Subgroups — #27384372

Order 13568.

1062 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20274858	C₂	1	2	yes	maximal, complemented
2	#20274832	C₂	1	2	yes	maximal, complemented
3	#20274783	C₂	1	2	yes	maximal
4	#20274695	C₂	1	2	yes	maximal
5	C₄×C₄⋊#88322	C₂	1	2	yes	maximal, complemented
6	C₄×C₂²⋊#88322	C₂	1	2	yes	maximal
7	#20274461	C₂	1	2	yes	maximal, complemented
8	C₂×C₄³×C₅₃	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄⋊#88322	C₂²	1	4	yes	—
10	C₂×C₂²⋊#88322	C₂²	1	4	yes	—
11	C₂×C₄×#88322	C₂²	1	4	yes	—
12	#16810378	C₂²	1	4	yes	—
13	#16810378	C₂²	1	4	yes	—
14	#16810378	C₂²	1	4	yes	—
15	#16810378	C₂²	1	4	yes	—
16	C₂²×C₄²×C₅₃	C₄	1	1	yes	characteristic
17	C₂²×C₄²×C₅₃	C₄	1	1	yes	characteristic
18	C₂²×C₄²×C₅₃	C₄	1	1	yes	characteristic
19	C₂²×C₄²×C₅₃	C₄	1	1	yes	characteristic
20	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
23	C₄³×C₅₃	C₄	1	1	yes	characteristic
24	C₄³×C₅₃	C₄	1	1	yes	characteristic
25	C₄³×C₅₃	C₄	1	1	yes	characteristic
26	C₄³×C₅₃	C₄	1	1	yes	characteristic
27	C₄³×C₅₃	C₂²	1	1	yes	characteristic
28	C₄³×C₅₃	C₂²	1	1	yes	characteristic
29	C₄³×C₅₃	C₂²	1	1	yes	characteristic
30	C₄³×C₅₃	C₂²	1	1	yes	characteristic
31	C₂²×#88322	C₂³	1	8	yes	—
32	C₄⋊#88322	—	2	8	no	—
33	C₂²⋊#88322	—	2	8	no	—
34	C₄×#88322	—	2	8	no	—
35	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
42	C₂×C₄²×C₅₃	—	2	4	no	—
43	C₂×C₄²×C₅₃	—	2	4	no	—
44	C₂×C₄²×C₅₃	—	2	4	no	—
45	C₂×C₄²×C₅₃	—	2	4	no	—
46	C₂×C₄²×C₅₃	—	2	4	no	—
47	C₂×C₄²×C₅₃	—	2	4	no	—
48	C₂×C₄²×C₅₃	C₈	1	8	yes	complemented
49	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
77	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₅₃	—	2	2	no	—
79	C₂²×C₄×C₅₃	—	2	2	no	—
80	C₂²×C₄×C₅₃	—	2	2	no	—
81	C₂²×C₄×C₅₃	—	2	2	no	—
82	C₂²×C₄×C₅₃	—	2	2	no	—
83	C₂²×C₄×C₅₃	—	2	2	no	—
84	C₂²×C₄×C₅₃	—	2	2	no	—
85	C₂²×C₄×C₅₃	—	2	2	no	—
86	C₂²×C₄×C₅₃	—	2	2	no	—
87	C₂²×C₄×C₅₃	—	2	2	no	—
88	C₂²×C₄×C₅₃	—	2	2	no	—
89	C₂²×C₄×C₅₃	—	2	2	no	—
90	C₂²×C₄×C₅₃	—	2	2	no	—
91	C₂²×C₄×C₅₃	—	2	2	no	—
92	C₂²×C₄×C₅₃	—	2	2	no	—
93	C₂²×C₄×C₅₃	—	2	2	no	—
94	C₂²×C₄×C₅₃	C₂×C₈	1	4	yes	—
95	C₂²×C₄×C₅₃	C₂×C₈	1	4	yes	—
96	C₂²×C₄×C₅₃	C₂×C₈	1	4	yes	—
97	C₂²×C₄×C₅₃	M₁₆	1	4	yes	—
98	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₅₃	#41	1	4	yes	—
