Subgroups — C₆₁×#63006 #29566439

Order 15616.

7230 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3524	C₂	1	8	yes	maximal, complemented
2	C₆₁×#3522	C₂	1	4	yes	maximal, complemented
3	C₆₁×#3517	C₂	1	4	yes	maximal, complemented
4	C₆₁×#3517	C₂	1	8	yes	maximal, complemented
5	C₆₁×#3508	C₂	1	6	yes	maximal, complemented
6	C₆₁×#3502	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3494	C₂	1	12	yes	maximal, complemented
8	C₆₁×#3487	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3483	C₂	1	4	yes	maximal, complemented
10	C₆₁×#3480	C₂	1	4	yes	maximal, complemented
11	C₆₁×#3475	C₂	1	6	yes	maximal, complemented
12	C₂×C₆₁×#550	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×2₋¹⁺⁴×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3428	C₂	1	2	yes	maximal, complemented
15	C₂×2₋¹⁺⁴×C₆₁	C₂²	1	1	yes	characteristic
16	C₂²×#41×C₆₁	C₂²	1	2	yes	—
17	C₆₁×#559	C₂²	1	12	yes	complemented
18	C₆₁×#559	C₂²	1	12	yes	complemented
19	Q₈²×C₆₁	C₂²	1	4	yes	complemented
20	C₆₁×#557	C₂²	1	4	yes	complemented
21	C₆₁×#557	C₂²	1	8	yes	complemented
22	C₆₁×#556	C₂²	1	6	yes	complemented
23	C₆₁×#555	C₂²	1	6	yes	complemented
24	C₆₁×#555	C₂²	1	24	yes	complemented
25	C₆₁×#554	C₂²	1	6	yes	complemented
26	C₆₁×#553	C₂²	1	12	yes	complemented
27	C₆₁×#553	C₂²	1	24	yes	complemented
28	C₆₁×#553	C₂²	1	24	yes	complemented
29	C₆₁×#552	C₂²	1	4	yes	—
30	C₆₁×#552	C₂²	1	12	yes	complemented
31	C₆₁×#551	C₂²	1	24	yes	—
32	C₆₁×#550	C₂²	1	4	yes	—
33	C₆₁×#550	C₂²	1	4	yes	—
34	C₆₁×#550	C₂²	1	8	yes	—
35	C₆₁×#550	C₂²	1	8	yes	complemented
36	C₆₁×#550	C₂²	1	12	yes	complemented
37	C₆₁×#550	C₂²	1	8	yes	complemented
38	C₆₁×#550	C₂²	1	12	yes	complemented
39	C₆₁×#548	C₂²	1	8	yes	complemented
40	C₆₁×#548	C₂²	1	8	yes	complemented
41	C₆₁×#547	C₂²	1	6	yes	complemented
42	C₆₁×#547	C₂²	1	24	yes	complemented
43	C₆₁×#546	C₂²	1	12	yes	—
44	C₆₁×#546	C₂²	1	24	yes	—
45	C₆₁×#544	C₂²	1	6	yes	—
46	C₆₁×#542	C₂²	1	24	yes	complemented
47	C₆₁×#540	C₂²	1	24	yes	complemented
48	C₆₁×#540	C₂²	1	24	yes	complemented
49	C₆₁×#535	C₂²	1	12	yes	—
50	C₆₁×#533	C₂²	1	6	yes	—
51	C₆₁×#532	C₂²	1	12	yes	complemented
52	C₆₁×#532	C₂²	1	24	yes	complemented
53	C₆₁×#532	C₂²	1	12	yes	complemented
54	C₂×#127×C₆₁	C₂²	1	3	yes	—
55	C₆₁×#529	C₂²	1	12	yes	complemented
56	C₆₁×#529	C₂²	1	24	yes	complemented
57	C₆₁×#529	C₂²	1	24	yes	complemented
58	C₆₁×#525	C₂²	1	12	yes	—
59	C₂×#121×C₆₁	C₂²	1	6	yes	—
60	C₆₁×#520	C₂²	1	6	yes	—
61	C₆₁×#520	C₂²	1	8	yes	complemented
62	C₆₁×#520	C₂²	1	8	yes	complemented
63	C₆₁×#520	C₂²	1	4	yes	complemented
64	C₆₁×#519	C₂²	1	1	yes	characteristic
65	C₆₁×#519	C₂²	1	2	yes	—
66	C₆₁×#519	C₂²	1	4	yes	complemented
67	C₆₁×#518	C₂²	1	12	yes	—
68	C₄×#41×C₆₁	C₂²	1	6	yes	—
69	C₄×#41×C₆₁	C₂²	1	8	yes	complemented
70	C₄×#41×C₆₁	C₂²	1	8	yes	complemented
71	C₄×#41×C₆₁	C₂²	1	4	yes	complemented
72	C₄×#41×C₆₁	C₂²	1	12	yes	complemented
73	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
74	C₂×C₄×Q₈×C₆₁	C₂²	1	4	yes	complemented
75	C₂×C₄×D₄×C₆₁	C₂²	1	3	yes	—
76	C₂×#117×C₆₁	C₂²	1	12	yes	—
77	2₋¹⁺⁴×C₆₁	—	2	8	no	—
78	C₂×#41×C₆₁	—	2	16	no	—
79	C₂×#41×C₆₁	C₂³	1	6	yes	—
80	C₂×#41×C₆₁	C₂³	1	8	yes	—
81	C₂×#41×C₆₁	C₂³	1	8	yes	—
82	C₂×#41×C₆₁	C₂³	1	4	yes	—
83	C₂×#41×C₆₁	C₂³	1	12	yes	—
84	C₂×#41×C₆₁	C₂³	1	24	yes	—
85	C₂²×Q₈×C₆₁	C₂³	1	4	yes	—
86	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₆₁	C₂³	1	6	yes	—
