Subgroups — C₆₁×#36969 #29540402

Order 15616.

2502 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#534	C₂	1	1	yes	maximal, characteristic
2	C₂²×#126×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2854	C₂	1	2	yes	maximal, complemented
4	C₆₁×#2718	C₂	1	8	yes	maximal, complemented
5	C₆₁×#2685	C₂	1	8	yes	maximal, complemented
6	C₆₁×#2618	C₂	1	2	yes	maximal, complemented
7	C₆₁×#2591	C₂	1	2	yes	maximal, complemented
8	C₆₁×#2501	C₂	1	2	yes	maximal, complemented
9	C₆₁×#2405	C₂	1	2	yes	maximal, complemented
10	C₆₁×#2405	C₂	1	2	yes	maximal, complemented
11	C₆₁×#2312	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₆₁	C₂²	1	2	yes	—
13	C₆₁×#534	—	2	8	no	—
14	C₂×#126×C₆₁	—	2	8	no	—
15	C₂×#126×C₆₁	C₂²	1	8	yes	complemented
16	C₂×#123×C₆₁	C₂²	1	4	yes	—
17	C₂×#123×C₆₁	C₂²	1	4	yes	complemented
18	C₂×#123×C₆₁	C₂²	1	4	yes	complemented
19	C₂×#121×C₆₁	C₂²	1	2	yes	—
20	C₂×#121×C₆₁	C₂²	1	2	yes	—
21	C₂×#120×C₆₁	C₂²	1	4	yes	—
22	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
27	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic, complemented
29	C₆₁×#400	C₂²	1	4	yes	complemented
30	C₆₁×#399	C₂²	1	8	yes	complemented
31	C₆₁×#398	C₂²	1	4	yes	complemented
32	C₆₁×#396	C₂²	1	8	yes	complemented
33	C₆₁×#394	C₂²	1	8	yes	—
34	C₆₁×#394	C₂²	1	8	yes	—
35	C₆₁×#394	C₂²	1	4	yes	complemented
36	C₆₁×#394	C₂²	1	4	yes	complemented
37	C₆₁×#390	C₂²	1	4	yes	complemented
38	C₆₁×#390	C₂²	1	4	yes	complemented
39	C₆₁×#389	C₂²	1	4	yes	complemented
40	C₆₁×#388	C₂²	1	8	yes	complemented
41	C₆₁×#388	C₂²	1	8	yes	complemented
42	C₆₁×#388	C₂²	1	8	yes	complemented
43	C₆₁×#386	C₂²	1	4	yes	complemented
44	C₆₁×#386	C₂²	1	4	yes	complemented
45	C₆₁×#385	C₂²	1	4	yes	complemented
46	C₆₁×#385	C₂²	1	4	yes	complemented
47	C₆₁×#384	C₂²	1	4	yes	complemented
48	C₆₁×#380	C₂²	1	2	yes	complemented
49	C₆₁×#379	C₂²	1	2	yes	—
50	C₆₁×#379	C₂²	1	4	yes	complemented
51	C₆₁×#379	C₂²	1	4	yes	complemented
52	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	complemented
53	C₂⁵×C₆₁	C₂³	1	1	yes	characteristic
54	C₂⁵×C₆₁	C₂³	1	2	yes	—
55	C₂²×D₄×C₆₁	—	2	8	no	—
56	C₂²×D₄×C₆₁	—	4	8	no	—
57	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
58	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
59	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
60	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
61	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
64	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
68	#126×C₆₁	—	2	32	no	—
69	#123×C₆₁	—	2	16	no	—
70	#123×C₆₁	—	4	8	no	—
71	#123×C₆₁	—	4	8	no	—
72	#121×C₆₁	—	2	8	no	—
73	#121×C₆₁	—	2	8	no	—
74	#120×C₆₁	—	2	16	no	—
75	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
76	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
77	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
78	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
