Subgroups — #28293141

Order 13568.

7390 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288771	C₂	1	8	yes	maximal, complemented
2	#20288737	C₂	1	8	yes	maximal, complemented
3	#20288666	C₂	1	8	yes	maximal, complemented
4	#20288643	C₂	1	8	yes	maximal, complemented
5	#20288567	C₂	1	2	yes	maximal, complemented
6	#20288554	C₂	1	4	yes	maximal, complemented
7	#20288518	C₂	1	1	yes	maximal, characteristic, complemented
8	#20288479	C₂	1	1	yes	maximal, characteristic, complemented
9	#20288435	C₂	1	2	yes	maximal, complemented
10	#20288404	C₂	1	4	yes	maximal, complemented
11	#20288350	C₂	1	2	yes	maximal, complemented
12	#20288137	C₂	1	2	yes	maximal, complemented
13	#20288124	C₂	1	4	yes	maximal, complemented
14	#20288105	C₂	1	2	yes	maximal, complemented
15	C₂×#16811211	C₂	1	4	yes	maximal, complemented
16	C₄×#13133262	C₂	1	2	yes	maximal, complemented
17	C₂×C₅₃×#518	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13133262	C₂²	1	2	yes	—
19	#16811356	C₂²	1	8	yes	complemented
20	#16811343	C₂²	1	4	yes	complemented
21	#16811341	C₂²	1	8	yes	complemented
22	#16811338	C₂²	1	4	yes	complemented
23	#16811336	C₂²	1	8	yes	complemented
24	#16811332	C₂²	1	8	yes	complemented
25	#16811330	C₂²	1	4	yes	complemented
26	#16811323	C₂²	1	8	yes	complemented
27	#16811322	C₂²	1	16	yes	complemented
28	#16811319	C₂²	1	8	yes	complemented
29	#16811317	C₂²	1	8	yes	complemented
30	#16811313	C₂²	1	8	yes	complemented
31	#16811312	C₂²	1	8	yes	complemented
32	#16811302	C₂²	1	16	yes	complemented
33	#16811299	C₂²	1	16	yes	complemented
34	#16811299	C₂²	1	16	yes	complemented
35	#16811294	C₂²	1	4	yes	complemented
36	D₄×Dic₁₀₆	C₂²	1	4	yes	complemented
37	#16811282	C₂²	1	8	yes	complemented
38	#16811278	C₂²	1	4	yes	complemented
39	#16811277	C₂²	1	4	yes	complemented
40	#16811269	C₂²	1	8	yes	complemented
41	#16811268	C₂²	1	8	yes	complemented
42	#16811267	C₂²	1	8	yes	complemented
43	#16811267	C₂²	1	8	yes	complemented
44	#16811263	C₂²	1	16	yes	complemented
45	#16811263	C₂²	1	16	yes	complemented
46	D₄×D₂₁₂	C₂²	1	4	yes	complemented
47	D₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
48	D₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
49	#16811254	C₂²	1	2	yes	complemented
50	#16811249	C₂²	1	4	yes	complemented
51	#16811244	C₂²	1	4	yes	complemented
52	#16811244	C₂²	1	4	yes	complemented
53	#16811238	C₂²	1	8	yes	complemented
54	#16811235	C₂²	1	4	yes	complemented
55	#16811228	C₂²	1	4	yes	complemented
56	#16811224	C₂²	1	8	yes	complemented
57	#16811220	C₂²	1	4	yes	complemented
58	#16811220	C₂²	1	4	yes	complemented
59	#16811215	C₂²	1	16	yes	complemented
60	#16811211	C₂²	1	4	yes	complemented
61	#16811211	C₂²	1	8	yes	complemented
62	#16811211	C₂²	1	4	yes	complemented
63	#16811211	C₂²	1	8	yes	complemented
64	#16811211	C₂²	1	8	yes	complemented
65	#16811211	C₂²	1	16	yes	complemented
66	#16811211	C₂²	1	16	yes	complemented
67	#16811206	C₂²	1	16	yes	complemented
68	#16811204	C₂²	1	2	yes	complemented
69	#16811190	C₂²	1	4	yes	complemented
70	#16811185	C₂²	1	4	yes	complemented
71	#16811182	C₂²	1	8	yes	complemented
72	#16811180	C₂²	1	2	yes	complemented
73	#16811173	C₂²	1	2	yes	complemented
74	#16811170	C₂²	1	8	yes	complemented
75	#16811157	C₂²	1	8	yes	complemented
76	#16811155	C₂²	1	8	yes	complemented
77	#16811153	C₂²	1	16	yes	complemented
78	#16811151	C₂²	1	8	yes	complemented
79	#16811151	C₂²	1	8	yes	complemented
80	C₂×#13133210	C₂²	1	8	yes	complemented
81	C₂×#13133203	C₂²	1	8	yes	complemented
82	#16811134	C₂²	1	4	yes	complemented
83	#16811134	C₂²	1	8	yes	complemented
84	#16811134	C₂²	1	8	yes	complemented
85	#16811132	C₂²	1	16	yes	complemented
86	C₂×#13133199	C₂²	1	8	yes	complemented
87	C₂×#13133196	C₂²	1	4	yes	complemented
88	C₂×#13133191	C₂²	1	4	yes	complemented
89	C₂×#13133190	C₂²	1	8	yes	complemented
90	C₂×#13133186	C₂²	1	8	yes	complemented
91	#16811104	C₂²	1	4	yes	complemented
92	#16811102	C₂²	1	8	yes	complemented
93	#16811098	C₂²	1	2	yes	—
94	#16811096	C₂²	1	8	yes	complemented
95	#16811095	C₂²	1	8	yes	complemented
96	C₄×#11719945	C₂²	1	4	yes	complemented
97	C₄×#11719947	C₂²	1	8	yes	complemented
98	C₂×C₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
99	C₄×D₄×D₅₃	C₂²	1	8	yes	complemented
100	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
101	C₅₃×#518	C₂²	1	8	yes	complemented
102	C₅₃×#518	C₂²	1	8	yes	complemented
103	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
104	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
105	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
106	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
107	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
108	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
109	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
110	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
111	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
112	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
113	#13133262	—	2	16	no	—
114	C₂×#11719945	C₂³	1	4	yes	—
115	C₂×#11719945	C₂³	1	8	yes	complemented
116	C₂×#11719945	C₂³	1	8	yes	complemented
117	C₂×#11719947	C₂³	1	8	yes	—
118	C₂²×Dic₁₀₆	C₂³	1	4	yes	complemented
