Subgroups — C₆₁×#22999 #29526432

Order 15616.

1034 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#463	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×SD₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×D₈×C₆₁	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2367	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2349	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#1958	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1949	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1934	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1933	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1879	C₂	1	1	yes	maximal, characteristic
11	C₆₁×#1877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#1864	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#1863	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×C₄⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#102×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
17	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
24	C₆₁×#463	C₄	1	8	yes	complemented
25	C₄×SD₁₆×C₆₁	—	2	4	no	—
26	C₄×D₈×C₆₁	—	2	4	no	—
27	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×#106×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×#102×C₆₁	C₂²	1	1	yes	characteristic
34	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
35	C₂×#102×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×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
41	C₆₁×#391	C₂²	1	1	yes	characteristic
42	C₆₁×#390	C₂²	1	1	yes	characteristic
43	C₆₁×#389	C₂²	1	1	yes	characteristic
44	C₆₁×#389	C₂²	1	1	yes	characteristic
45	C₆₁×#388	—	2	1	no	—
46	C₆₁×#388	—	2	1	no	—
47	C₆₁×#385	—	2	1	no	—
48	C₆₁×#385	—	2	1	no	—
49	C₆₁×#385	—	2	1	no	—
50	C₆₁×#382	C₂²	1	1	yes	characteristic
51	C₆₁×#380	—	2	1	no	—
52	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
53	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊C₄×C₆₁	—	2	1	no	—
55	C₂×#95×C₆₁	—	2	1	no	—
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×#340	C₂²	1	1	yes	characteristic
60	C₆₁×#336	C₂²	1	1	yes	characteristic
61	C₆₁×#336	C₂²	1	1	yes	characteristic
62	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₆₁	—	2	1	no	—
66	C₂³×C₄×C₆₁	—	2	1	no	—
67	C₂³×C₄×C₆₁	—	2	1	no	—
68	C₂³×C₄×C₆₁	—	2	1	no	—
69	C₂×SD₁₆×C₆₁	—	2	2	no	—
70	C₂×SD₁₆×C₆₁	—	2	2	no	—
71	C₂×SD₁₆×C₆₁	C₂×C₄	1	4	yes	complemented
72	C₂×D₈×C₆₁	—	2	2	no	—
73	C₂×D₈×C₆₁	—	2	2	no	—
74	C₂×D₈×C₆₁	C₂×C₄	1	4	yes	—
75	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
79	#124×C₆₁	—	2	2	no	—
80	#124×C₆₁	C₂×C₄	1	4	yes	complemented
81	C₄×Q₈×C₆₁	—	2	2	no	—
82	C₄×Q₈×C₆₁	—	4	1	no	—
83	C₄×D₄×C₆₁	—	2	2	no	—
84	C₄×D₄×C₆₁	—	2	2	no	—
85	C₄×D₄×C₆₁	—	2	2	no	—
86	C₄×D₄×C₆₁	—	2	2	no	—
87	C₄×D₄×C₆₁	—	4	1	no	—
88	C₄×D₄×C₆₁	—	4	1	no	—
89	C₄×D₄×C₆₁	—	4	1	no	—
90	C₄×D₄×C₆₁	C₂×C₄	1	4	yes	complemented
91	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
92	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
93	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
94	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
