Subgroups — C₆₁×#61452 #29564885

Order 15616.

2104 conjugacy classes of subgroups.

The subgroup lattice has 1196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3482	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3386	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3368	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3367	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3343	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3334	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#3310	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3308	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3298	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3294	C₂	1	1	yes	maximal, characteristic, complemented
13	D₄×SD₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3265	C₂	1	2	yes	maximal, complemented
15	C₆₁×#3182	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#3180	C₂	1	2	yes	maximal, complemented
17	C₆₁×#3115	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#3114	C₂	1	2	yes	maximal, complemented
19	C₆₁×#3112	C₂	1	2	yes	maximal, complemented
20	C₆₁×#3110	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#2970	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×AGL(1,ℤ/8)×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₆₁×#440	C₂	1	2	yes	maximal, complemented
24	C₂²×#41×C₆₁	—	2	1	no	—
25	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	1	yes	characteristic
26	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	—
27	C₆₁×#557	C₂²	1	1	yes	characteristic, complemented
28	C₆₁×#556	—	2	1	no	—
29	C₆₁×#556	C₂²	1	1	yes	characteristic, complemented
30	C₆₁×#552	—	2	2	no	—
31	C₆₁×#552	C₂²	1	2	yes	complemented
32	C₆₁×#550	C₂²	1	1	yes	characteristic
33	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
34	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
35	C₆₁×#548	—	2	1	no	—
36	C₆₁×#548	C₂²	1	2	yes	complemented
37	C₆₁×#547	—	2	1	no	—
38	C₆₁×#547	C₂²	1	1	yes	characteristic
39	C₆₁×#547	C₂²	1	2	yes	—
40	C₆₁×#547	C₂²	1	1	yes	characteristic, complemented
41	C₆₁×#546	—	2	1	no	—
42	C₆₁×#546	—	2	2	no	—
43	D₄²×C₆₁	C₂²	1	1	yes	characteristic
44	D₄²×C₆₁	C₂²	1	2	yes	—
45	C₆₁×#533	—	2	1	no	—
46	C₆₁×#533	C₂²	1	1	yes	characteristic, complemented
47	C₆₁×#532	C₂²	1	2	yes	—
48	C₆₁×#532	C₂²	1	1	yes	characteristic
49	C₆₁×#529	—	2	2	no	—
50	C₆₁×#529	C₂²	1	2	yes	complemented
51	C₆₁×#525	—	2	2	no	—
52	C₆₁×#525	—	2	1	no	—
53	C₄×#41×C₆₁	—	2	1	no	—
54	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
55	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	complemented
57	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
59	C₆₁×#501	C₂²	1	2	yes	complemented
60	C₆₁×#500	C₂²	1	1	yes	characteristic, complemented
61	C₆₁×#496	C₂²	1	2	yes	complemented
62	C₆₁×#492	C₂²	1	1	yes	characteristic, complemented
63	C₆₁×#490	C₂²	1	2	yes	complemented
64	C₆₁×#489	C₂²	1	2	yes	complemented
65	C₆₁×#487	C₂²	1	1	yes	characteristic, complemented
66	C₆₁×#486	C₂²	1	1	yes	characteristic, complemented
67	C₆₁×#484	C₂²	1	2	yes	complemented
68	C₆₁×#483	C₂²	1	2	yes	complemented
69	C₆₁×#482	C₂²	1	2	yes	complemented
70	C₆₁×#480	C₂²	1	2	yes	complemented
71	C₆₁×#480	C₂²	1	2	yes	complemented
72	C₆₁×#480	C₂²	1	2	yes	complemented
73	C₆₁×#478	C₂²	1	2	yes	—
74	C₆₁×#478	C₂²	1	2	yes	complemented
75	C₆₁×#477	C₂²	1	2	yes	complemented
76	C₆₁×#477	C₂²	1	2	yes	complemented
77	C₆₁×#475	C₂²	1	1	yes	characteristic, complemented
78	C₆₁×#474	C₂²	1	1	yes	characteristic
79	C₆₁×#474	C₂²	1	1	yes	characteristic, complemented
80	C₆₁×#474	C₂²	1	1	yes	characteristic, complemented
81	C₆₁×#468	C₂²	1	2	yes	complemented
82	C₆₁×#468	C₂²	1	2	yes	complemented
83	C₆₁×#466	C₂²	1	2	yes	complemented
84	C₆₁×#466	C₂²	1	2	yes	complemented
85	C₆₁×#465	C₂²	1	2	yes	complemented
86	C₆₁×#465	C₂²	1	2	yes	complemented
87	C₆₁×#463	C₂²	1	2	yes	—
88	C₆₁×#463	C₂²	1	2	yes	complemented
89	C₆₁×#461	C₂²	1	1	yes	characteristic
90	C₆₁×#461	C₂²	1	1	yes	characteristic, complemented
91	C₆₁×#460	C₂²	1	2	yes	complemented
92	C₆₁×#460	C₂²	1	2	yes	complemented
93	C₆₁×#460	C₂²	1	1	yes	characteristic, complemented
94	C₆₁×#459	C₂²	1	1	yes	characteristic, complemented
95	C₆₁×#450	C₂²	1	2	yes	—
96	C₆₁×#450	C₂²	1	2	yes	—
97	C₆₁×#449	C₂²	1	2	yes	complemented
98	C₆₁×#448	C₂²	1	2	yes	complemented
99	C₆₁×#448	C₂²	1	2	yes	complemented
100	C₆₁×#447	C₂²	1	2	yes	—
101	C₆₁×#446	C₂²	1	1	yes	characteristic, complemented
102	C₆₁×#446	C₂²	1	1	yes	characteristic, complemented
103	C₆₁×#442	C₂²	1	1	yes	characteristic
104	C₆₁×#442	C₂²	1	2	yes	complemented
105	C₆₁×#442	C₂²	1	1	yes	characteristic, complemented
106	C₆₁×#440	C₂²	1	2	yes	—
107	C₆₁×#440	C₂²	1	2	yes	—
108	C₆₁×#440	C₂²	1	2	yes	—
109	C₆₁×#440	C₂²	1	1	yes	characteristic
110	C₆₁×#440	C₂²	1	2	yes	complemented
111	C₆₁×#440	C₂²	1	2	yes	complemented
112	C₆₁×#440	C₂²	1	2	yes	complemented
113	C₆₁×#440	C₂²	1	1	yes	characteristic, complemented
114	C₆₁×#440	C₂²	1	2	yes	complemented
115	C₆₁×#440	C₂²	1	2	yes	complemented
116	C₆₁×#440	C₂²	1	2	yes	complemented
117	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
121	C₆₁×#435	C₂²	1	2	yes	complemented
122	C₆₁×#435	C₂²	1	2	yes	complemented
123	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
124	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
125	C₆₁×#432	C₂²	1	1	yes	characteristic, complemented
126	C₆₁×#432	C₂²	1	2	yes	complemented
127	C₆₁×#428	C₂²	1	1	yes	characteristic, complemented
128	C₂×#107×C₆₁	C₂²	1	2	yes	complemented
129	C₆₁×#418	C₂²	1	1	yes	characteristic
130	C₆₁×#417	C₂²	1	1	yes	characteristic, complemented
131	C₂×#103×C₆₁	C₂²	1	2	yes	complemented
132	C₂×#102×C₆₁	C₂²	1	2	yes	—
133	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
134	C₂×#97×C₆₁	C₂²	1	2	yes	complemented
135	C₂×#41×C₆₁	—	2	1	no	—
136	C₂×#41×C₆₁	—	2	2	no	—
137	C₂×#41×C₆₁	—	2	1	no	—
138	C₂×#41×C₆₁	—	2	1	no	—
