Subgroups — C₆₁×#61386 #29564819

Order 15616.

1690 conjugacy classes of subgroups.

The subgroup lattice has 1058 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3504	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3390	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3390	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3388	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3388	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3387	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3385	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3383	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3381	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3166	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3164	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3163	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3084	C₂	1	1	yes	maximal, characteristic
15	C₆₁×#3083	C₂	1	1	yes	maximal, characteristic
16	C₆₁×#3082	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3082	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#3076	C₂	1	1	yes	maximal, characteristic
19	C₂×C₆₁×#479	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₁×#2962	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#2947	C₂	1	1	yes	maximal, characteristic
22	C₆₁×#2947	C₂	1	1	yes	maximal, characteristic
23	C₄×#137×C₆₁	C₂	1	1	yes	maximal, characteristic
24	C₂×#137×C₆₁	C₂²	1	1	yes	characteristic
25	Q₈²×C₆₁	—	2	1	no	—
26	Q₈²×C₆₁	C₂²	1	2	yes	—
27	C₆₁×#557	—	2	1	no	—
28	C₆₁×#557	—	2	1	no	—
29	C₆₁×#557	—	2	1	no	—
30	C₆₁×#557	C₂²	1	2	yes	—
31	C₆₁×#557	C₂²	1	2	yes	—
32	C₆₁×#557	C₂²	1	2	yes	—
33	C₆₁×#557	C₂²	1	2	yes	—
34	C₆₁×#557	C₂²	1	2	yes	—
35	C₆₁×#554	—	2	2	no	—
36	C₆₁×#554	—	2	2	no	—
37	C₆₁×#554	C₂²	1	2	yes	—
38	C₆₁×#554	C₂²	1	2	yes	—
39	C₆₁×#544	—	2	1	no	—
40	C₆₁×#544	—	2	1	no	—
41	C₆₁×#544	—	2	2	no	—
42	C₆₁×#544	C₂²	1	1	yes	characteristic
43	C₆₁×#544	C₂²	1	1	yes	characteristic
44	C₆₁×#544	C₂²	1	1	yes	characteristic
45	C₆₁×#544	C₂²	1	1	yes	characteristic
46	C₆₁×#533	—	2	1	no	—
47	C₆₁×#533	—	2	2	no	—
48	C₆₁×#533	C₂²	1	1	yes	characteristic
49	C₆₁×#533	C₂²	1	1	yes	characteristic
50	C₂×#125×C₆₁	—	2	1	no	—
51	C₂×#125×C₆₁	C₂²	1	1	yes	characteristic
52	C₆₁×#520	C₂²	1	1	yes	characteristic
53	C₆₁×#520	C₂²	1	1	yes	characteristic
54	C₆₁×#519	C₂²	1	1	yes	characteristic
55	C₆₁×#519	C₂²	1	1	yes	characteristic
56	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
57	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
58	C₆₁×#501	C₂²	1	2	yes	—
59	C₆₁×#501	C₂²	1	2	yes	—
60	C₆₁×#501	C₂²	1	2	yes	—
61	C₆₁×#501	C₂²	1	2	yes	—
62	C₆₁×#501	C₂²	1	2	yes	—
63	C₆₁×#501	C₂²	1	2	yes	—
64	C₆₁×#500	C₂²	1	2	yes	—
65	C₆₁×#499	C₂²	1	2	yes	—
66	C₆₁×#499	C₂²	1	2	yes	—
67	C₆₁×#499	C₂²	1	2	yes	—
68	C₆₁×#499	C₂²	1	2	yes	—
69	C₆₁×#498	C₂²	1	2	yes	—
70	C₆₁×#479	C₂²	1	2	yes	—
71	C₆₁×#479	C₂²	1	2	yes	—
72	C₆₁×#479	C₂²	1	2	yes	—
73	C₆₁×#479	C₂²	1	2	yes	—
74	C₆₁×#479	C₂²	1	1	yes	characteristic
75	C₆₁×#479	C₂²	1	1	yes	characteristic
76	C₆₁×#479	C₂²	1	2	yes	—
77	C₆₁×#479	C₂²	1	2	yes	—
78	C₆₁×#479	C₂²	1	2	yes	—
79	C₆₁×#479	C₂²	1	2	yes	—
80	C₆₁×#479	C₂²	1	2	yes	—
81	C₆₁×#479	C₂²	1	2	yes	—
82	C₆₁×#478	C₂²	1	1	yes	characteristic
83	C₆₁×#478	C₂²	1	1	yes	characteristic
84	C₆₁×#478	C₂²	1	2	yes	—
85	C₆₁×#478	C₂²	1	2	yes	—
86	C₆₁×#477	C₂²	1	1	yes	characteristic
87	C₆₁×#477	C₂²	1	2	yes	—
88	C₆₁×#477	C₂²	1	2	yes	—
89	C₆₁×#477	C₂²	1	2	yes	—
90	C₆₁×#476	C₂²	1	1	yes	characteristic
91	C₆₁×#476	C₂²	1	2	yes	—
92	C₆₁×#475	C₂²	1	1	yes	characteristic
93	C₆₁×#475	C₂²	1	2	yes	—
94	C₆₁×#475	C₂²	1	2	yes	—
95	C₆₁×#475	C₂²	1	2	yes	—
96	C₆₁×#474	C₂²	1	1	yes	characteristic
97	C₆₁×#474	C₂²	1	2	yes	—
98	C₆₁×#446	C₂²	1	2	yes	—
99	C₆₁×#446	C₂²	1	2	yes	—
100	C₆₁×#446	C₂²	1	2	yes	—
101	C₈×Q₈×C₆₁	C₂²	1	2	yes	—
102	C₆₁×#441	C₂²	1	2	yes	—
103	C₆₁×#441	C₂²	1	2	yes	—
104	C₆₁×#441	C₂²	1	2	yes	—
105	C₆₁×#440	C₂²	1	2	yes	—
106	C₆₁×#440	C₂²	1	2	yes	—
107	C₆₁×#440	C₂²	1	2	yes	—
108	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
109	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
110	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
111	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
112	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
113	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
114	C₆₁×#428	C₂²	1	1	yes	characteristic
115	C₆₁×#428	C₂²	1	1	yes	characteristic
116	C₆₁×#428	C₂²	1	1	yes	characteristic
117	C₆₁×#428	C₂²	1	1	yes	characteristic
118	C₆₁×#428	C₂²	1	1	yes	characteristic