88	C₂²×D₄×C₆₁	C₂³	1	3	yes	—
89	C₂²×D₄×C₆₁	C₂³	1	6	yes	—
90	C₂³×C₄×C₆₁	C₂³	1	6	yes	—
91	C₄⋊Q₈×C₆₁	C₂³	1	6	yes	—
92	C₄⋊Q₈×C₆₁	C₂³	1	6	yes	—
93	C₄⋊Q₈×C₆₁	C₂³	1	24	yes	—
94	#127×C₆₁	C₂³	1	12	yes	—
95	#127×C₆₁	C₂³	1	12	yes	—
96	#127×C₆₁	C₂³	1	24	yes	—
97	#126×C₆₁	C₂³	1	24	yes	—
98	#126×C₆₁	C₂³	1	24	yes	—
99	#126×C₆₁	C₂³	1	8	yes	—
100	#125×C₆₁	C₂³	1	12	yes	—
101	#125×C₆₁	C₂³	1	24	yes	—
102	#125×C₆₁	C₂³	1	8	yes	—
103	#125×C₆₁	C₂³	1	4	yes	—
104	#124×C₆₁	C₂³	1	12	yes	—
105	#124×C₆₁	C₂³	1	24	yes	—
106	#124×C₆₁	C₂³	1	24	yes	—
107	#124×C₆₁	C₂³	1	24	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	48	yes	—
112	#123×C₆₁	C₂³	1	8	yes	—
113	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
114	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
115	C₂²⋊Q₈×C₆₁	C₂³	1	24	yes	—
116	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
117	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
118	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
119	#121×C₆₁	C₂³	1	12	yes	—
120	#121×C₆₁	C₂³	1	12	yes	—
121	#121×C₆₁	C₂³	1	24	yes	—
122	#121×C₆₁	C₂³	1	24	yes	—
123	#121×C₆₁	C₂³	1	24	yes	—
124	#121×C₆₁	C₂³	1	48	yes	—
125	#121×C₆₁	C₂³	1	24	yes	—
126	#121×C₆₁	C₂³	1	24	yes	—
127	#121×C₆₁	C₂³	1	12	yes	—
128	#121×C₆₁	C₂³	1	24	yes	—
129	#120×C₆₁	C₂³	1	24	yes	—
130	C₄×Q₈×C₆₁	C₂³	1	12	yes	—
131	C₄×Q₈×C₆₁	C₂³	1	12	yes	—
132	C₄×Q₈×C₆₁	C₂³	1	12	yes	—
133	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
134	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
135	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
136	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
137	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
138	C₄×Q₈×C₆₁	C₂³	1	6	yes	—
139	C₄×Q₈×C₆₁	C₂³	1	6	yes	—
140	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
141	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
142	C₄×D₄×C₆₁	C₂³	1	12	yes	—
143	C₄×D₄×C₆₁	C₂³	1	24	yes	—
144	C₄×D₄×C₆₁	C₂³	1	12	yes	—
145	C₄×D₄×C₆₁	C₂³	1	24	yes	—
146	C₄×D₄×C₆₁	C₂³	1	24	yes	—
147	C₄×D₄×C₆₁	C₂³	1	24	yes	—
148	C₄×D₄×C₆₁	C₂³	1	4	yes	—
149	C₄×D₄×C₆₁	C₂³	1	12	yes	—
150	C₄×D₄×C₆₁	C₂³	1	24	yes	—
151	C₄×D₄×C₆₁	C₂³	1	6	yes	—
152	C₄×D₄×C₆₁	C₂³	1	6	yes	—
153	C₄×D₄×C₆₁	C₂³	1	24	yes	—
154	C₄×D₄×C₆₁	C₂³	1	24	yes	—
155	C₄×D₄×C₆₁	C₂³	1	12	yes	—
156	C₄×D₄×C₆₁	C₂³	1	6	yes	—
157	C₄×D₄×C₆₁	C₂³	1	6	yes	—
158	C₄×D₄×C₆₁	C₂³	1	24	yes	—
159	#117×C₆₁	C₂³	1	12	yes	—
160	#117×C₆₁	C₂³	1	12	yes	—
161	#117×C₆₁	C₂³	1	24	yes	—
162	#117×C₆₁	C₂³	1	8	yes	—
163	#117×C₆₁	C₂³	1	24	yes	—
164	#117×C₆₁	C₂³	1	4	yes	—
165	#117×C₆₁	C₂³	1	12	yes	—
166	#117×C₆₁	C₂³	1	12	yes	—
167	#117×C₆₁	C₂³	1	12	yes	—
168	#117×C₆₁	C₂³	1	6	yes	—
169	C₂×C₄⋊C₄×C₆₁	C₂³	1	3	yes	—
170	C₂×C₄⋊C₄×C₆₁	C₂³	1	12	yes	—
171	C₂×C₄⋊C₄×C₆₁	C₂³	1	12	yes	—
172	C₂×C₄⋊C₄×C₆₁	C₂³	1	12	yes	—
173	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₆₁	C₂³	1	24	yes	—
175	C₂×C₂²⋊C₄×C₆₁	C₂³	1	6	yes	—
176	C₂×C₄²×C₆₁	C₂³	1	3	yes	—
177	C₂×C₄²×C₆₁	C₂³	1	12	yes	—
178	C₂×C₄²×C₆₁	C₂³	1	24	yes	—
179	C₂⁴×C₆₁	C₂⁴	1	6	yes	—
180	#41×C₆₁	—	2	32	no	—
181	#41×C₆₁	—	2	32	no	—
182	#41×C₆₁	—	2	16	no	—
183	#41×C₆₁	—	2	24	no	—
184	#41×C₆₁	—	4	24	no	—
185	#41×C₆₁	—	8	24	no	—
186	C₂×Q₈×C₆₁	—	2	16	no	—
187	C₂×Q₈×C₆₁	#41	1	8	yes	complemented
188	C₂×Q₈×C₆₁	C₂⁴	1	6	yes	—
189	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
190	C₂×Q₈×C₆₁	C₂⁴	1	12	yes	—
