Subgroups — #27292350

Order 13568.

886 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16810493	C₂	1	1	yes	maximal, characteristic
2	C₂×#16810385	C₂	1	2	yes	maximal
3	C₂×#16810385	C₂	1	2	yes	maximal
4	C₂×#16810378	C₂	1	1	yes	maximal, characteristic
5	C₅₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
6	C₂³×#88322	C₂²	1	2	yes	—
7	C₂²×C₄⋊Dic₅₃	—	2	1	no	—
8	C₂²×C₄⋊Dic₅₃	—	2	1	no	—
9	C₂²×C₄⋊Dic₅₃	C₂²	1	2	yes	—
10	#16810493	—	2	4	no	—
11	#16810385	—	2	4	no	—
12	#16810385	—	2	4	no	—
13	#16810378	C₄	1	4	yes	complemented
14	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
17	C₂×#95×C₅₃	—	2	1	no	—
18	C₂×#95×C₅₃	—	2	1	no	—
19	C₂³×Dic₅₃	—	2	2	no	—
20	C₂²×#88322	—	2	2	no	—
21	C₂²×#88322	—	2	2	no	—
22	C₂²×#88322	—	2	2	no	—
23	C₂²×#88322	—	2	2	no	—
24	C₂²×#88322	—	2	2	no	—
25	C₂²×#88322	—	2	2	no	—
26	C₂²×#88322	C₂×C₄	1	4	yes	—
27	C₂×C₄⋊Dic₅₃	—	2	4	no	—
28	C₂×C₄⋊Dic₅₃	—	2	4	no	—
29	C₂×C₄⋊Dic₅₃	—	2	2	no	—
30	C₂×C₄⋊Dic₅₃	—	2	2	no	—
31	C₂×C₄⋊Dic₅₃	—	2	2	no	—
32	C₂×C₄⋊Dic₅₃	—	2	2	no	—
33	C₂×C₄⋊Dic₅₃	—	2	2	no	—
34	C₂×C₄⋊Dic₅₃	—	4	2	no	—
35	C₂×C₄⋊Dic₅₃	—	4	2	no	—
36	C₂×C₄⋊Dic₅₃	—	4	2	no	—
37	C₂×C₄⋊Dic₅₃	—	4	2	no	—
38	C₂×C₄⋊Dic₅₃	D₄	1	4	yes	—
39	C₂³×C₄×C₅₃	—	2	1	no	—
40	C₂³×C₄×C₅₃	—	2	1	no	—
41	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
44	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
45	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
46	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
47	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
48	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
49	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
50	C₂×C₄⋊C₄×C₅₃	D₄	1	2	yes	—
51	C₂×C₄⋊C₄×C₅₃	Q₈	1	2	yes	—
52	C₂×C₄²×C₅₃	—	2	2	no	—
53	C₂×C₄²×C₅₃	—	2	2	no	—
54	C₂×C₄²×C₅₃	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₅₃	Q₈	1	2	yes	—
56	#95×C₅₃	—	4	2	no	—
57	#95×C₅₃	—	4	2	no	—
58	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₅₃	—	2	1	no	—
60	C₂²×C₄×C₅₃	—	2	1	no	—
61	C₂²×C₄×C₅₃	—	2	1	no	—
62	C₂²×C₄×C₅₃	—	2	1	no	—
63	C₂²×C₄×C₅₃	—	2	1	no	—
64	C₂²×C₄×C₅₃	—	2	1	no	—
65	C₂²×C₄×C₅₃	—	2	1	no	—
66	C₂²×C₄×C₅₃	—	2	1	no	—
67	C₂²×C₄×C₅₃	—	2	2	no	—
68	C₂²×C₄×C₅₃	—	2	2	no	—
69	C₂²×C₄×C₅₃	—	4	1	no	—
70	C₂²×C₄×C₅₃	—	4	1	no	—
