Subgroups — C₆₁×#60927 #29564360

Order 15616.

1772 conjugacy classes of subgroups.

The subgroup lattice has 1140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3461	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3263	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3262	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3258	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3258	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3256	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3252	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3250	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3248	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3082	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3081	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3078	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#3062	C₂	1	1	yes	maximal, characteristic
17	C₆₁×#3059	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#3057	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#3044	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₁×#3042	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#3040	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₆₁×#464	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₁×#2906	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	1	yes	characteristic
26	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
27	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
30	C₆₁×#559	—	2	1	no	—
31	C₆₁×#559	—	2	1	no	—
32	C₆₁×#556	—	2	1	no	—
33	C₆₁×#556	—	2	1	no	—
34	C₆₁×#551	—	2	2	no	—
35	C₆₁×#551	—	2	2	no	—
36	C₆₁×#544	C₂²	1	1	yes	characteristic
37	C₆₁×#542	—	2	1	no	—
38	C₆₁×#542	C₂²	1	2	yes	—
39	C₆₁×#542	C₂²	1	2	yes	—
40	C₆₁×#542	C₂²	1	2	yes	complemented
41	C₆₁×#541	—	2	1	no	—
42	C₆₁×#541	C₂²	1	2	yes	complemented
43	C₆₁×#539	—	2	2	no	—
44	C₆₁×#537	C₂²	1	1	yes	characteristic
45	C₆₁×#536	C₂²	1	1	yes	characteristic
46	C₆₁×#536	C₂²	1	1	yes	characteristic
47	C₆₁×#536	C₂²	1	1	yes	characteristic
48	C₆₁×#535	C₂²	1	1	yes	characteristic
49	C₆₁×#533	—	2	1	no	—
50	C₆₁×#533	C₂²	1	1	yes	characteristic
51	C₆₁×#533	C₂²	1	2	yes	complemented
52	C₆₁×#529	—	2	2	no	—
53	C₆₁×#529	—	2	1	no	—
54	C₆₁×#529	C₂²	1	2	yes	—
55	C₆₁×#529	C₂²	1	2	yes	—
56	C₆₁×#529	C₂²	1	2	yes	complemented
57	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
58	C₆₁×#519	C₂²	1	1	yes	characteristic
59	C₆₁×#518	C₂²	1	1	yes	characteristic
60	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
61	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
62	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
63	C₆₁×#479	C₂²	1	1	yes	characteristic, complemented
64	C₆₁×#479	C₂²	1	1	yes	characteristic, complemented
65	C₆₁×#479	C₂²	1	2	yes	complemented
66	C₆₁×#479	C₂²	1	2	yes	complemented
67	C₆₁×#479	C₂²	1	2	yes	complemented
68	C₆₁×#479	C₂²	1	2	yes	complemented
69	C₆₁×#478	C₂²	1	2	yes	—
70	C₆₁×#478	C₂²	1	2	yes	—
71	C₆₁×#478	C₂²	1	1	yes	characteristic, complemented
72	C₆₁×#478	C₂²	1	1	yes	characteristic, complemented
73	C₆₁×#477	C₂²	1	1	yes	characteristic, complemented
74	C₆₁×#477	C₂²	1	2	yes	complemented
75	C₆₁×#477	C₂²	1	2	yes	complemented
76	C₆₁×#476	C₂²	1	2	yes	—
77	C₆₁×#476	C₂²	1	1	yes	characteristic, complemented
78	C₆₁×#475	C₂²	1	1	yes	characteristic, complemented
79	C₆₁×#475	C₂²	1	2	yes	complemented
80	C₆₁×#475	C₂²	1	2	yes	complemented
81	C₆₁×#474	C₂²	1	2	yes	—
82	C₆₁×#474	C₂²	1	1	yes	characteristic, complemented
83	C₆₁×#470	C₂²	1	2	yes	complemented
84	C₆₁×#470	C₂²	1	2	yes	complemented
85	C₆₁×#470	C₂²	1	2	yes	complemented
86	C₆₁×#469	C₂²	1	2	yes	—
87	C₆₁×#468	C₂²	1	2	yes	—
88	C₆₁×#468	C₂²	1	2	yes	—
89	C₆₁×#468	C₂²	1	2	yes	—
90	C₆₁×#468	C₂²	1	2	yes	complemented
91	C₆₁×#467	C₂²	1	2	yes	complemented
92	C₆₁×#467	C₂²	1	2	yes	complemented
93	C₆₁×#467	C₂²	1	2	yes	complemented
94	C₆₁×#466	C₂²	1	2	yes	—
95	C₆₁×#465	C₂²	1	2	yes	—
96	C₆₁×#465	C₂²	1	2	yes	—
97	C₆₁×#465	C₂²	1	2	yes	—
98	C₆₁×#465	C₂²	1	2	yes	complemented
99	C₆₁×#464	C₂²	1	2	yes	—
100	C₆₁×#464	C₂²	1	2	yes	—
101	C₆₁×#464	C₂²	1	2	yes	—
102	C₆₁×#464	C₂²	1	2	yes	—
103	C₆₁×#464	C₂²	1	2	yes	—
104	C₆₁×#464	C₂²	1	2	yes	—
105	C₆₁×#464	C₂²	1	2	yes	complemented
106	C₆₁×#464	C₂²	1	2	yes	complemented
107	C₆₁×#463	C₂²	1	2	yes	—
108	C₆₁×#463	C₂²	1	2	yes	—
109	C₆₁×#463	C₂²	1	2	yes	—
110	C₆₁×#463	C₂²	1	2	yes	—
111	C₆₁×#462	C₂²	1	2	yes	complemented
112	C₆₁×#462	C₂²	1	2	yes	complemented
113	C₆₁×#461	C₂²	1	2	yes	—
114	C₆₁×#461	C₂²	1	2	yes	—
115	C₆₁×#428	C₂²	1	1	yes	characteristic
116	C₆₁×#428	C₂²	1	1	yes	characteristic
117	C₆₁×#427	C₂²	1	1	yes	characteristic
118	C₆₁×#427	C₂²	1	1	yes	characteristic
119	C₆₁×#424	C₂²	1	1	yes	characteristic
120	C₆₁×#424	C₂²	1	1	yes	characteristic
121	C₆₁×#424	C₂²	1	2	yes	complemented
122	C₆₁×#424	C₂²	1	2	yes	complemented
123	C₆₁×#423	C₂²	1	1	yes	characteristic
124	C₆₁×#423	C₂²	1	2	yes	complemented
125	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
126	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	complemented
127	C₆₁×#419	C₂²	1	1	yes	characteristic
128	C₆₁×#419	C₂²	1	1	yes	characteristic
