Subgroups — #28316270

Order 13568.

610 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20291410	C₂	1	2	yes	maximal
2	#20290287	C₂	1	2	yes	maximal, complemented
3	#20290286	C₂	1	2	yes	maximal, complemented
4	#20290282	C₂	1	2	yes	maximal, complemented
5	#20290277	C₂	1	1	yes	maximal, characteristic, complemented
6	#20290276	C₂	1	1	yes	maximal, characteristic, complemented
7	#20290272	C₂	1	1	yes	maximal, characteristic, complemented
8	#20290265	C₂	1	1	yes	maximal, characteristic, complemented
9	#20290262	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16811486	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×#11719947	C₂	1	1	yes	maximal, characteristic
12	#16811648	—	2	2	no	—
13	#16811647	—	2	2	no	—
14	#16811645	C₂²	1	2	yes	—
15	#16811644	C₂²	1	2	yes	—
16	#16811642	C₂²	1	2	yes	—
17	#16811639	C₂²	1	2	yes	—
18	#16811626	C₂²	1	2	yes	—
19	C₂×C₄⋊#88324	C₂²	1	2	yes	—
20	#16811596	—	2	2	no	—
21	#16811587	—	2	2	no	—
22	#16811487	C₂²	1	2	yes	—
23	#16811486	C₂²	1	1	yes	characteristic
24	#16811486	C₂²	1	1	yes	characteristic
25	#16811486	C₂²	1	2	yes	—
26	#16811486	C₂²	1	1	yes	characteristic
27	#16811486	C₂²	1	1	yes	characteristic
28	#16811485	C₂²	1	2	yes	—
29	#16811485	C₂²	1	2	yes	—
30	#16811484	C₂²	1	2	yes	—
31	#16811484	C₂²	1	2	yes	—
32	C₄×#11719947	C₂²	1	1	yes	characteristic
33	C₈×Dic₁₀₆	C₄	1	1	yes	characteristic
34	#16810747	C₄	1	1	yes	characteristic
35	D₄×#88322	C₄	1	1	yes	characteristic
36	C₈×C₂²⋊D₅₃	C₄	1	1	yes	characteristic
37	C₈×C₂²⋊D₅₃	C₄	1	1	yes	characteristic
38	#16810686	C₄	1	1	yes	characteristic
39	#16810686	C₄	1	1	yes	characteristic
40	#16810675	C₂²	1	1	yes	characteristic
41	#16810673	C₂²	1	1	yes	characteristic
42	#16810673	C₂²	1	1	yes	characteristic
43	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
44	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
45	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
46	C₈×D₄×C₅₃	C₄	1	1	yes	characteristic
47	C₂×#11719940	—	2	2	no	—
48	C₂²×#88324	—	2	2	no	—
49	#13133284	—	2	2	no	—
50	C₄⋊#88324	—	2	2	no	—
51	C₄⋊#88324	C₂³	1	2	yes	—
52	C₄⋊#88324	C₂³	1	2	yes	—
53	C₄⋊#88324	C₂³	1	2	yes	—
54	C₄⋊#88324	C₂³	1	2	yes	—
55	#13133274	—	2	2	no	—
56	#13133274	—	2	2	no	—
57	C₂²⋊#88324	—	2	2	no	—
58	C₂²⋊#88324	—	2	2	no	—
59	#13133272	—	2	2	no	—
60	#13133272	—	2	2	no	—
61	C₄×#88324	—	2	2	no	—
62	C₄×#88324	—	2	2	no	—
63	C₂×#11719947	D₄	1	1	yes	characteristic
64	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
65	C₂²×#88322	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	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
69	#13133182	Q₈	1	1	yes	characteristic
70	D₄×Dic₅₃	Q₈	1	1	yes	characteristic
71	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
72	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
73	#13133177	Q₈	1	1	yes	characteristic
74	#13133177	Q₈	1	1	yes	characteristic
75	#13133175	D₄	1	1	yes	characteristic
76	#13133173	D₄	1	1	yes	characteristic
77	#13133173	D₄	1	1	yes	characteristic
