Subgroups — C₂×C₆₁×#3341 #29564665

Order 15616.

1982 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#555	C₂	1	2	yes	maximal, complemented
2	C₆₁×#3341	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₆₁×#500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₆₁×#482	C₂	1	4	yes	maximal, complemented
5	C₂×C₆₁×#476	C₂	1	2	yes	maximal, complemented
6	C₂×C₆₁×#466	C₂	1	2	yes	maximal, complemented
7	C₂×C₄×D₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₈×D₄×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₆₁×#427	C₂	1	2	yes	maximal, complemented
10	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₆₁	C₂²	1	2	yes	—
12	C₆₁×#555	—	2	8	no	—
13	C₆₁×#555	C₂²	1	16	yes	complemented
14	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
15	C₂×#124×C₆₁	—	2	4	no	—
16	C₂×#121×C₆₁	—	2	2	no	—
17	C₂×#121×C₆₁	C₂²	1	4	yes	—
18	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×#117×C₆₁	—	2	2	no	—
21	C₂×#117×C₆₁	C₂²	1	4	yes	—
22	C₆₁×#500	C₂²	1	8	yes	complemented
23	C₆₁×#482	C₂²	1	32	yes	complemented
24	C₆₁×#476	C₂²	1	16	yes	complemented
25	C₆₁×#466	C₂²	1	16	yes	complemented
26	C₄×D₈×C₆₁	C₂²	1	8	yes	complemented
27	C₈×D₄×C₆₁	C₂²	1	8	yes	complemented
28	C₆₁×#427	C₂²	1	16	yes	complemented
29	C₂×#107×C₆₁	C₂²	1	2	yes	—
30	C₂×#107×C₆₁	C₂²	1	2	yes	—
31	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×#106×C₆₁	C₂²	1	4	yes	—
33	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
34	C₂×#102×C₆₁	C₂²	1	4	yes	—
35	C₂×#102×C₆₁	C₂²	1	2	yes	—
36	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
37	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
38	C₂²×Q₈×C₆₁	—	2	2	no	—
39	C₂²×D₄×C₆₁	—	2	4	no	—
40	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
41	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
42	C₂³×C₄×C₆₁	—	2	2	no	—
43	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
44	C₂×D₈×C₆₁	—	2	4	no	—
45	C₂×D₈×C₆₁	C₂³	1	4	yes	—
46	C₂²×C₈×C₆₁	—	2	8	no	—
47	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
48	C₂²×C₈×C₆₁	C₂³	1	8	yes	—
49	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
51	C₄⋊Q₈×C₆₁	—	2	4	no	—
52	C₄⋊Q₈×C₆₁	C₂³	1	8	yes	—
53	#124×C₆₁	—	2	32	no	—
54	#121×C₆₁	—	2	16	no	—
55	#121×C₆₁	—	2	8	no	—
56	#121×C₆₁	C₂³	1	16	yes	—
57	C₄×D₄×C₆₁	—	2	4	no	—
58	C₄×D₄×C₆₁	D₄	1	4	yes	—
59	C₄×D₄×C₆₁	C₂³	1	8	yes	—
60	C₄×D₄×C₆₁	C₂³	1	4	yes	—
61	#117×C₆₁	—	2	8	no	—
62	#117×C₆₁	—	2	16	no	—
63	#117×C₆₁	C₂³	1	16	yes	—
64	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
65	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
67	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
68	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
69	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
70	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
72	C₂×C₄²×C₆₁	—	2	4	no	—
73	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
74	#107×C₆₁	C₂³	1	4	yes	—