119	C₂²×D₂₁₂	C₂³	1	4	yes	complemented
120	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	—
121	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	—
122	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	—
123	C₂×D₄×D₅₃	C₂³	1	8	yes	—
124	C₂²×C₄×D₅₃	C₂³	1	8	yes	complemented
125	#13133217	C₂³	1	2	yes	complemented
126	#13133217	C₂³	1	2	yes	complemented
127	#13133217	C₂³	1	2	yes	complemented
128	#13133216	C₂³	1	8	yes	complemented
129	#13133214	C₂³	1	2	yes	complemented
130	#13133213	C₂³	1	8	yes	—
131	#13133212	C₂³	1	8	yes	complemented
132	#13133212	C₂³	1	8	yes	complemented
133	#13133211	C₂³	1	16	yes	complemented
134	#13133210	C₂³	1	8	yes	—
135	#13133210	C₂³	1	16	yes	—
136	#13133210	C₂³	1	8	yes	—
137	#13133210	C₂³	1	16	yes	complemented
138	#13133210	C₂³	1	16	yes	complemented
139	#13133209	C₂³	1	8	yes	complemented
140	#13133209	C₂³	1	4	yes	complemented
141	#13133208	C₂³	1	8	yes	complemented
142	#13133207	C₂³	1	8	yes	complemented
143	#13133207	C₂³	1	8	yes	complemented
144	#13133205	C₂³	1	4	yes	complemented
145	#13133205	C₂³	1	8	yes	complemented
146	#13133204	C₂³	1	8	yes	—
147	#13133203	C₂³	1	8	yes	—
148	#13133203	C₂³	1	16	yes	—
149	#13133203	C₂³	1	8	yes	—
150	#13133203	C₂³	1	16	yes	complemented
151	#13133203	C₂³	1	16	yes	complemented
152	#13133202	C₂³	1	8	yes	complemented
153	#13133202	C₂³	1	8	yes	complemented
154	#13133201	C₂³	1	16	yes	complemented
155	#13133200	C₂³	1	8	yes	—
156	#13133200	C₂³	1	16	yes	complemented
157	#13133200	C₂³	1	16	yes	complemented
158	#13133199	C₂³	1	8	yes	—
159	#13133199	C₂³	1	16	yes	—
160	#13133199	C₂³	1	8	yes	—
161	#13133199	C₂³	1	16	yes	complemented
162	#13133199	C₂³	1	16	yes	complemented
163	#13133198	C₂³	1	16	yes	—
164	#13133197	C₂³	1	8	yes	complemented
165	#13133196	C₂³	1	4	yes	—
166	#13133196	C₂³	1	4	yes	—
167	#13133196	C₂³	1	4	yes	—
168	#13133196	C₂³	1	8	yes	—
169	#13133196	C₂³	1	4	yes	—
170	#13133196	C₂³	1	8	yes	complemented
171	#13133196	C₂³	1	8	yes	complemented
172	#13133196	C₂³	1	8	yes	complemented
173	#13133196	C₂³	1	8	yes	complemented
174	#13133195	C₂³	1	8	yes	complemented
175	#13133195	C₂³	1	8	yes	complemented
176	#13133194	C₂³	1	16	yes	complemented
177	#13133194	C₂³	1	16	yes	complemented
178	#13133192	C₂³	1	8	yes	complemented
179	#13133191	C₂³	1	4	yes	—
180	#13133191	C₂³	1	4	yes	—
181	#13133191	C₂³	1	4	yes	—
182	#13133191	C₂³	1	8	yes	—
183	#13133191	C₂³	1	4	yes	—
184	#13133191	C₂³	1	8	yes	complemented
185	#13133191	C₂³	1	8	yes	complemented
186	#13133191	C₂³	1	8	yes	complemented
187	#13133191	C₂³	1	8	yes	complemented
188	#13133190	C₂³	1	16	yes	—
189	#13133190	C₂³	1	8	yes	—
190	#13133190	C₂³	1	8	yes	—
191	#13133190	C₂³	1	16	yes	complemented
192	#13133190	C₂³	1	16	yes	complemented
193	#13133189	C₂³	1	16	yes	—
194	#13133189	C₂³	1	16	yes	—
195	#13133188	C₂³	1	8	yes	—
196	#13133188	C₂³	1	8	yes	—
197	#13133187	C₂³	1	16	yes	complemented
198	#13133186	C₂³	1	16	yes	—
199	#13133186	C₂³	1	16	yes	—
200	#13133186	C₂³	1	8	yes	—
201	#13133186	C₂³	1	16	yes	—
202	#13133185	C₂³	1	16	yes	—
203	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
204	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
205	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
206	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
207	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
208	#13133182	C₂³	1	8	yes	complemented
209	C₄×D₂₁₂	C₂³	1	4	yes	complemented
210	C₄×D₂₁₂	C₂³	1	8	yes	complemented
211	C₄×D₂₁₂	C₂³	1	4	yes	complemented
212	C₄×D₂₁₂	C₂³	1	4	yes	complemented
213	C₄×D₂₁₂	C₂³	1	4	yes	complemented
214	D₄×Dic₅₃	C₂³	1	8	yes	—
215	D₄×Dic₅₃	C₂³	1	8	yes	—
216	#13133179	C₂³	1	8	yes	complemented
217	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
218	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
219	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
220	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	—
221	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
222	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
223	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
224	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
225	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
226	#13133177	C₂³	1	16	yes	complemented
227	#13133177	C₂³	1	16	yes	complemented
228	#13133176	C₂³	1	4	yes	—
229	#13133176	C₂³	1	8	yes	complemented
230	#13133176	C₂³	1	8	yes	complemented
231	#13133175	C₂³	1	8	yes	complemented
232	#13133174	C₂³	1	16	yes	complemented
233	#13133174	C₂³	1	8	yes	complemented
234	#13133173	C₂³	1	16	yes	complemented
235	C₂×C₄⋊Dic₅₃	C₂³	1	4	yes	complemented
236	C₂×C₄⋊Dic₅₃	C₂³	1	4	yes	complemented
237	C₂×#11719919	C₂³	1	8	yes	complemented
238	C₂×#11719919	C₂³	1	8	yes	complemented
239	C₄⋊C₄×D₅₃	C₂³	1	8	yes	complemented
240	C₂×C₂²⋊Dic₅₃	C₂³	1	8	yes	—
241	C₂×C₂²⋊Dic₅₃	C₂³	1	8	yes	—
242	C₂×C₂²⋊Dic₅₃	C₂³	1	8	yes	—
243	C₂×#11719921	C₂³	1	8	yes	complemented
244	C₂×#11719921	C₂³	1	8	yes	complemented
245	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
246	C₂×C₄×Dic₅₃	C₂³	1	8	yes	complemented
247	C₄²×D₅₃	C₂³	1	8	yes	complemented
248	C₂⁵×C₅₃	C₂³	1	2	yes	—
249	C₂²×D₄×C₅₃	—	2	8	no	—
250	C₂²×D₄×C₅₃	C₂³	1	8	yes	—
