Subgroups — C₆₁×#62103 #29565536

Order 15616.

1804 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3515	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3481	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3381	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3380	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3339	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3338	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#3337	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3335	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3297	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3296	C₂	1	2	yes	maximal, complemented
13	C₆₁×#3295	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3250	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3247	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3232	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#3105	C₂	1	2	yes	maximal, complemented
20	C₆₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₆₁×#478	C₂	1	2	yes	maximal, complemented
23	C₆₁×#2988	C₂	1	1	yes	maximal, characteristic, complemented
24	C₆₁×#559	C₂²	1	1	yes	characteristic
25	C₆₁×#557	C₂²	1	1	yes	characteristic, complemented
26	C₆₁×#554	C₂²	1	1	yes	characteristic
27	C₆₁×#554	C₂²	1	1	yes	characteristic
28	C₆₁×#554	C₂²	1	1	yes	characteristic
29	C₆₁×#554	C₂²	1	1	yes	characteristic, complemented
30	C₆₁×#553	—	2	1	no	—
31	C₆₁×#553	C₂²	1	2	yes	—
32	C₆₁×#553	C₂²	1	2	yes	complemented
33	C₆₁×#552	—	2	2	no	—
34	C₆₁×#552	—	2	1	no	—
35	C₆₁×#552	C₂²	1	2	yes	complemented
36	C₆₁×#551	—	2	2	no	—
37	C₆₁×#547	—	2	1	no	—
38	C₆₁×#547	C₂²	1	1	yes	characteristic
39	C₆₁×#546	—	2	1	no	—
40	C₆₁×#546	C₂²	1	2	yes	—
41	D₄²×C₆₁	C₂²	1	1	yes	characteristic
42	C₆₁×#541	—	2	1	no	—
43	C₆₁×#539	—	2	2	no	—
44	C₆₁×#533	C₂²	1	1	yes	characteristic, complemented
45	C₆₁×#532	C₂²	1	1	yes	characteristic
46	C₆₁×#529	—	2	1	no	—
47	C₆₁×#529	C₂²	1	2	yes	—
48	C₆₁×#529	C₂²	1	1	yes	characteristic, complemented
49	C₆₁×#529	C₂²	1	2	yes	complemented
50	C₂×#125×C₆₁	C₂²	1	2	yes	complemented
51	C₆₁×#525	—	2	2	no	—
52	C₆₁×#520	—	2	1	no	—
53	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
54	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄×C₆₁	—	2	1	no	—
56	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
57	C₆₁×#500	C₂²	1	1	yes	characteristic, complemented
58	C₆₁×#499	C₂²	1	2	yes	complemented
59	C₆₁×#499	C₂²	1	2	yes	complemented
60	C₆₁×#498	C₂²	1	1	yes	characteristic, complemented
61	C₆₁×#488	C₂²	1	2	yes	complemented
62	C₆₁×#488	C₂²	1	2	yes	complemented
63	C₆₁×#486	C₂²	1	1	yes	characteristic
64	C₆₁×#486	C₂²	1	1	yes	characteristic
65	C₆₁×#485	C₂²	1	1	yes	characteristic, complemented
66	C₆₁×#484	C₂²	1	2	yes	complemented
67	C₆₁×#484	C₂²	1	2	yes	complemented
68	C₆₁×#483	C₂²	1	2	yes	complemented
69	C₆₁×#482	C₂²	1	2	yes	complemented
70	C₆₁×#482	C₂²	1	2	yes	complemented
71	C₆₁×#482	C₂²	1	1	yes	characteristic, complemented
72	C₆₁×#481	C₂²	1	2	yes	—
73	C₆₁×#481	C₂²	1	2	yes	complemented
74	C₆₁×#480	C₂²	1	2	yes	—
75	C₆₁×#479	C₂²	1	2	yes	complemented
76	C₆₁×#479	C₂²	1	2	yes	complemented
77	C₆₁×#479	C₂²	1	1	yes	characteristic, complemented
78	C₆₁×#478	C₂²	1	2	yes	—
79	C₆₁×#478	C₂²	1	2	yes	—
80	C₆₁×#478	C₂²	1	1	yes	characteristic
81	C₆₁×#478	C₂²	1	2	yes	—
