Subgroups — #28313813

Order 13568.

874 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20291394	C₂	1	1	yes	maximal, characteristic
2	#20291393	C₂	1	1	yes	maximal, characteristic
3	#20289929	C₂	1	2	yes	maximal, complemented
4	#20289925	C₂	1	2	yes	maximal, complemented
5	#20289924	C₂	1	2	yes	maximal, complemented
6	#20289919	C₂	1	2	yes	maximal, complemented
7	C₈×#11719936	C₂	1	2	yes	maximal, complemented
8	C₈×#11719940	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₈×D₅₃	C₂	1	1	yes	maximal, characteristic
10	#16811646	C₄	1	2	yes	—
11	#16811646	C₄	1	2	yes	—
12	#16811645	C₄	1	2	yes	—
13	#16811643	C₄	1	2	yes	—
14	#16811642	C₂²	1	2	yes	—
15	#16811641	C₂²	1	2	yes	—
16	#16811641	C₂²	1	2	yes	—
17	#16811640	C₂²	1	2	yes	—
18	#16811628	C₄	1	2	yes	—
19	#16811626	C₄	1	2	yes	—
20	#16811595	C₄	1	2	yes	—
21	#16811594	C₄	1	2	yes	—
22	C₄×#11719936	C₂²	1	2	yes	—
23	C₄×#11719940	C₂²	1	2	yes	—
24	#88324⋊C₈	C₂²	1	4	yes	complemented
25	#88324⋊C₈	C₂²	1	4	yes	complemented
26	#16811464	C₂²	1	4	yes	complemented
27	C₈×#88324	C₂²	1	4	yes	complemented
28	C₂²×C₈×D₅₃	C₄	1	1	yes	characteristic
29	C₂²×C₈×D₅₃	C₄	1	1	yes	characteristic
30	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×#88322	C₄	1	1	yes	characteristic
32	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₅₃	C₄	1	1	yes	characteristic
35	C₄×C₈×D₅₃	C₄	1	1	yes	characteristic
36	C₄×C₈×D₅₃	C₄	1	1	yes	characteristic
37	C₄×C₈×D₅₃	C₄	1	1	yes	characteristic
38	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
39	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
40	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
41	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₅₃	C₄	1	1	yes	characteristic
43	C₂×#11719936	C₂×C₄	1	4	yes	—
44	C₂×#11719940	C₂×C₄	1	4	yes	—
45	#13133284	C₂×C₄	1	4	yes	—
46	#13133284	C₂×C₄	1	4	yes	—
47	#13133284	C₂×C₄	1	4	yes	—
48	C₄⋊#88324	C₂×C₄	1	4	yes	—
49	#13133274	C₂×C₄	1	4	yes	—
50	#13133274	C₂×C₄	1	4	yes	—
51	#13133274	C₂×C₄	1	4	yes	—
52	C₂²⋊#88324	C₂×C₄	1	4	yes	—
53	#13133272	C₂×C₄	1	4	yes	—
54	#13133272	C₂×C₄	1	4	yes	—
55	C₄×#88324	C₂³	1	4	yes	—
56	C₄×#88324	C₂³	1	4	yes	—
57	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
60	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
61	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₅₃	—	2	4	no	—
63	C₂×C₈×D₅₃	—	2	4	no	—
64	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
71	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
75	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
76	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
77	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
78	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
79	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
80	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
81	C₄²×D₅₃	C₂³	1	1	yes	characteristic
82	C₄²×D₅₃	C₂³	1	1	yes	characteristic
83	C₄×#88322	C₂×C₄	1	1	yes	characteristic
84	C₄×#88322	C₂×C₄	1	1	yes	characteristic
85	C₄×#88322	C₂×C₄	1	1	yes	characteristic
86	C₄×#88322	C₂×C₄	1	1	yes	characteristic
87	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
