Subgroups — C₆₁×#61912 #29565345

Order 15616.

1760 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3403	C₂	1	4	yes	maximal, complemented
4	C₆₁×#3397	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3393	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3375	C₂	1	4	yes	maximal, complemented
7	C₆₁×#3367	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3358	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3224	C₂	1	4	yes	maximal, complemented
10	C₆₁×#3214	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3210	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3124	C₂	1	4	yes	maximal, complemented
13	C₆₁×#3110	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3100	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#2985	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#563	—	2	2	no	—
17	C₆₁×#559	C₂²	1	4	yes	—
18	C₆₁×#559	C₂²	1	2	yes	complemented
19	Q₈²×C₆₁	C₂²	1	2	yes	complemented
20	C₆₁×#556	—	2	1	no	—
21	C₆₁×#556	C₂²	1	2	yes	—
22	C₆₁×#556	C₂²	1	2	yes	complemented
23	C₆₁×#555	—	2	1	no	—
24	C₆₁×#553	—	2	2	no	—
25	C₆₁×#550	C₂²	1	2	yes	—
26	D₄×Q₈×C₆₁	—	2	1	no	—
27	D₄×Q₈×C₆₁	C₂²	1	2	yes	complemented
28	C₆₁×#547	—	2	1	no	—
29	C₆₁×#542	—	2	2	no	—
30	C₆₁×#542	C₂²	1	4	yes	—
31	C₆₁×#538	—	2	2	no	—
32	C₆₁×#536	—	2	2	no	—
33	C₆₁×#535	C₂²	1	2	yes	—
34	C₆₁×#533	C₂²	1	1	yes	characteristic
35	C₆₁×#533	C₂²	1	1	yes	characteristic
36	C₆₁×#532	C₂²	1	1	yes	characteristic
37	C₆₁×#532	C₂²	1	1	yes	characteristic
38	C₆₁×#525	—	2	2	no	—
39	C₆₁×#520	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
41	C₆₁×#496	C₂²	1	4	yes	—
42	C₆₁×#496	C₂²	1	2	yes	complemented
43	C₆₁×#495	C₂²	1	4	yes	—
44	C₆₁×#494	C₂²	1	1	yes	characteristic, complemented
45	C₆₁×#492	C₂²	1	1	yes	characteristic, complemented
46	C₆₁×#489	C₂²	1	4	yes	—
47	C₆₁×#489	C₂²	1	2	yes	complemented
48	C₆₁×#487	C₂²	1	1	yes	characteristic, complemented
49	C₆₁×#486	C₂²	1	4	yes	—
50	C₆₁×#486	C₂²	1	1	yes	characteristic, complemented
51	C₆₁×#484	C₂²	1	2	yes	—
52	C₆₁×#480	C₂²	1	2	yes	—
53	C₆₁×#477	C₂²	1	4	yes	complemented
54	C₆₁×#474	C₂²	1	2	yes	—
55	C₆₁×#474	C₂²	1	2	yes	—
56	C₆₁×#474	C₂²	1	4	yes	complemented
57	C₆₁×#464	C₂²	1	4	yes	—
58	C₆₁×#464	C₂²	1	4	yes	complemented
59	C₆₁×#464	C₂²	1	4	yes	complemented
60	C₆₁×#463	C₂²	1	4	yes	—
61	C₆₁×#463	C₂²	1	4	yes	complemented
62	C₆₁×#461	C₂²	1	2	yes	—
63	C₆₁×#461	C₂²	1	2	yes	complemented
64	C₆₁×#460	C₂²	1	4	yes	—
65	C₆₁×#459	C₂²	1	2	yes	—
66	C₆₁×#459	C₂²	1	4	yes	—
67	C₆₁×#459	C₂²	1	2	yes	complemented
68	C₆₁×#452	C₂²	1	4	yes	—
69	C₆₁×#450	C₂²	1	2	yes	—
70	C₆₁×#449	C₂²	1	4	yes	—
71	C₆₁×#447	C₂²	1	2	yes	—
72	C₆₁×#446	C₂²	1	2	yes	complemented
73	C₆₁×#446	C₂²	1	4	yes	complemented
74	C₈×Q₈×C₆₁	C₂²	1	2	yes	complemented
75	C₆₁×#440	C₂²	1	4	yes	—
76	C₆₁×#440	C₂²	1	4	yes	complemented
77	C₆₁×#440	C₂²	1	4	yes	complemented
78	C₄×Q₁₆×C₆₁	C₂²	1	4	yes	complemented
79	C₄×D₈×C₆₁	C₂²	1	2	yes	—
80	C₄×D₈×C₆₁	C₂²	1	2	yes	—
81	C₄×D₈×C₆₁	C₂²	1	4	yes	complemented
82	C₆₁×#433	C₂²	1	4	yes	—
83	C₆₁×#432	C₂²	1	1	yes	characteristic
84	C₆₁×#431	C₂²	1	1	yes	characteristic
85	C₂×#41×C₆₁	—	2	2	no	—
86	C₂×#41×C₆₁	—	2	1	no	—
87	C₂×#41×C₆₁	C₂³	1	2	yes	—
88	C₂²×Q₈×C₆₁	—	2	2	no	—
89	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₆₁	—	2	1	no	—