129	C₆₁×#419	C₂²	1	1	yes	characteristic
130	C₆₁×#418	C₂²	1	1	yes	characteristic
131	C₆₁×#416	C₂²	1	1	yes	characteristic
132	C₆₁×#416	C₂²	1	1	yes	characteristic
133	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
134	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
135	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
136	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
139	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
140	#137×C₆₁	—	4	2	no	—
141	AGL(1,ℤ/8)×C₆₁	—	4	2	no	—
142	C₂×Q₁₆×C₆₁	—	4	2	no	—
143	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
144	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
145	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₆₁	—	4	2	no	—
147	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
151	C₂×D₈×C₆₁	C₂³	1	2	yes	—
152	#131×C₆₁	—	4	2	no	—
153	#131×C₆₁	—	4	2	no	—
154	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
155	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
156	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
157	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
158	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
159	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
160	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
161	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
162	C₄⋊Q₈×C₆₁	—	2	1	no	—
163	C₄⋊Q₈×C₆₁	—	2	1	no	—
164	C₄⋊Q₈×C₆₁	—	2	1	no	—
165	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
166	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
167	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
168	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
169	#127×C₆₁	—	2	1	no	—
170	#126×C₆₁	—	2	2	no	—
171	#126×C₆₁	—	2	2	no	—
172	#126×C₆₁	—	2	2	no	—
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	#125×C₆₁	—	2	2	no	—
179	#125×C₆₁	—	2	2	no	—
180	#125×C₆₁	—	2	1	no	—
181	#125×C₆₁	—	2	2	no	—
182	#125×C₆₁	C₂³	1	1	yes	characteristic
183	#125×C₆₁	C₂³	1	1	yes	characteristic
184	#125×C₆₁	C₂³	1	2	yes	—
185	#124×C₆₁	—	2	1	no	—
186	#124×C₆₁	—	2	1	no	—
187	#124×C₆₁	—	2	1	no	—
188	#124×C₆₁	—	2	2	no	—
189	#124×C₆₁	—	2	2	no	—
190	#124×C₆₁	—	2	2	no	—
191	#124×C₆₁	—	2	1	no	—
192	#124×C₆₁	—	2	1	no	—
193	#124×C₆₁	C₂³	1	2	yes	—
194	#124×C₆₁	C₂³	1	2	yes	—
195	#124×C₆₁	C₂³	1	2	yes	—
196	#123×C₆₁	—	2	2	no	—
197	#123×C₆₁	—	2	2	no	—
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	C₂²⋊Q₈×C₆₁	—	2	1	no	—
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	1	no	—
210	C₂²⋊Q₈×C₆₁	—	2	2	no	—
211	C₂²⋊Q₈×C₆₁	—	2	1	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	C₂³	1	2	yes	—
216	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
217	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
218	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
219	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
220	#121×C₆₁	—	2	2	no	—
221	#121×C₆₁	—	2	1	no	—
222	#121×C₆₁	C₂³	1	2	yes	—
223	#121×C₆₁	C₂³	1	2	yes	—
224	#121×C₆₁	C₂³	1	2	yes	—
225	#120×C₆₁	—	2	2	no	—
226	C₄×Q₈×C₆₁	—	2	1	no	—
227	C₄×Q₈×C₆₁	—	2	1	no	—
228	C₄×Q₈×C₆₁	—	2	2	no	—
229	C₄×Q₈×C₆₁	—	2	1	no	—
230	C₄×Q₈×C₆₁	—	2	1	no	—
231	C₄×Q₈×C₆₁	—	2	1	no	—
232	C₄×Q₈×C₆₁	—	2	1	no	—
233	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
234	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
235	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
237	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
238	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
239	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
240	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
241	C₄×D₄×C₆₁	—	2	1	no	—
242	C₄×D₄×C₆₁	—	2	2	no	—
243	C₄×D₄×C₆₁	—	2	2	no	—
244	C₄×D₄×C₆₁	—	2	1	no	—
245	C₄×D₄×C₆₁	—	2	2	no	—
246	C₄×D₄×C₆₁	—	2	1	no	—
247	C₄×D₄×C₆₁	—	2	1	no	—
248	C₄×D₄×C₆₁	D₄	1	2	yes	—
249	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
250	C₄×D₄×C₆₁	D₄	1	2	yes	—
251	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
252	C₄×D₄×C₆₁	C₂³	1	2	yes	—
253	C₄×D₄×C₆₁	C₂³	1	2	yes	—
254	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
256	#117×C₆₁	—	2	2	no	—
257	#117×C₆₁	—	2	2	no	—
258	#117×C₆₁	—	2	2	no	—
259	#117×C₆₁	—	2	1	no	—
260	#117×C₆₁	—	2	2	no	—
261	#117×C₆₁	—	2	2	no	—
262	#117×C₆₁	C₂³	1	1	yes	characteristic
263	#117×C₆₁	C₂³	1	1	yes	characteristic
264	#117×C₆₁	C₂³	1	1	yes	characteristic
265	#117×C₆₁	C₂³	1	1	yes	characteristic
266	#117×C₆₁	C₂³	1	2	yes	—
267	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
268	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
270	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
271	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
272	C₂×C₄²×C₆₁	—	2	1	no	—
273	C₂×C₄²×C₆₁	—	2	1	no	—
274	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
275	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
276	#107×C₆₁	C₂³	1	1	yes	characteristic
277	#107×C₆₁	C₂³	1	1	yes	characteristic
278	#107×C₆₁	C₂³	1	1	yes	characteristic
279	#107×C₆₁	C₂³	1	1	yes	characteristic
280	#107×C₆₁	C₂³	1	2	yes	—
281	#107×C₆₁	C₂³	1	2	yes	—
282	#106×C₆₁	C₂³	1	1	yes	characteristic
