Subgroups — C₆₁×#24825 #29528258

Order 15616.

880 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#478	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#440	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2565	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₄⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2085	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#2083	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#2068	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2066	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1992	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1940	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1877	C₂	1	1	yes	maximal, characteristic
12	C₆₁×#1877	C₂	1	1	yes	maximal, characteristic
13	C₆₁×#1804	C₂	1	1	yes	maximal, characteristic
14	C₆₁×#1803	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#1802	C₂	1	1	yes	maximal, characteristic
16	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×#125×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₆₁	—	2	1	no	—
23	C₆₁×#478	—	2	4	no	—
24	C₆₁×#440	—	2	4	no	—
25	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
33	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
34	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
35	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
36	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
37	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
38	C₆₁×#398	—	2	1	no	—
39	C₆₁×#398	—	2	1	no	—
40	C₆₁×#391	C₂²	1	1	yes	characteristic
41	C₆₁×#391	C₂²	1	1	yes	characteristic
42	C₆₁×#389	C₂²	1	1	yes	characteristic
43	C₆₁×#389	C₂²	1	1	yes	characteristic
44	C₆₁×#387	—	2	1	no	—
45	C₆₁×#387	—	2	1	no	—
46	C₆₁×#385	—	2	1	no	—
47	C₆₁×#385	—	2	1	no	—
48	C₆₁×#384	C₂²	1	1	yes	characteristic
49	C₆₁×#384	C₂²	1	1	yes	characteristic
50	C₆₁×#382	C₂²	1	1	yes	characteristic
51	C₆₁×#380	—	2	1	no	—
52	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
53	C₆₁×#340	C₂²	1	1	yes	characteristic
54	C₆₁×#340	C₂²	1	1	yes	characteristic
55	C₆₁×#340	C₂²	1	1	yes	characteristic
56	C₆₁×#340	C₂²	1	1	yes	characteristic
57	C₆₁×#340	C₂²	1	1	yes	characteristic
58	C₆₁×#340	C₂²	1	1	yes	characteristic
59	C₆₁×#336	C₂²	1	1	yes	characteristic
60	C₆₁×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₆₁	—	2	1	no	—
64	C₂³×C₄×C₆₁	—	2	1	no	—
65	C₂³×C₄×C₆₁	—	2	1	no	—
66	C₂×SD₁₆×C₆₁	—	2	2	no	—
67	C₂×SD₁₆×C₆₁	—	2	2	no	—
68	C₂×SD₁₆×C₆₁	Q₈	1	4	yes	—
69	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
73	#125×C₆₁	—	2	2	no	—
74	#125×C₆₁	—	2	2	no	—
75	C₄×Q₈×C₆₁	—	2	2	no	—
76	C₄×Q₈×C₆₁	—	2	2	no	—
77	C₄×D₄×C₆₁	—	2	2	no	—
78	C₄×D₄×C₆₁	—	2	2	no	—
