Subgroups — C₆₁×#61272 #29564705

Order 15616.

1866 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3492	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3354	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3351	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3348	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3346	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3345	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3345	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3339	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3335	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3163	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3099	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3096	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3091	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₆₁×#481	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#3084	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3081	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#3062	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#3055	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₁×#2946	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#2933	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₁×#2912	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₆₁×#428	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
26	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
27	C₆₁×#555	C₂²	1	2	yes	—
28	C₆₁×#554	—	2	1	no	—
29	C₆₁×#554	C₂²	1	2	yes	complemented
30	C₆₁×#553	—	2	1	no	—
31	C₆₁×#553	C₂²	1	2	yes	—
32	C₆₁×#553	C₂²	1	2	yes	—
33	C₆₁×#553	C₂²	1	2	yes	complemented
34	C₆₁×#552	—	2	1	no	—
35	C₆₁×#552	C₂²	1	2	yes	complemented
36	C₆₁×#551	—	2	2	no	—
37	C₆₁×#547	—	2	1	no	—
38	C₆₁×#547	C₂²	1	2	yes	—
39	C₆₁×#547	C₂²	1	2	yes	complemented
40	C₆₁×#546	—	2	2	no	—
41	C₆₁×#544	C₂²	1	1	yes	characteristic
42	C₆₁×#544	C₂²	1	1	yes	characteristic
43	C₆₁×#542	—	2	1	no	—
44	C₆₁×#540	—	2	1	no	—
45	C₆₁×#539	—	2	2	no	—
46	C₆₁×#537	C₂²	1	1	yes	characteristic
47	C₆₁×#535	C₂²	1	1	yes	characteristic
48	C₆₁×#532	—	2	1	no	—
49	C₆₁×#529	—	2	1	no	—
50	C₆₁×#525	—	2	2	no	—
51	C₆₁×#525	C₂²	1	1	yes	characteristic
52	C₆₁×#525	C₂²	1	1	yes	characteristic
53	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
54	C₆₁×#520	C₂²	1	1	yes	characteristic
55	C₆₁×#520	C₂²	1	1	yes	characteristic
56	C₆₁×#520	C₂²	1	1	yes	characteristic
57	C₆₁×#518	C₂²	1	1	yes	characteristic
58	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
59	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
60	C₆₁×#501	C₂²	1	2	yes	complemented
61	C₆₁×#501	C₂²	1	2	yes	complemented
62	C₆₁×#499	C₂²	1	2	yes	complemented
63	C₆₁×#498	C₂²	1	2	yes	complemented
64	C₆₁×#485	C₂²	1	2	yes	complemented
65	C₆₁×#485	C₂²	1	1	yes	characteristic, complemented
66	C₆₁×#485	C₂²	1	1	yes	characteristic, complemented
67	C₆₁×#484	C₂²	1	1	yes	characteristic, complemented
68	C₆₁×#483	C₂²	1	1	yes	characteristic, complemented
69	C₆₁×#483	C₂²	1	2	yes	complemented
70	C₆₁×#482	C₂²	1	2	yes	complemented
71	C₆₁×#482	C₂²	1	2	yes	complemented
72	C₆₁×#482	C₂²	1	1	yes	characteristic, complemented
73	C₆₁×#482	C₂²	1	2	yes	complemented
74	C₆₁×#482	C₂²	1	1	yes	characteristic, complemented
75	C₆₁×#481	C₂²	1	2	yes	—
76	C₆₁×#481	C₂²	1	2	yes	—
77	C₆₁×#481	C₂²	1	2	yes	—
78	C₆₁×#481	C₂²	1	2	yes	—
79	C₆₁×#481	C₂²	1	2	yes	complemented
80	C₆₁×#481	C₂²	1	1	yes	characteristic, complemented
81	C₆₁×#481	C₂²	1	2	yes	complemented
82	C₆₁×#480	C₂²	1	1	yes	characteristic, complemented
83	C₆₁×#480	C₂²	1	2	yes	complemented
84	C₆₁×#479	C₂²	1	2	yes	complemented
85	C₆₁×#478	C₂²	1	2	yes	complemented
86	C₆₁×#478	C₂²	1	2	yes	complemented
87	C₆₁×#478	C₂²	1	2	yes	complemented
88	C₆₁×#476	C₂²	1	2	yes	complemented
89	C₆₁×#476	C₂²	1	2	yes	complemented
90	C₆₁×#475	C₂²	1	2	yes	complemented
91	C₆₁×#474	C₂²	1	2	yes	complemented
92	C₆₁×#469	C₂²	1	2	yes	—
93	C₆₁×#469	C₂²	1	2	yes	complemented
94	C₆₁×#468	C₂²	1	2	yes	—
95	C₆₁×#468	C₂²	1	2	yes	complemented
96	C₆₁×#466	C₂²	1	2	yes	—
97	C₆₁×#466	C₂²	1	2	yes	complemented
98	C₆₁×#465	C₂²	1	2	yes	—
99	C₆₁×#465	C₂²	1	2	yes	complemented
100	C₆₁×#442	C₂²	1	2	yes	complemented
101	C₆₁×#440	C₂²	1	2	yes	complemented
102	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
103	C₄×D₈×C₆₁	C₂²	1	2	yes	complemented
104	C₆₁×#436	C₂²	1	2	yes	complemented
105	C₆₁×#435	C₂²	1	2	yes	complemented
106	C₆₁×#435	C₂²	1	2	yes	complemented
107	C₈×D₄×C₆₁	C₂²	1	2	yes	complemented
108	C₆₁×#428	C₂²	1	1	yes	characteristic
109	C₆₁×#428	C₂²	1	1	yes	characteristic
110	C₆₁×#428	C₂²	1	1	yes	characteristic
111	C₆₁×#428	C₂²	1	1	yes	characteristic
112	C₆₁×#428	C₂²	1	1	yes	characteristic
113	C₆₁×#428	C₂²	1	2	yes	complemented
114	C₆₁×#428	C₂²	1	2	yes	complemented
115	C₆₁×#428	C₂²	1	2	yes	complemented
116	C₆₁×#428	C₂²	1	2	yes	complemented
117	C₆₁×#427	C₂²	1	1	yes	characteristic
118	C₆₁×#427	C₂²	1	1	yes	characteristic
119	C₆₁×#427	C₂²	1	2	yes	complemented
120	C₂×#107×C₆₁	C₂²	1	2	yes	complemented
121	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
