Subgroups — C₆₁×#36962 #29540395

Order 15616.

1986 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#126×C₆₁	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2855	C₂	1	2	yes	maximal, complemented
4	C₆₁×#2721	C₂	1	8	yes	maximal, complemented
5	C₆₁×#2716	C₂	1	8	yes	maximal, complemented
6	C₆₁×#2626	C₂	1	2	yes	maximal
7	C₆₁×#2561	C₂	1	2	yes	maximal
8	C₆₁×#2502	C₂	1	2	yes	maximal, complemented
9	C₆₁×#2484	C₂	1	2	yes	maximal, complemented
10	C₆₁×#2482	C₂	1	2	yes	maximal
11	C₆₁×#2313	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#544	—	2	8	no	—
13	C₂×C₄⋊Q₈×C₆₁	C₂²	1	4	yes	complemented
14	C₂×#126×C₆₁	—	2	8	no	—
15	C₂×#126×C₆₁	C₂²	1	8	yes	—
16	C₂×#125×C₆₁	C₂²	1	4	yes	complemented
17	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
18	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
19	C₂×#117×C₆₁	C₂²	1	2	yes	—
20	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
27	C₆₁×#400	C₂²	1	4	yes	complemented
28	C₆₁×#399	C₂²	1	4	yes	—
29	C₆₁×#399	C₂²	1	4	yes	—
30	C₆₁×#398	C₂²	1	8	yes	complemented
31	C₆₁×#398	C₂²	1	4	yes	complemented
32	C₆₁×#397	C₂²	1	4	yes	—
33	C₆₁×#397	C₂²	1	4	yes	—
34	C₆₁×#396	C₂²	1	8	yes	—
35	C₆₁×#393	C₂²	1	4	yes	—
36	C₆₁×#393	C₂²	1	4	yes	—
37	C₆₁×#391	C₂²	1	4	yes	complemented
38	C₆₁×#391	C₂²	1	4	yes	complemented
39	C₆₁×#389	C₂²	1	4	yes	complemented
40	C₆₁×#388	C₂²	1	8	yes	—
41	C₆₁×#388	C₂²	1	8	yes	—
42	C₆₁×#387	C₂²	1	8	yes	complemented
43	C₆₁×#387	C₂²	1	8	yes	complemented
44	C₆₁×#387	C₂²	1	8	yes	complemented
45	C₆₁×#385	C₂²	1	4	yes	—
46	C₆₁×#385	C₂²	1	4	yes	—
47	C₆₁×#384	C₂²	1	4	yes	complemented
48	C₆₁×#381	C₂²	1	4	yes	—
49	C₆₁×#381	C₂²	1	2	yes	—
50	C₆₁×#380	C₂²	1	2	yes	—
51	C₆₁×#379	C₂²	1	4	yes	—
52	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
53	C₂⁵×C₆₁	C₂³	1	1	yes	characteristic
54	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
55	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
56	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
62	C₄⋊Q₈×C₆₁	—	2	16	no	—
63	#126×C₆₁	—	2	32	no	—
64	#125×C₆₁	—	2	16	no	—
65	C₂²⋊Q₈×C₆₁	—	2	8	no	—
66	C₂²⋊Q₈×C₆₁	—	2	8	no	—
67	#117×C₆₁	—	2	8	no	—
68	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
69	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
70	C₂×C₄⋊C₄×C₆₁	D₄	1	8	yes	—
71	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
73	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
74	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
76	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
77	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
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	8	yes	—
81	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
82	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
83	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
84	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
85	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
86	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
87	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
88	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	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	8	yes	—
92	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
93	C₂×C₄²×C₆₁	—	2	4	no	—
94	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