71	C₂²×C₄×C₅₃	—	4	1	no	—
72	C₂²×C₄×C₅₃	—	4	1	no	—
73	C₂²×C₄×C₅₃	—	4	1	no	—
74	C₂²×C₄×C₅₃	—	4	1	no	—
75	C₂²×C₄×C₅₃	—	4	1	no	—
76	C₂²×C₄×C₅₃	—	4	1	no	—
77	C₂²×C₄×C₅₃	—	4	1	no	—
78	C₂²×C₄×C₅₃	—	4	1	no	—
79	C₂²×C₄×C₅₃	—	4	1	no	—
80	C₂²×C₄×C₅₃	—	4	1	no	—
81	C₂²×C₄×C₅₃	C₄⋊C₄	1	2	yes	—
82	C₂²×C₄×C₅₃	C₄⋊C₄	1	2	yes	—
83	C₂²×C₄×C₅₃	D₈	1	2	yes	—
84	C₂²×C₄×C₅₃	SD₁₆	1	2	yes	—
85	C₂²×C₄×C₅₃	SD₁₆	1	2	yes	—
86	C₂²×C₄×C₅₃	Q₁₆	1	2	yes	—
87	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
91	C₂²×C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
92	C₂²×C₄×C₅₃	#41	1	2	yes	—
93	C₂²×C₄×C₅₃	#41	1	2	yes	—
94	C₂²×C₄×C₅₃	#41	1	2	yes	—
95	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
96	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
97	C₂²×Dic₅₃	—	2	4	no	—
98	C₂²×Dic₅₃	—	4	2	no	—
99	C₂²×Dic₅₃	—	4	2	no	—
100	C₂²×Dic₅₃	—	4	2	no	—
101	C₂²×Dic₅₃	—	4	2	no	—
102	C₂²×Dic₅₃	—	4	2	no	—
103	C₂²×Dic₅₃	—	4	2	no	—
104	C₄⋊C₄×C₅₃	—	2	4	no	—
105	C₄⋊C₄×C₅₃	—	2	4	no	—
106	C₄⋊C₄×C₅₃	—	4	2	no	—
107	C₄⋊C₄×C₅₃	—	4	2	no	—
108	C₄²×C₅₃	—	2	4	no	—
109	C₄²×C₅₃	—	2	4	no	—
110	C₄⋊Dic₅₃	—	2	4	no	—
111	C₄⋊Dic₅₃	—	2	4	no	—
112	C₄⋊Dic₅₃	—	4	8	no	—
113	C₄⋊Dic₅₃	—	4	8	no	—
114	C₄⋊Dic₅₃	—	4	2	no	—
115	C₄⋊Dic₅₃	—	4	2	no	—
116	C₂×#88322	—	2	4	no	—
117	C₂×#88322	—	2	4	no	—
118	C₂×#88322	—	2	4	no	—
119	C₂×#88322	—	4	2	no	—
120	C₂×#88322	—	4	2	no	—
121	C₂×#88322	—	4	2	no	—
122	C₂×#88322	—	4	2	no	—
123	C₂³×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
124	C₂³×C₅₃	#120	1	1	yes	characteristic
125	C₂³×C₅₃	#121	1	1	yes	characteristic
126	C₂³×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
127	C₂³×C₅₃	#123	1	1	yes	characteristic
128	C₂³×C₅₃	#124	1	1	yes	characteristic
129	C₂³×C₅₃	#124	1	1	yes	characteristic
130	C₂³×C₅₃	C₂×D₈	1	1	yes	characteristic
131	C₂³×C₅₃	C₂×SD₁₆	1	1	yes	characteristic
132	C₂³×C₅₃	C₂×SD₁₆	1	1	yes	characteristic
133	C₂³×C₅₃	C₂×Q₁₆	1	1	yes	characteristic
134	C₂³×C₅₃	AGL(1,ℤ/8)	1	1	yes	characteristic
135	C₂³×C₅₃	AGL(1,ℤ/8)	1	1	yes	characteristic
136	C₂³×C₅₃	#137	1	1	yes	characteristic
137	C₂³×C₅₃	#137	1	1	yes	characteristic
138	C₂×C₄×C₅₃	—	2	2	no	—
139	C₂×C₄×C₅₃	—	2	2	no	—
140	C₂×C₄×C₅₃	—	2	2	no	—
141	C₂×C₄×C₅₃	—	2	2	no	—
142	C₂×C₄×C₅₃	—	2	2	no	—