122	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
123	C₂×#106×C₆₁	C₂²	1	2	yes	complemented
124	C₂×#106×C₆₁	C₂²	1	2	yes	complemented
125	C₆₁×#424	C₂²	1	1	yes	characteristic
126	C₆₁×#418	C₂²	1	1	yes	characteristic
127	C₆₁×#417	C₂²	1	1	yes	characteristic
128	C₆₁×#416	C₂²	1	1	yes	characteristic
129	C₆₁×#416	C₂²	1	1	yes	characteristic
130	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
131	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
132	C₆₁×#408	C₂²	1	1	yes	characteristic
133	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
134	C₆₁×#405	C₂²	1	1	yes	characteristic
135	C₂×#41×C₆₁	—	2	2	no	—
136	C₂×#41×C₆₁	—	2	2	no	—
137	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
138	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
139	C₂²×D₄×C₆₁	—	2	1	no	—
140	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₆₁	—	2	1	no	—
142	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
143	AGL(1,ℤ/8)×C₆₁	—	2	4	no	—
144	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
145	C₂×D₈×C₆₁	C₂³	1	2	yes	—
146	#131×C₆₁	—	2	4	no	—
147	C₂×M₁₆×C₆₁	—	2	4	no	—
148	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
149	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
150	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
151	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
153	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
154	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
155	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
156	C₄⋊Q₈×C₆₁	—	2	1	no	—
157	C₄⋊Q₈×C₆₁	—	2	1	no	—
158	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
159	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
160	#127×C₆₁	—	2	1	no	—
161	#126×C₆₁	—	2	2	no	—
162	#126×C₆₁	—	2	2	no	—
163	#126×C₆₁	—	2	2	no	—
164	#126×C₆₁	—	2	2	no	—
165	#125×C₆₁	—	2	2	no	—
166	#125×C₆₁	—	2	2	no	—
167	#125×C₆₁	—	2	1	no	—
168	#125×C₆₁	—	2	1	no	—
169	#125×C₆₁	C₂³	1	2	yes	—
170	#125×C₆₁	C₂³	1	2	yes	—
171	#124×C₆₁	—	2	1	no	—
172	#124×C₆₁	—	2	2	no	—
173	#124×C₆₁	—	2	2	no	—
174	#123×C₆₁	—	2	2	no	—
175	#123×C₆₁	—	2	1	no	—
176	#123×C₆₁	—	2	2	no	—
177	#123×C₆₁	—	2	2	no	—
178	#123×C₆₁	—	2	2	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	D₄	1	2	yes	—
184	C₂²⋊Q₈×C₆₁	—	2	1	no	—
185	C₂²⋊Q₈×C₆₁	—	2	2	no	—
186	C₂²⋊Q₈×C₆₁	—	2	2	no	—
187	C₂²⋊Q₈×C₆₁	—	2	2	no	—
188	C₂²⋊Q₈×C₆₁	—	2	2	no	—
189	C₂²⋊Q₈×C₆₁	—	2	2	no	—
190	C₂²⋊Q₈×C₆₁	—	2	2	no	—
191	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
192	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
193	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
194	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
195	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
196	#121×C₆₁	—	2	2	no	—
197	#121×C₆₁	—	2	2	no	—
198	#121×C₆₁	—	2	1	no	—
199	#121×C₆₁	—	2	2	no	—
200	#121×C₆₁	—	2	2	no	—
201	#121×C₆₁	—	2	2	no	—
202	#121×C₆₁	—	2	1	no	—
203	#121×C₆₁	—	2	1	no	—
204	#121×C₆₁	D₄	1	1	yes	characteristic
205	#121×C₆₁	D₄	1	1	yes	characteristic
206	#121×C₆₁	C₂³	1	2	yes	—
207	#121×C₆₁	C₂³	1	2	yes	—
208	#121×C₆₁	C₂³	1	2	yes	—
209	#121×C₆₁	C₂³	1	2	yes	—
210	#121×C₆₁	C₂³	1	1	yes	characteristic
211	#121×C₆₁	C₂³	1	2	yes	—
212	#121×C₆₁	C₂³	1	1	yes	characteristic
213	#120×C₆₁	—	2	1	no	—
214	#120×C₆₁	—	2	2	no	—
215	#120×C₆₁	D₄	1	2	yes	—
216	C₄×Q₈×C₆₁	—	2	1	no	—
217	C₄×Q₈×C₆₁	—	2	1	no	—
218	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
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	1	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	—	2	1	no	—
227	C₄×D₄×C₆₁	—	2	1	no	—
228	C₄×D₄×C₆₁	—	2	2	no	—
229	C₄×D₄×C₆₁	—	2	2	no	—
230	C₄×D₄×C₆₁	—	2	2	no	—
231	C₄×D₄×C₆₁	—	2	2	no	—
232	C₄×D₄×C₆₁	C₂³	1	2	yes	—
233	C₄×D₄×C₆₁	C₂³	1	2	yes	—
234	C₄×D₄×C₆₁	C₂³	1	2	yes	—
235	C₄×D₄×C₆₁	C₂³	1	2	yes	—
236	C₄×D₄×C₆₁	C₂³	1	2	yes	—
237	#117×C₆₁	—	2	1	no	—
238	#117×C₆₁	—	2	1	no	—
239	#117×C₆₁	—	2	2	no	—
240	#117×C₆₁	—	2	1	no	—
241	#117×C₆₁	—	2	2	no	—
242	#117×C₆₁	C₂³	1	1	yes	characteristic
243	#117×C₆₁	C₂³	1	1	yes	characteristic
244	#117×C₆₁	C₂³	1	2	yes	—
245	#117×C₆₁	C₂³	1	1	yes	characteristic
246	#117×C₆₁	C₂³	1	2	yes	—
247	#117×C₆₁	C₂³	1	1	yes	characteristic
248	#117×C₆₁	C₂³	1	1	yes	characteristic
249	#117×C₆₁	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
251	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
252	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
253	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
254	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
264	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
265	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
266	C₂×C₄²×C₆₁	—	2	1	no	—
267	#107×C₆₁	C₂³	1	2	yes	—
268	#107×C₆₁	C₂³	1	2	yes	—
269	#107×C₆₁	C₂³	1	2	yes	—
270	#107×C₆₁	C₂³	1	2	yes	—
271	#107×C₆₁	C₂³	1	1	yes	characteristic
272	#107×C₆₁	C₂³	1	1	yes	characteristic
273	#107×C₆₁	C₂³	1	1	yes	characteristic
274	#107×C₆₁	C₂³	1	1	yes	characteristic
275	#107×C₆₁	C₂³	1	2	yes	—
276	#106×C₆₁	C₂³	1	2	yes	—
277	#106×C₆₁	C₂³	1	2	yes	—
278	#106×C₆₁	C₂³	1	2	yes	—
279	#106×C₆₁	C₂³	1	2	yes	—