95	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
96	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
97	#95×C₆₁	C₂³	1	4	yes	—
98	#95×C₆₁	C₂³	1	4	yes	—
99	#95×C₆₁	C₂³	1	4	yes	—
100	#95×C₆₁	C₂³	1	4	yes	—
101	#95×C₆₁	C₂³	1	8	yes	—
102	#95×C₆₁	C₂³	1	8	yes	—
103	#95×C₆₁	C₂³	1	8	yes	—
104	#95×C₆₁	C₂³	1	8	yes	—
105	C₂⁴×C₆₁	—	2	2	no	—
106	C₂⁴×C₆₁	—	2	4	no	—
107	C₂⁴×C₆₁	—	4	2	no	—
108	C₂⁴×C₆₁	—	4	2	no	—
109	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
110	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
111	C₂×Q₈×C₆₁	—	2	4	no	—
112	C₂×Q₈×C₆₁	—	2	4	no	—
113	C₂×Q₈×C₆₁	—	4	4	no	—
114	C₂×Q₈×C₆₁	—	4	4	no	—
115	C₂²×C₄×C₆₁	—	2	4	no	—
116	C₂²×C₄×C₆₁	—	2	2	no	—
117	C₂²×C₄×C₆₁	—	2	2	no	—
118	C₂²×C₄×C₆₁	—	2	2	no	—
119	C₂²×C₄×C₆₁	—	2	4	no	—
120	C₂²×C₄×C₆₁	—	4	2	no	—
121	C₂²×C₄×C₆₁	—	4	2	no	—
122	C₂²×C₄×C₆₁	—	4	2	no	—
123	C₂²×C₄×C₆₁	—	4	2	no	—
124	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
125	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
126	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
127	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
128	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
129	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
130	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
131	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
132	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
133	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
134	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
135	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
136	C₄⋊C₄×C₆₁	—	2	8	no	—
137	C₄⋊C₄×C₆₁	—	2	8	no	—
138	C₄⋊C₄×C₆₁	—	2	4	no	—
139	C₄⋊C₄×C₆₁	—	2	4	no	—
140	C₄⋊C₄×C₆₁	—	2	4	no	—
141	C₄⋊C₄×C₆₁	—	2	4	no	—
142	C₄⋊C₄×C₆₁	—	2	8	no	—
143	C₄⋊C₄×C₆₁	—	2	8	no	—
144	C₄⋊C₄×C₆₁	—	4	4	no	—
145	C₄⋊C₄×C₆₁	—	4	8	no	—
146	C₄⋊C₄×C₆₁	—	4	8	no	—
147	C₄⋊C₄×C₆₁	C₂×D₄	1	16	yes	—
148	C₂²⋊C₄×C₆₁	—	2	8	no	—
149	C₂²⋊C₄×C₆₁	—	2	8	no	—
150	C₂²⋊C₄×C₆₁	—	2	8	no	—
151	C₂²⋊C₄×C₆₁	—	2	8	no	—
152	C₂²⋊C₄×C₆₁	—	2	8	no	—
153	C₂²⋊C₄×C₆₁	—	4	8	no	—
154	C₂²⋊C₄×C₆₁	—	4	8	no	—
155	C₄²×C₆₁	—	2	8	no	—
156	C₄²×C₆₁	—	2	8	no	—
157	C₄²×C₆₁	—	4	4	no	—
158	C₂³×C₆₁	—	2	2	no	—
159	C₂³×C₆₁	—	2	2	no	—
160	C₂³×C₆₁	—	2	2	no	—
161	C₂³×C₆₁	—	2	4	no	—
162	C₂³×C₆₁	—	2	4	no	—
163	C₂³×C₆₁	—	2	4	no	—
164	C₂³×C₆₁	—	4	4	no	—
165	C₂³×C₆₁	—	4	4	no	—
166	C₂³×C₆₁	—	4	4	no	—
167	C₂³×C₆₁	—	8	8	no	—
168	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
169	C₂³×C₆₁	2₋¹⁺⁴	1	4	yes	—
170	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
171	Q₈×C₆₁	—	8	4	no	—
172	Q₈×C₆₁	—	8	4	no	—
173	C₂×C₄×C₆₁	—	2	8	no	—
174	C₂×C₄×C₆₁	—	2	4	no	—
175	C₂×C₄×C₆₁	—	2	4	no	—
176	C₂×C₄×C₆₁	—	2	4	no	—
177	C₂×C₄×C₆₁	—	2	2	no	—
178	C₂×C₄×C₆₁	—	2	2	no	—
179	C₂×C₄×C₆₁	—	2	4	no	—
180	C₂×C₄×C₆₁	—	2	4	no	—
181	C₂×C₄×C₆₁	—	2	2	no	—
182	C₂×C₄×C₆₁	—	2	8	no	—
183	C₂×C₄×C₆₁	—	2	4	no	—
184	C₂×C₄×C₆₁	—	2	8	no	—
185	C₂×C₄×C₆₁	—	2	8	no	—
186	C₂×C₄×C₆₁	—	2	8	no	—
187	C₂×C₄×C₆₁	—	2	8	no	—
188	C₂×C₄×C₆₁	—	2	4	no	—
189	C₂×C₄×C₆₁	—	2	4	no	—
190	C₂×C₄×C₆₁	—	4	4	no	—
191	C₂×C₄×C₆₁	—	4	4	no	—
192	C₂×C₄×C₆₁	—	4	4	no	—
193	C₂×C₄×C₆₁	—	4	4	no	—
194	C₂×C₄×C₆₁	—	4	4	no	—
195	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
196	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
