Subgroups — C₆₁×#62043 #29565476

Order 15616.

1766 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3554	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#3523	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3395	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3365	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3328	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3327	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3315	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3304	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×Q₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3278	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3276	C₂	1	2	yes	maximal, complemented
14	C₆₁×#3270	C₂	1	2	yes	maximal, complemented
15	C₆₁×#3258	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3255	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3223	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#3121	C₂	1	2	yes	maximal, complemented
20	C₆₁×#3104	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#3044	C₂	1	2	yes	maximal, complemented
22	C₆₁×#3037	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₁×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₆₁	C₂²	1	2	yes	—
25	C₂×#137×C₆₁	C₂²	1	2	yes	—
26	C₂²×Q₁₆×C₆₁	C₂²	1	2	yes	—
27	C₆₁×#562	—	2	2	no	—
28	C₆₁×#559	—	2	1	no	—
29	C₆₁×#559	C₂²	1	1	yes	characteristic
30	C₆₁×#557	—	2	1	no	—
31	C₆₁×#557	C₂²	1	1	yes	characteristic
32	C₆₁×#557	C₂²	1	1	yes	characteristic
33	C₆₁×#557	C₂²	1	1	yes	characteristic
34	C₆₁×#556	—	2	1	no	—
35	C₆₁×#556	C₂²	1	1	yes	characteristic
36	C₆₁×#554	—	2	1	no	—
37	C₆₁×#552	—	2	2	no	—
38	C₆₁×#552	C₂²	1	2	yes	—
39	C₆₁×#550	C₂²	1	1	yes	characteristic
40	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
41	D₄×Q₈×C₆₁	C₂²	1	2	yes	—
42	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
43	C₆₁×#548	C₂²	1	2	yes	—
44	C₆₁×#547	C₂²	1	2	yes	—
45	C₆₁×#542	—	2	1	no	—
46	C₆₁×#542	C₂²	1	2	yes	—
47	C₆₁×#541	—	2	2	no	—
48	C₆₁×#541	C₂²	1	2	yes	—
49	C₆₁×#540	—	2	1	no	—
50	C₆₁×#539	—	2	2	no	—
51	C₆₁×#536	C₂²	1	2	yes	—
52	C₆₁×#533	—	2	1	no	—
53	C₆₁×#533	C₂²	1	1	yes	characteristic
54	C₆₁×#533	C₂²	1	1	yes	characteristic
55	C₆₁×#532	C₂²	1	1	yes	characteristic
56	C₆₁×#529	—	2	1	no	—
57	C₆₁×#529	C₂²	1	1	yes	characteristic
58	C₆₁×#519	C₂²	1	2	yes	—
59	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
60	C₆₁×#497	C₂²	1	2	yes	—
61	C₆₁×#494	C₂²	1	1	yes	characteristic
62	C₆₁×#494	C₂²	1	2	yes	—
63	C₆₁×#492	C₂²	1	1	yes	characteristic
64	C₆₁×#491	C₂²	1	2	yes	—
65	C₆₁×#488	C₂²	1	2	yes	—
66	C₆₁×#487	C₂²	1	1	yes	characteristic
67	C₆₁×#486	C₂²	1	1	yes	characteristic
68	C₆₁×#485	C₂²	1	2	yes	—
69	C₆₁×#484	C₂²	1	1	yes	characteristic
70	C₆₁×#484	C₂²	1	1	yes	characteristic
71	C₆₁×#482	C₂²	1	2	yes	—
72	C₆₁×#479	C₂²	1	2	yes	—
73	C₆₁×#478	C₂²	1	2	yes	—
74	C₆₁×#477	C₂²	1	1	yes	characteristic
75	C₆₁×#477	C₂²	1	1	yes	characteristic
76	C₆₁×#475	C₂²	1	1	yes	characteristic
77	C₆₁×#475	C₂²	1	1	yes	characteristic
78	C₆₁×#475	C₂²	1	2	yes	—
79	C₆₁×#470	C₂²	1	2	yes	—
80	C₆₁×#470	C₂²	1	2	yes	—
81	C₆₁×#470	C₂²	1	2	yes	—
82	C₆₁×#468	C₂²	1	2	yes	—
83	C₆₁×#467	C₂²	1	2	yes	—
84	C₆₁×#465	C₂²	1	2	yes	—
85	C₆₁×#464	C₂²	1	2	yes	—
86	C₆₁×#464	C₂²	1	2	yes	—
87	C₆₁×#464	C₂²	1	2	yes	—
88	C₆₁×#464	C₂²	1	2	yes	—
89	C₆₁×#464	C₂²	1	2	yes	—
90	C₆₁×#464	C₂²	1	2	yes	—
91	C₆₁×#462	C₂²	1	1	yes	characteristic
92	C₆₁×#462	C₂²	1	1	yes	characteristic
93	C₆₁×#462	C₂²	1	1	yes	characteristic
94	C₆₁×#462	C₂²	1	2	yes	—
95	C₆₁×#462	C₂²	1	2	yes	—
96	C₆₁×#462	C₂²	1	2	yes	—
97	C₆₁×#462	C₂²	1	1	yes	characteristic
98	C₆₁×#462	C₂²	1	1	yes	characteristic
99	C₆₁×#462	C₂²	1	2	yes	—
100	C₆₁×#462	C₂²	1	1	yes	characteristic
101	C₆₁×#461	C₂²	1	2	yes	—
102	C₆₁×#460	C₂²	1	1	yes	characteristic
103	C₆₁×#460	C₂²	1	1	yes	characteristic
104	C₆₁×#452	C₂²	1	2	yes	—
105	C₆₁×#452	C₂²	1	2	yes	—
106	C₆₁×#452	C₂²	1	2	yes	—
107	C₆₁×#452	C₂²	1	2	yes	—
108	C₆₁×#451	C₂²	1	2	yes	—
109	C₆₁×#451	C₂²	1	2	yes	—
110	C₆₁×#451	C₂²	1	1	yes	characteristic
111	C₆₁×#451	C₂²	1	1	yes	characteristic
112	C₆₁×#451	C₂²	1	2	yes	—
113	C₆₁×#448	C₂²	1	2	yes	—
114	C₆₁×#446	C₂²	1	1	yes	characteristic
115	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic
116	C₆₁×#441	C₂²	1	2	yes	—
117	C₆₁×#440	C₂²	1	2	yes	—
118	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
119	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
120	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
121	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
122	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
123	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
124	C₆₁×#436	C₂²	1	2	yes	—
125	C₆₁×#436	C₂²	1	1	yes	characteristic
