Subgroups — #28316301

Order 13568.

616 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20291640	C₂	1	2	yes	maximal
2	#20290291	C₂	1	2	yes	maximal, complemented
3	#20290290	C₂	1	2	yes	maximal, complemented
4	#20290289	C₂	1	2	yes	maximal, complemented
5	#20290276	C₂	1	1	yes	maximal, characteristic, complemented
6	#20290275	C₂	1	1	yes	maximal, characteristic, complemented
7	#20290269	C₂	1	1	yes	maximal, characteristic, complemented
8	#20290262	C₂	1	1	yes	maximal, characteristic, complemented
9	D₅₃⋊#334	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16811484	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×#11719947	C₂	1	1	yes	maximal, characteristic
12	#16811675	—	2	2	no	—
13	#16811655	—	2	2	no	—
14	#16811654	—	2	2	no	—
15	#16811650	—	2	2	no	—
16	#16811645	C₂²	1	2	yes	—
17	#16811644	C₂²	1	2	yes	—
18	#16811639	C₂²	1	2	yes	—
19	#16811626	C₂²	1	2	yes	—
20	D₅₃⋊(C₄⋊C₈)	C₂²	1	2	yes	—
21	C₂×C₄⋊#88324	C₂²	1	2	yes	—
22	#16811487	C₂²	1	2	yes	—
23	#16811486	C₂²	1	2	yes	—
24	#16811486	C₂²	1	2	yes	—
25	#16811485	C₂²	1	2	yes	—
26	#16811485	C₂²	1	2	yes	—
27	#16811484	C₂²	1	1	yes	characteristic
28	#16811484	C₂²	1	1	yes	characteristic
29	#16811484	C₂²	1	2	yes	—
30	#16811484	C₂²	1	1	yes	characteristic
31	#16811484	C₂²	1	1	yes	characteristic
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	C₂×D₅₃⋊C₈	—	2	2	no	—
49	C₂²×#88324	—	2	2	no	—
50	#13133284	—	2	2	no	—
51	#13133284	—	2	2	no	—
52	C₄⋊#88324	—	2	2	no	—
53	C₄⋊#88324	C₂³	1	2	yes	—
54	C₄⋊#88324	C₂³	1	2	yes	—
55	C₄⋊#88324	C₂³	1	2	yes	—
56	C₄⋊#88324	C₂³	1	2	yes	—
57	#13133274	—	2	2	no	—
58	C₂²⋊#88324	—	2	2	no	—
59	C₂²⋊#88324	—	2	2	no	—
60	#13133272	—	2	2	no	—
61	#13133272	—	2	2	no	—
62	C₄×#88324	—	2	2	no	—
63	C₂×#11719947	Q₈	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	D₄	1	1	yes	characteristic
70	D₄×Dic₅₃	D₄	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	D₄	1	1	yes	characteristic
74	#13133177	D₄	1	1	yes	characteristic
75	#13133175	Q₈	1	1	yes	characteristic
76	#13133173	Q₈	1	1	yes	characteristic
77	#13133173	Q₈	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	4	no	—
116	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
119	C₂×Dic₁₀₆	C₄⋊C₄	1	1	yes	characteristic
120	#11719940	—	8	2	no	—
121	C₂×#88324	—	2	2	no	—
122	C₂×#88324	—	2	2	no	—
123	C₂×#88324	—	2	2	no	—
124	C₂×#88324	—	2	2	no	—
125	C₂×#88324	—	8	2	no	—
126	D₅₃⋊C₈	—	8	2	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	#108	1	4	yes	—
178	C₂×Dic₅₃	—	2	2	no	—
179	C₂×Dic₅₃	—	2	2	no	—
180	C₂×Dic₅₃	—	2	2	no	—