197	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
198	#36962	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂²×C₆₁	—	2	2	no	—
200	C₂²×C₆₁	—	2	2	no	—
201	C₂²×C₆₁	—	2	8	no	—
202	C₂²×C₆₁	—	4	2	no	—
203	C₂²×C₆₁	—	4	2	no	—
204	C₂²×C₆₁	—	4	2	no	—
205	C₂²×C₆₁	—	4	8	no	—
206	C₂²×C₆₁	—	8	8	no	—
207	C₂²×C₆₁	#536	1	4	yes	—
208	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
209	C₂²×C₆₁	C₂×2₋¹⁺⁴	1	2	yes	—
210	C₂²×C₆₁	#585	1	2	yes	—
211	C₂²×C₆₁	#585	1	2	yes	—
212	C₄×C₆₁	—	2	4	no	—
213	C₄×C₆₁	—	2	4	no	—
214	C₄×C₆₁	—	2	4	no	—
215	C₄×C₆₁	—	4	2	no	—
216	C₄×C₆₁	—	4	4	no	—
217	C₄×C₆₁	—	4	4	no	—
218	C₄×C₆₁	—	4	2	no	—
219	C₄×C₆₁	—	4	2	no	—
220	C₄×C₆₁	—	4	8	no	—
221	C₂×#544	C₂×C₆₁	1	1	yes	characteristic, complemented
222	C₂²×#126	C₂×C₆₁	1	1	yes	characteristic
223	#2855	C₂×C₆₁	1	2	yes	complemented
224	#2721	C₂×C₆₁	1	8	yes	complemented
225	#2716	C₂×C₆₁	1	8	yes	complemented
226	#2626	C₂×C₆₁	1	2	yes	—
227	#2561	C₂×C₆₁	1	2	yes	—
228	#2502	C₂×C₆₁	1	2	yes	complemented
229	#2484	C₂×C₆₁	1	2	yes	complemented
230	#2482	C₂×C₆₁	1	2	yes	—
231	#2313	C₂×C₆₁	1	1	yes	characteristic, complemented
232	C₂×C₆₁	—	2	4	no	—
233	C₂×C₆₁	—	8	2	no	—
234	C₂×C₆₁	C₂×#536	1	1	yes	characteristic
235	C₂×C₆₁	#3485	1	1	yes	characteristic
236	C₂×C₆₁	#3487	1	1	yes	characteristic
237	C₂×C₆₁	#3564	1	4	yes	—
238	#544	—	2	8	no	—
239	C₂×C₄⋊Q₈	C₂²×C₆₁	1	4	yes	complemented
240	C₂×#126	—	2	8	no	—
241	C₂×#126	C₂²×C₆₁	1	8	yes	—
242	C₂×#125	C₂²×C₆₁	1	4	yes	complemented
243	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
244	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
245	C₂×#117	C₂²×C₆₁	1	2	yes	—
246	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
247	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
248	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
249	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
250	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
251	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
252	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
253	#400	C₂²×C₆₁	1	4	yes	complemented
254	#399	C₂²×C₆₁	1	4	yes	—
255	#399	C₂²×C₆₁	1	4	yes	—
256	#398	C₂²×C₆₁	1	8	yes	complemented
257	#398	C₂²×C₆₁	1	4	yes	complemented
258	#397	C₂²×C₆₁	1	4	yes	—
259	#397	C₂²×C₆₁	1	4	yes	—
260	#396	C₂²×C₆₁	1	8	yes	—
261	#393	C₂²×C₆₁	1	4	yes	—
262	#393	C₂²×C₆₁	1	4	yes	—
263	#391	C₂²×C₆₁	1	4	yes	complemented
264	#391	C₂²×C₆₁	1	4	yes	complemented
265	#389	C₂²×C₆₁	1	4	yes	complemented
266	#388	C₂²×C₆₁	1	8	yes	—
267	#388	C₂²×C₆₁	1	8	yes	—
268	#387	C₂²×C₆₁	1	8	yes	complemented
269	#387	C₂²×C₆₁	1	8	yes	complemented
270	#387	C₂²×C₆₁	1	8	yes	complemented
271	#385	C₂²×C₆₁	1	4	yes	—
272	#385	C₂²×C₆₁	1	4	yes	—
273	#384	C₂²×C₆₁	1	4	yes	complemented
274	#381	C₂²×C₆₁	1	4	yes	—
275	#381	C₂²×C₆₁	1	2	yes	—
276	#380	C₂²×C₆₁	1	2	yes	—
277	#379	C₂²×C₆₁	1	4	yes	—
278	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
279	C₆₁	#36962	1	1	yes	characteristic, direct product factor, Sylow
280	C₂⁵	C₂³×C₆₁	1	1	yes	characteristic
281	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
282	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
283	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
284	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
285	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
