Subgroups — C₆₁×#62182 #29565615

Order 15616.

1684 conjugacy classes of subgroups.

The subgroup lattice has 1098 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3515	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3384	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3381	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3359	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3356	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3351	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3344	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3335	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3331	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3330	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3307	C₂	1	2	yes	maximal, complemented
14	C₆₁×#3302	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3258	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3252	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3242	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3229	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#3125	C₂	1	2	yes	maximal, complemented
20	C₆₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#3084	C₂	1	2	yes	maximal, complemented
22	C₆₁×#3079	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₁×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₆₁×#563	—	2	2	no	—
25	C₆₁×#557	C₂²	1	1	yes	characteristic
26	C₆₁×#557	C₂²	1	1	yes	characteristic
27	C₆₁×#556	C₂²	1	1	yes	characteristic
28	C₆₁×#554	C₂²	1	1	yes	characteristic
29	C₆₁×#554	C₂²	1	2	yes	—
30	C₆₁×#554	C₂²	1	1	yes	characteristic
31	C₆₁×#553	—	2	1	no	—
32	C₆₁×#553	C₂²	1	2	yes	—
33	C₆₁×#552	—	2	2	no	—
34	C₆₁×#552	—	2	1	no	—
35	C₆₁×#552	C₂²	1	2	yes	—
36	D₄×Q₈×C₆₁	—	2	1	no	—
37	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
38	C₆₁×#548	—	2	1	no	—
39	C₆₁×#547	C₂²	1	1	yes	characteristic
40	C₆₁×#547	C₂²	1	2	yes	—
41	C₆₁×#547	C₂²	1	1	yes	characteristic
42	C₆₁×#544	C₂²	1	2	yes	—
43	C₆₁×#542	C₂²	1	2	yes	—
44	C₆₁×#541	—	2	1	no	—
45	C₆₁×#541	C₂²	1	2	yes	—
46	C₆₁×#539	—	2	2	no	—
47	C₆₁×#539	—	2	2	no	—
48	C₆₁×#536	—	2	1	no	—
49	C₆₁×#533	C₂²	1	1	yes	characteristic
50	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
51	C₆₁×#529	—	2	1	no	—
52	C₆₁×#529	C₂²	1	1	yes	characteristic
53	C₆₁×#529	C₂²	1	1	yes	characteristic
54	C₂×#125×C₆₁	—	2	1	no	—
55	C₆₁×#520	C₂²	1	2	yes	—
56	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
57	C₆₁×#501	C₂²	1	2	yes	—
58	C₆₁×#499	C₂²	1	2	yes	—
59	C₆₁×#498	C₂²	1	1	yes	characteristic
60	C₆₁×#498	C₂²	1	1	yes	characteristic
61	C₆₁×#491	C₂²	1	2	yes	—
62	C₆₁×#487	C₂²	1	1	yes	characteristic
63	C₆₁×#487	C₂²	1	1	yes	characteristic
64	C₆₁×#487	C₂²	1	2	yes	—
65	C₆₁×#485	C₂²	1	2	yes	—
66	C₆₁×#485	C₂²	1	2	yes	—
67	C₆₁×#485	C₂²	1	1	yes	characteristic
68	C₆₁×#484	C₂²	1	2	yes	—
69	C₆₁×#483	C₂²	1	2	yes	—
70	C₆₁×#483	C₂²	1	2	yes	—
71	C₆₁×#483	C₂²	1	2	yes	—
72	C₆₁×#483	C₂²	1	2	yes	—
73	C₆₁×#482	C₂²	1	1	yes	characteristic
74	C₆₁×#481	C₂²	1	2	yes	—
75	C₆₁×#479	C₂²	1	2	yes	—
76	C₆₁×#479	C₂²	1	2	yes	—
77	C₆₁×#479	C₂²	1	2	yes	—
78	C₆₁×#479	C₂²	1	1	yes	characteristic
79	C₆₁×#478	C₂²	1	2	yes	—
80	C₆₁×#478	C₂²	1	1	yes	characteristic
81	C₆₁×#478	C₂²	1	2	yes	—
82	C₆₁×#477	C₂²	1	2	yes	—
83	C₆₁×#477	C₂²	1	1	yes	characteristic
84	C₆₁×#476	C₂²	1	2	yes	—
85	C₆₁×#476	C₂²	1	2	yes	—
86	C₆₁×#476	C₂²	1	1	yes	characteristic
87	C₆₁×#475	C₂²	1	1	yes	characteristic
88	C₆₁×#475	C₂²	1	1	yes	characteristic
89	C₆₁×#475	C₂²	1	2	yes	—
90	C₆₁×#475	C₂²	1	2	yes	—
91	C₆₁×#475	C₂²	1	2	yes	—
92	C₆₁×#474	C₂²	1	1	yes	characteristic
93	C₆₁×#474	C₂²	1	1	yes	characteristic
94	C₆₁×#470	C₂²	1	2	yes	—
95	C₆₁×#470	C₂²	1	2	yes	—
96	C₆₁×#468	C₂²	1	2	yes	—
97	C₆₁×#468	C₂²	1	2	yes	—
98	C₆₁×#467	C₂²	1	2	yes	—
99	C₆₁×#465	C₂²	1	2	yes	—
100	C₆₁×#464	C₂²	1	1	yes	characteristic
101	C₆₁×#464	C₂²	1	2	yes	—
102	C₆₁×#463	C₂²	1	1	yes	characteristic
103	C₆₁×#462	C₂²	1	1	yes	characteristic
104	C₆₁×#462	C₂²	1	2	yes	—
105	C₆₁×#461	C₂²	1	2	yes	—
106	C₆₁×#461	C₂²	1	1	yes	characteristic
107	C₆₁×#452	C₂²	1	2	yes	—
108	C₆₁×#452	C₂²	1	1	yes	characteristic
109	C₆₁×#449	C₂²	1	1	yes	characteristic
110	C₆₁×#449	C₂²	1	2	yes	—
111	C₆₁×#446	C₂²	1	1	yes	characteristic
112	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic
113	C₆₁×#442	C₂²	1	2	yes	—
114	C₆₁×#441	C₂²	1	2	yes	—
115	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
116	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
118	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
120	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
