Subgroups — C₆₁×#25229 #29528662

Order 15616.

808 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×#484	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#470	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2503	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2362	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2085	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#2074	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#2068	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2056	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1949	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1928	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1878	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#1873	C₂	1	1	yes	maximal, characteristic
13	C₆₁×#1851	C₂	1	1	yes	maximal, characteristic
14	C₆₁×#1805	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#1736	C₂	1	1	yes	maximal, characteristic
16	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
23	C₆₁×#484	—	2	4	no	—
24	C₆₁×#470	—	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×#103×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×#103×C₆₁	C₂²	1	1	yes	characteristic
35	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
37	C₆₁×#400	—	2	1	no	—
38	C₆₁×#400	—	2	1	no	—
39	C₆₁×#391	C₂²	1	1	yes	characteristic
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×#388	—	2	1	no	—
44	C₆₁×#388	—	2	1	no	—
45	C₆₁×#387	—	2	1	no	—
46	C₆₁×#382	C₂²	1	1	yes	characteristic
47	C₆₁×#382	C₂²	1	1	yes	characteristic
48	C₆₁×#381	—	2	1	no	—
49	C₆₁×#381	—	2	1	no	—
50	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
51	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
52	C₄×C₂²⋊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×Q₈×C₆₁	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₆₁	—	2	1	no	—
64	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
65	C₂×Q₁₆×C₆₁	—	2	2	no	—
66	C₂×Q₁₆×C₆₁	—	2	2	no	—
67	C₂×Q₁₆×C₆₁	—	4	1	no	—
68	C₂×M₁₆×C₆₁	—	2	2	no	—
69	C₂×M₁₆×C₆₁	—	2	2	no	—
70	C₂×M₁₆×C₆₁	—	4	1	no	—
71	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
75	C₂²⋊Q₈×C₆₁	—	2	2	no	—
76	C₂²⋊Q₈×C₆₁	—	2	2	no	—
77	C₂²⋊Q₈×C₆₁	—	2	2	no	—
78	C₂²⋊Q₈×C₆₁	D₄	1	4	yes	—
79	C₄×Q₈×C₆₁	—	2	2	no	—
80	C₄×Q₈×C₆₁	—	4	1	no	—
81	#117×C₆₁	—	2	2	no	—
82	#117×C₆₁	—	4	1	no	—
83	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
84	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
85	C₂×C₄⋊C₄×C₆₁	—	2	2	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	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₆₁	—	2	1	no	—
102	C₂×C₄²×C₆₁	—	2	1	no	—
103	C₂×C₄²×C₆₁	—	2	1	no	—
104	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
106	#107×C₆₁	—	2	2	no	—
107	#107×C₆₁	—	2	2	no	—
108	#106×C₆₁	—	2	2	no	—
109	C₄⋊C₈×C₆₁	—	2	2	no	—
110	C₄⋊C₈×C₆₁	—	4	1	no	—
111	#103×C₆₁	—	2	2	no	—
112	#103×C₆₁	—	2	2	no	—
113	#103×C₆₁	—	2	2	no	—
114	#103×C₆₁	—	2	2	no	—
115	#103×C₆₁	—	2	2	no	—
116	#103×C₆₁	—	4	1	no	—
117	C₂²⋊C₈×C₆₁	—	2	2	no	—
118	#95×C₆₁	—	2	1	no	—
119	#95×C₆₁	—	2	1	no	—
120	#95×C₆₁	—	2	1	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	—	2	1	no	—
130	#95×C₆₁	D₄	1	1	yes	characteristic
131	#95×C₆₁	D₄	1	1	yes	characteristic
132	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
138	C₂×Q₈×C₆₁	—	2	1	no	—
139	C₂×Q₈×C₆₁	—	2	1	no	—
140	C₂×Q₈×C₆₁	—	2	1	no	—
141	C₂×Q₈×C₆₁	—	2	1	no	—
142	C₂×Q₈×C₆₁	—	2	1	no	—
143	C₂×Q₈×C₆₁	—	2	1	no	—
144	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₆₁	—	2	1	no	—
146	C₂²×C₄×C₆₁	—	2	1	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	—	2	1	no	—
153	C₂²×C₄×C₆₁	—	2	1	no	—
