Subgroups — C₆₁×#61784 #29565217

Order 15616.

1810 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3546	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3355	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3354	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3353	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3340	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3339	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3334	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#3332	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#3325	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3322	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3305	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3297	C₂	1	2	yes	maximal, complemented
14	C₆₁×#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3233	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#3228	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3199	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3198	C₂	1	2	yes	maximal, complemented
19	C₆₁×#3105	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₁×#3100	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#3098	C₂	1	2	yes	maximal, complemented
22	C₆₁×#3096	C₂	1	2	yes	maximal, complemented
23	C₆₁×#2979	C₂	1	1	yes	maximal, characteristic, complemented
24	C₆₁×#560	—	2	2	no	—
25	C₆₁×#559	—	2	2	no	—
26	C₆₁×#556	—	2	1	no	—
27	C₆₁×#556	C₂²	1	1	yes	characteristic, complemented
28	C₆₁×#555	C₂²	1	1	yes	characteristic
29	C₆₁×#555	C₂²	1	1	yes	characteristic, complemented
30	C₆₁×#553	C₂²	1	2	yes	complemented
31	C₆₁×#553	C₂²	1	2	yes	complemented
32	C₆₁×#553	C₂²	1	2	yes	complemented
33	C₆₁×#550	—	2	1	no	—
34	C₆₁×#550	—	2	1	no	—
35	C₆₁×#550	C₂²	1	1	yes	characteristic, complemented
36	C₆₁×#547	C₂²	1	1	yes	characteristic
37	C₆₁×#547	C₂²	1	1	yes	characteristic, complemented
38	C₆₁×#547	C₂²	1	1	yes	characteristic, complemented
39	C₆₁×#546	—	2	1	no	—
40	C₆₁×#546	C₂²	1	2	yes	complemented
41	D₄²×C₆₁	C₂²	1	1	yes	characteristic, complemented
42	C₆₁×#542	—	2	1	no	—
43	C₆₁×#538	—	2	2	no	—
44	C₆₁×#538	—	2	2	no	—
45	C₆₁×#537	C₂²	1	2	yes	—
46	C₆₁×#535	—	2	1	no	—
47	C₆₁×#535	C₂²	1	2	yes	—
48	C₆₁×#535	C₂²	1	2	yes	complemented
49	C₆₁×#533	C₂²	1	1	yes	characteristic, complemented
50	C₆₁×#532	C₂²	1	1	yes	characteristic
51	C₆₁×#532	C₂²	1	1	yes	characteristic
52	C₆₁×#529	C₂²	1	1	yes	characteristic
53	C₆₁×#525	—	2	1	no	—
54	C₆₁×#525	—	2	1	no	—
55	C₆₁×#520	C₂²	1	2	yes	complemented
56	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
57	C₆₁×#500	C₂²	1	1	yes	characteristic, complemented
58	C₆₁×#499	C₂²	1	2	yes	complemented
59	C₆₁×#498	C₂²	1	1	yes	characteristic, complemented
60	C₆₁×#488	C₂²	1	2	yes	complemented
61	C₆₁×#486	C₂²	1	1	yes	characteristic, complemented
62	C₆₁×#486	C₂²	1	1	yes	characteristic, complemented
63	C₆₁×#485	C₂²	1	2	yes	complemented
64	C₆₁×#485	C₂²	1	2	yes	complemented
65	C₆₁×#484	C₂²	1	2	yes	complemented
66	C₆₁×#484	C₂²	1	1	yes	characteristic, complemented
67	C₆₁×#482	C₂²	1	2	yes	—
68	C₆₁×#482	C₂²	1	2	yes	complemented
69	C₆₁×#482	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	2	yes	complemented
73	C₆₁×#482	C₂²	1	2	yes	complemented
74	C₆₁×#482	C₂²	1	2	yes	complemented
75	C₆₁×#481	C₂²	1	1	yes	characteristic
76	C₆₁×#481	C₂²	1	2	yes	complemented
77	C₆₁×#481	C₂²	1	2	yes	complemented
78	C₆₁×#480	C₂²	1	2	yes	complemented
79	C₆₁×#480	C₂²	1	2	yes	complemented
80	C₆₁×#480	C₂²	1	2	yes	complemented
81	C₆₁×#480	C₂²	1	2	yes	complemented
82	C₆₁×#478	C₂²	1	2	yes	complemented
83	C₆₁×#478	C₂²	1	2	yes	complemented
84	C₆₁×#478	C₂²	1	1	yes	characteristic, complemented
85	C₆₁×#478	C₂²	1	1	yes	characteristic, complemented
86	C₆₁×#477	C₂²	1	1	yes	characteristic, complemented
87	C₆₁×#476	C₂²	1	1	yes	characteristic, complemented
88	C₆₁×#475	C₂²	1	1	yes	characteristic, complemented
89	C₆₁×#474	C₂²	1	1	yes	characteristic, complemented
90	C₆₁×#474	C₂²	1	1	yes	characteristic, complemented
91	C₆₁×#474	C₂²	1	1	yes	characteristic, complemented
92	C₆₁×#469	C₂²	1	2	yes	—
93	C₆₁×#469	C₂²	1	2	yes	—
94	C₆₁×#469	C₂²	1	2	yes	complemented
95	C₆₁×#468	C₂²	1	2	yes	complemented
96	C₆₁×#466	C₂²	1	2	yes	—
97	C₆₁×#466	C₂²	1	2	yes	—
98	C₆₁×#466	C₂²	1	2	yes	complemented
99	C₆₁×#465	C₂²	1	2	yes	complemented
100	C₆₁×#463	C₂²	1	1	yes	characteristic
101	C₆₁×#463	C₂²	1	1	yes	characteristic
102	C₆₁×#459	C₂²	1	1	yes	characteristic
103	C₆₁×#459	C₂²	1	1	yes	characteristic
104	C₆₁×#450	C₂²	1	1	yes	characteristic, complemented
105	C₆₁×#449	C₂²	1	2	yes	complemented
106	C₆₁×#449	C₂²	1	2	yes	complemented
107	C₆₁×#447	C₂²	1	2	yes	—
108	C₆₁×#447	C₂²	1	2	yes	—
109	C₆₁×#447	C₂²	1	1	yes	characteristic
110	C₆₁×#447	C₂²	1	2	yes	complemented
111	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
112	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
113	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
114	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
115	C₄×D₈×C₆₁	C₂²	1	2	yes	complemented
116	C₄×D₈×C₆₁	C₂²	1	2	yes	complemented
117	C₆₁×#436	C₂²	1	2	yes	complemented
118	C₆₁×#436	C₂²	1	1	yes	characteristic, complemented
119	C₆₁×#436	C₂²	1	1	yes	characteristic, complemented
120	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