112	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
113	C₄²×C₅₃	—	2	2	no	—
114	C₄²×C₅₃	—	2	2	no	—
115	C₄²×C₅₃	—	2	2	no	—
116	C₄²×C₅₃	—	2	2	no	—
117	C₄²×C₅₃	—	2	2	no	—
118	C₄²×C₅₃	—	2	2	no	—
119	C₄²×C₅₃	—	2	2	no	—
120	C₄²×C₅₃	—	2	2	no	—
121	C₄²×C₅₃	—	2	2	no	—
122	C₄²×C₅₃	—	2	2	no	—
123	C₄²×C₅₃	—	2	2	no	—
124	C₄²×C₅₃	—	2	2	no	—
125	C₄²×C₅₃	—	2	2	no	—
126	C₄²×C₅₃	—	2	2	no	—
127	C₄²×C₅₃	—	2	2	no	—
128	C₄²×C₅₃	—	2	2	no	—
129	C₄²×C₅₃	—	2	2	no	—
130	C₄²×C₅₃	—	2	2	no	—
131	C₄²×C₅₃	—	2	2	no	—
132	C₄²×C₅₃	—	2	2	no	—
133	C₄²×C₅₃	C₂×C₈	1	4	yes	—
134	C₄²×C₅₃	C₂×C₈	1	4	yes	—
135	C₄²×C₅₃	C₂×C₈	1	4	yes	—
136	C₄²×C₅₃	C₂×C₈	1	4	yes	—
137	C₄²×C₅₃	M₁₆	1	4	yes	—
138	C₄²×C₅₃	M₁₆	1	4	yes	—
139	C₄²×C₅₃	#41	1	4	yes	—
140	C₄²×C₅₃	#41	1	4	yes	—
141	C₂×#88322	—	2	8	no	—
142	C₂×#88322	—	2	8	no	—
143	C₂×#88322	—	2	8	no	—
144	C₂³×C₅₃	—	2	1	no	—
145	C₂³×C₅₃	—	2	1	no	—
146	C₂³×C₅₃	—	2	1	no	—
147	C₂³×C₅₃	—	2	1	no	—
148	C₂³×C₅₃	#117	1	2	yes	—
149	C₂³×C₅₃	C₂²×C₈	1	2	yes	—
150	C₂³×C₅₃	C₂×M₁₆	1	2	yes	—
151	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
152	C₂×C₄×C₅₃	—	2	8	no	—
153	C₂×C₄×C₅₃	—	2	8	no	—
154	C₂×C₄×C₅₃	—	2	1	no	—
155	C₂×C₄×C₅₃	—	2	1	no	—
156	C₂×C₄×C₅₃	—	2	1	no	—
157	C₂×C₄×C₅₃	—	2	1	no	—
158	C₂×C₄×C₅₃	—	2	1	no	—
159	C₂×C₄×C₅₃	—	2	1	no	—
160	C₂×C₄×C₅₃	—	2	1	no	—
161	C₂×C₄×C₅₃	—	2	1	no	—
162	C₂×C₄×C₅₃	—	2	1	no	—
163	C₂×C₄×C₅₃	—	2	1	no	—
164	C₂×C₄×C₅₃	—	2	1	no	—
165	C₂×C₄×C₅₃	—	2	1	no	—
166	C₂×C₄×C₅₃	—	2	1	no	—
167	C₂×C₄×C₅₃	—	2	1	no	—
168	C₂×C₄×C₅₃	—	2	1	no	—
169	C₂×C₄×C₅₃	—	2	1	no	—
170	C₂×C₄×C₅₃	—	2	1	no	—
171	C₂×C₄×C₅₃	—	2	1	no	—
172	C₂×C₄×C₅₃	—	2	1	no	—
173	C₂×C₄×C₅₃	—	2	1	no	—
174	C₂×C₄×C₅₃	—	2	8	no	—
175	C₂×C₄×C₅₃	—	2	8	no	—
176	C₂×C₄×C₅₃	—	2	8	no	—
177	C₂×C₄×C₅₃	—	2	8	no	—
178	C₂×C₄×C₅₃	—	2	8	no	—
179	C₂×C₄×C₅₃	#117	1	2	yes	—
180	C₂×C₄×C₅₃	#117	1	2	yes	—
181	C₂×C₄×C₅₃	#117	1	2	yes	—
182	C₂×C₄×C₅₃	#117	1	2	yes	—
183	C₂×C₄×C₅₃	#117	1	2	yes	—
184	C₂×C₄×C₅₃	C₂²×C₈	1	2	yes	—
185	C₂×C₄×C₅₃	C₂²×C₈	1	2	yes	—
186	C₂×C₄×C₅₃	C₂²×C₈	1	2	yes	—
187	C₂×C₄×C₅₃	C₂²×C₈	1	2	yes	—
188	C₂×C₄×C₅₃	C₂²×C₈	1	2	yes	—
189	C₂×C₄×C₅₃	C₂²×C₈	1	2	yes	—
190	C₂×C₄×C₅₃	C₂×M₁₆	1	2	yes	—
191	C₂×C₄×C₅₃	C₂×M₁₆	1	2	yes	—
192	C₂×C₄×C₅₃	C₂×M₁₆	1	2	yes	—
