Subgroups — #27289990

Order 13568.

982 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13133151	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×Dic₅₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#16810385	C₂	1	2	yes	maximal
4	#20272944	C₂	1	2	yes	maximal
5	C₂²×#107×C₅₃	C₂	1	1	yes	maximal, characteristic
6	C₂³×#88322	C₂²	1	1	yes	characteristic
7	C₂²×C₄⋊Dic₅₃	C₂²	1	2	yes	—
8	C₂²×C₄×Dic₅₃	C₂²	1	1	yes	characteristic
9	C₂×#13133151	—	2	2	no	—
10	C₂×#13133151	—	2	2	no	—
11	C₂×#13133151	C₄	1	4	yes	complemented
12	C₂×C₈×Dic₅₃	—	2	2	no	—
13	C₂×C₈×Dic₅₃	—	2	2	no	—
14	C₂×C₈×Dic₅₃	C₄	1	4	yes	complemented
15	C₂×#13133124	—	2	4	no	—
16	#16810385	—	2	4	no	—
17	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
19	C₂×#107×C₅₃	—	2	2	no	—
20	C₂×#107×C₅₃	—	2	2	no	—
21	C₂×#107×C₅₃	C₄	1	4	yes	complemented
22	C₂³×Dic₅₃	—	2	2	no	—
23	C₂³×Dic₅₃	D₄	1	2	yes	—
24	C₂²×#88322	—	2	1	no	—
25	C₂²×#88322	—	2	1	no	—
26	C₂²×#88322	—	2	1	no	—
27	C₂²×#88322	—	2	1	no	—
28	C₂²×#88322	C₂×C₄	1	2	yes	—
29	C₂²×#88322	D₄	1	2	yes	—
30	C₂²×#88322	Q₈	1	2	yes	—
31	C₂×C₄⋊Dic₅₃	—	2	2	no	—
32	C₂×C₄⋊Dic₅₃	—	2	2	no	—
33	C₂×C₄⋊Dic₅₃	—	2	2	no	—
34	C₂×C₄⋊Dic₅₃	—	2	2	no	—
35	C₂×C₄⋊Dic₅₃	—	2	2	no	—
36	C₂×C₄⋊Dic₅₃	C₂×C₄	1	4	yes	—
37	C₂×C₄×Dic₅₃	—	2	1	no	—
38	C₂×C₄×Dic₅₃	—	2	1	no	—
39	C₂×C₄×Dic₅₃	—	2	1	no	—
40	C₂×C₄×Dic₅₃	—	2	1	no	—
41	C₂×C₄×Dic₅₃	C₂×C₄	1	2	yes	—
42	C₂×C₄×Dic₅₃	Q₈	1	2	yes	—
43	#13133151	—	2	8	no	—
44	C₈×Dic₅₃	—	2	8	no	—
45	#13133124	—	4	8	no	—
46	C₂³×C₄×C₅₃	—	2	2	no	—
47	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₅₃	C₂×C₄	1	2	yes	—
49	C₂²×C₈×C₅₃	C₂×C₄	1	2	yes	—
50	C₂²×C₈×C₅₃	C₂×C₄	1	2	yes	—
51	C₂²×C₈×C₅₃	D₄	1	2	yes	—
52	C₂²×C₈×C₅₃	D₄	1	2	yes	—
53	C₂²×C₈×C₅₃	D₄	1	2	yes	—
54	C₂²×C₈×C₅₃	Q₈	1	2	yes	—
55	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
56	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
57	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
58	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
59	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
60	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	4	yes	—
61	#107×C₅₃	—	2	8	no	—
62	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₅₃	—	2	4	no	—
64	C₂²×C₄×C₅₃	—	4	2	no	—
65	C₂²×C₄×C₅₃	—	4	2	no	—
66	C₂²×C₄×C₅₃	—	4	4	no	—
67	C₂²×C₄×C₅₃	—	4	4	no	—
68	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
76	C₂²×C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
77	C₂²×C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
78	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
