Subgroups — C₆₁×#62098 #29565531

Order 15616.

1794 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3380	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3360	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3341	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3337	C₂	1	4	yes	maximal, complemented
7	C₆₁×#3303	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3297	C₂	1	4	yes	maximal, complemented
9	C₆₁×#3247	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3246	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3233	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3230	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3106	C₂	1	2	yes	maximal, complemented
14	C₆₁×#3100	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3076	C₂	1	2	yes	maximal, complemented
16	C₂×C₆₁×#476	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#2988	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#556	—	2	1	no	—
19	C₆₁×#556	C₂²	1	1	yes	characteristic
20	C₆₁×#555	C₂²	1	1	yes	characteristic
21	C₆₁×#555	C₂²	1	2	yes	complemented
22	C₆₁×#554	C₂²	1	1	yes	characteristic
23	C₆₁×#554	C₂²	1	2	yes	complemented
24	C₆₁×#553	—	2	1	no	—
25	C₆₁×#553	C₂²	1	4	yes	—
26	C₆₁×#552	—	2	1	no	—
27	C₆₁×#552	C₂²	1	2	yes	—
28	C₆₁×#551	—	2	2	no	—
29	C₆₁×#548	—	2	2	no	—
30	C₆₁×#547	—	2	1	no	—
31	C₆₁×#547	C₂²	1	1	yes	characteristic
32	C₆₁×#546	C₂²	1	2	yes	—
33	C₆₁×#542	—	2	2	no	—
34	C₆₁×#537	—	2	1	no	—
35	C₆₁×#533	C₂²	1	1	yes	characteristic
36	C₆₁×#533	C₂²	1	2	yes	complemented
37	C₆₁×#532	C₂²	1	1	yes	characteristic
38	C₆₁×#532	C₂²	1	2	yes	complemented
39	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
40	C₆₁×#529	—	2	2	no	—
41	C₆₁×#529	C₂²	1	2	yes	—
42	C₆₁×#525	—	2	1	no	—
43	C₆₁×#520	—	2	1	no	—
44	C₄×#41×C₆₁	C₂²	1	2	yes	—
45	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
47	C₂×#117×C₆₁	—	2	1	no	—
48	C₆₁×#500	C₂²	1	2	yes	complemented
49	C₆₁×#499	C₂²	1	4	yes	complemented
50	C₆₁×#488	C₂²	1	4	yes	—
51	C₆₁×#487	C₂²	1	2	yes	complemented
52	C₆₁×#485	C₂²	1	4	yes	complemented
53	C₆₁×#484	C₂²	1	4	yes	—
54	C₆₁×#482	C₂²	1	4	yes	—
55	C₆₁×#482	C₂²	1	4	yes	complemented
56	C₆₁×#480	C₂²	1	2	yes	—
57	C₆₁×#479	C₂²	1	4	yes	complemented
58	C₆₁×#478	C₂²	1	4	yes	—
59	C₆₁×#478	C₂²	1	4	yes	complemented
60	C₆₁×#477	C₂²	1	2	yes	complemented
61	C₆₁×#477	C₂²	1	2	yes	complemented
62	C₆₁×#476	C₂²	1	2	yes	—
63	C₆₁×#476	C₂²	1	2	yes	—
64	C₆₁×#476	C₂²	1	2	yes	—
65	C₆₁×#476	C₂²	1	2	yes	—
66	C₆₁×#476	C₂²	1	2	yes	complemented
67	C₆₁×#475	C₂²	1	2	yes	complemented
68	C₆₁×#474	C₂²	1	1	yes	characteristic
69	C₆₁×#474	C₂²	1	1	yes	characteristic
70	C₆₁×#466	C₂²	1	4	yes	—
71	C₆₁×#465	C₂²	1	4	yes	—
72	C₆₁×#465	C₂²	1	4	yes	complemented
73	C₆₁×#463	C₂²	1	4	yes	—
74	C₆₁×#461	C₂²	1	2	yes	complemented
75	C₆₁×#460	C₂²	1	2	yes	complemented
76	C₆₁×#459	C₂²	1	1	yes	characteristic
77	C₆₁×#459	C₂²	1	1	yes	characteristic
78	C₆₁×#449	C₂²	1	4	yes	—
79	C₆₁×#447	C₂²	1	2	yes	—
80	C₈×Q₈×C₆₁	C₂²	1	2	yes	complemented
81	C₄×SD₁₆×C₆₁	C₂²	1	4	yes	complemented
82	C₄×D₈×C₆₁	C₂²	1	4	yes	—
83	C₄×D₈×C₆₁	C₂²	1	2	yes	—
84	C₄×D₈×C₆₁	C₂²	1	2	yes	—
85	C₈×D₄×C₆₁	C₂²	1	4	yes	—
86	C₈×D₄×C₆₁	C₂²	1	2	yes	complemented
87	C₆₁×#431	C₂²	1	1	yes	characteristic
88	C₆₁×#431	C₂²	1	2	yes	complemented
89	C₆₁×#427	C₂²	1	4	yes	complemented
90	C₂×#106×C₆₁	C₂²	1	2	yes	—
91	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
92	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	complemented
93	C₆₁×#416	C₂²	1	4	yes	—
94	C₂×#102×C₆₁	C₂²	1	2	yes	—
95	C₂×#41×C₆₁	—	2	1	no	—
96	C₂×#41×C₆₁	—	2	2	no	—
97	C₂×#41×C₆₁	D₄	1	1	yes	characteristic
98	C₂×#41×C₆₁	C₂³	1	2	yes	—
99	C₂²×Q₈×C₆₁	—	2	1	no	—
100	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₆₁	—	2	1	no	—
102	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
103	C₂×D₈×C₆₁	C₂³	1	2	yes	—
