Subgroups — C₂×#20272543 #27273487

Order 13568.

758 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16810676	C₂	1	1	yes	maximal, characteristic
2	C₂×#16810469	C₂	1	1	yes	maximal, characteristic
3	#20272543	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₅₃×#431	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄×Dic₅₃	C₄	1	2	yes	—
6	#16810676	—	2	1	no	—
7	#16810676	—	2	1	no	—
8	#16810676	C₄	1	2	yes	complemented
9	#16810676	C₂²	1	2	yes	—
10	C₂×C₄⋊#88322	—	2	1	no	—
11	C₂×C₂²⋊#88322	—	2	1	no	—
12	C₂×C₄×#88322	C₄	1	2	yes	complemented
13	#16810469	—	2	1	no	—
14	#16810469	—	2	1	no	—
15	#16810469	C₄	1	2	yes	—
16	#16810469	C₂²	1	2	yes	—
17	C₂×#13133124	—	2	1	no	—
18	C₂×#13133124	—	2	1	no	—
19	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
20	C₅₃×#431	—	2	1	no	—
21	C₅₃×#431	—	2	1	no	—
22	C₅₃×#431	C₄	1	2	yes	complemented
23	C₅₃×#431	C₂²	1	2	yes	—
24	C₂×C₄⋊C₈×C₅₃	—	2	1	no	—
25	C₂×C₂²⋊C₈×C₅₃	—	2	1	no	—
26	C₂×C₄×C₈×C₅₃	C₄	1	2	yes	complemented
27	C₂³×Dic₅₃	—	2	2	no	—
28	C₂²×#88322	—	2	2	no	—
29	C₂×C₄×Dic₅₃	—	2	2	no	—
30	C₂×C₄×Dic₅₃	—	2	4	no	—
31	C₂×C₄×Dic₅₃	C₈	1	8	yes	complemented
32	C₂×C₄×Dic₅₃	C₂×C₄	1	4	yes	—
33	C₄⋊#88322	—	2	2	no	—
34	C₄⋊#88322	—	2	2	no	—
35	C₂²⋊#88322	—	2	2	no	—
36	C₂²⋊#88322	—	2	2	no	—
37	C₄×#88322	—	2	2	no	—
38	C₄×#88322	C₂×C₄	1	4	yes	complemented
39	#13133124	—	2	2	no	—
40	#13133124	—	2	2	no	—
41	#13133124	—	2	2	no	—
42	#13133124	—	2	2	no	—
43	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
46	C₂²×C₈×C₅₃	—	2	2	no	—
47	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₅₃	Q₈	1	1	yes	characteristic
57	C₂×C₄²×C₅₃	Q₈	1	1	yes	characteristic
58	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
59	C₄⋊C₈×C₅₃	—	2	2	no	—
60	C₄⋊C₈×C₅₃	—	2	2	no	—
61	C₂²⋊C₈×C₅₃	—	2	2	no	—
62	C₂²⋊C₈×C₅₃	—	2	2	no	—
63	C₄×C₈×C₅₃	—	2	2	no	—
64	C₄×C₈×C₅₃	C₂×C₄	1	4	yes	complemented
65	C₂⁴×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₅₃	—	4	2	no	—
67	C₂²×C₄×C₅₃	—	4	2	no	—
68	C₂²×C₄×C₅₃	C₄²	1	1	yes	characteristic
69	C₂²×C₄×C₅₃	C₄²	1	1	yes	characteristic
70	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₅₃	C₂×C₈	1	4	yes	—
84	C₂²×C₄×C₅₃	M₁₆	1	4	yes	—
85	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
88	C₂²×Dic₅₃	—	2	8	no	—
89	C₂²×Dic₅₃	—	2	4	no	—
90	C₂²×Dic₅₃	—	4	4	no	—
91	C₂²×Dic₅₃	—	4	4	no	—
92	C₂×C₈×C₅₃	—	2	4	no	—
93	C₂×C₈×C₅₃	—	4	4	no	—
94	C₄²×C₅₃	C₄²	1	1	yes	characteristic
95	C₄²×C₅₃	C₄²	1	1	yes	characteristic
96	C₄²×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