143	C₂×C₄×C₅₃	—	2	2	no	—
144	C₂×C₄×C₅₃	—	2	2	no	—
145	C₂×C₄×C₅₃	—	2	2	no	—
146	C₂×C₄×C₅₃	—	2	2	no	—
147	C₂×C₄×C₅₃	—	2	2	no	—
148	C₂×C₄×C₅₃	—	2	2	no	—
149	C₂×C₄×C₅₃	—	2	2	no	—
150	C₂×C₄×C₅₃	—	4	2	no	—
151	C₂×C₄×C₅₃	—	4	2	no	—
152	C₂×C₄×C₅₃	—	4	2	no	—
153	C₂×C₄×C₅₃	—	4	2	no	—
154	C₂×C₄×C₅₃	—	4	2	no	—
155	C₂×C₄×C₅₃	—	4	2	no	—
156	C₂×C₄×C₅₃	—	8	1	no	—
157	C₂×C₄×C₅₃	—	8	1	no	—
158	C₂×C₄×C₅₃	—	8	1	no	—
159	C₂×C₄×C₅₃	—	8	1	no	—
160	C₂×C₄×C₅₃	—	8	1	no	—
161	C₂×C₄×C₅₃	—	8	1	no	—
162	C₂×C₄×C₅₃	—	8	1	no	—
163	C₂×C₄×C₅₃	—	8	1	no	—
164	C₂×C₄×C₅₃	#106	1	4	yes	—
165	C₂×C₄×C₅₃	#107	1	4	yes	—
166	C₂×C₄×C₅₃	#117	1	2	yes	—
167	C₂×C₄×C₅₃	C₄×D₄	1	2	yes	—
168	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₅₃	C₄×Q₈	1	1	yes	characteristic
170	C₂×C₄×C₅₃	#121	1	2	yes	—
171	C₂×C₄×C₅₃	C₂²⋊Q₈	1	2	yes	—
172	C₂×C₄×C₅₃	C₂²⋊Q₈	1	2	yes	—
173	C₂×C₄×C₅₃	#123	1	2	yes	—
174	C₂×C₄×C₅₃	#123	1	2	yes	—
175	C₂×C₄×C₅₃	#124	1	2	yes	—
176	C₂×C₄×C₅₃	#125	1	2	yes	—
177	C₂×C₄×C₅₃	#125	1	2	yes	—
178	C₂×C₄×C₅₃	#125	1	1	yes	characteristic
179	C₂×C₄×C₅₃	#126	1	2	yes	—
180	C₂×C₄×C₅₃	#126	1	2	yes	—
181	C₂×C₄×C₅₃	C₄⋊Q₈	1	1	yes	characteristic
182	C₂×Dic₅₃	—	4	4	no	—
183	C₂×Dic₅₃	—	4	4	no	—
184	C₂×Dic₅₃	—	4	4	no	—
185	C₂×Dic₅₃	—	8	2	no	—
186	C₂×Dic₅₃	—	8	2	no	—
187	C₂×Dic₅₃	—	8	2	no	—
188	C₂×Dic₅₃	—	8	2	no	—
189	#88322	—	4	4	no	—
190	#11267	—	53	1	no	maximal, Sylow
191	C₂²×C₅₃	#382	1	1	yes	characteristic
192	C₂²×C₅₃	#385	1	1	yes	characteristic
193	C₂²×C₅₃	#389	1	1	yes	characteristic
194	C₂²×C₅₃	#393	1	1	yes	characteristic
195	C₂²×C₅₃	#394	1	1	yes	characteristic
196	C₂²×C₅₃	#397	1	1	yes	characteristic
197	C₂²×C₅₃	#400	1	1	yes	characteristic
198	C₂²×C₅₃	C₂×#106	1	1	yes	characteristic
199	C₂²×C₅₃	C₂×#107	1	1	yes	characteristic
200	C₂²×C₅₃	#428	1	1	yes	characteristic
201	C₂²×C₅₃	#428	1	1	yes	characteristic
202	C₂²×C₅₃	#447	1	1	yes	characteristic
203	C₂²×C₅₃	#448	1	1	yes	characteristic
204	C₂²×C₅₃	#450	1	1	yes	characteristic
205	C₂²×C₅₃	#451	1	1	yes	characteristic
206	C₂²×C₅₃	#459	1	1	yes	characteristic
207	C₂²×C₅₃	#460	1	1	yes	characteristic
208	C₂²×C₅₃	#461	1	1	yes	characteristic
209	C₂²×C₅₃	#462	1	1	yes	characteristic
210	C₂²×C₅₃	#474	1	1	yes	characteristic
211	C₂²×C₅₃	#475	1	1	yes	characteristic
