Subgroups — #28328330

Order 13568.

734 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅₃⋊M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#13133291	C₂	1	1	yes	maximal, characteristic, complemented
3	#20291100	C₂	1	2	yes	maximal, complemented
4	#20291097	C₂	1	2	yes	maximal, complemented
5	#20291096	C₂	1	2	yes	maximal, complemented
6	#20291093	C₂	1	2	yes	maximal, complemented
7	#20291049	C₂	1	1	yes	maximal, characteristic, complemented
8	#20290944	C₂	1	1	yes	maximal, characteristic, complemented
9	#20290942	C₂	1	1	yes	maximal, characteristic, complemented
10	#20290921	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#16810686	C₂	1	1	yes	maximal, characteristic
12	C₂×#13133292	C₂²	1	2	yes	complemented
13	D₅₃⋊M₃₂	—	2	4	no	—
14	C₂×#13133291	—	2	4	no	—
15	C₂×#13133291	C₂²	1	1	yes	characteristic
16	C₂×#13133291	C₂²	1	1	yes	characteristic
17	C₂×#13133291	C₂²	1	1	yes	characteristic
18	C₂×#13133291	C₂²	1	1	yes	characteristic
19	C₂×#13133291	C₂²	1	2	yes	complemented
20	C₂×D₅₃⋊C₁₆	C₂²	1	2	yes	complemented
21	C₂²×#11719910	C₂²	1	2	yes	complemented
22	#16811544	C₂²	1	2	yes	complemented
23	#16811544	C₂²	1	2	yes	complemented
24	#16811518	C₂²	1	2	yes	complemented
25	#16811518	C₂²	1	2	yes	complemented
26	C₂²⋊#11719910	C₂²	1	2	yes	complemented
27	C₂²⋊#11719910	C₂²	1	2	yes	complemented
28	#16811512	C₂²	1	2	yes	complemented
29	#16811509	C₂²	1	2	yes	complemented
30	C₂³×#88322	C₂²	1	1	yes	characteristic
31	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₂²⋊D₅₃	C₄	1	1	yes	characteristic
33	#16810686	C₄	1	1	yes	characteristic
34	#16810686	C₄	1	1	yes	characteristic
35	#16810686	C₄	1	1	yes	characteristic
36	#16810686	C₄	1	1	yes	characteristic
37	#16810686	C₂²	1	1	yes	characteristic
38	#16810686	C₂²	1	1	yes	characteristic
39	#16810686	C₂²	1	1	yes	characteristic
40	#16810686	C₂²	1	1	yes	characteristic
41	C₂×#13133146	C₄	1	1	yes	characteristic
42	C₂×#13133129	C₄	1	1	yes	characteristic
43	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
44	C₂×C₂²⋊C₈×C₅₃	C₄	1	1	yes	characteristic
45	#13133292	—	2	4	no	—
46	#13133291	—	2	2	no	—
47	#13133291	—	2	2	no	—
48	#13133291	—	2	2	no	—
49	#13133291	—	2	4	no	—
50	#13133291	D₄	1	4	yes	complemented
51	D₅₃⋊C₁₆	—	2	4	no	—
52	C₂×#11719910	—	2	4	no	—
53	C₂×#11719910	C₂³	1	2	yes	—
54	C₂×#11719910	C₂³	1	2	yes	—
55	C₂×#11719910	C₂³	1	2	yes	—
56	C₂×#11719910	C₂³	1	2	yes	—
57	C₂²×C₂²⋊D₅₃	C₈	1	1	yes	characteristic
58	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
59	C₂²×#88322	—	2	2	no	—
60	C₂²×#88322	—	2	2	no	—
61	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