91	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
92	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
93	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
94	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
95	C₂×D₈×C₆₁	C₂³	1	2	yes	—
96	C₂×D₈×C₆₁	C₂³	1	2	yes	—
97	C₂×D₈×C₆₁	C₂³	1	4	yes	—
98	C₄⋊Q₈×C₆₁	—	2	4	no	—
99	C₄⋊Q₈×C₆₁	—	2	2	no	—
100	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
101	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
102	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
103	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
104	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
105	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
106	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
107	#127×C₆₁	C₂³	1	1	yes	characteristic
108	#127×C₆₁	C₂³	1	1	yes	characteristic
109	#127×C₆₁	C₂³	1	4	yes	—
110	#126×C₆₁	—	2	4	no	—
111	#126×C₆₁	—	2	4	no	—
112	#126×C₆₁	—	2	4	no	—
113	#125×C₆₁	—	2	1	no	—
114	#125×C₆₁	D₄	1	2	yes	—
115	#124×C₆₁	—	2	4	no	—
116	#124×C₆₁	—	2	2	no	—
117	#124×C₆₁	—	2	4	no	—
118	#124×C₆₁	—	2	1	no	—
119	#124×C₆₁	C₂³	1	2	yes	—
120	#124×C₆₁	C₂³	1	4	yes	—
121	#124×C₆₁	C₂³	1	4	yes	—
122	#123×C₆₁	—	2	4	no	—
123	#123×C₆₁	—	2	4	no	—
124	#123×C₆₁	—	2	4	no	—
125	#123×C₆₁	—	2	4	no	—
126	C₂²⋊Q₈×C₆₁	—	2	2	no	—
127	C₂²⋊Q₈×C₆₁	—	2	2	no	—
128	C₂²⋊Q₈×C₆₁	—	2	1	no	—
129	C₂²⋊Q₈×C₆₁	—	2	2	no	—
130	C₂²⋊Q₈×C₆₁	—	2	4	no	—
131	C₂²⋊Q₈×C₆₁	—	2	4	no	—
132	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
133	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
134	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
135	#121×C₆₁	—	2	1	no	—
136	#121×C₆₁	—	2	1	no	—
137	#121×C₆₁	—	2	1	no	—
138	#121×C₆₁	—	2	2	no	—
139	#121×C₆₁	—	2	2	no	—
140	#121×C₆₁	—	2	4	no	—
141	#121×C₆₁	—	2	2	no	—
142	#121×C₆₁	C₂³	1	2	yes	—
143	#120×C₆₁	—	2	4	no	—
144	C₄×Q₈×C₆₁	—	2	2	no	—
145	C₄×Q₈×C₆₁	—	2	1	no	—
146	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
147	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
148	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
149	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
150	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
151	C₄×D₄×C₆₁	—	2	2	no	—
152	C₄×D₄×C₆₁	—	2	4	no	—
153	C₄×D₄×C₆₁	—	2	4	no	—
154	C₄×D₄×C₆₁	—	2	1	no	—
155	C₄×D₄×C₆₁	—	2	1	no	—
156	C₄×D₄×C₆₁	—	2	1	no	—
157	C₄×D₄×C₆₁	—	2	1	no	—
158	C₄×D₄×C₆₁	—	2	1	no	—
159	C₄×D₄×C₆₁	C₂³	1	2	yes	—
160	C₄×D₄×C₆₁	C₂³	1	4	yes	—
161	C₄×D₄×C₆₁	C₂³	1	2	yes	—
162	C₄×D₄×C₆₁	C₂³	1	4	yes	—
163	C₄×D₄×C₆₁	C₂³	1	2	yes	—
164	#117×C₆₁	—	2	1	no	—
165	#117×C₆₁	—	2	2	no	—
166	#117×C₆₁	—	2	2	no	—
167	#117×C₆₁	—	2	2	no	—
168	#117×C₆₁	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
170	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
171	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
172	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
173	#107×C₆₁	C₂³	1	2	yes	—
174	#107×C₆₁	C₂³	1	2	yes	—
175	#107×C₆₁	C₂³	1	4	yes	—
176	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
177	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
178	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
179	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
180	#103×C₆₁	C₂³	1	4	yes	—
