C₅₃	—	4	1	no	—
379	C₂²×C₄×C₅₃	—	4	1	no	—
380	C₂²×C₄×C₅₃	—	4	1	no	—
381	C₂²×C₄×C₅₃	—	4	1	no	—
382	C₂²×C₄×C₅₃	—	4	1	no	—
383	C₂²×C₄×C₅₃	—	4	1	no	—
384	C₂²×C₄×C₅₃	—	4	1	no	—
385	C₂²×C₄×C₅₃	—	4	1	no	—
386	C₂²×C₄×C₅₃	—	4	1	no	—
387	C₂²×C₄×C₅₃	—	4	1	no	—
388	C₂²×C₄×C₅₃	—	4	1	no	—
389	C₂²×C₄×C₅₃	—	4	1	no	—
390	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
391	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
392	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
393	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
394	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
395	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
396	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
397	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
399	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
400	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
401	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
402	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
406	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
407	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
409	C₂²×Dic₅₃	—	2	2	no	—
410	C₂²×Dic₅₃	—	2	2	no	—
411	C₂²×Dic₅₃	—	2	2	no	—
412	C₂²×Dic₅₃	—	2	2	no	—
413	C₂²×Dic₅₃	—	2	2	no	—
414	C₂²×Dic₅₃	—	4	1	no	—
415	C₂²×Dic₅₃	—	4	1	no	—
416	C₂²×Dic₅₃	—	4	1	no	—
417	C₂²×Dic₅₃	—	4	1	no	—
418	C₂²×Dic₅₃	—	4	1	no	—
419	C₂²×Dic₅₃	—	4	1	no	—
420	C₂²×Dic₅₃	—	4	1	no	—
421	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
422	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
423	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
424	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
425	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
426	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
427	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
428	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
429	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
430	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
431	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
432	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
433	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
434	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
435	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
436	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
437	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
438	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
439	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
440	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
441	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
442	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
443	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
444	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
445	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
446	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
447	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
448	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
449	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
450	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
451	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
452	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
453	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
454	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
455	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
456	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
457	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
458	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
459	C₄²×C₅₃	C₂²×C₄	1	4	yes	—
460	C₄²×C₅₃	C₂²×C₄	1	4	yes	—
461	C₄²×C₅₃	C₂²×C₄	1	4	yes	—
462	C₂²⋊Dic₅₃	—	2	2	no	—
463	C₂²⋊Dic₅₃	—	2	2	no	—
464	C₂²⋊Dic₅₃	—	2	2	no	—
465	C₂²⋊Dic₅₃	—	2	2	no	—
466	C₂²⋊Dic₅₃	—	2	2	no	—
467	C₂²⋊Dic₅₃	—	4	1	no	—
468	C₂²⋊Dic₅₃	—	4	1	no	—
