Subgroups — C₆₁×#60862 #29564295

Order 15616.

1778 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#533	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3240	C₂	1	8	yes	maximal, complemented
4	C₆₁×#3231	C₂	1	4	yes	maximal, complemented
5	C₆₁×#3228	C₂	1	4	yes	maximal, complemented
6	C₆₁×#3165	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3141	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3093	C₂	1	4	yes	maximal, complemented
9	C₆₁×#3080	C₂	1	4	yes	maximal, complemented
10	C₆₁×#2920	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#533	—	2	2	no	—
12	C₆₁×#533	—	2	2	no	—
13	C₆₁×#533	C₂²	1	2	yes	—
14	C₆₁×#533	C₂²	1	1	yes	characteristic
15	C₆₁×#533	C₂²	1	4	yes	—
16	C₆₁×#533	C₂²	1	4	yes	—
17	C₆₁×#532	C₂²	1	1	yes	characteristic
18	C₆₁×#532	C₂²	1	2	yes	—
19	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
20	C₆₁×#529	—	2	2	no	—
21	C₆₁×#529	—	2	2	no	—
22	C₆₁×#529	C₂²	1	4	yes	—
23	C₂×#125×C₆₁	C₂²	1	2	yes	—
24	C₆₁×#525	—	2	2	no	—
25	C₆₁×#525	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₆₁	—	2	2	no	—
27	C₄×#41×C₆₁	—	2	2	no	—
28	C₄×#41×C₆₁	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₆₁	—	2	2	no	—
30	C₂×#117×C₆₁	C₂²	1	2	yes	—
31	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
32	C₆₁×#501	C₂²	1	8	yes	complemented
33	C₆₁×#500	C₂²	1	4	yes	complemented
34	C₆₁×#498	C₂²	1	4	yes	complemented
35	C₆₁×#489	C₂²	1	8	yes	complemented
36	C₆₁×#487	C₂²	1	4	yes	complemented
37	C₆₁×#486	C₂²	1	4	yes	complemented
38	C₆₁×#485	C₂²	1	16	yes	—
39	C₆₁×#482	C₂²	1	16	yes	—
40	C₆₁×#479	C₂²	1	16	yes	complemented
41	C₆₁×#478	C₂²	1	16	yes	complemented
42	C₆₁×#432	C₂²	1	4	yes	—
43	C₆₁×#431	C₂²	1	4	yes	—
44	C₆₁×#428	C₂²	1	8	yes	—
45	C₆₁×#423	C₂²	1	2	yes	—
46	C₆₁×#417	C₂²	1	8	yes	—
47	C₆₁×#407	C₂²	1	2	yes	—
48	C₄×M₁₆×C₆₁	C₂²	1	2	yes	—
49	C₂×#41×C₆₁	—	2	2	no	—
50	C₂×#41×C₆₁	C₂³	1	2	yes	—
51	C₂²×Q₈×C₆₁	—	2	2	no	—
52	C₂³×C₄×C₆₁	D₄	1	2	yes	—
53	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
54	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
55	C₄⋊Q₈×C₆₁	—	2	2	no	—
56	C₄⋊Q₈×C₆₁	—	2	2	no	—
57	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
58	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
59	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
60	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
61	#127×C₆₁	C₂³	1	1	yes	characteristic
62	#126×C₆₁	—	2	4	no	—
63	#125×C₆₁	—	2	2	no	—
64	#125×C₆₁	—	2	2	no	—
65	#125×C₆₁	—	2	2	no	—
66	#125×C₆₁	C₂³	1	8	yes	—
67	#125×C₆₁	C₂³	1	2	yes	—
68	#124×C₆₁	—	2	2	no	—
69	#124×C₆₁	C₂³	1	2	yes	—
70	#123×C₆₁	—	2	4	no	—
71	#123×C₆₁	—	2	2	no	—
72	C₂²⋊Q₈×C₆₁	—	2	4	no	—
73	C₂²⋊Q₈×C₆₁	—	2	4	no	—
74	C₂²⋊Q₈×C₆₁	—	2	4	no	—
75	C₂²⋊Q₈×C₆₁	—	2	4	no	—