62	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
63	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
64	C₂²×#88322	C₂³	1	1	yes	characteristic
65	C₂²×#88322	C₂³	1	1	yes	characteristic
66	C₂²×#88322	C₂³	1	1	yes	characteristic
67	C₂×C₈×D₅₃	—	2	2	no	—
68	C₂×C₈×D₅₃	—	2	2	no	—
69	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
71	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
72	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
73	C₄×C₂²⋊D₅₃	C₈	1	1	yes	characteristic
74	C₄×C₂²⋊D₅₃	C₈	1	1	yes	characteristic
75	C₄×C₂²⋊D₅₃	C₈	1	1	yes	characteristic
76	C₄×C₂²⋊D₅₃	C₈	1	1	yes	characteristic
77	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
78	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
79	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
80	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
81	C₂×#11719919	C₈	1	1	yes	characteristic
82	C₂×C₂²⋊Dic₅₃	C₈	1	1	yes	characteristic
83	C₂×#11719921	C₈	1	1	yes	characteristic
84	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
85	#13133146	C₂×C₄	1	1	yes	characteristic
86	#13133146	C₂×C₄	1	1	yes	characteristic
87	#13133146	C₂×C₄	1	1	yes	characteristic
88	#13133146	C₂×C₄	1	1	yes	characteristic
89	#13133129	C₂×C₄	1	1	yes	characteristic
90	#13133129	C₂×C₄	1	1	yes	characteristic
91	#13133129	C₂×C₄	1	1	yes	characteristic
92	#13133129	C₂×C₄	1	1	yes	characteristic
93	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
94	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
95	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
96	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
98	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
99	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
100	C₂²⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
101	C₂²⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
102	C₂²⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
103	C₂²⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
104	C₂⁴×C₅₃	C₂×C₈	1	1	yes	characteristic
105	C₂³×D₅₃	C₂×C₈	1	1	yes	characteristic
106	C₂²×C₄×C₅₃	—	2	2	no	—
107	C₂²×C₄×C₅₃	—	2	2	no	—
108	C₂²×C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
109	C₂²×C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
110	C₂²×C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
111	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₂²⋊D₅₃	—	2	4	no	—
115	C₂×C₂²⋊D₅₃	C₂×C₈	1	1	yes	characteristic
116	C₂×C₂²⋊D₅₃	C₂×C₈	1	1	yes	characteristic
117	C₂×C₂²⋊D₅₃	C₂×C₈	1	1	yes	characteristic
