Subgroups — C₆₁×#23808 #29527241

Order 15616.

1086 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#442	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#440	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×SD₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×D₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2328	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#2326	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#2097	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2094	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#2093	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#2092	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#2014	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#2012	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#2012	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#2011	C₂	1	1	yes	maximal, characteristic
15	C₆₁×#1746	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
18	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
26	C₆₁×#442	—	2	4	no	—
27	C₆₁×#440	—	2	4	no	—
28	C₄×SD₁₆×C₆₁	—	2	4	no	—
29	C₄×D₈×C₆₁	—	2	4	no	—
30	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
33	C₂×#106×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×#102×C₆₁	C₂²	1	1	yes	characteristic
37	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
38	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
39	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
40	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
41	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
42	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
44	C₆₁×#391	C₂²	1	1	yes	characteristic
45	C₆₁×#390	C₂²	1	1	yes	characteristic
46	C₆₁×#390	C₂²	1	1	yes	characteristic
47	C₆₁×#390	C₂²	1	1	yes	characteristic
48	C₆₁×#388	—	2	2	no	—
49	C₆₁×#386	—	2	2	no	—
50	C₆₁×#386	—	2	2	no	—
51	C₆₁×#385	—	2	2	no	—
52	C₆₁×#384	C₂²	1	1	yes	characteristic
53	C₆₁×#382	C₂²	1	1	yes	characteristic
54	C₆₁×#376	C₂²	1	1	yes	characteristic
55	C₆₁×#336	C₂²	1	1	yes	characteristic
56	C₆₁×#336	C₂²	1	1	yes	characteristic
57	C₆₁×#336	C₂²	1	1	yes	characteristic
58	C₆₁×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₆₁	—	2	2	no	—
61	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₆₁	—	2	1	no	—
65	C₂³×C₄×C₆₁	—	2	1	no	—
66	C₂³×C₄×C₆₁	—	2	1	no	—
67	C₂×SD₁₆×C₆₁	—	2	2	no	—
68	C₂×SD₁₆×C₆₁	—	2	2	no	—
69	C₂×SD₁₆×C₆₁	—	2	2	no	—
70	C₂×SD₁₆×C₆₁	—	2	2	no	—
71	C₂×SD₁₆×C₆₁	—	2	2	no	—
72	C₂×SD₁₆×C₆₁	—	2	2	no	—
73	C₂×D₈×C₆₁	—	2	2	no	—
74	C₂×D₈×C₆₁	—	2	2	no	—
75	C₂×D₈×C₆₁	—	2	2	no	—
76	C₂×D₈×C₆₁	—	2	2	no	—
77	C₂×D₈×C₆₁	—	2	2	no	—
78	C₂×D₈×C₆₁	—	2	2	no	—
79	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
83	#127×C₆₁	—	2	2	no	—
84	#127×C₆₁	—	2	2	no	—