193	C₂×C₄×C₅₃	C₂×M₁₆	1	2	yes	—
194	C₂×C₄×C₅₃	C₂×M₁₆	1	2	yes	—
195	C₂×C₄×C₅₃	C₂×M₁₆	1	2	yes	—
196	C₂×C₄×C₅₃	C₂×M₁₆	1	2	yes	—
197	C₂×C₄×C₅₃	C₂×M₁₆	1	2	yes	—
198	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
199	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
200	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
201	#88322	—	4	8	no	—
202	#20777	—	53	1	no	maximal, Sylow
203	C₂²×C₅₃	—	2	2	no	—
204	C₂²×C₅₃	—	2	2	no	—
205	C₂²×C₅₃	—	2	2	no	—
206	C₂²×C₅₃	—	2	2	no	—
207	C₂²×C₅₃	—	2	2	no	—
208	C₂²×C₅₃	—	2	2	no	—
209	C₂²×C₅₃	#431	1	4	yes	—
210	C₂²×C₅₃	C₂×#117	1	1	yes	characteristic
211	C₂²×C₅₃	C₂×#117	1	1	yes	characteristic
212	C₂²×C₅₃	C₂×#117	1	1	yes	characteristic
213	C₂²×C₅₃	C₂³×C₈	1	1	yes	characteristic
214	C₂²×C₅₃	C₂²×M₁₆	1	1	yes	characteristic
215	C₂²×C₅₃	C₂²×M₁₆	1	1	yes	characteristic
216	C₂²×C₅₃	C₂²×M₁₆	1	1	yes	characteristic
217	C₄×C₅₃	—	2	2	no	—
218	C₄×C₅₃	—	2	2	no	—
219	C₄×C₅₃	—	2	2	no	—
220	C₄×C₅₃	—	2	2	no	—
221	C₄×C₅₃	—	2	2	no	—
222	C₄×C₅₃	—	2	2	no	—
223	C₄×C₅₃	—	2	2	no	—
224	C₄×C₅₃	—	2	2	no	—
225	C₄×C₅₃	—	2	2	no	—
226	C₄×C₅₃	—	2	2	no	—
227	C₄×C₅₃	#431	1	4	yes	—
228	C₄×C₅₃	#431	1	4	yes	—
229	C₄×C₅₃	#432	1	4	yes	—
230	C₄×C₅₃	#529	1	4	yes	—
231	C₂×C₄³	D₅₃	1	1	yes	characteristic
232	#1839	—	53	2	no	—
233	#1831	—	53	2	no	—
234	#1817	—	53	2	no	—
235	#1797	—	53	2	no	—
236	C₄×C₄⋊C₈	—	53	2	no	—
237	C₄×C₂²⋊C₈	—	53	2	no	—
238	#1744	—	53	2	no	—
239	C₂×C₅₃	—	2	4	no	—
240	C₂×C₅₃	#2283	1	1	yes	characteristic
241	C₂×C₅₃	C₂×#431	1	1	yes	characteristic
242	C₂×C₅₃	C₂×#431	1	1	yes	characteristic
243	C₂×C₅₃	C₂×#431	1	1	yes	characteristic
244	C₂×C₅₃	C₂×#432	1	1	yes	characteristic
245	C₂×C₅₃	#2920	1	1	yes	characteristic
246	C₂×C₅₃	#2920	1	1	yes	characteristic
247	C₂²×C₄²	Dic₅₃	1	1	yes	characteristic
248	C₂²×C₄²	Dic₅₃	1	1	yes	characteristic
249	C₂²×C₄²	Dic₅₃	1	1	yes	characteristic
250	C₂²×C₄²	Dic₅₃	1	1	yes	characteristic
251	C₂²×C₄²	C₂×D₅₃	1	1	yes	characteristic
252	C₂²×C₄²	C₂×D₅₃	1	1	yes	characteristic
253	C₂²×C₄²	C₂×D₅₃	1	1	yes	characteristic
254	C₂×C₄⋊C₈	—	53	4	no	—
255	C₂×C₂²⋊C₈	—	53	4	no	—
256	C₂×C₄×C₈	—	53	4	no	—
257	C₄³	Dic₅₃	1	1	yes	characteristic
258	C₄³	Dic₅₃	1	1	yes	characteristic
259	C₄³	Dic₅₃	1	1	yes	characteristic
260	C₄³	Dic₅₃	1	1	yes	characteristic