82	C₆₁×#478	C₂²	1	2	yes	complemented
83	C₆₁×#478	C₂²	1	2	yes	complemented
84	C₆₁×#478	C₂²	1	2	yes	complemented
85	C₆₁×#478	C₂²	1	2	yes	complemented
86	C₆₁×#478	C₂²	1	2	yes	complemented
87	C₆₁×#478	C₂²	1	2	yes	complemented
88	C₆₁×#477	C₂²	1	1	yes	characteristic, complemented
89	C₆₁×#477	C₂²	1	1	yes	characteristic, complemented
90	C₆₁×#476	C₂²	1	1	yes	characteristic
91	C₆₁×#476	C₂²	1	1	yes	characteristic, complemented
92	C₆₁×#475	C₂²	1	1	yes	characteristic, complemented
93	C₆₁×#474	C₂²	1	1	yes	characteristic
94	C₆₁×#467	C₂²	1	2	yes	complemented
95	C₆₁×#466	C₂²	1	2	yes	—
96	C₆₁×#466	C₂²	1	2	yes	complemented
97	C₆₁×#465	C₂²	1	2	yes	—
98	C₆₁×#465	C₂²	1	2	yes	complemented
99	C₆₁×#465	C₂²	1	2	yes	complemented
100	C₆₁×#464	C₂²	1	2	yes	complemented
101	C₆₁×#464	C₂²	1	1	yes	characteristic, complemented
102	C₆₁×#463	C₂²	1	1	yes	characteristic
103	C₆₁×#463	C₂²	1	2	yes	complemented
104	C₆₁×#463	C₂²	1	2	yes	complemented
105	C₆₁×#460	C₂²	1	1	yes	characteristic
106	C₆₁×#459	C₂²	1	1	yes	characteristic
107	C₆₁×#452	C₂²	1	1	yes	characteristic
108	C₆₁×#450	C₂²	1	2	yes	—
109	C₆₁×#449	C₂²	1	1	yes	characteristic
110	C₆₁×#447	C₂²	1	2	yes	—
111	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
113	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
114	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
115	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
116	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
117	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
118	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
119	C₄×D₈×C₆₁	C₂²	1	2	yes	—
120	C₄×D₈×C₆₁	C₂²	1	2	yes	complemented
121	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
122	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
123	C₈×D₄×C₆₁	C₂²	1	2	yes	complemented
124	C₈×D₄×C₆₁	C₂²	1	2	yes	complemented
125	C₆₁×#431	C₂²	1	1	yes	characteristic, complemented
126	C₆₁×#431	C₂²	1	2	yes	complemented
127	C₆₁×#427	C₂²	1	2	yes	complemented
128	C₂×#107×C₆₁	C₂²	1	2	yes	complemented
129	C₂×#106×C₆₁	C₂²	1	2	yes	complemented
130	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	complemented
131	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
132	C₆₁×#416	C₂²	1	2	yes	—
133	C₂×#102×C₆₁	C₂²	1	2	yes	—
134	C₂×#102×C₆₁	C₂²	1	2	yes	—
135	C₂×#41×C₆₁	—	2	1	no	—
136	C₂×#41×C₆₁	—	2	1	no	—
137	C₂×#41×C₆₁	D₄	1	1	yes	characteristic
138	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
139	C₂²×D₄×C₆₁	—	2	1	no	—
140	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
141	C₂³×C₄×C₆₁	—	2	2	no	—
142	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
146	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
147	C₂×D₈×C₆₁	C₂³	1	2	yes	—
148	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
149	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
150	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
151	C₄⋊Q₈×C₆₁	—	2	1	no	—
152	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
153	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
154	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
155	#127×C₆₁	C₂³	1	1	yes	characteristic
156	#126×C₆₁	—	2	2	no	—
157	#126×C₆₁	—	2	2	no	—
158	#126×C₆₁	—	2	2	no	—
159	#126×C₆₁	—	2	2	no	—
160	#126×C₆₁	—	2	2	no	—
161	#126×C₆₁	—	2	1	no	—
162	#125×C₆₁	—	2	2	no	—
163	#125×C₆₁	—	2	2	no	—