126	C₆₁×#435	C₂²	1	2	yes	—
127	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
128	C₆₁×#433	C₂²	1	2	yes	—
129	C₆₁×#431	C₂²	1	1	yes	characteristic
130	C₆₁×#424	C₂²	1	2	yes	—
131	C₆₁×#423	C₂²	1	1	yes	characteristic
132	C₆₁×#419	C₂²	1	2	yes	—
133	C₆₁×#417	C₂²	1	2	yes	—
134	C₆₁×#416	C₂²	1	2	yes	—
135	C₂×#41×C₆₁	C₂³	1	2	yes	—
136	C₂×#41×C₆₁	C₂³	1	2	yes	—
137	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
138	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
139	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
140	#137×C₆₁	—	4	4	no	—
141	#137×C₆₁	—	4	4	no	—
142	C₂×Q₁₆×C₆₁	—	4	4	no	—
143	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
144	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
145	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
146	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
149	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
150	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
151	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
152	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
153	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
157	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
158	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
159	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
160	C₄⋊Q₈×C₆₁	—	2	1	no	—
161	C₄⋊Q₈×C₆₁	—	2	1	no	—
162	C₄⋊Q₈×C₆₁	—	2	2	no	—
163	C₄⋊Q₈×C₆₁	—	2	1	no	—
164	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
166	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
167	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
168	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
169	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
170	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
171	#127×C₆₁	—	2	1	no	—
172	#127×C₆₁	C₂³	1	1	yes	characteristic
173	#126×C₆₁	—	2	2	no	—
174	#126×C₆₁	—	2	2	no	—
175	#126×C₆₁	—	2	2	no	—
176	#126×C₆₁	—	2	2	no	—
177	#126×C₆₁	—	2	2	no	—
178	#126×C₆₁	D₄	1	2	yes	—
179	#125×C₆₁	—	2	2	no	—
180	#125×C₆₁	—	2	2	no	—
181	#125×C₆₁	—	2	1	no	—
182	#125×C₆₁	—	2	2	no	—
183	#125×C₆₁	—	2	2	no	—
184	#125×C₆₁	—	2	2	no	—
185	#125×C₆₁	—	2	2	no	—
186	#125×C₆₁	—	2	1	no	—
187	#125×C₆₁	—	2	1	no	—
188	#125×C₆₁	—	2	1	no	—
189	#125×C₆₁	D₄	1	1	yes	characteristic
190	#125×C₆₁	C₂³	1	2	yes	—
191	#124×C₆₁	—	2	1	no	—
192	#124×C₆₁	—	2	1	no	—
193	#124×C₆₁	—	2	2	no	—
194	#124×C₆₁	—	2	2	no	—
195	#124×C₆₁	D₄	1	1	yes	characteristic
196	#124×C₆₁	C₂³	1	2	yes	—
197	#124×C₆₁	C₂³	1	2	yes	—
198	#123×C₆₁	—	2	2	no	—
199	#123×C₆₁	—	2	2	no	—
200	#123×C₆₁	—	2	2	no	—
201	#123×C₆₁	—	2	2	no	—
202	#123×C₆₁	—	2	2	no	—
203	#123×C₆₁	—	2	2	no	—
204	#123×C₆₁	—	2	2	no	—
205	#123×C₆₁	D₄	1	2	yes	—
206	C₂²⋊Q₈×C₆₁	—	2	1	no	—
207	C₂²⋊Q₈×C₆₁	—	2	1	no	—
208	C₂²⋊Q₈×C₆₁	—	2	2	no	—
209	C₂²⋊Q₈×C₆₁	—	2	2	no	—
210	C₂²⋊Q₈×C₆₁	—	2	2	no	—
211	C₂²⋊Q₈×C₆₁	—	2	2	no	—
212	C₂²⋊Q₈×C₆₁	—	2	2	no	—
213	C₂²⋊Q₈×C₆₁	—	2	2	no	—
214	C₂²⋊Q₈×C₆₁	—	2	2	no	—
215	C₂²⋊Q₈×C₆₁	—	2	2	no	—
216	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
217	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
218	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
219	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
220	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
221	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
222	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
223	#121×C₆₁	—	2	2	no	—
224	#121×C₆₁	—	2	2	no	—
225	#121×C₆₁	—	2	1	no	—
226	#121×C₆₁	—	2	1	no	—
227	#121×C₆₁	—	2	2	no	—
228	#121×C₆₁	D₄	1	1	yes	characteristic
229	#121×C₆₁	C₂³	1	2	yes	—
230	C₄×Q₈×C₆₁	—	2	1	no	—
231	C₄×Q₈×C₆₁	—	2	1	no	—
232	C₄×Q₈×C₆₁	—	2	2	no	—
233	C₄×Q₈×C₆₁	—	2	1	no	—
234	C₄×Q₈×C₆₁	—	2	2	no	—
235	C₄×Q₈×C₆₁	—	2	1	no	—
236	C₄×Q₈×C₆₁	—	2	1	no	—
237	C₄×Q₈×C₆₁	—	2	1	no	—
238	C₄×Q₈×C₆₁	—	2	1	no	—
239	C₄×Q₈×C₆₁	—	2	1	no	—
240	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
241	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
242	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
243	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
244	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
245	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
246	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
247	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
248	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
249	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
250	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₆₁	—	2	1	no	—
252	C₄×D₄×C₆₁	—	2	2	no	—
253	C₄×D₄×C₆₁	—	2	1	no	—
254	C₄×D₄×C₆₁	—	2	1	no	—
255	C₄×D₄×C₆₁	—	2	1	no	—
256	C₄×D₄×C₆₁	—	2	2	no	—
257	C₄×D₄×C₆₁	—	2	1	no	—