121	C₈×D₄×C₆₁	C₂²	1	2	yes	complemented
122	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
123	C₆₁×#431	C₂²	1	1	yes	characteristic, complemented
124	C₆₁×#431	C₂²	1	1	yes	characteristic, complemented
125	C₆₁×#428	C₂²	1	2	yes	complemented
126	C₆₁×#428	C₂²	1	2	yes	complemented
127	C₆₁×#427	C₂²	1	2	yes	complemented
128	C₂×#107×C₆₁	C₂²	1	2	yes	complemented
129	C₆₁×#418	C₂²	1	2	yes	complemented
130	C₆₁×#417	C₂²	1	2	yes	complemented
131	C₆₁×#416	C₂²	1	2	yes	complemented
132	C₂×#102×C₆₁	C₂²	1	2	yes	complemented
133	C₆₁×#408	C₂²	1	2	yes	complemented
134	C₆₁×#408	C₂²	1	2	yes	complemented
135	C₂×#41×C₆₁	—	2	1	no	—
136	C₂×#41×C₆₁	—	2	1	no	—
137	C₂×#41×C₆₁	—	2	1	no	—
138	C₂×#41×C₆₁	—	2	1	no	—
139	C₂×#41×C₆₁	C₂³	1	2	yes	—
140	C₂×#41×C₆₁	C₂³	1	2	yes	—
141	C₂²×D₄×C₆₁	—	2	1	no	—
142	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
143	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₆₁	—	2	1	no	—
145	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
147	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
148	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
149	C₂×D₈×C₆₁	C₂³	1	2	yes	—
150	C₂×D₈×C₆₁	C₂³	1	2	yes	—
151	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
152	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
153	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
154	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
155	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
156	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
157	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
159	#127×C₆₁	—	2	1	no	—
160	#127×C₆₁	—	2	2	no	—
161	#127×C₆₁	—	2	2	no	—
162	#127×C₆₁	D₄	1	1	yes	characteristic
163	#127×C₆₁	C₂³	1	1	yes	characteristic
164	#126×C₆₁	—	2	2	no	—
165	#126×C₆₁	—	2	2	no	—
166	#126×C₆₁	—	2	2	no	—
167	#126×C₆₁	—	2	2	no	—
168	#126×C₆₁	—	2	1	no	—
169	#125×C₆₁	C₂³	1	2	yes	—
170	#125×C₆₁	C₂³	1	1	yes	characteristic
171	#124×C₆₁	—	2	2	no	—
172	#124×C₆₁	—	2	2	no	—
173	#124×C₆₁	—	2	1	no	—
174	#124×C₆₁	—	2	2	no	—
175	#124×C₆₁	—	2	2	no	—
176	#124×C₆₁	—	2	1	no	—
177	#124×C₆₁	D₄	1	2	yes	—
178	#124×C₆₁	C₂³	1	1	yes	characteristic
179	#123×C₆₁	—	2	1	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	#123×C₆₁	—	2	2	no	—
186	#123×C₆₁	—	2	2	no	—
187	C₂²⋊Q₈×C₆₁	—	2	2	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	1	no	—
192	C₂²⋊Q₈×C₆₁	—	2	1	no	—
193	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
194	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
195	#121×C₆₁	—	2	2	no	—
196	#121×C₆₁	—	2	2	no	—
197	#121×C₆₁	—	2	2	no	—
198	#121×C₆₁	—	2	2	no	—
199	#121×C₆₁	—	2	2	no	—
200	#121×C₆₁	—	2	2	no	—
201	#121×C₆₁	—	2	1	no	—
202	#121×C₆₁	—	2	1	no	—
203	#121×C₆₁	—	2	1	no	—
204	#121×C₆₁	—	2	1	no	—
205	#121×C₆₁	—	2	2	no	—
206	#121×C₆₁	—	2	2	no	—
207	#121×C₆₁	D₄	1	2	yes	—
208	#121×C₆₁	D₄	1	1	yes	characteristic
209	#121×C₆₁	D₄	1	1	yes	characteristic
210	#121×C₆₁	C₂³	1	2	yes	—
211	#121×C₆₁	C₂³	1	1	yes	characteristic
212	#121×C₆₁	C₂³	1	2	yes	—
213	#121×C₆₁	C₂³	1	2	yes	—
214	#121×C₆₁	C₂³	1	2	yes	—
215	#121×C₆₁	C₂³	1	2	yes	—
216	#121×C₆₁	C₂³	1	2	yes	—
217	#121×C₆₁	C₂³	1	2	yes	—
218	#121×C₆₁	C₂³	1	2	yes	—
219	#120×C₆₁	—	2	2	no	—
220	#120×C₆₁	—	2	2	no	—
221	#120×C₆₁	—	2	2	no	—
222	#120×C₆₁	—	2	2	no	—
223	#120×C₆₁	—	2	2	no	—
224	#120×C₆₁	—	2	2	no	—
225	C₄×Q₈×C₆₁	—	2	2	no	—
226	C₄×Q₈×C₆₁	—	2	1	no	—
227	C₄×Q₈×C₆₁	—	2	1	no	—
228	C₄×Q₈×C₆₁	—	2	1	no	—
229	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
230	C₄×D₄×C₆₁	—	2	2	no	—
231	C₄×D₄×C₆₁	—	2	2	no	—
232	C₄×D₄×C₆₁	—	2	2	no	—
233	C₄×D₄×C₆₁	—	2	1	no	—
234	C₄×D₄×C₆₁	—	2	1	no	—
235	C₄×D₄×C₆₁	—	2	2	no	—
236	C₄×D₄×C₆₁	—	2	2	no	—
237	C₄×D₄×C₆₁	—	2	2	no	—
238	C₄×D₄×C₆₁	—	2	1	no	—
239	C₄×D₄×C₆₁	—	2	1	no	—
240	C₄×D₄×C₆₁	—	2	1	no	—
241	C₄×D₄×C₆₁	C₂³	1	2	yes	—
242	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₆₁	C₂³	1	2	yes	—
249	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
250	#117×C₆₁	—	2	1	no	—
251	#117×C₆₁	—	2	1	no	—
252	#117×C₆₁	—	2	1	no	—
253	#117×C₆₁	C₂³	1	2	yes	—
254	#117×C₆₁	C₂³	1	2	yes	—
255	#117×C₆₁	C₂³	1	2	yes	—
256	#117×C₆₁	C₂³	1	2	yes	—
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×C₂²⋊C₄×C₆₁	—	2	1	no	—
262	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
263	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
264	#107×C₆₁	C₂³	1	1	yes	characteristic
265	#107×C₆₁	C₂³	1	2	yes	—
266	#107×C₆₁	C₂³	1	2	yes	—
267	#107×C₆₁	C₂³	1	2	yes	—
268	#107×C₆₁	C₂³	1	2	yes	—
269	#107×C₆₁	C₂³	1	1	yes	characteristic
270	#107×C₆₁	C₂³	1	2	yes	—
271	#107×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	1	yes	characteristic
275	#106×C₆₁	C₂³	1	2	yes	—
276	#106×C₆₁	C₂³	1	2	yes	—
277	#106×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	1	yes	characteristic
282	#103×C₆₁	C₂³	1	1	yes	characteristic
283	#103×C₆₁	C₂³	1	2	yes	—
284	#103×C₆₁	C₂³	1	1	yes	characteristic
285	#103×C₆₁	C₂³	1	2	yes	—
286	#102×C₆₁	C₂³	1	1	yes	characteristic
287	#102×C₆₁	C₂³	1	2	yes	—
288	#102×C₆₁	C₂³	1	2	yes	—
289	#102×C₆₁	C₂³	1	2	yes	—
290	#102×C₆₁	C₂³	1	2	yes	—
291	#102×C₆₁	C₂³	1	2	yes	—
292	#102×C₆₁	C₂³	1	2	yes	—
293	#102×C₆₁	C₂³	1	1	yes	characteristic