283	#106×C₆₁	C₂³	1	1	yes	characteristic
284	#106×C₆₁	C₂³	1	1	yes	characteristic
285	#106×C₆₁	C₂³	1	1	yes	characteristic
286	#106×C₆₁	C₂³	1	2	yes	—
287	#106×C₆₁	C₂³	1	2	yes	—
288	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
289	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
290	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
291	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
292	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
293	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
294	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
295	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
296	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
297	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
298	#103×C₆₁	C₂³	1	2	yes	—
299	#103×C₆₁	C₂³	1	2	yes	—
300	#103×C₆₁	C₂³	1	1	yes	characteristic
301	#103×C₆₁	C₂³	1	1	yes	characteristic
302	#103×C₆₁	C₂³	1	1	yes	characteristic
303	#103×C₆₁	C₂³	1	1	yes	characteristic
304	#103×C₆₁	C₂³	1	2	yes	—
305	#103×C₆₁	C₂³	1	2	yes	—
306	#103×C₆₁	C₂³	1	2	yes	—
307	#103×C₆₁	C₂³	1	2	yes	—
308	#103×C₆₁	C₂³	1	2	yes	—
309	#103×C₆₁	C₂³	1	2	yes	—
310	#102×C₆₁	C₂³	1	2	yes	—
311	#102×C₆₁	C₂³	1	2	yes	—
312	#102×C₆₁	C₂³	1	1	yes	characteristic
313	#102×C₆₁	C₂³	1	1	yes	characteristic
314	#102×C₆₁	C₂³	1	1	yes	characteristic
315	#102×C₆₁	C₂³	1	1	yes	characteristic
316	#102×C₆₁	C₂³	1	2	yes	—
317	#102×C₆₁	C₂³	1	2	yes	—
318	C₂⁴×C₆₁	—	2	1	no	—
319	#41×C₆₁	—	2	2	no	—
320	#41×C₆₁	—	2	2	no	—
321	#41×C₆₁	—	2	2	no	—
322	#41×C₆₁	—	2	2	no	—
323	C₂×Q₈×C₆₁	—	2	1	no	—
324	C₂×Q₈×C₆₁	—	2	1	no	—
325	C₂×Q₈×C₆₁	—	2	1	no	—
326	C₂×Q₈×C₆₁	—	2	1	no	—
327	C₂×Q₈×C₆₁	—	2	2	no	—
328	C₂×Q₈×C₆₁	—	2	2	no	—
329	C₂×Q₈×C₆₁	—	2	2	no	—
330	C₂×Q₈×C₆₁	—	2	2	no	—
331	C₂×Q₈×C₆₁	—	2	2	no	—
332	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
333	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
334	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
335	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
336	C₂×D₄×C₆₁	—	2	1	no	—
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	2	no	—
342	C₂×D₄×C₆₁	—	2	2	no	—
343	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
344	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
345	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
346	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
347	C₂²×C₄×C₆₁	—	2	1	no	—
348	C₂²×C₄×C₆₁	—	2	1	no	—
349	C₂²×C₄×C₆₁	—	2	1	no	—
350	C₂²×C₄×C₆₁	—	2	1	no	—
351	C₂²×C₄×C₆₁	—	2	1	no	—
352	C₂²×C₄×C₆₁	—	2	1	no	—
353	C₂²×C₄×C₆₁	—	2	2	no	—
354	C₂²×C₄×C₆₁	—	2	2	no	—
355	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
357	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
358	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
359	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
360	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
361	Q₁₆×C₆₁	—	4	2	no	—
362	Q₁₆×C₆₁	—	4	2	no	—
363	Q₁₆×C₆₁	—	4	2	no	—
364	SD₁₆×C₆₁	—	4	2	no	—
365	SD₁₆×C₆₁	—	4	2	no	—
366	SD₁₆×C₆₁	—	4	2	no	—
367	SD₁₆×C₆₁	—	4	2	no	—
368	D₈×C₆₁	—	4	2	no	—
369	M₁₆×C₆₁	—	2	2	no	—
370	M₁₆×C₆₁	—	2	2	no	—
371	M₁₆×C₆₁	—	4	2	no	—
372	M₁₆×C₆₁	—	4	2	no	—
373	C₂×C₈×C₆₁	—	2	2	no	—
374	C₂×C₈×C₆₁	—	2	2	no	—
375	C₂×C₈×C₆₁	—	4	2	no	—
376	C₂×C₈×C₆₁	—	4	2	no	—
377	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
378	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
379	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
380	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
381	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
382	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
383	C₄⋊C₄×C₆₁	—	2	2	no	—
384	C₄⋊C₄×C₆₁	—	2	2	no	—
385	C₄⋊C₄×C₆₁	—	2	1	no	—
386	C₄⋊C₄×C₆₁	—	2	1	no	—
387	C₄⋊C₄×C₆₁	—	2	1	no	—
388	C₄⋊C₄×C₆₁	—	2	1	no	—
389	C₄⋊C₄×C₆₁	—	2	1	no	—
390	C₄⋊C₄×C₆₁	—	2	2	no	—
391	C₄⋊C₄×C₆₁	—	2	2	no	—
392	C₄⋊C₄×C₆₁	—	2	2	no	—
393	C₄⋊C₄×C₆₁	—	2	2	no	—
394	C₄⋊C₄×C₆₁	—	2	2	no	—
395	C₄⋊C₄×C₆₁	—	2	2	no	—
396	C₄⋊C₄×C₆₁	—	2	2	no	—
397	C₄⋊C₄×C₆₁	—	2	2	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	2	no	—
402	C₄⋊C₄×C₆₁	—	2	2	no	—
403	C₄⋊C₄×C₆₁	—	2	2	no	—
404	C₄⋊C₄×C₆₁	—	2	1	no	—
405	C₄⋊C₄×C₆₁	—	2	1	no	—
406	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
407	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
409	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
411	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
417	C₂²⋊C₄×C₆₁	—	2	1	no	—
418	C₂²⋊C₄×C₆₁	—	2	1	no	—
419	C₂²⋊C₄×C₆₁	—	2	2	no	—
420	C₂²⋊C₄×C₆₁	—	2	2	no	—
421	C₂²⋊C₄×C₆₁	—	2	1	no	—
422	C₂²⋊C₄×C₆₁	—	2	2	no	—
423	C₂²⋊C₄×C₆₁	—	2	2	no	—
424	C₂²⋊C₄×C₆₁	—	2	2	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	1	no	—
432	C₂²⋊C₄×C₆₁	—	2	1	no	—
433	C₂²⋊C₄×C₆₁	—	2	2	no	—
434	C₂²⋊C₄×C₆₁	—	2	2	no	—
435	C₂²⋊C₄×C₆₁	—	2	2	no	—
436	C₂²⋊C₄×C₆₁	—	2	2	no	—
437	C₂²⋊C₄×C₆₁	—	2	2	no	—
438	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
441	C₄²×C₆₁	—	2	2	no	—
442	C₄²×C₆₁	—	2	1	no	—
443	C₄²×C₆₁	—	2	1	no	—
444	C₄²×C₆₁	—	2	1	no	—
445	C₄²×C₆₁	—	2	2	no	—
446	C₄²×C₆₁	—	2	2	no	—
447	C₄²×C₆₁	—	2	2	no	—
448	C₄²×C₆₁	—	2	1	no	—
449	C₄²×C₆₁	—	2	1	no	—
