Subgroups — C₆₁×#23643 #29527076

Order 15616.

1014 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#428	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#408	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2311	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2311	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2077	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2077	C₂	1	2	yes	maximal, complemented
7	C₆₁×#2076	C₂	1	2	yes	maximal, complemented
8	C₆₁×#2075	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1736	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1735	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₆₁×#340	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
19	C₆₁×#428	—	2	4	no	—
20	C₂×#107×C₆₁	C₂²	1	2	yes	—
21	C₂×#106×C₆₁	C₂²	1	2	yes	—
22	C₆₁×#408	—	2	4	no	—
23	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
24	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
25	C₆₁×#391	—	2	1	no	—
26	C₆₁×#391	—	2	1	no	—
27	C₆₁×#390	—	2	1	no	—
28	C₆₁×#390	—	2	1	no	—
29	C₆₁×#386	—	2	2	no	—
30	C₆₁×#386	—	2	2	no	—
31	C₆₁×#380	C₂²	1	2	yes	—
32	C₆₁×#380	C₂²	1	2	yes	—
33	C₆₁×#380	C₂²	1	2	yes	—
34	C₆₁×#380	C₂²	1	2	yes	—
35	C₆₁×#340	C₂²	1	1	yes	characteristic
36	C₆₁×#340	C₂²	1	2	yes	—
37	C₆₁×#340	C₂²	1	2	yes	—
38	C₆₁×#340	C₂²	1	1	yes	characteristic
39	C₆₁×#340	C₂²	1	2	yes	—
40	C₆₁×#340	C₂²	1	2	yes	—
41	C₆₁×#340	C₂²	1	1	yes	characteristic
42	C₆₁×#340	C₂²	1	1	yes	characteristic
43	C₂×#41×C₆₁	—	2	2	no	—
44	C₂×#41×C₆₁	—	2	2	no	—
45	C₂×#41×C₆₁	—	2	2	no	—
46	C₂×#41×C₆₁	—	2	2	no	—
47	C₂×#41×C₆₁	—	2	2	no	—
48	C₂×#41×C₆₁	—	2	2	no	—
49	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
50	C₂²×D₄×C₆₁	D₄	1	2	yes	—
51	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₆₁	—	2	1	no	—
53	C₂³×C₄×C₆₁	—	2	1	no	—
54	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
55	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
56	C₂×M₁₆×C₆₁	—	2	2	no	—
57	C₂×M₁₆×C₆₁	—	2	2	no	—
58	C₂×M₁₆×C₆₁	D₄	1	4	yes	—
59	C₂²×C₈×C₆₁	—	2	2	no	—
60	C₂²×C₈×C₆₁	—	2	2	no	—
61	C₂²×C₈×C₆₁	—	2	2	no	—
62	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
65	#117×C₆₁	—	2	2	no	—
66	#117×C₆₁	—	2	2	no	—
67	#117×C₆₁	—	2	2	no	—
68	#117×C₆₁	—	2	2	no	—
69	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
70	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
71	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
72	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
73	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
74	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