251	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
252	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
253	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
254	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
255	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
256	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
257	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
258	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
259	C₄×D₄×C₅₃	C₂³	1	4	yes	—
260	C₄×D₄×C₅₃	C₂³	1	8	yes	—
261	C₄×D₄×C₅₃	C₂³	1	4	yes	—
262	C₄×D₄×C₅₃	C₂³	1	4	yes	—
263	C₄×D₄×C₅₃	C₂³	1	8	yes	—
264	C₄×D₄×C₅₃	C₂³	1	8	yes	—
265	C₄×D₄×C₅₃	C₂³	1	4	yes	—
266	C₄×D₄×C₅₃	C₂³	1	16	yes	—
267	C₄×D₄×C₅₃	C₂³	1	8	yes	—
268	#117×C₅₃	C₂³	1	8	yes	—
269	#117×C₅₃	C₂³	1	4	yes	—
270	#117×C₅₃	C₂³	1	4	yes	—
271	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
275	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
277	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
278	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
279	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
280	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
281	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
282	C₂×C₂²⋊C₄×C₅₃	C₂³	1	16	yes	—
283	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
284	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
285	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
286	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
287	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
288	C₂⁴×C₅₃	—	2	8	no	—
289	C₂⁴×C₅₃	—	8	2	no	—
290	C₂⁴×C₅₃	—	8	2	no	—
291	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
292	C₂⁴×C₅₃	C₂⁴	1	8	yes	—
293	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
294	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
295	C₂³×D₅₃	C₂⁴	1	8	yes	—
296	C₂×D₄×C₅₃	—	2	8	no	—
297	C₂×D₄×C₅₃	—	2	32	no	—
298	C₂×D₄×C₅₃	—	2	4	no	—
299	C₂×D₄×C₅₃	#41	1	8	yes	complemented
300	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
301	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
302	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
303	C₂²×C₄×C₅₃	—	2	4	no	—
304	C₂²×C₄×C₅₃	—	8	2	no	—
305	C₂²×C₄×C₅₃	—	8	2	no	—
306	C₂²×C₄×C₅₃	—	8	2	no	—
307	C₂²×C₄×C₅₃	—	8	2	no	—
308	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
310	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
317	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
318	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
319	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
320	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
321	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
322	C₂×C₂²⋊D₅₃	—	2	32	no	—
323	C₂×C₂²⋊D₅₃	—	8	8	no	—
324	C₂×C₂²⋊D₅₃	—	8	8	no	—
325	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
326	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
327	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
328	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
329	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
330	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
331	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
332	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
333	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
334	#11719947	—	2	32	no	—
335	D₄×D₅₃	—	2	32	no	—
336	#11719945	—	2	16	no	—
337	#11719945	—	8	8	no	—
338	#11719945	—	8	8	no	—
339	C₂×D₂₁₂	—	8	4	no	—
340	C₂×D₂₁₂	C₂⁴	1	4	yes	—
341	C₂×D₂₁₂	C₂⁴	1	4	yes	—
342	C₂×D₂₁₂	C₂⁴	1	8	yes	—
343	C₂×D₂₁₂	C₂⁴	1	4	yes	—
344	C₂×C₄×D₅₃	—	8	8	no	—
345	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
346	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
347	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
348	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
349	C₂×Dic₁₀₆	—	8	4	no	—
350	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
351	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
352	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
353	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
354	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
355	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
356	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
357	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
358	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
359	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
360	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
361	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
362	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
363	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
364	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
365	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
366	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
367	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
368	C₄²×C₅₃	C₂⁴	1	4	yes	—
369	C₄²×C₅₃	C₂⁴	1	8	yes	—
370	C₄²×C₅₃	C₂⁴	1	2	yes	—
371	C₄²×C₅₃	C₂⁴	1	2	yes	—
372	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
373	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