258	C₄×D₄×C₆₁	—	2	1	no	—
259	C₄×D₄×C₆₁	C₂³	1	2	yes	—
260	C₄×D₄×C₆₁	C₂³	1	2	yes	—
261	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
262	#117×C₆₁	—	2	1	no	—
263	#117×C₆₁	—	2	1	no	—
264	#117×C₆₁	—	2	2	no	—
265	#117×C₆₁	—	2	2	no	—
266	#117×C₆₁	—	2	2	no	—
267	#117×C₆₁	C₂³	1	2	yes	—
268	#117×C₆₁	C₂³	1	2	yes	—
269	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
270	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
271	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
272	C₂×C₄²×C₆₁	—	2	1	no	—
273	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
274	#107×C₆₁	C₂³	1	1	yes	characteristic
275	#107×C₆₁	C₂³	1	1	yes	characteristic
276	#107×C₆₁	C₂³	1	1	yes	characteristic
277	#107×C₆₁	C₂³	1	1	yes	characteristic
278	#106×C₆₁	C₂³	1	2	yes	—
279	#106×C₆₁	C₂³	1	2	yes	—
280	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
281	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
285	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
286	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
287	#103×C₆₁	C₂³	1	1	yes	characteristic
288	#103×C₆₁	C₂³	1	2	yes	—
289	#103×C₆₁	C₂³	1	2	yes	—
290	#103×C₆₁	C₂³	1	2	yes	—
291	#103×C₆₁	C₂³	1	1	yes	characteristic
292	#103×C₆₁	C₂³	1	2	yes	—
293	#103×C₆₁	C₂³	1	2	yes	—
294	#103×C₆₁	C₂³	1	1	yes	characteristic
295	#103×C₆₁	C₂³	1	1	yes	characteristic
296	#103×C₆₁	C₂³	1	2	yes	—
297	#103×C₆₁	C₂³	1	1	yes	characteristic
298	#103×C₆₁	C₂³	1	1	yes	characteristic
299	#103×C₆₁	C₂³	1	1	yes	characteristic
300	#103×C₆₁	C₂³	1	1	yes	characteristic
301	#103×C₆₁	C₂³	1	2	yes	—
302	#103×C₆₁	C₂³	1	2	yes	—
303	#102×C₆₁	C₂³	1	2	yes	—
304	#102×C₆₁	C₂³	1	2	yes	—
305	#102×C₆₁	C₂³	1	2	yes	—
306	#102×C₆₁	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
311	#97×C₆₁	C₂³	1	2	yes	—
312	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₆₁	C₂³	1	2	yes	—
315	#41×C₆₁	—	4	2	no	—
316	#41×C₆₁	—	4	2	no	—
317	#41×C₆₁	—	4	2	no	—
318	#41×C₆₁	—	4	2	no	—
319	C₂×Q₈×C₆₁	—	2	1	no	—
320	C₂×Q₈×C₆₁	—	2	2	no	—
321	C₂×Q₈×C₆₁	—	2	1	no	—
322	C₂×Q₈×C₆₁	—	2	1	no	—
323	C₂×Q₈×C₆₁	—	2	2	no	—
324	C₂×Q₈×C₆₁	—	2	4	no	—
325	C₂×Q₈×C₆₁	—	2	2	no	—
326	C₂×Q₈×C₆₁	—	4	2	no	—
327	C₂×Q₈×C₆₁	—	4	1	no	—
328	C₂×Q₈×C₆₁	—	4	2	no	—
329	C₂×Q₈×C₆₁	—	4	2	no	—
330	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
332	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
333	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
334	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
335	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
336	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
337	C₂×D₄×C₆₁	—	2	2	no	—
338	C₂×D₄×C₆₁	—	2	2	no	—
339	C₂×D₄×C₆₁	—	2	2	no	—
340	C₂×D₄×C₆₁	—	2	1	no	—
341	C₂×D₄×C₆₁	—	2	1	no	—
342	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
343	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
344	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
345	C₂²×C₄×C₆₁	—	2	1	no	—
346	C₂²×C₄×C₆₁	—	2	1	no	—
347	C₂²×C₄×C₆₁	—	2	2	no	—
348	C₂²×C₄×C₆₁	—	2	2	no	—
349	C₂²×C₄×C₆₁	—	2	2	no	—
350	C₂²×C₄×C₆₁	—	2	2	no	—
351	C₂²×C₄×C₆₁	—	2	2	no	—
352	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
353	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
354	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
356	Q₁₆×C₆₁	—	2	2	no	—
357	Q₁₆×C₆₁	—	2	4	no	—
358	Q₁₆×C₆₁	—	2	2	no	—
359	Q₁₆×C₆₁	—	4	2	no	—
360	Q₁₆×C₆₁	—	4	2	no	—
361	Q₁₆×C₆₁	—	4	1	no	—
362	Q₁₆×C₆₁	—	4	2	no	—
363	Q₁₆×C₆₁	—	4	1	no	—
364	Q₁₆×C₆₁	—	4	2	no	—
365	Q₁₆×C₆₁	—	4	2	no	—
366	SD₁₆×C₆₁	—	2	4	no	—
367	SD₁₆×C₆₁	—	4	2	no	—
368	SD₁₆×C₆₁	—	4	2	no	—
369	SD₁₆×C₆₁	—	4	2	no	—
370	M₁₆×C₆₁	—	4	2	no	—
371	M₁₆×C₆₁	—	4	2	no	—
372	C₂×C₈×C₆₁	—	4	2	no	—
373	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
377	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
378	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
379	C₄⋊C₄×C₆₁	—	2	1	no	—
380	C₄⋊C₄×C₆₁	—	2	1	no	—
381	C₄⋊C₄×C₆₁	—	2	1	no	—
382	C₄⋊C₄×C₆₁	—	2	1	no	—
383	C₄⋊C₄×C₆₁	—	2	1	no	—
384	C₄⋊C₄×C₆₁	—	2	2	no	—
385	C₄⋊C₄×C₆₁	—	2	2	no	—
386	C₄⋊C₄×C₆₁	—	2	1	no	—
387	C₄⋊C₄×C₆₁	—	2	2	no	—
388	C₄⋊C₄×C₆₁	—	2	2	no	—
389	C₄⋊C₄×C₆₁	—	2	2	no	—
390	C₄⋊C₄×C₆₁	—	2	1	no	—
391	C₄⋊C₄×C₆₁	—	2	1	no	—
392	C₄⋊C₄×C₆₁	—	2	2	no	—
393	C₄⋊C₄×C₆₁	—	2	1	no	—
394	C₄⋊C₄×C₆₁	—	2	1	no	—
395	C₄⋊C₄×C₆₁	—	2	2	no	—
396	C₄⋊C₄×C₆₁	—	2	1	no	—
397	C₄⋊C₄×C₆₁	—	2	1	no	—
398	C₄⋊C₄×C₆₁	—	2	1	no	—
399	C₄⋊C₄×C₆₁	—	2	1	no	—
400	C₄⋊C₄×C₆₁	—	2	2	no	—
401	C₄⋊C₄×C₆₁	—	2	1	no	—
402	C₄⋊C₄×C₆₁	—	2	2	no	—
403	C₄⋊C₄×C₆₁	—	2	2	no	—
404	C₄⋊C₄×C₆₁	—	2	2	no	—
405	C₄⋊C₄×C₆₁	—	2	2	no	—
406	C₄⋊C₄×C₆₁	—	2	2	no	—
407	C₄⋊C₄×C₆₁	—	2	1	no	—
408	C₄⋊C₄×C₆₁	—	2	2	no	—
409	C₄⋊C₄×C₆₁	—	2	1	no	—
410	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