139	C₂×#41×C₆₁	—	2	2	no	—
140	C₂×#41×C₆₁	—	2	1	no	—
141	C₂×#41×C₆₁	—	4	8	no	—
142	C₂×#41×C₆₁	D₄	1	1	yes	characteristic
143	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
144	C₂²×Q₈×C₆₁	—	2	1	no	—
145	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
146	C₂²×D₄×C₆₁	—	2	2	no	—
147	C₂²×D₄×C₆₁	—	2	1	no	—
148	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
149	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
150	C₂³×C₄×C₆₁	—	2	2	no	—
151	C₂³×C₄×C₆₁	—	2	1	no	—
152	AGL(1,ℤ/8)×C₆₁	—	2	4	no	—
153	C₂×SD₁₆×C₆₁	—	2	8	no	—
154	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
158	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
161	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
162	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
163	C₂×D₈×C₆₁	C₂³	1	2	yes	—
164	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
165	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
166	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
167	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
168	C₄⋊Q₈×C₆₁	—	2	1	no	—
169	C₄⋊Q₈×C₆₁	—	2	1	no	—
170	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
171	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
172	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
173	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
174	#127×C₆₁	C₂³	1	1	yes	characteristic
175	#127×C₆₁	C₂³	1	2	yes	—
176	#126×C₆₁	—	2	2	no	—
177	#126×C₆₁	—	2	2	no	—
178	#126×C₆₁	—	2	2	no	—
179	#125×C₆₁	—	2	2	no	—
180	#125×C₆₁	—	2	2	no	—
181	#125×C₆₁	—	2	1	no	—
182	#125×C₆₁	C₂³	1	2	yes	—
183	#124×C₆₁	—	2	2	no	—
184	#124×C₆₁	—	2	1	no	—
185	#124×C₆₁	—	2	2	no	—
186	#124×C₆₁	C₂³	1	2	yes	—
187	#123×C₆₁	—	2	2	no	—
188	#123×C₆₁	—	2	2	no	—
189	#123×C₆₁	—	2	2	no	—
190	#123×C₆₁	—	2	2	no	—
191	#123×C₆₁	—	2	2	no	—
192	#123×C₆₁	—	2	2	no	—
193	C₂²⋊Q₈×C₆₁	—	2	1	no	—
194	C₂²⋊Q₈×C₆₁	—	2	1	no	—
195	C₂²⋊Q₈×C₆₁	—	2	1	no	—
196	C₂²⋊Q₈×C₆₁	—	2	2	no	—
197	C₂²⋊Q₈×C₆₁	—	2	1	no	—
198	C₂²⋊Q₈×C₆₁	—	2	2	no	—
199	C₂²⋊Q₈×C₆₁	—	2	2	no	—
200	C₂²⋊Q₈×C₆₁	—	2	1	no	—
201	C₂²⋊Q₈×C₆₁	—	2	2	no	—
202	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
203	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
204	#121×C₆₁	—	2	2	no	—
205	#121×C₆₁	—	2	2	no	—
206	#121×C₆₁	—	2	1	no	—
207	#121×C₆₁	—	2	2	no	—
208	#121×C₆₁	—	2	1	no	—
209	#121×C₆₁	—	2	1	no	—
210	#121×C₆₁	—	2	2	no	—
211	#121×C₆₁	C₂³	1	2	yes	—
212	#121×C₆₁	C₂³	1	2	yes	—
213	#121×C₆₁	C₂³	1	2	yes	—
214	#121×C₆₁	C₂³	1	2	yes	—
215	#120×C₆₁	—	2	2	no	—
216	#120×C₆₁	—	2	2	no	—
217	#120×C₆₁	—	2	2	no	—
218	C₄×Q₈×C₆₁	—	2	1	no	—
219	C₄×Q₈×C₆₁	—	2	1	no	—
220	C₄×Q₈×C₆₁	—	2	2	no	—
221	C₄×Q₈×C₆₁	—	2	2	no	—
222	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
223	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
224	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
225	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
227	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
229	C₄×D₄×C₆₁	—	2	1	no	—
230	C₄×D₄×C₆₁	—	2	1	no	—
231	C₄×D₄×C₆₁	—	2	2	no	—
232	C₄×D₄×C₆₁	—	2	1	no	—
233	C₄×D₄×C₆₁	—	2	2	no	—
234	C₄×D₄×C₆₁	—	2	1	no	—
235	C₄×D₄×C₆₁	—	2	2	no	—
236	C₄×D₄×C₆₁	—	2	1	no	—
237	C₄×D₄×C₆₁	—	2	2	no	—
238	C₄×D₄×C₆₁	—	2	1	no	—
239	C₄×D₄×C₆₁	—	2	2	no	—
240	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
241	C₄×D₄×C₆₁	D₄	1	2	yes	—
242	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₆₁	C₂³	1	2	yes	—
244	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₆₁	C₂³	1	2	yes	—
246	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₆₁	C₂³	1	2	yes	—
248	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₆₁	C₂³	1	2	yes	—
253	#117×C₆₁	—	2	1	no	—
254	#117×C₆₁	—	2	1	no	—
255	#117×C₆₁	—	2	2	no	—
256	#117×C₆₁	—	2	2	no	—
257	#117×C₆₁	—	2	1	no	—
258	#117×C₆₁	D₄	1	2	yes	—
259	#117×C₆₁	D₄	1	1	yes	characteristic
260	#117×C₆₁	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
262	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
265	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
266	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
267	C₂×C₄²×C₆₁	—	2	2	no	—
268	C₂×C₄²×C₆₁	—	2	1	no	—
269	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
270	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
271	#107×C₆₁	C₂³	1	1	yes	characteristic
272	#107×C₆₁	C₂³	1	2	yes	—
273	#107×C₆₁	C₂³	1	2	yes	—
274	#107×C₆₁	C₂³	1	2	yes	—
275	#107×C₆₁	C₂³	1	1	yes	characteristic
276	#107×C₆₁	C₂³	1	2	yes	—
277	#107×C₆₁	C₂³	1	2	yes	—
278	#106×C₆₁	C₂³	1	1	yes	characteristic
279	#106×C₆₁	C₂³	1	1	yes	characteristic
280	#106×C₆₁	C₂³	1	2	yes	—
281	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
284	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
285	#103×C₆₁	C₂³	1	1	yes	characteristic
286	#103×C₆₁	C₂³	1	2	yes	—
287	#103×C₆₁	C₂³	1	2	yes	—
288	#103×C₆₁	C₂³	1	2	yes	—
289	#103×C₆₁	C₂³	1	1	yes	characteristic
290	#103×C₆₁	C₂³	1	2	yes	—
291	#103×C₆₁	C₂³	1	2	yes	—
292	#102×C₆₁	C₂³	1	1	yes	characteristic
293	#102×C₆₁	C₂³	1	2	yes	—
294	#102×C₆₁	C₂³	1	2	yes	—
295	#102×C₆₁	C₂³	1	2	yes	—
296	#102×C₆₁	C₂³	1	1	yes	characteristic
297	#102×C₆₁	C₂³	1	1	yes	characteristic
298	#102×C₆₁	C₂³	1	1	yes	characteristic
299	#102×C₆₁	C₂³	1	1	yes	characteristic
300	#102×C₆₁	C₂³	1	1	yes	characteristic
301	#102×C₆₁	C₂³	1	2	yes	—
302	#102×C₆₁	C₂³	1	2	yes	—
303	#102×C₆₁	C₂³	1	2	yes	—
304	#102×C₆₁	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
308	#97×C₆₁	C₂³	1	1	yes	characteristic
309	#97×C₆₁	C₂³	1	2	yes	—
310	#97×C₆₁	C₂³	1	2	yes	—
311	#97×C₆₁	C₂³	1	2	yes	—
312	#97×C₆₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
315	C₂⁴×C₆₁	—	2	1	no	—
316	C₂⁴×C₆₁	—	2	2	no	—
317	#41×C₆₁	—	2	4	no	—
318	#41×C₆₁	—	2	2	no	—
319	#41×C₆₁	—	4	1	no	—
320	#41×C₆₁	—	4	8	no	—
321	#41×C₆₁	—	4	4	no	—
322	#41×C₆₁	—	4	8	no	—
323	#41×C₆₁	—	4	4	no	—
324	#41×C₆₁	—	4	4	no	—
325	#41×C₆₁	—	4	4	no	—