118	C₂×C₂²⋊D₅₃	C₂×C₈	1	1	yes	characteristic
119	C₂²×Dic₅₃	C₂×C₈	1	1	yes	characteristic
120	C₂²×Dic₅₃	C₂×C₈	1	1	yes	characteristic
121	C₂²×Dic₅₃	C₂×C₈	1	1	yes	characteristic
122	C₂×C₄×D₅₃	—	2	2	no	—
123	C₂×C₄×D₅₃	—	2	2	no	—
124	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
125	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
126	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₅₃	—	2	2	no	—
129	C₂×C₈×C₅₃	—	2	2	no	—
130	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
134	C₂²⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
135	C₂²⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
136	C₂²⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
137	C₂²⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
138	#11719921	C₂×C₈	1	1	yes	characteristic
139	#11719921	C₂×C₈	1	1	yes	characteristic
140	#11719921	C₂×C₈	1	1	yes	characteristic
141	#11719921	C₂×C₈	1	1	yes	characteristic
142	#11719919	C₂×C₈	1	1	yes	characteristic
143	#11719919	C₂×C₈	1	1	yes	characteristic
144	#11719919	C₂×C₈	1	1	yes	characteristic
145	#11719919	C₂×C₈	1	1	yes	characteristic
146	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
147	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
148	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
149	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
150	C₂×#88322	—	2	2	no	—
151	C₂×#88322	—	2	2	no	—
152	C₂×#88322	—	2	2	no	—
153	C₂×#88322	—	2	1	no	—
154	C₂×#88322	—	2	1	no	—
155	C₂×#88322	—	2	1	no	—
156	C₂×#88322	—	2	1	no	—
157	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
158	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
159	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
160	C₂×#88322	C₂×D₄	1	2	yes	—
161	C₂×#88322	#41	1	2	yes	—
162	C₂×#88322	C₂⁴	1	1	yes	characteristic
163	C₈×D₅₃	—	2	2	no	—
164	C₈×D₅₃	—	2	2	no	—
165	C₈×D₅₃	—	2	1	no	—
166	C₈×D₅₃	—	2	1	no	—
167	C₈×D₅₃	—	2	1	no	—
168	C₈×D₅₃	—	2	1	no	—
169	#11719910	—	2	2	no	—
170	#11719910	—	2	2	no	—
171	#11719910	—	2	2	no	—
172	#11719910	C₂×D₄	1	4	yes	complemented
173	C₂³×C₅₃	—	2	2	no	—
174	C₂³×C₅₃	—	2	2	no	—
175	C₂³×C₅₃	—	4	1	no	—
176	C₂³×C₅₃	C₂²×C₈	1	1	yes	characteristic
177	C₂³×C₅₃	C₂²×C₈	1	1	yes	characteristic
178	C₂³×C₅₃	C₂²×C₈	1	1	yes	characteristic
179	C₂²×D₅₃	—	2	2	no	—
180	C₂²×D₅₃	—	2	2	no	—
181	C₂²×D₅₃	—	4	1	no	—
182	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
183	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
184	C₂×C₄×C₅₃	—	2	2	no	—
185	C₂×C₄×C₅₃	—	2	1	no	—
186	C₂×C₄×C₅₃	—	2	1	no	—
187	C₂×C₄×C₅₃	—	2	1	no	—
188	C₂×C₄×C₅₃	—	2	1	no	—