79	C₄×D₄×C₆₁	—	2	2	no	—
80	C₄×D₄×C₆₁	—	4	1	no	—
81	C₄×D₄×C₆₁	—	4	1	no	—
82	C₄×D₄×C₆₁	D₄	1	4	yes	—
83	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
84	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
85	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
86	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
87	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
88	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
89	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
90	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
91	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
92	C₂×C₄⋊C₄×C₆₁	—	4	4	no	—
93	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
104	C₂×C₄²×C₆₁	—	2	1	no	—
105	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
108	#107×C₆₁	—	2	2	no	—
109	#107×C₆₁	—	2	2	no	—
110	#106×C₆₁	—	2	2	no	—
111	C₄⋊C₈×C₆₁	—	2	2	no	—
112	C₄⋊C₈×C₆₁	—	4	1	no	—
113	C₄⋊C₈×C₆₁	—	4	1	no	—
114	#103×C₆₁	—	2	2	no	—
115	#103×C₆₁	—	4	1	no	—
116	#103×C₆₁	—	4	1	no	—
117	#102×C₆₁	—	2	2	no	—
118	#102×C₆₁	—	2	2	no	—
119	#102×C₆₁	—	2	2	no	—
120	#97×C₆₁	—	2	2	no	—
121	#95×C₆₁	—	2	1	no	—
122	#95×C₆₁	—	2	1	no	—
123	#95×C₆₁	—	2	1	no	—
124	#95×C₆₁	—	2	1	no	—
125	#95×C₆₁	—	2	1	no	—
126	#95×C₆₁	—	2	1	no	—
127	#95×C₆₁	—	2	1	no	—
128	#95×C₆₁	—	2	1	no	—
129	#95×C₆₁	D₄	1	1	yes	characteristic
130	#95×C₆₁	D₄	1	1	yes	characteristic
131	C₂⁴×C₆₁	—	2	1	no	—
132	C₂×Q₈×C₆₁	—	2	1	no	—
133	C₂×Q₈×C₆₁	—	2	1	no	—
134	C₂×Q₈×C₆₁	—	2	1	no	—
135	C₂×Q₈×C₆₁	—	2	1	no	—
136	C₂×Q₈×C₆₁	—	2	1	no	—
137	C₂×Q₈×C₆₁	C₂×Q₈	1	2	yes	—
138	C₂×D₄×C₆₁	—	2	1	no	—
139	C₂×D₄×C₆₁	—	2	1	no	—
140	C₂×D₄×C₆₁	—	2	1	no	—
141	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
142	C₂×D₄×C₆₁	C₂×Q₈	1	2	yes	—
143	C₂×D₄×C₆₁	#41	1	2	yes	—
144	C₂²×C₄×C₆₁	—	2	1	no	—
145	C₂²×C₄×C₆₁	—	2	1	no	—
146	C₂²×C₄×C₆₁	—	2	4	no	—
147	C₂²×C₄×C₆₁	—	2	1	no	—
148	C₂²×C₄×C₆₁	—	2	1	no	—
149	C₂²×C₄×C₆₁	—	2	1	no	—
150	C₂²×C₄×C₆₁	—	2	1	no	—
151	C₂²×C₄×C₆₁	—	2	1	no	—
152	C₂²×C₄×C₆₁	—	4	2	no	—
153	C₂²×C₄×C₆₁	—	4	2	no	—
154	C₂²×C₄×C₆₁	—	4	2	no	—
155	C₂²×C₄×C₆₁	—	4	2	no	—
156	C₂²×C₄×C₆₁	—	4	2	no	—
157	C₂²×C₄×C₆₁	—	4	2	no	—
158	C₂²×C₄×C₆₁	—	8	1	no	—
159	C₂²×C₄×C₆₁	—	8	1	no	—
160	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
167	SD₁₆×C₆₁	—	2	8	no	—
168	C₂×C₈×C₆₁	—	2	1	no	—
169	C₂×C₈×C₆₁	—	2	1	no	—
170	C₂×C₈×C₆₁	—	2	1	no	—
171	C₂×C₈×C₆₁	—	2	1	no	—
172	C₂×C₈×C₆₁	—	2	1	no	—
173	C₂×C₈×C₆₁	—	2	1	no	—
174	C₂×C₈×C₆₁	—	2	1	no	—
175	C₂×C₈×C₆₁	—	2	1	no	—
176	C₂×C₈×C₆₁	—	2	1	no	—
177	C₂×C₈×C₆₁	—	2	1	no	—
178	C₂×C₈×C₆₁	—	2	1	no	—
179	C₂×C₈×C₆₁	C₂×Q₈	1	2	yes	—
180	C₄⋊C₄×C₆₁	—	2	2	no	—
181	C₄⋊C₄×C₆₁	—	2	1	no	—
182	C₄⋊C₄×C₆₁	—	2	1	no	—