280	#106×C₆₁	C₂³	1	1	yes	characteristic
281	#106×C₆₁	C₂³	1	2	yes	—
282	#106×C₆₁	C₂³	1	2	yes	—
283	#106×C₆₁	C₂³	1	2	yes	—
284	#106×C₆₁	C₂³	1	2	yes	—
285	#106×C₆₁	C₂³	1	2	yes	—
286	#106×C₆₁	C₂³	1	1	yes	characteristic
287	#106×C₆₁	C₂³	1	1	yes	characteristic
288	#106×C₆₁	C₂³	1	1	yes	characteristic
289	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
290	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
291	#103×C₆₁	C₂³	1	1	yes	characteristic
292	#103×C₆₁	C₂³	1	1	yes	characteristic
293	#103×C₆₁	C₂³	1	1	yes	characteristic
294	#103×C₆₁	C₂³	1	1	yes	characteristic
295	#103×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	2	yes	—
300	#102×C₆₁	C₂³	1	1	yes	characteristic
301	#102×C₆₁	C₂³	1	1	yes	characteristic
302	#102×C₆₁	C₂³	1	1	yes	characteristic
303	#102×C₆₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
310	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
311	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
312	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
313	#97×C₆₁	C₂³	1	2	yes	—
314	C₄×C₈×C₆₁	C₂³	1	2	yes	—
315	C₂⁴×C₆₁	—	2	1	no	—
316	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
317	#41×C₆₁	—	2	2	no	—
318	#41×C₆₁	—	2	2	no	—
319	#41×C₆₁	—	2	2	no	—
320	#41×C₆₁	—	2	2	no	—
321	#41×C₆₁	—	8	4	no	—
322	#41×C₆₁	—	8	4	no	—
323	C₂×Q₈×C₆₁	—	2	2	no	—
324	C₂×Q₈×C₆₁	—	2	2	no	—
325	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
327	C₂×D₄×C₆₁	—	2	1	no	—
328	C₂×D₄×C₆₁	—	2	1	no	—
329	C₂×D₄×C₆₁	—	2	1	no	—
330	C₂×D₄×C₆₁	—	2	2	no	—
331	C₂×D₄×C₆₁	—	2	2	no	—
332	C₂×D₄×C₆₁	—	2	2	no	—
333	C₂×D₄×C₆₁	—	2	2	no	—
334	C₂×D₄×C₆₁	—	2	2	no	—
335	C₂×D₄×C₆₁	—	2	1	no	—
336	C₂×D₄×C₆₁	—	2	2	no	—
337	C₂×D₄×C₆₁	—	2	2	no	—
338	C₂×D₄×C₆₁	—	8	2	no	—
339	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
340	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
341	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
342	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
343	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
344	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
345	C₂²×C₄×C₆₁	—	2	2	no	—
346	C₂²×C₄×C₆₁	—	2	2	no	—
347	C₂²×C₄×C₆₁	—	2	1	no	—
348	C₂²×C₄×C₆₁	—	2	2	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	2	no	—
353	C₂²×C₄×C₆₁	—	2	1	no	—
354	C₂²×C₄×C₆₁	—	2	2	no	—
355	C₂²×C₄×C₆₁	—	2	2	no	—
356	C₂²×C₄×C₆₁	—	2	1	no	—
357	C₂²×C₄×C₆₁	—	2	2	no	—
358	C₂²×C₄×C₆₁	—	2	2	no	—
359	C₂²×C₄×C₆₁	—	2	2	no	—
360	C₂²×C₄×C₆₁	—	8	2	no	—
361	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
362	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
366	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
368	SD₁₆×C₆₁	—	2	4	no	—
369	D₈×C₆₁	—	2	4	no	—
370	M₁₆×C₆₁	—	2	2	no	—
371	M₁₆×C₆₁	—	2	4	no	—
372	M₁₆×C₆₁	—	2	4	no	—
373	M₁₆×C₆₁	#41	1	4	yes	complemented
374	C₂×C₈×C₆₁	—	2	2	no	—
375	C₂×C₈×C₆₁	—	2	2	no	—
376	C₂×C₈×C₆₁	—	2	4	no	—
377	C₂×C₈×C₆₁	—	2	4	no	—
378	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
379	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
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	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
384	C₄⋊C₄×C₆₁	—	2	1	no	—
385	C₄⋊C₄×C₆₁	—	2	1	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	1	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	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	2	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	1	no	—
403	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
404	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
406	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
408	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
409	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
410	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
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	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	1	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	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	—	2	1	no	—
435	C₂²⋊C₄×C₆₁	—	2	1	no	—
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	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
441	C₄²×C₆₁	—	2	1	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	C₂⁴	1	2	yes	—
450	C₂³×C₆₁	—	2	2	no	—
451	C₂³×C₆₁	—	2	2	no	—
452	C₂³×C₆₁	—	2	1	no	—
453	C₂³×C₆₁	—	2	2	no	—
454	C₂³×C₆₁	—	4	1	no	—
455	C₂³×C₆₁	—	4	2	no	—
456	C₂³×C₆₁	—	8	1	no	—
457	C₂³×C₆₁	—	8	1	no	—
458	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
459	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
460	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
461	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
462	Q₈×C₆₁	—	2	2	no	—
463	Q₈×C₆₁	—	2	1	no	—
464	Q₈×C₆₁	—	2	1	no	—
465	Q₈×C₆₁	—	8	2	no	—
466	Q₈×C₆₁	—	8	2	no	—
467	D₄×C₆₁	—	2	4	no	—
468	D₄×C₆₁	—	2	4	no	—
469	D₄×C₆₁	—	2	2	no	—
470	D₄×C₆₁	—	2	1	no	—
471	D₄×C₆₁	—	2	2	no	—
472	D₄×C₆₁	—	2	2	no	—
473	D₄×C₆₁	—	2	1	no	—
474	D₄×C₆₁	—	4	2	no	—
475	D₄×C₆₁	—	4	2	no	—
476	D₄×C₆₁	—	4	2	no	—
477	D₄×C₆₁	—	4	2	no	—
478	D₄×C₆₁	—	4	4	no	—
479	D₄×C₆₁	—	4	2	no	—
480	D₄×C₆₁	—	8	2	no	—