189	C₂×C₄×C₅₃	—	2	2	no	—
190	C₂×C₄×C₅₃	—	2	2	no	—
191	C₂×C₄×C₅₃	C₄×D₄	1	2	yes	—
192	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
193	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
194	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
195	C₂×C₄×C₅₃	#131	1	2	yes	—
196	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
197	C₂²⋊D₅₃	—	2	2	no	—
198	C₂²⋊D₅₃	—	2	2	no	—
199	C₂²⋊D₅₃	—	2	2	no	—
200	C₂²⋊D₅₃	M₃₂	1	4	yes	complemented
201	C₂×Dic₅₃	—	2	2	no	—
202	C₂×Dic₅₃	—	2	2	no	—
203	C₂×Dic₅₃	—	4	1	no	—
204	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
205	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
206	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
207	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
208	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
209	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
210	C₄×D₅₃	—	2	1	no	—
211	C₄×D₅₃	—	2	1	no	—
212	C₄×D₅₃	—	2	1	no	—
213	C₄×D₅₃	—	2	1	no	—
214	C₄×D₅₃	—	2	2	no	—
215	C₄×D₅₃	—	2	2	no	—
216	C₈×C₅₃	—	2	1	no	—
217	C₈×C₅₃	—	2	1	no	—
218	C₈×C₅₃	—	2	1	no	—
219	C₈×C₅₃	—	2	1	no	—
220	#88322	—	2	1	no	—
221	#88322	—	2	1	no	—
222	#88322	C₄×D₄	1	2	yes	—
223	#88322	C₂²×D₄	1	1	yes	characteristic
224	#88322	C₂×#41	1	1	yes	characteristic
225	D₄×M₃₂	—	53	1	no	maximal, Sylow
226	C₂²×C₅₃	—	2	1	no	—
227	C₂²×C₅₃	—	2	1	no	—
228	C₂²×C₅₃	—	2	1	no	—
229	C₂²×C₅₃	—	2	1	no	—
230	C₂²×C₅₃	—	2	1	no	—
231	C₂²×C₅₃	—	2	1	no	—
232	C₂²×C₅₃	—	2	1	no	—
233	C₂²×C₅₃	—	4	4	no	—
234	C₂²×C₅₃	C₈×D₄	1	2	yes	—
235	C₂²×C₅₃	C₂×M₃₂	1	2	yes	complemented
236	C₂²×C₅₃	C₂³×C₈	1	1	yes	characteristic
237	C₂×D₅₃	—	2	1	no	—
238	C₂×D₅₃	—	2	1	no	—
239	C₂×D₅₃	—	2	1	no	—
240	C₂×D₅₃	—	2	1	no	—
241	C₂×D₅₃	—	2	1	no	—
242	C₂×D₅₃	—	4	4	no	—
243	C₂×D₅₃	C₂×M₃₂	1	2	yes	complemented
244	C₄×C₅₃	—	2	1	no	—
245	C₄×C₅₃	—	2	1	no	—
246	C₄×C₅₃	C₈×D₄	1	2	yes	—
247	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
248	C₄×C₅₃	C₂×#131	1	1	yes	characteristic
249	Dic₅₃	—	2	1	no	—
250	Dic₅₃	—	2	1	no	—
251	Dic₅₃	—	2	1	no	—
252	Dic₅₃	—	2	1	no	—
253	Dic₅₃	—	2	1	no	—
254	Dic₅₃	C₂×M₃₂	1	2	yes	complemented
255	C₂²×M₃₂	—	53	1	no	—
256	C₂²×M₃₂	—	53	1	no	—
257	C₂×C₈×D₄	—	53	1	no	—
258	#2169	—	53	2	no	—
259	#2168	—	53	2	no	—
260	#2168	—	53	2	no	—
261	D₄×C₁₆	—	53	2	no	—
262	#2150	—	53	1	no	—
263	#2112	—	53	1	no	—
264	#2112	—	53	1	no	—
265	C₄×M₃₂	—	53	1	no	—
266	C₂×C₅₃	—	2	2	no	—
267	C₂×C₅₃	—	2	2	no	—
268	C₂×C₅₃	—	4	1	no	—
269	C₂×C₅₃	C₂×C₈×D₄	1	1	yes	characteristic
270	C₂×C₅₃	C₂²×M₃₂	1	1	yes	characteristic
271	C₂×C₅₃	#3407	1	1	yes	characteristic
272	D₅₃	—	2	2	no	—