119	C₆₁×#427	C₂²	1	1	yes	characteristic
120	C₆₁×#427	C₂²	1	1	yes	characteristic
121	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
122	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
123	C₆₁×#424	C₂²	1	1	yes	characteristic
124	C₆₁×#424	C₂²	1	1	yes	characteristic
125	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
126	C₆₁×#419	C₂²	1	1	yes	characteristic
127	C₆₁×#417	C₂²	1	1	yes	characteristic
128	C₆₁×#416	C₂²	1	1	yes	characteristic
129	C₆₁×#416	C₂²	1	1	yes	characteristic
130	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
131	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
132	C₆₁×#405	C₂²	1	1	yes	characteristic
133	C₆₁×#405	C₂²	1	1	yes	characteristic
134	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
135	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
136	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
137	#137×C₆₁	Q₈	1	8	yes	complemented
138	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
139	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
140	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
141	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
143	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
144	C₄⋊Q₈×C₆₁	—	2	2	no	—
145	C₄⋊Q₈×C₆₁	—	2	2	no	—
146	C₄⋊Q₈×C₆₁	—	2	2	no	—
147	C₄⋊Q₈×C₆₁	—	2	2	no	—
148	C₄⋊Q₈×C₆₁	—	2	2	no	—
149	C₄⋊Q₈×C₆₁	—	2	1	no	—
150	C₄⋊Q₈×C₆₁	—	2	1	no	—
151	C₄⋊Q₈×C₆₁	—	2	2	no	—
152	C₄⋊Q₈×C₆₁	—	2	2	no	—
153	C₄⋊Q₈×C₆₁	—	2	2	no	—
154	C₄⋊Q₈×C₆₁	—	2	1	no	—
155	C₄⋊Q₈×C₆₁	—	2	1	no	—
156	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
157	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
158	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
161	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
162	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
163	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
164	#125×C₆₁	—	2	2	no	—
165	#125×C₆₁	—	2	2	no	—
166	#125×C₆₁	—	2	1	no	—
167	#125×C₆₁	—	2	1	no	—
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	1	no	—
175	#125×C₆₁	—	2	1	no	—
176	#125×C₆₁	—	2	2	no	—
177	#125×C₆₁	—	2	2	no	—
178	#125×C₆₁	—	2	1	no	—
179	#125×C₆₁	—	2	1	no	—
180	#125×C₆₁	D₄	1	1	yes	characteristic
181	#125×C₆₁	D₄	1	1	yes	characteristic
182	#125×C₆₁	C₂³	1	1	yes	characteristic
183	#125×C₆₁	C₂³	1	1	yes	characteristic
184	#125×C₆₁	C₂³	1	2	yes	—
185	#125×C₆₁	C₂³	1	2	yes	—
186	#125×C₆₁	C₂³	1	2	yes	—
187	#125×C₆₁	C₂³	1	2	yes	—
188	#125×C₆₁	C₂³	1	2	yes	—
189	#125×C₆₁	C₂³	1	2	yes	—
190	C₂²⋊Q₈×C₆₁	—	2	2	no	—
191	C₂²⋊Q₈×C₆₁	—	2	2	no	—
192	C₂²⋊Q₈×C₆₁	—	2	1	no	—
193	C₂²⋊Q₈×C₆₁	—	2	1	no	—
194	C₂²⋊Q₈×C₆₁	—	2	2	no	—
195	C₂²⋊Q₈×C₆₁	—	2	2	no	—
196	C₂²⋊Q₈×C₆₁	—	2	2	no	—
197	C₂²⋊Q₈×C₆₁	—	2	2	no	—
198	C₂²⋊Q₈×C₆₁	—	2	2	no	—
199	C₂²⋊Q₈×C₆₁	—	2	2	no	—
200	C₂²⋊Q₈×C₆₁	—	2	2	no	—
201	C₂²⋊Q₈×C₆₁	—	2	2	no	—
202	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
203	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
204	C₄×Q₈×C₆₁	—	2	2	no	—
205	C₄×Q₈×C₆₁	—	2	2	no	—
206	C₄×Q₈×C₆₁	—	2	2	no	—
207	C₄×Q₈×C₆₁	—	2	2	no	—
208	C₄×Q₈×C₆₁	—	2	2	no	—
209	C₄×Q₈×C₆₁	—	2	2	no	—
210	C₄×Q₈×C₆₁	—	2	1	no	—
211	C₄×Q₈×C₆₁	—	2	1	no	—
212	C₄×Q₈×C₆₁	—	2	1	no	—
213	C₄×Q₈×C₆₁	—	2	1	no	—
214	C₄×Q₈×C₆₁	—	2	1	no	—
215	C₄×Q₈×C₆₁	—	2	1	no	—
216	C₄×Q₈×C₆₁	—	2	1	no	—
217	C₄×Q₈×C₆₁	—	2	1	no	—
218	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
219	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
220	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
222	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
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	2	yes	—
228	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
229	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
230	C₄×D₄×C₆₁	—	2	1	no	—
231	C₄×D₄×C₆₁	—	2	1	no	—
232	C₄×D₄×C₆₁	—	2	2	no	—
233	C₄×D₄×C₆₁	—	2	2	no	—
234	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₆₁	C₂³	1	2	yes	—
236	C₄×D₄×C₆₁	C₂³	1	2	yes	—
237	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
238	#117×C₆₁	—	2	1	no	—
239	#117×C₆₁	—	2	1	no	—
240	#117×C₆₁	—	2	2	no	—
241	#117×C₆₁	—	2	2	no	—
242	#117×C₆₁	—	2	1	no	—
243	#117×C₆₁	C₂³	1	1	yes	characteristic
244	#117×C₆₁	C₂³	1	1	yes	characteristic
245	#117×C₆₁	C₂³	1	1	yes	characteristic
246	#117×C₆₁	C₂³	1	1	yes	characteristic
247	#117×C₆₁	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
249	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
250	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
251	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
252	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
