Subgroups — #28328491

Order 13568.

618 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20291098	C₂	1	2	yes	maximal, complemented
2	#20291097	C₂	1	2	yes	maximal, complemented
3	#20291096	C₂	1	2	yes	maximal, complemented
4	#20291095	C₂	1	2	yes	maximal, complemented
5	#20291079	C₂	1	1	yes	maximal, characteristic, complemented
6	#20291078	C₂	1	1	yes	maximal, characteristic, complemented
7	#20290944	C₂	1	1	yes	maximal, characteristic, complemented
8	#20290943	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#16811518	C₂	1	1	yes	maximal, characteristic, complemented
10	D₅₃⋊(C₂²⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic
12	C₂×#13133292	C₂²	1	2	yes	complemented
13	C₂×#13133291	C₂²	1	2	yes	complemented
14	C₂×D₅₃⋊C₁₆	C₂²	1	2	yes	complemented
15	C₂²×#11719910	C₂²	1	2	yes	complemented
16	#16811544	C₂²	1	2	yes	complemented
17	C₄⋊#11719910	C₂²	1	2	yes	complemented
18	#16811518	C₂²	1	1	yes	characteristic
19	#16811518	C₂²	1	1	yes	characteristic
20	#16811518	C₂²	1	1	yes	characteristic
21	#16811518	C₂²	1	1	yes	characteristic
22	#16811518	C₂²	1	2	yes	complemented
23	#16811518	C₂²	1	2	yes	complemented
24	C₂²⋊#11719910	C₂²	1	2	yes	complemented
25	C₂²⋊#11719910	C₂²	1	2	yes	complemented
26	#16811512	C₂²	1	2	yes	complemented
27	#16811511	C₂²	1	2	yes	complemented
28	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
29	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
30	C₄×D₄×D₅₃	C₄	1	1	yes	characteristic
31	C₈×D₂₁₂	C₄	1	1	yes	characteristic
32	D₄×#88322	C₂²	1	1	yes	characteristic
33	#16810688	C₂²	1	1	yes	characteristic
34	C₈×C₂²⋊D₅₃	C₄	1	1	yes	characteristic
35	C₈×C₂²⋊D₅₃	C₄	1	1	yes	characteristic
36	#16810686	C₂²	1	1	yes	characteristic
37	#16810686	C₂²	1	1	yes	characteristic
38	C₄⋊C₈×D₅₃	C₄	1	1	yes	characteristic
39	C₂²⋊C₈×D₅₃	C₄	1	1	yes	characteristic
40	C₂²⋊C₈×D₅₃	C₄	1	1	yes	characteristic
41	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
42	C₈×D₄×C₅₃	C₄	1	1	yes	characteristic
43	#13133292	—	4	2	no	—
44	#13133291	—	4	2	no	—
45	D₅₃⋊C₁₆	—	4	2	no	—
46	C₂×#11719910	—	4	2	no	—
47	C₂×#11719910	C₂³	1	2	yes	—
48	C₂×#11719910	C₂³	1	2	yes	—
49	C₂×#11719910	C₂³	1	2	yes	—
50	C₂×#11719910	C₂³	1	2	yes	—
51	C₂×D₄×D₅₃	C₈	1	1	yes	characteristic
52	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
54	C₂²×#88322	C₂³	1	1	yes	characteristic
55	C₂²×#88322	C₂³	1	1	yes	characteristic
56	C₂×C₈×D₅₃	—	4	2	no	—
57	C₂×C₈×D₅₃	—	4	2	no	—
58	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
64	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
65	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
66	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
67	D₄×Dic₅₃	C₈	1	1	yes	characteristic
68	#13133179	C₈	1	1	yes	characteristic
69	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
