Subgroups — C₆₁×#21506 #29524939

Order 15616.

972 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#462	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#441	C₂	1	2	yes	maximal
3	C₄×C₄⋊Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic
4	C₄²×Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#1981	C₂	1	1	yes	maximal, characteristic
6	C₆₁×#1948	C₂	1	1	yes	maximal, characteristic
7	C₆₁×#1927	C₂	1	2	yes	maximal
8	C₆₁×#1878	C₂	1	2	yes	maximal
9	C₆₁×#1803	C₂	1	1	yes	maximal, characteristic
10	C₆₁×#1767	C₂	1	1	yes	maximal, characteristic
11	C₆₁×#1763	C₂	1	2	yes	maximal
12	C₂²×Q₁₆×C₆₁	C₂²	1	2	yes	—
13	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
18	C₆₁×#462	C₄	1	8	yes	complemented
19	C₆₁×#441	—	2	8	no	—
20	C₂×#106×C₆₁	C₂²	1	2	yes	—
21	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×#103×C₆₁	C₂²	1	2	yes	—
24	C₂×#103×C₆₁	C₂²	1	2	yes	—
25	C₂×#103×C₆₁	C₂²	1	2	yes	—
26	C₂×#103×C₆₁	C₂²	1	2	yes	—
27	C₂×#97×C₆₁	C₂²	1	2	yes	—
28	C₆₁×#391	C₂²	1	2	yes	—
29	C₆₁×#389	—	2	1	no	—
30	C₆₁×#389	—	2	1	no	—
31	C₆₁×#384	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
33	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
34	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
35	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
36	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
37	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
40	C₄³×C₆₁	—	2	1	no	—
41	C₄³×C₆₁	C₂²	1	1	yes	characteristic
42	C₆₁×#340	C₂²	1	2	yes	—
43	C₆₁×#340	C₂²	1	2	yes	—
44	C₆₁×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
46	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
47	C₂×Q₁₆×C₆₁	—	2	4	no	—
48	C₂×Q₁₆×C₆₁	—	2	4	no	—
49	C₂×Q₁₆×C₆₁	C₂×C₄	1	8	yes	—
50	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
51	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
52	C₄⋊Q₈×C₆₁	—	2	2	no	—
53	C₄⋊Q₈×C₆₁	C₂×C₄	1	4	yes	—
54	C₄×Q₈×C₆₁	—	2	2	no	—
55	C₄×Q₈×C₆₁	—	2	2	no	—
56	C₄×Q₈×C₆₁	—	2	2	no	—
57	C₄×Q₈×C₆₁	—	2	2	no	—
58	C₄×Q₈×C₆₁	—	2	4	no	—
59	C₄×Q₈×C₆₁	—	2	4	no	—
60	C₄×Q₈×C₆₁	C₂×C₄	1	4	yes	—
61	C₄×Q₈×C₆₁	D₄	1	4	yes	—
62	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
63	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
66	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
67	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
68	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
69	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
70	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₆₁	—	2	1	no	—
75	C₂×C₄²×C₆₁	—	2	1	no	—
76	C₂×C₄²×C₆₁	—	2	1	no	—
77	C₂×C₄²×C₆₁	—	2	1	no	—
78	C₂×C₄²×C₆₁	—	2	1	no	—
79	C₂×C₄²×C₆₁	—	2	1	no	—
80	C₂×C₄²×C₆₁	—	2	2	no	—
81	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
88	#106×C₆₁	—	2	4	no	—
89	C₄⋊C₈×C₆₁	—	2	2	no	—
90	C₄⋊C₈×C₆₁	C₂×C₄	1	4	yes	—
91	#103×C₆₁	—	2	4	no	—
92	#103×C₆₁	—	2	4	no	—
93	#103×C₆₁	—	2	4	no	—
94	#103×C₆₁	C₂×C₄	1	8	yes	—