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	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	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
303	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
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	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
309	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₆₁	C₂³	1	2	yes	—
312	C₂⁴×C₆₁	—	2	1	no	—
313	C₂⁴×C₆₁	—	2	2	no	—
314	#41×C₆₁	—	4	2	no	—
315	#41×C₆₁	—	4	2	no	—
316	#41×C₆₁	—	4	2	no	—
317	#41×C₆₁	—	4	2	no	—
318	#41×C₆₁	—	8	2	no	—
319	#41×C₆₁	—	8	2	no	—
320	#41×C₆₁	—	8	2	no	—
321	#41×C₆₁	—	8	2	no	—
322	C₂×Q₈×C₆₁	—	2	1	no	—
323	C₂×Q₈×C₆₁	—	2	1	no	—
324	C₂×Q₈×C₆₁	—	2	1	no	—
325	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
326	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
327	C₂×D₄×C₆₁	—	2	1	no	—
328	C₂×D₄×C₆₁	—	2	2	no	—
329	C₂×D₄×C₆₁	—	2	2	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	2	no	—
336	C₂×D₄×C₆₁	—	2	2	no	—
337	C₂×D₄×C₆₁	—	2	1	no	—
338	C₂×D₄×C₆₁	—	2	1	no	—
339	C₂×D₄×C₆₁	—	2	1	no	—
340	C₂×D₄×C₆₁	—	2	2	no	—
341	C₂×D₄×C₆₁	—	4	1	no	—
342	C₂×D₄×C₆₁	—	4	1	no	—
343	C₂×D₄×C₆₁	—	4	2	no	—
344	C₂×D₄×C₆₁	—	4	2	no	—
345	C₂×D₄×C₆₁	—	8	2	no	—
346	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
347	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
348	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
349	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
350	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
351	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
352	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
353	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
354	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
355	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
361	C₂²×C₄×C₆₁	—	2	1	no	—
362	C₂²×C₄×C₆₁	—	2	1	no	—
363	C₂²×C₄×C₆₁	—	2	2	no	—
364	C₂²×C₄×C₆₁	—	2	2	no	—
365	C₂²×C₄×C₆₁	—	2	1	no	—
366	C₂²×C₄×C₆₁	—	2	1	no	—
367	C₂²×C₄×C₆₁	—	8	2	no	—
368	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
369	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
370	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
372	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
373	SD₁₆×C₆₁	—	4	1	no	—
374	SD₁₆×C₆₁	—	4	1	no	—
375	D₈×C₆₁	—	4	2	no	—
376	D₈×C₆₁	—	4	1	no	—
377	D₈×C₆₁	—	4	2	no	—
378	D₈×C₆₁	—	4	1	no	—
379	M₁₆×C₆₁	—	4	2	no	—
380	M₁₆×C₆₁	—	4	2	no	—
381	C₂×C₈×C₆₁	—	4	2	no	—
382	C₂×C₈×C₆₁	—	4	2	no	—
383	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
387	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
389	C₄⋊C₄×C₆₁	—	2	1	no	—
390	C₄⋊C₄×C₆₁	—	2	2	no	—
391	C₄⋊C₄×C₆₁	—	2	2	no	—
392	C₄⋊C₄×C₆₁	—	2	2	no	—
393	C₄⋊C₄×C₆₁	—	2	1	no	—
394	C₄⋊C₄×C₆₁	—	2	1	no	—
395	C₄⋊C₄×C₆₁	—	2	1	no	—
396	C₄⋊C₄×C₆₁	—	2	1	no	—
397	C₄⋊C₄×C₆₁	—	2	2	no	—
398	C₄⋊C₄×C₆₁	—	2	1	no	—
399	C₄⋊C₄×C₆₁	—	2	2	no	—
400	C₄⋊C₄×C₆₁	—	2	2	no	—
401	C₄⋊C₄×C₆₁	—	2	1	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	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
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	C₂²⋊C₄×C₆₁	—	2	2	no	—
414	C₂²⋊C₄×C₆₁	—	2	2	no	—
415	C₂²⋊C₄×C₆₁	—	2	2	no	—
416	C₂²⋊C₄×C₆₁	—	2	2	no	—
417	C₂²⋊C₄×C₆₁	—	2	2	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	1	no	—
423	C₂²⋊C₄×C₆₁	—	2	1	no	—
424	C₂²⋊C₄×C₆₁	—	2	2	no	—
425	C₂²⋊C₄×C₆₁	—	2	1	no	—
426	C₂²⋊C₄×C₆₁	—	2	1	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	2	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	C₄²×C₆₁	—	2	2	no	—
441	C₄²×C₆₁	—	2	2	no	—
442	C₄²×C₆₁	—	2	1	no	—
443	C₄²×C₆₁	—	2	2	no	—
444	C₄²×C₆₁	—	2	2	no	—
445	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
446	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
447	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
448	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
449	C₂³×C₆₁	—	2	1	no	—
450	C₂³×C₆₁	—	2	1	no	—
451	C₂³×C₆₁	—	2	1	no	—
452	C₂³×C₆₁	—	2	2	no	—
453	C₂³×C₆₁	—	4	2	no	—
454	C₂³×C₆₁	—	8	1	no	—
455	C₂³×C₆₁	—	8	1	no	—
456	C₂³×C₆₁	—	8	2	no	—
457	C₂³×C₆₁	—	8	2	no	—
458	C₂³×C₆₁	—	8	2	no	—
459	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
460	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
461	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
462	Q₈×C₆₁	—	2	1	no	—
463	Q₈×C₆₁	—	2	1	no	—
464	Q₈×C₆₁	—	4	2	no	—
465	Q₈×C₆₁	—	4	2	no	—
466	Q₈×C₆₁	—	4	2	no	—
467	Q₈×C₆₁	—	8	1	no	—
468	D₄×C₆₁	—	2	2	no	—
469	D₄×C₆₁	—	2	2	no	—
470	D₄×C₆₁	—	2	1	no	—
471	D₄×C₆₁	—	2	1	no	—
472	D₄×C₆₁	—	2	1	no	—
473	D₄×C₆₁	—	2	1	no	—
474	D₄×C₆₁	—	2	1	no	—
475	D₄×C₆₁	—	2	1	no	—
476	D₄×C₆₁	—	2	2	no	—
477	D₄×C₆₁	—	2	2	no	—
478	D₄×C₆₁	—	4	2	no	—
479	D₄×C₆₁	—	4	2	no	—
480	D₄×C₆₁	—	4	2	no	—
481	D₄×C₆₁	—	4	2	no	—
482	D₄×C₆₁	—	4	2	no	—
483	D₄×C₆₁	—	4	2	no	—
484	D₄×C₆₁	—	8	1	no	—
485	D₄×C₆₁	—	8	2	no	—
486	D₄×C₆₁	—	8	1	no	—
487	D₄×C₆₁	—	8	2	no	—
488	D₄×C₆₁	—	8	2	no	—
489	D₄×C₆₁	—	8	2	no	—
490	D₄×C₆₁	—	8	2	no	—
491	D₄×C₆₁	—	8	2	no	—
492	D₄×C₆₁	—	8	2	no	—
493	D₄×C₆₁	—	8	2	no	—
494	D₄×C₆₁	—	8	2	no	—
495	D₄×C₆₁	—	8	2	no	—
496	C₂×C₄×C₆₁	—	2	2	no	—
497	C₂×C₄×C₆₁	—	2	2	no	—
498	C₂×C₄×C₆₁	—	2	2	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	1	no	—
503	C₂×C₄×C₆₁	—	2	1	no	—
504	C₂×C₄×C₆₁	—	2	2	no	—
505	C₂×C₄×C₆₁	—	2	1	no	—
506	C₂×C₄×C₆₁	—	2	1	no	—
507	C₂×C₄×C₆₁	—	2	1	no	—