75	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₆₁	C₂³	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×C₂²⋊C₄×C₆₁	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
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	2	no	—
87	C₂×C₄²×C₆₁	—	2	1	no	—
88	C₂×C₄²×C₆₁	—	2	1	no	—
89	#107×C₆₁	—	2	4	no	—
90	#106×C₆₁	—	2	4	no	—
91	C₂²⋊C₈×C₆₁	—	2	4	no	—
92	C₂²⋊C₈×C₆₁	—	2	4	no	—
93	#95×C₆₁	—	2	2	no	—
94	#95×C₆₁	—	2	2	no	—
95	#95×C₆₁	—	2	2	no	—
96	#95×C₆₁	—	2	2	no	—
97	C₂⁴×C₆₁	C₂×D₄	1	2	yes	—
98	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
99	#41×C₆₁	—	4	4	no	—
100	#41×C₆₁	—	4	4	no	—
101	#41×C₆₁	—	4	4	no	—
102	#41×C₆₁	—	4	4	no	—
103	C₂×Q₈×C₆₁	—	2	2	no	—
104	C₂×Q₈×C₆₁	—	2	2	no	—
105	C₂×Q₈×C₆₁	—	2	2	no	—
106	C₂×D₄×C₆₁	—	2	4	no	—
107	C₂×D₄×C₆₁	—	2	4	no	—
108	C₂×D₄×C₆₁	—	2	4	no	—
109	C₂×D₄×C₆₁	—	2	2	no	—
110	C₂×D₄×C₆₁	—	2	2	no	—
111	C₂×D₄×C₆₁	—	2	2	no	—
112	C₂²×C₄×C₆₁	—	2	2	no	—
113	C₂²×C₄×C₆₁	—	2	2	no	—
114	C₂²×C₄×C₆₁	—	2	2	no	—
115	C₂²×C₄×C₆₁	—	2	2	no	—
116	C₂²×C₄×C₆₁	—	2	2	no	—
117	C₂²×C₄×C₆₁	—	2	2	no	—
118	C₂²×C₄×C₆₁	—	2	1	no	—
119	C₂²×C₄×C₆₁	—	2	1	no	—
120	C₂²×C₄×C₆₁	—	2	1	no	—
121	C₂²×C₄×C₆₁	—	2	1	no	—
122	C₂²×C₄×C₆₁	—	2	2	no	—
123	C₂²×C₄×C₆₁	—	2	2	no	—
124	C₂²×C₄×C₆₁	—	4	2	no	—
125	C₂²×C₄×C₆₁	—	4	2	no	—
126	C₂²×C₄×C₆₁	—	8	1	no	—
127	C₂²×C₄×C₆₁	—	8	1	no	—
128	C₂²×C₄×C₆₁	—	8	1	no	—
129	C₂²×C₄×C₆₁	—	8	1	no	—
130	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₆₁	#41	1	2	yes	—
134	C₂²×C₄×C₆₁	#41	1	2	yes	—
135	C₂²×C₄×C₆₁	#41	1	2	yes	—
136	C₂²×C₄×C₆₁	#41	1	2	yes	—
137	C₂²×C₄×C₆₁	#41	1	2	yes	—
138	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
139	M₁₆×C₆₁	—	2	8	no	—
140	C₂×C₈×C₆₁	—	2	2	no	—
141	C₂×C₈×C₆₁	—	2	2	no	—
142	C₂×C₈×C₆₁	—	2	1	no	—
143	C₂×C₈×C₆₁	—	2	1	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	1	no	—
148	C₂×C₈×C₆₁	—	4	4	no	—
149	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
150	C₄⋊C₄×C₆₁	—	2	1	no	—
151	C₄⋊C₄×C₆₁	—	2	2	no	—
152	C₄⋊C₄×C₆₁	—	2	1	no	—
153	C₄⋊C₄×C₆₁	—	2	2	no	—
154	C₄⋊C₄×C₆₁	—	2	2	no	—
155	C₄⋊C₄×C₆₁	—	2	2	no	—
156	C₄⋊C₄×C₆₁	—	2	1	no	—
157	C₄⋊C₄×C₆₁	—	2	1	no	—
158	C₄⋊C₄×C₆₁	—	2	1	no	—
159	C₄⋊C₄×C₆₁	—	2	1	no	—
160	C₄⋊C₄×C₆₁	—	2	1	no	—
161	C₄⋊C₄×C₆₁	—	2	1	no	—
162	C₄⋊C₄×C₆₁	—	4	2	no	—
163	C₄⋊C₄×C₆₁	—	4	2	no	—
164	C₂²⋊C₄×C₆₁	—	4	2	no	—
165	C₂²⋊C₄×C₆₁	—	4	2	no	—
166	C₂²⋊C₄×C₆₁	—	8	2	no	—
167	C₂²⋊C₄×C₆₁	—	8	2	no	—
168	C₂²⋊C₄×C₆₁	—	8	2	no	—
169	C₂²⋊C₄×C₆₁	—	8	2	no	—
170	C₄²×C₆₁	—	4	2	no	—
171	C₄²×C₆₁	—	4	2	no	—
172	C₂³×C₆₁	—	2	1	no	—
173	C₂³×C₆₁	—	2	1	no	—
174	C₂³×C₆₁	—	2	1	no	—
175	C₂³×C₆₁	—	2	1	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	#121	1	2	yes	—
184	C₂³×C₆₁	#123	1	2	yes	—
185	C₂³×C₆₁	#123	1	2	yes	—