191	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
192	C₂×D₄×C₆₁	—	2	24	no	—
193	C₂×D₄×C₆₁	—	4	6	no	—
194	C₂×D₄×C₆₁	—	8	6	no	—
195	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
196	C₂×D₄×C₆₁	C₂⁴	1	24	yes	—
197	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
198	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
199	C₂×D₄×C₆₁	C₂⁴	1	24	yes	—
200	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
201	C₂×D₄×C₆₁	C₂⁴	1	24	yes	—
202	C₂×D₄×C₆₁	C₂⁴	1	24	yes	—
203	C₂²×C₄×C₆₁	—	2	24	no	—
204	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
206	C₂²×C₄×C₆₁	C₂⁴	1	12	yes	—
207	C₂²×C₄×C₆₁	C₂⁴	1	12	yes	—
208	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₆₁	C₂⁴	1	12	yes	—
210	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
211	C₂²×C₄×C₆₁	C₂⁴	1	24	yes	—
212	C₂²×C₄×C₆₁	C₂⁴	1	24	yes	—
213	C₂²×C₄×C₆₁	C₂⁴	1	12	yes	—
214	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
215	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
216	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
217	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
218	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
219	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
220	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
221	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
222	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
223	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
224	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
225	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
226	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
227	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
228	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
229	C₄⋊C₄×C₆₁	C₂⁴	1	24	yes	—
230	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
231	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
232	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
233	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
234	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
235	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
236	C₂²⋊C₄×C₆₁	C₂⁴	1	24	yes	—
237	C₂²⋊C₄×C₆₁	C₂⁴	1	24	yes	—
238	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
239	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
240	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
241	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
242	C₂²⋊C₄×C₆₁	C₂⁴	1	24	yes	—
243	C₂²⋊C₄×C₆₁	C₂⁴	1	24	yes	—
244	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
245	C₄²×C₆₁	C₂⁴	1	8	yes	—
246	C₄²×C₆₁	C₂⁴	1	12	yes	—
247	C₄²×C₆₁	C₂⁴	1	8	yes	—
248	C₄²×C₆₁	C₂⁴	1	4	yes	—
249	C₄²×C₆₁	C₂⁴	1	6	yes	—
250	C₄²×C₆₁	C₂⁴	1	12	yes	—
251	C₄²×C₆₁	C₂⁴	1	24	yes	—
252	C₄²×C₆₁	C₂⁴	1	6	yes	—
253	C₂³×C₆₁	—	2	12	no	—
254	C₂³×C₆₁	—	4	6	no	—
255	C₂³×C₆₁	—	4	6	no	—
256	C₂³×C₆₁	C₂⁵	1	12	yes	—
257	C₂³×C₆₁	C₂⁵	1	4	yes	—
258	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
259	Q₈×C₆₁	—	2	12	no	—
260	Q₈×C₆₁	—	2	8	no	—
261	Q₈×C₆₁	—	4	12	no	—
262	Q₈×C₆₁	C₂×#41	1	16	yes	—
263	D₄×C₆₁	—	2	8	no	—
264	D₄×C₆₁	—	2	48	no	—
265	D₄×C₆₁	—	2	12	no	—
266	D₄×C₆₁	—	2	12	no	—
267	D₄×C₆₁	—	4	6	no	—
268	D₄×C₆₁	—	4	24	no	—
269	D₄×C₆₁	—	4	24	no	—
270	D₄×C₆₁	—	4	24	no	—
271	C₂×C₄×C₆₁	—	2	4	no	—
272	C₂×C₄×C₆₁	—	2	24	no	—