481	D₄×C₆₁	—	8	2	no	—
482	D₄×C₆₁	—	8	2	no	—
483	D₄×C₆₁	—	8	2	no	—
484	C₂×C₄×C₆₁	—	2	2	no	—
485	C₂×C₄×C₆₁	—	2	2	no	—
486	C₂×C₄×C₆₁	—	2	2	no	—
487	C₂×C₄×C₆₁	—	2	1	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	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	1	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	2	no	—
501	C₂×C₄×C₆₁	—	2	1	no	—
502	C₂×C₄×C₆₁	—	2	2	no	—
503	C₂×C₄×C₆₁	—	4	4	no	—
504	C₂×C₄×C₆₁	—	4	2	no	—
505	C₂×C₄×C₆₁	—	4	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	—	8	1	no	—
510	C₂×C₄×C₆₁	—	8	1	no	—
511	C₂×C₄×C₆₁	—	8	2	no	—
512	C₂×C₄×C₆₁	—	8	1	no	—
513	C₂×C₄×C₆₁	—	8	1	no	—
514	C₂×C₄×C₆₁	—	8	2	no	—
515	C₂×C₄×C₆₁	—	8	2	no	—
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	2	yes	—
519	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
520	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
523	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
524	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
525	C₈×C₆₁	—	2	1	no	—
526	C₈×C₆₁	—	2	1	no	—
527	C₈×C₆₁	—	2	2	no	—
528	C₈×C₆₁	—	2	1	no	—
529	C₈×C₆₁	—	2	1	no	—
530	C₈×C₆₁	C₂×#41	1	4	yes	—
531	#61272	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
532	C₂²×C₆₁	—	2	1	no	—
533	C₂²×C₆₁	—	2	1	no	—
534	C₂²×C₆₁	—	2	1	no	—
535	C₂²×C₆₁	—	2	1	no	—
536	C₂²×C₆₁	—	2	1	no	—
537	C₂²×C₆₁	—	2	2	no	—
538	C₂²×C₆₁	—	2	1	no	—
539	C₂²×C₆₁	—	2	2	no	—
540	C₂²×C₆₁	—	2	2	no	—
541	C₂²×C₆₁	—	2	1	no	—
542	C₂²×C₆₁	—	4	4	no	—
543	C₂²×C₆₁	—	4	1	no	—
544	C₂²×C₆₁	—	4	2	no	—
545	C₂²×C₆₁	—	4	1	no	—
546	C₂²×C₆₁	—	4	2	no	—
547	C₂²×C₆₁	—	4	2	no	—
548	C₂²×C₆₁	—	4	1	no	—
549	C₂²×C₆₁	—	16	2	no	—
550	C₂²×C₆₁	#547	1	2	yes	—
551	C₂²×C₆₁	#577	1	2	yes	—
552	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
553	C₄×C₆₁	—	2	2	no	—
554	C₄×C₆₁	—	2	1	no	—
555	C₄×C₆₁	—	2	1	no	—
556	C₄×C₆₁	—	2	2	no	—
557	C₄×C₆₁	—	2	2	no	—
558	C₄×C₆₁	—	4	2	no	—
559	C₄×C₆₁	—	4	2	no	—
560	C₄×C₆₁	—	4	1	no	—
561	C₄×C₆₁	—	4	1	no	—
562	C₄×C₆₁	—	4	1	no	—
563	C₄×C₆₁	—	4	1	no	—
564	C₄×C₆₁	—	4	1	no	—
565	C₄×C₆₁	—	4	1	no	—
566	C₄×C₆₁	—	4	2	no	—
567	C₄×C₆₁	—	4	1	no	—
568	C₄×C₆₁	#547	1	2	yes	—
569	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
570	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
571	#3494	C₂×C₆₁	1	1	yes	characteristic, complemented
572	#3492	C₂×C₆₁	1	1	yes	characteristic, complemented
573	#3354	C₂×C₆₁	1	2	yes	complemented
574	#3351	C₂×C₆₁	1	2	yes	complemented
575	#3348	C₂×C₆₁	1	2	yes	complemented
576	#3346	C₂×C₆₁	1	2	yes	complemented
577	#3345	C₂×C₆₁	1	2	yes	complemented
578	#3345	C₂×C₆₁	1	2	yes	complemented
579	#3339	C₂×C₆₁	1	2	yes	complemented
580	#3335	C₂×C₆₁	1	2	yes	complemented
581	#3163	C₂×C₆₁	1	1	yes	characteristic, complemented
582	#3099	C₂×C₆₁	1	1	yes	characteristic, complemented
583	#3096	C₂×C₆₁	1	1	yes	characteristic, complemented
584	#3091	C₂×C₆₁	1	1	yes	characteristic, complemented
585	C₂×#481	C₂×C₆₁	1	1	yes	characteristic, complemented
586	#3084	C₂×C₆₁	1	1	yes	characteristic, complemented
587	#3081	C₂×C₆₁	1	1	yes	characteristic, complemented
588	#3062	C₂×C₆₁	1	1	yes	characteristic, complemented
589	#3055	C₂×C₆₁	1	1	yes	characteristic, complemented
590	#2946	C₂×C₆₁	1	1	yes	characteristic, complemented
591	#2933	C₂×C₆₁	1	1	yes	characteristic, complemented
592	#2912	C₂×C₆₁	1	1	yes	characteristic, complemented
593	C₂×#428	C₂×C₆₁	1	1	yes	characteristic, complemented
594	C₂×C₆₁	—	2	2	no	—
595	C₂×C₆₁	—	2	2	no	—
596	C₂×C₆₁	—	4	2	no	—
597	C₂×C₆₁	—	4	1	no	—
598	C₂×C₆₁	—	8	1	no	—
599	C₂×C₆₁	—	8	2	no	—
600	C₂×C₆₁	C₂×#547	1	1	yes	characteristic
601	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
602	C₂×C₆₁	#3585	1	1	yes	characteristic
603	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	1	yes	characteristic
604	C₂×#131	C₂²×C₆₁	1	1	yes	characteristic
605	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
606	#555	C₂²×C₆₁	1	2	yes	—
607	#554	—	2	1	no	—
608	#554	C₂²×C₆₁	1	2	yes	complemented
609	#553	—	2	1	no	—
610	#553	C₂²×C₆₁	1	2	yes	—
611	#553	C₂²×C₆₁	1	2	yes	—
612	#553	C₂²×C₆₁	1	2	yes	complemented
613	#552	—	2	1	no	—
614	#552	C₂²×C₆₁	1	2	yes	complemented
615	#551	—	2	2	no	—
616	#547	—	2	1	no	—
617	#547	C₂²×C₆₁	1	2	yes	—
618	#547	C₂²×C₆₁	1	2	yes	complemented
619	#546	—	2	2	no	—
620	#544	C₂²×C₆₁	1	1	yes	characteristic
621	#544	C₂²×C₆₁	1	1	yes	characteristic
622	#542	—	2	1	no	—
623	#540	—	2	1	no	—
624	#539	—	2	2	no	—
625	#537	C₂²×C₆₁	1	1	yes	characteristic
626	#535	C₂²×C₆₁	1	1	yes	characteristic
627	#532	—	2	1	no	—
628	#529	—	2	1	no	—
629	#525	—	2	2	no	—
630	#525	C₂²×C₆₁	1	1	yes	characteristic
631	#525	C₂²×C₆₁	1	1	yes	characteristic
632	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
633	#520	C₂²×C₆₁	1	1	yes	characteristic
634	#520	C₂²×C₆₁	1	1	yes	characteristic
635	#520	C₂²×C₆₁	1	1	yes	characteristic
636	#518	C₂²×C₆₁	1	1	yes	characteristic
637	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
638	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
639	#501	C₂²×C₆₁	1	2	yes	complemented
640	#501	C₂²×C₆₁	1	2	yes	complemented
641	#499	C₂²×C₆₁	1	2	yes	complemented