97	C₄²×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
98	C₄²×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
99	C₄²×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
100	C₄²×C₅₃	C₄⋊C₄	1	1	yes	characteristic
101	C₄²×C₅₃	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₅₃	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₅₃	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₅₃	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₅₃	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
107	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
108	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
109	C₄²×C₅₃	C₂×Q₈	1	1	yes	characteristic
110	C₄×Dic₅₃	—	2	8	no	—
111	C₄×Dic₅₃	—	2	4	no	—
112	C₄×Dic₅₃	C₂×C₈	1	8	yes	complemented
113	C₂×#88322	—	2	4	no	—
114	C₂×#88322	—	4	4	no	—
115	C₂³×C₅₃	—	2	2	no	—
116	C₂³×C₅₃	—	2	2	no	—
117	C₂³×C₅₃	#95	1	1	yes	characteristic
118	C₂³×C₅₃	#95	1	1	yes	characteristic
119	C₂³×C₅₃	C₂²⋊C₈	1	4	yes	—
120	C₂³×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂×C₄×C₅₃	—	2	2	no	—
122	C₂×C₄×C₅₃	—	2	2	no	—
123	C₂×C₄×C₅₃	—	2	2	no	—
124	C₂×C₄×C₅₃	—	2	2	no	—
125	C₂×C₄×C₅₃	—	4	1	no	—
126	C₂×C₄×C₅₃	—	4	1	no	—
127	C₂×C₄×C₅₃	—	4	1	no	—
128	C₂×C₄×C₅₃	—	4	1	no	—
129	C₂×C₄×C₅₃	—	4	1	no	—
130	C₂×C₄×C₅₃	—	4	1	no	—
131	C₂×C₄×C₅₃	—	4	1	no	—
132	C₂×C₄×C₅₃	—	4	1	no	—
133	C₂×C₄×C₅₃	#95	1	1	yes	characteristic
134	C₂×C₄×C₅₃	#95	1	1	yes	characteristic
135	C₂×C₄×C₅₃	#95	1	1	yes	characteristic
136	C₂×C₄×C₅₃	#95	1	1	yes	characteristic
137	C₂×C₄×C₅₃	#95	1	1	yes	characteristic
138	C₂×C₄×C₅₃	#95	1	1	yes	characteristic
139	C₂×C₄×C₅₃	C₄×C₈	1	2	yes	—
140	C₂×C₄×C₅₃	C₄×C₈	1	2	yes	—
141	C₂×C₄×C₅₃	#97	1	2	yes	—
142	C₂×C₄×C₅₃	#97	1	2	yes	—
143	C₂×C₄×C₅₃	C₂²⋊C₈	1	4	yes	—
144	C₂×C₄×C₅₃	C₄⋊C₈	1	4	yes	—
145	C₂×C₄×C₅₃	C₄⋊C₈	1	4	yes	—
146	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
147	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₅₃	C₂²×C₈	1	2	yes	—
153	C₂×C₄×C₅₃	C₂×M₁₆	1	2	yes	—
154	C₂×Dic₅₃	—	2	8	no	—
155	C₂×Dic₅₃	—	4	4	no	—
156	C₂×Dic₅₃	—	4	4	no	—
157	C₂×Dic₅₃	—	4	16	no	—
158	C₈×C₅₃	—	4	4	no	—
159	#88322	—	4	4	no	—
160	C₂×#1274	—	53	1	no	maximal, Sylow
161	C₂²×C₅₃	—	2	1	no	—
162	C₂²×C₅₃	—	2	1	no	—
163	C₂²×C₅₃	—	2	1	no	—
164	C₂²×C₅₃	—	2	1	no	—
165	C₂²×C₅₃	—	2	8	no	—
166	C₂²×C₅₃	#336	1	2	yes	—
167	C₂²×C₅₃	#336	1	2	yes	—
168	C₂²×C₅₃	H(3,ℤ/4)	1	2	yes	—
169	C₂²×C₅₃	H(3,ℤ/4)	1	2	yes	—
170	C₂²×C₅₃	C₂×#95	1	1	yes	characteristic
171	C₂²×C₅₃	C₂×C₂²⋊C₈	1	2	yes	—
