Subgroups — C₂×C₆₁×#1970 #29524656

Order 15616.

2046 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₈×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×#107×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#102×C₆₁	C₂	1	2	yes	maximal, complemented
4	C₂²×C₄×C₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₆₁×#390	C₂	1	2	yes	maximal, complemented
6	C₆₁×#1970	C₂	1	8	yes	maximal, direct product factor
7	C₂³×D₄×C₆₁	C₂²	1	2	yes	—
8	C₂²×D₈×C₆₁	—	2	4	no	—
9	C₂²×D₈×C₆₁	—	2	4	no	—
10	C₂²×D₈×C₆₁	C₄	1	8	yes	complemented
11	C₂²×D₈×C₆₁	C₂²	1	4	yes	—
12	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
15	C₂²×C₂²⋊C₄×C₆₁	—	2	4	no	—
16	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×#107×C₆₁	—	2	4	no	—
18	C₂×#107×C₆₁	C₂²	1	4	yes	complemented
19	C₂×#102×C₆₁	—	2	8	no	—
20	C₂×#102×C₆₁	C₂²	1	8	yes	complemented
21	C₂×C₄×C₈×C₆₁	—	2	4	no	—
22	C₂×C₄×C₈×C₆₁	C₂²	1	4	yes	complemented
23	C₆₁×#390	—	2	4	no	—
24	C₆₁×#390	C₂²	1	8	yes	complemented
25	C₂⁵×C₆₁	—	2	2	no	—
26	C₂²×D₄×C₆₁	—	2	4	no	—
27	C₂²×D₄×C₆₁	—	2	4	no	—
28	C₂²×D₄×C₆₁	—	2	4	no	—
29	C₂²×D₄×C₆₁	—	2	2	no	—
30	C₂²×D₄×C₆₁	—	2	4	no	—
31	C₂²×D₄×C₆₁	—	2	4	no	—
32	C₂²×D₄×C₆₁	C₂×C₄	1	8	yes	—
33	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
34	C₂³×C₄×C₆₁	—	2	2	no	—
35	C₂³×C₄×C₆₁	D₄	1	2	yes	—
36	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
37	C₂×D₈×C₆₁	—	2	32	no	—
38	C₂×D₈×C₆₁	—	2	8	no	—
39	C₂×D₈×C₆₁	—	2	8	no	—
40	C₂×D₈×C₆₁	C₂×C₄	1	16	yes	complemented
41	C₂²×C₈×C₆₁	—	2	2	no	—
42	C₂²×C₈×C₆₁	—	2	2	no	—
43	C₂²×C₈×C₆₁	C₂×C₄	1	4	yes	—
44	C₂²×C₈×C₆₁	D₄	1	4	yes	—
45	C₂²×C₈×C₆₁	D₄	1	4	yes	—
46	C₂²×C₈×C₆₁	D₄	1	4	yes	—
47	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
48	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
49	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
50	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
51	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
52	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
53	C₂×C₂²⋊C₄×C₆₁	—	2	16	no	—
54	C₂×C₂²⋊C₄×C₆₁	—	4	16	no	—
55	C₂×C₄²×C₆₁	—	2	2	no	—
56	C₂×C₄²×C₆₁	—	2	2	no	—
57	C₂×C₄²×C₆₁	D₄	1	2	yes	—
58	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
59	#107×C₆₁	—	2	8	no	—
60	#102×C₆₁	—	2	16	no	—
61	C₄×C₈×C₆₁	—	2	8	no	—
62	C₂⁴×C₆₁	—	2	8	no	—
63	C₂⁴×C₆₁	—	2	4	no	—
64	C₂⁴×C₆₁	—	4	4	no	—
65	C₂⁴×C₆₁	—	4	4	no	—
66	C₂⁴×C₆₁	—	4	8	no	—
67	C₂⁴×C₆₁	—	4	8	no	—
68	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
69	C₂×D₄×C₆₁	—	2	16	no	—
70	C₂×D₄×C₆₁	—	2	16	no	—
71	C₂×D₄×C₆₁	—	2	8	no	—
72	C₂×D₄×C₆₁	—	2	4	no	—
73	C₂×D₄×C₆₁	—	2	4	no	—
74	C₂×D₄×C₆₁	—	2	4	no	—
75	C₂×D₄×C₆₁	—	2	4	no	—
76	C₂×D₄×C₆₁	—	2	4	no	—
77	C₂×D₄×C₆₁	—	4	8	no	—
78	C₂×D₄×C₆₁	—	4	4	no	—
79	C₂×D₄×C₆₁	—	4	8	no	—
80	C₂×D₄×C₆₁	—	4	4	no	—
