Subgroups — C₆₁×#34995 #29538428

Order 15616.

2214 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#2852	C₂	1	4	yes	maximal, complemented
2	C₆₁×#2643	C₂	1	4	yes	maximal, complemented
3	C₆₁×#2510	C₂	1	4	yes	maximal, complemented
4	C₆₁×#2493	C₂	1	4	yes	maximal, complemented
5	C₆₁×#2481	C₂	1	4	yes	maximal, complemented
6	C₆₁×#2480	C₂	1	4	yes	maximal, complemented
7	C₆₁×#2315	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2315	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#2308	C₂	1	1	yes	maximal, characteristic
10	C₆₁×#2308	C₂	1	1	yes	maximal, characteristic
11	C₂×C₆₁×#386	C₂	1	1	yes	maximal, characteristic
12	C₂×C₆₁×#385	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄×C₂²⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂³×D₄×C₆₁	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×#126×C₆₁	C₂²	1	4	yes	complemented
17	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	complemented
18	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
24	C₂²×C₄²×C₆₁	C₂²	1	2	yes	complemented
25	C₆₁×#401	C₂²	1	4	yes	complemented
26	C₆₁×#400	C₂²	1	4	yes	complemented
27	C₆₁×#400	C₂²	1	4	yes	complemented
28	C₆₁×#400	C₂²	1	4	yes	complemented
29	C₆₁×#397	C₂²	1	4	yes	complemented
30	C₆₁×#397	C₂²	1	4	yes	complemented
31	C₆₁×#397	C₂²	1	4	yes	complemented
32	C₆₁×#396	C₂²	1	4	yes	complemented
33	C₆₁×#388	C₂²	1	4	yes	complemented
34	C₆₁×#388	C₂²	1	4	yes	complemented
35	C₆₁×#388	C₂²	1	4	yes	complemented
36	C₆₁×#387	C₂²	1	4	yes	complemented
37	C₆₁×#387	C₂²	1	4	yes	complemented
38	C₆₁×#387	C₂²	1	4	yes	complemented
39	C₆₁×#386	C₂²	1	2	yes	—
40	C₆₁×#386	C₂²	1	2	yes	—
41	C₆₁×#386	C₂²	1	4	yes	—
42	C₆₁×#386	C₂²	1	4	yes	—
43	C₆₁×#386	C₂²	1	4	yes	—
44	C₆₁×#386	C₂²	1	2	yes	—
45	C₆₁×#386	C₂²	1	4	yes	—
46	C₆₁×#386	C₂²	1	2	yes	—
47	C₆₁×#385	C₂²	1	4	yes	—
48	C₆₁×#385	C₂²	1	4	yes	—
49	C₆₁×#385	C₂²	1	2	yes	complemented
50	C₆₁×#385	C₂²	1	2	yes	complemented
51	C₆₁×#385	C₂²	1	4	yes	complemented
52	C₆₁×#385	C₂²	1	4	yes	complemented
53	C₆₁×#385	C₂²	1	4	yes	complemented
54	C₆₁×#383	C₂²	1	4	yes	complemented
55	C₆₁×#381	C₂²	1	2	yes	—
56	C₆₁×#381	C₂²	1	2	yes	—
57	C₆₁×#380	C₂²	1	4	yes	—
58	C₆₁×#380	C₂²	1	2	yes	complemented
59	C₆₁×#380	C₂²	1	2	yes	complemented
60	C₆₁×#379	C₂²	1	2	yes	—
61	C₆₁×#379	C₂²	1	2	yes	—
62	C₄×C₂²⋊C₄×C₆₁	C₂²	1	4	yes	—
63	C₄×C₂²⋊C₄×C₆₁	C₂²	1	4	yes	complemented
64	C₂×#95×C₆₁	C₂²	1	2	yes	—
65	C₂×#95×C₆₁	C₂²	1	2	yes	complemented
66	C₂×#95×C₆₁	C₂²	1	2	yes	complemented
67	C₂⁵×C₆₁	C₂³	1	1	yes	characteristic
68	C₂⁵×C₆₁	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₆₁	—	2	4	no	—
70	C₂²×D₄×C₆₁	—	2	4	no	—
71	C₂²×D₄×C₆₁	—	2	4	no	—
72	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
73	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
74	C₂³×C₄×C₆₁	—	2	4	no	—
75	C₂³×C₄×C₆₁	—	4	4	no	—
76	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
79	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
80	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