273	C₂×C₄×C₆₁	—	2	24	no	—
274	C₂×C₄×C₆₁	—	2	24	no	—
275	C₂×C₄×C₆₁	—	2	2	no	—
276	C₂×C₄×C₆₁	—	2	8	no	—
277	C₂×C₄×C₆₁	—	4	3	no	—
278	C₂×C₄×C₆₁	—	4	24	no	—
279	C₂×C₄×C₆₁	—	4	12	no	—
280	C₂×C₄×C₆₁	—	4	24	no	—
281	C₂×C₄×C₆₁	C₂×#41	1	12	yes	—
282	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
283	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
284	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
285	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
286	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
287	C₂×C₄×C₆₁	C₂⁵	1	8	yes	—
288	C₂×C₄×C₆₁	C₂⁵	1	8	yes	—
289	C₂×C₄×C₆₁	C₂⁵	1	6	yes	—
290	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
291	C₂×C₄×C₆₁	C₂⁵	1	6	yes	—
292	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
293	#63006	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
294	C₂²×C₆₁	—	2	1	no	—
295	C₂²×C₆₁	—	2	1	no	—
296	C₂²×C₆₁	—	2	4	no	—
297	C₂²×C₆₁	—	2	12	no	—
298	C₂²×C₆₁	—	2	4	no	—
299	C₂²×C₆₁	—	2	12	no	—
300	C₂²×C₆₁	—	2	4	no	—
301	C₂²×C₆₁	—	2	12	no	—
302	C₂²×C₆₁	—	8	12	no	—
303	C₂²×C₆₁	C₂²×#41	1	2	yes	—
304	C₂²×C₆₁	C₂⁶	1	1	yes	characteristic
305	C₄×C₆₁	—	2	2	no	—
306	C₄×C₆₁	—	2	2	no	—
307	C₄×C₆₁	—	2	4	no	—
308	C₄×C₆₁	—	2	4	no	—
309	C₄×C₆₁	—	2	1	no	—
310	C₄×C₆₁	—	2	8	no	—
311	C₄×C₆₁	—	2	4	no	—
312	C₄×C₆₁	—	2	6	no	—
313	C₄×C₆₁	—	2	8	no	—
314	C₄×C₆₁	C₂²×#41	1	12	yes	—
315	C₄×C₆₁	#585	1	2	yes	—
316	#3524	C₂×C₆₁	1	8	yes	complemented
317	#3522	C₂×C₆₁	1	4	yes	complemented
318	#3517	C₂×C₆₁	1	8	yes	complemented
319	#3517	C₂×C₆₁	1	4	yes	complemented
320	#3508	C₂×C₆₁	1	6	yes	complemented
321	#3502	C₂×C₆₁	1	1	yes	characteristic, complemented
322	#3494	C₂×C₆₁	1	12	yes	complemented
323	#3487	C₂×C₆₁	1	2	yes	complemented
324	#3483	C₂×C₆₁	1	4	yes	complemented
325	#3480	C₂×C₆₁	1	4	yes	complemented
326	#3475	C₂×C₆₁	1	6	yes	complemented
327	C₂×#550	C₂×C₆₁	1	1	yes	characteristic, complemented
328	C₄×2₋¹⁺⁴	C₂×C₆₁	1	1	yes	characteristic, complemented
329	#3428	C₂×C₆₁	1	2	yes	complemented
330	C₂×C₆₁	—	2	2	no	—
331	C₂×C₆₁	—	4	4	no	—
332	C₂×C₆₁	—	4	12	no	—
333	C₂×C₆₁	C₂³×#41	1	1	yes	characteristic
334	C₂×C₆₁	C₂×#585	1	1	yes	characteristic
335	C₂×C₆₁	H(7,𝔽₂)	1	1	yes	characteristic
336	C₂×2₋¹⁺⁴	C₂²×C₆₁	1	1	yes	characteristic
337	C₂²×#41	C₂²×C₆₁	1	2	yes	—
338	#559	C₂²×C₆₁	1	12	yes	complemented
339	#559	C₂²×C₆₁	1	12	yes	complemented
340	Q₈²	C₂²×C₆₁	1	4	yes	complemented
341	#557	C₂²×C₆₁	1	4	yes	complemented
342	#557	C₂²×C₆₁	1	8	yes	complemented
343	#556	C₂²×C₆₁	1	6	yes	complemented
344	#555	C₂²×C₆₁	1	6	yes	complemented
345	#555	C₂²×C₆₁	1	24	yes	complemented
346	#554	C₂²×C₆₁	1	6	yes	complemented
347	#553	C₂²×C₆₁	1	12	yes	complemented
348	#553	C₂²×C₆₁	1	24	yes	complemented
349	#553	C₂²×C₆₁	1	24	yes	complemented
350	#552	C₂²×C₆₁	1	4	yes	—
351	#552	C₂²×C₆₁	1	12	yes	complemented
352	#551	C₂²×C₆₁	1	24	yes	—
353	#550	C₂²×C₆₁	1	4	yes	—
354	#550	C₂²×C₆₁	1	4	yes	—
355	#550	C₂²×C₆₁	1	8	yes	—
356	#550	C₂²×C₆₁	1	8	yes	complemented
357	#550	C₂²×C₆₁	1	12	yes	complemented
358	#550	C₂²×C₆₁	1	8	yes	complemented
359	#550	C₂²×C₆₁	1	12	yes	complemented
360	#548	C₂²×C₆₁	1	8	yes	complemented
361	#548	C₂²×C₆₁	1	8	yes	complemented
362	#547	C₂²×C₆₁	1	6	yes	complemented
363	#547	C₂²×C₆₁	1	24	yes	complemented
364	#546	C₂²×C₆₁	1	12	yes	—
365	#546	C₂²×C₆₁	1	24	yes	—
366	#544	C₂²×C₆₁	1	6	yes	—
367	#542	C₂²×C₆₁	1	24	yes	complemented