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	1	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	1	no	—
106	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
109	C₂×C₄²×C₆₁	—	2	1	no	—
110	C₂×C₄²×C₆₁	—	2	1	no	—
111	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
114	#107×C₆₁	—	2	2	no	—
115	#106×C₆₁	—	2	2	no	—
116	C₄⋊C₈×C₆₁	C₂×C₄	1	4	yes	complemented
117	#103×C₆₁	—	2	2	no	—
118	#103×C₆₁	—	4	1	no	—
119	#103×C₆₁	C₂×C₄	1	4	yes	complemented
120	#102×C₆₁	—	2	2	no	—
121	#102×C₆₁	—	2	2	no	—
122	#102×C₆₁	—	4	1	no	—
123	#102×C₆₁	C₂×C₄	1	4	yes	complemented
124	#102×C₆₁	D₄	1	4	yes	—
125	C₄×C₈×C₆₁	—	2	2	no	—
126	C₄×C₈×C₆₁	—	2	2	no	—
127	C₄×C₈×C₆₁	—	2	2	no	—
128	#95×C₆₁	—	2	1	no	—
129	#95×C₆₁	—	2	1	no	—
130	#95×C₆₁	—	2	1	no	—
131	#95×C₆₁	—	2	1	no	—
132	#95×C₆₁	—	2	1	no	—
133	#95×C₆₁	—	2	1	no	—
134	#95×C₆₁	—	2	1	no	—
135	#95×C₆₁	D₄	1	1	yes	characteristic
136	#95×C₆₁	D₄	1	1	yes	characteristic
137	C₂⁴×C₆₁	—	2	1	no	—
138	C₂⁴×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	C₂²×C₄	1	2	yes	—
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	C₂²×C₄	1	2	yes	—
154	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
155	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
156	C₂×D₄×C₆₁	#41	1	2	yes	—
157	C₂²×C₄×C₆₁	—	2	1	no	—
158	C₂²×C₄×C₆₁	—	2	1	no	—
159	C₂²×C₄×C₆₁	—	2	1	no	—
160	C₂²×C₄×C₆₁	—	2	4	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	—	4	2	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	—	4	2	no	—
169	C₂²×C₄×C₆₁	—	4	2	no	—
170	C₂²×C₄×C₆₁	—	8	1	no	—
171	C₂²×C₄×C₆₁	—	8	1	no	—
172	C₂²×C₄×C₆₁	—	8	1	no	—
173	C₂²×C₄×C₆₁	—	8	1	no	—
174	C₂²×C₄×C₆₁	—	8	1	no	—
175	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
182	SD₁₆×C₆₁	—	2	8	no	—
183	D₈×C₆₁	—	2	8	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	—	2	1	no	—
189	C₂×C₈×C₆₁	—	2	1	no	—
190	C₂×C₈×C₆₁	—	2	1	no	—
191	C₂×C₈×C₆₁	—	2	1	no	—
192	C₂×C₈×C₆₁	—	2	1	no	—
193	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
194	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
195	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
196	C₄⋊C₄×C₆₁	—	2	2	no	—
197	C₄⋊C₄×C₆₁	—	2	2	no	—
198	C₄⋊C₄×C₆₁	—	2	1	no	—
199	C₄⋊C₄×C₆₁	—	2	1	no	—
200	C₄⋊C₄×C₆₁	—	2	1	no	—
201	C₄⋊C₄×C₆₁	—	2	1	no	—
202	C₄⋊C₄×C₆₁	—	2	1	no	—
203	C₄⋊C₄×C₆₁	—	2	1	no	—
204	C₄⋊C₄×C₆₁	—	2	1	no	—
205	C₄⋊C₄×C₆₁	—	2	1	no	—
206	C₄⋊C₄×C₆₁	—	4	2	no	—
207	C₄⋊C₄×C₆₁	—	8	1	no	—
208	C₄⋊C₄×C₆₁	—	8	1	no	—
209	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
210	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
211	C₂²⋊C₄×C₆₁	—	2	4	no	—
212	C₂²⋊C₄×C₆₁	—	2	4	no	—
213	C₂²⋊C₄×C₆₁	—	2	4	no	—
214	C₂²⋊C₄×C₆₁	—	4	2	no	—
215	C₂²⋊C₄×C₆₁	—	4	2	no	—
216	C₂²⋊C₄×C₆₁	—	4	2	no	—
217	C₂²⋊C₄×C₆₁	—	4	2	no	—
218	C₂²⋊C₄×C₆₁	—	8	1	no	—
219	C₄²×C₆₁	—	2	1	no	—
220	C₄²×C₆₁	—	2	1	no	—
221	C₄²×C₆₁	—	2	1	no	—
222	C₄²×C₆₁	—	2	1	no	—
223	C₄²×C₆₁	—	4	2	no	—
224	C₄²×C₆₁	—	8	1	no	—
225	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
226	C₄²×C₆₁	#41	1	2	yes	—
227	C₂³×C₆₁	—	2	2	no	—
228	C₂³×C₆₁	—	2	2	no	—
229	C₂³×C₆₁	—	2	2	no	—
230	C₂³×C₆₁	—	2	2	no	—