374	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
375	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
376	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
377	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
378	#11719921	C₂⁴	1	8	yes	—
379	#11719921	C₂⁴	1	16	yes	—
380	#11719921	C₂⁴	1	8	yes	—
381	#11719921	C₂⁴	1	8	yes	—
382	#11719921	C₂⁴	1	16	yes	—
383	#11719921	C₂⁴	1	8	yes	—
384	#11719921	C₂⁴	1	8	yes	—
385	#11719921	C₂⁴	1	8	yes	—
386	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
387	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
388	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
389	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
390	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
391	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
392	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
393	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
394	#11719919	C₂⁴	1	16	yes	—
395	#11719919	C₂⁴	1	8	yes	—
396	#11719919	C₂⁴	1	8	yes	—
397	#11719919	C₂⁴	1	16	yes	—
398	#11719919	C₂⁴	1	8	yes	—
399	#11719919	C₂⁴	1	8	yes	—
400	#11719919	C₂⁴	1	8	yes	—
401	#11719919	C₂⁴	1	8	yes	—
402	C₄×Dic₅₃	C₂⁴	1	8	yes	—
403	C₄×Dic₅₃	C₂⁴	1	8	yes	—
404	C₄×Dic₅₃	C₂⁴	1	8	yes	—
405	C₄×Dic₅₃	C₂⁴	1	16	yes	—
406	C₂³×C₅₃	—	2	2	no	—
407	C₂³×C₅₃	—	2	4	no	—
408	C₂³×C₅₃	—	2	16	no	—
409	C₂³×C₅₃	—	4	2	no	—
410	C₂³×C₅₃	—	4	2	no	—
411	C₂³×C₅₃	—	4	2	no	—
412	C₂³×C₅₃	—	4	2	no	—
413	C₂³×C₅₃	—	4	1	no	—
414	C₂³×C₅₃	—	4	1	no	—
415	C₂³×C₅₃	—	4	8	no	—
416	C₂³×C₅₃	—	4	8	no	—
417	C₂³×C₅₃	—	8	16	no	—
418	C₂³×C₅₃	C₂×#41	1	8	yes	—
419	C₂³×C₅₃	C₂⁵	1	4	yes	—
420	C₂³×C₅₃	C₂⁵	1	2	yes	—
421	C₂³×C₅₃	C₂⁵	1	4	yes	—
422	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
423	C₂²×D₅₃	—	2	16	no	—
424	C₂²×D₅₃	—	4	8	no	—
425	C₂²×D₅₃	—	4	8	no	—
426	C₂²×D₅₃	C₂⁵	1	8	yes	—
427	D₄×C₅₃	—	2	16	no	—
428	D₄×C₅₃	—	2	8	no	—
429	D₄×C₅₃	C₂×#41	1	16	yes	—
430	C₂×C₄×C₅₃	—	2	2	no	—
431	C₂×C₄×C₅₃	—	2	8	no	—
432	C₂×C₄×C₅₃	—	4	4	no	—
433	C₂×C₄×C₅₃	—	4	8	no	—
434	C₂×C₄×C₅₃	—	4	4	no	—
435	C₂×C₄×C₅₃	—	4	8	no	—
436	C₂×C₄×C₅₃	—	4	8	no	—
437	C₂×C₄×C₅₃	—	4	1	no	—
438	C₂×C₄×C₅₃	—	4	2	no	—
439	C₂×C₄×C₅₃	—	4	1	no	—
440	C₂×C₄×C₅₃	—	4	1	no	—
441	C₂×C₄×C₅₃	—	4	2	no	—
442	C₂×C₄×C₅₃	—	4	1	no	—
443	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
444	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
445	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
446	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
447	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
448	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
449	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
450	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
451	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
452	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
453	C₂²⋊D₅₃	—	2	16	no	—
454	C₂²⋊D₅₃	—	2	32	no	—
455	C₂²⋊D₅₃	—	4	16	no	—
456	C₂²⋊D₅₃	—	4	16	no	—
457	C₂²⋊D₅₃	—	4	8	no	—
458	C₂²⋊D₅₃	—	4	8	no	—
459	C₂×Dic₅₃	—	2	16	no	—
460	C₂×Dic₅₃	—	4	8	no	—
461	C₂×Dic₅₃	—	4	8	no	—
462	C₂×Dic₅₃	C₂⁵	1	8	yes	—
463	C₂×Dic₅₃	C₂⁵	1	8	yes	—
464	C₂×Dic₅₃	C₂⁵	1	8	yes	—
465	D₂₁₂	—	2	8	no	—
466	D₂₁₂	—	4	4	no	—
467	D₂₁₂	—	4	8	no	—
468	D₂₁₂	—	4	4	no	—
469	C₄×D₅₃	—	2	16	no	—
470	C₄×D₅₃	—	4	8	no	—
471	C₄×D₅₃	—	4	16	no	—
472	C₄×D₅₃	—	4	8	no	—
473	Dic₁₀₆	—	2	8	no	—
474	Dic₁₀₆	—	4	4	no	—
475	Dic₁₀₆	—	4	8	no	—
476	Dic₁₀₆	—	4	4	no	—
477	#62846	—	53	1	no	maximal, Sylow
478	C₂²×C₅₃	—	2	4	no	—
479	C₂²×C₅₃	—	2	4	no	—
480	C₂²×C₅₃	—	2	1	no	—
481	C₂²×C₅₃	—	2	1	no	—
482	C₂²×C₅₃	—	2	2	no	—
483	C₂²×C₅₃	—	2	4	no	—
484	C₂²×C₅₃	—	2	4	no	—
485	C₂²×C₅₃	—	2	4	no	—
486	C₂²×C₅₃	—	2	2	no	—
487	C₂²×C₅₃	—	2	2	no	—
488	C₂²×C₅₃	—	4	8	no	—
489	C₂²×C₅₃	—	4	8	no	—
490	C₂²×C₅₃	—	4	4	no	—
491	C₂²×C₅₃	—	8	16	no	—
492	C₂²×C₅₃	C₂²×#41	1	8	yes	—
493	C₂²×C₅₃	C₂²×#41	1	2	yes	—
494	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
495	C₂×D₅₃	—	2	8	no	—
496	C₂×D₅₃	—	2	8	no	—
497	C₂×D₅₃	—	2	8	no	—
498	C₂×D₅₃	—	8	16	no	—
499	C₄×C₅₃	—	2	2	no	—
500	C₄×C₅₃	—	2	1	no	—
501	C₄×C₅₃	—	2	4	no	—
502	C₄×C₅₃	—	2	2	no	—
503	C₄×C₅₃	—	2	2	no	—
504	C₄×C₅₃	—	2	4	no	—
505	C₄×C₅₃	—	2	2	no	—
506	C₄×C₅₃	—	2	1	no	—
507	C₄×C₅₃	C₂²×#41	1	4	yes	—
508	Dic₅₃	—	2	8	no	—
509	Dic₅₃	—	2	8	no	—
510	Dic₅₃	—	2	8	no	—
511	#3521	—	53	8	no	—
512	#3519	—	53	8	no	—
513	#3514	—	53	8	no	—
514	#3513	—	53	8	no	—
515	#3506	—	53	2	no	—
516	#3505	—	53	4	no	—
517	#3501	—	53	1	no	—
518	#3496	—	53	1	no	—
519	#3493	—	53	2	no	—
520	#3490	—	53	4	no	—
521	#3484	—	53	2	no	—
522	#3460	—	53	2	no	—
523	#3459	—	53	4	no	—
524	#3455	—	53	2	no	—
525	C₂×#538	—	53	4	no	—
526	C₄×H(5,𝔽₂)	—	53	2	no	—
527	C₂×#518	D₅₃	1	1	yes	characteristic, complemented
528	C₂×C₅₃	—	2	8	no	—
529	C₂×C₅₃	—	2	2	no	—
530	C₂×C₅₃	—	4	4	no	—
531	C₂×C₅₃	—	4	2	no	—
532	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
533	C₂×C₅₃	H(7,𝔽₂)	1	1	yes	characteristic
534	C₂×C₅₃	H(7,𝔽₂)	1	1	yes	characteristic
535	D₅₃	—	4	8	no	—
536	C₂×H(5,𝔽₂)	—	53	2	no	—
537	C₂³×D₄	C₂×D₅₃	1	1	yes	characteristic
538	#559	—	53	8	no	—
539	#556	—	53	4	no	—
540	#556	—	53	8	no	—
541	#555	—	53	4	no	—
542	#555	—	53	8	no	—
543	#554	—	53	4	no	—
544	#554	—	53	8	no	—
545	#553	—	53	8	no	—
