Subgroups — C₂×#20290521 #28318344

Order 13568.

1062 conjugacy classes of subgroups.

The subgroup lattice has 466 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	#20290521	C₂	1	8	yes	maximal, direct product factor
5	C₂×#16811494	C₂	1	2	yes	maximal
6	C₂×#97×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×#13133128	C₄	1	1	yes	characteristic, complemented
26	C₂×#13133127	C₄	1	1	yes	characteristic, complemented
27	C₂×#13133127	C₄	1	1	yes	characteristic, complemented
28	#97×D₅₃	C₄	1	4	yes	complemented
29	#97×D₅₃	C₂²	1	4	yes	—
30	C₂×#97×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	2	yes	—
64	C₂×C₈×D₅₃	D₄	1	2	yes	—
65	C₂×C₈×D₅₃	Q₈	1	2	yes	—
66	C₂×C₈×D₅₃	Q₈	1	2	yes	—
67	C₂×C₈×D₅₃	C₂³	1	2	yes	—
68	C₂×C₈×D₅₃	C₂³	1	2	yes	—
69	C₂×C₄×Dic₅₃	—	2	1	no	—
70	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
71	C₄²×D₅₃	—	2	1	no	—
72	C₄²×D₅₃	—	2	1	no	—
73	C₄²×D₅₃	C₂×C₄	1	2	yes	—
74	C₄²×D₅₃	C₂³	1	2	yes	—
75	#13133128	C₂×C₄	1	4	yes	complemented
76	#13133127	C₂×C₄	1	4	yes	complemented
77	#13133127	C₂×C₄	1	4	yes	complemented
78	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
79	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
81	#97×C₅₃	C₂×C₄	1	4	yes	complemented
82	C₂³×D₅₃	#41	1	1	yes	characteristic
83	C₂²×#6157	—	2	4	no	—
84	C₂²×C₄×C₅₃	—	2	1	no	—
85	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
86	C₂²×Dic₅₃	—	2	1	no	—
87	C₂²×Dic₅₃	#41	1	1	yes	characteristic
88	C₂×C₄×D₅₃	—	2	2	no	—
89	C₂×C₄×D₅₃	—	2	2	no	—
90	C₂×C₄×D₅₃	—	4	4	no	—
91	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
97	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
98	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
99	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
100	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
101	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
102	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
103	C₂²⋊#6157	—	2	4	no	—
104	C₂²⋊#6157	—	2	4	no	—
105	#11719940	—	2	4	no	—
106	#11719940	—	2	4	no	—
107	C₂×#88324	—	2	4	no	—
108	C₄⋊#6157	—	2	4	no	—
109	C₄⋊#6157	C₂²×C₄	1	8	yes	—
110	C₄×#6157	—	2	4	no	—
111	C₄×#6157	—	2	4	no	—
112	#11719936	—	2	4	no	—
113	#11719936	C₂²×C₄	1	8	yes	—
114	D₅₃⋊C₈	—	2	4	no	—
115	D₅₃⋊C₈	—	2	4	no	—
116	C₂×C₈×C₅₃	C₄²	1	1	yes	characteristic
117	C₂×C₈×C₅₃	C₄²	1	1	yes	characteristic
118	C₂×C₈×C₅₃	C₄²	1	2	yes	—
119	C₂×C₈×C₅₃	C₄⋊C₄	1	2	yes	—
120	C₂×C₈×C₅₃	C₄⋊C₄	1	2	yes	—
121	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
122	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
123	C₄²×C₅₃	—	2	1	no	—
124	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
125	C₄×Dic₅₃	—	2	1	no	—
126	C₄×Dic₅₃	—	2	2	no	—
127	C₄×Dic₅₃	—	2	2	no	—
128	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