326	C₂×Q₈×C₆₁	—	2	2	no	—
327	C₂×Q₈×C₆₁	—	2	1	no	—
328	C₂×Q₈×C₆₁	—	2	2	no	—
329	C₂×Q₈×C₆₁	—	2	1	no	—
330	C₂×Q₈×C₆₁	—	2	4	no	—
331	C₂×Q₈×C₆₁	—	4	2	no	—
332	C₂×Q₈×C₆₁	—	4	4	no	—
333	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
334	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
335	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
336	C₂×D₄×C₆₁	—	2	4	no	—
337	C₂×D₄×C₆₁	—	2	2	no	—
338	C₂×D₄×C₆₁	—	2	1	no	—
339	C₂×D₄×C₆₁	—	2	2	no	—
340	C₂×D₄×C₆₁	—	2	2	no	—
341	C₂×D₄×C₆₁	—	2	2	no	—
342	C₂×D₄×C₆₁	—	2	2	no	—
343	C₂×D₄×C₆₁	—	2	1	no	—
344	C₂×D₄×C₆₁	—	2	2	no	—
345	C₂×D₄×C₆₁	—	2	2	no	—
346	C₂×D₄×C₆₁	—	2	1	no	—
347	C₂×D₄×C₆₁	—	2	2	no	—
348	C₂×D₄×C₆₁	—	2	1	no	—
349	C₂×D₄×C₆₁	—	4	2	no	—
350	C₂×D₄×C₆₁	—	4	1	no	—
351	C₂×D₄×C₆₁	—	4	8	no	—
352	C₂×D₄×C₆₁	—	4	4	no	—
353	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
354	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
355	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
356	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
357	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
358	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄×C₆₁	—	2	2	no	—
360	C₂²×C₄×C₆₁	—	2	2	no	—
361	C₂²×C₄×C₆₁	—	2	1	no	—
362	C₂²×C₄×C₆₁	—	2	2	no	—
363	C₂²×C₄×C₆₁	—	2	1	no	—
364	C₂²×C₄×C₆₁	—	2	1	no	—
365	C₂²×C₄×C₆₁	—	2	1	no	—
366	C₂²×C₄×C₆₁	—	2	1	no	—
367	C₂²×C₄×C₆₁	—	2	2	no	—
368	C₂²×C₄×C₆₁	—	2	1	no	—
369	C₂²×C₄×C₆₁	—	2	2	no	—
370	C₂²×C₄×C₆₁	—	2	1	no	—
371	C₂²×C₄×C₆₁	—	2	2	no	—
372	C₂²×C₄×C₆₁	—	2	1	no	—
373	C₂²×C₄×C₆₁	—	4	8	no	—
374	C₂²×C₄×C₆₁	—	4	4	no	—
375	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
376	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
377	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
378	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
379	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
380	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
381	SD₁₆×C₆₁	—	2	4	no	—
382	SD₁₆×C₆₁	—	2	2	no	—
383	SD₁₆×C₆₁	—	2	4	no	—
384	SD₁₆×C₆₁	—	2	4	no	—
385	SD₁₆×C₆₁	—	4	2	no	—
386	SD₁₆×C₆₁	—	4	2	no	—
387	SD₁₆×C₆₁	#41	1	4	yes	complemented
388	D₈×C₆₁	—	2	2	no	—
389	D₈×C₆₁	—	2	2	no	—
390	D₈×C₆₁	—	4	2	no	—
391	M₁₆×C₆₁	—	2	2	no	—
392	M₁₆×C₆₁	—	4	1	no	—
393	C₂×C₈×C₆₁	—	2	4	no	—
394	C₂×C₈×C₆₁	—	4	2	no	—
395	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
396	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
397	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
398	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
399	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
400	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₆₁	—	2	1	no	—
402	C₄⋊C₄×C₆₁	—	2	2	no	—
403	C₄⋊C₄×C₆₁	—	2	2	no	—
404	C₄⋊C₄×C₆₁	—	2	2	no	—
405	C₄⋊C₄×C₆₁	—	2	1	no	—
406	C₄⋊C₄×C₆₁	—	2	2	no	—
407	C₄⋊C₄×C₆₁	—	2	2	no	—
408	C₄⋊C₄×C₆₁	—	2	1	no	—
409	C₄⋊C₄×C₆₁	—	2	2	no	—
410	C₄⋊C₄×C₆₁	—	2	2	no	—
411	C₄⋊C₄×C₆₁	—	2	1	no	—
412	C₄⋊C₄×C₆₁	—	2	1	no	—
413	C₄⋊C₄×C₆₁	—	2	2	no	—
414	C₄⋊C₄×C₆₁	—	2	1	no	—
415	C₄⋊C₄×C₆₁	—	2	2	no	—
416	C₄⋊C₄×C₆₁	—	2	2	no	—
417	C₄⋊C₄×C₆₁	—	2	1	no	—
418	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
419	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
420	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
421	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
422	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
425	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
426	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
427	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
428	C₂²⋊C₄×C₆₁	—	2	2	no	—
429	C₂²⋊C₄×C₆₁	—	2	2	no	—
430	C₂²⋊C₄×C₆₁	—	2	1	no	—
431	C₂²⋊C₄×C₆₁	—	2	1	no	—
432	C₂²⋊C₄×C₆₁	—	2	2	no	—
433	C₂²⋊C₄×C₆₁	—	2	1	no	—
434	C₂²⋊C₄×C₆₁	—	2	2	no	—
435	C₂²⋊C₄×C₆₁	—	2	1	no	—
436	C₂²⋊C₄×C₆₁	—	2	2	no	—
437	C₂²⋊C₄×C₆₁	—	2	1	no	—
438	C₂²⋊C₄×C₆₁	—	2	2	no	—
439	C₂²⋊C₄×C₆₁	—	2	1	no	—
440	C₂²⋊C₄×C₆₁	—	2	1	no	—
441	C₂²⋊C₄×C₆₁	—	2	2	no	—
442	C₂²⋊C₄×C₆₁	—	2	2	no	—
443	C₂²⋊C₄×C₆₁	—	2	2	no	—
444	C₂²⋊C₄×C₆₁	—	2	2	no	—
445	C₂²⋊C₄×C₆₁	—	2	2	no	—
446	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
447	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
448	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
449	C₄²×C₆₁	—	2	1	no	—
450	C₄²×C₆₁	—	2	1	no	—
451	C₄²×C₆₁	—	2	2	no	—
452	C₄²×C₆₁	—	2	2	no	—
453	C₄²×C₆₁	—	2	1	no	—
454	C₄²×C₆₁	—	2	2	no	—
455	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
456	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
457	C₄²×C₆₁	C₂×D₄	1	2	yes	—
458	C₄²×C₆₁	C₂×D₄	1	2	yes	—
459	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
460	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
461	C₄²×C₆₁	C₂⁴	1	2	yes	—
462	C₂³×C₆₁	—	2	1	no	—
463	C₂³×C₆₁	—	2	1	no	—
464	C₂³×C₆₁	—	2	1	no	—
465	C₂³×C₆₁	—	2	2	no	—
466	C₂³×C₆₁	—	4	4	no	—
467	C₂³×C₆₁	—	4	2	no	—
468	C₂³×C₆₁	—	4	2	no	—
469	C₂³×C₆₁	—	4	4	no	—
470	C₂³×C₆₁	—	8	2	no	—
471	C₂³×C₆₁	—	8	1	no	—
472	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
473	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
474	Q₈×C₆₁	—	2	2	no	—
475	Q₈×C₆₁	—	2	1	no	—
476	Q₈×C₆₁	—	2	2	no	—
477	Q₈×C₆₁	—	2	2	no	—
478	Q₈×C₆₁	—	4	4	no	—
479	Q₈×C₆₁	—	4	4	no	—
480	Q₈×C₆₁	—	4	2	no	—
481	Q₈×C₆₁	—	4	2	no	—
482	Q₈×C₆₁	C₂×#41	1	2	yes	complemented
483	D₄×C₆₁	—	2	4	no	—
484	D₄×C₆₁	—	2	1	no	—
485	D₄×C₆₁	—	2	1	no	—
486	D₄×C₆₁	—	2	2	no	—
487	D₄×C₆₁	—	2	1	no	—
488	D₄×C₆₁	—	2	1	no	—
489	D₄×C₆₁	—	2	2	no	—
490	D₄×C₆₁	—	2	1	no	—
491	D₄×C₆₁	—	4	2	no	—
492	D₄×C₆₁	—	4	4	no	—
493	D₄×C₆₁	—	4	2	no	—
494	D₄×C₆₁	—	4	4	no	—
495	D₄×C₆₁	—	4	4	no	—
496	D₄×C₆₁	—	4	4	no	—
497	D₄×C₆₁	—	4	4	no	—
498	D₄×C₆₁	—	4	4	no	—
499	D₄×C₆₁	—	4	2	no	—
500	D₄×C₆₁	—	8	2	no	—
501	D₄×C₆₁	—	8	1	no	—
502	D₄×C₆₁	AGL(1,ℤ/8)	1	4	yes	complemented
503	D₄×C₆₁	C₂×#41	1	2	yes	—
504	C₂×C₄×C₆₁	—	2	4	no	—
505	C₂×C₄×C₆₁	—	2	1	no	—
506	C₂×C₄×C₆₁	—	2	2	no	—
507	C₂×C₄×C₆₁	—	2	2	no	—
508	C₂×C₄×C₆₁	—	2	1	no	—