450	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
451	C₄²×C₆₁	C₂×D₄	1	2	yes	—
452	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
453	C₄²×C₆₁	C₂×D₄	1	2	yes	—
454	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
455	C₄²×C₆₁	C₂⁴	1	2	yes	—
456	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
457	C₂³×C₆₁	—	2	1	no	—
458	C₂³×C₆₁	—	2	2	no	—
459	C₂³×C₆₁	—	4	2	no	—
460	C₂³×C₆₁	—	8	1	no	—
461	C₂³×C₆₁	—	8	1	no	—
462	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
463	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
464	Q₈×C₆₁	—	2	2	no	—
465	Q₈×C₆₁	—	2	2	no	—
466	Q₈×C₆₁	—	2	1	no	—
467	Q₈×C₆₁	—	2	2	no	—
468	Q₈×C₆₁	—	2	2	no	—
469	Q₈×C₆₁	—	2	2	no	—
470	Q₈×C₆₁	—	2	1	no	—
471	Q₈×C₆₁	—	4	2	no	—
472	Q₈×C₆₁	—	4	2	no	—
473	Q₈×C₆₁	—	8	1	no	—
474	Q₈×C₆₁	—	8	2	no	—
475	Q₈×C₆₁	—	8	1	no	—
476	D₄×C₆₁	—	2	4	no	—
477	D₄×C₆₁	—	2	2	no	—
478	D₄×C₆₁	—	2	1	no	—
479	D₄×C₆₁	—	2	2	no	—
480	D₄×C₆₁	—	2	2	no	—
481	D₄×C₆₁	—	2	1	no	—
482	D₄×C₆₁	—	4	2	no	—
483	D₄×C₆₁	—	4	2	no	—
484	D₄×C₆₁	—	8	2	no	—
485	D₄×C₆₁	—	8	2	no	—
486	D₄×C₆₁	—	8	2	no	—
487	C₂×C₄×C₆₁	—	2	2	no	—
488	C₂×C₄×C₆₁	—	2	2	no	—
489	C₂×C₄×C₆₁	—	2	1	no	—
490	C₂×C₄×C₆₁	—	2	1	no	—
491	C₂×C₄×C₆₁	—	2	2	no	—
492	C₂×C₄×C₆₁	—	2	1	no	—
493	C₂×C₄×C₆₁	—	2	2	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	—	4	1	no	—
500	C₂×C₄×C₆₁	—	4	2	no	—
501	C₂×C₄×C₆₁	—	4	2	no	—
502	C₂×C₄×C₆₁	—	4	1	no	—
503	C₂×C₄×C₆₁	—	4	2	no	—
504	C₂×C₄×C₆₁	—	4	2	no	—
505	C₂×C₄×C₆₁	—	4	2	no	—
506	C₂×C₄×C₆₁	—	4	2	no	—
507	C₂×C₄×C₆₁	—	8	2	no	—
508	C₂×C₄×C₆₁	—	8	1	no	—
509	C₂×C₄×C₆₁	—	8	2	no	—
510	C₂×C₄×C₆₁	—	8	1	no	—
511	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
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	2	yes	—
516	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
518	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
520	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
521	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
522	C₈×C₆₁	—	2	1	no	—
523	C₈×C₆₁	—	2	1	no	—
524	C₈×C₆₁	—	2	1	no	—
525	C₈×C₆₁	—	2	1	no	—
526	C₈×C₆₁	—	2	2	no	—
527	C₈×C₆₁	—	2	2	no	—
528	#60927	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
529	C₂²×C₆₁	—	2	1	no	—
530	C₂²×C₆₁	—	2	1	no	—
531	C₂²×C₆₁	—	2	2	no	—
532	C₂²×C₆₁	—	2	2	no	—
533	C₂²×C₆₁	—	2	2	no	—
534	C₂²×C₆₁	—	4	1	no	—
535	C₂²×C₆₁	—	4	2	no	—
536	C₂²×C₆₁	—	4	1	no	—
537	C₂²×C₆₁	—	4	2	no	—
538	C₂²×C₆₁	—	4	1	no	—
539	C₂²×C₆₁	—	4	2	no	—
540	C₂²×C₆₁	—	16	2	no	—
541	C₂²×C₆₁	#537	1	2	yes	—
542	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
543	C₄×C₆₁	—	2	1	no	—
544	C₄×C₆₁	—	2	1	no	—
545	C₄×C₆₁	—	2	2	no	—
546	C₄×C₆₁	—	2	1	no	—
547	C₄×C₆₁	—	2	2	no	—
548	C₄×C₆₁	—	2	1	no	—
549	C₄×C₆₁	—	2	2	no	—
550	C₄×C₆₁	—	4	1	no	—
551	C₄×C₆₁	—	4	2	no	—
552	C₄×C₆₁	—	4	1	no	—
553	C₄×C₆₁	—	4	1	no	—
554	C₄×C₆₁	—	4	1	no	—
555	C₄×C₆₁	—	4	1	no	—
556	C₄×C₆₁	—	4	1	no	—
557	C₄×C₆₁	—	4	1	no	—
558	C₄×C₆₁	—	4	2	no	—
559	C₄×C₆₁	—	4	2	no	—
560	C₄×C₆₁	#537	1	2	yes	—
561	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
562	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
563	#3510	C₂×C₆₁	1	1	yes	characteristic, complemented
564	#3461	C₂×C₆₁	1	1	yes	characteristic, complemented
565	#3263	C₂×C₆₁	1	2	yes	complemented
566	#3262	C₂×C₆₁	1	2	yes	complemented
567	#3258	C₂×C₆₁	1	2	yes	complemented
568	#3258	C₂×C₆₁	1	2	yes	complemented
569	#3256	C₂×C₆₁	1	2	yes	complemented
570	#3252	C₂×C₆₁	1	2	yes	complemented
571	#3250	C₂×C₆₁	1	2	yes	complemented
572	#3248	C₂×C₆₁	1	2	yes	complemented
573	#3082	C₂×C₆₁	1	1	yes	characteristic, complemented
574	#3081	C₂×C₆₁	1	1	yes	characteristic, complemented
575	#3078	C₂×C₆₁	1	1	yes	characteristic, complemented
576	#3076	C₂×C₆₁	1	1	yes	characteristic, complemented
577	#3063	C₂×C₆₁	1	1	yes	characteristic, complemented
578	#3062	C₂×C₆₁	1	1	yes	characteristic
579	#3059	C₂×C₆₁	1	1	yes	characteristic, complemented
580	#3057	C₂×C₆₁	1	1	yes	characteristic, complemented
581	#3044	C₂×C₆₁	1	1	yes	characteristic, complemented
582	#3042	C₂×C₆₁	1	1	yes	characteristic, complemented
583	#3040	C₂×C₆₁	1	1	yes	characteristic, complemented
584	C₂×#464	C₂×C₆₁	1	1	yes	characteristic, complemented
585	#2906	C₂×C₆₁	1	1	yes	characteristic, complemented
586	C₂×C₆₁	—	2	2	no	—
587	C₂×C₆₁	—	4	2	no	—
588	C₂×C₆₁	—	8	1	no	—
589	C₂×C₆₁	—	8	2	no	—
590	C₂×C₆₁	C₂×#537	1	1	yes	characteristic
591	C₂×C₆₁	#3584	1	1	yes	characteristic
592	C₂×C₆₁	#3586	1	1	yes	characteristic
593	C₂×#137	C₂²×C₆₁	1	1	yes	characteristic
594	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	1	yes	characteristic
595	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
596	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
597	C₂×#131	C₂²×C₆₁	1	1	yes	characteristic
598	C₂×#131	C₂²×C₆₁	1	1	yes	characteristic
599	#559	—	2	1	no	—
600	#559	—	2	1	no	—
601	#556	—	2	1	no	—
602	#556	—	2	1	no	—
603	#551	—	2	2	no	—
604	#551	—	2	2	no	—
605	#544	C₂²×C₆₁	1	1	yes	characteristic
606	#542	—	2	1	no	—
607	#542	C₂²×C₆₁	1	2	yes	—
608	#542	C₂²×C₆₁	1	2	yes	—
609	#542	C₂²×C₆₁	1	2	yes	complemented
610	#541	—	2	1	no	—
611	#541	C₂²×C₆₁	1	2	yes	complemented
612	#539	—	2	2	no	—
