Subgroups — C₆₁×#62152 #29565585

Order 15616.

1730 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3515	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3381	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3380	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3364	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3354	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#3352	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3351	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3331	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3330	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3323	C₂	1	2	yes	maximal, complemented
14	C₆₁×#3322	C₂	1	2	yes	maximal, complemented
15	C₆₁×#3256	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3252	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3232	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3231	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#3105	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₁×#3102	C₂	1	2	yes	maximal, complemented
21	C₆₁×#3080	C₂	1	2	yes	maximal, complemented
22	C₆₁×#3077	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₁×#2991	C₂	1	1	yes	maximal, characteristic, complemented
24	C₆₁×#557	C₂²	1	1	yes	characteristic, complemented
25	C₆₁×#556	C₂²	1	1	yes	characteristic
26	C₆₁×#555	C₂²	1	1	yes	characteristic
27	C₆₁×#554	C₂²	1	1	yes	characteristic
28	C₆₁×#554	C₂²	1	1	yes	characteristic, complemented
29	C₆₁×#554	C₂²	1	1	yes	characteristic, complemented
30	C₆₁×#553	—	2	1	no	—
31	C₆₁×#553	C₂²	1	2	yes	—
32	C₆₁×#552	—	2	1	no	—
33	C₆₁×#552	—	2	2	no	—
34	C₆₁×#552	—	2	1	no	—
35	C₆₁×#552	C₂²	1	2	yes	—
36	C₆₁×#552	C₂²	1	2	yes	—
37	C₆₁×#551	—	2	2	no	—
38	C₆₁×#547	—	2	1	no	—
39	C₆₁×#547	C₂²	1	1	yes	characteristic
40	C₆₁×#547	C₂²	1	1	yes	characteristic, complemented
41	C₆₁×#546	C₂²	1	2	yes	—
42	C₆₁×#541	—	2	1	no	—
43	C₆₁×#539	—	2	2	no	—
44	C₆₁×#533	C₂²	1	1	yes	characteristic
45	C₆₁×#533	C₂²	1	1	yes	characteristic
46	C₆₁×#529	—	2	2	no	—
47	C₆₁×#529	C₂²	1	1	yes	characteristic
48	C₆₁×#529	C₂²	1	2	yes	—
49	C₆₁×#529	C₂²	1	2	yes	complemented
50	C₂×#125×C₆₁	C₂²	1	2	yes	complemented
51	C₆₁×#525	—	2	1	no	—
52	C₆₁×#520	—	2	1	no	—
53	C₄×#41×C₆₁	C₂²	1	2	yes	—
54	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
56	C₂×#117×C₆₁	—	2	1	no	—
57	C₆₁×#500	C₂²	1	1	yes	characteristic, complemented
58	C₆₁×#499	C₂²	1	2	yes	complemented
59	C₆₁×#499	C₂²	1	2	yes	complemented
60	C₆₁×#498	C₂²	1	1	yes	characteristic, complemented
61	C₆₁×#488	C₂²	1	2	yes	—
62	C₆₁×#488	C₂²	1	2	yes	—
63	C₆₁×#487	C₂²	1	1	yes	characteristic, complemented
64	C₆₁×#487	C₂²	1	1	yes	characteristic, complemented
65	C₆₁×#485	C₂²	1	2	yes	—
66	C₆₁×#485	C₂²	1	2	yes	—
67	C₆₁×#485	C₂²	1	2	yes	complemented
68	C₆₁×#484	C₂²	1	1	yes	characteristic
69	C₆₁×#484	C₂²	1	2	yes	complemented
70	C₆₁×#483	C₂²	1	2	yes	complemented
71	C₆₁×#482	C₂²	1	2	yes	complemented
72	C₆₁×#481	C₂²	1	2	yes	—
73	C₆₁×#481	C₂²	1	1	yes	characteristic
74	C₆₁×#480	C₂²	1	2	yes	—
75	C₆₁×#479	C₂²	1	2	yes	complemented
76	C₆₁×#479	C₂²	1	2	yes	complemented
77	C₆₁×#479	C₂²	1	2	yes	complemented
78	C₆₁×#479	C₂²	1	2	yes	complemented
79	C₆₁×#479	C₂²	1	2	yes	complemented
80	C₆₁×#479	C₂²	1	2	yes	complemented
81	C₆₁×#478	C₂²	1	2	yes	—
82	C₆₁×#478	C₂²	1	2	yes	—
83	C₆₁×#478	C₂²	1	2	yes	—
84	C₆₁×#478	C₂²	1	2	yes	—
85	C₆₁×#478	C₂²	1	1	yes	characteristic
86	C₆₁×#478	C₂²	1	1	yes	characteristic
87	C₆₁×#478	C₂²	1	2	yes	complemented
88	C₆₁×#477	C₂²	1	1	yes	characteristic, complemented
89	C₆₁×#476	C₂²	1	1	yes	characteristic
90	C₆₁×#476	C₂²	1	1	yes	characteristic
91	C₆₁×#476	C₂²	1	1	yes	characteristic, complemented
92	C₆₁×#474	C₂²	1	1	yes	characteristic
93	C₆₁×#474	C₂²	1	1	yes	characteristic
94	C₆₁×#470	C₂²	1	2	yes	—
95	C₆₁×#470	C₂²	1	2	yes	complemented
96	C₆₁×#469	C₂²	1	2	yes	—
97	C₆₁×#468	C₂²	1	2	yes	—
98	C₆₁×#468	C₂²	1	2	yes	—
99	C₆₁×#468	C₂²	1	2	yes	complemented
100	C₆₁×#464	C₂²	1	2	yes	—
101	C₆₁×#464	C₂²	1	2	yes	complemented
102	C₆₁×#463	C₂²	1	2	yes	—
103	C₆₁×#463	C₂²	1	1	yes	characteristic
104	C₆₁×#463	C₂²	1	1	yes	characteristic
105	C₆₁×#462	C₂²	1	1	yes	characteristic, complemented
106	C₆₁×#461	C₂²	1	1	yes	characteristic, complemented
107	C₆₁×#452	C₂²	1	2	yes	—
108	C₆₁×#450	C₂²	1	1	yes	characteristic
109	C₆₁×#449	C₂²	1	2	yes	—
110	C₆₁×#447	C₂²	1	1	yes	characteristic
111	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
113	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	complemented
114	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
115	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
116	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
118	C₄×D₈×C₆₁	C₂²	1	2	yes	—
119	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
121	C₆₁×#436	C₂²	1	2	yes	—
122	C₆₁×#436	C₂²	1	2	yes	—
123	C₆₁×#436	C₂²	1	1	yes	characteristic, complemented
124	C₆₁×#436	C₂²	1	1	yes	characteristic, complemented
125	C₆₁×#431	C₂²	1	1	yes	characteristic
126	C₆₁×#431	C₂²	1	2	yes	complemented
127	C₆₁×#428	C₂²	1	2	yes	—