469	C₂²⋊Dic₅₃	—	4	1	no	—
470	C₂²⋊Dic₅₃	—	4	1	no	—
471	C₂²⋊Dic₅₃	—	4	1	no	—
472	C₂²⋊Dic₅₃	—	4	1	no	—
473	C₂²⋊Dic₅₃	—	4	1	no	—
474	C₄⋊Dic₅₃	—	2	2	no	—
475	C₄⋊Dic₅₃	—	2	2	no	—
476	C₄⋊Dic₅₃	—	2	2	no	—
477	C₄⋊Dic₅₃	—	4	1	no	—
478	C₄⋊Dic₅₃	—	4	1	no	—
479	C₄⋊Dic₅₃	—	4	1	no	—
480	C₄⋊Dic₅₃	—	4	1	no	—
481	C₄⋊Dic₅₃	—	4	1	no	—
482	C₄⋊Dic₅₃	—	4	1	no	—
483	C₄⋊Dic₅₃	—	4	1	no	—
484	C₄⋊Dic₅₃	—	4	1	no	—
485	C₄⋊Dic₅₃	—	4	1	no	—
486	C₄⋊Dic₅₃	—	4	1	no	—
487	C₄⋊Dic₅₃	—	4	1	no	—
488	C₄⋊Dic₅₃	—	4	1	no	—
489	C₄⋊Dic₅₃	—	4	1	no	—
490	C₄⋊Dic₅₃	—	4	1	no	—
491	C₄⋊Dic₅₃	—	4	1	no	—
492	C₄⋊Dic₅₃	—	4	1	no	—
493	C₄⋊Dic₅₃	—	4	1	no	—
494	C₄⋊Dic₅₃	—	4	1	no	—
495	C₄⋊Dic₅₃	—	4	1	no	—
496	C₄×Dic₅₃	—	2	2	no	—
497	C₄×Dic₅₃	—	2	2	no	—
498	C₄×Dic₅₃	—	2	2	no	—
499	C₄×Dic₅₃	—	2	2	no	—
500	C₄×Dic₅₃	—	4	1	no	—
501	C₄×Dic₅₃	—	4	1	no	—
502	C₄×Dic₅₃	—	4	1	no	—
503	C₄×Dic₅₃	—	4	1	no	—
504	C₄×Dic₅₃	—	4	1	no	—
505	C₄×Dic₅₃	—	4	1	no	—
506	C₄×Dic₅₃	—	4	1	no	—
507	C₄×Dic₅₃	—	4	1	no	—
508	C₄×Dic₅₃	—	4	1	no	—
509	C₄×Dic₅₃	—	4	1	no	—
510	C₄×Dic₅₃	—	4	1	no	—
511	C₄×Dic₅₃	—	4	1	no	—
512	C₄×Dic₅₃	—	4	1	no	—
513	C₄×Dic₅₃	—	4	1	no	—
514	C₄×Dic₅₃	—	4	1	no	—
515	C₄×Dic₅₃	—	4	1	no	—
516	C₄×Dic₅₃	—	4	1	no	—
517	C₄×Dic₅₃	—	4	1	no	—
518	C₂³×C₅₃	—	2	1	no	—
519	C₂³×C₅₃	—	2	1	no	—
520	C₂³×C₅₃	—	2	1	no	—
521	C₂³×C₅₃	—	2	1	no	—
522	C₂³×C₅₃	—	2	1	no	—
523	C₂³×C₅₃	—	2	1	no	—
524	C₂³×C₅₃	—	2	1	no	—
525	C₂³×C₅₃	—	2	1	no	—
526	C₂³×C₅₃	—	2	1	no	—
527	C₂³×C₅₃	—	2	1	no	—
528	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
529	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
530	C₂³×C₅₃	2₋¹⁺⁴	1	2	yes	—
531	C₂³×C₅₃	2₋¹⁺⁴	1	2	yes	—
532	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
533	Q₈×C₅₃	—	4	4	no	—
534	Q₈×C₅₃	—	4	4	no	—
535	Q₈×C₅₃	—	4	4	no	—
536	D₄×C₅₃	—	2	8	no	—
537	C₂×C₄×C₅₃	—	2	1	no	—
538	C₂×C₄×C₅₃	—	2	1	no	—
539	C₂×C₄×C₅₃	—	2	1	no	—
540	C₂×C₄×C₅₃	—	2	1	no	—
541	C₂×C₄×C₅₃	—	2	1	no	—
542	C₂×C₄×C₅₃	—	2	1	no	—
543	C₂×C₄×C₅₃	—	2	1	no	—
544	C₂×C₄×C₅₃	—	2	1	no	—
545	C₂×C₄×C₅₃	—	2	1	no	—
546	C₂×C₄×C₅₃	—	2	1	no	—
547	C₂×C₄×C₅₃	—	2	1	no	—
548	C₂×C₄×C₅₃	—	2	1	no	—
549	C₂×C₄×C₅₃	—	2	1	no	—
550	C₂×C₄×C₅₃	—	2	1	no	—
551	C₂×C₄×C₅₃	—	2	1	no	—
552	C₂×C₄×C₅₃	—	2	1	no	—
553	C₂×C₄×C₅₃	—	2	1	no	—
554	C₂×C₄×C₅₃	—	2	1	no	—
555	C₂×C₄×C₅₃	—	2	1	no	—
556	C₂×C₄×C₅₃	—	2	1	no	—
557	C₂×C₄×C₅₃	—	2	1	no	—
558	C₂×C₄×C₅₃	—	2	1	no	—
559	C₂×C₄×C₅₃	—	2	1	no	—
560	C₂×C₄×C₅₃	—	2	1	no	—
561	C₂×C₄×C₅₃	—	2	1	no	—
562	C₂×C₄×C₅₃	—	2	1	no	—
563	C₂×C₄×C₅₃	—	4	4	no	—
564	C₂×C₄×C₅₃	—	4	4	no	—
565	C₂×C₄×C₅₃	—	4	4	no	—
566	C₂×C₄×C₅₃	—	4	4	no	—
567	C₂×C₄×C₅₃	—	4	4	no	—
568	C₂×C₄×C₅₃	—	4	4	no	—
569	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
570	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
571	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
572	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
573	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
574	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
575	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
576	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
577	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
578	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
579	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
580	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
581	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
582	C₂×Dic₅₃	—	2	1	no	—
583	C₂×Dic₅₃	—	2	1	no	—
584	C₂×Dic₅₃	—	2	1	no	—
585	C₂×Dic₅₃	—	2	1	no	—
586	C₂×Dic₅₃	—	2	1	no	—
587	C₂×Dic₅₃	—	2	1	no	—
588	C₂×Dic₅₃	—	2	1	no	—
589	C₂×Dic₅₃	—	2	1	no	—
590	C₂×Dic₅₃	—	2	1	no	—
591	C₂×Dic₅₃	—	2	1	no	—
592	C₂×Dic₅₃	—	2	1	no	—
593	C₂×Dic₅₃	—	2	1	no	—
594	C₂×Dic₅₃	—	2	1	no	—
595	C₂×Dic₅₃	—	2	1	no	—
596	C₂×Dic₅₃	—	2	1	no	—
597	C₂×Dic₅₃	—	2	1	no	—
598	C₂×Dic₅₃	—	2	1	no	—
599	C₂×Dic₅₃	—	2	1	no	—
600	C₂×Dic₅₃	—	2	1	no	—
601	C₂×Dic₅₃	—	2	1	no	—
602	C₂×Dic₅₃	—	2	1	no	—
603	C₂×Dic₅₃	—	2	1	no	—
604	C₂×Dic₅₃	—	2	1	no	—
605	C₂×Dic₅₃	—	2	1	no	—
606	C₂×Dic₅₃	—	2	1	no	—
