Subgroups — C₆₁×#61796 #29565229

Order 15616.

1738 conjugacy classes of subgroups.

The subgroup lattice has 1026 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3348	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3347	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3346	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3343	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3321	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3320	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3308	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3307	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3240	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3237	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3200	C₂	1	2	yes	maximal, complemented
14	C₆₁×#3198	C₂	1	2	yes	maximal, complemented
15	C₆₁×#3114	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#3110	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3098	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3097	C₂	1	2	yes	maximal, complemented
19	C₆₁×#2980	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₁×#562	—	2	2	no	—
21	C₆₁×#559	—	2	2	no	—
22	C₆₁×#556	—	2	1	no	—
23	C₆₁×#555	—	2	1	no	—
24	C₆₁×#555	C₂²	1	2	yes	—
25	C₆₁×#555	C₂²	1	1	yes	characteristic, complemented
26	C₆₁×#554	C₂²	1	1	yes	characteristic, complemented
27	C₆₁×#553	—	2	1	no	—
28	C₆₁×#553	C₂²	1	2	yes	—
29	C₆₁×#553	C₂²	1	2	yes	—
30	C₆₁×#552	C₂²	1	2	yes	complemented
31	C₆₁×#550	—	2	1	no	—
32	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
33	C₆₁×#548	C₂²	1	2	yes	complemented
34	C₆₁×#547	C₂²	1	2	yes	—
35	C₆₁×#547	C₂²	1	1	yes	characteristic, complemented
36	C₆₁×#544	—	2	1	no	—
37	C₆₁×#542	—	2	2	no	—
38	C₆₁×#540	—	2	1	no	—
39	C₆₁×#538	—	2	1	no	—
40	C₆₁×#538	—	2	1	no	—
41	C₆₁×#537	C₂²	1	2	yes	—
42	C₆₁×#536	C₂²	1	2	yes	—
43	C₆₁×#535	C₂²	1	2	yes	—
44	C₆₁×#533	C₂²	1	1	yes	characteristic
45	C₆₁×#533	C₂²	1	1	yes	characteristic
46	C₆₁×#532	C₂²	1	1	yes	characteristic
47	C₆₁×#529	C₂²	1	1	yes	characteristic
48	C₆₁×#525	—	2	2	no	—
49	C₆₁×#520	C₂²	1	2	yes	—
50	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
51	C₆₁×#501	C₂²	1	1	yes	characteristic, complemented
52	C₆₁×#501	C₂²	1	2	yes	complemented
53	C₆₁×#501	C₂²	1	1	yes	characteristic, complemented
54	C₆₁×#491	C₂²	1	2	yes	complemented
55	C₆₁×#489	C₂²	1	1	yes	characteristic, complemented
56	C₆₁×#489	C₂²	1	1	yes	characteristic, complemented
57	C₆₁×#485	C₂²	1	2	yes	—
58	C₆₁×#485	C₂²	1	2	yes	—
59	C₆₁×#485	C₂²	1	2	yes	—
60	C₆₁×#485	C₂²	1	2	yes	complemented
61	C₆₁×#485	C₂²	1	2	yes	complemented
62	C₆₁×#485	C₂²	1	2	yes	complemented
63	C₆₁×#484	C₂²	1	2	yes	—
64	C₆₁×#484	C₂²	1	2	yes	complemented
65	C₆₁×#484	C₂²	1	2	yes	complemented
66	C₆₁×#483	C₂²	1	1	yes	characteristic
67	C₆₁×#483	C₂²	1	2	yes	complemented
68	C₆₁×#482	C₂²	1	2	yes	—
69	C₆₁×#482	C₂²	1	2	yes	—
70	C₆₁×#482	C₂²	1	2	yes	—
71	C₆₁×#482	C₂²	1	2	yes	complemented
72	C₆₁×#481	C₂²	1	2	yes	—
73	C₆₁×#480	C₂²	1	2	yes	—
74	C₆₁×#480	C₂²	1	1	yes	characteristic
75	C₆₁×#480	C₂²	1	2	yes	complemented
76	C₆₁×#479	C₂²	1	2	yes	complemented
77	C₆₁×#478	C₂²	1	2	yes	—
78	C₆₁×#478	C₂²	1	2	yes	complemented
79	C₆₁×#477	C₂²	1	2	yes	complemented
80	C₆₁×#475	C₂²	1	2	yes	complemented
81	C₆₁×#474	C₂²	1	2	yes	—
82	C₆₁×#469	C₂²	1	2	yes	—
83	C₆₁×#468	C₂²	1	2	yes	—
84	C₆₁×#468	C₂²	1	2	yes	—
85	C₆₁×#468	C₂²	1	2	yes	—
86	C₆₁×#466	C₂²	1	2	yes	—
87	C₆₁×#465	C₂²	1	2	yes	—
88	C₆₁×#465	C₂²	1	2	yes	—
89	C₆₁×#465	C₂²	1	2	yes	—
90	C₆₁×#463	C₂²	1	2	yes	—
91	C₆₁×#461	C₂²	1	2	yes	—
92	C₆₁×#450	C₂²	1	2	yes	—
93	C₆₁×#450	C₂²	1	1	yes	characteristic
94	C₆₁×#449	C₂²	1	2	yes	—
95	C₆₁×#449	C₂²	1	2	yes	—
96	C₆₁×#448	C₂²	1	2	yes	—
97	C₆₁×#448	C₂²	1	2	yes	—
98	C₆₁×#447	C₂²	1	1	yes	characteristic
99	C₆₁×#442	C₂²	1	2	yes	—
100	C₆₁×#440	C₂²	1	2	yes	—
101	C₆₁×#440	C₂²	1	2	yes	—
102	C₆₁×#440	C₂²	1	2	yes	—
103	C₆₁×#435	C₂²	1	2	yes	complemented
104	C₆₁×#435	C₂²	1	2	yes	complemented
105	C₆₁×#435	C₂²	1	2	yes	complemented
106	C₆₁×#435	C₂²	1	2	yes	complemented
107	C₆₁×#432	C₂²	1	1	yes	characteristic
108	C₆₁×#432	C₂²	1	1	yes	characteristic
109	C₆₁×#428	C₂²	1	2	yes	complemented
110	C₆₁×#428	C₂²	1	2	yes	complemented
111	C₆₁×#427	C₂²	1	2	yes	complemented
112	C₂×#107×C₆₁	C₂²	1	2	yes	complemented
113	C₆₁×#419	C₂²	1	2	yes	complemented
114	C₆₁×#417	C₂²	1	2	yes	complemented
115	C₆₁×#416	C₂²	1	2	yes	complemented
116	C₂×#103×C₆₁	C₂²	1	2	yes	complemented
117	C₆₁×#408	C₂²	1	2	yes	—
118	C₆₁×#408	C₂²	1	2	yes	—
119	C₂×#41×C₆₁	—	2	2	no	—
120	C₂×#41×C₆₁	C₂³	1	2	yes	—
121	C₂×#41×C₆₁	C₂³	1	2	yes	—
122	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