183	C₄⋊C₄×C₆₁	—	2	1	no	—
184	C₄⋊C₄×C₆₁	—	2	1	no	—
185	C₄⋊C₄×C₆₁	—	2	1	no	—
186	C₄⋊C₄×C₆₁	—	2	1	no	—
187	C₄⋊C₄×C₆₁	—	2	1	no	—
188	C₄⋊C₄×C₆₁	—	2	1	no	—
189	C₄⋊C₄×C₆₁	—	2	1	no	—
190	C₄⋊C₄×C₆₁	—	2	1	no	—
191	C₄⋊C₄×C₆₁	—	2	1	no	—
192	C₄⋊C₄×C₆₁	—	4	1	no	—
193	C₄⋊C₄×C₆₁	—	4	2	no	—
194	C₄⋊C₄×C₆₁	—	4	2	no	—
195	C₄⋊C₄×C₆₁	—	4	2	no	—
196	C₄⋊C₄×C₆₁	—	4	2	no	—
197	C₄⋊C₄×C₆₁	—	4	2	no	—
198	C₄⋊C₄×C₆₁	—	4	2	no	—
199	C₄⋊C₄×C₆₁	—	4	2	no	—
200	C₄⋊C₄×C₆₁	—	4	2	no	—
201	C₄⋊C₄×C₆₁	—	8	1	no	—
202	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
203	C₂²⋊C₄×C₆₁	—	2	4	no	—
204	C₂²⋊C₄×C₆₁	—	4	2	no	—
205	C₂²⋊C₄×C₆₁	—	4	2	no	—
206	C₄²×C₆₁	—	2	1	no	—
207	C₄²×C₆₁	—	2	1	no	—
208	C₄²×C₆₁	—	2	1	no	—
209	C₄²×C₆₁	—	2	1	no	—
210	C₄²×C₆₁	—	4	2	no	—
211	C₄²×C₆₁	C₂×D₄	1	2	yes	—
212	C₄²×C₆₁	#41	1	2	yes	—
213	C₂³×C₆₁	—	2	2	no	—
214	C₂³×C₆₁	—	2	2	no	—
215	C₂³×C₆₁	—	2	2	no	—
216	C₂³×C₆₁	—	4	1	no	—
217	C₂³×C₆₁	—	4	1	no	—
218	C₂³×C₆₁	—	4	1	no	—
219	C₂³×C₆₁	—	4	1	no	—
220	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
221	Q₈×C₆₁	—	2	2	no	—
222	Q₈×C₆₁	—	2	2	no	—
223	Q₈×C₆₁	—	4	1	no	—
224	Q₈×C₆₁	—	4	1	no	—
225	D₄×C₆₁	—	2	2	no	—
226	D₄×C₆₁	—	2	2	no	—
227	D₄×C₆₁	—	2	2	no	—
228	D₄×C₆₁	C₂²⋊Q₈	1	4	yes	—
229	C₂×C₄×C₆₁	—	2	1	no	—
230	C₂×C₄×C₆₁	—	2	1	no	—
231	C₂×C₄×C₆₁	—	2	1	no	—
232	C₂×C₄×C₆₁	—	2	1	no	—
233	C₂×C₄×C₆₁	—	2	1	no	—
234	C₂×C₄×C₆₁	—	2	1	no	—
235	C₂×C₄×C₆₁	—	2	2	no	—
236	C₂×C₄×C₆₁	—	2	1	no	—
237	C₂×C₄×C₆₁	—	2	1	no	—
238	C₂×C₄×C₆₁	—	2	1	no	—
239	C₂×C₄×C₆₁	—	2	2	no	—
240	C₂×C₄×C₆₁	—	2	1	no	—
241	C₂×C₄×C₆₁	—	2	1	no	—
242	C₂×C₄×C₆₁	—	2	1	no	—
243	C₂×C₄×C₆₁	—	2	1	no	—
244	C₂×C₄×C₆₁	—	2	1	no	—
245	C₂×C₄×C₆₁	—	2	1	no	—
246	C₂×C₄×C₆₁	—	4	8	no	—
247	C₂×C₄×C₆₁	—	4	1	no	—
248	C₂×C₄×C₆₁	—	4	1	no	—
249	C₂×C₄×C₆₁	—	4	1	no	—
250	C₂×C₄×C₆₁	—	4	1	no	—
251	C₂×C₄×C₆₁	—	4	1	no	—
252	C₂×C₄×C₆₁	—	4	1	no	—
253	C₂×C₄×C₆₁	—	4	1	no	—
254	C₂×C₄×C₆₁	—	4	1	no	—
255	C₂×C₄×C₆₁	—	4	1	no	—
256	C₂×C₄×C₆₁	—	4	1	no	—
257	C₂×C₄×C₆₁	—	4	1	no	—
258	C₂×C₄×C₆₁	—	4	1	no	—
259	C₂×C₄×C₆₁	—	4	1	no	—
260	C₂×C₄×C₆₁	—	4	1	no	—
261	C₂×C₄×C₆₁	—	4	1	no	—
262	C₂×C₄×C₆₁	—	4	1	no	—
263	C₂×C₄×C₆₁	—	4	1	no	—
264	C₂×C₄×C₆₁	—	4	1	no	—
265	C₂×C₄×C₆₁	—	4	1	no	—
266	C₂×C₄×C₆₁	—	8	4	no	—
267	C₂×C₄×C₆₁	—	8	4	no	—
268	C₂×C₄×C₆₁	#121	1	2	yes	—
269	C₂×C₄×C₆₁	#121	1	2	yes	—
270	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
271	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
272	C₂×C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
273	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
274	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
275	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
276	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