78	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
79	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
80	C₄²×D₅₃	C₂³	1	1	yes	characteristic
81	C₄⋊#88322	C₂×C₄	1	1	yes	characteristic
82	#13133146	C₂×C₄	1	1	yes	characteristic
83	#13133146	C₂×C₄	1	1	yes	characteristic
84	#13133146	C₂×C₄	1	1	yes	characteristic
85	#13133146	C₂×C₄	1	1	yes	characteristic
86	C₂²⋊#88322	C₂×C₄	1	1	yes	characteristic
87	C₂²⋊#88322	C₂×C₄	1	1	yes	characteristic
88	#13133129	C₂×C₄	1	1	yes	characteristic
89	#13133129	C₂×C₄	1	1	yes	characteristic
90	C₄×#88322	C₂×C₄	1	1	yes	characteristic
91	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
92	C₈×Dic₅₃	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	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
98	C₈×Dic₅₃	C₂³	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	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
102	C₄⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
103	C₂²⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
104	C₂²⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
105	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
106	C₂×D₄×C₅₃	C₄⋊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	C₂×C₂²⋊D₅₃	C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₂²⋊D₅₃	C₄⋊C₄	1	1	yes	characteristic
111	C₂²×Dic₅₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×Dic₅₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
114	C₂²×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
115	#11719947	—	2	2	no	—
116	#11719947	—	2	2	no	—
117	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
120	C₂×Dic₁₀₆	C₄⋊C₄	1	1	yes	characteristic
121	#11719940	—	4	4	no	—
122	C₂×#88324	—	2	2	no	—
123	C₂×#88324	—	2	2	no	—
124	C₂×#88324	—	2	2	no	—
125	C₂×#88324	—	2	2	no	—
126	C₂×#88324	—	4	4	no	—
127	C₂×C₈×C₅₃	—	2	2	no	—
128	C₂×C₈×C₅₃	—	2	2	no	—
129	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
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	C₄⋊C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
134	C₂²⋊C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
135	C₂²⋊C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
136	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
137	C₂²⋊Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
138	C₂²⋊Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
139	#11719921	C₄⋊C₄	1	1	yes	characteristic
140	#11719921	C₄⋊C₄	1	1	yes	characteristic
141	C₄⋊Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
142	#11719919	C₄⋊C₄	1	1	yes	characteristic
143	#11719919	C₄⋊C₄	1	1	yes	characteristic
144	#11719919	C₄⋊C₄	1	1	yes	characteristic
145	#11719919	C₄⋊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	C₂×D₄	1	1	yes	characteristic
149	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
150	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
151	C₄×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
152	C₄×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