642	#498	C₂²×C₆₁	1	2	yes	complemented
643	#485	C₂²×C₆₁	1	2	yes	complemented
644	#485	C₂²×C₆₁	1	1	yes	characteristic, complemented
645	#485	C₂²×C₆₁	1	1	yes	characteristic, complemented
646	#484	C₂²×C₆₁	1	1	yes	characteristic, complemented
647	#483	C₂²×C₆₁	1	1	yes	characteristic, complemented
648	#483	C₂²×C₆₁	1	2	yes	complemented
649	#482	C₂²×C₆₁	1	2	yes	complemented
650	#482	C₂²×C₆₁	1	2	yes	complemented
651	#482	C₂²×C₆₁	1	1	yes	characteristic, complemented
652	#482	C₂²×C₆₁	1	2	yes	complemented
653	#482	C₂²×C₆₁	1	1	yes	characteristic, complemented
654	#481	C₂²×C₆₁	1	2	yes	—
655	#481	C₂²×C₆₁	1	2	yes	—
656	#481	C₂²×C₆₁	1	2	yes	—
657	#481	C₂²×C₆₁	1	2	yes	—
658	#481	C₂²×C₆₁	1	2	yes	complemented
659	#481	C₂²×C₆₁	1	1	yes	characteristic, complemented
660	#481	C₂²×C₆₁	1	2	yes	complemented
661	#480	C₂²×C₆₁	1	1	yes	characteristic, complemented
662	#480	C₂²×C₆₁	1	2	yes	complemented
663	#479	C₂²×C₆₁	1	2	yes	complemented
664	#478	C₂²×C₆₁	1	2	yes	complemented
665	#478	C₂²×C₆₁	1	2	yes	complemented
666	#478	C₂²×C₆₁	1	2	yes	complemented
667	#476	C₂²×C₆₁	1	2	yes	complemented
668	#476	C₂²×C₆₁	1	2	yes	complemented
669	#475	C₂²×C₆₁	1	2	yes	complemented
670	#474	C₂²×C₆₁	1	2	yes	complemented
671	#469	C₂²×C₆₁	1	2	yes	—
672	#469	C₂²×C₆₁	1	2	yes	complemented
673	#468	C₂²×C₆₁	1	2	yes	—
674	#468	C₂²×C₆₁	1	2	yes	complemented
675	#466	C₂²×C₆₁	1	2	yes	—
676	#466	C₂²×C₆₁	1	2	yes	complemented
677	#465	C₂²×C₆₁	1	2	yes	—
678	#465	C₂²×C₆₁	1	2	yes	complemented
679	#442	C₂²×C₆₁	1	2	yes	complemented
680	#440	C₂²×C₆₁	1	2	yes	complemented
681	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
682	C₄×D₈	C₂²×C₆₁	1	2	yes	complemented
683	#436	C₂²×C₆₁	1	2	yes	complemented
684	#435	C₂²×C₆₁	1	2	yes	complemented
685	#435	C₂²×C₆₁	1	2	yes	complemented
686	C₈×D₄	C₂²×C₆₁	1	2	yes	complemented
687	#428	C₂²×C₆₁	1	1	yes	characteristic
688	#428	C₂²×C₆₁	1	1	yes	characteristic
689	#428	C₂²×C₆₁	1	1	yes	characteristic
690	#428	C₂²×C₆₁	1	1	yes	characteristic
691	#428	C₂²×C₆₁	1	1	yes	characteristic
692	#428	C₂²×C₆₁	1	2	yes	complemented
693	#428	C₂²×C₆₁	1	2	yes	complemented
694	#428	C₂²×C₆₁	1	2	yes	complemented
695	#428	C₂²×C₆₁	1	2	yes	complemented
696	#427	C₂²×C₆₁	1	1	yes	characteristic
697	#427	C₂²×C₆₁	1	1	yes	characteristic
698	#427	C₂²×C₆₁	1	2	yes	complemented
699	C₂×#107	C₂²×C₆₁	1	2	yes	complemented
700	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
701	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
702	C₂×#106	C₂²×C₆₁	1	2	yes	complemented
703	C₂×#106	C₂²×C₆₁	1	2	yes	complemented
704	#424	C₂²×C₆₁	1	1	yes	characteristic
705	#418	C₂²×C₆₁	1	1	yes	characteristic
706	#417	C₂²×C₆₁	1	1	yes	characteristic
707	#416	C₂²×C₆₁	1	1	yes	characteristic
708	#416	C₂²×C₆₁	1	1	yes	characteristic
709	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
710	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
711	#408	C₂²×C₆₁	1	1	yes	characteristic
712	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
713	#405	C₂²×C₆₁	1	1	yes	characteristic
714	C₆₁	#61272	1	1	yes	characteristic, direct product factor, Sylow
715	C₂×#41	—	2	2	no	—
716	C₂×#41	—	2	2	no	—
717	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
718	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
719	C₂²×D₄	—	2	1	no	—
720	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
721	C₂³×C₄	—	2	1	no	—
722	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
723	AGL(1,ℤ/8)	—	2	4	no	—
724	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
725	C₂×D₈	C₂³×C₆₁	1	2	yes	—
726	#131	—	2	4	no	—
727	C₂×M₁₆	—	2	4	no	—
728	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
729	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
730	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
731	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
732	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
733	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
734	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
735	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
736	C₄⋊Q₈	—	2	1	no	—
737	C₄⋊Q₈	—	2	1	no	—
738	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
739	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
740	#127	—	2	1	no	—
741	#126	—	2	2	no	—
742	#126	—	2	2	no	—
743	#126	—	2	2	no	—
744	#126	—	2	2	no	—
745	#125	—	2	1	no	—
746	#125	—	2	2	no	—
747	#125	—	2	2	no	—
748	#125	—	2	1	no	—
749	#125	C₂³×C₆₁	1	2	yes	—
750	#125	C₂³×C₆₁	1	2	yes	—
751	#124	—	2	1	no	—
752	#124	—	2	2	no	—
753	#124	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	1	no	—
756	#123	—	2	2	no	—
757	#123	—	2	2	no	—
758	#123	—	2	2	no	—
759	#123	—	2	2	no	—
760	#123	—	2	2	no	—
761	#123	—	2	2	no	—
762	#123	—	2	2	no	—
763	#123	D₄×C₆₁	1	2	yes	—
764	C₂²⋊Q₈	—	2	1	no	—
765	C₂²⋊Q₈	—	2	2	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
772	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
773	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
774	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
775	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
776	#121	—	2	2	no	—