121	C₆₁×#436	C₂²	1	1	yes	characteristic
122	C₆₁×#436	C₂²	1	2	yes	—
123	C₆₁×#435	C₂²	1	2	yes	—
124	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
125	C₆₁×#433	C₂²	1	2	yes	—
126	C₆₁×#431	C₂²	1	1	yes	characteristic
127	C₆₁×#428	C₂²	1	2	yes	—
128	C₆₁×#428	C₂²	1	2	yes	—
129	C₂×#106×C₆₁	C₂²	1	2	yes	—
130	C₆₁×#424	C₂²	1	2	yes	—
131	C₆₁×#423	C₂²	1	1	yes	characteristic
132	C₆₁×#417	C₂²	1	2	yes	—
133	C₆₁×#417	C₂²	1	2	yes	—
134	C₆₁×#416	C₂²	1	2	yes	—
135	C₂×#41×C₆₁	—	2	1	no	—
136	C₂×#41×C₆₁	C₂³	1	2	yes	—
137	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₆₁	—	2	1	no	—
139	C₂²×Q₈×C₆₁	—	2	1	no	—
140	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
141	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
142	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
145	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
146	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
147	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
148	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
149	C₄⋊Q₈×C₆₁	—	2	1	no	—
150	C₄⋊Q₈×C₆₁	—	2	2	no	—
151	C₄⋊Q₈×C₆₁	—	2	1	no	—
152	C₄⋊Q₈×C₆₁	—	2	1	no	—
153	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
154	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
155	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
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	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
160	#126×C₆₁	—	2	2	no	—
161	#126×C₆₁	—	2	2	no	—
162	#126×C₆₁	—	2	2	no	—
163	#126×C₆₁	—	2	2	no	—
164	#126×C₆₁	—	2	2	no	—
165	#126×C₆₁	—	2	2	no	—
166	#126×C₆₁	—	2	1	no	—
167	#126×C₆₁	D₄	1	2	yes	—
168	#125×C₆₁	—	2	2	no	—
169	#125×C₆₁	—	2	2	no	—
170	#125×C₆₁	—	2	2	no	—
171	#125×C₆₁	—	2	2	no	—
172	#125×C₆₁	—	2	2	no	—
173	#125×C₆₁	—	2	2	no	—
174	#125×C₆₁	—	2	2	no	—
175	#125×C₆₁	—	2	1	no	—
176	#125×C₆₁	—	2	1	no	—
177	#125×C₆₁	—	2	1	no	—
178	#125×C₆₁	D₄	1	1	yes	characteristic
179	#125×C₆₁	C₂³	1	2	yes	—
180	#125×C₆₁	C₂³	1	1	yes	characteristic
181	#125×C₆₁	C₂³	1	2	yes	—
182	#124×C₆₁	—	2	1	no	—
183	#124×C₆₁	—	2	2	no	—
184	#124×C₆₁	D₄	1	1	yes	characteristic
185	#124×C₆₁	C₂³	1	1	yes	characteristic
186	#123×C₆₁	—	2	2	no	—
187	#123×C₆₁	—	2	1	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	#123×C₆₁	—	2	2	no	—
194	#123×C₆₁	D₄	1	2	yes	—
195	C₂²⋊Q₈×C₆₁	—	2	1	no	—
196	C₂²⋊Q₈×C₆₁	—	2	1	no	—
197	C₂²⋊Q₈×C₆₁	—	2	2	no	—
198	C₂²⋊Q₈×C₆₁	—	2	2	no	—
199	C₂²⋊Q₈×C₆₁	—	2	1	no	—
200	C₂²⋊Q₈×C₆₁	—	2	1	no	—
201	C₂²⋊Q₈×C₆₁	—	2	2	no	—
202	C₂²⋊Q₈×C₆₁	—	2	2	no	—
203	C₂²⋊Q₈×C₆₁	—	2	2	no	—
204	C₂²⋊Q₈×C₆₁	—	2	2	no	—
205	C₂²⋊Q₈×C₆₁	—	2	2	no	—
206	C₂²⋊Q₈×C₆₁	—	2	2	no	—
207	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
208	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
209	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
210	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
211	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
212	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
213	#121×C₆₁	—	2	2	no	—
214	#121×C₆₁	—	2	2	no	—
215	#121×C₆₁	—	2	1	no	—
216	#121×C₆₁	D₄	1	1	yes	characteristic
217	#121×C₆₁	C₂³	1	2	yes	—
218	#121×C₆₁	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₆₁	—	2	1	no	—
220	C₄×Q₈×C₆₁	—	2	1	no	—
221	C₄×Q₈×C₆₁	—	2	1	no	—
222	C₄×Q₈×C₆₁	—	2	1	no	—
223	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
224	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
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×Q₈×C₆₁	C₂³	1	1	yes	characteristic
230	C₄×D₄×C₆₁	—	2	2	no	—
231	C₄×D₄×C₆₁	—	2	1	no	—
232	C₄×D₄×C₆₁	—	2	1	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	C₂³	1	2	yes	—
239	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
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	2	yes	—
245	#117×C₆₁	—	2	1	no	—
246	#117×C₆₁	—	2	2	no	—
247	#117×C₆₁	—	2	2	no	—
248	#117×C₆₁	—	2	1	no	—
249	#117×C₆₁	—	2	1	no	—
250	#117×C₆₁	C₂³	1	2	yes	—
251	#117×C₆₁	C₂³	1	1	yes	characteristic
252	#117×C₆₁	C₂³	1	2	yes	—
253	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
254	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
255	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
256	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
257	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
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	2	yes	—
261	C₂×C₄²×C₆₁	—	2	1	no	—
262	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
263	#107×C₆₁	C₂³	1	1	yes	characteristic
264	#107×C₆₁	C₂³	1	2	yes	—
265	#107×C₆₁	C₂³	1	2	yes	—
266	#107×C₆₁	C₂³	1	2	yes	—
267	#107×C₆₁	C₂³	1	1	yes	characteristic