546	#553	—	53	16	no	—
547	#553	—	53	8	no	—
548	#553	—	53	8	no	—
549	#552	—	53	8	no	—
550	#552	—	53	8	no	—
551	#551	—	53	16	no	—
552	#551	—	53	16	no	—
553	#551	—	53	16	no	—
554	#550	—	53	4	no	—
555	D₄×Q₈	—	53	4	no	—
556	#548	—	53	8	no	—
557	#547	—	53	4	no	—
558	#547	—	53	4	no	—
559	#546	—	53	8	no	—
560	#546	—	53	8	no	—
561	#546	—	53	8	no	—
562	#546	—	53	8	no	—
563	#546	—	53	16	no	—
564	#546	—	53	16	no	—
565	D₄²	—	53	8	no	—
566	D₄²	—	53	8	no	—
567	D₄²	—	53	4	no	—
568	#544	—	53	2	no	—
569	#543	—	53	4	no	—
570	#542	—	53	8	no	—
571	#542	—	53	4	no	—
572	#542	—	53	4	no	—
573	#541	—	53	4	no	—
574	#540	—	53	8	no	—
575	#540	—	53	4	no	—
576	#539	—	53	16	no	—
577	#539	—	53	4	no	—
578	#539	—	53	4	no	—
579	#538	—	53	16	no	—
580	#538	—	53	4	no	—
581	#538	—	53	8	no	—
582	#538	—	53	8	no	—
583	#538	—	53	8	no	—
584	#538	—	53	16	no	—
585	#538	—	53	16	no	—
586	#538	—	53	4	no	—
587	#537	—	53	2	no	—
588	#535	—	53	4	no	—
589	#534	—	53	8	no	—
590	#534	—	53	4	no	—
591	#533	—	53	2	no	—
592	#532	—	53	8	no	—
593	#532	—	53	2	no	—
594	#529	—	53	16	no	—
595	#529	—	53	8	no	—
596	#529	—	53	8	no	—
597	#529	—	53	8	no	—
598	#529	—	53	8	no	—
599	C₂×#126	—	53	8	no	—
600	C₂×#124	—	53	8	no	—
601	#525	—	53	4	no	—
602	#525	—	53	8	no	—
603	#525	—	53	8	no	—
604	#525	—	53	16	no	—
605	C₂×#123	—	53	8	no	—
606	C₂×C₂²⋊Q₈	—	53	4	no	—
607	C₂×#121	—	53	4	no	—
608	C₂×#121	—	53	8	no	—
609	C₂×#120	—	53	8	no	—
610	#520	—	53	8	no	—
611	#520	—	53	4	no	—
612	#518	—	53	2	no	—
613	#518	—	53	8	no	—
614	#518	—	53	8	no	—
615	#518	C₂×D₅₃	1	8	yes	complemented
616	#518	C₂×D₅₃	1	8	yes	complemented
617	C₄×#41	—	53	8	no	—
618	C₄×#41	—	53	4	no	—
619	C₂×C₄×D₄	—	53	8	no	—
620	C₂×C₄×D₄	—	53	8	no	—
621	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
622	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
623	C₂×C₄×D₄	C₂×D₅₃	1	2	yes	complemented
624	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
625	C₂×C₄×D₄	C₂×D₅₃	1	2	yes	complemented
626	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
627	C₂×#117	C₂×D₅₃	1	1	yes	characteristic, complemented
628	C₂×#117	C₂×D₅₃	1	1	yes	characteristic, complemented
629	C₂²×C₂²⋊C₄	C₂×D₅₃	1	2	yes	complemented
630	C₂²×C₂²⋊C₄	C₂×D₅₃	1	2	yes	complemented
631	C₅₃	#62846	1	1	yes	characteristic, complemented, Sylow
632	C₂⁵	C₂²×D₅₃	1	2	yes	—
633	H(5,𝔽₂)	—	106	16	no	—
634	C₂×#41	—	53	8	no	—
635	C₂×#41	—	53	4	no	—
636	C₂×#41	—	53	8	no	—
637	C₂×#41	—	53	8	no	—
638	C₂²×Q₈	—	53	4	no	—
639	C₂²×D₄	—	2	8	no	—
640	C₂²×D₄	—	53	8	no	—
641	C₂²×D₄	—	53	8	no	—
642	C₂²×D₄	—	53	8	no	—
643	C₂²×D₄	—	53	8	no	—
644	C₂²×D₄	—	53	4	no	—
645	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
646	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
647	C₂²×D₄	C₂²×D₅₃	1	8	yes	—
648	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
649	C₂³×C₄	—	53	8	no	—
650	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
651	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
652	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
653	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
654	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
655	C₄⋊Q₈	—	53	8	no	—
656	C₄⋊Q₈	—	53	2	no	—
657	C₄⋊Q₈	—	53	2	no	—
658	C₄⋊Q₈	—	53	2	no	—
659	#127	—	53	8	no	—
660	#127	—	53	2	no	—
661	#126	—	53	8	no	—
662	#126	—	53	8	no	—
663	#126	—	53	8	no	—
664	#126	—	53	16	no	—
665	#126	—	53	16	no	—
666	#126	—	53	16	no	—
667	#126	—	53	8	no	—
668	#126	—	53	16	no	—
669	#125	—	53	8	no	—
670	#125	—	53	8	no	—
671	#125	—	53	8	no	—
672	#125	—	53	8	no	—
673	#125	—	53	4	no	—
674	#124	—	53	8	no	—
675	#124	—	53	8	no	—
676	#124	—	53	16	no	—
677	#124	—	53	16	no	—
678	#124	—	53	16	no	—
679	#124	—	53	8	no	—
680	#124	—	53	8	no	—
681	#124	—	53	4	no	—
682	#123	—	53	16	no	—
683	#123	—	53	8	no	—
684	#123	—	53	16	no	—
685	#123	—	53	16	no	—
686	#123	—	53	8	no	—
687	#123	—	53	8	no	—
688	#123	—	53	8	no	—
689	#123	—	53	16	no	—
690	#123	—	53	16	no	—
691	#123	—	53	16	no	—
692	#123	—	53	16	no	—
693	#123	—	53	8	no	—
694	C₂²⋊Q₈	—	53	4	no	—
695	C₂²⋊Q₈	—	53	8	no	—
696	C₂²⋊Q₈	—	53	8	no	—
697	C₂²⋊Q₈	—	53	8	no	—
698	C₂²⋊Q₈	—	53	4	no	—
699	C₂²⋊Q₈	—	53	8	no	—
700	C₂²⋊Q₈	—	53	4	no	—
701	C₂²⋊Q₈	—	53	4	no	—
702	C₂²⋊Q₈	—	53	8	no	—
703	C₂²⋊Q₈	—	53	8	no	—
704	C₂²⋊Q₈	—	53	8	no	—
705	C₂²⋊Q₈	—	53	8	no	—
706	C₂²⋊Q₈	—	53	16	no	—
707	C₂²⋊Q₈	—	53	16	no	—
708	#121	—	53	16	no	—
709	#121	—	53	16	no	—
710	#121	—	53	8	no	—
711	#121	—	53	8	no	—
712	#121	—	53	4	no	—
713	#121	—	53	8	no	—
714	#121	—	53	8	no	—
715	#121	—	53	8	no	—
716	#121	—	53	4	no	—
717	#121	—	53	8	no	—
718	#121	—	53	8	no	—
719	#121	—	53	4	no	—
720	#121	—	53	4	no	—
721	#121	—	53	8	no	—
722	#121	—	53	8	no	—
723	#121	—	53	16	no	—
724	#121	—	53	16	no	—
725	#121	—	53	16	no	—
726	#121	—	53	8	no	—
727	#120	—	53	8	no	—
728	#120	—	53	16	no	—
729	#120	—	53	16	no	—
730	#120	—	53	16	no	—
731	#120	—	53	16	no	—
732	#120	—	53	16	no	—
733	C₄×Q₈	—	53	8	no	—
734	C₄×Q₈	—	53	4	no	—
735	C₄×Q₈	—	53	4	no	—
736	C₄×Q₈	—	53	8	no	—
737	C₄×Q₈	—	53	4	no	—
738	C₄×Q₈	—	53	4	no	—
739	C₄×D₄	—	53	8	no	—
740	C₄×D₄	—	53	8	no	—
741	C₄×D₄	—	53	8	no	—
742	C₄×D₄	—	53	16	no	—
743	C₄×D₄	—	53	16	no	—
744	C₄×D₄	—	53	16	no	—
745	C₄×D₄	—	53	8	no	—
746	C₄×D₄	—	53	16	no	—