261	C₄³	C₂×D₅₃	1	1	yes	characteristic
262	C₄³	C₂×D₅₃	1	1	yes	characteristic
263	C₄³	C₂×D₅₃	1	1	yes	characteristic
264	C₄³	C₂×D₅₃	1	1	yes	characteristic
265	#336	—	53	4	no	—
266	#336	—	53	4	no	—
267	#336	—	53	4	no	—
268	#336	—	53	4	no	—
269	C₅₃	#20777	1	1	yes	characteristic, complemented, Sylow
270	C₂³×C₄	C₂×Dic₅₃	1	1	yes	characteristic
271	C₂³×C₄	C₂×Dic₅₃	1	1	yes	characteristic
272	C₂³×C₄	C₂×Dic₅₃	1	1	yes	characteristic
273	C₂³×C₄	C₂×Dic₅₃	1	1	yes	characteristic
274	C₂³×C₄	C₂×Dic₅₃	1	1	yes	characteristic
275	C₂³×C₄	C₂×Dic₅₃	1	1	yes	characteristic
276	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
277	C₂²×C₈	—	53	8	no	—
278	C₂×C₄²	—	2	4	no	—
279	C₂×C₄²	—	2	4	no	—
280	C₂×C₄²	—	2	4	no	—
281	C₂×C₄²	—	2	4	no	—
282	C₂×C₄²	—	2	4	no	—
283	C₂×C₄²	—	2	4	no	—
284	C₂×C₄²	#88322	1	8	yes	complemented
285	C₂×C₄²	C₂×Dic₅₃	1	1	yes	characteristic
286	C₂×C₄²	C₂×Dic₅₃	1	1	yes	characteristic
287	C₂×C₄²	C₂×Dic₅₃	1	1	yes	characteristic
288	C₂×C₄²	C₂×Dic₅₃	1	1	yes	characteristic
289	C₂×C₄²	C₂×Dic₅₃	1	1	yes	characteristic
290	C₂×C₄²	C₂×Dic₅₃	1	1	yes	characteristic
291	C₂×C₄²	C₂×Dic₅₃	1	1	yes	characteristic
292	C₂×C₄²	C₂×Dic₅₃	1	1	yes	characteristic
293	C₂×C₄²	C₂×Dic₅₃	1	1	yes	characteristic
294	C₂×C₄²	C₂×Dic₅₃	1	1	yes	characteristic
295	C₂×C₄²	C₂×Dic₅₃	1	1	yes	characteristic
296	C₂×C₄²	C₂×Dic₅₃	1	1	yes	characteristic
297	C₂×C₄²	C₂×Dic₅₃	1	1	yes	characteristic
298	C₂×C₄²	C₂×Dic₅₃	1	1	yes	characteristic
299	C₂×C₄²	C₂×Dic₅₃	1	1	yes	characteristic
300	C₂×C₄²	C₂×Dic₅₃	1	1	yes	characteristic
301	C₂×C₄²	C₂×Dic₅₃	1	1	yes	characteristic
302	C₂×C₄²	C₂×Dic₅₃	1	1	yes	characteristic
303	C₂×C₄²	C₂×Dic₅₃	1	1	yes	characteristic
304	C₂×C₄²	C₂×Dic₅₃	1	1	yes	characteristic
305	C₂×C₄²	C₂×Dic₅₃	1	1	yes	characteristic
306	C₂×C₄²	C₂×Dic₅₃	1	1	yes	characteristic
307	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
308	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
309	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
310	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
311	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
312	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
313	C₄⋊C₈	—	106	8	no	—
314	C₂²⋊C₈	—	106	8	no	—
315	C₄×C₈	—	106	8	no	—