253	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
254	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
255	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
258	C₂×C₄²×C₆₁	—	2	1	no	—
259	C₂×C₄²×C₆₁	—	2	1	no	—
260	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
261	#107×C₆₁	C₂³	1	2	yes	—
262	#107×C₆₁	C₂³	1	2	yes	—
263	#107×C₆₁	C₂³	1	1	yes	characteristic
264	#107×C₆₁	C₂³	1	1	yes	characteristic
265	#107×C₆₁	C₂³	1	1	yes	characteristic
266	#107×C₆₁	C₂³	1	1	yes	characteristic
267	#107×C₆₁	C₂³	1	2	yes	—
268	#107×C₆₁	C₂³	1	2	yes	—
269	#107×C₆₁	C₂³	1	2	yes	—
270	#107×C₆₁	C₂³	1	2	yes	—
271	#107×C₆₁	C₂³	1	2	yes	—
272	#106×C₆₁	C₂³	1	2	yes	—
273	#106×C₆₁	C₂³	1	2	yes	—
274	#106×C₆₁	C₂³	1	1	yes	characteristic
275	#106×C₆₁	C₂³	1	1	yes	characteristic
276	#106×C₆₁	C₂³	1	1	yes	characteristic
277	#106×C₆₁	C₂³	1	1	yes	characteristic
278	#106×C₆₁	C₂³	1	2	yes	—
279	#106×C₆₁	C₂³	1	2	yes	—
280	#106×C₆₁	C₂³	1	2	yes	—
281	#106×C₆₁	C₂³	1	2	yes	—
282	#106×C₆₁	C₂³	1	2	yes	—
283	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
285	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
286	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
287	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
288	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
289	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
290	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
291	#103×C₆₁	C₂³	1	2	yes	—
292	#103×C₆₁	C₂³	1	2	yes	—
293	#103×C₆₁	C₂³	1	2	yes	—
294	#103×C₆₁	C₂³	1	2	yes	—
295	#103×C₆₁	C₂³	1	1	yes	characteristic
296	#103×C₆₁	C₂³	1	1	yes	characteristic
297	#103×C₆₁	C₂³	1	1	yes	characteristic
298	#103×C₆₁	C₂³	1	1	yes	characteristic
299	#103×C₆₁	C₂³	1	2	yes	—
300	#103×C₆₁	C₂³	1	2	yes	—
301	#103×C₆₁	C₂³	1	2	yes	—
302	#102×C₆₁	C₂³	1	1	yes	characteristic
303	#102×C₆₁	C₂³	1	1	yes	characteristic
304	#102×C₆₁	C₂³	1	1	yes	characteristic
305	#102×C₆₁	C₂³	1	1	yes	characteristic
306	#102×C₆₁	C₂³	1	2	yes	—
307	#97×C₆₁	C₂³	1	2	yes	—
308	#97×C₆₁	C₂³	1	2	yes	—
309	#97×C₆₁	C₂³	1	2	yes	—
310	C₄×C₈×C₆₁	C₂³	1	2	yes	—
311	C₄×C₈×C₆₁	C₂³	1	2	yes	—
312	C₄×C₈×C₆₁	C₂³	1	2	yes	—
313	#41×C₆₁	—	2	2	no	—
314	#41×C₆₁	C₂×Q₈	1	4	yes	—
315	C₂×Q₈×C₆₁	—	2	1	no	—
316	C₂×Q₈×C₆₁	—	2	1	no	—
317	C₂×Q₈×C₆₁	—	2	2	no	—
318	C₂×Q₈×C₆₁	—	2	2	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	—	2	2	no	—
323	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
324	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
325	C₂×Q₈×C₆₁	C₂×Q₈	1	4	yes	—
326	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
327	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₆₁	—	2	1	no	—
329	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₆₁	—	2	1	no	—
331	C₂²×C₄×C₆₁	—	2	1	no	—
332	C₂²×C₄×C₆₁	—	2	1	no	—
333	C₂²×C₄×C₆₁	—	2	1	no	—
334	C₂²×C₄×C₆₁	—	2	1	no	—
335	C₂²×C₄×C₆₁	—	2	1	no	—
336	C₂²×C₄×C₆₁	—	2	1	no	—
337	C₂²×C₄×C₆₁	—	2	2	no	—
338	C₂²×C₄×C₆₁	—	2	2	no	—
339	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
340	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
341	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
342	Q₁₆×C₆₁	C₂×Q₈	1	8	yes	—
343	SD₁₆×C₆₁	C₂×Q₈	1	8	yes	—
344	M₁₆×C₆₁	—	2	2	no	—
345	M₁₆×C₆₁	C₂×Q₈	1	4	yes	—
346	C₂×C₈×C₆₁	—	2	2	no	—
347	C₂×C₈×C₆₁	—	2	2	no	—
348	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
349	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
350	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
351	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
352	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
353	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
354	C₄⋊C₄×C₆₁	—	2	2	no	—
355	C₄⋊C₄×C₆₁	—	2	2	no	—
356	C₄⋊C₄×C₆₁	—	2	1	no	—
357	C₄⋊C₄×C₆₁	—	2	1	no	—
358	C₄⋊C₄×C₆₁	—	2	2	no	—
359	C₄⋊C₄×C₆₁	—	2	2	no	—
360	C₄⋊C₄×C₆₁	—	2	2	no	—
361	C₄⋊C₄×C₆₁	—	2	2	no	—
362	C₄⋊C₄×C₆₁	—	2	2	no	—
363	C₄⋊C₄×C₆₁	—	2	2	no	—
364	C₄⋊C₄×C₆₁	—	2	2	no	—
365	C₄⋊C₄×C₆₁	—	2	2	no	—
366	C₄⋊C₄×C₆₁	—	2	2	no	—
367	C₄⋊C₄×C₆₁	—	2	2	no	—
368	C₄⋊C₄×C₆₁	—	2	1	no	—
369	C₄⋊C₄×C₆₁	—	2	1	no	—
370	C₄⋊C₄×C₆₁	—	2	1	no	—
371	C₄⋊C₄×C₆₁	—	2	2	no	—
372	C₄⋊C₄×C₆₁	—	2	2	no	—
373	C₄⋊C₄×C₆₁	—	2	2	no	—
374	C₄⋊C₄×C₆₁	—	2	2	no	—
375	C₄⋊C₄×C₆₁	—	2	1	no	—
376	C₄⋊C₄×C₆₁	—	2	1	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	2	no	—
382	C₄⋊C₄×C₆₁	—	2	2	no	—
383	C₄⋊C₄×C₆₁	—	2	2	no	—
384	C₄⋊C₄×C₆₁	—	2	2	no	—
385	C₄⋊C₄×C₆₁	—	2	1	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	C₂×D₄	1	1	yes	characteristic
390	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