95	#97×C₆₁	—	2	4	no	—
96	#95×C₆₁	—	2	1	no	—
97	#95×C₆₁	—	2	1	no	—
98	#95×C₆₁	—	2	1	no	—
99	#95×C₆₁	—	2	2	no	—
100	#95×C₆₁	—	2	2	no	—
101	C₂×Q₈×C₆₁	—	2	1	no	—
102	C₂×Q₈×C₆₁	—	2	1	no	—
103	C₂×Q₈×C₆₁	—	2	1	no	—
104	C₂×Q₈×C₆₁	—	2	2	no	—
105	C₂×Q₈×C₆₁	—	2	2	no	—
106	C₂×Q₈×C₆₁	—	2	2	no	—
107	C₂×Q₈×C₆₁	—	2	2	no	—
108	C₂×Q₈×C₆₁	—	2	2	no	—
109	C₂×Q₈×C₆₁	C₂²×C₄	1	4	yes	—
110	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
111	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
112	C₂×Q₈×C₆₁	#41	1	2	yes	—
113	C₂²×C₄×C₆₁	—	2	1	no	—
114	C₂²×C₄×C₆₁	—	2	1	no	—
115	C₂²×C₄×C₆₁	—	2	1	no	—
116	C₂²×C₄×C₆₁	—	2	1	no	—
117	C₂²×C₄×C₆₁	—	2	2	no	—
118	C₂²×C₄×C₆₁	—	2	2	no	—
119	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
126	Q₁₆×C₆₁	—	2	16	no	—
127	C₂×C₈×C₆₁	—	2	2	no	—
128	C₂×C₈×C₆₁	—	2	2	no	—
129	C₂×C₈×C₆₁	—	2	2	no	—
130	C₂×C₈×C₆₁	—	2	2	no	—
131	C₂×C₈×C₆₁	—	2	2	no	—
132	C₂×C₈×C₆₁	C₂²×C₄	1	4	yes	—
133	C₄⋊C₄×C₆₁	—	2	4	no	—
134	C₄⋊C₄×C₆₁	—	2	4	no	—
135	C₄⋊C₄×C₆₁	—	2	4	no	—
136	C₄⋊C₄×C₆₁	—	2	4	no	—
137	C₄⋊C₄×C₆₁	—	2	4	no	—
138	C₄⋊C₄×C₆₁	—	2	1	no	—
139	C₄⋊C₄×C₆₁	—	2	1	no	—
140	C₄⋊C₄×C₆₁	—	2	1	no	—
141	C₄⋊C₄×C₆₁	—	2	2	no	—
142	C₄⋊C₄×C₆₁	—	2	2	no	—
143	C₄⋊C₄×C₆₁	—	4	2	no	—
144	C₄⋊C₄×C₆₁	—	4	4	no	—
145	C₄⋊C₄×C₆₁	—	4	2	no	—
146	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
147	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
148	C₄⋊C₄×C₆₁	#41	1	2	yes	—
149	C₄²×C₆₁	—	2	4	no	—
150	C₄²×C₆₁	—	2	4	no	—
151	C₄²×C₆₁	—	2	4	no	—
152	C₄²×C₆₁	—	2	2	no	—
153	C₄²×C₆₁	—	2	2	no	—
154	C₄²×C₆₁	—	2	2	no	—
155	C₄²×C₆₁	—	2	1	no	—
156	C₄²×C₆₁	—	2	1	no	—
157	C₄²×C₆₁	—	4	1	no	—
158	C₄²×C₆₁	—	4	2	no	—
159	C₄²×C₆₁	—	4	4	no	—
160	C₄²×C₆₁	—	4	2	no	—
161	C₄²×C₆₁	—	4	2	no	—
162	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
163	C₄²×C₆₁	C₂×D₄	1	2	yes	—
164	C₄²×C₆₁	#41	1	2	yes	—
165	C₄²×C₆₁	#41	1	2	yes	—
166	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
167	Q₈×C₆₁	—	2	2	no	—
168	Q₈×C₆₁	—	2	2	no	—
169	Q₈×C₆₁	—	2	2	no	—
170	Q₈×C₆₁	—	2	4	no	—
171	Q₈×C₆₁	—	2	4	no	—
172	Q₈×C₆₁	—	4	2	no	—
173	Q₈×C₆₁	—	4	2	no	—
174	Q₈×C₆₁	C₄×D₄	1	4	yes	—
175	C₂×C₄×C₆₁	—	2	2	no	—
176	C₂×C₄×C₆₁	—	2	2	no	—
177	C₂×C₄×C₆₁	—	2	1	no	—
178	C₂×C₄×C₆₁	—	2	2	no	—
179	C₂×C₄×C₆₁	—	2	1	no	—
180	C₂×C₄×C₆₁	—	2	1	no	—
181	C₂×C₄×C₆₁	—	2	1	no	—
182	C₂×C₄×C₆₁	—	2	1	no	—
183	C₂×C₄×C₆₁	—	2	1	no	—
184	C₂×C₄×C₆₁	—	2	1	no	—
185	C₂×C₄×C₆₁	—	2	1	no	—
186	C₂×C₄×C₆₁	—	2	2	no	—
187	C₂×C₄×C₆₁	—	2	4	no	—
188	C₂×C₄×C₆₁	—	2	2	no	—
189	C₂×C₄×C₆₁	—	2	1	no	—
190	C₂×C₄×C₆₁	—	2	2	no	—
191	C₂×C₄×C₆₁	—	2	1	no	—
192	C₂×C₄×C₆₁	—	2	1	no	—
193	C₂×C₄×C₆₁	—	4	2	no	—
194	C₂×C₄×C₆₁	—	4	2	no	—
195	C₂×C₄×C₆₁	—	4	1	no	—
196	C₂×C₄×C₆₁	—	4	1	no	—
197	C₂×C₄×C₆₁	—	4	1	no	—
198	C₂×C₄×C₆₁	—	4	1	no	—
199	C₂×C₄×C₆₁	—	4	1	no	—
200	C₂×C₄×C₆₁	—	4	1	no	—
201	C₂×C₄×C₆₁	—	4	2	no	—
202	C₂×C₄×C₆₁	—	4	2	no	—
203	C₂×C₄×C₆₁	—	4	2	no	—
204	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