412	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
413	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
414	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
415	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
416	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
417	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
421	C₂²⋊C₄×C₆₁	—	2	2	no	—
422	C₂²⋊C₄×C₆₁	—	2	2	no	—
423	C₂²⋊C₄×C₆₁	—	2	1	no	—
424	C₂²⋊C₄×C₆₁	—	2	1	no	—
425	C₂²⋊C₄×C₆₁	—	2	2	no	—
426	C₂²⋊C₄×C₆₁	—	2	2	no	—
427	C₂²⋊C₄×C₆₁	—	2	2	no	—
428	C₂²⋊C₄×C₆₁	—	2	2	no	—
429	C₂²⋊C₄×C₆₁	—	2	2	no	—
430	C₂²⋊C₄×C₆₁	—	2	2	no	—
431	C₂²⋊C₄×C₆₁	—	2	2	no	—
432	C₂²⋊C₄×C₆₁	—	2	2	no	—
433	C₂²⋊C₄×C₆₁	—	2	2	no	—
434	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
439	C₄²×C₆₁	—	2	1	no	—
440	C₄²×C₆₁	—	2	1	no	—
441	C₄²×C₆₁	—	2	1	no	—
442	C₄²×C₆₁	—	2	1	no	—
443	C₄²×C₆₁	—	2	2	no	—
444	C₄²×C₆₁	—	2	2	no	—
445	C₄²×C₆₁	—	2	2	no	—
446	C₄²×C₆₁	—	2	1	no	—
447	C₄²×C₆₁	—	2	1	no	—
448	C₄²×C₆₁	—	2	2	no	—
449	C₄²×C₆₁	—	2	2	no	—
450	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
451	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
452	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
453	C₄²×C₆₁	C₂⁴	1	2	yes	—
454	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
455	C₂³×C₆₁	—	2	2	no	—
456	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
457	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
458	Q₈×C₆₁	—	2	2	no	—
459	Q₈×C₆₁	—	2	1	no	—
460	Q₈×C₆₁	—	2	1	no	—
461	Q₈×C₆₁	—	2	2	no	—
462	Q₈×C₆₁	—	2	1	no	—
463	Q₈×C₆₁	—	2	2	no	—
464	Q₈×C₆₁	—	2	1	no	—
465	Q₈×C₆₁	—	2	2	no	—
466	Q₈×C₆₁	—	2	1	no	—
467	Q₈×C₆₁	—	2	1	no	—
468	Q₈×C₆₁	—	2	2	no	—
469	Q₈×C₆₁	—	2	1	no	—
470	Q₈×C₆₁	—	4	2	no	—
471	Q₈×C₆₁	—	4	4	no	—
472	Q₈×C₆₁	—	4	2	no	—
473	Q₈×C₆₁	—	8	1	no	—
474	Q₈×C₆₁	—	8	2	no	—
475	Q₈×C₆₁	H(5,𝔽₂)	1	2	yes	—
476	D₄×C₆₁	—	2	2	no	—
477	D₄×C₆₁	—	2	2	no	—
478	D₄×C₆₁	—	2	2	no	—
479	D₄×C₆₁	—	4	2	no	—
480	D₄×C₆₁	—	4	2	no	—
481	D₄×C₆₁	—	8	1	no	—
482	D₄×C₆₁	—	8	2	no	—
483	D₄×C₆₁	—	8	2	no	—
484	D₄×C₆₁	—	8	2	no	—
485	C₂×C₄×C₆₁	—	2	1	no	—
486	C₂×C₄×C₆₁	—	2	2	no	—
487	C₂×C₄×C₆₁	—	2	2	no	—
488	C₂×C₄×C₆₁	—	2	1	no	—
489	C₂×C₄×C₆₁	—	2	2	no	—
490	C₂×C₄×C₆₁	—	2	1	no	—
491	C₂×C₄×C₆₁	—	2	1	no	—
492	C₂×C₄×C₆₁	—	2	2	no	—
493	C₂×C₄×C₆₁	—	2	1	no	—
494	C₂×C₄×C₆₁	—	2	1	no	—
495	C₂×C₄×C₆₁	—	2	1	no	—
496	C₂×C₄×C₆₁	—	2	2	no	—
497	C₂×C₄×C₆₁	—	2	1	no	—
498	C₂×C₄×C₆₁	—	2	1	no	—
499	C₂×C₄×C₆₁	—	2	2	no	—
500	C₂×C₄×C₆₁	—	2	1	no	—
501	C₂×C₄×C₆₁	—	4	1	no	—
502	C₂×C₄×C₆₁	—	4	4	no	—
503	C₂×C₄×C₆₁	—	4	2	no	—
504	C₂×C₄×C₆₁	—	4	2	no	—
505	C₂×C₄×C₆₁	—	8	2	no	—
506	C₂×C₄×C₆₁	—	8	2	no	—
507	C₂×C₄×C₆₁	—	8	2	no	—
508	C₂×C₄×C₆₁	—	8	2	no	—
509	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
512	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
513	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
514	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
518	C₈×C₆₁	—	2	1	no	—
519	C₈×C₆₁	—	2	2	no	—
520	C₈×C₆₁	—	2	2	no	—
521	C₈×C₆₁	—	2	1	no	—
522	C₈×C₆₁	—	2	1	no	—
523	C₈×C₆₁	—	2	1	no	—
524	#62043	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
525	C₂²×C₆₁	—	2	1	no	—
526	C₂²×C₆₁	—	2	2	no	—
527	C₂²×C₆₁	—	2	2	no	—
528	C₂²×C₆₁	—	2	1	no	—
529	C₂²×C₆₁	—	2	1	no	—
530	C₂²×C₆₁	—	2	2	no	—
531	C₂²×C₆₁	—	4	2	no	—
532	C₂²×C₆₁	—	4	2	no	—
533	C₂²×C₆₁	—	4	2	no	—
534	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
535	C₄×C₆₁	—	2	1	no	—
536	C₄×C₆₁	—	2	1	no	—
537	C₄×C₆₁	—	2	2	no	—
538	C₄×C₆₁	—	2	1	no	—
539	C₄×C₆₁	—	2	2	no	—
540	C₄×C₆₁	—	2	2	no	—
541	C₄×C₆₁	—	2	1	no	—
542	C₄×C₆₁	—	2	2	no	—
543	C₄×C₆₁	—	4	1	no	—
544	C₄×C₆₁	—	4	1	no	—
545	C₄×C₆₁	—	4	1	no	—
546	C₄×C₆₁	—	4	1	no	—
547	C₄×C₆₁	—	4	1	no	—
548	C₄×C₆₁	—	4	2	no	—
549	C₄×C₆₁	—	4	1	no	—
550	C₄×C₆₁	—	4	2	no	—
551	C₄×C₆₁	—	4	1	no	—
552	C₄×C₆₁	—	4	2	no	—
553	C₄×C₆₁	#578	1	2	yes	—
554	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
555	C₄×C₆₁	#585	1	1	yes	characteristic
556	#3554	C₂×C₆₁	1	1	yes	characteristic
557	#3523	C₂×C₆₁	1	1	yes	characteristic, complemented
558	#3400	C₂×C₆₁	1	1	yes	characteristic, complemented
559	#3395	C₂×C₆₁	1	1	yes	characteristic, complemented
560	#3374	C₂×C₆₁	1	1	yes	characteristic, complemented
561	#3365	C₂×C₆₁	1	1	yes	characteristic, complemented
562	#3328	C₂×C₆₁	1	1	yes	characteristic, complemented
563	#3327	C₂×C₆₁	1	2	yes	complemented
564	#3315	C₂×C₆₁	1	2	yes	complemented
565	#3304	C₂×C₆₁	1	1	yes	characteristic, complemented
566	D₄×Q₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
567	#3278	C₂×C₆₁	1	1	yes	characteristic, complemented
568	#3276	C₂×C₆₁	1	2	yes	complemented
569	#3270	C₂×C₆₁	1	2	yes	complemented
570	#3258	C₂×C₆₁	1	2	yes	complemented