509	C₂×C₄×C₆₁	—	2	2	no	—
510	C₂×C₄×C₆₁	—	2	1	no	—
511	C₂×C₄×C₆₁	—	2	1	no	—
512	C₂×C₄×C₆₁	—	2	1	no	—
513	C₂×C₄×C₆₁	—	2	2	no	—
514	C₂×C₄×C₆₁	—	2	2	no	—
515	C₂×C₄×C₆₁	—	2	1	no	—
516	C₂×C₄×C₆₁	—	2	2	no	—
517	C₂×C₄×C₆₁	—	2	1	no	—
518	C₂×C₄×C₆₁	—	4	2	no	—
519	C₂×C₄×C₆₁	—	4	1	no	—
520	C₂×C₄×C₆₁	—	4	2	no	—
521	C₂×C₄×C₆₁	—	4	4	no	—
522	C₂×C₄×C₆₁	—	4	2	no	—
523	C₂×C₄×C₆₁	—	4	2	no	—
524	C₂×C₄×C₆₁	—	4	4	no	—
525	C₂×C₄×C₆₁	—	4	4	no	—
526	C₂×C₄×C₆₁	—	4	2	no	—
527	C₂×C₄×C₆₁	—	4	4	no	—
528	C₂×C₄×C₆₁	—	4	2	no	—
529	C₂×C₄×C₆₁	—	4	4	no	—
530	C₂×C₄×C₆₁	—	4	4	no	—
531	C₂×C₄×C₆₁	—	4	2	no	—
532	C₂×C₄×C₆₁	—	4	2	no	—
533	C₂×C₄×C₆₁	—	4	2	no	—
534	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
536	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
539	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
540	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
541	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
542	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
543	C₈×C₆₁	—	2	2	no	—
544	C₈×C₆₁	—	2	1	no	—
545	C₈×C₆₁	—	2	1	no	—
546	C₈×C₆₁	—	2	2	no	—
547	C₈×C₆₁	—	2	1	no	—
548	C₈×C₆₁	C₂×#41	1	2	yes	complemented
549	#61452	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
550	C₂²×C₆₁	—	2	2	no	—
551	C₂²×C₆₁	—	2	2	no	—
552	C₂²×C₆₁	—	2	1	no	—
553	C₂²×C₆₁	—	2	1	no	—
554	C₂²×C₆₁	—	2	2	no	—
555	C₂²×C₆₁	—	2	1	no	—
556	C₂²×C₆₁	—	4	1	no	—
557	C₂²×C₆₁	—	4	1	no	—
558	C₂²×C₆₁	—	4	1	no	—
559	C₂²×C₆₁	—	4	2	no	—
560	C₂²×C₆₁	—	4	1	no	—
561	C₂²×C₆₁	—	4	1	no	—
562	C₂²×C₆₁	—	4	1	no	—
563	C₂²×C₆₁	—	4	2	no	—
564	C₂²×C₆₁	—	4	2	no	—
565	C₂²×C₆₁	—	4	1	no	—
566	C₂²×C₆₁	—	4	1	no	—
567	C₂²×C₆₁	—	8	8	no	—
568	C₂²×C₆₁	—	8	4	no	—
569	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	4	yes	—
570	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
571	C₄×C₆₁	—	2	1	no	—
572	C₄×C₆₁	—	2	2	no	—
573	C₄×C₆₁	—	2	1	no	—
574	C₄×C₆₁	—	2	1	no	—
575	C₄×C₆₁	—	2	2	no	—
576	C₄×C₆₁	—	2	2	no	—
577	C₄×C₆₁	—	2	1	no	—
578	C₄×C₆₁	—	2	2	no	—
579	C₄×C₆₁	—	4	1	no	—
580	C₄×C₆₁	—	4	2	no	—
581	C₄×C₆₁	—	4	1	no	—
582	C₄×C₆₁	—	4	1	no	—
583	C₄×C₆₁	—	4	2	no	—
584	C₄×C₆₁	—	4	1	no	—
585	C₄×C₆₁	—	4	2	no	—
586	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
587	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
588	C₄×C₆₁	#585	1	1	yes	characteristic
589	#3482	C₂×C₆₁	1	1	yes	characteristic, complemented
590	D₄×#41	C₂×C₆₁	1	1	yes	characteristic, complemented
591	#3397	C₂×C₆₁	1	1	yes	characteristic, complemented
592	#3386	C₂×C₆₁	1	1	yes	characteristic, complemented
593	#3368	C₂×C₆₁	1	1	yes	characteristic, complemented
594	#3367	C₂×C₆₁	1	1	yes	characteristic, complemented
595	#3343	C₂×C₆₁	1	2	yes	complemented
596	#3334	C₂×C₆₁	1	1	yes	characteristic, complemented
597	#3310	C₂×C₆₁	1	2	yes	complemented
598	#3308	C₂×C₆₁	1	2	yes	complemented
599	#3298	C₂×C₆₁	1	1	yes	characteristic, complemented
600	#3294	C₂×C₆₁	1	1	yes	characteristic, complemented
601	D₄×SD₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
602	#3265	C₂×C₆₁	1	2	yes	complemented
603	#3182	C₂×C₆₁	1	1	yes	characteristic, complemented
604	#3180	C₂×C₆₁	1	2	yes	complemented
605	#3115	C₂×C₆₁	1	1	yes	characteristic, complemented
606	#3114	C₂×C₆₁	1	2	yes	complemented
607	#3112	C₂×C₆₁	1	2	yes	complemented
608	#3110	C₂×C₆₁	1	1	yes	characteristic, complemented
609	#2970	C₂×C₆₁	1	1	yes	characteristic, complemented
610	C₄×AGL(1,ℤ/8)	C₂×C₆₁	1	1	yes	characteristic, complemented
611	C₂×#440	C₂×C₆₁	1	2	yes	complemented
612	C₂×C₆₁	—	2	4	no	—
613	C₂×C₆₁	—	4	1	no	—
614	C₂×C₆₁	—	4	2	no	—
615	C₂×C₆₁	—	8	1	no	—
616	C₂×C₆₁	—	8	2	no	—
617	C₂×C₆₁	—	8	1	no	—
618	C₂×C₆₁	D₄×#41	1	1	yes	characteristic
619	C₂×C₆₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
620	C₂×C₆₁	#3586	1	1	yes	characteristic
621	C₂²×#41	—	2	1	no	—
622	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	1	yes	characteristic
623	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	—
624	#557	C₂²×C₆₁	1	1	yes	characteristic, complemented
625	#556	—	2	1	no	—
626	#556	C₂²×C₆₁	1	1	yes	characteristic, complemented
627	#552	—	2	2	no	—
628	#552	C₂²×C₆₁	1	2	yes	complemented
629	#550	C₂²×C₆₁	1	1	yes	characteristic
630	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
631	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
632	#548	—	2	1	no	—
633	#548	C₂²×C₆₁	1	2	yes	complemented
634	#547	—	2	1	no	—
635	#547	C₂²×C₆₁	1	1	yes	characteristic
636	#547	C₂²×C₆₁	1	2	yes	—
637	#547	C₂²×C₆₁	1	1	yes	characteristic, complemented
638	#546	—	2	1	no	—
639	#546	—	2	2	no	—
640	D₄²	C₂²×C₆₁	1	2	yes	—
641	D₄²	C₂²×C₆₁	1	1	yes	characteristic
642	#533	—	2	1	no	—
643	#533	C₂²×C₆₁	1	1	yes	characteristic, complemented
644	#532	C₂²×C₆₁	1	2	yes	—
645	#532	C₂²×C₆₁	1	1	yes	characteristic
646	#529	—	2	2	no	—
647	#529	C₂²×C₆₁	1	2	yes	complemented
648	#525	—	2	2	no	—
649	#525	—	2	1	no	—
650	C₄×#41	—	2	1	no	—
651	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
652	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic, complemented
653	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	complemented
654	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
655	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
656	#501	C₂²×C₆₁	1	2	yes	complemented
657	#500	C₂²×C₆₁	1	1	yes	characteristic, complemented
658	#496	C₂²×C₆₁	1	2	yes	complemented
659	#492	C₂²×C₆₁	1	1	yes	characteristic, complemented
660	#490	C₂²×C₆₁	1	2	yes	complemented
661	#489	C₂²×C₆₁	1	2	yes	complemented
662	#487	C₂²×C₆₁	1	1	yes	characteristic, complemented
663	#486	C₂²×C₆₁	1	1	yes	characteristic, complemented
664	#484	C₂²×C₆₁	1	2	yes	complemented
665	#483	C₂²×C₆₁	1	2	yes	complemented
666	#482	C₂²×C₆₁	1	2	yes	complemented
667	#480	C₂²×C₆₁	1	2	yes	complemented
668	#480	C₂²×C₆₁	1	2	yes	complemented
669	#480	C₂²×C₆₁	1	2	yes	complemented
670	#478	C₂²×C₆₁	1	2	yes	—
671	#478	C₂²×C₆₁	1	2	yes	complemented