70	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
71	#13133177	C₈	1	1	yes	characteristic
72	#13133177	C₈	1	1	yes	characteristic
73	C₄⋊C₄×D₅₃	C₈	1	1	yes	characteristic
74	C₂²⋊C₄×D₅₃	C₈	1	1	yes	characteristic
75	C₂²⋊C₄×D₅₃	C₈	1	1	yes	characteristic
76	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
77	C₄⋊#88322	C₂×C₄	1	1	yes	characteristic
78	#13133146	C₂×C₄	1	1	yes	characteristic
79	#13133146	C₂×C₄	1	1	yes	characteristic
80	C₂²⋊#88322	C₂×C₄	1	1	yes	characteristic
81	C₂²⋊#88322	C₂×C₄	1	1	yes	characteristic
82	#13133129	C₂×C₄	1	1	yes	characteristic
83	#13133129	C₂×C₄	1	1	yes	characteristic
84	#13133129	C₂×C₄	1	1	yes	characteristic
85	#13133129	C₂×C₄	1	1	yes	characteristic
86	C₄×#88322	C₂³	1	1	yes	characteristic
87	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
88	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
90	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
91	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
92	C₄⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
93	C₂²⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
94	C₂²⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
95	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
96	C₂³×D₅₃	C₂×C₈	1	1	yes	characteristic
97	C₂³×D₅₃	C₂×C₈	1	1	yes	characteristic
98	C₂×D₄×C₅₃	C₂×C₈	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	C₂×C₂²⋊D₅₃	C₂×C₈	1	1	yes	characteristic
102	C₂×C₂²⋊D₅₃	C₂×C₈	1	1	yes	characteristic
103	C₂²×Dic₅₃	C₂×C₈	1	1	yes	characteristic
104	C₂²×Dic₅₃	C₂×C₈	1	1	yes	characteristic
105	D₄×D₅₃	—	2	4	no	—
106	C₂×D₂₁₂	C₂×C₈	1	1	yes	characteristic
107	C₂×C₄×D₅₃	—	4	1	no	—
108	C₂×C₄×D₅₃	—	4	1	no	—
109	C₂×C₄×D₅₃	—	4	1	no	—
110	C₂×C₄×D₅₃	—	4	1	no	—
111	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
112	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
113	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
114	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
115	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
116	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
117	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₈×C₅₃	—	4	1	no	—
121	C₂×C₈×C₅₃	—	4	1	no	—
122	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
126	C₄⋊C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
127	C₂²⋊C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
128	C₂²⋊C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
129	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
131	C₂²⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
132	#11719921	C₂×C₈	1	1	yes	characteristic
133	#11719921	C₂×C₈	1	1	yes	characteristic
134	#11719921	C₂×C₈	1	1	yes	characteristic
135	#11719921	C₂×C₈	1	1	yes	characteristic
136	C₄⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