747	C₄×D₄	—	53	8	no	—
748	C₄×D₄	—	53	8	no	—
749	C₄×D₄	—	53	16	no	—
750	C₄×D₄	—	53	8	no	—
751	C₄×D₄	—	53	16	no	—
752	C₄×D₄	—	53	16	no	—
753	C₄×D₄	—	53	4	no	—
754	C₄×D₄	—	53	4	no	—
755	C₄×D₄	—	53	8	no	—
756	C₄×D₄	—	53	4	no	—
757	C₄×D₄	—	53	4	no	—
758	C₄×D₄	C₂²×D₅₃	1	8	yes	—
759	C₄×D₄	C₂²×D₅₃	1	4	yes	—
760	C₄×D₄	C₂²×D₅₃	1	4	yes	—
761	C₄×D₄	C₂²×D₅₃	1	16	yes	—
762	C₄×D₄	C₂²×D₅₃	1	8	yes	—
763	C₄×D₄	C₂²×D₅₃	1	8	yes	—
764	C₄×D₄	C₂²×D₅₃	1	4	yes	—
765	C₄×D₄	C₂²×D₅₃	1	8	yes	—
766	C₄×D₄	C₂²×D₅₃	1	4	yes	—
767	#117	—	53	4	no	—
768	#117	—	53	8	no	—
769	#117	—	53	8	no	—
770	#117	—	53	8	no	—
771	#117	—	53	16	no	—
772	#117	—	53	8	no	—
773	#117	—	53	16	no	—
774	#117	C₂²×D₅₃	1	4	yes	—
775	#117	C₂²×D₅₃	1	4	yes	—
776	#117	C₂²×D₅₃	1	8	yes	—
777	C₂×C₄⋊C₄	—	53	8	no	—
778	C₂×C₄⋊C₄	—	53	8	no	—
779	C₂×C₄⋊C₄	—	53	4	no	—
780	C₂×C₄⋊C₄	—	53	4	no	—
781	C₂×C₄⋊C₄	—	53	8	no	—
782	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
783	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
784	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
785	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
786	C₂×C₂²⋊C₄	—	53	8	no	—
787	C₂×C₂²⋊C₄	—	53	8	no	—
788	C₂×C₂²⋊C₄	—	53	8	no	—
789	C₂×C₂²⋊C₄	—	53	8	no	—
790	C₂×C₂²⋊C₄	—	53	8	no	—
791	C₂×C₂²⋊C₄	—	53	16	no	—
792	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
793	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
794	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
795	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
796	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
797	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
798	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
799	C₂×C₂²⋊C₄	C₂²×D₅₃	1	8	yes	—
800	C₂×C₂²⋊C₄	C₂²×D₅₃	1	8	yes	—
801	C₂×C₂²⋊C₄	C₂²×D₅₃	1	16	yes	—
802	C₂×C₄²	—	53	8	no	—
803	C₂×C₄²	—	53	8	no	—
804	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
805	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
806	C₂×C₄²	C₂²×D₅₃	1	2	yes	—
807	C₂⁴	—	2	8	no	—
808	C₂⁴	—	8	2	no	—
809	C₂⁴	—	8	2	no	—
810	C₂⁴	—	53	8	no	—
811	C₂⁴	C₂³×D₅₃	1	8	yes	—
812	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
813	C₂⁴	C₂³×D₅₃	1	2	yes	—
814	C₂⁴	C₂³×D₅₃	1	2	yes	—
815	#41	—	106	32	no	—
816	#41	—	106	16	no	—
817	#41	—	424	8	no	—
818	#41	—	424	8	no	—
819	C₂×Q₈	—	53	4	no	—
820	C₂×Q₈	—	53	4	no	—
821	C₂×Q₈	—	53	4	no	—
822	C₂×Q₈	—	53	8	no	—
823	C₂×Q₈	—	424	4	no	—
824	C₂×D₄	—	2	8	no	—
825	C₂×D₄	—	2	32	no	—
826	C₂×D₄	—	2	4	no	—
827	C₂×D₄	—	53	8	no	—
828	C₂×D₄	—	53	16	no	—
829	C₂×D₄	—	53	8	no	—
830	C₂×D₄	—	53	16	no	—
831	C₂×D₄	—	53	8	no	—
832	C₂×D₄	—	53	16	no	—
833	C₂×D₄	—	53	4	no	—
834	C₂×D₄	—	53	4	no	—
835	C₂×D₄	—	53	8	no	—
836	C₂×D₄	—	53	4	no	—
837	C₂×D₄	—	106	32	no	—
838	C₂×D₄	—	106	32	no	—
839	C₂×D₄	—	424	4	no	—
840	C₂×D₄	—	424	8	no	—
841	C₂×D₄	—	424	8	no	—
842	C₂×D₄	#11719945	1	8	yes	complemented
843	C₂×D₄	C₂³×D₅₃	1	8	yes	—
844	C₂×D₄	C₂³×D₅₃	1	4	yes	—
845	C₂×D₄	C₂³×D₅₃	1	4	yes	—
846	C₂²×C₄	—	2	4	no	—
847	C₂²×C₄	—	8	2	no	—
848	C₂²×C₄	—	8	2	no	—
849	C₂²×C₄	—	8	2	no	—
850	C₂²×C₄	—	8	2	no	—
851	C₂²×C₄	—	53	8	no	—
852	C₂²×C₄	—	53	8	no	—
853	C₂²×C₄	—	53	8	no	—
854	C₂²×C₄	—	53	8	no	—
855	C₂²×C₄	—	53	8	no	—
856	C₂²×C₄	—	53	8	no	—
857	C₂²×C₄	—	53	16	no	—
858	C₂²×C₄	—	424	8	no	—
859	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
860	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
861	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
862	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
863	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
864	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
865	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
866	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
867	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
868	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
869	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
870	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
871	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
872	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
873	C₄⋊C₄	—	53	4	no	—
874	C₄⋊C₄	—	53	8	no	—
875	C₄⋊C₄	—	53	16	no	—
876	C₄⋊C₄	—	53	4	no	—
877	C₄⋊C₄	—	53	8	no	—
878	C₄⋊C₄	—	53	4	no	—
879	C₄⋊C₄	—	53	16	no	—
880	C₄⋊C₄	—	53	8	no	—
881	C₄⋊C₄	—	53	8	no	—
882	C₄⋊C₄	—	53	4	no	—
883	C₄⋊C₄	—	53	8	no	—
884	C₄⋊C₄	—	53	8	no	—
885	C₄⋊C₄	—	53	4	no	—
886	C₄⋊C₄	—	53	4	no	—
887	C₄⋊C₄	—	53	8	no	—
888	C₄⋊C₄	—	53	8	no	—
889	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
890	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
891	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
892	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
893	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
894	C₂²⋊C₄	—	53	8	no	—
895	C₂²⋊C₄	—	53	16	no	—
896	C₂²⋊C₄	—	53	8	no	—
897	C₂²⋊C₄	—	53	8	no	—
898	C₂²⋊C₄	—	53	16	no	—
899	C₂²⋊C₄	—	53	16	no	—
900	C₂²⋊C₄	—	53	8	no	—
901	C₂²⋊C₄	—	53	8	no	—
902	C₂²⋊C₄	—	53	16	no	—
903	C₂²⋊C₄	—	53	8	no	—
904	C₂²⋊C₄	—	53	16	no	—
905	C₂²⋊C₄	—	53	8	no	—
906	C₂²⋊C₄	—	53	8	no	—
907	C₂²⋊C₄	—	53	8	no	—
908	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
909	C₂²⋊C₄	C₂³×D₅₃	1	2	yes	—