368	#540	C₂²×C₆₁	1	24	yes	complemented
369	#540	C₂²×C₆₁	1	24	yes	complemented
370	#535	C₂²×C₆₁	1	12	yes	—
371	#533	C₂²×C₆₁	1	6	yes	—
372	#532	C₂²×C₆₁	1	12	yes	complemented
373	#532	C₂²×C₆₁	1	24	yes	complemented
374	#532	C₂²×C₆₁	1	12	yes	complemented
375	C₂×#127	C₂²×C₆₁	1	3	yes	—
376	#529	C₂²×C₆₁	1	12	yes	complemented
377	#529	C₂²×C₆₁	1	24	yes	complemented
378	#529	C₂²×C₆₁	1	24	yes	complemented
379	#525	C₂²×C₆₁	1	12	yes	—
380	C₂×#121	C₂²×C₆₁	1	6	yes	—
381	#520	C₂²×C₆₁	1	6	yes	—
382	#520	C₂²×C₆₁	1	8	yes	complemented
383	#520	C₂²×C₆₁	1	8	yes	complemented
384	#520	C₂²×C₆₁	1	4	yes	complemented
385	#519	C₂²×C₆₁	1	1	yes	characteristic
386	#519	C₂²×C₆₁	1	2	yes	—
387	#519	C₂²×C₆₁	1	4	yes	complemented
388	#518	C₂²×C₆₁	1	12	yes	—
389	C₄×#41	C₂²×C₆₁	1	6	yes	—
390	C₄×#41	C₂²×C₆₁	1	8	yes	complemented
391	C₄×#41	C₂²×C₆₁	1	8	yes	complemented
392	C₄×#41	C₂²×C₆₁	1	4	yes	complemented
393	C₄×#41	C₂²×C₆₁	1	12	yes	complemented
394	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
395	C₂×C₄×Q₈	C₂²×C₆₁	1	4	yes	complemented
396	C₂×C₄×D₄	C₂²×C₆₁	1	3	yes	—
397	C₂×#117	C₂²×C₆₁	1	12	yes	—
398	C₆₁	#63006	1	1	yes	characteristic, direct product factor, Sylow
399	2₋¹⁺⁴	—	2	8	no	—
400	C₂×#41	—	2	16	no	—
401	C₂×#41	C₂³×C₆₁	1	6	yes	—
402	C₂×#41	C₂³×C₆₁	1	8	yes	—
403	C₂×#41	C₂³×C₆₁	1	4	yes	—
404	C₂×#41	C₂³×C₆₁	1	8	yes	—
405	C₂×#41	C₂³×C₆₁	1	12	yes	—
406	C₂×#41	C₂³×C₆₁	1	24	yes	—
407	C₂²×Q₈	C₂³×C₆₁	1	4	yes	—
408	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
409	C₂²×D₄	C₂³×C₆₁	1	6	yes	—
410	C₂²×D₄	C₂³×C₆₁	1	3	yes	—
411	C₂²×D₄	C₂³×C₆₁	1	6	yes	—
412	C₂³×C₄	C₂³×C₆₁	1	6	yes	—
413	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	—
414	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	—
415	C₄⋊Q₈	C₂³×C₆₁	1	24	yes	—
416	#127	C₂³×C₆₁	1	12	yes	—
417	#127	C₂³×C₆₁	1	12	yes	—
418	#127	C₂³×C₆₁	1	24	yes	—
419	#126	C₂³×C₆₁	1	24	yes	—
420	#126	C₂³×C₆₁	1	8	yes	—
421	#126	C₂³×C₆₁	1	24	yes	—
422	#125	C₂³×C₆₁	1	8	yes	—
423	#125	C₂³×C₆₁	1	4	yes	—
424	#125	C₂³×C₆₁	1	24	yes	—
425	#125	C₂³×C₆₁	1	12	yes	—
426	#124	C₂³×C₆₁	1	12	yes	—
427	#124	C₂³×C₆₁	1	24	yes	—
428	#124	C₂³×C₆₁	1	24	yes	—
429	#124	C₂³×C₆₁	1	24	yes	—
430	#123	C₂³×C₆₁	1	8	yes	—
431	#123	C₂³×C₆₁	1	24	yes	—
432	#123	C₂³×C₆₁	1	24	yes	—
433	#123	C₂³×C₆₁	1	24	yes	—
434	#123	C₂³×C₆₁	1	48	yes	—
435	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
436	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
437	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
438	C₂²⋊Q₈	C₂³×C₆₁	1	24	yes	—
439	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
440	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
441	#121	C₂³×C₆₁	1	24	yes	—
442	#121	C₂³×C₆₁	1	24	yes	—
443	#121	C₂³×C₆₁	1	12	yes	—
444	#121	C₂³×C₆₁	1	12	yes	—
445	#121	C₂³×C₆₁	1	12	yes	—
446	#121	C₂³×C₆₁	1	24	yes	—
447	#121	C₂³×C₆₁	1	24	yes	—
448	#121	C₂³×C₆₁	1	24	yes	—
449	#121	C₂³×C₆₁	1	24	yes	—
450	#121	C₂³×C₆₁	1	48	yes	—
451	#120	C₂³×C₆₁	1	24	yes	—
452	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
453	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
454	C₄×Q₈	C₂³×C₆₁	1	6	yes	—
455	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
456	C₄×Q₈	C₂³×C₆₁	1	12	yes	—
457	C₄×Q₈	C₂³×C₆₁	1	6	yes	—
458	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
459	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