607	C₂×Dic₅₃	—	2	1	no	—
608	C₂×Dic₅₃	—	2	1	no	—
609	C₂×Dic₅₃	—	2	1	no	—
610	C₂×Dic₅₃	—	2	1	no	—
611	C₂×Dic₅₃	—	2	1	no	—
612	C₂×Dic₅₃	—	2	1	no	—
613	C₂×Dic₅₃	—	2	1	no	—
614	C₂×Dic₅₃	—	2	1	no	—
615	C₂×Dic₅₃	—	2	1	no	—
616	C₂×Dic₅₃	—	2	1	no	—
617	C₂×Dic₅₃	—	2	1	no	—
618	C₂×Dic₅₃	—	2	1	no	—
619	C₂×Dic₅₃	—	2	1	no	—
620	C₂×Dic₅₃	—	2	1	no	—
621	C₂×Dic₅₃	—	2	1	no	—
622	C₂×Dic₅₃	—	2	1	no	—
623	C₂×Dic₅₃	—	2	1	no	—
624	C₂×Dic₅₃	—	2	1	no	—
625	C₂×Dic₅₃	—	2	1	no	—
626	C₂×Dic₅₃	—	2	1	no	—
627	C₂×Dic₅₃	—	2	1	no	—
628	C₂×Dic₅₃	—	2	1	no	—
629	C₂×Dic₅₃	—	4	4	no	—
630	C₂×Dic₅₃	—	4	4	no	—
631	C₂×Dic₅₃	—	8	2	no	—
632	C₂×Dic₅₃	—	8	2	no	—
633	C₂×Dic₅₃	H(5,𝔽₂)	1	2	yes	—
634	#34486	—	53	1	no	maximal, Sylow
635	C₂²×C₅₃	—	2	2	no	—
636	C₂²×C₅₃	—	2	2	no	—
637	C₂²×C₅₃	—	2	2	no	—
638	C₂²×C₅₃	—	2	2	no	—
639	C₂²×C₅₃	—	2	2	no	—
640	C₂²×C₅₃	—	2	2	no	—
641	C₂²×C₅₃	—	2	2	no	—
642	C₂²×C₅₃	—	2	2	no	—
643	C₂²×C₅₃	—	2	2	no	—
644	C₂²×C₅₃	—	4	1	no	—
645	C₂²×C₅₃	—	4	1	no	—
646	C₂²×C₅₃	—	4	1	no	—
647	C₂²×C₅₃	—	4	1	no	—
648	C₂²×C₅₃	#519	1	4	yes	—
649	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
650	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
651	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
652	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
653	C₂²×C₅₃	#585	1	1	yes	characteristic
654	C₂²×C₅₃	#585	1	1	yes	characteristic
655	C₂²×C₅₃	#585	1	1	yes	characteristic
656	C₄×C₅₃	—	2	2	no	—
657	C₄×C₅₃	—	2	2	no	—
658	C₄×C₅₃	—	2	2	no	—
659	C₄×C₅₃	—	2	2	no	—
660	C₄×C₅₃	—	2	2	no	—
661	C₄×C₅₃	—	2	2	no	—
662	C₄×C₅₃	—	2	2	no	—
663	C₄×C₅₃	—	2	2	no	—
664	C₄×C₅₃	—	2	2	no	—
665	C₄×C₅₃	—	2	2	no	—
666	C₄×C₅₃	—	2	2	no	—
667	C₄×C₅₃	—	2	2	no	—
668	C₄×C₅₃	—	2	2	no	—
669	Dic₅₃	—	2	2	no	—
670	Dic₅₃	—	4	1	no	—
671	Dic₅₃	—	4	1	no	—
672	Dic₅₃	—	4	1	no	—
673	Dic₅₃	—	4	1	no	—
674	Dic₅₃	—	4	1	no	—
675	Dic₅₃	—	4	1	no	—
676	Dic₅₃	—	4	1	no	—
677	Dic₅₃	—	4	1	no	—
678	Dic₅₃	—	4	1	no	—
679	Dic₅₃	—	4	1	no	—
680	Dic₅₃	—	4	1	no	—
681	Dic₅₃	—	4	1	no	—
682	Dic₅₃	—	4	1	no	—
683	Dic₅₃	—	4	1	no	—
684	Dic₅₃	—	4	1	no	—
685	C₂×#554	D₅₃	1	1	yes	characteristic
686	#2382	—	53	1	no	—
687	#2381	—	53	1	no	—
688	#2378	—	53	1	no	—
689	#2378	—	53	1	no	—
690	#2371	—	53	1	no	—
691	#2368	—	53	1	no	—
692	#2368	—	53	1	no	—
693	#2362	—	53	1	no	—
694	#2360	—	53	1	no	—
695	#2356	—	53	1	no	—
696	#2353	—	53	1	no	—
697	#2353	—	53	1	no	—
698	#2352	—	53	1	no	—
699	#2345	—	53	1	no	—
700	#2344	—	53	1	no	—
701	#2336	—	53	1	no	—
702	#2336	—	53	1	no	—
703	#2332	—	53	1	no	—
704	#2332	—	53	1	no	—
705	#2329	—	53	1	no	—
706	#2329	—	53	1	no	—
707	#2327	—	53	1	no	—
708	#2323	—	53	1	no	—
709	#2320	—	53	1	no	—
710	#2318	—	53	1	no	—
711	#2318	—	53	1	no	—
712	#2313	—	53	1	no	—
713	C₄×C₂²⋊Q₈	—	53	1	no	—
714	#2290	—	53	1	no	—
715	C₂×#387	—	53	1	no	—
716	C₂×C₅₃	—	2	4	no	—
717	C₂×C₅₃	—	4	2	no	—
718	C₂×C₅₃	C₂×#519	1	1	yes	characteristic
719	C₂×C₅₃	#3428	1	1	yes	characteristic
720	C₂×C₅₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
721	C₂×C₅₃	#3535	1	1	yes	characteristic
722	C₂×C₅₃	#3541	1	1	yes	characteristic
723	C₂×C₅₃	#3553	1	1	yes	characteristic
724	C₂×C₅₃	#3564	1	1	yes	characteristic
725	#554	Dic₅₃	1	16	yes	complemented
726	C₂×C₄⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
727	C₂×#125	C₂×D₅₃	1	1	yes	characteristic
728	C₂×#125	C₂×D₅₃	1	1	yes	characteristic
729	C₂×C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
730	C₂×C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
731	C₂×C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
732	C₂×C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
733	C₂×C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
734	C₂×C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
735	C₂×C₄×Q₈	—	53	1	no	—
736	C₂×C₄×Q₈	—	53	1	no	—
737	C₂×C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic
738	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
739	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
740	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