128	C₆₁×#428	C₂²	1	2	yes	complemented
129	C₆₁×#428	C₂²	1	2	yes	complemented
130	C₆₁×#423	C₂²	1	1	yes	characteristic
131	C₆₁×#423	C₂²	1	2	yes	complemented
132	C₆₁×#418	C₂²	1	2	yes	—
133	C₆₁×#417	C₂²	1	2	yes	—
134	C₆₁×#417	C₂²	1	2	yes	—
135	C₂×#41×C₆₁	—	2	1	no	—
136	C₂×#41×C₆₁	D₄	1	1	yes	characteristic
137	C₂×#41×C₆₁	C₂³	1	2	yes	—
138	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₆₁	—	2	1	no	—
140	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
141	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
142	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
144	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
145	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
146	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
147	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
148	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
149	C₄⋊Q₈×C₆₁	—	2	1	no	—
150	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
151	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
152	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
153	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
154	#126×C₆₁	—	2	2	no	—
155	#126×C₆₁	—	2	2	no	—
156	#126×C₆₁	—	2	2	no	—
157	#126×C₆₁	—	2	2	no	—
158	#126×C₆₁	—	2	2	no	—
159	#126×C₆₁	—	2	2	no	—
160	#126×C₆₁	—	2	1	no	—
161	#125×C₆₁	—	2	2	no	—
162	#125×C₆₁	—	2	2	no	—
163	#125×C₆₁	—	2	1	no	—
164	#125×C₆₁	—	2	2	no	—
165	#125×C₆₁	—	2	1	no	—
166	#125×C₆₁	—	2	2	no	—
167	#125×C₆₁	—	2	2	no	—
168	#125×C₆₁	C₂³	1	2	yes	—
169	#125×C₆₁	C₂³	1	2	yes	—
170	#125×C₆₁	C₂³	1	2	yes	—
171	#125×C₆₁	C₂³	1	2	yes	—
172	#125×C₆₁	C₂³	1	1	yes	characteristic
173	#124×C₆₁	—	2	2	no	—
174	#124×C₆₁	C₂³	1	2	yes	—
175	#124×C₆₁	C₂³	1	1	yes	characteristic
176	#123×C₆₁	—	2	2	no	—
177	#123×C₆₁	—	2	2	no	—
178	#123×C₆₁	—	2	1	no	—
179	#123×C₆₁	—	2	2	no	—
180	#123×C₆₁	—	2	2	no	—
181	#123×C₆₁	—	2	2	no	—
182	#123×C₆₁	—	2	2	no	—
183	#123×C₆₁	—	2	2	no	—
184	#123×C₆₁	—	2	2	no	—
185	C₂²⋊Q₈×C₆₁	—	2	1	no	—
186	C₂²⋊Q₈×C₆₁	—	2	1	no	—
187	C₂²⋊Q₈×C₆₁	—	2	1	no	—
188	C₂²⋊Q₈×C₆₁	—	2	1	no	—
189	C₂²⋊Q₈×C₆₁	—	2	1	no	—
190	C₂²⋊Q₈×C₆₁	—	2	1	no	—
191	C₂²⋊Q₈×C₆₁	—	2	2	no	—
192	C₂²⋊Q₈×C₆₁	—	2	1	no	—
193	C₂²⋊Q₈×C₆₁	—	2	2	no	—
194	C₂²⋊Q₈×C₆₁	—	2	2	no	—
195	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
196	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
197	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
198	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
199	#121×C₆₁	—	2	2	no	—
200	#121×C₆₁	—	2	1	no	—
201	#121×C₆₁	—	2	1	no	—
202	#121×C₆₁	—	2	2	no	—
203	#121×C₆₁	C₂³	1	2	yes	—
204	#121×C₆₁	C₂³	1	2	yes	—
205	#121×C₆₁	C₂³	1	1	yes	characteristic
206	#120×C₆₁	—	2	2	no	—
207	C₄×Q₈×C₆₁	—	2	1	no	—
208	C₄×Q₈×C₆₁	—	2	1	no	—
209	C₄×Q₈×C₆₁	—	2	1	no	—
210	C₄×Q₈×C₆₁	—	2	1	no	—
211	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
212	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
213	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
214	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
215	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
216	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
217	C₄×D₄×C₆₁	—	2	1	no	—
218	C₄×D₄×C₆₁	—	2	2	no	—
219	C₄×D₄×C₆₁	—	2	1	no	—
220	C₄×D₄×C₆₁	—	2	2	no	—
221	C₄×D₄×C₆₁	—	2	2	no	—
222	C₄×D₄×C₆₁	—	2	2	no	—
223	C₄×D₄×C₆₁	—	2	2	no	—
224	C₄×D₄×C₆₁	—	2	1	no	—
225	C₄×D₄×C₆₁	—	2	1	no	—
226	C₄×D₄×C₆₁	D₄	1	2	yes	—
227	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
228	C₄×D₄×C₆₁	C₂³	1	2	yes	—
229	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
230	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
231	C₄×D₄×C₆₁	C₂³	1	2	yes	—
232	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
233	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₆₁	C₂³	1	2	yes	—
236	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
237	#117×C₆₁	—	2	1	no	—
238	#117×C₆₁	—	2	1	no	—
239	#117×C₆₁	—	2	1	no	—
240	#117×C₆₁	—	2	2	no	—
241	#117×C₆₁	—	2	2	no	—
242	#117×C₆₁	—	2	1	no	—
243	#117×C₆₁	—	2	2	no	—
244	#117×C₆₁	—	2	2	no	—
245	#117×C₆₁	—	2	2	no	—
246	#117×C₆₁	D₄	1	1	yes	characteristic
247	#117×C₆₁	D₄	1	2	yes	—
248	#117×C₆₁	C₂³	1	2	yes	—
249	#117×C₆₁	C₂³	1	2	yes	—
250	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
251	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
252	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
253	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
254	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
255	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
258	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
259	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
260	C₂×C₄²×C₆₁	—	2	2	no	—
261	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
262	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
263	#107×C₆₁	C₂³	1	2	yes	—
264	#107×C₆₁	C₂³	1	2	yes	—
265	#107×C₆₁	C₂³	1	1	yes	characteristic
266	#107×C₆₁	C₂³	1	2	yes	—
267	#107×C₆₁	C₂³	1	2	yes	—
268	#107×C₆₁	C₂³	1	1	yes	characteristic
269	#107×C₆₁	C₂³	1	2	yes	—
270	#106×C₆₁	C₂³	1	2	yes	—