391	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
392	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
393	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
394	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
395	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
396	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
400	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
408	C₂²⋊C₄×C₆₁	—	2	1	no	—
409	C₂²⋊C₄×C₆₁	—	2	1	no	—
410	C₂²⋊C₄×C₆₁	—	2	1	no	—
411	C₂²⋊C₄×C₆₁	—	2	1	no	—
412	C₂²⋊C₄×C₆₁	—	2	1	no	—
413	C₂²⋊C₄×C₆₁	—	2	2	no	—
414	C₂²⋊C₄×C₆₁	—	2	2	no	—
415	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
416	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
417	C₄²×C₆₁	—	2	1	no	—
418	C₄²×C₆₁	—	2	1	no	—
419	C₄²×C₆₁	—	2	1	no	—
420	C₄²×C₆₁	—	2	2	no	—
421	C₄²×C₆₁	—	2	2	no	—
422	C₄²×C₆₁	—	2	2	no	—
423	C₄²×C₆₁	—	2	2	no	—
424	C₄²×C₆₁	—	2	2	no	—
425	C₄²×C₆₁	—	2	2	no	—
426	C₄²×C₆₁	—	2	2	no	—
427	C₄²×C₆₁	—	2	2	no	—
428	C₄²×C₆₁	—	2	1	no	—
429	C₄²×C₆₁	—	2	1	no	—
430	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
431	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
432	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
433	C₄²×C₆₁	C₂⁴	1	2	yes	—
434	C₄²×C₆₁	C₂⁴	1	2	yes	—
435	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
436	C₂³×C₆₁	—	2	1	no	—
437	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
438	Q₈×C₆₁	—	2	4	no	—
439	Q₈×C₆₁	—	2	2	no	—
440	Q₈×C₆₁	—	2	1	no	—
441	Q₈×C₆₁	—	4	2	no	—
442	Q₈×C₆₁	—	4	2	no	—
443	Q₈×C₆₁	—	4	2	no	—
444	Q₈×C₆₁	—	8	1	no	—
445	Q₈×C₆₁	—	8	2	no	—
446	Q₈×C₆₁	—	8	2	no	—
447	Q₈×C₆₁	—	8	2	no	—
448	Q₈×C₆₁	—	8	2	no	—
449	Q₈×C₆₁	C₂²×Q₈	1	4	yes	—
450	Q₈×C₆₁	C₂²×Q₈	1	2	yes	—
451	D₄×C₆₁	—	2	4	no	—
452	D₄×C₆₁	—	2	1	no	—
453	D₄×C₆₁	C₂²×Q₈	1	2	yes	—
454	C₂×C₄×C₆₁	—	2	4	no	—
455	C₂×C₄×C₆₁	—	2	1	no	—
456	C₂×C₄×C₆₁	—	2	2	no	—
457	C₂×C₄×C₆₁	—	2	4	no	—
458	C₂×C₄×C₆₁	—	2	1	no	—
459	C₂×C₄×C₆₁	—	2	1	no	—
460	C₂×C₄×C₆₁	—	2	1	no	—
461	C₂×C₄×C₆₁	—	2	1	no	—
462	C₂×C₄×C₆₁	—	2	1	no	—
463	C₂×C₄×C₆₁	—	2	1	no	—
464	C₂×C₄×C₆₁	—	2	2	no	—
465	C₂×C₄×C₆₁	—	2	2	no	—
466	C₂×C₄×C₆₁	—	2	2	no	—
467	C₂×C₄×C₆₁	—	4	1	no	—
468	C₂×C₄×C₆₁	—	4	1	no	—
469	C₂×C₄×C₆₁	—	8	1	no	—
470	C₂×C₄×C₆₁	—	8	2	no	—
471	C₂×C₄×C₆₁	—	8	1	no	—
472	C₂×C₄×C₆₁	—	8	2	no	—
473	C₂×C₄×C₆₁	—	8	1	no	—
474	C₂×C₄×C₆₁	—	8	1	no	—
475	C₂×C₄×C₆₁	—	8	1	no	—
476	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
479	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
480	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
481	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
482	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
483	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₆₁	C₂²×Q₈	1	2	yes	—
486	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
487	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
488	C₈×C₆₁	—	2	1	no	—
489	C₈×C₆₁	—	2	1	no	—
490	C₈×C₆₁	—	2	1	no	—
491	C₈×C₆₁	—	2	1	no	—
492	C₈×C₆₁	—	2	2	no	—
493	C₈×C₆₁	C₂²×Q₈	1	4	yes	—
494	#61386	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
495	C₂²×C₆₁	—	2	1	no	—
496	C₂²×C₆₁	—	2	1	no	—
497	C₂²×C₆₁	—	2	2	no	—
498	C₂²×C₆₁	—	4	1	no	—
499	C₂²×C₆₁	—	4	1	no	—
500	C₂²×C₆₁	D₄×Q₈	1	2	yes	—
501	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
502	C₄×C₆₁	—	2	1	no	—
503	C₄×C₆₁	—	2	1	no	—
504	C₄×C₆₁	—	2	2	no	—
505	C₄×C₆₁	—	2	2	no	—
506	C₄×C₆₁	—	2	1	no	—
507	C₄×C₆₁	—	2	1	no	—
508	C₄×C₆₁	—	2	2	no	—
509	C₄×C₆₁	—	2	2	no	—
510	C₄×C₆₁	—	2	2	no	—
511	C₄×C₆₁	—	2	4	no	—
512	C₄×C₆₁	—	4	2	no	—
513	C₄×C₆₁	—	4	1	no	—
514	C₄×C₆₁	—	4	2	no	—
515	C₄×C₆₁	—	4	1	no	—
516	C₄×C₆₁	—	4	1	no	—
517	C₄×C₆₁	—	4	2	no	—
518	C₄×C₆₁	—	4	1	no	—
519	C₄×C₆₁	—	4	1	no	—
520	C₄×C₆₁	—	4	1	no	—
521	C₄×C₆₁	D₄×Q₈	1	2	yes	—
522	C₄×C₆₁	C₂³×Q₈	1	1	yes	characteristic
523	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
524	#3504	C₂×C₆₁	1	1	yes	characteristic
525	#3502	C₂×C₆₁	1	1	yes	characteristic, complemented
526	#3390	C₂×C₆₁	1	2	yes	complemented
527	#3390	C₂×C₆₁	1	2	yes	complemented
528	#3388	C₂×C₆₁	1	2	yes	complemented
529	#3388	C₂×C₆₁	1	2	yes	complemented
530	#3387	C₂×C₆₁	1	2	yes	complemented
531	#3385	C₂×C₆₁	1	2	yes	complemented
532	#3383	C₂×C₆₁	1	2	yes	complemented
533	#3381	C₂×C₆₁	1	2	yes	complemented
534	#3166	C₂×C₆₁	1	1	yes	characteristic, complemented
535	#3164	C₂×C₆₁	1	1	yes	characteristic, complemented
536	#3163	C₂×C₆₁	1	1	yes	characteristic, complemented
537	#3084	C₂×C₆₁	1	1	yes	characteristic
538	#3083	C₂×C₆₁	1	1	yes	characteristic
539	#3082	C₂×C₆₁	1	1	yes	characteristic, complemented
