Subgroups — C₂×#20290517 #28318339

Order 13568.

1102 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅₃⋊#108	C₂	1	1	yes	maximal, characteristic
2	C₂×#16811633	C₂	1	1	yes	maximal, characteristic
3	C₂×#16811586	C₂	1	2	yes	maximal
4	#20290517	C₂	1	8	yes	maximal, direct product factor
5	C₂×#16811494	C₂	1	2	yes	maximal
6	C₂×C₄×C₈×D₅₃	C₂	1	1	yes	maximal, characteristic
7	C₂×D₅₃⋊M₁₆	C₂²	1	2	yes	—
8	C₂×#13133296	C₂²	1	2	yes	—
9	C₂×#13133288	C₄	1	2	yes	complemented
10	D₅₃⋊#108	C₄	1	4	yes	complemented
11	D₅₃⋊#108	C₂²	1	4	yes	—
12	C₂×#13133287	C₄	1	2	yes	complemented
13	#16811633	C₄	1	4	yes	complemented
14	#16811633	C₂²	1	4	yes	—
15	C₂×#13133286	C₄	1	2	yes	complemented
16	C₂×#13133285	C₄	1	2	yes	complemented
17	#16811586	—	2	4	no	—
18	#16811586	C₂²	1	8	yes	—
19	C₂×#13133271	—	2	2	no	—
20	C₂×C₈×#6157	—	2	2	no	—
21	#16811494	C₂²	1	8	yes	—
22	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
23	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
24	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×#88322	C₄	1	1	yes	characteristic, complemented
26	C₂×C₈×Dic₅₃	C₄	1	1	yes	characteristic, complemented
27	C₂×C₈×Dic₅₃	C₄	1	1	yes	characteristic, complemented
28	C₄×C₈×D₅₃	C₄	1	4	yes	complemented
29	C₄×C₈×D₅₃	C₂²	1	4	yes	—
30	C₂×C₄×C₈×C₅₃	C₄	1	1	yes	characteristic, complemented
31	C₂×#11719936	C₂×C₄	1	4	yes	—
32	D₅₃⋊M₁₆	—	2	2	no	—
33	D₅₃⋊M₁₆	—	2	2	no	—
34	D₅₃⋊M₁₆	C₂×C₄	1	4	yes	—
35	D₅₃⋊M₁₆	C₂³	1	4	yes	—
36	C₂×#11719940	—	2	2	no	—
37	C₂×D₅₃⋊C₈	—	2	2	no	—
38	#13133296	—	2	2	no	—
39	#13133296	—	2	2	no	—
40	#13133296	C₂×C₄	1	4	yes	—
41	#13133296	C₂³	1	4	yes	—
42	C₂×C₄⋊#6157	C₂×C₄	1	4	yes	—
43	C₂×C₂²⋊#6157	—	2	2	no	—
44	C₂×C₄×#6157	—	2	2	no	—
45	#13133288	C₂×C₄	1	8	yes	complemented
46	#13133287	C₂×C₄	1	8	yes	complemented
47	#13133286	C₂×C₄	1	8	yes	complemented
48	#13133285	C₂×C₄	1	8	yes	complemented
49	#13133271	—	2	8	no	—
50	C₈×#6157	—	2	8	no	—
51	C₂²×C₄×D₅₃	—	2	1	no	—
52	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
53	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
54	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
56	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
59	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
61	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
63	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
64	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
65	C₂×C₈×D₅₃	D₄	1	2	yes	—
66	C₂×C₈×D₅₃	Q₈	1	2	yes	—
67	C₂×C₈×D₅₃	Q₈	1	1	yes	characteristic
68	C₂×C₈×D₅₃	Q₈	1	1	yes	characteristic
69	C₂×C₈×D₅₃	C₂³	1	2	yes	—
70	C₂×C₈×D₅₃	C₂³	1	2	yes	—
71	C₂×C₄×Dic₅₃	—	2	1	no	—
72	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
73	C₄²×D₅₃	—	2	1	no	—