271	#106×C₆₁	C₂³	1	2	yes	—
272	#106×C₆₁	C₂³	1	1	yes	characteristic
273	#106×C₆₁	C₂³	1	2	yes	—
274	#106×C₆₁	C₂³	1	2	yes	—
275	#106×C₆₁	C₂³	1	1	yes	characteristic
276	#106×C₆₁	C₂³	1	2	yes	—
277	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
278	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
279	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
282	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
283	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
284	#103×C₆₁	C₂³	1	2	yes	—
285	#103×C₆₁	C₂³	1	2	yes	—
286	#103×C₆₁	C₂³	1	2	yes	—
287	#103×C₆₁	C₂³	1	2	yes	—
288	#103×C₆₁	C₂³	1	1	yes	characteristic
289	#103×C₆₁	C₂³	1	1	yes	characteristic
290	#103×C₆₁	C₂³	1	2	yes	—
291	#103×C₆₁	C₂³	1	2	yes	—
292	#103×C₆₁	C₂³	1	2	yes	—
293	#102×C₆₁	C₂³	1	1	yes	characteristic
294	#102×C₆₁	C₂³	1	1	yes	characteristic
295	#102×C₆₁	C₂³	1	2	yes	—
296	#102×C₆₁	C₂³	1	2	yes	—
297	#102×C₆₁	C₂³	1	2	yes	—
298	#102×C₆₁	C₂³	1	2	yes	—
299	#102×C₆₁	C₂³	1	1	yes	characteristic
300	#102×C₆₁	C₂³	1	1	yes	characteristic
301	#102×C₆₁	C₂³	1	1	yes	characteristic
302	#102×C₆₁	C₂³	1	2	yes	—
303	#102×C₆₁	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
305	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
306	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
308	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₆₁	C₂³	1	2	yes	—
311	C₄×C₈×C₆₁	C₂³	1	2	yes	—
312	C₂⁴×C₆₁	—	2	1	no	—
313	#41×C₆₁	—	2	4	no	—
314	#41×C₆₁	—	4	2	no	—
315	#41×C₆₁	—	4	2	no	—
316	#41×C₆₁	—	4	4	no	—
317	C₂×Q₈×C₆₁	—	2	1	no	—
318	C₂×Q₈×C₆₁	—	2	1	no	—
319	C₂×Q₈×C₆₁	—	2	1	no	—
320	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
321	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
322	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
323	C₂×D₄×C₆₁	—	2	2	no	—
324	C₂×D₄×C₆₁	—	2	2	no	—
325	C₂×D₄×C₆₁	—	2	2	no	—
326	C₂×D₄×C₆₁	—	2	2	no	—
327	C₂×D₄×C₆₁	—	2	1	no	—
328	C₂×D₄×C₆₁	—	2	1	no	—
329	C₂×D₄×C₆₁	—	4	1	no	—
330	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
331	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
332	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
333	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
334	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₆₁	—	2	1	no	—
336	C₂²×C₄×C₆₁	—	2	2	no	—
337	C₂²×C₄×C₆₁	—	2	2	no	—
338	C₂²×C₄×C₆₁	—	2	1	no	—
339	C₂²×C₄×C₆₁	—	2	2	no	—
340	C₂²×C₄×C₆₁	—	2	1	no	—
341	C₂²×C₄×C₆₁	—	2	1	no	—
342	C₂²×C₄×C₆₁	—	2	1	no	—
343	C₂²×C₄×C₆₁	—	2	1	no	—
344	C₂²×C₄×C₆₁	—	2	2	no	—
345	C₂²×C₄×C₆₁	—	2	2	no	—
346	C₂²×C₄×C₆₁	—	4	4	no	—
347	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
349	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
350	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
351	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
352	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
353	Q₁₆×C₆₁	—	4	2	no	—
354	SD₁₆×C₆₁	—	2	2	no	—
355	SD₁₆×C₆₁	—	4	2	no	—
356	SD₁₆×C₆₁	—	4	1	no	—
357	D₈×C₆₁	—	2	2	no	—
358	D₈×C₆₁	—	4	1	no	—
359	M₁₆×C₆₁	—	4	2	no	—
360	M₁₆×C₆₁	—	4	2	no	—
361	M₁₆×C₆₁	—	4	2	no	—
362	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
363	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
365	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
366	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
367	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
368	C₄⋊C₄×C₆₁	—	2	2	no	—
369	C₄⋊C₄×C₆₁	—	2	1	no	—
370	C₄⋊C₄×C₆₁	—	2	1	no	—
371	C₄⋊C₄×C₆₁	—	2	1	no	—
372	C₄⋊C₄×C₆₁	—	2	1	no	—
373	C₄⋊C₄×C₆₁	—	2	2	no	—
374	C₄⋊C₄×C₆₁	—	2	2	no	—
375	C₄⋊C₄×C₆₁	—	2	2	no	—
376	C₄⋊C₄×C₆₁	—	2	1	no	—
377	C₄⋊C₄×C₆₁	—	2	2	no	—
378	C₄⋊C₄×C₆₁	—	2	2	no	—
379	C₄⋊C₄×C₆₁	—	2	2	no	—
380	C₄⋊C₄×C₆₁	—	2	2	no	—
381	C₄⋊C₄×C₆₁	—	2	1	no	—
382	C₄⋊C₄×C₆₁	—	2	2	no	—
383	C₄⋊C₄×C₆₁	—	2	2	no	—
384	C₄⋊C₄×C₆₁	—	2	1	no	—
385	C₄⋊C₄×C₆₁	—	2	2	no	—
386	C₄⋊C₄×C₆₁	—	2	2	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	1	no	—
393	C₄⋊C₄×C₆₁	—	2	2	no	—
394	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
395	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
396	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
399	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
401	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
402	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
405	C₂²⋊C₄×C₆₁	—	2	2	no	—
406	C₂²⋊C₄×C₆₁	—	2	2	no	—
407	C₂²⋊C₄×C₆₁	—	2	2	no	—
408	C₂²⋊C₄×C₆₁	—	2	2	no	—
409	C₂²⋊C₄×C₆₁	—	2	2	no	—
410	C₂²⋊C₄×C₆₁	—	2	1	no	—
411	C₂²⋊C₄×C₆₁	—	2	1	no	—
412	C₂²⋊C₄×C₆₁	—	2	2	no	—
413	C₂²⋊C₄×C₆₁	—	2	2	no	—
414	C₂²⋊C₄×C₆₁	—	2	1	no	—
415	C₂²⋊C₄×C₆₁	—	2	1	no	—
416	C₂²⋊C₄×C₆₁	—	2	1	no	—
417	C₂²⋊C₄×C₆₁	—	2	1	no	—
418	C₂²⋊C₄×C₆₁	—	2	1	no	—
419	C₂²⋊C₄×C₆₁	—	2	1	no	—
420	C₂²⋊C₄×C₆₁	—	2	2	no	—
421	C₂²⋊C₄×C₆₁	—	2	2	no	—
422	C₂²⋊C₄×C₆₁	—	2	2	no	—
423	C₂²⋊C₄×C₆₁	—	2	2	no	—
424	C₂²⋊C₄×C₆₁	—	2	1	no	—
425	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
426	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
427	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
428	C₄²×C₆₁	—	2	2	no	—