540	#3082	C₂×C₆₁	1	1	yes	characteristic, complemented
541	#3076	C₂×C₆₁	1	1	yes	characteristic
542	C₂×#479	C₂×C₆₁	1	1	yes	characteristic, complemented
543	#2962	C₂×C₆₁	1	1	yes	characteristic, complemented
544	#2947	C₂×C₆₁	1	1	yes	characteristic
545	#2947	C₂×C₆₁	1	1	yes	characteristic
546	C₄×#137	C₂×C₆₁	1	1	yes	characteristic
547	C₂×C₆₁	—	2	2	no	—
548	C₂×C₆₁	—	4	2	no	—
549	C₂×C₆₁	C₂×D₄×Q₈	1	1	yes	characteristic
550	C₂×C₆₁	#3584	1	1	yes	characteristic
551	C₂×C₆₁	#3586	1	1	yes	characteristic
552	C₂×#137	C₂²×C₆₁	1	1	yes	characteristic
553	Q₈²	—	2	1	no	—
554	Q₈²	C₂²×C₆₁	1	2	yes	—
555	#557	—	2	1	no	—
556	#557	—	2	1	no	—
557	#557	—	2	1	no	—
558	#557	C₂²×C₆₁	1	2	yes	—
559	#557	C₂²×C₆₁	1	2	yes	—
560	#557	C₂²×C₆₁	1	2	yes	—
561	#557	C₂²×C₆₁	1	2	yes	—
562	#557	C₂²×C₆₁	1	2	yes	—
563	#554	—	2	2	no	—
564	#554	—	2	2	no	—
565	#554	C₂²×C₆₁	1	2	yes	—
566	#554	C₂²×C₆₁	1	2	yes	—
567	#544	—	2	1	no	—
568	#544	—	2	1	no	—
569	#544	—	2	2	no	—
570	#544	C₂²×C₆₁	1	1	yes	characteristic
571	#544	C₂²×C₆₁	1	1	yes	characteristic
572	#544	C₂²×C₆₁	1	1	yes	characteristic
573	#544	C₂²×C₆₁	1	1	yes	characteristic
574	#533	—	2	1	no	—
575	#533	—	2	2	no	—
576	#533	C₂²×C₆₁	1	1	yes	characteristic
577	#533	C₂²×C₆₁	1	1	yes	characteristic
578	C₂×#125	—	2	1	no	—
579	C₂×#125	C₂²×C₆₁	1	1	yes	characteristic
580	#520	C₂²×C₆₁	1	1	yes	characteristic
581	#520	C₂²×C₆₁	1	1	yes	characteristic
582	#519	C₂²×C₆₁	1	1	yes	characteristic
583	#519	C₂²×C₆₁	1	1	yes	characteristic
584	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
585	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
586	#501	C₂²×C₆₁	1	2	yes	—
587	#501	C₂²×C₆₁	1	2	yes	—
588	#501	C₂²×C₆₁	1	2	yes	—
589	#501	C₂²×C₆₁	1	2	yes	—
590	#501	C₂²×C₆₁	1	2	yes	—
591	#501	C₂²×C₆₁	1	2	yes	—
592	#500	C₂²×C₆₁	1	2	yes	—
593	#499	C₂²×C₆₁	1	2	yes	—
594	#499	C₂²×C₆₁	1	2	yes	—
595	#499	C₂²×C₆₁	1	2	yes	—
596	#499	C₂²×C₆₁	1	2	yes	—
597	#498	C₂²×C₆₁	1	2	yes	—
598	#479	C₂²×C₆₁	1	2	yes	—
599	#479	C₂²×C₆₁	1	2	yes	—
600	#479	C₂²×C₆₁	1	2	yes	—
601	#479	C₂²×C₆₁	1	2	yes	—
602	#479	C₂²×C₆₁	1	1	yes	characteristic
603	#479	C₂²×C₆₁	1	1	yes	characteristic
604	#479	C₂²×C₆₁	1	2	yes	—
605	#479	C₂²×C₆₁	1	2	yes	—
606	#479	C₂²×C₆₁	1	2	yes	—
607	#479	C₂²×C₆₁	1	2	yes	—
608	#479	C₂²×C₆₁	1	2	yes	—
609	#479	C₂²×C₆₁	1	2	yes	—
610	#478	C₂²×C₆₁	1	1	yes	characteristic
611	#478	C₂²×C₆₁	1	1	yes	characteristic
612	#478	C₂²×C₆₁	1	2	yes	—
613	#478	C₂²×C₆₁	1	2	yes	—
614	#477	C₂²×C₆₁	1	1	yes	characteristic
615	#477	C₂²×C₆₁	1	2	yes	—
616	#477	C₂²×C₆₁	1	2	yes	—
617	#477	C₂²×C₆₁	1	2	yes	—
618	#476	C₂²×C₆₁	1	1	yes	characteristic
619	#476	C₂²×C₆₁	1	2	yes	—
620	#475	C₂²×C₆₁	1	1	yes	characteristic
621	#475	C₂²×C₆₁	1	2	yes	—
622	#475	C₂²×C₆₁	1	2	yes	—
623	#475	C₂²×C₆₁	1	2	yes	—
624	#474	C₂²×C₆₁	1	1	yes	characteristic
625	#474	C₂²×C₆₁	1	2	yes	—
626	#446	C₂²×C₆₁	1	2	yes	—
627	#446	C₂²×C₆₁	1	2	yes	—
628	#446	C₂²×C₆₁	1	2	yes	—
629	C₈×Q₈	C₂²×C₆₁	1	2	yes	—
630	#441	C₂²×C₆₁	1	2	yes	—
631	#441	C₂²×C₆₁	1	2	yes	—
632	#441	C₂²×C₆₁	1	2	yes	—
633	#440	C₂²×C₆₁	1	2	yes	—
634	#440	C₂²×C₆₁	1	2	yes	—
635	#440	C₂²×C₆₁	1	2	yes	—
636	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
637	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
638	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
639	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
640	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
641	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
642	#428	C₂²×C₆₁	1	1	yes	characteristic
643	#428	C₂²×C₆₁	1	1	yes	characteristic
644	#428	C₂²×C₆₁	1	1	yes	characteristic
645	#428	C₂²×C₆₁	1	1	yes	characteristic
646	#428	C₂²×C₆₁	1	1	yes	characteristic
647	#427	C₂²×C₆₁	1	1	yes	characteristic
648	#427	C₂²×C₆₁	1	1	yes	characteristic
649	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
650	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
651	#424	C₂²×C₆₁	1	1	yes	characteristic
652	#424	C₂²×C₆₁	1	1	yes	characteristic
653	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
654	#419	C₂²×C₆₁	1	1	yes	characteristic
655	#417	C₂²×C₆₁	1	1	yes	characteristic
656	#416	C₂²×C₆₁	1	1	yes	characteristic
657	#416	C₂²×C₆₁	1	1	yes	characteristic
658	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
659	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
660	#405	C₂²×C₆₁	1	1	yes	characteristic
661	#405	C₂²×C₆₁	1	1	yes	characteristic
662	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
663	C₆₁	#61386	1	1	yes	characteristic, direct product factor, Sylow
664	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