186	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
187	Q₈×C₆₁	—	4	4	no	—
188	D₄×C₆₁	—	4	8	no	—
189	D₄×C₆₁	—	4	4	no	—
190	C₂×C₄×C₆₁	—	2	2	no	—
191	C₂×C₄×C₆₁	—	2	2	no	—
192	C₂×C₄×C₆₁	—	2	2	no	—
193	C₂×C₄×C₆₁	—	4	2	no	—
194	C₂×C₄×C₆₁	—	4	2	no	—
195	C₂×C₄×C₆₁	—	4	2	no	—
196	C₂×C₄×C₆₁	—	4	2	no	—
197	C₂×C₄×C₆₁	—	4	1	no	—
198	C₂×C₄×C₆₁	—	4	1	no	—
199	C₂×C₄×C₆₁	—	4	2	no	—
200	C₂×C₄×C₆₁	—	4	1	no	—
201	C₂×C₄×C₆₁	—	4	1	no	—
202	C₂×C₄×C₆₁	—	4	2	no	—
203	C₂×C₄×C₆₁	—	4	1	no	—
204	C₂×C₄×C₆₁	—	4	1	no	—
205	C₂×C₄×C₆₁	—	4	2	no	—
206	C₂×C₄×C₆₁	—	4	2	no	—
207	C₂×C₄×C₆₁	—	4	1	no	—
208	C₂×C₄×C₆₁	—	4	1	no	—
209	C₂×C₄×C₆₁	—	4	2	no	—
210	C₂×C₄×C₆₁	—	4	2	no	—
211	C₂×C₄×C₆₁	—	4	1	no	—
212	C₂×C₄×C₆₁	—	4	1	no	—
213	C₂×C₄×C₆₁	—	4	1	no	—
214	C₂×C₄×C₆₁	—	4	1	no	—
215	C₂×C₄×C₆₁	—	8	4	no	—
216	C₂×C₄×C₆₁	—	8	4	no	—
217	C₂×C₄×C₆₁	#121	1	2	yes	—
218	C₂×C₄×C₆₁	#123	1	4	yes	—
219	C₂×C₄×C₆₁	#123	1	2	yes	—
220	C₂×C₄×C₆₁	#123	1	2	yes	—
221	C₂×C₄×C₆₁	#124	1	4	yes	—
222	C₂×C₄×C₆₁	#126	1	4	yes	—
223	C₂×C₄×C₆₁	#126	1	4	yes	—
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	C₂×#41	1	1	yes	characteristic
228	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
229	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
230	C₈×C₆₁	—	2	4	no	—
231	C₈×C₆₁	—	4	1	no	—
232	C₈×C₆₁	—	4	1	no	—
233	#23643	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂²×C₆₁	—	2	2	no	—
235	C₂²×C₆₁	—	2	2	no	—
236	C₂²×C₆₁	—	2	2	no	—
237	C₂²×C₆₁	—	2	2	no	—
238	C₂²×C₆₁	—	2	2	no	—
239	C₂²×C₆₁	—	2	2	no	—
240	C₂²×C₆₁	—	4	2	no	—
241	C₂²×C₆₁	—	4	2	no	—
242	C₂²×C₆₁	—	4	2	no	—
243	C₂²×C₆₁	—	4	2	no	—
244	C₂²×C₆₁	—	4	2	no	—
245	C₂²×C₆₁	—	4	2	no	—
246	C₂²×C₆₁	—	4	2	no	—
247	C₂²×C₆₁	#397	1	4	yes	—
248	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
249	C₂²×C₆₁	C₂×#123	1	1	yes	characteristic
250	C₂²×C₆₁	C₂×#123	1	1	yes	characteristic
251	C₂²×C₆₁	#576	1	1	yes	characteristic
252	C₂²×C₆₁	#577	1	1	yes	characteristic
253	C₂²×C₆₁	#577	1	1	yes	characteristic
254	C₂²×C₆₁	#578	1	1	yes	characteristic
255	C₄×C₆₁	—	4	2	no	—
256	C₄×C₆₁	—	8	2	no	—
257	C₄×C₆₁	—	8	1	no	—
258	C₄×C₆₁	—	8	1	no	—
259	C₄×C₆₁	—	8	1	no	—
260	C₄×C₆₁	—	8	2	no	—
261	C₄×C₆₁	—	8	1	no	—
262	C₄×C₆₁	#397	1	4	yes	—
263	C₄×C₆₁	C₂×#123	1	1	yes	characteristic
264	C₄×C₆₁	C₂×#124	1	1	yes	characteristic
265	C₄×C₆₁	C₂×#126	1	1	yes	characteristic
266	C₄×C₆₁	C₂×#126	1	1	yes	characteristic
267	C₂×#428	C₂×C₆₁	1	1	yes	characteristic, complemented
268	C₂×#408	C₂×C₆₁	1	1	yes	characteristic
269	#2311	C₂×C₆₁	1	1	yes	characteristic
270	#2311	C₂×C₆₁	1	1	yes	characteristic
271	#2077	C₂×C₆₁	1	2	yes	complemented
272	#2077	C₂×C₆₁	1	2	yes	complemented
273	#2076	C₂×C₆₁	1	2	yes	complemented