164	#125×C₆₁	—	2	1	no	—
165	#125×C₆₁	—	2	1	no	—
166	#125×C₆₁	—	2	2	no	—
167	#125×C₆₁	—	2	2	no	—
168	#125×C₆₁	C₂³	1	2	yes	—
169	#125×C₆₁	C₂³	1	2	yes	—
170	#125×C₆₁	C₂³	1	2	yes	—
171	#125×C₆₁	C₂³	1	2	yes	—
172	#125×C₆₁	C₂³	1	1	yes	characteristic
173	#124×C₆₁	—	2	1	no	—
174	#124×C₆₁	—	2	1	no	—
175	#124×C₆₁	C₂³	1	2	yes	—
176	#124×C₆₁	C₂³	1	1	yes	characteristic
177	#123×C₆₁	—	2	2	no	—
178	#123×C₆₁	—	2	1	no	—
179	#123×C₆₁	—	2	2	no	—
180	#123×C₆₁	—	2	2	no	—
181	#123×C₆₁	—	2	2	no	—
182	#123×C₆₁	—	2	2	no	—
183	#123×C₆₁	—	2	2	no	—
184	#123×C₆₁	—	2	2	no	—
185	#123×C₆₁	—	2	2	no	—
186	C₂²⋊Q₈×C₆₁	—	2	1	no	—
187	C₂²⋊Q₈×C₆₁	—	2	1	no	—
188	C₂²⋊Q₈×C₆₁	—	2	1	no	—
189	C₂²⋊Q₈×C₆₁	—	2	1	no	—
190	C₂²⋊Q₈×C₆₁	—	2	2	no	—
191	C₂²⋊Q₈×C₆₁	—	2	1	no	—
192	C₂²⋊Q₈×C₆₁	—	2	2	no	—
193	C₂²⋊Q₈×C₆₁	—	2	2	no	—
194	C₂²⋊Q₈×C₆₁	—	2	2	no	—
195	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
196	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
197	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
198	#121×C₆₁	—	2	2	no	—
199	#121×C₆₁	—	2	2	no	—
200	#121×C₆₁	—	2	1	no	—
201	#121×C₆₁	—	2	1	no	—
202	#121×C₆₁	—	2	2	no	—
203	#121×C₆₁	C₂³	1	2	yes	—
204	#121×C₆₁	C₂³	1	2	yes	—
205	#121×C₆₁	C₂³	1	2	yes	—
206	#121×C₆₁	C₂³	1	1	yes	characteristic
207	#120×C₆₁	—	2	2	no	—
208	#120×C₆₁	—	2	2	no	—
209	C₄×Q₈×C₆₁	—	2	1	no	—
210	C₄×Q₈×C₆₁	—	2	1	no	—
211	C₄×Q₈×C₆₁	—	2	1	no	—
212	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
213	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
214	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
215	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
216	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
218	C₄×D₄×C₆₁	—	2	1	no	—
219	C₄×D₄×C₆₁	—	2	1	no	—
220	C₄×D₄×C₆₁	—	2	2	no	—
221	C₄×D₄×C₆₁	—	2	1	no	—
222	C₄×D₄×C₆₁	—	2	1	no	—
223	C₄×D₄×C₆₁	—	2	2	no	—
224	C₄×D₄×C₆₁	—	2	1	no	—
225	C₄×D₄×C₆₁	—	2	1	no	—
226	C₄×D₄×C₆₁	—	2	2	no	—
227	C₄×D₄×C₆₁	—	2	2	no	—
228	C₄×D₄×C₆₁	—	2	1	no	—
229	C₄×D₄×C₆₁	—	2	2	no	—
230	C₄×D₄×C₆₁	—	2	2	no	—
231	C₄×D₄×C₆₁	D₄	1	2	yes	—
232	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
233	C₄×D₄×C₆₁	C₂³	1	2	yes	—
234	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₆₁	C₂³	1	2	yes	—
236	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₆₁	C₂³	1	2	yes	—
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	#117×C₆₁	—	2	2	no	—
243	#117×C₆₁	—	2	1	no	—
244	#117×C₆₁	—	2	1	no	—
245	#117×C₆₁	—	2	2	no	—
246	#117×C₆₁	—	2	2	no	—
247	#117×C₆₁	D₄	1	2	yes	—
248	#117×C₆₁	D₄	1	1	yes	characteristic
249	#117×C₆₁	C₂³	1	2	yes	—
250	#117×C₆₁	C₂³	1	1	yes	characteristic
251	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
252	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
253	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
254	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
255	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
258	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
259	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
260	C₂×C₄²×C₆₁	—	2	1	no	—
261	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
262	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
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	2	yes	—
268	#107×C₆₁	C₂³	1	2	yes	—
269	#107×C₆₁	C₂³	1	1	yes	characteristic
270	#106×C₆₁	C₂³	1	1	yes	characteristic