88	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
89	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
90	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
91	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
92	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
93	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
94	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
96	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
98	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
99	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
100	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
101	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
102	C₂³×D₅₃	C₄²	1	1	yes	characteristic
103	C₂²×C₄×C₅₃	C₄²	1	1	yes	characteristic
104	C₂²×C₄×C₅₃	C₄²	1	1	yes	characteristic
105	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
106	C₂²×Dic₅₃	C₄²	1	1	yes	characteristic
107	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
108	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₄×D₅₃	—	2	4	no	—
110	C₂×C₄×D₅₃	—	2	2	no	—
111	C₂×C₄×D₅₃	—	2	2	no	—
112	C₂×C₄×D₅₃	—	2	4	no	—
113	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
114	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
115	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
116	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
117	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
118	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
119	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
125	#11719940	—	2	8	no	—
126	C₂×#88324	C₂²×C₄	1	8	yes	—
127	C₂×#88324	C₂²×C₄	1	8	yes	—
128	#11719936	—	2	8	no	—
129	C₂×C₈×C₅₃	—	2	2	no	—
130	C₂×C₈×C₅₃	—	2	2	no	—
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	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
135	C₄²×C₅₃	C₄²	1	1	yes	characteristic
136	C₄²×C₅₃	C₄²	1	1	yes	characteristic
137	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
138	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
139	C₄×Dic₅₃	C₄²	1	1	yes	characteristic
140	C₄×Dic₅₃	C₄²	1	1	yes	characteristic
141	C₄×Dic₅₃	C₄²	1	1	yes	characteristic
142	C₄×Dic₅₃	C₄²	1	1	yes	characteristic
143	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
144	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
145	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
146	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
147	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
148	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
149	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
150	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
151	C₂×#88322	—	2	2	no	—
152	C₂×#88322	—	2	2	no	—
153	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
154	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
155	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
156	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
157	C₈×D₅₃	—	2	2	no	—
158	C₈×D₅₃	—	2	2	no	—
159	C₈×D₅₃	—	2	2	no	—
160	C₈×D₅₃	—	2	2	no	—
161	C₈×D₅₃	—	2	2	no	—
162	C₈×D₅₃	—	2	2	no	—
163	C₈×D₅₃	M₁₆	1	4	yes	complemented