665	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
666	#137	Q₈×C₆₁	1	8	yes	complemented
667	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
668	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
669	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
670	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
671	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
672	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
673	C₄⋊Q₈	—	2	2	no	—
674	C₄⋊Q₈	—	2	2	no	—
675	C₄⋊Q₈	—	2	2	no	—
676	C₄⋊Q₈	—	2	2	no	—
677	C₄⋊Q₈	—	2	2	no	—
678	C₄⋊Q₈	—	2	1	no	—
679	C₄⋊Q₈	—	2	1	no	—
680	C₄⋊Q₈	—	2	2	no	—
681	C₄⋊Q₈	—	2	2	no	—
682	C₄⋊Q₈	—	2	2	no	—
683	C₄⋊Q₈	—	2	1	no	—
684	C₄⋊Q₈	—	2	1	no	—
685	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
686	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
687	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
688	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
689	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
690	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
691	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
692	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
693	#125	—	2	1	no	—
694	#125	—	2	1	no	—
695	#125	—	2	2	no	—
696	#125	—	2	2	no	—
697	#125	—	2	2	no	—
698	#125	—	2	2	no	—
699	#125	—	2	2	no	—
700	#125	—	2	2	no	—
701	#125	—	2	2	no	—
702	#125	—	2	2	no	—
703	#125	—	2	2	no	—
704	#125	—	2	2	no	—
705	#125	—	2	1	no	—
706	#125	—	2	1	no	—
707	#125	—	2	1	no	—
708	#125	—	2	1	no	—
709	#125	D₄×C₆₁	1	1	yes	characteristic
710	#125	D₄×C₆₁	1	1	yes	characteristic
711	#125	C₂³×C₆₁	1	2	yes	—
712	#125	C₂³×C₆₁	1	2	yes	—
713	#125	C₂³×C₆₁	1	1	yes	characteristic
714	#125	C₂³×C₆₁	1	1	yes	characteristic
715	#125	C₂³×C₆₁	1	2	yes	—
716	#125	C₂³×C₆₁	1	2	yes	—
717	#125	C₂³×C₆₁	1	2	yes	—
718	#125	C₂³×C₆₁	1	2	yes	—
719	C₂²⋊Q₈	—	2	2	no	—
720	C₂²⋊Q₈	—	2	2	no	—
721	C₂²⋊Q₈	—	2	1	no	—
722	C₂²⋊Q₈	—	2	1	no	—
723	C₂²⋊Q₈	—	2	2	no	—
724	C₂²⋊Q₈	—	2	2	no	—
725	C₂²⋊Q₈	—	2	2	no	—
726	C₂²⋊Q₈	—	2	2	no	—
727	C₂²⋊Q₈	—	2	2	no	—
728	C₂²⋊Q₈	—	2	2	no	—
729	C₂²⋊Q₈	—	2	2	no	—
730	C₂²⋊Q₈	—	2	2	no	—
731	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
732	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
733	C₄×Q₈	—	2	2	no	—
734	C₄×Q₈	—	2	1	no	—
735	C₄×Q₈	—	2	1	no	—
736	C₄×Q₈	—	2	1	no	—
737	C₄×Q₈	—	2	1	no	—
738	C₄×Q₈	—	2	2	no	—
739	C₄×Q₈	—	2	2	no	—
740	C₄×Q₈	—	2	2	no	—
741	C₄×Q₈	—	2	2	no	—
742	C₄×Q₈	—	2	2	no	—
743	C₄×Q₈	—	2	1	no	—
744	C₄×Q₈	—	2	1	no	—
745	C₄×Q₈	—	2	1	no	—
746	C₄×Q₈	—	2	1	no	—
747	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
748	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
749	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
750	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
751	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
752	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
753	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
754	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
755	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
756	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
757	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
758	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
759	C₄×D₄	—	2	1	no	—
760	C₄×D₄	—	2	1	no	—
761	C₄×D₄	—	2	2	no	—
762	C₄×D₄	—	2	2	no	—
763	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
764	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
765	C₄×D₄	C₂³×C₆₁	1	2	yes	—
766	C₄×D₄	C₂³×C₆₁	1	2	yes	—
767	#117	—	2	1	no	—
768	#117	—	2	1	no	—
769	#117	—	2	2	no	—
770	#117	—	2	2	no	—
771	#117	—	2	1	no	—
772	#117	C₂³×C₆₁	1	1	yes	characteristic
773	#117	C₂³×C₆₁	1	1	yes	characteristic
774	#117	C₂³×C₆₁	1	1	yes	characteristic
775	#117	C₂³×C₆₁	1	1	yes	characteristic
776	#117	C₂³×C₆₁	1	1	yes	characteristic
777	C₂×C₄⋊C₄	—	2	1	no	—
778	C₂×C₄⋊C₄	—	2	1	no	—
779	C₂×C₄⋊C₄	—	2	1	no	—
780	C₂×C₄⋊C₄	—	2	1	no	—
781	C₂×C₄⋊C₄	—	2	1	no	—
782	C₂×C₄⋊C₄	—	2	2	no	—
783	C₂×C₄⋊C₄	—	2	2	no	—
784	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
785	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
786	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
787	C₂×C₄²	—	2	1	no	—
788	C₂×C₄²	—	2	1	no	—
789	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
790	#107	C₂³×C₆₁	1	2	yes	—
791	#107	C₂³×C₆₁	1	2	yes	—
792	#107	C₂³×C₆₁	1	1	yes	characteristic
793	#107	C₂³×C₆₁	1	1	yes	characteristic
794	#107	C₂³×C₆₁	1	1	yes	characteristic
795	#107	C₂³×C₆₁	1	1	yes	characteristic
796	#107	C₂³×C₆₁	1	2	yes	—
797	#107	C₂³×C₆₁	1	2	yes	—
798	#107	C₂³×C₆₁	1	2	yes	—