571	#3255	C₂×C₆₁	1	1	yes	characteristic, complemented
572	#3223	C₂×C₆₁	1	2	yes	complemented
573	#3210	C₂×C₆₁	1	1	yes	characteristic, complemented
574	#3121	C₂×C₆₁	1	2	yes	complemented
575	#3104	C₂×C₆₁	1	1	yes	characteristic, complemented
576	#3044	C₂×C₆₁	1	2	yes	complemented
577	#3037	C₂×C₆₁	1	1	yes	characteristic, complemented
578	#2993	C₂×C₆₁	1	1	yes	characteristic, complemented
579	C₂×C₆₁	—	4	1	no	—
580	C₂×C₆₁	—	4	2	no	—
581	C₂×C₆₁	—	8	2	no	—
582	C₂×C₆₁	#3488	1	1	yes	characteristic
583	C₂×C₆₁	C₂×#578	1	1	yes	characteristic
584	C₂×C₆₁	#3586	1	1	yes	characteristic
585	C₂×#137	C₂²×C₆₁	1	2	yes	—
586	C₂×#137	C₂²×C₆₁	1	2	yes	—
587	C₂²×Q₁₆	C₂²×C₆₁	1	2	yes	—
588	#562	—	2	2	no	—
589	#559	—	2	1	no	—
590	#559	C₂²×C₆₁	1	1	yes	characteristic
591	#557	—	2	1	no	—
592	#557	C₂²×C₆₁	1	1	yes	characteristic
593	#557	C₂²×C₆₁	1	1	yes	characteristic
594	#557	C₂²×C₆₁	1	1	yes	characteristic
595	#556	—	2	1	no	—
596	#556	C₂²×C₆₁	1	1	yes	characteristic
597	#554	—	2	1	no	—
598	#552	—	2	2	no	—
599	#552	C₂²×C₆₁	1	2	yes	—
600	#550	C₂²×C₆₁	1	1	yes	characteristic
601	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
602	D₄×Q₈	C₂²×C₆₁	1	2	yes	—
603	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
604	#548	C₂²×C₆₁	1	2	yes	—
605	#547	C₂²×C₆₁	1	2	yes	—
606	#542	—	2	1	no	—
607	#542	C₂²×C₆₁	1	2	yes	—
608	#541	—	2	2	no	—
609	#541	C₂²×C₆₁	1	2	yes	—
610	#540	—	2	1	no	—
611	#539	—	2	2	no	—
612	#536	C₂²×C₆₁	1	2	yes	—
613	#533	—	2	1	no	—
614	#533	C₂²×C₆₁	1	1	yes	characteristic
615	#533	C₂²×C₆₁	1	1	yes	characteristic
616	#532	C₂²×C₆₁	1	1	yes	characteristic
617	#529	—	2	1	no	—
618	#529	C₂²×C₆₁	1	1	yes	characteristic
619	#519	C₂²×C₆₁	1	2	yes	—
620	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
621	#497	C₂²×C₆₁	1	2	yes	—
622	#494	C₂²×C₆₁	1	1	yes	characteristic
623	#494	C₂²×C₆₁	1	2	yes	—
624	#492	C₂²×C₆₁	1	1	yes	characteristic
625	#491	C₂²×C₆₁	1	2	yes	—
626	#488	C₂²×C₆₁	1	2	yes	—
627	#487	C₂²×C₆₁	1	1	yes	characteristic
628	#486	C₂²×C₆₁	1	1	yes	characteristic
629	#485	C₂²×C₆₁	1	2	yes	—
630	#484	C₂²×C₆₁	1	1	yes	characteristic
631	#484	C₂²×C₆₁	1	1	yes	characteristic
632	#482	C₂²×C₆₁	1	2	yes	—
633	#479	C₂²×C₆₁	1	2	yes	—
634	#478	C₂²×C₆₁	1	2	yes	—
635	#477	C₂²×C₆₁	1	1	yes	characteristic
636	#477	C₂²×C₆₁	1	1	yes	characteristic
637	#475	C₂²×C₆₁	1	1	yes	characteristic
638	#475	C₂²×C₆₁	1	1	yes	characteristic
639	#475	C₂²×C₆₁	1	2	yes	—
640	#470	C₂²×C₆₁	1	2	yes	—
641	#470	C₂²×C₆₁	1	2	yes	—
642	#470	C₂²×C₆₁	1	2	yes	—
643	#468	C₂²×C₆₁	1	2	yes	—
644	#467	C₂²×C₆₁	1	2	yes	—
645	#465	C₂²×C₆₁	1	2	yes	—
646	#464	C₂²×C₆₁	1	2	yes	—
647	#464	C₂²×C₆₁	1	2	yes	—
648	#464	C₂²×C₆₁	1	2	yes	—
649	#464	C₂²×C₆₁	1	2	yes	—
650	#464	C₂²×C₆₁	1	2	yes	—
651	#464	C₂²×C₆₁	1	2	yes	—
652	#462	C₂²×C₆₁	1	1	yes	characteristic
653	#462	C₂²×C₆₁	1	1	yes	characteristic
654	#462	C₂²×C₆₁	1	1	yes	characteristic
655	#462	C₂²×C₆₁	1	2	yes	—
656	#462	C₂²×C₆₁	1	1	yes	characteristic
657	#462	C₂²×C₆₁	1	1	yes	characteristic
658	#462	C₂²×C₆₁	1	2	yes	—
659	#462	C₂²×C₆₁	1	2	yes	—
660	#462	C₂²×C₆₁	1	1	yes	characteristic
661	#462	C₂²×C₆₁	1	2	yes	—
662	#461	C₂²×C₆₁	1	2	yes	—
663	#460	C₂²×C₆₁	1	1	yes	characteristic
664	#460	C₂²×C₆₁	1	1	yes	characteristic
665	#452	C₂²×C₆₁	1	2	yes	—
666	#452	C₂²×C₆₁	1	2	yes	—
667	#452	C₂²×C₆₁	1	2	yes	—
668	#452	C₂²×C₆₁	1	2	yes	—
669	#451	C₂²×C₆₁	1	2	yes	—
670	#451	C₂²×C₆₁	1	1	yes	characteristic
671	#451	C₂²×C₆₁	1	1	yes	characteristic
672	#451	C₂²×C₆₁	1	2	yes	—
673	#451	C₂²×C₆₁	1	2	yes	—
674	#448	C₂²×C₆₁	1	2	yes	—
675	#446	C₂²×C₆₁	1	1	yes	characteristic
676	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic
677	#441	C₂²×C₆₁	1	2	yes	—
678	#440	C₂²×C₆₁	1	2	yes	—
679	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
680	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
681	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
682	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
683	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
684	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
685	#436	C₂²×C₆₁	1	1	yes	characteristic
686	#436	C₂²×C₆₁	1	2	yes	—
687	#435	C₂²×C₆₁	1	2	yes	—
688	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic
689	#433	C₂²×C₆₁	1	2	yes	—
690	#431	C₂²×C₆₁	1	1	yes	characteristic
691	#424	C₂²×C₆₁	1	2	yes	—
692	#423	C₂²×C₆₁	1	1	yes	characteristic
693	#419	C₂²×C₆₁	1	2	yes	—
694	#417	C₂²×C₆₁	1	2	yes	—
695	#416	C₂²×C₆₁	1	2	yes	—
696	C₆₁	#62043	1	1	yes	characteristic, direct product factor, Sylow
697	C₂×#41	C₂³×C₆₁	1	2	yes	—
698	C₂×#41	C₂³×C₆₁	1	2	yes	—
699	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
700	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
701	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