164	C₈×D₅₃	M₁₆	1	4	yes	complemented
165	C₂³×C₅₃	C₂×C₄²	1	1	yes	characteristic
166	C₂²×D₅₃	—	2	2	no	—
167	C₂²×D₅₃	—	2	2	no	—
168	C₂²×D₅₃	—	2	2	no	—
169	C₂²×D₅₃	C₂×C₄²	1	1	yes	characteristic
170	C₂²×D₅₃	C₂×C₄²	1	1	yes	characteristic
171	C₂×C₄×C₅₃	—	2	2	no	—
172	C₂×C₄×C₅₃	—	2	1	no	—
173	C₂×C₄×C₅₃	—	2	1	no	—
174	C₂×C₄×C₅₃	—	2	2	no	—
175	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
176	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
177	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
178	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
179	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
180	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
181	C₂×Dic₅₃	—	2	2	no	—
182	C₂×Dic₅₃	—	2	2	no	—
183	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
184	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
185	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
186	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
187	C₂×Dic₅₃	#131	1	4	yes	—
188	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
189	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
190	C₄×D₅₃	—	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	2	no	—
195	C₄×D₅₃	—	2	2	no	—
196	C₄×D₅₃	—	2	2	no	—
197	C₄×D₅₃	—	2	2	no	—
198	C₄×D₅₃	—	2	2	no	—
199	C₄×D₅₃	—	2	2	no	—
200	C₄×D₅₃	—	2	2	no	—
201	C₄×D₅₃	C₂×M₁₆	1	2	yes	—
202	C₄×D₅₃	C₂×M₁₆	1	2	yes	—
203	C₄×D₅₃	#131	1	4	yes	—
204	#88324	—	2	8	no	—
205	#88324	—	2	8	no	—
206	C₈×C₅₃	—	2	1	no	—
207	C₈×C₅₃	—	2	1	no	—
208	C₈×C₅₃	C₂×M₁₆	1	2	yes	—
209	C₈×C₅₃	C₂×M₁₆	1	2	yes	—
210	#88322	—	2	1	no	—
211	#88322	—	2	1	no	—
212	#88322	C₂×M₁₆	1	2	yes	—
213	#88322	C₂×M₁₆	1	2	yes	—
214	#17323	—	53	1	no	maximal, Sylow
215	C₂²×C₅₃	—	2	1	no	—
216	C₂²×C₅₃	—	2	1	no	—
217	C₂²×C₅₃	#405	1	2	yes	—
218	C₂²×C₅₃	C₂²×C₄²	1	1	yes	characteristic
219	C₂×D₅₃	—	2	8	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	C₄×M₁₆	1	2	yes	—
225	C₂×D₅₃	#405	1	2	yes	—
226	C₄×C₅₃	—	2	1	no	—
227	C₄×C₅₃	—	2	1	no	—
228	C₄×C₅₃	—	2	1	no	—
229	C₄×C₅₃	—	2	1	no	—
230	C₄×C₅₃	#405	1	2	yes	—
231	C₄×C₅₃	C₂²×M₁₆	1	1	yes	characteristic
232	C₄×C₅₃	C₂²×M₁₆	1	1	yes	characteristic
233	Dic₅₃	—	2	1	no	—
234	Dic₅₃	—	2	1	no	—
235	Dic₅₃	C₄×M₁₆	1	2	yes	—
236	Dic₅₃	#405	1	2	yes	—
237	Dic₅₃	C₂×#131	1	2	yes	—
238	Dic₅₃	C₂×#131	1	2	yes	—
239	#2920	—	53	1	no	—
240	#2920	—	53	1	no	—
241	C₂²×C₄×C₈	—	53	1	no	—
242	#1452	—	53	2	no	—
243	#1451	—	53	2	no	—
244	#1451	—	53	2	no	—
245	#1450	—	53	2	no	—
246	C₈×M₁₆	—	53	2	no	—
247	C₈×M₁₆	—	53	2	no	—
248	C₂×C₅₃	—	2	2	no	—
249	C₂×C₅₃	C₂×C₄×M₁₆	1	1	yes	characteristic
250	C₂×C₅₃	C₂×#405	1	1	yes	characteristic
251	C₂×C₅₃	C₂×#405	1	1	yes	characteristic
252	D₅₃	—	2	2	no	—
253	D₅₃	—	2	2	no	—
254	C₂³×C₈	—	53	1	no	—
255	C₂³×C₈	—	53	1	no	—
256	C₂²×C₄²	—	53	1	no	—
257	#432	—	53	2	no	—
258	#432	—	53	2	no	—
259	#432	—	53	2	no	—
260	#432	—	53	2	no	—
261	#431	—	53	2	no	—
262	#431	—	53	2	no	—
263	#431	—	53	2	no	—
264	#431	—	53	2	no	—
265	#423	—	53	2	no	—
266	#423	—	53	2	no	—
267	#407	—	53	2	no	—
268	#407	—	53	2	no	—
269	C₄×M₁₆	—	53	2	no	—
270	C₄×M₁₆	—	53	2	no	—
271	C₂×C₄×C₈	—	53	1	no	—
272	C₂×C₄×C₈	—	53	1	no	—