74	C₄²×D₅₃	—	2	1	no	—
75	C₄²×D₅₃	C₂×C₄	1	2	yes	—
76	C₄²×D₅₃	C₂³	1	2	yes	—
77	C₄×#88322	C₂×C₄	1	4	yes	complemented
78	C₈×Dic₅₃	C₂×C₄	1	4	yes	complemented
79	C₈×Dic₅₃	C₂×C₄	1	4	yes	complemented
80	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
81	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
83	C₄×C₈×C₅₃	C₂×C₄	1	4	yes	complemented
84	C₂³×D₅₃	#41	1	1	yes	characteristic
85	C₂²×#6157	—	2	4	no	—
86	C₂²×C₄×C₅₃	—	2	1	no	—
87	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
88	C₂²×Dic₅₃	—	2	1	no	—
89	C₂²×Dic₅₃	#41	1	1	yes	characteristic
90	C₂×C₄×D₅₃	—	2	8	no	—
91	C₂×C₄×D₅₃	—	2	2	no	—
92	C₂×C₄×D₅₃	—	2	2	no	—
93	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
99	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
100	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
101	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
102	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
103	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
104	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
105	C₂²⋊#6157	—	2	4	no	—
106	C₂²⋊#6157	—	2	4	no	—
107	#11719940	—	2	4	no	—
108	#11719940	—	2	4	no	—
109	C₂×#88324	—	2	4	no	—
110	C₄⋊#6157	—	2	4	no	—
111	C₄⋊#6157	C₂²×C₄	1	8	yes	—
112	C₄×#6157	—	2	4	no	—
113	C₄×#6157	—	2	4	no	—
114	#11719936	—	2	4	no	—
115	#11719936	C₂²×C₄	1	8	yes	—
116	D₅₃⋊C₈	—	2	4	no	—
117	D₅₃⋊C₈	—	2	4	no	—
118	C₂×C₈×C₅₃	C₄²	1	1	yes	characteristic
119	C₂×C₈×C₅₃	C₄²	1	1	yes	characteristic
120	C₂×C₈×C₅₃	C₄²	1	2	yes	—
121	C₂×C₈×C₅₃	C₄⋊C₄	1	1	yes	characteristic
122	C₂×C₈×C₅₃	C₄⋊C₄	1	2	yes	—
123	C₂×C₈×C₅₃	C₄⋊C₄	1	1	yes	characteristic
124	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
126	C₄²×C₅₃	—	2	1	no	—
127	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
128	C₄×Dic₅₃	—	2	1	no	—
129	C₄×Dic₅₃	—	2	2	no	—
130	C₄×Dic₅₃	—	2	2	no	—
131	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
132	C₂×#88322	C₄²	1	1	yes	characteristic
133	C₂×#88322	C₄²	1	1	yes	characteristic
134	C₂×#88322	C₄²	1	2	yes	—
135	C₂×#88322	C₄⋊C₄	1	1	yes	characteristic
136	C₂×#88322	C₄⋊C₄	1	1	yes	characteristic
137	C₂×#88322	C₄⋊C₄	1	2	yes	—
138	C₂×#88322	C₂²×C₄	1	2	yes	—
139	C₂×#88322	C₂²×C₄	1	2	yes	—
140	C₈×D₅₃	C₄²	1	2	yes	—
141	C₈×D₅₃	C₄²	1	2	yes	—
142	C₈×D₅₃	C₄²	1	2	yes	—
143	C₈×D₅₃	C₄²	1	2	yes	—
144	C₈×D₅₃	C₄⋊C₄	1	2	yes	—
145	C₈×D₅₃	C₄⋊C₄	1	2	yes	—
146	C₈×D₅₃	C₄⋊C₄	1	2	yes	—
147	C₈×D₅₃	C₄⋊C₄	1	2	yes	—
148	C₈×D₅₃	C₂²×C₄	1	2	yes	—
149	C₈×D₅₃	C₂²×C₄	1	2	yes	—
150	C₈×D₅₃	C₂²×C₄	1	2	yes	—
151	C₈×D₅₃	C₂²×C₄	1	2	yes	—
152	C₈×D₅₃	C₂×D₄	1	2	yes	—
153	C₈×D₅₃	C₂×D₄	1	2	yes	—
154	C₈×D₅₃	C₂×Q₈	1	2	yes	—
155	C₈×D₅₃	C₂×Q₈	1	2	yes	—
156	C₂³×C₅₃	#117	1	1	yes	characteristic
157	C₂²×D₅₃	—	2	4	no	—
158	C₂²×D₅₃	#117	1	1	yes	characteristic