81	C₂×D₄×C₆₁	C₂²×C₄	1	8	yes	—
82	C₂²×C₄×C₆₁	—	2	4	no	—
83	C₂²×C₄×C₆₁	—	2	4	no	—
84	C₂²×C₄×C₆₁	—	2	4	no	—
85	C₂²×C₄×C₆₁	—	4	4	no	—
86	C₂²×C₄×C₆₁	—	4	8	no	—
87	C₂²×C₄×C₆₁	D₈	1	8	yes	complemented
88	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
90	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₆₁	#41	1	2	yes	—
95	C₂²×C₄×C₆₁	#41	1	2	yes	—
96	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
97	D₈×C₆₁	—	2	32	no	—
98	C₂×C₈×C₆₁	—	2	8	no	—
99	C₂×C₈×C₆₁	—	2	2	no	—
100	C₂×C₈×C₆₁	—	2	2	no	—
101	C₂×C₈×C₆₁	C₂²⋊C₄	1	16	yes	complemented
102	C₂×C₈×C₆₁	C₂²×C₄	1	4	yes	—
103	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
104	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
105	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
106	C₄⋊C₄×C₆₁	—	2	4	no	—
107	C₄⋊C₄×C₆₁	—	2	4	no	—
108	C₄⋊C₄×C₆₁	—	4	4	no	—
109	C₂²⋊C₄×C₆₁	—	4	32	no	—
110	C₄²×C₆₁	—	2	4	no	—
111	C₄²×C₆₁	—	2	2	no	—
112	C₄²×C₆₁	—	2	2	no	—
113	C₂³×C₆₁	—	2	8	no	—
114	C₂³×C₆₁	—	4	4	no	—
115	C₂³×C₆₁	—	4	4	no	—
116	C₂³×C₆₁	—	4	8	no	—
117	C₂³×C₆₁	—	4	8	no	—
118	C₂³×C₆₁	—	4	16	no	—
119	C₂³×C₆₁	—	4	32	no	—
120	C₂³×C₆₁	—	8	16	no	—
121	C₂³×C₆₁	—	8	8	no	—
122	C₂³×C₆₁	—	8	8	no	—
123	C₂³×C₆₁	C₄×D₄	1	2	yes	—
124	C₂³×C₆₁	#121	1	2	yes	—
125	C₂³×C₆₁	#127	1	2	yes	—
126	C₂³×C₆₁	C₂×D₈	1	4	yes	—
127	C₂³×C₆₁	#135	1	4	yes	—
128	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
129	D₄×C₆₁	—	2	8	no	—
130	D₄×C₆₁	—	2	8	no	—
131	D₄×C₆₁	—	4	4	no	—
132	D₄×C₆₁	—	4	4	no	—
133	D₄×C₆₁	—	4	16	no	—
134	C₂×C₄×C₆₁	—	2	4	no	—
135	C₂×C₄×C₆₁	—	2	4	no	—
136	C₂×C₄×C₆₁	—	2	16	no	—
137	C₂×C₄×C₆₁	—	4	4	no	—
138	C₂×C₄×C₆₁	—	4	8	no	—
139	C₂×C₄×C₆₁	—	8	8	no	—
140	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	4	yes	—
141	C₂×C₄×C₆₁	C₄×D₄	1	4	yes	—
142	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
143	C₂×C₄×C₆₁	#121	1	4	yes	—
144	C₂×C₄×C₆₁	#121	1	2	yes	—
145	C₂×C₄×C₆₁	#124	1	4	yes	—
146	C₂×C₄×C₆₁	#127	1	2	yes	—
147	C₂×C₄×C₆₁	C₂×D₈	1	8	yes	complemented
148	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
149	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
150	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
153	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
154	C₈×C₆₁	—	2	4	no	—
155	C₈×C₆₁	C₂×C₂²⋊C₄	1	8	yes	complemented
156	C₂×#1970	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂²×C₆₁	—	4	16	no	—
158	C₂²×C₆₁	—	4	8	no	—
159	C₂²×C₆₁	—	8	4	no	—
160	C₂²×C₆₁	—	8	4	no	—
161	C₂²×C₆₁	—	8	32	no	—
162	C₂²×C₆₁	—	8	8	no	—
163	C₂²×C₆₁	#390	1	4	yes	—
164	C₂²×C₆₁	C₄×D₈	1	8	yes	—
165	C₂²×C₆₁	#466	1	8	yes	—
166	C₂²×C₆₁	#493	1	4	yes	—
167	C₂²×C₆₁	#495	1	4	yes	—
168	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
169	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
