Subgroups — C₆₁×#24131 #29527564

Order 15616.

1140 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#476	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#440	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2535	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2035	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2000	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1993	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1955	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1875	C₂	1	2	yes	maximal, complemented
10	C₆₁×#1854	C₂	1	2	yes	maximal, complemented
11	C₆₁×#1805	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
13	C₆₁×#556	—	2	4	no	—
14	C₆₁×#556	—	2	4	no	—
15	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×#126×C₆₁	—	2	2	no	—
17	C₂×#124×C₆₁	—	2	1	no	—
18	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
19	C₂×#121×C₆₁	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
21	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×#117×C₆₁	C₂²	1	2	yes	—
25	C₆₁×#476	—	2	4	no	—
26	C₆₁×#440	—	2	4	no	—
27	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×#106×C₆₁	C₂²	1	2	yes	—
29	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×#103×C₆₁	C₂²	1	2	yes	—
32	C₂×#102×C₆₁	C₂²	1	2	yes	—
33	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
35	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
36	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
37	C₆₁×#397	—	2	1	no	—
38	C₆₁×#392	—	2	1	no	—
39	C₆₁×#386	—	2	2	no	—
40	C₆₁×#382	C₂²	1	1	yes	characteristic
41	C₆₁×#380	C₂²	1	2	yes	—
42	C₆₁×#340	C₂²	1	2	yes	—
43	C₆₁×#340	C₂²	1	2	yes	—
44	C₆₁×#340	C₂²	1	2	yes	—
45	C₂²×Q₈×C₆₁	—	2	1	no	—
46	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₆₁	—	2	2	no	—
48	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
49	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₆₁	—	2	1	no	—
51	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
52	C₂×SD₁₆×C₆₁	—	2	2	no	—
53	C₂×SD₁₆×C₆₁	—	2	2	no	—
54	C₂×SD₁₆×C₆₁	—	2	2	no	—
55	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
57	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
58	C₄⋊Q₈×C₆₁	—	2	2	no	—
59	C₄⋊Q₈×C₆₁	D₄	1	4	yes	complemented
60	#126×C₆₁	—	2	16	no	—
61	#124×C₆₁	—	2	8	no	—
62	C₂²⋊Q₈×C₆₁	—	2	4	no	—
63	C₂²⋊Q₈×C₆₁	—	2	4	no	—
64	#121×C₆₁	—	2	4	no	—
65	#121×C₆₁	—	4	2	no	—
66	C₄×Q₈×C₆₁	—	2	8	no	—
67	C₄×Q₈×C₆₁	—	2	2	no	—
68	C₄×Q₈×C₆₁	D₄	1	4	yes	complemented
69	C₄×D₄×C₆₁	—	2	2	no	—
70	C₄×D₄×C₆₁	—	2	2	no	—
71	C₄×D₄×C₆₁	—	2	2	no	—
72	C₄×D₄×C₆₁	—	2	2	no	—
73	#117×C₆₁	—	2	4	no	—
74	#117×C₆₁	—	2	4	no	—
75	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