273	C₂×C₄×C₈	—	53	1	no	—
274	C₂×C₄×C₈	—	53	1	no	—
275	C₂×C₄×C₈	—	53	1	no	—
276	C₂×C₄×C₈	—	53	1	no	—
277	C₂×C₄×C₈	—	53	1	no	—
278	C₂×C₄×C₈	—	53	1	no	—
279	C₂×C₄×C₈	—	53	1	no	—
280	C₂×C₄×C₈	—	53	1	no	—
281	C₂×C₄×C₈	—	53	1	no	—
282	C₂×C₄×C₈	#6157	1	1	yes	characteristic
283	#322	—	53	4	no	—
284	#322	—	53	4	no	—
285	#322	—	53	4	no	—
286	C₈²	—	53	4	no	—
287	C₅₃	#17323	1	1	yes	characteristic, complemented, Sylow
288	C₂³×C₄	—	53	1	no	—
289	C₂³×C₄	—	53	1	no	—
290	C₂³×C₄	—	53	1	no	—
291	C₂×M₁₆	—	53	4	no	—
292	C₂×M₁₆	—	53	4	no	—
293	C₂²×C₈	—	53	1	no	—
294	C₂²×C₈	—	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	—	106	4	no	—
304	C₂²×C₈	—	106	4	no	—
305	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
306	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
307	C₂×C₄²	—	53	1	no	—
308	C₂×C₄²	—	53	1	no	—
309	C₂×C₄²	—	53	1	no	—
310	C₂×C₄²	—	53	1	no	—
311	C₂×C₄²	—	53	1	no	—
312	C₂×C₄²	—	53	1	no	—
313	C₂×C₄²	—	53	1	no	—
314	C₂×C₄²	—	53	1	no	—
315	C₂×C₄²	—	53	1	no	—
316	C₂×C₄²	—	53	1	no	—
317	C₂×C₄²	—	53	1	no	—
318	C₂×C₄²	C₂×#6157	1	1	yes	characteristic
319	C₄⋊C₈	—	53	4	no	—
320	C₄⋊C₈	—	53	4	no	—
321	C₄⋊C₈	—	53	4	no	—
322	C₄⋊C₈	—	53	4	no	—
323	C₂²⋊C₈	—	53	4	no	—
324	C₂²⋊C₈	—	53	4	no	—
325	C₂²⋊C₈	—	53	4	no	—
326	C₂²⋊C₈	—	53	4	no	—
327	#97	—	53	4	no	—
328	#97	—	53	4	no	—
329	C₄×C₈	—	53	4	no	—
330	C₄×C₈	—	53	4	no	—
331	C₄×C₈	—	53	1	no	—
332	C₄×C₈	—	53	1	no	—
333	C₄×C₈	—	53	1	no	—
334	C₄×C₈	—	53	1	no	—
335	C₄×C₈	—	53	1	no	—
336	C₄×C₈	—	53	1	no	—
337	C₄×C₈	—	53	1	no	—
338	C₄×C₈	—	53	1	no	—
339	C₄×C₈	—	53	1	no	—
340	C₄×C₈	—	53	1	no	—
341	C₄×C₈	—	53	1	no	—
342	C₄×C₈	—	53	1	no	—
343	C₄×C₈	C₂×#6157	1	1	yes	characteristic
344	C₄×C₈	C₂×#6157	1	1	yes	characteristic
345	C₄×C₈	C₂×#6157	1	1	yes	characteristic
346	C₄×C₈	C₂×#6157	1	1	yes	characteristic
347	C₂⁴	—	53	1	no	—
348	C₂²×C₄	—	53	1	no	—
349	C₂²×C₄	—	53	1	no	—
350	C₂²×C₄	—	53	1	no	—
351	C₂²×C₄	—	53	1	no	—
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	—	106	2	no	—
364	C₂²×C₄	—	106	2	no	—
365	C₂²×C₄	—	106	4	no	—
366	C₂²×C₄	—	106	4	no	—
367	C₂²×C₄	C₄×#6157	1	1	yes	characteristic
368	C₂²×C₄	C₄×#6157	1	1	yes	characteristic
369	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
370	M₁₆	—	106	8	no	—
371	M₁₆	—	106	8	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	53	1	no	—
375	C₂×C₈	—	53	1	no	—
376	C₂×C₈	—	53	4	no	—
377	C₂×C₈	—	53	4	no	—
378	C₂×C₈	—	53	8	no	—
379	C₂×C₈	—	53	8	no	—
380	C₂×C₈	—	53	1	no	—
381	C₂×C₈	—	53	1	no	—
382	C₂×C₈	—	106	2	no	—
383	C₂×C₈	—	106	2	no	—
384	C₂×C₈	—	106	2	no	—
385	C₂×C₈	—	106	2	no	—
386	C₂×C₈	—	106	2	no	—
387	C₂×C₈	—	106	2	no	—
388	C₂×C₈	—	106	2	no	—
389	C₂×C₈	—	106	2	no	—
390	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
391	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
392	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
393	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
394	C₄²	—	53	1	no	—
395	C₄²	—	53	1	no	—
396	C₄²	—	53	1	no	—
397	C₄²	—	53	1	no	—
398	C₄²	—	53	1	no	—
399	C₄²	—	53	1	no	—
400	C₄²	—	53	1	no	—
401	C₄²	—	53	1	no	—
402	C₄²	—	53	1	no	—
403	C₄²	—	53	1	no	—
404	C₄²	—	53	1	no	—