79	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
80	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
81	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
83	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
84	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
85	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
86	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
87	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
88	C₂×C₂²⋊C₄×C₆₁	D₄	1	8	yes	—
89	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
90	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
91	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
92	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
93	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
94	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
95	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
96	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
97	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
98	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
99	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
100	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
101	C₂×C₄²×C₆₁	—	2	4	no	—
102	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
103	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
104	#95×C₆₁	C₂³	1	4	yes	—
105	#95×C₆₁	C₂³	1	4	yes	—
106	#95×C₆₁	C₂³	1	8	yes	—
107	#95×C₆₁	C₂³	1	8	yes	—
108	C₂⁴×C₆₁	—	2	4	no	—
109	C₂⁴×C₆₁	—	2	4	no	—
110	C₂⁴×C₆₁	—	4	4	no	—
111	C₂⁴×C₆₁	—	4	2	no	—
112	C₂⁴×C₆₁	—	4	2	no	—
113	C₂⁴×C₆₁	—	4	4	no	—
114	C₂⁴×C₆₁	—	4	4	no	—
115	C₂⁴×C₆₁	C₂×D₄	1	4	yes	—
116	C₂⁴×C₆₁	C₂⁴	1	4	yes	—
117	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
118	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
119	C₂×D₄×C₆₁	—	2	8	no	—
120	C₂×D₄×C₆₁	—	2	8	no	—
121	C₂×D₄×C₆₁	—	2	8	no	—
122	C₂×D₄×C₆₁	—	2	8	no	—
123	C₂×D₄×C₆₁	—	2	4	no	—
124	C₂×D₄×C₆₁	—	2	4	no	—
125	C₂×D₄×C₆₁	—	4	4	no	—
126	C₂×D₄×C₆₁	—	4	4	no	—
127	C₂×D₄×C₆₁	—	4	4	no	—
128	C₂×D₄×C₆₁	—	4	4	no	—
129	C₂×D₄×C₆₁	—	4	32	no	—
130	C₂²×C₄×C₆₁	—	2	2	no	—
131	C₂²×C₄×C₆₁	—	2	2	no	—
132	C₂²×C₄×C₆₁	—	2	2	no	—
133	C₂²×C₄×C₆₁	—	2	2	no	—
134	C₂²×C₄×C₆₁	—	2	4	no	—
135	C₂²×C₄×C₆₁	—	2	4	no	—
136	C₂²×C₄×C₆₁	—	2	4	no	—
137	C₂²×C₄×C₆₁	—	4	2	no	—
138	C₂²×C₄×C₆₁	—	4	2	no	—
139	C₂²×C₄×C₆₁	—	4	2	no	—
140	C₂²×C₄×C₆₁	—	4	2	no	—
141	C₂²×C₄×C₆₁	—	4	4	no	—
142	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
143	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
144	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
145	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
146	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
147	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
149	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