123	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₆₁	—	2	1	no	—
125	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
128	C₂×D₈×C₆₁	C₂³	1	2	yes	—
129	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
130	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
131	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
132	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
133	C₄⋊Q₈×C₆₁	—	2	2	no	—
134	C₄⋊Q₈×C₆₁	—	2	1	no	—
135	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
136	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
137	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
138	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
139	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
140	#127×C₆₁	—	2	2	no	—
141	#127×C₆₁	D₄	1	1	yes	characteristic
142	#126×C₆₁	—	2	2	no	—
143	#126×C₆₁	—	2	2	no	—
144	#126×C₆₁	—	2	2	no	—
145	#126×C₆₁	—	2	1	no	—
146	#125×C₆₁	—	2	2	no	—
147	#125×C₆₁	—	2	1	no	—
148	#125×C₆₁	—	2	1	no	—
149	#125×C₆₁	C₂³	1	2	yes	—
150	#125×C₆₁	C₂³	1	1	yes	characteristic
151	#124×C₆₁	—	2	2	no	—
152	#124×C₆₁	—	2	2	no	—
153	#124×C₆₁	—	2	2	no	—
154	#124×C₆₁	—	2	2	no	—
155	#124×C₆₁	—	2	2	no	—
156	#124×C₆₁	—	2	2	no	—
157	#124×C₆₁	D₄	1	2	yes	—
158	#124×C₆₁	C₂³	1	1	yes	characteristic
159	#123×C₆₁	—	2	2	no	—
160	#123×C₆₁	—	2	2	no	—
161	#123×C₆₁	—	2	2	no	—
162	#123×C₆₁	—	2	1	no	—
163	#123×C₆₁	—	2	2	no	—
164	#123×C₆₁	—	2	2	no	—
165	#123×C₆₁	—	2	2	no	—
166	#123×C₆₁	—	2	2	no	—
167	#123×C₆₁	—	2	2	no	—
168	C₂²⋊Q₈×C₆₁	—	2	2	no	—
169	C₂²⋊Q₈×C₆₁	—	2	1	no	—
170	C₂²⋊Q₈×C₆₁	—	2	1	no	—
171	C₂²⋊Q₈×C₆₁	—	2	1	no	—
172	C₂²⋊Q₈×C₆₁	—	2	2	no	—
173	C₂²⋊Q₈×C₆₁	—	2	2	no	—
174	C₂²⋊Q₈×C₆₁	—	2	2	no	—
175	C₂²⋊Q₈×C₆₁	—	2	2	no	—
176	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
177	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
178	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
179	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
180	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
181	#121×C₆₁	—	2	2	no	—
182	#121×C₆₁	—	2	2	no	—
183	#121×C₆₁	—	2	2	no	—
184	#121×C₆₁	—	2	2	no	—
185	#121×C₆₁	—	2	2	no	—
186	#121×C₆₁	—	2	1	no	—
187	#121×C₆₁	—	2	2	no	—
188	#121×C₆₁	—	2	1	no	—
189	#121×C₆₁	—	2	2	no	—
190	#121×C₆₁	D₄	1	1	yes	characteristic
191	#121×C₆₁	D₄	1	1	yes	characteristic
192	#121×C₆₁	D₄	1	2	yes	—
193	#121×C₆₁	C₂³	1	2	yes	—
194	#121×C₆₁	C₂³	1	2	yes	—
195	#121×C₆₁	C₂³	1	2	yes	—
196	#121×C₆₁	C₂³	1	2	yes	—
197	#121×C₆₁	C₂³	1	1	yes	characteristic
198	#121×C₆₁	C₂³	1	2	yes	—
199	#120×C₆₁	—	2	2	no	—
200	#120×C₆₁	—	2	2	no	—
201	C₄×Q₈×C₆₁	—	2	2	no	—
202	C₄×Q₈×C₆₁	—	2	1	no	—
203	C₄×Q₈×C₆₁	—	2	1	no	—
204	C₄×Q₈×C₆₁	—	2	1	no	—
205	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
206	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
207	C₄×D₄×C₆₁	—	2	2	no	—
208	C₄×D₄×C₆₁	—	2	2	no	—
209	C₄×D₄×C₆₁	—	2	1	no	—
210	C₄×D₄×C₆₁	—	2	1	no	—
211	C₄×D₄×C₆₁	—	2	2	no	—
212	C₄×D₄×C₆₁	—	2	1	no	—
213	C₄×D₄×C₆₁	—	2	2	no	—
214	C₄×D₄×C₆₁	—	2	2	no	—
215	C₄×D₄×C₆₁	—	2	2	no	—
216	C₄×D₄×C₆₁	—	2	1	no	—
217	C₄×D₄×C₆₁	—	2	1	no	—
218	C₄×D₄×C₆₁	C₂³	1	2	yes	—
219	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
220	C₄×D₄×C₆₁	C₂³	1	2	yes	—
221	C₄×D₄×C₆₁	C₂³	1	2	yes	—
222	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
223	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
224	#117×C₆₁	—	2	1	no	—
225	#117×C₆₁	—	2	1	no	—
226	#117×C₆₁	—	2	2	no	—
227	#117×C₆₁	—	2	2	no	—
228	#117×C₆₁	—	2	1	no	—
229	#117×C₆₁	C₂³	1	2	yes	—
230	#117×C₆₁	C₂³	1	2	yes	—
231	#117×C₆₁	C₂³	1	2	yes	—
232	#117×C₆₁	C₂³	1	2	yes	—
233	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
234	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
235	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
236	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
237	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
238	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
239	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
240	#107×C₆₁	C₂³	1	2	yes	—
241	#107×C₆₁	C₂³	1	2	yes	—
242	#107×C₆₁	C₂³	1	2	yes	—
243	#107×C₆₁	C₂³	1	2	yes	—
244	#107×C₆₁	C₂³	1	2	yes	—
245	#107×C₆₁	C₂³	1	2	yes	—
246	#107×C₆₁	C₂³	1	2	yes	—
247	#106×C₆₁	C₂³	1	2	yes	—
248	#106×C₆₁	C₂³	1	2	yes	—
249	#106×C₆₁	C₂³	1	2	yes	—
250	#106×C₆₁	C₂³	1	2	yes	—
251	#106×C₆₁	C₂³	1	2	yes	—
252	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
253	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
254	#103×C₆₁	C₂³	1	2	yes	—
255	#103×C₆₁	C₂³	1	2	yes	—
256	#103×C₆₁	C₂³	1	2	yes	—
257	#103×C₆₁	C₂³	1	2	yes	—
258	#103×C₆₁	C₂³	1	2	yes	—
259	#103×C₆₁	C₂³	1	2	yes	—