79	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
80	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
81	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
82	C₂²×Dic₅₃	—	2	2	no	—
83	C₂²×Dic₅₃	—	2	2	no	—
84	C₂²×Dic₅₃	—	2	2	no	—
85	C₂²×Dic₅₃	—	2	2	no	—
86	C₂²×Dic₅₃	—	2	4	no	—
87	C₂²×Dic₅₃	—	4	2	no	—
88	C₂²×Dic₅₃	—	4	2	no	—
89	C₂²×Dic₅₃	—	4	4	no	—
90	C₂²×Dic₅₃	—	4	4	no	—
91	C₂²×Dic₅₃	C₄⋊C₄	1	4	yes	—
92	C₂²×Dic₅₃	D₈	1	4	yes	—
93	C₂²×Dic₅₃	Q₁₆	1	4	yes	—
94	C₂×C₈×C₅₃	C₄²	1	4	yes	—
95	C₂×C₈×C₅₃	C₂²⋊C₄	1	4	yes	—
96	C₂×C₈×C₅₃	C₂²⋊C₄	1	4	yes	—
97	C₂×C₈×C₅₃	C₂²⋊C₄	1	4	yes	—
98	C₂×C₈×C₅₃	C₄⋊C₄	1	4	yes	—
99	C₂×C₈×C₅₃	C₄⋊C₄	1	4	yes	—
100	C₂×C₈×C₅₃	C₄⋊C₄	1	4	yes	—
101	C₄⋊C₄×C₅₃	—	2	4	no	—
102	C₄⋊C₄×C₅₃	—	2	4	no	—
103	C₄⋊C₄×C₅₃	—	4	2	no	—
104	C₄⋊C₄×C₅₃	—	4	2	no	—
105	C₄⋊Dic₅₃	—	2	4	no	—
106	C₄⋊Dic₅₃	—	2	4	no	—
107	C₄⋊Dic₅₃	—	4	2	no	—
108	C₄⋊Dic₅₃	—	4	2	no	—
109	C₄×Dic₅₃	—	2	2	no	—
110	C₄×Dic₅₃	—	2	2	no	—
111	C₄×Dic₅₃	—	2	2	no	—
112	C₄×Dic₅₃	—	2	2	no	—
113	C₂×#88322	—	2	2	no	—
114	C₂×#88322	—	2	2	no	—
115	C₂×#88322	—	2	2	no	—
116	C₂×#88322	—	2	2	no	—
117	C₂×#88322	—	2	2	no	—
118	C₂×#88322	—	2	2	no	—
119	C₂×#88322	C₄⋊C₄	1	4	yes	—
120	C₂³×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
121	C₂³×C₅₃	C₄×D₄	1	1	yes	characteristic
122	C₂³×C₅₃	C₄×D₄	1	1	yes	characteristic
123	C₂³×C₅₃	#121	1	1	yes	characteristic
124	C₂³×C₅₃	#121	1	1	yes	characteristic
125	C₂³×C₅₃	#127	1	1	yes	characteristic
126	C₂³×C₅₃	C₄⋊Q₈	1	1	yes	characteristic
127	C₂³×C₅₃	C₂×D₈	1	2	yes	—
128	C₂³×C₅₃	C₂×Q₁₆	1	2	yes	—
129	C₂³×C₅₃	#135	1	2	yes	—
130	C₂³×C₅₃	#135	1	2	yes	—
131	C₂×C₄×C₅₃	—	4	4	no	—
132	C₂×C₄×C₅₃	—	4	8	no	—
133	C₂×C₄×C₅₃	—	8	4	no	—
134	C₂×C₄×C₅₃	—	8	2	no	—
135	C₂×C₄×C₅₃	—	8	2	no	—
136	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
137	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₅₃	#117	1	1	yes	characteristic
145	C₂×C₄×C₅₃	#117	1	1	yes	characteristic
146	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₅₃	C₄×Q₈	1	1	yes	characteristic
149	C₂×C₄×C₅₃	C₄×Q₈	1	1	yes	characteristic
150	C₂×C₄×C₅₃	C₄×Q₈	1	1	yes	characteristic
151	C₂×C₄×C₅₃	C₄×Q₈	1	1	yes	characteristic
152	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
153	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
154	C₂×C₄×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
155	C₂×C₄×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
156	C₂×C₄×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
157	C₂×C₄×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