150	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
151	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
152	C₄⋊C₄×C₆₁	—	2	8	no	—
153	C₄⋊C₄×C₆₁	—	2	8	no	—
154	C₄⋊C₄×C₆₁	—	2	8	no	—
155	C₄⋊C₄×C₆₁	—	2	4	no	—
156	C₄⋊C₄×C₆₁	—	2	4	no	—
157	C₄⋊C₄×C₆₁	—	4	4	no	—
158	C₄⋊C₄×C₆₁	—	4	8	no	—
159	C₄⋊C₄×C₆₁	—	4	8	no	—
160	C₂²⋊C₄×C₆₁	—	2	8	no	—
161	C₂²⋊C₄×C₆₁	—	2	8	no	—
162	C₂²⋊C₄×C₆₁	—	2	8	no	—
163	C₂²⋊C₄×C₆₁	—	2	8	no	—
164	C₂²⋊C₄×C₆₁	—	2	8	no	—
165	C₂²⋊C₄×C₆₁	—	4	4	no	—
166	C₂²⋊C₄×C₆₁	—	4	8	no	—
167	C₂²⋊C₄×C₆₁	—	4	4	no	—
168	C₂²⋊C₄×C₆₁	—	4	8	no	—
169	C₂²⋊C₄×C₆₁	—	4	8	no	—
170	C₂²⋊C₄×C₆₁	—	4	8	no	—
171	C₂²⋊C₄×C₆₁	C₂×D₄	1	16	yes	—
172	C₄²×C₆₁	—	2	8	no	—
173	C₄²×C₆₁	—	4	4	no	—
174	C₂³×C₆₁	—	2	2	no	—
175	C₂³×C₆₁	—	2	2	no	—
176	C₂³×C₆₁	—	2	4	no	—
177	C₂³×C₆₁	—	2	4	no	—
178	C₂³×C₆₁	—	2	4	no	—
179	C₂³×C₆₁	—	2	8	no	—
180	C₂³×C₆₁	—	2	4	no	—
181	C₂³×C₆₁	—	2	4	no	—
182	C₂³×C₆₁	—	2	4	no	—
183	C₂³×C₆₁	—	2	8	no	—
184	C₂³×C₆₁	—	2	8	no	—
185	C₂³×C₆₁	—	4	4	no	—
186	C₂³×C₆₁	—	4	4	no	—
187	C₂³×C₆₁	—	4	8	no	—
188	C₂³×C₆₁	—	8	8	no	—
189	C₂³×C₆₁	—	8	4	no	—
190	C₂³×C₆₁	—	8	4	no	—
191	C₂³×C₆₁	—	8	16	no	—
192	C₂³×C₆₁	C₂²×D₄	1	4	yes	—
193	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
194	C₂³×C₆₁	H(5,𝔽₂)	1	4	yes	—
195	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
196	D₄×C₆₁	—	4	16	no	—
197	D₄×C₆₁	—	4	16	no	—
198	D₄×C₆₁	—	8	4	no	—
199	D₄×C₆₁	—	8	4	no	—
200	C₂×C₄×C₆₁	—	2	4	no	—
201	C₂×C₄×C₆₁	—	2	4	no	—
202	C₂×C₄×C₆₁	—	2	2	no	—
203	C₂×C₄×C₆₁	—	2	2	no	—
204	C₂×C₄×C₆₁	—	2	2	no	—
205	C₂×C₄×C₆₁	—	2	2	no	—
206	C₂×C₄×C₆₁	—	2	4	no	—
207	C₂×C₄×C₆₁	—	2	8	no	—
208	C₂×C₄×C₆₁	—	2	4	no	—
209	C₂×C₄×C₆₁	—	2	4	no	—
210	C₂×C₄×C₆₁	—	2	4	no	—
211	C₂×C₄×C₆₁	—	2	4	no	—
212	C₂×C₄×C₆₁	—	2	8	no	—
213	C₂×C₄×C₆₁	—	2	8	no	—
214	C₂×C₄×C₆₁	—	2	4	no	—
215	C₂×C₄×C₆₁	—	2	4	no	—
216	C₂×C₄×C₆₁	—	4	4	no	—
217	C₂×C₄×C₆₁	—	4	4	no	—
218	C₂×C₄×C₆₁	—	4	4	no	—
219	C₂×C₄×C₆₁	—	4	4	no	—
220	C₂×C₄×C₆₁	—	4	8	no	—
221	C₂×C₄×C₆₁	—	4	4	no	—
222	C₂×C₄×C₆₁	—	4	4	no	—
223	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
224	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
225	#36969	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
226	C₂²×C₆₁	—	2	2	no	—
227	C₂²×C₆₁	—	2	2	no	—
228	C₂²×C₆₁	—	2	8	no	—
229	C₂²×C₆₁	—	2	4	no	—
230	C₂²×C₆₁	—	2	4	no	—
231	C₂²×C₆₁	—	2	4	no	—
232	C₂²×C₆₁	—	4	8	no	—
233	C₂²×C₆₁	—	4	4	no	—
234	C₂²×C₆₁	—	4	4	no	—
235	C₂²×C₆₁	—	4	4	no	—
236	C₂²×C₆₁	—	4	8	no	—
237	C₂²×C₆₁	—	4	8	no	—
238	C₂²×C₆₁	—	8	8	no	—
239	C₂²×C₆₁	—	8	16	no	—
240	C₂²×C₆₁	#535	1	4	yes	—
241	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
242	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	2	yes	—
243	C₂²×C₆₁	#585	1	2	yes	—
244	C₂²×C₆₁	#585	1	2	yes	—
245	C₄×C₆₁	—	2	4	no	—
246	C₄×C₆₁	—	2	4	no	—
247	C₄×C₆₁	—	4	2	no	—
248	C₄×C₆₁	—	4	2	no	—
249	C₄×C₆₁	—	4	4	no	—
250	C₄×C₆₁	—	4	2	no	—
251	C₄×C₆₁	—	4	2	no	—