508	C₂×C₄×C₆₁	—	2	2	no	—
509	C₂×C₄×C₆₁	—	2	2	no	—
510	C₂×C₄×C₆₁	—	2	1	no	—
511	C₂×C₄×C₆₁	—	4	1	no	—
512	C₂×C₄×C₆₁	—	4	2	no	—
513	C₂×C₄×C₆₁	—	4	2	no	—
514	C₂×C₄×C₆₁	—	4	2	no	—
515	C₂×C₄×C₆₁	—	8	1	no	—
516	C₂×C₄×C₆₁	—	8	1	no	—
517	C₂×C₄×C₆₁	—	8	2	no	—
518	C₂×C₄×C₆₁	—	8	2	no	—
519	C₂×C₄×C₆₁	—	8	1	no	—
520	C₂×C₄×C₆₁	—	8	2	no	—
521	C₂×C₄×C₆₁	—	8	2	no	—
522	C₂×C₄×C₆₁	—	8	2	no	—
523	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
525	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
526	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
531	C₈×C₆₁	—	2	1	no	—
532	C₈×C₆₁	—	2	2	no	—
533	C₈×C₆₁	—	2	1	no	—
534	C₈×C₆₁	—	2	1	no	—
535	C₈×C₆₁	—	2	2	no	—
536	C₈×C₆₁	—	2	1	no	—
537	#61784	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	—	2	2	no	—
543	C₂²×C₆₁	—	2	2	no	—
544	C₂²×C₆₁	—	2	1	no	—
545	C₂²×C₆₁	—	2	2	no	—
546	C₂²×C₆₁	—	2	2	no	—
547	C₂²×C₆₁	—	4	1	no	—
548	C₂²×C₆₁	—	4	1	no	—
549	C₂²×C₆₁	—	4	2	no	—
550	C₂²×C₆₁	—	4	1	no	—
551	C₂²×C₆₁	—	4	2	no	—
552	C₂²×C₆₁	—	4	1	no	—
553	C₂²×C₆₁	—	4	1	no	—
554	C₂²×C₆₁	—	4	1	no	—
555	C₂²×C₆₁	—	4	1	no	—
556	C₂²×C₆₁	—	4	1	no	—
557	C₂²×C₆₁	—	4	1	no	—
558	C₂²×C₆₁	—	4	2	no	—
559	C₂²×C₆₁	—	8	4	no	—
560	C₂²×C₆₁	—	16	4	no	—
561	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
562	C₄×C₆₁	—	2	1	no	—
563	C₄×C₆₁	—	2	1	no	—
564	C₄×C₆₁	—	2	2	no	—
565	C₄×C₆₁	—	2	1	no	—
566	C₄×C₆₁	—	2	2	no	—
567	C₄×C₆₁	—	2	1	no	—
568	C₄×C₆₁	—	4	1	no	—
569	C₄×C₆₁	—	4	2	no	—
570	C₄×C₆₁	—	4	1	no	—
571	C₄×C₆₁	—	4	1	no	—
572	C₄×C₆₁	—	4	1	no	—
573	C₄×C₆₁	—	4	1	no	—
574	C₄×C₆₁	—	4	2	no	—
575	C₄×C₆₁	—	4	2	no	—
576	C₄×C₆₁	#576	1	2	yes	—
577	C₄×C₆₁	#585	1	1	yes	characteristic
578	C₄×C₆₁	#585	1	1	yes	characteristic
579	#3546	C₂×C₆₁	1	1	yes	characteristic, complemented
580	#3506	C₂×C₆₁	1	1	yes	characteristic, complemented
581	#3355	C₂×C₆₁	1	2	yes	complemented
582	#3354	C₂×C₆₁	1	1	yes	characteristic, complemented
583	#3353	C₂×C₆₁	1	1	yes	characteristic, complemented
584	#3340	C₂×C₆₁	1	1	yes	characteristic, complemented
585	#3339	C₂×C₆₁	1	2	yes	complemented
586	#3334	C₂×C₆₁	1	1	yes	characteristic, complemented
587	#3332	C₂×C₆₁	1	1	yes	characteristic, complemented
588	#3325	C₂×C₆₁	1	1	yes	characteristic, complemented
589	#3322	C₂×C₆₁	1	2	yes	complemented
590	#3305	C₂×C₆₁	1	1	yes	characteristic, complemented
591	#3297	C₂×C₆₁	1	2	yes	complemented
592	#3294	C₂×C₆₁	1	1	yes	characteristic, complemented
593	#3233	C₂×C₆₁	1	1	yes	characteristic, complemented
594	#3228	C₂×C₆₁	1	1	yes	characteristic, complemented
595	#3199	C₂×C₆₁	1	2	yes	complemented
596	#3198	C₂×C₆₁	1	2	yes	complemented
597	#3105	C₂×C₆₁	1	1	yes	characteristic, complemented
598	#3100	C₂×C₆₁	1	1	yes	characteristic, complemented
599	#3098	C₂×C₆₁	1	2	yes	complemented
600	#3096	C₂×C₆₁	1	2	yes	complemented
601	#2979	C₂×C₆₁	1	1	yes	characteristic, complemented
602	C₂×C₆₁	—	4	2	no	—
603	C₂×C₆₁	—	4	1	no	—
604	C₂×C₆₁	—	4	2	no	—
605	C₂×C₆₁	—	8	1	no	—
606	C₂×C₆₁	—	8	1	no	—
607	C₂×C₆₁	—	8	2	no	—
608	C₂×C₆₁	—	8	1	no	—
609	C₂×C₆₁	#3485	1	1	yes	characteristic
610	C₂×C₆₁	C₂×#576	1	1	yes	characteristic
611	C₂×C₆₁	#3584	1	1	yes	characteristic
612	#560	—	2	2	no	—
613	#559	—	2	2	no	—
614	#556	—	2	1	no	—
615	#556	C₂²×C₆₁	1	1	yes	characteristic, complemented
616	#555	C₂²×C₆₁	1	1	yes	characteristic
617	#555	C₂²×C₆₁	1	1	yes	characteristic, complemented
618	#553	C₂²×C₆₁	1	2	yes	complemented
619	#553	C₂²×C₆₁	1	2	yes	complemented
620	#553	C₂²×C₆₁	1	2	yes	complemented
621	#550	—	2	1	no	—
622	#550	—	2	1	no	—
623	#550	C₂²×C₆₁	1	1	yes	characteristic, complemented
624	#547	C₂²×C₆₁	1	1	yes	characteristic
625	#547	C₂²×C₆₁	1	1	yes	characteristic, complemented
626	#547	C₂²×C₆₁	1	1	yes	characteristic, complemented
627	#546	—	2	1	no	—
628	#546	C₂²×C₆₁	1	2	yes	complemented
629	D₄²	C₂²×C₆₁	1	1	yes	characteristic, complemented
630	#542	—	2	1	no	—
631	#538	—	2	2	no	—
632	#538	—	2	2	no	—
633	#537	C₂²×C₆₁	1	2	yes	—
634	#535	—	2	1	no	—
635	#535	C₂²×C₆₁	1	2	yes	—
636	#535	C₂²×C₆₁	1	2	yes	complemented
637	#533	C₂²×C₆₁	1	1	yes	characteristic, complemented
638	#532	C₂²×C₆₁	1	1	yes	characteristic
639	#532	C₂²×C₆₁	1	1	yes	characteristic
640	#529	C₂²×C₆₁	1	1	yes	characteristic
641	#525	—	2	1	no	—
642	#525	—	2	1	no	—
643	#520	C₂²×C₆₁	1	2	yes	complemented
644	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
645	#500	C₂²×C₆₁	1	1	yes	characteristic, complemented
646	#499	C₂²×C₆₁	1	2	yes	complemented
647	#498	C₂²×C₆₁	1	1	yes	characteristic, complemented
648	#488	C₂²×C₆₁	1	2	yes	complemented
649	#486	C₂²×C₆₁	1	1	yes	characteristic, complemented
650	#486	C₂²×C₆₁	1	1	yes	characteristic, complemented
651	#485	C₂²×C₆₁	1	2	yes	complemented
652	#485	C₂²×C₆₁	1	2	yes	complemented
653	#484	C₂²×C₆₁	1	2	yes	complemented
654	#484	C₂²×C₆₁	1	1	yes	characteristic, complemented
655	#482	C₂²×C₆₁	1	2	yes	—
656	#482	C₂²×C₆₁	1	2	yes	complemented
657	#482	C₂²×C₆₁	1	2	yes	complemented
658	#482	C₂²×C₆₁	1	2	yes	complemented
659	#482	C₂²×C₆₁	1	2	yes	complemented
660	#482	C₂²×C₆₁	1	2	yes	complemented
661	#482	C₂²×C₆₁	1	2	yes	complemented
662	#482	C₂²×C₆₁	1	2	yes	complemented
663	#481	C₂²×C₆₁	1	1	yes	characteristic
664	#481	C₂²×C₆₁	1	2	yes	complemented
665	#481	C₂²×C₆₁	1	2	yes	complemented
666	#480	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	1	yes	characteristic, complemented