613	#537	C₂²×C₆₁	1	1	yes	characteristic
614	#536	C₂²×C₆₁	1	1	yes	characteristic
615	#536	C₂²×C₆₁	1	1	yes	characteristic
616	#536	C₂²×C₆₁	1	1	yes	characteristic
617	#535	C₂²×C₆₁	1	1	yes	characteristic
618	#533	—	2	1	no	—
619	#533	C₂²×C₆₁	1	1	yes	characteristic
620	#533	C₂²×C₆₁	1	2	yes	complemented
621	#529	—	2	2	no	—
622	#529	—	2	1	no	—
623	#529	C₂²×C₆₁	1	2	yes	—
624	#529	C₂²×C₆₁	1	2	yes	—
625	#529	C₂²×C₆₁	1	2	yes	complemented
626	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
627	#519	C₂²×C₆₁	1	1	yes	characteristic
628	#518	C₂²×C₆₁	1	1	yes	characteristic
629	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
630	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
631	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
632	#479	C₂²×C₆₁	1	1	yes	characteristic, complemented
633	#479	C₂²×C₆₁	1	1	yes	characteristic, complemented
634	#479	C₂²×C₆₁	1	2	yes	complemented
635	#479	C₂²×C₆₁	1	2	yes	complemented
636	#479	C₂²×C₆₁	1	2	yes	complemented
637	#479	C₂²×C₆₁	1	2	yes	complemented
638	#478	C₂²×C₆₁	1	2	yes	—
639	#478	C₂²×C₆₁	1	2	yes	—
640	#478	C₂²×C₆₁	1	1	yes	characteristic, complemented
641	#478	C₂²×C₆₁	1	1	yes	characteristic, complemented
642	#477	C₂²×C₆₁	1	1	yes	characteristic, complemented
643	#477	C₂²×C₆₁	1	2	yes	complemented
644	#477	C₂²×C₆₁	1	2	yes	complemented
645	#476	C₂²×C₆₁	1	2	yes	—
646	#476	C₂²×C₆₁	1	1	yes	characteristic, complemented
647	#475	C₂²×C₆₁	1	1	yes	characteristic, complemented
648	#475	C₂²×C₆₁	1	2	yes	complemented
649	#475	C₂²×C₆₁	1	2	yes	complemented
650	#474	C₂²×C₆₁	1	2	yes	—
651	#474	C₂²×C₆₁	1	1	yes	characteristic, complemented
652	#470	C₂²×C₆₁	1	2	yes	complemented
653	#470	C₂²×C₆₁	1	2	yes	complemented
654	#470	C₂²×C₆₁	1	2	yes	complemented
655	#469	C₂²×C₆₁	1	2	yes	—
656	#468	C₂²×C₆₁	1	2	yes	—
657	#468	C₂²×C₆₁	1	2	yes	—
658	#468	C₂²×C₆₁	1	2	yes	—
659	#468	C₂²×C₆₁	1	2	yes	complemented
660	#467	C₂²×C₆₁	1	2	yes	complemented
661	#467	C₂²×C₆₁	1	2	yes	complemented
662	#467	C₂²×C₆₁	1	2	yes	complemented
663	#466	C₂²×C₆₁	1	2	yes	—
664	#465	C₂²×C₆₁	1	2	yes	—
665	#465	C₂²×C₆₁	1	2	yes	—
666	#465	C₂²×C₆₁	1	2	yes	—
667	#465	C₂²×C₆₁	1	2	yes	complemented
668	#464	C₂²×C₆₁	1	2	yes	—
669	#464	C₂²×C₆₁	1	2	yes	—
670	#464	C₂²×C₆₁	1	2	yes	—
671	#464	C₂²×C₆₁	1	2	yes	—
672	#464	C₂²×C₆₁	1	2	yes	—
673	#464	C₂²×C₆₁	1	2	yes	—
674	#464	C₂²×C₆₁	1	2	yes	complemented
675	#464	C₂²×C₆₁	1	2	yes	complemented
676	#463	C₂²×C₆₁	1	2	yes	—
677	#463	C₂²×C₆₁	1	2	yes	—
678	#463	C₂²×C₆₁	1	2	yes	—
679	#463	C₂²×C₆₁	1	2	yes	—
680	#462	C₂²×C₆₁	1	2	yes	complemented
681	#462	C₂²×C₆₁	1	2	yes	complemented
682	#461	C₂²×C₆₁	1	2	yes	—
683	#461	C₂²×C₆₁	1	2	yes	—
684	#428	C₂²×C₆₁	1	1	yes	characteristic
685	#428	C₂²×C₆₁	1	1	yes	characteristic
686	#427	C₂²×C₆₁	1	1	yes	characteristic
687	#427	C₂²×C₆₁	1	1	yes	characteristic
688	#424	C₂²×C₆₁	1	1	yes	characteristic
689	#424	C₂²×C₆₁	1	1	yes	characteristic
690	#424	C₂²×C₆₁	1	2	yes	complemented
691	#424	C₂²×C₆₁	1	2	yes	complemented
692	#423	C₂²×C₆₁	1	1	yes	characteristic
693	#423	C₂²×C₆₁	1	2	yes	complemented
694	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
695	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	complemented
696	#419	C₂²×C₆₁	1	1	yes	characteristic
697	#419	C₂²×C₆₁	1	1	yes	characteristic
698	#419	C₂²×C₆₁	1	1	yes	characteristic
699	#418	C₂²×C₆₁	1	1	yes	characteristic
700	#416	C₂²×C₆₁	1	1	yes	characteristic
701	#416	C₂²×C₆₁	1	1	yes	characteristic
702	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
703	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
704	C₆₁	#60927	1	1	yes	characteristic, direct product factor, Sylow
705	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
706	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
707	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
708	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
709	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
710	#137	—	4	2	no	—
711	AGL(1,ℤ/8)	—	4	2	no	—
712	C₂×Q₁₆	—	4	2	no	—
713	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
714	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
715	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
716	C₂×SD₁₆	—	4	2	no	—
717	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
718	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
719	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
720	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
721	C₂×D₈	C₂³×C₆₁	1	2	yes	—
722	#131	—	4	2	no	—
723	#131	—	4	2	no	—
724	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
725	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
726	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
727	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
728	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
729	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
730	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
731	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
732	C₄⋊Q₈	—	2	1	no	—
733	C₄⋊Q₈	—	2	1	no	—
734	C₄⋊Q₈	—	2	1	no	—
735	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