129	C₂×#88322	C₄²	1	1	yes	characteristic
130	C₂×#88322	C₄²	1	1	yes	characteristic
131	C₂×#88322	C₄²	1	2	yes	—
132	C₂×#88322	C₄⋊C₄	1	2	yes	—
133	C₂×#88322	C₄⋊C₄	1	2	yes	—
134	C₂×#88322	C₂²×C₄	1	2	yes	—
135	C₂×#88322	C₂²×C₄	1	2	yes	—
136	C₈×D₅₃	C₄²	1	2	yes	—
137	C₈×D₅₃	C₄²	1	2	yes	—
138	C₈×D₅₃	C₄²	1	2	yes	—
139	C₈×D₅₃	C₄²	1	2	yes	—
140	C₈×D₅₃	C₄⋊C₄	1	4	yes	—
141	C₈×D₅₃	C₄⋊C₄	1	4	yes	—
142	C₈×D₅₃	C₂²×C₄	1	2	yes	—
143	C₈×D₅₃	C₂²×C₄	1	2	yes	—
144	C₈×D₅₃	C₂²×C₄	1	2	yes	—
145	C₈×D₅₃	C₂²×C₄	1	2	yes	—
146	C₈×D₅₃	C₂×D₄	1	4	yes	—
147	C₈×D₅₃	C₂×Q₈	1	4	yes	—
148	C₂³×C₅₃	#117	1	1	yes	characteristic
149	C₂²×D₅₃	—	2	4	no	—
150	C₂²×D₅₃	#117	1	1	yes	characteristic
151	C₂²×D₅₃	C₄×D₄	1	1	yes	characteristic
152	C₂²×D₅₃	C₄×D₄	1	1	yes	characteristic
153	C₂²×D₅₃	C₄×Q₈	1	1	yes	characteristic
154	C₂²×D₅₃	C₄×Q₈	1	1	yes	characteristic
155	C₂²×D₅₃	C₂×#41	1	1	yes	characteristic
156	C₂×#6157	—	2	8	no	—
157	C₂×#6157	—	4	8	no	—
158	C₂×C₄×C₅₃	—	2	2	no	—
159	C₂×C₄×C₅₃	—	4	2	no	—
160	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
161	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
162	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₅₃	#117	1	1	yes	characteristic
165	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
166	C₂×Dic₅₃	—	2	2	no	—
167	C₂×Dic₅₃	—	4	2	no	—
168	C₂×Dic₅₃	#117	1	1	yes	characteristic
169	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
170	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
171	C₂×Dic₅₃	C₄×Q₈	1	1	yes	characteristic
172	C₂×Dic₅₃	C₄×Q₈	1	1	yes	characteristic
173	C₂×Dic₅₃	C₂×#41	1	1	yes	characteristic
174	C₄×D₅₃	—	4	4	no	—
175	C₄×D₅₃	—	4	4	no	—
176	C₄×D₅₃	C₂×C₄²	1	1	yes	characteristic
177	C₄×D₅₃	C₂×C₄²	1	1	yes	characteristic
178	C₄×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₄×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
181	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
182	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
183	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
184	C₄×D₅₃	C₄×Q₈	1	1	yes	characteristic
185	C₄×D₅₃	C₄×Q₈	1	1	yes	characteristic
186	C₄×D₅₃	C₄×Q₈	1	1	yes	characteristic
187	C₄×D₅₃	C₄×Q₈	1	1	yes	characteristic
188	C₄×D₅₃	C₂³×C₄	1	1	yes	characteristic
189	C₄×D₅₃	C₂³×C₄	1	1	yes	characteristic
190	C₄×D₅₃	C₂²×D₄	1	1	yes	characteristic
191	C₄×D₅₃	C₂²×Q₈	1	1	yes	characteristic
192	#88324	—	2	8	no	—
193	C₈×C₅₃	C₂×C₄²	1	2	yes	—
194	C₈×C₅₃	C₂×C₄²	1	2	yes	—
195	C₈×C₅₃	C₂×C₄⋊C₄	1	4	yes	—
196	#88322	C₂×C₄²	1	2	yes	—
197	#88322	C₂×C₄²	1	2	yes	—
198	#88322	C₂×C₄⋊C₄	1	4	yes	—
199	C₂×#1773	—	53	1	no	maximal, Sylow
200	C₂²×C₅₃	—	2	2	no	—
201	C₂²×C₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
202	C₂²×C₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