273	D₅₃	—	4	1	no	—
274	C₂³×C₈	—	53	1	no	—
275	C₂³×C₈	—	53	1	no	—
276	C₂×C₄×D₄	—	53	1	no	—
277	C₂×M₃₂	—	53	1	no	—
278	C₂×M₃₂	—	53	1	no	—
279	C₂×M₃₂	—	53	1	no	—
280	C₂×M₃₂	—	53	1	no	—
281	C₂×M₃₂	—	53	2	no	—
282	C₂×M₃₂	—	53	2	no	—
283	C₂×M₃₂	—	106	4	no	—
284	C₂×M₃₂	—	106	4	no	—
285	C₂²×C₁₆	—	53	2	no	—
286	C₂²×C₁₆	—	53	2	no	—
287	C₈×D₄	—	53	1	no	—
288	C₈×D₄	—	53	1	no	—
289	C₈×D₄	—	53	1	no	—
290	C₈×D₄	—	53	1	no	—
291	C₈×D₄	—	53	1	no	—
292	C₈×D₄	—	53	1	no	—
293	C₈×D₄	—	53	1	no	—
294	C₈×D₄	—	53	1	no	—
295	C₂×C₄⋊C₈	—	53	1	no	—
296	C₂×C₂²⋊C₈	—	53	1	no	—
297	C₂×C₂²⋊C₈	#6157	1	1	yes	characteristic
298	C₂×C₄×C₈	—	53	1	no	—
299	C₄⋊C₁₆	—	53	2	no	—
300	C₄⋊C₁₆	—	53	2	no	—
301	C₂²⋊C₁₆	—	53	2	no	—
302	C₂²⋊C₁₆	—	53	2	no	—
303	C₂²⋊C₁₆	—	53	2	no	—
304	C₂²⋊C₁₆	—	53	2	no	—
305	#346	—	53	2	no	—
306	C₄×C₁₆	—	53	2	no	—
307	C₅₃	D₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
308	C₂²×D₄	—	53	1	no	—
309	C₂³×C₄	—	53	1	no	—
310	C₂³×C₄	C₂×#6157	1	1	yes	characteristic
311	C₂²×C₈	—	53	1	no	—
312	C₂²×C₈	—	53	1	no	—
313	C₂²×C₈	—	53	1	no	—
314	C₂²×C₈	—	53	1	no	—
315	C₂²×C₈	—	53	1	no	—
316	C₂²×C₈	—	53	1	no	—
317	C₂²×C₈	—	53	1	no	—
318	C₂²×C₈	—	53	1	no	—
319	C₂²×C₈	—	53	1	no	—
320	C₂²×C₈	—	53	1	no	—
321	C₂²×C₈	—	106	2	no	—
322	C₂²×C₈	—	106	2	no	—
323	C₂²×C₈	—	106	2	no	—
324	C₂²×C₈	—	106	2	no	—
325	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
326	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
327	C₄×D₄	—	53	1	no	—
328	C₄×D₄	—	53	1	no	—
329	C₄×D₄	—	53	1	no	—
330	C₄×D₄	—	53	1	no	—
331	C₄×D₄	—	53	1	no	—
332	C₄×D₄	—	53	1	no	—
333	C₄×D₄	—	53	1	no	—
334	C₄×D₄	—	53	1	no	—
335	C₂×C₄⋊C₄	—	53	1	no	—
336	C₂×C₂²⋊C₄	—	53	1	no	—
337	C₂×C₂²⋊C₄	—	53	1	no	—
338	C₂×C₄²	—	53	1	no	—
339	M₃₂	—	53	4	no	—
340	M₃₂	—	106	4	no	—
341	M₃₂	—	106	4	no	—
342	M₃₂	—	106	2	no	—
343	M₃₂	—	106	2	no	—
344	M₃₂	—	106	2	no	—
345	C₂×C₁₆	—	53	2	no	—
346	C₂×C₁₆	—	53	2	no	—
347	C₂×C₁₆	—	53	2	no	—
348	C₂×C₁₆	—	53	2	no	—
349	C₂×C₁₆	—	106	4	no	—
350	C₂×C₁₆	—	106	4	no	—
351	C₄⋊C₈	—	53	1	no	—
352	C₄⋊C₈	—	53	1	no	—
353	C₄⋊C₈	—	53	1	no	—
354	C₄⋊C₈	—	53	1	no	—
355	C₂²⋊C₈	—	53	1	no	—
356	C₂²⋊C₈	—	53	1	no	—
357	C₂²⋊C₈	—	53	1	no	—
358	C₂²⋊C₈	—	53	1	no	—
359	C₂²⋊C₈	C₂×#6157	1	1	yes	characteristic
360	C₂²⋊C₈	C₂×#6157	1	1	yes	characteristic
361	C₂²⋊C₈	C₂×#6157	1	1	yes	characteristic
362	C₂²⋊C₈	C₂×#6157	1	1	yes	characteristic
363	C₄×C₈	—	53	1	no	—
364	C₄×C₈	—	53	1	no	—
365	C₄×C₈	—	53	1	no	—
366	C₄×C₈	—	53	1	no	—
367	C₂⁴	—	53	1	no	—
368	C₂⁴	D₅₃⋊C₈	1	1	yes	characteristic
369	C₂×D₄	—	53	1	no	—
370	C₂×D₄	—	53	1	no	—
371	C₂×D₄	—	53	1	no	—
372	C₂×D₄	—	53	1	no	—