672	#477	C₂²×C₆₁	1	2	yes	complemented
673	#477	C₂²×C₆₁	1	2	yes	complemented
674	#475	C₂²×C₆₁	1	1	yes	characteristic, complemented
675	#474	C₂²×C₆₁	1	1	yes	characteristic
676	#474	C₂²×C₆₁	1	1	yes	characteristic, complemented
677	#474	C₂²×C₆₁	1	1	yes	characteristic, complemented
678	#468	C₂²×C₆₁	1	2	yes	complemented
679	#468	C₂²×C₆₁	1	2	yes	complemented
680	#466	C₂²×C₆₁	1	2	yes	complemented
681	#466	C₂²×C₆₁	1	2	yes	complemented
682	#465	C₂²×C₆₁	1	2	yes	complemented
683	#465	C₂²×C₆₁	1	2	yes	complemented
684	#463	C₂²×C₆₁	1	2	yes	—
685	#463	C₂²×C₆₁	1	2	yes	complemented
686	#461	C₂²×C₆₁	1	1	yes	characteristic
687	#461	C₂²×C₆₁	1	1	yes	characteristic, complemented
688	#460	C₂²×C₆₁	1	2	yes	complemented
689	#460	C₂²×C₆₁	1	2	yes	complemented
690	#460	C₂²×C₆₁	1	1	yes	characteristic, complemented
691	#459	C₂²×C₆₁	1	1	yes	characteristic, complemented
692	#450	C₂²×C₆₁	1	2	yes	—
693	#450	C₂²×C₆₁	1	2	yes	—
694	#449	C₂²×C₆₁	1	2	yes	complemented
695	#448	C₂²×C₆₁	1	2	yes	complemented
696	#448	C₂²×C₆₁	1	2	yes	complemented
697	#447	C₂²×C₆₁	1	2	yes	—
698	#446	C₂²×C₆₁	1	1	yes	characteristic, complemented
699	#446	C₂²×C₆₁	1	1	yes	characteristic, complemented
700	#442	C₂²×C₆₁	1	1	yes	characteristic
701	#442	C₂²×C₆₁	1	2	yes	complemented
702	#442	C₂²×C₆₁	1	1	yes	characteristic, complemented
703	#440	C₂²×C₆₁	1	2	yes	—
704	#440	C₂²×C₆₁	1	2	yes	—
705	#440	C₂²×C₆₁	1	2	yes	—
706	#440	C₂²×C₆₁	1	1	yes	characteristic
707	#440	C₂²×C₆₁	1	2	yes	complemented
708	#440	C₂²×C₆₁	1	2	yes	complemented
709	#440	C₂²×C₆₁	1	1	yes	characteristic, complemented
710	#440	C₂²×C₆₁	1	2	yes	complemented
711	#440	C₂²×C₆₁	1	2	yes	complemented
712	#440	C₂²×C₆₁	1	2	yes	complemented
713	#440	C₂²×C₆₁	1	2	yes	complemented
714	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
715	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
716	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
717	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
718	#435	C₂²×C₆₁	1	2	yes	complemented
719	#435	C₂²×C₆₁	1	2	yes	complemented
720	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
721	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
722	#432	C₂²×C₆₁	1	1	yes	characteristic, complemented
723	#432	C₂²×C₆₁	1	2	yes	complemented
724	#428	C₂²×C₆₁	1	1	yes	characteristic, complemented
725	C₂×#107	C₂²×C₆₁	1	2	yes	complemented
726	#418	C₂²×C₆₁	1	1	yes	characteristic
727	#417	C₂²×C₆₁	1	1	yes	characteristic, complemented
728	C₂×#103	C₂²×C₆₁	1	2	yes	complemented
729	C₂×#102	C₂²×C₆₁	1	2	yes	—
730	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
731	C₂×#97	C₂²×C₆₁	1	2	yes	complemented
732	C₆₁	#61452	1	1	yes	characteristic, direct product factor, Sylow
733	C₂×#41	—	2	1	no	—
734	C₂×#41	—	2	1	no	—
735	C₂×#41	—	2	2	no	—
736	C₂×#41	—	2	1	no	—
737	C₂×#41	—	2	2	no	—
738	C₂×#41	—	2	1	no	—
739	C₂×#41	—	4	8	no	—
740	C₂×#41	D₄×C₆₁	1	1	yes	characteristic
741	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
742	C₂²×Q₈	—	2	1	no	—
743	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
744	C₂²×D₄	—	2	2	no	—
745	C₂²×D₄	—	2	1	no	—
746	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
747	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
748	C₂³×C₄	—	2	2	no	—
749	C₂³×C₄	—	2	1	no	—
750	AGL(1,ℤ/8)	—	2	4	no	—
751	C₂×SD₁₆	—	2	8	no	—
752	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
753	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
754	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
755	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
756	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
757	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
758	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
759	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
760	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
761	C₂×D₈	C₂³×C₆₁	1	2	yes	—
762	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
763	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
764	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
765	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
766	C₄⋊Q₈	—	2	1	no	—
767	C₄⋊Q₈	—	2	1	no	—
768	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
769	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
770	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
771	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
772	#127	C₂³×C₆₁	1	1	yes	characteristic
773	#127	C₂³×C₆₁	1	2	yes	—
774	#126	—	2	2	no	—
775	#126	—	2	2	no	—
776	#126	—	2	2	no	—
777	#125	—	2	2	no	—
778	#125	—	2	2	no	—
779	#125	—	2	1	no	—
780	#125	C₂³×C₆₁	1	2	yes	—
781	#124	—	2	2	no	—
782	#124	—	2	1	no	—
783	#124	—	2	2	no	—
784	#124	C₂³×C₆₁	1	2	yes	—
785	#123	—	2	2	no	—
786	#123	—	2	2	no	—
787	#123	—	2	2	no	—
788	#123	—	2	2	no	—
789	#123	—	2	2	no	—
790	#123	—	2	2	no	—
791	C₂²⋊Q₈	—	2	1	no	—
792	C₂²⋊Q₈	—	2	1	no	—
793	C₂²⋊Q₈	—	2	1	no	—
794	C₂²⋊Q₈	—	2	2	no	—
795	C₂²⋊Q₈	—	2	2	no	—
796	C₂²⋊Q₈	—	2	1	no	—
797	C₂²⋊Q₈	—	2	1	no	—
798	C₂²⋊Q₈	—	2	2	no	—
799	C₂²⋊Q₈	—	2	2	no	—
800	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
801	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
802	#121	—	2	2	no	—
803	#121	—	2	2	no	—
804	#121	—	2	1	no	—
805	#121	—	2	2	no	—
806	#121	—	2	1	no	—
807	#121	—	2	1	no	—
808	#121	—	2	2	no	—
809	#121	C₂³×C₆₁	1	2	yes	—
810	#121	C₂³×C₆₁	1	2	yes	—
811	#121	C₂³×C₆₁	1	2	yes	—
812	#121	C₂³×C₆₁	1	2	yes	—
813	#120	—	2	2	no	—
814	#120	—	2	2	no	—
815	#120	—	2	2	no	—
816	C₄×Q₈	—	2	1	no	—
817	C₄×Q₈	—	2	2	no	—
818	C₄×Q₈	—	2	2	no	—
819	C₄×Q₈	—	2	1	no	—
820	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
821	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
822	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
823	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
824	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
825	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