82	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
84	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
85	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
86	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
87	#126×C₆₁	—	4	8	no	—
88	C₂×C₄⋊C₄×C₆₁	—	4	4	no	—
89	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
90	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
91	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
92	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
94	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
95	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
96	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
97	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
98	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
99	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
100	C₂×C₂²⋊C₄×C₆₁	—	4	4	no	—
101	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
102	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
103	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
104	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
105	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
106	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
107	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
108	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
109	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
110	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
111	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
112	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
113	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
114	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
115	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
116	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
117	C₂×C₄²×C₆₁	—	4	4	no	—
118	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
119	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
120	#95×C₆₁	C₂³	1	4	yes	—
121	#95×C₆₁	C₂³	1	4	yes	—
122	#95×C₆₁	C₂³	1	4	yes	—
123	#95×C₆₁	C₂³	1	4	yes	—
124	#95×C₆₁	C₂³	1	4	yes	—
125	#95×C₆₁	C₂³	1	4	yes	—
126	#95×C₆₁	C₂³	1	4	yes	—
127	#95×C₆₁	C₂³	1	4	yes	—
128	#95×C₆₁	C₂³	1	4	yes	—
129	#95×C₆₁	C₂³	1	4	yes	—
130	#95×C₆₁	C₂³	1	4	yes	—
131	#95×C₆₁	C₂³	1	4	yes	—
132	#95×C₆₁	C₂³	1	4	yes	—
133	#95×C₆₁	C₂³	1	4	yes	—
134	C₂⁴×C₆₁	—	2	2	no	—
135	C₂⁴×C₆₁	—	2	2	no	—
136	C₂⁴×C₆₁	—	2	2	no	—
137	C₂⁴×C₆₁	—	4	2	no	—
138	C₂⁴×C₆₁	—	4	2	no	—
139	C₂⁴×C₆₁	—	4	2	no	—
140	C₂⁴×C₆₁	—	4	2	no	—
141	C₂⁴×C₆₁	#41	1	4	yes	—
142	C₂⁴×C₆₁	#41	1	4	yes	—
143	C₂⁴×C₆₁	#41	1	4	yes	—
144	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
145	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
146	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
147	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
148	C₂×D₄×C₆₁	—	2	4	no	—
149	C₂×D₄×C₆₁	—	2	4	no	—
150	C₂×D₄×C₆₁	—	2	4	no	—
151	C₂×D₄×C₆₁	—	2	4	no	—
152	C₂×D₄×C₆₁	—	2	4	no	—
153	C₂×D₄×C₆₁	—	2	4	no	—