405	C₄²	—	53	1	no	—
406	C₄²	C₄×#6157	1	1	yes	characteristic
407	C₄²	C₄×#6157	1	1	yes	characteristic
408	C₄²	C₂²×#6157	1	1	yes	characteristic
409	C₄²	C₂²×#6157	1	1	yes	characteristic
410	C₂³	—	53	1	no	—
411	C₂³	—	53	1	no	—
412	C₂³	—	106	2	no	—
413	C₂³	—	106	2	no	—
414	C₂³	—	106	2	no	—
415	C₂³	C₂×C₄×#6157	1	1	yes	characteristic
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	53	4	no	—
421	C₂×C₄	—	53	1	no	—
422	C₂×C₄	—	53	1	no	—
423	C₂×C₄	—	53	1	no	—
424	C₂×C₄	—	53	1	no	—
425	C₂×C₄	—	53	4	no	—
426	C₂×C₄	—	53	2	no	—
427	C₂×C₄	—	53	2	no	—
428	C₂×C₄	—	53	1	no	—
429	C₂×C₄	—	53	1	no	—
430	C₂×C₄	—	106	2	no	—
431	C₂×C₄	—	106	2	no	—
432	C₂×C₄	—	106	2	no	—
433	C₂×C₄	—	106	2	no	—
434	C₂×C₄	—	106	2	no	—
435	C₂×C₄	—	106	2	no	—
436	C₂×C₄	—	106	2	no	—
437	C₂×C₄	—	106	2	no	—
438	C₂×C₄	—	106	2	no	—
439	C₂×C₄	—	106	2	no	—
440	C₂×C₄	—	106	2	no	—
441	C₂×C₄	—	106	1	no	—
442	C₂×C₄	—	106	1	no	—
443	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
444	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
445	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
446	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
447	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
448	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
449	C₈	—	2	1	no	—
450	C₈	—	2	1	no	—
451	C₈	—	53	2	no	—
452	C₈	—	53	2	no	—
453	C₈	—	106	8	no	—
454	C₈	—	106	8	no	—
455	C₈	—	106	1	no	—
456	C₈	—	106	1	no	—
457	C₈	D₅₃⋊M₁₆	1	2	yes	—
458	C₈	D₅₃⋊M₁₆	1	2	yes	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	53	2	no	—
462	C₂²	—	53	2	no	—
463	C₂²	—	106	8	no	—
464	C₂²	—	106	1	no	—
465	C₂²	—	106	1	no	—
466	C₂²	—	106	1	no	—
467	C₂²	—	106	1	no	—
468	C₂²	#16811586	1	2	yes	—
469	C₂²	C₂²×C₄×#6157	1	1	yes	characteristic
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	1	no	—
473	C₄	—	2	1	no	—
474	C₄	—	53	2	no	—
475	C₄	—	53	2	no	—
476	C₄	—	53	2	no	—
477	C₄	—	53	2	no	—
478	C₄	—	106	1	no	—
479	C₄	—	106	1	no	—
480	C₄	#16811586	1	2	yes	—
481	C₄	C₂×D₅₃⋊M₁₆	1	1	yes	characteristic
482	C₄	C₂×D₅₃⋊M₁₆	1	1	yes	characteristic
483	C₂	—	2	2	no	—
484	C₂	—	106	2	no	—
485	C₂	—	106	2	no	—
486	C₂	C₄×D₅₃⋊M₁₆	1	1	yes	characteristic
487	C₂	C₂×#16811586	1	1	yes	characteristic
488	C₂	C₂×#16811586	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×#6157
commutator, socle	C₂²×C₅₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#6157
Fitting	C₂×C₄×C₈×C₅₃	C₄
prime radical	C₂³×D₅₃	C₄²
cosocle	C₄×Dic₅₃	C₂⁴
hypercenter	C₂×C₄×C₈	#6157
hypocenter	C₅₃	#17323
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
3. #20289929	C₂	semidirect
4. #20289925	C₂	semidirect
5. #20289924	C₂	semidirect
6. #20289919	C₂	semidirect
7. C₈×#11719936	C₂	semidirect
8. C₈×#11719940	C₂	semidirect
24. #88324⋊C₈	C₂²	semidirect
25. #88324⋊C₈	C₂²	semidirect
26. #16811464	C₂²	semidirect
27. C₈×#88324	C₂²	semidirect
163. C₈×D₅₃	M₁₆	semidirect
164. C₈×D₅₃	M₁₆	semidirect
287. C₅₃	#17323	semidirect

Maximal subgroups

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

subgroup	index
#20291394	2
#20291393	2
#20289929	2
#20289925	2
#20289924	2
#20289919	2
C₈×#11719936	2
C₈×#11719940	2
C₂×C₄×C₈×D₅₃	2
#17323	53