286	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
287	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
288	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
289	C₄⋊Q₈	—	2	16	no	—
290	#126	—	2	32	no	—
291	#125	—	2	16	no	—
292	C₂²⋊Q₈	—	2	8	no	—
293	C₂²⋊Q₈	—	2	8	no	—
294	#117	—	2	8	no	—
295	C₂×C₄⋊C₄	—	2	4	no	—
296	C₂×C₄⋊C₄	—	2	4	no	—
297	C₂×C₄⋊C₄	D₄×C₆₁	1	8	yes	—
298	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
299	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
300	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
301	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
302	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
303	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
304	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
305	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
306	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
307	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
308	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
309	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
310	C₂×C₂²⋊C₄	—	2	4	no	—
311	C₂×C₂²⋊C₄	—	2	4	no	—
312	C₂×C₂²⋊C₄	—	2	4	no	—
313	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
314	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
315	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
316	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
317	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
318	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
319	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
320	C₂×C₄²	—	2	4	no	—
321	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
322	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
323	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
324	#95	C₂³×C₆₁	1	4	yes	—
325	#95	C₂³×C₆₁	1	4	yes	—
326	#95	C₂³×C₆₁	1	4	yes	—
327	#95	C₂³×C₆₁	1	4	yes	—
328	#95	C₂³×C₆₁	1	8	yes	—
329	#95	C₂³×C₆₁	1	8	yes	—
330	#95	C₂³×C₆₁	1	8	yes	—
331	#95	C₂³×C₆₁	1	8	yes	—
332	C₂⁴	—	2	2	no	—
333	C₂⁴	—	2	4	no	—
334	C₂⁴	—	4	2	no	—
335	C₂⁴	—	4	2	no	—
336	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
337	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
338	C₂×Q₈	—	2	4	no	—
339	C₂×Q₈	—	2	4	no	—
340	C₂×Q₈	—	4	4	no	—
341	C₂×Q₈	—	4	4	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	—	4	2	no	—
351	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
352	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
353	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
354	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
355	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
356	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
357	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
358	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
359	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
360	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
361	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
362	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
363	C₄⋊C₄	—	2	8	no	—
364	C₄⋊C₄	—	2	8	no	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	—	2	8	no	—
370	C₄⋊C₄	—	2	8	no	—
371	C₄⋊C₄	—	4	4	no	—
372	C₄⋊C₄	—	4	8	no	—
373	C₄⋊C₄	—	4	8	no	—