181	C₂×Dic₅₃	—	2	2	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	C₂²×D₄	1	1	yes	characteristic
188	C₂×Dic₅₃	C₂²×Q₈	1	1	yes	characteristic
189	C₄×D₅₃	—	2	2	no	—
190	C₄×D₅₃	—	2	1	no	—
191	C₄×D₅₃	—	2	1	no	—
192	C₄×D₅₃	—	2	2	no	—
193	Dic₁₀₆	—	2	2	no	—
194	#88324	—	4	2	no	—
195	#88324	—	4	2	no	—
196	#88324	—	4	2	no	—
197	#88324	—	4	2	no	—
198	C₈×C₅₃	—	2	1	no	—
199	C₈×C₅₃	—	2	1	no	—
200	C₈×C₅₃	—	2	1	no	—
201	C₈×C₅₃	#131	1	2	yes	—
202	#88322	—	2	1	no	—
203	#88322	—	2	1	no	—
204	#88322	—	2	1	no	—
205	#88322	—	2	1	no	—
206	#17834	—	53	1	no	maximal, Sylow
207	C₂²×C₅₃	—	2	1	no	—
208	C₂²×C₅₃	—	2	1	no	—
209	C₂²×C₅₃	—	2	1	no	—
210	C₂²×C₅₃	—	2	1	no	—
211	C₂²×C₅₃	—	2	1	no	—
212	C₂²×C₅₃	C₂×#108	1	2	yes	—
213	C₂²×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
214	C₂×D₅₃	—	2	1	no	—
215	C₂×D₅₃	—	2	1	no	—
216	C₂×D₅₃	C₂×#108	1	2	yes	—
217	C₄×C₅₃	—	2	1	no	—
218	C₄×C₅₃	—	2	1	no	—
219	C₄×C₅₃	—	2	1	no	—
220	C₄×C₅₃	—	2	1	no	—
221	C₄×C₅₃	C₂×#131	1	1	yes	characteristic
222	C₄×C₅₃	#568	1	1	yes	characteristic
223	Dic₅₃	—	2	1	no	—
224	Dic₅₃	—	2	1	no	—
225	Dic₅₃	—	2	1	no	—
226	Dic₅₃	—	2	1	no	—
227	Dic₅₃	—	2	1	no	—
228	Dic₅₃	C₂×#108	1	2	yes	—
229	Dic₅₃	#577	1	2	yes	—
230	#2990	—	53	2	no	—
231	C₈×#41	—	53	1	no	—
232	#1574	—	53	2	no	—
233	#1573	—	53	2	no	—
234	#1573	—	53	2	no	—
235	#1568	—	53	1	no	—
236	#1568	—	53	1	no	—
237	#1566	—	53	1	no	—
238	#1564	—	53	1	no	—
239	C₂×#334	—	53	1	no	—
240	C₂×#334	—	53	1	no	—
241	C₂×C₅₃	—	2	2	no	—
242	C₂×C₅₃	—	4	1	no	—
243	C₂×C₅₃	#2906	1	1	yes	characteristic
244	C₂×C₅₃	#2912	1	1	yes	characteristic
245	C₂×C₅₃	C₂²×#108	1	1	yes	characteristic
246	D₅₃	—	2	2	no	—
247	C₄×#41	—	53	1	no	—
248	#446	—	106	2	no	—
249	C₈×Q₈	—	53	1	no	—
250	C₈×Q₈	—	53	1	no	—
251	#435	—	106	2	no	—
252	#435	—	106	2	no	—
253	C₈×D₄	—	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	—	106	2	no	—
259	C₈×D₄	#6157	1	1	yes	characteristic
260	#432	—	53	2	no	—
261	#432	—	53	2	no	—
262	#431	—	53	1	no	—
263	#431	—	53	1	no	—
264	#431	—	53	1	no	—
265	#431	—	53	2	no	—
266	#423	—	53	2	no	—
267	C₂×C₄⋊C₈	—	53	2	no	—
268	C₂×C₄⋊C₈	—	53	2	no	—
269	C₂×C₄×C₈	—	53	1	no	—
270	C₂×C₄×C₈	—	53	1	no	—
271	C₂×C₄×C₈	—	53	1	no	—
272	#335	—	53	2	no	—
273	#335	—	53	2	no	—
274	#335	—	53	2	no	—
275	#334	—	53	1	no	—
276	#334	—	53	1	no	—
277	#334	—	53	1	no	—
278	#334	—	53	2	no	—
279	#334	—	53	2	no	—
280	#334	—	53	1	no	—
281	#334	—	53	2	no	—
282	C₅₃	#17834	1	1	yes	characteristic, complemented, Sylow
283	C₂×#41	—	53	1	no	—
284	C₂×M₁₆	—	106	2	no	—
285	C₂²×C₈	—	53	1	no	—
286	C₂²×C₈	—	53	1	no	—
287	C₂²×C₈	—	53	1	no	—