172	C₄×C₅₃	—	2	1	no	—
173	C₄×C₅₃	—	2	1	no	—
174	C₄×C₅₃	—	2	1	no	—
175	C₄×C₅₃	—	2	1	no	—
176	C₄×C₅₃	—	2	1	no	—
177	C₄×C₅₃	—	2	1	no	—
178	C₄×C₅₃	—	2	1	no	—
179	C₄×C₅₃	—	2	1	no	—
180	C₄×C₅₃	#336	1	2	yes	—
181	C₄×C₅₃	#336	1	2	yes	—
182	C₄×C₅₃	C₂×C₄×C₈	1	1	yes	characteristic
183	C₄×C₅₃	C₂×#97	1	1	yes	characteristic
184	C₄×C₅₃	C₂×C₄⋊C₈	1	2	yes	—
185	Dic₅₃	—	4	8	no	—
186	C₂×#431	—	53	1	no	—
187	C₂×#431	D₅₃	1	1	yes	characteristic
188	C₂×#376	—	53	1	no	—
189	#1274	—	53	4	no	—
190	C₂×C₅₃	—	2	2	no	—
191	C₂×C₅₃	—	2	2	no	—
192	C₂×C₅₃	#1274	1	4	yes	complemented
193	C₂×C₅₃	C₂×#336	1	1	yes	characteristic
194	C₂×C₅₃	C₂×H(3,ℤ/4)	1	1	yes	characteristic
195	C₂×C₅₃	C₂×H(3,ℤ/4)	1	1	yes	characteristic
196	C₂²×C₄²	—	53	2	no	—
197	C₂²×C₄²	C₂×D₅₃	1	1	yes	characteristic
198	#431	—	2	1	no	—
199	#431	—	2	1	no	—
200	#431	—	53	2	no	—
201	#431	—	53	2	no	—
202	#431	—	106	1	no	—
203	#431	—	106	1	no	—
204	#431	Dic₅₃	1	2	yes	complemented
205	#431	C₂×D₅₃	1	2	yes	—
206	C₂×C₄⋊C₈	—	2	1	no	—
207	C₂×C₄⋊C₈	—	106	1	no	—
208	C₂×C₂²⋊C₈	—	2	1	no	—
209	C₂×C₂²⋊C₈	—	106	1	no	—
210	C₂×C₄×C₈	—	53	2	no	—
211	C₂×C₄×C₈	Dic₅₃	1	2	yes	complemented
212	#376	—	53	2	no	—
213	#376	—	53	2	no	—
214	#376	—	106	1	no	—
215	#376	—	106	1	no	—
216	C₂×#95	—	106	1	no	—
217	C₂×#95	—	106	1	no	—
218	C₅₃	C₂×#1274	1	1	yes	characteristic, complemented, Sylow
219	C₂³×C₄	—	106	2	no	—
220	C₂³×C₄	C₄×D₅₃	1	1	yes	characteristic
221	C₂³×C₄	D₂₁₂	1	1	yes	characteristic
222	C₂³×C₄	C₂²⋊D₅₃	1	1	yes	characteristic
223	C₂²×C₈	—	2	2	no	—
224	C₂²×C₈	—	106	2	no	—
225	C₂×C₄²	—	53	4	no	—
226	C₂×C₄²	—	53	8	no	—
227	C₂×C₄²	—	106	4	no	—
228	C₂×C₄²	—	106	2	no	—
229	C₂×C₄²	Dic₁₀₆	1	1	yes	characteristic
230	C₂×C₄²	Dic₁₀₆	1	1	yes	characteristic
231	C₂×C₄²	C₄×D₅₃	1	1	yes	characteristic
232	C₂×C₄²	C₄×D₅₃	1	1	yes	characteristic
233	C₂×C₄²	C₄×D₅₃	1	1	yes	characteristic
234	C₂×C₄²	D₂₁₂	1	1	yes	characteristic
235	C₂×C₄²	C₂×Dic₅₃	1	1	yes	characteristic
236	C₂×C₄²	C₂×Dic₅₃	1	1	yes	characteristic
237	C₂×C₄²	C₂²⋊D₅₃	1	1	yes	characteristic
238	C₂×C₄²	C₂²⋊D₅₃	1	1	yes	characteristic
239	C₂×C₄²	C₂²⋊D₅₃	1	1	yes	characteristic
240	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
241	C₄⋊C₈	—	2	2	no	—
242	C₄⋊C₈	—	2	2	no	—
243	C₄⋊C₈	—	106	2	no	—
244	C₄⋊C₈	—	106	2	no	—
245	C₂²⋊C₈	—	2	2	no	—
246	C₂²⋊C₈	—	2	2	no	—
247	C₂²⋊C₈	—	106	2	no	—
248	C₂²⋊C₈	—	106	2	no	—
249	C₄×C₈	—	2	2	no	—
250	C₄×C₈	—	53	4	no	—
251	C₄×C₈	—	106	2	no	—
252	C₄×C₈	C₂×Dic₅₃	1	4	yes	complemented
253	#95	—	106	2	no	—