910	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
911	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
912	C₂²⋊C₄	C₂³×D₅₃	1	2	yes	—
913	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
914	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
915	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
916	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
917	C₄²	—	53	8	no	—
918	C₄²	—	53	8	no	—
919	C₄²	—	53	16	no	—
920	C₄²	—	53	8	no	—
921	C₄²	C₂³×D₅₃	1	4	yes	—
922	C₄²	C₂³×D₅₃	1	8	yes	—
923	C₄²	C₂³×D₅₃	1	2	yes	—
924	C₄²	C₂³×D₅₃	1	2	yes	—
925	C₂³	—	2	2	no	—
926	C₂³	—	2	4	no	—
927	C₂³	—	2	16	no	—
928	C₂³	—	4	2	no	—
929	C₂³	—	4	2	no	—
930	C₂³	—	4	2	no	—
931	C₂³	—	4	2	no	—
932	C₂³	—	4	1	no	—
933	C₂³	—	4	1	no	—
934	C₂³	—	4	8	no	—
935	C₂³	—	4	8	no	—
936	C₂³	—	8	16	no	—
937	C₂³	—	53	8	no	—
938	C₂³	—	106	16	no	—
939	C₂³	—	212	8	no	—
940	C₂³	—	212	8	no	—
941	C₂³	C₂×#11719945	1	8	yes	—
942	C₂³	C₂⁴×D₅₃	1	2	yes	—
943	C₂³	C₂⁴×D₅₃	1	4	yes	—
944	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
945	C₂³	C₂⁴×D₅₃	1	4	yes	—
946	Q₈	—	106	8	no	—
947	Q₈	—	212	4	no	—
948	Q₈	—	212	8	no	—
949	Q₈	—	212	4	no	—
950	D₄	—	2	16	no	—
951	D₄	—	2	8	no	—
952	D₄	—	106	16	no	—
953	D₄	—	106	32	no	—
954	D₄	—	106	8	no	—
955	D₄	—	212	4	no	—
956	D₄	—	212	8	no	—
957	D₄	—	212	4	no	—
958	D₄	—	212	8	no	—
959	D₄	—	212	8	no	—
960	D₄	—	212	16	no	—
961	D₄	—	212	16	no	—
962	D₄	C₂×#11719945	1	16	yes	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	8	no	—
965	C₂×C₄	—	4	1	no	—
966	C₂×C₄	—	4	2	no	—
967	C₂×C₄	—	4	1	no	—
968	C₂×C₄	—	4	1	no	—
969	C₂×C₄	—	4	2	no	—
970	C₂×C₄	—	4	1	no	—
971	C₂×C₄	—	4	8	no	—
972	C₂×C₄	—	4	4	no	—
973	C₂×C₄	—	4	4	no	—
974	C₂×C₄	—	4	8	no	—
975	C₂×C₄	—	4	8	no	—
976	C₂×C₄	—	53	8	no	—
977	C₂×C₄	—	53	8	no	—
978	C₂×C₄	—	53	8	no	—
979	C₂×C₄	—	106	16	no	—
980	C₂×C₄	—	106	16	no	—
981	C₂×C₄	—	212	8	no	—
982	C₂×C₄	—	212	16	no	—
983	C₂×C₄	—	212	8	no	—
984	C₂×C₄	—	212	8	no	—
985	C₂×C₄	—	212	8	no	—
986	C₂×C₄	C₂×#11719945	1	4	yes	—
987	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
988	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
989	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
990	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
991	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
992	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
993	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
994	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
995	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
996	C₂²	—	2	1	no	—
997	C₂²	—	2	1	no	—
998	C₂²	—	2	4	no	—
999	C₂²	—	2	4	no	—
1000	C₂²	—	2	2	no	—
1001	C₂²	—	2	4	no	—
1002	C₂²	—	2	4	no	—
1003	C₂²	—	2	4	no	—
1004	C₂²	—	2	2	no	—
1005	C₂²	—	2	2	no	—
1006	C₂²	—	4	8	no	—
1007	C₂²	—	4	4	no	—
1008	C₂²	—	4	8	no	—
1009	C₂²	—	8	16	no	—
1010	C₂²	—	106	8	no	—
1011	C₂²	—	106	8	no	—
1012	C₂²	—	106	8	no	—
1013	C₂²	—	424	16	no	—
1014	C₂²	C₂²×#11719945	1	2	yes	—
1015	C₂²	C₂²×#11719945	1	8	yes	—
1016	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1017	C₄	—	2	2	no	—
1018	C₄	—	2	2	no	—
1019	C₄	—	2	4	no	—
1020	C₄	—	2	2	no	—
1021	C₄	—	2	1	no	—
1022	C₄	—	2	4	no	—
1023	C₄	—	2	2	no	—
1024	C₄	—	2	1	no	—
1025	C₄	—	106	8	no	—
1026	C₄	—	106	8	no	—
1027	C₄	—	106	8	no	—
1028	C₄	C₂²×#11719945	1	4	yes	—
1029	C₂	—	2	2	no	—
1030	C₂	—	2	8	no	—
1031	C₂	—	4	2	no	—
1032	C₂	—	4	4	no	—
1033	C₂	—	212	8	no	—
1034	C₂	C₂³×#11719945	1	1	yes	characteristic
1035	C₂	#20289525	1	1	yes	characteristic
1036	C₂	#20289525	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₂×C₅₃×#518	C₂
hypercenter	C₂×#518	D₅₃
hypocenter	C₅₃	#62846
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂×#518

Complements

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

N	H ≅ G/N	type
1. #20288771	C₂	semidirect
2. #20288737	C₂	semidirect
3. #20288666	C₂	semidirect
4. #20288643	C₂	semidirect
5. #20288567	C₂	semidirect
6. #20288554	C₂	semidirect
7. #20288518	C₂	semidirect
8. #20288479	C₂	semidirect
9. #20288435	C₂	semidirect
10. #20288404	C₂	semidirect
11. #20288350	C₂	semidirect
12. #20288137	C₂	semidirect
13. #20288124	C₂	semidirect
14. #20288105	C₂	semidirect
15. C₂×#16811211	C₂	semidirect
16. C₄×#13133262	C₂	semidirect
17. C₂×C₅₃×#518	C₂	semidirect
19. #16811356	C₂²	semidirect
20. #16811343	C₂²	semidirect
21. #16811341	C₂²	semidirect
22. #16811338	C₂²	semidirect
23. #16811336	C₂²	semidirect
24. #16811332	C₂²	semidirect
25. #16811330	C₂²	semidirect
26. #16811323	C₂²	semidirect
27. #16811322	C₂²	semidirect
28. #16811319	C₂²	semidirect
29. #16811317	C₂²	semidirect
30. #16811313	C₂²	semidirect
31. #16811312	C₂²	semidirect
32. #16811302	C₂²	semidirect
33. #16811299	C₂²	semidirect
34. #16811299	C₂²	semidirect
35. #16811294	C₂²	semidirect
36. D₄×Dic₁₀₆	C₂²	semidirect
37. #16811282	C₂²	semidirect
38. #16811278	C₂²	semidirect
39. #16811277	C₂²	semidirect
40. #16811269	C₂²	semidirect
41. #16811268	C₂²	semidirect
42. #16811267	C₂²	semidirect
43. #16811267	C₂²	semidirect
44. #16811263	C₂²	semidirect
45. #16811263	C₂²	semidirect
46. D₄×D₂₁₂	C₂²	semidirect
47. D₄×C₂²⋊D₅₃	C₂²	semidirect
48. D₄×C₂²⋊D₅₃	C₂²	semidirect
49. #16811254	C₂²	semidirect
50. #16811249	C₂²	semidirect