260	#103×C₆₁	C₂³	1	2	yes	—
261	#103×C₆₁	C₂³	1	2	yes	—
262	#103×C₆₁	C₂³	1	2	yes	—
263	#102×C₆₁	C₂³	1	2	yes	—
264	#102×C₆₁	C₂³	1	2	yes	—
265	#102×C₆₁	C₂³	1	2	yes	—
266	#102×C₆₁	C₂³	1	2	yes	—
267	#102×C₆₁	C₂³	1	2	yes	—
268	#102×C₆₁	C₂³	1	2	yes	—
269	#102×C₆₁	C₂³	1	2	yes	—
270	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
271	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
272	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
273	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
274	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
275	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
276	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
277	#97×C₆₁	C₂³	1	1	yes	characteristic
278	#97×C₆₁	C₂³	1	1	yes	characteristic
279	#97×C₆₁	C₂³	1	2	yes	—
280	C₂⁴×C₆₁	—	2	1	no	—
281	#41×C₆₁	—	4	2	no	—
282	#41×C₆₁	—	4	2	no	—
283	#41×C₆₁	—	4	2	no	—
284	#41×C₆₁	—	4	2	no	—
285	#41×C₆₁	—	8	4	no	—
286	C₂×Q₈×C₆₁	—	2	1	no	—
287	C₂×Q₈×C₆₁	—	2	1	no	—
288	C₂×Q₈×C₆₁	—	2	1	no	—
289	C₂×Q₈×C₆₁	—	2	2	no	—
290	C₂×Q₈×C₆₁	—	4	2	no	—
291	C₂×Q₈×C₆₁	—	4	2	no	—
292	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
293	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
294	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
295	C₂×D₄×C₆₁	—	2	2	no	—
296	C₂×D₄×C₆₁	—	2	2	no	—
297	C₂×D₄×C₆₁	—	2	1	no	—
298	C₂×D₄×C₆₁	—	2	2	no	—
299	C₂×D₄×C₆₁	—	2	2	no	—
300	C₂×D₄×C₆₁	—	2	2	no	—
301	C₂×D₄×C₆₁	—	2	2	no	—
302	C₂×D₄×C₆₁	—	2	1	no	—
303	C₂×D₄×C₆₁	—	4	2	no	—
304	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
305	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
306	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
307	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
308	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
309	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
310	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
311	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₆₁	—	2	1	no	—
313	C₂²×C₄×C₆₁	—	2	2	no	—
314	C₂²×C₄×C₆₁	—	2	2	no	—
315	C₂²×C₄×C₆₁	—	2	2	no	—
316	C₂²×C₄×C₆₁	—	2	2	no	—
317	C₂²×C₄×C₆₁	—	2	1	no	—
318	C₂²×C₄×C₆₁	—	2	2	no	—
319	C₂²×C₄×C₆₁	—	2	2	no	—
320	C₂²×C₄×C₆₁	—	2	2	no	—
321	C₂²×C₄×C₆₁	—	8	2	no	—
322	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
323	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
324	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
326	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
327	SD₁₆×C₆₁	—	4	2	no	—
328	SD₁₆×C₆₁	—	4	2	no	—
329	SD₁₆×C₆₁	—	4	2	no	—
330	D₈×C₆₁	—	4	2	no	—
331	M₁₆×C₆₁	—	4	2	no	—
332	M₁₆×C₆₁	—	4	2	no	—
333	C₂×C₈×C₆₁	—	4	2	no	—
334	C₂×C₈×C₆₁	—	4	2	no	—
335	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
336	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
337	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
338	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
339	C₄⋊C₄×C₆₁	—	2	1	no	—
340	C₄⋊C₄×C₆₁	—	2	2	no	—
341	C₄⋊C₄×C₆₁	—	2	1	no	—
342	C₄⋊C₄×C₆₁	—	2	2	no	—
343	C₄⋊C₄×C₆₁	—	2	2	no	—
344	C₄⋊C₄×C₆₁	—	2	2	no	—
345	C₄⋊C₄×C₆₁	—	2	1	no	—
346	C₄⋊C₄×C₆₁	—	2	1	no	—
347	C₄⋊C₄×C₆₁	—	2	1	no	—
348	C₄⋊C₄×C₆₁	—	2	2	no	—
349	C₄⋊C₄×C₆₁	—	2	1	no	—
350	C₄⋊C₄×C₆₁	—	2	1	no	—
351	C₄⋊C₄×C₆₁	—	2	2	no	—
352	C₄⋊C₄×C₆₁	—	2	2	no	—
353	C₄⋊C₄×C₆₁	—	2	2	no	—
354	C₄⋊C₄×C₆₁	—	2	2	no	—
355	C₄⋊C₄×C₆₁	—	2	1	no	—
356	C₄⋊C₄×C₆₁	—	2	1	no	—
357	C₄⋊C₄×C₆₁	—	2	2	no	—
358	C₄⋊C₄×C₆₁	—	2	1	no	—
359	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
360	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
361	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
362	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
363	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
364	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
366	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
367	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
368	C₂²⋊C₄×C₆₁	—	2	2	no	—
369	C₂²⋊C₄×C₆₁	—	2	2	no	—
370	C₂²⋊C₄×C₆₁	—	2	2	no	—
371	C₂²⋊C₄×C₆₁	—	2	2	no	—
372	C₂²⋊C₄×C₆₁	—	2	2	no	—
373	C₂²⋊C₄×C₆₁	—	2	2	no	—
374	C₂²⋊C₄×C₆₁	—	2	2	no	—
375	C₂²⋊C₄×C₆₁	—	2	2	no	—
376	C₂²⋊C₄×C₆₁	—	2	1	no	—
377	C₂²⋊C₄×C₆₁	—	2	2	no	—
378	C₂²⋊C₄×C₆₁	—	2	2	no	—
379	C₂²⋊C₄×C₆₁	—	2	2	no	—
380	C₂²⋊C₄×C₆₁	—	2	2	no	—
381	C₂²⋊C₄×C₆₁	—	2	1	no	—
382	C₂²⋊C₄×C₆₁	—	2	1	no	—
383	C₂²⋊C₄×C₆₁	—	2	2	no	—
384	C₂²⋊C₄×C₆₁	—	2	1	no	—
385	C₂²⋊C₄×C₆₁	—	2	2	no	—
386	C₂²⋊C₄×C₆₁	—	2	2	no	—
387	C₂²⋊C₄×C₆₁	—	2	1	no	—
388	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
389	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
390	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