252	C₄×C₆₁	—	4	8	no	—
253	C₂×#534	C₂×C₆₁	1	1	yes	characteristic
254	C₂²×#126	C₂×C₆₁	1	1	yes	characteristic, complemented
255	#2854	C₂×C₆₁	1	2	yes	complemented
256	#2718	C₂×C₆₁	1	8	yes	complemented
257	#2685	C₂×C₆₁	1	8	yes	complemented
258	#2618	C₂×C₆₁	1	2	yes	complemented
259	#2591	C₂×C₆₁	1	2	yes	complemented
260	#2501	C₂×C₆₁	1	2	yes	complemented
261	#2405	C₂×C₆₁	1	2	yes	complemented
262	#2405	C₂×C₆₁	1	2	yes	complemented
263	#2312	C₂×C₆₁	1	1	yes	characteristic, complemented
264	C₂×C₆₁	—	2	4	no	—
265	C₂×C₆₁	—	4	4	no	—
266	C₂×C₆₁	—	8	4	no	—
267	C₂×C₆₁	C₂×#535	1	1	yes	characteristic
268	C₂×C₆₁	#3485	1	1	yes	characteristic
269	C₂×C₆₁	#3485	1	1	yes	characteristic
270	C₂×C₆₁	#3560	1	4	yes	—
271	C₂³×D₄	C₂²×C₆₁	1	2	yes	—
272	#534	—	2	8	no	—
273	C₂×#126	—	2	8	no	—
274	C₂×#126	C₂²×C₆₁	1	8	yes	complemented
275	C₂×#123	C₂²×C₆₁	1	4	yes	—
276	C₂×#123	C₂²×C₆₁	1	4	yes	complemented
277	C₂×#123	C₂²×C₆₁	1	4	yes	complemented
278	C₂×#121	C₂²×C₆₁	1	2	yes	—
279	C₂×#121	C₂²×C₆₁	1	2	yes	—
280	C₂×#120	C₂²×C₆₁	1	4	yes	—
281	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
282	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
283	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
284	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
285	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
286	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
287	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic, complemented
288	#400	C₂²×C₆₁	1	4	yes	complemented
289	#399	C₂²×C₆₁	1	8	yes	complemented
290	#398	C₂²×C₆₁	1	4	yes	complemented
291	#396	C₂²×C₆₁	1	8	yes	complemented
292	#394	C₂²×C₆₁	1	8	yes	—
293	#394	C₂²×C₆₁	1	8	yes	—
294	#394	C₂²×C₆₁	1	4	yes	complemented
295	#394	C₂²×C₆₁	1	4	yes	complemented
296	#390	C₂²×C₆₁	1	4	yes	complemented
297	#390	C₂²×C₆₁	1	4	yes	complemented
298	#389	C₂²×C₆₁	1	4	yes	complemented
299	#388	C₂²×C₆₁	1	8	yes	complemented
300	#388	C₂²×C₆₁	1	8	yes	complemented
301	#388	C₂²×C₆₁	1	8	yes	complemented
302	#386	C₂²×C₆₁	1	4	yes	complemented
303	#386	C₂²×C₆₁	1	4	yes	complemented
304	#385	C₂²×C₆₁	1	4	yes	complemented
305	#385	C₂²×C₆₁	1	4	yes	complemented
306	#384	C₂²×C₆₁	1	4	yes	complemented
307	#380	C₂²×C₆₁	1	2	yes	complemented
308	#379	C₂²×C₆₁	1	2	yes	—
309	#379	C₂²×C₆₁	1	4	yes	complemented
310	#379	C₂²×C₆₁	1	4	yes	complemented
311	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	complemented
312	C₆₁	#36969	1	1	yes	characteristic, direct product factor, Sylow
313	C₂⁵	C₂³×C₆₁	1	1	yes	characteristic
314	C₂⁵	C₂³×C₆₁	1	2	yes	—
315	C₂²×D₄	—	2	8	no	—
316	C₂²×D₄	—	4	8	no	—
317	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
318	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
319	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
320	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
321	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