702	#137	—	4	4	no	—
703	#137	—	4	4	no	—
704	C₂×Q₁₆	—	4	4	no	—
705	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
706	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
707	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
708	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
709	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
710	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
711	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
712	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
713	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
714	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
715	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
716	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
717	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
718	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
719	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
720	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
721	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
722	C₄⋊Q₈	—	2	1	no	—
723	C₄⋊Q₈	—	2	1	no	—
724	C₄⋊Q₈	—	2	2	no	—
725	C₄⋊Q₈	—	2	1	no	—
726	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
727	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
728	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
729	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
730	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
731	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
732	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
733	#127	—	2	1	no	—
734	#127	C₂³×C₆₁	1	1	yes	characteristic
735	#126	—	2	2	no	—
736	#126	—	2	2	no	—
737	#126	—	2	2	no	—
738	#126	—	2	2	no	—
739	#126	—	2	2	no	—
740	#126	D₄×C₆₁	1	2	yes	—
741	#125	—	2	1	no	—
742	#125	—	2	2	no	—
743	#125	—	2	2	no	—
744	#125	—	2	1	no	—
745	#125	—	2	2	no	—
746	#125	—	2	2	no	—
747	#125	—	2	2	no	—
748	#125	—	2	2	no	—
749	#125	—	2	1	no	—
750	#125	—	2	1	no	—
751	#125	D₄×C₆₁	1	1	yes	characteristic
752	#125	C₂³×C₆₁	1	2	yes	—
753	#124	—	2	1	no	—
754	#124	—	2	1	no	—
755	#124	—	2	2	no	—
756	#124	—	2	2	no	—
757	#124	D₄×C₆₁	1	1	yes	characteristic
758	#124	C₂³×C₆₁	1	2	yes	—
759	#124	C₂³×C₆₁	1	2	yes	—
760	#123	—	2	2	no	—
761	#123	—	2	2	no	—
762	#123	—	2	2	no	—
763	#123	—	2	2	no	—
764	#123	—	2	2	no	—
765	#123	—	2	2	no	—
766	#123	—	2	2	no	—
767	#123	D₄×C₆₁	1	2	yes	—
768	C₂²⋊Q₈	—	2	1	no	—
769	C₂²⋊Q₈	—	2	1	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	—	2	2	no	—
774	C₂²⋊Q₈	—	2	2	no	—
775	C₂²⋊Q₈	—	2	2	no	—
776	C₂²⋊Q₈	—	2	2	no	—
777	C₂²⋊Q₈	—	2	2	no	—
778	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
779	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
780	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
781	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
782	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
783	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
784	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
785	#121	—	2	2	no	—
786	#121	—	2	2	no	—
787	#121	—	2	1	no	—
788	#121	—	2	1	no	—
789	#121	—	2	2	no	—
790	#121	D₄×C₆₁	1	1	yes	characteristic
791	#121	C₂³×C₆₁	1	2	yes	—
792	C₄×Q₈	—	2	1	no	—
793	C₄×Q₈	—	2	1	no	—
794	C₄×Q₈	—	2	2	no	—
795	C₄×Q₈	—	2	2	no	—
796	C₄×Q₈	—	2	1	no	—
797	C₄×Q₈	—	2	1	no	—
798	C₄×Q₈	—	2	1	no	—
799	C₄×Q₈	—	2	1	no	—
800	C₄×Q₈	—	2	1	no	—
801	C₄×Q₈	—	2	1	no	—
802	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
803	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
804	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
805	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
806	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
807	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
808	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
809	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
810	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
811	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
812	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
813	C₄×D₄	—	2	2	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	1	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	C₂³×C₆₁	1	2	yes	—
822	C₄×D₄	C₂³×C₆₁	1	2	yes	—
823	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
824	#117	—	2	1	no	—
825	#117	—	2	1	no	—
826	#117	—	2	2	no	—
827	#117	—	2	2	no	—
828	#117	—	2	2	no	—
829	#117	C₂³×C₆₁	1	2	yes	—
830	#117	C₂³×C₆₁	1	2	yes	—
831	C₂×C₄⋊C₄	—	2	1	no	—
832	C₂×C₄⋊C₄	—	2	2	no	—
833	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
834	C₂×C₄²	—	2	1	no	—
835	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
836	#107	C₂³×C₆₁	1	1	yes	characteristic
837	#107	C₂³×C₆₁	1	1	yes	characteristic