429	C₄²×C₆₁	—	2	2	no	—
430	C₄²×C₆₁	—	2	2	no	—
431	C₄²×C₆₁	—	2	2	no	—
432	C₄²×C₆₁	—	2	2	no	—
433	C₄²×C₆₁	—	2	1	no	—
434	C₄²×C₆₁	C₂×D₄	1	2	yes	—
435	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
436	C₄²×C₆₁	C₂×D₄	1	2	yes	—
437	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
438	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
439	C₄²×C₆₁	C₂⁴	1	2	yes	—
440	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
441	C₂³×C₆₁	—	2	1	no	—
442	C₂³×C₆₁	—	2	1	no	—
443	C₂³×C₆₁	—	2	1	no	—
444	C₂³×C₆₁	—	4	2	no	—
445	C₂³×C₆₁	—	4	2	no	—
446	C₂³×C₆₁	—	8	1	no	—
447	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
448	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
449	Q₈×C₆₁	—	2	2	no	—
450	Q₈×C₆₁	—	2	1	no	—
451	Q₈×C₆₁	—	2	2	no	—
452	Q₈×C₆₁	—	2	1	no	—
453	Q₈×C₆₁	—	2	2	no	—
454	Q₈×C₆₁	—	4	2	no	—
455	Q₈×C₆₁	—	8	1	no	—
456	Q₈×C₆₁	—	8	1	no	—
457	D₄×C₆₁	—	2	2	no	—
458	D₄×C₆₁	—	2	1	no	—
459	D₄×C₆₁	—	2	1	no	—
460	D₄×C₆₁	—	2	1	no	—
461	D₄×C₆₁	—	2	1	no	—
462	D₄×C₆₁	—	2	1	no	—
463	D₄×C₆₁	—	4	2	no	—
464	D₄×C₆₁	—	4	2	no	—
465	D₄×C₆₁	—	4	4	no	—
466	D₄×C₆₁	—	4	4	no	—
467	D₄×C₆₁	—	8	1	no	—
468	D₄×C₆₁	—	8	2	no	—
469	D₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
470	C₂×C₄×C₆₁	—	2	2	no	—
471	C₂×C₄×C₆₁	—	2	1	no	—
472	C₂×C₄×C₆₁	—	2	2	no	—
473	C₂×C₄×C₆₁	—	2	1	no	—
474	C₂×C₄×C₆₁	—	2	2	no	—
475	C₂×C₄×C₆₁	—	2	1	no	—
476	C₂×C₄×C₆₁	—	2	1	no	—
477	C₂×C₄×C₆₁	—	2	2	no	—
478	C₂×C₄×C₆₁	—	2	2	no	—
479	C₂×C₄×C₆₁	—	2	2	no	—
480	C₂×C₄×C₆₁	—	2	2	no	—
481	C₂×C₄×C₆₁	—	2	1	no	—
482	C₂×C₄×C₆₁	—	2	1	no	—
483	C₂×C₄×C₆₁	—	2	1	no	—
484	C₂×C₄×C₆₁	—	4	2	no	—
485	C₂×C₄×C₆₁	—	4	1	no	—
486	C₂×C₄×C₆₁	—	4	2	no	—
487	C₂×C₄×C₆₁	—	4	4	no	—
488	C₂×C₄×C₆₁	—	4	2	no	—
489	C₂×C₄×C₆₁	—	4	2	no	—
490	C₂×C₄×C₆₁	—	4	2	no	—
491	C₂×C₄×C₆₁	—	4	4	no	—
492	C₂×C₄×C₆₁	—	4	2	no	—
493	C₂×C₄×C₆₁	—	4	2	no	—
494	C₂×C₄×C₆₁	—	4	2	no	—
495	C₂×C₄×C₆₁	—	8	2	no	—
496	C₂×C₄×C₆₁	—	8	2	no	—
497	C₂×C₄×C₆₁	—	8	2	no	—
498	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
501	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
502	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
505	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
507	C₈×C₆₁	—	2	1	no	—
508	C₈×C₆₁	—	2	1	no	—
509	C₈×C₆₁	—	2	1	no	—
510	C₈×C₆₁	—	2	1	no	—
511	C₈×C₆₁	—	2	2	no	—
512	C₈×C₆₁	—	2	2	no	—
513	#62152	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
514	C₂²×C₆₁	—	2	2	no	—
515	C₂²×C₆₁	—	2	1	no	—
516	C₂²×C₆₁	—	2	2	no	—
517	C₂²×C₆₁	—	2	1	no	—
518	C₂²×C₆₁	—	2	2	no	—
519	C₂²×C₆₁	—	2	1	no	—
520	C₂²×C₆₁	—	2	2	no	—
521	C₂²×C₆₁	—	4	1	no	—
522	C₂²×C₆₁	—	4	1	no	—
523	C₂²×C₆₁	—	4	1	no	—
524	C₂²×C₆₁	—	4	1	no	—
525	C₂²×C₆₁	—	4	1	no	—
526	C₂²×C₆₁	—	4	1	no	—
527	C₂²×C₆₁	—	4	1	no	—
528	C₂²×C₆₁	—	4	1	no	—
529	C₂²×C₆₁	—	8	4	no	—
530	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
531	C₄×C₆₁	—	2	1	no	—
532	C₄×C₆₁	—	2	2	no	—
533	C₄×C₆₁	—	2	1	no	—
534	C₄×C₆₁	—	2	2	no	—
535	C₄×C₆₁	—	2	1	no	—
536	C₄×C₆₁	—	2	1	no	—
537	C₄×C₆₁	—	2	2	no	—
538	C₄×C₆₁	—	4	1	no	—
539	C₄×C₆₁	—	4	2	no	—
540	C₄×C₆₁	—	4	2	no	—
541	C₄×C₆₁	—	4	2	no	—
542	C₄×C₆₁	—	4	1	no	—
543	C₄×C₆₁	—	4	1	no	—
544	C₄×C₆₁	—	4	1	no	—
545	C₄×C₆₁	—	4	1	no	—
546	C₄×C₆₁	—	4	2	no	—
547	C₄×C₆₁	#575	1	2	yes	—
548	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
549	C₄×C₆₁	#585	1	1	yes	characteristic
550	#3515	C₂×C₆₁	1	1	yes	characteristic, complemented
551	#3475	C₂×C₆₁	1	1	yes	characteristic, complemented
552	#3381	C₂×C₆₁	1	1	yes	characteristic, complemented
553	#3380	C₂×C₆₁	1	1	yes	characteristic, complemented
554	#3364	C₂×C₆₁	1	1	yes	characteristic, complemented
555	#3360	C₂×C₆₁	1	1	yes	characteristic, complemented
556	#3357	C₂×C₆₁	1	1	yes	characteristic, complemented
557	#3354	C₂×C₆₁	1	1	yes	characteristic, complemented
558	#3352	C₂×C₆₁	1	2	yes	complemented
559	#3351	C₂×C₆₁	1	2	yes	complemented
560	#3331	C₂×C₆₁	1	1	yes	characteristic, complemented
561	#3330	C₂×C₆₁	1	1	yes	characteristic, complemented
562	#3323	C₂×C₆₁	1	2	yes	complemented
563	#3322	C₂×C₆₁	1	2	yes	complemented
564	#3256	C₂×C₆₁	1	2	yes	complemented
565	#3252	C₂×C₆₁	1	1	yes	characteristic, complemented
566	#3232	C₂×C₆₁	1	2	yes	complemented
567	#3231	C₂×C₆₁	1	1	yes	characteristic, complemented
568	#3105	C₂×C₆₁	1	1	yes	characteristic, complemented
569	#3102	C₂×C₆₁	1	2	yes	complemented
570	#3080	C₂×C₆₁	1	2	yes	complemented
571	#3077	C₂×C₆₁	1	1	yes	characteristic, complemented
572	#2991	C₂×C₆₁	1	1	yes	characteristic, complemented
573	C₂×C₆₁	—	4	2	no	—
574	C₂×C₆₁	—	4	1	no	—
575	C₂×C₆₁	—	4	2	no	—
576	C₂×C₆₁	—	8	1	no	—
577	C₂×C₆₁	—	8	1	no	—
578	C₂×C₆₁	#3489	1	1	yes	characteristic
579	C₂×C₆₁	C₂×#575	1	1	yes	characteristic
580	C₂×C₆₁	#3584	1	1	yes	characteristic
581	#557	C₂²×C₆₁	1	1	yes	characteristic, complemented
582	#556	C₂²×C₆₁	1	1	yes	characteristic
583	#555	C₂²×C₆₁	1	1	yes	characteristic
584	#554	C₂²×C₆₁	1	1	yes	characteristic
585	#554	C₂²×C₆₁	1	1	yes	characteristic, complemented
586	#554	C₂²×C₆₁	1	1	yes	characteristic, complemented
587	#553	—	2	1	no	—
588	#553	C₂²×C₆₁	1	2	yes	—
589	#552	—	2	1	no	—
590	#552	—	2	2	no	—