181	#103×C₆₁	C₂³	1	4	yes	—
182	#103×C₆₁	C₂³	1	4	yes	—
183	#102×C₆₁	C₂³	1	2	yes	—
184	#102×C₆₁	C₂³	1	2	yes	—
185	#102×C₆₁	C₂³	1	2	yes	—
186	#102×C₆₁	C₂³	1	2	yes	—
187	#102×C₆₁	C₂³	1	4	yes	—
188	#102×C₆₁	C₂³	1	4	yes	—
189	#102×C₆₁	C₂³	1	4	yes	—
190	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
191	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
192	#97×C₆₁	C₂³	1	2	yes	—
193	#97×C₆₁	C₂³	1	4	yes	—
194	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₆₁	C₂³	1	4	yes	—
197	C₂⁴×C₆₁	—	2	1	no	—
198	#41×C₆₁	—	4	4	no	—
199	#41×C₆₁	—	8	2	no	—
200	#41×C₆₁	—	8	4	no	—
201	C₂×Q₈×C₆₁	—	2	1	no	—
202	C₂×Q₈×C₆₁	—	2	4	no	—
203	C₂×Q₈×C₆₁	—	2	1	no	—
204	C₂×Q₈×C₆₁	—	8	4	no	—
205	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
206	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
207	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
208	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
209	C₂×D₄×C₆₁	—	2	2	no	—
210	C₂×D₄×C₆₁	—	2	2	no	—
211	C₂×D₄×C₆₁	—	2	1	no	—
212	C₂×D₄×C₆₁	—	2	1	no	—
213	C₂×D₄×C₆₁	—	2	1	no	—
214	C₂×D₄×C₆₁	—	2	4	no	—
215	C₂×D₄×C₆₁	—	2	1	no	—
216	C₂×D₄×C₆₁	—	2	4	no	—
217	C₂×D₄×C₆₁	—	2	1	no	—
218	C₂×D₄×C₆₁	—	4	2	no	—
219	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
220	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
221	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₆₁	—	2	1	no	—
223	C₂²×C₄×C₆₁	—	2	2	no	—
224	C₂²×C₄×C₆₁	—	2	2	no	—
225	C₂²×C₄×C₆₁	—	2	2	no	—
226	C₂²×C₄×C₆₁	—	2	4	no	—
227	C₂²×C₄×C₆₁	—	2	2	no	—
228	C₂²×C₄×C₆₁	—	2	4	no	—
229	C₂²×C₄×C₆₁	—	8	2	no	—
230	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
233	Q₁₆×C₆₁	—	4	4	no	—
234	SD₁₆×C₆₁	—	4	4	no	—
235	SD₁₆×C₆₁	—	4	4	no	—
236	SD₁₆×C₆₁	—	4	4	no	—
237	D₈×C₆₁	—	4	4	no	—
238	D₈×C₆₁	—	4	2	no	—
239	D₈×C₆₁	—	4	2	no	—
240	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
241	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
242	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
243	C₄⋊C₄×C₆₁	—	2	1	no	—
244	C₄⋊C₄×C₆₁	—	2	4	no	—
245	C₄⋊C₄×C₆₁	—	2	1	no	—
246	C₄⋊C₄×C₆₁	—	2	1	no	—
247	C₄⋊C₄×C₆₁	—	2	1	no	—
248	C₄⋊C₄×C₆₁	—	2	1	no	—
249	C₄⋊C₄×C₆₁	—	2	1	no	—
250	C₄⋊C₄×C₆₁	—	2	1	no	—
251	C₄⋊C₄×C₆₁	—	2	2	no	—
252	C₄⋊C₄×C₆₁	—	2	4	no	—
253	C₄⋊C₄×C₆₁	—	2	4	no	—
254	C₄⋊C₄×C₆₁	—	2	2	no	—
255	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
256	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
257	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
258	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
259	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
260	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
261	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
263	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
264	C₂²⋊C₄×C₆₁	—	2	2	no	—
265	C₂²⋊C₄×C₆₁	—	2	2	no	—
266	C₂²⋊C₄×C₆₁	—	2	2	no	—
267	C₂²⋊C₄×C₆₁	—	2	4	no	—
268	C₂²⋊C₄×C₆₁	—	2	4	no	—
269	C₂²⋊C₄×C₆₁	—	2	4	no	—
270	C₂²⋊C₄×C₆₁	—	2	2	no	—
271	C₂²⋊C₄×C₆₁	—	2	4	no	—
272	C₂²⋊C₄×C₆₁	—	2	2	no	—
273	C₂²⋊C₄×C₆₁	—	2	2	no	—
274	C₂²⋊C₄×C₆₁	—	2	4	no	—
275	C₂²⋊C₄×C₆₁	—	2	2	no	—
276	C₂²⋊C₄×C₆₁	—	2	4	no	—
277	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
278	C₄²×C₆₁	—	2	4	no	—
279	C₄²×C₆₁	—	2	2	no	—
280	C₄²×C₆₁	—	2	4	no	—