799	#107	C₂³×C₆₁	1	2	yes	—
800	#107	C₂³×C₆₁	1	2	yes	—
801	#106	C₂³×C₆₁	1	2	yes	—
802	#106	C₂³×C₆₁	1	2	yes	—
803	#106	C₂³×C₆₁	1	1	yes	characteristic
804	#106	C₂³×C₆₁	1	1	yes	characteristic
805	#106	C₂³×C₆₁	1	1	yes	characteristic
806	#106	C₂³×C₆₁	1	1	yes	characteristic
807	#106	C₂³×C₆₁	1	2	yes	—
808	#106	C₂³×C₆₁	1	2	yes	—
809	#106	C₂³×C₆₁	1	2	yes	—
810	#106	C₂³×C₆₁	1	2	yes	—
811	#106	C₂³×C₆₁	1	2	yes	—
812	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
813	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
814	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
815	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
816	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
817	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
818	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
819	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
820	#103	C₂³×C₆₁	1	2	yes	—
821	#103	C₂³×C₆₁	1	2	yes	—
822	#103	C₂³×C₆₁	1	2	yes	—
823	#103	C₂³×C₆₁	1	2	yes	—
824	#103	C₂³×C₆₁	1	1	yes	characteristic
825	#103	C₂³×C₆₁	1	1	yes	characteristic
826	#103	C₂³×C₆₁	1	1	yes	characteristic
827	#103	C₂³×C₆₁	1	1	yes	characteristic
828	#103	C₂³×C₆₁	1	2	yes	—
829	#103	C₂³×C₆₁	1	2	yes	—
830	#103	C₂³×C₆₁	1	2	yes	—
831	#102	C₂³×C₆₁	1	1	yes	characteristic
832	#102	C₂³×C₆₁	1	1	yes	characteristic
833	#102	C₂³×C₆₁	1	1	yes	characteristic
834	#102	C₂³×C₆₁	1	1	yes	characteristic
835	#102	C₂³×C₆₁	1	2	yes	—
836	#97	C₂³×C₆₁	1	2	yes	—
837	#97	C₂³×C₆₁	1	2	yes	—
838	#97	C₂³×C₆₁	1	2	yes	—
839	C₄×C₈	C₂³×C₆₁	1	2	yes	—
840	C₄×C₈	C₂³×C₆₁	1	2	yes	—
841	C₄×C₈	C₂³×C₆₁	1	2	yes	—
842	#41	—	2	2	no	—
843	#41	C₂×Q₈×C₆₁	1	4	yes	—
844	C₂×Q₈	—	2	1	no	—
845	C₂×Q₈	—	2	1	no	—
846	C₂×Q₈	—	2	2	no	—
847	C₂×Q₈	—	2	2	no	—
848	C₂×Q₈	—	2	1	no	—
849	C₂×Q₈	—	2	2	no	—
850	C₂×Q₈	—	2	2	no	—
851	C₂×Q₈	—	2	2	no	—
852	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
853	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
854	C₂×Q₈	C₂×Q₈×C₆₁	1	4	yes	—
855	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
856	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
857	C₂×D₄	—	2	1	no	—
858	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
859	C₂²×C₄	—	2	1	no	—
860	C₂²×C₄	—	2	1	no	—
861	C₂²×C₄	—	2	1	no	—
862	C₂²×C₄	—	2	1	no	—
863	C₂²×C₄	—	2	1	no	—
864	C₂²×C₄	—	2	1	no	—
865	C₂²×C₄	—	2	1	no	—
866	C₂²×C₄	—	2	2	no	—
867	C₂²×C₄	—	2	2	no	—
868	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
869	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
871	Q₁₆	C₂×Q₈×C₆₁	1	8	yes	—
872	SD₁₆	C₂×Q₈×C₆₁	1	8	yes	—
873	M₁₆	—	2	2	no	—
874	M₁₆	C₂×Q₈×C₆₁	1	4	yes	—
875	C₂×C₈	—	2	2	no	—
876	C₂×C₈	—	2	2	no	—
877	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
878	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
879	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
880	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
881	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
882	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
883	C₄⋊C₄	—	2	2	no	—
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	—	2	1	no	—
886	C₄⋊C₄	—	2	1	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	1	no	—
898	C₄⋊C₄	—	2	1	no	—
899	C₄⋊C₄	—	2	1	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
919	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
920	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
921	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
922	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
923	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
924	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
925	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
926	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
927	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
928	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
929	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
930	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
931	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
932	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
933	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
934	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
935	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
936	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
937	C₂²⋊C₄	—	2	1	no	—
938	C₂²⋊C₄	—	2	1	no	—
939	C₂²⋊C₄	—	2	1	no	—
940	C₂²⋊C₄	—	2	1	no	—
941	C₂²⋊C₄	—	2	1	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
945	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