104	C₂×D₈×C₆₁	C₂³	1	2	yes	—
105	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
106	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
107	C₄⋊Q₈×C₆₁	—	2	1	no	—
108	C₄⋊Q₈×C₆₁	—	2	1	no	—
109	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
110	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
111	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
112	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
113	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
114	#127×C₆₁	C₂³	1	1	yes	characteristic
115	#126×C₆₁	—	2	4	no	—
116	#126×C₆₁	—	2	2	no	—
117	#126×C₆₁	—	2	2	no	—
118	#126×C₆₁	—	2	2	no	—
119	#125×C₆₁	—	2	2	no	—
120	#125×C₆₁	—	2	1	no	—
121	#125×C₆₁	C₂³	1	4	yes	—
122	#125×C₆₁	C₂³	1	2	yes	—
123	#124×C₆₁	—	2	4	no	—
124	#124×C₆₁	—	2	2	no	—
125	#124×C₆₁	—	2	1	no	—
126	#124×C₆₁	—	2	2	no	—
127	#124×C₆₁	C₂³	1	2	yes	—
128	#123×C₆₁	—	2	2	no	—
129	#123×C₆₁	—	2	2	no	—
130	#123×C₆₁	—	2	2	no	—
131	#123×C₆₁	—	2	4	no	—
132	#123×C₆₁	—	2	2	no	—
133	C₂²⋊Q₈×C₆₁	—	2	2	no	—
134	C₂²⋊Q₈×C₆₁	—	2	1	no	—
135	C₂²⋊Q₈×C₆₁	—	2	1	no	—
136	C₂²⋊Q₈×C₆₁	—	2	1	no	—
137	C₂²⋊Q₈×C₆₁	—	2	2	no	—
138	C₂²⋊Q₈×C₆₁	—	2	2	no	—
139	C₂²⋊Q₈×C₆₁	—	2	4	no	—
140	C₂²⋊Q₈×C₆₁	—	2	2	no	—
141	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
142	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
143	#121×C₆₁	—	2	2	no	—
144	#121×C₆₁	—	2	4	no	—
145	#121×C₆₁	—	2	1	no	—
146	#121×C₆₁	—	2	1	no	—
147	#121×C₆₁	—	2	1	no	—
148	#121×C₆₁	—	2	2	no	—
149	#121×C₆₁	—	2	2	no	—
150	#121×C₆₁	C₂³	1	2	yes	—
151	#121×C₆₁	C₂³	1	4	yes	—
152	#121×C₆₁	C₂³	1	2	yes	—
153	#120×C₆₁	—	2	2	no	—
154	C₄×Q₈×C₆₁	—	2	1	no	—
155	C₄×Q₈×C₆₁	—	2	2	no	—
156	C₄×Q₈×C₆₁	—	2	2	no	—
157	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
158	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
159	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
160	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
161	C₄×D₄×C₆₁	—	2	2	no	—
162	C₄×D₄×C₆₁	—	2	2	no	—
163	C₄×D₄×C₆₁	—	2	2	no	—
164	C₄×D₄×C₆₁	—	2	4	no	—
165	C₄×D₄×C₆₁	—	2	1	no	—
166	C₄×D₄×C₆₁	—	2	2	no	—
167	C₄×D₄×C₆₁	—	2	1	no	—
168	C₄×D₄×C₆₁	—	2	1	no	—
169	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
170	C₄×D₄×C₆₁	D₄	1	2	yes	—
171	C₄×D₄×C₆₁	C₂³	1	2	yes	—
172	C₄×D₄×C₆₁	C₂³	1	4	yes	—
173	C₄×D₄×C₆₁	C₂³	1	2	yes	—
174	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
175	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
177	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₆₁	C₂³	1	2	yes	—
179	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
180	#117×C₆₁	—	2	1	no	—
181	#117×C₆₁	—	2	1	no	—
182	#117×C₆₁	—	2	1	no	—
183	#117×C₆₁	—	2	2	no	—
184	#117×C₆₁	—	2	2	no	—
185	#117×C₆₁	—	2	2	no	—
186	#117×C₆₁	—	2	2	no	—
187	#117×C₆₁	D₄	1	2	yes	—
188	#117×C₆₁	D₄	1	1	yes	characteristic
189	#117×C₆₁	C₂³	1	4	yes	—
190	#117×C₆₁	C₂³	1	2	yes	—
191	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
192	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
193	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
194	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
195	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
198	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
199	C₂×C₄²×C₆₁	—	2	2	no	—
200	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
202	#107×C₆₁	C₂³	1	2	yes	—
203	#107×C₆₁	C₂³	1	4	yes	—
204	#107×C₆₁	C₂³	1	2	yes	—
205	#107×C₆₁	C₂³	1	4	yes	—
206	#106×C₆₁	C₂³	1	4	yes	—
207	#106×C₆₁	C₂³	1	4	yes	—
208	#106×C₆₁	C₂³	1	4	yes	—
209	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
210	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
211	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
212	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
213	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
214	#103×C₆₁	C₂³	1	4	yes	—
215	#103×C₆₁	C₂³	1	4	yes	—