268	#106×C₆₁	C₂³	1	1	yes	characteristic
269	#106×C₆₁	C₂³	1	2	yes	—
270	#106×C₆₁	C₂³	1	2	yes	—
271	#106×C₆₁	C₂³	1	2	yes	—
272	#106×C₆₁	C₂³	1	2	yes	—
273	#106×C₆₁	C₂³	1	2	yes	—
274	#106×C₆₁	C₂³	1	2	yes	—
275	#106×C₆₁	C₂³	1	1	yes	characteristic
276	#106×C₆₁	C₂³	1	2	yes	—
277	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
278	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
279	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
282	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
283	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
284	#103×C₆₁	C₂³	1	2	yes	—
285	#103×C₆₁	C₂³	1	2	yes	—
286	#103×C₆₁	C₂³	1	2	yes	—
287	#103×C₆₁	C₂³	1	2	yes	—
288	#103×C₆₁	C₂³	1	2	yes	—
289	#103×C₆₁	C₂³	1	2	yes	—
290	#103×C₆₁	C₂³	1	2	yes	—
291	#103×C₆₁	C₂³	1	1	yes	characteristic
292	#103×C₆₁	C₂³	1	1	yes	characteristic
293	#103×C₆₁	C₂³	1	2	yes	—
294	#103×C₆₁	C₂³	1	1	yes	characteristic
295	#103×C₆₁	C₂³	1	1	yes	characteristic
296	#103×C₆₁	C₂³	1	2	yes	—
297	#102×C₆₁	C₂³	1	1	yes	characteristic
298	#102×C₆₁	C₂³	1	2	yes	—
299	#102×C₆₁	C₂³	1	1	yes	characteristic
300	#102×C₆₁	C₂³	1	2	yes	—
301	#102×C₆₁	C₂³	1	1	yes	characteristic
302	#102×C₆₁	C₂³	1	1	yes	characteristic
303	#102×C₆₁	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
305	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
306	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
308	#97×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	#41×C₆₁	—	2	4	no	—
313	#41×C₆₁	—	2	2	no	—
314	#41×C₆₁	—	4	2	no	—
315	#41×C₆₁	—	4	1	no	—
316	#41×C₆₁	—	8	2	no	—
317	C₂×Q₈×C₆₁	—	2	1	no	—
318	C₂×Q₈×C₆₁	—	2	1	no	—
319	C₂×Q₈×C₆₁	—	2	1	no	—
320	C₂×Q₈×C₆₁	—	2	2	no	—
321	C₂×Q₈×C₆₁	—	2	2	no	—
322	C₂×Q₈×C₆₁	—	8	2	no	—
323	C₂×Q₈×C₆₁	—	8	2	no	—
324	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
326	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₆₁	—	2	1	no	—
329	C₂×D₄×C₆₁	—	2	2	no	—
330	C₂×D₄×C₆₁	—	2	1	no	—
331	C₂×D₄×C₆₁	—	2	2	no	—
332	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
333	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
334	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
335	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₆₁	—	2	2	no	—
337	C₂²×C₄×C₆₁	—	2	2	no	—
338	C₂²×C₄×C₆₁	—	2	2	no	—
339	C₂²×C₄×C₆₁	—	2	1	no	—
340	C₂²×C₄×C₆₁	—	2	1	no	—
341	C₂²×C₄×C₆₁	—	2	2	no	—
342	C₂²×C₄×C₆₁	—	2	1	no	—
343	C₂²×C₄×C₆₁	—	2	1	no	—
344	C₂²×C₄×C₆₁	—	2	2	no	—
345	C₂²×C₄×C₆₁	—	2	2	no	—
346	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
347	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
350	Q₁₆×C₆₁	—	4	2	no	—
351	Q₁₆×C₆₁	—	4	1	no	—
352	SD₁₆×C₆₁	—	2	2	no	—
353	SD₁₆×C₆₁	—	4	1	no	—
354	SD₁₆×C₆₁	—	4	2	no	—
355	D₈×C₆₁	—	2	2	no	—
356	M₁₆×C₆₁	—	4	2	no	—
357	M₁₆×C₆₁	—	4	2	no	—
358	C₂×C₈×C₆₁	—	4	2	no	—
359	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
362	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
363	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
364	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₆₁	—	2	2	no	—
366	C₄⋊C₄×C₆₁	—	2	1	no	—
367	C₄⋊C₄×C₆₁	—	2	1	no	—
368	C₄⋊C₄×C₆₁	—	2	2	no	—
369	C₄⋊C₄×C₆₁	—	2	2	no	—
370	C₄⋊C₄×C₆₁	—	2	2	no	—
371	C₄⋊C₄×C₆₁	—	2	2	no	—
372	C₄⋊C₄×C₆₁	—	2	1	no	—
373	C₄⋊C₄×C₆₁	—	2	2	no	—
374	C₄⋊C₄×C₆₁	—	2	2	no	—
375	C₄⋊C₄×C₆₁	—	2	2	no	—
376	C₄⋊C₄×C₆₁	—	2	2	no	—
377	C₄⋊C₄×C₆₁	—	2	1	no	—
378	C₄⋊C₄×C₆₁	—	2	2	no	—
379	C₄⋊C₄×C₆₁	—	2	2	no	—
380	C₄⋊C₄×C₆₁	—	2	1	no	—
381	C₄⋊C₄×C₆₁	—	2	1	no	—
382	C₄⋊C₄×C₆₁	—	2	1	no	—
383	C₄⋊C₄×C₆₁	—	2	1	no	—
384	C₄⋊C₄×C₆₁	—	2	2	no	—
385	C₄⋊C₄×C₆₁	—	2	2	no	—
386	C₄⋊C₄×C₆₁	—	2	1	no	—
387	C₄⋊C₄×C₆₁	—	2	2	no	—
388	C₄⋊C₄×C₆₁	—	2	2	no	—
389	C₄⋊C₄×C₆₁	—	2	2	no	—
390	C₄⋊C₄×C₆₁	—	2	1	no	—
391	C₄⋊C₄×C₆₁	—	2	2	no	—
392	C₄⋊C₄×C₆₁	—	2	2	no	—
393	C₄⋊C₄×C₆₁	—	2	1	no	—
394	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
395	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
396	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
398	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
402	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
403	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
406	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
407	C₂²⋊C₄×C₆₁	—	2	2	no	—
408	C₂²⋊C₄×C₆₁	—	2	2	no	—
409	C₂²⋊C₄×C₆₁	—	2	1	no	—
410	C₂²⋊C₄×C₆₁	—	2	2	no	—
411	C₂²⋊C₄×C₆₁	—	2	1	no	—
412	C₂²⋊C₄×C₆₁	—	2	2	no	—
413	C₂²⋊C₄×C₆₁	—	2	2	no	—
414	C₂²⋊C₄×C₆₁	—	2	1	no	—
415	C₂²⋊C₄×C₆₁	—	2	1	no	—
416	C₂²⋊C₄×C₆₁	—	2	2	no	—
417	C₂²⋊C₄×C₆₁	—	2	1	no	—
418	C₂²⋊C₄×C₆₁	—	2	1	no	—
419	C₂²⋊C₄×C₆₁	—	2	2	no	—
420	C₂²⋊C₄×C₆₁	—	2	1	no	—
421	C₂²⋊C₄×C₆₁	—	2	2	no	—
422	C₂²⋊C₄×C₆₁	—	2	1	no	—