212	C₂²×C₅₃	#476	1	1	yes	characteristic
213	C₂²×C₅₃	#477	1	1	yes	characteristic
214	C₂²×C₅₃	#480	1	1	yes	characteristic
215	C₂²×C₅₃	#481	1	1	yes	characteristic
216	C₂²×C₅₃	#483	1	1	yes	characteristic
217	C₂²×C₅₃	#484	1	1	yes	characteristic
218	C₂²×C₅₃	#486	1	1	yes	characteristic
219	C₂²×C₅₃	#486	1	1	yes	characteristic
220	C₂²×C₅₃	#487	1	1	yes	characteristic
221	C₂²×C₅₃	#487	1	1	yes	characteristic
222	C₂²×C₅₃	#489	1	1	yes	characteristic
223	C₂²×C₅₃	#489	1	1	yes	characteristic
224	C₂²×C₅₃	#490	1	1	yes	characteristic
225	C₂²×C₅₃	#491	1	1	yes	characteristic
226	C₄×C₅₃	—	2	4	no	—
227	C₄×C₅₃	—	2	4	no	—
228	C₄×C₅₃	—	8	2	no	—
229	C₄×C₅₃	—	8	2	no	—
230	C₄×C₅₃	#387	1	2	yes	—
231	C₄×C₅₃	#388	1	2	yes	—
232	C₄×C₅₃	#398	1	2	yes	—
233	C₄×C₅₃	#400	1	2	yes	—
234	Dic₅₃	—	8	4	no	—
235	C₂×#384	—	53	1	no	—
236	C₂×#340	—	53	2	no	—
237	C₂×#340	—	53	2	no	—
238	C₂×#336	—	53	1	no	—
239	C₄⋊#95	D₅₃	1	1	yes	characteristic
240	C₂×C₅₃	#1442	1	1	yes	characteristic
241	C₂×C₅₃	#1834	1	1	yes	characteristic
242	C₂×C₅₃	#1836	1	1	yes	characteristic
243	C₂×C₅₃	#1852	1	1	yes	characteristic
244	C₂×C₅₃	#1853	1	1	yes	characteristic
245	C₂×C₅₃	#1947	1	1	yes	characteristic
246	C₂×C₅₃	#1948	1	1	yes	characteristic
247	C₂×C₅₃	#2023	1	1	yes	characteristic
248	C₂×C₅₃	#2024	1	1	yes	characteristic
249	C₂×C₅₃	#2041	1	1	yes	characteristic
250	C₂×C₅₃	#2043	1	1	yes	characteristic
251	C₂×C₅₃	#2071	1	1	yes	characteristic
252	C₂×C₅₃	#2072	1	1	yes	characteristic
253	C₂×C₅₃	#2099	1	1	yes	characteristic
254	C₂×C₅₃	#2100	1	1	yes	characteristic
255	C₂³×C₈	—	53	2	no	—
256	C₂²×C₄⋊C₄	—	53	2	no	—
257	C₂²×C₄⋊C₄	—	106	1	no	—
258	C₂²×C₄⋊C₄	—	106	1	no	—
259	C₂²×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
260	C₂²×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
261	C₂²×C₄²	C₂×D₅₃	1	1	yes	characteristic
262	#384	—	106	4	no	—
263	C₂×#95	—	2	1	no	—
264	C₂×#95	—	2	1	no	—
265	#340	—	106	4	no	—
266	#340	—	106	4	no	—
267	#336	—	53	4	no	—
268	C₅₃	#11267	1	1	yes	characteristic, complemented, Sylow
269	C₂³×C₄	—	2	1	no	—
270	C₂³×C₄	—	2	1	no	—
271	C₂³×C₄	—	106	2	no	—
272	C₂³×C₄	C₂²⋊D₅₃	1	1	yes	characteristic
273	C₂³×C₄	C₂²⋊D₅₃	1	1	yes	characteristic
274	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