281	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
282	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
284	C₄²×C₆₁	C₂⁴	1	4	yes	—
285	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
286	C₂³×C₆₁	—	2	2	no	—
287	C₂³×C₆₁	—	2	2	no	—
288	C₂³×C₆₁	—	2	2	no	—
289	C₂³×C₆₁	—	4	2	no	—
290	C₂³×C₆₁	—	8	1	no	—
291	C₂³×C₆₁	—	8	1	no	—
292	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
293	Q₈×C₆₁	—	2	4	no	—
294	Q₈×C₆₁	—	2	4	no	—
295	Q₈×C₆₁	—	2	4	no	—
296	Q₈×C₆₁	—	4	2	no	—
297	Q₈×C₆₁	—	4	2	no	—
298	Q₈×C₆₁	—	8	4	no	—
299	Q₈×C₆₁	—	8	1	no	—
300	D₄×C₆₁	—	2	2	no	—
301	D₄×C₆₁	—	2	2	no	—
302	D₄×C₆₁	—	2	2	no	—
303	D₄×C₆₁	—	2	4	no	—
304	D₄×C₆₁	—	2	2	no	—
305	D₄×C₆₁	—	4	2	no	—
306	D₄×C₆₁	—	4	2	no	—
307	D₄×C₆₁	—	4	4	no	—
308	D₄×C₆₁	—	4	2	no	—
309	D₄×C₆₁	—	8	1	no	—
310	D₄×C₆₁	—	8	4	no	—
311	D₄×C₆₁	—	8	1	no	—
312	D₄×C₆₁	—	8	4	no	—
313	D₄×C₆₁	—	8	2	no	—
314	C₂×C₄×C₆₁	—	2	2	no	—
315	C₂×C₄×C₆₁	—	2	2	no	—
316	C₂×C₄×C₆₁	—	2	2	no	—
317	C₂×C₄×C₆₁	—	2	2	no	—
318	C₂×C₄×C₆₁	—	2	2	no	—
319	C₂×C₄×C₆₁	—	2	2	no	—
320	C₂×C₄×C₆₁	—	2	2	no	—
321	C₂×C₄×C₆₁	—	4	1	no	—
322	C₂×C₄×C₆₁	—	4	4	no	—
323	C₂×C₄×C₆₁	—	4	4	no	—
324	C₂×C₄×C₆₁	—	4	4	no	—
325	C₂×C₄×C₆₁	—	8	2	no	—
326	C₂×C₄×C₆₁	—	8	4	no	—
327	C₂×C₄×C₆₁	—	8	4	no	—
328	C₂×C₄×C₆₁	—	8	1	no	—
329	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
331	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
335	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
337	C₈×C₆₁	—	2	2	no	—
338	C₈×C₆₁	—	2	4	no	—
339	C₈×C₆₁	—	2	2	no	—
340	#61912	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
341	C₂²×C₆₁	—	2	1	no	—
342	C₂²×C₆₁	—	2	1	no	—
343	C₂²×C₆₁	—	2	1	no	—
344	C₂²×C₆₁	—	4	2	no	—
345	C₂²×C₆₁	—	4	2	no	—
346	C₂²×C₆₁	—	4	2	no	—
347	C₂²×C₆₁	—	4	2	no	—
348	C₂²×C₆₁	—	4	2	no	—
349	C₂²×C₆₁	—	4	2	no	—
350	C₂²×C₆₁	—	4	2	no	—
351	C₂²×C₆₁	—	4	2	no	—
352	C₂²×C₆₁	—	4	2	no	—
353	C₂²×C₆₁	—	8	4	no	—
354	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
355	C₄×C₆₁	—	2	1	no	—
356	C₄×C₆₁	—	2	1	no	—
357	C₄×C₆₁	—	2	4	no	—
358	C₄×C₆₁	—	2	1	no	—
359	C₄×C₆₁	—	2	1	no	—
360	C₄×C₆₁	—	2	4	no	—
361	C₄×C₆₁	—	4	2	no	—
362	C₄×C₆₁	—	4	2	no	—
363	C₄×C₆₁	—	4	2	no	—
364	C₄×C₆₁	—	4	2	no	—
365	C₄×C₆₁	—	4	2	no	—
366	C₄×C₆₁	#576	1	2	yes	—
367	C₄×C₆₁	#585	1	2	yes	—
368	#3550	C₂×C₆₁	1	1	yes	characteristic, complemented
369	#3506	C₂×C₆₁	1	1	yes	characteristic, complemented
370	#3403	C₂×C₆₁	1	4	yes	complemented
371	#3397	C₂×C₆₁	1	2	yes	complemented
372	#3393	C₂×C₆₁	1	2	yes	complemented
373	#3375	C₂×C₆₁	1	4	yes	complemented
374	#3367	C₂×C₆₁	1	2	yes	complemented
375	#3358	C₂×C₆₁	1	2	yes	complemented
376	#3224	C₂×C₆₁	1	4	yes	complemented
377	#3214	C₂×C₆₁	1	1	yes	characteristic, complemented
378	#3210	C₂×C₆₁	1	1	yes	characteristic, complemented
379	#3124	C₂×C₆₁	1	4	yes	complemented
380	#3110	C₂×C₆₁	1	1	yes	characteristic, complemented
381	#3100	C₂×C₆₁	1	1	yes	characteristic, complemented
382	#2985	C₂×C₆₁	1	1	yes	characteristic, complemented
383	C₂×C₆₁	—	4	1	no	—
384	C₂×C₆₁	—	8	2	no	—
385	C₂×C₆₁	—	8	2	no	—
386	C₂×C₆₁	—	8	2	no	—
387	C₂×C₆₁	#3487	1	1	yes	characteristic
388	C₂×C₆₁	C₂×#576	1	1	yes	characteristic
389	C₂×C₆₁	#3586	1	1	yes	characteristic
390	#563	—	2	2	no	—
391	#559	C₂²×C₆₁	1	4	yes	—
392	#559	C₂²×C₆₁	1	2	yes	complemented