75	#107×C₆₁	C₂³	1	8	yes	—
76	#107×C₆₁	C₂³	1	8	yes	—
77	#106×C₆₁	C₂³	1	16	yes	—
78	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
79	#102×C₆₁	C₂³	1	8	yes	—
80	#102×C₆₁	C₂³	1	16	yes	—
81	C₂²⋊C₈×C₆₁	C₂³	1	8	yes	—
82	C₄×C₈×C₆₁	C₂³	1	4	yes	—
83	C₂⁴×C₆₁	—	2	2	no	—
84	C₂⁴×C₆₁	C₂×D₄	1	2	yes	—
85	C₂×Q₈×C₆₁	—	2	8	no	—
86	C₂×Q₈×C₆₁	—	8	4	no	—
87	C₂×D₄×C₆₁	—	2	16	no	—
88	C₂×D₄×C₆₁	—	2	4	no	—
89	C₂×D₄×C₆₁	—	2	2	no	—
90	C₂×D₄×C₆₁	—	2	4	no	—
91	C₂×D₄×C₆₁	—	2	4	no	—
92	C₂×D₄×C₆₁	—	8	8	no	—
93	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
94	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
95	C₂²×C₄×C₆₁	—	2	4	no	—
96	C₂²×C₄×C₆₁	—	2	4	no	—
97	C₂²×C₄×C₆₁	—	2	2	no	—
98	C₂²×C₄×C₆₁	—	2	4	no	—
99	C₂²×C₄×C₆₁	—	2	8	no	—
100	C₂²×C₄×C₆₁	—	4	8	no	—
101	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
102	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
106	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
107	D₈×C₆₁	—	2	8	no	—
108	C₂×C₈×C₆₁	—	2	4	no	—
109	C₂×C₈×C₆₁	—	2	2	no	—
110	C₂×C₈×C₆₁	—	2	16	no	—
111	C₂×C₈×C₆₁	#41	1	4	yes	—
112	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
113	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
114	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
115	C₄⋊C₄×C₆₁	—	2	8	no	—
116	C₄⋊C₄×C₆₁	—	2	2	no	—
117	C₄⋊C₄×C₆₁	—	2	4	no	—
118	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
119	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
120	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
121	C₂²⋊C₄×C₆₁	—	2	16	no	—
122	C₂²⋊C₄×C₆₁	—	2	16	no	—
123	C₂²⋊C₄×C₆₁	—	2	8	no	—
124	C₂²⋊C₄×C₆₁	C₂×D₄	1	8	yes	—
125	C₄²×C₆₁	—	2	16	no	—
126	C₄²×C₆₁	C₂×D₄	1	2	yes	—
127	C₄²×C₆₁	C₂⁴	1	2	yes	—
128	C₂³×C₆₁	—	2	4	no	—
129	C₂³×C₆₁	—	2	4	no	—
130	C₂³×C₆₁	—	2	4	no	—
131	C₂³×C₆₁	—	2	4	no	—
132	C₂³×C₆₁	—	4	4	no	—
133	C₂³×C₆₁	—	4	4	no	—
134	C₂³×C₆₁	—	4	4	no	—
135	C₂³×C₆₁	C₂²×D₄	1	4	yes	—
136	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
137	Q₈×C₆₁	—	8	8	no	—
138	D₄×C₆₁	—	2	8	no	—
139	D₄×C₆₁	—	2	4	no	—
140	D₄×C₆₁	—	2	4	no	—
141	D₄×C₆₁	—	4	4	no	—
142	D₄×C₆₁	—	8	16	no	—
143	C₂×C₄×C₆₁	—	2	4	no	—
144	C₂×C₄×C₆₁	—	2	2	no	—
145	C₂×C₄×C₆₁	—	2	8	no	—
146	C₂×C₄×C₆₁	—	2	4	no	—
147	C₂×C₄×C₆₁	—	2	4	no	—
148	C₂×C₄×C₆₁	—	2	4	no	—
149	C₂×C₄×C₆₁	—	2	8	no	—
150	C₂×C₄×C₆₁	—	4	4	no	—
151	C₂×C₄×C₆₁	—	4	8	no	—
152	C₂×C₄×C₆₁	—	4	16	no	—
153	C₂×C₄×C₆₁	#135	1	4	yes	—
154	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
155	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
156	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
158	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
159	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
160	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
161	C₈×C₆₁	—	2	4	no	—
162	C₈×C₆₁	—	2	2	no	—
163	C₈×C₆₁	C₂×#41	1	4	yes	—
164	C₂×#3341	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂²×C₆₁	—	2	4	no	—