216	#103×C₆₁	C₂³	1	4	yes	—
217	#102×C₆₁	C₂³	1	4	yes	—
218	#102×C₆₁	C₂³	1	4	yes	—
219	#102×C₆₁	C₂³	1	2	yes	—
220	#102×C₆₁	C₂³	1	2	yes	—
221	#102×C₆₁	C₂³	1	2	yes	—
222	#102×C₆₁	C₂³	1	2	yes	—
223	#102×C₆₁	C₂³	1	4	yes	—
224	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
225	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
226	C₄×C₈×C₆₁	C₂³	1	2	yes	—
227	C₄×C₈×C₆₁	C₂³	1	4	yes	—
228	C₂⁴×C₆₁	—	2	1	no	—
229	#41×C₆₁	—	2	4	no	—
230	#41×C₆₁	—	2	4	no	—
231	#41×C₆₁	—	4	2	no	—
232	#41×C₆₁	—	4	4	no	—
233	#41×C₆₁	—	8	4	no	—
234	C₂×Q₈×C₆₁	—	2	1	no	—
235	C₂×Q₈×C₆₁	—	2	2	no	—
236	C₂×Q₈×C₆₁	—	2	1	no	—
237	C₂×Q₈×C₆₁	—	2	2	no	—
238	C₂×Q₈×C₆₁	—	8	2	no	—
239	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
240	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
241	C₂×D₄×C₆₁	—	2	2	no	—
242	C₂×D₄×C₆₁	—	2	2	no	—
243	C₂×D₄×C₆₁	—	2	2	no	—
244	C₂×D₄×C₆₁	—	2	2	no	—
245	C₂×D₄×C₆₁	—	2	4	no	—
246	C₂×D₄×C₆₁	—	2	1	no	—
247	C₂×D₄×C₆₁	—	2	1	no	—
248	C₂×D₄×C₆₁	—	2	1	no	—
249	C₂×D₄×C₆₁	—	4	1	no	—
250	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
251	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
252	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
253	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
254	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₆₁	—	2	1	no	—
256	C₂²×C₄×C₆₁	—	2	2	no	—
257	C₂²×C₄×C₆₁	—	2	1	no	—
258	C₂²×C₄×C₆₁	—	2	2	no	—
259	C₂²×C₄×C₆₁	—	2	1	no	—
260	C₂²×C₄×C₆₁	—	2	2	no	—
261	C₂²×C₄×C₆₁	—	2	1	no	—
262	C₂²×C₄×C₆₁	—	2	1	no	—
263	C₂²×C₄×C₆₁	—	2	2	no	—
264	C₂²×C₄×C₆₁	—	2	4	no	—
265	C₂²×C₄×C₆₁	—	4	4	no	—
266	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
267	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
269	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
272	SD₁₆×C₆₁	—	4	4	no	—
273	D₈×C₆₁	—	2	4	no	—
274	D₈×C₆₁	—	4	2	no	—
275	C₂×C₈×C₆₁	—	4	4	no	—
276	C₂×C₈×C₆₁	—	4	2	no	—
277	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
278	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
279	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
280	C₄⋊C₄×C₆₁	—	2	2	no	—
281	C₄⋊C₄×C₆₁	—	2	1	no	—
282	C₄⋊C₄×C₆₁	—	2	1	no	—
283	C₄⋊C₄×C₆₁	—	2	2	no	—
284	C₄⋊C₄×C₆₁	—	2	2	no	—
285	C₄⋊C₄×C₆₁	—	2	2	no	—
286	C₄⋊C₄×C₆₁	—	2	4	no	—
287	C₄⋊C₄×C₆₁	—	2	1	no	—
288	C₄⋊C₄×C₆₁	—	2	2	no	—
289	C₄⋊C₄×C₆₁	—	2	2	no	—
290	C₄⋊C₄×C₆₁	—	2	2	no	—
291	C₄⋊C₄×C₆₁	—	2	1	no	—
292	C₄⋊C₄×C₆₁	—	2	2	no	—
293	C₄⋊C₄×C₆₁	—	2	4	no	—
294	C₄⋊C₄×C₆₁	—	2	2	no	—
295	C₄⋊C₄×C₆₁	—	2	1	no	—
296	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
297	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
298	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
300	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
301	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
302	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
303	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
304	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
305	C₂²⋊C₄×C₆₁	—	2	2	no	—
306	C₂²⋊C₄×C₆₁	—	2	2	no	—
307	C₂²⋊C₄×C₆₁	—	2	4	no	—
308	C₂²⋊C₄×C₆₁	—	2	2	no	—
309	C₂²⋊C₄×C₆₁	—	2	1	no	—
310	C₂²⋊C₄×C₆₁	—	2	2	no	—
311	C₂²⋊C₄×C₆₁	—	2	2	no	—
312	C₂²⋊C₄×C₆₁	—	2	1	no	—
313	C₂²⋊C₄×C₆₁	—	2	1	no	—
314	C₂²⋊C₄×C₆₁	—	2	1	no	—
315	C₂²⋊C₄×C₆₁	—	2	4	no	—
316	C₂²⋊C₄×C₆₁	—	2	2	no	—
317	C₂²⋊C₄×C₆₁	—	2	2	no	—
318	C₂²⋊C₄×C₆₁	—	2	2	no	—
319	C₂²⋊C₄×C₆₁	—	2	4	no	—
320	C₂²⋊C₄×C₆₁	—	2	2	no	—
321	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
322	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
323	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
324	C₄²×C₆₁	—	2	2	no	—
325	C₄²×C₆₁	—	2	2	no	—
326	C₄²×C₆₁	—	2	2	no	—
327	C₄²×C₆₁	—	2	4	no	—
328	C₄²×C₆₁	C₂×D₄	1	2	yes	—
329	C₄²×C₆₁	C₂×D₄	1	2	yes	—
330	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
333	C₄²×C₆₁	C₂⁴	1	2	yes	—