838	#107	C₂³×C₆₁	1	1	yes	characteristic
839	#107	C₂³×C₆₁	1	1	yes	characteristic
840	#106	C₂³×C₆₁	1	2	yes	—
841	#106	C₂³×C₆₁	1	2	yes	—
842	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
843	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
844	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
845	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
846	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
847	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
848	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
849	#103	C₂³×C₆₁	1	1	yes	characteristic
850	#103	C₂³×C₆₁	1	2	yes	—
851	#103	C₂³×C₆₁	1	2	yes	—
852	#103	C₂³×C₆₁	1	2	yes	—
853	#103	C₂³×C₆₁	1	1	yes	characteristic
854	#103	C₂³×C₆₁	1	2	yes	—
855	#103	C₂³×C₆₁	1	2	yes	—
856	#103	C₂³×C₆₁	1	1	yes	characteristic
857	#103	C₂³×C₆₁	1	1	yes	characteristic
858	#103	C₂³×C₆₁	1	2	yes	—
859	#103	C₂³×C₆₁	1	1	yes	characteristic
860	#103	C₂³×C₆₁	1	1	yes	characteristic
861	#103	C₂³×C₆₁	1	1	yes	characteristic
862	#103	C₂³×C₆₁	1	1	yes	characteristic
863	#103	C₂³×C₆₁	1	2	yes	—
864	#103	C₂³×C₆₁	1	2	yes	—
865	#102	C₂³×C₆₁	1	2	yes	—
866	#102	C₂³×C₆₁	1	2	yes	—
867	#102	C₂³×C₆₁	1	2	yes	—
868	#102	C₂³×C₆₁	1	2	yes	—
869	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
870	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
871	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
872	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
873	#97	C₂³×C₆₁	1	2	yes	—
874	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
875	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
876	C₄×C₈	C₂³×C₆₁	1	2	yes	—
877	#41	—	4	2	no	—
878	#41	—	4	2	no	—
879	#41	—	4	2	no	—
880	#41	—	4	2	no	—
881	C₂×Q₈	—	2	1	no	—
882	C₂×Q₈	—	2	2	no	—
883	C₂×Q₈	—	2	1	no	—
884	C₂×Q₈	—	2	1	no	—
885	C₂×Q₈	—	2	2	no	—
886	C₂×Q₈	—	2	4	no	—
887	C₂×Q₈	—	2	2	no	—
888	C₂×Q₈	—	4	2	no	—
889	C₂×Q₈	—	4	1	no	—
890	C₂×Q₈	—	4	2	no	—
891	C₂×Q₈	—	4	2	no	—
892	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
893	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
894	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
895	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
896	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
897	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
898	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	2	2	no	—
902	C₂×D₄	—	2	1	no	—
903	C₂×D₄	—	2	1	no	—
904	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
905	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
906	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
907	C₂²×C₄	—	2	1	no	—
908	C₂²×C₄	—	2	1	no	—
909	C₂²×C₄	—	2	2	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
915	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
916	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
917	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
918	Q₁₆	—	2	2	no	—
919	Q₁₆	—	2	4	no	—
920	Q₁₆	—	2	2	no	—
921	Q₁₆	—	4	2	no	—
922	Q₁₆	—	4	2	no	—
923	Q₁₆	—	4	1	no	—
924	Q₁₆	—	4	2	no	—
925	Q₁₆	—	4	1	no	—
926	Q₁₆	—	4	2	no	—
927	Q₁₆	—	4	2	no	—
928	SD₁₆	—	2	4	no	—
929	SD₁₆	—	4	2	no	—
930	SD₁₆	—	4	2	no	—
931	SD₁₆	—	4	2	no	—
932	M₁₆	—	4	2	no	—
933	M₁₆	—	4	2	no	—
934	C₂×C₈	—	4	2	no	—
935	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
936	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
937	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
938	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
939	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
940	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
973	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
974	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
975	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
976	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
977	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
978	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
979	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
980	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
981	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
982	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	1	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
997	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
998	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
999	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1000	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1001	C₄²	—	2	1	no	—
1002	C₄²	—	2	1	no	—
1003	C₄²	—	2	1	no	—
1004	C₄²	—	2	1	no	—
1005	C₄²	—	2	2	no	—
1006	C₄²	—	2	2	no	—
1007	C₄²	—	2	2	no	—
1008	C₄²	—	2	1	no	—
1009	C₄²	—	2	1	no	—
1010	C₄²	—	2	2	no	—