76	C₂²⋊Q₈×C₆₁	—	2	2	no	—
77	C₂²⋊Q₈×C₆₁	—	2	2	no	—
78	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
79	#121×C₆₁	—	2	2	no	—
80	#121×C₆₁	—	2	2	no	—
81	#121×C₆₁	C₂³	1	4	yes	—
82	#120×C₆₁	—	2	2	no	—
83	C₄×Q₈×C₆₁	—	2	4	no	—
84	C₄×Q₈×C₆₁	—	2	4	no	—
85	C₄×Q₈×C₆₁	—	2	4	no	—
86	C₄×Q₈×C₆₁	—	2	4	no	—
87	C₄×Q₈×C₆₁	—	2	2	no	—
88	C₄×Q₈×C₆₁	—	2	2	no	—
89	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
90	C₄×D₄×C₆₁	—	2	4	no	—
91	C₄×D₄×C₆₁	—	2	4	no	—
92	C₄×D₄×C₆₁	—	2	4	no	—
93	C₄×D₄×C₆₁	—	2	2	no	—
94	C₄×D₄×C₆₁	—	2	2	no	—
95	C₄×D₄×C₆₁	C₂³	1	4	yes	—
96	#117×C₆₁	—	2	4	no	—
97	#117×C₆₁	—	2	2	no	—
98	#117×C₆₁	—	2	4	no	—
99	#117×C₆₁	—	2	2	no	—
100	#117×C₆₁	C₂³	1	8	yes	—
101	#117×C₆₁	C₂³	1	2	yes	—
102	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
103	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
104	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
105	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
106	C₂×C₄²×C₆₁	—	2	2	no	—
107	C₂×C₄²×C₆₁	—	2	2	no	—
108	C₂×C₄²×C₆₁	D₄	1	2	yes	—
109	C₂×C₄²×C₆₁	D₄	1	2	yes	—
110	C₂×C₄²×C₆₁	D₄	1	2	yes	—
111	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
113	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
114	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
115	#107×C₆₁	C₂³	1	16	yes	—
116	#106×C₆₁	C₂³	1	16	yes	—
117	C₄⋊C₈×C₆₁	C₂³	1	8	yes	—
118	#103×C₆₁	C₂³	1	16	yes	—
119	#102×C₆₁	C₂³	1	16	yes	—
120	C₂²⋊C₈×C₆₁	C₂³	1	8	yes	—
121	#97×C₆₁	C₂³	1	4	yes	—
122	C₄×C₈×C₆₁	C₂³	1	4	yes	—
123	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
124	#41×C₆₁	—	2	8	no	—
125	#41×C₆₁	—	4	8	no	—
126	C₂×Q₈×C₆₁	—	2	2	no	—
127	C₂×Q₈×C₆₁	—	2	4	no	—
128	C₂×Q₈×C₆₁	—	2	4	no	—
129	C₂×Q₈×C₆₁	—	4	8	no	—
130	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
131	C₂×D₄×C₆₁	—	2	2	no	—
132	C₂×D₄×C₆₁	—	2	4	no	—
133	C₂×D₄×C₆₁	—	2	2	no	—
134	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
135	C₂²×C₄×C₆₁	—	2	4	no	—
136	C₂²×C₄×C₆₁	—	2	4	no	—
137	C₂²×C₄×C₆₁	—	2	2	no	—
138	C₂²×C₄×C₆₁	—	2	4	no	—
139	C₂²×C₄×C₆₁	—	4	4	no	—
140	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
149	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
150	M₁₆×C₆₁	—	2	8	no	—
151	C₂×C₈×C₆₁	C₂⁴	1	8	yes	—
152	C₄⋊C₄×C₆₁	—	2	8	no	—
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	4	no	—
157	C₄⋊C₄×C₆₁	—	2	2	no	—
158	C₄⋊C₄×C₆₁	—	2	2	no	—
159	C₄⋊C₄×C₆₁	—	2	4	no	—
160	C₄⋊C₄×C₆₁	—	2	4	no	—
161	C₄⋊C₄×C₆₁	—	2	4	no	—
162	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
163	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
164	C₂²⋊C₄×C₆₁	—	2	8	no	—
165	C₂²⋊C₄×C₆₁	—	2	4	no	—
166	C₂²⋊C₄×C₆₁	—	2	2	no	—
167	C₂²⋊C₄×C₆₁	—	2	4	no	—
168	C₂²⋊C₄×C₆₁	—	2	4	no	—
169	C₂²⋊C₄×C₆₁	—	2	4	no	—
170	C₄²×C₆₁	—	2	4	no	—