274	#2075	C₂×C₆₁	1	2	yes	complemented
275	#1736	C₂×C₆₁	1	1	yes	characteristic, complemented
276	#1735	C₂×C₆₁	1	1	yes	characteristic, complemented
277	C₂×#340	C₂×C₆₁	1	1	yes	characteristic, complemented
278	C₂×C₆₁	—	2	4	no	—
279	C₂×C₆₁	—	8	2	no	—
280	C₂×C₆₁	C₂×#397	1	1	yes	characteristic
281	C₂×C₆₁	#3062	1	1	yes	characteristic
282	C₂×C₆₁	#3063	1	1	yes	characteristic
283	C₂×C₆₁	#3096	1	1	yes	characteristic
284	C₂×C₆₁	#3097	1	1	yes	characteristic
285	C₂×C₆₁	#3098	1	1	yes	characteristic
286	C₂×C₆₁	#3099	1	1	yes	characteristic
287	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
288	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
289	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
290	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
291	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
292	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
293	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
294	#428	—	2	4	no	—
295	C₂×#107	C₂²×C₆₁	1	2	yes	—
296	C₂×#106	C₂²×C₆₁	1	2	yes	—
297	#408	—	2	4	no	—
298	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
299	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
300	#391	—	2	1	no	—
301	#391	—	2	1	no	—
302	#390	—	2	1	no	—
303	#390	—	2	1	no	—
304	#386	—	2	2	no	—
305	#386	—	2	2	no	—
306	#380	C₂²×C₆₁	1	2	yes	—
307	#380	C₂²×C₆₁	1	2	yes	—
308	#380	C₂²×C₆₁	1	2	yes	—
309	#380	C₂²×C₆₁	1	2	yes	—
310	#340	C₂²×C₆₁	1	1	yes	characteristic
311	#340	C₂²×C₆₁	1	2	yes	—
312	#340	C₂²×C₆₁	1	2	yes	—
313	#340	C₂²×C₆₁	1	1	yes	characteristic
314	#340	C₂²×C₆₁	1	2	yes	—
315	#340	C₂²×C₆₁	1	2	yes	—
316	#340	C₂²×C₆₁	1	1	yes	characteristic
317	#340	C₂²×C₆₁	1	1	yes	characteristic
318	C₆₁	#23643	1	1	yes	characteristic, direct product factor, Sylow
319	C₂×#41	—	2	2	no	—
320	C₂×#41	—	2	2	no	—
321	C₂×#41	—	2	2	no	—
322	C₂×#41	—	2	2	no	—
323	C₂×#41	—	2	2	no	—
324	C₂×#41	—	2	2	no	—
325	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
326	C₂²×D₄	D₄×C₆₁	1	2	yes	—
327	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
328	C₂³×C₄	—	2	1	no	—
329	C₂³×C₄	—	2	1	no	—
330	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
331	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
332	C₂×M₁₆	—	2	2	no	—
333	C₂×M₁₆	—	2	2	no	—
334	C₂×M₁₆	D₄×C₆₁	1	4	yes	—
335	C₂²×C₈	—	2	2	no	—
336	C₂²×C₈	—	2	2	no	—
337	C₂²×C₈	—	2	2	no	—
338	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
339	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
340	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
341	#117	—	2	2	no	—
342	#117	—	2	2	no	—
343	#117	—	2	2	no	—
344	#117	—	2	2	no	—
345	C₂×C₄⋊C₄	—	2	2	no	—