277	C₈×C₆₁	—	2	2	no	—
278	C₈×C₆₁	—	4	1	no	—
279	C₈×C₆₁	—	4	1	no	—
280	C₈×C₆₁	—	4	1	no	—
281	#24825	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
282	C₂²×C₆₁	—	2	4	no	—
283	C₂²×C₆₁	—	4	2	no	—
284	C₂²×C₆₁	—	4	2	no	—
285	C₂²×C₆₁	—	4	2	no	—
286	C₂²×C₆₁	—	4	2	no	—
287	C₂²×C₆₁	—	4	2	no	—
288	C₂²×C₆₁	—	4	2	no	—
289	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
290	C₂²×C₆₁	#546	1	1	yes	characteristic
291	C₂²×C₆₁	D₄×Q₈	1	1	yes	characteristic
292	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
293	C₂²×C₆₁	#575	1	1	yes	characteristic
294	C₂²×C₆₁	#577	1	1	yes	characteristic
295	C₂²×C₆₁	#578	1	1	yes	characteristic
296	C₄×C₆₁	—	2	2	no	—
297	C₄×C₆₁	—	2	2	no	—
298	C₄×C₆₁	—	2	2	no	—
299	C₄×C₆₁	—	4	2	no	—
300	C₄×C₆₁	—	4	2	no	—
301	C₄×C₆₁	—	4	1	no	—
302	C₄×C₆₁	—	4	1	no	—
303	C₄×C₆₁	—	4	1	no	—
304	C₄×C₆₁	—	8	1	no	—
305	C₄×C₆₁	—	8	1	no	—
306	C₄×C₆₁	—	8	1	no	—
307	C₄×C₆₁	—	8	1	no	—
308	C₄×C₆₁	—	8	1	no	—
309	C₄×C₆₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
310	C₄×C₆₁	#537	1	1	yes	characteristic
311	C₄×C₆₁	#552	1	1	yes	characteristic
312	C₄×C₆₁	#554	1	1	yes	characteristic
313	C₂×#478	C₂×C₆₁	1	1	yes	characteristic
314	C₂×#440	C₂×C₆₁	1	1	yes	characteristic
315	#2565	C₂×C₆₁	1	1	yes	characteristic, complemented
316	D₄×C₄⋊C₄	C₂×C₆₁	1	1	yes	characteristic
317	#2085	C₂×C₆₁	1	1	yes	characteristic, complemented
318	#2083	C₂×C₆₁	1	1	yes	characteristic, complemented
319	#2068	C₂×C₆₁	1	1	yes	characteristic, complemented
320	#2066	C₂×C₆₁	1	1	yes	characteristic, complemented
321	#1992	C₂×C₆₁	1	1	yes	characteristic, complemented
322	#1940	C₂×C₆₁	1	1	yes	characteristic, complemented
323	#1877	C₂×C₆₁	1	1	yes	characteristic
324	#1877	C₂×C₆₁	1	1	yes	characteristic
325	#1804	C₂×C₆₁	1	1	yes	characteristic
326	#1803	C₂×C₆₁	1	1	yes	characteristic, complemented
327	#1802	C₂×C₆₁	1	1	yes	characteristic
328	C₂×C₆₁	—	4	4	no	—
329	C₂×C₆₁	#2417	1	1	yes	characteristic
330	C₂×C₆₁	#3036	1	1	yes	characteristic
331	C₂×C₆₁	#3046	1	1	yes	characteristic
332	C₂×C₆₁	#3310	1	1	yes	characteristic
333	C₂×C₆₁	#3315	1	1	yes	characteristic
334	C₂×C₆₁	#3386	1	1	yes	characteristic
335	C₂×C₆₁	#3388	1	1	yes	characteristic
336	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
337	C₂×#125	C₂²×C₆₁	1	1	yes	characteristic
338	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
339	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
340	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
341	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
342	C₂²×C₄⋊C₄	—	2	1	no	—
343	#478	—	2	4	no	—
344	#440	—	2	4	no	—
345	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