423	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
424	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
425	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
426	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
427	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
428	C₄²×C₆₁	—	2	1	no	—
429	C₄²×C₆₁	—	2	1	no	—
430	C₄²×C₆₁	—	2	1	no	—
431	C₄²×C₆₁	—	2	2	no	—
432	C₄²×C₆₁	—	2	2	no	—
433	C₄²×C₆₁	—	2	1	no	—
434	C₄²×C₆₁	—	2	2	no	—
435	C₄²×C₆₁	—	2	2	no	—
436	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
437	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
438	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
439	C₄²×C₆₁	C₂⁴	1	2	yes	—
440	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
441	C₂³×C₆₁	—	2	1	no	—
442	C₂³×C₆₁	—	2	1	no	—
443	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
444	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
445	Q₈×C₆₁	—	2	2	no	—
446	Q₈×C₆₁	—	2	1	no	—
447	Q₈×C₆₁	—	2	2	no	—
448	Q₈×C₆₁	—	2	1	no	—
449	Q₈×C₆₁	—	2	1	no	—
450	Q₈×C₆₁	—	2	2	no	—
451	Q₈×C₆₁	—	2	1	no	—
452	Q₈×C₆₁	—	4	2	no	—
453	Q₈×C₆₁	—	4	2	no	—
454	Q₈×C₆₁	—	8	1	no	—
455	Q₈×C₆₁	—	8	2	no	—
456	Q₈×C₆₁	—	8	2	no	—
457	D₄×C₆₁	—	2	2	no	—
458	D₄×C₆₁	—	2	1	no	—
459	D₄×C₆₁	—	2	1	no	—
460	D₄×C₆₁	—	2	1	no	—
461	D₄×C₆₁	—	4	2	no	—
462	D₄×C₆₁	—	4	4	no	—
463	D₄×C₆₁	—	4	2	no	—
464	D₄×C₆₁	—	4	2	no	—
465	D₄×C₆₁	—	8	2	no	—
466	D₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
467	C₂×C₄×C₆₁	—	2	2	no	—
468	C₂×C₄×C₆₁	—	2	1	no	—
469	C₂×C₄×C₆₁	—	2	2	no	—
470	C₂×C₄×C₆₁	—	2	2	no	—
471	C₂×C₄×C₆₁	—	2	1	no	—
472	C₂×C₄×C₆₁	—	2	1	no	—
473	C₂×C₄×C₆₁	—	2	1	no	—
474	C₂×C₄×C₆₁	—	2	1	no	—
475	C₂×C₄×C₆₁	—	2	1	no	—
476	C₂×C₄×C₆₁	—	2	1	no	—
477	C₂×C₄×C₆₁	—	2	2	no	—
478	C₂×C₄×C₆₁	—	2	2	no	—
479	C₂×C₄×C₆₁	—	2	2	no	—
480	C₂×C₄×C₆₁	—	2	2	no	—
481	C₂×C₄×C₆₁	—	2	1	no	—
482	C₂×C₄×C₆₁	—	4	1	no	—
483	C₂×C₄×C₆₁	—	4	2	no	—
484	C₂×C₄×C₆₁	—	4	4	no	—
485	C₂×C₄×C₆₁	—	4	2	no	—
486	C₂×C₄×C₆₁	—	4	2	no	—
487	C₂×C₄×C₆₁	—	8	1	no	—
488	C₂×C₄×C₆₁	—	8	2	no	—
489	C₂×C₄×C₆₁	—	8	2	no	—
490	C₂×C₄×C₆₁	—	8	2	no	—
491	C₂×C₄×C₆₁	—	8	2	no	—
492	C₂×C₄×C₆₁	—	8	2	no	—
493	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
497	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
498	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
499	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
502	C₈×C₆₁	—	2	1	no	—
503	C₈×C₆₁	—	2	1	no	—
504	C₈×C₆₁	—	2	1	no	—
505	C₈×C₆₁	—	2	2	no	—
506	C₈×C₆₁	—	2	2	no	—
507	C₈×C₆₁	—	2	1	no	—
508	#62182	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
509	C₂²×C₆₁	—	2	1	no	—
510	C₂²×C₆₁	—	2	2	no	—
511	C₂²×C₆₁	—	2	2	no	—
512	C₂²×C₆₁	—	2	1	no	—
513	C₂²×C₆₁	—	2	2	no	—
514	C₂²×C₆₁	—	2	1	no	—
515	C₂²×C₆₁	—	2	2	no	—
516	C₂²×C₆₁	—	4	1	no	—
517	C₂²×C₆₁	—	4	1	no	—
518	C₂²×C₆₁	—	4	1	no	—
519	C₂²×C₆₁	—	4	1	no	—
520	C₂²×C₆₁	—	4	1	no	—
521	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
522	C₄×C₆₁	—	2	1	no	—
523	C₄×C₆₁	—	2	1	no	—
524	C₄×C₆₁	—	2	2	no	—
525	C₄×C₆₁	—	2	2	no	—
526	C₄×C₆₁	—	2	1	no	—
527	C₄×C₆₁	—	2	1	no	—
528	C₄×C₆₁	—	2	2	no	—
529	C₄×C₆₁	—	4	1	no	—
530	C₄×C₆₁	—	4	2	no	—
531	C₄×C₆₁	—	4	1	no	—
532	C₄×C₆₁	—	4	1	no	—
533	C₄×C₆₁	—	4	2	no	—
534	C₄×C₆₁	—	4	1	no	—
535	C₄×C₆₁	—	4	1	no	—
536	C₄×C₆₁	—	4	1	no	—
537	C₄×C₆₁	—	4	2	no	—
538	C₄×C₆₁	—	4	2	no	—
539	C₄×C₆₁	#577	1	2	yes	—
540	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
541	C₄×C₆₁	#585	1	1	yes	characteristic
542	#3552	C₂×C₆₁	1	1	yes	characteristic, complemented
543	#3515	C₂×C₆₁	1	1	yes	characteristic, complemented
544	#3384	C₂×C₆₁	1	1	yes	characteristic, complemented
545	#3381	C₂×C₆₁	1	1	yes	characteristic, complemented
546	#3374	C₂×C₆₁	1	1	yes	characteristic, complemented
547	#3359	C₂×C₆₁	1	1	yes	characteristic, complemented
548	#3356	C₂×C₆₁	1	1	yes	characteristic, complemented
549	#3351	C₂×C₆₁	1	2	yes	complemented
550	#3344	C₂×C₆₁	1	2	yes	complemented
551	#3335	C₂×C₆₁	1	1	yes	characteristic, complemented
552	#3331	C₂×C₆₁	1	2	yes	complemented
553	#3330	C₂×C₆₁	1	1	yes	characteristic, complemented
554	#3307	C₂×C₆₁	1	2	yes	complemented
555	#3302	C₂×C₆₁	1	1	yes	characteristic, complemented
556	#3258	C₂×C₆₁	1	2	yes	complemented
557	#3252	C₂×C₆₁	1	1	yes	characteristic, complemented
558	#3242	C₂×C₆₁	1	2	yes	complemented
559	#3229	C₂×C₆₁	1	1	yes	characteristic, complemented
560	#3125	C₂×C₆₁	1	2	yes	complemented
561	#3102	C₂×C₆₁	1	1	yes	characteristic, complemented
562	#3084	C₂×C₆₁	1	2	yes	complemented
563	#3079	C₂×C₆₁	1	1	yes	characteristic, complemented
564	#2993	C₂×C₆₁	1	1	yes	characteristic, complemented
565	C₂×C₆₁	—	4	1	no	—