393	Q₈²	C₂²×C₆₁	1	2	yes	complemented
394	#556	—	2	1	no	—
395	#556	C₂²×C₆₁	1	2	yes	—
396	#556	C₂²×C₆₁	1	2	yes	complemented
397	#555	—	2	1	no	—
398	#553	—	2	2	no	—
399	#550	C₂²×C₆₁	1	2	yes	—
400	D₄×Q₈	—	2	1	no	—
401	D₄×Q₈	C₂²×C₆₁	1	2	yes	complemented
402	#547	—	2	1	no	—
403	#542	—	2	2	no	—
404	#542	C₂²×C₆₁	1	4	yes	—
405	#538	—	2	2	no	—
406	#536	—	2	2	no	—
407	#535	C₂²×C₆₁	1	2	yes	—
408	#533	C₂²×C₆₁	1	1	yes	characteristic
409	#533	C₂²×C₆₁	1	1	yes	characteristic
410	#532	C₂²×C₆₁	1	1	yes	characteristic
411	#532	C₂²×C₆₁	1	1	yes	characteristic
412	#525	—	2	2	no	—
413	#520	C₂²×C₆₁	1	2	yes	—
414	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
415	#496	C₂²×C₆₁	1	4	yes	—
416	#496	C₂²×C₆₁	1	2	yes	complemented
417	#495	C₂²×C₆₁	1	4	yes	—
418	#494	C₂²×C₆₁	1	1	yes	characteristic, complemented
419	#492	C₂²×C₆₁	1	1	yes	characteristic, complemented
420	#489	C₂²×C₆₁	1	4	yes	—
421	#489	C₂²×C₆₁	1	2	yes	complemented
422	#487	C₂²×C₆₁	1	1	yes	characteristic, complemented
423	#486	C₂²×C₆₁	1	4	yes	—
424	#486	C₂²×C₆₁	1	1	yes	characteristic, complemented
425	#484	C₂²×C₆₁	1	2	yes	—
426	#480	C₂²×C₆₁	1	2	yes	—
427	#477	C₂²×C₆₁	1	4	yes	complemented
428	#474	C₂²×C₆₁	1	2	yes	—
429	#474	C₂²×C₆₁	1	2	yes	—
430	#474	C₂²×C₆₁	1	4	yes	complemented
431	#464	C₂²×C₆₁	1	4	yes	—
432	#464	C₂²×C₆₁	1	4	yes	complemented
433	#464	C₂²×C₆₁	1	4	yes	complemented
434	#463	C₂²×C₆₁	1	4	yes	—
435	#463	C₂²×C₆₁	1	4	yes	complemented
436	#461	C₂²×C₆₁	1	2	yes	—
437	#461	C₂²×C₆₁	1	2	yes	complemented
438	#460	C₂²×C₆₁	1	4	yes	—
439	#459	C₂²×C₆₁	1	2	yes	—
440	#459	C₂²×C₆₁	1	4	yes	—
441	#459	C₂²×C₆₁	1	2	yes	complemented
442	#452	C₂²×C₆₁	1	4	yes	—
443	#450	C₂²×C₆₁	1	2	yes	—
444	#449	C₂²×C₆₁	1	4	yes	—
445	#447	C₂²×C₆₁	1	2	yes	—
446	#446	C₂²×C₆₁	1	2	yes	complemented
447	#446	C₂²×C₆₁	1	4	yes	complemented
448	C₈×Q₈	C₂²×C₆₁	1	2	yes	complemented
449	#440	C₂²×C₆₁	1	4	yes	—
450	#440	C₂²×C₆₁	1	4	yes	complemented
451	#440	C₂²×C₆₁	1	4	yes	complemented
452	C₄×Q₁₆	C₂²×C₆₁	1	4	yes	complemented
453	C₄×D₈	C₂²×C₆₁	1	2	yes	—
454	C₄×D₈	C₂²×C₆₁	1	2	yes	—
455	C₄×D₈	C₂²×C₆₁	1	4	yes	complemented
456	#433	C₂²×C₆₁	1	4	yes	—
457	#432	C₂²×C₆₁	1	1	yes	characteristic
458	#431	C₂²×C₆₁	1	1	yes	characteristic
459	C₆₁	#61912	1	1	yes	characteristic, direct product factor, Sylow
460	C₂×#41	—	2	2	no	—
461	C₂×#41	—	2	1	no	—
462	C₂×#41	C₂³×C₆₁	1	2	yes	—
463	C₂²×Q₈	—	2	2	no	—
464	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
465	C₂³×C₄	—	2	1	no	—
466	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
467	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
468	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
469	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
470	C₂×D₈	C₂³×C₆₁	1	2	yes	—
471	C₂×D₈	C₂³×C₆₁	1	2	yes	—
472	C₂×D₈	C₂³×C₆₁	1	4	yes	—
473	C₄⋊Q₈	—	2	4	no	—
474	C₄⋊Q₈	—	2	2	no	—
475	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
476	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
477	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
478	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
479	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
480	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
481	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
482	#127	C₂³×C₆₁	1	1	yes	characteristic