203	C₂²×C₅₃	C₂×#117	1	1	yes	characteristic
204	C₂×D₅₃	—	2	2	no	—
205	C₂×D₅₃	—	2	2	no	—
206	C₂×D₅₃	—	2	2	no	—
207	C₂×D₅₃	—	2	2	no	—
208	C₂×D₅₃	—	2	2	no	—
209	C₂×D₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
210	C₂×D₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
211	C₂×D₅₃	#444	1	4	yes	—
212	C₂×D₅₃	C₂×C₄×D₄	1	1	yes	characteristic
213	C₂×D₅₃	C₂×C₄×Q₈	1	1	yes	characteristic
214	#6157	—	4	8	no	—
215	C₄×C₅₃	—	4	2	no	—
216	C₄×C₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
217	C₄×C₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
218	C₄×C₅₃	C₂²×C₄²	1	1	yes	characteristic
219	C₄×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
220	Dic₅₃	—	4	2	no	—
221	Dic₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
222	Dic₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
223	Dic₅₃	C₂×C₄×D₄	1	1	yes	characteristic
224	Dic₅₃	C₂×C₄×Q₈	1	1	yes	characteristic
225	C₂²×#108	—	53	1	no	—
226	C₂×#427	—	53	1	no	—
227	C₂×#405	—	53	2	no	—
228	C₂²×#97	—	53	1	no	—
229	#1773	—	53	8	no	—
230	C₂×#339	—	53	2	no	—
231	C₂×C₅₃	—	2	1	no	—
232	C₂×C₅₃	—	2	1	no	—
233	C₂×C₅₃	#1773	1	2	yes	complemented
234	C₂×C₅₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
235	D₅₃	—	2	1	no	—
236	D₅₃	—	2	1	no	—
237	D₅₃	#1773	1	2	yes	complemented
238	D₅₃	C₂×#444	1	2	yes	—
239	C₂²×M₁₆	—	53	2	no	—
240	C₂³×C₈	—	53	1	no	—
241	C₂³×C₈	—	53	1	no	—
242	C₂×#117	—	53	2	no	—
243	C₂²×C₄²	—	53	1	no	—
244	C₂×#108	—	53	2	no	—
245	C₂×#108	—	53	4	no	—
246	C₂×#108	—	53	4	no	—
247	C₂×#108	—	53	2	no	—
248	#427	—	53	4	no	—
249	#427	—	53	4	no	—
250	C₂×#107	—	53	2	no	—
251	C₂×#106	—	53	2	no	—
252	#405	—	53	8	no	—
253	#405	—	106	4	no	—
254	C₂×#97	—	53	1	no	—
255	C₂×#97	—	53	1	no	—
256	C₂×#97	—	53	1	no	—
257	C₂×#97	—	53	4	no	—
258	C₂×#97	—	53	4	no	—
259	C₂×#97	—	106	2	no	—
260	C₂×#97	#6157	1	1	yes	characteristic, complemented
261	C₂×C₄×C₈	—	106	2	no	—
262	#339	—	53	8	no	—
263	C₅₃	C₂×#1773	1	1	yes	characteristic, complemented, Sylow
264	C₂³×C₄	—	53	1	no	—
265	C₂³×C₄	—	106	1	no	—
266	C₂×M₁₆	—	53	4	no	—
267	C₂×M₁₆	—	53	4	no	—
268	C₂×M₁₆	—	53	4	no	—
269	C₂×M₁₆	—	106	2	no	—
270	C₂×M₁₆	—	106	2	no	—
271	C₂×M₁₆	—	106	2	no	—
272	C₂²×C₈	—	53	1	no	—
273	C₂²×C₈	—	53	1	no	—
274	C₂²×C₈	—	53	1	no	—
275	C₂²×C₈	—	53	1	no	—
276	C₂²×C₈	—	53	2	no	—
277	C₂²×C₈	—	53	1	no	—
278	C₂²×C₈	—	53	2	no	—
279	C₂²×C₈	—	53	1	no	—
280	C₂²×C₈	—	53	2	no	—
281	C₂²×C₈	—	53	2	no	—
282	C₂²×C₈	—	53	2	no	—
283	C₂²×C₈	—	53	2	no	—
284	C₂²×C₈	—	53	2	no	—
285	C₂²×C₈	—	53	2	no	—
286	C₂²×C₈	—	53	2	no	—
287	C₂²×C₈	—	53	2	no	—
288	C₂²×C₈	—	106	2	no	—
289	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
290	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
291	#117	—	53	4	no	—
292	#117	—	53	4	no	—
293	#117	—	106	2	no	—
294	#117	—	106	2	no	—
