Subgroups — C₆₁×#62905 #29566338

Order 15616.

7326 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3560	C₂	1	12	yes	maximal, complemented
2	C₆₁×#3559	C₂	1	6	yes	maximal, complemented
3	C₆₁×#3537	C₂	1	6	yes	maximal, complemented
4	C₆₁×#3534	C₂	1	12	yes	maximal, complemented
5	C₆₁×#3519	C₂	1	6	yes	maximal, complemented
6	C₆₁×#3496	C₂	1	3	yes	maximal, complemented
7	C₆₁×#3496	C₂	1	6	yes	maximal, complemented
8	C₆₁×#3494	C₂	1	6	yes	maximal, complemented
9	C₂×C₆₁×#553	C₂	1	3	yes	maximal, complemented
10	C₆₁×#3459	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3459	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×H(5,𝔽₂)×C₆₁	C₂²	1	6	yes	complemented
13	C₆₁×#563	C₂²	1	12	yes	complemented
14	C₆₁×#562	C₂²	1	12	yes	complemented
15	C₆₁×#560	C₂²	1	24	yes	complemented
16	C₆₁×#555	C₂²	1	6	yes	complemented
17	C₆₁×#554	C₂²	1	6	yes	complemented
18	C₆₁×#553	C₂²	1	12	yes	complemented
19	C₆₁×#553	C₂²	1	12	yes	complemented
20	C₆₁×#553	C₂²	1	12	yes	complemented
21	C₆₁×#553	C₂²	1	24	yes	complemented
22	C₆₁×#553	C₂²	1	12	yes	complemented
23	C₆₁×#551	C₂²	1	24	yes	complemented
24	C₆₁×#550	C₂²	1	2	yes	complemented
25	C₆₁×#547	C₂²	1	24	yes	complemented
26	C₆₁×#547	C₂²	1	12	yes	complemented
27	C₆₁×#546	C₂²	1	24	yes	complemented
28	C₆₁×#546	C₂²	1	24	yes	complemented
29	C₆₁×#546	C₂²	1	24	yes	complemented
30	C₆₁×#546	C₂²	1	12	yes	complemented
31	D₄²×C₆₁	C₂²	1	12	yes	complemented
32	D₄²×C₆₁	C₂²	1	24	yes	complemented
33	D₄²×C₆₁	C₂²	1	6	yes	complemented
34	C₆₁×#544	C₂²	1	6	yes	complemented
35	C₆₁×#543	C₂²	1	1	yes	characteristic, complemented
36	C₆₁×#542	C₂²	1	12	yes	complemented
37	C₆₁×#540	C₂²	1	12	yes	complemented
38	C₆₁×#540	C₂²	1	12	yes	complemented
39	C₆₁×#539	C₂²	1	24	yes	complemented
40	C₆₁×#539	C₂²	1	12	yes	complemented
41	C₆₁×#539	C₂²	1	6	yes	complemented
42	C₆₁×#538	C₂²	1	12	yes	complemented
43	C₆₁×#538	C₂²	1	12	yes	complemented
44	C₆₁×#538	C₂²	1	24	yes	complemented
45	C₆₁×#538	C₂²	1	6	yes	complemented
46	C₆₁×#537	C₂²	1	12	yes	complemented
47	C₆₁×#537	C₂²	1	6	yes	complemented
48	C₆₁×#535	C₂²	1	6	yes	complemented
49	C₆₁×#534	C₂²	1	12	yes	complemented
50	C₆₁×#534	C₂²	1	3	yes	complemented
51	C₆₁×#534	C₂²	1	6	yes	complemented
52	C₆₁×#534	C₂²	1	6	yes	complemented
53	C₆₁×#534	C₂²	1	12	yes	complemented
54	C₆₁×#532	C₂²	1	6	yes	complemented
55	C₆₁×#532	C₂²	1	12	yes	complemented
56	C₆₁×#529	C₂²	1	6	yes	complemented
57	C₆₁×#529	C₂²	1	12	yes	complemented
58	C₂×#126×C₆₁	C₂²	1	6	yes	complemented
59	C₂×#125×C₆₁	C₂²	1	3	yes	complemented
60	C₆₁×#525	C₂²	1	6	yes	complemented
61	C₆₁×#525	C₂²	1	12	yes	complemented
62	C₂×#123×C₆₁	C₂²	1	6	yes	complemented
63	C₂×#121×C₆₁	C₂²	1	6	yes	complemented
64	C₂×#121×C₆₁	C₂²	1	3	yes	complemented
65	C₂×#121×C₆₁	C₂²	1	3	yes	complemented
66	C₂×#121×C₆₁	C₂²	1	6	yes	complemented
67	C₂×#121×C₆₁	C₂²	1	12	yes	complemented
68	C₆₁×#520	C₂²	1	2	yes	complemented
69	C₆₁×#518	C₂²	1	6	yes	complemented
70	C₂×C₄×D₄×C₆₁	C₂²	1	6	yes	complemented
71	C₂×C₄×D₄×C₆₁	C₂²	1	3	yes	complemented
72	C₂×C₄×D₄×C₆₁	C₂²	1	3	yes	complemented
73	C₂×#117×C₆₁	C₂²	1	3	yes	complemented
74	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
75	H(5,𝔽₂)×C₆₁	—	4	24	no	—
76	C₂×#41×C₆₁	C₂³	1	12	yes	—
77	C₂×#41×C₆₁	C₂³	1	24	yes	—
78	C₂×#41×C₆₁	C₂³	1	2	yes	—
79	C₂×#41×C₆₁	C₂³	1	4	yes	—
80	C₂²×D₄×C₆₁	C₂³	1	6	yes	—
81	C₂²×D₄×C₆₁	C₂³	1	3	yes	—
82	C₂²×D₄×C₆₁	C₂³	1	24	yes	—
83	C₂²×D₄×C₆₁	C₂³	1	12	yes	—
84	C₂²×D₄×C₆₁	C₂³	1	6	yes	—
85	C₂²×D₄×C₆₁	C₂³	1	3	yes	—
86	C₂²×D₄×C₆₁	C₂³	1	12	yes	—
87	C₂²×D₄×C₆₁	C₂³	1	6	yes	—
88	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₆₁	C₂³	1	3	yes	—
90	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