170	C₂²×C₆₁	C₂×#127	1	1	yes	characteristic
171	C₂²×C₆₁	C₂²×D₈	1	2	yes	—
172	C₂²×C₆₁	C₂×#135	1	2	yes	—
173	C₄×C₆₁	—	2	8	no	—
174	C₄×C₆₁	—	8	4	no	—
175	C₄×C₆₁	#390	1	4	yes	—
176	C₄×C₆₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
177	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
178	C₄×C₆₁	C₂×#121	1	1	yes	characteristic
179	C₄×C₆₁	C₂×#124	1	1	yes	characteristic
180	C₂³×D₈	C₂×C₆₁	1	1	yes	characteristic
181	C₂²×#107	C₂×C₆₁	1	1	yes	characteristic, complemented
182	C₂²×#102	C₂×C₆₁	1	2	yes	complemented
183	C₂²×C₄×C₈	C₂×C₆₁	1	1	yes	characteristic, complemented
184	C₂×#390	C₂×C₆₁	1	2	yes	complemented
185	#1970	C₂×C₆₁	1	8	yes	direct product factor
186	C₂×C₆₁	—	8	8	no	—
187	C₂×C₆₁	#1970	1	8	yes	direct product factor
188	C₂×C₆₁	C₂×#390	1	1	yes	characteristic
189	C₂×C₆₁	C₂×C₄×D₈	1	2	yes	—
190	C₂×C₆₁	C₂×#466	1	2	yes	—
191	C₂×C₆₁	C₂×#493	1	1	yes	characteristic
192	C₂×C₆₁	C₂×#495	1	1	yes	characteristic
193	C₂³×D₄	C₂²×C₆₁	1	2	yes	—
194	C₂²×D₈	—	2	4	no	—
195	C₂²×D₈	—	2	4	no	—
196	C₂²×D₈	C₄×C₆₁	1	8	yes	complemented
197	C₂²×D₈	C₂²×C₆₁	1	4	yes	—
198	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
199	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
200	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
201	C₂²×C₂²⋊C₄	—	2	4	no	—
202	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
203	C₂×#107	—	2	4	no	—
204	C₂×#107	C₂²×C₆₁	1	4	yes	complemented
205	C₂×#102	—	2	8	no	—
206	C₂×#102	C₂²×C₆₁	1	8	yes	complemented
207	C₂×C₄×C₈	—	2	4	no	—
208	C₂×C₄×C₈	C₂²×C₆₁	1	4	yes	complemented
209	#390	—	2	4	no	—
210	#390	C₂²×C₆₁	1	8	yes	complemented
211	C₆₁	C₂×#1970	1	1	yes	characteristic, direct product factor, Sylow
212	C₂⁵	—	2	2	no	—
213	C₂²×D₄	—	2	4	no	—
214	C₂²×D₄	—	2	4	no	—
215	C₂²×D₄	—	2	4	no	—
216	C₂²×D₄	—	2	2	no	—
217	C₂²×D₄	—	2	4	no	—
218	C₂²×D₄	—	2	4	no	—
219	C₂²×D₄	C₂×C₄×C₆₁	1	8	yes	—
220	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
221	C₂³×C₄	—	2	2	no	—
222	C₂³×C₄	D₄×C₆₁	1	2	yes	—
223	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
224	C₂×D₈	—	2	32	no	—
225	C₂×D₈	—	2	8	no	—
226	C₂×D₈	—	2	8	no	—
227	C₂×D₈	C₂×C₄×C₆₁	1	16	yes	complemented
228	C₂²×C₈	—	2	2	no	—
229	C₂²×C₈	—	2	2	no	—
230	C₂²×C₈	C₂×C₄×C₆₁	1	4	yes	—
231	C₂²×C₈	D₄×C₆₁	1	4	yes	—
232	C₂²×C₈	D₄×C₆₁	1	4	yes	—
233	C₂²×C₈	D₄×C₆₁	1	4	yes	—
234	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
235	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
236	C₂×C₄⋊C₄	—	2	4	no	—
237	C₂×C₄⋊C₄	—	2	4	no	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
240	C₂×C₂²⋊C₄	—	2	16	no	—
241	C₂×C₂²⋊C₄	—	4	16	no	—
242	C₂×C₄²	—	2	2	no	—
243	C₂×C₄²	—	2	2	no	—
244	C₂×C₄²	D₄×C₆₁	1	2	yes	—
245	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
246	#107	—	2	8	no	—
247	#102	—	2	16	no	—