154	C₂×D₄×C₆₁	—	4	16	no	—
155	C₂²×C₄×C₆₁	—	2	2	no	—
156	C₂²×C₄×C₆₁	—	2	4	no	—
157	C₂²×C₄×C₆₁	—	2	4	no	—
158	C₂²×C₄×C₆₁	—	2	4	no	—
159	C₂²×C₄×C₆₁	—	2	4	no	—
160	C₂²×C₄×C₆₁	—	2	4	no	—
161	C₂²×C₄×C₆₁	—	2	4	no	—
162	C₂²×C₄×C₆₁	—	2	2	no	—
163	C₂²×C₄×C₆₁	—	2	2	no	—
164	C₂²×C₄×C₆₁	—	2	2	no	—
165	C₂²×C₄×C₆₁	—	2	2	no	—
166	C₂²×C₄×C₆₁	—	2	4	no	—
167	C₂²×C₄×C₆₁	—	2	2	no	—
168	C₂²×C₄×C₆₁	—	2	2	no	—
169	C₂²×C₄×C₆₁	—	2	4	no	—
170	C₂²×C₄×C₆₁	—	2	4	no	—
171	C₂²×C₄×C₆₁	—	4	2	no	—
172	C₂²×C₄×C₆₁	—	4	2	no	—
173	C₂²×C₄×C₆₁	—	4	2	no	—
174	C₂²×C₄×C₆₁	—	4	2	no	—
175	C₂²×C₄×C₆₁	—	4	2	no	—
176	C₂²×C₄×C₆₁	—	4	2	no	—
177	C₂²×C₄×C₆₁	—	4	2	no	—
178	C₂²×C₄×C₆₁	—	4	2	no	—
179	C₂²×C₄×C₆₁	—	4	2	no	—
180	C₂²×C₄×C₆₁	—	4	2	no	—
181	C₂²×C₄×C₆₁	—	4	2	no	—
182	C₂²×C₄×C₆₁	—	4	2	no	—
183	C₂²×C₄×C₆₁	—	4	2	no	—
184	C₂²×C₄×C₆₁	—	4	16	no	—
185	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
189	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
190	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
191	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
192	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
194	C₄⋊C₄×C₆₁	—	2	8	no	—
195	C₄⋊C₄×C₆₁	—	4	4	no	—
196	C₄⋊C₄×C₆₁	—	4	4	no	—
197	C₄⋊C₄×C₆₁	—	4	4	no	—
198	C₄⋊C₄×C₆₁	—	4	4	no	—
199	C₄⋊C₄×C₆₁	—	4	4	no	—
200	C₂²⋊C₄×C₆₁	—	2	4	no	—
201	C₂²⋊C₄×C₆₁	—	2	4	no	—
202	C₂²⋊C₄×C₆₁	—	2	4	no	—
203	C₂²⋊C₄×C₆₁	—	2	4	no	—
204	C₂²⋊C₄×C₆₁	—	2	4	no	—
205	C₂²⋊C₄×C₆₁	—	2	4	no	—
206	C₂²⋊C₄×C₆₁	—	2	4	no	—
207	C₂²⋊C₄×C₆₁	—	2	4	no	—
208	C₂²⋊C₄×C₆₁	—	2	4	no	—
209	C₂²⋊C₄×C₆₁	—	2	4	no	—
210	C₂²⋊C₄×C₆₁	—	2	8	no	—
211	C₂²⋊C₄×C₆₁	—	4	4	no	—
212	C₂²⋊C₄×C₆₁	—	4	4	no	—
213	C₂²⋊C₄×C₆₁	—	4	4	no	—
214	C₂²⋊C₄×C₆₁	—	4	4	no	—
215	C₂²⋊C₄×C₆₁	—	4	4	no	—
216	C₄²×C₆₁	—	2	8	no	—
217	C₄²×C₆₁	—	4	4	no	—
218	C₂³×C₆₁	—	2	2	no	—
219	C₂³×C₆₁	—	2	2	no	—
220	C₂³×C₆₁	—	2	2	no	—
221	C₂³×C₆₁	—	2	2	no	—
222	C₂³×C₆₁	—	2	2	no	—
223	C₂³×C₆₁	—	2	2	no	—
224	C₂³×C₆₁	—	2	2	no	—
225	C₂³×C₆₁	—	2	2	no	—
226	C₂³×C₆₁	—	2	2	no	—
227	C₂³×C₆₁	—	2	4	no	—
228	C₂³×C₆₁	—	2	4	no	—
229	C₂³×C₆₁	—	4	4	no	—
230	C₂³×C₆₁	—	4	8	no	—
231	C₂³×C₆₁	—	4	4	no	—
232	C₂³×C₆₁	—	4	8	no	—
233	C₂³×C₆₁	—	4	8	no	—
234	C₂³×C₆₁	—	4	4	no	—
235	C₂³×C₆₁	—	8	2	no	—
236	C₂³×C₆₁	—	8	2	no	—
237	C₂³×C₆₁	—	8	4	no	—
238	C₂³×C₆₁	#126	1	16	yes	complemented
239	C₂³×C₆₁	C₂×#41	1	2	yes	—
240	C₂³×C₆₁	C₂×#41	1	2	yes	—
241	C₂³×C₆₁	C₂×#41	1	2	yes	—
242	C₂³×C₆₁	C₂×#41	1	2	yes	—
243	C₂³×C₆₁	C₂×#41	1	2	yes	—
244	C₂³×C₆₁	C₂×#41	1	2	yes	—
245	C₂³×C₆₁	C₂×#41	1	2	yes	—
246	C₂³×C₆₁	C₂×#41	1	2	yes	—
247	C₂³×C₆₁	C₂×#41	1	2	yes	—
248	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
249	D₄×C₆₁	—	4	8	no	—
250	D₄×C₆₁	—	4	8	no	—
251	C₂×C₄×C₆₁	—	2	8	no	—
252	C₂×C₄×C₆₁	—	2	2	no	—
253	C₂×C₄×C₆₁	—	2	2	no	—
254	C₂×C₄×C₆₁	—	2	4	no	—
255	C₂×C₄×C₆₁	—	2	4	no	—
256	C₂×C₄×C₆₁	—	2	2	no	—
257	C₂×C₄×C₆₁	—	2	2	no	—
258	C₂×C₄×C₆₁	—	2	4	no	—
259	C₂×C₄×C₆₁	—	2	4	no	—
260	C₂×C₄×C₆₁	—	2	2	no	—
261	C₂×C₄×C₆₁	—	2	2	no	—
262	C₂×C₄×C₆₁	—	2	2	no	—
263	C₂×C₄×C₆₁	—	2	2	no	—
264	C₂×C₄×C₆₁	—	2	4	no	—