671	#478	C₂²×C₆₁	1	2	yes	complemented
672	#478	C₂²×C₆₁	1	1	yes	characteristic, complemented
673	#478	C₂²×C₆₁	1	2	yes	complemented
674	#477	C₂²×C₆₁	1	1	yes	characteristic, complemented
675	#476	C₂²×C₆₁	1	1	yes	characteristic, complemented
676	#475	C₂²×C₆₁	1	1	yes	characteristic, complemented
677	#474	C₂²×C₆₁	1	1	yes	characteristic, complemented
678	#474	C₂²×C₆₁	1	1	yes	characteristic, complemented
679	#474	C₂²×C₆₁	1	1	yes	characteristic, complemented
680	#469	C₂²×C₆₁	1	2	yes	—
681	#469	C₂²×C₆₁	1	2	yes	—
682	#469	C₂²×C₆₁	1	2	yes	complemented
683	#468	C₂²×C₆₁	1	2	yes	complemented
684	#466	C₂²×C₆₁	1	2	yes	—
685	#466	C₂²×C₆₁	1	2	yes	—
686	#466	C₂²×C₆₁	1	2	yes	complemented
687	#465	C₂²×C₆₁	1	2	yes	complemented
688	#463	C₂²×C₆₁	1	1	yes	characteristic
689	#463	C₂²×C₆₁	1	1	yes	characteristic
690	#459	C₂²×C₆₁	1	1	yes	characteristic
691	#459	C₂²×C₆₁	1	1	yes	characteristic
692	#450	C₂²×C₆₁	1	1	yes	characteristic, complemented
693	#449	C₂²×C₆₁	1	2	yes	complemented
694	#449	C₂²×C₆₁	1	2	yes	complemented
695	#447	C₂²×C₆₁	1	1	yes	characteristic
696	#447	C₂²×C₆₁	1	2	yes	—
697	#447	C₂²×C₆₁	1	2	yes	—
698	#447	C₂²×C₆₁	1	2	yes	complemented
699	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
700	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
701	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
702	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
703	C₄×D₈	C₂²×C₆₁	1	2	yes	complemented
704	C₄×D₈	C₂²×C₆₁	1	2	yes	complemented
705	#436	C₂²×C₆₁	1	1	yes	characteristic, complemented
706	#436	C₂²×C₆₁	1	1	yes	characteristic, complemented
707	#436	C₂²×C₆₁	1	2	yes	complemented
708	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
709	C₈×D₄	C₂²×C₆₁	1	2	yes	complemented
710	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
711	#431	C₂²×C₆₁	1	1	yes	characteristic, complemented
712	#431	C₂²×C₆₁	1	1	yes	characteristic, complemented
713	#428	C₂²×C₆₁	1	2	yes	complemented
714	#428	C₂²×C₆₁	1	2	yes	complemented
715	#427	C₂²×C₆₁	1	2	yes	complemented
716	C₂×#107	C₂²×C₆₁	1	2	yes	complemented
717	#418	C₂²×C₆₁	1	2	yes	complemented
718	#417	C₂²×C₆₁	1	2	yes	complemented
719	#416	C₂²×C₆₁	1	2	yes	complemented
720	C₂×#102	C₂²×C₆₁	1	2	yes	complemented
721	#408	C₂²×C₆₁	1	2	yes	complemented
722	#408	C₂²×C₆₁	1	2	yes	complemented
723	C₆₁	#61784	1	1	yes	characteristic, direct product factor, Sylow
724	C₂×#41	—	2	1	no	—
725	C₂×#41	—	2	1	no	—
726	C₂×#41	—	2	1	no	—
727	C₂×#41	—	2	1	no	—
728	C₂×#41	C₂³×C₆₁	1	2	yes	—
729	C₂×#41	C₂³×C₆₁	1	2	yes	—
730	C₂²×D₄	—	2	1	no	—
731	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
732	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
733	C₂³×C₄	—	2	1	no	—
734	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
735	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
736	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
737	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
738	C₂×D₈	C₂³×C₆₁	1	2	yes	—
739	C₂×D₈	C₂³×C₆₁	1	2	yes	—
740	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
741	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
742	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
743	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
744	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
745	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
746	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
747	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
748	#127	—	2	1	no	—
749	#127	—	2	2	no	—
750	#127	—	2	2	no	—
751	#127	D₄×C₆₁	1	1	yes	characteristic
752	#127	C₂³×C₆₁	1	1	yes	characteristic
753	#126	—	2	2	no	—
754	#126	—	2	2	no	—
755	#126	—	2	2	no	—
756	#126	—	2	2	no	—
757	#126	—	2	1	no	—
758	#125	C₂³×C₆₁	1	1	yes	characteristic
759	#125	C₂³×C₆₁	1	2	yes	—
760	#124	—	2	2	no	—
761	#124	—	2	2	no	—
762	#124	—	2	1	no	—
763	#124	—	2	2	no	—
764	#124	—	2	2	no	—
765	#124	—	2	1	no	—
766	#124	D₄×C₆₁	1	2	yes	—
767	#124	C₂³×C₆₁	1	1	yes	characteristic
768	#123	—	2	1	no	—
769	#123	—	2	2	no	—
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	#123	—	2	2	no	—
776	C₂²⋊Q₈	—	2	2	no	—
777	C₂²⋊Q₈	—	2	1	no	—
778	C₂²⋊Q₈	—	2	1	no	—
779	C₂²⋊Q₈	—	2	1	no	—
780	C₂²⋊Q₈	—	2	1	no	—
781	C₂²⋊Q₈	—	2	1	no	—
782	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
783	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
784	#121	—	2	1	no	—
785	#121	—	2	1	no	—
786	#121	—	2	2	no	—
787	#121	—	2	2	no	—
788	#121	—	2	2	no	—
789	#121	—	2	2	no	—
790	#121	—	2	2	no	—
791	#121	—	2	2	no	—
792	#121	—	2	1	no	—
793	#121	—	2	1	no	—
794	#121	—	2	2	no	—
795	#121	—	2	2	no	—
796	#121	D₄×C₆₁	1	1	yes	characteristic
797	#121	D₄×C₆₁	1	1	yes	characteristic
798	#121	D₄×C₆₁	1	2	yes	—
799	#121	C₂³×C₆₁	1	1	yes	characteristic
800	#121	C₂³×C₆₁	1	2	yes	—
801	#121	C₂³×C₆₁	1	2	yes	—
802	#121	C₂³×C₆₁	1	2	yes	—
803	#121	C₂³×C₆₁	1	2	yes	—
804	#121	C₂³×C₆₁	1	2	yes	—
805	#121	C₂³×C₆₁	1	2	yes	—
806	#121	C₂³×C₆₁	1	2	yes	—
807	#121	C₂³×C₆₁	1	2	yes	—
808	#120	—	2	2	no	—
809	#120	—	2	2	no	—
810	#120	—	2	2	no	—
811	#120	—	2	2	no	—
812	#120	—	2	2	no	—
813	#120	—	2	2	no	—
814	C₄×Q₈	—	2	2	no	—
815	C₄×Q₈	—	2	1	no	—
816	C₄×Q₈	—	2	1	no	—
817	C₄×Q₈	—	2	1	no	—
818	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	—	2	2	no	—