137	#11719919	C₂×C₈	1	1	yes	characteristic
138	#11719919	C₂×C₈	1	1	yes	characteristic
139	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
140	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
141	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
142	C₂×#88322	—	2	2	no	—
143	C₂×#88322	—	2	2	no	—
144	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
145	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
146	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
147	C₂×#88322	C₂⁴	1	1	yes	characteristic
148	C₈×D₅₃	—	2	2	no	—
149	C₈×D₅₃	—	2	2	no	—
150	C₈×D₅₃	—	2	2	no	—
151	C₈×D₅₃	—	4	1	no	—
152	C₈×D₅₃	—	4	1	no	—
153	C₈×D₅₃	—	4	1	no	—
154	C₈×D₅₃	—	4	1	no	—
155	C₈×D₅₃	—	4	1	no	—
156	#11719910	—	2	2	no	—
157	#11719910	—	2	2	no	—
158	#11719910	—	2	2	no	—
159	#11719910	—	2	2	no	—
160	C₂³×C₅₃	C₂²×C₈	1	1	yes	characteristic
161	C₂³×C₅₃	C₂²×C₈	1	1	yes	characteristic
162	C₂²×D₅₃	—	2	2	no	—
163	C₂²×D₅₃	—	4	1	no	—
164	C₂²×D₅₃	—	4	1	no	—
165	C₂²×D₅₃	—	4	1	no	—
166	C₂²×D₅₃	—	4	1	no	—
167	C₂²×D₅₃	M₃₂	1	4	yes	complemented
168	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
169	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
170	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
171	D₄×C₅₃	—	2	2	no	—
172	C₂×C₄×C₅₃	—	2	1	no	—
173	C₂×C₄×C₅₃	—	2	1	no	—
174	C₂×C₄×C₅₃	—	2	1	no	—
175	C₂×C₄×C₅₃	—	2	1	no	—
176	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
177	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
178	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
179	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
180	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
181	C₂²⋊D₅₃	—	2	2	no	—
182	C₂²⋊D₅₃	—	2	2	no	—
183	C₂×Dic₅₃	—	4	1	no	—
184	C₂×Dic₅₃	—	4	1	no	—
185	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
186	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
187	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
188	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
189	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
190	D₂₁₂	—	2	2	no	—
191	C₄×D₅₃	—	2	2	no	—
192	C₄×D₅₃	—	2	1	no	—
193	C₄×D₅₃	—	2	1	no	—
194	C₄×D₅₃	—	2	1	no	—
195	C₄×D₅₃	—	2	1	no	—
196	C₄×D₅₃	—	2	1	no	—
197	C₄×D₅₃	—	2	1	no	—
198	C₄×D₅₃	—	4	1	no	—
199	C₄×D₅₃	—	4	1	no	—
200	C₄×D₅₃	—	4	1	no	—
201	C₄×D₅₃	—	4	1	no	—
202	C₄×D₅₃	—	4	1	no	—
203	C₈×C₅₃	—	2	1	no	—
204	C₈×C₅₃	—	2	1	no	—
205	C₈×C₅₃	—	2	1	no	—
206	C₈×C₅₃	—	2	1	no	—
207	#88322	—	2	1	no	—
208	#88322	—	2	1	no	—
209	#88322	—	2	1	no	—
210	#88322	H(5,𝔽₂)	1	2	yes	—
211	#33487	—	53	1	no	maximal, Sylow
212	C₂²×C₅₃	—	2	1	no	—
213	C₂²×C₅₃	—	2	1	no	—
214	C₂²×C₅₃	—	2	1	no	—
215	C₂²×C₅₃	—	2	1	no	—
216	C₂²×C₅₃	—	2	1	no	—
217	C₂²×C₅₃	C₂×M₃₂	1	2	yes	—
218	C₂²×C₅₃	C₂³×C₈	1	1	yes	characteristic
219	C₂×D₅₃	—	2	1	no	—