91	C₂³×C₄×C₆₁	C₂³	1	6	yes	—
92	C₄⋊Q₈×C₆₁	C₂³	1	12	yes	—
93	C₄⋊Q₈×C₆₁	C₂³	1	6	yes	—
94	#127×C₆₁	C₂³	1	12	yes	—
95	#127×C₆₁	C₂³	1	6	yes	—
96	#126×C₆₁	C₂³	1	12	yes	—
97	#126×C₆₁	C₂³	1	24	yes	—
98	#126×C₆₁	C₂³	1	24	yes	—
99	#126×C₆₁	C₂³	1	24	yes	—
100	#125×C₆₁	C₂³	1	12	yes	—
101	#125×C₆₁	C₂³	1	12	yes	—
102	#125×C₆₁	C₂³	1	6	yes	—
103	#125×C₆₁	C₂³	1	12	yes	—
104	#124×C₆₁	C₂³	1	12	yes	—
105	#124×C₆₁	C₂³	1	24	yes	—
106	#124×C₆₁	C₂³	1	12	yes	—
107	#124×C₆₁	C₂³	1	6	yes	—
108	#123×C₆₁	C₂³	1	24	yes	—
109	#123×C₆₁	C₂³	1	24	yes	—
110	#123×C₆₁	C₂³	1	24	yes	—
111	#123×C₆₁	C₂³	1	24	yes	—
112	#123×C₆₁	C₂³	1	12	yes	—
113	#123×C₆₁	C₂³	1	24	yes	—
114	#123×C₆₁	C₂³	1	24	yes	—
115	#123×C₆₁	C₂³	1	12	yes	—
116	#123×C₆₁	C₂³	1	24	yes	—
117	C₂²⋊Q₈×C₆₁	C₂³	1	24	yes	—
118	C₂²⋊Q₈×C₆₁	C₂³	1	24	yes	—
119	C₂²⋊Q₈×C₆₁	C₂³	1	24	yes	—
120	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
121	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
122	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
123	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
124	#121×C₆₁	C₂³	1	6	yes	—
125	#121×C₆₁	C₂³	1	12	yes	—
126	#121×C₆₁	C₂³	1	12	yes	—
127	#121×C₆₁	C₂³	1	12	yes	—
128	#121×C₆₁	C₂³	1	24	yes	—
129	#121×C₆₁	C₂³	1	6	yes	—
130	#121×C₆₁	C₂³	1	6	yes	—
131	#121×C₆₁	C₂³	1	24	yes	—
132	#121×C₆₁	C₂³	1	24	yes	—
133	#121×C₆₁	C₂³	1	12	yes	—
134	#121×C₆₁	C₂³	1	12	yes	—
135	#121×C₆₁	C₂³	1	12	yes	—
136	#121×C₆₁	C₂³	1	12	yes	—
137	#121×C₆₁	C₂³	1	24	yes	—
138	#121×C₆₁	C₂³	1	24	yes	—
139	#121×C₆₁	C₂³	1	12	yes	—
140	#121×C₆₁	C₂³	1	12	yes	—
141	#121×C₆₁	C₂³	1	24	yes	—
142	#121×C₆₁	C₂³	1	12	yes	—
143	#121×C₆₁	C₂³	1	12	yes	—
144	#120×C₆₁	C₂³	1	24	yes	—
145	#120×C₆₁	C₂³	1	24	yes	—
146	#120×C₆₁	C₂³	1	24	yes	—
147	#120×C₆₁	C₂³	1	12	yes	—
148	#120×C₆₁	C₂³	1	24	yes	—
149	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
150	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
151	C₄×D₄×C₆₁	C₂³	1	24	yes	—
152	C₄×D₄×C₆₁	C₂³	1	12	yes	—
153	C₄×D₄×C₆₁	C₂³	1	12	yes	—
154	C₄×D₄×C₆₁	C₂³	1	12	yes	—
155	C₄×D₄×C₆₁	C₂³	1	12	yes	—
156	C₄×D₄×C₆₁	C₂³	1	12	yes	—
157	C₄×D₄×C₆₁	C₂³	1	12	yes	—
158	C₄×D₄×C₆₁	C₂³	1	24	yes	—
159	C₄×D₄×C₆₁	C₂³	1	12	yes	—
160	C₄×D₄×C₆₁	C₂³	1	6	yes	—
161	C₄×D₄×C₆₁	C₂³	1	12	yes	—
162	C₄×D₄×C₆₁	C₂³	1	6	yes	—
163	C₄×D₄×C₆₁	C₂³	1	24	yes	—
164	C₄×D₄×C₆₁	C₂³	1	6	yes	—
165	#117×C₆₁	C₂³	1	6	yes	—
166	#117×C₆₁	C₂³	1	6	yes	—
167	#117×C₆₁	C₂³	1	12	yes	—
168	#117×C₆₁	C₂³	1	12	yes	—
169	#117×C₆₁	C₂³	1	6	yes	—
170	C₂×C₄⋊C₄×C₆₁	C₂³	1	6	yes	—
171	C₂×C₄⋊C₄×C₆₁	C₂³	1	3	yes	—
172	C₂×C₄⋊C₄×C₆₁	C₂³	1	12	yes	—
173	C₂×C₄⋊C₄×C₆₁	C₂³	1	6	yes	—
174	C₂×C₄⋊C₄×C₆₁	C₂³	1	3	yes	—
175	C₂×C₄⋊C₄×C₆₁	C₂³	1	6	yes	—
176	C₂×C₄⋊C₄×C₆₁	C₂³	1	3	yes	—
177	C₂×C₄⋊C₄×C₆₁	C₂³	1	3	yes	—
178	C₂×C₄⋊C₄×C₆₁	C₂³	1	6	yes	—
179	C₂×C₂²⋊C₄×C₆₁	C₂³	1	3	yes	—
180	C₂×C₂²⋊C₄×C₆₁	C₂³	1	6	yes	—
181	C₂×C₂²⋊C₄×C₆₁	C₂³	1	3	yes	—
182	C₂×C₂²⋊C₄×C₆₁	C₂³	1	12	yes	—
183	C₂×C₂²⋊C₄×C₆₁	C₂³	1	24	yes	—
184	C₂×C₂²⋊C₄×C₆₁	C₂³	1	6	yes	—
185	C₂×C₂²⋊C₄×C₆₁	C₂³	1	6	yes	—
186	C₂×C₂²⋊C₄×C₆₁	C₂³	1	6	yes	—
187	C₂×C₄²×C₆₁	C₂³	1	6	yes	—
188	C₂×C₄²×C₆₁	C₂³	1	3	yes	—
189	C₂⁴×C₆₁	C₂⁴	1	3	yes	—
190	C₂⁴×C₆₁	C₂⁴	1	6	yes	—
191	C₂⁴×C₆₁	C₂⁴	1	12	yes	—
192	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
193	#41×C₆₁	—	4	4	no	—
194	#41×C₆₁	—	4	24	no	—
195	#41×C₆₁	—	4	48	no	—
196	#41×C₆₁	—	8	4	no	—
197	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
198	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
199	C₂×Q₈×C₆₁	C₂⁴	1	12	yes	—
200	C₂×D₄×C₆₁	—	2	24	no	—
201	C₂×D₄×C₆₁	—	2	12	no	—
202	C₂×D₄×C₆₁	—	4	6	no	—
203	C₂×D₄×C₆₁	—	4	12	no	—
204	C₂×D₄×C₆₁	—	4	48	no	—
205	C₂×D₄×C₆₁	—	4	24	no	—
206	C₂×D₄×C₆₁	—	8	6	no	—
207	C₂×D₄×C₆₁	—	8	12	no	—