275	C₂²×C₈	—	53	4	no	—
276	C₂²×C₈	—	106	2	no	—
277	C₂²×C₈	—	106	2	no	—
278	C₂²×C₈	—	106	2	no	—
279	C₂²×C₈	—	106	2	no	—
280	C₂²×C₈	—	106	2	no	—
281	C₂²×C₈	—	106	2	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	53	4	no	—
289	C₂×C₄⋊C₄	—	106	2	no	—
290	C₂×C₄⋊C₄	—	106	2	no	—
291	C₂×C₄⋊C₄	—	106	2	no	—
292	C₂×C₄⋊C₄	—	106	2	no	—
293	C₂×C₄⋊C₄	—	106	4	no	—
294	C₂×C₄⋊C₄	—	106	4	no	—
295	C₂×C₄⋊C₄	—	106	2	no	—
296	C₂×C₄⋊C₄	—	212	2	no	—
297	C₂×C₄⋊C₄	—	212	2	no	—
298	C₂×C₄⋊C₄	—	212	2	no	—
299	C₂×C₄⋊C₄	—	212	2	no	—
300	C₂×C₄⋊C₄	Dic₁₀₆	1	2	yes	—
301	C₂×C₄⋊C₄	D₂₁₂	1	2	yes	—
302	C₂×C₄²	—	2	2	no	—
303	C₂×C₄²	—	2	2	no	—
304	C₂×C₄²	Dic₁₀₆	1	2	yes	—
305	C₂×C₄²	C₄×D₅₃	1	2	yes	—
306	#95	—	4	2	no	—
307	#95	—	4	2	no	—
308	C₂⁴	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	4	1	no	—
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	—	4	1	no	—
324	C₂²×C₄	—	4	1	no	—
325	C₂²×C₄	—	4	1	no	—
326	C₂²×C₄	—	4	1	no	—
327	C₂²×C₄	—	4	1	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	—	106	4	no	—
332	C₂²×C₄	—	212	2	no	—
333	C₂²×C₄	—	212	2	no	—
334	C₂²×C₄	—	212	2	no	—
335	C₂²×C₄	—	212	2	no	—
336	C₂²×C₄	—	212	2	no	—
337	C₂²×C₄	—	212	2	no	—
338	C₂²×C₄	#11719919	1	2	yes	—
339	C₂²×C₄	#11719919	1	2	yes	—
340	C₂²×C₄	#11719922	1	2	yes	—
341	C₂²×C₄	#11719923	1	2	yes	—
342	C₂²×C₄	#11719924	1	2	yes	—
343	C₂²×C₄	#11719925	1	2	yes	—
344	C₂²×C₄	C₂×Dic₁₀₆	1	1	yes	characteristic
345	C₂²×C₄	C₂×Dic₁₀₆	1	1	yes	characteristic
346	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₂₁₂	1	1	yes	characteristic
348	C₂²×C₄	#11719945	1	1	yes	characteristic
349	C₂²×C₄	#11719945	1	1	yes	characteristic
350	C₂²×C₄	D₄×D₅₃	1	2	yes	—
351	C₂²×C₄	#11719947	1	2	yes	—
352	C₂²×C₄	#11719947	1	2	yes	—
353	C₂²×C₄	#11719949	1	2	yes	—
354	C₂×C₈	—	106	4	no	—
355	C₂×C₈	—	106	4	no	—
356	C₂×C₈	—	106	4	no	—
357	C₂×C₈	—	212	2	no	—
358	C₂×C₈	—	212	2	no	—
359	C₂×C₈	—	212	2	no	—
360	C₂×C₈	—	212	2	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	4	no	—
363	C₄⋊C₄	—	4	2	no	—
364	C₄⋊C₄	—	4	2	no	—
365	C₄⋊C₄	—	106	4	no	—
366	C₄⋊C₄	—	106	4	no	—
367	C₄⋊C₄	—	212	8	no	—
368	C₄⋊C₄	—	212	8	no	—
369	C₄⋊C₄	—	212	2	no	—
370	C₄⋊C₄	—	212	2	no	—
371	C₄²	—	2	4	no	—
372	C₄²	—	2	4	no	—
373	C₂³	C₂×#11719919	1	1	yes	characteristic