460	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
461	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
462	C₄×Q₈	C₂³×C₆₁	1	12	yes	—
463	C₄×Q₈	C₂³×C₆₁	1	12	yes	—
464	C₄×D₄	C₂³×C₆₁	1	6	yes	—
465	C₄×D₄	C₂³×C₆₁	1	6	yes	—
466	C₄×D₄	C₂³×C₆₁	1	12	yes	—
467	C₄×D₄	C₂³×C₆₁	1	4	yes	—
468	C₄×D₄	C₂³×C₆₁	1	6	yes	—
469	C₄×D₄	C₂³×C₆₁	1	12	yes	—
470	C₄×D₄	C₂³×C₆₁	1	6	yes	—
471	C₄×D₄	C₂³×C₆₁	1	24	yes	—
472	C₄×D₄	C₂³×C₆₁	1	24	yes	—
473	C₄×D₄	C₂³×C₆₁	1	24	yes	—
474	C₄×D₄	C₂³×C₆₁	1	24	yes	—
475	C₄×D₄	C₂³×C₆₁	1	12	yes	—
476	C₄×D₄	C₂³×C₆₁	1	24	yes	—
477	C₄×D₄	C₂³×C₆₁	1	12	yes	—
478	C₄×D₄	C₂³×C₆₁	1	24	yes	—
479	C₄×D₄	C₂³×C₆₁	1	24	yes	—
480	C₄×D₄	C₂³×C₆₁	1	24	yes	—
481	#117	C₂³×C₆₁	1	8	yes	—
482	#117	C₂³×C₆₁	1	6	yes	—
483	#117	C₂³×C₆₁	1	12	yes	—
484	#117	C₂³×C₆₁	1	12	yes	—
485	#117	C₂³×C₆₁	1	12	yes	—
486	#117	C₂³×C₆₁	1	24	yes	—
487	#117	C₂³×C₆₁	1	12	yes	—
488	#117	C₂³×C₆₁	1	4	yes	—
489	#117	C₂³×C₆₁	1	12	yes	—
490	#117	C₂³×C₆₁	1	24	yes	—
491	C₂×C₄⋊C₄	C₂³×C₆₁	1	12	yes	—
492	C₂×C₄⋊C₄	C₂³×C₆₁	1	12	yes	—
493	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
494	C₂×C₄⋊C₄	C₂³×C₆₁	1	3	yes	—
495	C₂×C₄⋊C₄	C₂³×C₆₁	1	12	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₆₁	1	24	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₆₁	1	6	yes	—
498	C₂×C₄²	C₂³×C₆₁	1	24	yes	—
499	C₂×C₄²	C₂³×C₆₁	1	3	yes	—
500	C₂×C₄²	C₂³×C₆₁	1	12	yes	—
501	C₂⁴	C₂⁴×C₆₁	1	6	yes	—
502	#41	—	2	32	no	—
503	#41	—	2	32	no	—
504	#41	—	2	16	no	—
505	#41	—	2	24	no	—
506	#41	—	4	24	no	—
507	#41	—	8	24	no	—
508	C₂×Q₈	—	2	16	no	—
509	C₂×Q₈	#41×C₆₁	1	8	yes	complemented
510	C₂×Q₈	C₂⁴×C₆₁	1	6	yes	—
511	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
512	C₂×Q₈	C₂⁴×C₆₁	1	12	yes	—
513	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
514	C₂×D₄	—	2	24	no	—
515	C₂×D₄	—	4	6	no	—
516	C₂×D₄	—	8	6	no	—
517	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
518	C₂×D₄	C₂⁴×C₆₁	1	24	yes	—
519	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
520	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
521	C₂×D₄	C₂⁴×C₆₁	1	24	yes	—
522	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
523	C₂×D₄	C₂⁴×C₆₁	1	24	yes	—
524	C₂×D₄	C₂⁴×C₆₁	1	24	yes	—
525	C₂²×C₄	—	2	24	no	—
526	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
527	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
528	C₂²×C₄	C₂⁴×C₆₁	1	12	yes	—
529	C₂²×C₄	C₂⁴×C₆₁	1	12	yes	—
530	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
531	C₂²×C₄	C₂⁴×C₆₁	1	12	yes	—
532	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
533	C₂²×C₄	C₂⁴×C₆₁	1	24	yes	—
534	C₂²×C₄	C₂⁴×C₆₁	1	24	yes	—
535	C₂²×C₄	C₂⁴×C₆₁	1	12	yes	—
536	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
537	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
538	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
539	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
540	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
541	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
542	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
543	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
544	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
545	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
546	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
547	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