159	C₂²×D₅₃	C₄×D₄	1	1	yes	characteristic
160	C₂²×D₅₃	C₄×D₄	1	1	yes	characteristic
161	C₂²×D₅₃	C₄×Q₈	1	1	yes	characteristic
162	C₂²×D₅₃	C₄×Q₈	1	1	yes	characteristic
163	C₂²×D₅₃	C₂×#41	1	1	yes	characteristic
164	C₂×#6157	—	2	8	no	—
165	C₂×#6157	—	4	8	no	—
166	C₂×C₄×C₅₃	—	2	4	no	—
167	C₂×C₄×C₅₃	—	2	2	no	—
168	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
169	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
170	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₅₃	#117	1	1	yes	characteristic
173	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
174	C₂×Dic₅₃	—	2	4	no	—
175	C₂×Dic₅₃	—	2	2	no	—
176	C₂×Dic₅₃	#117	1	1	yes	characteristic
177	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
178	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
179	C₂×Dic₅₃	C₄×Q₈	1	1	yes	characteristic
180	C₂×Dic₅₃	C₄×Q₈	1	1	yes	characteristic
181	C₂×Dic₅₃	C₂×#41	1	1	yes	characteristic
182	C₄×D₅₃	—	2	8	no	—
183	C₄×D₅₃	—	2	8	no	—
184	C₄×D₅₃	C₂×C₄²	1	1	yes	characteristic
185	C₄×D₅₃	C₂×C₄²	1	1	yes	characteristic
186	C₄×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₄×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
189	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
190	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
191	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
192	C₄×D₅₃	C₄×Q₈	1	1	yes	characteristic
193	C₄×D₅₃	C₄×Q₈	1	1	yes	characteristic
194	C₄×D₅₃	C₄×Q₈	1	1	yes	characteristic
195	C₄×D₅₃	C₄×Q₈	1	1	yes	characteristic
196	C₄×D₅₃	C₂³×C₄	1	1	yes	characteristic
197	C₄×D₅₃	C₂³×C₄	1	1	yes	characteristic
198	C₄×D₅₃	C₂²×D₄	1	1	yes	characteristic
199	C₄×D₅₃	C₂²×Q₈	1	1	yes	characteristic
200	#88324	—	2	8	no	—
201	C₈×C₅₃	C₂×C₄²	1	2	yes	—
202	C₈×C₅₃	C₂×C₄²	1	2	yes	—
203	C₈×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
204	C₈×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
205	#88322	C₂×C₄²	1	2	yes	—
206	#88322	C₂×C₄²	1	2	yes	—
207	#88322	C₂×C₄⋊C₄	1	2	yes	—
208	#88322	C₂×C₄⋊C₄	1	2	yes	—
209	C₂×#1772	—	53	1	no	maximal, Sylow
210	C₂²×C₅₃	—	2	2	no	—
211	C₂²×C₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
212	C₂²×C₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
213	C₂²×C₅₃	C₂×#117	1	1	yes	characteristic
214	C₂×D₅₃	—	2	2	no	—
215	C₂×D₅₃	—	2	2	no	—
216	C₂×D₅₃	—	2	2	no	—
217	C₂×D₅₃	—	2	2	no	—
218	C₂×D₅₃	—	2	2	no	—
219	C₂×D₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
220	C₂×D₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
221	C₂×D₅₃	#443	1	4	yes	—
222	C₂×D₅₃	C₂×C₄×D₄	1	1	yes	characteristic
223	C₂×D₅₃	C₂×C₄×Q₈	1	1	yes	characteristic
224	#6157	—	4	8	no	—
225	C₄×C₅₃	—	2	4	no	—
226	C₄×C₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