85	#124×C₆₁	—	2	2	no	—
86	#124×C₆₁	—	2	2	no	—
87	C₄×Q₈×C₆₁	—	2	2	no	—
88	C₄×Q₈×C₆₁	—	2	2	no	—
89	C₄×D₄×C₆₁	—	2	2	no	—
90	C₄×D₄×C₆₁	—	2	2	no	—
91	C₄×D₄×C₆₁	—	2	2	no	—
92	C₄×D₄×C₆₁	—	2	2	no	—
93	C₄×D₄×C₆₁	—	2	2	no	—
94	C₄×D₄×C₆₁	—	2	2	no	—
95	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
96	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
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	2	no	—
102	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
106	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
107	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
108	C₂×C₄²×C₆₁	—	2	1	no	—
109	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
112	#107×C₆₁	—	2	2	no	—
113	#107×C₆₁	—	2	2	no	—
114	#106×C₆₁	—	2	2	no	—
115	#106×C₆₁	—	2	2	no	—
116	#103×C₆₁	—	2	2	no	—
117	#103×C₆₁	—	2	2	no	—
118	#102×C₆₁	—	2	2	no	—
119	#102×C₆₁	—	2	2	no	—
120	#102×C₆₁	—	2	2	no	—
121	#102×C₆₁	—	2	2	no	—
122	#102×C₆₁	—	2	2	no	—
123	#102×C₆₁	—	2	2	no	—
124	#97×C₆₁	D₄	1	4	yes	complemented
125	C₄×C₈×C₆₁	D₄	1	4	yes	complemented
126	#95×C₆₁	—	2	2	no	—
127	#95×C₆₁	—	2	2	no	—
128	#95×C₆₁	D₄	1	2	yes	—
129	#95×C₆₁	D₄	1	2	yes	—
130	C₂⁴×C₆₁	—	2	1	no	—
131	C₂⁴×C₆₁	—	2	1	no	—
132	C₂⁴×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	—	2	1	no	—
138	C₂×Q₈×C₆₁	#41	1	2	yes	—
139	C₂×D₄×C₆₁	—	2	8	no	—
140	C₂×D₄×C₆₁	—	2	1	no	—
141	C₂×D₄×C₆₁	—	2	1	no	—
142	C₂×D₄×C₆₁	—	2	1	no	—
143	C₂×D₄×C₆₁	—	2	1	no	—
144	C₂×D₄×C₆₁	—	2	1	no	—
145	C₂×D₄×C₆₁	—	2	1	no	—
146	C₂×D₄×C₆₁	—	2	1	no	—
147	C₂×D₄×C₆₁	—	2	1	no	—
148	C₂×D₄×C₆₁	—	2	1	no	—
149	C₂×D₄×C₆₁	—	2	1	no	—
150	C₂×D₄×C₆₁	—	2	1	no	—
151	C₂×D₄×C₆₁	—	2	1	no	—
152	C₂×D₄×C₆₁	—	2	1	no	—
153	C₂×D₄×C₆₁	—	2	1	no	—
154	C₂×D₄×C₆₁	—	2	1	no	—
155	C₂×D₄×C₆₁	—	8	2	no	—
156	C₂×D₄×C₆₁	—	8	2	no	—
157	C₂×D₄×C₆₁	#41	1	2	yes	—
158	C₂×D₄×C₆₁	#41	1	2	yes	—
159	C₂×D₄×C₆₁	#41	1	2	yes	—
160	C₂²×C₄×C₆₁	—	2	1	no	—
161	C₂²×C₄×C₆₁	—	2	1	no	—
162	C₂²×C₄×C₆₁	—	2	1	no	—
163	C₂²×C₄×C₆₁	—	2	1	no	—
164	C₂²×C₄×C₆₁	—	2	1	no	—
165	C₂²×C₄×C₆₁	—	4	2	no	—
166	C₂²×C₄×C₆₁	—	4	2	no	—
167	C₂²×C₄×C₆₁	—	4	2	no	—
168	C₂²×C₄×C₆₁	—	8	2	no	—
169	C₂²×C₄×C₆₁	—	8	2	no	—
170	C₂²×C₄×C₆₁	—	8	2	no	—
171	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
173	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
176	SD₁₆×C₆₁	—	2	8	no	—
177	SD₁₆×C₆₁	—	2	8	no	—
178	D₈×C₆₁	—	2	8	no	—
179	D₈×C₆₁	—	2	8	no	—
180	C₂×C₈×C₆₁	—	2	1	no	—
181	C₂×C₈×C₆₁	—	2	1	no	—
182	C₂×C₈×C₆₁	—	2	1	no	—
183	C₂×C₈×C₆₁	—	2	1	no	—
184	C₂×C₈×C₆₁	—	2	1	no	—
185	C₂×C₈×C₆₁	—	2	1	no	—
186	C₂×C₈×C₆₁	—	2	1	no	—
187	C₂×C₈×C₆₁	—	2	1	no	—
188	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
189	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
190	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
191	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