741	C₂×#117	—	53	1	no	—
742	C₂×#117	—	53	1	no	—
743	C₂²×C₄⋊C₄	—	53	1	no	—
744	C₂²×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
745	C₂²×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
746	C₂²×C₄²	—	53	1	no	—
747	#391	—	53	1	no	—
748	#391	—	53	1	no	—
749	#391	—	53	1	no	—
750	#391	—	53	1	no	—
751	#391	—	53	1	no	—
752	#391	—	53	1	no	—
753	#391	—	53	1	no	—
754	#391	—	53	1	no	—
755	#391	—	53	1	no	—
756	#391	—	53	1	no	—
757	#389	—	53	1	no	—
758	#389	—	53	1	no	—
759	#389	—	53	1	no	—
760	#389	—	53	1	no	—
761	#389	—	53	1	no	—
762	#389	—	53	1	no	—
763	#389	—	53	1	no	—
764	#389	—	53	1	no	—
765	#389	—	53	1	no	—
766	#389	—	53	1	no	—
767	#388	—	53	1	no	—
768	#388	—	53	1	no	—
769	#388	—	53	1	no	—
770	#388	—	53	1	no	—
771	#388	—	53	1	no	—
772	#388	—	53	1	no	—
773	#388	—	53	1	no	—
774	#388	—	53	1	no	—
775	#388	—	53	1	no	—
776	#388	—	53	1	no	—
777	#388	—	53	1	no	—
778	#388	—	53	1	no	—
779	#387	—	53	1	no	—
780	#387	—	53	1	no	—
781	#387	—	53	1	no	—
782	#387	—	53	1	no	—
783	#387	—	53	1	no	—
784	#387	—	53	1	no	—
785	#387	—	53	1	no	—
786	#387	—	53	1	no	—
787	#387	—	53	1	no	—
788	#387	—	53	1	no	—
789	#387	—	53	1	no	—
790	#387	—	53	1	no	—
791	#387	—	53	1	no	—
792	#387	—	53	1	no	—
793	#387	—	53	1	no	—
794	#387	—	53	1	no	—
795	#387	—	53	1	no	—
796	#387	—	53	1	no	—
797	#387	—	53	1	no	—
798	#387	—	53	1	no	—
799	#387	—	53	1	no	—
800	#387	—	53	1	no	—
801	#387	—	53	1	no	—
802	#387	—	53	1	no	—
803	#387	—	53	1	no	—
804	#387	—	53	1	no	—
805	#387	—	53	1	no	—
806	#387	—	53	1	no	—
807	#387	—	53	1	no	—
808	#387	—	53	1	no	—
809	#387	—	53	1	no	—
810	#387	—	53	1	no	—
811	#387	—	53	1	no	—
812	#387	—	53	1	no	—
813	#387	—	53	1	no	—
814	#387	—	53	1	no	—
815	#387	—	53	1	no	—
816	#387	—	53	1	no	—
817	#387	—	53	1	no	—
818	#387	—	53	1	no	—
819	#387	—	53	1	no	—
820	#387	—	53	1	no	—
821	#387	—	53	1	no	—
822	#387	—	53	1	no	—
823	#386	—	53	1	no	—
824	#386	—	53	1	no	—
825	#386	—	53	1	no	—
826	#386	—	53	1	no	—
827	#385	—	53	1	no	—
828	#385	—	53	1	no	—
829	#385	—	53	1	no	—
830	#385	—	53	1	no	—
831	#385	—	53	1	no	—
832	#385	—	53	1	no	—
833	#383	—	53	1	no	—
834	#383	—	53	1	no	—
835	#383	—	53	1	no	—
836	#383	—	53	1	no	—
837	#382	—	53	1	no	—
838	#382	—	53	1	no	—
839	#382	—	53	1	no	—
840	#381	—	53	1	no	—
841	#381	—	53	1	no	—
842	#381	—	53	1	no	—
843	#381	—	53	1	no	—
844	#380	—	53	1	no	—
845	#380	—	53	1	no	—
846	#380	—	53	1	no	—
847	#380	—	53	1	no	—
848	#380	—	53	1	no	—
849	#380	—	53	1	no	—
850	C₄×C₄⋊C₄	—	53	1	no	—
851	C₄×C₄⋊C₄	—	53	1	no	—
852	C₄×C₄⋊C₄	—	53	1	no	—
853	C₄×C₄⋊C₄	—	53	1	no	—
854	C₄×C₄⋊C₄	—	53	1	no	—
855	C₄×C₄⋊C₄	—	53	1	no	—
856	C₄×C₄⋊C₄	—	53	1	no	—
857	C₄×C₄⋊C₄	—	53	1	no	—
858	C₄×C₄⋊C₄	—	53	1	no	—
859	C₄×C₄⋊C₄	—	53	1	no	—
860	C₄×C₄⋊C₄	—	53	1	no	—
861	C₄×C₄⋊C₄	—	53	1	no	—
862	C₄×C₂²⋊C₄	—	53	1	no	—
863	C₄×C₂²⋊C₄	—	53	1	no	—
864	C₄×C₂²⋊C₄	—	53	1	no	—
865	C₄×C₂²⋊C₄	—	53	1	no	—
866	C₄×C₂²⋊C₄	—	53	1	no	—
867	C₄×C₂²⋊C₄	—	53	1	no	—
868	C₄×C₂²⋊C₄	—	53	1	no	—
869	C₄×C₂²⋊C₄	—	53	1	no	—
870	C₄×C₂²⋊C₄	—	53	1	no	—
871	C₄×C₂²⋊C₄	—	53	1	no	—
872	C₄×C₂²⋊C₄	—	53	1	no	—
873	C₄×C₂²⋊C₄	—	53	1	no	—
874	#376	—	53	1	no	—
875	#376	—	53	1	no	—
876	#376	—	53	1	no	—
877	C₂×#95	—	53	1	no	—
878	C₂×#95	—	53	1	no	—
879	C₂×#95	—	53	1	no	—
880	C₂×#95	—	53	1	no	—
881	C₅₃	#34486	1	1	yes	characteristic, complemented, Sylow
882	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
883	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
884	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
885	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
886	C₂³×C₄	—	53	1	no	—
887	C₂³×C₄	—	53	1	no	—
888	C₂³×C₄	—	53	1	no	—
889	C₂³×C₄	—	53	1	no	—
890	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
891	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
892	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
893	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
894	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