826	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	—	2	1	no	—
831	C₄×D₄	—	2	2	no	—
832	C₄×D₄	—	2	1	no	—
833	C₄×D₄	—	2	2	no	—
834	C₄×D₄	—	2	1	no	—
835	C₄×D₄	—	2	2	no	—
836	C₄×D₄	—	2	1	no	—
837	C₄×D₄	—	2	2	no	—
838	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
839	C₄×D₄	D₄×C₆₁	1	2	yes	—
840	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
841	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
842	C₄×D₄	C₂³×C₆₁	1	2	yes	—
843	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
844	C₄×D₄	C₂³×C₆₁	1	2	yes	—
845	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
846	C₄×D₄	C₂³×C₆₁	1	2	yes	—
847	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
848	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
849	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
850	C₄×D₄	C₂³×C₆₁	1	2	yes	—
851	#117	—	2	1	no	—
852	#117	—	2	1	no	—
853	#117	—	2	2	no	—
854	#117	—	2	1	no	—
855	#117	—	2	2	no	—
856	#117	D₄×C₆₁	1	2	yes	—
857	#117	D₄×C₆₁	1	1	yes	characteristic
858	#117	C₂³×C₆₁	1	1	yes	characteristic
859	C₂×C₄⋊C₄	—	2	2	no	—
860	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
861	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
862	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
863	C₂×C₂²⋊C₄	—	2	2	no	—
864	C₂×C₂²⋊C₄	—	2	1	no	—
865	C₂×C₄²	—	2	2	no	—
866	C₂×C₄²	—	2	1	no	—
867	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
868	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
869	#107	C₂³×C₆₁	1	1	yes	characteristic
870	#107	C₂³×C₆₁	1	2	yes	—
871	#107	C₂³×C₆₁	1	2	yes	—
872	#107	C₂³×C₆₁	1	2	yes	—
873	#107	C₂³×C₆₁	1	1	yes	characteristic
874	#107	C₂³×C₆₁	1	2	yes	—
875	#107	C₂³×C₆₁	1	2	yes	—
876	#106	C₂³×C₆₁	1	1	yes	characteristic
877	#106	C₂³×C₆₁	1	1	yes	characteristic
878	#106	C₂³×C₆₁	1	2	yes	—
879	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
880	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
881	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
882	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
883	#103	C₂³×C₆₁	1	1	yes	characteristic
884	#103	C₂³×C₆₁	1	2	yes	—
885	#103	C₂³×C₆₁	1	2	yes	—
886	#103	C₂³×C₆₁	1	2	yes	—
887	#103	C₂³×C₆₁	1	1	yes	characteristic
888	#103	C₂³×C₆₁	1	2	yes	—
889	#103	C₂³×C₆₁	1	2	yes	—
890	#102	C₂³×C₆₁	1	1	yes	characteristic
891	#102	C₂³×C₆₁	1	2	yes	—
892	#102	C₂³×C₆₁	1	2	yes	—
893	#102	C₂³×C₆₁	1	2	yes	—
894	#102	C₂³×C₆₁	1	1	yes	characteristic
895	#102	C₂³×C₆₁	1	1	yes	characteristic
896	#102	C₂³×C₆₁	1	1	yes	characteristic
897	#102	C₂³×C₆₁	1	1	yes	characteristic
898	#102	C₂³×C₆₁	1	1	yes	characteristic
899	#102	C₂³×C₆₁	1	2	yes	—
900	#102	C₂³×C₆₁	1	2	yes	—
901	#102	C₂³×C₆₁	1	2	yes	—
902	#102	C₂³×C₆₁	1	2	yes	—
903	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
904	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
905	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
906	#97	C₂³×C₆₁	1	1	yes	characteristic
907	#97	C₂³×C₆₁	1	2	yes	—
908	#97	C₂³×C₆₁	1	2	yes	—
909	#97	C₂³×C₆₁	1	2	yes	—
910	#97	C₂³×C₆₁	1	1	yes	characteristic
911	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
912	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
913	C₂⁴	—	2	1	no	—
914	C₂⁴	—	2	2	no	—
915	#41	—	2	4	no	—
916	#41	—	2	2	no	—
917	#41	—	4	1	no	—
918	#41	—	4	8	no	—
919	#41	—	4	4	no	—
920	#41	—	4	8	no	—
921	#41	—	4	4	no	—
922	#41	—	4	4	no	—
923	#41	—	4	4	no	—
924	C₂×Q₈	—	2	2	no	—
925	C₂×Q₈	—	2	1	no	—
926	C₂×Q₈	—	2	2	no	—
927	C₂×Q₈	—	2	1	no	—
928	C₂×Q₈	—	2	4	no	—
929	C₂×Q₈	—	4	2	no	—
930	C₂×Q₈	—	4	4	no	—
931	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
932	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
933	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
934	C₂×D₄	—	2	4	no	—
935	C₂×D₄	—	2	2	no	—
936	C₂×D₄	—	2	1	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	1	no	—
942	C₂×D₄	—	2	2	no	—
943	C₂×D₄	—	2	2	no	—
944	C₂×D₄	—	2	1	no	—
945	C₂×D₄	—	2	2	no	—
946	C₂×D₄	—	2	1	no	—
947	C₂×D₄	—	4	2	no	—
948	C₂×D₄	—	4	1	no	—
949	C₂×D₄	—	4	8	no	—
950	C₂×D₄	—	4	4	no	—
951	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
952	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
953	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
954	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
955	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
956	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
957	C₂²×C₄	—	2	2	no	—
958	C₂²×C₄	—	2	2	no	—
959	C₂²×C₄	—	2	1	no	—
960	C₂²×C₄	—	2	2	no	—
961	C₂²×C₄	—	2	1	no	—
962	C₂²×C₄	—	2	1	no	—
963	C₂²×C₄	—	2	1	no	—
964	C₂²×C₄	—	2	1	no	—
965	C₂²×C₄	—	2	1	no	—
966	C₂²×C₄	—	2	2	no	—
967	C₂²×C₄	—	2	2	no	—
968	C₂²×C₄	—	2	1	no	—
969	C₂²×C₄	—	2	2	no	—
970	C₂²×C₄	—	2	1	no	—
971	C₂²×C₄	—	4	8	no	—
972	C₂²×C₄	—	4	4	no	—
973	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
974	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
975	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
976	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
977	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
978	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
979	SD₁₆	—	2	4	no	—
980	SD₁₆	—	2	2	no	—
981	SD₁₆	—	2	4	no	—
982	SD₁₆	—	2	4	no	—
983	SD₁₆	—	4	2	no	—
984	SD₁₆	—	4	2	no	—
985	SD₁₆	#41×C₆₁	1	4	yes	complemented
986	D₈	—	2	2	no	—
987	D₈	—	2	2	no	—
988	D₈	—	4	2	no	—
989	M₁₆	—	2	2	no	—
990	M₁₆	—	4	1	no	—
991	C₂×C₈	—	2	4	no	—
992	C₂×C₈	—	4	2	no	—
993	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
994	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
995	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
996	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
997	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
998	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
999	C₄⋊C₄	—	2	1	no	—
1000	C₄⋊C₄	—	2	2	no	—
1001	C₄⋊C₄	—	2	2	no	—
1002	C₄⋊C₄	—	2	2	no	—