295	C₂×C₄⋊C₄	—	53	4	no	—
296	C₂×C₂²⋊C₄	—	106	2	no	—
297	C₂×C₄²	—	53	1	no	—
298	C₂×C₄²	—	53	2	no	—
299	C₂×C₄²	—	53	2	no	—
300	C₂×C₄²	—	106	1	no	—
301	C₂×C₄²	—	106	1	no	—
302	C₂×C₄²	—	106	1	no	—
303	C₂×C₄²	—	106	2	no	—
304	C₂×C₄²	C₂×#6157	1	1	yes	characteristic
305	#108	—	53	8	no	—
306	#108	—	53	8	no	—
307	#107	—	53	8	no	—
308	#106	—	53	8	no	—
309	#97	—	53	4	no	—
310	#97	—	53	4	no	—
311	#97	—	53	4	no	—
312	#97	—	106	8	no	—
313	#97	C₂×#6157	1	4	yes	complemented
314	C₄×C₈	—	106	8	no	—
315	C₂⁴	—	53	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	53	1	no	—
318	C₂²×C₄	—	53	1	no	—
319	C₂²×C₄	—	53	1	no	—
320	C₂²×C₄	—	53	1	no	—
321	C₂²×C₄	—	53	1	no	—
322	C₂²×C₄	—	53	1	no	—
323	C₂²×C₄	—	53	1	no	—
324	C₂²×C₄	—	53	1	no	—
325	C₂²×C₄	—	53	1	no	—
326	C₂²×C₄	—	53	1	no	—
327	C₂²×C₄	—	53	1	no	—
328	C₂²×C₄	—	53	1	no	—
329	C₂²×C₄	—	53	1	no	—
330	C₂²×C₄	—	106	2	no	—
331	C₂²×C₄	—	106	2	no	—
332	C₂²×C₄	—	106	4	no	—
333	C₂²×C₄	—	106	1	no	—
334	C₂²×C₄	—	212	4	no	—
335	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
336	M₁₆	—	53	8	no	—
337	M₁₆	—	106	4	no	—
338	M₁₆	—	106	4	no	—
339	M₁₆	—	106	4	no	—
340	C₂×C₈	—	53	1	no	—
341	C₂×C₈	—	53	1	no	—
342	C₂×C₈	—	53	2	no	—
343	C₂×C₈	—	53	2	no	—
344	C₂×C₈	—	53	2	no	—
345	C₂×C₈	—	53	2	no	—
346	C₂×C₈	—	53	2	no	—
347	C₂×C₈	—	53	2	no	—
348	C₂×C₈	—	53	2	no	—
349	C₂×C₈	—	53	2	no	—
350	C₂×C₈	—	53	2	no	—
351	C₂×C₈	—	53	2	no	—
352	C₂×C₈	—	53	2	no	—
353	C₂×C₈	—	53	2	no	—
354	C₂×C₈	—	53	2	no	—
355	C₂×C₈	—	53	4	no	—
356	C₂×C₈	—	53	4	no	—
357	C₂×C₈	—	53	4	no	—
358	C₂×C₈	—	53	4	no	—
359	C₂×C₈	—	106	4	no	—
360	C₂×C₈	—	106	4	no	—
361	C₂×C₈	—	106	4	no	—
362	C₂×C₈	C₄×#6157	1	1	yes	characteristic
363	C₂×C₈	C₄×#6157	1	1	yes	characteristic
364	C₂×C₈	C₄×#6157	1	2	yes	—
365	C₂×C₈	C₄⋊#6157	1	2	yes	—
366	C₂×C₈	C₄⋊#6157	1	2	yes	—
367	C₂×C₈	C₂²×#6157	1	2	yes	—
368	C₂×C₈	C₂²×#6157	1	2	yes	—
369	C₄⋊C₄	—	53	8	no	—
370	C₄⋊C₄	—	106	4	no	—
371	C₂²⋊C₄	—	106	4	no	—
372	C₂²⋊C₄	—	106	4	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	53	2	no	—
375	C₄²	—	106	2	no	—
376	C₄²	—	106	2	no	—
377	C₄²	—	106	4	no	—
378	C₄²	—	106	4	no	—
379	C₄²	—	106	1	no	—
380	C₄²	C₂²×#6157	1	2	yes	—
381	C₂³	—	53	1	no	—
382	C₂³	—	53	1	no	—
383	C₂³	—	53	1	no	—
384	C₂³	—	53	1	no	—
385	C₂³	—	53	1	no	—
386	C₂³	—	53	1	no	—
387	C₂³	—	106	4	no	—
388	C₂³	#13133296	1	1	yes	characteristic
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	53	1	no	—
392	C₂×C₄	—	53	1	no	—
393	C₂×C₄	—	53	1	no	—
394	C₂×C₄	—	53	1	no	—
395	C₂×C₄	—	53	1	no	—
396	C₂×C₄	—	53	1	no	—
397	C₂×C₄	—	53	1	no	—
398	C₂×C₄	—	53	1	no	—
399	C₂×C₄	—	53	1	no	—
400	C₂×C₄	—	53	1	no	—
401	C₂×C₄	—	53	1	no	—
402	C₂×C₄	—	53	1	no	—
403	C₂×C₄	—	53	1	no	—
404	C₂×C₄	—	53	1	no	—
405	C₂×C₄	—	53	1	no	—
406	C₂×C₄	—	53	1	no	—
407	C₂×C₄	—	53	1	no	—