153	C₄×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
154	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
155	C₂×#88322	—	4	1	no	—
156	C₂×#88322	—	4	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	C₂²×C₄	1	1	yes	characteristic
161	C₈×D₅₃	—	2	2	no	—
162	C₈×D₅₃	—	4	1	no	—
163	C₂³×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂³×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂²×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
166	D₄×C₅₃	—	2	2	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	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
176	C₂²⋊D₅₃	—	2	2	no	—
177	C₂²⋊D₅₃	—	2	2	no	—
178	C₂×Dic₅₃	—	2	1	no	—
179	C₂×Dic₅₃	—	2	1	no	—
180	C₂×Dic₅₃	—	4	1	no	—
181	C₂×Dic₅₃	—	4	1	no	—
182	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂×Dic₅₃	#135	1	2	yes	—
188	C₂×Dic₅₃	#135	1	2	yes	—
189	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
190	C₂×Dic₅₃	C₂²×Q₈	1	1	yes	characteristic
191	C₄×D₅₃	—	2	1	no	—
192	C₄×D₅₃	—	2	1	no	—
193	C₄×D₅₃	—	2	1	no	—
194	C₄×D₅₃	—	2	1	no	—
195	C₄×D₅₃	—	4	1	no	—
196	Dic₁₀₆	—	2	2	no	—
197	#88324	—	4	2	no	—
198	#88324	—	4	2	no	—
199	#88324	—	4	2	no	—
200	#88324	—	4	2	no	—
201	C₈×C₅₃	—	2	1	no	—
202	C₈×C₅₃	—	2	1	no	—
203	C₈×C₅₃	—	2	1	no	—
204	C₈×C₅₃	#131	1	2	yes	—
205	#88322	—	2	1	no	—
206	#88322	—	2	1	no	—
207	#88322	—	2	1	no	—
208	#88322	—	2	1	no	—
209	#17829	—	53	1	no	maximal, Sylow
210	C₂²×C₅₃	—	2	1	no	—
211	C₂²×C₅₃	—	2	1	no	—
212	C₂²×C₅₃	—	2	1	no	—
213	C₂²×C₅₃	—	2	1	no	—
214	C₂²×C₅₃	—	2	1	no	—
215	C₂²×C₅₃	#427	1	2	yes	—
216	C₂²×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
217	C₂×D₅₃	—	2	1	no	—
218	C₂×D₅₃	—	2	1	no	—
219	C₂×D₅₃	—	2	1	no	—
220	C₄×C₅₃	—	2	1	no	—
221	C₄×C₅₃	—	2	1	no	—
222	C₄×C₅₃	—	2	1	no	—
223	C₄×C₅₃	—	2	1	no	—
224	C₄×C₅₃	C₂×#131	1	1	yes	characteristic
225	C₄×C₅₃	#568	1	1	yes	characteristic
226	Dic₅₃	—	2	1	no	—
227	Dic₅₃	—	2	1	no	—
228	Dic₅₃	—	2	1	no	—
229	Dic₅₃	—	2	1	no	—
230	Dic₅₃	—	2	1	no	—
231	Dic₅₃	#427	1	2	yes	—
232	Dic₅₃	C₂×#135	1	1	yes	characteristic
233	Dic₅₃	C₂×#135	1	1	yes	characteristic
234	C₈×#41	—	53	1	no	—
235	#2925	—	53	2	no	—
236	#1572	—	53	2	no	—
237	#1572	—	53	2	no	—
238	#1570	—	53	2	no	—
239	#1568	—	53	1	no	—
240	#1568	—	53	1	no	—
241	#1567	—	53	1	no	—
242	#1564	—	53	1	no	—
243	#1564	—	53	1	no	—
244	C₂×#335	—	53	1	no	—
245	C₂×C₅₃	—	2	2	no	—
246	C₂×C₅₃	—	4	1	no	—
247	C₂×C₅₃	#2906	1	1	yes	characteristic
248	C₂×C₅₃	C₂×#427	1	1	yes	characteristic
249	C₂×C₅₃	#2916	1	1	yes	characteristic
250	D₅₃	—	4	1	no	—
251	C₄×#41	—	53	1	no	—
252	C₈×Q₈	—	53	1	no	—
253	C₈×Q₈	—	53	1	no	—
254	C₈×D₄	—	53	1	no	—
255	C₈×D₄	—	53	1	no	—
256	C₈×D₄	—	53	1	no	—
257	C₈×D₄	—	53	1	no	—
258	C₈×D₄	—	53	1	no	—
259	C₈×D₄	#6157	1	1	yes	characteristic
260	#433	—	106	2	no	—
261	#433	—	106	2	no	—
262	#432	—	53	2	no	—
263	#432	—	53	2	no	—
264	#431	—	53	1	no	—
265	#431	—	53	1	no	—
266	#431	—	53	1	no	—
267	#431	—	53	2	no	—
268	#431	—	53	2	no	—
269	#423	—	53	2	no	—