171	C₄²×C₆₁	—	2	2	no	—
172	C₄²×C₆₁	—	2	8	no	—
173	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₆₁	C₂×D₄	1	2	yes	—
175	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₆₁	C₂×D₄	1	2	yes	—
177	C₄²×C₆₁	C₂×D₄	1	2	yes	—
178	C₄²×C₆₁	C₂×D₄	1	2	yes	—
179	C₄²×C₆₁	C₂×D₄	1	2	yes	—
180	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
181	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
182	C₄²×C₆₁	C₂⁴	1	2	yes	—
183	C₂³×C₆₁	—	2	2	no	—
184	C₂³×C₆₁	—	2	2	no	—
185	C₂³×C₆₁	—	4	2	no	—
186	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
187	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
188	Q₈×C₆₁	—	2	4	no	—
189	Q₈×C₆₁	—	4	8	no	—
190	Q₈×C₆₁	—	4	8	no	—
191	Q₈×C₆₁	—	4	4	no	—
192	D₄×C₆₁	—	2	4	no	—
193	D₄×C₆₁	—	4	8	no	—
194	D₄×C₆₁	—	4	4	no	—
195	D₄×C₆₁	—	4	4	no	—
196	C₂×C₄×C₆₁	—	2	2	no	—
197	C₂×C₄×C₆₁	—	2	4	no	—
198	C₂×C₄×C₆₁	—	2	4	no	—
199	C₂×C₄×C₆₁	—	2	4	no	—
200	C₂×C₄×C₆₁	—	2	4	no	—
201	C₂×C₄×C₆₁	—	2	4	no	—
202	C₂×C₄×C₆₁	—	2	2	no	—
203	C₂×C₄×C₆₁	—	2	4	no	—
204	C₂×C₄×C₆₁	—	2	8	no	—
205	C₂×C₄×C₆₁	—	4	2	no	—
206	C₂×C₄×C₆₁	—	4	2	no	—
207	C₂×C₄×C₆₁	—	4	2	no	—
208	C₂×C₄×C₆₁	—	4	8	no	—
209	C₂×C₄×C₆₁	—	4	8	no	—
210	C₂×C₄×C₆₁	—	4	4	no	—
211	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
212	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
213	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
214	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
215	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
217	C₂×C₄×C₆₁	2₋¹⁺⁴	1	4	yes	—
218	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
219	C₈×C₆₁	—	2	8	no	—
220	#60862	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
221	C₂²×C₆₁	—	2	2	no	—
222	C₂²×C₆₁	—	2	2	no	—
223	C₂²×C₆₁	—	2	2	no	—
224	C₂²×C₆₁	—	2	2	no	—
225	C₂²×C₆₁	—	4	4	no	—
226	C₂²×C₆₁	—	4	2	no	—
227	C₂²×C₆₁	—	4	4	no	—
228	C₂²×C₆₁	#536	1	2	yes	—
229	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
230	C₄×C₆₁	—	2	2	no	—
231	C₄×C₆₁	—	2	2	no	—
232	C₄×C₆₁	—	2	2	no	—
233	C₄×C₆₁	—	2	2	no	—
234	C₄×C₆₁	—	4	2	no	—
235	C₄×C₆₁	—	4	4	no	—
236	C₄×C₆₁	—	4	8	no	—
237	C₄×C₆₁	#536	1	2	yes	—
238	C₄×C₆₁	#575	1	4	yes	—
239	C₄×C₆₁	C₂×2₋¹⁺⁴	1	2	yes	—
240	#3444	C₂×C₆₁	1	1	yes	characteristic
241	C₂×#533	C₂×C₆₁	1	1	yes	characteristic, complemented
242	#3240	C₂×C₆₁	1	8	yes	complemented
243	#3231	C₂×C₆₁	1	4	yes	complemented
244	#3228	C₂×C₆₁	1	4	yes	complemented
245	#3165	C₂×C₆₁	1	2	yes	complemented
246	#3141	C₂×C₆₁	1	2	yes	complemented
247	#3093	C₂×C₆₁	1	4	yes	complemented
248	#3080	C₂×C₆₁	1	4	yes	complemented
249	#2920	C₂×C₆₁	1	1	yes	characteristic, complemented
250	C₂×C₆₁	—	2	2	no	—
251	C₂×C₆₁	—	4	2	no	—
252	C₂×C₆₁	—	8	2	no	—
253	C₂×C₆₁	C₂×#536	1	1	yes	characteristic
254	C₂×C₆₁	C₂×#575	1	2	yes	—