227	C₄×C₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
228	C₄×C₅₃	C₂²×C₄²	1	1	yes	characteristic
229	C₄×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
230	Dic₅₃	—	2	4	no	—
231	Dic₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
232	Dic₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
233	Dic₅₃	C₂×C₄×D₄	1	1	yes	characteristic
234	Dic₅₃	C₂×C₄×Q₈	1	1	yes	characteristic
235	C₂²×#108	—	53	1	no	—
236	C₂×#427	—	53	1	no	—
237	C₂×#405	—	53	2	no	—
238	C₂²×C₄×C₈	—	53	1	no	—
239	#1772	—	53	8	no	—
240	C₂×#339	—	53	2	no	—
241	C₂×C₅₃	—	2	1	no	—
242	C₂×C₅₃	—	2	1	no	—
243	C₂×C₅₃	#1772	1	2	yes	complemented
244	C₂×C₅₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
245	D₅₃	—	2	1	no	—
246	D₅₃	—	2	1	no	—
247	D₅₃	#1772	1	2	yes	complemented
248	D₅₃	C₂×#443	1	2	yes	—
249	C₂²×M₁₆	—	53	2	no	—
250	C₂³×C₈	—	53	1	no	—
251	C₂³×C₈	—	53	1	no	—
252	C₂×#117	—	53	2	no	—
253	C₂²×C₄²	—	53	1	no	—
254	C₂×#108	—	53	2	no	—
255	C₂×#108	—	53	4	no	—
256	C₂×#108	—	53	4	no	—
257	C₂×#108	—	53	2	no	—
258	#427	—	53	4	no	—
259	#427	—	53	4	no	—
260	C₂×#107	—	53	2	no	—
261	C₂×#106	—	53	2	no	—
262	#405	—	53	8	no	—
263	#405	—	106	4	no	—
264	C₂×#97	—	106	2	no	—
265	C₂×C₄×C₈	—	53	1	no	—
266	C₂×C₄×C₈	—	53	1	no	—
267	C₂×C₄×C₈	—	53	1	no	—
268	C₂×C₄×C₈	—	53	4	no	—
269	C₂×C₄×C₈	—	53	4	no	—
270	C₂×C₄×C₈	—	106	2	no	—
271	C₂×C₄×C₈	#6157	1	1	yes	characteristic, complemented
272	#339	—	53	8	no	—
273	C₅₃	C₂×#1772	1	1	yes	characteristic, complemented, Sylow
274	C₂³×C₄	—	53	1	no	—
275	C₂³×C₄	—	106	1	no	—
276	C₂×M₁₆	—	53	4	no	—
277	C₂×M₁₆	—	53	4	no	—
278	C₂×M₁₆	—	53	4	no	—
279	C₂×M₁₆	—	106	2	no	—
280	C₂×M₁₆	—	106	2	no	—
281	C₂×M₁₆	—	106	2	no	—
282	C₂²×C₈	—	53	1	no	—
283	C₂²×C₈	—	53	1	no	—
284	C₂²×C₈	—	53	1	no	—
285	C₂²×C₈	—	53	1	no	—
286	C₂²×C₈	—	53	2	no	—
287	C₂²×C₈	—	53	1	no	—
288	C₂²×C₈	—	53	2	no	—
289	C₂²×C₈	—	53	1	no	—
290	C₂²×C₈	—	53	1	no	—
291	C₂²×C₈	—	53	2	no	—
292	C₂²×C₈	—	53	2	no	—
293	C₂²×C₈	—	53	1	no	—
294	C₂²×C₈	—	53	1	no	—
295	C₂²×C₈	—	53	1	no	—
296	C₂²×C₈	—	53	2	no	—
297	C₂²×C₈	—	53	2	no	—
298	C₂²×C₈	—	53	2	no	—
299	C₂²×C₈	—	53	2	no	—
300	C₂²×C₈	—	106	2	no	—
301	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
302	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
303	#117	—	53	4	no	—
304	#117	—	53	4	no	—
305	#117	—	106	2	no	—
306	#117	—	106	2	no	—
307	C₂×C₄⋊C₄	—	53	4	no	—
308	C₂×C₂²⋊C₄	—	106	2	no	—
309	C₂×C₄²	—	53	1	no	—
310	C₂×C₄²	—	53	2	no	—
311	C₂×C₄²	—	53	2	no	—
312	C₂×C₄²	—	106	1	no	—
313	C₂×C₄²	—	106	1	no	—
314	C₂×C₄²	—	106	1	no	—
315	C₂×C₄²	—	106	2	no	—
316	C₂×C₄²	C₂×#6157	1	1	yes	characteristic
317	#108	—	53	8	no	—
318	#108	—	53	8	no	—
319	#107	—	53	8	no	—
320	#106	—	53	8	no	—
321	#97	—	106	8	no	—