158	C₂×C₄×C₅₃	#124	1	1	yes	characteristic
159	C₂×C₄×C₅₃	#124	1	1	yes	characteristic
160	C₂×C₄×C₅₃	#125	1	1	yes	characteristic
161	C₂×C₄×C₅₃	#125	1	1	yes	characteristic
162	C₂×C₄×C₅₃	C₄⋊Q₈	1	1	yes	characteristic
163	C₂×C₄×C₅₃	C₄⋊Q₈	1	1	yes	characteristic
164	C₂×Dic₅₃	—	2	4	no	—
165	C₂×Dic₅₃	—	2	4	no	—
166	C₂×Dic₅₃	—	2	4	no	—
167	C₂×Dic₅₃	—	2	4	no	—
168	C₂×Dic₅₃	—	2	4	no	—
169	C₂×Dic₅₃	—	2	4	no	—
170	C₂×Dic₅₃	—	4	4	no	—
171	C₂×Dic₅₃	—	4	8	no	—
172	C₂×Dic₅₃	—	8	4	no	—
173	C₂×Dic₅₃	—	8	2	no	—
174	C₂×Dic₅₃	—	8	2	no	—
175	C₂×Dic₅₃	#107	1	8	yes	complemented
176	C₈×C₅₃	#95	1	8	yes	complemented
177	#88322	—	2	4	no	—
178	#10862	—	53	1	no	maximal, Sylow
179	C₂²×C₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
180	C₂²×C₅₃	#380	1	1	yes	characteristic
181	C₂²×C₅₃	#384	1	1	yes	characteristic
182	C₂²×C₅₃	#389	1	1	yes	characteristic
183	C₂²×C₅₃	#389	1	1	yes	characteristic
184	C₂²×C₅₃	#390	1	1	yes	characteristic
185	C₂²×C₅₃	#390	1	1	yes	characteristic
186	C₂²×C₅₃	C₂×#107	1	2	yes	—
187	C₂²×C₅₃	#427	1	2	yes	—
188	C₂²×C₅₃	C₄×D₈	1	2	yes	—
189	C₂²×C₅₃	C₄×D₈	1	2	yes	—
190	C₂²×C₅₃	C₄×Q₁₆	1	2	yes	—
191	C₂²×C₅₃	C₄×Q₁₆	1	2	yes	—
192	C₂²×C₅₃	#466	1	2	yes	—
193	C₂²×C₅₃	#466	1	2	yes	—
194	C₂²×C₅₃	#467	1	2	yes	—
195	C₂²×C₅₃	#467	1	2	yes	—
196	C₂²×C₅₃	#493	1	1	yes	characteristic
197	C₂²×C₅₃	#494	1	1	yes	characteristic
198	C₂²×C₅₃	#495	1	1	yes	characteristic
199	C₂²×C₅₃	#495	1	1	yes	characteristic
200	C₂²×C₅₃	#499	1	2	yes	—
201	C₂²×C₅₃	#500	1	2	yes	—
202	C₄×C₅₃	—	8	4	no	—
203	C₄×C₅₃	C₂×#95	1	1	yes	characteristic
204	C₄×C₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
205	C₄×C₅₃	#380	1	1	yes	characteristic
206	C₄×C₅₃	#382	1	1	yes	characteristic
207	C₄×C₅₃	#389	1	1	yes	characteristic
208	C₄×C₅₃	#389	1	1	yes	characteristic
209	C₄×C₅₃	#391	1	1	yes	characteristic
210	C₄×C₅₃	#391	1	1	yes	characteristic
211	Dic₅₃	—	2	8	no	—
212	Dic₅₃	—	8	4	no	—
213	C₂²×#107	—	53	1	no	—
214	C₂²×#107	D₅₃	1	1	yes	characteristic
215	C₂²×C₄×C₈	—	53	1	no	—
216	C₂×#340	—	53	2	no	—
217	C₄⋊#95	—	53	2	no	—
218	C₂×C₅₃	C₄⋊#95	1	1	yes	characteristic
219	C₂×C₅₃	C₄×#107	1	2	yes	—
220	C₂×C₅₃	#1808	1	2	yes	—
221	C₂×C₅₃	#1845	1	1	yes	characteristic
222	C₂×C₅₃	#1846	1	1	yes	characteristic
223	C₂×C₅₃	#1942	1	2	yes	—
224	C₂×C₅₃	#1942	1	2	yes	—
225	C₂×C₅₃	#1969	1	1	yes	characteristic
226	C₂×C₅₃	#1969	1	1	yes	characteristic
227	C₂×C₅₃	#1970	1	1	yes	characteristic
228	C₂×C₅₃	#1970	1	1	yes	characteristic
229	C₂³×C₈	—	53	1	no	—
230	C₂³×C₈	C₂×D₅₃	1	1	yes	characteristic
231	C₂²×C₄⋊C₄	—	53	2	no	—