591	#552	—	2	1	no	—
592	#552	C₂²×C₆₁	1	2	yes	—
593	#552	C₂²×C₆₁	1	2	yes	—
594	#551	—	2	2	no	—
595	#547	—	2	1	no	—
596	#547	C₂²×C₆₁	1	1	yes	characteristic
597	#547	C₂²×C₆₁	1	1	yes	characteristic, complemented
598	#546	C₂²×C₆₁	1	2	yes	—
599	#541	—	2	1	no	—
600	#539	—	2	2	no	—
601	#533	C₂²×C₆₁	1	1	yes	characteristic
602	#533	C₂²×C₆₁	1	1	yes	characteristic
603	#529	—	2	2	no	—
604	#529	C₂²×C₆₁	1	1	yes	characteristic
605	#529	C₂²×C₆₁	1	2	yes	—
606	#529	C₂²×C₆₁	1	2	yes	complemented
607	C₂×#125	C₂²×C₆₁	1	2	yes	complemented
608	#525	—	2	1	no	—
609	#520	—	2	1	no	—
610	C₄×#41	C₂²×C₆₁	1	2	yes	—
611	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
612	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
613	C₂×#117	—	2	1	no	—
614	#500	C₂²×C₆₁	1	1	yes	characteristic, complemented
615	#499	C₂²×C₆₁	1	2	yes	complemented
616	#499	C₂²×C₆₁	1	2	yes	complemented
617	#498	C₂²×C₆₁	1	1	yes	characteristic, complemented
618	#488	C₂²×C₆₁	1	2	yes	—
619	#488	C₂²×C₆₁	1	2	yes	—
620	#487	C₂²×C₆₁	1	1	yes	characteristic, complemented
621	#487	C₂²×C₆₁	1	1	yes	characteristic, complemented
622	#485	C₂²×C₆₁	1	2	yes	—
623	#485	C₂²×C₆₁	1	2	yes	—
624	#485	C₂²×C₆₁	1	2	yes	complemented
625	#484	C₂²×C₆₁	1	1	yes	characteristic
626	#484	C₂²×C₆₁	1	2	yes	complemented
627	#483	C₂²×C₆₁	1	2	yes	complemented
628	#482	C₂²×C₆₁	1	2	yes	complemented
629	#481	C₂²×C₆₁	1	1	yes	characteristic
630	#481	C₂²×C₆₁	1	2	yes	—
631	#480	C₂²×C₆₁	1	2	yes	—
632	#479	C₂²×C₆₁	1	2	yes	complemented
633	#479	C₂²×C₆₁	1	2	yes	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
641	#478	C₂²×C₆₁	1	2	yes	—
642	#478	C₂²×C₆₁	1	2	yes	—
643	#478	C₂²×C₆₁	1	1	yes	characteristic
644	#478	C₂²×C₆₁	1	2	yes	complemented
645	#477	C₂²×C₆₁	1	1	yes	characteristic, complemented
646	#476	C₂²×C₆₁	1	1	yes	characteristic
647	#476	C₂²×C₆₁	1	1	yes	characteristic
648	#476	C₂²×C₆₁	1	1	yes	characteristic, complemented
649	#474	C₂²×C₆₁	1	1	yes	characteristic
650	#474	C₂²×C₆₁	1	1	yes	characteristic
651	#470	C₂²×C₆₁	1	2	yes	—
652	#470	C₂²×C₆₁	1	2	yes	complemented
653	#469	C₂²×C₆₁	1	2	yes	—
654	#468	C₂²×C₆₁	1	2	yes	—
655	#468	C₂²×C₆₁	1	2	yes	—
656	#468	C₂²×C₆₁	1	2	yes	complemented
657	#464	C₂²×C₆₁	1	2	yes	—
658	#464	C₂²×C₆₁	1	2	yes	complemented
659	#463	C₂²×C₆₁	1	1	yes	characteristic
660	#463	C₂²×C₆₁	1	2	yes	—
661	#463	C₂²×C₆₁	1	1	yes	characteristic
662	#462	C₂²×C₆₁	1	1	yes	characteristic, complemented
663	#461	C₂²×C₆₁	1	1	yes	characteristic, complemented
664	#452	C₂²×C₆₁	1	2	yes	—
665	#450	C₂²×C₆₁	1	1	yes	characteristic
666	#449	C₂²×C₆₁	1	2	yes	—
667	#447	C₂²×C₆₁	1	1	yes	characteristic
668	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
669	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
670	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	complemented
671	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
672	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
673	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
674	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
675	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
676	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
677	C₄×D₈	C₂²×C₆₁	1	2	yes	—
678	#436	C₂²×C₆₁	1	2	yes	—
679	#436	C₂²×C₆₁	1	2	yes	—
680	#436	C₂²×C₆₁	1	1	yes	characteristic, complemented
681	#436	C₂²×C₆₁	1	1	yes	characteristic, complemented
682	#431	C₂²×C₆₁	1	1	yes	characteristic
683	#431	C₂²×C₆₁	1	2	yes	complemented
684	#428	C₂²×C₆₁	1	2	yes	—
685	#428	C₂²×C₆₁	1	2	yes	complemented
686	#428	C₂²×C₆₁	1	2	yes	complemented
687	#423	C₂²×C₆₁	1	1	yes	characteristic
688	#423	C₂²×C₆₁	1	2	yes	complemented
689	#418	C₂²×C₆₁	1	2	yes	—
690	#417	C₂²×C₆₁	1	2	yes	—
691	#417	C₂²×C₆₁	1	2	yes	—
692	C₆₁	#62152	1	1	yes	characteristic, direct product factor, Sylow
693	C₂×#41	—	2	1	no	—
694	C₂×#41	D₄×C₆₁	1	1	yes	characteristic
695	C₂×#41	C₂³×C₆₁	1	2	yes	—
696	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
697	C₂³×C₄	—	2	1	no	—
698	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
699	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
700	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
701	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
702	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
703	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
704	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
705	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
706	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
707	C₄⋊Q₈	—	2	1	no	—
708	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
709	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
710	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
711	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
712	#126	—	2	2	no	—
713	#126	—	2	2	no	—
714	#126	—	2	2	no	—
715	#126	—	2	2	no	—
716	#126	—	2	2	no	—
717	#126	—	2	1	no	—
718	#126	—	2	2	no	—
719	#125	—	2	2	no	—
720	#125	—	2	2	no	—
721	#125	—	2	2	no	—
722	#125	—	2	1	no	—
723	#125	—	2	2	no	—
724	#125	—	2	2	no	—
725	#125	—	2	1	no	—