736	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
737	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
738	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
739	#127	—	2	1	no	—
740	#126	—	2	2	no	—
741	#126	—	2	2	no	—
742	#126	—	2	2	no	—
743	#126	—	2	2	no	—
744	#126	—	2	2	no	—
745	#126	—	2	2	no	—
746	#126	—	2	2	no	—
747	#126	—	2	2	no	—
748	#125	—	2	2	no	—
749	#125	—	2	1	no	—
750	#125	—	2	2	no	—
751	#125	—	2	2	no	—
752	#125	C₂³×C₆₁	1	1	yes	characteristic
753	#125	C₂³×C₆₁	1	1	yes	characteristic
754	#125	C₂³×C₆₁	1	2	yes	—
755	#124	—	2	1	no	—
756	#124	—	2	1	no	—
757	#124	—	2	1	no	—
758	#124	—	2	2	no	—
759	#124	—	2	2	no	—
760	#124	—	2	2	no	—
761	#124	—	2	1	no	—
762	#124	—	2	1	no	—
763	#124	C₂³×C₆₁	1	2	yes	—
764	#124	C₂³×C₆₁	1	2	yes	—
765	#124	C₂³×C₆₁	1	2	yes	—
766	#123	—	2	2	no	—
767	#123	—	2	2	no	—
768	#123	—	2	2	no	—
769	#123	—	2	2	no	—
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	C₂²⋊Q₈	—	2	1	no	—
776	C₂²⋊Q₈	—	2	1	no	—
777	C₂²⋊Q₈	—	2	1	no	—
778	C₂²⋊Q₈	—	2	2	no	—
779	C₂²⋊Q₈	—	2	1	no	—
780	C₂²⋊Q₈	—	2	1	no	—
781	C₂²⋊Q₈	—	2	2	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	—	2	2	no	—
785	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
786	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
787	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
788	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
789	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
790	#121	—	2	2	no	—
791	#121	—	2	1	no	—
792	#121	C₂³×C₆₁	1	2	yes	—
793	#121	C₂³×C₆₁	1	2	yes	—
794	#121	C₂³×C₆₁	1	2	yes	—
795	#120	—	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	2	no	—
801	C₄×Q₈	—	2	1	no	—
802	C₄×Q₈	—	2	1	no	—
803	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
804	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
805	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
806	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
807	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
808	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
809	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
810	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	2	no	—
814	C₄×D₄	—	2	2	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	D₄×C₆₁	1	2	yes	—
819	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
820	C₄×D₄	D₄×C₆₁	1	2	yes	—
821	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
822	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
823	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
824	C₄×D₄	C₂³×C₆₁	1	2	yes	—
825	C₄×D₄	C₂³×C₆₁	1	2	yes	—
826	#117	—	2	2	no	—
827	#117	—	2	2	no	—
828	#117	—	2	1	no	—
829	#117	—	2	2	no	—
830	#117	—	2	2	no	—
831	#117	—	2	2	no	—
832	#117	C₂³×C₆₁	1	1	yes	characteristic
833	#117	C₂³×C₆₁	1	1	yes	characteristic
834	#117	C₂³×C₆₁	1	1	yes	characteristic
835	#117	C₂³×C₆₁	1	1	yes	characteristic
836	#117	C₂³×C₆₁	1	2	yes	—
837	C₂×C₄⋊C₄	—	2	1	no	—
838	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
839	C₂×C₂²⋊C₄	—	2	1	no	—
840	C₂×C₂²⋊C₄	—	2	1	no	—
841	C₂×C₂²⋊C₄	—	2	2	no	—
842	C₂×C₄²	—	2	1	no	—
843	C₂×C₄²	—	2	1	no	—
844	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
845	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
846	#107	C₂³×C₆₁	1	1	yes	characteristic
847	#107	C₂³×C₆₁	1	1	yes	characteristic
848	#107	C₂³×C₆₁	1	1	yes	characteristic
849	#107	C₂³×C₆₁	1	1	yes	characteristic
850	#107	C₂³×C₆₁	1	2	yes	—
851	#107	C₂³×C₆₁	1	2	yes	—
852	#106	C₂³×C₆₁	1	1	yes	characteristic
853	#106	C₂³×C₆₁	1	1	yes	characteristic
854	#106	C₂³×C₆₁	1	1	yes	characteristic
855	#106	C₂³×C₆₁	1	1	yes	characteristic
856	#106	C₂³×C₆₁	1	2	yes	—
857	#106	C₂³×C₆₁	1	2	yes	—
858	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
859	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
860	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
861	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
862	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
863	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
864	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
865	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
866	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
867	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
868	#103	C₂³×C₆₁	1	2	yes	—
869	#103	C₂³×C₆₁	1	2	yes	—
870	#103	C₂³×C₆₁	1	1	yes	characteristic
871	#103	C₂³×C₆₁	1	1	yes	characteristic
872	#103	C₂³×C₆₁	1	1	yes	characteristic
873	#103	C₂³×C₆₁	1	1	yes	characteristic
874	#103	C₂³×C₆₁	1	2	yes	—
875	#103	C₂³×C₆₁	1	2	yes	—
876	#103	C₂³×C₆₁	1	2	yes	—
877	#103	C₂³×C₆₁	1	2	yes	—
878	#103	C₂³×C₆₁	1	2	yes	—
879	#103	C₂³×C₆₁	1	2	yes	—
880	#102	C₂³×C₆₁	1	2	yes	—
881	#102	C₂³×C₆₁	1	2	yes	—
882	#102	C₂³×C₆₁	1	1	yes	characteristic
883	#102	C₂³×C₆₁	1	1	yes	characteristic
884	#102	C₂³×C₆₁	1	1	yes	characteristic
885	#102	C₂³×C₆₁	1	1	yes	characteristic
886	#102	C₂³×C₆₁	1	2	yes	—
887	#102	C₂³×C₆₁	1	2	yes	—
888	C₂⁴	—	2	1	no	—
889	#41	—	2	2	no	—
890	#41	—	2	2	no	—
891	#41	—	2	2	no	—
892	#41	—	2	2	no	—
893	C₂×Q₈	—	2	1	no	—
894	C₂×Q₈	—	2	1	no	—
895	C₂×Q₈	—	2	1	no	—
896	C₂×Q₈	—	2	1	no	—