566	C₂×C₆₁	—	4	2	no	—
567	C₂×C₆₁	—	4	2	no	—
568	C₂×C₆₁	—	8	1	no	—
569	C₂×C₆₁	#3489	1	1	yes	characteristic
570	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
571	C₂×C₆₁	#3586	1	1	yes	characteristic
572	#563	—	2	2	no	—
573	#557	C₂²×C₆₁	1	1	yes	characteristic
574	#557	C₂²×C₆₁	1	1	yes	characteristic
575	#556	C₂²×C₆₁	1	1	yes	characteristic
576	#554	C₂²×C₆₁	1	1	yes	characteristic
577	#554	C₂²×C₆₁	1	2	yes	—
578	#554	C₂²×C₆₁	1	1	yes	characteristic
579	#553	—	2	1	no	—
580	#553	C₂²×C₆₁	1	2	yes	—
581	#552	—	2	2	no	—
582	#552	—	2	1	no	—
583	#552	C₂²×C₆₁	1	2	yes	—
584	D₄×Q₈	—	2	1	no	—
585	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
586	#548	—	2	1	no	—
587	#547	C₂²×C₆₁	1	1	yes	characteristic
588	#547	C₂²×C₆₁	1	2	yes	—
589	#547	C₂²×C₆₁	1	1	yes	characteristic
590	#544	C₂²×C₆₁	1	2	yes	—
591	#542	C₂²×C₆₁	1	2	yes	—
592	#541	—	2	1	no	—
593	#541	C₂²×C₆₁	1	2	yes	—
594	#539	—	2	2	no	—
595	#539	—	2	2	no	—
596	#536	—	2	1	no	—
597	#533	C₂²×C₆₁	1	1	yes	characteristic
598	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
599	#529	—	2	1	no	—
600	#529	C₂²×C₆₁	1	1	yes	characteristic
601	#529	C₂²×C₆₁	1	1	yes	characteristic
602	C₂×#125	—	2	1	no	—
603	#520	C₂²×C₆₁	1	2	yes	—
604	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
605	#501	C₂²×C₆₁	1	2	yes	—
606	#499	C₂²×C₆₁	1	2	yes	—
607	#498	C₂²×C₆₁	1	1	yes	characteristic
608	#498	C₂²×C₆₁	1	1	yes	characteristic
609	#491	C₂²×C₆₁	1	2	yes	—
610	#487	C₂²×C₆₁	1	1	yes	characteristic
611	#487	C₂²×C₆₁	1	2	yes	—
612	#487	C₂²×C₆₁	1	1	yes	characteristic
613	#485	C₂²×C₆₁	1	1	yes	characteristic
614	#485	C₂²×C₆₁	1	2	yes	—
615	#485	C₂²×C₆₁	1	2	yes	—
616	#484	C₂²×C₆₁	1	2	yes	—
617	#483	C₂²×C₆₁	1	2	yes	—
618	#483	C₂²×C₆₁	1	2	yes	—
619	#483	C₂²×C₆₁	1	2	yes	—
620	#483	C₂²×C₆₁	1	2	yes	—
621	#482	C₂²×C₆₁	1	1	yes	characteristic
622	#481	C₂²×C₆₁	1	2	yes	—
623	#479	C₂²×C₆₁	1	2	yes	—
624	#479	C₂²×C₆₁	1	2	yes	—
625	#479	C₂²×C₆₁	1	2	yes	—
626	#479	C₂²×C₆₁	1	1	yes	characteristic
627	#478	C₂²×C₆₁	1	1	yes	characteristic
628	#478	C₂²×C₆₁	1	2	yes	—
629	#478	C₂²×C₆₁	1	2	yes	—
630	#477	C₂²×C₆₁	1	2	yes	—
631	#477	C₂²×C₆₁	1	1	yes	characteristic
632	#476	C₂²×C₆₁	1	2	yes	—
633	#476	C₂²×C₆₁	1	2	yes	—
634	#476	C₂²×C₆₁	1	1	yes	characteristic
635	#475	C₂²×C₆₁	1	1	yes	characteristic
636	#475	C₂²×C₆₁	1	1	yes	characteristic
637	#475	C₂²×C₆₁	1	2	yes	—
638	#475	C₂²×C₆₁	1	2	yes	—
639	#475	C₂²×C₆₁	1	2	yes	—
640	#474	C₂²×C₆₁	1	1	yes	characteristic
641	#474	C₂²×C₆₁	1	1	yes	characteristic
642	#470	C₂²×C₆₁	1	2	yes	—
643	#470	C₂²×C₆₁	1	2	yes	—
644	#468	C₂²×C₆₁	1	2	yes	—
645	#468	C₂²×C₆₁	1	2	yes	—
646	#467	C₂²×C₆₁	1	2	yes	—
647	#465	C₂²×C₆₁	1	2	yes	—
648	#464	C₂²×C₆₁	1	1	yes	characteristic
649	#464	C₂²×C₆₁	1	2	yes	—
650	#463	C₂²×C₆₁	1	1	yes	characteristic
651	#462	C₂²×C₆₁	1	2	yes	—
652	#462	C₂²×C₆₁	1	1	yes	characteristic
653	#461	C₂²×C₆₁	1	1	yes	characteristic
654	#461	C₂²×C₆₁	1	2	yes	—
655	#452	C₂²×C₆₁	1	1	yes	characteristic
656	#452	C₂²×C₆₁	1	2	yes	—
657	#449	C₂²×C₆₁	1	2	yes	—
658	#449	C₂²×C₆₁	1	1	yes	characteristic
659	#446	C₂²×C₆₁	1	1	yes	characteristic
660	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic
661	#442	C₂²×C₆₁	1	2	yes	—
662	#441	C₂²×C₆₁	1	2	yes	—
663	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
664	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
665	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
666	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
667	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
668	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
669	#436	C₂²×C₆₁	1	1	yes	characteristic
670	#436	C₂²×C₆₁	1	2	yes	—
671	#435	C₂²×C₆₁	1	2	yes	—
672	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic
673	#433	C₂²×C₆₁	1	2	yes	—
674	#431	C₂²×C₆₁	1	1	yes	characteristic
675	#428	C₂²×C₆₁	1	2	yes	—
676	#428	C₂²×C₆₁	1	2	yes	—
677	C₂×#106	C₂²×C₆₁	1	2	yes	—
678	#424	C₂²×C₆₁	1	2	yes	—
679	#423	C₂²×C₆₁	1	1	yes	characteristic
680	#417	C₂²×C₆₁	1	2	yes	—
681	#417	C₂²×C₆₁	1	2	yes	—
682	#416	C₂²×C₆₁	1	2	yes	—
683	C₆₁	#62182	1	1	yes	characteristic, direct product factor, Sylow
684	C₂×#41	—	2	1	no	—
685	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
686	C₂×#41	C₂³×C₆₁	1	2	yes	—
687	C₂²×Q₈	—	2	1	no	—
688	C₂²×Q₈	—	2	1	no	—
689	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
690	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
691	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
692	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
693	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