288	C₂²×C₈	—	53	1	no	—
289	C₂²×C₈	—	106	2	no	—
290	C₂²×C₈	—	106	2	no	—
291	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
292	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
293	C₄×Q₈	—	53	1	no	—
294	C₄×Q₈	—	53	1	no	—
295	C₄×D₄	—	53	1	no	—
296	C₄×D₄	—	53	1	no	—
297	C₄×D₄	—	53	1	no	—
298	C₄×D₄	—	53	1	no	—
299	C₄×D₄	—	53	1	no	—
300	C₄×D₄	C₂×#6157	1	1	yes	characteristic
301	#117	—	53	1	no	—
302	#117	—	53	1	no	—
303	#117	—	53	1	no	—
304	C₂×C₄²	—	53	1	no	—
305	C₂×C₄²	—	53	1	no	—
306	C₂×C₄²	—	53	1	no	—
307	C₄⋊C₈	—	53	1	no	—
308	C₄⋊C₈	—	53	1	no	—
309	C₄⋊C₈	—	53	1	no	—
310	C₄⋊C₈	—	53	1	no	—
311	C₄⋊C₈	—	53	2	no	—
312	C₄⋊C₈	—	53	2	no	—
313	C₄⋊C₈	—	53	2	no	—
314	C₄⋊C₈	—	53	2	no	—
315	C₄⋊C₈	—	53	1	no	—
316	C₄⋊C₈	—	106	2	no	—
317	C₄⋊C₈	—	106	2	no	—
318	C₄⋊C₈	—	106	2	no	—
319	C₄⋊C₈	C₂×#6157	1	1	yes	characteristic
320	C₂²⋊C₈	—	53	1	no	—
321	C₂²⋊C₈	—	53	1	no	—
322	C₂²⋊C₈	—	53	1	no	—
323	C₂²⋊C₈	—	53	1	no	—
324	C₂²⋊C₈	—	106	2	no	—
325	C₂²⋊C₈	—	106	2	no	—
326	C₂²⋊C₈	—	106	2	no	—
327	C₂²⋊C₈	C₂×#6157	1	1	yes	characteristic
328	C₂²⋊C₈	C₂×#6157	1	1	yes	characteristic
329	#97	—	106	2	no	—
330	#97	—	106	2	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	—	106	2	no	—
341	C₄×C₈	C₂×#6157	1	1	yes	characteristic
342	#41	—	106	4	no	—
343	C₂×Q₈	—	53	1	no	—
344	C₂×D₄	—	53	1	no	—
345	C₂×D₄	—	53	1	no	—
346	C₂×D₄	C₄⋊#6157	1	1	yes	characteristic
347	C₂²×C₄	—	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	C₂²×#6157	1	1	yes	characteristic
355	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
356	M₁₆	—	424	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	53	1	no	—
360	C₂×C₈	—	53	1	no	—
361	C₂×C₈	—	53	1	no	—
362	C₂×C₈	—	53	1	no	—
363	C₂×C₈	—	106	2	no	—
364	C₂×C₈	—	106	2	no	—
365	C₂×C₈	—	106	2	no	—
366	C₂×C₈	—	106	2	no	—
367	C₂×C₈	—	106	2	no	—
368	C₂×C₈	—	424	2	no	—
369	C₂×C₈	—	424	2	no	—
370	C₂×C₈	—	212	1	no	—
371	C₂×C₈	—	212	1	no	—
372	C₂×C₈	—	212	1	no	—
373	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
374	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
375	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
376	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
377	C₄⋊C₄	—	53	1	no	—
378	C₄⋊C₄	—	53	1	no	—
379	C₄⋊C₄	—	53	1	no	—
380	C₄⋊C₄	—	53	1	no	—
381	C₄⋊C₄	—	53	1	no	—
382	C₄⋊C₄	C₄⋊#6157	1	1	yes	characteristic
383	C₂²⋊C₄	—	53	1	no	—
384	C₂²⋊C₄	—	53	1	no	—
385	C₂²⋊C₄	—	53	1	no	—
386	C₂²⋊C₄	—	53	1	no	—
387	C₂²⋊C₄	C₄⋊#6157	1	1	yes	characteristic
388	C₂²⋊C₄	C₄⋊#6157	1	1	yes	characteristic
389	C₄²	—	53	1	no	—
390	C₄²	—	53	1	no	—
391	C₄²	—	53	1	no	—