265	C₂×C₄×C₆₁	—	2	4	no	—
266	C₂×C₄×C₆₁	—	2	4	no	—
267	C₂×C₄×C₆₁	—	2	2	no	—
268	C₂×C₄×C₆₁	—	2	4	no	—
269	C₂×C₄×C₆₁	—	2	4	no	—
270	C₂×C₄×C₆₁	—	2	2	no	—
271	C₂×C₄×C₆₁	—	2	4	no	—
272	C₂×C₄×C₆₁	—	2	4	no	—
273	C₂×C₄×C₆₁	—	2	4	no	—
274	C₂×C₄×C₆₁	—	2	4	no	—
275	C₂×C₄×C₆₁	—	2	4	no	—
276	C₂×C₄×C₆₁	—	4	8	no	—
277	C₂×C₄×C₆₁	—	4	8	no	—
278	C₂×C₄×C₆₁	—	4	8	no	—
279	C₂×C₄×C₆₁	—	4	8	no	—
280	C₂×C₄×C₆₁	—	4	8	no	—
281	C₂×C₄×C₆₁	—	4	4	no	—
282	C₂×C₄×C₆₁	—	4	4	no	—
283	C₂×C₄×C₆₁	—	8	2	no	—
284	C₂×C₄×C₆₁	—	8	2	no	—
285	C₂×C₄×C₆₁	—	8	4	no	—
286	C₂×C₄×C₆₁	H(5,𝔽₂)	1	4	yes	—
287	#34995	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
288	C₂²×C₆₁	—	2	4	no	—
289	C₂²×C₆₁	—	2	4	no	—
290	C₂²×C₆₁	—	2	4	no	—
291	C₂²×C₆₁	—	2	2	no	—
292	C₂²×C₆₁	—	2	2	no	—
293	C₂²×C₆₁	—	2	2	no	—
294	C₂²×C₆₁	—	2	2	no	—
295	C₂²×C₆₁	—	2	2	no	—
296	C₂²×C₆₁	—	2	2	no	—
297	C₂²×C₆₁	—	2	4	no	—
298	C₂²×C₆₁	—	2	4	no	—
299	C₂²×C₆₁	—	2	4	no	—
300	C₂²×C₆₁	—	4	16	no	—
301	C₂²×C₆₁	—	4	2	no	—
302	C₂²×C₆₁	—	4	4	no	—
303	C₂²×C₆₁	—	4	2	no	—
304	C₂²×C₆₁	—	4	2	no	—
305	C₂²×C₆₁	—	4	4	no	—
306	C₂²×C₆₁	—	8	8	no	—
307	C₂²×C₆₁	C₂×#126	1	4	yes	—
308	C₂²×C₆₁	C₂×#126	1	4	yes	—
309	C₂²×C₆₁	C₂×#126	1	4	yes	—
310	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
311	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
312	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
313	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	2	yes	—
314	C₂²×C₆₁	#585	1	2	yes	—
315	C₄×C₆₁	—	2	4	no	—
316	C₄×C₆₁	—	4	2	no	—
317	C₄×C₆₁	—	4	4	no	—
318	C₄×C₆₁	—	4	4	no	—
319	C₄×C₆₁	—	4	2	no	—
320	C₄×C₆₁	—	4	2	no	—
321	C₄×C₆₁	—	4	2	no	—
322	C₄×C₆₁	—	4	4	no	—
323	C₄×C₆₁	—	4	4	no	—
324	#2852	C₂×C₆₁	1	4	yes	complemented
325	#2643	C₂×C₆₁	1	4	yes	complemented
326	#2510	C₂×C₆₁	1	4	yes	complemented
327	#2493	C₂×C₆₁	1	4	yes	complemented
328	#2481	C₂×C₆₁	1	4	yes	complemented
329	#2480	C₂×C₆₁	1	4	yes	complemented
330	#2315	C₂×C₆₁	1	1	yes	characteristic, complemented
331	#2315	C₂×C₆₁	1	1	yes	characteristic, complemented
332	#2308	C₂×C₆₁	1	1	yes	characteristic
333	#2308	C₂×C₆₁	1	1	yes	characteristic
334	C₂×#386	C₂×C₆₁	1	1	yes	characteristic
335	C₂×#385	C₂×C₆₁	1	1	yes	characteristic, complemented
336	C₂×C₄×C₂²⋊C₄	C₂×C₆₁	1	1	yes	characteristic, complemented
337	C₂×C₆₁	—	2	4	no	—
338	C₂×C₆₁	—	2	4	no	—
339	C₂×C₆₁	—	2	4	no	—
340	C₂×C₆₁	—	8	2	no	—
341	C₂×C₆₁	C₂²×#126	1	1	yes	characteristic
342	C₂×C₆₁	#3459	1	2	yes	—
343	C₂×C₆₁	#3490	1	1	yes	characteristic
344	C₂×C₆₁	#3491	1	1	yes	characteristic
345	C₂×C₆₁	#3505	1	2	yes	—
346	C₂³×D₄	C₂²×C₆₁	1	1	yes	characteristic
347	C₂⁴×C₄	C₂²×C₆₁	1	1	yes	characteristic
348	C₂×#126	C₂²×C₆₁	1	4	yes	complemented
349	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	complemented
350	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
351	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
352	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
353	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
354	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