322	C₄×C₈	—	53	4	no	—
323	C₄×C₈	—	53	4	no	—
324	C₄×C₈	—	53	4	no	—
325	C₄×C₈	—	106	8	no	—
326	C₄×C₈	C₂×#6157	1	4	yes	complemented
327	C₂⁴	—	53	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	53	1	no	—
330	C₂²×C₄	—	53	1	no	—
331	C₂²×C₄	—	53	1	no	—
332	C₂²×C₄	—	53	1	no	—
333	C₂²×C₄	—	53	1	no	—
334	C₂²×C₄	—	53	1	no	—
335	C₂²×C₄	—	53	1	no	—
336	C₂²×C₄	—	53	1	no	—
337	C₂²×C₄	—	53	1	no	—
338	C₂²×C₄	—	53	1	no	—
339	C₂²×C₄	—	53	1	no	—
340	C₂²×C₄	—	53	1	no	—
341	C₂²×C₄	—	53	1	no	—
342	C₂²×C₄	—	106	2	no	—
343	C₂²×C₄	—	106	2	no	—
344	C₂²×C₄	—	106	8	no	—
345	C₂²×C₄	—	106	1	no	—
346	C₂²×C₄	—	106	4	no	—
347	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
348	M₁₆	—	53	8	no	—
349	M₁₆	—	106	4	no	—
350	M₁₆	—	106	4	no	—
351	M₁₆	—	106	4	no	—
352	C₂×C₈	—	53	1	no	—
353	C₂×C₈	—	53	1	no	—
354	C₂×C₈	—	53	2	no	—
355	C₂×C₈	—	53	2	no	—
356	C₂×C₈	—	53	1	no	—
357	C₂×C₈	—	53	1	no	—
358	C₂×C₈	—	53	2	no	—
359	C₂×C₈	—	53	2	no	—
360	C₂×C₈	—	53	2	no	—
361	C₂×C₈	—	53	2	no	—
362	C₂×C₈	—	53	2	no	—
363	C₂×C₈	—	53	2	no	—
364	C₂×C₈	—	53	2	no	—
365	C₂×C₈	—	53	2	no	—
366	C₂×C₈	—	53	2	no	—
367	C₂×C₈	—	53	2	no	—
368	C₂×C₈	—	53	2	no	—
369	C₂×C₈	—	53	2	no	—
370	C₂×C₈	—	53	2	no	—
371	C₂×C₈	—	53	2	no	—
372	C₂×C₈	—	53	2	no	—
373	C₂×C₈	—	53	2	no	—
374	C₂×C₈	—	53	2	no	—
375	C₂×C₈	—	53	2	no	—
376	C₂×C₈	—	106	4	no	—
377	C₂×C₈	—	106	4	no	—
378	C₂×C₈	—	106	4	no	—
379	C₂×C₈	C₄×#6157	1	1	yes	characteristic
380	C₂×C₈	C₄×#6157	1	1	yes	characteristic
381	C₂×C₈	C₄×#6157	1	2	yes	—
382	C₂×C₈	C₄⋊#6157	1	1	yes	characteristic
383	C₂×C₈	C₄⋊#6157	1	2	yes	—
384	C₂×C₈	C₄⋊#6157	1	1	yes	characteristic
385	C₂×C₈	C₂²×#6157	1	2	yes	—
386	C₂×C₈	C₂²×#6157	1	2	yes	—
387	C₄⋊C₄	—	53	8	no	—
388	C₄⋊C₄	—	106	4	no	—
389	C₂²⋊C₄	—	106	4	no	—
390	C₂²⋊C₄	—	106	4	no	—
391	C₄²	—	2	1	no	—
392	C₄²	—	53	2	no	—
393	C₄²	—	106	2	no	—
394	C₄²	—	106	2	no	—
395	C₄²	—	106	4	no	—
396	C₄²	—	106	4	no	—
397	C₄²	—	106	1	no	—
398	C₄²	C₂²×#6157	1	2	yes	—
399	C₂³	—	53	1	no	—
400	C₂³	—	53	1	no	—
401	C₂³	—	53	1	no	—
402	C₂³	—	53	1	no	—
403	C₂³	—	53	1	no	—
404	C₂³	—	53	1	no	—
405	C₂³	—	106	4	no	—
406	C₂³	#13133296	1	1	yes	characteristic
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	53	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	—	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	—	53	1	no	—
424	C₂×C₄	—	53	1	no	—
425	C₂×C₄	—	53	1	no	—
426	C₂×C₄	—	53	1	no	—
427	C₂×C₄	—	53	1	no	—
428	C₂×C₄	—	53	1	no	—
429	C₂×C₄	—	53	1	no	—
430	C₂×C₄	—	53	1	no	—
431	C₂×C₄	—	106	8	no	—
432	C₂×C₄	—	106	8	no	—
433	C₂×C₄	—	106	4	no	—
434	C₂×C₄	—	106	2	no	—
435	C₂×C₄	—	106	8	no	—
436	C₂×C₄	—	212	8	no	—
437	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
438	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