231	C₂³×C₆₁	—	4	1	no	—
232	C₂³×C₆₁	—	4	1	no	—
233	C₂³×C₆₁	—	4	1	no	—
234	C₂³×C₆₁	—	4	1	no	—
235	C₂³×C₆₁	—	4	1	no	—
236	C₂³×C₆₁	—	4	1	no	—
237	C₂³×C₆₁	—	4	1	no	—
238	C₂³×C₆₁	—	4	1	no	—
239	C₂³×C₆₁	—	4	1	no	—
240	C₂³×C₆₁	—	4	1	no	—
241	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
242	Q₈×C₆₁	—	2	2	no	—
243	Q₈×C₆₁	—	2	2	no	—
244	Q₈×C₆₁	—	4	1	no	—
245	Q₈×C₆₁	—	4	1	no	—
246	D₄×C₆₁	—	2	2	no	—
247	D₄×C₆₁	—	2	2	no	—
248	D₄×C₆₁	—	2	2	no	—
249	D₄×C₆₁	—	2	2	no	—
250	D₄×C₆₁	—	2	2	no	—
251	D₄×C₆₁	—	4	1	no	—
252	D₄×C₆₁	—	4	1	no	—
253	D₄×C₆₁	C₄×D₄	1	4	yes	—
254	C₂×C₄×C₆₁	—	2	1	no	—
255	C₂×C₄×C₆₁	—	2	1	no	—
256	C₂×C₄×C₆₁	—	2	1	no	—
257	C₂×C₄×C₆₁	—	2	1	no	—
258	C₂×C₄×C₆₁	—	2	1	no	—
259	C₂×C₄×C₆₁	—	2	1	no	—
260	C₂×C₄×C₆₁	—	2	1	no	—
261	C₂×C₄×C₆₁	—	2	1	no	—
262	C₂×C₄×C₆₁	—	2	2	no	—
263	C₂×C₄×C₆₁	—	2	2	no	—
264	C₂×C₄×C₆₁	—	2	1	no	—
265	C₂×C₄×C₆₁	—	2	1	no	—
266	C₂×C₄×C₆₁	—	2	2	no	—
267	C₂×C₄×C₆₁	—	2	1	no	—
268	C₂×C₄×C₆₁	—	2	1	no	—
269	C₂×C₄×C₆₁	—	2	1	no	—
270	C₂×C₄×C₆₁	—	2	1	no	—
271	C₂×C₄×C₆₁	—	4	1	no	—
272	C₂×C₄×C₆₁	—	4	1	no	—
273	C₂×C₄×C₆₁	—	4	1	no	—
274	C₂×C₄×C₆₁	—	4	1	no	—
275	C₂×C₄×C₆₁	—	4	1	no	—
276	C₂×C₄×C₆₁	—	4	1	no	—
277	C₂×C₄×C₆₁	—	4	1	no	—
278	C₂×C₄×C₆₁	—	4	1	no	—
279	C₂×C₄×C₆₁	—	4	1	no	—
280	C₂×C₄×C₆₁	—	4	1	no	—
281	C₂×C₄×C₆₁	—	4	1	no	—
282	C₂×C₄×C₆₁	—	4	1	no	—
283	C₂×C₄×C₆₁	—	4	1	no	—
284	C₂×C₄×C₆₁	—	4	1	no	—
285	C₂×C₄×C₆₁	—	4	1	no	—
286	C₂×C₄×C₆₁	—	8	4	no	—
287	C₂×C₄×C₆₁	—	8	4	no	—
288	C₂×C₄×C₆₁	—	8	4	no	—
289	C₂×C₄×C₆₁	—	8	4	no	—
290	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
291	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
292	C₂×C₄×C₆₁	#135	1	2	yes	—
293	C₂×C₄×C₆₁	#135	1	2	yes	—
294	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
295	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
296	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
297	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
298	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
299	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
300	C₈×C₆₁	—	2	2	no	—
301	C₈×C₆₁	—	2	2	no	—
302	C₈×C₆₁	—	2	2	no	—
303	C₈×C₆₁	—	4	1	no	—
304	#22999	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
305	C₂²×C₆₁	—	2	4	no	—
306	C₂²×C₆₁	—	4	2	no	—
307	C₂²×C₆₁	—	4	2	no	—
308	C₂²×C₆₁	—	4	2	no	—
309	C₂²×C₆₁	—	4	2	no	—
310	C₂²×C₆₁	—	4	2	no	—
311	C₂²×C₆₁	—	4	2	no	—
312	C₂²×C₆₁	—	4	2	no	—
313	C₂²×C₆₁	—	4	2	no	—
314	C₂²×C₆₁	—	4	2	no	—
315	C₂²×C₆₁	—	8	1	no	—
316	C₂²×C₆₁	—	8	1	no	—
317	C₂²×C₆₁	—	8	1	no	—
318	C₂²×C₆₁	—	8	1	no	—
319	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
320	C₂²×C₆₁	D₄²	1	1	yes	characteristic
321	C₂²×C₆₁	#548	1	1	yes	characteristic
322	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
323	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
324	C₂²×C₆₁	#576	1	1	yes	characteristic
325	C₂²×C₆₁	#577	1	1	yes	characteristic
326	C₄×C₆₁	—	2	2	no	—
327	C₄×C₆₁	—	2	2	no	—
328	C₄×C₆₁	—	2	2	no	—
329	C₄×C₆₁	—	2	2	no	—
330	C₄×C₆₁	—	4	2	no	—
331	C₄×C₆₁	—	4	2	no	—
332	C₄×C₆₁	—	4	1	no	—
333	C₄×C₆₁	—	4	2	no	—
334	C₄×C₆₁	—	4	1	no	—
335	C₄×C₆₁	—	8	1	no	—
336	C₄×C₆₁	—	8	1	no	—