777	#121	—	2	2	no	—
778	#121	—	2	2	no	—
779	#121	—	2	1	no	—
780	#121	—	2	2	no	—
781	#121	—	2	2	no	—
782	#121	—	2	1	no	—
783	#121	—	2	1	no	—
784	#121	D₄×C₆₁	1	1	yes	characteristic
785	#121	D₄×C₆₁	1	1	yes	characteristic
786	#121	C₂³×C₆₁	1	2	yes	—
787	#121	C₂³×C₆₁	1	2	yes	—
788	#121	C₂³×C₆₁	1	1	yes	characteristic
789	#121	C₂³×C₆₁	1	1	yes	characteristic
790	#121	C₂³×C₆₁	1	2	yes	—
791	#121	C₂³×C₆₁	1	2	yes	—
792	#121	C₂³×C₆₁	1	2	yes	—
793	#120	—	2	1	no	—
794	#120	—	2	2	no	—
795	#120	D₄×C₆₁	1	2	yes	—
796	C₄×Q₈	—	2	1	no	—
797	C₄×Q₈	—	2	1	no	—
798	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
799	C₄×D₄	—	2	2	no	—
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	—	2	2	no	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	2	no	—
812	C₄×D₄	C₂³×C₆₁	1	2	yes	—
813	C₄×D₄	C₂³×C₆₁	1	2	yes	—
814	C₄×D₄	C₂³×C₆₁	1	2	yes	—
815	C₄×D₄	C₂³×C₆₁	1	2	yes	—
816	C₄×D₄	C₂³×C₆₁	1	2	yes	—
817	#117	—	2	1	no	—
818	#117	—	2	1	no	—
819	#117	—	2	1	no	—
820	#117	—	2	2	no	—
821	#117	—	2	2	no	—
822	#117	C₂³×C₆₁	1	1	yes	characteristic
823	#117	C₂³×C₆₁	1	1	yes	characteristic
824	#117	C₂³×C₆₁	1	1	yes	characteristic
825	#117	C₂³×C₆₁	1	1	yes	characteristic
826	#117	C₂³×C₆₁	1	1	yes	characteristic
827	#117	C₂³×C₆₁	1	2	yes	—
828	#117	C₂³×C₆₁	1	2	yes	—
829	#117	C₂³×C₆₁	1	1	yes	characteristic
830	C₂×C₄⋊C₄	—	2	1	no	—
831	C₂×C₄⋊C₄	—	2	1	no	—
832	C₂×C₄⋊C₄	—	2	1	no	—
833	C₂×C₄⋊C₄	—	2	1	no	—
834	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
835	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
836	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
837	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
838	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
839	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
840	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
841	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
842	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
843	C₂×C₂²⋊C₄	—	2	1	no	—
844	C₂×C₂²⋊C₄	—	2	1	no	—
845	C₂×C₂²⋊C₄	—	2	2	no	—
846	C₂×C₄²	—	2	1	no	—
847	#107	C₂³×C₆₁	1	2	yes	—
848	#107	C₂³×C₆₁	1	2	yes	—
849	#107	C₂³×C₆₁	1	2	yes	—
850	#107	C₂³×C₆₁	1	2	yes	—
851	#107	C₂³×C₆₁	1	1	yes	characteristic
852	#107	C₂³×C₆₁	1	1	yes	characteristic
853	#107	C₂³×C₆₁	1	1	yes	characteristic
854	#107	C₂³×C₆₁	1	1	yes	characteristic
855	#107	C₂³×C₆₁	1	2	yes	—
856	#106	C₂³×C₆₁	1	2	yes	—
857	#106	C₂³×C₆₁	1	2	yes	—
858	#106	C₂³×C₆₁	1	2	yes	—
859	#106	C₂³×C₆₁	1	2	yes	—
860	#106	C₂³×C₆₁	1	1	yes	characteristic
861	#106	C₂³×C₆₁	1	2	yes	—
862	#106	C₂³×C₆₁	1	2	yes	—
863	#106	C₂³×C₆₁	1	2	yes	—
864	#106	C₂³×C₆₁	1	2	yes	—
865	#106	C₂³×C₆₁	1	2	yes	—
866	#106	C₂³×C₆₁	1	1	yes	characteristic
867	#106	C₂³×C₆₁	1	1	yes	characteristic
868	#106	C₂³×C₆₁	1	1	yes	characteristic
869	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
870	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
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	1	yes	characteristic
875	#103	C₂³×C₆₁	1	2	yes	—
876	#102	C₂³×C₆₁	1	2	yes	—
877	#102	C₂³×C₆₁	1	2	yes	—
878	#102	C₂³×C₆₁	1	2	yes	—
879	#102	C₂³×C₆₁	1	2	yes	—
880	#102	C₂³×C₆₁	1	1	yes	characteristic
881	#102	C₂³×C₆₁	1	1	yes	characteristic
882	#102	C₂³×C₆₁	1	1	yes	characteristic
883	#102	C₂³×C₆₁	1	1	yes	characteristic
884	#102	C₂³×C₆₁	1	2	yes	—
885	#102	C₂³×C₆₁	1	2	yes	—
886	#102	C₂³×C₆₁	1	2	yes	—
887	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
888	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
889	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
890	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
891	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
892	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
893	#97	C₂³×C₆₁	1	2	yes	—
894	C₄×C₈	C₂³×C₆₁	1	2	yes	—
895	C₂⁴	—	2	1	no	—
896	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
897	#41	—	2	2	no	—
898	#41	—	2	2	no	—
899	#41	—	2	2	no	—
900	#41	—	2	2	no	—
901	#41	—	8	4	no	—
902	#41	—	8	4	no	—
903	C₂×Q₈	—	2	2	no	—
904	C₂×Q₈	—	2	2	no	—
905	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
906	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
907	C₂×D₄	—	2	1	no	—
908	C₂×D₄	—	2	1	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	2	2	no	—
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	8	2	no	—
919	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
920	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
921	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
922	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
923	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
924	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	—	2	1	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	1	no	—
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	2	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	2	2	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	8	2	no	—
941	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
942	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
943	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