392	C₄²	—	53	1	no	—
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	C₂²×#6157	1	1	yes	characteristic
399	C₂³	—	53	1	no	—
400	C₂³	C₂×C₄⋊#6157	1	1	yes	characteristic
401	C₂³	C₂×C₄⋊#6157	1	1	yes	characteristic
402	Q₈	—	106	2	no	—
403	D₄	—	2	2	no	—
404	D₄	—	53	4	no	—
405	D₄	—	106	2	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	—	53	1	no	—
411	C₂×C₄	—	53	1	no	—
412	C₂×C₄	—	53	1	no	—
413	C₂×C₄	—	53	1	no	—
414	C₂×C₄	—	53	1	no	—
415	C₂×C₄	—	53	1	no	—
416	C₂×C₄	—	53	1	no	—
417	C₂×C₄	—	106	2	no	—
418	C₂×C₄	—	106	2	no	—
419	C₂×C₄	—	106	2	no	—
420	C₂×C₄	—	106	2	no	—
421	C₂×C₄	—	106	2	no	—
422	C₂×C₄	—	106	2	no	—
423	C₂×C₄	—	106	1	no	—
424	C₂×C₄	—	106	1	no	—
425	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
426	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
427	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
428	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
429	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
430	C₈	—	2	1	no	—
431	C₈	—	2	1	no	—
432	C₈	—	2	1	no	—
433	C₈	—	106	1	no	—
434	C₈	—	106	1	no	—
435	C₈	—	106	1	no	—
436	C₈	—	106	1	no	—
437	C₈	—	212	2	no	—
438	C₈	—	212	2	no	—
439	C₈	—	212	2	no	—
440	C₈	—	212	2	no	—
441	C₈	#13133304	1	2	yes	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	1	no	—
447	C₂²	—	53	2	no	—
448	C₂²	—	106	1	no	—
449	C₂²	—	106	1	no	—
450	C₂²	D₅₃⋊#108	1	2	yes	—
451	C₂²	C₂²×C₄⋊#6157	1	1	yes	characteristic
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	53	2	no	—
457	C₄	—	53	2	no	—
458	C₄	—	106	1	no	—
459	C₄	—	106	1	no	—
460	C₄	—	106	1	no	—
461	C₄	—	106	1	no	—
462	C₄	—	106	1	no	—
463	C₄	C₂×#13133304	1	1	yes	characteristic
464	C₄	#16811702	1	1	yes	characteristic
465	C₂	—	2	2	no	—
466	C₂	—	4	1	no	—
467	C₂	—	106	2	no	—
468	C₂	#20291360	1	1	yes	characteristic
469	C₂	#20291369	1	1	yes	characteristic
470	C₂	C₂×D₅₃⋊#108	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	Q₈
cosocle	C₄×Dic₅₃	C₂⁴
hypercenter	C₈×D₄	#6157
hypocenter	C₅₃	#17834
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. #20290291	C₂	semidirect
3. #20290290	C₂	semidirect
4. #20290289	C₂	semidirect
5. #20290276	C₂	semidirect
6. #20290275	C₂	semidirect
7. #20290269	C₂	semidirect
8. #20290262	C₂	semidirect
9. D₅₃⋊#334	C₂	semidirect
10. C₂×#16811484	C₂	semidirect
282. C₅₃	#17834	semidirect

Maximal subgroups

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

subgroup	index
#20291640	2
#20290291	2
#20290290	2
#20290289	2
#20290276	2
#20290275	2
#20290269	2
#20290262	2
D₅₃⋊#334	2
C₂×#16811484	2
C₈×#11719947	2
#17834	53