334	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
335	C₂³×C₆₁	—	2	1	no	—
336	C₂³×C₆₁	—	2	1	no	—
337	C₂³×C₆₁	—	2	2	no	—
338	C₂³×C₆₁	—	4	2	no	—
339	C₂³×C₆₁	—	4	2	no	—
340	C₂³×C₆₁	—	8	1	no	—
341	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
342	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
343	Q₈×C₆₁	—	2	2	no	—
344	Q₈×C₆₁	—	2	2	no	—
345	Q₈×C₆₁	—	2	2	no	—
346	Q₈×C₆₁	—	4	4	no	—
347	Q₈×C₆₁	—	4	2	no	—
348	Q₈×C₆₁	—	8	1	no	—
349	Q₈×C₆₁	—	8	2	no	—
350	D₄×C₆₁	—	2	4	no	—
351	D₄×C₆₁	—	2	2	no	—
352	D₄×C₆₁	—	2	2	no	—
353	D₄×C₆₁	—	2	1	no	—
354	D₄×C₆₁	—	2	1	no	—
355	D₄×C₆₁	—	2	1	no	—
356	D₄×C₆₁	—	2	2	no	—
357	D₄×C₆₁	—	4	2	no	—
358	D₄×C₆₁	—	4	2	no	—
359	D₄×C₆₁	—	4	4	no	—
360	D₄×C₆₁	—	4	4	no	—
361	D₄×C₆₁	—	4	2	no	—
362	D₄×C₆₁	—	8	2	no	—
363	D₄×C₆₁	—	8	4	no	—
364	D₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
365	C₂×C₄×C₆₁	—	2	4	no	—
366	C₂×C₄×C₆₁	—	2	1	no	—
367	C₂×C₄×C₆₁	—	2	2	no	—
368	C₂×C₄×C₆₁	—	2	1	no	—
369	C₂×C₄×C₆₁	—	2	2	no	—
370	C₂×C₄×C₆₁	—	2	1	no	—
371	C₂×C₄×C₆₁	—	2	2	no	—
372	C₂×C₄×C₆₁	—	2	2	no	—
373	C₂×C₄×C₆₁	—	2	2	no	—
374	C₂×C₄×C₆₁	—	2	4	no	—
375	C₂×C₄×C₆₁	—	2	1	no	—
376	C₂×C₄×C₆₁	—	4	1	no	—
377	C₂×C₄×C₆₁	—	4	2	no	—
378	C₂×C₄×C₆₁	—	4	4	no	—
379	C₂×C₄×C₆₁	—	4	2	no	—
380	C₂×C₄×C₆₁	—	4	2	no	—
381	C₂×C₄×C₆₁	—	4	2	no	—
382	C₂×C₄×C₆₁	—	4	2	no	—
383	C₂×C₄×C₆₁	—	4	2	no	—
384	C₂×C₄×C₆₁	—	4	4	no	—
385	C₂×C₄×C₆₁	—	8	2	no	—
386	C₂×C₄×C₆₁	—	8	4	no	—
387	C₂×C₄×C₆₁	—	8	2	no	—
388	C₂×C₄×C₆₁	#135	1	4	yes	—
389	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
390	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
391	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
395	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
398	C₈×C₆₁	—	2	2	no	—
399	C₈×C₆₁	—	2	2	no	—
400	C₈×C₆₁	—	2	4	no	—
401	#62098	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
402	C₂²×C₆₁	—	2	1	no	—
403	C₂²×C₆₁	—	2	1	no	—
404	C₂²×C₆₁	—	2	2	no	—
405	C₂²×C₆₁	—	2	2	no	—
406	C₂²×C₆₁	—	2	2	no	—
407	C₂²×C₆₁	—	2	2	no	—
408	C₂²×C₆₁	—	4	1	no	—
409	C₂²×C₆₁	—	4	1	no	—
410	C₂²×C₆₁	—	4	2	no	—
411	C₂²×C₆₁	—	4	1	no	—
412	C₂²×C₆₁	—	4	1	no	—
413	C₂²×C₆₁	—	4	2	no	—
414	C₂²×C₆₁	—	4	1	no	—
415	C₂²×C₆₁	—	4	2	no	—
416	C₂²×C₆₁	—	8	4	no	—
417	C₂²×C₆₁	C₂×#135	1	2	yes	—
418	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
419	C₄×C₆₁	—	2	1	no	—
420	C₄×C₆₁	—	2	2	no	—
421	C₄×C₆₁	—	2	1	no	—
422	C₄×C₆₁	—	2	2	no	—
423	C₄×C₆₁	—	2	1	no	—
424	C₄×C₆₁	—	2	2	no	—
425	C₄×C₆₁	—	4	4	no	—
426	C₄×C₆₁	—	4	2	no	—
427	C₄×C₆₁	—	4	2	no	—
428	C₄×C₆₁	—	4	1	no	—
429	C₄×C₆₁	—	4	1	no	—
430	C₄×C₆₁	—	4	2	no	—
431	C₄×C₆₁	C₂×#135	1	2	yes	—
432	C₄×C₆₁	C₂×#135	1	2	yes	—
433	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
434	C₄×C₆₁	#585	1	1	yes	characteristic
435	#3511	C₂×C₆₁	1	1	yes	characteristic, complemented
436	#3475	C₂×C₆₁	1	1	yes	characteristic, complemented
437	#3380	C₂×C₆₁	1	2	yes	complemented
438	#3360	C₂×C₆₁	1	2	yes	complemented
439	#3341	C₂×C₆₁	1	2	yes	complemented
440	#3337	C₂×C₆₁	1	4	yes	complemented
441	#3303	C₂×C₆₁	1	2	yes	complemented
442	#3297	C₂×C₆₁	1	4	yes	complemented
443	#3247	C₂×C₆₁	1	2	yes	complemented
444	#3246	C₂×C₆₁	1	1	yes	characteristic, complemented
445	#3233	C₂×C₆₁	1	2	yes	complemented
446	#3230	C₂×C₆₁	1	1	yes	characteristic, complemented
447	#3106	C₂×C₆₁	1	2	yes	complemented
448	#3100	C₂×C₆₁	1	1	yes	characteristic, complemented
449	#3076	C₂×C₆₁	1	2	yes	complemented
450	C₂×#476	C₂×C₆₁	1	1	yes	characteristic, complemented
451	#2988	C₂×C₆₁	1	1	yes	characteristic, complemented
452	C₂×C₆₁	—	2	2	no	—
453	C₂×C₆₁	—	4	2	no	—
454	C₂×C₆₁	—	4	2	no	—
455	C₂×C₆₁	—	8	2	no	—
456	C₂×C₆₁	—	8	1	no	—
457	C₂×C₆₁	#3489	1	1	yes	characteristic
458	C₂×C₆₁	C₂²×#135	1	1	yes	characteristic
459	C₂×C₆₁	#3585	1	1	yes	characteristic
460	#556	—	2	1	no	—
461	#556	C₂²×C₆₁	1	1	yes	characteristic