726	#125	C₂³×C₆₁	1	1	yes	characteristic
727	#125	C₂³×C₆₁	1	2	yes	—
728	#125	C₂³×C₆₁	1	2	yes	—
729	#125	C₂³×C₆₁	1	2	yes	—
730	#125	C₂³×C₆₁	1	2	yes	—
731	#124	—	2	2	no	—
732	#124	C₂³×C₆₁	1	1	yes	characteristic
733	#124	C₂³×C₆₁	1	2	yes	—
734	#123	—	2	2	no	—
735	#123	—	2	2	no	—
736	#123	—	2	1	no	—
737	#123	—	2	2	no	—
738	#123	—	2	2	no	—
739	#123	—	2	2	no	—
740	#123	—	2	2	no	—
741	#123	—	2	2	no	—
742	#123	—	2	2	no	—
743	C₂²⋊Q₈	—	2	1	no	—
744	C₂²⋊Q₈	—	2	1	no	—
745	C₂²⋊Q₈	—	2	1	no	—
746	C₂²⋊Q₈	—	2	1	no	—
747	C₂²⋊Q₈	—	2	1	no	—
748	C₂²⋊Q₈	—	2	1	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	1	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
754	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
755	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
756	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
757	#121	—	2	1	no	—
758	#121	—	2	1	no	—
759	#121	—	2	2	no	—
760	#121	—	2	2	no	—
761	#121	C₂³×C₆₁	1	2	yes	—
762	#121	C₂³×C₆₁	1	1	yes	characteristic
763	#121	C₂³×C₆₁	1	2	yes	—
764	#120	—	2	2	no	—
765	C₄×Q₈	—	2	1	no	—
766	C₄×Q₈	—	2	1	no	—
767	C₄×Q₈	—	2	1	no	—
768	C₄×Q₈	—	2	1	no	—
769	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
770	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
771	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
772	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
773	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
774	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
775	C₄×D₄	—	2	1	no	—
776	C₄×D₄	—	2	2	no	—
777	C₄×D₄	—	2	2	no	—
778	C₄×D₄	—	2	2	no	—
779	C₄×D₄	—	2	2	no	—
780	C₄×D₄	—	2	1	no	—
781	C₄×D₄	—	2	2	no	—
782	C₄×D₄	—	2	1	no	—
783	C₄×D₄	—	2	1	no	—
784	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
785	C₄×D₄	D₄×C₆₁	1	2	yes	—
786	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
787	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
788	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
789	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
790	C₄×D₄	C₂³×C₆₁	1	2	yes	—
791	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
792	C₄×D₄	C₂³×C₆₁	1	2	yes	—
793	C₄×D₄	C₂³×C₆₁	1	2	yes	—
794	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
795	#117	—	2	1	no	—
796	#117	—	2	1	no	—
797	#117	—	2	1	no	—
798	#117	—	2	2	no	—
799	#117	—	2	2	no	—
800	#117	—	2	2	no	—
801	#117	—	2	2	no	—
802	#117	—	2	1	no	—
803	#117	—	2	2	no	—
804	#117	D₄×C₆₁	1	1	yes	characteristic
805	#117	D₄×C₆₁	1	2	yes	—
806	#117	C₂³×C₆₁	1	2	yes	—
807	#117	C₂³×C₆₁	1	2	yes	—
808	C₂×C₄⋊C₄	—	2	2	no	—
809	C₂×C₄⋊C₄	—	2	2	no	—
810	C₂×C₄⋊C₄	—	2	1	no	—
811	C₂×C₄⋊C₄	—	2	1	no	—
812	C₂×C₄⋊C₄	—	2	1	no	—
813	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
814	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
815	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
816	C₂×C₂²⋊C₄	—	2	1	no	—
817	C₂×C₂²⋊C₄	—	2	2	no	—
818	C₂×C₄²	—	2	2	no	—
819	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
820	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
821	#107	C₂³×C₆₁	1	2	yes	—
822	#107	C₂³×C₆₁	1	2	yes	—
823	#107	C₂³×C₆₁	1	1	yes	characteristic
824	#107	C₂³×C₆₁	1	2	yes	—
825	#107	C₂³×C₆₁	1	2	yes	—
826	#107	C₂³×C₆₁	1	1	yes	characteristic
827	#107	C₂³×C₆₁	1	2	yes	—
828	#106	C₂³×C₆₁	1	2	yes	—
829	#106	C₂³×C₆₁	1	2	yes	—
830	#106	C₂³×C₆₁	1	1	yes	characteristic
831	#106	C₂³×C₆₁	1	2	yes	—
832	#106	C₂³×C₆₁	1	2	yes	—
833	#106	C₂³×C₆₁	1	1	yes	characteristic
834	#106	C₂³×C₆₁	1	2	yes	—
835	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
836	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
837	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
838	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
839	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
840	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
841	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
842	#103	C₂³×C₆₁	1	2	yes	—
843	#103	C₂³×C₆₁	1	2	yes	—
844	#103	C₂³×C₆₁	1	2	yes	—
845	#103	C₂³×C₆₁	1	2	yes	—
846	#103	C₂³×C₆₁	1	1	yes	characteristic
847	#103	C₂³×C₆₁	1	1	yes	characteristic
848	#103	C₂³×C₆₁	1	2	yes	—
849	#103	C₂³×C₆₁	1	2	yes	—
850	#103	C₂³×C₆₁	1	2	yes	—
851	#102	C₂³×C₆₁	1	1	yes	characteristic
852	#102	C₂³×C₆₁	1	1	yes	characteristic
853	#102	C₂³×C₆₁	1	2	yes	—
854	#102	C₂³×C₆₁	1	2	yes	—
855	#102	C₂³×C₆₁	1	2	yes	—
856	#102	C₂³×C₆₁	1	2	yes	—
857	#102	C₂³×C₆₁	1	1	yes	characteristic
858	#102	C₂³×C₆₁	1	1	yes	characteristic
859	#102	C₂³×C₆₁	1	1	yes	characteristic
860	#102	C₂³×C₆₁	1	2	yes	—
861	#102	C₂³×C₆₁	1	1	yes	characteristic
862	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
863	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
864	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
865	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
866	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
867	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
868	C₄×C₈	C₂³×C₆₁	1	2	yes	—
869	C₄×C₈	C₂³×C₆₁	1	2	yes	—
870	C₂⁴	—	2	1	no	—
871	#41	—	2	4	no	—
872	#41	—	4	2	no	—
873	#41	—	4	2	no	—
874	#41	—	4	4	no	—