337	C₄×C₆₁	—	8	1	no	—
338	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
339	C₄×C₆₁	#520	1	1	yes	characteristic
340	C₄×C₆₁	#547	1	1	yes	characteristic
341	C₄×C₆₁	#553	1	1	yes	characteristic
342	C₂×#463	C₂×C₆₁	1	1	yes	characteristic
343	C₂×C₄×SD₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
344	C₂×C₄×D₈	C₂×C₆₁	1	1	yes	characteristic
345	#2367	C₂×C₆₁	1	1	yes	characteristic, complemented
346	#2349	C₂×C₆₁	1	1	yes	characteristic, complemented
347	#1958	C₂×C₆₁	1	1	yes	characteristic, complemented
348	#1949	C₂×C₆₁	1	1	yes	characteristic, complemented
349	#1934	C₂×C₆₁	1	1	yes	characteristic, complemented
350	#1933	C₂×C₆₁	1	1	yes	characteristic, complemented
351	#1879	C₂×C₆₁	1	1	yes	characteristic
352	#1877	C₂×C₆₁	1	1	yes	characteristic, complemented
353	#1864	C₂×C₆₁	1	1	yes	characteristic, complemented
354	#1863	C₂×C₆₁	1	1	yes	characteristic, complemented
355	C₈×C₄⋊C₄	C₂×C₆₁	1	1	yes	characteristic, complemented
356	C₄×#102	C₂×C₆₁	1	1	yes	characteristic, complemented
357	C₂×C₆₁	—	4	4	no	—
358	C₂×C₆₁	—	8	2	no	—
359	C₂×C₆₁	#2361	1	1	yes	characteristic
360	C₂×C₆₁	C₄×#135	1	1	yes	characteristic
361	C₂×C₆₁	#2946	1	1	yes	characteristic
362	C₂×C₆₁	#3280	1	1	yes	characteristic
363	C₂×C₆₁	#3282	1	1	yes	characteristic
364	C₂×C₆₁	#3360	1	1	yes	characteristic
365	C₂×C₆₁	#3361	1	1	yes	characteristic
366	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
367	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
368	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
369	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
370	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
371	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
372	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
373	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
374	#463	C₄×C₆₁	1	8	yes	complemented
375	C₄×SD₁₆	—	2	4	no	—
376	C₄×D₈	—	2	4	no	—
377	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
378	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
379	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
380	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
381	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
382	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
383	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
384	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
385	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
386	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
387	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
388	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
389	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
390	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
391	#391	C₂²×C₆₁	1	1	yes	characteristic
392	#390	C₂²×C₆₁	1	1	yes	characteristic
393	#389	C₂²×C₆₁	1	1	yes	characteristic
394	#389	C₂²×C₆₁	1	1	yes	characteristic
395	#388	—	2	1	no	—
396	#388	—	2	1	no	—
397	#385	—	2	1	no	—
398	#385	—	2	1	no	—
399	#385	—	2	1	no	—
400	#382	C₂²×C₆₁	1	1	yes	characteristic
401	#380	—	2	1	no	—