373	C₂×D₄	—	106	4	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	53	1	no	—
377	C₂²×C₄	—	53	1	no	—
378	C₂²×C₄	—	53	1	no	—
379	C₂²×C₄	—	53	1	no	—
380	C₂²×C₄	—	53	1	no	—
381	C₂²×C₄	—	53	1	no	—
382	C₂²×C₄	—	53	1	no	—
383	C₂²×C₄	—	106	2	no	—
384	C₂²×C₄	—	106	2	no	—
385	C₂²×C₄	D₅₃⋊C₈	1	1	yes	characteristic
386	C₂²×C₄	D₅₃⋊C₈	1	1	yes	characteristic
387	C₂²×C₄	D₅₃⋊C₈	1	1	yes	characteristic
388	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
389	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
390	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	53	2	no	—
394	C₂×C₈	—	53	2	no	—
395	C₂×C₈	—	53	1	no	—
396	C₂×C₈	—	53	1	no	—
397	C₂×C₈	—	53	1	no	—
398	C₂×C₈	—	53	1	no	—
399	C₂×C₈	—	106	1	no	—
400	C₂×C₈	—	106	1	no	—
401	C₂×C₈	—	106	2	no	—
402	C₂×C₈	—	106	2	no	—
403	C₂×C₈	—	106	1	no	—
404	C₂×C₈	—	106	1	no	—
405	C₂×C₈	—	106	1	no	—
406	C₂×C₈	—	106	1	no	—
407	C₂×C₈	—	106	2	no	—
408	C₂×C₈	—	106	2	no	—
409	C₂×C₈	—	106	1	no	—
410	C₂×C₈	—	106	1	no	—
411	C₂×C₈	—	106	2	no	—
412	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
413	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
414	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
415	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
416	C₄⋊C₄	—	53	1	no	—
417	C₄⋊C₄	—	53	1	no	—
418	C₄⋊C₄	—	53	1	no	—
419	C₄⋊C₄	—	53	1	no	—
420	C₂²⋊C₄	—	53	1	no	—
421	C₂²⋊C₄	—	53	1	no	—
422	C₂²⋊C₄	—	53	1	no	—
423	C₂²⋊C₄	—	53	1	no	—
424	C₂²⋊C₄	—	53	1	no	—
425	C₂²⋊C₄	—	53	1	no	—
426	C₂²⋊C₄	—	53	1	no	—
427	C₂²⋊C₄	—	53	1	no	—
428	C₄²	—	53	1	no	—
429	C₄²	—	53	1	no	—
430	C₄²	—	53	1	no	—
431	C₄²	—	53	1	no	—
432	C₁₆	—	53	4	no	—
433	C₁₆	—	106	2	no	—
434	C₁₆	—	106	2	no	—
435	C₁₆	—	106	2	no	—
436	C₂³	—	2	2	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	4	1	no	—
439	C₂³	—	53	1	no	—
440	C₂³	—	53	1	no	—
441	C₂³	—	106	2	no	—
442	C₂³	—	106	2	no	—
443	C₂³	—	212	1	no	—
444	C₂³	C₂×D₅₃⋊C₈	1	1	yes	characteristic
445	C₂³	C₂×D₅₃⋊C₈	1	1	yes	characteristic
446	C₂³	C₂×D₅₃⋊C₈	1	1	yes	characteristic
447	D₄	—	53	4	no	—
448	D₄	—	106	2	no	—
449	D₄	—	106	2	no	—
450	D₄	—	106	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	53	1	no	—
459	C₂×C₄	—	53	1	no	—
460	C₂×C₄	—	53	1	no	—
461	C₂×C₄	—	53	1	no	—
462	C₂×C₄	—	53	1	no	—
463	C₂×C₄	—	53	1	no	—
464	C₂×C₄	—	106	2	no	—
465	C₂×C₄	—	106	2	no	—
466	C₂×C₄	—	106	2	no	—
467	C₂×C₄	—	106	2	no	—
468	C₂×C₄	—	106	1	no	—
469	C₂×C₄	—	106	1	no	—
470	C₂×C₄	—	106	1	no	—
471	C₂×C₄	—	106	1	no	—
472	C₂×C₄	—	212	1	no	—
473	C₂×C₄	D₄×#6157	1	2	yes	—
474	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