897	C₂×Q₈	—	2	2	no	—
898	C₂×Q₈	—	2	2	no	—
899	C₂×Q₈	—	2	2	no	—
900	C₂×Q₈	—	2	2	no	—
901	C₂×Q₈	—	2	2	no	—
902	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
903	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
904	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
905	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	2	2	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	2	no	—
910	C₂×D₄	—	2	1	no	—
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
914	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
915	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
916	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	1	no	—
919	C₂²×C₄	—	2	1	no	—
920	C₂²×C₄	—	2	1	no	—
921	C₂²×C₄	—	2	1	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	2	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
926	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
927	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
928	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
929	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
930	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
931	Q₁₆	—	4	2	no	—
932	Q₁₆	—	4	2	no	—
933	Q₁₆	—	4	2	no	—
934	SD₁₆	—	4	2	no	—
935	SD₁₆	—	4	2	no	—
936	SD₁₆	—	4	2	no	—
937	SD₁₆	—	4	2	no	—
938	D₈	—	4	2	no	—
939	M₁₆	—	2	2	no	—
940	M₁₆	—	2	2	no	—
941	M₁₆	—	4	2	no	—
942	M₁₆	—	4	2	no	—
943	C₂×C₈	—	2	2	no	—
944	C₂×C₈	—	2	2	no	—
945	C₂×C₈	—	4	2	no	—
946	C₂×C₈	—	4	2	no	—
947	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
948	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
949	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
950	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
951	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
952	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	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	1	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
977	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
978	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
979	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
980	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
981	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
982	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
983	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
984	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
985	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
986	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	1	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	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1009	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1010	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1011	C₄²	—	2	2	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	—	2	1	no	—
1014	C₄²	—	2	1	no	—
1015	C₄²	—	2	2	no	—
1016	C₄²	—	2	2	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	1	no	—
1020	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1021	C₄²	C₂×D₄×C₆₁	1	2	yes	—
1022	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1023	C₄²	C₂×D₄×C₆₁	1	2	yes	—
1024	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1025	C₄²	C₂⁴×C₆₁	1	2	yes	—
1026	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1027	C₂³	—	2	1	no	—
1028	C₂³	—	2	2	no	—
1029	C₂³	—	4	2	no	—
1030	C₂³	—	8	1	no	—
1031	C₂³	—	8	1	no	—
1032	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1033	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1034	Q₈	—	2	2	no	—
1035	Q₈	—	2	2	no	—
1036	Q₈	—	2	1	no	—
1037	Q₈	—	2	2	no	—
1038	Q₈	—	2	2	no	—
1039	Q₈	—	2	2	no	—
1040	Q₈	—	2	1	no	—
1041	Q₈	—	4	2	no	—
1042	Q₈	—	4	2	no	—
1043	Q₈	—	8	1	no	—
1044	Q₈	—	8	2	no	—
1045	Q₈	—	8	1	no	—
1046	D₄	—	2	4	no	—
1047	D₄	—	2	2	no	—
1048	D₄	—	2	1	no	—
1049	D₄	—	2	2	no	—
1050	D₄	—	2	2	no	—
1051	D₄	—	2	1	no	—
1052	D₄	—	4	2	no	—
1053	D₄	—	4	2	no	—
1054	D₄	—	8	2	no	—
1055	D₄	—	8	2	no	—
1056	D₄	—	8	2	no	—
1057	C₂×C₄	—	2	2	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	—	2	2	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	4	1	no	—
1070	C₂×C₄	—	4	2	no	—
1071	C₂×C₄	—	4	2	no	—
1072	C₂×C₄	—	4	1	no	—
1073	C₂×C₄	—	4	2	no	—
1074	C₂×C₄	—	4	2	no	—
1075	C₂×C₄	—	4	2	no	—
1076	C₂×C₄	—	4	2	no	—
1077	C₂×C₄	—	8	2	no	—
1078	C₂×C₄	—	8	1	no	—
1079	C₂×C₄	—	8	2	no	—
1080	C₂×C₄	—	8	1	no	—
1081	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1082	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1083	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1084	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1085	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1086	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1087	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1088	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1089	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
1090	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
1091	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1092	C₈	—	2	1	no	—
1093	C₈	—	2	1	no	—
1094	C₈	—	2	1	no	—
1095	C₈	—	2	1	no	—