322	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
323	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
324	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
325	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
326	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
327	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
328	#126	—	2	32	no	—
329	#123	—	2	16	no	—
330	#123	—	4	8	no	—
331	#123	—	4	8	no	—
332	#121	—	2	8	no	—
333	#121	—	2	8	no	—
334	#120	—	2	16	no	—
335	C₂×C₄⋊C₄	—	2	4	no	—
336	C₂×C₄⋊C₄	—	2	4	no	—
337	C₂×C₄⋊C₄	—	2	4	no	—
338	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
339	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
340	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
341	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
342	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
343	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
344	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
345	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
346	C₂×C₂²⋊C₄	—	2	4	no	—
347	C₂×C₂²⋊C₄	—	2	4	no	—
348	C₂×C₂²⋊C₄	D₄×C₆₁	1	8	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
350	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
351	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
352	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
354	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
355	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
356	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
357	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
358	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
359	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
360	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
361	C₂×C₄²	—	2	4	no	—
362	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
363	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
364	#95	C₂³×C₆₁	1	4	yes	—
365	#95	C₂³×C₆₁	1	4	yes	—
366	#95	C₂³×C₆₁	1	8	yes	—
367	#95	C₂³×C₆₁	1	8	yes	—
368	C₂⁴	—	2	4	no	—
369	C₂⁴	—	2	4	no	—
370	C₂⁴	—	4	4	no	—
371	C₂⁴	—	4	2	no	—
372	C₂⁴	—	4	2	no	—
373	C₂⁴	—	4	4	no	—
374	C₂⁴	—	4	4	no	—
375	C₂⁴	C₂×D₄×C₆₁	1	4	yes	—
376	C₂⁴	C₂⁴×C₆₁	1	4	yes	—
377	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
378	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
379	C₂×D₄	—	2	8	no	—
380	C₂×D₄	—	2	8	no	—
381	C₂×D₄	—	2	8	no	—
382	C₂×D₄	—	2	8	no	—
383	C₂×D₄	—	2	4	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	4	4	no	—
386	C₂×D₄	—	4	4	no	—
387	C₂×D₄	—	4	4	no	—
388	C₂×D₄	—	4	4	no	—
389	C₂×D₄	—	4	32	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	4	no	—
395	C₂²×C₄	—	2	4	no	—
396	C₂²×C₄	—	2	4	no	—
397	C₂²×C₄	—	4	4	no	—
398	C₂²×C₄	—	4	2	no	—
399	C₂²×C₄	—	4	2	no	—
400	C₂²×C₄	—	4	2	no	—
401	C₂²×C₄	—	4	2	no	—