192	C₄⋊C₄×C₆₁	—	2	1	no	—
193	C₄⋊C₄×C₆₁	—	2	1	no	—
194	C₄⋊C₄×C₆₁	—	2	1	no	—
195	C₄⋊C₄×C₆₁	—	2	1	no	—
196	C₄⋊C₄×C₆₁	—	2	1	no	—
197	C₄⋊C₄×C₆₁	—	2	1	no	—
198	C₄⋊C₄×C₆₁	—	2	1	no	—
199	C₄⋊C₄×C₆₁	—	2	1	no	—
200	C₄⋊C₄×C₆₁	—	4	2	no	—
201	C₄⋊C₄×C₆₁	—	8	2	no	—
202	C₂²⋊C₄×C₆₁	—	2	8	no	—
203	C₂²⋊C₄×C₆₁	—	4	2	no	—
204	C₂²⋊C₄×C₆₁	—	4	2	no	—
205	C₂²⋊C₄×C₆₁	—	4	2	no	—
206	C₂²⋊C₄×C₆₁	—	8	2	no	—
207	C₂²⋊C₄×C₆₁	—	8	2	no	—
208	C₂²⋊C₄×C₆₁	—	8	2	no	—
209	C₄²×C₆₁	—	2	1	no	—
210	C₄²×C₆₁	—	2	1	no	—
211	C₄²×C₆₁	—	2	1	no	—
212	C₄²×C₆₁	—	2	1	no	—
213	C₄²×C₆₁	—	4	2	no	—
214	C₄²×C₆₁	C₂×D₄	1	2	yes	—
215	C₄²×C₆₁	C₂×D₄	1	2	yes	—
216	C₂³×C₆₁	—	2	2	no	—
217	C₂³×C₆₁	—	2	2	no	—
218	C₂³×C₆₁	—	2	2	no	—
219	C₂³×C₆₁	—	4	1	no	—
220	C₂³×C₆₁	—	4	1	no	—
221	C₂³×C₆₁	—	4	1	no	—
222	C₂³×C₆₁	—	4	1	no	—
223	C₂³×C₆₁	—	4	1	no	—
224	C₂³×C₆₁	—	4	1	no	—
225	C₂³×C₆₁	—	4	2	no	—
226	C₂³×C₆₁	—	4	2	no	—
227	C₂³×C₆₁	—	4	2	no	—
228	C₂³×C₆₁	—	4	2	no	—
229	C₂³×C₆₁	—	4	2	no	—
230	C₂³×C₆₁	—	4	2	no	—
231	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
232	Q₈×C₆₁	—	2	2	no	—
233	Q₈×C₆₁	—	2	2	no	—
234	Q₈×C₆₁	—	4	1	no	—
235	Q₈×C₆₁	—	4	1	no	—
236	D₄×C₆₁	—	2	2	no	—
237	D₄×C₆₁	—	2	2	no	—
238	D₄×C₆₁	—	2	2	no	—
239	D₄×C₆₁	—	2	2	no	—
240	D₄×C₆₁	—	2	2	no	—
241	D₄×C₆₁	—	2	2	no	—
242	D₄×C₆₁	—	4	1	no	—
243	D₄×C₆₁	—	4	1	no	—
244	D₄×C₆₁	—	4	1	no	—
245	D₄×C₆₁	—	4	1	no	—
246	D₄×C₆₁	—	4	1	no	—
247	D₄×C₆₁	—	4	1	no	—
248	D₄×C₆₁	—	8	8	no	—
249	C₂×C₄×C₆₁	—	2	2	no	—
250	C₂×C₄×C₆₁	—	2	2	no	—
251	C₂×C₄×C₆₁	—	2	2	no	—
252	C₂×C₄×C₆₁	—	2	2	no	—
253	C₂×C₄×C₆₁	—	2	2	no	—
254	C₂×C₄×C₆₁	—	2	2	no	—
255	C₂×C₄×C₆₁	—	2	2	no	—
256	C₂×C₄×C₆₁	—	2	2	no	—
257	C₂×C₄×C₆₁	—	2	2	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	2	no	—
265	C₂×C₄×C₆₁	—	4	2	no	—
266	C₂×C₄×C₆₁	—	4	2	no	—
267	C₂×C₄×C₆₁	—	4	2	no	—
268	C₂×C₄×C₆₁	—	8	4	no	—
269	C₂×C₄×C₆₁	—	8	4	no	—
270	C₂×C₄×C₆₁	—	8	4	no	—
271	C₂×C₄×C₆₁	#127	1	2	yes	—
272	C₂×C₄×C₆₁	#127	1	2	yes	—
273	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
276	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
277	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
278	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
279	C₈×C₆₁	—	2	2	no	—
280	C₈×C₆₁	—	2	2	no	—
281	C₈×C₆₁	—	2	2	no	—
282	C₈×C₆₁	—	2	2	no	—
283	#23808	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
284	C₂²×C₆₁	—	4	4	no	—
285	C₂²×C₆₁	—	4	4	no	—
286	C₂²×C₆₁	—	4	4	no	—
287	C₂²×C₆₁	—	4	2	no	—
288	C₂²×C₆₁	—	4	2	no	—
289	C₂²×C₆₁	—	4	2	no	—
290	C₂²×C₆₁	—	8	2	no	—
291	C₂²×C₆₁	—	8	2	no	—
292	C₂²×C₆₁	—	8	2	no	—
293	C₂²×C₆₁	—	8	1	no	—
294	C₂²×C₆₁	—	8	1	no	—
295	C₂²×C₆₁	—	8	1	no	—
296	C₂²×C₆₁	—	8	1	no	—
297	C₂²×C₆₁	—	8	1	no	—
298	C₂²×C₆₁	—	8	1	no	—
299	C₂²×C₆₁	#525	1	1	yes	characteristic
300	C₂²×C₆₁	#525	1	1	yes	characteristic