408	C₂×C₄	—	53	1	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	—	106	8	no	—
414	C₂×C₄	—	106	2	no	—
415	C₂×C₄	—	212	4	no	—
416	C₂×C₄	—	212	4	no	—
417	C₂×C₄	—	212	2	no	—
418	C₂×C₄	—	212	8	no	—
419	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
420	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
421	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
422	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
423	C₂×C₄	#13133296	1	1	yes	characteristic
424	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
425	C₈	—	53	2	no	—
426	C₈	—	53	2	no	—
427	C₈	—	53	4	no	—
428	C₈	—	106	8	no	—
429	C₈	C₂×C₄×#6157	1	2	yes	—
430	C₈	C₂×C₄×#6157	1	2	yes	—
431	C₈	C₂×C₄⋊#6157	1	4	yes	—
432	C₂²	—	2	2	no	—
433	C₂²	—	53	1	no	—
434	C₂²	—	53	1	no	—
435	C₂²	—	53	4	no	—
436	C₂²	—	53	1	no	—
437	C₂²	—	53	1	no	—
438	C₂²	—	106	2	no	—
439	C₂²	—	106	2	no	—
440	C₂²	—	106	2	no	—
441	C₂²	—	106	2	no	—
442	C₂²	—	106	2	no	—
443	C₂²	C₄×C₄⋊#6157	1	1	yes	characteristic
444	C₂²	C₄×C₄⋊#6157	1	1	yes	characteristic
445	C₂²	C₂×#13133296	1	1	yes	characteristic
446	C₄	—	4	2	no	—
447	C₄	—	53	1	no	—
448	C₄	—	53	1	no	—
449	C₄	—	53	1	no	—
450	C₄	—	53	1	no	—
451	C₄	—	212	2	no	—
452	C₄	—	212	8	no	—
453	C₄	C₄×C₄⋊#6157	1	1	yes	characteristic
454	C₄	C₄×C₄⋊#6157	1	1	yes	characteristic
455	C₄	C₂²×C₄×#6157	1	1	yes	characteristic
456	C₄	C₂²×C₄⋊#6157	1	1	yes	characteristic
457	C₂	—	2	1	no	—
458	C₂	—	2	1	no	—
459	C₂	—	53	2	no	—
460	C₂	—	53	2	no	—
461	C₂	—	106	1	no	—
462	C₂	—	106	1	no	—
463	C₂	#20290521	1	2	yes	direct product factor
464	C₂	C₂×C₄×C₄⋊#6157	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₄⋊#6157
commutator	C₄×C₅₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#6157
Fitting	C₂×#97×C₅₃	C₄
socle	C₂²×C₅₃	C₄×C₄⋊C₄
prime radical	C₂³×D₅₃	#41
cosocle	C₂×C₄×D₅₃	C₂⁴
hypercenter	C₂×#97	#6157
hypocenter	C₅₃	C₂×#1773
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
4. #20290521	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×#13133128	C₄	semidirect
26. C₂×#13133127	C₄	semidirect
27. C₂×#13133127	C₄	semidirect
28. #97×D₅₃	C₄	semidirect
30. C₂×#97×C₅₃	C₄	semidirect
45. #13133288	C₂×C₄	semidirect
46. #13133287	C₂×C₄	semidirect
47. #13133286	C₂×C₄	semidirect
48. #13133285	C₂×C₄	semidirect
75. #13133128	C₂×C₄	semidirect
76. #13133127	C₂×C₄	semidirect
77. #13133127	C₂×C₄	semidirect
81. #97×C₅₃	C₂×C₄	semidirect
233. C₂×C₅₃	#1773	semidirect
237. D₅₃	#1773	semidirect
260. C₂×#97	#6157	semidirect
263. C₅₃	C₂×#1773	semidirect
313. #97	C₂×#6157	semidirect
463. C₂	#20290521	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
#20290521	2
C₂×#16811494	2
C₂×#97×D₅₃	2
C₂×#1773	53

Subgroups — C2×#20290521 #28318344

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20290521 #28318344