166	C₂²×C₆₁	—	2	4	no	—
167	C₂²×C₆₁	—	2	4	no	—
168	C₂²×C₆₁	—	4	8	no	—
169	C₂²×C₆₁	—	4	4	no	—
170	C₂²×C₆₁	—	4	4	no	—
171	C₂²×C₆₁	—	4	4	no	—
172	C₂²×C₆₁	—	8	8	no	—
173	C₂²×C₆₁	#547	1	2	yes	—
174	C₂²×C₆₁	C₂×#135	1	2	yes	—
175	C₂²×C₆₁	#576	1	2	yes	—
176	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
177	C₄×C₆₁	—	2	4	no	—
178	C₄×C₆₁	—	2	2	no	—
179	C₄×C₆₁	—	4	4	no	—
180	C₄×C₆₁	—	4	8	no	—
181	C₄×C₆₁	#547	1	2	yes	—
182	C₄×C₆₁	C₂×#135	1	4	yes	—
183	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
184	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
185	C₂×#555	C₂×C₆₁	1	2	yes	complemented
186	#3341	C₂×C₆₁	1	16	yes	direct product factor
187	C₂×#500	C₂×C₆₁	1	1	yes	characteristic, complemented
188	C₂×#482	C₂×C₆₁	1	4	yes	complemented
189	C₂×#476	C₂×C₆₁	1	2	yes	complemented
190	C₂×#466	C₂×C₆₁	1	2	yes	complemented
191	C₂×C₄×D₈	C₂×C₆₁	1	1	yes	characteristic, complemented
192	C₂×C₈×D₄	C₂×C₆₁	1	1	yes	characteristic, complemented
193	C₂×#427	C₂×C₆₁	1	2	yes	complemented
194	C₂×C₆₁	—	4	4	no	—
195	C₂×C₆₁	—	8	4	no	—
196	C₂×C₆₁	#3341	1	4	yes	direct product factor
197	C₂×C₆₁	C₂×#547	1	1	yes	characteristic
198	C₂×C₆₁	C₂²×#135	1	1	yes	characteristic
199	C₂×C₆₁	C₂×#576	1	1	yes	characteristic
200	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
201	C₂³×C₈	C₂²×C₆₁	1	2	yes	—
202	#555	—	2	8	no	—
203	#555	C₂²×C₆₁	1	16	yes	complemented
204	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	—
205	C₂×#124	—	2	4	no	—
206	C₂×#121	—	2	2	no	—
207	C₂×#121	C₂²×C₆₁	1	4	yes	—
208	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
209	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
210	C₂×#117	—	2	2	no	—
211	C₂×#117	C₂²×C₆₁	1	4	yes	—
212	#500	C₂²×C₆₁	1	8	yes	complemented
213	#482	C₂²×C₆₁	1	32	yes	complemented
214	#476	C₂²×C₆₁	1	16	yes	complemented
215	#466	C₂²×C₆₁	1	16	yes	complemented
216	C₄×D₈	C₂²×C₆₁	1	8	yes	complemented
217	C₈×D₄	C₂²×C₆₁	1	8	yes	complemented
218	#427	C₂²×C₆₁	1	16	yes	complemented
219	C₂×#107	C₂²×C₆₁	1	2	yes	—
220	C₂×#107	C₂²×C₆₁	1	2	yes	—
221	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
222	C₂×#106	C₂²×C₆₁	1	4	yes	—
223	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
224	C₂×#102	C₂²×C₆₁	1	2	yes	—
225	C₂×#102	C₂²×C₆₁	1	4	yes	—
226	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
227	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
228	C₆₁	C₂×#3341	1	1	yes	characteristic, direct product factor, Sylow
229	C₂²×Q₈	—	2	2	no	—
230	C₂²×D₄	—	2	4	no	—
231	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
232	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
233	C₂³×C₄	—	2	2	no	—
234	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
235	C₂×D₈	—	2	4	no	—
236	C₂×D₈	C₂³×C₆₁	1	4	yes	—
237	C₂²×C₈	—	2	8	no	—
238	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
239	C₂²×C₈	C₂³×C₆₁	1	8	yes	—