270	C₂×C₄⋊C₈	—	53	2	no	—
271	#408	—	106	2	no	—
272	#405	—	106	2	no	—
273	C₂×C₄×C₈	—	53	1	no	—
274	C₂×C₄×C₈	—	53	1	no	—
275	C₂×C₄×C₈	—	53	1	no	—
276	#335	—	53	1	no	—
277	#335	—	53	1	no	—
278	#335	—	53	2	no	—
279	#335	—	53	1	no	—
280	#335	—	53	1	no	—
281	#335	—	53	2	no	—
282	#334	—	53	2	no	—
283	#334	—	53	2	no	—
284	#334	—	53	2	no	—
285	#334	—	53	2	no	—
286	C₅₃	#17829	1	1	yes	characteristic, complemented, Sylow
287	C₂×#41	—	53	1	no	—
288	C₂×M₁₆	—	106	2	no	—
289	C₂²×C₈	—	53	1	no	—
290	C₂²×C₈	—	53	1	no	—
291	C₂²×C₈	—	53	1	no	—
292	C₂²×C₈	—	53	1	no	—
293	C₂²×C₈	—	106	2	no	—
294	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
295	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
296	C₄×Q₈	—	53	1	no	—
297	C₄×Q₈	—	53	1	no	—
298	C₄×D₄	—	53	1	no	—
299	C₄×D₄	—	53	1	no	—
300	C₄×D₄	—	53	1	no	—
301	C₄×D₄	—	53	1	no	—
302	C₄×D₄	—	53	1	no	—
303	C₄×D₄	C₂×#6157	1	1	yes	characteristic
304	#117	—	53	1	no	—
305	#117	—	53	1	no	—
306	#117	—	53	1	no	—
307	C₂×C₄²	—	53	1	no	—
308	C₂×C₄²	—	53	1	no	—
309	C₂×C₄²	—	53	1	no	—
310	C₄⋊C₈	—	53	1	no	—
311	C₄⋊C₈	—	53	1	no	—
312	C₄⋊C₈	—	53	1	no	—
313	C₄⋊C₈	—	53	1	no	—
314	C₄⋊C₈	—	53	2	no	—
315	C₄⋊C₈	—	53	2	no	—
316	C₄⋊C₈	—	53	2	no	—
317	C₄⋊C₈	—	53	2	no	—
318	C₄⋊C₈	—	53	1	no	—
319	C₄⋊C₈	—	106	2	no	—
320	C₄⋊C₈	—	106	2	no	—
321	C₄⋊C₈	C₂×#6157	1	1	yes	characteristic
322	C₂²⋊C₈	—	53	1	no	—
323	C₂²⋊C₈	—	53	1	no	—
324	C₂²⋊C₈	—	53	1	no	—
325	C₂²⋊C₈	—	53	1	no	—
326	C₂²⋊C₈	—	106	2	no	—
327	C₂²⋊C₈	—	106	2	no	—
328	C₂²⋊C₈	—	106	2	no	—
329	C₂²⋊C₈	—	106	2	no	—
330	C₂²⋊C₈	C₂×#6157	1	1	yes	characteristic
331	C₂²⋊C₈	C₂×#6157	1	1	yes	characteristic
332	#97	—	106	2	no	—
333	#97	—	106	2	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	—	106	2	no	—
344	C₄×C₈	—	106	2	no	—
345	C₄×C₈	C₂×#6157	1	1	yes	characteristic
346	#41	—	106	2	no	—
347	#41	—	106	2	no	—
348	C₂×Q₈	—	53	1	no	—
349	C₂×D₄	—	53	1	no	—
350	C₂×D₄	—	53	1	no	—
351	C₂×D₄	C₄⋊#6157	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	C₂²×#6157	1	1	yes	characteristic
360	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
361	M₁₆	—	212	4	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	53	1	no	—
365	C₂×C₈	—	53	1	no	—
366	C₂×C₈	—	53	1	no	—
367	C₂×C₈	—	53	1	no	—
368	C₂×C₈	—	106	2	no	—
369	C₂×C₈	—	106	2	no	—
370	C₂×C₈	—	106	2	no	—
371	C₂×C₈	—	106	2	no	—
372	C₂×C₈	—	106	2	no	—
373	C₂×C₈	—	212	1	no	—
374	C₂×C₈	—	212	1	no	—
375	C₂×C₈	—	212	1	no	—
376	C₂×C₈	—	212	4	no	—
377	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
378	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
379	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
380	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
381	C₄⋊C₄	—	53	1	no	—
382	C₄⋊C₄	—	53	1	no	—
383	C₄⋊C₄	—	53	1	no	—
384	C₄⋊C₄	—	53	1	no	—
385	C₄⋊C₄	—	53	1	no	—
386	C₄⋊C₄	C₄⋊#6157	1	1	yes	characteristic
387	C₂²⋊C₄	—	53	1	no	—
388	C₂²⋊C₄	—	53	1	no	—
389	C₂²⋊C₄	—	53	1	no	—
390	C₂²⋊C₄	—	53	1	no	—
391	C₂²⋊C₄	C₄⋊#6157	1	1	yes	characteristic