462	#555	C₂²×C₆₁	1	1	yes	characteristic
463	#555	C₂²×C₆₁	1	2	yes	complemented
464	#554	C₂²×C₆₁	1	1	yes	characteristic
465	#554	C₂²×C₆₁	1	2	yes	complemented
466	#553	—	2	1	no	—
467	#553	C₂²×C₆₁	1	4	yes	—
468	#552	—	2	1	no	—
469	#552	C₂²×C₆₁	1	2	yes	—
470	#551	—	2	2	no	—
471	#548	—	2	2	no	—
472	#547	—	2	1	no	—
473	#547	C₂²×C₆₁	1	1	yes	characteristic
474	#546	C₂²×C₆₁	1	2	yes	—
475	#542	—	2	2	no	—
476	#537	—	2	1	no	—
477	#533	C₂²×C₆₁	1	1	yes	characteristic
478	#533	C₂²×C₆₁	1	2	yes	complemented
479	#532	C₂²×C₆₁	1	1	yes	characteristic
480	#532	C₂²×C₆₁	1	2	yes	complemented
481	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
482	#529	—	2	2	no	—
483	#529	C₂²×C₆₁	1	2	yes	—
484	#525	—	2	1	no	—
485	#520	—	2	1	no	—
486	C₄×#41	C₂²×C₆₁	1	2	yes	—
487	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
488	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
489	C₂×#117	—	2	1	no	—
490	#500	C₂²×C₆₁	1	2	yes	complemented
491	#499	C₂²×C₆₁	1	4	yes	complemented
492	#488	C₂²×C₆₁	1	4	yes	—
493	#487	C₂²×C₆₁	1	2	yes	complemented
494	#485	C₂²×C₆₁	1	4	yes	complemented
495	#484	C₂²×C₆₁	1	4	yes	—
496	#482	C₂²×C₆₁	1	4	yes	—
497	#482	C₂²×C₆₁	1	4	yes	complemented
498	#480	C₂²×C₆₁	1	2	yes	—
499	#479	C₂²×C₆₁	1	4	yes	complemented
500	#478	C₂²×C₆₁	1	4	yes	—
501	#478	C₂²×C₆₁	1	4	yes	complemented
502	#477	C₂²×C₆₁	1	2	yes	complemented
503	#477	C₂²×C₆₁	1	2	yes	complemented
504	#476	C₂²×C₆₁	1	2	yes	—
505	#476	C₂²×C₆₁	1	2	yes	—
506	#476	C₂²×C₆₁	1	2	yes	—
507	#476	C₂²×C₆₁	1	2	yes	—
508	#476	C₂²×C₆₁	1	2	yes	complemented
509	#475	C₂²×C₆₁	1	2	yes	complemented
510	#474	C₂²×C₆₁	1	1	yes	characteristic
511	#474	C₂²×C₆₁	1	1	yes	characteristic
512	#466	C₂²×C₆₁	1	4	yes	—
513	#465	C₂²×C₆₁	1	4	yes	—
514	#465	C₂²×C₆₁	1	4	yes	complemented
515	#463	C₂²×C₆₁	1	4	yes	—
516	#461	C₂²×C₆₁	1	2	yes	complemented
517	#460	C₂²×C₆₁	1	2	yes	complemented
518	#459	C₂²×C₆₁	1	1	yes	characteristic
519	#459	C₂²×C₆₁	1	1	yes	characteristic
520	#449	C₂²×C₆₁	1	4	yes	—
521	#447	C₂²×C₆₁	1	2	yes	—
522	C₈×Q₈	C₂²×C₆₁	1	2	yes	complemented
523	C₄×SD₁₆	C₂²×C₆₁	1	4	yes	complemented
524	C₄×D₈	C₂²×C₆₁	1	2	yes	—
525	C₄×D₈	C₂²×C₆₁	1	2	yes	—
526	C₄×D₈	C₂²×C₆₁	1	4	yes	—
527	C₈×D₄	C₂²×C₆₁	1	4	yes	—
528	C₈×D₄	C₂²×C₆₁	1	2	yes	complemented
529	#431	C₂²×C₆₁	1	1	yes	characteristic
530	#431	C₂²×C₆₁	1	2	yes	complemented
531	#427	C₂²×C₆₁	1	4	yes	complemented
532	C₂×#106	C₂²×C₆₁	1	2	yes	—
533	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
534	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	complemented
535	#416	C₂²×C₆₁	1	4	yes	—
536	C₂×#102	C₂²×C₆₁	1	2	yes	—
537	C₆₁	#62098	1	1	yes	characteristic, direct product factor, Sylow
538	C₂×#41	—	2	1	no	—
539	C₂×#41	—	2	2	no	—
540	C₂×#41	D₄×C₆₁	1	1	yes	characteristic
541	C₂×#41	C₂³×C₆₁	1	2	yes	—
542	C₂²×Q₈	—	2	1	no	—
543	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
544	C₂³×C₄	—	2	1	no	—
545	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
546	C₂×D₈	C₂³×C₆₁	1	2	yes	—
547	C₂×D₈	C₂³×C₆₁	1	2	yes	—
548	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
549	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
550	C₄⋊Q₈	—	2	1	no	—
551	C₄⋊Q₈	—	2	1	no	—
552	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
553	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
554	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
555	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
556	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
557	#127	C₂³×C₆₁	1	1	yes	characteristic
558	#126	—	2	2	no	—
559	#126	—	2	4	no	—
560	#126	—	2	2	no	—
561	#126	—	2	2	no	—
562	#125	—	2	2	no	—
563	#125	—	2	1	no	—
564	#125	C₂³×C₆₁	1	2	yes	—
565	#125	C₂³×C₆₁	1	4	yes	—
566	#124	—	2	2	no	—
567	#124	—	2	4	no	—
568	#124	—	2	1	no	—
569	#124	—	2	2	no	—
570	#124	C₂³×C₆₁	1	2	yes	—
571	#123	—	2	2	no	—
572	#123	—	2	2	no	—
573	#123	—	2	2	no	—