301	C₂²×C₆₁	C₂×#127	1	1	yes	characteristic
302	C₂²×C₆₁	#576	1	2	yes	—
303	C₂²×C₆₁	#577	1	2	yes	—
304	C₄×C₆₁	—	2	2	no	—
305	C₄×C₆₁	—	2	2	no	—
306	C₄×C₆₁	—	4	2	no	—
307	C₄×C₆₁	—	4	2	no	—
308	C₄×C₆₁	—	4	2	no	—
309	C₄×C₆₁	—	8	1	no	—
310	C₄×C₆₁	—	8	1	no	—
311	C₄×C₆₁	—	8	1	no	—
312	C₄×C₆₁	—	8	1	no	—
313	C₄×C₆₁	#525	1	1	yes	characteristic
314	C₄×C₆₁	#525	1	1	yes	characteristic
315	C₄×C₆₁	#525	1	1	yes	characteristic
316	C₄×C₆₁	#525	1	1	yes	characteristic
317	C₂×#442	C₂×C₆₁	1	1	yes	characteristic, complemented
318	C₂×#440	C₂×C₆₁	1	1	yes	characteristic, complemented
319	C₂×C₄×SD₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
320	C₂×C₄×D₈	C₂×C₆₁	1	1	yes	characteristic, complemented
321	#2328	C₂×C₆₁	1	1	yes	characteristic, complemented
322	#2326	C₂×C₆₁	1	1	yes	characteristic, complemented
323	#2097	C₂×C₆₁	1	1	yes	characteristic, complemented
324	#2094	C₂×C₆₁	1	1	yes	characteristic, complemented
325	#2093	C₂×C₆₁	1	1	yes	characteristic, complemented
326	#2092	C₂×C₆₁	1	1	yes	characteristic, complemented
327	#2014	C₂×C₆₁	1	1	yes	characteristic, complemented
328	#2012	C₂×C₆₁	1	1	yes	characteristic, complemented
329	#2012	C₂×C₆₁	1	1	yes	characteristic, complemented
330	#2011	C₂×C₆₁	1	1	yes	characteristic
331	#1746	C₂×C₆₁	1	1	yes	characteristic, complemented
332	C₂×C₆₁	—	8	2	no	—
333	C₂×C₆₁	—	8	2	no	—
334	C₂×C₆₁	—	8	2	no	—
335	C₂×C₆₁	#2397	1	1	yes	characteristic
336	C₂×C₆₁	#3118	1	2	yes	—
337	C₂×C₆₁	#3119	1	2	yes	—
338	C₂×C₆₁	#3154	1	1	yes	characteristic
339	C₂×C₆₁	#3155	1	1	yes	characteristic
340	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
341	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
342	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
343	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
344	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
345	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
346	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
347	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
348	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
349	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
350	#442	—	2	4	no	—
351	#440	—	2	4	no	—
352	C₄×SD₁₆	—	2	4	no	—
353	C₄×D₈	—	2	4	no	—
354	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
355	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
356	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
357	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
358	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
359	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
360	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
361	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
362	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