826	C₄×D₄	—	2	2	no	—
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
831	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
832	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
833	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
834	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
835	C₄×D₄	C₂³×C₆₁	1	2	yes	—
836	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
837	C₄×D₄	C₂³×C₆₁	1	2	yes	—
838	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
839	#117	—	2	1	no	—
840	#117	—	2	1	no	—
841	#117	—	2	1	no	—
842	#117	C₂³×C₆₁	1	2	yes	—
843	#117	C₂³×C₆₁	1	2	yes	—
844	#117	C₂³×C₆₁	1	2	yes	—
845	#117	C₂³×C₆₁	1	2	yes	—
846	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
847	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
848	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
849	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
850	C₂×C₂²⋊C₄	—	2	1	no	—
851	C₂×C₂²⋊C₄	—	2	2	no	—
852	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
853	#107	C₂³×C₆₁	1	1	yes	characteristic
854	#107	C₂³×C₆₁	1	2	yes	—
855	#107	C₂³×C₆₁	1	2	yes	—
856	#107	C₂³×C₆₁	1	2	yes	—
857	#107	C₂³×C₆₁	1	2	yes	—
858	#107	C₂³×C₆₁	1	1	yes	characteristic
859	#107	C₂³×C₆₁	1	2	yes	—
860	#107	C₂³×C₆₁	1	2	yes	—
861	#106	C₂³×C₆₁	1	1	yes	characteristic
862	#106	C₂³×C₆₁	1	2	yes	—
863	#106	C₂³×C₆₁	1	1	yes	characteristic
864	#106	C₂³×C₆₁	1	2	yes	—
865	#106	C₂³×C₆₁	1	2	yes	—
866	#106	C₂³×C₆₁	1	2	yes	—
867	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
868	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
869	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
870	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
871	#103	C₂³×C₆₁	1	1	yes	characteristic
872	#103	C₂³×C₆₁	1	2	yes	—
873	#103	C₂³×C₆₁	1	1	yes	characteristic
874	#103	C₂³×C₆₁	1	2	yes	—
875	#102	C₂³×C₆₁	1	1	yes	characteristic
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	2	yes	—
881	#102	C₂³×C₆₁	1	2	yes	—
882	#102	C₂³×C₆₁	1	1	yes	characteristic
883	#102	C₂³×C₆₁	1	2	yes	—
884	#102	C₂³×C₆₁	1	2	yes	—
885	#102	C₂³×C₆₁	1	1	yes	characteristic
886	#102	C₂³×C₆₁	1	1	yes	characteristic
887	#102	C₂³×C₆₁	1	2	yes	—
888	#102	C₂³×C₆₁	1	2	yes	—
889	#102	C₂³×C₆₁	1	1	yes	characteristic
890	#102	C₂³×C₆₁	1	1	yes	characteristic
891	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
892	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
893	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
894	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
895	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
896	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
897	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
898	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
899	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
900	C₄×C₈	C₂³×C₆₁	1	2	yes	—
901	C₂⁴	—	2	1	no	—
902	C₂⁴	—	2	2	no	—
903	#41	—	4	2	no	—
904	#41	—	4	2	no	—
905	#41	—	4	2	no	—
906	#41	—	4	2	no	—
907	#41	—	8	2	no	—
908	#41	—	8	2	no	—
909	#41	—	8	2	no	—
910	#41	—	8	2	no	—
911	C₂×Q₈	—	2	1	no	—
912	C₂×Q₈	—	2	1	no	—
913	C₂×Q₈	—	2	1	no	—
914	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
915	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	4	1	no	—
931	C₂×D₄	—	4	1	no	—
932	C₂×D₄	—	4	2	no	—
933	C₂×D₄	—	4	2	no	—
934	C₂×D₄	—	8	2	no	—
935	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
936	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
937	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
938	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
939	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
940	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
941	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
942	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
943	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
944	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
945	C₂²×C₄	—	2	1	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	2	2	no	—
953	C₂²×C₄	—	2	2	no	—
954	C₂²×C₄	—	2	1	no	—
955	C₂²×C₄	—	2	1	no	—
956	C₂²×C₄	—	8	2	no	—
957	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
958	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
959	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
960	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
961	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
962	SD₁₆	—	4	1	no	—
963	SD₁₆	—	4	1	no	—
964	D₈	—	4	2	no	—
965	D₈	—	4	1	no	—
966	D₈	—	4	2	no	—
967	D₈	—	4	1	no	—
968	M₁₆	—	4	2	no	—
969	M₁₆	—	4	2	no	—
970	C₂×C₈	—	4	2	no	—
971	C₂×C₈	—	4	2	no	—
972	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
973	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
974	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
975	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
976	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
977	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	1	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
993	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
994	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
995	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
996	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