76	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
77	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
78	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
83	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
89	C₂×C₄²×C₆₁	—	2	2	no	—
90	C₂×C₄²×C₆₁	—	2	1	no	—
91	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
92	#107×C₆₁	—	2	2	no	—
93	#106×C₆₁	—	2	4	no	—
94	C₄⋊C₈×C₆₁	—	2	2	no	—
95	#103×C₆₁	—	2	2	no	—
96	#103×C₆₁	—	4	2	no	—
97	#102×C₆₁	—	2	2	no	—
98	#102×C₆₁	—	2	4	no	—
99	C₂²⋊C₈×C₆₁	—	2	4	no	—
100	C₂²⋊C₈×C₆₁	—	4	2	no	—
101	#97×C₆₁	—	2	2	no	—
102	#95×C₆₁	—	2	2	no	—
103	#95×C₆₁	—	2	1	no	—
104	#95×C₆₁	—	2	1	no	—
105	C₂⁴×C₆₁	—	2	1	no	—
106	C₂⁴×C₆₁	C₂×D₄	1	2	yes	—
107	C₂×Q₈×C₆₁	—	2	4	no	—
108	C₂×Q₈×C₆₁	—	2	1	no	—
109	C₂×Q₈×C₆₁	—	2	1	no	—
110	C₂×Q₈×C₆₁	—	2	1	no	—
111	C₂×Q₈×C₆₁	—	2	1	no	—
112	C₂×Q₈×C₆₁	—	2	1	no	—
113	C₂×Q₈×C₆₁	—	4	4	no	—
114	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
115	C₂×D₄×C₆₁	—	2	2	no	—
116	C₂×D₄×C₆₁	—	2	1	no	—
117	C₂×D₄×C₆₁	—	2	1	no	—
118	C₂×D₄×C₆₁	—	2	1	no	—
119	C₂×D₄×C₆₁	—	2	1	no	—
120	C₂×D₄×C₆₁	—	2	1	no	—
121	C₂×D₄×C₆₁	—	4	2	no	—
122	C₂×D₄×C₆₁	—	4	4	no	—
123	C₂×D₄×C₆₁	—	4	4	no	—
124	C₂×D₄×C₆₁	—	8	2	no	—
125	C₂×D₄×C₆₁	#41	1	2	yes	—
126	C₂²×C₄×C₆₁	—	2	1	no	—
127	C₂²×C₄×C₆₁	—	2	1	no	—
128	C₂²×C₄×C₆₁	—	2	2	no	—
129	C₂²×C₄×C₆₁	—	2	2	no	—
130	C₂²×C₄×C₆₁	—	2	2	no	—
131	C₂²×C₄×C₆₁	—	2	2	no	—
132	C₂²×C₄×C₆₁	—	2	2	no	—
133	C₂²×C₄×C₆₁	—	2	2	no	—
134	C₂²×C₄×C₆₁	—	2	2	no	—
135	C₂²×C₄×C₆₁	—	2	2	no	—
136	C₂²×C₄×C₆₁	—	2	1	no	—
137	C₂²×C₄×C₆₁	—	4	2	no	—
138	C₂²×C₄×C₆₁	—	8	2	no	—
139	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
143	SD₁₆×C₆₁	—	2	8	no	—
144	C₂×C₈×C₆₁	—	2	1	no	—
145	C₂×C₈×C₆₁	—	2	1	no	—
146	C₂×C₈×C₆₁	—	2	1	no	—
147	C₂×C₈×C₆₁	—	2	2	no	—
148	C₂×C₈×C₆₁	—	2	2	no	—
149	C₂×C₈×C₆₁	—	2	1	no	—
150	C₂×C₈×C₆₁	—	2	2	no	—
151	C₂×C₈×C₆₁	—	2	1	no	—
152	C₂×C₈×C₆₁	#41	1	2	yes	—
153	C₄⋊C₄×C₆₁	—	2	8	no	—
154	C₄⋊C₄×C₆₁	—	2	4	no	—
155	C₄⋊C₄×C₆₁	—	2	4	no	—
156	C₄⋊C₄×C₆₁	—	2	2	no	—
157	C₄⋊C₄×C₆₁	—	2	1	no	—
158	C₄⋊C₄×C₆₁	—	2	2	no	—
159	C₄⋊C₄×C₆₁	—	2	1	no	—
160	C₄⋊C₄×C₆₁	—	2	1	no	—
161	C₄⋊C₄×C₆₁	—	2	2	no	—
162	C₄⋊C₄×C₆₁	—	2	2	no	—
163	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
164	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
165	C₂²⋊C₄×C₆₁	—	2	8	no	—
166	C₂²⋊C₄×C₆₁	—	2	8	no	—
167	C₂²⋊C₄×C₆₁	—	2	4	no	—
168	C₂²⋊C₄×C₆₁	—	4	4	no	—
169	C₂²⋊C₄×C₆₁	—	4	2	no	—
170	C₂²⋊C₄×C₆₁	—	8	2	no	—
171	C₄²×C₆₁	—	2	8	no	—
172	C₄²×C₆₁	—	2	4	no	—
173	C₄²×C₆₁	C₂×D₄	1	2	yes	—
174	C₄²×C₆₁	C₂×D₄	1	2	yes	—
175	C₂³×C₆₁	—	2	2	no	—
176	C₂³×C₆₁	—	2	2	no	—
177	C₂³×C₆₁	—	2	2	no	—
178	C₂³×C₆₁	—	2	2	no	—
179	C₂³×C₆₁	—	2	2	no	—
180	C₂³×C₆₁	—	2	2	no	—