363	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
364	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
365	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
366	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
367	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
368	#391	C₂²×C₆₁	1	1	yes	characteristic
369	#390	C₂²×C₆₁	1	1	yes	characteristic
370	#390	C₂²×C₆₁	1	1	yes	characteristic
371	#390	C₂²×C₆₁	1	1	yes	characteristic
372	#388	—	2	2	no	—
373	#386	—	2	2	no	—
374	#386	—	2	2	no	—
375	#385	—	2	2	no	—
376	#384	C₂²×C₆₁	1	1	yes	characteristic
377	#382	C₂²×C₆₁	1	1	yes	characteristic
378	#376	C₂²×C₆₁	1	1	yes	characteristic
379	#336	C₂²×C₆₁	1	1	yes	characteristic
380	#336	C₂²×C₆₁	1	1	yes	characteristic
381	#336	C₂²×C₆₁	1	1	yes	characteristic
382	#336	C₂²×C₆₁	1	1	yes	characteristic
383	C₆₁	#23808	1	1	yes	characteristic, direct product factor, Sylow
384	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
385	C₂²×D₄	—	2	2	no	—
386	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
387	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
388	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
389	C₂³×C₄	—	2	1	no	—
390	C₂³×C₄	—	2	1	no	—
391	C₂³×C₄	—	2	1	no	—
392	C₂×SD₁₆	—	2	2	no	—
393	C₂×SD₁₆	—	2	2	no	—
394	C₂×SD₁₆	—	2	2	no	—
395	C₂×SD₁₆	—	2	2	no	—
396	C₂×SD₁₆	—	2	2	no	—
397	C₂×SD₁₆	—	2	2	no	—
398	C₂×D₈	—	2	2	no	—
399	C₂×D₈	—	2	2	no	—
400	C₂×D₈	—	2	2	no	—
401	C₂×D₈	—	2	2	no	—
402	C₂×D₈	—	2	2	no	—
403	C₂×D₈	—	2	2	no	—
404	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
405	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
406	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
407	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
408	#127	—	2	2	no	—
409	#127	—	2	2	no	—
410	#124	—	2	2	no	—
411	#124	—	2	2	no	—
412	C₄×Q₈	—	2	2	no	—
413	C₄×Q₈	—	2	2	no	—
414	C₄×D₄	—	2	2	no	—
415	C₄×D₄	—	2	2	no	—
416	C₄×D₄	—	2	2	no	—
417	C₄×D₄	—	2	2	no	—
418	C₄×D₄	—	2	2	no	—
419	C₄×D₄	—	2	2	no	—
420	C₂×C₄⋊C₄	—	2	1	no	—
421	C₂×C₄⋊C₄	—	2	2	no	—
422	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
426	C₂×C₂²⋊C₄	—	2	2	no	—
427	C₂×C₂²⋊C₄	—	2	1	no	—
428	C₂×C₂²⋊C₄	—	2	1	no	—
429	C₂×C₂²⋊C₄	—	2	1	no	—
430	C₂×C₂²⋊C₄	—	2	2	no	—
431	C₂×C₂²⋊C₄	—	2	2	no	—
432	C₂×C₂²⋊C₄	—	2	2	no	—
433	C₂×C₄²	—	2	1	no	—
434	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
435	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
436	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
437	#107	—	2	2	no	—
438	#107	—	2	2	no	—
439	#106	—	2	2	no	—
440	#106	—	2	2	no	—
441	#103	—	2	2	no	—
442	#103	—	2	2	no	—
443	#102	—	2	2	no	—
444	#102	—	2	2	no	—
445	#102	—	2	2	no	—
446	#102	—	2	2	no	—
447	#102	—	2	2	no	—
448	#102	—	2	2	no	—
449	#97	D₄×C₆₁	1	4	yes	complemented
450	C₄×C₈	D₄×C₆₁	1	4	yes	complemented