232	C₂²×C₄⋊C₄	C₂×D₅₃	1	2	yes	—
233	C₂²×C₄²	—	53	1	no	—
234	C₂×#107	—	2	2	no	—
235	C₂×#107	—	2	2	no	—
236	C₂×#107	—	53	4	no	—
237	C₂×#107	—	106	2	no	—
238	C₂×#107	—	106	2	no	—
239	C₂×#107	Dic₅₃	1	4	yes	complemented
240	C₂×C₄×C₈	—	53	4	no	—
241	C₂×C₄×C₈	—	106	2	no	—
242	C₂×C₄×C₈	—	106	2	no	—
243	C₂×#95	—	106	4	no	—
244	#340	—	106	4	no	—
245	C₅₃	#10862	1	1	yes	characteristic, complemented, Sylow
246	C₂³×C₄	—	2	2	no	—
247	C₂³×C₄	—	53	2	no	—
248	C₂³×C₄	—	106	2	no	—
249	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
250	C₂²×C₈	—	53	2	no	—
251	C₂²×C₈	—	53	2	no	—
252	C₂²×C₈	—	53	2	no	—
253	C₂²×C₈	—	106	1	no	—
254	C₂²×C₈	—	106	1	no	—
255	C₂²×C₈	—	106	1	no	—
256	C₂²×C₈	—	106	1	no	—
257	C₂²×C₈	Dic₁₀₆	1	2	yes	—
258	C₂²×C₈	C₄×D₅₃	1	2	yes	—
259	C₂²×C₈	C₄×D₅₃	1	2	yes	—
260	C₂²×C₈	D₂₁₂	1	2	yes	—
261	C₂²×C₈	C₂×Dic₅₃	1	2	yes	—
262	C₂²×C₈	C₂²⋊D₅₃	1	2	yes	—
263	C₂²×C₈	C₂²⋊D₅₃	1	2	yes	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	53	4	no	—
270	C₂×C₄⋊C₄	—	106	2	no	—
271	C₂×C₄⋊C₄	—	106	2	no	—
272	C₂×C₄⋊C₄	—	106	2	no	—
273	C₂×C₄⋊C₄	—	106	2	no	—
274	C₂×C₄⋊C₄	—	106	2	no	—
275	C₂×C₄⋊C₄	C₂×Dic₅₃	1	4	yes	—
276	C₂×C₄²	—	53	2	no	—
277	C₂×C₄²	—	53	2	no	—
278	C₂×C₄²	—	106	1	no	—
279	C₂×C₄²	—	106	1	no	—
280	C₂×C₄²	—	106	1	no	—
281	C₂×C₄²	—	106	1	no	—
282	#107	—	2	8	no	—
283	#107	—	106	8	no	—
284	C₄×C₈	—	106	8	no	—
285	#95	—	212	8	no	—
286	C₂⁴	D₄×D₅₃	1	1	yes	characteristic
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	—	4	2	no	—
290	C₂²×C₄	—	4	4	no	—
291	C₂²×C₄	—	4	4	no	—
292	C₂²×C₄	—	53	4	no	—
293	C₂²×C₄	—	53	4	no	—
294	C₂²×C₄	—	53	4	no	—
295	C₂²×C₄	—	106	2	no	—
296	C₂²×C₄	—	106	2	no	—
297	C₂²×C₄	—	106	2	no	—
298	C₂²×C₄	—	106	2	no	—
299	C₂²×C₄	—	106	4	no	—
300	C₂²×C₄	—	212	2	no	—
301	C₂²×C₄	—	212	2	no	—
302	C₂²×C₄	—	212	4	no	—
303	C₂²×C₄	—	212	4	no	—
304	C₂²×C₄	C₂×Dic₁₀₆	1	1	yes	characteristic
305	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
306	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₂₁₂	1	1	yes	characteristic
308	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
309	C₂²×C₄	#11719947	1	1	yes	characteristic
310	C₂²×C₄	#11719947	1	1	yes	characteristic
311	C₂²×C₄	Q₈×D₅₃	1	1	yes	characteristic
312	C₂²×C₄	Q₈×D₅₃	1	1	yes	characteristic
313	C₂²×C₄	#11719949	1	1	yes	characteristic
314	C₂²×C₄	#11719949	1	1	yes	characteristic
315	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
316	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
317	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
318	C₂×C₈	—	53	4	no	—
319	C₂×C₈	—	106	2	no	—