391	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
392	C₄²×C₆₁	—	2	2	no	—
393	C₄²×C₆₁	—	2	2	no	—
394	C₄²×C₆₁	—	2	2	no	—
395	C₄²×C₆₁	—	2	2	no	—
396	C₄²×C₆₁	—	2	1	no	—
397	C₄²×C₆₁	—	2	2	no	—
398	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
399	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
400	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
401	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
402	C₂³×C₆₁	—	2	1	no	—
403	C₂³×C₆₁	—	2	2	no	—
404	C₂³×C₆₁	—	4	2	no	—
405	C₂³×C₆₁	—	8	1	no	—
406	C₂³×C₆₁	—	8	1	no	—
407	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
408	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
409	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
410	Q₈×C₆₁	—	2	2	no	—
411	Q₈×C₆₁	—	2	2	no	—
412	Q₈×C₆₁	—	2	2	no	—
413	Q₈×C₆₁	—	4	2	no	—
414	Q₈×C₆₁	—	4	2	no	—
415	Q₈×C₆₁	—	8	1	no	—
416	Q₈×C₆₁	—	8	1	no	—
417	Q₈×C₆₁	—	8	2	no	—
418	D₄×C₆₁	—	2	2	no	—
419	D₄×C₆₁	—	2	2	no	—
420	D₄×C₆₁	—	2	2	no	—
421	D₄×C₆₁	—	4	1	no	—
422	D₄×C₆₁	—	4	1	no	—
423	D₄×C₆₁	—	4	2	no	—
424	D₄×C₆₁	—	4	2	no	—
425	D₄×C₆₁	—	4	2	no	—
426	D₄×C₆₁	—	4	2	no	—
427	D₄×C₆₁	—	4	2	no	—
428	D₄×C₆₁	—	8	1	no	—
429	D₄×C₆₁	—	8	2	no	—
430	D₄×C₆₁	—	8	2	no	—
431	D₄×C₆₁	—	8	2	no	—
432	D₄×C₆₁	—	8	2	no	—
433	D₄×C₆₁	—	8	2	no	—
434	D₄×C₆₁	—	8	2	no	—
435	C₂×C₄×C₆₁	—	2	2	no	—
436	C₂×C₄×C₆₁	—	2	2	no	—
437	C₂×C₄×C₆₁	—	2	2	no	—
438	C₂×C₄×C₆₁	—	2	2	no	—
439	C₂×C₄×C₆₁	—	2	2	no	—
440	C₂×C₄×C₆₁	—	2	2	no	—
441	C₂×C₄×C₆₁	—	2	1	no	—
442	C₂×C₄×C₆₁	—	2	2	no	—
443	C₂×C₄×C₆₁	—	2	2	no	—
444	C₂×C₄×C₆₁	—	2	1	no	—
445	C₂×C₄×C₆₁	—	2	1	no	—
446	C₂×C₄×C₆₁	—	2	2	no	—
447	C₂×C₄×C₆₁	—	2	2	no	—
448	C₂×C₄×C₆₁	—	4	1	no	—
449	C₂×C₄×C₆₁	—	4	1	no	—
450	C₂×C₄×C₆₁	—	4	2	no	—
451	C₂×C₄×C₆₁	—	4	4	no	—
452	C₂×C₄×C₆₁	—	8	2	no	—
453	C₂×C₄×C₆₁	—	8	2	no	—
454	C₂×C₄×C₆₁	—	8	2	no	—
455	C₂×C₄×C₆₁	—	8	1	no	—
456	C₂×C₄×C₆₁	—	8	2	no	—
457	C₂×C₄×C₆₁	—	8	2	no	—
458	C₂×C₄×C₆₁	—	8	2	no	—
459	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
462	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
463	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
464	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
467	C₈×C₆₁	—	2	2	no	—
468	C₈×C₆₁	—	2	2	no	—
469	C₈×C₆₁	—	2	2	no	—
470	C₈×C₆₁	—	2	2	no	—
471	#61796	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
472	C₂²×C₆₁	—	2	1	no	—
473	C₂²×C₆₁	—	2	2	no	—
474	C₂²×C₆₁	—	2	2	no	—
475	C₂²×C₆₁	—	2	1	no	—
476	C₂²×C₆₁	—	2	2	no	—
477	C₂²×C₆₁	—	2	2	no	—
478	C₂²×C₆₁	—	2	2	no	—
479	C₂²×C₆₁	—	2	1	no	—
480	C₂²×C₆₁	—	2	2	no	—
481	C₂²×C₆₁	—	4	2	no	—
482	C₂²×C₆₁	—	4	1	no	—
483	C₂²×C₆₁	—	4	1	no	—
484	C₂²×C₆₁	—	4	2	no	—
485	C₂²×C₆₁	—	4	1	no	—
486	C₂²×C₆₁	—	4	2	no	—
487	C₂²×C₆₁	—	8	4	no	—
488	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
489	C₄×C₆₁	—	2	1	no	—
490	C₄×C₆₁	—	2	1	no	—
491	C₄×C₆₁	—	2	1	no	—
492	C₄×C₆₁	—	2	1	no	—
493	C₄×C₆₁	—	2	2	no	—
494	C₄×C₆₁	—	2	1	no	—
495	C₄×C₆₁	—	2	2	no	—
496	C₄×C₆₁	—	4	2	no	—
497	C₄×C₆₁	—	4	1	no	—
498	C₄×C₆₁	—	4	2	no	—
499	C₄×C₆₁	—	4	2	no	—
500	C₄×C₆₁	—	4	1	no	—
501	C₄×C₆₁	—	4	2	no	—
502	C₄×C₆₁	—	4	2	no	—
503	C₄×C₆₁	—	4	1	no	—
504	C₄×C₆₁	#585	1	2	yes	—
505	#3547	C₂×C₆₁	1	1	yes	characteristic, complemented
506	#3506	C₂×C₆₁	1	1	yes	characteristic, complemented
507	#3348	C₂×C₆₁	1	2	yes	complemented
508	#3347	C₂×C₆₁	1	2	yes	complemented
509	#3346	C₂×C₆₁	1	2	yes	complemented
510	#3343	C₂×C₆₁	1	2	yes	complemented
511	#3321	C₂×C₆₁	1	2	yes	complemented
512	#3320	C₂×C₆₁	1	2	yes	complemented
513	#3308	C₂×C₆₁	1	2	yes	complemented
514	#3307	C₂×C₆₁	1	2	yes	complemented
515	#3240	C₂×C₆₁	1	1	yes	characteristic, complemented
516	#3237	C₂×C₆₁	1	1	yes	characteristic, complemented
517	#3200	C₂×C₆₁	1	2	yes	complemented
518	#3198	C₂×C₆₁	1	2	yes	complemented
519	#3114	C₂×C₆₁	1	1	yes	characteristic, complemented
520	#3110	C₂×C₆₁	1	1	yes	characteristic, complemented
521	#3098	C₂×C₆₁	1	2	yes	complemented
522	#3097	C₂×C₆₁	1	2	yes	complemented
523	#2980	C₂×C₆₁	1	1	yes	characteristic, complemented
524	C₂×C₆₁	—	4	2	no	—
525	C₂×C₆₁	—	4	2	no	—
526	C₂×C₆₁	—	4	1	no	—
527	C₂×C₆₁	—	8	1	no	—
528	C₂×C₆₁	—	8	2	no	—
529	C₂×C₆₁	#3485	1	1	yes	characteristic
530	C₂×C₆₁	#3585	1	1	yes	characteristic
531	C₂×C₆₁	#3586	1	1	yes	characteristic
532	#562	—	2	2	no	—
533	#559	—	2	2	no	—
534	#556	—	2	1	no	—
535	#555	—	2	1	no	—
536	#555	C₂²×C₆₁	1	2	yes	—
537	#555	C₂²×C₆₁	1	1	yes	characteristic, complemented
538	#554	C₂²×C₆₁	1	1	yes	characteristic, complemented
539	#553	—	2	1	no	—
540	#553	C₂²×C₆₁	1	2	yes	—
541	#553	C₂²×C₆₁	1	2	yes	—
542	#552	C₂²×C₆₁	1	2	yes	complemented
543	#550	—	2	1	no	—
544	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