154	C₂²×C₄×C₆₁	—	2	1	no	—
155	C₂²×C₄×C₆₁	—	2	1	no	—
156	C₂²×C₄×C₆₁	—	2	1	no	—
157	C₂²×C₄×C₆₁	—	4	2	no	—
158	C₂²×C₄×C₆₁	—	4	2	no	—
159	C₂²×C₄×C₆₁	—	4	2	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	2	yes	—
166	C₂²×C₄×C₆₁	#41	1	2	yes	—
167	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
168	Q₁₆×C₆₁	—	4	4	no	—
169	M₁₆×C₆₁	—	4	4	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	—	2	1	no	—
180	C₂×C₈×C₆₁	—	2	1	no	—
181	C₂×C₈×C₆₁	#41	1	2	yes	—
182	C₄⋊C₄×C₆₁	—	2	4	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	—	2	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	C₂×D₄	1	2	yes	—
198	C₄⋊C₄×C₆₁	#41	1	2	yes	—
199	C₂²⋊C₄×C₆₁	—	2	4	no	—
200	C₂²⋊C₄×C₆₁	—	4	1	no	—
201	C₂²⋊C₄×C₆₁	—	4	1	no	—
202	C₂²⋊C₄×C₆₁	—	4	2	no	—
203	C₂²⋊C₄×C₆₁	—	4	2	no	—
204	C₄²×C₆₁	—	2	1	no	—
205	C₄²×C₆₁	—	2	1	no	—
206	C₄²×C₆₁	—	2	1	no	—
207	C₄²×C₆₁	—	2	1	no	—
208	C₄²×C₆₁	—	4	2	no	—
209	C₄²×C₆₁	—	4	2	no	—
210	C₄²×C₆₁	—	4	2	no	—
211	C₂³×C₆₁	—	2	1	no	—
212	C₂³×C₆₁	—	2	1	no	—
213	C₂³×C₆₁	—	2	1	no	—
214	C₂³×C₆₁	—	2	1	no	—
215	C₂³×C₆₁	—	2	1	no	—
216	C₂³×C₆₁	—	2	1	no	—
217	C₂³×C₆₁	#121	1	2	yes	—
218	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
219	Q₈×C₆₁	—	2	2	no	—
220	Q₈×C₆₁	—	2	2	no	—
221	Q₈×C₆₁	—	4	1	no	—
222	Q₈×C₆₁	—	4	1	no	—
223	Q₈×C₆₁	—	4	1	no	—
224	Q₈×C₆₁	—	4	1	no	—
225	Q₈×C₆₁	—	4	1	no	—
226	Q₈×C₆₁	—	4	1	no	—
227	C₂×C₄×C₆₁	—	2	1	no	—
228	C₂×C₄×C₆₁	—	2	1	no	—
229	C₂×C₄×C₆₁	—	2	2	no	—
230	C₂×C₄×C₆₁	—	2	2	no	—
231	C₂×C₄×C₆₁	—	2	2	no	—
232	C₂×C₄×C₆₁	—	2	2	no	—
233	C₂×C₄×C₆₁	—	2	2	no	—
234	C₂×C₄×C₆₁	—	2	2	no	—
235	C₂×C₄×C₆₁	—	2	1	no	—
236	C₂×C₄×C₆₁	—	2	1	no	—
237	C₂×C₄×C₆₁	—	2	2	no	—
238	C₂×C₄×C₆₁	—	2	1	no	—
239	C₂×C₄×C₆₁	—	2	1	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	—	2	1	no	—
247	C₂×C₄×C₆₁	—	2	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	—	4	1	no	—
267	C₂×C₄×C₆₁	—	4	1	no	—
268	C₂×C₄×C₆₁	—	4	1	no	—
269	C₂×C₄×C₆₁	—	8	4	no	—
270	C₂×C₄×C₆₁	#121	1	2	yes	—
271	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
272	C₂×C₄×C₆₁	C₂×#41	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	#25229	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
282	C₂²×C₆₁	—	2	2	no	—
283	C₂²×C₆₁	—	2	2	no	—
284	C₂²×C₆₁	—	2	2	no	—
285	C₂²×C₆₁	—	4	1	no	—
286	C₂²×C₆₁	—	4	1	no	—
287	C₂²×C₆₁	—	4	1	no	—
288	C₂²×C₆₁	—	4	1	no	—
289	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
290	C₂²×C₆₁	#546	1	1	yes	characteristic
291	C₂²×C₆₁	#547	1	1	yes	characteristic
292	C₂²×C₆₁	#575	1	1	yes	characteristic
293	C₂²×C₆₁	#575	1	1	yes	characteristic
294	C₂²×C₆₁	#578	1	1	yes	characteristic
295	C₂²×C₆₁	#578	1	1	yes	characteristic
296	C₄×C₆₁	—	2	2	no	—
297	C₄×C₆₁	—	4	1	no	—
298	C₄×C₆₁	—	4	1	no	—
299	C₄×C₆₁	—	4	2	no	—
300	C₄×C₆₁	—	4	2	no	—
301	C₄×C₆₁	—	4	1	no	—
302	C₄×C₆₁	—	4	2	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	#529	1	1	yes	characteristic
310	C₄×C₆₁	#539	1	1	yes	characteristic
311	C₄×C₆₁	#546	1	1	yes	characteristic
312	C₄×C₆₁	#547	1	1	yes	characteristic
313	C₂×#484	C₂×C₆₁	1	1	yes	characteristic
314	C₂×#470	C₂×C₆₁	1	1	yes	characteristic
315	#2503	C₂×C₆₁	1	1	yes	characteristic
316	#2362	C₂×C₆₁	1	1	yes	characteristic
317	#2085	C₂×C₆₁	1	1	yes	characteristic, complemented
318	#2074	C₂×C₆₁	1	1	yes	characteristic, complemented
319	#2068	C₂×C₆₁	1	1	yes	characteristic, complemented
320	#2056	C₂×C₆₁	1	1	yes	characteristic, complemented
321	#1949	C₂×C₆₁	1	1	yes	characteristic, complemented
322	#1928	C₂×C₆₁	1	1	yes	characteristic, complemented
323	#1878	C₂×C₆₁	1	1	yes	characteristic, complemented
324	#1873	C₂×C₆₁	1	1	yes	characteristic
325	#1851	C₂×C₆₁	1	1	yes	characteristic