574	#123	—	2	2	no	—
575	#123	—	2	4	no	—
576	C₂²⋊Q₈	—	2	1	no	—
577	C₂²⋊Q₈	—	2	1	no	—
578	C₂²⋊Q₈	—	2	2	no	—
579	C₂²⋊Q₈	—	2	1	no	—
580	C₂²⋊Q₈	—	2	2	no	—
581	C₂²⋊Q₈	—	2	2	no	—
582	C₂²⋊Q₈	—	2	2	no	—
583	C₂²⋊Q₈	—	2	4	no	—
584	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
585	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
586	#121	—	2	1	no	—
587	#121	—	2	1	no	—
588	#121	—	2	2	no	—
589	#121	—	2	4	no	—
590	#121	—	2	1	no	—
591	#121	—	2	2	no	—
592	#121	—	2	2	no	—
593	#121	C₂³×C₆₁	1	2	yes	—
594	#121	C₂³×C₆₁	1	2	yes	—
595	#121	C₂³×C₆₁	1	4	yes	—
596	#120	—	2	2	no	—
597	C₄×Q₈	—	2	2	no	—
598	C₄×Q₈	—	2	1	no	—
599	C₄×Q₈	—	2	2	no	—
600	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
601	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
602	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
603	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	—	2	2	no	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	—	2	4	no	—
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
613	C₄×D₄	D₄×C₆₁	1	2	yes	—
614	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
615	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
616	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
617	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
618	C₄×D₄	C₂³×C₆₁	1	2	yes	—
619	C₄×D₄	C₂³×C₆₁	1	2	yes	—
620	C₄×D₄	C₂³×C₆₁	1	4	yes	—
621	C₄×D₄	C₂³×C₆₁	1	2	yes	—
622	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
623	#117	—	2	1	no	—
624	#117	—	2	1	no	—
625	#117	—	2	1	no	—
626	#117	—	2	2	no	—
627	#117	—	2	2	no	—
628	#117	—	2	2	no	—
629	#117	—	2	2	no	—
630	#117	D₄×C₆₁	1	1	yes	characteristic
631	#117	D₄×C₆₁	1	2	yes	—
632	#117	C₂³×C₆₁	1	2	yes	—
633	#117	C₂³×C₆₁	1	4	yes	—
634	C₂×C₄⋊C₄	—	2	1	no	—
635	C₂×C₄⋊C₄	—	2	1	no	—
636	C₂×C₄⋊C₄	—	2	1	no	—
637	C₂×C₄⋊C₄	—	2	2	no	—
638	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
640	C₂×C₂²⋊C₄	—	2	1	no	—
641	C₂×C₂²⋊C₄	—	2	2	no	—
642	C₂×C₄²	—	2	2	no	—
643	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
644	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
645	#107	C₂³×C₆₁	1	2	yes	—
646	#107	C₂³×C₆₁	1	4	yes	—
647	#107	C₂³×C₆₁	1	2	yes	—
648	#107	C₂³×C₆₁	1	4	yes	—
649	#106	C₂³×C₆₁	1	4	yes	—
650	#106	C₂³×C₆₁	1	4	yes	—
651	#106	C₂³×C₆₁	1	4	yes	—
652	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
653	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
654	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
655	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
656	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
657	#103	C₂³×C₆₁	1	4	yes	—
658	#103	C₂³×C₆₁	1	4	yes	—
659	#103	C₂³×C₆₁	1	4	yes	—
660	#102	C₂³×C₆₁	1	4	yes	—
661	#102	C₂³×C₆₁	1	4	yes	—
662	#102	C₂³×C₆₁	1	2	yes	—
663	#102	C₂³×C₆₁	1	2	yes	—
664	#102	C₂³×C₆₁	1	2	yes	—
665	#102	C₂³×C₆₁	1	2	yes	—
666	#102	C₂³×C₆₁	1	4	yes	—
667	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
668	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
669	C₄×C₈	C₂³×C₆₁	1	2	yes	—
670	C₄×C₈	C₂³×C₆₁	1	4	yes	—
671	C₂⁴	—	2	1	no	—
672	#41	—	2	4	no	—
673	#41	—	2	4	no	—
674	#41	—	4	2	no	—
675	#41	—	4	4	no	—
676	#41	—	8	4	no	—
677	C₂×Q₈	—	2	1	no	—
678	C₂×Q₈	—	2	2	no	—
679	C₂×Q₈	—	2	1	no	—
680	C₂×Q₈	—	2	2	no	—
681	C₂×Q₈	—	8	2	no	—
682	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
683	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	2	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	2	1	no	—
690	C₂×D₄	—	2	1	no	—
691	C₂×D₄	—	2	1	no	—
692	C₂×D₄	—	4	1	no	—
693	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
694	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
695	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
696	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
697	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