694	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
695	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
696	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
697	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
698	C₄⋊Q₈	—	2	1	no	—
699	C₄⋊Q₈	—	2	2	no	—
700	C₄⋊Q₈	—	2	1	no	—
701	C₄⋊Q₈	—	2	1	no	—
702	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
703	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
704	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
705	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
706	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
707	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
708	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
709	#126	—	2	2	no	—
710	#126	—	2	2	no	—
711	#126	—	2	2	no	—
712	#126	—	2	2	no	—
713	#126	—	2	2	no	—
714	#126	—	2	2	no	—
715	#126	—	2	1	no	—
716	#126	D₄×C₆₁	1	2	yes	—
717	#125	—	2	2	no	—
718	#125	—	2	2	no	—
719	#125	—	2	1	no	—
720	#125	—	2	1	no	—
721	#125	—	2	2	no	—
722	#125	—	2	2	no	—
723	#125	—	2	2	no	—
724	#125	—	2	2	no	—
725	#125	—	2	2	no	—
726	#125	—	2	1	no	—
727	#125	D₄×C₆₁	1	1	yes	characteristic
728	#125	C₂³×C₆₁	1	1	yes	characteristic
729	#125	C₂³×C₆₁	1	2	yes	—
730	#125	C₂³×C₆₁	1	2	yes	—
731	#124	—	2	1	no	—
732	#124	—	2	2	no	—
733	#124	D₄×C₆₁	1	1	yes	characteristic
734	#124	C₂³×C₆₁	1	1	yes	characteristic
735	#123	—	2	2	no	—
736	#123	—	2	1	no	—
737	#123	—	2	2	no	—
738	#123	—	2	2	no	—
739	#123	—	2	2	no	—
740	#123	—	2	2	no	—
741	#123	—	2	2	no	—
742	#123	—	2	2	no	—
743	#123	D₄×C₆₁	1	2	yes	—
744	C₂²⋊Q₈	—	2	1	no	—
745	C₂²⋊Q₈	—	2	1	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	—	2	2	no	—
748	C₂²⋊Q₈	—	2	1	no	—
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
757	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
758	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
759	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
760	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
761	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
762	#121	—	2	1	no	—
763	#121	—	2	2	no	—
764	#121	—	2	2	no	—
765	#121	D₄×C₆₁	1	1	yes	characteristic
766	#121	C₂³×C₆₁	1	1	yes	characteristic
767	#121	C₂³×C₆₁	1	2	yes	—
768	C₄×Q₈	—	2	1	no	—
769	C₄×Q₈	—	2	1	no	—
770	C₄×Q₈	—	2	1	no	—
771	C₄×Q₈	—	2	1	no	—
772	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
773	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
774	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
775	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
776	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
777	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
778	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
779	C₄×D₄	—	2	1	no	—
780	C₄×D₄	—	2	2	no	—
781	C₄×D₄	—	2	1	no	—
782	C₄×D₄	—	2	1	no	—
783	C₄×D₄	—	2	1	no	—
784	C₄×D₄	—	2	2	no	—
785	C₄×D₄	—	2	2	no	—
786	C₄×D₄	—	2	2	no	—
787	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
788	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
789	C₄×D₄	C₂³×C₆₁	1	2	yes	—
790	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
791	C₄×D₄	C₂³×C₆₁	1	2	yes	—
792	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
793	C₄×D₄	C₂³×C₆₁	1	2	yes	—
794	#117	—	2	1	no	—
795	#117	—	2	2	no	—
796	#117	—	2	2	no	—
797	#117	—	2	1	no	—
798	#117	—	2	1	no	—
799	#117	C₂³×C₆₁	1	1	yes	characteristic
800	#117	C₂³×C₆₁	1	2	yes	—
801	#117	C₂³×C₆₁	1	2	yes	—
802	C₂×C₄⋊C₄	—	2	1	no	—
803	C₂×C₄⋊C₄	—	2	2	no	—
804	C₂×C₄⋊C₄	—	2	1	no	—
805	C₂×C₄⋊C₄	—	2	2	no	—
806	C₂×C₄⋊C₄	—	2	1	no	—
807	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
808	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
809	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
810	C₂×C₄²	—	2	1	no	—
811	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
812	#107	C₂³×C₆₁	1	1	yes	characteristic
813	#107	C₂³×C₆₁	1	2	yes	—
814	#107	C₂³×C₆₁	1	2	yes	—
815	#107	C₂³×C₆₁	1	2	yes	—
816	#107	C₂³×C₆₁	1	1	yes	characteristic
817	#106	C₂³×C₆₁	1	1	yes	characteristic
818	#106	C₂³×C₆₁	1	2	yes	—
819	#106	C₂³×C₆₁	1	2	yes	—
820	#106	C₂³×C₆₁	1	2	yes	—
821	#106	C₂³×C₆₁	1	2	yes	—
822	#106	C₂³×C₆₁	1	2	yes	—
823	#106	C₂³×C₆₁	1	2	yes	—
824	#106	C₂³×C₆₁	1	1	yes	characteristic
825	#106	C₂³×C₆₁	1	2	yes	—
826	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
827	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
828	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
829	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
830	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
831	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