895	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
896	C₄⋊Q₈	C₂×Dic₅₃	1	8	yes	complemented
897	#125	C₂×Dic₅₃	1	8	yes	complemented
898	#125	C₂×Dic₅₃	1	8	yes	complemented
899	C₂²⋊Q₈	C₂×Dic₅₃	1	8	yes	—
900	C₂²⋊Q₈	C₂×Dic₅₃	1	8	yes	—
901	C₂²⋊Q₈	C₂×Dic₅₃	1	8	yes	—
902	C₂²⋊Q₈	C₂×Dic₅₃	1	8	yes	complemented
903	C₂²⋊Q₈	C₂×Dic₅₃	1	8	yes	complemented
904	C₂²⋊Q₈	C₂×Dic₅₃	1	8	yes	complemented
905	C₄×Q₈	—	212	2	no	—
906	C₄×Q₈	—	212	2	no	—
907	C₄×Q₈	C₂×Dic₅₃	1	8	yes	complemented
908	C₄×D₄	C₂×Dic₅₃	1	8	yes	—
909	C₄×D₄	C₂×Dic₅₃	1	8	yes	—
910	C₄×D₄	C₂×Dic₅₃	1	8	yes	—
911	#117	—	212	2	no	—
912	#117	—	212	2	no	—
913	C₂×C₄⋊C₄	—	53	1	no	—
914	C₂×C₄⋊C₄	—	53	1	no	—
915	C₂×C₄⋊C₄	—	53	1	no	—
916	C₂×C₄⋊C₄	—	53	1	no	—
917	C₂×C₄⋊C₄	—	53	1	no	—
918	C₂×C₄⋊C₄	—	53	1	no	—
919	C₂×C₄⋊C₄	—	53	1	no	—
920	C₂×C₄⋊C₄	—	53	1	no	—
921	C₂×C₄⋊C₄	—	53	1	no	—
922	C₂×C₄⋊C₄	—	53	1	no	—
923	C₂×C₄⋊C₄	—	53	1	no	—
924	C₂×C₄⋊C₄	—	53	1	no	—
925	C₂×C₄⋊C₄	—	53	1	no	—
926	C₂×C₄⋊C₄	—	53	1	no	—
927	C₂×C₄⋊C₄	—	53	1	no	—
928	C₂×C₄⋊C₄	—	53	1	no	—
929	C₂×C₄⋊C₄	—	53	1	no	—
930	C₂×C₄⋊C₄	—	53	1	no	—
931	C₂×C₄⋊C₄	—	53	1	no	—
932	C₂×C₄⋊C₄	—	53	1	no	—
933	C₂×C₄⋊C₄	—	53	1	no	—
934	C₂×C₄⋊C₄	—	53	1	no	—
935	C₂×C₄⋊C₄	—	212	2	no	—
936	C₂×C₄⋊C₄	C₂×Dic₅₃	1	8	yes	—
937	C₂×C₄⋊C₄	C₂×Dic₅₃	1	8	yes	complemented
938	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
939	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
940	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
941	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
942	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
943	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
944	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
945	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
946	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
947	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
948	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
949	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
950	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
951	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
952	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
953	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
954	C₂×C₂²⋊C₄	—	53	1	no	—
955	C₂×C₂²⋊C₄	—	53	1	no	—
956	C₂×C₂²⋊C₄	—	53	1	no	—
957	C₂×C₂²⋊C₄	—	53	1	no	—
958	C₂×C₂²⋊C₄	—	53	1	no	—
959	C₂×C₂²⋊C₄	—	53	1	no	—
960	C₂×C₂²⋊C₄	—	53	1	no	—
961	C₂×C₂²⋊C₄	—	53	1	no	—
962	C₂×C₂²⋊C₄	—	53	1	no	—
963	C₂×C₂²⋊C₄	—	53	1	no	—
964	C₂×C₂²⋊C₄	—	53	1	no	—
965	C₂×C₂²⋊C₄	—	53	1	no	—
966	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
967	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
968	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
969	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
970	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
971	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
972	C₂×C₄²	—	53	1	no	—
973	C₂×C₄²	—	53	1	no	—
974	C₂×C₄²	—	53	1	no	—
975	C₂×C₄²	—	53	1	no	—
976	C₂×C₄²	—	53	1	no	—
977	C₂×C₄²	—	53	1	no	—
978	C₂×C₄²	—	53	1	no	—
979	C₂×C₄²	—	53	1	no	—
980	C₂×C₄²	—	53	1	no	—
981	C₂×C₄²	—	53	1	no	—
982	C₂×C₄²	—	53	1	no	—
983	C₂×C₄²	—	53	1	no	—
984	C₂×C₄²	—	53	1	no	—
985	C₂×C₄²	—	53	1	no	—
986	C₂×C₄²	—	53	1	no	—
987	C₂×C₄²	—	53	1	no	—
988	C₂×C₄²	—	53	1	no	—
989	C₂×C₄²	—	53	1	no	—
990	C₂×C₄²	—	53	1	no	—
991	C₂×C₄²	—	53	1	no	—
992	C₂×C₄²	—	53	1	no	—
993	C₂×C₄²	—	53	1	no	—
994	C₂×C₄²	—	212	2	no	—
995	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
996	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
997	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
998	#95	—	53	1	no	—
999	#95	—	53	1	no	—
1000	#95	—	53	1	no	—
1001	#95	—	53	1	no	—
1002	#95	—	53	1	no	—
1003	#95	—	53	1	no	—
1004	#95	—	53	1	no	—
1005	#95	—	53	1	no	—
1006	#95	—	53	1	no	—
1007	#95	—	53	1	no	—
1008	#95	—	53	1	no	—
1009	#95	—	53	1	no	—
1010	#95	—	53	1	no	—
1011	#95	—	53	1	no	—
1012	#95	—	53	1	no	—
1013	#95	—	53	1	no	—
1014	#95	—	53	1	no	—