220	C₂×D₅₃	—	2	1	no	—
221	C₂×D₅₃	—	2	1	no	—
222	C₂×D₅₃	—	2	1	no	—
223	C₂×D₅₃	—	2	1	no	—
224	C₂×D₅₃	—	2	1	no	—
225	C₂×D₅₃	—	2	1	no	—
226	C₂×D₅₃	—	4	4	no	—
227	C₂×D₅₃	—	4	4	no	—
228	C₂×D₅₃	C₂×M₃₂	1	2	yes	—
229	C₂×D₅₃	C₂×M₃₂	1	2	yes	—
230	C₄×C₅₃	—	2	1	no	—
231	C₄×C₅₃	—	2	1	no	—
232	C₄×C₅₃	—	2	1	no	—
233	C₄×C₅₃	—	2	1	no	—
234	C₄×C₅₃	#518	1	1	yes	characteristic
235	C₄×C₅₃	#568	1	1	yes	characteristic
236	Dic₅₃	—	2	1	no	—
237	Dic₅₃	—	2	1	no	—
238	Dic₅₃	—	2	1	no	—
239	Dic₅₃	—	2	1	no	—
240	Dic₅₃	—	2	1	no	—
241	C₂×C₈×D₄	—	53	1	no	—
242	#2168	—	53	2	no	—
243	#2168	—	53	2	no	—
244	#2168	—	53	2	no	—
245	#2168	—	53	2	no	—
246	#2163	—	53	1	no	—
247	#2163	—	53	1	no	—
248	#2112	—	53	1	no	—
249	#2112	—	53	1	no	—
250	C₂×C₂²⋊C₁₆	—	53	1	no	—
251	C₂×C₂²⋊C₁₆	—	53	1	no	—
252	C₂×C₅₃	—	2	2	no	—
253	C₂×C₅₃	—	4	1	no	—
254	C₂×C₅₃	#2972	1	1	yes	characteristic
255	C₂×C₅₃	C₂²×M₃₂	1	1	yes	characteristic
256	C₂×C₅₃	#3407	1	1	yes	characteristic
257	D₅₃	—	2	2	no	—
258	D₅₃	—	2	2	no	—
259	D₅₃	—	4	1	no	—
260	C₂³×C₈	—	53	1	no	—
261	C₂³×C₈	—	53	1	no	—
262	C₂×C₄×D₄	—	53	1	no	—
263	C₂×M₃₂	—	53	2	no	—
264	C₂×M₃₂	—	53	2	no	—
265	C₂²×C₁₆	—	53	2	no	—
266	C₂²×C₁₆	—	53	2	no	—
267	C₈×D₄	—	53	1	no	—
268	C₈×D₄	—	53	1	no	—
269	C₈×D₄	—	53	1	no	—
270	C₈×D₄	—	53	1	no	—
271	C₈×D₄	—	53	1	no	—
272	C₈×D₄	—	53	1	no	—
273	C₈×D₄	—	53	1	no	—
274	C₈×D₄	#6157	1	1	yes	characteristic
275	C₂×C₄⋊C₈	—	53	1	no	—
276	C₂×C₂²⋊C₈	—	53	1	no	—
277	C₂×C₂²⋊C₈	—	53	1	no	—
278	C₂×C₄×C₈	—	53	1	no	—
279	C₄⋊C₁₆	—	53	2	no	—
280	C₄⋊C₁₆	—	53	2	no	—
281	C₂²⋊C₁₆	—	53	1	no	—
282	C₂²⋊C₁₆	—	53	1	no	—
283	C₂²⋊C₁₆	—	53	1	no	—
284	C₂²⋊C₁₆	—	53	1	no	—
285	C₂²⋊C₁₆	—	53	2	no	—
286	C₂²⋊C₁₆	—	53	2	no	—
287	C₂²⋊C₁₆	—	53	2	no	—
288	C₂²⋊C₁₆	—	53	2	no	—
289	#346	—	53	2	no	—
290	#346	—	53	2	no	—
291	C₅₃	#33487	1	1	yes	characteristic, complemented, Sylow
292	C₂²×D₄	—	53	1	no	—
293	C₂³×C₄	—	53	1	no	—
294	C₂³×C₄	—	53	1	no	—
295	C₂²×C₈	—	53	1	no	—
296	C₂²×C₈	—	53	1	no	—
297	C₂²×C₈	—	53	1	no	—
298	C₂²×C₈	—	53	1	no	—
299	C₂²×C₈	—	53	1	no	—
300	C₂²×C₈	—	53	1	no	—
301	C₂²×C₈	—	53	1	no	—
302	C₂²×C₈	—	53	1	no	—
303	C₂²×C₈	—	53	1	no	—
304	C₂²×C₈	—	53	1	no	—
305	C₂²×C₈	—	212	2	no	—
306	C₂²×C₈	—	212	2	no	—
307	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
308	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
309	C₄×D₄	—	53	1	no	—
310	C₄×D₄	—	53	1	no	—
311	C₄×D₄	—	53	1	no	—
312	C₄×D₄	—	53	1	no	—
313	C₄×D₄	—	53	1	no	—
314	C₄×D₄	—	53	1	no	—
315	C₄×D₄	—	53	1	no	—
316	C₄×D₄	C₂×#6157	1	1	yes	characteristic
317	C₂×C₄⋊C₄	—	53	1	no	—
318	C₂×C₂²⋊C₄	—	53	1	no	—
319	C₂×C₂²⋊C₄	—	53	1	no	—
320	C₂×C₄²	—	53	1	no	—
321	M₃₂	—	212	2	no	—
322	M₃₂	—	212	2	no	—
323	C₂×C₁₆	—	53	2	no	—
324	C₂×C₁₆	—	53	2	no	—
325	C₂×C₁₆	—	53	2	no	—
326	C₂×C₁₆	—	53	2	no	—
327	C₂×C₁₆	—	212	2	no	—
328	C₂×C₁₆	—	212	2	no	—
329	C₄⋊C₈	—	53	1	no	—