832	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
833	#103	C₂³×C₆₁	1	2	yes	—
834	#103	C₂³×C₆₁	1	2	yes	—
835	#103	C₂³×C₆₁	1	2	yes	—
836	#103	C₂³×C₆₁	1	2	yes	—
837	#103	C₂³×C₆₁	1	2	yes	—
838	#103	C₂³×C₆₁	1	2	yes	—
839	#103	C₂³×C₆₁	1	2	yes	—
840	#103	C₂³×C₆₁	1	1	yes	characteristic
841	#103	C₂³×C₆₁	1	1	yes	characteristic
842	#103	C₂³×C₆₁	1	2	yes	—
843	#103	C₂³×C₆₁	1	1	yes	characteristic
844	#103	C₂³×C₆₁	1	1	yes	characteristic
845	#103	C₂³×C₆₁	1	2	yes	—
846	#102	C₂³×C₆₁	1	1	yes	characteristic
847	#102	C₂³×C₆₁	1	2	yes	—
848	#102	C₂³×C₆₁	1	1	yes	characteristic
849	#102	C₂³×C₆₁	1	2	yes	—
850	#102	C₂³×C₆₁	1	1	yes	characteristic
851	#102	C₂³×C₆₁	1	1	yes	characteristic
852	#102	C₂³×C₆₁	1	2	yes	—
853	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
854	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
855	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
856	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
857	#97	C₂³×C₆₁	1	2	yes	—
858	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
859	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
860	C₄×C₈	C₂³×C₆₁	1	2	yes	—
861	#41	—	2	2	no	—
862	#41	—	2	4	no	—
863	#41	—	4	2	no	—
864	#41	—	4	1	no	—
865	#41	—	8	2	no	—
866	C₂×Q₈	—	2	1	no	—
867	C₂×Q₈	—	2	1	no	—
868	C₂×Q₈	—	2	1	no	—
869	C₂×Q₈	—	2	2	no	—
870	C₂×Q₈	—	2	2	no	—
871	C₂×Q₈	—	8	2	no	—
872	C₂×Q₈	—	8	2	no	—
873	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
874	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
875	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
876	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
877	C₂×D₄	—	2	1	no	—
878	C₂×D₄	—	2	2	no	—
879	C₂×D₄	—	2	1	no	—
880	C₂×D₄	—	2	2	no	—
881	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
882	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
883	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
884	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
885	C₂²×C₄	—	2	2	no	—
886	C₂²×C₄	—	2	2	no	—
887	C₂²×C₄	—	2	2	no	—
888	C₂²×C₄	—	2	1	no	—
889	C₂²×C₄	—	2	1	no	—
890	C₂²×C₄	—	2	2	no	—
891	C₂²×C₄	—	2	1	no	—
892	C₂²×C₄	—	2	1	no	—
893	C₂²×C₄	—	2	2	no	—
894	C₂²×C₄	—	2	2	no	—
895	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
896	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
897	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
898	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
899	Q₁₆	—	4	2	no	—
900	Q₁₆	—	4	1	no	—
901	SD₁₆	—	2	2	no	—
902	SD₁₆	—	4	1	no	—
903	SD₁₆	—	4	2	no	—
904	D₈	—	2	2	no	—
905	M₁₆	—	4	2	no	—
906	M₁₆	—	4	2	no	—
907	C₂×C₈	—	4	2	no	—
908	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
909	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
910	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
911	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
912	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
913	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	1	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
944	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
945	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
946	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
947	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
948	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
949	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
950	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
951	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
952	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
953	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
954	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
955	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	2	1	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	1	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	1	no	—
964	C₂²⋊C₄	—	2	1	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	1	no	—
967	C₂²⋊C₄	—	2	1	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	1	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	1	no	—
972	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
973	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
974	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
975	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
976	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
977	C₄²	—	2	1	no	—
978	C₄²	—	2	1	no	—
979	C₄²	—	2	1	no	—
980	C₄²	—	2	2	no	—
981	C₄²	—	2	2	no	—
982	C₄²	—	2	1	no	—
983	C₄²	—	2	2	no	—
984	C₄²	—	2	2	no	—
985	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