545	#548	C₂²×C₆₁	1	2	yes	complemented
546	#547	C₂²×C₆₁	1	2	yes	—
547	#547	C₂²×C₆₁	1	1	yes	characteristic, complemented
548	#544	—	2	1	no	—
549	#542	—	2	2	no	—
550	#540	—	2	1	no	—
551	#538	—	2	1	no	—
552	#538	—	2	1	no	—
553	#537	C₂²×C₆₁	1	2	yes	—
554	#536	C₂²×C₆₁	1	2	yes	—
555	#535	C₂²×C₆₁	1	2	yes	—
556	#533	C₂²×C₆₁	1	1	yes	characteristic
557	#533	C₂²×C₆₁	1	1	yes	characteristic
558	#532	C₂²×C₆₁	1	1	yes	characteristic
559	#529	C₂²×C₆₁	1	1	yes	characteristic
560	#525	—	2	2	no	—
561	#520	C₂²×C₆₁	1	2	yes	—
562	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
563	#501	C₂²×C₆₁	1	1	yes	characteristic, complemented
564	#501	C₂²×C₆₁	1	2	yes	complemented
565	#501	C₂²×C₆₁	1	1	yes	characteristic, complemented
566	#491	C₂²×C₆₁	1	2	yes	complemented
567	#489	C₂²×C₆₁	1	1	yes	characteristic, complemented
568	#489	C₂²×C₆₁	1	1	yes	characteristic, complemented
569	#485	C₂²×C₆₁	1	2	yes	—
570	#485	C₂²×C₆₁	1	2	yes	—
571	#485	C₂²×C₆₁	1	2	yes	—
572	#485	C₂²×C₆₁	1	2	yes	complemented
573	#485	C₂²×C₆₁	1	2	yes	complemented
574	#485	C₂²×C₆₁	1	2	yes	complemented
575	#484	C₂²×C₆₁	1	2	yes	—
576	#484	C₂²×C₆₁	1	2	yes	complemented
577	#484	C₂²×C₆₁	1	2	yes	complemented
578	#483	C₂²×C₆₁	1	1	yes	characteristic
579	#483	C₂²×C₆₁	1	2	yes	complemented
580	#482	C₂²×C₆₁	1	2	yes	—
581	#482	C₂²×C₆₁	1	2	yes	—
582	#482	C₂²×C₆₁	1	2	yes	—
583	#482	C₂²×C₆₁	1	2	yes	complemented
584	#481	C₂²×C₆₁	1	2	yes	—
585	#480	C₂²×C₆₁	1	2	yes	—
586	#480	C₂²×C₆₁	1	1	yes	characteristic
587	#480	C₂²×C₆₁	1	2	yes	complemented
588	#479	C₂²×C₆₁	1	2	yes	complemented
589	#478	C₂²×C₆₁	1	2	yes	—
590	#478	C₂²×C₆₁	1	2	yes	complemented
591	#477	C₂²×C₆₁	1	2	yes	complemented
592	#475	C₂²×C₆₁	1	2	yes	complemented
593	#474	C₂²×C₆₁	1	2	yes	—
594	#469	C₂²×C₆₁	1	2	yes	—
595	#468	C₂²×C₆₁	1	2	yes	—
596	#468	C₂²×C₆₁	1	2	yes	—
597	#468	C₂²×C₆₁	1	2	yes	—
598	#466	C₂²×C₆₁	1	2	yes	—
599	#465	C₂²×C₆₁	1	2	yes	—
600	#465	C₂²×C₆₁	1	2	yes	—
601	#465	C₂²×C₆₁	1	2	yes	—
602	#463	C₂²×C₆₁	1	2	yes	—
603	#461	C₂²×C₆₁	1	2	yes	—
604	#450	C₂²×C₆₁	1	2	yes	—
605	#450	C₂²×C₆₁	1	1	yes	characteristic
606	#449	C₂²×C₆₁	1	2	yes	—
607	#449	C₂²×C₆₁	1	2	yes	—
608	#448	C₂²×C₆₁	1	2	yes	—
609	#448	C₂²×C₆₁	1	2	yes	—
610	#447	C₂²×C₆₁	1	1	yes	characteristic
611	#442	C₂²×C₆₁	1	2	yes	—
612	#440	C₂²×C₆₁	1	2	yes	—
613	#440	C₂²×C₆₁	1	2	yes	—
614	#440	C₂²×C₆₁	1	2	yes	—
615	#435	C₂²×C₆₁	1	2	yes	complemented
616	#435	C₂²×C₆₁	1	2	yes	complemented
617	#435	C₂²×C₆₁	1	2	yes	complemented
618	#435	C₂²×C₆₁	1	2	yes	complemented
619	#432	C₂²×C₆₁	1	1	yes	characteristic
620	#432	C₂²×C₆₁	1	1	yes	characteristic
621	#428	C₂²×C₆₁	1	2	yes	complemented
622	#428	C₂²×C₆₁	1	2	yes	complemented
623	#427	C₂²×C₆₁	1	2	yes	complemented
624	C₂×#107	C₂²×C₆₁	1	2	yes	complemented
625	#419	C₂²×C₆₁	1	2	yes	complemented
626	#417	C₂²×C₆₁	1	2	yes	complemented
627	#416	C₂²×C₆₁	1	2	yes	complemented
628	C₂×#103	C₂²×C₆₁	1	2	yes	complemented
629	#408	C₂²×C₆₁	1	2	yes	—
630	#408	C₂²×C₆₁	1	2	yes	—
631	C₆₁	#61796	1	1	yes	characteristic, direct product factor, Sylow
632	C₂×#41	—	2	2	no	—
633	C₂×#41	C₂³×C₆₁	1	2	yes	—
634	C₂×#41	C₂³×C₆₁	1	2	yes	—
635	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
636	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
637	C₂³×C₄	—	2	1	no	—
638	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
639	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
640	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
641	C₂×D₈	C₂³×C₆₁	1	2	yes	—
642	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
643	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
644	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
645	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
646	C₄⋊Q₈	—	2	2	no	—
647	C₄⋊Q₈	—	2	1	no	—
648	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
649	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
650	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
651	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
652	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
653	#127	—	2	2	no	—
654	#127	D₄×C₆₁	1	1	yes	characteristic
655	#126	—	2	2	no	—
656	#126	—	2	2	no	—
657	#126	—	2	2	no	—
658	#126	—	2	1	no	—
659	#125	—	2	2	no	—
660	#125	—	2	1	no	—
661	#125	—	2	1	no	—
662	#125	C₂³×C₆₁	1	1	yes	characteristic
663	#125	C₂³×C₆₁	1	2	yes	—
664	#124	—	2	2	no	—
665	#124	—	2	2	no	—
666	#124	—	2	2	no	—
667	#124	—	2	2	no	—
668	#124	—	2	2	no	—
669	#124	—	2	2	no	—
670	#124	D₄×C₆₁	1	2	yes	—
671	#124	C₂³×C₆₁	1	1	yes	characteristic
672	#123	—	2	2	no	—
673	#123	—	2	2	no	—
674	#123	—	2	2	no	—
675	#123	—	2	1	no	—
676	#123	—	2	2	no	—