374	C₄⋊C₄	C₂×D₄×C₆₁	1	16	yes	—
375	C₂²⋊C₄	—	2	8	no	—
376	C₂²⋊C₄	—	2	8	no	—
377	C₂²⋊C₄	—	2	8	no	—
378	C₂²⋊C₄	—	2	8	no	—
379	C₂²⋊C₄	—	2	8	no	—
380	C₂²⋊C₄	—	4	8	no	—
381	C₂²⋊C₄	—	4	8	no	—
382	C₄²	—	2	8	no	—
383	C₄²	—	2	8	no	—
384	C₄²	—	4	4	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	4	no	—
389	C₂³	—	2	4	no	—
390	C₂³	—	2	4	no	—
391	C₂³	—	4	4	no	—
392	C₂³	—	4	4	no	—
393	C₂³	—	4	4	no	—
394	C₂³	—	8	8	no	—
395	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
396	C₂³	2₋¹⁺⁴×C₆₁	1	4	yes	—
397	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
398	Q₈	—	8	4	no	—
399	Q₈	—	8	4	no	—
400	C₂×C₄	—	2	8	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	8	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	8	no	—
412	C₂×C₄	—	2	8	no	—
413	C₂×C₄	—	2	8	no	—
414	C₂×C₄	—	2	8	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	4	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
423	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
424	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
425	C₂²	—	2	8	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	4	8	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	8	8	no	—
433	C₂²	C₆₁×#536	1	4	yes	—
434	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
435	C₂²	C₂×2₋¹⁺⁴×C₆₁	1	2	yes	—
436	C₂²	C₆₁×#585	1	2	yes	—
437	C₂²	C₆₁×#585	1	2	yes	—
438	C₄	—	2	4	no	—
439	C₄	—	2	4	no	—
440	C₄	—	2	4	no	—
441	C₄	—	4	8	no	—
442	C₄	—	4	2	no	—
443	C₄	—	4	4	no	—
444	C₄	—	4	4	no	—
445	C₄	—	4	2	no	—
446	C₄	—	4	2	no	—
447	C₂	—	2	4	no	—
448	C₂	—	8	2	no	—
449	C₂	C₂×C₆₁×#536	1	1	yes	characteristic
450	C₂	C₆₁×#3485	1	1	yes	characteristic
451	C₂	C₆₁×#3487	1	1	yes	characteristic
452	C₂	C₆₁×#3564	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₁
prime radical	C₂⁵×C₆₁	C₂³
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. C₂×C₆₁×#544	C₂	semidirect
3. C₆₁×#2855	C₂	semidirect
4. C₆₁×#2721	C₂	semidirect
5. C₆₁×#2716	C₂	semidirect
8. C₆₁×#2502	C₂	semidirect
9. C₆₁×#2484	C₂	semidirect
11. C₆₁×#2313	C₂	semidirect
13. C₂×C₄⋊Q₈×C₆₁	C₂²	semidirect
16. C₂×#125×C₆₁	C₂²	semidirect
27. C₆₁×#400	C₂²	semidirect
30. C₆₁×#398	C₂²	semidirect
31. C₆₁×#398	C₂²	semidirect
37. C₆₁×#391	C₂²	semidirect
38. C₆₁×#391	C₂²	semidirect
39. C₆₁×#389	C₂²	semidirect
42. C₆₁×#387	C₂²	semidirect
43. C₆₁×#387	C₂²	semidirect
44. C₆₁×#387	C₂²	semidirect
47. C₆₁×#384	C₂²	semidirect
198. #36962	C₆₁	direct (N × H)
221. C₂×#544	C₂×C₆₁	semidirect
223. #2855	C₂×C₆₁	semidirect
224. #2721	C₂×C₆₁	semidirect
225. #2716	C₂×C₆₁	semidirect
228. #2502	C₂×C₆₁	semidirect
229. #2484	C₂×C₆₁	semidirect
231. #2313	C₂×C₆₁	semidirect
239. C₂×C₄⋊Q₈	C₂²×C₆₁	semidirect
242. C₂×#125	C₂²×C₆₁	semidirect
253. #400	C₂²×C₆₁	semidirect
256. #398	C₂²×C₆₁	semidirect
257. #398	C₂²×C₆₁	semidirect
263. #391	C₂²×C₆₁	semidirect
264. #391	C₂²×C₆₁	semidirect
265. #389	C₂²×C₆₁	semidirect
268. #387	C₂²×C₆₁	semidirect
269. #387	C₂²×C₆₁	semidirect
270. #387	C₂²×C₆₁	semidirect
273. #384	C₂²×C₆₁	semidirect
279. C₆₁	#36962	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×#544	2
C₂²×#126×C₆₁	2
C₆₁×#2855	2
C₆₁×#2721	2
C₆₁×#2716	2
C₆₁×#2626	2
C₆₁×#2561	2
C₆₁×#2502	2
C₆₁×#2484	2
C₆₁×#2482	2
C₆₁×#2313	2
#36962	61

Subgroups — C61×#36962 #29540395

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#36962 #29540395