205	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
206	C₂×C₄×C₆₁	#121	1	2	yes	—
207	C₂×C₄×C₆₁	#121	1	2	yes	—
208	C₂×C₄×C₆₁	#137	1	2	yes	—
209	C₂×C₄×C₆₁	#137	1	2	yes	—
210	C₂×C₄×C₆₁	#137	1	2	yes	—
211	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
212	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
217	C₈×C₆₁	—	2	4	no	—
218	C₈×C₆₁	—	4	2	no	—
219	#21506	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
221	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
222	C₂²×C₆₁	#525	1	1	yes	characteristic
223	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
224	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
225	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
226	C₂²×C₆₁	#575	1	1	yes	characteristic
227	C₄×C₆₁	—	2	2	no	—
228	C₄×C₆₁	—	2	2	no	—
229	C₄×C₆₁	—	2	2	no	—
230	C₄×C₆₁	—	2	2	no	—
231	C₄×C₆₁	—	2	4	no	—
232	C₄×C₆₁	—	4	1	no	—
233	C₄×C₆₁	—	4	2	no	—
234	C₄×C₆₁	—	4	2	no	—
235	C₄×C₆₁	—	4	2	no	—
236	C₄×C₆₁	—	4	4	no	—
237	C₄×C₆₁	—	8	2	no	—
238	C₄×C₆₁	#441	1	4	yes	complemented
239	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
240	C₄×C₆₁	C₄×#41	1	1	yes	characteristic
241	C₄×C₆₁	#529	1	1	yes	characteristic
242	C₄×C₆₁	#532	1	1	yes	characteristic
243	C₂×#462	C₂×C₆₁	1	1	yes	characteristic
244	C₂×#441	C₂×C₆₁	1	2	yes	—
245	C₄×C₄⋊Q₈	C₂×C₆₁	1	1	yes	characteristic
246	C₄²×Q₈	C₂×C₆₁	1	1	yes	characteristic
247	#1981	C₂×C₆₁	1	1	yes	characteristic
248	#1948	C₂×C₆₁	1	1	yes	characteristic
249	#1927	C₂×C₆₁	1	2	yes	—
250	#1878	C₂×C₆₁	1	2	yes	—
251	#1803	C₂×C₆₁	1	1	yes	characteristic
252	#1767	C₂×C₆₁	1	1	yes	characteristic
253	#1763	C₂×C₆₁	1	2	yes	—
254	C₂×C₆₁	C₄×#121	1	1	yes	characteristic
255	C₂×C₆₁	C₂×#441	1	1	yes	characteristic
256	C₂×C₆₁	C₄×#137	1	1	yes	characteristic
257	C₂×C₆₁	#3037	1	1	yes	characteristic
258	C₂×C₆₁	#3039	1	1	yes	characteristic
259	C₂×C₆₁	#3113	1	1	yes	characteristic
260	C₂×C₆₁	#3116	1	1	yes	characteristic
261	C₂²×Q₁₆	C₂²×C₆₁	1	2	yes	—
262	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
263	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
264	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
265	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
266	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
267	#462	C₄×C₆₁	1	8	yes	complemented
268	#441	—	2	8	no	—
269	C₂×#106	C₂²×C₆₁	1	2	yes	—
270	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
271	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
272	C₂×#103	C₂²×C₆₁	1	2	yes	—
273	C₂×#103	C₂²×C₆₁	1	2	yes	—
274	C₂×#103	C₂²×C₆₁	1	2	yes	—
275	C₂×#103	C₂²×C₆₁	1	2	yes	—
276	C₂×#97	C₂²×C₆₁	1	2	yes	—
277	#391	C₂²×C₆₁	1	2	yes	—
278	#389	—	2	1	no	—
279	#389	—	2	1	no	—
280	#384	C₂²×C₆₁	1	1	yes	characteristic
281	C₄×C₄⋊C₄	—	2	1	no	—
282	C₄×C₄⋊C₄	—	2	1	no	—
283	C₄×C₄⋊C₄	—	2	1	no	—
284	C₄×C₄⋊C₄	—	2	1	no	—
285	C₄×C₄⋊C₄	—	2	1	no	—
286	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