483	#127	C₂³×C₆₁	1	1	yes	characteristic
484	#127	C₂³×C₆₁	1	4	yes	—
485	#126	—	2	4	no	—
486	#126	—	2	4	no	—
487	#126	—	2	4	no	—
488	#125	—	2	1	no	—
489	#125	D₄×C₆₁	1	2	yes	—
490	#124	—	2	4	no	—
491	#124	—	2	2	no	—
492	#124	—	2	4	no	—
493	#124	—	2	1	no	—
494	#124	C₂³×C₆₁	1	2	yes	—
495	#124	C₂³×C₆₁	1	4	yes	—
496	#124	C₂³×C₆₁	1	4	yes	—
497	#123	—	2	4	no	—
498	#123	—	2	4	no	—
499	#123	—	2	4	no	—
500	#123	—	2	4	no	—
501	C₂²⋊Q₈	—	2	2	no	—
502	C₂²⋊Q₈	—	2	2	no	—
503	C₂²⋊Q₈	—	2	1	no	—
504	C₂²⋊Q₈	—	2	2	no	—
505	C₂²⋊Q₈	—	2	4	no	—
506	C₂²⋊Q₈	—	2	4	no	—
507	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
508	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
509	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
510	#121	—	2	1	no	—
511	#121	—	2	1	no	—
512	#121	—	2	1	no	—
513	#121	—	2	2	no	—
514	#121	—	2	2	no	—
515	#121	—	2	2	no	—
516	#121	—	2	4	no	—
517	#121	C₂³×C₆₁	1	2	yes	—
518	#120	—	2	4	no	—
519	C₄×Q₈	—	2	2	no	—
520	C₄×Q₈	—	2	1	no	—
521	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
522	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
523	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
524	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
525	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
526	C₄×D₄	—	2	4	no	—
527	C₄×D₄	—	2	2	no	—
528	C₄×D₄	—	2	4	no	—
529	C₄×D₄	—	2	1	no	—
530	C₄×D₄	—	2	1	no	—
531	C₄×D₄	—	2	1	no	—
532	C₄×D₄	—	2	1	no	—
533	C₄×D₄	—	2	1	no	—
534	C₄×D₄	C₂³×C₆₁	1	2	yes	—
535	C₄×D₄	C₂³×C₆₁	1	2	yes	—
536	C₄×D₄	C₂³×C₆₁	1	4	yes	—
537	C₄×D₄	C₂³×C₆₁	1	2	yes	—
538	C₄×D₄	C₂³×C₆₁	1	4	yes	—
539	#117	—	2	1	no	—
540	#117	—	2	2	no	—
541	#117	—	2	2	no	—
542	#117	—	2	2	no	—
543	#117	C₂³×C₆₁	1	2	yes	—
544	C₂×C₄⋊C₄	—	2	2	no	—
545	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
546	C₂×C₂²⋊C₄	—	2	1	no	—
547	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
548	#107	C₂³×C₆₁	1	2	yes	—
549	#107	C₂³×C₆₁	1	2	yes	—
550	#107	C₂³×C₆₁	1	4	yes	—
551	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
552	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
553	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
554	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
555	#103	C₂³×C₆₁	1	4	yes	—
556	#103	C₂³×C₆₁	1	4	yes	—
557	#103	C₂³×C₆₁	1	4	yes	—
558	#102	C₂³×C₆₁	1	2	yes	—
559	#102	C₂³×C₆₁	1	2	yes	—
560	#102	C₂³×C₆₁	1	2	yes	—
561	#102	C₂³×C₆₁	1	2	yes	—
562	#102	C₂³×C₆₁	1	4	yes	—
563	#102	C₂³×C₆₁	1	4	yes	—
564	#102	C₂³×C₆₁	1	4	yes	—
565	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
566	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
567	#97	C₂³×C₆₁	1	2	yes	—
568	#97	C₂³×C₆₁	1	4	yes	—
569	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
570	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
571	C₄×C₈	C₂³×C₆₁	1	4	yes	—
572	C₂⁴	—	2	1	no	—
573	#41	—	4	4	no	—
574	#41	—	8	2	no	—
575	#41	—	8	4	no	—
576	C₂×Q₈	—	2	1	no	—
577	C₂×Q₈	—	2	4	no	—
578	C₂×Q₈	—	2	1	no	—
579	C₂×Q₈	—	8	4	no	—
580	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
581	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
582	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
583	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	2	1	no	—
587	C₂×D₄	—	2	1	no	—