330	C₄⋊C₈	—	53	1	no	—
331	C₄⋊C₈	—	53	1	no	—
332	C₄⋊C₈	C₂×#6157	1	1	yes	characteristic
333	C₂²⋊C₈	—	53	1	no	—
334	C₂²⋊C₈	—	53	1	no	—
335	C₂²⋊C₈	—	53	1	no	—
336	C₂²⋊C₈	—	53	1	no	—
337	C₂²⋊C₈	—	53	1	no	—
338	C₂²⋊C₈	—	53	1	no	—
339	C₂²⋊C₈	C₂×#6157	1	1	yes	characteristic
340	C₂²⋊C₈	C₂×#6157	1	1	yes	characteristic
341	C₄×C₈	—	53	1	no	—
342	C₄×C₈	—	53	1	no	—
343	C₄×C₈	—	53	1	no	—
344	C₄×C₈	C₂×#6157	1	1	yes	characteristic
345	C₂⁴	—	53	1	no	—
346	C₂⁴	—	53	1	no	—
347	C₂×D₄	—	53	1	no	—
348	C₂×D₄	—	53	1	no	—
349	C₂×D₄	—	53	1	no	—
350	C₂×D₄	—	106	4	no	—
351	C₂×D₄	D₅₃⋊C₈	1	1	yes	characteristic
352	C₂²×C₄	—	53	1	no	—
353	C₂²×C₄	—	53	1	no	—
354	C₂²×C₄	—	53	1	no	—
355	C₂²×C₄	—	53	1	no	—
356	C₂²×C₄	—	53	1	no	—
357	C₂²×C₄	—	53	1	no	—
358	C₂²×C₄	—	53	1	no	—
359	C₂²×C₄	—	53	1	no	—
360	C₂²×C₄	—	53	1	no	—
361	C₂²×C₄	—	53	1	no	—
362	C₂²×C₄	—	53	1	no	—
363	C₂²×C₄	—	212	1	no	—
364	C₂²×C₄	—	212	1	no	—
365	C₂²×C₄	—	212	1	no	—
366	C₂²×C₄	—	212	1	no	—
367	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
368	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
369	C₂×C₈	—	4	1	no	—
370	C₂×C₈	—	4	1	no	—
371	C₂×C₈	—	53	1	no	—
372	C₂×C₈	—	53	1	no	—
373	C₂×C₈	—	53	1	no	—
374	C₂×C₈	—	53	1	no	—
375	C₂×C₈	—	106	2	no	—
376	C₂×C₈	—	106	2	no	—
377	C₂×C₈	—	106	2	no	—
378	C₂×C₈	—	106	2	no	—
379	C₂×C₈	—	106	2	no	—
380	C₂×C₈	—	212	1	no	—
381	C₂×C₈	—	212	1	no	—
382	C₂×C₈	—	212	1	no	—
383	C₂×C₈	—	212	1	no	—
384	C₂×C₈	—	212	1	no	—
385	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
386	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
387	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
388	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
389	C₄⋊C₄	—	53	1	no	—
390	C₄⋊C₄	—	53	1	no	—
391	C₄⋊C₄	—	53	1	no	—
392	C₄⋊C₄	D₅₃⋊C₈	1	1	yes	characteristic
393	C₂²⋊C₄	—	53	1	no	—
394	C₂²⋊C₄	—	53	1	no	—
395	C₂²⋊C₄	—	53	1	no	—
396	C₂²⋊C₄	—	53	1	no	—
397	C₂²⋊C₄	—	53	1	no	—
398	C₂²⋊C₄	—	53	1	no	—
399	C₂²⋊C₄	D₅₃⋊C₈	1	1	yes	characteristic
400	C₂²⋊C₄	D₅₃⋊C₈	1	1	yes	characteristic
401	C₄²	—	53	1	no	—
402	C₄²	—	53	1	no	—
403	C₄²	—	53	1	no	—
404	C₄²	C₂²×#6157	1	1	yes	characteristic
405	C₁₆	—	106	2	no	—
406	C₁₆	—	106	2	no	—
407	C₁₆	—	106	2	no	—
408	C₁₆	—	106	2	no	—
409	C₂³	—	53	1	no	—
410	C₂³	—	53	1	no	—
411	C₂³	—	53	4	no	—
412	C₂³	—	53	1	no	—
413	C₂³	—	106	2	no	—
414	C₂³	—	212	1	no	—
415	C₂³	—	212	1	no	—
416	C₂³	—	212	1	no	—
417	C₂³	—	212	1	no	—
418	C₂³	C₂×D₅₃⋊C₈	1	1	yes	characteristic
419	C₂³	C₂×D₅₃⋊C₈	1	1	yes	characteristic
420	D₄	—	2	2	no	—
421	D₄	—	106	2	no	—
422	D₄	—	106	2	no	—
423	D₄	—	106	2	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	53	1	no	—
429	C₂×C₄	—	53	1	no	—
430	C₂×C₄	—	53	1	no	—
431	C₂×C₄	—	53	1	no	—
432	C₂×C₄	—	53	1	no	—
433	C₂×C₄	—	106	2	no	—
434	C₂×C₄	—	106	1	no	—
435	C₂×C₄	—	106	1	no	—