1003	C₄⋊C₄	—	2	1	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	2	no	—
1006	C₄⋊C₄	—	2	1	no	—
1007	C₄⋊C₄	—	2	2	no	—
1008	C₄⋊C₄	—	2	2	no	—
1009	C₄⋊C₄	—	2	1	no	—
1010	C₄⋊C₄	—	2	1	no	—
1011	C₄⋊C₄	—	2	2	no	—
1012	C₄⋊C₄	—	2	1	no	—
1013	C₄⋊C₄	—	2	2	no	—
1014	C₄⋊C₄	—	2	2	no	—
1015	C₄⋊C₄	—	2	1	no	—
1016	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1017	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1018	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1019	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1020	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1021	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1022	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1023	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1024	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1025	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	1	no	—
1029	C₂²⋊C₄	—	2	1	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	1	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	—	2	1	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	1	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	1	no	—
1038	C₂²⋊C₄	—	2	1	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	2	no	—
1044	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1045	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1046	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1047	C₄²	—	2	1	no	—
1048	C₄²	—	2	1	no	—
1049	C₄²	—	2	2	no	—
1050	C₄²	—	2	2	no	—
1051	C₄²	—	2	1	no	—
1052	C₄²	—	2	2	no	—
1053	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1054	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1055	C₄²	C₂×D₄×C₆₁	1	2	yes	—
1056	C₄²	C₂×D₄×C₆₁	1	2	yes	—
1057	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1058	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1059	C₄²	C₂⁴×C₆₁	1	2	yes	—
1060	C₂³	—	2	1	no	—
1061	C₂³	—	2	1	no	—
1062	C₂³	—	2	2	no	—
1063	C₂³	—	2	1	no	—
1064	C₂³	—	4	4	no	—
1065	C₂³	—	4	2	no	—
1066	C₂³	—	4	2	no	—
1067	C₂³	—	4	4	no	—
1068	C₂³	—	8	2	no	—
1069	C₂³	—	8	1	no	—
1070	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1071	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1072	Q₈	—	2	2	no	—
1073	Q₈	—	2	1	no	—
1074	Q₈	—	2	2	no	—
1075	Q₈	—	2	2	no	—
1076	Q₈	—	4	4	no	—
1077	Q₈	—	4	4	no	—
1078	Q₈	—	4	2	no	—
1079	Q₈	—	4	2	no	—
1080	Q₈	C₂×#41×C₆₁	1	2	yes	complemented
1081	D₄	—	2	4	no	—
1082	D₄	—	2	1	no	—
1083	D₄	—	2	1	no	—
1084	D₄	—	2	2	no	—
1085	D₄	—	2	1	no	—
1086	D₄	—	2	1	no	—
1087	D₄	—	2	2	no	—
1088	D₄	—	2	1	no	—
1089	D₄	—	4	2	no	—
1090	D₄	—	4	4	no	—
1091	D₄	—	4	2	no	—
1092	D₄	—	4	4	no	—
1093	D₄	—	4	4	no	—
1094	D₄	—	4	4	no	—
1095	D₄	—	4	4	no	—
1096	D₄	—	4	4	no	—
1097	D₄	—	4	2	no	—
1098	D₄	—	8	2	no	—
1099	D₄	—	8	1	no	—
1100	D₄	AGL(1,ℤ/8)×C₆₁	1	4	yes	complemented
1101	D₄	C₂×#41×C₆₁	1	2	yes	—
1102	C₂×C₄	—	2	4	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	2	no	—
1112	C₂×C₄	—	2	2	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	4	2	no	—
1117	C₂×C₄	—	4	1	no	—
1118	C₂×C₄	—	4	2	no	—
1119	C₂×C₄	—	4	4	no	—
1120	C₂×C₄	—	4	2	no	—
1121	C₂×C₄	—	4	2	no	—
1122	C₂×C₄	—	4	4	no	—
1123	C₂×C₄	—	4	4	no	—
1124	C₂×C₄	—	4	2	no	—
1125	C₂×C₄	—	4	4	no	—
1126	C₂×C₄	—	4	2	no	—
1127	C₂×C₄	—	4	4	no	—
1128	C₂×C₄	—	4	4	no	—
1129	C₂×C₄	—	4	2	no	—
1130	C₂×C₄	—	4	2	no	—
1131	C₂×C₄	—	4	2	no	—
1132	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1133	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1134	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1135	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1136	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1137	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1138	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1139	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1140	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1141	C₈	—	2	2	no	—
1142	C₈	—	2	1	no	—
1143	C₈	—	2	1	no	—
1144	C₈	—	2	2	no	—
1145	C₈	—	2	1	no	—
1146	C₈	C₂×#41×C₆₁	1	2	yes	complemented
1147	C₂²	—	2	2	no	—
1148	C₂²	—	2	2	no	—
1149	C₂²	—	2	1	no	—
1150	C₂²	—	2	1	no	—
1151	C₂²	—	2	1	no	—
1152	C₂²	—	2	2	no	—
1153	C₂²	—	4	1	no	—
1154	C₂²	—	4	1	no	—
1155	C₂²	—	4	2	no	—
1156	C₂²	—	4	1	no	—
1157	C₂²	—	4	1	no	—
1158	C₂²	—	4	1	no	—
1159	C₂²	—	4	2	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	4	1	no	—
1162	C₂²	—	4	1	no	—
1163	C₂²	—	4	2	no	—
1164	C₂²	—	8	8	no	—
1165	C₂²	—	8	4	no	—
1166	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	4	yes	—
1167	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1168	C₄	—	2	1	no	—
1169	C₄	—	2	2	no	—
1170	C₄	—	2	1	no	—
1171	C₄	—	2	2	no	—
1172	C₄	—	2	1	no	—
1173	C₄	—	2	1	no	—
1174	C₄	—	2	2	no	—
1175	C₄	—	2	2	no	—
1176	C₄	—	4	1	no	—
1177	C₄	—	4	1	no	—
1178	C₄	—	4	2	no	—
1179	C₄	—	4	1	no	—
1180	C₄	—	4	2	no	—
1181	C₄	—	4	1	no	—
1182	C₄	—	4	2	no	—
1183	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	2	yes	—
1184	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
1185	C₄	C₆₁×#585	1	1	yes	characteristic
1186	C₂	—	2	4	no	—
1187	C₂	—	4	1	no	—
1188	C₂	—	4	2	no	—
1189	C₂	—	8	2	no	—
1190	C₂	—	8	1	no	—
1191	C₂	—	8	1	no	—
1192	C₂	D₄×#41×C₆₁	1	1	yes	characteristic
1193	C₂	C₂²×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
1194	C₂	C₆₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₄×#41×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3482	C₂	semidirect
2. D₄×#41×C₆₁	C₂	semidirect
3. C₆₁×#3397	C₂	semidirect
4. C₆₁×#3386	C₂	semidirect
5. C₆₁×#3368	C₂	semidirect
6. C₆₁×#3367	C₂	semidirect
7. C₆₁×#3343	C₂	semidirect
8. C₆₁×#3334	C₂	semidirect
9. C₆₁×#3310	C₂	semidirect
10. C₆₁×#3308	C₂	semidirect
11. C₆₁×#3298	C₂	semidirect
12. C₆₁×#3294	C₂	semidirect
13. D₄×SD₁₆×C₆₁	C₂	semidirect
14. C₆₁×#3265	C₂	semidirect
15. C₆₁×#3182	C₂	semidirect
16. C₆₁×#3180	C₂	semidirect
17. C₆₁×#3115	C₂	semidirect