320	C₂×C₈	—	106	2	no	—
321	C₂×C₈	—	106	2	no	—
322	C₂×C₈	—	106	2	no	—
323	C₂×C₈	—	106	2	no	—
324	C₂×C₈	—	106	2	no	—
325	C₂×C₈	C₄×Dic₅₃	1	4	yes	—
326	C₂×C₈	#11719919	1	4	yes	—
327	C₂×C₈	#11719919	1	4	yes	—
328	C₂×C₈	C₄⋊Dic₅₃	1	4	yes	—
329	C₂×C₈	#11719921	1	4	yes	—
330	C₂×C₈	#11719921	1	4	yes	—
331	C₂×C₈	C₂²⋊Dic₅₃	1	4	yes	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	4	2	no	—
335	C₄⋊C₄	—	4	2	no	—
336	C₄⋊C₄	—	106	4	no	—
337	C₄⋊C₄	—	106	4	no	—
338	C₄⋊C₄	—	212	2	no	—
339	C₄⋊C₄	—	212	2	no	—
340	C₄²	—	106	2	no	—
341	C₄²	—	106	2	no	—
342	C₄²	—	106	2	no	—
343	C₄²	—	106	2	no	—
344	C₂³	C₄⋊C₄×D₅₃	1	1	yes	characteristic
345	C₂³	#13133179	1	1	yes	characteristic
346	C₂³	D₄×Dic₅₃	1	1	yes	characteristic
347	C₂³	#13133188	1	1	yes	characteristic
348	C₂³	#13133192	1	1	yes	characteristic
349	C₂³	#13133213	1	1	yes	characteristic
350	C₂³	#13133216	1	1	yes	characteristic
351	C₂³	D₈×D₅₃	1	2	yes	—
352	C₂³	Q₁₆×D₅₃	1	2	yes	—
353	C₂³	#13133236	1	2	yes	—
354	C₂³	#13133240	1	2	yes	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	8	no	—
357	C₂×C₄	—	8	4	no	—
358	C₂×C₄	—	8	2	no	—
359	C₂×C₄	—	8	2	no	—
360	C₂×C₄	—	53	8	no	—
361	C₂×C₄	—	106	4	no	—
362	C₂×C₄	—	106	4	no	—
363	C₂×C₄	—	106	4	no	—
364	C₂×C₄	—	106	4	no	—
365	C₂×C₄	—	106	4	no	—
366	C₂×C₄	—	106	4	no	—
367	C₂×C₄	—	424	2	no	—
368	C₂×C₄	—	424	4	no	—
369	C₂×C₄	—	424	2	no	—
370	C₂×C₄	—	212	4	no	—
371	C₂×C₄	—	212	8	no	—
372	C₂×C₄	C₂×C₄×Dic₅₃	1	1	yes	characteristic
373	C₂×C₄	C₂×#11719921	1	1	yes	characteristic
374	C₂×C₄	C₂×#11719921	1	1	yes	characteristic
375	C₂×C₄	C₂×C₂²⋊Dic₅₃	1	1	yes	characteristic
376	C₂×C₄	C₄⋊C₄×D₅₃	1	1	yes	characteristic
377	C₂×C₄	C₂×#11719919	1	1	yes	characteristic
378	C₂×C₄	C₂×#11719919	1	1	yes	characteristic
379	C₂×C₄	C₂×C₄⋊Dic₅₃	1	1	yes	characteristic
380	C₂×C₄	#13133175	1	1	yes	characteristic
381	C₂×C₄	#13133175	1	1	yes	characteristic
382	C₂×C₄	#13133179	1	1	yes	characteristic
383	C₂×C₄	D₄×Dic₅₃	1	1	yes	characteristic
384	C₂×C₄	#13133182	1	1	yes	characteristic
385	C₂×C₄	#13133182	1	1	yes	characteristic
386	C₂×C₄	Q₈×Dic₅₃	1	1	yes	characteristic
387	C₂×C₄	Q₈×Dic₅₃	1	1	yes	characteristic
388	C₂×C₄	#13133188	1	1	yes	characteristic
389	C₂×C₄	#13133192	1	1	yes	characteristic
390	C₂×C₄	#13133193	1	1	yes	characteristic
391	C₂×C₄	#13133193	1	1	yes	characteristic
392	C₂×C₄	#13133197	1	1	yes	characteristic
393	C₂×C₄	#13133197	1	1	yes	characteristic
394	C₂×C₄	#13133204	1	1	yes	characteristic
395	C₂×C₄	#13133206	1	1	yes	characteristic
396	C₂×C₄	#13133208	1	1	yes	characteristic