997	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
998	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
999	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1000	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1001	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	1	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1026	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1027	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1028	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1029	C₄²	—	2	2	no	—
1030	C₄²	—	2	2	no	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	2	no	—
1033	C₄²	—	2	2	no	—
1034	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1035	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1036	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1037	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1038	C₂³	—	2	1	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	2	1	no	—
1041	C₂³	—	2	2	no	—
1042	C₂³	—	4	2	no	—
1043	C₂³	—	8	1	no	—
1044	C₂³	—	8	1	no	—
1045	C₂³	—	8	2	no	—
1046	C₂³	—	8	2	no	—
1047	C₂³	—	8	2	no	—
1048	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1049	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1050	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1051	Q₈	—	2	1	no	—
1052	Q₈	—	2	1	no	—
1053	Q₈	—	4	2	no	—
1054	Q₈	—	4	2	no	—
1055	Q₈	—	4	2	no	—
1056	Q₈	—	8	1	no	—
1057	D₄	—	2	2	no	—
1058	D₄	—	2	2	no	—
1059	D₄	—	2	1	no	—
1060	D₄	—	2	1	no	—
1061	D₄	—	2	1	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	1	no	—
1064	D₄	—	2	1	no	—
1065	D₄	—	2	2	no	—
1066	D₄	—	2	2	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	4	2	no	—
1070	D₄	—	4	2	no	—
1071	D₄	—	4	2	no	—
1072	D₄	—	4	2	no	—
1073	D₄	—	8	1	no	—
1074	D₄	—	8	2	no	—
1075	D₄	—	8	1	no	—
1076	D₄	—	8	2	no	—
1077	D₄	—	8	2	no	—
1078	D₄	—	8	2	no	—
1079	D₄	—	8	2	no	—
1080	D₄	—	8	2	no	—
1081	D₄	—	8	2	no	—
1082	D₄	—	8	2	no	—
1083	D₄	—	8	2	no	—
1084	D₄	—	8	2	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	4	1	no	—
1101	C₂×C₄	—	4	2	no	—
1102	C₂×C₄	—	4	2	no	—
1103	C₂×C₄	—	4	2	no	—
1104	C₂×C₄	—	8	1	no	—
1105	C₂×C₄	—	8	1	no	—
1106	C₂×C₄	—	8	2	no	—
1107	C₂×C₄	—	8	2	no	—
1108	C₂×C₄	—	8	1	no	—
1109	C₂×C₄	—	8	2	no	—
1110	C₂×C₄	—	8	2	no	—
1111	C₂×C₄	—	8	2	no	—
1112	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1113	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1114	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1115	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1116	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1117	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1118	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1119	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1120	C₈	—	2	1	no	—
1121	C₈	—	2	2	no	—
1122	C₈	—	2	1	no	—
1123	C₈	—	2	1	no	—
1124	C₈	—	2	2	no	—
1125	C₈	—	2	1	no	—
1126	C₂²	—	2	1	no	—
1127	C₂²	—	2	2	no	—
1128	C₂²	—	2	2	no	—
1129	C₂²	—	2	1	no	—
1130	C₂²	—	2	2	no	—
1131	C₂²	—	2	2	no	—
1132	C₂²	—	2	1	no	—
1133	C₂²	—	2	2	no	—
1134	C₂²	—	2	2	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	4	2	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	4	1	no	—
1141	C₂²	—	4	2	no	—
1142	C₂²	—	4	1	no	—
1143	C₂²	—	4	2	no	—
1144	C₂²	—	4	1	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	4	1	no	—
1147	C₂²	—	8	4	no	—
1148	C₂²	—	16	4	no	—
1149	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1150	C₄	—	2	1	no	—
1151	C₄	—	2	1	no	—
1152	C₄	—	2	1	no	—
1153	C₄	—	2	2	no	—
1154	C₄	—	2	1	no	—
1155	C₄	—	2	2	no	—
1156	C₄	—	4	1	no	—
1157	C₄	—	4	1	no	—
1158	C₄	—	4	1	no	—
1159	C₄	—	4	2	no	—
1160	C₄	—	4	2	no	—
1161	C₄	—	4	1	no	—
1162	C₄	—	4	2	no	—
1163	C₄	—	4	1	no	—
1164	C₄	C₆₁×#576	1	2	yes	—
1165	C₄	C₆₁×#585	1	1	yes	characteristic
1166	C₄	C₆₁×#585	1	1	yes	characteristic
1167	C₂	—	4	1	no	—
1168	C₂	—	4	2	no	—
1169	C₂	—	4	2	no	—
1170	C₂	—	8	1	no	—
1171	C₂	—	8	1	no	—
1172	C₂	—	8	1	no	—
1173	C₂	—	8	2	no	—
1174	C₂	C₆₁×#3485	1	1	yes	characteristic
1175	C₂	C₂×C₆₁×#576	1	1	yes	characteristic
1176	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 ◁ C₆₁×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3546	C₂	semidirect
2. C₆₁×#3506	C₂	semidirect
3. C₆₁×#3355	C₂	semidirect
4. C₆₁×#3354	C₂	semidirect
5. C₆₁×#3353	C₂	semidirect
6. C₆₁×#3340	C₂	semidirect
7. C₆₁×#3339	C₂	semidirect
8. C₆₁×#3334	C₂	semidirect
9. C₆₁×#3332	C₂	semidirect
10. C₆₁×#3325	C₂	semidirect
11. C₆₁×#3322	C₂	semidirect
12. C₆₁×#3305	C₂	semidirect
13. C₆₁×#3297	C₂	semidirect
14. C₆₁×#3294	C₂	semidirect
15. C₆₁×#3233	C₂	semidirect
16. C₆₁×#3228	C₂	semidirect
17. C₆₁×#3199	C₂	semidirect
18. C₆₁×#3198	C₂	semidirect
19. C₆₁×#3105	C₂	semidirect
20. C₆₁×#3100	C₂	semidirect
21. C₆₁×#3098	C₂	semidirect
22. C₆₁×#3096	C₂	semidirect
23. C₆₁×#2979	C₂	semidirect
27. C₆₁×#556	C₂²	semidirect
29. C₆₁×#555	C₂²	semidirect
30. C₆₁×#553	C₂²	semidirect
31. C₆₁×#553	C₂²	semidirect
32. C₆₁×#553	C₂²	semidirect
35. C₆₁×#550	C₂²	semidirect
37. C₆₁×#547	C₂²	semidirect
38. C₆₁×#547	C₂²	semidirect
40. C₆₁×#546	C₂²	semidirect
41. D₄²×C₆₁	C₂²	semidirect
48. C₆₁×#535	C₂²	semidirect
49. C₆₁×#533	C₂²	semidirect
55. C₆₁×#520	C₂²	semidirect
56. C₂×C₄×D₄×C₆₁	C₂²	semidirect