255	#533	—	2	2	no	—
256	#533	—	2	2	no	—
257	#533	C₂²×C₆₁	1	2	yes	—
258	#533	C₂²×C₆₁	1	1	yes	characteristic
259	#533	C₂²×C₆₁	1	4	yes	—
260	#533	C₂²×C₆₁	1	4	yes	—
261	#532	C₂²×C₆₁	1	1	yes	characteristic
262	#532	C₂²×C₆₁	1	2	yes	—
263	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	—
264	#529	—	2	2	no	—
265	#529	—	2	2	no	—
266	#529	C₂²×C₆₁	1	4	yes	—
267	C₂×#125	C₂²×C₆₁	1	2	yes	—
268	#525	—	2	2	no	—
269	#525	C₂²×C₆₁	1	2	yes	—
270	C₂×C₂²⋊Q₈	—	2	2	no	—
271	C₄×#41	—	2	2	no	—
272	C₄×#41	C₂²×C₆₁	1	2	yes	—
273	C₂×C₄×Q₈	—	2	2	no	—
274	C₂×#117	C₂²×C₆₁	1	2	yes	—
275	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
276	#501	C₂²×C₆₁	1	8	yes	complemented
277	#500	C₂²×C₆₁	1	4	yes	complemented
278	#498	C₂²×C₆₁	1	4	yes	complemented
279	#489	C₂²×C₆₁	1	8	yes	complemented
280	#487	C₂²×C₆₁	1	4	yes	complemented
281	#486	C₂²×C₆₁	1	4	yes	complemented
282	#485	C₂²×C₆₁	1	16	yes	—
283	#482	C₂²×C₆₁	1	16	yes	—
284	#479	C₂²×C₆₁	1	16	yes	complemented
285	#478	C₂²×C₆₁	1	16	yes	complemented
286	#432	C₂²×C₆₁	1	4	yes	—
287	#431	C₂²×C₆₁	1	4	yes	—
288	#428	C₂²×C₆₁	1	8	yes	—
289	#423	C₂²×C₆₁	1	2	yes	—
290	#417	C₂²×C₆₁	1	8	yes	—
291	#407	C₂²×C₆₁	1	2	yes	—
292	C₄×M₁₆	C₂²×C₆₁	1	2	yes	—
293	C₆₁	#60862	1	1	yes	characteristic, direct product factor, Sylow
294	C₂×#41	—	2	2	no	—
295	C₂×#41	C₂³×C₆₁	1	2	yes	—
296	C₂²×Q₈	—	2	2	no	—
297	C₂³×C₄	D₄×C₆₁	1	2	yes	—
298	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
299	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
300	C₄⋊Q₈	—	2	2	no	—
301	C₄⋊Q₈	—	2	2	no	—
302	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
303	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
304	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
305	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
306	#127	C₂³×C₆₁	1	1	yes	characteristic
307	#126	—	2	4	no	—
308	#125	—	2	2	no	—
309	#125	—	2	2	no	—
310	#125	—	2	2	no	—
311	#125	C₂³×C₆₁	1	8	yes	—
312	#125	C₂³×C₆₁	1	2	yes	—
313	#124	—	2	2	no	—
314	#124	C₂³×C₆₁	1	2	yes	—
315	#123	—	2	4	no	—
316	#123	—	2	2	no	—
317	C₂²⋊Q₈	—	2	4	no	—
318	C₂²⋊Q₈	—	2	4	no	—
319	C₂²⋊Q₈	—	2	4	no	—
320	C₂²⋊Q₈	—	2	4	no	—
321	C₂²⋊Q₈	—	2	2	no	—
322	C₂²⋊Q₈	—	2	2	no	—
323	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
324	#121	—	2	2	no	—
325	#121	—	2	2	no	—
326	#121	C₂³×C₆₁	1	4	yes	—
327	#120	—	2	2	no	—
328	C₄×Q₈	—	2	4	no	—
329	C₄×Q₈	—	2	4	no	—
330	C₄×Q₈	—	2	4	no	—
331	C₄×Q₈	—	2	4	no	—
332	C₄×Q₈	—	2	2	no	—
333	C₄×Q₈	—	2	2	no	—
334	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
335	C₄×D₄	—	2	4	no	—
336	C₄×D₄	—	2	4	no	—
337	C₄×D₄	—	2	4	no	—
338	C₄×D₄	—	2	2	no	—
339	C₄×D₄	—	2	2	no	—
340	C₄×D₄	C₂³×C₆₁	1	4	yes	—
341	#117	—	2	4	no	—
342	#117	—	2	2	no	—
343	#117	—	2	4	no	—