51. #16811244	C₂²	semidirect
52. #16811244	C₂²	semidirect
53. #16811238	C₂²	semidirect
54. #16811235	C₂²	semidirect
55. #16811228	C₂²	semidirect
56. #16811224	C₂²	semidirect
57. #16811220	C₂²	semidirect
58. #16811220	C₂²	semidirect
59. #16811215	C₂²	semidirect
60. #16811211	C₂²	semidirect
61. #16811211	C₂²	semidirect
62. #16811211	C₂²	semidirect
63. #16811211	C₂²	semidirect
64. #16811211	C₂²	semidirect
65. #16811211	C₂²	semidirect
66. #16811211	C₂²	semidirect
67. #16811206	C₂²	semidirect
68. #16811204	C₂²	semidirect
69. #16811190	C₂²	semidirect
70. #16811185	C₂²	semidirect
71. #16811182	C₂²	semidirect
72. #16811180	C₂²	semidirect
73. #16811173	C₂²	semidirect
74. #16811170	C₂²	semidirect
75. #16811157	C₂²	semidirect
76. #16811155	C₂²	semidirect
77. #16811153	C₂²	semidirect
78. #16811151	C₂²	semidirect
79. #16811151	C₂²	semidirect
80. C₂×#13133210	C₂²	semidirect
81. C₂×#13133203	C₂²	semidirect
82. #16811134	C₂²	semidirect
83. #16811134	C₂²	semidirect
84. #16811134	C₂²	semidirect
85. #16811132	C₂²	semidirect
86. C₂×#13133199	C₂²	semidirect
87. C₂×#13133196	C₂²	semidirect
88. C₂×#13133191	C₂²	semidirect
89. C₂×#13133190	C₂²	semidirect
90. C₂×#13133186	C₂²	semidirect
91. #16811104	C₂²	semidirect
92. #16811102	C₂²	semidirect
94. #16811096	C₂²	semidirect
95. #16811095	C₂²	semidirect
96. C₄×#11719945	C₂²	semidirect
97. C₄×#11719947	C₂²	semidirect
98. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
99. C₄×D₄×D₅₃	C₂²	semidirect
101. C₅₃×#518	C₂²	semidirect
102. C₅₃×#518	C₂²	semidirect
105. C₂×C₄×D₄×C₅₃	C₂²	semidirect
106. C₂×C₄×D₄×C₅₃	C₂²	semidirect
107. C₂×C₄×D₄×C₅₃	C₂²	semidirect
108. C₂×C₄×D₄×C₅₃	C₂²	semidirect
109. C₂×#117×C₅₃	C₂²	semidirect
110. C₂×#117×C₅₃	C₂²	semidirect
111. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
112. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
115. C₂×#11719945	C₂³	semidirect
116. C₂×#11719945	C₂³	semidirect
118. C₂²×Dic₁₀₆	C₂³	semidirect
119. C₂²×D₂₁₂	C₂³	semidirect
124. C₂²×C₄×D₅₃	C₂³	semidirect
125. #13133217	C₂³	semidirect
126. #13133217	C₂³	semidirect
127. #13133217	C₂³	semidirect
128. #13133216	C₂³	semidirect
129. #13133214	C₂³	semidirect
131. #13133212	C₂³	semidirect
132. #13133212	C₂³	semidirect
133. #13133211	C₂³	semidirect
137. #13133210	C₂³	semidirect
138. #13133210	C₂³	semidirect
139. #13133209	C₂³	semidirect
140. #13133209	C₂³	semidirect
141. #13133208	C₂³	semidirect
142. #13133207	C₂³	semidirect
143. #13133207	C₂³	semidirect
144. #13133205	C₂³	semidirect
145. #13133205	C₂³	semidirect
150. #13133203	C₂³	semidirect
151. #13133203	C₂³	semidirect
152. #13133202	C₂³	semidirect
153. #13133202	C₂³	semidirect
154. #13133201	C₂³	semidirect
156. #13133200	C₂³	semidirect
157. #13133200	C₂³	semidirect
161. #13133199	C₂³	semidirect
162. #13133199	C₂³	semidirect
164. #13133197	C₂³	semidirect
170. #13133196	C₂³	semidirect
171. #13133196	C₂³	semidirect
172. #13133196	C₂³	semidirect
173. #13133196	C₂³	semidirect
174. #13133195	C₂³	semidirect
175. #13133195	C₂³	semidirect
176. #13133194	C₂³	semidirect
177. #13133194	C₂³	semidirect
178. #13133192	C₂³	semidirect
184. #13133191	C₂³	semidirect
185. #13133191	C₂³	semidirect
186. #13133191	C₂³	semidirect
187. #13133191	C₂³	semidirect
191. #13133190	C₂³	semidirect
192. #13133190	C₂³	semidirect
197. #13133187	C₂³	semidirect
203. C₄×Dic₁₀₆	C₂³	semidirect
204. C₄×Dic₁₀₆	C₂³	semidirect
205. C₄×Dic₁₀₆	C₂³	semidirect
206. C₄×Dic₁₀₆	C₂³	semidirect
207. C₄×Dic₁₀₆	C₂³	semidirect
208. #13133182	C₂³	semidirect
209. C₄×D₂₁₂	C₂³	semidirect
210. C₄×D₂₁₂	C₂³	semidirect
211. C₄×D₂₁₂	C₂³	semidirect
212. C₄×D₂₁₂	C₂³	semidirect
213. C₄×D₂₁₂	C₂³	semidirect
216. #13133179	C₂³	semidirect
222. C₄×C₂²⋊D₅₃	C₂³	semidirect
223. C₄×C₂²⋊D₅₃	C₂³	semidirect
224. C₄×C₂²⋊D₅₃	C₂³	semidirect
225. C₄×C₂²⋊D₅₃	C₂³	semidirect
226. #13133177	C₂³	semidirect
227. #13133177	C₂³	semidirect
229. #13133176	C₂³	semidirect
230. #13133176	C₂³	semidirect
231. #13133175	C₂³	semidirect
232. #13133174	C₂³	semidirect
233. #13133174	C₂³	semidirect
234. #13133173	C₂³	semidirect
235. C₂×C₄⋊Dic₅₃	C₂³	semidirect
236. C₂×C₄⋊Dic₅₃	C₂³	semidirect
237. C₂×#11719919	C₂³	semidirect
238. C₂×#11719919	C₂³	semidirect
239. C₄⋊C₄×D₅₃	C₂³	semidirect
243. C₂×#11719921	C₂³	semidirect
244. C₂×#11719921	C₂³	semidirect
245. C₂²⋊C₄×D₅₃	C₂³	semidirect
246. C₂×C₄×Dic₅₃	C₂³	semidirect
247. C₄²×D₅₃	C₂³	semidirect
299. C₂×D₄×C₅₃	#41	semidirect
527. C₂×#518	D₅₃	semidirect
615. #518	C₂×D₅₃	semidirect
616. #518	C₂×D₅₃	semidirect
623. C₂×C₄×D₄	C₂×D₅₃	semidirect
624. C₂×C₄×D₄	C₂×D₅₃	semidirect
625. C₂×C₄×D₄	C₂×D₅₃	semidirect
626. C₂×C₄×D₄	C₂×D₅₃	semidirect
627. C₂×#117	C₂×D₅₃	semidirect
628. C₂×#117	C₂×D₅₃	semidirect
629. C₂²×C₂²⋊C₄	C₂×D₅₃	semidirect
630. C₂²×C₂²⋊C₄	C₂×D₅₃	semidirect
631. C₅₃	#62846	semidirect
842. C₂×D₄	#11719945	semidirect

Maximal subgroups

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

subgroup	index
#20288771	2
#20288737	2
#20288666	2
#20288643	2
#20288567	2
#20288554	2
#20288518	2
#20288479	2
#20288435	2
#20288404	2
#20288350	2
#20288137	2
#20288124	2
#20288105	2
C₂×#16811211	2
C₄×#13133262	2
C₂×C₅₃×#518	2
#62846	53