451	#95	—	2	2	no	—
452	#95	—	2	2	no	—
453	#95	D₄×C₆₁	1	2	yes	—
454	#95	D₄×C₆₁	1	2	yes	—
455	C₂⁴	—	2	1	no	—
456	C₂⁴	—	2	1	no	—
457	C₂⁴	—	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	#41×C₆₁	1	2	yes	—
464	C₂×D₄	—	2	8	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	2	1	no	—
474	C₂×D₄	—	2	1	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	—	8	2	no	—
481	C₂×D₄	—	8	2	no	—
482	C₂×D₄	#41×C₆₁	1	2	yes	—
483	C₂×D₄	#41×C₆₁	1	2	yes	—
484	C₂×D₄	#41×C₆₁	1	2	yes	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	4	2	no	—
491	C₂²×C₄	—	4	2	no	—
492	C₂²×C₄	—	4	2	no	—
493	C₂²×C₄	—	8	2	no	—
494	C₂²×C₄	—	8	2	no	—
495	C₂²×C₄	—	8	2	no	—
496	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
497	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
498	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
499	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
500	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
501	SD₁₆	—	2	8	no	—
502	SD₁₆	—	2	8	no	—
503	D₈	—	2	8	no	—
504	D₈	—	2	8	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
514	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
515	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
516	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	4	2	no	—
526	C₄⋊C₄	—	8	2	no	—
527	C₂²⋊C₄	—	2	8	no	—
528	C₂²⋊C₄	—	4	2	no	—
529	C₂²⋊C₄	—	4	2	no	—
530	C₂²⋊C₄	—	4	2	no	—
531	C₂²⋊C₄	—	8	2	no	—
532	C₂²⋊C₄	—	8	2	no	—
533	C₂²⋊C₄	—	8	2	no	—
534	C₄²	—	2	1	no	—
535	C₄²	—	2	1	no	—
536	C₄²	—	2	1	no	—
537	C₄²	—	2	1	no	—
538	C₄²	—	4	2	no	—
539	C₄²	C₂×D₄×C₆₁	1	2	yes	—
540	C₄²	C₂×D₄×C₆₁	1	2	yes	—
541	C₂³	—	2	2	no	—
542	C₂³	—	2	2	no	—
543	C₂³	—	2	2	no	—
544	C₂³	—	4	1	no	—
545	C₂³	—	4	1	no	—
546	C₂³	—	4	1	no	—
547	C₂³	—	4	2	no	—
548	C₂³	—	4	2	no	—
549	C₂³	—	4	2	no	—
550	C₂³	—	4	2	no	—
551	C₂³	—	4	2	no	—
552	C₂³	—	4	2	no	—
553	C₂³	—	4	1	no	—
554	C₂³	—	4	1	no	—
555	C₂³	—	4	1	no	—
556	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
557	Q₈	—	2	2	no	—
558	Q₈	—	2	2	no	—
559	Q₈	—	4	1	no	—
560	Q₈	—	4	1	no	—
561	D₄	—	2	2	no	—
562	D₄	—	2	2	no	—
563	D₄	—	2	2	no	—
564	D₄	—	2	2	no	—
565	D₄	—	2	2	no	—
566	D₄	—	2	2	no	—
567	D₄	—	4	1	no	—
568	D₄	—	4	1	no	—
569	D₄	—	4	1	no	—
570	D₄	—	4	1	no	—
571	D₄	—	4	1	no	—
572	D₄	—	4	1	no	—
573	D₄	—	8	8	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	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	2	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	2	no	—
592	C₂×C₄	—	4	2	no	—
593	C₂×C₄	—	8	4	no	—
594	C₂×C₄	—	8	4	no	—
595	C₂×C₄	—	8	4	no	—
596	C₂×C₄	#127×C₆₁	1	2	yes	—
597	C₂×C₄	#127×C₆₁	1	2	yes	—
598	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
599	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
600	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