397	C₂×C₄	#13133208	1	1	yes	characteristic
398	C₂×C₄	#13133215	1	1	yes	characteristic
399	C₂×C₄	#13133216	1	1	yes	characteristic
400	C₈	—	106	4	no	—
401	C₈	#13133124	1	8	yes	complemented
402	C₂²	C₄⋊C₄×Dic₅₃	1	1	yes	characteristic
403	C₂²	#16810480	1	1	yes	characteristic
404	C₂²	#16810492	1	1	yes	characteristic
405	C₂²	#16810519	1	1	yes	characteristic
406	C₂²	#16810522	1	1	yes	characteristic
407	C₂²	#16810524	1	1	yes	characteristic
408	C₂²	#16810526	1	1	yes	characteristic
409	C₂²	#107×D₅₃	1	2	yes	—
410	C₂²	#16810660	1	2	yes	—
411	C₂²	#16810705	1	2	yes	—
412	C₂²	D₈×Dic₅₃	1	2	yes	—
413	C₂²	#16810717	1	2	yes	—
414	C₂²	Q₁₆×Dic₅₃	1	2	yes	—
415	C₂²	#16810856	1	2	yes	—
416	C₂²	#16810860	1	2	yes	—
417	C₂²	#16810861	1	2	yes	—
418	C₂²	#16810865	1	2	yes	—
419	C₂²	#16810998	1	1	yes	characteristic
420	C₂²	#16811001	1	1	yes	characteristic
421	C₂²	#16811006	1	1	yes	characteristic
422	C₂²	#16811008	1	1	yes	characteristic
423	C₂²	#16811024	1	2	yes	—
424	C₂²	#16811027	1	2	yes	—
425	C₄	—	8	4	no	—
426	C₄	—	106	8	no	—
427	C₄	—	424	4	no	—
428	C₄	C₂×#13133124	1	1	yes	characteristic
429	C₄	C₄⋊C₄×Dic₅₃	1	1	yes	characteristic
430	C₄	#16810480	1	1	yes	characteristic
431	C₄	#16810488	1	1	yes	characteristic
432	C₄	#16810519	1	1	yes	characteristic
433	C₄	#16810522	1	1	yes	characteristic
434	C₄	#16810528	1	1	yes	characteristic
435	C₄	#16810530	1	1	yes	characteristic
436	C₂	#20272944	1	1	yes	characteristic
437	C₂	#107×Dic₅₃	1	2	yes	—
438	C₂	#20274741	1	2	yes	—
439	C₂	#20274873	1	1	yes	characteristic
440	C₂	#20274878	1	1	yes	characteristic
441	C₂	#20275446	1	2	yes	—
442	C₂	#20275449	1	2	yes	—
443	C₂	#20275574	1	1	yes	characteristic
444	C₂	#20275577	1	1	yes	characteristic
445	C₂	#20275579	1	1	yes	characteristic
446	C₂	#20275582	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	D₄×D₅₃
commutator	C₂×C₄×C₅₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₅₃
Fitting	C₂²×#107×C₅₃	C₂
socle, prime radical	C₂⁴×C₅₃	C₂×D₄
cosocle	C₂³×C₄×C₅₃	C₂³
hypercenter	C₂²×#107	D₅₃
hypocenter	C₅₃	#10862
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂²×#107

Complements

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

N	H ≅ G/N	type
11. C₂×#13133151	C₄	semidirect
14. C₂×C₈×Dic₅₃	C₄	semidirect
21. C₂×#107×C₅₃	C₄	semidirect
175. C₂×Dic₅₃	#107	semidirect
176. C₈×C₅₃	#95	semidirect
239. C₂×#107	Dic₅₃	semidirect
245. C₅₃	#10862	semidirect
401. C₈	#13133124	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13133151	2
C₂²×C₈×Dic₅₃	2
C₂×#16810385	2
#20272944	2
C₂²×#107×C₅₃	2
#10862	53