346	C₂×C₄⋊C₄	—	2	2	no	—
347	C₂×C₄⋊C₄	—	2	2	no	—
348	C₂×C₄⋊C₄	—	2	2	no	—
349	C₂×C₄⋊C₄	—	2	1	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
352	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
353	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
354	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
355	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
357	C₂×C₂²⋊C₄	—	2	1	no	—
358	C₂×C₂²⋊C₄	—	2	1	no	—
359	C₂×C₂²⋊C₄	—	2	2	no	—
360	C₂×C₂²⋊C₄	—	2	2	no	—
361	C₂×C₂²⋊C₄	—	2	2	no	—
362	C₂×C₂²⋊C₄	—	2	2	no	—
363	C₂×C₄²	—	2	1	no	—
364	C₂×C₄²	—	2	1	no	—
365	#107	—	2	4	no	—
366	#106	—	2	4	no	—
367	C₂²⋊C₈	—	2	4	no	—
368	C₂²⋊C₈	—	2	4	no	—
369	#95	—	2	2	no	—
370	#95	—	2	2	no	—
371	#95	—	2	2	no	—
372	#95	—	2	2	no	—
373	C₂⁴	C₂×D₄×C₆₁	1	2	yes	—
374	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
375	#41	—	4	4	no	—
376	#41	—	4	4	no	—
377	#41	—	4	4	no	—
378	#41	—	4	4	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	2	2	no	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×D₄	—	2	4	no	—
383	C₂×D₄	—	2	4	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	4	2	no	—
401	C₂²×C₄	—	4	2	no	—
402	C₂²×C₄	—	8	1	no	—
403	C₂²×C₄	—	8	1	no	—
404	C₂²×C₄	—	8	1	no	—
405	C₂²×C₄	—	8	1	no	—
406	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
407	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
408	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
409	C₂²×C₄	#41×C₆₁	1	2	yes	—
410	C₂²×C₄	#41×C₆₁	1	2	yes	—
411	C₂²×C₄	#41×C₆₁	1	2	yes	—
412	C₂²×C₄	#41×C₆₁	1	2	yes	—
413	C₂²×C₄	#41×C₆₁	1	2	yes	—
414	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
415	M₁₆	—	2	8	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	2	1	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	4	4	no	—
425	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	4	2	no	—
439	C₄⋊C₄	—	4	2	no	—
440	C₂²⋊C₄	—	4	2	no	—
441	C₂²⋊C₄	—	4	2	no	—
442	C₂²⋊C₄	—	8	2	no	—
443	C₂²⋊C₄	—	8	2	no	—
444	C₂²⋊C₄	—	8	2	no	—
445	C₂²⋊C₄	—	8	2	no	—
446	C₄²	—	4	2	no	—
447	C₄²	—	4	2	no	—
448	C₂³	—	2	1	no	—
449	C₂³	—	2	1	no	—
450	C₂³	—	2	1	no	—
451	C₂³	—	2	1	no	—
452	C₂³	—	2	2	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	2	2	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	2	2	no	—
458	C₂³	—	2	2	no	—
459	C₂³	#121×C₆₁	1	2	yes	—
460	C₂³	#123×C₆₁	1	2	yes	—
461	C₂³	#123×C₆₁	1	2	yes	—
462	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
463	Q₈	—	4	4	no	—
464	D₄	—	4	8	no	—
465	D₄	—	4	4	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	8	4	no	—
492	C₂×C₄	—	8	4	no	—
493	C₂×C₄	#121×C₆₁	1	2	yes	—
494	C₂×C₄	#123×C₆₁	1	2	yes	—
495	C₂×C₄	#123×C₆₁	1	2	yes	—
496	C₂×C₄	#123×C₆₁	1	4	yes	—