677	#123	—	2	2	no	—
678	#123	—	2	2	no	—
679	#123	—	2	2	no	—
680	#123	—	2	2	no	—
681	C₂²⋊Q₈	—	2	2	no	—
682	C₂²⋊Q₈	—	2	1	no	—
683	C₂²⋊Q₈	—	2	1	no	—
684	C₂²⋊Q₈	—	2	1	no	—
685	C₂²⋊Q₈	—	2	2	no	—
686	C₂²⋊Q₈	—	2	2	no	—
687	C₂²⋊Q₈	—	2	2	no	—
688	C₂²⋊Q₈	—	2	2	no	—
689	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
690	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
691	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
692	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
693	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
694	#121	—	2	2	no	—
695	#121	—	2	2	no	—
696	#121	—	2	2	no	—
697	#121	—	2	2	no	—
698	#121	—	2	2	no	—
699	#121	—	2	2	no	—
700	#121	—	2	1	no	—
701	#121	—	2	2	no	—
702	#121	—	2	1	no	—
703	#121	D₄×C₆₁	1	2	yes	—
704	#121	D₄×C₆₁	1	1	yes	characteristic
705	#121	D₄×C₆₁	1	1	yes	characteristic
706	#121	C₂³×C₆₁	1	1	yes	characteristic
707	#121	C₂³×C₆₁	1	2	yes	—
708	#121	C₂³×C₆₁	1	2	yes	—
709	#121	C₂³×C₆₁	1	2	yes	—
710	#121	C₂³×C₆₁	1	2	yes	—
711	#121	C₂³×C₆₁	1	2	yes	—
712	#120	—	2	2	no	—
713	#120	—	2	2	no	—
714	C₄×Q₈	—	2	2	no	—
715	C₄×Q₈	—	2	1	no	—
716	C₄×Q₈	—	2	1	no	—
717	C₄×Q₈	—	2	1	no	—
718	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
719	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
720	C₄×D₄	—	2	2	no	—
721	C₄×D₄	—	2	2	no	—
722	C₄×D₄	—	2	2	no	—
723	C₄×D₄	—	2	1	no	—
724	C₄×D₄	—	2	1	no	—
725	C₄×D₄	—	2	1	no	—
726	C₄×D₄	—	2	2	no	—
727	C₄×D₄	—	2	2	no	—
728	C₄×D₄	—	2	2	no	—
729	C₄×D₄	—	2	1	no	—
730	C₄×D₄	—	2	1	no	—
731	C₄×D₄	C₂³×C₆₁	1	2	yes	—
732	C₄×D₄	C₂³×C₆₁	1	2	yes	—
733	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
734	C₄×D₄	C₂³×C₆₁	1	2	yes	—
735	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
736	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
737	#117	—	2	1	no	—
738	#117	—	2	2	no	—
739	#117	—	2	1	no	—
740	#117	—	2	2	no	—
741	#117	—	2	1	no	—
742	#117	C₂³×C₆₁	1	2	yes	—
743	#117	C₂³×C₆₁	1	2	yes	—
744	#117	C₂³×C₆₁	1	2	yes	—
745	#117	C₂³×C₆₁	1	2	yes	—
746	C₂×C₄⋊C₄	—	2	1	no	—
747	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
748	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
749	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
750	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
751	C₂×C₂²⋊C₄	—	2	1	no	—
752	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
753	#107	C₂³×C₆₁	1	2	yes	—
754	#107	C₂³×C₆₁	1	2	yes	—
755	#107	C₂³×C₆₁	1	2	yes	—
756	#107	C₂³×C₆₁	1	2	yes	—
757	#107	C₂³×C₆₁	1	2	yes	—
758	#107	C₂³×C₆₁	1	2	yes	—
759	#107	C₂³×C₆₁	1	2	yes	—
760	#106	C₂³×C₆₁	1	2	yes	—
761	#106	C₂³×C₆₁	1	2	yes	—
762	#106	C₂³×C₆₁	1	2	yes	—
763	#106	C₂³×C₆₁	1	2	yes	—
764	#106	C₂³×C₆₁	1	2	yes	—
765	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
766	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
767	#103	C₂³×C₆₁	1	2	yes	—
768	#103	C₂³×C₆₁	1	2	yes	—
769	#103	C₂³×C₆₁	1	2	yes	—
770	#103	C₂³×C₆₁	1	2	yes	—
771	#103	C₂³×C₆₁	1	2	yes	—
772	#103	C₂³×C₆₁	1	2	yes	—
773	#103	C₂³×C₆₁	1	2	yes	—
774	#103	C₂³×C₆₁	1	2	yes	—
775	#103	C₂³×C₆₁	1	2	yes	—
776	#102	C₂³×C₆₁	1	2	yes	—
777	#102	C₂³×C₆₁	1	2	yes	—
778	#102	C₂³×C₆₁	1	2	yes	—
779	#102	C₂³×C₆₁	1	2	yes	—
780	#102	C₂³×C₆₁	1	2	yes	—
781	#102	C₂³×C₆₁	1	2	yes	—
782	#102	C₂³×C₆₁	1	2	yes	—
783	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
784	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
785	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
786	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
787	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
788	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
789	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
790	#97	C₂³×C₆₁	1	1	yes	characteristic
791	#97	C₂³×C₆₁	1	1	yes	characteristic
792	#97	C₂³×C₆₁	1	2	yes	—
793	C₂⁴	—	2	1	no	—
794	#41	—	4	2	no	—
795	#41	—	4	2	no	—
796	#41	—	4	2	no	—
797	#41	—	4	2	no	—
798	#41	—	8	4	no	—
799	C₂×Q₈	—	2	1	no	—
800	C₂×Q₈	—	2	1	no	—
801	C₂×Q₈	—	2	1	no	—
802	C₂×Q₈	—	2	2	no	—
803	C₂×Q₈	—	4	2	no	—
804	C₂×Q₈	—	4	2	no	—
805	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
806	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
807	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
808	C₂×D₄	—	2	2	no	—
809	C₂×D₄	—	2	2	no	—
810	C₂×D₄	—	2	1	no	—
811	C₂×D₄	—	2	2	no	—
812	C₂×D₄	—	2	2	no	—
813	C₂×D₄	—	2	2	no	—
814	C₂×D₄	—	2	2	no	—
815	C₂×D₄	—	2	1	no	—
816	C₂×D₄	—	4	2	no	—
817	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
818	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
819	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
820	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