208	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
209	C₂×D₄×C₆₁	C₂⁴	1	24	yes	—
210	C₂×D₄×C₆₁	C₂⁴	1	12	yes	—
211	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
212	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
213	C₂×D₄×C₆₁	C₂⁴	1	12	yes	—
214	C₂×D₄×C₆₁	C₂⁴	1	12	yes	—
215	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
216	C₂×D₄×C₆₁	C₂⁴	1	24	yes	—
217	C₂×D₄×C₆₁	C₂⁴	1	24	yes	—
218	C₂×D₄×C₆₁	C₂⁴	1	12	yes	—
219	C₂²×C₄×C₆₁	—	4	2	no	—
220	C₂²×C₄×C₆₁	—	4	6	no	—
221	C₂²×C₄×C₆₁	—	8	2	no	—
222	C₂²×C₄×C₆₁	—	8	6	no	—
223	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
224	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
225	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
226	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
227	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
228	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
229	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
230	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
231	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
232	C₂²×C₄×C₆₁	C₂⁴	1	12	yes	—
233	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
234	C₂²×C₄×C₆₁	C₂⁴	1	12	yes	—
235	C₂²×C₄×C₆₁	C₂⁴	1	24	yes	—
236	C₂²×C₄×C₆₁	C₂⁴	1	12	yes	—
237	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
238	C₄⋊C₄×C₆₁	C₂⁴	1	3	yes	—
239	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
240	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
241	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
242	C₄⋊C₄×C₆₁	C₂⁴	1	24	yes	—
243	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
244	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
245	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
246	C₄⋊C₄×C₆₁	C₂⁴	1	24	yes	—
247	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
248	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
249	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
250	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
251	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
252	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
253	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
254	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
255	C₂²⋊C₄×C₆₁	C₂⁴	1	24	yes	—
256	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
257	C₂²⋊C₄×C₆₁	C₂⁴	1	24	yes	—
258	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
259	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
260	C₂²⋊C₄×C₆₁	C₂⁴	1	24	yes	—
261	C₂²⋊C₄×C₆₁	C₂⁴	1	24	yes	—
262	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
263	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
264	C₄²×C₆₁	C₂⁴	1	12	yes	—
265	C₄²×C₆₁	C₂⁴	1	6	yes	—
266	C₄²×C₆₁	C₂⁴	1	12	yes	—
267	C₄²×C₆₁	C₂⁴	1	6	yes	—
268	C₂³×C₆₁	—	2	6	no	—
269	C₂³×C₆₁	—	2	12	no	—
270	C₂³×C₆₁	—	4	1	no	—
271	C₂³×C₆₁	—	4	1	no	—
272	C₂³×C₆₁	—	4	3	no	—
273	C₂³×C₆₁	—	4	6	no	—
274	C₂³×C₆₁	—	4	6	no	—
275	C₂³×C₆₁	—	4	3	no	—
276	C₂³×C₆₁	—	4	12	no	—
277	C₂³×C₆₁	—	4	12	no	—
278	C₂³×C₆₁	—	4	12	no	—
279	C₂³×C₆₁	H(5,𝔽₂)	1	4	yes	—
280	C₂³×C₆₁	C₂⁵	1	6	yes	—
281	C₂³×C₆₁	C₂⁵	1	12	yes	—
282	C₂³×C₆₁	C₂⁵	1	3	yes	—
283	Q₈×C₆₁	—	4	2	no	—
284	Q₈×C₆₁	—	4	12	no	—
285	Q₈×C₆₁	—	4	2	no	—
286	D₄×C₆₁	—	2	48	no	—
287	D₄×C₆₁	—	2	24	no	—
288	D₄×C₆₁	—	2	12	no	—
289	D₄×C₆₁	—	4	24	no	—
290	D₄×C₆₁	—	4	12	no	—
291	D₄×C₆₁	—	4	6	no	—
292	D₄×C₆₁	—	4	12	no	—
293	D₄×C₆₁	—	4	24	no	—
294	D₄×C₆₁	—	4	6	no	—
295	D₄×C₆₁	—	4	12	no	—
296	D₄×C₆₁	—	4	6	no	—
297	C₂×C₄×C₆₁	—	2	12	no	—
298	C₂×C₄×C₆₁	—	2	6	no	—
299	C₂×C₄×C₆₁	—	2	6	no	—
300	C₂×C₄×C₆₁	—	2	12	no	—
301	C₂×C₄×C₆₁	—	4	3	no	—
302	C₂×C₄×C₆₁	—	4	6	no	—
303	C₂×C₄×C₆₁	—	4	3	no	—
304	C₂×C₄×C₆₁	—	4	6	no	—