240	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
241	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
242	C₄⋊Q₈	—	2	4	no	—
243	C₄⋊Q₈	C₂³×C₆₁	1	8	yes	—
244	#124	—	2	32	no	—
245	#121	—	2	16	no	—
246	#121	—	2	8	no	—
247	#121	C₂³×C₆₁	1	16	yes	—
248	C₄×D₄	—	2	4	no	—
249	C₄×D₄	D₄×C₆₁	1	4	yes	—
250	C₄×D₄	C₂³×C₆₁	1	8	yes	—
251	C₄×D₄	C₂³×C₆₁	1	4	yes	—
252	#117	—	2	8	no	—
253	#117	—	2	16	no	—
254	#117	C₂³×C₆₁	1	16	yes	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
258	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
259	C₂×C₂²⋊C₄	—	2	4	no	—
260	C₂×C₂²⋊C₄	—	2	4	no	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
263	C₂×C₄²	—	2	4	no	—
264	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
265	#107	C₂³×C₆₁	1	4	yes	—
266	#107	C₂³×C₆₁	1	8	yes	—
267	#107	C₂³×C₆₁	1	8	yes	—
268	#106	C₂³×C₆₁	1	16	yes	—
269	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
270	#102	C₂³×C₆₁	1	8	yes	—
271	#102	C₂³×C₆₁	1	16	yes	—
272	C₂²⋊C₈	C₂³×C₆₁	1	8	yes	—
273	C₄×C₈	C₂³×C₆₁	1	4	yes	—
274	C₂⁴	—	2	2	no	—
275	C₂⁴	C₂×D₄×C₆₁	1	2	yes	—
276	C₂×Q₈	—	2	8	no	—
277	C₂×Q₈	—	8	4	no	—
278	C₂×D₄	—	2	16	no	—
279	C₂×D₄	—	2	4	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	4	no	—
282	C₂×D₄	—	2	4	no	—
283	C₂×D₄	—	8	8	no	—
284	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
285	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	2	8	no	—
291	C₂²×C₄	—	4	8	no	—
292	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
293	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
294	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
295	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
296	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
297	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
298	D₈	—	2	8	no	—
299	C₂×C₈	—	2	4	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	16	no	—
302	C₂×C₈	#41×C₆₁	1	4	yes	—
303	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
304	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
305	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
306	C₄⋊C₄	—	2	8	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
310	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
311	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
312	C₂²⋊C₄	—	2	16	no	—
313	C₂²⋊C₄	—	2	16	no	—
314	C₂²⋊C₄	—	2	8	no	—
315	C₂²⋊C₄	C₂×D₄×C₆₁	1	8	yes	—
316	C₄²	—	2	16	no	—
317	C₄²	C₂×D₄×C₆₁	1	2	yes	—
318	C₄²	C₂⁴×C₆₁	1	2	yes	—
319	C₂³	—	2	4	no	—
320	C₂³	—	2	4	no	—
321	C₂³	—	2	4	no	—
322	C₂³	—	2	4	no	—
323	C₂³	—	4	4	no	—
324	C₂³	—	4	4	no	—
325	C₂³	—	4	4	no	—
326	C₂³	C₂²×D₄×C₆₁	1	4	yes	—
327	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
328	Q₈	—	8	8	no	—
329	D₄	—	2	8	no	—
330	D₄	—	2	4	no	—
331	D₄	—	2	4	no	—
332	D₄	—	4	4	no	—
333	D₄	—	8	16	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	8	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	8	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	8	no	—