326	#1805	C₂×C₆₁	1	1	yes	characteristic, complemented
327	#1736	C₂×C₆₁	1	1	yes	characteristic
328	C₂×C₆₁	—	4	2	no	—
329	C₂×C₆₁	#2425	1	1	yes	characteristic
330	C₂×C₆₁	#3040	1	1	yes	characteristic
331	C₂×C₆₁	#3044	1	1	yes	characteristic
332	C₂×C₆₁	#3315	1	1	yes	characteristic
333	C₂×C₆₁	#3327	1	1	yes	characteristic
334	C₂×C₆₁	#3349	1	1	yes	characteristic
335	C₂×C₆₁	#3352	1	1	yes	characteristic
336	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
337	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
338	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
339	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
340	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
341	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
342	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
343	#484	—	2	4	no	—
344	#470	—	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×#103	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×#103	C₂²×C₆₁	1	1	yes	characteristic
355	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
356	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
357	#400	—	2	1	no	—
358	#400	—	2	1	no	—
359	#391	C₂²×C₆₁	1	1	yes	characteristic
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	#388	—	2	1	no	—
364	#388	—	2	1	no	—
365	#387	—	2	1	no	—
366	#382	C₂²×C₆₁	1	1	yes	characteristic
367	#382	C₂²×C₆₁	1	1	yes	characteristic
368	#381	—	2	1	no	—
369	#381	—	2	1	no	—
370	C₄×C₄⋊C₄	—	2	1	no	—
371	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
372	C₄×C₂²⋊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	#25229	1	1	yes	characteristic, direct product factor, Sylow
382	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
383	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
384	C₂³×C₄	—	2	1	no	—
385	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
386	C₂×Q₁₆	—	2	2	no	—
387	C₂×Q₁₆	—	2	2	no	—
388	C₂×Q₁₆	—	4	1	no	—
389	C₂×M₁₆	—	2	2	no	—
390	C₂×M₁₆	—	2	2	no	—
391	C₂×M₁₆	—	4	1	no	—
392	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
393	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
394	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
395	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
396	C₂²⋊Q₈	—	2	2	no	—
397	C₂²⋊Q₈	—	2	2	no	—
398	C₂²⋊Q₈	—	2	2	no	—
399	C₂²⋊Q₈	D₄×C₆₁	1	4	yes	—
400	C₄×Q₈	—	2	2	no	—
401	C₄×Q₈	—	4	1	no	—
402	#117	—	2	2	no	—
403	#117	—	4	1	no	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	—	2	2	no	—
406	C₂×C₄⋊C₄	—	2	2	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	C₂³×C₆₁	1	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₂²⋊C₄	—	2	1	no	—
420	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
421	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
422	C₂×C₄²	—	2	1	no	—
423	C₂×C₄²	—	2	1	no	—
424	C₂×C₄²	—	2	1	no	—
425	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
426	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
427	#107	—	2	2	no	—
428	#107	—	2	2	no	—
429	#106	—	2	2	no	—
430	C₄⋊C₈	—	2	2	no	—
431	C₄⋊C₈	—	4	1	no	—
432	#103	—	2	2	no	—
433	#103	—	2	2	no	—
434	#103	—	2	2	no	—
435	#103	—	2	2	no	—
436	#103	—	2	2	no	—
437	#103	—	4	1	no	—
438	C₂²⋊C₈	—	2	2	no	—
439	#95	—	2	1	no	—
440	#95	—	2	1	no	—
441	#95	—	2	1	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	—	2	1	no	—
451	#95	D₄×C₆₁	1	1	yes	characteristic
452	#95	D₄×C₆₁	1	1	yes	characteristic
453	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
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	—	2	1	no	—
459	C₂×Q₈	—	2	1	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×Q₈	—	2	1	no	—
464	C₂×Q₈	—	2	1	no	—