944	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
945	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
946	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
947	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
948	SD₁₆	—	2	4	no	—
949	D₈	—	2	4	no	—
950	M₁₆	—	2	2	no	—
951	M₁₆	—	2	4	no	—
952	M₁₆	—	2	4	no	—
953	M₁₆	#41×C₆₁	1	4	yes	complemented
954	C₂×C₈	—	2	2	no	—
955	C₂×C₈	—	2	2	no	—
956	C₂×C₈	—	2	4	no	—
957	C₂×C₈	—	2	4	no	—
958	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
959	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
960	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
961	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
962	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
963	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	1	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	1	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
984	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
985	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
986	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
987	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
988	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
989	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
990	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
991	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
992	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
993	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
994	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
995	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1017	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1018	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1019	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1020	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1021	C₄²	—	2	1	no	—
1022	C₄²	—	2	1	no	—
1023	C₄²	—	2	1	no	—
1024	C₄²	—	2	1	no	—
1025	C₄²	—	2	2	no	—
1026	C₄²	—	2	2	no	—
1027	C₄²	—	2	2	no	—
1028	C₄²	—	2	1	no	—
1029	C₄²	C₂⁴×C₆₁	1	2	yes	—
1030	C₂³	—	2	2	no	—
1031	C₂³	—	2	2	no	—
1032	C₂³	—	2	1	no	—
1033	C₂³	—	2	2	no	—
1034	C₂³	—	4	1	no	—
1035	C₂³	—	4	2	no	—
1036	C₂³	—	8	1	no	—
1037	C₂³	—	8	1	no	—
1038	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1039	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1040	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1041	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1042	Q₈	—	2	2	no	—
1043	Q₈	—	2	1	no	—
1044	Q₈	—	2	1	no	—
1045	Q₈	—	8	2	no	—
1046	Q₈	—	8	2	no	—
1047	D₄	—	2	4	no	—
1048	D₄	—	2	4	no	—
1049	D₄	—	2	2	no	—
1050	D₄	—	2	1	no	—
1051	D₄	—	2	2	no	—
1052	D₄	—	2	2	no	—
1053	D₄	—	2	1	no	—
1054	D₄	—	4	2	no	—
1055	D₄	—	4	2	no	—
1056	D₄	—	4	2	no	—
1057	D₄	—	4	2	no	—
1058	D₄	—	4	4	no	—
1059	D₄	—	4	2	no	—
1060	D₄	—	8	2	no	—
1061	D₄	—	8	2	no	—
1062	D₄	—	8	2	no	—
1063	D₄	—	8	2	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	4	4	no	—
1084	C₂×C₄	—	4	2	no	—
1085	C₂×C₄	—	4	2	no	—
1086	C₂×C₄	—	8	2	no	—
1087	C₂×C₄	—	8	2	no	—
1088	C₂×C₄	—	8	2	no	—
1089	C₂×C₄	—	8	1	no	—
1090	C₂×C₄	—	8	1	no	—
1091	C₂×C₄	—	8	2	no	—
1092	C₂×C₄	—	8	1	no	—
1093	C₂×C₄	—	8	1	no	—
1094	C₂×C₄	—	8	2	no	—
1095	C₂×C₄	—	8	2	no	—
1096	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1097	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1098	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1099	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1100	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1101	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1102	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
1103	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
1104	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1105	C₈	—	2	1	no	—
1106	C₈	—	2	1	no	—
1107	C₈	—	2	2	no	—
1108	C₈	—	2	1	no	—
1109	C₈	—	2	1	no	—
1110	C₈	C₂×#41×C₆₁	1	4	yes	—
1111	C₂²	—	2	1	no	—
1112	C₂²	—	2	1	no	—
1113	C₂²	—	2	1	no	—
1114	C₂²	—	2	1	no	—
1115	C₂²	—	2	2	no	—
1116	C₂²	—	2	1	no	—
1117	C₂²	—	2	1	no	—
1118	C₂²	—	2	2	no	—
1119	C₂²	—	2	1	no	—
1120	C₂²	—	2	2	no	—
1121	C₂²	—	4	4	no	—
1122	C₂²	—	4	2	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	2	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	16	2	no	—
1129	C₂²	C₆₁×#547	1	2	yes	—
1130	C₂²	C₆₁×#577	1	2	yes	—
1131	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1132	C₄	—	2	2	no	—
1133	C₄	—	2	2	no	—
1134	C₄	—	2	1	no	—
1135	C₄	—	2	1	no	—
1136	C₄	—	2	2	no	—
1137	C₄	—	4	1	no	—
1138	C₄	—	4	1	no	—
1139	C₄	—	4	2	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	2	no	—
1142	C₄	—	4	2	no	—
1143	C₄	—	4	1	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	1	no	—
1146	C₄	—	4	1	no	—
1147	C₄	C₆₁×#547	1	2	yes	—
1148	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
1149	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
1150	C₂	—	2	2	no	—
1151	C₂	—	2	2	no	—
1152	C₂	—	4	1	no	—
1153	C₂	—	4	2	no	—
1154	C₂	—	8	2	no	—
1155	C₂	—	8	1	no	—
1156	C₂	C₂×C₆₁×#547	1	1	yes	characteristic
1157	C₂	C₂×C₆₁×#577	1	1	yes	characteristic