287	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
288	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
289	C₄³	—	2	1	no	—
290	C₄³	C₂²×C₆₁	1	1	yes	characteristic
291	#340	C₂²×C₆₁	1	2	yes	—
292	#340	C₂²×C₆₁	1	2	yes	—
293	#336	C₂²×C₆₁	1	2	yes	—
294	C₆₁	#21506	1	1	yes	characteristic, direct product factor, Sylow
295	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
296	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
297	C₂×Q₁₆	—	2	4	no	—
298	C₂×Q₁₆	—	2	4	no	—
299	C₂×Q₁₆	C₂×C₄×C₆₁	1	8	yes	—
300	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
301	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
302	C₄⋊Q₈	—	2	2	no	—
303	C₄⋊Q₈	C₂×C₄×C₆₁	1	4	yes	—
304	C₄×Q₈	—	2	2	no	—
305	C₄×Q₈	—	2	2	no	—
306	C₄×Q₈	—	2	2	no	—
307	C₄×Q₈	—	2	2	no	—
308	C₄×Q₈	—	2	4	no	—
309	C₄×Q₈	—	2	4	no	—
310	C₄×Q₈	C₂×C₄×C₆₁	1	4	yes	—
311	C₄×Q₈	D₄×C₆₁	1	4	yes	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
321	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
322	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
324	C₂×C₄²	—	2	1	no	—
325	C₂×C₄²	—	2	1	no	—
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	—	2	2	no	—
328	C₂×C₄²	—	2	1	no	—
329	C₂×C₄²	—	2	1	no	—
330	C₂×C₄²	—	2	1	no	—
331	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
332	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
333	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
334	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
335	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
336	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
337	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
338	#106	—	2	4	no	—
339	C₄⋊C₈	—	2	2	no	—
340	C₄⋊C₈	C₂×C₄×C₆₁	1	4	yes	—
341	#103	—	2	4	no	—
342	#103	—	2	4	no	—
343	#103	—	2	4	no	—
344	#103	C₂×C₄×C₆₁	1	8	yes	—
345	#97	—	2	4	no	—
346	#95	—	2	1	no	—
347	#95	—	2	1	no	—
348	#95	—	2	1	no	—
349	#95	—	2	2	no	—
350	#95	—	2	2	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	C₂²×C₄×C₆₁	1	4	yes	—
360	C₂×Q₈	C₂²×C₄×C₆₁	1	2	yes	—
361	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
362	C₂×Q₈	#41×C₆₁	1	2	yes	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
373	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
374	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
375	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
376	Q₁₆	—	2	16	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	C₂²×C₄×C₆₁	1	4	yes	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	2	4	no	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	4	no	—
387	C₄⋊C₄	—	2	4	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	4	2	no	—
394	C₄⋊C₄	—	4	4	no	—
395	C₄⋊C₄	—	4	2	no	—
396	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
397	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
398	C₄⋊C₄	#41×C₆₁	1	2	yes	—
399	C₄²	—	2	4	no	—
400	C₄²	—	2	4	no	—
401	C₄²	—	2	4	no	—
402	C₄²	—	2	2	no	—