875	C₂×Q₈	—	2	1	no	—
876	C₂×Q₈	—	2	1	no	—
877	C₂×Q₈	—	2	1	no	—
878	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
879	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
880	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
881	C₂×D₄	—	2	2	no	—
882	C₂×D₄	—	2	2	no	—
883	C₂×D₄	—	2	2	no	—
884	C₂×D₄	—	2	2	no	—
885	C₂×D₄	—	2	1	no	—
886	C₂×D₄	—	2	1	no	—
887	C₂×D₄	—	4	1	no	—
888	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
889	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
890	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
891	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
892	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
893	C₂²×C₄	—	2	1	no	—
894	C₂²×C₄	—	2	2	no	—
895	C₂²×C₄	—	2	2	no	—
896	C₂²×C₄	—	2	1	no	—
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	2	1	no	—
899	C₂²×C₄	—	2	1	no	—
900	C₂²×C₄	—	2	1	no	—
901	C₂²×C₄	—	2	1	no	—
902	C₂²×C₄	—	2	2	no	—
903	C₂²×C₄	—	2	2	no	—
904	C₂²×C₄	—	4	4	no	—
905	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
906	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
907	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
908	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
909	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
910	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
911	Q₁₆	—	4	2	no	—
912	SD₁₆	—	2	2	no	—
913	SD₁₆	—	4	2	no	—
914	SD₁₆	—	4	1	no	—
915	D₈	—	2	2	no	—
916	D₈	—	4	1	no	—
917	M₁₆	—	4	2	no	—
918	M₁₆	—	4	2	no	—
919	M₁₆	—	4	2	no	—
920	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
921	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
922	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
923	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
924	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
925	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
953	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
954	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
955	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
956	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
957	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
958	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
959	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
960	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
961	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
962	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	1	no	—
969	C₂²⋊C₄	—	2	1	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	1	no	—
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
984	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
985	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
986	C₄²	—	2	2	no	—
987	C₄²	—	2	2	no	—
988	C₄²	—	2	2	no	—
989	C₄²	—	2	2	no	—
990	C₄²	—	2	2	no	—
991	C₄²	—	2	1	no	—
992	C₄²	C₂×D₄×C₆₁	1	2	yes	—
993	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
994	C₄²	C₂×D₄×C₆₁	1	2	yes	—
995	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
996	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
997	C₄²	C₂⁴×C₆₁	1	2	yes	—
998	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
999	C₂³	—	2	1	no	—
1000	C₂³	—	2	1	no	—
1001	C₂³	—	2	1	no	—
1002	C₂³	—	4	2	no	—
1003	C₂³	—	4	2	no	—
1004	C₂³	—	8	1	no	—
1005	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1006	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1007	Q₈	—	2	2	no	—
1008	Q₈	—	2	1	no	—
1009	Q₈	—	2	2	no	—
1010	Q₈	—	2	1	no	—
1011	Q₈	—	2	2	no	—
1012	Q₈	—	4	2	no	—
1013	Q₈	—	8	1	no	—
1014	Q₈	—	8	1	no	—
1015	D₄	—	2	2	no	—
1016	D₄	—	2	1	no	—
1017	D₄	—	2	1	no	—
1018	D₄	—	2	1	no	—
1019	D₄	—	2	1	no	—
1020	D₄	—	2	1	no	—
1021	D₄	—	4	2	no	—
1022	D₄	—	4	2	no	—
1023	D₄	—	4	4	no	—
1024	D₄	—	4	4	no	—
1025	D₄	—	8	1	no	—
1026	D₄	—	8	2	no	—
1027	D₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	2	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	4	2	no	—
1043	C₂×C₄	—	4	1	no	—
1044	C₂×C₄	—	4	2	no	—
1045	C₂×C₄	—	4	4	no	—
1046	C₂×C₄	—	4	2	no	—
1047	C₂×C₄	—	4	2	no	—
1048	C₂×C₄	—	4	2	no	—
1049	C₂×C₄	—	4	4	no	—
1050	C₂×C₄	—	4	2	no	—
1051	C₂×C₄	—	4	2	no	—
1052	C₂×C₄	—	4	2	no	—
1053	C₂×C₄	—	8	2	no	—
1054	C₂×C₄	—	8	2	no	—
1055	C₂×C₄	—	8	2	no	—
1056	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1057	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1058	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1059	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1060	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1061	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1062	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1063	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1064	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1065	C₈	—	2	1	no	—
1066	C₈	—	2	1	no	—
1067	C₈	—	2	1	no	—
1068	C₈	—	2	1	no	—
1069	C₈	—	2	2	no	—
1070	C₈	—	2	2	no	—
1071	C₂²	—	2	1	no	—
1072	C₂²	—	2	2	no	—
1073	C₂²	—	2	2	no	—
1074	C₂²	—	2	1	no	—
1075	C₂²	—	2	2	no	—
1076	C₂²	—	2	1	no	—
1077	C₂²	—	2	2	no	—
1078	C₂²	—	4	1	no	—