436	C₂×C₄	—	106	1	no	—
437	C₂×C₄	—	106	1	no	—
438	C₂×C₄	—	106	1	no	—
439	C₂×C₄	—	106	1	no	—
440	C₂×C₄	—	212	1	no	—
441	C₂×C₄	—	212	1	no	—
442	C₂×C₄	—	212	1	no	—
443	C₂×C₄	—	212	1	no	—
444	C₂×C₄	—	212	1	no	—
445	C₂×C₄	—	212	1	no	—
446	C₂×C₄	—	212	1	no	—
447	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
448	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
449	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
450	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
451	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
452	C₈	—	2	1	no	—
453	C₈	—	2	1	no	—
454	C₈	—	2	1	no	—
455	C₈	—	2	1	no	—
456	C₈	—	53	2	no	—
457	C₈	—	106	1	no	—
458	C₈	—	106	1	no	—
459	C₈	—	106	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	53	2	no	—
466	C₂²	—	53	2	no	—
467	C₂²	—	106	1	no	—
468	C₂²	—	106	1	no	—
469	C₂²	—	106	1	no	—
470	C₂²	—	106	1	no	—
471	C₂²	—	106	1	no	—
472	C₂²	—	106	1	no	—
473	C₂²	—	106	1	no	—
474	C₂²	—	212	4	no	—
475	C₂²	—	212	4	no	—
476	C₂²	D₅₃⋊M₃₂	1	2	yes	—
477	C₂²	C₂²×D₅₃⋊C₈	1	1	yes	characteristic
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	106	1	no	—
483	C₄	—	106	1	no	—
484	C₄	—	106	1	no	—
485	C₄	—	106	1	no	—
486	C₄	—	106	1	no	—
487	C₄	#16811690	1	1	yes	characteristic
488	C₄	#16811702	1	1	yes	characteristic
489	C₂	—	2	2	no	—
490	C₂	—	4	1	no	—
491	C₂	—	106	2	no	—
492	C₂	—	106	2	no	—
493	C₂	—	212	1	no	—
494	C₂	#20291563	1	1	yes	characteristic
495	C₂	C₂×D₅₃⋊M₃₂	1	1	yes	characteristic
496	C₂	#20291683	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#6157
commutator, socle	C₂²×C₅₃	C₂³×C₈
Fitting	C₈×D₄×C₅₃	C₄
prime radical	C₂×D₄×D₅₃	C₈
cosocle	C₂×#88322	C₂⁴
hypercenter	C₈×D₄	#6157
hypocenter	C₅₃	#33487
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₈×D₄

Complements

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

N	H ≅ G/N	type
1. #20291098	C₂	semidirect
2. #20291097	C₂	semidirect
3. #20291096	C₂	semidirect
4. #20291095	C₂	semidirect
5. #20291079	C₂	semidirect
6. #20291078	C₂	semidirect
7. #20290944	C₂	semidirect
8. #20290943	C₂	semidirect
9. C₂×#16811518	C₂	semidirect
10. D₅₃⋊(C₂²⋊C₁₆)	C₂	semidirect
12. C₂×#13133292	C₂²	semidirect
13. C₂×#13133291	C₂²	semidirect
14. C₂×D₅₃⋊C₁₆	C₂²	semidirect
15. C₂²×#11719910	C₂²	semidirect
16. #16811544	C₂²	semidirect
17. C₄⋊#11719910	C₂²	semidirect
22. #16811518	C₂²	semidirect
23. #16811518	C₂²	semidirect
24. C₂²⋊#11719910	C₂²	semidirect
25. C₂²⋊#11719910	C₂²	semidirect
26. #16811512	C₂²	semidirect
27. #16811511	C₂²	semidirect
167. C₂²×D₅₃	M₃₂	semidirect
291. C₅₃	#33487	semidirect

Maximal subgroups

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

subgroup	index
#20291098	2
#20291097	2
#20291096	2
#20291095	2
#20291079	2
#20291078	2
#20290944	2
#20290943	2
C₂×#16811518	2
D₅₃⋊(C₂²⋊C₁₆)	2
C₈×D₄×D₅₃	2
#33487	53