355	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
356	C₂²×C₄²	C₂²×C₆₁	1	2	yes	complemented
357	#401	C₂²×C₆₁	1	4	yes	complemented
358	#400	C₂²×C₆₁	1	4	yes	complemented
359	#400	C₂²×C₆₁	1	4	yes	complemented
360	#400	C₂²×C₆₁	1	4	yes	complemented
361	#397	C₂²×C₆₁	1	4	yes	complemented
362	#397	C₂²×C₆₁	1	4	yes	complemented
363	#397	C₂²×C₆₁	1	4	yes	complemented
364	#396	C₂²×C₆₁	1	4	yes	complemented
365	#388	C₂²×C₆₁	1	4	yes	complemented
366	#388	C₂²×C₆₁	1	4	yes	complemented
367	#388	C₂²×C₆₁	1	4	yes	complemented
368	#387	C₂²×C₆₁	1	4	yes	complemented
369	#387	C₂²×C₆₁	1	4	yes	complemented
370	#387	C₂²×C₆₁	1	4	yes	complemented
371	#386	C₂²×C₆₁	1	4	yes	—
372	#386	C₂²×C₆₁	1	4	yes	—
373	#386	C₂²×C₆₁	1	2	yes	—
374	#386	C₂²×C₆₁	1	4	yes	—
375	#386	C₂²×C₆₁	1	2	yes	—
376	#386	C₂²×C₆₁	1	2	yes	—
377	#386	C₂²×C₆₁	1	2	yes	—
378	#386	C₂²×C₆₁	1	4	yes	—
379	#385	C₂²×C₆₁	1	4	yes	—
380	#385	C₂²×C₆₁	1	4	yes	—
381	#385	C₂²×C₆₁	1	4	yes	complemented
382	#385	C₂²×C₆₁	1	4	yes	complemented
383	#385	C₂²×C₆₁	1	4	yes	complemented
384	#385	C₂²×C₆₁	1	2	yes	complemented
385	#385	C₂²×C₆₁	1	2	yes	complemented
386	#383	C₂²×C₆₁	1	4	yes	complemented
387	#381	C₂²×C₆₁	1	2	yes	—
388	#381	C₂²×C₆₁	1	2	yes	—
389	#380	C₂²×C₆₁	1	4	yes	—
390	#380	C₂²×C₆₁	1	2	yes	complemented
391	#380	C₂²×C₆₁	1	2	yes	complemented
392	#379	C₂²×C₆₁	1	2	yes	—
393	#379	C₂²×C₆₁	1	2	yes	—
394	C₄×C₂²⋊C₄	C₂²×C₆₁	1	4	yes	—
395	C₄×C₂²⋊C₄	C₂²×C₆₁	1	4	yes	complemented
396	C₂×#95	C₂²×C₆₁	1	2	yes	—
397	C₂×#95	C₂²×C₆₁	1	2	yes	complemented
398	C₂×#95	C₂²×C₆₁	1	2	yes	complemented
399	C₆₁	#34995	1	1	yes	characteristic, direct product factor, Sylow
400	C₂⁵	C₂³×C₆₁	1	1	yes	characteristic
401	C₂⁵	C₂³×C₆₁	1	1	yes	characteristic
402	C₂²×D₄	—	2	4	no	—
403	C₂²×D₄	—	2	4	no	—
404	C₂²×D₄	—	2	4	no	—
405	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
406	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
407	C₂³×C₄	—	2	4	no	—
408	C₂³×C₄	—	4	4	no	—
409	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
410	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
411	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
412	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
413	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
414	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
415	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
416	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
417	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
418	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
419	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
420	#126	—	4	8	no	—
421	C₂×C₄⋊C₄	—	4	4	no	—
422	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
423	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
424	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
425	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
426	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
427	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