475	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
476	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
477	C₂×C₄	#13133304	1	2	yes	—
478	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
479	C₈	—	2	1	no	—
480	C₈	—	2	1	no	—
481	C₈	—	2	1	no	—
482	C₈	—	2	1	no	—
483	C₈	—	53	2	no	—
484	C₈	—	53	1	no	—
485	C₈	—	53	1	no	—
486	C₈	—	106	1	no	—
487	C₈	—	106	1	no	—
488	C₂²	—	2	1	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	2	1	no	—
495	C₂²	—	4	4	no	—
496	C₂²	—	53	2	no	—
497	C₂²	—	106	1	no	—
498	C₂²	—	106	1	no	—
499	C₂²	—	106	1	no	—
500	C₂²	—	106	1	no	—
501	C₂²	—	106	1	no	—
502	C₂²	—	212	4	no	—
503	C₂²	#16811650	1	2	yes	—
504	C₂²	D₅₃⋊M₃₂	1	2	yes	complemented
505	C₂²	C₂²×D₅₃⋊C₈	1	1	yes	characteristic
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	53	2	no	—
509	C₄	—	106	1	no	—
510	C₄	—	106	1	no	—
511	C₄	—	106	1	no	—
512	C₄	—	106	1	no	—
513	C₄	—	106	1	no	—
514	C₄	#16811650	1	2	yes	—
515	C₄	C₂×D₄×#6157	1	1	yes	characteristic
516	C₄	C₂×#13133304	1	1	yes	characteristic
517	C₂	—	2	2	no	—
518	C₂	—	2	2	no	—
519	C₂	—	4	1	no	—
520	C₂	—	106	2	no	—
521	C₂	—	212	1	no	—
522	C₂	C₂×#16811650	1	1	yes	characteristic
523	C₂	C₂×D₅₃⋊M₃₂	1	1	yes	characteristic
524	C₂	#20291684	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#6157
commutator, socle	C₂²×C₅₃	C₂³×C₈
Fitting	C₂×C₂²⋊C₈×C₅₃	C₄
prime radical	C₂²×C₂²⋊D₅₃	C₈
cosocle	C₂×#88322	C₂⁴
hypercenter	C₂×C₂²⋊C₈	#6157
hypocenter	C₅₃	D₄×M₃₂
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
1. C₂×D₅₃⋊M₃₂	C₂	semidirect
2. C₂²×#13133291	C₂	semidirect
3. #20291100	C₂	semidirect
4. #20291097	C₂	semidirect
5. #20291096	C₂	semidirect
6. #20291093	C₂	semidirect
7. #20291049	C₂	semidirect
8. #20290944	C₂	semidirect
9. #20290942	C₂	semidirect
10. #20290921	C₂	semidirect
12. C₂×#13133292	C₂²	semidirect
19. C₂×#13133291	C₂²	semidirect
20. C₂×D₅₃⋊C₁₆	C₂²	semidirect
21. C₂²×#11719910	C₂²	semidirect
22. #16811544	C₂²	semidirect
23. #16811544	C₂²	semidirect
24. #16811518	C₂²	semidirect
25. #16811518	C₂²	semidirect
26. C₂²⋊#11719910	C₂²	semidirect
27. C₂²⋊#11719910	C₂²	semidirect
28. #16811512	C₂²	semidirect
29. #16811509	C₂²	semidirect
50. #13133291	D₄	semidirect
172. #11719910	C₂×D₄	semidirect
200. C₂²⋊D₅₃	M₃₂	semidirect
235. C₂²×C₅₃	C₂×M₃₂	semidirect
243. C₂×D₅₃	C₂×M₃₂	semidirect
254. Dic₅₃	C₂×M₃₂	semidirect
307. C₅₃	D₄×M₃₂	semidirect
504. C₂²	D₅₃⋊M₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₅₃⋊M₃₂	2
C₂²×#13133291	2
#20291100	2
#20291097	2
#20291096	2
#20291093	2
#20291049	2
#20290944	2
#20290942	2
#20290921	2
C₂×#16810686	2
D₄×M₃₂	53