57. C₆₁×#500	C₂²	semidirect
58. C₆₁×#499	C₂²	semidirect
59. C₆₁×#498	C₂²	semidirect
60. C₆₁×#488	C₂²	semidirect
61. C₆₁×#486	C₂²	semidirect
62. C₆₁×#486	C₂²	semidirect
63. C₆₁×#485	C₂²	semidirect
64. C₆₁×#485	C₂²	semidirect
65. C₆₁×#484	C₂²	semidirect
66. C₆₁×#484	C₂²	semidirect
68. C₆₁×#482	C₂²	semidirect
69. C₆₁×#482	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
76. C₆₁×#481	C₂²	semidirect
77. C₆₁×#481	C₂²	semidirect
78. C₆₁×#480	C₂²	semidirect
79. C₆₁×#480	C₂²	semidirect
80. C₆₁×#480	C₂²	semidirect
81. C₆₁×#480	C₂²	semidirect
82. C₆₁×#478	C₂²	semidirect
83. C₆₁×#478	C₂²	semidirect
84. C₆₁×#478	C₂²	semidirect
85. C₆₁×#478	C₂²	semidirect
86. C₆₁×#477	C₂²	semidirect
87. C₆₁×#476	C₂²	semidirect
88. C₆₁×#475	C₂²	semidirect
89. C₆₁×#474	C₂²	semidirect
90. C₆₁×#474	C₂²	semidirect
91. C₆₁×#474	C₂²	semidirect
94. C₆₁×#469	C₂²	semidirect
95. C₆₁×#468	C₂²	semidirect
98. C₆₁×#466	C₂²	semidirect
99. C₆₁×#465	C₂²	semidirect
104. C₆₁×#450	C₂²	semidirect
105. C₆₁×#449	C₂²	semidirect
106. C₆₁×#449	C₂²	semidirect
110. C₆₁×#447	C₂²	semidirect
111. C₄×SD₁₆×C₆₁	C₂²	semidirect
112. C₄×SD₁₆×C₆₁	C₂²	semidirect
115. C₄×D₈×C₆₁	C₂²	semidirect
116. C₄×D₈×C₆₁	C₂²	semidirect
117. C₆₁×#436	C₂²	semidirect
118. C₆₁×#436	C₂²	semidirect
119. C₆₁×#436	C₂²	semidirect
120. C₈×D₄×C₆₁	C₂²	semidirect
121. C₈×D₄×C₆₁	C₂²	semidirect
122. C₈×D₄×C₆₁	C₂²	semidirect
123. C₆₁×#431	C₂²	semidirect
124. C₆₁×#431	C₂²	semidirect
125. C₆₁×#428	C₂²	semidirect
126. C₆₁×#428	C₂²	semidirect
127. C₆₁×#427	C₂²	semidirect
128. C₂×#107×C₆₁	C₂²	semidirect
129. C₆₁×#418	C₂²	semidirect
130. C₆₁×#417	C₂²	semidirect
131. C₆₁×#416	C₂²	semidirect
132. C₂×#102×C₆₁	C₂²	semidirect
133. C₆₁×#408	C₂²	semidirect
134. C₆₁×#408	C₂²	semidirect
537. #61784	C₆₁	direct (N × H)
579. #3546	C₂×C₆₁	semidirect
580. #3506	C₂×C₆₁	semidirect
581. #3355	C₂×C₆₁	semidirect
582. #3354	C₂×C₆₁	semidirect
583. #3353	C₂×C₆₁	semidirect
584. #3340	C₂×C₆₁	semidirect
585. #3339	C₂×C₆₁	semidirect
586. #3334	C₂×C₆₁	semidirect
587. #3332	C₂×C₆₁	semidirect
588. #3325	C₂×C₆₁	semidirect
589. #3322	C₂×C₆₁	semidirect
590. #3305	C₂×C₆₁	semidirect
591. #3297	C₂×C₆₁	semidirect
592. #3294	C₂×C₆₁	semidirect
593. #3233	C₂×C₆₁	semidirect
594. #3228	C₂×C₆₁	semidirect
595. #3199	C₂×C₆₁	semidirect
596. #3198	C₂×C₆₁	semidirect
597. #3105	C₂×C₆₁	semidirect
598. #3100	C₂×C₆₁	semidirect
599. #3098	C₂×C₆₁	semidirect
600. #3096	C₂×C₆₁	semidirect
601. #2979	C₂×C₆₁	semidirect
615. #556	C₂²×C₆₁	semidirect
617. #555	C₂²×C₆₁	semidirect
618. #553	C₂²×C₆₁	semidirect
619. #553	C₂²×C₆₁	semidirect
620. #553	C₂²×C₆₁	semidirect
623. #550	C₂²×C₆₁	semidirect
625. #547	C₂²×C₆₁	semidirect
626. #547	C₂²×C₆₁	semidirect
628. #546	C₂²×C₆₁	semidirect
629. D₄²	C₂²×C₆₁	semidirect
636. #535	C₂²×C₆₁	semidirect
637. #533	C₂²×C₆₁	semidirect
643. #520	C₂²×C₆₁	semidirect
644. C₂×C₄×D₄	C₂²×C₆₁	semidirect
645. #500	C₂²×C₆₁	semidirect
646. #499	C₂²×C₆₁	semidirect
647. #498	C₂²×C₆₁	semidirect
648. #488	C₂²×C₆₁	semidirect
649. #486	C₂²×C₆₁	semidirect
650. #486	C₂²×C₆₁	semidirect
651. #485	C₂²×C₆₁	semidirect
652. #485	C₂²×C₆₁	semidirect
653. #484	C₂²×C₆₁	semidirect
654. #484	C₂²×C₆₁	semidirect
656. #482	C₂²×C₆₁	semidirect
657. #482	C₂²×C₆₁	semidirect
658. #482	C₂²×C₆₁	semidirect
659. #482	C₂²×C₆₁	semidirect
660. #482	C₂²×C₆₁	semidirect
661. #482	C₂²×C₆₁	semidirect
662. #482	C₂²×C₆₁	semidirect
664. #481	C₂²×C₆₁	semidirect
665. #481	C₂²×C₆₁	semidirect
666. #480	C₂²×C₆₁	semidirect
667. #480	C₂²×C₆₁	semidirect
668. #480	C₂²×C₆₁	semidirect
669. #480	C₂²×C₆₁	semidirect
670. #478	C₂²×C₆₁	semidirect
671. #478	C₂²×C₆₁	semidirect
672. #478	C₂²×C₆₁	semidirect
673. #478	C₂²×C₆₁	semidirect
674. #477	C₂²×C₆₁	semidirect
675. #476	C₂²×C₆₁	semidirect
676. #475	C₂²×C₆₁	semidirect
677. #474	C₂²×C₆₁	semidirect
678. #474	C₂²×C₆₁	semidirect
679. #474	C₂²×C₆₁	semidirect
682. #469	C₂²×C₆₁	semidirect
683. #468	C₂²×C₆₁	semidirect
686. #466	C₂²×C₆₁	semidirect
687. #465	C₂²×C₆₁	semidirect
692. #450	C₂²×C₆₁	semidirect
693. #449	C₂²×C₆₁	semidirect
694. #449	C₂²×C₆₁	semidirect
698. #447	C₂²×C₆₁	semidirect
699. C₄×SD₁₆	C₂²×C₆₁	semidirect
700. C₄×SD₁₆	C₂²×C₆₁	semidirect
703. C₄×D₈	C₂²×C₆₁	semidirect
704. C₄×D₈	C₂²×C₆₁	semidirect
705. #436	C₂²×C₆₁	semidirect
706. #436	C₂²×C₆₁	semidirect
707. #436	C₂²×C₆₁	semidirect
708. C₈×D₄	C₂²×C₆₁	semidirect
709. C₈×D₄	C₂²×C₆₁	semidirect
710. C₈×D₄	C₂²×C₆₁	semidirect
711. #431	C₂²×C₆₁	semidirect
712. #431	C₂²×C₆₁	semidirect
713. #428	C₂²×C₆₁	semidirect
714. #428	C₂²×C₆₁	semidirect
715. #427	C₂²×C₆₁	semidirect
716. C₂×#107	C₂²×C₆₁	semidirect
717. #418	C₂²×C₆₁	semidirect
718. #417	C₂²×C₆₁	semidirect
719. #416	C₂²×C₆₁	semidirect
720. C₂×#102	C₂²×C₆₁	semidirect
721. #408	C₂²×C₆₁	semidirect
722. #408	C₂²×C₆₁	semidirect
723. C₆₁	#61784	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×#3546	2
C₆₁×#3506	2
C₆₁×#3355	2
C₆₁×#3354	2
C₆₁×#3353	2
C₆₁×#3340	2
C₆₁×#3339	2
C₆₁×#3334	2
C₆₁×#3332	2
C₆₁×#3325	2
C₆₁×#3322	2
C₆₁×#3305	2
C₆₁×#3297	2
C₆₁×#3294	2
C₆₁×#3233	2
C₆₁×#3228	2
C₆₁×#3199	2
C₆₁×#3198	2
C₆₁×#3105	2
C₆₁×#3100	2
C₆₁×#3098	2
C₆₁×#3096	2
C₆₁×#2979	2
#61784	61

Subgroups — C61×#61784 #29565217

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61784 #29565217