316	C₂⁴	C₂²×Dic₅₃	1	1	yes	characteristic
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	C₂×#88322	1	4	yes	—
334	C₂²×C₄	C₂×#88322	1	4	yes	—
335	C₂²×C₄	C₂×#88322	1	4	yes	—
336	C₂²×C₄	#11719917	1	4	yes	—
337	C₂²×C₄	#11719945	1	4	yes	—
338	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
339	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
340	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
341	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
342	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
343	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
344	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
345	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
346	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
347	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
348	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
349	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
350	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
351	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
352	C₂×C₈	—	106	8	no	—
353	C₂×C₈	—	106	8	no	—
354	C₂×C₈	—	106	8	no	—
355	C₄²	—	2	2	no	—
356	C₄²	—	2	2	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	2	2	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	C₂×#88322	1	4	yes	—
376	C₄²	C₂×#88322	1	4	yes	—
377	C₄²	C₂×#88322	1	4	yes	—
378	C₄²	C₂×#88322	1	4	yes	—
379	C₄²	#11719917	1	4	yes	—
380	C₄²	#11719917	1	4	yes	—
381	C₄²	#11719945	1	4	yes	—
382	C₄²	#11719945	1	4	yes	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	1	no	—
387	C₂³	#13133176	1	2	yes	—
388	C₂³	C₂²×#88322	1	2	yes	—
389	C₂³	C₂×#11719917	1	2	yes	—
390	C₂³	C₂³×Dic₅₃	1	1	yes	characteristic
391	C₂×C₄	—	2	8	no	—
392	C₂×C₄	—	2	8	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	8	no	—
414	C₂×C₄	—	2	8	no	—
415	C₂×C₄	—	2	8	no	—
416	C₂×C₄	—	2	8	no	—
417	C₂×C₄	—	2	8	no	—
418	C₂×C₄	#13133176	1	2	yes	—
419	C₂×C₄	#13133176	1	2	yes	—
420	C₂×C₄	#13133176	1	2	yes	—
421	C₂×C₄	#13133176	1	2	yes	—
422	C₂×C₄	#13133176	1	2	yes	—
423	C₂×C₄	C₂²×#88322	1	2	yes	—
424	C₂×C₄	C₂²×#88322	1	2	yes	—
425	C₂×C₄	C₂²×#88322	1	2	yes	—
426	C₂×C₄	C₂²×#88322	1	2	yes	—
427	C₂×C₄	C₂²×#88322	1	2	yes	—