346	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
347	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
348	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
349	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
350	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
351	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
352	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
353	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
354	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
355	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
356	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
357	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
358	#398	—	2	1	no	—
359	#398	—	2	1	no	—
360	#391	C₂²×C₆₁	1	1	yes	characteristic
361	#391	C₂²×C₆₁	1	1	yes	characteristic
362	#389	C₂²×C₆₁	1	1	yes	characteristic
363	#389	C₂²×C₆₁	1	1	yes	characteristic
364	#387	—	2	1	no	—
365	#387	—	2	1	no	—
366	#385	—	2	1	no	—
367	#385	—	2	1	no	—
368	#384	C₂²×C₆₁	1	1	yes	characteristic
369	#384	C₂²×C₆₁	1	1	yes	characteristic
370	#382	C₂²×C₆₁	1	1	yes	characteristic
371	#380	—	2	1	no	—
372	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
373	#340	C₂²×C₆₁	1	1	yes	characteristic
374	#340	C₂²×C₆₁	1	1	yes	characteristic
375	#340	C₂²×C₆₁	1	1	yes	characteristic
376	#340	C₂²×C₆₁	1	1	yes	characteristic
377	#340	C₂²×C₆₁	1	1	yes	characteristic
378	#340	C₂²×C₆₁	1	1	yes	characteristic
379	#336	C₂²×C₆₁	1	1	yes	characteristic
380	#336	C₂²×C₆₁	1	1	yes	characteristic
381	C₆₁	#24825	1	1	yes	characteristic, direct product factor, Sylow
382	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
383	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
384	C₂³×C₄	—	2	1	no	—
385	C₂³×C₄	—	2	1	no	—
386	C₂³×C₄	—	2	1	no	—
387	C₂×SD₁₆	—	2	2	no	—
388	C₂×SD₁₆	—	2	2	no	—
389	C₂×SD₁₆	Q₈×C₆₁	1	4	yes	—
390	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
391	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
392	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
393	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
394	#125	—	2	2	no	—
395	#125	—	2	2	no	—
396	C₄×Q₈	—	2	2	no	—
397	C₄×Q₈	—	2	2	no	—
398	C₄×D₄	—	2	2	no	—
399	C₄×D₄	—	2	2	no	—
400	C₄×D₄	—	2	2	no	—
401	C₄×D₄	—	4	1	no	—
402	C₄×D₄	—	4	1	no	—
403	C₄×D₄	D₄×C₆₁	1	4	yes	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	—	2	1	no	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	—	2	1	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	—	2	1	no	—
412	C₂×C₄⋊C₄	—	2	1	no	—
413	C₂×C₄⋊C₄	—	4	4	no	—
414	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
415	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
422	C₂×C₂²⋊C₄	—	2	1	no	—