402	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
403	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
404	C₄×C₂²⋊C₄	—	2	1	no	—
405	C₂×#95	—	2	1	no	—
406	#340	C₂²×C₆₁	1	1	yes	characteristic
407	#340	C₂²×C₆₁	1	1	yes	characteristic
408	#340	C₂²×C₆₁	1	1	yes	characteristic
409	#340	C₂²×C₆₁	1	1	yes	characteristic
410	#336	C₂²×C₆₁	1	1	yes	characteristic
411	#336	C₂²×C₆₁	1	1	yes	characteristic
412	C₆₁	#22999	1	1	yes	characteristic, direct product factor, Sylow
413	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
414	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
415	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
416	C₂³×C₄	—	2	1	no	—
417	C₂³×C₄	—	2	1	no	—
418	C₂³×C₄	—	2	1	no	—
419	C₂³×C₄	—	2	1	no	—
420	C₂×SD₁₆	—	2	2	no	—
421	C₂×SD₁₆	—	2	2	no	—
422	C₂×SD₁₆	C₂×C₄×C₆₁	1	4	yes	complemented
423	C₂×D₈	—	2	2	no	—
424	C₂×D₈	—	2	2	no	—
425	C₂×D₈	C₂×C₄×C₆₁	1	4	yes	—
426	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
427	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
428	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
429	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
430	#124	—	2	2	no	—
431	#124	C₂×C₄×C₆₁	1	4	yes	complemented
432	C₄×Q₈	—	2	2	no	—
433	C₄×Q₈	—	4	1	no	—
434	C₄×D₄	—	2	2	no	—
435	C₄×D₄	—	2	2	no	—
436	C₄×D₄	—	2	2	no	—
437	C₄×D₄	—	2	2	no	—
438	C₄×D₄	—	4	1	no	—
439	C₄×D₄	—	4	1	no	—
440	C₄×D₄	—	4	1	no	—
441	C₄×D₄	C₂×C₄×C₆₁	1	4	yes	complemented
442	C₂×C₄⋊C₄	—	2	1	no	—
443	C₂×C₄⋊C₄	—	2	1	no	—
444	C₂×C₄⋊C₄	—	2	1	no	—
445	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
446	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
451	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
452	C₂×C₂²⋊C₄	—	2	1	no	—
453	C₂×C₂²⋊C₄	—	2	1	no	—
454	C₂×C₂²⋊C₄	—	2	1	no	—
455	C₂×C₂²⋊C₄	—	2	1	no	—
456	C₂×C₂²⋊C₄	—	2	1	no	—
457	C₂×C₂²⋊C₄	—	2	1	no	—
458	C₂×C₂²⋊C₄	—	2	1	no	—
459	C₂×C₂²⋊C₄	—	2	1	no	—
460	C₂×C₄²	—	2	1	no	—
461	C₂×C₄²	—	2	1	no	—
462	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
463	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
464	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
465	#107	—	2	2	no	—
466	#106	—	2	2	no	—
467	C₄⋊C₈	C₂×C₄×C₆₁	1	4	yes	complemented
468	#103	—	2	2	no	—
469	#103	—	4	1	no	—
470	#103	C₂×C₄×C₆₁	1	4	yes	complemented
471	#102	—	2	2	no	—
472	#102	—	2	2	no	—
473	#102	—	4	1	no	—
474	#102	C₂×C₄×C₆₁	1	4	yes	complemented
475	#102	D₄×C₆₁	1	4	yes	—
476	C₄×C₈	—	2	2	no	—
477	C₄×C₈	—	2	2	no	—
478	C₄×C₈	—	2	2	no	—
479	#95	—	2	1	no	—
480	#95	—	2	1	no	—
481	#95	—	2	1	no	—
482	#95	—	2	1	no	—
483	#95	—	2	1	no	—
484	#95	—	2	1	no	—
485	#95	—	2	1	no	—
486	#95	D₄×C₆₁	1	1	yes	characteristic
487	#95	D₄×C₆₁	1	1	yes	characteristic
488	C₂⁴	—	2	1	no	—
489	C₂⁴	—	2	1	no	—
490	C₂×Q₈	—	2	1	no	—
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	—	2	1	no	—
494	C₂×Q₈	—	2	1	no	—
495	C₂×Q₈	C₂²×C₄×C₆₁	1	2	yes	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	—	2	1	no	—
498	C₂×D₄	—	2	1	no	—
499	C₂×D₄	—	2	1	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	2	1	no	—
502	C₂×D₄	—	2	1	no	—
503	C₂×D₄	—	2	1	no	—
504	C₂×D₄	C₂²×C₄×C₆₁	1	2	yes	—