305	C₂×C₄×C₆₁	—	4	3	no	—
306	C₂×C₄×C₆₁	—	4	6	no	—
307	C₂×C₄×C₆₁	—	4	12	no	—
308	C₂×C₄×C₆₁	—	4	12	no	—
309	C₂×C₄×C₆₁	—	4	12	no	—
310	C₂×C₄×C₆₁	—	4	24	no	—
311	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
312	C₂×C₄×C₆₁	C₂⁵	1	6	yes	—
313	C₂×C₄×C₆₁	C₂⁵	1	3	yes	—
314	C₂×C₄×C₆₁	C₂⁵	1	6	yes	—
315	C₂×C₄×C₆₁	C₂⁵	1	6	yes	—
316	C₂×C₄×C₆₁	C₂⁵	1	12	yes	—
317	C₂×C₄×C₆₁	C₂⁵	1	6	yes	—
318	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
319	#62905	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
320	C₂²×C₆₁	—	2	3	no	—
321	C₂²×C₆₁	—	2	3	no	—
322	C₂²×C₆₁	—	2	6	no	—
323	C₂²×C₆₁	—	2	12	no	—
324	C₂²×C₆₁	—	2	6	no	—
325	C₂²×C₆₁	—	2	12	no	—
326	C₂²×C₆₁	—	2	12	no	—
327	C₂²×C₆₁	—	2	6	no	—
328	C₂²×C₆₁	—	4	4	no	—
329	C₂²×C₆₁	—	8	6	no	—
330	C₂²×C₆₁	—	8	12	no	—
331	C₂²×C₆₁	—	16	12	no	—
332	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	6	yes	—
333	C₂²×C₆₁	C₂⁶	1	1	yes	characteristic
334	C₄×C₆₁	—	2	12	no	—
335	C₄×C₆₁	—	2	6	no	—
336	C₄×C₆₁	—	2	3	no	—
337	C₄×C₆₁	—	2	6	no	—
338	C₄×C₆₁	—	2	2	no	—
339	C₄×C₆₁	—	2	6	no	—
340	C₄×C₆₁	—	2	6	no	—
341	C₄×C₆₁	#585	1	2	yes	—
342	#3560	C₂×C₆₁	1	12	yes	complemented
343	#3559	C₂×C₆₁	1	6	yes	complemented
344	#3537	C₂×C₆₁	1	6	yes	complemented
345	#3534	C₂×C₆₁	1	12	yes	complemented
346	#3519	C₂×C₆₁	1	6	yes	complemented
347	#3496	C₂×C₆₁	1	3	yes	complemented
348	#3496	C₂×C₆₁	1	6	yes	complemented
349	#3494	C₂×C₆₁	1	6	yes	complemented
350	C₂×#553	C₂×C₆₁	1	3	yes	complemented
351	#3459	C₂×C₆₁	1	1	yes	characteristic, complemented
352	#3459	C₂×C₆₁	1	2	yes	complemented
353	C₂×C₆₁	—	2	6	no	—
354	C₂×C₆₁	—	4	6	no	—
355	C₂×C₆₁	—	4	12	no	—
356	C₂×C₆₁	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
357	C₂×C₆₁	C₂×#585	1	1	yes	characteristic
358	C₂×C₆₁	H(7,𝔽₂)	1	1	yes	characteristic
359	C₂×H(5,𝔽₂)	C₂²×C₆₁	1	6	yes	complemented
360	#563	C₂²×C₆₁	1	12	yes	complemented
361	#562	C₂²×C₆₁	1	12	yes	complemented
362	#560	C₂²×C₆₁	1	24	yes	complemented
363	#555	C₂²×C₆₁	1	6	yes	complemented
364	#554	C₂²×C₆₁	1	6	yes	complemented
365	#553	C₂²×C₆₁	1	12	yes	complemented
366	#553	C₂²×C₆₁	1	24	yes	complemented
367	#553	C₂²×C₆₁	1	12	yes	complemented
368	#553	C₂²×C₆₁	1	12	yes	complemented
369	#553	C₂²×C₆₁	1	12	yes	complemented
370	#551	C₂²×C₆₁	1	24	yes	complemented
371	#550	C₂²×C₆₁	1	2	yes	complemented
372	#547	C₂²×C₆₁	1	12	yes	complemented
373	#547	C₂²×C₆₁	1	24	yes	complemented
374	#546	C₂²×C₆₁	1	24	yes	complemented
375	#546	C₂²×C₆₁	1	24	yes	complemented
376	#546	C₂²×C₆₁	1	24	yes	complemented
377	#546	C₂²×C₆₁	1	12	yes	complemented
378	D₄²	C₂²×C₆₁	1	12	yes	complemented
379	D₄²	C₂²×C₆₁	1	24	yes	complemented
380	D₄²	C₂²×C₆₁	1	6	yes	complemented
381	#544	C₂²×C₆₁	1	6	yes	complemented
382	#543	C₂²×C₆₁	1	1	yes	characteristic, complemented
383	#542	C₂²×C₆₁	1	12	yes	complemented
384	#540	C₂²×C₆₁	1	12	yes	complemented
385	#540	C₂²×C₆₁	1	12	yes	complemented
386	#539	C₂²×C₆₁	1	12	yes	complemented
387	#539	C₂²×C₆₁	1	6	yes	complemented
388	#539	C₂²×C₆₁	1	24	yes	complemented
389	#538	C₂²×C₆₁	1	6	yes	complemented
390	#538	C₂²×C₆₁	1	12	yes	complemented
391	#538	C₂²×C₆₁	1	24	yes	complemented
392	#538	C₂²×C₆₁	1	12	yes	complemented
393	#537	C₂²×C₆₁	1	12	yes	complemented
394	#537	C₂²×C₆₁	1	6	yes	complemented
395	#535	C₂²×C₆₁	1	6	yes	complemented
396	#534	C₂²×C₆₁	1	3	yes	complemented
397	#534	C₂²×C₆₁	1	6	yes	complemented
398	#534	C₂²×C₆₁	1	6	yes	complemented
399	#534	C₂²×C₆₁	1	12	yes	complemented
400	#534	C₂²×C₆₁	1	12	yes	complemented
401	#532	C₂²×C₆₁	1	12	yes	complemented
402	#532	C₂²×C₆₁	1	6	yes	complemented
403	#529	C₂²×C₆₁	1	12	yes	complemented
404	#529	C₂²×C₆₁	1	6	yes	complemented
405	C₂×#126	C₂²×C₆₁	1	6	yes	complemented