403	C₄²	—	2	2	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	2	1	no	—
406	C₄²	—	2	1	no	—
407	C₄²	—	4	1	no	—
408	C₄²	—	4	2	no	—
409	C₄²	—	4	4	no	—
410	C₄²	—	4	2	no	—
411	C₄²	—	4	2	no	—
412	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
413	C₄²	C₂×D₄×C₆₁	1	2	yes	—
414	C₄²	#41×C₆₁	1	2	yes	—
415	C₄²	#41×C₆₁	1	2	yes	—
416	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
417	Q₈	—	2	2	no	—
418	Q₈	—	2	2	no	—
419	Q₈	—	2	2	no	—
420	Q₈	—	2	4	no	—
421	Q₈	—	2	4	no	—
422	Q₈	—	4	2	no	—
423	Q₈	—	4	2	no	—
424	Q₈	C₄×D₄×C₆₁	1	4	yes	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
455	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
456	C₂×C₄	#121×C₆₁	1	2	yes	—
457	C₂×C₄	#121×C₆₁	1	2	yes	—
458	C₂×C₄	#137×C₆₁	1	2	yes	—
459	C₂×C₄	#137×C₆₁	1	2	yes	—
460	C₂×C₄	#137×C₆₁	1	2	yes	—
461	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
462	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
463	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
464	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
465	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
466	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
467	C₈	—	2	4	no	—
468	C₈	—	4	2	no	—
469	C₂²	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
470	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
471	C₂²	C₆₁×#525	1	1	yes	characteristic
472	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
473	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
474	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
475	C₂²	C₆₁×#575	1	1	yes	characteristic
476	C₄	—	2	2	no	—
477	C₄	—	2	2	no	—
478	C₄	—	2	4	no	—
479	C₄	—	2	2	no	—
480	C₄	—	2	2	no	—
481	C₄	—	4	2	no	—
482	C₄	—	4	4	no	—
483	C₄	—	4	1	no	—
484	C₄	—	4	2	no	—
485	C₄	—	4	2	no	—
486	C₄	—	8	2	no	—
487	C₄	C₆₁×#441	1	4	yes	complemented
488	C₄	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
489	C₄	C₄×#41×C₆₁	1	1	yes	characteristic
490	C₄	C₆₁×#529	1	1	yes	characteristic
491	C₄	C₆₁×#532	1	1	yes	characteristic
492	C₂	C₄×#121×C₆₁	1	1	yes	characteristic
493	C₂	C₂×C₆₁×#441	1	1	yes	characteristic
494	C₂	C₄×#137×C₆₁	1	1	yes	characteristic
495	C₂	C₆₁×#3037	1	1	yes	characteristic
496	C₂	C₆₁×#3039	1	1	yes	characteristic
497	C₂	C₆₁×#3113	1	1	yes	characteristic
498	C₂	C₆₁×#3116	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₆₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₄³×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
18. C₆₁×#462	C₄	semidirect
219. #21506	C₆₁	direct (N × H)
238. C₄×C₆₁	#441	semidirect
267. #462	C₄×C₆₁	semidirect
294. C₆₁	#21506	direct (N × H)
487. C₄	C₆₁×#441	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#462	2
C₂×C₆₁×#441	2
C₄×C₄⋊Q₈×C₆₁	2
C₄²×Q₈×C₆₁	2
C₆₁×#1981	2
C₆₁×#1948	2
C₆₁×#1927	2
C₆₁×#1878	2
C₆₁×#1803	2
C₆₁×#1767	2
C₆₁×#1763	2
#21506	61

Subgroups — C61×#21506 #29524939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#21506 #29524939