428	C₂×C₄	C₂²×#88322	1	2	yes	—
429	C₂×C₄	C₂×#11719917	1	2	yes	—
430	C₂×C₄	C₂×#11719917	1	2	yes	—
431	C₂×C₄	C₂×#11719917	1	2	yes	—
432	C₂×C₄	C₂×#11719917	1	2	yes	—
433	C₂×C₄	C₂×#11719917	1	2	yes	—
434	C₂×C₄	C₂×#11719917	1	2	yes	—
435	C₂×C₄	C₂×#11719917	1	2	yes	—
436	C₂×C₄	C₂×#11719917	1	2	yes	—
437	C₂×C₄	C₂×#11719945	1	2	yes	—
438	C₂×C₄	C₂×#11719945	1	2	yes	—
439	C₂×C₄	C₂×#11719945	1	2	yes	—
440	C₈	—	212	8	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	2	no	—
447	C₂²	#16810676	1	4	yes	—
448	C₂²	C₂×#13133176	1	1	yes	characteristic
449	C₂²	C₂×#13133176	1	1	yes	characteristic
450	C₂²	C₂×#13133176	1	1	yes	characteristic
451	C₂²	C₂³×#88322	1	1	yes	characteristic
452	C₂²	C₂²×#11719917	1	1	yes	characteristic
453	C₂²	C₂²×#11719917	1	1	yes	characteristic
454	C₂²	C₂²×#11719917	1	1	yes	characteristic
455	C₄	—	2	2	no	—
456	C₄	—	2	2	no	—
457	C₄	—	2	2	no	—
458	C₄	—	2	2	no	—
459	C₄	—	2	2	no	—
460	C₄	—	2	2	no	—
461	C₄	—	2	2	no	—
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	2	2	no	—
465	C₄	#16810676	1	4	yes	—
466	C₄	#16810676	1	4	yes	—
467	C₄	#16810680	1	4	yes	—
468	C₄	#16811157	1	4	yes	—
469	C₂	—	2	4	no	—
470	C₂	#20277113	1	1	yes	characteristic
471	C₂	C₂×#16810676	1	1	yes	characteristic
472	C₂	C₂×#16810676	1	1	yes	characteristic
473	C₂	C₂×#16810676	1	1	yes	characteristic
474	C₂	C₂×#16810680	1	1	yes	characteristic
475	C₂	#20283348	1	1	yes	characteristic
476	C₂	#20283348	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄²	C₂²×D₅₃
commutator	C₂²×C₅₃	C₂³×C₈
Frattini	C₂²×C₄	C₂³×D₅₃
Fitting	C₂×C₄³×C₅₃	C₂
socle	C₂³×C₅₃	C₂³×C₄
prime radical	C₂⁴×C₅₃	C₂²×C₄
cosocle	C₂²×C₄×C₅₃	C₂⁴
hypercenter	C₂×C₄³	D₅₃
hypocenter	C₅₃	#20777
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₄³

Complements

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

N	H ≅ G/N	type
1. #20274858	C₂	semidirect
2. #20274832	C₂	semidirect
5. C₄×C₄⋊#88322	C₂	semidirect
7. #20274461	C₂	semidirect
48. C₂×C₄²×C₅₃	C₈	semidirect
269. C₅₃	#20777	semidirect
284. C₂×C₄²	#88322	semidirect

Maximal subgroups

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

subgroup	index
#20274858	2
#20274832	2
#20274783	2
#20274695	2
C₄×C₄⋊#88322	2
C₄×C₂²⋊#88322	2
#20274461	2
C₂×C₄³×C₅₃	2
#20777	53