248	C₄×C₈	—	2	8	no	—
249	C₂⁴	—	2	8	no	—
250	C₂⁴	—	2	4	no	—
251	C₂⁴	—	4	4	no	—
252	C₂⁴	—	4	4	no	—
253	C₂⁴	—	4	8	no	—
254	C₂⁴	—	4	8	no	—
255	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
256	C₂×D₄	—	2	16	no	—
257	C₂×D₄	—	2	16	no	—
258	C₂×D₄	—	2	8	no	—
259	C₂×D₄	—	2	4	no	—
260	C₂×D₄	—	2	4	no	—
261	C₂×D₄	—	2	4	no	—
262	C₂×D₄	—	2	4	no	—
263	C₂×D₄	—	2	4	no	—
264	C₂×D₄	—	4	4	no	—
265	C₂×D₄	—	4	8	no	—
266	C₂×D₄	—	4	8	no	—
267	C₂×D₄	—	4	4	no	—
268	C₂×D₄	C₂²×C₄×C₆₁	1	8	yes	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	4	4	no	—
273	C₂²×C₄	—	4	8	no	—
274	C₂²×C₄	D₈×C₆₁	1	8	yes	complemented
275	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
276	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
277	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
278	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
279	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
280	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
281	C₂²×C₄	#41×C₆₁	1	2	yes	—
282	C₂²×C₄	#41×C₆₁	1	2	yes	—
283	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
284	D₈	—	2	32	no	—
285	C₂×C₈	—	2	8	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	C₂²⋊C₄×C₆₁	1	16	yes	complemented
289	C₂×C₈	C₂²×C₄×C₆₁	1	4	yes	—
290	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
291	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
292	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
293	C₄⋊C₄	—	2	4	no	—
294	C₄⋊C₄	—	2	4	no	—
295	C₄⋊C₄	—	4	4	no	—
296	C₂²⋊C₄	—	4	32	no	—
297	C₄²	—	2	4	no	—
298	C₄²	—	2	2	no	—
299	C₄²	—	2	2	no	—
300	C₂³	—	2	8	no	—
301	C₂³	—	4	4	no	—
302	C₂³	—	4	8	no	—
303	C₂³	—	4	8	no	—
304	C₂³	—	4	16	no	—
305	C₂³	—	4	32	no	—
306	C₂³	—	4	4	no	—
307	C₂³	—	8	16	no	—
308	C₂³	—	8	8	no	—
309	C₂³	—	8	8	no	—
310	C₂³	C₄×D₄×C₆₁	1	2	yes	—
311	C₂³	#121×C₆₁	1	2	yes	—
312	C₂³	#127×C₆₁	1	2	yes	—
313	C₂³	C₂×D₈×C₆₁	1	4	yes	—
314	C₂³	#135×C₆₁	1	4	yes	—
315	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
316	D₄	—	2	8	no	—
317	D₄	—	2	8	no	—
318	D₄	—	4	16	no	—
319	D₄	—	4	4	no	—
320	D₄	—	4	4	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	16	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	—	4	8	no	—
326	C₂×C₄	—	8	8	no	—
327	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	4	yes	—
328	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
329	C₂×C₄	C₄×D₄×C₆₁	1	4	yes	—
330	C₂×C₄	#121×C₆₁	1	2	yes	—
331	C₂×C₄	#121×C₆₁	1	4	yes	—
332	C₂×C₄	#124×C₆₁	1	4	yes	—
333	C₂×C₄	#127×C₆₁	1	2	yes	—
334	C₂×C₄	C₂×D₈×C₆₁	1	8	yes	complemented
335	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
336	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
337	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
338	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