406	C₂×#125	C₂²×C₆₁	1	3	yes	complemented
407	#525	C₂²×C₆₁	1	6	yes	complemented
408	#525	C₂²×C₆₁	1	12	yes	complemented
409	C₂×#123	C₂²×C₆₁	1	6	yes	complemented
410	C₂×#121	C₂²×C₆₁	1	6	yes	complemented
411	C₂×#121	C₂²×C₆₁	1	3	yes	complemented
412	C₂×#121	C₂²×C₆₁	1	3	yes	complemented
413	C₂×#121	C₂²×C₆₁	1	6	yes	complemented
414	C₂×#121	C₂²×C₆₁	1	12	yes	complemented
415	#520	C₂²×C₆₁	1	2	yes	complemented
416	#518	C₂²×C₆₁	1	6	yes	complemented
417	C₂×C₄×D₄	C₂²×C₆₁	1	6	yes	complemented
418	C₂×C₄×D₄	C₂²×C₆₁	1	3	yes	complemented
419	C₂×C₄×D₄	C₂²×C₆₁	1	3	yes	complemented
420	C₂×#117	C₂²×C₆₁	1	3	yes	complemented
421	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
422	C₆₁	#62905	1	1	yes	characteristic, direct product factor, Sylow
423	H(5,𝔽₂)	—	4	24	no	—
424	C₂×#41	C₂³×C₆₁	1	2	yes	—
425	C₂×#41	C₂³×C₆₁	1	24	yes	—
426	C₂×#41	C₂³×C₆₁	1	12	yes	—
427	C₂×#41	C₂³×C₆₁	1	4	yes	—
428	C₂²×D₄	C₂³×C₆₁	1	6	yes	—
429	C₂²×D₄	C₂³×C₆₁	1	3	yes	—
430	C₂²×D₄	C₂³×C₆₁	1	3	yes	—
431	C₂²×D₄	C₂³×C₆₁	1	6	yes	—
432	C₂²×D₄	C₂³×C₆₁	1	12	yes	—
433	C₂²×D₄	C₂³×C₆₁	1	24	yes	—
434	C₂²×D₄	C₂³×C₆₁	1	6	yes	—
435	C₂²×D₄	C₂³×C₆₁	1	12	yes	—
436	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
437	C₂³×C₄	C₂³×C₆₁	1	3	yes	—
438	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
439	C₂³×C₄	C₂³×C₆₁	1	6	yes	—
440	C₄⋊Q₈	C₂³×C₆₁	1	12	yes	—
441	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	—
442	#127	C₂³×C₆₁	1	12	yes	—
443	#127	C₂³×C₆₁	1	6	yes	—
444	#126	C₂³×C₆₁	1	24	yes	—
445	#126	C₂³×C₆₁	1	24	yes	—
446	#126	C₂³×C₆₁	1	12	yes	—
447	#126	C₂³×C₆₁	1	24	yes	—
448	#125	C₂³×C₆₁	1	12	yes	—
449	#125	C₂³×C₆₁	1	12	yes	—
450	#125	C₂³×C₆₁	1	12	yes	—
451	#125	C₂³×C₆₁	1	6	yes	—
452	#124	C₂³×C₆₁	1	12	yes	—
453	#124	C₂³×C₆₁	1	6	yes	—
454	#124	C₂³×C₆₁	1	12	yes	—
455	#124	C₂³×C₆₁	1	24	yes	—
456	#123	C₂³×C₆₁	1	24	yes	—
457	#123	C₂³×C₆₁	1	24	yes	—
458	#123	C₂³×C₆₁	1	24	yes	—
459	#123	C₂³×C₆₁	1	12	yes	—
460	#123	C₂³×C₆₁	1	12	yes	—
461	#123	C₂³×C₆₁	1	24	yes	—
462	#123	C₂³×C₆₁	1	24	yes	—
463	#123	C₂³×C₆₁	1	24	yes	—
464	#123	C₂³×C₆₁	1	24	yes	—
465	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
466	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
467	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
468	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
469	C₂²⋊Q₈	C₂³×C₆₁	1	24	yes	—
470	C₂²⋊Q₈	C₂³×C₆₁	1	24	yes	—
471	C₂²⋊Q₈	C₂³×C₆₁	1	24	yes	—
472	#121	C₂³×C₆₁	1	6	yes	—
473	#121	C₂³×C₆₁	1	12	yes	—
474	#121	C₂³×C₆₁	1	24	yes	—
475	#121	C₂³×C₆₁	1	12	yes	—
476	#121	C₂³×C₆₁	1	12	yes	—
477	#121	C₂³×C₆₁	1	24	yes	—
478	#121	C₂³×C₆₁	1	12	yes	—
479	#121	C₂³×C₆₁	1	12	yes	—
480	#121	C₂³×C₆₁	1	12	yes	—
481	#121	C₂³×C₆₁	1	12	yes	—
482	#121	C₂³×C₆₁	1	12	yes	—
483	#121	C₂³×C₆₁	1	24	yes	—
484	#121	C₂³×C₆₁	1	12	yes	—
485	#121	C₂³×C₆₁	1	12	yes	—
486	#121	C₂³×C₆₁	1	6	yes	—
487	#121	C₂³×C₆₁	1	6	yes	—
488	#121	C₂³×C₆₁	1	12	yes	—
489	#121	C₂³×C₆₁	1	24	yes	—
490	#121	C₂³×C₆₁	1	24	yes	—
491	#121	C₂³×C₆₁	1	24	yes	—
492	#120	C₂³×C₆₁	1	12	yes	—
493	#120	C₂³×C₆₁	1	24	yes	—
494	#120	C₂³×C₆₁	1	24	yes	—
495	#120	C₂³×C₆₁	1	24	yes	—
496	#120	C₂³×C₆₁	1	24	yes	—
497	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
498	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
499	C₄×D₄	C₂³×C₆₁	1	6	yes	—
500	C₄×D₄	C₂³×C₆₁	1	12	yes	—
501	C₄×D₄	C₂³×C₆₁	1	24	yes	—
502	C₄×D₄	C₂³×C₆₁	1	12	yes	—
503	C₄×D₄	C₂³×C₆₁	1	24	yes	—
504	C₄×D₄	C₂³×C₆₁	1	12	yes	—
505	C₄×D₄	C₂³×C₆₁	1	6	yes	—
506	C₄×D₄	C₂³×C₆₁	1	12	yes	—
507	C₄×D₄	C₂³×C₆₁	1	12	yes	—
508	C₄×D₄	C₂³×C₆₁	1	12	yes	—
509	C₄×D₄	C₂³×C₆₁	1	12	yes	—
510	C₄×D₄	C₂³×C₆₁	1	6	yes	—
511	C₄×D₄	C₂³×C₆₁	1	24	yes	—
512	C₄×D₄	C₂³×C₆₁	1	12	yes	—
513	#117	C₂³×C₆₁	1	6	yes	—