497	C₂×C₄	#124×C₆₁	1	4	yes	—
498	C₂×C₄	#126×C₆₁	1	4	yes	—
499	C₂×C₄	#126×C₆₁	1	4	yes	—
500	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
501	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
502	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
503	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
504	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
505	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
506	C₈	—	2	4	no	—
507	C₈	—	4	1	no	—
508	C₈	—	4	1	no	—
509	C₂²	—	2	2	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	2	2	no	—
513	C₂²	—	2	2	no	—
514	C₂²	—	2	2	no	—
515	C₂²	—	4	2	no	—
516	C₂²	—	4	2	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	C₆₁×#397	1	4	yes	—
523	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
524	C₂²	C₂×#123×C₆₁	1	1	yes	characteristic
525	C₂²	C₂×#123×C₆₁	1	1	yes	characteristic
526	C₂²	C₆₁×#576	1	1	yes	characteristic
527	C₂²	C₆₁×#577	1	1	yes	characteristic
528	C₂²	C₆₁×#577	1	1	yes	characteristic
529	C₂²	C₆₁×#578	1	1	yes	characteristic
530	C₄	—	4	2	no	—
531	C₄	—	8	1	no	—
532	C₄	—	8	2	no	—
533	C₄	—	8	1	no	—
534	C₄	—	8	2	no	—
535	C₄	—	8	1	no	—
536	C₄	—	8	1	no	—
537	C₄	C₆₁×#397	1	4	yes	—
538	C₄	C₂×#123×C₆₁	1	1	yes	characteristic
539	C₄	C₂×#124×C₆₁	1	1	yes	characteristic
540	C₄	C₂×#126×C₆₁	1	1	yes	characteristic
541	C₄	C₂×#126×C₆₁	1	1	yes	characteristic
542	C₂	—	2	4	no	—
543	C₂	—	8	2	no	—
544	C₂	C₂×C₆₁×#397	1	1	yes	characteristic
545	C₂	C₆₁×#3062	1	1	yes	characteristic
546	C₂	C₆₁×#3063	1	1	yes	characteristic
547	C₂	C₆₁×#3096	1	1	yes	characteristic
548	C₂	C₆₁×#3097	1	1	yes	characteristic
549	C₂	C₆₁×#3098	1	1	yes	characteristic
550	C₂	C₆₁×#3099	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂²×#41×C₆₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂²×#41×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#428	C₂	semidirect
5. C₆₁×#2077	C₂	semidirect
6. C₆₁×#2077	C₂	semidirect
7. C₆₁×#2076	C₂	semidirect
8. C₆₁×#2075	C₂	semidirect
9. C₆₁×#1736	C₂	semidirect
10. C₆₁×#1735	C₂	semidirect
11. C₂×C₆₁×#340	C₂	semidirect
233. #23643	C₆₁	direct (N × H)
267. C₂×#428	C₂×C₆₁	semidirect
271. #2077	C₂×C₆₁	semidirect
272. #2077	C₂×C₆₁	semidirect
273. #2076	C₂×C₆₁	semidirect
274. #2075	C₂×C₆₁	semidirect
275. #1736	C₂×C₆₁	semidirect
276. #1735	C₂×C₆₁	semidirect
277. C₂×#340	C₂×C₆₁	semidirect
318. C₆₁	#23643	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×#428	2
C₂×C₆₁×#408	2
C₆₁×#2311	2
C₆₁×#2077	2
C₆₁×#2076	2
C₆₁×#2075	2
C₆₁×#1736	2
C₆₁×#1735	2
C₂×C₆₁×#340	2
#23643	61

Subgroups — C61×#23643 #29527076

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#23643 #29527076