428	C₂×C₂²⋊C₄	—	2	4	no	—
429	C₂×C₂²⋊C₄	—	2	4	no	—
430	C₂×C₂²⋊C₄	—	2	4	no	—
431	C₂×C₂²⋊C₄	—	2	4	no	—
432	C₂×C₂²⋊C₄	—	2	4	no	—
433	C₂×C₂²⋊C₄	—	4	4	no	—
434	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
441	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
442	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
443	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
444	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
445	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
446	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
447	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
448	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
449	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
450	C₂×C₄²	—	4	4	no	—
451	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
452	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
453	#95	C₂³×C₆₁	1	4	yes	—
454	#95	C₂³×C₆₁	1	4	yes	—
455	#95	C₂³×C₆₁	1	4	yes	—
456	#95	C₂³×C₆₁	1	4	yes	—
457	#95	C₂³×C₆₁	1	4	yes	—
458	#95	C₂³×C₆₁	1	4	yes	—
459	#95	C₂³×C₆₁	1	4	yes	—
460	#95	C₂³×C₆₁	1	4	yes	—
461	#95	C₂³×C₆₁	1	4	yes	—
462	#95	C₂³×C₆₁	1	4	yes	—
463	#95	C₂³×C₆₁	1	4	yes	—
464	#95	C₂³×C₆₁	1	4	yes	—
465	#95	C₂³×C₆₁	1	4	yes	—
466	#95	C₂³×C₆₁	1	4	yes	—
467	C₂⁴	—	2	2	no	—
468	C₂⁴	—	2	2	no	—
469	C₂⁴	—	2	2	no	—
470	C₂⁴	—	4	2	no	—
471	C₂⁴	—	4	2	no	—
472	C₂⁴	—	4	2	no	—
473	C₂⁴	—	4	2	no	—
474	C₂⁴	#41×C₆₁	1	4	yes	—
475	C₂⁴	#41×C₆₁	1	4	yes	—
476	C₂⁴	#41×C₆₁	1	4	yes	—
477	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
478	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
479	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
480	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
481	C₂×D₄	—	2	4	no	—
482	C₂×D₄	—	2	4	no	—
483	C₂×D₄	—	2	4	no	—
484	C₂×D₄	—	2	4	no	—
485	C₂×D₄	—	2	4	no	—
486	C₂×D₄	—	2	4	no	—
487	C₂×D₄	—	4	16	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	4	no	—
490	C₂²×C₄	—	2	4	no	—
491	C₂²×C₄	—	2	4	no	—
492	C₂²×C₄	—	2	4	no	—
493	C₂²×C₄	—	2	4	no	—
494	C₂²×C₄	—	2	4	no	—
495	C₂²×C₄	—	2	2	no	—
496	C₂²×C₄	—	2	2	no	—
497	C₂²×C₄	—	2	2	no	—
498	C₂²×C₄	—	2	2	no	—
499	C₂²×C₄	—	2	4	no	—
500	C₂²×C₄	—	2	2	no	—
501	C₂²×C₄	—	2	2	no	—
502	C₂²×C₄	—	2	4	no	—
503	C₂²×C₄	—	2	4	no	—
504	C₂²×C₄	—	4	2	no	—
505	C₂²×C₄	—	4	2	no	—
506	C₂²×C₄	—	4	2	no	—
507	C₂²×C₄	—	4	2	no	—
508	C₂²×C₄	—	4	2	no	—
509	C₂²×C₄	—	4	2	no	—
510	C₂²×C₄	—	4	2	no	—
511	C₂²×C₄	—	4	2	no	—
512	C₂²×C₄	—	4	2	no	—
513	C₂²×C₄	—	4	2	no	—
514	C₂²×C₄	—	4	2	no	—
515	C₂²×C₄	—	4	2	no	—
516	C₂²×C₄	—	4	2	no	—
517	C₂²×C₄	—	4	16	no	—
518	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
519	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
520	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
521	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
522	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
523	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
524	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