1096	C₈	—	2	2	no	—
1097	C₈	—	2	2	no	—
1098	C₂²	—	2	1	no	—
1099	C₂²	—	2	1	no	—
1100	C₂²	—	2	2	no	—
1101	C₂²	—	2	2	no	—
1102	C₂²	—	2	2	no	—
1103	C₂²	—	4	1	no	—
1104	C₂²	—	4	2	no	—
1105	C₂²	—	4	1	no	—
1106	C₂²	—	4	2	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	—	4	2	no	—
1109	C₂²	—	16	2	no	—
1110	C₂²	C₆₁×#537	1	2	yes	—
1111	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1112	C₄	—	2	1	no	—
1113	C₄	—	2	1	no	—
1114	C₄	—	2	2	no	—
1115	C₄	—	2	1	no	—
1116	C₄	—	2	2	no	—
1117	C₄	—	2	1	no	—
1118	C₄	—	2	2	no	—
1119	C₄	—	4	1	no	—
1120	C₄	—	4	2	no	—
1121	C₄	—	4	1	no	—
1122	C₄	—	4	1	no	—
1123	C₄	—	4	1	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	1	no	—
1127	C₄	—	4	2	no	—
1128	C₄	—	4	2	no	—
1129	C₄	C₆₁×#537	1	2	yes	—
1130	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1131	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
1132	C₂	—	2	2	no	—
1133	C₂	—	4	2	no	—
1134	C₂	—	8	2	no	—
1135	C₂	—	8	1	no	—
1136	C₂	C₂×C₆₁×#537	1	1	yes	characteristic
1137	C₂	C₆₁×#3584	1	1	yes	characteristic
1138	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×#3062	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₄×#41×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3510	C₂	semidirect
2. C₆₁×#3461	C₂	semidirect
3. C₆₁×#3263	C₂	semidirect
4. C₆₁×#3262	C₂	semidirect
5. C₆₁×#3258	C₂	semidirect
6. C₆₁×#3258	C₂	semidirect
7. C₆₁×#3256	C₂	semidirect
8. C₆₁×#3252	C₂	semidirect
9. C₆₁×#3250	C₂	semidirect
10. C₆₁×#3248	C₂	semidirect
11. C₆₁×#3082	C₂	semidirect
12. C₆₁×#3081	C₂	semidirect
13. C₆₁×#3078	C₂	semidirect
14. C₆₁×#3076	C₂	semidirect
15. C₆₁×#3063	C₂	semidirect
17. C₆₁×#3059	C₂	semidirect
18. C₆₁×#3057	C₂	semidirect
19. C₆₁×#3044	C₂	semidirect
20. C₆₁×#3042	C₂	semidirect
21. C₆₁×#3040	C₂	semidirect
22. C₂×C₆₁×#464	C₂	semidirect
23. C₆₁×#2906	C₂	semidirect
40. C₆₁×#542	C₂²	semidirect
42. C₆₁×#541	C₂²	semidirect
51. C₆₁×#533	C₂²	semidirect
56. C₆₁×#529	C₂²	semidirect
63. C₆₁×#479	C₂²	semidirect
64. C₆₁×#479	C₂²	semidirect
65. C₆₁×#479	C₂²	semidirect
66. C₆₁×#479	C₂²	semidirect
67. C₆₁×#479	C₂²	semidirect
68. C₆₁×#479	C₂²	semidirect
71. C₆₁×#478	C₂²	semidirect
72. C₆₁×#478	C₂²	semidirect
73. C₆₁×#477	C₂²	semidirect
74. C₆₁×#477	C₂²	semidirect
75. C₆₁×#477	C₂²	semidirect
77. C₆₁×#476	C₂²	semidirect
78. C₆₁×#475	C₂²	semidirect
79. C₆₁×#475	C₂²	semidirect
80. C₆₁×#475	C₂²	semidirect
82. C₆₁×#474	C₂²	semidirect
83. C₆₁×#470	C₂²	semidirect
84. C₆₁×#470	C₂²	semidirect
85. C₆₁×#470	C₂²	semidirect
90. C₆₁×#468	C₂²	semidirect
91. C₆₁×#467	C₂²	semidirect
92. C₆₁×#467	C₂²	semidirect
93. C₆₁×#467	C₂²	semidirect
98. C₆₁×#465	C₂²	semidirect
105. C₆₁×#464	C₂²	semidirect
106. C₆₁×#464	C₂²	semidirect
111. C₆₁×#462	C₂²	semidirect
112. C₆₁×#462	C₂²	semidirect
121. C₆₁×#424	C₂²	semidirect
122. C₆₁×#424	C₂²	semidirect
124. C₆₁×#423	C₂²	semidirect
126. C₂×C₄⋊C₈×C₆₁	C₂²	semidirect
528. #60927	C₆₁	direct (N × H)
563. #3510	C₂×C₆₁	semidirect
564. #3461	C₂×C₆₁	semidirect
565. #3263	C₂×C₆₁	semidirect
566. #3262	C₂×C₆₁	semidirect
567. #3258	C₂×C₆₁	semidirect
568. #3258	C₂×C₆₁	semidirect
569. #3256	C₂×C₆₁	semidirect
570. #3252	C₂×C₆₁	semidirect
571. #3250	C₂×C₆₁	semidirect
572. #3248	C₂×C₆₁	semidirect
573. #3082	C₂×C₆₁	semidirect
574. #3081	C₂×C₆₁	semidirect
575. #3078	C₂×C₆₁	semidirect
576. #3076	C₂×C₆₁	semidirect
577. #3063	C₂×C₆₁	semidirect
579. #3059	C₂×C₆₁	semidirect
580. #3057	C₂×C₆₁	semidirect
581. #3044	C₂×C₆₁	semidirect
582. #3042	C₂×C₆₁	semidirect
583. #3040	C₂×C₆₁	semidirect
584. C₂×#464	C₂×C₆₁	semidirect
585. #2906	C₂×C₆₁	semidirect
609. #542	C₂²×C₆₁	semidirect
611. #541	C₂²×C₆₁	semidirect
620. #533	C₂²×C₆₁	semidirect
625. #529	C₂²×C₆₁	semidirect
632. #479	C₂²×C₆₁	semidirect
633. #479	C₂²×C₆₁	semidirect
634. #479	C₂²×C₆₁	semidirect
635. #479	C₂²×C₆₁	semidirect
636. #479	C₂²×C₆₁	semidirect
637. #479	C₂²×C₆₁	semidirect
640. #478	C₂²×C₆₁	semidirect
641. #478	C₂²×C₆₁	semidirect
642. #477	C₂²×C₆₁	semidirect
643. #477	C₂²×C₆₁	semidirect
644. #477	C₂²×C₆₁	semidirect
646. #476	C₂²×C₆₁	semidirect
647. #475	C₂²×C₆₁	semidirect
648. #475	C₂²×C₆₁	semidirect
649. #475	C₂²×C₆₁	semidirect
651. #474	C₂²×C₆₁	semidirect
652. #470	C₂²×C₆₁	semidirect
653. #470	C₂²×C₆₁	semidirect
654. #470	C₂²×C₆₁	semidirect
659. #468	C₂²×C₆₁	semidirect
660. #467	C₂²×C₆₁	semidirect
661. #467	C₂²×C₆₁	semidirect
662. #467	C₂²×C₆₁	semidirect
667. #465	C₂²×C₆₁	semidirect
674. #464	C₂²×C₆₁	semidirect
675. #464	C₂²×C₆₁	semidirect
680. #462	C₂²×C₆₁	semidirect
681. #462	C₂²×C₆₁	semidirect
690. #424	C₂²×C₆₁	semidirect
691. #424	C₂²×C₆₁	semidirect
693. #423	C₂²×C₆₁	semidirect
695. C₂×C₄⋊C₈	C₂²×C₆₁	semidirect
704. C₆₁	#60927	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×#3510	2
C₆₁×#3461	2
C₆₁×#3263	2
C₆₁×#3262	2
C₆₁×#3258	2
C₆₁×#3256	2
C₆₁×#3252	2
C₆₁×#3250	2
C₆₁×#3248	2
C₆₁×#3082	2
C₆₁×#3081	2
C₆₁×#3078	2
C₆₁×#3076	2
C₆₁×#3063	2
C₆₁×#3062	2
C₆₁×#3059	2
C₆₁×#3057	2
C₆₁×#3044	2
C₆₁×#3042	2
C₆₁×#3040	2
C₂×C₆₁×#464	2
C₆₁×#2906	2
#60927	61

Subgroups — C61×#60927 #29564360

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#60927 #29564360