588	C₂×D₄	—	2	1	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	1	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	4	2	no	—
594	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
595	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
596	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	4	no	—
604	C₂²×C₄	—	8	2	no	—
605	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
606	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
608	Q₁₆	—	4	4	no	—
609	SD₁₆	—	4	4	no	—
610	SD₁₆	—	4	4	no	—
611	SD₁₆	—	4	4	no	—
612	D₈	—	4	4	no	—
613	D₈	—	4	2	no	—
614	D₈	—	4	2	no	—
615	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
616	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
617	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	2	no	—
630	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
631	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
632	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
633	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
634	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
635	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
636	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
637	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
638	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	—	2	2	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	2	no	—
648	C₂²⋊C₄	—	2	2	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	2	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
653	C₄²	—	2	4	no	—
654	C₄²	—	2	2	no	—
655	C₄²	—	2	4	no	—
656	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
657	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
658	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
659	C₄²	C₂⁴×C₆₁	1	4	yes	—
660	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
661	C₂³	—	2	2	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	4	2	no	—
665	C₂³	—	8	1	no	—
666	C₂³	—	8	1	no	—
667	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
668	Q₈	—	2	4	no	—
669	Q₈	—	2	4	no	—
670	Q₈	—	2	4	no	—
671	Q₈	—	4	2	no	—
672	Q₈	—	4	2	no	—
673	Q₈	—	8	4	no	—
674	Q₈	—	8	1	no	—
675	D₄	—	2	2	no	—
676	D₄	—	2	2	no	—
677	D₄	—	2	2	no	—
678	D₄	—	2	4	no	—
679	D₄	—	2	2	no	—
680	D₄	—	4	2	no	—
681	D₄	—	4	2	no	—
682	D₄	—	4	4	no	—
683	D₄	—	4	2	no	—
684	D₄	—	8	1	no	—
685	D₄	—	8	4	no	—
686	D₄	—	8	1	no	—
687	D₄	—	8	4	no	—
688	D₄	—	8	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	4	no	—
698	C₂×C₄	—	4	4	no	—
699	C₂×C₄	—	4	4	no	—
700	C₂×C₄	—	8	2	no	—
701	C₂×C₄	—	8	4	no	—
702	C₂×C₄	—	8	4	no	—
703	C₂×C₄	—	8	1	no	—
704	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
705	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
706	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
707	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
708	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
709	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
710	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
711	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
712	C₈	—	2	2	no	—
713	C₈	—	2	4	no	—
714	C₈	—	2	2	no	—
715	C₂²	—	2	1	no	—
716	C₂²	—	2	1	no	—
717	C₂²	—	2	1	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	8	4	no	—