514	#117	C₂³×C₆₁	1	6	yes	—
515	#117	C₂³×C₆₁	1	12	yes	—
516	#117	C₂³×C₆₁	1	6	yes	—
517	#117	C₂³×C₆₁	1	12	yes	—
518	C₂×C₄⋊C₄	C₂³×C₆₁	1	3	yes	—
519	C₂×C₄⋊C₄	C₂³×C₆₁	1	3	yes	—
520	C₂×C₄⋊C₄	C₂³×C₆₁	1	6	yes	—
521	C₂×C₄⋊C₄	C₂³×C₆₁	1	3	yes	—
522	C₂×C₄⋊C₄	C₂³×C₆₁	1	6	yes	—
523	C₂×C₄⋊C₄	C₂³×C₆₁	1	3	yes	—
524	C₂×C₄⋊C₄	C₂³×C₆₁	1	6	yes	—
525	C₂×C₄⋊C₄	C₂³×C₆₁	1	6	yes	—
526	C₂×C₄⋊C₄	C₂³×C₆₁	1	12	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₆₁	1	6	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₆₁	1	3	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₆₁	1	6	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₆₁	1	6	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₆₁	1	3	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₆₁	1	24	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₆₁	1	6	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₆₁	1	12	yes	—
535	C₂×C₄²	C₂³×C₆₁	1	6	yes	—
536	C₂×C₄²	C₂³×C₆₁	1	3	yes	—
537	C₂⁴	C₂⁴×C₆₁	1	3	yes	—
538	C₂⁴	C₂⁴×C₆₁	1	6	yes	—
539	C₂⁴	C₂⁴×C₆₁	1	12	yes	—
540	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
541	#41	—	4	4	no	—
542	#41	—	4	48	no	—
543	#41	—	4	24	no	—
544	#41	—	8	4	no	—
545	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
546	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
547	C₂×Q₈	C₂⁴×C₆₁	1	12	yes	—
548	C₂×D₄	—	2	24	no	—
549	C₂×D₄	—	2	12	no	—
550	C₂×D₄	—	4	6	no	—
551	C₂×D₄	—	4	12	no	—
552	C₂×D₄	—	4	24	no	—
553	C₂×D₄	—	4	48	no	—
554	C₂×D₄	—	8	6	no	—
555	C₂×D₄	—	8	12	no	—
556	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
557	C₂×D₄	C₂⁴×C₆₁	1	12	yes	—
558	C₂×D₄	C₂⁴×C₆₁	1	24	yes	—
559	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
560	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
561	C₂×D₄	C₂⁴×C₆₁	1	12	yes	—
562	C₂×D₄	C₂⁴×C₆₁	1	12	yes	—
563	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
564	C₂×D₄	C₂⁴×C₆₁	1	24	yes	—
565	C₂×D₄	C₂⁴×C₆₁	1	24	yes	—
566	C₂×D₄	C₂⁴×C₆₁	1	12	yes	—
567	C₂²×C₄	—	4	2	no	—
568	C₂²×C₄	—	4	6	no	—
569	C₂²×C₄	—	8	2	no	—
570	C₂²×C₄	—	8	6	no	—
571	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
572	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
573	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
574	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
575	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
576	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
577	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
578	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
579	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
580	C₂²×C₄	C₂⁴×C₆₁	1	12	yes	—
581	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
582	C₂²×C₄	C₂⁴×C₆₁	1	24	yes	—
583	C₂²×C₄	C₂⁴×C₆₁	1	12	yes	—
584	C₂²×C₄	C₂⁴×C₆₁	1	12	yes	—
585	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
586	C₄⋊C₄	C₂⁴×C₆₁	1	3	yes	—
587	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
588	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
589	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
590	C₄⋊C₄	C₂⁴×C₆₁	1	24	yes	—
591	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
592	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
593	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
594	C₄⋊C₄	C₂⁴×C₆₁	1	24	yes	—
595	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
596	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
597	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
598	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
599	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
600	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
601	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