1079	C₂²	—	4	1	no	—
1080	C₂²	—	4	1	no	—
1081	C₂²	—	4	1	no	—
1082	C₂²	—	4	1	no	—
1083	C₂²	—	4	1	no	—
1084	C₂²	—	4	1	no	—
1085	C₂²	—	4	1	no	—
1086	C₂²	—	8	4	no	—
1087	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1088	C₄	—	2	1	no	—
1089	C₄	—	2	2	no	—
1090	C₄	—	2	1	no	—
1091	C₄	—	2	2	no	—
1092	C₄	—	2	1	no	—
1093	C₄	—	2	2	no	—
1094	C₄	—	2	1	no	—
1095	C₄	—	4	1	no	—
1096	C₄	—	4	1	no	—
1097	C₄	—	4	1	no	—
1098	C₄	—	4	2	no	—
1099	C₄	—	4	1	no	—
1100	C₄	—	4	2	no	—
1101	C₄	—	4	2	no	—
1102	C₄	—	4	2	no	—
1103	C₄	—	4	1	no	—
1104	C₄	C₆₁×#575	1	2	yes	—
1105	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
1106	C₄	C₆₁×#585	1	1	yes	characteristic
1107	C₂	—	4	1	no	—
1108	C₂	—	4	2	no	—
1109	C₂	—	4	2	no	—
1110	C₂	—	8	1	no	—
1111	C₂	—	8	1	no	—
1112	C₂	C₆₁×#3489	1	1	yes	characteristic
1113	C₂	C₂×C₆₁×#575	1	1	yes	characteristic
1114	C₂	C₆₁×#3584	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 ◁ C₄×#41×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3515	C₂	semidirect
2. C₆₁×#3475	C₂	semidirect
3. C₆₁×#3381	C₂	semidirect
4. C₆₁×#3380	C₂	semidirect
5. C₆₁×#3364	C₂	semidirect
6. C₆₁×#3360	C₂	semidirect
7. C₆₁×#3357	C₂	semidirect
8. C₆₁×#3354	C₂	semidirect
9. C₆₁×#3352	C₂	semidirect
10. C₆₁×#3351	C₂	semidirect
11. C₆₁×#3331	C₂	semidirect
12. C₆₁×#3330	C₂	semidirect
13. C₆₁×#3323	C₂	semidirect
14. C₆₁×#3322	C₂	semidirect
15. C₆₁×#3256	C₂	semidirect
16. C₆₁×#3252	C₂	semidirect
17. C₆₁×#3232	C₂	semidirect
18. C₆₁×#3231	C₂	semidirect
19. C₆₁×#3105	C₂	semidirect
20. C₆₁×#3102	C₂	semidirect
21. C₆₁×#3080	C₂	semidirect
22. C₆₁×#3077	C₂	semidirect
23. C₆₁×#2991	C₂	semidirect
24. C₆₁×#557	C₂²	semidirect
28. C₆₁×#554	C₂²	semidirect
29. C₆₁×#554	C₂²	semidirect
40. C₆₁×#547	C₂²	semidirect
49. C₆₁×#529	C₂²	semidirect
50. C₂×#125×C₆₁	C₂²	semidirect
57. C₆₁×#500	C₂²	semidirect
58. C₆₁×#499	C₂²	semidirect
59. C₆₁×#499	C₂²	semidirect
60. C₆₁×#498	C₂²	semidirect
63. C₆₁×#487	C₂²	semidirect
64. C₆₁×#487	C₂²	semidirect
67. C₆₁×#485	C₂²	semidirect
69. C₆₁×#484	C₂²	semidirect
70. C₆₁×#483	C₂²	semidirect
71. C₆₁×#482	C₂²	semidirect
75. C₆₁×#479	C₂²	semidirect
76. C₆₁×#479	C₂²	semidirect
77. C₆₁×#479	C₂²	semidirect
78. C₆₁×#479	C₂²	semidirect
79. C₆₁×#479	C₂²	semidirect
80. C₆₁×#479	C₂²	semidirect
87. C₆₁×#478	C₂²	semidirect
88. C₆₁×#477	C₂²	semidirect
91. C₆₁×#476	C₂²	semidirect
95. C₆₁×#470	C₂²	semidirect
99. C₆₁×#468	C₂²	semidirect
101. C₆₁×#464	C₂²	semidirect
105. C₆₁×#462	C₂²	semidirect
106. C₆₁×#461	C₂²	semidirect
111. C₈×Q₈×C₆₁	C₂²	semidirect
112. C₈×Q₈×C₆₁	C₂²	semidirect
113. C₄×Q₁₆×C₆₁	C₂²	semidirect
117. C₄×SD₁₆×C₆₁	C₂²	semidirect
123. C₆₁×#436	C₂²	semidirect
124. C₆₁×#436	C₂²	semidirect
126. C₆₁×#431	C₂²	semidirect
128. C₆₁×#428	C₂²	semidirect
129. C₆₁×#428	C₂²	semidirect
131. C₆₁×#423	C₂²	semidirect
513. #62152	C₆₁	direct (N × H)
550. #3515	C₂×C₆₁	semidirect
551. #3475	C₂×C₆₁	semidirect
552. #3381	C₂×C₆₁	semidirect
553. #3380	C₂×C₆₁	semidirect
554. #3364	C₂×C₆₁	semidirect
555. #3360	C₂×C₆₁	semidirect
556. #3357	C₂×C₆₁	semidirect
557. #3354	C₂×C₆₁	semidirect
558. #3352	C₂×C₆₁	semidirect
559. #3351	C₂×C₆₁	semidirect
560. #3331	C₂×C₆₁	semidirect
561. #3330	C₂×C₆₁	semidirect
562. #3323	C₂×C₆₁	semidirect
563. #3322	C₂×C₆₁	semidirect
564. #3256	C₂×C₆₁	semidirect
565. #3252	C₂×C₆₁	semidirect
566. #3232	C₂×C₆₁	semidirect
567. #3231	C₂×C₆₁	semidirect
568. #3105	C₂×C₆₁	semidirect
569. #3102	C₂×C₆₁	semidirect
570. #3080	C₂×C₆₁	semidirect
571. #3077	C₂×C₆₁	semidirect
572. #2991	C₂×C₆₁	semidirect
581. #557	C₂²×C₆₁	semidirect
585. #554	C₂²×C₆₁	semidirect
586. #554	C₂²×C₆₁	semidirect
597. #547	C₂²×C₆₁	semidirect
606. #529	C₂²×C₆₁	semidirect
607. C₂×#125	C₂²×C₆₁	semidirect
614. #500	C₂²×C₆₁	semidirect
615. #499	C₂²×C₆₁	semidirect
616. #499	C₂²×C₆₁	semidirect
617. #498	C₂²×C₆₁	semidirect
620. #487	C₂²×C₆₁	semidirect
621. #487	C₂²×C₆₁	semidirect
624. #485	C₂²×C₆₁	semidirect
626. #484	C₂²×C₆₁	semidirect
627. #483	C₂²×C₆₁	semidirect
628. #482	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
644. #478	C₂²×C₆₁	semidirect
645. #477	C₂²×C₆₁	semidirect
648. #476	C₂²×C₆₁	semidirect
652. #470	C₂²×C₆₁	semidirect
656. #468	C₂²×C₆₁	semidirect
658. #464	C₂²×C₆₁	semidirect
662. #462	C₂²×C₆₁	semidirect
663. #461	C₂²×C₆₁	semidirect
668. C₈×Q₈	C₂²×C₆₁	semidirect
669. C₈×Q₈	C₂²×C₆₁	semidirect
670. C₄×Q₁₆	C₂²×C₆₁	semidirect
674. C₄×SD₁₆	C₂²×C₆₁	semidirect
680. #436	C₂²×C₆₁	semidirect
681. #436	C₂²×C₆₁	semidirect
683. #431	C₂²×C₆₁	semidirect
685. #428	C₂²×C₆₁	semidirect
686. #428	C₂²×C₆₁	semidirect
688. #423	C₂²×C₆₁	semidirect
692. C₆₁	#62152	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×#3515	2
C₆₁×#3475	2
C₆₁×#3381	2
C₆₁×#3380	2
C₆₁×#3364	2
C₆₁×#3360	2
C₆₁×#3357	2
C₆₁×#3354	2
C₆₁×#3352	2
C₆₁×#3351	2
C₆₁×#3331	2
C₆₁×#3330	2
C₆₁×#3323	2
C₆₁×#3322	2
C₆₁×#3256	2
C₆₁×#3252	2
C₆₁×#3232	2
C₆₁×#3231	2
C₆₁×#3105	2
C₆₁×#3102	2
C₆₁×#3080	2
C₆₁×#3077	2
C₆₁×#2991	2
#62152	61

Subgroups — C61×#62152 #29565585

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62152 #29565585