1015	#95	—	53	1	no	—
1016	#95	—	53	1	no	—
1017	#95	—	53	1	no	—
1018	#95	—	53	1	no	—
1019	#95	—	53	1	no	—
1020	#95	—	53	1	no	—
1021	#95	—	53	1	no	—
1022	#95	—	53	1	no	—
1023	#95	—	53	1	no	—
1024	#95	—	53	1	no	—
1025	#95	—	53	1	no	—
1026	#95	—	53	1	no	—
1027	#95	—	53	1	no	—
1028	#95	—	53	1	no	—
1029	#95	—	53	1	no	—
1030	#95	—	53	1	no	—
1031	#95	—	53	1	no	—
1032	#95	—	53	1	no	—
1033	#95	—	53	1	no	—
1034	#95	—	53	1	no	—
1035	#95	—	53	1	no	—
1036	#95	—	53	1	no	—
1037	#95	—	53	1	no	—
1038	#95	—	53	1	no	—
1039	#95	—	53	1	no	—
1040	#95	—	53	1	no	—
1041	#95	—	53	1	no	—
1042	#95	—	53	1	no	—
1043	#95	—	53	1	no	—
1044	#95	—	53	1	no	—
1045	#95	—	53	1	no	—
1046	#95	—	53	1	no	—
1047	#95	—	53	1	no	—
1048	#95	—	53	1	no	—
1049	#95	—	53	1	no	—
1050	#95	—	53	1	no	—
1051	#95	—	53	1	no	—
1052	#95	—	53	1	no	—
1053	#95	—	53	1	no	—
1054	#95	—	53	1	no	—
1055	#95	—	53	1	no	—
1056	#95	—	53	1	no	—
1057	#95	—	53	1	no	—
1058	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1059	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1060	C₂×Q₈	—	4	1	no	—
1061	C₂×Q₈	—	4	1	no	—
1062	C₂×Q₈	—	4	1	no	—
1063	C₂×Q₈	—	4	1	no	—
1064	C₂×Q₈	—	4	1	no	—
1065	C₂×Q₈	—	4	1	no	—
1066	C₂×Q₈	C₂²×Dic₅₃	1	4	yes	—
1067	C₂×Q₈	C₂²×Dic₅₃	1	4	yes	—
1068	C₂×Q₈	C₂²×Dic₅₃	1	4	yes	—
1069	C₂×D₄	—	2	2	no	—
1070	C₂×D₄	—	2	2	no	—
1071	C₂×D₄	C₂²×Dic₅₃	1	4	yes	—
1072	C₂²×C₄	—	4	1	no	—
1073	C₂²×C₄	—	4	1	no	—
1074	C₂²×C₄	—	4	1	no	—
1075	C₂²×C₄	—	4	1	no	—
1076	C₂²×C₄	—	4	1	no	—
1077	C₂²×C₄	—	4	1	no	—
1078	C₂²×C₄	—	4	1	no	—
1079	C₂²×C₄	—	4	1	no	—
1080	C₂²×C₄	—	4	1	no	—
1081	C₂²×C₄	—	4	1	no	—
1082	C₂²×C₄	—	4	1	no	—
1083	C₂²×C₄	—	4	1	no	—
1084	C₂²×C₄	—	53	1	no	—
1085	C₂²×C₄	—	53	1	no	—
1086	C₂²×C₄	—	53	1	no	—
1087	C₂²×C₄	—	53	1	no	—
1088	C₂²×C₄	—	53	1	no	—
1089	C₂²×C₄	—	53	1	no	—
1090	C₂²×C₄	—	53	1	no	—
1091	C₂²×C₄	—	53	1	no	—
1092	C₂²×C₄	—	53	1	no	—
1093	C₂²×C₄	—	53	1	no	—
1094	C₂²×C₄	—	53	1	no	—
1095	C₂²×C₄	—	53	1	no	—
1096	C₂²×C₄	—	53	1	no	—
1097	C₂²×C₄	—	53	1	no	—
1098	C₂²×C₄	—	53	1	no	—
1099	C₂²×C₄	—	53	1	no	—
1100	C₂²×C₄	—	106	2	no	—
1101	C₂²×C₄	—	106	2	no	—
1102	C₂²×C₄	—	106	2	no	—
1103	C₂²×C₄	—	106	2	no	—
1104	C₂²×C₄	—	106	2	no	—
1105	C₂²×C₄	—	212	1	no	—
1106	C₂²×C₄	—	212	1	no	—
1107	C₂²×C₄	—	212	1	no	—
1108	C₂²×C₄	—	212	1	no	—
1109	C₂²×C₄	—	212	1	no	—
1110	C₂²×C₄	—	212	1	no	—
1111	C₂²×C₄	—	212	1	no	—
1112	C₂²×C₄	C₂²×Dic₅₃	1	4	yes	—
1113	C₂²×C₄	C₂²×Dic₅₃	1	4	yes	—
1114	C₂²×C₄	C₂²×Dic₅₃	1	4	yes	—
1115	C₂²×C₄	C₂²×Dic₅₃	1	4	yes	—
1116	C₂²×C₄	C₂²×Dic₅₃	1	4	yes	—
1117	C₂²×C₄	C₂²×Dic₅₃	1	4	yes	—
1118	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1119	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1120	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1121	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1122	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1123	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1124	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1125	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1126	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1127	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1128	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1129	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1130	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1131	C₄⋊C₄	—	106	2	no	—
1132	C₄⋊C₄	—	106	2	no	—
1133	C₄⋊C₄	—	106	2	no	—
1134	C₄⋊C₄	—	212	1	no	—
1135	C₄⋊C₄	—	212	1	no	—
1136	C₄⋊C₄	—	212	1	no	—
1137	C₄⋊C₄	—	212	1	no	—
1138	C₄⋊C₄	—	212	1	no	—
1139	C₄⋊C₄	—	212	1	no	—
1140	C₄⋊C₄	—	212	1	no	—
1141	C₄⋊C₄	—	212	1	no	—
1142	C₄⋊C₄	—	212	1	no	—
1143	C₄⋊C₄	—	212	1	no	—
1144	C₄⋊C₄	—	212	1	no	—
1145	C₄⋊C₄	—	212	1	no	—
1146	C₄⋊C₄	—	212	1	no	—
1147	C₄⋊C₄	—	212	1	no	—
1148	C₄⋊C₄	—	212	1	no	—
1149	C₄⋊C₄	—	212	1	no	—
1150	C₄⋊C₄	—	212	1	no	—
1151	C₄⋊C₄	—	212	1	no	—
1152	C₄⋊C₄	—	212	1	no	—
1153	C₄⋊C₄	C₂²×Dic₅₃	1	4	yes	—
1154	C₄⋊C₄	C₂²×Dic₅₃	1	4	yes	—
1155	C₄⋊C₄	C₂²×Dic₅₃	1	4	yes	—
1156	C₄⋊C₄	C₂²×Dic₅₃	1	4	yes	—