1011	C₄²	—	2	2	no	—
1012	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1013	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1014	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1015	C₄²	C₂⁴×C₆₁	1	2	yes	—
1016	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1017	C₂³	—	2	2	no	—
1018	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1019	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1020	Q₈	—	2	2	no	—
1021	Q₈	—	2	1	no	—
1022	Q₈	—	2	1	no	—
1023	Q₈	—	2	2	no	—
1024	Q₈	—	2	1	no	—
1025	Q₈	—	2	2	no	—
1026	Q₈	—	2	1	no	—
1027	Q₈	—	2	2	no	—
1028	Q₈	—	2	1	no	—
1029	Q₈	—	2	1	no	—
1030	Q₈	—	2	2	no	—
1031	Q₈	—	2	1	no	—
1032	Q₈	—	4	2	no	—
1033	Q₈	—	4	4	no	—
1034	Q₈	—	4	2	no	—
1035	Q₈	—	8	1	no	—
1036	Q₈	—	8	2	no	—
1037	Q₈	H(5,𝔽₂)×C₆₁	1	2	yes	—
1038	D₄	—	2	2	no	—
1039	D₄	—	2	2	no	—
1040	D₄	—	2	2	no	—
1041	D₄	—	4	2	no	—
1042	D₄	—	4	2	no	—
1043	D₄	—	8	1	no	—
1044	D₄	—	8	2	no	—
1045	D₄	—	8	2	no	—
1046	D₄	—	8	2	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	4	1	no	—
1064	C₂×C₄	—	4	4	no	—
1065	C₂×C₄	—	4	2	no	—
1066	C₂×C₄	—	4	2	no	—
1067	C₂×C₄	—	8	2	no	—
1068	C₂×C₄	—	8	2	no	—
1069	C₂×C₄	—	8	2	no	—
1070	C₂×C₄	—	8	2	no	—
1071	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1072	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1073	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1074	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1075	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1076	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1077	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1078	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1079	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1080	C₈	—	2	1	no	—
1081	C₈	—	2	2	no	—
1082	C₈	—	2	2	no	—
1083	C₈	—	2	1	no	—
1084	C₈	—	2	1	no	—
1085	C₈	—	2	1	no	—
1086	C₂²	—	2	1	no	—
1087	C₂²	—	2	2	no	—
1088	C₂²	—	2	1	no	—
1089	C₂²	—	2	2	no	—
1090	C₂²	—	2	2	no	—
1091	C₂²	—	2	1	no	—
1092	C₂²	—	4	2	no	—
1093	C₂²	—	4	2	no	—
1094	C₂²	—	4	2	no	—
1095	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1096	C₄	—	2	1	no	—
1097	C₄	—	2	2	no	—
1098	C₄	—	2	1	no	—
1099	C₄	—	2	1	no	—
1100	C₄	—	2	2	no	—
1101	C₄	—	2	1	no	—
1102	C₄	—	2	2	no	—
1103	C₄	—	2	2	no	—
1104	C₄	—	4	2	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	1	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	2	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	2	no	—
1113	C₄	—	4	1	no	—
1114	C₄	C₆₁×#578	1	2	yes	—
1115	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1116	C₄	C₆₁×#585	1	1	yes	characteristic
1117	C₂	—	4	1	no	—
1118	C₂	—	4	2	no	—
1119	C₂	—	8	2	no	—
1120	C₂	C₆₁×#3488	1	1	yes	characteristic
1121	C₂	C₂×C₆₁×#578	1	1	yes	characteristic
1122	C₂	C₆₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₆₁×#3554	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₆₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₁×#3523	C₂	semidirect
3. C₆₁×#3400	C₂	semidirect
4. C₆₁×#3395	C₂	semidirect
5. C₆₁×#3374	C₂	semidirect
6. C₆₁×#3365	C₂	semidirect
7. C₆₁×#3328	C₂	semidirect
8. C₆₁×#3327	C₂	semidirect
9. C₆₁×#3315	C₂	semidirect
10. C₆₁×#3304	C₂	semidirect
11. D₄×Q₁₆×C₆₁	C₂	semidirect
12. C₆₁×#3278	C₂	semidirect
13. C₆₁×#3276	C₂	semidirect
14. C₆₁×#3270	C₂	semidirect
15. C₆₁×#3258	C₂	semidirect
16. C₆₁×#3255	C₂	semidirect
17. C₆₁×#3223	C₂	semidirect
18. C₆₁×#3210	C₂	semidirect
19. C₆₁×#3121	C₂	semidirect
20. C₆₁×#3104	C₂	semidirect
21. C₆₁×#3044	C₂	semidirect
22. C₆₁×#3037	C₂	semidirect
23. C₆₁×#2993	C₂	semidirect
524. #62043	C₆₁	direct (N × H)
557. #3523	C₂×C₆₁	semidirect
558. #3400	C₂×C₆₁	semidirect
559. #3395	C₂×C₆₁	semidirect
560. #3374	C₂×C₆₁	semidirect
561. #3365	C₂×C₆₁	semidirect
562. #3328	C₂×C₆₁	semidirect
563. #3327	C₂×C₆₁	semidirect
564. #3315	C₂×C₆₁	semidirect
565. #3304	C₂×C₆₁	semidirect
566. D₄×Q₁₆	C₂×C₆₁	semidirect
567. #3278	C₂×C₆₁	semidirect
568. #3276	C₂×C₆₁	semidirect
569. #3270	C₂×C₆₁	semidirect
570. #3258	C₂×C₆₁	semidirect
571. #3255	C₂×C₆₁	semidirect
572. #3223	C₂×C₆₁	semidirect
573. #3210	C₂×C₆₁	semidirect
574. #3121	C₂×C₆₁	semidirect
575. #3104	C₂×C₆₁	semidirect
576. #3044	C₂×C₆₁	semidirect
577. #3037	C₂×C₆₁	semidirect
578. #2993	C₂×C₆₁	semidirect
696. C₆₁	#62043	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×#3554	2
C₆₁×#3523	2
C₆₁×#3400	2
C₆₁×#3395	2
C₆₁×#3374	2
C₆₁×#3365	2
C₆₁×#3328	2
C₆₁×#3327	2
C₆₁×#3315	2
C₆₁×#3304	2
D₄×Q₁₆×C₆₁	2
C₆₁×#3278	2
C₆₁×#3276	2
C₆₁×#3270	2
C₆₁×#3258	2
C₆₁×#3255	2
C₆₁×#3223	2
C₆₁×#3210	2
C₆₁×#3121	2
C₆₁×#3104	2
C₆₁×#3044	2
C₆₁×#3037	2
C₆₁×#2993	2
#62043	61

Subgroups — C61×#62043 #29565476

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62043 #29565476