423	C₂×C₂²⋊C₄	—	2	1	no	—
424	C₂×C₂²⋊C₄	—	2	1	no	—
425	C₂×C₄²	—	2	1	no	—
426	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
427	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
428	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
429	#107	—	2	2	no	—
430	#107	—	2	2	no	—
431	#106	—	2	2	no	—
432	C₄⋊C₈	—	2	2	no	—
433	C₄⋊C₈	—	4	1	no	—
434	C₄⋊C₈	—	4	1	no	—
435	#103	—	2	2	no	—
436	#103	—	4	1	no	—
437	#103	—	4	1	no	—
438	#102	—	2	2	no	—
439	#102	—	2	2	no	—
440	#102	—	2	2	no	—
441	#97	—	2	2	no	—
442	#95	—	2	1	no	—
443	#95	—	2	1	no	—
444	#95	—	2	1	no	—
445	#95	—	2	1	no	—
446	#95	—	2	1	no	—
447	#95	—	2	1	no	—
448	#95	—	2	1	no	—
449	#95	—	2	1	no	—
450	#95	D₄×C₆₁	1	1	yes	characteristic
451	#95	D₄×C₆₁	1	1	yes	characteristic
452	C₂⁴	—	2	1	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	C₂×Q₈×C₆₁	1	2	yes	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
463	C₂×D₄	C₂×Q₈×C₆₁	1	2	yes	—
464	C₂×D₄	#41×C₆₁	1	2	yes	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	4	2	no	—
474	C₂²×C₄	—	4	2	no	—
475	C₂²×C₄	—	4	2	no	—
476	C₂²×C₄	—	4	2	no	—
477	C₂²×C₄	—	4	2	no	—
478	C₂²×C₄	—	4	2	no	—
479	C₂²×C₄	—	8	1	no	—
480	C₂²×C₄	—	8	1	no	—
481	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
482	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
483	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
484	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
485	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
486	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
487	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
488	SD₁₆	—	2	8	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	C₂×Q₈×C₆₁	1	2	yes	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	4	1	no	—
514	C₄⋊C₄	—	4	2	no	—
515	C₄⋊C₄	—	4	2	no	—
516	C₄⋊C₄	—	4	2	no	—
517	C₄⋊C₄	—	4	2	no	—
518	C₄⋊C₄	—	4	2	no	—
519	C₄⋊C₄	—	4	2	no	—
520	C₄⋊C₄	—	4	2	no	—
521	C₄⋊C₄	—	4	2	no	—
522	C₄⋊C₄	—	8	1	no	—
523	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
524	C₂²⋊C₄	—	2	4	no	—
525	C₂²⋊C₄	—	4	2	no	—
526	C₂²⋊C₄	—	4	2	no	—
527	C₄²	—	2	1	no	—
528	C₄²	—	2	1	no	—
529	C₄²	—	2	1	no	—
530	C₄²	—	2	1	no	—
531	C₄²	—	4	2	no	—
532	C₄²	C₂×D₄×C₆₁	1	2	yes	—
533	C₄²	#41×C₆₁	1	2	yes	—
534	C₂³	—	2	2	no	—
535	C₂³	—	2	2	no	—
536	C₂³	—	2	2	no	—
537	C₂³	—	4	1	no	—
538	C₂³	—	4	1	no	—
539	C₂³	—	4	1	no	—
540	C₂³	—	4	1	no	—
541	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
542	Q₈	—	2	2	no	—
543	Q₈	—	2	2	no	—
544	Q₈	—	4	1	no	—
545	Q₈	—	4	1	no	—
546	D₄	—	2	2	no	—
547	D₄	—	2	2	no	—
548	D₄	—	2	2	no	—
549	D₄	C₂²⋊Q₈×C₆₁	1	4	yes	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	4	8	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	8	4	no	—