728	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
729	C₄	—	2	1	no	—
730	C₄	—	2	4	no	—
731	C₄	—	2	1	no	—
732	C₄	—	2	1	no	—
733	C₄	—	2	4	no	—
734	C₄	—	2	1	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	2	no	—
738	C₄	—	4	2	no	—
739	C₄	—	4	2	no	—
740	C₄	C₆₁×#576	1	2	yes	—
741	C₄	C₆₁×#585	1	2	yes	—
742	C₂	—	4	1	no	—
743	C₂	—	8	2	no	—
744	C₂	—	8	2	no	—
745	C₂	—	8	2	no	—
746	C₂	C₆₁×#3487	1	1	yes	characteristic
747	C₂	C₂×C₆₁×#576	1	1	yes	characteristic
748	C₂	C₆₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₆₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3550	C₂	semidirect
2. C₆₁×#3506	C₂	semidirect
3. C₆₁×#3403	C₂	semidirect
4. C₆₁×#3397	C₂	semidirect
5. C₆₁×#3393	C₂	semidirect
6. C₆₁×#3375	C₂	semidirect
7. C₆₁×#3367	C₂	semidirect
8. C₆₁×#3358	C₂	semidirect
9. C₆₁×#3224	C₂	semidirect
10. C₆₁×#3214	C₂	semidirect
11. C₆₁×#3210	C₂	semidirect
12. C₆₁×#3124	C₂	semidirect
13. C₆₁×#3110	C₂	semidirect
14. C₆₁×#3100	C₂	semidirect
15. C₆₁×#2985	C₂	semidirect
18. C₆₁×#559	C₂²	semidirect
19. Q₈²×C₆₁	C₂²	semidirect
22. C₆₁×#556	C₂²	semidirect
27. D₄×Q₈×C₆₁	C₂²	semidirect
42. C₆₁×#496	C₂²	semidirect
44. C₆₁×#494	C₂²	semidirect
45. C₆₁×#492	C₂²	semidirect
47. C₆₁×#489	C₂²	semidirect
48. C₆₁×#487	C₂²	semidirect
50. C₆₁×#486	C₂²	semidirect
53. C₆₁×#477	C₂²	semidirect
56. C₆₁×#474	C₂²	semidirect
58. C₆₁×#464	C₂²	semidirect
59. C₆₁×#464	C₂²	semidirect
61. C₆₁×#463	C₂²	semidirect
63. C₆₁×#461	C₂²	semidirect
67. C₆₁×#459	C₂²	semidirect
72. C₆₁×#446	C₂²	semidirect
73. C₆₁×#446	C₂²	semidirect
74. C₈×Q₈×C₆₁	C₂²	semidirect
76. C₆₁×#440	C₂²	semidirect
77. C₆₁×#440	C₂²	semidirect
78. C₄×Q₁₆×C₆₁	C₂²	semidirect
81. C₄×D₈×C₆₁	C₂²	semidirect
340. #61912	C₆₁	direct (N × H)
368. #3550	C₂×C₆₁	semidirect
369. #3506	C₂×C₆₁	semidirect
370. #3403	C₂×C₆₁	semidirect
371. #3397	C₂×C₆₁	semidirect
372. #3393	C₂×C₆₁	semidirect
373. #3375	C₂×C₆₁	semidirect
374. #3367	C₂×C₆₁	semidirect
375. #3358	C₂×C₆₁	semidirect
376. #3224	C₂×C₆₁	semidirect
377. #3214	C₂×C₆₁	semidirect
378. #3210	C₂×C₆₁	semidirect
379. #3124	C₂×C₆₁	semidirect
380. #3110	C₂×C₆₁	semidirect
381. #3100	C₂×C₆₁	semidirect
382. #2985	C₂×C₆₁	semidirect
392. #559	C₂²×C₆₁	semidirect
393. Q₈²	C₂²×C₆₁	semidirect
396. #556	C₂²×C₆₁	semidirect
401. D₄×Q₈	C₂²×C₆₁	semidirect
416. #496	C₂²×C₆₁	semidirect
418. #494	C₂²×C₆₁	semidirect
419. #492	C₂²×C₆₁	semidirect
421. #489	C₂²×C₆₁	semidirect
422. #487	C₂²×C₆₁	semidirect
424. #486	C₂²×C₆₁	semidirect
427. #477	C₂²×C₆₁	semidirect
430. #474	C₂²×C₆₁	semidirect
432. #464	C₂²×C₆₁	semidirect
433. #464	C₂²×C₆₁	semidirect
435. #463	C₂²×C₆₁	semidirect
437. #461	C₂²×C₆₁	semidirect
441. #459	C₂²×C₆₁	semidirect
446. #446	C₂²×C₆₁	semidirect
447. #446	C₂²×C₆₁	semidirect
448. C₈×Q₈	C₂²×C₆₁	semidirect
450. #440	C₂²×C₆₁	semidirect
451. #440	C₂²×C₆₁	semidirect
452. C₄×Q₁₆	C₂²×C₆₁	semidirect
455. C₄×D₈	C₂²×C₆₁	semidirect
459. C₆₁	#61912	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×#3550	2
C₆₁×#3506	2
C₆₁×#3403	2
C₆₁×#3397	2
C₆₁×#3393	2
C₆₁×#3375	2
C₆₁×#3367	2
C₆₁×#3358	2
C₆₁×#3224	2
C₆₁×#3214	2
C₆₁×#3210	2
C₆₁×#3124	2
C₆₁×#3110	2
C₆₁×#3100	2
C₆₁×#2985	2
#61912	61

Subgroups — C61×#61912 #29565345

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61912 #29565345