343	C₂×C₄	—	4	16	no	—
344	C₂×C₄	#135×C₆₁	1	4	yes	—
345	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
346	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
347	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
348	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
349	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
350	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
351	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
352	C₈	—	2	4	no	—
353	C₈	—	2	2	no	—
354	C₈	C₂×#41×C₆₁	1	4	yes	—
355	C₂²	—	2	4	no	—
356	C₂²	—	2	4	no	—
357	C₂²	—	2	4	no	—
358	C₂²	—	4	8	no	—
359	C₂²	—	4	4	no	—
360	C₂²	—	4	4	no	—
361	C₂²	—	4	4	no	—
362	C₂²	—	8	8	no	—
363	C₂²	C₆₁×#547	1	2	yes	—
364	C₂²	C₂×#135×C₆₁	1	2	yes	—
365	C₂²	C₆₁×#576	1	2	yes	—
366	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
367	C₄	—	2	2	no	—
368	C₄	—	2	4	no	—
369	C₄	—	4	4	no	—
370	C₄	—	4	8	no	—
371	C₄	C₆₁×#547	1	2	yes	—
372	C₄	C₂×#135×C₆₁	1	4	yes	—
373	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
374	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
375	C₂	—	4	4	no	—
376	C₂	—	8	4	no	—
377	C₂	C₆₁×#3341	1	4	yes	direct product factor
378	C₂	C₂×C₆₁×#547	1	1	yes	characteristic
379	C₂	C₂²×#135×C₆₁	1	1	yes	characteristic
380	C₂	C₂×C₆₁×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂×C₄×D₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#555	C₂	semidirect
2. C₆₁×#3341	C₂	direct (N × H)
3. C₂×C₆₁×#500	C₂	semidirect
4. C₂×C₆₁×#482	C₂	semidirect
5. C₂×C₆₁×#476	C₂	semidirect
6. C₂×C₆₁×#466	C₂	semidirect
7. C₂×C₄×D₈×C₆₁	C₂	semidirect
8. C₂×C₈×D₄×C₆₁	C₂	semidirect
9. C₂×C₆₁×#427	C₂	semidirect
13. C₆₁×#555	C₂²	semidirect
22. C₆₁×#500	C₂²	semidirect
23. C₆₁×#482	C₂²	semidirect
24. C₆₁×#476	C₂²	semidirect
25. C₆₁×#466	C₂²	semidirect
26. C₄×D₈×C₆₁	C₂²	semidirect
27. C₈×D₄×C₆₁	C₂²	semidirect
28. C₆₁×#427	C₂²	semidirect
164. C₂×#3341	C₆₁	direct (N × H)
185. C₂×#555	C₂×C₆₁	semidirect
186. #3341	C₂×C₆₁	direct (N × H)
187. C₂×#500	C₂×C₆₁	semidirect
188. C₂×#482	C₂×C₆₁	semidirect
189. C₂×#476	C₂×C₆₁	semidirect
190. C₂×#466	C₂×C₆₁	semidirect
191. C₂×C₄×D₈	C₂×C₆₁	semidirect
192. C₂×C₈×D₄	C₂×C₆₁	semidirect
193. C₂×#427	C₂×C₆₁	semidirect
196. C₂×C₆₁	#3341	direct (N × H)
203. #555	C₂²×C₆₁	semidirect
212. #500	C₂²×C₆₁	semidirect
213. #482	C₂²×C₆₁	semidirect
214. #476	C₂²×C₆₁	semidirect
215. #466	C₂²×C₆₁	semidirect
216. C₄×D₈	C₂²×C₆₁	semidirect
217. C₈×D₄	C₂²×C₆₁	semidirect
218. #427	C₂²×C₆₁	semidirect
228. C₆₁	C₂×#3341	direct (N × H)
377. C₂	C₆₁×#3341	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×C₆₁×#555	2
C₆₁×#3341	2
C₂×C₆₁×#500	2
C₂×C₆₁×#482	2
C₂×C₆₁×#476	2
C₂×C₆₁×#466	2
C₂×C₄×D₈×C₆₁	2
C₂×C₈×D₄×C₆₁	2
C₂×C₆₁×#427	2
C₂×#3341	61

Subgroups — C2×C61×#3341 #29564665

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#3341 #29564665