505	C₂×D₄	C₂²×C₄×C₆₁	1	2	yes	—
506	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
507	C₂×D₄	#41×C₆₁	1	2	yes	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	4	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	4	2	no	—
516	C₂²×C₄	—	4	2	no	—
517	C₂²×C₄	—	4	2	no	—
518	C₂²×C₄	—	4	2	no	—
519	C₂²×C₄	—	4	2	no	—
520	C₂²×C₄	—	4	2	no	—
521	C₂²×C₄	—	8	1	no	—
522	C₂²×C₄	—	8	1	no	—
523	C₂²×C₄	—	8	1	no	—
524	C₂²×C₄	—	8	1	no	—
525	C₂²×C₄	—	8	1	no	—
526	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
527	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
528	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
529	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
530	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
531	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
532	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
533	SD₁₆	—	2	8	no	—
534	D₈	—	2	8	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
545	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
546	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
547	C₄⋊C₄	—	2	2	no	—
548	C₄⋊C₄	—	2	2	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	—	2	1	no	—
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	—	4	2	no	—
558	C₄⋊C₄	—	8	1	no	—
559	C₄⋊C₄	—	8	1	no	—
560	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
561	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
562	C₂²⋊C₄	—	2	4	no	—
563	C₂²⋊C₄	—	2	4	no	—
564	C₂²⋊C₄	—	2	4	no	—
565	C₂²⋊C₄	—	4	2	no	—
566	C₂²⋊C₄	—	4	2	no	—
567	C₂²⋊C₄	—	4	2	no	—
568	C₂²⋊C₄	—	4	2	no	—
569	C₂²⋊C₄	—	8	1	no	—
570	C₄²	—	2	1	no	—
571	C₄²	—	2	1	no	—
572	C₄²	—	2	1	no	—
573	C₄²	—	2	1	no	—
574	C₄²	—	4	2	no	—
575	C₄²	—	8	1	no	—
576	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
577	C₄²	#41×C₆₁	1	2	yes	—
578	C₂³	—	2	2	no	—
579	C₂³	—	2	2	no	—
580	C₂³	—	2	2	no	—
581	C₂³	—	2	2	no	—
582	C₂³	—	4	1	no	—
583	C₂³	—	4	1	no	—
584	C₂³	—	4	1	no	—
585	C₂³	—	4	1	no	—
586	C₂³	—	4	1	no	—
587	C₂³	—	4	1	no	—
588	C₂³	—	4	1	no	—
589	C₂³	—	4	1	no	—
590	C₂³	—	4	1	no	—
591	C₂³	—	4	1	no	—
592	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
593	Q₈	—	2	2	no	—
594	Q₈	—	2	2	no	—
595	Q₈	—	4	1	no	—
596	Q₈	—	4	1	no	—
597	D₄	—	2	2	no	—
598	D₄	—	2	2	no	—
599	D₄	—	2	2	no	—
600	D₄	—	2	2	no	—
601	D₄	—	2	2	no	—
602	D₄	—	4	1	no	—
603	D₄	—	4	1	no	—
604	D₄	C₄×D₄×C₆₁	1	4	yes	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	8	4	no	—
638	C₂×C₄	—	8	4	no	—
639	C₂×C₄	—	8	4	no	—
640	C₂×C₄	—	8	4	no	—
641	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
642	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
643	C₂×C₄	#135×C₆₁	1	2	yes	—
644	C₂×C₄	#135×C₆₁	1	2	yes	—
645	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
646	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
647	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
648	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
649	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
650	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
651	C₈	—	2	2	no	—
652	C₈	—	2	2	no	—
653	C₈	—	2	2	no	—