946	C₄²	—	2	1	no	—
947	C₄²	—	2	1	no	—
948	C₄²	—	2	1	no	—
949	C₄²	—	2	2	no	—
950	C₄²	—	2	2	no	—
951	C₄²	—	2	2	no	—
952	C₄²	—	2	2	no	—
953	C₄²	—	2	2	no	—
954	C₄²	—	2	2	no	—
955	C₄²	—	2	2	no	—
956	C₄²	—	2	2	no	—
957	C₄²	—	2	1	no	—
958	C₄²	—	2	1	no	—
959	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
960	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
961	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
962	C₄²	C₂⁴×C₆₁	1	2	yes	—
963	C₄²	C₂⁴×C₆₁	1	2	yes	—
964	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
965	C₂³	—	2	1	no	—
966	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
967	Q₈	—	2	4	no	—
968	Q₈	—	2	2	no	—
969	Q₈	—	2	1	no	—
970	Q₈	—	4	2	no	—
971	Q₈	—	4	2	no	—
972	Q₈	—	4	2	no	—
973	Q₈	—	8	1	no	—
974	Q₈	—	8	2	no	—
975	Q₈	—	8	2	no	—
976	Q₈	—	8	2	no	—
977	Q₈	—	8	2	no	—
978	Q₈	C₂²×Q₈×C₆₁	1	4	yes	—
979	Q₈	C₂²×Q₈×C₆₁	1	2	yes	—
980	D₄	—	2	4	no	—
981	D₄	—	2	1	no	—
982	D₄	C₂²×Q₈×C₆₁	1	2	yes	—
983	C₂×C₄	—	2	4	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	4	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	4	1	no	—
997	C₂×C₄	—	4	1	no	—
998	C₂×C₄	—	8	1	no	—
999	C₂×C₄	—	8	2	no	—
1000	C₂×C₄	—	8	1	no	—
1001	C₂×C₄	—	8	2	no	—
1002	C₂×C₄	—	8	1	no	—
1003	C₂×C₄	—	8	1	no	—
1004	C₂×C₄	—	8	1	no	—
1005	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1006	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1007	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1008	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1009	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1010	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1011	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1012	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1013	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1014	C₂×C₄	C₂²×Q₈×C₆₁	1	2	yes	—
1015	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
1016	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1017	C₈	—	2	1	no	—
1018	C₈	—	2	1	no	—
1019	C₈	—	2	1	no	—
1020	C₈	—	2	1	no	—
1021	C₈	—	2	2	no	—
1022	C₈	C₂²×Q₈×C₆₁	1	4	yes	—
1023	C₂²	—	2	1	no	—
1024	C₂²	—	2	1	no	—
1025	C₂²	—	2	2	no	—
1026	C₂²	—	4	1	no	—
1027	C₂²	—	4	1	no	—
1028	C₂²	D₄×Q₈×C₆₁	1	2	yes	—
1029	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1030	C₄	—	2	1	no	—
1031	C₄	—	2	1	no	—
1032	C₄	—	2	2	no	—
1033	C₄	—	2	2	no	—
1034	C₄	—	2	1	no	—
1035	C₄	—	2	1	no	—
1036	C₄	—	2	2	no	—
1037	C₄	—	2	2	no	—
1038	C₄	—	2	2	no	—
1039	C₄	—	2	4	no	—
1040	C₄	—	4	2	no	—
1041	C₄	—	4	1	no	—
1042	C₄	—	4	2	no	—
1043	C₄	—	4	1	no	—
1044	C₄	—	4	1	no	—
1045	C₄	—	4	2	no	—
1046	C₄	—	4	1	no	—
1047	C₄	—	4	1	no	—
1048	C₄	—	4	1	no	—
1049	C₄	D₄×Q₈×C₆₁	1	2	yes	—
1050	C₄	C₂³×Q₈×C₆₁	1	1	yes	characteristic
1051	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
1052	C₂	—	2	2	no	—
1053	C₂	—	4	2	no	—
1054	C₂	C₂×D₄×Q₈×C₆₁	1	1	yes	characteristic
1055	C₂	C₆₁×#3584	1	1	yes	characteristic
1056	C₂	C₆₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₂×#41×C₆₁	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₆₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₁×#3502	C₂	semidirect
3. C₆₁×#3390	C₂	semidirect
4. C₆₁×#3390	C₂	semidirect
5. C₆₁×#3388	C₂	semidirect
6. C₆₁×#3388	C₂	semidirect
7. C₆₁×#3387	C₂	semidirect
8. C₆₁×#3385	C₂	semidirect
9. C₆₁×#3383	C₂	semidirect
10. C₆₁×#3381	C₂	semidirect
11. C₆₁×#3166	C₂	semidirect
12. C₆₁×#3164	C₂	semidirect
13. C₆₁×#3163	C₂	semidirect
16. C₆₁×#3082	C₂	semidirect
17. C₆₁×#3082	C₂	semidirect
19. C₂×C₆₁×#479	C₂	semidirect
20. C₆₁×#2962	C₂	semidirect
137. #137×C₆₁	Q₈	semidirect
494. #61386	C₆₁	direct (N × H)
525. #3502	C₂×C₆₁	semidirect
526. #3390	C₂×C₆₁	semidirect
527. #3390	C₂×C₆₁	semidirect
528. #3388	C₂×C₆₁	semidirect
529. #3388	C₂×C₆₁	semidirect
530. #3387	C₂×C₆₁	semidirect
531. #3385	C₂×C₆₁	semidirect
532. #3383	C₂×C₆₁	semidirect
533. #3381	C₂×C₆₁	semidirect
534. #3166	C₂×C₆₁	semidirect
535. #3164	C₂×C₆₁	semidirect
536. #3163	C₂×C₆₁	semidirect
539. #3082	C₂×C₆₁	semidirect
540. #3082	C₂×C₆₁	semidirect
542. C₂×#479	C₂×C₆₁	semidirect
543. #2962	C₂×C₆₁	semidirect
663. C₆₁	#61386	direct (N × H)
666. #137	Q₈×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3504	2
C₆₁×#3502	2
C₆₁×#3390	2
C₆₁×#3388	2
C₆₁×#3387	2
C₆₁×#3385	2
C₆₁×#3383	2
C₆₁×#3381	2
C₆₁×#3166	2
C₆₁×#3164	2
C₆₁×#3163	2
C₆₁×#3084	2
C₆₁×#3083	2
C₆₁×#3082	2
C₆₁×#3076	2
C₂×C₆₁×#479	2
C₆₁×#2962	2
C₆₁×#2947	2
C₄×#137×C₆₁	2
#61386	61

Subgroups — C61×#61386 #29564819

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61386 #29564819