1157	C₄⋊C₄	C₂²×Dic₅₃	1	4	yes	—
1158	C₄⋊C₄	C₂²×Dic₅₃	1	4	yes	—
1159	C₄⋊C₄	C₂²×Dic₅₃	1	4	yes	—
1160	C₄⋊C₄	C₂²×Dic₅₃	1	4	yes	—
1161	C₄⋊C₄	C₂²×Dic₅₃	1	4	yes	—
1162	C₄⋊C₄	C₂²×Dic₅₃	1	4	yes	—
1163	C₄⋊C₄	C₂²×Dic₅₃	1	4	yes	—
1164	C₄⋊C₄	C₂²×Dic₅₃	1	4	yes	—
1165	C₄⋊C₄	C₂²×Dic₅₃	1	4	yes	—
1166	C₄⋊C₄	C₂²×Dic₅₃	1	4	yes	—
1167	C₄⋊C₄	C₂²×Dic₅₃	1	4	yes	—
1168	C₄⋊C₄	C₂²×Dic₅₃	1	4	yes	—
1169	C₂²⋊C₄	—	106	2	no	—
1170	C₂²⋊C₄	—	106	2	no	—
1171	C₂²⋊C₄	—	106	2	no	—
1172	C₂²⋊C₄	—	106	2	no	—
1173	C₂²⋊C₄	—	106	2	no	—
1174	C₂²⋊C₄	—	212	1	no	—
1175	C₂²⋊C₄	—	212	1	no	—
1176	C₂²⋊C₄	—	212	1	no	—
1177	C₂²⋊C₄	—	212	1	no	—
1178	C₂²⋊C₄	—	212	1	no	—
1179	C₂²⋊C₄	—	212	1	no	—
1180	C₂²⋊C₄	—	212	1	no	—
1181	C₂²⋊C₄	C₂²×Dic₅₃	1	4	yes	—
1182	C₂²⋊C₄	C₂²×Dic₅₃	1	4	yes	—
1183	C₂²⋊C₄	C₂²×Dic₅₃	1	4	yes	—
1184	C₂²⋊C₄	C₂²×Dic₅₃	1	4	yes	—
1185	C₂²⋊C₄	C₂²×Dic₅₃	1	4	yes	—
1186	C₂²⋊C₄	C₂²×Dic₅₃	1	4	yes	—
1187	C₄²	—	106	2	no	—
1188	C₄²	—	106	2	no	—
1189	C₄²	—	106	2	no	—
1190	C₄²	—	106	2	no	—
1191	C₄²	—	212	1	no	—
1192	C₄²	—	212	1	no	—
1193	C₄²	—	212	1	no	—
1194	C₄²	—	212	1	no	—
1195	C₄²	—	212	1	no	—
1196	C₄²	—	212	1	no	—
1197	C₄²	—	212	1	no	—
1198	C₄²	—	212	1	no	—
1199	C₄²	—	212	1	no	—
1200	C₄²	—	212	1	no	—
1201	C₄²	—	212	1	no	—
1202	C₄²	—	212	1	no	—
1203	C₄²	—	212	1	no	—
1204	C₄²	—	212	1	no	—
1205	C₄²	—	212	1	no	—
1206	C₄²	—	212	1	no	—
1207	C₄²	—	212	1	no	—
1208	C₄²	—	212	1	no	—
1209	C₄²	C₂²×Dic₅₃	1	4	yes	—
1210	C₄²	C₂²×Dic₅₃	1	4	yes	—
1211	C₄²	C₂²×Dic₅₃	1	4	yes	—
1212	C₂³	—	2	1	no	—
1213	C₂³	—	2	1	no	—
1214	C₂³	—	2	1	no	—
1215	C₂³	—	2	1	no	—
1216	C₂³	—	2	1	no	—
1217	C₂³	—	2	1	no	—
1218	C₂³	—	2	1	no	—
1219	C₂³	—	2	1	no	—
1220	C₂³	—	2	1	no	—
1221	C₂³	—	2	1	no	—
1222	C₂³	C₂³×Dic₅₃	1	2	yes	—
1223	C₂³	C₂³×Dic₅₃	1	2	yes	—
1224	C₂³	#13133265	1	2	yes	—
1225	C₂³	#13133265	1	2	yes	—
1226	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1227	Q₈	—	4	4	no	—
1228	Q₈	—	4	4	no	—
1229	Q₈	—	4	4	no	—
1230	D₄	—	2	8	no	—
1231	C₂×C₄	—	2	1	no	—
1232	C₂×C₄	—	2	1	no	—
1233	C₂×C₄	—	2	1	no	—
1234	C₂×C₄	—	2	1	no	—
1235	C₂×C₄	—	2	1	no	—
1236	C₂×C₄	—	2	1	no	—
1237	C₂×C₄	—	2	1	no	—
1238	C₂×C₄	—	2	1	no	—
1239	C₂×C₄	—	2	1	no	—
1240	C₂×C₄	—	2	1	no	—
1241	C₂×C₄	—	2	1	no	—
1242	C₂×C₄	—	2	1	no	—
1243	C₂×C₄	—	2	1	no	—
1244	C₂×C₄	—	2	1	no	—
1245	C₂×C₄	—	2	1	no	—
1246	C₂×C₄	—	2	1	no	—
1247	C₂×C₄	—	2	1	no	—
1248	C₂×C₄	—	2	1	no	—
1249	C₂×C₄	—	2	1	no	—
1250	C₂×C₄	—	2	1	no	—
1251	C₂×C₄	—	2	1	no	—
1252	C₂×C₄	—	2	1	no	—
1253	C₂×C₄	—	2	1	no	—
1254	C₂×C₄	—	2	1	no	—
1255	C₂×C₄	—	2	1	no	—
1256	C₂×C₄	—	2	1	no	—
1257	C₂×C₄	—	4	4	no	—
1258	C₂×C₄	—	4	4	no	—
1259	C₂×C₄	—	4	4	no	—
1260	C₂×C₄	—	4	4	no	—
1261	C₂×C₄	—	4	4	no	—
1262	C₂×C₄	—	4	4	no	—
1263	C₂×C₄	—	53	2	no	—
1264	C₂×C₄	—	106	1	no	—
1265	C₂×C₄	—	106	1	no	—
1266	C₂×C₄	—	106	1	no	—
1267	C₂×C₄	—	106	1	no	—
1268	C₂×C₄	—	106	1	no	—
1269	C₂×C₄	—	106	1	no	—
1270	C₂×C₄	—	106	1	no	—
1271	C₂×C₄	—	106	1	no	—
1272	C₂×C₄	—	106	1	no	—
1273	C₂×C₄	—	106	1	no	—
1274	C₂×C₄	—	106	1	no	—
1275	C₂×C₄	—	106	1	no	—
1276	C₂×C₄	—	106	1	no	—
1277	C₂×C₄	—	106	1	no	—
1278	C₂×C₄	—	106	1	no	—
1279	C₂×C₄	—	106	1	no	—
1280	C₂×C₄	—	106	1	no	—
1281	C₂×C₄	—	106	1	no	—
1282	C₂×C₄	—	106	1	no	—
1283	C₂×C₄	—	106	1	no	—
1284	C₂×C₄	—	106	1	no	—
1285	C₂×C₄	—	106	1	no	—
1286	C₂×C₄	—	106	1	no	—
1287	C₂×C₄	—	106	1	no	—
1288	C₂×C₄	—	106	1	no	—
1289	C₂×C₄	—	106	1	no	—
1290	C₂×C₄	—	106	1	no	—
1291	C₂×C₄	—	106	1	no	—
1292	C₂×C₄	—	106	1	no	—
1293	C₂×C₄	—	106	1	no	—
1294	C₂×C₄	—	106	1	no	—
1295	C₂×C₄	—	106	1	no	—
1296	C₂×C₄	—	106	1	no	—
1297	C₂×C₄	—	106	1	no	—
1298	C₂×C₄	—	106	1	no	—
1299	C₂×C₄	—	106	1	no	—
1300	C₂×C₄	—	106	1	no	—
1301	C₂×C₄	—	106	1	no	—
1302	C₂×C₄	—	106	1	no	—
1303	C₂×C₄	—	106	1	no	—
1304	C₂×C₄	—	106	1	no	—
1305	C₂×C₄	—	106	1	no	—
1306	C₂×C₄	—	106	1	no	—
1307	C₂×C₄	—	106	1	no	—
1308	C₂×C₄	—	106	1	no	—
1309	C₂×C₄	—	106	1	no	—
1310	C₂×C₄	—	106	1	no	—
1311	C₂×C₄	—	424	2	no	—
1312	C₂×C₄	—	424	2	no	—
1313	C₂×C₄	—	212	4	no	—
1314	C₂×C₄	—	212	4	no	—
1315	C₂×C₄	C₂³×Dic₅₃	1	2	yes	—