254	#95	—	106	2	no	—
255	#95	—	106	2	no	—
256	#95	—	106	2	no	—
257	C₂⁴	#11719921	1	1	yes	characteristic
258	C₂²×C₄	—	4	2	no	—
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	—	106	8	no	—
261	C₂²×C₄	—	106	4	no	—
262	C₂²×C₄	—	212	4	no	—
263	C₂²×C₄	—	212	4	no	—
264	C₂²×C₄	C₈×D₅₃	1	4	yes	—
265	C₂²×C₄	#11719912	1	4	yes	—
266	C₂²×C₄	C₄×Dic₅₃	1	1	yes	characteristic
267	C₂²×C₄	C₄×Dic₅₃	1	1	yes	characteristic
268	C₂²×C₄	#11719919	1	1	yes	characteristic
269	C₂²×C₄	#11719919	1	1	yes	characteristic
270	C₂²×C₄	#11719919	1	1	yes	characteristic
271	C₂²×C₄	#11719919	1	1	yes	characteristic
272	C₂²×C₄	C₄⋊Dic₅₃	1	1	yes	characteristic
273	C₂²×C₄	C₄⋊Dic₅₃	1	1	yes	characteristic
274	C₂²×C₄	#11719921	1	1	yes	characteristic
275	C₂²×C₄	#11719921	1	1	yes	characteristic
276	C₂²×C₄	#11719921	1	1	yes	characteristic
277	C₂²×C₄	#11719921	1	1	yes	characteristic
278	C₂²×C₄	#11719921	1	1	yes	characteristic
279	C₂²×C₄	C₂²⋊Dic₅₃	1	1	yes	characteristic
280	C₂²×C₄	C₂²⋊Dic₅₃	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
282	C₂²×C₄	C₂×D₂₁₂	1	1	yes	characteristic
283	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
284	C₂×C₈	—	2	4	no	—
285	C₂×C₈	—	4	4	no	—
286	C₂×C₈	—	106	4	no	—
287	C₂×C₈	—	212	4	no	—
288	C₄²	—	53	8	no	—
289	C₄²	—	106	8	no	—
290	C₄²	—	106	4	no	—
291	C₄²	C₄×Dic₅₃	1	1	yes	characteristic
292	C₄²	C₄×Dic₅₃	1	1	yes	characteristic
293	C₄²	#11719919	1	1	yes	characteristic
294	C₄²	#11719919	1	1	yes	characteristic
295	C₄²	#11719919	1	1	yes	characteristic
296	C₄²	#11719919	1	1	yes	characteristic
297	C₄²	C₄⋊Dic₅₃	1	1	yes	characteristic
298	C₄²	C₄⋊Dic₅₃	1	1	yes	characteristic
299	C₄²	#11719921	1	1	yes	characteristic
300	C₄²	#11719921	1	1	yes	characteristic
301	C₄²	C₂²⋊Dic₅₃	1	1	yes	characteristic
302	C₄²	C₂²⋊Dic₅₃	1	1	yes	characteristic
303	C₄²	C₂×Dic₁₀₆	1	1	yes	characteristic
304	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
305	C₄²	C₂²×Dic₅₃	1	1	yes	characteristic
306	C₄²	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
307	C₂³	—	2	2	no	—
308	C₂³	—	2	2	no	—
309	C₂³	#13133124	1	1	yes	characteristic
310	C₂³	#13133124	1	1	yes	characteristic
311	C₂³	#13133129	1	4	yes	—
312	C₂³	C₂×#11719921	1	1	yes	characteristic
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	1	no	—
319	C₂×C₄	—	4	1	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	106	8	no	—
326	C₂×C₄	—	212	16	no	—
327	C₂×C₄	—	212	4	no	—
328	C₂×C₄	—	212	4	no	—
329	C₂×C₄	#13133124	1	1	yes	characteristic
330	C₂×C₄	#13133124	1	1	yes	characteristic