392	C₂²⋊C₄	C₄⋊#6157	1	1	yes	characteristic
393	C₄²	—	53	1	no	—
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	C₂²×#6157	1	1	yes	characteristic
403	C₂³	—	53	1	no	—
404	C₂³	C₂×C₄⋊#6157	1	1	yes	characteristic
405	C₂³	C₂×C₄⋊#6157	1	1	yes	characteristic
406	Q₈	—	106	2	no	—
407	D₄	—	2	2	no	—
408	D₄	—	106	2	no	—
409	D₄	—	106	2	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	53	2	no	—
415	C₂×C₄	—	53	2	no	—
416	C₂×C₄	—	53	1	no	—
417	C₂×C₄	—	53	1	no	—
418	C₂×C₄	—	53	1	no	—
419	C₂×C₄	—	53	1	no	—
420	C₂×C₄	—	53	1	no	—
421	C₂×C₄	—	53	1	no	—
422	C₂×C₄	—	53	1	no	—
423	C₂×C₄	—	106	1	no	—
424	C₂×C₄	—	106	1	no	—
425	C₂×C₄	—	106	1	no	—
426	C₂×C₄	—	106	1	no	—
427	C₂×C₄	—	106	1	no	—
428	C₂×C₄	—	106	1	no	—
429	C₂×C₄	—	212	1	no	—
430	C₂×C₄	—	212	1	no	—
431	C₂×C₄	—	212	1	no	—
432	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
433	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
434	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
435	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
436	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
437	C₈	—	2	1	no	—
438	C₈	—	2	1	no	—
439	C₈	—	2	1	no	—
440	C₈	—	106	1	no	—
441	C₈	—	106	1	no	—
442	C₈	—	106	1	no	—
443	C₈	—	106	1	no	—
444	C₈	—	212	2	no	—
445	C₈	—	212	2	no	—
446	C₈	—	212	2	no	—
447	C₈	—	212	2	no	—
448	C₈	#13133304	1	2	yes	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	2	1	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	106	1	no	—
455	C₂²	—	106	1	no	—
456	C₂²	—	106	1	no	—
457	C₂²	#16811633	1	2	yes	—
458	C₂²	C₂²×C₄⋊#6157	1	1	yes	characteristic
459	C₄	—	2	1	no	—
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	53	1	no	—
464	C₄	—	53	1	no	—
465	C₄	—	53	2	no	—
466	C₄	—	106	1	no	—
467	C₄	—	106	1	no	—
468	C₄	—	106	1	no	—
469	C₄	—	106	1	no	—
470	C₄	—	106	1	no	—
471	C₄	C₂×#13133304	1	1	yes	characteristic
472	C₄	#16811702	1	1	yes	characteristic
473	C₂	—	2	2	no	—
474	C₂	—	4	1	no	—
475	C₂	—	212	1	no	—
476	C₂	#20291360	1	1	yes	characteristic
477	C₂	C₂×#16811633	1	1	yes	characteristic
478	C₂	#20291377	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₄⋊#6157
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#6157
Fitting	C₈×D₄×C₅₃	C₄
socle	C₂²×C₅₃	C₂²×C₄⋊C₄
prime radical	C₂×#11719947	D₄
cosocle	C₄×Dic₅₃	C₂⁴
hypercenter	C₈×D₄	#6157
hypocenter	C₅₃	#17829
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ C₈×D₄

Complements

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

N	H ≅ G/N	type
2. #20290287	C₂	semidirect
3. #20290286	C₂	semidirect
4. #20290282	C₂	semidirect
5. #20290277	C₂	semidirect
6. #20290276	C₂	semidirect
7. #20290272	C₂	semidirect
8. #20290265	C₂	semidirect
9. #20290262	C₂	semidirect
10. C₂×#16811486	C₂	semidirect
286. C₅₃	#17829	semidirect

Maximal subgroups

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

subgroup	index
#20291410	2
#20290287	2
#20290286	2
#20290282	2
#20290277	2
#20290276	2
#20290272	2
#20290265	2
#20290262	2
C₂×#16811486	2
C₈×#11719947	2
#17829	53