1158	C₂	C₆₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₆₁×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3494	C₂	semidirect
2. C₆₁×#3492	C₂	semidirect
3. C₆₁×#3354	C₂	semidirect
4. C₆₁×#3351	C₂	semidirect
5. C₆₁×#3348	C₂	semidirect
6. C₆₁×#3346	C₂	semidirect
7. C₆₁×#3345	C₂	semidirect
8. C₆₁×#3345	C₂	semidirect
9. C₆₁×#3339	C₂	semidirect
10. C₆₁×#3335	C₂	semidirect
11. C₆₁×#3163	C₂	semidirect
12. C₆₁×#3099	C₂	semidirect
13. C₆₁×#3096	C₂	semidirect
14. C₆₁×#3091	C₂	semidirect
15. C₂×C₆₁×#481	C₂	semidirect
16. C₆₁×#3084	C₂	semidirect
17. C₆₁×#3081	C₂	semidirect
18. C₆₁×#3062	C₂	semidirect
19. C₆₁×#3055	C₂	semidirect
20. C₆₁×#2946	C₂	semidirect
21. C₆₁×#2933	C₂	semidirect
22. C₆₁×#2912	C₂	semidirect
23. C₂×C₆₁×#428	C₂	semidirect
29. C₆₁×#554	C₂²	semidirect
33. C₆₁×#553	C₂²	semidirect
35. C₆₁×#552	C₂²	semidirect
39. C₆₁×#547	C₂²	semidirect
60. C₆₁×#501	C₂²	semidirect
61. C₆₁×#501	C₂²	semidirect
62. C₆₁×#499	C₂²	semidirect
63. C₆₁×#498	C₂²	semidirect
64. C₆₁×#485	C₂²	semidirect
65. C₆₁×#485	C₂²	semidirect
66. C₆₁×#485	C₂²	semidirect
67. C₆₁×#484	C₂²	semidirect
68. C₆₁×#483	C₂²	semidirect
69. C₆₁×#483	C₂²	semidirect
70. C₆₁×#482	C₂²	semidirect
71. C₆₁×#482	C₂²	semidirect
72. C₆₁×#482	C₂²	semidirect
73. C₆₁×#482	C₂²	semidirect
74. C₆₁×#482	C₂²	semidirect
79. C₆₁×#481	C₂²	semidirect
80. C₆₁×#481	C₂²	semidirect
81. C₆₁×#481	C₂²	semidirect
82. C₆₁×#480	C₂²	semidirect
83. C₆₁×#480	C₂²	semidirect
84. C₆₁×#479	C₂²	semidirect
85. C₆₁×#478	C₂²	semidirect
86. C₆₁×#478	C₂²	semidirect
87. C₆₁×#478	C₂²	semidirect
88. C₆₁×#476	C₂²	semidirect
89. C₆₁×#476	C₂²	semidirect
90. C₆₁×#475	C₂²	semidirect
91. C₆₁×#474	C₂²	semidirect
93. C₆₁×#469	C₂²	semidirect
95. C₆₁×#468	C₂²	semidirect
97. C₆₁×#466	C₂²	semidirect
99. C₆₁×#465	C₂²	semidirect
100. C₆₁×#442	C₂²	semidirect
101. C₆₁×#440	C₂²	semidirect
102. C₄×SD₁₆×C₆₁	C₂²	semidirect
103. C₄×D₈×C₆₁	C₂²	semidirect
104. C₆₁×#436	C₂²	semidirect
105. C₆₁×#435	C₂²	semidirect
106. C₆₁×#435	C₂²	semidirect
107. C₈×D₄×C₆₁	C₂²	semidirect
113. C₆₁×#428	C₂²	semidirect
114. C₆₁×#428	C₂²	semidirect
115. C₆₁×#428	C₂²	semidirect
116. C₆₁×#428	C₂²	semidirect
119. C₆₁×#427	C₂²	semidirect
120. C₂×#107×C₆₁	C₂²	semidirect
123. C₂×#106×C₆₁	C₂²	semidirect
124. C₂×#106×C₆₁	C₂²	semidirect
373. M₁₆×C₆₁	#41	semidirect
531. #61272	C₆₁	direct (N × H)
571. #3494	C₂×C₆₁	semidirect
572. #3492	C₂×C₆₁	semidirect
573. #3354	C₂×C₆₁	semidirect
574. #3351	C₂×C₆₁	semidirect
575. #3348	C₂×C₆₁	semidirect
576. #3346	C₂×C₆₁	semidirect
577. #3345	C₂×C₆₁	semidirect
578. #3345	C₂×C₆₁	semidirect
579. #3339	C₂×C₆₁	semidirect
580. #3335	C₂×C₆₁	semidirect
581. #3163	C₂×C₆₁	semidirect
582. #3099	C₂×C₆₁	semidirect
583. #3096	C₂×C₆₁	semidirect
584. #3091	C₂×C₆₁	semidirect
585. C₂×#481	C₂×C₆₁	semidirect
586. #3084	C₂×C₆₁	semidirect
587. #3081	C₂×C₆₁	semidirect
588. #3062	C₂×C₆₁	semidirect
589. #3055	C₂×C₆₁	semidirect
590. #2946	C₂×C₆₁	semidirect
591. #2933	C₂×C₆₁	semidirect
592. #2912	C₂×C₆₁	semidirect
593. C₂×#428	C₂×C₆₁	semidirect
608. #554	C₂²×C₆₁	semidirect
612. #553	C₂²×C₆₁	semidirect
614. #552	C₂²×C₆₁	semidirect
618. #547	C₂²×C₆₁	semidirect
639. #501	C₂²×C₆₁	semidirect
640. #501	C₂²×C₆₁	semidirect
641. #499	C₂²×C₆₁	semidirect
642. #498	C₂²×C₆₁	semidirect
643. #485	C₂²×C₆₁	semidirect
644. #485	C₂²×C₆₁	semidirect
645. #485	C₂²×C₆₁	semidirect
646. #484	C₂²×C₆₁	semidirect
647. #483	C₂²×C₆₁	semidirect
648. #483	C₂²×C₆₁	semidirect
649. #482	C₂²×C₆₁	semidirect
650. #482	C₂²×C₆₁	semidirect
651. #482	C₂²×C₆₁	semidirect
652. #482	C₂²×C₆₁	semidirect
653. #482	C₂²×C₆₁	semidirect
658. #481	C₂²×C₆₁	semidirect
659. #481	C₂²×C₆₁	semidirect
660. #481	C₂²×C₆₁	semidirect
661. #480	C₂²×C₆₁	semidirect
662. #480	C₂²×C₆₁	semidirect
663. #479	C₂²×C₆₁	semidirect
664. #478	C₂²×C₆₁	semidirect
665. #478	C₂²×C₆₁	semidirect
666. #478	C₂²×C₆₁	semidirect
667. #476	C₂²×C₆₁	semidirect
668. #476	C₂²×C₆₁	semidirect
669. #475	C₂²×C₆₁	semidirect
670. #474	C₂²×C₆₁	semidirect
672. #469	C₂²×C₆₁	semidirect
674. #468	C₂²×C₆₁	semidirect
676. #466	C₂²×C₆₁	semidirect
678. #465	C₂²×C₆₁	semidirect
679. #442	C₂²×C₆₁	semidirect
680. #440	C₂²×C₆₁	semidirect
681. C₄×SD₁₆	C₂²×C₆₁	semidirect
682. C₄×D₈	C₂²×C₆₁	semidirect
683. #436	C₂²×C₆₁	semidirect
684. #435	C₂²×C₆₁	semidirect
685. #435	C₂²×C₆₁	semidirect
686. C₈×D₄	C₂²×C₆₁	semidirect
692. #428	C₂²×C₆₁	semidirect
693. #428	C₂²×C₆₁	semidirect
694. #428	C₂²×C₆₁	semidirect
695. #428	C₂²×C₆₁	semidirect
698. #427	C₂²×C₆₁	semidirect
699. C₂×#107	C₂²×C₆₁	semidirect
702. C₂×#106	C₂²×C₆₁	semidirect
703. C₂×#106	C₂²×C₆₁	semidirect
714. C₆₁	#61272	direct (N × H)
953. M₁₆	#41×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3494	2
C₆₁×#3492	2
C₆₁×#3354	2
C₆₁×#3351	2
C₆₁×#3348	2
C₆₁×#3346	2
C₆₁×#3345	2
C₆₁×#3339	2
C₆₁×#3335	2
C₆₁×#3163	2
C₆₁×#3099	2
C₆₁×#3096	2
C₆₁×#3091	2
C₂×C₆₁×#481	2
C₆₁×#3084	2
C₆₁×#3081	2
C₆₁×#3062	2
C₆₁×#3055	2
C₆₁×#2946	2
C₆₁×#2933	2
C₆₁×#2912	2
C₂×C₆₁×#428	2
#61272	61

Subgroups — C61×#61272 #29564705

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61272 #29564705