601	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
602	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
603	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
604	C₈	—	2	2	no	—
605	C₈	—	2	2	no	—
606	C₈	—	2	2	no	—
607	C₈	—	2	2	no	—
608	C₂²	—	4	4	no	—
609	C₂²	—	4	4	no	—
610	C₂²	—	4	4	no	—
611	C₂²	—	4	2	no	—
612	C₂²	—	4	2	no	—
613	C₂²	—	4	2	no	—
614	C₂²	—	8	2	no	—
615	C₂²	—	8	2	no	—
616	C₂²	—	8	2	no	—
617	C₂²	—	8	1	no	—
618	C₂²	—	8	1	no	—
619	C₂²	—	8	1	no	—
620	C₂²	—	8	1	no	—
621	C₂²	—	8	1	no	—
622	C₂²	—	8	1	no	—
623	C₂²	C₆₁×#525	1	1	yes	characteristic
624	C₂²	C₆₁×#525	1	1	yes	characteristic
625	C₂²	C₂×#127×C₆₁	1	1	yes	characteristic
626	C₂²	C₆₁×#576	1	2	yes	—
627	C₂²	C₆₁×#577	1	2	yes	—
628	C₄	—	2	2	no	—
629	C₄	—	2	2	no	—
630	C₄	—	4	2	no	—
631	C₄	—	4	2	no	—
632	C₄	—	4	2	no	—
633	C₄	—	8	1	no	—
634	C₄	—	8	1	no	—
635	C₄	—	8	1	no	—
636	C₄	—	8	1	no	—
637	C₄	C₆₁×#525	1	1	yes	characteristic
638	C₄	C₆₁×#525	1	1	yes	characteristic
639	C₄	C₆₁×#525	1	1	yes	characteristic
640	C₄	C₆₁×#525	1	1	yes	characteristic
641	C₂	—	8	2	no	—
642	C₂	—	8	2	no	—
643	C₂	—	8	2	no	—
644	C₂	C₆₁×#2397	1	1	yes	characteristic
645	C₂	C₆₁×#3118	1	2	yes	—
646	C₂	C₆₁×#3119	1	2	yes	—
647	C₂	C₆₁×#3154	1	1	yes	characteristic
648	C₂	C₆₁×#3155	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₆₁×#2011	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₆₁×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#442	C₂	semidirect
2. C₂×C₆₁×#440	C₂	semidirect
3. C₂×C₄×SD₁₆×C₆₁	C₂	semidirect
4. C₂×C₄×D₈×C₆₁	C₂	semidirect
5. C₆₁×#2328	C₂	semidirect
6. C₆₁×#2326	C₂	semidirect
7. C₆₁×#2097	C₂	semidirect
8. C₆₁×#2094	C₂	semidirect
9. C₆₁×#2093	C₂	semidirect
10. C₆₁×#2092	C₂	semidirect
11. C₆₁×#2014	C₂	semidirect
12. C₆₁×#2012	C₂	semidirect
13. C₆₁×#2012	C₂	semidirect
15. C₆₁×#1746	C₂	semidirect
124. #97×C₆₁	D₄	semidirect
125. C₄×C₈×C₆₁	D₄	semidirect
283. #23808	C₆₁	direct (N × H)
317. C₂×#442	C₂×C₆₁	semidirect
318. C₂×#440	C₂×C₆₁	semidirect
319. C₂×C₄×SD₁₆	C₂×C₆₁	semidirect
320. C₂×C₄×D₈	C₂×C₆₁	semidirect
321. #2328	C₂×C₆₁	semidirect
322. #2326	C₂×C₆₁	semidirect
323. #2097	C₂×C₆₁	semidirect
324. #2094	C₂×C₆₁	semidirect
325. #2093	C₂×C₆₁	semidirect
326. #2092	C₂×C₆₁	semidirect
327. #2014	C₂×C₆₁	semidirect
328. #2012	C₂×C₆₁	semidirect
329. #2012	C₂×C₆₁	semidirect
331. #1746	C₂×C₆₁	semidirect
383. C₆₁	#23808	direct (N × H)
449. #97	D₄×C₆₁	semidirect
450. C₄×C₈	D₄×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#442	2
C₂×C₆₁×#440	2
C₂×C₄×SD₁₆×C₆₁	2
C₂×C₄×D₈×C₆₁	2
C₆₁×#2328	2
C₆₁×#2326	2
C₆₁×#2097	2
C₆₁×#2094	2
C₆₁×#2093	2
C₆₁×#2092	2
C₆₁×#2014	2
C₆₁×#2012	2
C₆₁×#2011	2
C₆₁×#1746	2
#23808	61

Subgroups — C61×#23808 #29527241

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#23808 #29527241