1316	C₂×C₄	C₂³×Dic₅₃	1	2	yes	—
1317	C₂×C₄	C₂³×Dic₅₃	1	2	yes	—
1318	C₂×C₄	C₂³×Dic₅₃	1	2	yes	—
1319	C₂×C₄	C₂³×Dic₅₃	1	2	yes	—
1320	C₂×C₄	C₂³×Dic₅₃	1	2	yes	—
1321	C₂×C₄	C₂³×Dic₅₃	1	2	yes	—
1322	C₂×C₄	C₂³×Dic₅₃	1	2	yes	—
1323	C₂×C₄	C₂³×Dic₅₃	1	2	yes	—
1324	C₂×C₄	C₂³×Dic₅₃	1	2	yes	—
1325	C₂×C₄	C₂³×Dic₅₃	1	2	yes	—
1326	C₂×C₄	C₂³×Dic₅₃	1	2	yes	—
1327	C₂×C₄	C₂³×Dic₅₃	1	2	yes	—
1328	C₂²	—	2	2	no	—
1329	C₂²	—	2	2	no	—
1330	C₂²	—	2	2	no	—
1331	C₂²	—	2	2	no	—
1332	C₂²	—	2	2	no	—
1333	C₂²	—	2	2	no	—
1334	C₂²	—	2	2	no	—
1335	C₂²	—	2	2	no	—
1336	C₂²	—	2	2	no	—
1337	C₂²	—	4	1	no	—
1338	C₂²	—	4	1	no	—
1339	C₂²	—	4	1	no	—
1340	C₂²	—	4	1	no	—
1341	C₂²	#16811101	1	4	yes	—
1342	C₂²	C₂⁴×Dic₅₃	1	1	yes	characteristic
1343	C₂²	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1344	C₂²	C₂×#13133265	1	1	yes	characteristic
1345	C₂²	C₂×#13133265	1	1	yes	characteristic
1346	C₂²	#16811458	1	1	yes	characteristic
1347	C₂²	#16811459	1	1	yes	characteristic
1348	C₂²	#16811459	1	1	yes	characteristic
1349	C₄	—	2	2	no	—
1350	C₄	—	2	2	no	—
1351	C₄	—	2	2	no	—
1352	C₄	—	2	2	no	—
1353	C₄	—	2	2	no	—
1354	C₄	—	2	2	no	—
1355	C₄	—	2	2	no	—
1356	C₄	—	2	2	no	—
1357	C₄	—	2	2	no	—
1358	C₄	—	2	2	no	—
1359	C₄	—	2	2	no	—
1360	C₄	—	2	2	no	—
1361	C₄	—	2	2	no	—
1362	C₄	—	106	2	no	—
1363	C₄	—	212	1	no	—
1364	C₄	—	212	1	no	—
1365	C₄	—	212	1	no	—
1366	C₄	—	212	1	no	—
1367	C₄	—	212	1	no	—
1368	C₄	—	212	1	no	—
1369	C₄	—	212	1	no	—
1370	C₄	—	212	1	no	—
1371	C₄	—	212	1	no	—
1372	C₄	—	212	1	no	—
1373	C₄	—	212	1	no	—
1374	C₄	—	212	1	no	—
1375	C₄	—	212	1	no	—
1376	C₄	—	212	1	no	—
1377	C₄	—	212	1	no	—
1378	C₂	—	2	4	no	—
1379	C₂	—	4	2	no	—
1380	C₂	C₂×#16811101	1	1	yes	characteristic
1381	C₂	#20287918	1	1	yes	characteristic
1382	C₂	H(5,𝔽₂)×Dic₅₃	1	1	yes	characteristic
1383	C₂	#20288919	1	1	yes	characteristic
1384	C₂	#20289001	1	1	yes	characteristic
1385	C₂	#20289167	1	1	yes	characteristic
1386	C₂	#20289338	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₅₃
commutator	C₂²×C₅₃	C₂⁴×C₄
Fitting	C₂×C₅₃×#554	C₂
socle, cosocle	C₂³×C₅₃	C₂⁵
prime radical	C₂²×D₄×C₅₃	C₂³
hypercenter	C₂×#554	D₅₃
hypocenter	C₅₃	#34486
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂×#554

Complements

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

N	H ≅ G/N	type
1. #20277901	C₂	semidirect
2. #20277896	C₂	semidirect
3. #20277881	C₂	semidirect
4. #20277881	C₂	semidirect
5. #20277821	C₂	semidirect
6. #20277800	C₂	semidirect
7. #20277800	C₂	semidirect
8. #20277746	C₂	semidirect
9. #20277724	C₂	semidirect
10. #20277680	C₂	semidirect
14. #20277592	C₂	semidirect
15. #20277584	C₂	semidirect
16. #20277521	C₂	semidirect
17. #20277521	C₂	semidirect
18. #20277473	C₂	semidirect
19. #20277473	C₂	semidirect
20. #20277450	C₂	semidirect
21. #20277450	C₂	semidirect
22. #20277435	C₂	semidirect
23. #20277399	C₂	semidirect
24. #20277366	C₂	semidirect
27. #20277318	C₂	semidirect
28. C₂²⋊Q₈×Dic₅₃	C₂	semidirect
30. C₂×#16810509	C₂	semidirect
172. C₅₃×#554	C₄	semidirect
324. C₄⋊Q₈×C₅₃	C₂×C₄	semidirect
325. #125×C₅₃	C₂×C₄	semidirect
326. #125×C₅₃	C₂×C₄	semidirect
330. C₂²⋊Q₈×C₅₃	C₂×C₄	semidirect
331. C₂²⋊Q₈×C₅₃	C₂×C₄	semidirect
332. C₂²⋊Q₈×C₅₃	C₂×C₄	semidirect
333. C₄×Q₈×C₅₃	C₂×C₄	semidirect
338. C₂×C₄⋊C₄×C₅₃	C₂×C₄	semidirect
725. #554	Dic₅₃	semidirect
881. C₅₃	#34486	semidirect
896. C₄⋊Q₈	C₂×Dic₅₃	semidirect
897. #125	C₂×Dic₅₃	semidirect
898. #125	C₂×Dic₅₃	semidirect
902. C₂²⋊Q₈	C₂×Dic₅₃	semidirect
903. C₂²⋊Q₈	C₂×Dic₅₃	semidirect
904. C₂²⋊Q₈	C₂×Dic₅₃	semidirect
907. C₄×Q₈	C₂×Dic₅₃	semidirect
937. C₂×C₄⋊C₄	C₂×Dic₅₃	semidirect

Maximal subgroups

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

subgroup	index
#20277901	2
#20277896	2
#20277881	2
#20277821	2
#20277800	2
#20277746	2
#20277724	2
#20277680	2
#20277655	2
#20277644	2
#20277592	2
#20277584	2
#20277521	2
#20277473	2
#20277450	2
#20277435	2
#20277399	2
#20277366	2
#20277348	2
#20277318	2
C₂²⋊Q₈×Dic₅₃	2
#20277160	2
C₂×#16810509	2
C₂×C₅₃×#554	2
#34486	53