821	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
822	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
823	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
824	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
825	C₂²×C₄	—	2	1	no	—
826	C₂²×C₄	—	2	2	no	—
827	C₂²×C₄	—	2	2	no	—
828	C₂²×C₄	—	2	2	no	—
829	C₂²×C₄	—	2	2	no	—
830	C₂²×C₄	—	2	1	no	—
831	C₂²×C₄	—	2	2	no	—
832	C₂²×C₄	—	2	2	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	8	2	no	—
835	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
836	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
837	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
838	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
839	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
840	SD₁₆	—	4	2	no	—
841	SD₁₆	—	4	2	no	—
842	SD₁₆	—	4	2	no	—
843	D₈	—	4	2	no	—
844	M₁₆	—	4	2	no	—
845	M₁₆	—	4	2	no	—
846	C₂×C₈	—	4	2	no	—
847	C₂×C₈	—	4	2	no	—
848	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
849	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
850	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
851	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
852	C₄⋊C₄	—	2	1	no	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	2	1	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	1	no	—
859	C₄⋊C₄	—	2	1	no	—
860	C₄⋊C₄	—	2	1	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	1	no	—
863	C₄⋊C₄	—	2	1	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	—	2	2	no	—
868	C₄⋊C₄	—	2	1	no	—
869	C₄⋊C₄	—	2	1	no	—
870	C₄⋊C₄	—	2	2	no	—
871	C₄⋊C₄	—	2	1	no	—
872	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
873	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
874	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
875	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
876	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
877	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
878	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
879	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
880	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	2	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	1	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	2	no	—
894	C₂²⋊C₄	—	2	1	no	—
895	C₂²⋊C₄	—	2	1	no	—
896	C₂²⋊C₄	—	2	2	no	—
897	C₂²⋊C₄	—	2	1	no	—
898	C₂²⋊C₄	—	2	2	no	—
899	C₂²⋊C₄	—	2	2	no	—
900	C₂²⋊C₄	—	2	1	no	—
901	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
902	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
903	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
904	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
905	C₄²	—	2	2	no	—
906	C₄²	—	2	2	no	—
907	C₄²	—	2	2	no	—
908	C₄²	—	2	2	no	—
909	C₄²	—	2	1	no	—
910	C₄²	—	2	2	no	—
911	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
912	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
913	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
914	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
915	C₂³	—	2	1	no	—
916	C₂³	—	2	2	no	—
917	C₂³	—	4	2	no	—
918	C₂³	—	8	1	no	—
919	C₂³	—	8	1	no	—
920	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
921	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
922	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
923	Q₈	—	2	2	no	—
924	Q₈	—	2	2	no	—
925	Q₈	—	2	2	no	—
926	Q₈	—	4	2	no	—
927	Q₈	—	4	2	no	—
928	Q₈	—	8	1	no	—
929	Q₈	—	8	1	no	—
930	Q₈	—	8	2	no	—
931	D₄	—	2	2	no	—
932	D₄	—	2	2	no	—
933	D₄	—	2	2	no	—
934	D₄	—	4	1	no	—
935	D₄	—	4	1	no	—
936	D₄	—	4	2	no	—
937	D₄	—	4	2	no	—
938	D₄	—	4	2	no	—
939	D₄	—	4	2	no	—
940	D₄	—	4	2	no	—
941	D₄	—	8	1	no	—
942	D₄	—	8	2	no	—
943	D₄	—	8	2	no	—
944	D₄	—	8	2	no	—
945	D₄	—	8	2	no	—
946	D₄	—	8	2	no	—
947	D₄	—	8	2	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	4	1	no	—
962	C₂×C₄	—	4	1	no	—
963	C₂×C₄	—	4	2	no	—
964	C₂×C₄	—	4	4	no	—
965	C₂×C₄	—	8	2	no	—
966	C₂×C₄	—	8	2	no	—
967	C₂×C₄	—	8	2	no	—
968	C₂×C₄	—	8	1	no	—
969	C₂×C₄	—	8	2	no	—
970	C₂×C₄	—	8	2	no	—
971	C₂×C₄	—	8	2	no	—
972	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
973	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
974	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
975	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
976	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
977	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
978	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
979	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
980	C₈	—	2	2	no	—
981	C₈	—	2	2	no	—
982	C₈	—	2	2	no	—
983	C₈	—	2	2	no	—
984	C₂²	—	2	1	no	—
985	C₂²	—	2	2	no	—
986	C₂²	—	2	2	no	—