181	C₂³×C₆₁	—	2	2	no	—
182	C₂³×C₆₁	—	2	2	no	—
183	C₂³×C₆₁	—	4	1	no	—
184	C₂³×C₆₁	—	4	1	no	—
185	C₂³×C₆₁	—	4	2	no	—
186	C₂³×C₆₁	—	4	2	no	—
187	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
188	Q₈×C₆₁	—	2	2	no	—
189	Q₈×C₆₁	—	2	2	no	—
190	Q₈×C₆₁	—	4	8	no	—
191	Q₈×C₆₁	—	4	1	no	—
192	Q₈×C₆₁	—	4	1	no	—
193	D₄×C₆₁	—	2	2	no	—
194	D₄×C₆₁	—	2	2	no	—
195	D₄×C₆₁	—	4	4	no	—
196	D₄×C₆₁	—	4	1	no	—
197	D₄×C₆₁	—	4	1	no	—
198	D₄×C₆₁	—	8	8	no	—
199	C₂×C₄×C₆₁	—	2	2	no	—
200	C₂×C₄×C₆₁	—	2	2	no	—
201	C₂×C₄×C₆₁	—	2	2	no	—
202	C₂×C₄×C₆₁	—	2	2	no	—
203	C₂×C₄×C₆₁	—	2	2	no	—
204	C₂×C₄×C₆₁	—	2	4	no	—
205	C₂×C₄×C₆₁	—	2	2	no	—
206	C₂×C₄×C₆₁	—	2	2	no	—
207	C₂×C₄×C₆₁	—	4	1	no	—
208	C₂×C₄×C₆₁	—	4	1	no	—
209	C₂×C₄×C₆₁	—	4	4	no	—
210	C₂×C₄×C₆₁	—	4	2	no	—
211	C₂×C₄×C₆₁	—	4	2	no	—
212	C₂×C₄×C₆₁	—	4	2	no	—
213	C₂×C₄×C₆₁	—	4	2	no	—
214	C₂×C₄×C₆₁	—	4	2	no	—
215	C₂×C₄×C₆₁	—	4	1	no	—
216	C₂×C₄×C₆₁	—	4	2	no	—
217	C₂×C₄×C₆₁	—	4	2	no	—
218	C₂×C₄×C₆₁	—	4	2	no	—
219	C₂×C₄×C₆₁	—	4	2	no	—
220	C₂×C₄×C₆₁	—	8	4	no	—
221	C₂×C₄×C₆₁	#120	1	2	yes	—
222	C₂×C₄×C₆₁	#120	1	2	yes	—
223	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
226	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
227	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
228	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
229	C₈×C₆₁	—	2	2	no	—
230	C₈×C₆₁	—	4	1	no	—
231	C₈×C₆₁	—	4	2	no	—
232	#24131	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
233	C₂²×C₆₁	—	4	2	no	—
234	C₂²×C₆₁	—	4	2	no	—
235	C₂²×C₆₁	—	4	2	no	—
236	C₂²×C₆₁	—	4	2	no	—
237	C₂²×C₆₁	—	4	2	no	—
238	C₂²×C₆₁	—	4	2	no	—
239	C₂²×C₆₁	—	4	2	no	—
240	C₂²×C₆₁	—	4	4	no	—
241	C₂²×C₆₁	—	4	2	no	—
242	C₂²×C₆₁	—	8	2	no	—
243	C₂²×C₆₁	—	8	1	no	—
244	C₂²×C₆₁	—	8	1	no	—
245	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
246	C₂²×C₆₁	#546	1	1	yes	characteristic
247	C₂²×C₆₁	#547	1	1	yes	characteristic
248	C₂²×C₆₁	#575	1	2	yes	—
249	C₂²×C₆₁	#577	1	2	yes	—
250	C₄×C₆₁	—	2	2	no	—
251	C₄×C₆₁	—	2	2	no	—
252	C₄×C₆₁	—	4	2	no	—
253	C₄×C₆₁	—	4	2	no	—
254	C₄×C₆₁	—	4	4	no	—
255	C₄×C₆₁	—	4	2	no	—
256	C₄×C₆₁	—	8	1	no	—
257	C₄×C₆₁	—	8	2	no	—
258	C₄×C₆₁	#525	1	1	yes	characteristic
259	C₄×C₆₁	#537	1	1	yes	characteristic
260	C₄×C₆₁	#548	1	1	yes	characteristic
261	C₄×C₆₁	#550	1	1	yes	characteristic
262	C₂×#556	C₂×C₆₁	1	1	yes	characteristic, complemented
263	C₂×#476	C₂×C₆₁	1	1	yes	characteristic, complemented
264	C₂×#440	C₂×C₆₁	1	1	yes	characteristic, complemented
265	#2535	C₂×C₆₁	1	1	yes	characteristic
266	#2035	C₂×C₆₁	1	2	yes	complemented
267	#2000	C₂×C₆₁	1	2	yes	complemented
268	#1993	C₂×C₆₁	1	1	yes	characteristic, complemented
269	#1955	C₂×C₆₁	1	1	yes	characteristic, complemented