344	#117	—	2	2	no	—
345	#117	C₂³×C₆₁	1	8	yes	—
346	#117	C₂³×C₆₁	1	2	yes	—
347	C₂×C₄⋊C₄	—	2	4	no	—
348	C₂×C₄⋊C₄	—	2	2	no	—
349	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
350	C₂×C₂²⋊C₄	—	2	2	no	—
351	C₂×C₄²	—	2	2	no	—
352	C₂×C₄²	—	2	2	no	—
353	C₂×C₄²	D₄×C₆₁	1	2	yes	—
354	C₂×C₄²	D₄×C₆₁	1	2	yes	—
355	C₂×C₄²	D₄×C₆₁	1	2	yes	—
356	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
357	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
358	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
359	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
360	#107	C₂³×C₆₁	1	16	yes	—
361	#106	C₂³×C₆₁	1	16	yes	—
362	C₄⋊C₈	C₂³×C₆₁	1	8	yes	—
363	#103	C₂³×C₆₁	1	16	yes	—
364	#102	C₂³×C₆₁	1	16	yes	—
365	C₂²⋊C₈	C₂³×C₆₁	1	8	yes	—
366	#97	C₂³×C₆₁	1	4	yes	—
367	C₄×C₈	C₂³×C₆₁	1	4	yes	—
368	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
369	#41	—	2	8	no	—
370	#41	—	4	8	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	4	no	—
373	C₂×Q₈	—	2	4	no	—
374	C₂×Q₈	—	4	8	no	—
375	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	4	4	no	—
385	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
387	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
388	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
389	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
390	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
391	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
392	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
393	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
394	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
395	M₁₆	—	2	8	no	—
396	C₂×C₈	C₂⁴×C₆₁	1	8	yes	—
397	C₄⋊C₄	—	2	8	no	—
398	C₄⋊C₄	—	2	8	no	—
399	C₄⋊C₄	—	2	4	no	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	4	no	—
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
408	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
409	C₂²⋊C₄	—	2	8	no	—
410	C₂²⋊C₄	—	2	4	no	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	2	4	no	—
413	C₂²⋊C₄	—	2	4	no	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₄²	—	2	4	no	—
416	C₄²	—	2	2	no	—
417	C₄²	—	2	8	no	—
418	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
419	C₄²	C₂×D₄×C₆₁	1	2	yes	—
420	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
421	C₄²	C₂×D₄×C₆₁	1	2	yes	—
422	C₄²	C₂×D₄×C₆₁	1	2	yes	—
423	C₄²	C₂×D₄×C₆₁	1	2	yes	—
424	C₄²	C₂×D₄×C₆₁	1	2	yes	—
425	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
426	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
427	C₄²	C₂⁴×C₆₁	1	2	yes	—
428	C₂³	—	2	2	no	—
429	C₂³	—	2	2	no	—
430	C₂³	—	4	2	no	—
431	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
432	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