374	C₂³	#13133185	1	1	yes	characteristic
375	C₂³	#13133191	1	1	yes	characteristic
376	C₂³	#13133196	1	1	yes	characteristic
377	C₂³	#13133198	1	1	yes	characteristic
378	C₂³	#13133204	1	1	yes	characteristic
379	C₂³	#13133206	1	1	yes	characteristic
380	C₂³	C₂×#11719922	1	1	yes	characteristic
381	C₂³	C₂×#11719924	1	1	yes	characteristic
382	C₂³	C₂×#11719923	1	1	yes	characteristic
383	C₂³	C₂×#11719925	1	1	yes	characteristic
384	C₂³	#13133242	1	1	yes	characteristic
385	C₂³	#13133242	1	1	yes	characteristic
386	C₂³	#13133247	1	1	yes	characteristic
387	C₂³	#13133247	1	1	yes	characteristic
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	8	1	no	—
407	C₂×C₄	—	8	1	no	—
408	C₂×C₄	—	8	1	no	—
409	C₂×C₄	—	8	1	no	—
410	C₂×C₄	—	8	1	no	—
411	C₂×C₄	—	8	1	no	—
412	C₂×C₄	—	8	1	no	—
413	C₂×C₄	—	8	1	no	—
414	C₂×C₄	—	424	2	no	—
415	C₂×C₄	—	424	2	no	—
416	C₂×C₄	—	424	2	no	—
417	C₂×C₄	—	424	2	no	—
418	C₂×C₄	—	212	4	no	—
419	C₂×C₄	—	212	4	no	—
420	C₂×C₄	—	212	4	no	—
421	C₂×C₄	#13133148	1	4	yes	—
422	C₂×C₄	#13133150	1	4	yes	—
423	C₂×C₄	#13133175	1	2	yes	—
424	C₂×C₄	#13133177	1	2	yes	—
425	C₂×C₄	C₄×D₂₁₂	1	1	yes	characteristic
426	C₂×C₄	C₄×Dic₁₀₆	1	1	yes	characteristic
427	C₂×C₄	#13133192	1	2	yes	—
428	C₂×C₄	#13133194	1	2	yes	—
429	C₂×C₄	#13133194	1	2	yes	—
430	C₂×C₄	#13133201	1	2	yes	—
431	C₂×C₄	#13133202	1	2	yes	—
432	C₂×C₄	#13133203	1	2	yes	—
433	C₂×C₄	#13133208	1	2	yes	—
434	C₂×C₄	#13133208	1	2	yes	—
435	C₂×C₄	#13133209	1	1	yes	characteristic
436	C₂×C₄	#13133210	1	2	yes	—
437	C₂×C₄	#13133212	1	2	yes	—
438	C₂×C₄	#13133217	1	1	yes	characteristic
439	C₈	—	212	4	no	—
440	C₂²	#16810488	1	1	yes	characteristic
441	C₂²	#16810495	1	1	yes	characteristic
442	C₂²	#16810521	1	1	yes	characteristic
443	C₂²	#16810535	1	1	yes	characteristic
444	C₂²	#16810540	1	1	yes	characteristic
445	C₂²	#16810548	1	1	yes	characteristic
446	C₂²	#16810562	1	1	yes	characteristic
447	C₂²	C₂×#13133148	1	1	yes	characteristic
448	C₂²	C₂×#13133150	1	1	yes	characteristic
449	C₂²	#16810666	1	1	yes	characteristic
450	C₂²	#16810666	1	1	yes	characteristic
451	C₂²	#16810756	1	1	yes	characteristic
452	C₂²	#16810761	1	1	yes	characteristic
453	C₂²	#16810773	1	1	yes	characteristic
454	C₂²	#16810778	1	1	yes	characteristic