602	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
603	C₂²⋊C₄	C₂⁴×C₆₁	1	24	yes	—
604	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
605	C₂²⋊C₄	C₂⁴×C₆₁	1	24	yes	—
606	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
607	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
608	C₂²⋊C₄	C₂⁴×C₆₁	1	24	yes	—
609	C₂²⋊C₄	C₂⁴×C₆₁	1	24	yes	—
610	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
611	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
612	C₄²	C₂⁴×C₆₁	1	12	yes	—
613	C₄²	C₂⁴×C₆₁	1	6	yes	—
614	C₄²	C₂⁴×C₆₁	1	12	yes	—
615	C₄²	C₂⁴×C₆₁	1	6	yes	—
616	C₂³	—	2	6	no	—
617	C₂³	—	2	12	no	—
618	C₂³	—	4	1	no	—
619	C₂³	—	4	1	no	—
620	C₂³	—	4	3	no	—
621	C₂³	—	4	6	no	—
622	C₂³	—	4	6	no	—
623	C₂³	—	4	3	no	—
624	C₂³	—	4	12	no	—
625	C₂³	—	4	12	no	—
626	C₂³	—	4	12	no	—
627	C₂³	H(5,𝔽₂)×C₆₁	1	4	yes	—
628	C₂³	C₂⁵×C₆₁	1	6	yes	—
629	C₂³	C₂⁵×C₆₁	1	12	yes	—
630	C₂³	C₂⁵×C₆₁	1	3	yes	—
631	Q₈	—	4	2	no	—
632	Q₈	—	4	12	no	—
633	Q₈	—	4	2	no	—
634	D₄	—	2	24	no	—
635	D₄	—	2	48	no	—
636	D₄	—	2	12	no	—
637	D₄	—	4	24	no	—
638	D₄	—	4	12	no	—
639	D₄	—	4	6	no	—
640	D₄	—	4	12	no	—
641	D₄	—	4	24	no	—
642	D₄	—	4	6	no	—
643	D₄	—	4	12	no	—
644	D₄	—	4	6	no	—
645	C₂×C₄	—	2	12	no	—
646	C₂×C₄	—	2	6	no	—
647	C₂×C₄	—	2	6	no	—
648	C₂×C₄	—	2	12	no	—
649	C₂×C₄	—	4	3	no	—
650	C₂×C₄	—	4	6	no	—
651	C₂×C₄	—	4	3	no	—
652	C₂×C₄	—	4	6	no	—
653	C₂×C₄	—	4	3	no	—
654	C₂×C₄	—	4	6	no	—
655	C₂×C₄	—	4	12	no	—
656	C₂×C₄	—	4	12	no	—
657	C₂×C₄	—	4	24	no	—
658	C₂×C₄	—	4	12	no	—
659	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
660	C₂×C₄	C₂⁵×C₆₁	1	6	yes	—
661	C₂×C₄	C₂⁵×C₆₁	1	3	yes	—
662	C₂×C₄	C₂⁵×C₆₁	1	6	yes	—
663	C₂×C₄	C₂⁵×C₆₁	1	6	yes	—
664	C₂×C₄	C₂⁵×C₆₁	1	12	yes	—
665	C₂×C₄	C₂⁵×C₆₁	1	6	yes	—
666	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
667	C₂²	—	2	3	no	—
668	C₂²	—	2	3	no	—
669	C₂²	—	2	6	no	—
670	C₂²	—	2	12	no	—
671	C₂²	—	2	6	no	—
672	C₂²	—	2	12	no	—
673	C₂²	—	2	12	no	—
674	C₂²	—	2	6	no	—
675	C₂²	—	4	4	no	—
676	C₂²	—	8	6	no	—
677	C₂²	—	8	12	no	—
678	C₂²	—	16	12	no	—
679	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	6	yes	—
680	C₂²	C₂⁶×C₆₁	1	1	yes	characteristic
681	C₄	—	2	12	no	—
682	C₄	—	2	6	no	—
683	C₄	—	2	3	no	—
684	C₄	—	2	6	no	—
685	C₄	—	2	2	no	—
686	C₄	—	2	6	no	—
687	C₄	—	2	6	no	—
688	C₄	C₆₁×#585	1	2	yes	—
689	C₂	—	2	6	no	—
690	C₂	—	4	6	no	—
691	C₂	—	4	12	no	—
692	C₂	C₂²×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
693	C₂	C₂×C₆₁×#585	1	1	yes	characteristic
694	C₂	C₆₁×H(7,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₆₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3560	C₂	semidirect
2. C₆₁×#3559	C₂	semidirect
3. C₆₁×#3537	C₂	semidirect
4. C₆₁×#3534	C₂	semidirect
5. C₆₁×#3519	C₂	semidirect
6. C₆₁×#3496	C₂	semidirect
7. C₆₁×#3496	C₂	semidirect
8. C₆₁×#3494	C₂	semidirect
9. C₂×C₆₁×#553	C₂	semidirect
10. C₆₁×#3459	C₂	semidirect
11. C₆₁×#3459	C₂	semidirect
12. C₂×H(5,𝔽₂)×C₆₁	C₂²	semidirect
13. C₆₁×#563	C₂²	semidirect
14. C₆₁×#562	C₂²	semidirect
15. C₆₁×#560	C₂²	semidirect
16. C₆₁×#555	C₂²	semidirect
17. C₆₁×#554	C₂²	semidirect
18. C₆₁×#553	C₂²	semidirect
19. C₆₁×#553	C₂²	semidirect
20. C₆₁×#553	C₂²	semidirect
21. C₆₁×#553	C₂²	semidirect
22. C₆₁×#553	C₂²	semidirect
23. C₆₁×#551	C₂²	semidirect
24. C₆₁×#550	C₂²	semidirect
25. C₆₁×#547	C₂²	semidirect
26. C₆₁×#547	C₂²	semidirect
27. C₆₁×#546	C₂²	semidirect
28. C₆₁×#546	C₂²	semidirect
29. C₆₁×#546	C₂²	semidirect
30. C₆₁×#546	C₂²	semidirect
31. D₄²×C₆₁	C₂²	semidirect
32. D₄²×C₆₁	C₂²	semidirect
33. D₄²×C₆₁	C₂²	semidirect
34. C₆₁×#544	C₂²	semidirect
35. C₆₁×#543	C₂²	semidirect
36. C₆₁×#542	C₂²	semidirect
37. C₆₁×#540	C₂²	semidirect
38. C₆₁×#540	C₂²	semidirect