439	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
440	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
441	C₂×C₄	#13133296	1	1	yes	characteristic
442	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
443	C₈	—	53	2	no	—
444	C₈	—	53	2	no	—
445	C₈	—	53	2	no	—
446	C₈	—	53	2	no	—
447	C₈	—	106	8	no	—
448	C₈	C₂×C₄×#6157	1	2	yes	—
449	C₈	C₂×C₄×#6157	1	2	yes	—
450	C₈	C₂×C₄⋊#6157	1	2	yes	—
451	C₈	C₂×C₄⋊#6157	1	2	yes	—
452	C₂²	—	2	2	no	—
453	C₂²	—	53	1	no	—
454	C₂²	—	53	1	no	—
455	C₂²	—	53	4	no	—
456	C₂²	—	53	1	no	—
457	C₂²	—	53	1	no	—
458	C₂²	—	106	2	no	—
459	C₂²	—	106	2	no	—
460	C₂²	—	106	2	no	—
461	C₂²	—	106	2	no	—
462	C₂²	—	106	2	no	—
463	C₂²	C₄×C₄⋊#6157	1	1	yes	characteristic
464	C₂²	C₄×C₄⋊#6157	1	1	yes	characteristic
465	C₂²	C₂×#13133296	1	1	yes	characteristic
466	C₄	—	2	4	no	—
467	C₄	—	53	1	no	—
468	C₄	—	53	1	no	—
469	C₄	—	53	1	no	—
470	C₄	—	53	1	no	—
471	C₄	—	106	4	no	—
472	C₄	—	212	8	no	—
473	C₄	C₄×C₄⋊#6157	1	1	yes	characteristic
474	C₄	C₄×C₄⋊#6157	1	1	yes	characteristic
475	C₄	C₂²×C₄×#6157	1	1	yes	characteristic
476	C₄	C₂²×C₄⋊#6157	1	1	yes	characteristic
477	C₂	—	2	1	no	—
478	C₂	—	2	1	no	—
479	C₂	—	53	2	no	—
480	C₂	—	53	2	no	—
481	C₂	—	106	1	no	—
482	C₂	—	106	1	no	—
483	C₂	#20290517	1	2	yes	direct product factor
484	C₂	C₂×C₄×C₄⋊#6157	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₄⋊#6157
commutator	C₄×C₅₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#6157
Fitting	C₂×C₄×C₈×C₅₃	C₄
socle	C₂²×C₅₃	C₄×C₄⋊C₄
prime radical	C₂³×D₅₃	#41
cosocle	C₂×C₄×D₅₃	C₂⁴
hypercenter	C₂×C₄×C₈	#6157
hypocenter	C₅₃	C₂×#1772
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
4. #20290517	C₂	direct (N × H)
9. C₂×#13133288	C₄	semidirect
10. D₅₃⋊#108	C₄	semidirect
12. C₂×#13133287	C₄	semidirect
13. #16811633	C₄	semidirect
15. C₂×#13133286	C₄	semidirect
16. C₂×#13133285	C₄	semidirect
25. C₂×C₄×#88322	C₄	semidirect
26. C₂×C₈×Dic₅₃	C₄	semidirect
27. C₂×C₈×Dic₅₃	C₄	semidirect
28. C₄×C₈×D₅₃	C₄	semidirect
30. C₂×C₄×C₈×C₅₃	C₄	semidirect
45. #13133288	C₂×C₄	semidirect
46. #13133287	C₂×C₄	semidirect
47. #13133286	C₂×C₄	semidirect
48. #13133285	C₂×C₄	semidirect
77. C₄×#88322	C₂×C₄	semidirect
78. C₈×Dic₅₃	C₂×C₄	semidirect
79. C₈×Dic₅₃	C₂×C₄	semidirect
83. C₄×C₈×C₅₃	C₂×C₄	semidirect
243. C₂×C₅₃	#1772	semidirect
247. D₅₃	#1772	semidirect
271. C₂×C₄×C₈	#6157	semidirect
273. C₅₃	C₂×#1772	semidirect
326. C₄×C₈	C₂×#6157	semidirect
483. C₂	#20290517	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×D₅₃⋊#108	2
C₂×#16811633	2
C₂×#16811586	2
#20290517	2
C₂×#16811494	2
C₂×C₄×C₈×D₅₃	2
C₂×#1772	53

Subgroups — C2×#20290517 #28318339

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20290517 #28318339