18. C₆₁×#3114	C₂	semidirect
19. C₆₁×#3112	C₂	semidirect
20. C₆₁×#3110	C₂	semidirect
21. C₆₁×#2970	C₂	semidirect
22. C₄×AGL(1,ℤ/8)×C₆₁	C₂	semidirect
23. C₂×C₆₁×#440	C₂	semidirect
27. C₆₁×#557	C₂²	semidirect
29. C₆₁×#556	C₂²	semidirect
31. C₆₁×#552	C₂²	semidirect
34. D₄×Q₈×C₆₁	C₂²	semidirect
36. C₆₁×#548	C₂²	semidirect
40. C₆₁×#547	C₂²	semidirect
46. C₆₁×#533	C₂²	semidirect
50. C₆₁×#529	C₂²	semidirect
55. C₄×#41×C₆₁	C₂²	semidirect
56. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
59. C₆₁×#501	C₂²	semidirect
60. C₆₁×#500	C₂²	semidirect
61. C₆₁×#496	C₂²	semidirect
62. C₆₁×#492	C₂²	semidirect
63. C₆₁×#490	C₂²	semidirect
64. C₆₁×#489	C₂²	semidirect
65. C₆₁×#487	C₂²	semidirect
66. C₆₁×#486	C₂²	semidirect
67. C₆₁×#484	C₂²	semidirect
68. C₆₁×#483	C₂²	semidirect
69. C₆₁×#482	C₂²	semidirect
70. C₆₁×#480	C₂²	semidirect
71. C₆₁×#480	C₂²	semidirect
72. C₆₁×#480	C₂²	semidirect
74. C₆₁×#478	C₂²	semidirect
75. C₆₁×#477	C₂²	semidirect
76. C₆₁×#477	C₂²	semidirect
77. C₆₁×#475	C₂²	semidirect
79. C₆₁×#474	C₂²	semidirect
80. C₆₁×#474	C₂²	semidirect
81. C₆₁×#468	C₂²	semidirect
82. C₆₁×#468	C₂²	semidirect
83. C₆₁×#466	C₂²	semidirect
84. C₆₁×#466	C₂²	semidirect
85. C₆₁×#465	C₂²	semidirect
86. C₆₁×#465	C₂²	semidirect
88. C₆₁×#463	C₂²	semidirect
90. C₆₁×#461	C₂²	semidirect
91. C₆₁×#460	C₂²	semidirect
92. C₆₁×#460	C₂²	semidirect
93. C₆₁×#460	C₂²	semidirect
94. C₆₁×#459	C₂²	semidirect
97. C₆₁×#449	C₂²	semidirect
98. C₆₁×#448	C₂²	semidirect
99. C₆₁×#448	C₂²	semidirect
101. C₆₁×#446	C₂²	semidirect
102. C₆₁×#446	C₂²	semidirect
104. C₆₁×#442	C₂²	semidirect
105. C₆₁×#442	C₂²	semidirect
110. C₆₁×#440	C₂²	semidirect
111. C₆₁×#440	C₂²	semidirect
112. C₆₁×#440	C₂²	semidirect
113. C₆₁×#440	C₂²	semidirect
114. C₆₁×#440	C₂²	semidirect
115. C₆₁×#440	C₂²	semidirect
116. C₆₁×#440	C₂²	semidirect
118. C₄×SD₁₆×C₆₁	C₂²	semidirect
120. C₄×D₈×C₆₁	C₂²	semidirect
121. C₆₁×#435	C₂²	semidirect
122. C₆₁×#435	C₂²	semidirect
123. C₈×D₄×C₆₁	C₂²	semidirect
124. C₈×D₄×C₆₁	C₂²	semidirect
125. C₆₁×#432	C₂²	semidirect
126. C₆₁×#432	C₂²	semidirect
127. C₆₁×#428	C₂²	semidirect
128. C₂×#107×C₆₁	C₂²	semidirect
130. C₆₁×#417	C₂²	semidirect
131. C₂×#103×C₆₁	C₂²	semidirect
133. C₄×M₁₆×C₆₁	C₂²	semidirect
134. C₂×#97×C₆₁	C₂²	semidirect
387. SD₁₆×C₆₁	#41	semidirect
482. Q₈×C₆₁	C₂×#41	semidirect
502. D₄×C₆₁	AGL(1,ℤ/8)	semidirect
548. C₈×C₆₁	C₂×#41	semidirect
549. #61452	C₆₁	direct (N × H)
589. #3482	C₂×C₆₁	semidirect
590. D₄×#41	C₂×C₆₁	semidirect
591. #3397	C₂×C₆₁	semidirect
592. #3386	C₂×C₆₁	semidirect
593. #3368	C₂×C₆₁	semidirect
594. #3367	C₂×C₆₁	semidirect
595. #3343	C₂×C₆₁	semidirect
596. #3334	C₂×C₆₁	semidirect
597. #3310	C₂×C₆₁	semidirect
598. #3308	C₂×C₆₁	semidirect
599. #3298	C₂×C₆₁	semidirect
600. #3294	C₂×C₆₁	semidirect
601. D₄×SD₁₆	C₂×C₆₁	semidirect
602. #3265	C₂×C₆₁	semidirect
603. #3182	C₂×C₆₁	semidirect
604. #3180	C₂×C₆₁	semidirect
605. #3115	C₂×C₆₁	semidirect
606. #3114	C₂×C₆₁	semidirect
607. #3112	C₂×C₆₁	semidirect
608. #3110	C₂×C₆₁	semidirect
609. #2970	C₂×C₆₁	semidirect
610. C₄×AGL(1,ℤ/8)	C₂×C₆₁	semidirect
611. C₂×#440	C₂×C₆₁	semidirect
624. #557	C₂²×C₆₁	semidirect
626. #556	C₂²×C₆₁	semidirect
628. #552	C₂²×C₆₁	semidirect
631. D₄×Q₈	C₂²×C₆₁	semidirect
633. #548	C₂²×C₆₁	semidirect
637. #547	C₂²×C₆₁	semidirect
643. #533	C₂²×C₆₁	semidirect
647. #529	C₂²×C₆₁	semidirect
652. C₄×#41	C₂²×C₆₁	semidirect
653. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
656. #501	C₂²×C₆₁	semidirect
657. #500	C₂²×C₆₁	semidirect
658. #496	C₂²×C₆₁	semidirect
659. #492	C₂²×C₆₁	semidirect
660. #490	C₂²×C₆₁	semidirect
661. #489	C₂²×C₆₁	semidirect
662. #487	C₂²×C₆₁	semidirect
663. #486	C₂²×C₆₁	semidirect
664. #484	C₂²×C₆₁	semidirect
665. #483	C₂²×C₆₁	semidirect
666. #482	C₂²×C₆₁	semidirect
667. #480	C₂²×C₆₁	semidirect
668. #480	C₂²×C₆₁	semidirect
669. #480	C₂²×C₆₁	semidirect
671. #478	C₂²×C₆₁	semidirect
672. #477	C₂²×C₆₁	semidirect
673. #477	C₂²×C₆₁	semidirect
674. #475	C₂²×C₆₁	semidirect
676. #474	C₂²×C₆₁	semidirect
677. #474	C₂²×C₆₁	semidirect
678. #468	C₂²×C₆₁	semidirect
679. #468	C₂²×C₆₁	semidirect
680. #466	C₂²×C₆₁	semidirect
681. #466	C₂²×C₆₁	semidirect
682. #465	C₂²×C₆₁	semidirect
683. #465	C₂²×C₆₁	semidirect
685. #463	C₂²×C₆₁	semidirect
687. #461	C₂²×C₆₁	semidirect
688. #460	C₂²×C₆₁	semidirect
689. #460	C₂²×C₆₁	semidirect
690. #460	C₂²×C₆₁	semidirect
691. #459	C₂²×C₆₁	semidirect
694. #449	C₂²×C₆₁	semidirect
695. #448	C₂²×C₆₁	semidirect
696. #448	C₂²×C₆₁	semidirect
698. #446	C₂²×C₆₁	semidirect
699. #446	C₂²×C₆₁	semidirect
701. #442	C₂²×C₆₁	semidirect
702. #442	C₂²×C₆₁	semidirect
707. #440	C₂²×C₆₁	semidirect
708. #440	C₂²×C₆₁	semidirect
709. #440	C₂²×C₆₁	semidirect
710. #440	C₂²×C₆₁	semidirect
711. #440	C₂²×C₆₁	semidirect
712. #440	C₂²×C₆₁	semidirect
713. #440	C₂²×C₆₁	semidirect
715. C₄×SD₁₆	C₂²×C₆₁	semidirect
717. C₄×D₈	C₂²×C₆₁	semidirect
718. #435	C₂²×C₆₁	semidirect
719. #435	C₂²×C₆₁	semidirect
720. C₈×D₄	C₂²×C₆₁	semidirect
721. C₈×D₄	C₂²×C₆₁	semidirect
722. #432	C₂²×C₆₁	semidirect
723. #432	C₂²×C₆₁	semidirect
724. #428	C₂²×C₆₁	semidirect
725. C₂×#107	C₂²×C₆₁	semidirect
727. #417	C₂²×C₆₁	semidirect
728. C₂×#103	C₂²×C₆₁	semidirect
730. C₄×M₁₆	C₂²×C₆₁	semidirect
731. C₂×#97	C₂²×C₆₁	semidirect
732. C₆₁	#61452	direct (N × H)
985. SD₁₆	#41×C₆₁	semidirect
1080. Q₈	C₂×#41×C₆₁	semidirect
1100. D₄	AGL(1,ℤ/8)×C₆₁	semidirect
1146. C₈	C₂×#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×#3482	2
D₄×#41×C₆₁	2
C₆₁×#3397	2
C₆₁×#3386	2
C₆₁×#3368	2
C₆₁×#3367	2
C₆₁×#3343	2
C₆₁×#3334	2
C₆₁×#3310	2
C₆₁×#3308	2
C₆₁×#3298	2
C₆₁×#3294	2
D₄×SD₁₆×C₆₁	2
C₆₁×#3265	2
C₆₁×#3182	2
C₆₁×#3180	2
C₆₁×#3115	2
C₆₁×#3114	2
C₆₁×#3112	2
C₆₁×#3110	2
C₆₁×#2970	2
C₄×AGL(1,ℤ/8)×C₆₁	2
C₂×C₆₁×#440	2
#61452	61

Subgroups — C61×#61452 #29564885

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61452 #29564885