987	C₂²	—	2	1	no	—
988	C₂²	—	2	2	no	—
989	C₂²	—	2	2	no	—
990	C₂²	—	2	2	no	—
991	C₂²	—	2	1	no	—
992	C₂²	—	2	2	no	—
993	C₂²	—	4	2	no	—
994	C₂²	—	4	1	no	—
995	C₂²	—	4	1	no	—
996	C₂²	—	4	2	no	—
997	C₂²	—	4	1	no	—
998	C₂²	—	4	2	no	—
999	C₂²	—	8	4	no	—
1000	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1001	C₄	—	2	1	no	—
1002	C₄	—	2	1	no	—
1003	C₄	—	2	1	no	—
1004	C₄	—	2	1	no	—
1005	C₄	—	2	2	no	—
1006	C₄	—	2	1	no	—
1007	C₄	—	2	2	no	—
1008	C₄	—	4	2	no	—
1009	C₄	—	4	1	no	—
1010	C₄	—	4	2	no	—
1011	C₄	—	4	2	no	—
1012	C₄	—	4	1	no	—
1013	C₄	—	4	2	no	—
1014	C₄	—	4	2	no	—
1015	C₄	—	4	1	no	—
1016	C₄	C₆₁×#585	1	2	yes	—
1017	C₂	—	4	1	no	—
1018	C₂	—	4	2	no	—
1019	C₂	—	4	2	no	—
1020	C₂	—	8	2	no	—
1021	C₂	—	8	1	no	—
1022	C₂	C₆₁×#3485	1	1	yes	characteristic
1023	C₂	C₆₁×#3585	1	1	yes	characteristic
1024	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 ◁ C₆₁×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3547	C₂	semidirect
2. C₆₁×#3506	C₂	semidirect
3. C₆₁×#3348	C₂	semidirect
4. C₆₁×#3347	C₂	semidirect
5. C₆₁×#3346	C₂	semidirect
6. C₆₁×#3343	C₂	semidirect
7. C₆₁×#3321	C₂	semidirect
8. C₆₁×#3320	C₂	semidirect
9. C₆₁×#3308	C₂	semidirect
10. C₆₁×#3307	C₂	semidirect
11. C₆₁×#3240	C₂	semidirect
12. C₆₁×#3237	C₂	semidirect
13. C₆₁×#3200	C₂	semidirect
14. C₆₁×#3198	C₂	semidirect
15. C₆₁×#3114	C₂	semidirect
16. C₆₁×#3110	C₂	semidirect
17. C₆₁×#3098	C₂	semidirect
18. C₆₁×#3097	C₂	semidirect
19. C₆₁×#2980	C₂	semidirect
25. C₆₁×#555	C₂²	semidirect
26. C₆₁×#554	C₂²	semidirect
30. C₆₁×#552	C₂²	semidirect
32. D₄×Q₈×C₆₁	C₂²	semidirect
33. C₆₁×#548	C₂²	semidirect
35. C₆₁×#547	C₂²	semidirect
51. C₆₁×#501	C₂²	semidirect
52. C₆₁×#501	C₂²	semidirect
53. C₆₁×#501	C₂²	semidirect
54. C₆₁×#491	C₂²	semidirect
55. C₆₁×#489	C₂²	semidirect
56. C₆₁×#489	C₂²	semidirect
60. C₆₁×#485	C₂²	semidirect
61. C₆₁×#485	C₂²	semidirect
62. C₆₁×#485	C₂²	semidirect
64. C₆₁×#484	C₂²	semidirect
65. C₆₁×#484	C₂²	semidirect
67. C₆₁×#483	C₂²	semidirect
71. C₆₁×#482	C₂²	semidirect
75. C₆₁×#480	C₂²	semidirect
76. C₆₁×#479	C₂²	semidirect
78. C₆₁×#478	C₂²	semidirect
79. C₆₁×#477	C₂²	semidirect
80. C₆₁×#475	C₂²	semidirect
103. C₆₁×#435	C₂²	semidirect
104. C₆₁×#435	C₂²	semidirect
105. C₆₁×#435	C₂²	semidirect
106. C₆₁×#435	C₂²	semidirect
109. C₆₁×#428	C₂²	semidirect
110. C₆₁×#428	C₂²	semidirect
111. C₆₁×#427	C₂²	semidirect
112. C₂×#107×C₆₁	C₂²	semidirect
113. C₆₁×#419	C₂²	semidirect
114. C₆₁×#417	C₂²	semidirect
115. C₆₁×#416	C₂²	semidirect
116. C₂×#103×C₆₁	C₂²	semidirect
471. #61796	C₆₁	direct (N × H)
505. #3547	C₂×C₆₁	semidirect
506. #3506	C₂×C₆₁	semidirect
507. #3348	C₂×C₆₁	semidirect
508. #3347	C₂×C₆₁	semidirect
509. #3346	C₂×C₆₁	semidirect
510. #3343	C₂×C₆₁	semidirect
511. #3321	C₂×C₆₁	semidirect
512. #3320	C₂×C₆₁	semidirect
513. #3308	C₂×C₆₁	semidirect
514. #3307	C₂×C₆₁	semidirect
515. #3240	C₂×C₆₁	semidirect
516. #3237	C₂×C₆₁	semidirect
517. #3200	C₂×C₆₁	semidirect
518. #3198	C₂×C₆₁	semidirect
519. #3114	C₂×C₆₁	semidirect
520. #3110	C₂×C₆₁	semidirect
521. #3098	C₂×C₆₁	semidirect
522. #3097	C₂×C₆₁	semidirect
523. #2980	C₂×C₆₁	semidirect
537. #555	C₂²×C₆₁	semidirect
538. #554	C₂²×C₆₁	semidirect
542. #552	C₂²×C₆₁	semidirect
544. D₄×Q₈	C₂²×C₆₁	semidirect
545. #548	C₂²×C₆₁	semidirect
547. #547	C₂²×C₆₁	semidirect
563. #501	C₂²×C₆₁	semidirect
564. #501	C₂²×C₆₁	semidirect
565. #501	C₂²×C₆₁	semidirect
566. #491	C₂²×C₆₁	semidirect
567. #489	C₂²×C₆₁	semidirect
568. #489	C₂²×C₆₁	semidirect
572. #485	C₂²×C₆₁	semidirect
573. #485	C₂²×C₆₁	semidirect
574. #485	C₂²×C₆₁	semidirect
576. #484	C₂²×C₆₁	semidirect
577. #484	C₂²×C₆₁	semidirect
579. #483	C₂²×C₆₁	semidirect
583. #482	C₂²×C₆₁	semidirect
587. #480	C₂²×C₆₁	semidirect
588. #479	C₂²×C₆₁	semidirect
590. #478	C₂²×C₆₁	semidirect
591. #477	C₂²×C₆₁	semidirect
592. #475	C₂²×C₆₁	semidirect
615. #435	C₂²×C₆₁	semidirect
616. #435	C₂²×C₆₁	semidirect
617. #435	C₂²×C₆₁	semidirect
618. #435	C₂²×C₆₁	semidirect
621. #428	C₂²×C₆₁	semidirect
622. #428	C₂²×C₆₁	semidirect
623. #427	C₂²×C₆₁	semidirect
624. C₂×#107	C₂²×C₆₁	semidirect
625. #419	C₂²×C₆₁	semidirect
626. #417	C₂²×C₆₁	semidirect
627. #416	C₂²×C₆₁	semidirect
628. C₂×#103	C₂²×C₆₁	semidirect
631. C₆₁	#61796	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×#3547	2
C₆₁×#3506	2
C₆₁×#3348	2
C₆₁×#3347	2
C₆₁×#3346	2
C₆₁×#3343	2
C₆₁×#3321	2
C₆₁×#3320	2
C₆₁×#3308	2
C₆₁×#3307	2
C₆₁×#3240	2
C₆₁×#3237	2
C₆₁×#3200	2
C₆₁×#3198	2
C₆₁×#3114	2
C₆₁×#3110	2
C₆₁×#3098	2
C₆₁×#3097	2
C₆₁×#2980	2
#61796	61

Subgroups — C61×#61796 #29565229

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61796 #29565229