270	#1875	C₂×C₆₁	1	2	yes	complemented
271	#1854	C₂×C₆₁	1	2	yes	complemented
272	#1805	C₂×C₆₁	1	1	yes	characteristic, complemented
273	C₂×C₆₁	—	8	2	no	—
274	C₂×C₆₁	—	8	2	no	—
275	C₂×C₆₁	#2407	1	1	yes	characteristic
276	C₂×C₆₁	#3005	1	1	yes	characteristic
277	C₂×C₆₁	#3010	1	1	yes	characteristic
278	C₂×C₆₁	#3311	1	2	yes	—
279	C₂×C₆₁	#3350	1	2	yes	—
280	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
281	#556	—	2	4	no	—
282	#556	—	2	4	no	—
283	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
284	C₂×#126	—	2	2	no	—
285	C₂×#124	—	2	1	no	—
286	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
287	C₂×#121	C₂²×C₆₁	1	2	yes	—
288	C₂×C₄×Q₈	—	2	1	no	—
289	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
290	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
291	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
292	C₂×#117	C₂²×C₆₁	1	2	yes	—
293	#476	—	2	4	no	—
294	#440	—	2	4	no	—
295	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
296	C₂×#106	C₂²×C₆₁	1	2	yes	—
297	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
298	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
299	C₂×#103	C₂²×C₆₁	1	2	yes	—
300	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
301	C₂×#102	C₂²×C₆₁	1	2	yes	—
302	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
303	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
304	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
305	#397	—	2	1	no	—
306	#392	—	2	1	no	—
307	#386	—	2	2	no	—
308	#382	C₂²×C₆₁	1	1	yes	characteristic
309	#380	C₂²×C₆₁	1	2	yes	—
310	#340	C₂²×C₆₁	1	2	yes	—
311	#340	C₂²×C₆₁	1	2	yes	—
312	#340	C₂²×C₆₁	1	2	yes	—
313	C₆₁	#24131	1	1	yes	characteristic, direct product factor, Sylow
314	C₂²×Q₈	—	2	1	no	—
315	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
316	C₂²×D₄	—	2	2	no	—
317	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
318	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
319	C₂³×C₄	—	2	1	no	—
320	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
321	C₂×SD₁₆	—	2	2	no	—
322	C₂×SD₁₆	—	2	2	no	—
323	C₂×SD₁₆	—	2	2	no	—
324	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
325	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
326	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
327	C₄⋊Q₈	—	2	2	no	—
328	C₄⋊Q₈	D₄×C₆₁	1	4	yes	complemented
329	#126	—	2	16	no	—
330	#124	—	2	8	no	—
331	C₂²⋊Q₈	—	2	4	no	—
332	C₂²⋊Q₈	—	2	4	no	—
333	#121	—	2	4	no	—
334	#121	—	4	2	no	—
335	C₄×Q₈	—	2	8	no	—
336	C₄×Q₈	—	2	2	no	—
337	C₄×Q₈	D₄×C₆₁	1	4	yes	complemented
338	C₄×D₄	—	2	2	no	—
339	C₄×D₄	—	2	2	no	—
340	C₄×D₄	—	2	2	no	—
341	C₄×D₄	—	2	2	no	—
342	#117	—	2	4	no	—