588	C₂×C₄	—	8	4	no	—
589	C₂×C₄	#121×C₆₁	1	2	yes	—
590	C₂×C₄	#121×C₆₁	1	2	yes	—
591	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
592	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
593	C₂×C₄	C₂²×Q₈×C₆₁	1	1	yes	characteristic
594	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
595	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
596	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
597	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
598	C₈	—	2	2	no	—
599	C₈	—	4	1	no	—
600	C₈	—	4	1	no	—
601	C₈	—	4	1	no	—
602	C₂²	—	2	4	no	—
603	C₂²	—	4	2	no	—
604	C₂²	—	4	2	no	—
605	C₂²	—	4	2	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	4	2	no	—
609	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
610	C₂²	C₆₁×#546	1	1	yes	characteristic
611	C₂²	D₄×Q₈×C₆₁	1	1	yes	characteristic
612	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
613	C₂²	C₆₁×#575	1	1	yes	characteristic
614	C₂²	C₆₁×#577	1	1	yes	characteristic
615	C₂²	C₆₁×#578	1	1	yes	characteristic
616	C₄	—	2	2	no	—
617	C₄	—	2	2	no	—
618	C₄	—	2	2	no	—
619	C₄	—	4	2	no	—
620	C₄	—	4	1	no	—
621	C₄	—	4	1	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	2	no	—
624	C₄	—	8	1	no	—
625	C₄	—	8	1	no	—
626	C₄	—	8	1	no	—
627	C₄	—	8	1	no	—
628	C₄	—	8	1	no	—
629	C₄	C₂×C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
630	C₄	C₆₁×#537	1	1	yes	characteristic
631	C₄	C₆₁×#552	1	1	yes	characteristic
632	C₄	C₆₁×#554	1	1	yes	characteristic
633	C₂	—	4	4	no	—
634	C₂	C₆₁×#2417	1	1	yes	characteristic
635	C₂	C₆₁×#3036	1	1	yes	characteristic
636	C₂	C₆₁×#3046	1	1	yes	characteristic
637	C₂	C₆₁×#3310	1	1	yes	characteristic
638	C₂	C₆₁×#3315	1	1	yes	characteristic
639	C₂	C₆₁×#3386	1	1	yes	characteristic
640	C₂	C₆₁×#3388	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₆₁×#2565	C₂	semidirect
5. C₆₁×#2085	C₂	semidirect
6. C₆₁×#2083	C₂	semidirect
7. C₆₁×#2068	C₂	semidirect
8. C₆₁×#2066	C₂	semidirect
9. C₆₁×#1992	C₂	semidirect
10. C₆₁×#1940	C₂	semidirect
14. C₆₁×#1803	C₂	semidirect
281. #24825	C₆₁	direct (N × H)
315. #2565	C₂×C₆₁	semidirect
317. #2085	C₂×C₆₁	semidirect
318. #2083	C₂×C₆₁	semidirect
319. #2068	C₂×C₆₁	semidirect
320. #2066	C₂×C₆₁	semidirect
321. #1992	C₂×C₆₁	semidirect
322. #1940	C₂×C₆₁	semidirect
326. #1803	C₂×C₆₁	semidirect
381. C₆₁	#24825	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×#478	2
C₂×C₆₁×#440	2
C₆₁×#2565	2
D₄×C₄⋊C₄×C₆₁	2
C₆₁×#2085	2
C₆₁×#2083	2
C₆₁×#2068	2
C₆₁×#2066	2
C₆₁×#1992	2
C₆₁×#1940	2
C₆₁×#1877	2
C₆₁×#1804	2
C₆₁×#1803	2
C₆₁×#1802	2
#24825	61

Subgroups — C61×#24825 #29528258

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24825 #29528258