455	C₂²	#16810818	1	1	yes	characteristic
456	C₂²	#16810823	1	1	yes	characteristic
457	C₂²	#16810828	1	1	yes	characteristic
458	C₂²	#16810833	1	1	yes	characteristic
459	C₂²	#16810903	1	1	yes	characteristic
460	C₂²	#16810908	1	1	yes	characteristic
461	C₂²	#16810913	1	1	yes	characteristic
462	C₂²	#16810918	1	1	yes	characteristic
463	C₂²	#16810934	1	1	yes	characteristic
464	C₂²	#16810939	1	1	yes	characteristic
465	C₂²	#16810951	1	1	yes	characteristic
466	C₂²	#16810956	1	1	yes	characteristic
467	C₂²	#16810969	1	1	yes	characteristic
468	C₂²	#16810971	1	1	yes	characteristic
469	C₂²	#16810973	1	1	yes	characteristic
470	C₂²	#16810975	1	1	yes	characteristic
471	C₂²	#16810982	1	1	yes	characteristic
472	C₂²	#16810982	1	1	yes	characteristic
473	C₂²	#16810989	1	1	yes	characteristic
474	C₂²	#16810993	1	1	yes	characteristic
475	C₄	—	2	4	no	—
476	C₄	—	2	4	no	—
477	C₄	—	8	2	no	—
478	C₄	—	8	2	no	—
479	C₄	—	424	4	no	—
480	C₄	#16810510	1	2	yes	—
481	C₄	#16810515	1	2	yes	—
482	C₄	#16810555	1	2	yes	—
483	C₄	#16810565	1	2	yes	—
484	C₂	#20272971	1	1	yes	characteristic
485	C₂	#20274842	1	1	yes	characteristic
486	C₂	#20274848	1	1	yes	characteristic
487	C₂	#20274902	1	1	yes	characteristic
488	C₂	#20274907	1	1	yes	characteristic
489	C₂	#20275473	1	1	yes	characteristic
490	C₂	#20275478	1	1	yes	characteristic
491	C₂	#20275851	1	1	yes	characteristic
492	C₂	#20275856	1	1	yes	characteristic
493	C₂	#20275949	1	1	yes	characteristic
494	C₂	#20275961	1	1	yes	characteristic
495	C₂	#20276118	1	1	yes	characteristic
496	C₂	#20276123	1	1	yes	characteristic
497	C₂	#20276273	1	1	yes	characteristic
498	C₂	#20276278	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₅₃
commutator	C₂²×C₄×C₅₃	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₅₃
Fitting	C₅₃×C₄⋊#95	C₂
socle, prime radical	C₂⁴×C₅₃	C₂×D₄
cosocle	C₂³×C₄×C₅₃	C₂³
hypercenter	C₄⋊#95	D₅₃
hypocenter	C₅₃	#11267
LCS	G ▷ C₂²×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₄⋊#95

Complements

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

N	H ≅ G/N	type
13. #16810378	C₄	semidirect
268. C₅₃	#11267	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16810493	2
C₂×#16810385	2
C₂×#16810378	2
C₅₃×C₄⋊#95	2
#11267	53