698	C₂²×C₄	—	2	1	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	1	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	1	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	4	no	—
708	C₂²×C₄	—	4	4	no	—
709	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
710	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
711	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
712	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
713	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
714	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
715	SD₁₆	—	4	4	no	—
716	D₈	—	2	4	no	—
717	D₈	—	4	2	no	—
718	C₂×C₈	—	4	4	no	—
719	C₂×C₈	—	4	2	no	—
720	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
721	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
722	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	4	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
740	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
741	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
742	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
743	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
744	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
745	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
746	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
747	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	1	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	1	no	—
756	C₂²⋊C₄	—	2	1	no	—
757	C₂²⋊C₄	—	2	1	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
765	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
766	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
767	C₄²	—	2	2	no	—
768	C₄²	—	2	2	no	—
769	C₄²	—	2	2	no	—
770	C₄²	—	2	4	no	—
771	C₄²	C₂×D₄×C₆₁	1	2	yes	—
772	C₄²	C₂×D₄×C₆₁	1	2	yes	—
773	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
774	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
775	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
776	C₄²	C₂⁴×C₆₁	1	2	yes	—
777	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
778	C₂³	—	2	1	no	—
779	C₂³	—	2	1	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	4	2	no	—
782	C₂³	—	4	2	no	—
783	C₂³	—	8	1	no	—
784	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
785	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
786	Q₈	—	2	2	no	—
787	Q₈	—	2	2	no	—
788	Q₈	—	2	2	no	—
789	Q₈	—	4	4	no	—
790	Q₈	—	4	2	no	—
791	Q₈	—	8	1	no	—
792	Q₈	—	8	2	no	—
793	D₄	—	2	4	no	—
794	D₄	—	2	2	no	—
795	D₄	—	2	2	no	—
796	D₄	—	2	1	no	—
797	D₄	—	2	1	no	—
798	D₄	—	2	1	no	—
799	D₄	—	2	2	no	—
800	D₄	—	4	2	no	—
801	D₄	—	4	2	no	—
802	D₄	—	4	4	no	—
803	D₄	—	4	4	no	—
804	D₄	—	4	2	no	—
805	D₄	—	8	2	no	—
806	D₄	—	8	4	no	—
807	D₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
808	C₂×C₄	—	2	4	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	4	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	4	1	no	—
820	C₂×C₄	—	4	2	no	—
821	C₂×C₄	—	4	4	no	—
822	C₂×C₄	—	4	2	no	—
823	C₂×C₄	—	4	2	no	—
824	C₂×C₄	—	4	2	no	—
825	C₂×C₄	—	4	2	no	—
826	C₂×C₄	—	4	2	no	—
827	C₂×C₄	—	4	4	no	—
828	C₂×C₄	—	8	2	no	—
829	C₂×C₄	—	8	4	no	—
830	C₂×C₄	—	8	2	no	—
831	C₂×C₄	#135×C₆₁	1	4	yes	—
832	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
833	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
834	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
835	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
836	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
837	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
838	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
839	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
840	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
841	C₈	—	2	2	no	—
842	C₈	—	2	2	no	—
843	C₈	—	2	4	no	—
844	C₂²	—	2	1	no	—
845	C₂²	—	2	1	no	—
846	C₂²	—	2	2	no	—