343	#117	—	2	4	no	—
344	C₂×C₄⋊C₄	—	2	2	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
348	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
349	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
350	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
352	C₂×C₂²⋊C₄	—	2	2	no	—
353	C₂×C₂²⋊C₄	—	2	2	no	—
354	C₂×C₂²⋊C₄	—	2	1	no	—
355	C₂×C₂²⋊C₄	—	2	2	no	—
356	C₂×C₂²⋊C₄	—	2	2	no	—
357	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
358	C₂×C₄²	—	2	2	no	—
359	C₂×C₄²	—	2	1	no	—
360	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
361	#107	—	2	2	no	—
362	#106	—	2	4	no	—
363	C₄⋊C₈	—	2	2	no	—
364	#103	—	2	2	no	—
365	#103	—	4	2	no	—
366	#102	—	2	2	no	—
367	#102	—	2	4	no	—
368	C₂²⋊C₈	—	2	4	no	—
369	C₂²⋊C₈	—	4	2	no	—
370	#97	—	2	2	no	—
371	#95	—	2	2	no	—
372	#95	—	2	1	no	—
373	#95	—	2	1	no	—
374	C₂⁴	—	2	1	no	—
375	C₂⁴	C₂×D₄×C₆₁	1	2	yes	—
376	C₂×Q₈	—	2	4	no	—
377	C₂×Q₈	—	2	1	no	—
378	C₂×Q₈	—	2	1	no	—
379	C₂×Q₈	—	2	1	no	—
380	C₂×Q₈	—	2	1	no	—
381	C₂×Q₈	—	2	1	no	—
382	C₂×Q₈	—	4	4	no	—
383	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	2	1	no	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	4	2	no	—
391	C₂×D₄	—	4	4	no	—
392	C₂×D₄	—	4	4	no	—
393	C₂×D₄	—	8	2	no	—
394	C₂×D₄	#41×C₆₁	1	2	yes	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	4	2	no	—
407	C₂²×C₄	—	8	2	no	—
408	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
409	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
410	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
411	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
412	SD₁₆	—	2	8	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	1	no	—
415	C₂×C₈	—	2	1	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	#41×C₆₁	1	2	yes	—
422	C₄⋊C₄	—	2	8	no	—
423	C₄⋊C₄	—	2	4	no	—
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
433	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
434	C₂²⋊C₄	—	2	8	no	—
435	C₂²⋊C₄	—	2	8	no	—
436	C₂²⋊C₄	—	2	4	no	—
437	C₂²⋊C₄	—	4	4	no	—
438	C₂²⋊C₄	—	4	2	no	—
439	C₂²⋊C₄	—	8	2	no	—
440	C₄²	—	2	8	no	—
441	C₄²	—	2	4	no	—
442	C₄²	C₂×D₄×C₆₁	1	2	yes	—
443	C₄²	C₂×D₄×C₆₁	1	2	yes	—
444	C₂³	—	2	2	no	—
445	C₂³	—	2	2	no	—
446	C₂³	—	2	2	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	2	2	no	—
450	C₂³	—	2	2	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	4	1	no	—
453	C₂³	—	4	2	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	4	1	no	—
456	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
457	Q₈	—	2	2	no	—
458	Q₈	—	2	2	no	—
459	Q₈	—	4	8	no	—
460	Q₈	—	4	1	no	—
461	Q₈	—	4	1	no	—
462	D₄	—	2	2	no	—
463	D₄	—	2	2	no	—
464	D₄	—	4	4	no	—
465	D₄	—	4	1	no	—
466	D₄	—	4	1	no	—