525	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
526	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
527	C₄⋊C₄	—	2	8	no	—
528	C₄⋊C₄	—	4	4	no	—
529	C₄⋊C₄	—	4	4	no	—
530	C₄⋊C₄	—	4	4	no	—
531	C₄⋊C₄	—	4	4	no	—
532	C₄⋊C₄	—	4	4	no	—
533	C₂²⋊C₄	—	2	4	no	—
534	C₂²⋊C₄	—	2	4	no	—
535	C₂²⋊C₄	—	2	4	no	—
536	C₂²⋊C₄	—	2	4	no	—
537	C₂²⋊C₄	—	2	4	no	—
538	C₂²⋊C₄	—	2	4	no	—
539	C₂²⋊C₄	—	2	4	no	—
540	C₂²⋊C₄	—	2	4	no	—
541	C₂²⋊C₄	—	2	4	no	—
542	C₂²⋊C₄	—	2	4	no	—
543	C₂²⋊C₄	—	2	8	no	—
544	C₂²⋊C₄	—	4	4	no	—
545	C₂²⋊C₄	—	4	4	no	—
546	C₂²⋊C₄	—	4	4	no	—
547	C₂²⋊C₄	—	4	4	no	—
548	C₂²⋊C₄	—	4	4	no	—
549	C₄²	—	2	8	no	—
550	C₄²	—	4	4	no	—
551	C₂³	—	2	2	no	—
552	C₂³	—	2	2	no	—
553	C₂³	—	2	2	no	—
554	C₂³	—	2	2	no	—
555	C₂³	—	2	2	no	—
556	C₂³	—	2	2	no	—
557	C₂³	—	2	2	no	—
558	C₂³	—	2	2	no	—
559	C₂³	—	2	2	no	—
560	C₂³	—	2	4	no	—
561	C₂³	—	2	4	no	—
562	C₂³	—	4	4	no	—
563	C₂³	—	4	8	no	—
564	C₂³	—	4	4	no	—
565	C₂³	—	4	8	no	—
566	C₂³	—	4	8	no	—
567	C₂³	—	4	4	no	—
568	C₂³	—	8	2	no	—
569	C₂³	—	8	2	no	—
570	C₂³	—	8	4	no	—
571	C₂³	#126×C₆₁	1	16	yes	complemented
572	C₂³	C₂×#41×C₆₁	1	2	yes	—
573	C₂³	C₂×#41×C₆₁	1	2	yes	—
574	C₂³	C₂×#41×C₆₁	1	2	yes	—
575	C₂³	C₂×#41×C₆₁	1	2	yes	—
576	C₂³	C₂×#41×C₆₁	1	2	yes	—
577	C₂³	C₂×#41×C₆₁	1	2	yes	—
578	C₂³	C₂×#41×C₆₁	1	2	yes	—
579	C₂³	C₂×#41×C₆₁	1	2	yes	—
580	C₂³	C₂×#41×C₆₁	1	2	yes	—
581	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
582	D₄	—	4	8	no	—
583	D₄	—	4	8	no	—
584	C₂×C₄	—	2	8	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	2	4	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	4	no	—
599	C₂×C₄	—	2	4	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	4	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	4	no	—
605	C₂×C₄	—	2	4	no	—
606	C₂×C₄	—	2	4	no	—
607	C₂×C₄	—	2	4	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	4	8	no	—
610	C₂×C₄	—	4	8	no	—
611	C₂×C₄	—	4	8	no	—
612	C₂×C₄	—	4	8	no	—
613	C₂×C₄	—	4	8	no	—
614	C₂×C₄	—	4	4	no	—
615	C₂×C₄	—	4	4	no	—
616	C₂×C₄	—	8	2	no	—
617	C₂×C₄	—	8	2	no	—
618	C₂×C₄	—	8	4	no	—
619	C₂×C₄	H(5,𝔽₂)×C₆₁	1	4	yes	—
620	C₂²	—	2	4	no	—
621	C₂²	—	2	4	no	—
622	C₂²	—	2	4	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	2	2	no	—
625	C₂²	—	2	2	no	—
626	C₂²	—	2	2	no	—
627	C₂²	—	2	2	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	4	no	—
630	C₂²	—	2	4	no	—
631	C₂²	—	2	4	no	—
632	C₂²	—	4	16	no	—
633	C₂²	—	4	2	no	—
634	C₂²	—	4	4	no	—
635	C₂²	—	4	2	no	—
636	C₂²	—	4	2	no	—
637	C₂²	—	4	4	no	—
638	C₂²	—	8	8	no	—
639	C₂²	C₂×#126×C₆₁	1	4	yes	—
640	C₂²	C₂×#126×C₆₁	1	4	yes	—
641	C₂²	C₂×#126×C₆₁	1	4	yes	—
642	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
643	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
644	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
645	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	2	yes	—
646	C₂²	C₆₁×#585	1	2	yes	—
647	C₄	—	2	4	no	—
648	C₄	—	4	2	no	—
649	C₄	—	4	4	no	—
650	C₄	—	4	4	no	—
651	C₄	—	4	2	no	—
652	C₄	—	4	2	no	—
653	C₄	—	4	2	no	—
654	C₄	—	4	4	no	—
655	C₄	—	4	4	no	—