339	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
340	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
341	C₈	—	2	4	no	—
342	C₈	C₂×C₂²⋊C₄×C₆₁	1	8	yes	complemented
343	C₂²	—	4	8	no	—
344	C₂²	—	4	16	no	—
345	C₂²	—	8	8	no	—
346	C₂²	—	8	4	no	—
347	C₂²	—	8	4	no	—
348	C₂²	—	8	32	no	—
349	C₂²	C₆₁×#390	1	4	yes	—
350	C₂²	C₄×D₈×C₆₁	1	8	yes	—
351	C₂²	C₆₁×#466	1	8	yes	—
352	C₂²	C₆₁×#493	1	4	yes	—
353	C₂²	C₆₁×#495	1	4	yes	—
354	C₂²	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
355	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
356	C₂²	C₂×#127×C₆₁	1	1	yes	characteristic
357	C₂²	C₂²×D₈×C₆₁	1	2	yes	—
358	C₂²	C₂×#135×C₆₁	1	2	yes	—
359	C₄	—	2	8	no	—
360	C₄	—	8	4	no	—
361	C₄	C₆₁×#390	1	4	yes	—
362	C₄	C₂²×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
363	C₄	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
364	C₄	C₂×#121×C₆₁	1	1	yes	characteristic
365	C₄	C₂×#124×C₆₁	1	1	yes	characteristic
366	C₂	—	8	8	no	—
367	C₂	C₆₁×#1970	1	8	yes	direct product factor
368	C₂	C₂×C₆₁×#390	1	1	yes	characteristic
369	C₂	C₂×C₄×D₈×C₆₁	1	2	yes	—
370	C₂	C₂×C₆₁×#466	1	2	yes	—
371	C₂	C₂×C₆₁×#493	1	1	yes	characteristic
372	C₂	C₂×C₆₁×#495	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₆₁	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂³×D₈×C₆₁	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₆₁ ◁ C₂²×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#107×C₆₁	C₂	semidirect
3. C₂²×#102×C₆₁	C₂	semidirect
4. C₂²×C₄×C₈×C₆₁	C₂	semidirect
5. C₂×C₆₁×#390	C₂	semidirect
6. C₆₁×#1970	C₂	direct (N × H)
10. C₂²×D₈×C₆₁	C₄	semidirect
18. C₂×#107×C₆₁	C₂²	semidirect
20. C₂×#102×C₆₁	C₂²	semidirect
22. C₂×C₄×C₈×C₆₁	C₂²	semidirect
24. C₆₁×#390	C₂²	semidirect
40. C₂×D₈×C₆₁	C₂×C₄	semidirect
87. C₂²×C₄×C₆₁	D₈	semidirect
101. C₂×C₈×C₆₁	C₂²⋊C₄	semidirect
147. C₂×C₄×C₆₁	C₂×D₈	semidirect
155. C₈×C₆₁	C₂×C₂²⋊C₄	semidirect
156. C₂×#1970	C₆₁	direct (N × H)
181. C₂²×#107	C₂×C₆₁	semidirect
182. C₂²×#102	C₂×C₆₁	semidirect
183. C₂²×C₄×C₈	C₂×C₆₁	semidirect
184. C₂×#390	C₂×C₆₁	semidirect
185. #1970	C₂×C₆₁	direct (N × H)
187. C₂×C₆₁	#1970	direct (N × H)
196. C₂²×D₈	C₄×C₆₁	semidirect
204. C₂×#107	C₂²×C₆₁	semidirect
206. C₂×#102	C₂²×C₆₁	semidirect
208. C₂×C₄×C₈	C₂²×C₆₁	semidirect
210. #390	C₂²×C₆₁	semidirect
211. C₆₁	C₂×#1970	direct (N × H)
227. C₂×D₈	C₂×C₄×C₆₁	semidirect
274. C₂²×C₄	D₈×C₆₁	semidirect
288. C₂×C₈	C₂²⋊C₄×C₆₁	semidirect
334. C₂×C₄	C₂×D₈×C₆₁	semidirect
342. C₈	C₂×C₂²⋊C₄×C₆₁	semidirect
367. C₂	C₆₁×#1970	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₈×C₆₁	2
C₂²×#107×C₆₁	2
C₂²×#102×C₆₁	2
C₂²×C₄×C₈×C₆₁	2
C₂×C₆₁×#390	2
C₆₁×#1970	2
C₂×#1970	61

Subgroups — C2×C61×#1970 #29524656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#1970 #29524656