39. C₆₁×#539	C₂²	semidirect
40. C₆₁×#539	C₂²	semidirect
41. C₆₁×#539	C₂²	semidirect
42. C₆₁×#538	C₂²	semidirect
43. C₆₁×#538	C₂²	semidirect
44. C₆₁×#538	C₂²	semidirect
45. C₆₁×#538	C₂²	semidirect
46. C₆₁×#537	C₂²	semidirect
47. C₆₁×#537	C₂²	semidirect
48. C₆₁×#535	C₂²	semidirect
49. C₆₁×#534	C₂²	semidirect
50. C₆₁×#534	C₂²	semidirect
51. C₆₁×#534	C₂²	semidirect
52. C₆₁×#534	C₂²	semidirect
53. C₆₁×#534	C₂²	semidirect
54. C₆₁×#532	C₂²	semidirect
55. C₆₁×#532	C₂²	semidirect
56. C₆₁×#529	C₂²	semidirect
57. C₆₁×#529	C₂²	semidirect
58. C₂×#126×C₆₁	C₂²	semidirect
59. C₂×#125×C₆₁	C₂²	semidirect
60. C₆₁×#525	C₂²	semidirect
61. C₆₁×#525	C₂²	semidirect
62. C₂×#123×C₆₁	C₂²	semidirect
63. C₂×#121×C₆₁	C₂²	semidirect
64. C₂×#121×C₆₁	C₂²	semidirect
65. C₂×#121×C₆₁	C₂²	semidirect
66. C₂×#121×C₆₁	C₂²	semidirect
67. C₂×#121×C₆₁	C₂²	semidirect
68. C₆₁×#520	C₂²	semidirect
69. C₆₁×#518	C₂²	semidirect
70. C₂×C₄×D₄×C₆₁	C₂²	semidirect
71. C₂×C₄×D₄×C₆₁	C₂²	semidirect
72. C₂×C₄×D₄×C₆₁	C₂²	semidirect
73. C₂×#117×C₆₁	C₂²	semidirect
74. C₂²×C₄⋊C₄×C₆₁	C₂²	semidirect
319. #62905	C₆₁	direct (N × H)
342. #3560	C₂×C₆₁	semidirect
343. #3559	C₂×C₆₁	semidirect
344. #3537	C₂×C₆₁	semidirect
345. #3534	C₂×C₆₁	semidirect
346. #3519	C₂×C₆₁	semidirect
347. #3496	C₂×C₆₁	semidirect
348. #3496	C₂×C₆₁	semidirect
349. #3494	C₂×C₆₁	semidirect
350. C₂×#553	C₂×C₆₁	semidirect
351. #3459	C₂×C₆₁	semidirect
352. #3459	C₂×C₆₁	semidirect
359. C₂×H(5,𝔽₂)	C₂²×C₆₁	semidirect
360. #563	C₂²×C₆₁	semidirect
361. #562	C₂²×C₆₁	semidirect
362. #560	C₂²×C₆₁	semidirect
363. #555	C₂²×C₆₁	semidirect
364. #554	C₂²×C₆₁	semidirect
365. #553	C₂²×C₆₁	semidirect
366. #553	C₂²×C₆₁	semidirect
367. #553	C₂²×C₆₁	semidirect
368. #553	C₂²×C₆₁	semidirect
369. #553	C₂²×C₆₁	semidirect
370. #551	C₂²×C₆₁	semidirect
371. #550	C₂²×C₆₁	semidirect
372. #547	C₂²×C₆₁	semidirect
373. #547	C₂²×C₆₁	semidirect
374. #546	C₂²×C₆₁	semidirect
375. #546	C₂²×C₆₁	semidirect
376. #546	C₂²×C₆₁	semidirect
377. #546	C₂²×C₆₁	semidirect
378. D₄²	C₂²×C₆₁	semidirect
379. D₄²	C₂²×C₆₁	semidirect
380. D₄²	C₂²×C₆₁	semidirect
381. #544	C₂²×C₆₁	semidirect
382. #543	C₂²×C₆₁	semidirect
383. #542	C₂²×C₆₁	semidirect
384. #540	C₂²×C₆₁	semidirect
385. #540	C₂²×C₆₁	semidirect
386. #539	C₂²×C₆₁	semidirect
387. #539	C₂²×C₆₁	semidirect
388. #539	C₂²×C₆₁	semidirect
389. #538	C₂²×C₆₁	semidirect
390. #538	C₂²×C₆₁	semidirect
391. #538	C₂²×C₆₁	semidirect
392. #538	C₂²×C₆₁	semidirect
393. #537	C₂²×C₆₁	semidirect
394. #537	C₂²×C₆₁	semidirect
395. #535	C₂²×C₆₁	semidirect
396. #534	C₂²×C₆₁	semidirect
397. #534	C₂²×C₆₁	semidirect
398. #534	C₂²×C₆₁	semidirect
399. #534	C₂²×C₆₁	semidirect
400. #534	C₂²×C₆₁	semidirect
401. #532	C₂²×C₆₁	semidirect
402. #532	C₂²×C₆₁	semidirect
403. #529	C₂²×C₆₁	semidirect
404. #529	C₂²×C₆₁	semidirect
405. C₂×#126	C₂²×C₆₁	semidirect
406. C₂×#125	C₂²×C₆₁	semidirect
407. #525	C₂²×C₆₁	semidirect
408. #525	C₂²×C₆₁	semidirect
409. C₂×#123	C₂²×C₆₁	semidirect
410. C₂×#121	C₂²×C₆₁	semidirect
411. C₂×#121	C₂²×C₆₁	semidirect
412. C₂×#121	C₂²×C₆₁	semidirect
413. C₂×#121	C₂²×C₆₁	semidirect
414. C₂×#121	C₂²×C₆₁	semidirect
415. #520	C₂²×C₆₁	semidirect
416. #518	C₂²×C₆₁	semidirect
417. C₂×C₄×D₄	C₂²×C₆₁	semidirect
418. C₂×C₄×D₄	C₂²×C₆₁	semidirect
419. C₂×C₄×D₄	C₂²×C₆₁	semidirect
420. C₂×#117	C₂²×C₆₁	semidirect
421. C₂²×C₄⋊C₄	C₂²×C₆₁	semidirect
422. C₆₁	#62905	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₁×#3560	2
C₆₁×#3559	2
C₆₁×#3537	2
C₆₁×#3534	2
C₆₁×#3519	2
C₆₁×#3496	2
C₆₁×#3494	2
C₂×C₆₁×#553	2
C₆₁×#3459	2
#62905	61

Subgroups — C61×#62905 #29566338

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62905 #29566338