548	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
549	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
550	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
551	C₄⋊C₄	C₂⁴×C₆₁	1	24	yes	—
552	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
553	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
554	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
555	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
556	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
557	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
558	C₂²⋊C₄	C₂⁴×C₆₁	1	24	yes	—
559	C₂²⋊C₄	C₂⁴×C₆₁	1	24	yes	—
560	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
561	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
562	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
563	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
564	C₂²⋊C₄	C₂⁴×C₆₁	1	24	yes	—
565	C₂²⋊C₄	C₂⁴×C₆₁	1	24	yes	—
566	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
567	C₄²	C₂⁴×C₆₁	1	8	yes	—
568	C₄²	C₂⁴×C₆₁	1	12	yes	—
569	C₄²	C₂⁴×C₆₁	1	8	yes	—
570	C₄²	C₂⁴×C₆₁	1	4	yes	—
571	C₄²	C₂⁴×C₆₁	1	6	yes	—
572	C₄²	C₂⁴×C₆₁	1	12	yes	—
573	C₄²	C₂⁴×C₆₁	1	24	yes	—
574	C₄²	C₂⁴×C₆₁	1	6	yes	—
575	C₂³	—	2	12	no	—
576	C₂³	—	4	6	no	—
577	C₂³	—	4	6	no	—
578	C₂³	C₂⁵×C₆₁	1	12	yes	—
579	C₂³	C₂⁵×C₆₁	1	4	yes	—
580	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
581	Q₈	—	2	12	no	—
582	Q₈	—	2	8	no	—
583	Q₈	—	4	12	no	—
584	Q₈	C₂×#41×C₆₁	1	16	yes	—
585	D₄	—	2	8	no	—
586	D₄	—	2	48	no	—
587	D₄	—	2	12	no	—
588	D₄	—	2	12	no	—
589	D₄	—	4	6	no	—
590	D₄	—	4	24	no	—
591	D₄	—	4	24	no	—
592	D₄	—	4	24	no	—
593	C₂×C₄	—	2	4	no	—
594	C₂×C₄	—	2	24	no	—
595	C₂×C₄	—	2	24	no	—
596	C₂×C₄	—	2	24	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	8	no	—
599	C₂×C₄	—	4	3	no	—
600	C₂×C₄	—	4	24	no	—
601	C₂×C₄	—	4	12	no	—
602	C₂×C₄	—	4	24	no	—
603	C₂×C₄	C₂×#41×C₆₁	1	12	yes	—
604	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
605	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
606	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
607	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
608	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
609	C₂×C₄	C₂⁵×C₆₁	1	8	yes	—
610	C₂×C₄	C₂⁵×C₆₁	1	8	yes	—
611	C₂×C₄	C₂⁵×C₆₁	1	6	yes	—
612	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
613	C₂×C₄	C₂⁵×C₆₁	1	6	yes	—
614	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	4	no	—
618	C₂²	—	2	12	no	—
619	C₂²	—	2	4	no	—
620	C₂²	—	2	12	no	—
621	C₂²	—	2	4	no	—
622	C₂²	—	2	12	no	—
623	C₂²	—	8	12	no	—
624	C₂²	C₂²×#41×C₆₁	1	2	yes	—
625	C₂²	C₂⁶×C₆₁	1	1	yes	characteristic
626	C₄	—	2	2	no	—
627	C₄	—	2	2	no	—
628	C₄	—	2	4	no	—
629	C₄	—	2	4	no	—
630	C₄	—	2	1	no	—
631	C₄	—	2	8	no	—
632	C₄	—	2	4	no	—
633	C₄	—	2	6	no	—
634	C₄	—	2	8	no	—
635	C₄	C₂²×#41×C₆₁	1	12	yes	—
636	C₄	C₆₁×#585	1	2	yes	—
637	C₂	—	2	2	no	—
638	C₂	—	4	12	no	—
639	C₂	—	4	4	no	—
640	C₂	C₂³×#41×C₆₁	1	1	yes	characteristic
641	C₂	C₂×C₆₁×#585	1	1	yes	characteristic
642	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×#3524	C₂	semidirect
2. C₆₁×#3522	C₂	semidirect
3. C₆₁×#3517	C₂	semidirect
4. C₆₁×#3517	C₂	semidirect
5. C₆₁×#3508	C₂	semidirect
6. C₆₁×#3502	C₂	semidirect
7. C₆₁×#3494	C₂	semidirect
8. C₆₁×#3487	C₂	semidirect
9. C₆₁×#3483	C₂	semidirect
10. C₆₁×#3480	C₂	semidirect