433	Q₈	—	2	4	no	—
434	Q₈	—	4	8	no	—
435	Q₈	—	4	8	no	—
436	Q₈	—	4	4	no	—
437	D₄	—	2	4	no	—
438	D₄	—	4	8	no	—
439	D₄	—	4	4	no	—
440	D₄	—	4	4	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	8	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	8	no	—
454	C₂×C₄	—	4	8	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
457	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
458	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
459	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
460	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
461	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
462	C₂×C₄	2₋¹⁺⁴×C₆₁	1	4	yes	—
463	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
464	C₈	—	2	8	no	—
465	C₂²	—	2	2	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	4	4	no	—
470	C₂²	—	4	4	no	—
471	C₂²	—	4	2	no	—
472	C₂²	C₆₁×#536	1	2	yes	—
473	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	2	2	no	—
478	C₄	—	4	4	no	—
479	C₄	—	4	8	no	—
480	C₄	—	4	2	no	—
481	C₄	C₆₁×#536	1	2	yes	—
482	C₄	C₆₁×#575	1	4	yes	—
483	C₄	C₂×2₋¹⁺⁴×C₆₁	1	2	yes	—
484	C₂	—	2	2	no	—
485	C₂	—	4	2	no	—
486	C₂	—	8	2	no	—
487	C₂	C₂×C₆₁×#536	1	1	yes	characteristic
488	C₂	C₂×C₆₁×#575	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₆₁×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂²×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₆₁×#533	C₂	semidirect
3. C₆₁×#3240	C₂	semidirect
4. C₆₁×#3231	C₂	semidirect
5. C₆₁×#3228	C₂	semidirect
6. C₆₁×#3165	C₂	semidirect
7. C₆₁×#3141	C₂	semidirect
8. C₆₁×#3093	C₂	semidirect
9. C₆₁×#3080	C₂	semidirect
10. C₆₁×#2920	C₂	semidirect
32. C₆₁×#501	C₂²	semidirect
33. C₆₁×#500	C₂²	semidirect
34. C₆₁×#498	C₂²	semidirect
35. C₆₁×#489	C₂²	semidirect
36. C₆₁×#487	C₂²	semidirect
37. C₆₁×#486	C₂²	semidirect
40. C₆₁×#479	C₂²	semidirect
41. C₆₁×#478	C₂²	semidirect
220. #60862	C₆₁	direct (N × H)
241. C₂×#533	C₂×C₆₁	semidirect
242. #3240	C₂×C₆₁	semidirect
243. #3231	C₂×C₆₁	semidirect
244. #3228	C₂×C₆₁	semidirect
245. #3165	C₂×C₆₁	semidirect
246. #3141	C₂×C₆₁	semidirect
247. #3093	C₂×C₆₁	semidirect
248. #3080	C₂×C₆₁	semidirect
249. #2920	C₂×C₆₁	semidirect
276. #501	C₂²×C₆₁	semidirect
277. #500	C₂²×C₆₁	semidirect
278. #498	C₂²×C₆₁	semidirect
279. #489	C₂²×C₆₁	semidirect
280. #487	C₂²×C₆₁	semidirect
281. #486	C₂²×C₆₁	semidirect
284. #479	C₂²×C₆₁	semidirect
285. #478	C₂²×C₆₁	semidirect
293. C₆₁	#60862	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₁×#3444	2
C₂×C₆₁×#533	2
C₆₁×#3240	2
C₆₁×#3231	2
C₆₁×#3228	2
C₆₁×#3165	2
C₆₁×#3141	2
C₆₁×#3093	2
C₆₁×#3080	2
C₆₁×#2920	2
#60862	61

Subgroups — C61×#60862 #29564295

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#60862 #29564295