465	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	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	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	4	2	no	—
479	C₂²×C₄	—	4	2	no	—
480	C₂²×C₄	—	4	2	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	2	yes	—
487	C₂²×C₄	#41×C₆₁	1	2	yes	—
488	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
489	Q₁₆	—	4	4	no	—
490	M₁₆	—	4	4	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	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	#41×C₆₁	1	2	yes	—
503	C₄⋊C₄	—	2	4	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	—	2	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	C₂×D₄×C₆₁	1	2	yes	—
519	C₄⋊C₄	#41×C₆₁	1	2	yes	—
520	C₂²⋊C₄	—	2	4	no	—
521	C₂²⋊C₄	—	4	1	no	—
522	C₂²⋊C₄	—	4	1	no	—
523	C₂²⋊C₄	—	4	2	no	—
524	C₂²⋊C₄	—	4	2	no	—
525	C₄²	—	2	1	no	—
526	C₄²	—	2	1	no	—
527	C₄²	—	2	1	no	—
528	C₄²	—	2	1	no	—
529	C₄²	—	4	2	no	—
530	C₄²	—	4	2	no	—
531	C₄²	—	4	2	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	2	1	no	—
534	C₂³	—	2	1	no	—
535	C₂³	—	2	1	no	—
536	C₂³	—	2	1	no	—
537	C₂³	—	2	1	no	—
538	C₂³	#121×C₆₁	1	2	yes	—
539	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
540	Q₈	—	2	2	no	—
541	Q₈	—	2	2	no	—
542	Q₈	—	4	1	no	—
543	Q₈	—	4	1	no	—
544	Q₈	—	4	1	no	—
545	Q₈	—	4	1	no	—
546	Q₈	—	4	1	no	—
547	Q₈	—	4	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	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	1	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	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	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	8	4	no	—
591	C₂×C₄	#121×C₆₁	1	2	yes	—
592	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
593	C₂×C₄	C₂×#41×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	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	1	no	—
609	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
610	C₂²	C₆₁×#546	1	1	yes	characteristic
611	C₂²	C₆₁×#547	1	1	yes	characteristic
612	C₂²	C₆₁×#575	1	1	yes	characteristic
613	C₂²	C₆₁×#575	1	1	yes	characteristic
614	C₂²	C₆₁×#578	1	1	yes	characteristic
615	C₂²	C₆₁×#578	1	1	yes	characteristic
616	C₄	—	2	2	no	—
617	C₄	—	4	2	no	—
618	C₄	—	4	1	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	C₆₁×#529	1	1	yes	characteristic
630	C₄	C₆₁×#539	1	1	yes	characteristic
631	C₄	C₆₁×#546	1	1	yes	characteristic
632	C₄	C₆₁×#547	1	1	yes	characteristic
633	C₂	—	4	2	no	—
634	C₂	C₆₁×#2425	1	1	yes	characteristic
635	C₂	C₆₁×#3040	1	1	yes	characteristic
636	C₂	C₆₁×#3044	1	1	yes	characteristic
637	C₂	C₆₁×#3315	1	1	yes	characteristic
638	C₂	C₆₁×#3327	1	1	yes	characteristic
639	C₂	C₆₁×#3349	1	1	yes	characteristic
640	C₂	C₆₁×#3352	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
5. C₆₁×#2085	C₂	semidirect
6. C₆₁×#2074	C₂	semidirect
7. C₆₁×#2068	C₂	semidirect
8. C₆₁×#2056	C₂	semidirect
9. C₆₁×#1949	C₂	semidirect
10. C₆₁×#1928	C₂	semidirect
11. C₆₁×#1878	C₂	semidirect
14. C₆₁×#1805	C₂	semidirect
281. #25229	C₆₁	direct (N × H)
317. #2085	C₂×C₆₁	semidirect
318. #2074	C₂×C₆₁	semidirect
319. #2068	C₂×C₆₁	semidirect
320. #2056	C₂×C₆₁	semidirect
321. #1949	C₂×C₆₁	semidirect
322. #1928	C₂×C₆₁	semidirect
323. #1878	C₂×C₆₁	semidirect
326. #1805	C₂×C₆₁	semidirect
381. C₆₁	#25229	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×#484	2
C₂×C₆₁×#470	2
C₆₁×#2503	2
C₆₁×#2362	2
C₆₁×#2085	2
C₆₁×#2074	2
C₆₁×#2068	2
C₆₁×#2056	2
C₆₁×#1949	2
C₆₁×#1928	2
C₆₁×#1878	2
C₆₁×#1873	2
C₆₁×#1851	2
C₆₁×#1805	2
C₆₁×#1736	2
#25229	61

Subgroups — C61×#25229 #29528662

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25229 #29528662