654	C₈	—	4	1	no	—
655	C₂²	—	2	4	no	—
656	C₂²	—	4	2	no	—
657	C₂²	—	4	2	no	—
658	C₂²	—	4	2	no	—
659	C₂²	—	4	2	no	—
660	C₂²	—	4	2	no	—
661	C₂²	—	4	2	no	—
662	C₂²	—	4	2	no	—
663	C₂²	—	4	2	no	—
664	C₂²	—	4	2	no	—
665	C₂²	—	8	1	no	—
666	C₂²	—	8	1	no	—
667	C₂²	—	8	1	no	—
668	C₂²	—	8	1	no	—
669	C₂²	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
670	C₂²	D₄²×C₆₁	1	1	yes	characteristic
671	C₂²	C₆₁×#548	1	1	yes	characteristic
672	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
673	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
674	C₂²	C₆₁×#576	1	1	yes	characteristic
675	C₂²	C₆₁×#577	1	1	yes	characteristic
676	C₄	—	2	2	no	—
677	C₄	—	2	2	no	—
678	C₄	—	2	2	no	—
679	C₄	—	2	2	no	—
680	C₄	—	4	2	no	—
681	C₄	—	4	2	no	—
682	C₄	—	4	1	no	—
683	C₄	—	4	2	no	—
684	C₄	—	4	1	no	—
685	C₄	—	8	1	no	—
686	C₄	—	8	1	no	—
687	C₄	—	8	1	no	—
688	C₄	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
689	C₄	C₆₁×#520	1	1	yes	characteristic
690	C₄	C₆₁×#547	1	1	yes	characteristic
691	C₄	C₆₁×#553	1	1	yes	characteristic
692	C₂	—	4	4	no	—
693	C₂	—	8	2	no	—
694	C₂	C₆₁×#2361	1	1	yes	characteristic
695	C₂	C₄×#135×C₆₁	1	1	yes	characteristic
696	C₂	C₆₁×#2946	1	1	yes	characteristic
697	C₂	C₆₁×#3280	1	1	yes	characteristic
698	C₂	C₆₁×#3282	1	1	yes	characteristic
699	C₂	C₆₁×#3360	1	1	yes	characteristic
700	C₂	C₆₁×#3361	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂²×D₈×C₆₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₄×C₄⋊C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×SD₁₆×C₆₁	C₂	semidirect
4. C₆₁×#2367	C₂	semidirect
5. C₆₁×#2349	C₂	semidirect
6. C₆₁×#1958	C₂	semidirect
7. C₆₁×#1949	C₂	semidirect
8. C₆₁×#1934	C₂	semidirect
9. C₆₁×#1933	C₂	semidirect
11. C₆₁×#1877	C₂	semidirect
12. C₆₁×#1864	C₂	semidirect
13. C₆₁×#1863	C₂	semidirect
14. C₈×C₄⋊C₄×C₆₁	C₂	semidirect
15. C₄×#102×C₆₁	C₂	semidirect
24. C₆₁×#463	C₄	semidirect
71. C₂×SD₁₆×C₆₁	C₂×C₄	semidirect
80. #124×C₆₁	C₂×C₄	semidirect
90. C₄×D₄×C₆₁	C₂×C₄	semidirect
116. C₄⋊C₈×C₆₁	C₂×C₄	semidirect
119. #103×C₆₁	C₂×C₄	semidirect
123. #102×C₆₁	C₂×C₄	semidirect
304. #22999	C₆₁	direct (N × H)
343. C₂×C₄×SD₁₆	C₂×C₆₁	semidirect
345. #2367	C₂×C₆₁	semidirect
346. #2349	C₂×C₆₁	semidirect
347. #1958	C₂×C₆₁	semidirect
348. #1949	C₂×C₆₁	semidirect
349. #1934	C₂×C₆₁	semidirect
350. #1933	C₂×C₆₁	semidirect
352. #1877	C₂×C₆₁	semidirect
353. #1864	C₂×C₆₁	semidirect
354. #1863	C₂×C₆₁	semidirect
355. C₈×C₄⋊C₄	C₂×C₆₁	semidirect
356. C₄×#102	C₂×C₆₁	semidirect
374. #463	C₄×C₆₁	semidirect
412. C₆₁	#22999	direct (N × H)
422. C₂×SD₁₆	C₂×C₄×C₆₁	semidirect
431. #124	C₂×C₄×C₆₁	semidirect
441. C₄×D₄	C₂×C₄×C₆₁	semidirect
467. C₄⋊C₈	C₂×C₄×C₆₁	semidirect
470. #103	C₂×C₄×C₆₁	semidirect
474. #102	C₂×C₄×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×#463	2
C₂×C₄×SD₁₆×C₆₁	2
C₂×C₄×D₈×C₆₁	2
C₆₁×#2367	2
C₆₁×#2349	2
C₆₁×#1958	2
C₆₁×#1949	2
C₆₁×#1934	2
C₆₁×#1933	2
C₆₁×#1879	2
C₆₁×#1877	2
C₆₁×#1864	2
C₆₁×#1863	2
C₈×C₄⋊C₄×C₆₁	2
C₄×#102×C₆₁	2
#22999	61

Subgroups — C61×#22999 #29526432

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#22999 #29526432