11. C₆₁×#3475	C₂	semidirect
12. C₂×C₆₁×#550	C₂	semidirect
13. C₄×2₋¹⁺⁴×C₆₁	C₂	semidirect
14. C₆₁×#3428	C₂	semidirect
17. C₆₁×#559	C₂²	semidirect
18. C₆₁×#559	C₂²	semidirect
19. Q₈²×C₆₁	C₂²	semidirect
20. C₆₁×#557	C₂²	semidirect
21. C₆₁×#557	C₂²	semidirect
22. C₆₁×#556	C₂²	semidirect
23. C₆₁×#555	C₂²	semidirect
24. C₆₁×#555	C₂²	semidirect
25. C₆₁×#554	C₂²	semidirect
26. C₆₁×#553	C₂²	semidirect
27. C₆₁×#553	C₂²	semidirect
28. C₆₁×#553	C₂²	semidirect
30. C₆₁×#552	C₂²	semidirect
35. C₆₁×#550	C₂²	semidirect
36. C₆₁×#550	C₂²	semidirect
37. C₆₁×#550	C₂²	semidirect
38. C₆₁×#550	C₂²	semidirect
39. C₆₁×#548	C₂²	semidirect
40. C₆₁×#548	C₂²	semidirect
41. C₆₁×#547	C₂²	semidirect
42. C₆₁×#547	C₂²	semidirect
46. C₆₁×#542	C₂²	semidirect
47. C₆₁×#540	C₂²	semidirect
48. C₆₁×#540	C₂²	semidirect
51. C₆₁×#532	C₂²	semidirect
52. C₆₁×#532	C₂²	semidirect
53. C₆₁×#532	C₂²	semidirect
55. C₆₁×#529	C₂²	semidirect
56. C₆₁×#529	C₂²	semidirect
57. C₆₁×#529	C₂²	semidirect
61. C₆₁×#520	C₂²	semidirect
62. C₆₁×#520	C₂²	semidirect
63. C₆₁×#520	C₂²	semidirect
66. C₆₁×#519	C₂²	semidirect
69. C₄×#41×C₆₁	C₂²	semidirect
70. C₄×#41×C₆₁	C₂²	semidirect
71. C₄×#41×C₆₁	C₂²	semidirect
72. C₄×#41×C₆₁	C₂²	semidirect
74. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
187. C₂×Q₈×C₆₁	#41	semidirect
293. #63006	C₆₁	direct (N × H)
316. #3524	C₂×C₆₁	semidirect
317. #3522	C₂×C₆₁	semidirect
318. #3517	C₂×C₆₁	semidirect
319. #3517	C₂×C₆₁	semidirect
320. #3508	C₂×C₆₁	semidirect
321. #3502	C₂×C₆₁	semidirect
322. #3494	C₂×C₆₁	semidirect
323. #3487	C₂×C₆₁	semidirect
324. #3483	C₂×C₆₁	semidirect
325. #3480	C₂×C₆₁	semidirect
326. #3475	C₂×C₆₁	semidirect
327. C₂×#550	C₂×C₆₁	semidirect
328. C₄×2₋¹⁺⁴	C₂×C₆₁	semidirect
329. #3428	C₂×C₆₁	semidirect
338. #559	C₂²×C₆₁	semidirect
339. #559	C₂²×C₆₁	semidirect
340. Q₈²	C₂²×C₆₁	semidirect
341. #557	C₂²×C₆₁	semidirect
342. #557	C₂²×C₆₁	semidirect
343. #556	C₂²×C₆₁	semidirect
344. #555	C₂²×C₆₁	semidirect
345. #555	C₂²×C₆₁	semidirect
346. #554	C₂²×C₆₁	semidirect
347. #553	C₂²×C₆₁	semidirect
348. #553	C₂²×C₆₁	semidirect
349. #553	C₂²×C₆₁	semidirect
351. #552	C₂²×C₆₁	semidirect
356. #550	C₂²×C₆₁	semidirect
357. #550	C₂²×C₆₁	semidirect
358. #550	C₂²×C₆₁	semidirect
359. #550	C₂²×C₆₁	semidirect
360. #548	C₂²×C₆₁	semidirect
361. #548	C₂²×C₆₁	semidirect
362. #547	C₂²×C₆₁	semidirect
363. #547	C₂²×C₆₁	semidirect
367. #542	C₂²×C₆₁	semidirect
368. #540	C₂²×C₆₁	semidirect
369. #540	C₂²×C₆₁	semidirect
372. #532	C₂²×C₆₁	semidirect
373. #532	C₂²×C₆₁	semidirect
374. #532	C₂²×C₆₁	semidirect
376. #529	C₂²×C₆₁	semidirect
377. #529	C₂²×C₆₁	semidirect
378. #529	C₂²×C₆₁	semidirect
382. #520	C₂²×C₆₁	semidirect
383. #520	C₂²×C₆₁	semidirect
384. #520	C₂²×C₆₁	semidirect
387. #519	C₂²×C₆₁	semidirect
390. C₄×#41	C₂²×C₆₁	semidirect
391. C₄×#41	C₂²×C₆₁	semidirect
392. C₄×#41	C₂²×C₆₁	semidirect
393. C₄×#41	C₂²×C₆₁	semidirect
395. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
398. C₆₁	#63006	direct (N × H)
509. C₂×Q₈	#41×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3524	2
C₆₁×#3522	2
C₆₁×#3517	2
C₆₁×#3508	2
C₆₁×#3502	2
C₆₁×#3494	2
C₆₁×#3487	2
C₆₁×#3483	2
C₆₁×#3480	2
C₆₁×#3475	2
C₂×C₆₁×#550	2
C₄×2₋¹⁺⁴×C₆₁	2
C₆₁×#3428	2
#63006	61

Subgroups — C61×#63006 #29566439

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#63006 #29566439