402	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
403	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
404	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
405	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
406	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
407	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
408	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
409	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
410	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
411	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
412	C₄⋊C₄	—	2	8	no	—
413	C₄⋊C₄	—	2	8	no	—
414	C₄⋊C₄	—	2	8	no	—
415	C₄⋊C₄	—	2	4	no	—
416	C₄⋊C₄	—	2	4	no	—
417	C₄⋊C₄	—	4	8	no	—
418	C₄⋊C₄	—	4	8	no	—
419	C₄⋊C₄	—	4	4	no	—
420	C₂²⋊C₄	—	2	8	no	—
421	C₂²⋊C₄	—	2	8	no	—
422	C₂²⋊C₄	—	2	8	no	—
423	C₂²⋊C₄	—	2	8	no	—
424	C₂²⋊C₄	—	2	8	no	—
425	C₂²⋊C₄	—	4	8	no	—
426	C₂²⋊C₄	—	4	8	no	—
427	C₂²⋊C₄	—	4	4	no	—
428	C₂²⋊C₄	—	4	8	no	—
429	C₂²⋊C₄	—	4	4	no	—
430	C₂²⋊C₄	—	4	8	no	—
431	C₂²⋊C₄	C₂×D₄×C₆₁	1	16	yes	—
432	C₄²	—	2	8	no	—
433	C₄²	—	4	4	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	2	2	no	—
436	C₂³	—	2	4	no	—
437	C₂³	—	2	4	no	—
438	C₂³	—	2	4	no	—
439	C₂³	—	2	8	no	—
440	C₂³	—	2	4	no	—
441	C₂³	—	2	4	no	—
442	C₂³	—	2	4	no	—
443	C₂³	—	2	8	no	—
444	C₂³	—	2	8	no	—
445	C₂³	—	4	4	no	—
446	C₂³	—	4	4	no	—
447	C₂³	—	4	8	no	—
448	C₂³	—	8	8	no	—
449	C₂³	—	8	4	no	—
450	C₂³	—	8	4	no	—
451	C₂³	—	8	16	no	—
452	C₂³	C₂²×D₄×C₆₁	1	4	yes	—
453	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
454	C₂³	H(5,𝔽₂)×C₆₁	1	4	yes	—
455	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
456	D₄	—	4	16	no	—
457	D₄	—	4	16	no	—
458	D₄	—	8	4	no	—
459	D₄	—	8	4	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	8	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	8	no	—
473	C₂×C₄	—	2	8	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	—	4	4	no	—
479	C₂×C₄	—	4	4	no	—
480	C₂×C₄	—	4	8	no	—
481	C₂×C₄	—	4	4	no	—
482	C₂×C₄	—	4	4	no	—
483	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
484	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
485	C₂²	—	2	8	no	—
486	C₂²	—	2	2	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	2	4	no	—
489	C₂²	—	2	4	no	—
490	C₂²	—	2	4	no	—
491	C₂²	—	4	8	no	—
492	C₂²	—	4	8	no	—
493	C₂²	—	4	8	no	—
494	C₂²	—	4	4	no	—
495	C₂²	—	4	4	no	—
496	C₂²	—	4	4	no	—
497	C₂²	—	8	8	no	—
498	C₂²	—	8	16	no	—
499	C₂²	C₆₁×#535	1	4	yes	—
500	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
501	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	2	yes	—
502	C₂²	C₆₁×#585	1	2	yes	—
503	C₂²	C₆₁×#585	1	2	yes	—
504	C₄	—	2	4	no	—
505	C₄	—	2	4	no	—
506	C₄	—	4	8	no	—
507	C₄	—	4	2	no	—
508	C₄	—	4	2	no	—
509	C₄	—	4	4	no	—
510	C₄	—	4	2	no	—
511	C₄	—	4	2	no	—
512	C₂	—	2	4	no	—
513	C₂	—	4	4	no	—
514	C₂	—	8	4	no	—
515	C₂	C₂×C₆₁×#535	1	1	yes	characteristic