847	C₂²	—	2	2	no	—
848	C₂²	—	2	2	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	4	1	no	—
851	C₂²	—	4	1	no	—
852	C₂²	—	4	1	no	—
853	C₂²	—	4	2	no	—
854	C₂²	—	4	2	no	—
855	C₂²	—	4	1	no	—
856	C₂²	—	4	1	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	8	4	no	—
859	C₂²	C₂×#135×C₆₁	1	2	yes	—
860	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
861	C₄	—	2	2	no	—
862	C₄	—	2	1	no	—
863	C₄	—	2	2	no	—
864	C₄	—	2	1	no	—
865	C₄	—	2	2	no	—
866	C₄	—	2	1	no	—
867	C₄	—	4	1	no	—
868	C₄	—	4	1	no	—
869	C₄	—	4	2	no	—
870	C₄	—	4	4	no	—
871	C₄	—	4	2	no	—
872	C₄	—	4	2	no	—
873	C₄	C₂×#135×C₆₁	1	2	yes	—
874	C₄	C₂×#135×C₆₁	1	2	yes	—
875	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
876	C₄	C₆₁×#585	1	1	yes	characteristic
877	C₂	—	2	2	no	—
878	C₂	—	4	2	no	—
879	C₂	—	4	2	no	—
880	C₂	—	8	1	no	—
881	C₂	—	8	2	no	—
882	C₂	C₆₁×#3489	1	1	yes	characteristic
883	C₂	C₂²×#135×C₆₁	1	1	yes	characteristic
884	C₂	C₆₁×#3585	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3511	C₂	semidirect
2. C₆₁×#3475	C₂	semidirect
3. C₆₁×#3380	C₂	semidirect
4. C₆₁×#3360	C₂	semidirect
5. C₆₁×#3341	C₂	semidirect
6. C₆₁×#3337	C₂	semidirect
7. C₆₁×#3303	C₂	semidirect
8. C₆₁×#3297	C₂	semidirect
9. C₆₁×#3247	C₂	semidirect
10. C₆₁×#3246	C₂	semidirect
11. C₆₁×#3233	C₂	semidirect
12. C₆₁×#3230	C₂	semidirect
13. C₆₁×#3106	C₂	semidirect
14. C₆₁×#3100	C₂	semidirect
15. C₆₁×#3076	C₂	semidirect
16. C₂×C₆₁×#476	C₂	semidirect
17. C₆₁×#2988	C₂	semidirect
21. C₆₁×#555	C₂²	semidirect
23. C₆₁×#554	C₂²	semidirect
36. C₆₁×#533	C₂²	semidirect
38. C₆₁×#532	C₂²	semidirect
48. C₆₁×#500	C₂²	semidirect
49. C₆₁×#499	C₂²	semidirect
51. C₆₁×#487	C₂²	semidirect
52. C₆₁×#485	C₂²	semidirect
55. C₆₁×#482	C₂²	semidirect
57. C₆₁×#479	C₂²	semidirect
59. C₆₁×#478	C₂²	semidirect
60. C₆₁×#477	C₂²	semidirect
61. C₆₁×#477	C₂²	semidirect
66. C₆₁×#476	C₂²	semidirect
67. C₆₁×#475	C₂²	semidirect
72. C₆₁×#465	C₂²	semidirect
74. C₆₁×#461	C₂²	semidirect
75. C₆₁×#460	C₂²	semidirect
80. C₈×Q₈×C₆₁	C₂²	semidirect
81. C₄×SD₁₆×C₆₁	C₂²	semidirect
86. C₈×D₄×C₆₁	C₂²	semidirect
88. C₆₁×#431	C₂²	semidirect
89. C₆₁×#427	C₂²	semidirect
92. C₂×C₄⋊C₈×C₆₁	C₂²	semidirect
401. #62098	C₆₁	direct (N × H)
435. #3511	C₂×C₆₁	semidirect
436. #3475	C₂×C₆₁	semidirect
437. #3380	C₂×C₆₁	semidirect
438. #3360	C₂×C₆₁	semidirect
439. #3341	C₂×C₆₁	semidirect
440. #3337	C₂×C₆₁	semidirect
441. #3303	C₂×C₆₁	semidirect
442. #3297	C₂×C₆₁	semidirect
443. #3247	C₂×C₆₁	semidirect
444. #3246	C₂×C₆₁	semidirect
445. #3233	C₂×C₆₁	semidirect
446. #3230	C₂×C₆₁	semidirect
447. #3106	C₂×C₆₁	semidirect
448. #3100	C₂×C₆₁	semidirect
449. #3076	C₂×C₆₁	semidirect
450. C₂×#476	C₂×C₆₁	semidirect
451. #2988	C₂×C₆₁	semidirect
463. #555	C₂²×C₆₁	semidirect
465. #554	C₂²×C₆₁	semidirect
478. #533	C₂²×C₆₁	semidirect
480. #532	C₂²×C₆₁	semidirect
490. #500	C₂²×C₆₁	semidirect
491. #499	C₂²×C₆₁	semidirect
493. #487	C₂²×C₆₁	semidirect
494. #485	C₂²×C₆₁	semidirect
497. #482	C₂²×C₆₁	semidirect
499. #479	C₂²×C₆₁	semidirect
501. #478	C₂²×C₆₁	semidirect
502. #477	C₂²×C₆₁	semidirect
503. #477	C₂²×C₆₁	semidirect
508. #476	C₂²×C₆₁	semidirect
509. #475	C₂²×C₆₁	semidirect
514. #465	C₂²×C₆₁	semidirect
516. #461	C₂²×C₆₁	semidirect
517. #460	C₂²×C₆₁	semidirect
522. C₈×Q₈	C₂²×C₆₁	semidirect
523. C₄×SD₁₆	C₂²×C₆₁	semidirect
528. C₈×D₄	C₂²×C₆₁	semidirect
530. #431	C₂²×C₆₁	semidirect
531. #427	C₂²×C₆₁	semidirect
534. C₂×C₄⋊C₈	C₂²×C₆₁	semidirect
537. C₆₁	#62098	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×#3511	2
C₆₁×#3475	2
C₆₁×#3380	2
C₆₁×#3360	2
C₆₁×#3341	2
C₆₁×#3337	2
C₆₁×#3303	2
C₆₁×#3297	2
C₆₁×#3247	2
C₆₁×#3246	2
C₆₁×#3233	2
C₆₁×#3230	2
C₆₁×#3106	2
C₆₁×#3100	2
C₆₁×#3076	2
C₂×C₆₁×#476	2
C₆₁×#2988	2
#62098	61

Subgroups — C61×#62098 #29565531

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62098 #29565531