656	C₂	—	2	4	no	—
657	C₂	—	2	4	no	—
658	C₂	—	2	4	no	—
659	C₂	—	8	2	no	—
660	C₂	C₂²×#126×C₆₁	1	1	yes	characteristic
661	C₂	C₆₁×#3459	1	2	yes	—
662	C₂	C₆₁×#3490	1	1	yes	characteristic
663	C₂	C₆₁×#3491	1	1	yes	characteristic
664	C₂	C₆₁×#3505	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₆₁×#2852	C₂	semidirect
2. C₆₁×#2643	C₂	semidirect
3. C₆₁×#2510	C₂	semidirect
4. C₆₁×#2493	C₂	semidirect
5. C₆₁×#2481	C₂	semidirect
6. C₆₁×#2480	C₂	semidirect
7. C₆₁×#2315	C₂	semidirect
8. C₆₁×#2315	C₂	semidirect
12. C₂×C₆₁×#385	C₂	semidirect
13. C₂×C₄×C₂²⋊C₄×C₆₁	C₂	semidirect
16. C₂×#126×C₆₁	C₂²	semidirect
17. C₂²×C₄⋊C₄×C₆₁	C₂²	semidirect
24. C₂²×C₄²×C₆₁	C₂²	semidirect
25. C₆₁×#401	C₂²	semidirect
26. C₆₁×#400	C₂²	semidirect
27. C₆₁×#400	C₂²	semidirect
28. C₆₁×#400	C₂²	semidirect
29. C₆₁×#397	C₂²	semidirect
30. C₆₁×#397	C₂²	semidirect
31. C₆₁×#397	C₂²	semidirect
32. C₆₁×#396	C₂²	semidirect
33. C₆₁×#388	C₂²	semidirect
34. C₆₁×#388	C₂²	semidirect
35. C₆₁×#388	C₂²	semidirect
36. C₆₁×#387	C₂²	semidirect
37. C₆₁×#387	C₂²	semidirect
38. C₆₁×#387	C₂²	semidirect
49. C₆₁×#385	C₂²	semidirect
50. C₆₁×#385	C₂²	semidirect
51. C₆₁×#385	C₂²	semidirect
52. C₆₁×#385	C₂²	semidirect
53. C₆₁×#385	C₂²	semidirect
54. C₆₁×#383	C₂²	semidirect
58. C₆₁×#380	C₂²	semidirect
59. C₆₁×#380	C₂²	semidirect
63. C₄×C₂²⋊C₄×C₆₁	C₂²	semidirect
65. C₂×#95×C₆₁	C₂²	semidirect
66. C₂×#95×C₆₁	C₂²	semidirect
238. C₂³×C₆₁	#126	semidirect
287. #34995	C₆₁	direct (N × H)
324. #2852	C₂×C₆₁	semidirect
325. #2643	C₂×C₆₁	semidirect
326. #2510	C₂×C₆₁	semidirect
327. #2493	C₂×C₆₁	semidirect
328. #2481	C₂×C₆₁	semidirect
329. #2480	C₂×C₆₁	semidirect
330. #2315	C₂×C₆₁	semidirect
331. #2315	C₂×C₆₁	semidirect
335. C₂×#385	C₂×C₆₁	semidirect
336. C₂×C₄×C₂²⋊C₄	C₂×C₆₁	semidirect
348. C₂×#126	C₂²×C₆₁	semidirect
349. C₂²×C₄⋊C₄	C₂²×C₆₁	semidirect
356. C₂²×C₄²	C₂²×C₆₁	semidirect
357. #401	C₂²×C₆₁	semidirect
358. #400	C₂²×C₆₁	semidirect
359. #400	C₂²×C₆₁	semidirect
360. #400	C₂²×C₆₁	semidirect
361. #397	C₂²×C₆₁	semidirect
362. #397	C₂²×C₆₁	semidirect
363. #397	C₂²×C₆₁	semidirect
364. #396	C₂²×C₆₁	semidirect
365. #388	C₂²×C₆₁	semidirect
366. #388	C₂²×C₆₁	semidirect
367. #388	C₂²×C₆₁	semidirect
368. #387	C₂²×C₆₁	semidirect
369. #387	C₂²×C₆₁	semidirect
370. #387	C₂²×C₆₁	semidirect
381. #385	C₂²×C₆₁	semidirect
382. #385	C₂²×C₆₁	semidirect
383. #385	C₂²×C₆₁	semidirect
384. #385	C₂²×C₆₁	semidirect
385. #385	C₂²×C₆₁	semidirect
386. #383	C₂²×C₆₁	semidirect
390. #380	C₂²×C₆₁	semidirect
391. #380	C₂²×C₆₁	semidirect
395. C₄×C₂²⋊C₄	C₂²×C₆₁	semidirect
397. C₂×#95	C₂²×C₆₁	semidirect
398. C₂×#95	C₂²×C₆₁	semidirect
399. C₆₁	#34995	direct (N × H)
571. C₂³	#126×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#2852	2
C₆₁×#2643	2
C₆₁×#2510	2
C₆₁×#2493	2
C₆₁×#2481	2
C₆₁×#2480	2
C₆₁×#2315	2
C₆₁×#2308	2
C₂×C₆₁×#386	2
C₂×C₆₁×#385	2
C₂×C₄×C₂²⋊C₄×C₆₁	2
#34995	61

Subgroups — C61×#34995 #29538428

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#34995 #29538428