331	C₂×C₄	#13133124	1	1	yes	characteristic
332	C₂×C₄	#13133124	1	1	yes	characteristic
333	C₂×C₄	#13133124	1	1	yes	characteristic
334	C₂×C₄	#13133124	1	1	yes	characteristic
335	C₂×C₄	C₈×Dic₅₃	1	2	yes	—
336	C₂×C₄	C₈×Dic₅₃	1	2	yes	—
337	C₂×C₄	#13133127	1	2	yes	—
338	C₂×C₄	#13133127	1	2	yes	—
339	C₂×C₄	#13133129	1	4	yes	—
340	C₂×C₄	#13133146	1	4	yes	—
341	C₂×C₄	#13133146	1	4	yes	—
342	C₂×C₄	C₂×C₄×Dic₅₃	1	1	yes	characteristic
343	C₂×C₄	C₂×#11719921	1	1	yes	characteristic
344	C₂×C₄	C₂×C₂²⋊Dic₅₃	1	1	yes	characteristic
345	C₂×C₄	C₂×#11719919	1	1	yes	characteristic
346	C₂×C₄	C₂×#11719919	1	1	yes	characteristic
347	C₂×C₄	C₂×C₄⋊Dic₅₃	1	1	yes	characteristic
348	C₂×C₄	C₂×C₈×D₅₃	1	2	yes	—
349	C₂×C₄	C₂×#11719912	1	2	yes	—
350	C₈	—	4	4	no	—
351	C₈	—	212	4	no	—
352	C₂²	—	2	8	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	#16810377	1	2	yes	—
358	C₂²	#16810377	1	2	yes	—
359	C₂²	#16810379	1	2	yes	—
360	C₂²	#16810380	1	2	yes	—
361	C₂²	C₂×#13133124	1	1	yes	characteristic
362	C₂²	C₂×#13133129	1	2	yes	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	212	8	no	—
372	C₄	#16810377	1	2	yes	—
373	C₄	#16810377	1	2	yes	—
374	C₄	C₂×C₈×Dic₅₃	1	1	yes	characteristic
375	C₄	C₂×#13133127	1	1	yes	characteristic
376	C₄	C₂×#13133146	1	2	yes	—
377	C₂	—	2	2	no	—
378	C₂	—	2	2	no	—
379	C₂	#20272543	1	4	yes	direct product factor
380	C₂	C₂×#16810377	1	1	yes	characteristic
381	C₂	C₂×#16810379	1	1	yes	characteristic
382	C₂	C₂×#16810380	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₄×Dic₅₃
commutator	C₄×C₅₃	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₅₃
Fitting	C₂×C₅₃×#431	C₂
socle	C₂³×C₅₃	#95
prime radical	C₂⁴×C₅₃	C₂²⋊C₄
cosocle	C₂×C₄²×C₅₃	C₂³
hypercenter	C₂×#431	D₅₃
hypocenter	C₅₃	C₂×#1274
LCS	G ▷ C₄×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #20272543	C₂	direct (N × H)
8. #16810676	C₄	semidirect
12. C₂×C₄×#88322	C₄	semidirect
22. C₅₃×#431	C₄	semidirect
26. C₂×C₄×C₈×C₅₃	C₄	semidirect
31. C₂×C₄×Dic₅₃	C₈	semidirect
38. C₄×#88322	C₂×C₄	semidirect
64. C₄×C₈×C₅₃	C₂×C₄	semidirect
112. C₄×Dic₅₃	C₂×C₈	semidirect
192. C₂×C₅₃	#1274	semidirect
204. #431	Dic₅₃	semidirect
211. C₂×C₄×C₈	Dic₅₃	semidirect
218. C₅₃	C₂×#1274	semidirect
252. C₄×C₈	C₂×Dic₅₃	semidirect
379. C₂	#20272543	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×#16810676	2
C₂×#16810469	2
#20272543	2
C₂×C₅₃×#431	2
C₂×#1274	53

Subgroups — C2×#20272543 #27273487

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20272543 #27273487