516	C₂	C₆₁×#3485	1	1	yes	characteristic
517	C₂	C₆₁×#3485	1	1	yes	characteristic
518	C₂	C₆₁×#3560	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₁
prime radical	C₂×C₆₁×#534	C₂
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
2. C₂²×#126×C₆₁	C₂	semidirect
3. C₆₁×#2854	C₂	semidirect
4. C₆₁×#2718	C₂	semidirect
5. C₆₁×#2685	C₂	semidirect
6. C₆₁×#2618	C₂	semidirect
7. C₆₁×#2591	C₂	semidirect
8. C₆₁×#2501	C₂	semidirect
9. C₆₁×#2405	C₂	semidirect
10. C₆₁×#2405	C₂	semidirect
11. C₆₁×#2312	C₂	semidirect
15. C₂×#126×C₆₁	C₂²	semidirect
17. C₂×#123×C₆₁	C₂²	semidirect
18. C₂×#123×C₆₁	C₂²	semidirect
22. C₂²×C₄⋊C₄×C₆₁	C₂²	semidirect
23. C₂²×C₄⋊C₄×C₆₁	C₂²	semidirect
24. C₂²×C₄⋊C₄×C₆₁	C₂²	semidirect
28. C₂²×C₄²×C₆₁	C₂²	semidirect
29. C₆₁×#400	C₂²	semidirect
30. C₆₁×#399	C₂²	semidirect
31. C₆₁×#398	C₂²	semidirect
32. C₆₁×#396	C₂²	semidirect
35. C₆₁×#394	C₂²	semidirect
36. C₆₁×#394	C₂²	semidirect
37. C₆₁×#390	C₂²	semidirect
38. C₆₁×#390	C₂²	semidirect
39. C₆₁×#389	C₂²	semidirect
40. C₆₁×#388	C₂²	semidirect
41. C₆₁×#388	C₂²	semidirect
42. C₆₁×#388	C₂²	semidirect
43. C₆₁×#386	C₂²	semidirect
44. C₆₁×#386	C₂²	semidirect
45. C₆₁×#385	C₂²	semidirect
46. C₆₁×#385	C₂²	semidirect
47. C₆₁×#384	C₂²	semidirect
48. C₆₁×#380	C₂²	semidirect
50. C₆₁×#379	C₂²	semidirect
51. C₆₁×#379	C₂²	semidirect
52. C₄×C₂²⋊C₄×C₆₁	C₂²	semidirect
225. #36969	C₆₁	direct (N × H)
254. C₂²×#126	C₂×C₆₁	semidirect
255. #2854	C₂×C₆₁	semidirect
256. #2718	C₂×C₆₁	semidirect
257. #2685	C₂×C₆₁	semidirect
258. #2618	C₂×C₆₁	semidirect
259. #2591	C₂×C₆₁	semidirect
260. #2501	C₂×C₆₁	semidirect
261. #2405	C₂×C₆₁	semidirect
262. #2405	C₂×C₆₁	semidirect
263. #2312	C₂×C₆₁	semidirect
274. C₂×#126	C₂²×C₆₁	semidirect
276. C₂×#123	C₂²×C₆₁	semidirect
277. C₂×#123	C₂²×C₆₁	semidirect
281. C₂²×C₄⋊C₄	C₂²×C₆₁	semidirect
282. C₂²×C₄⋊C₄	C₂²×C₆₁	semidirect
283. C₂²×C₄⋊C₄	C₂²×C₆₁	semidirect
287. C₂²×C₄²	C₂²×C₆₁	semidirect
288. #400	C₂²×C₆₁	semidirect
289. #399	C₂²×C₆₁	semidirect
290. #398	C₂²×C₆₁	semidirect
291. #396	C₂²×C₆₁	semidirect
294. #394	C₂²×C₆₁	semidirect
295. #394	C₂²×C₆₁	semidirect
296. #390	C₂²×C₆₁	semidirect
297. #390	C₂²×C₆₁	semidirect
298. #389	C₂²×C₆₁	semidirect
299. #388	C₂²×C₆₁	semidirect
300. #388	C₂²×C₆₁	semidirect
301. #388	C₂²×C₆₁	semidirect
302. #386	C₂²×C₆₁	semidirect
303. #386	C₂²×C₆₁	semidirect
304. #385	C₂²×C₆₁	semidirect
305. #385	C₂²×C₆₁	semidirect
306. #384	C₂²×C₆₁	semidirect
307. #380	C₂²×C₆₁	semidirect
309. #379	C₂²×C₆₁	semidirect
310. #379	C₂²×C₆₁	semidirect
311. C₄×C₂²⋊C₄	C₂²×C₆₁	semidirect
312. C₆₁	#36969	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×#534	2
C₂²×#126×C₆₁	2
C₆₁×#2854	2
C₆₁×#2718	2
C₆₁×#2685	2
C₆₁×#2618	2
C₆₁×#2591	2
C₆₁×#2501	2
C₆₁×#2405	2
C₆₁×#2312	2
#36969	61

Subgroups — C61×#36969 #29540402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#36969 #29540402