986	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
987	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
988	C₄²	C₂⁴×C₆₁	1	2	yes	—
989	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
990	C₂³	—	2	1	no	—
991	C₂³	—	2	1	no	—
992	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
993	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
994	Q₈	—	2	2	no	—
995	Q₈	—	2	1	no	—
996	Q₈	—	2	2	no	—
997	Q₈	—	2	1	no	—
998	Q₈	—	2	1	no	—
999	Q₈	—	2	2	no	—
1000	Q₈	—	2	1	no	—
1001	Q₈	—	4	2	no	—
1002	Q₈	—	4	2	no	—
1003	Q₈	—	8	1	no	—
1004	Q₈	—	8	2	no	—
1005	Q₈	—	8	2	no	—
1006	D₄	—	2	2	no	—
1007	D₄	—	2	1	no	—
1008	D₄	—	2	1	no	—
1009	D₄	—	2	1	no	—
1010	D₄	—	4	2	no	—
1011	D₄	—	4	4	no	—
1012	D₄	—	4	2	no	—
1013	D₄	—	4	2	no	—
1014	D₄	—	8	2	no	—
1015	D₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	4	1	no	—
1032	C₂×C₄	—	4	2	no	—
1033	C₂×C₄	—	4	4	no	—
1034	C₂×C₄	—	4	2	no	—
1035	C₂×C₄	—	4	2	no	—
1036	C₂×C₄	—	8	1	no	—
1037	C₂×C₄	—	8	2	no	—
1038	C₂×C₄	—	8	2	no	—
1039	C₂×C₄	—	8	2	no	—
1040	C₂×C₄	—	8	2	no	—
1041	C₂×C₄	—	8	2	no	—
1042	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1043	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1044	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1045	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1046	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1047	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1048	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1049	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1050	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1051	C₈	—	2	1	no	—
1052	C₈	—	2	1	no	—
1053	C₈	—	2	1	no	—
1054	C₈	—	2	2	no	—
1055	C₈	—	2	2	no	—
1056	C₈	—	2	1	no	—
1057	C₂²	—	2	1	no	—
1058	C₂²	—	2	2	no	—
1059	C₂²	—	2	1	no	—
1060	C₂²	—	2	2	no	—
1061	C₂²	—	2	2	no	—
1062	C₂²	—	2	1	no	—
1063	C₂²	—	2	2	no	—
1064	C₂²	—	4	1	no	—
1065	C₂²	—	4	1	no	—
1066	C₂²	—	4	1	no	—
1067	C₂²	—	4	1	no	—
1068	C₂²	—	4	1	no	—
1069	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1070	C₄	—	2	1	no	—
1071	C₄	—	2	2	no	—
1072	C₄	—	2	1	no	—
1073	C₄	—	2	1	no	—
1074	C₄	—	2	2	no	—
1075	C₄	—	2	2	no	—
1076	C₄	—	2	1	no	—
1077	C₄	—	4	1	no	—
1078	C₄	—	4	1	no	—
1079	C₄	—	4	2	no	—
1080	C₄	—	4	2	no	—
1081	C₄	—	4	1	no	—
1082	C₄	—	4	2	no	—
1083	C₄	—	4	1	no	—
1084	C₄	—	4	1	no	—
1085	C₄	—	4	2	no	—
1086	C₄	—	4	1	no	—
1087	C₄	C₆₁×#577	1	2	yes	—
1088	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
1089	C₄	C₆₁×#585	1	1	yes	characteristic
1090	C₂	—	4	1	no	—
1091	C₂	—	4	2	no	—
1092	C₂	—	4	2	no	—
1093	C₂	—	8	1	no	—
1094	C₂	C₆₁×#3489	1	1	yes	characteristic
1095	C₂	C₂×C₆₁×#577	1	1	yes	characteristic
1096	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×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3552	C₂	semidirect
2. C₆₁×#3515	C₂	semidirect
3. C₆₁×#3384	C₂	semidirect
4. C₆₁×#3381	C₂	semidirect
5. C₆₁×#3374	C₂	semidirect
6. C₆₁×#3359	C₂	semidirect
7. C₆₁×#3356	C₂	semidirect
8. C₆₁×#3351	C₂	semidirect
9. C₆₁×#3344	C₂	semidirect
10. C₆₁×#3335	C₂	semidirect
11. C₆₁×#3331	C₂	semidirect
12. C₆₁×#3330	C₂	semidirect
13. C₆₁×#3307	C₂	semidirect
14. C₆₁×#3302	C₂	semidirect
15. C₆₁×#3258	C₂	semidirect
16. C₆₁×#3252	C₂	semidirect
17. C₆₁×#3242	C₂	semidirect
18. C₆₁×#3229	C₂	semidirect
19. C₆₁×#3125	C₂	semidirect
20. C₆₁×#3102	C₂	semidirect
21. C₆₁×#3084	C₂	semidirect
22. C₆₁×#3079	C₂	semidirect
23. C₆₁×#2993	C₂	semidirect
508. #62182	C₆₁	direct (N × H)
542. #3552	C₂×C₆₁	semidirect
543. #3515	C₂×C₆₁	semidirect
544. #3384	C₂×C₆₁	semidirect
545. #3381	C₂×C₆₁	semidirect
546. #3374	C₂×C₆₁	semidirect
547. #3359	C₂×C₆₁	semidirect
548. #3356	C₂×C₆₁	semidirect
549. #3351	C₂×C₆₁	semidirect
550. #3344	C₂×C₆₁	semidirect
551. #3335	C₂×C₆₁	semidirect
552. #3331	C₂×C₆₁	semidirect
553. #3330	C₂×C₆₁	semidirect
554. #3307	C₂×C₆₁	semidirect
555. #3302	C₂×C₆₁	semidirect
556. #3258	C₂×C₆₁	semidirect
557. #3252	C₂×C₆₁	semidirect
558. #3242	C₂×C₆₁	semidirect
559. #3229	C₂×C₆₁	semidirect
560. #3125	C₂×C₆₁	semidirect
561. #3102	C₂×C₆₁	semidirect
562. #3084	C₂×C₆₁	semidirect
563. #3079	C₂×C₆₁	semidirect
564. #2993	C₂×C₆₁	semidirect
683. C₆₁	#62182	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×#3552	2
C₆₁×#3515	2
C₆₁×#3384	2
C₆₁×#3381	2
C₆₁×#3374	2
C₆₁×#3359	2
C₆₁×#3356	2
C₆₁×#3351	2
C₆₁×#3344	2
C₆₁×#3335	2
C₆₁×#3331	2
C₆₁×#3330	2
C₆₁×#3307	2
C₆₁×#3302	2
C₆₁×#3258	2
C₆₁×#3252	2
C₆₁×#3242	2
C₆₁×#3229	2
C₆₁×#3125	2
C₆₁×#3102	2
C₆₁×#3084	2
C₆₁×#3079	2
C₆₁×#2993	2
#62182	61

Subgroups — C61×#62182 #29565615

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62182 #29565615