467	D₄	—	8	8	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	4	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	8	4	no	—
490	C₂×C₄	#120×C₆₁	1	2	yes	—
491	C₂×C₄	#120×C₆₁	1	2	yes	—
492	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
493	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
494	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
495	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
496	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
497	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
498	C₈	—	2	2	no	—
499	C₈	—	4	1	no	—
500	C₈	—	4	2	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	4	4	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	2	no	—
510	C₂²	—	8	2	no	—
511	C₂²	—	8	1	no	—
512	C₂²	—	8	1	no	—
513	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
514	C₂²	C₆₁×#546	1	1	yes	characteristic
515	C₂²	C₆₁×#547	1	1	yes	characteristic
516	C₂²	C₆₁×#575	1	2	yes	—
517	C₂²	C₆₁×#577	1	2	yes	—
518	C₄	—	2	2	no	—
519	C₄	—	2	2	no	—
520	C₄	—	4	2	no	—
521	C₄	—	4	2	no	—
522	C₄	—	4	4	no	—
523	C₄	—	4	2	no	—
524	C₄	—	8	2	no	—
525	C₄	—	8	1	no	—
526	C₄	C₆₁×#525	1	1	yes	characteristic
527	C₄	C₆₁×#537	1	1	yes	characteristic
528	C₄	C₆₁×#548	1	1	yes	characteristic
529	C₄	C₆₁×#550	1	1	yes	characteristic
530	C₂	—	8	2	no	—
531	C₂	—	8	2	no	—
532	C₂	C₆₁×#2407	1	1	yes	characteristic
533	C₂	C₆₁×#3005	1	1	yes	characteristic
534	C₂	C₆₁×#3010	1	1	yes	characteristic
535	C₂	C₆₁×#3311	1	2	yes	—
536	C₂	C₆₁×#3350	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₆₁×#2535	C₂
LCS	G ▷ C₂²×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×#556	C₂	semidirect
2. C₂×C₆₁×#476	C₂	semidirect
3. C₂×C₆₁×#440	C₂	semidirect
5. C₆₁×#2035	C₂	semidirect
6. C₆₁×#2000	C₂	semidirect
7. C₆₁×#1993	C₂	semidirect
8. C₆₁×#1955	C₂	semidirect
9. C₆₁×#1875	C₂	semidirect
10. C₆₁×#1854	C₂	semidirect
11. C₆₁×#1805	C₂	semidirect
59. C₄⋊Q₈×C₆₁	D₄	semidirect
68. C₄×Q₈×C₆₁	D₄	semidirect
232. #24131	C₆₁	direct (N × H)
262. C₂×#556	C₂×C₆₁	semidirect
263. C₂×#476	C₂×C₆₁	semidirect
264. C₂×#440	C₂×C₆₁	semidirect
266. #2035	C₂×C₆₁	semidirect
267. #2000	C₂×C₆₁	semidirect
268. #1993	C₂×C₆₁	semidirect
269. #1955	C₂×C₆₁	semidirect
270. #1875	C₂×C₆₁	semidirect
271. #1854	C₂×C₆₁	semidirect
272. #1805	C₂×C₆₁	semidirect
313. C₆₁	#24131	direct (N × H)
328. C₄⋊Q₈	D₄×C₆₁	semidirect
337. C₄×Q₈	D₄×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#556	2
C₂×C₆₁×#476	2
C₂×C₆₁×#440	2
C₆₁×#2535	2
C₆₁×#2035	2
C₆₁×#2000	2
C₆₁×#1993	2
C₆₁×#1955	2
C₆₁×#1875	2
C₆₁×#1854	2
C₆₁×#1805	2
#24131	61

Subgroups — C61×#24131 #29527564

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24131 #29527564