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	2	yes	—
276	#106×C₆₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
288	#103×C₆₁	C₂³	1	1	yes	characteristic
289	#103×C₆₁	C₂³	1	1	yes	characteristic
290	#103×C₆₁	C₂³	1	1	yes	characteristic
291	#102×C₆₁	C₂³	1	1	yes	characteristic
292	#102×C₆₁	C₂³	1	1	yes	characteristic
293	#102×C₆₁	C₂³	1	2	yes	—
294	#102×C₆₁	C₂³	1	2	yes	—
295	#102×C₆₁	C₂³	1	2	yes	—
296	#102×C₆₁	C₂³	1	2	yes	—
297	#102×C₆₁	C₂³	1	2	yes	—
298	#102×C₆₁	C₂³	1	2	yes	—
299	#102×C₆₁	C₂³	1	2	yes	—
300	#102×C₆₁	C₂³	1	1	yes	characteristic
301	#102×C₆₁	C₂³	1	1	yes	characteristic
302	#102×C₆₁	C₂³	1	2	yes	—
303	#102×C₆₁	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
307	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
308	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₆₁	C₂³	1	2	yes	—
311	C₄×C₈×C₆₁	C₂³	1	2	yes	—
312	C₂⁴×C₆₁	—	2	2	no	—
313	#41×C₆₁	—	2	4	no	—
314	#41×C₆₁	—	2	2	no	—
315	#41×C₆₁	—	4	1	no	—
316	#41×C₆₁	—	4	4	no	—
317	#41×C₆₁	—	8	2	no	—
318	C₂×Q₈×C₆₁	—	2	1	no	—
319	C₂×Q₈×C₆₁	—	2	1	no	—
320	C₂×Q₈×C₆₁	—	2	1	no	—
321	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
322	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
323	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
324	C₂×D₄×C₆₁	—	2	4	no	—
325	C₂×D₄×C₆₁	—	2	1	no	—
326	C₂×D₄×C₆₁	—	2	2	no	—
327	C₂×D₄×C₆₁	—	2	2	no	—
328	C₂×D₄×C₆₁	—	2	1	no	—
329	C₂×D₄×C₆₁	—	2	2	no	—
330	C₂×D₄×C₆₁	—	2	2	no	—
331	C₂×D₄×C₆₁	—	2	1	no	—
332	C₂×D₄×C₆₁	—	2	1	no	—
333	C₂×D₄×C₆₁	—	4	2	no	—
334	C₂×D₄×C₆₁	—	4	4	no	—
335	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
336	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
337	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
338	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
339	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₆₁	—	2	2	no	—
341	C₂²×C₄×C₆₁	—	2	2	no	—
342	C₂²×C₄×C₆₁	—	2	2	no	—
343	C₂²×C₄×C₆₁	—	2	1	no	—
344	C₂²×C₄×C₆₁	—	2	1	no	—
345	C₂²×C₄×C₆₁	—	2	1	no	—
346	C₂²×C₄×C₆₁	—	2	1	no	—
347	C₂²×C₄×C₆₁	—	2	2	no	—
348	C₂²×C₄×C₆₁	—	2	2	no	—
349	C₂²×C₄×C₆₁	—	2	2	no	—
350	C₂²×C₄×C₆₁	—	2	2	no	—
351	C₂²×C₄×C₆₁	—	8	4	no	—
352	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
353	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
354	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
355	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
357	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
358	Q₁₆×C₆₁	—	4	1	no	—
359	SD₁₆×C₆₁	—	2	2	no	—
360	SD₁₆×C₆₁	—	4	1	no	—
361	SD₁₆×C₆₁	—	4	2	no	—
362	D₈×C₆₁	—	2	2	no	—
363	D₈×C₆₁	—	4	2	no	—
364	C₂×C₈×C₆₁	—	4	2	no	—
365	C₂×C₈×C₆₁	—	4	2	no	—
366	C₂×C₈×C₆₁	—	4	2	no	—
367	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
368	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
372	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
373	C₄⋊C₄×C₆₁	—	2	2	no	—
374	C₄⋊C₄×C₆₁	—	2	1	no	—
375	C₄⋊C₄×C₆₁	—	2	1	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	1	no	—
380	C₄⋊C₄×C₆₁	—	2	2	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	2	no	—
386	C₄⋊C₄×C₆₁	—	2	2	no	—
387	C₄⋊C₄×C₆₁	—	2	1	no	—
388	C₄⋊C₄×C₆₁	—	2	1	no	—
389	C₄⋊C₄×C₆₁	—	2	1	no	—
390	C₄⋊C₄×C₆₁	—	2	2	no	—
391	C₄⋊C₄×C₆₁	—	2	2	no	—
392	C₄⋊C₄×C₆₁	—	2	2	no	—
393	C₄⋊C₄×C₆₁	—	2	1	no	—
394	C₄⋊C₄×C₆₁	—	2	1	no	—
395	C₄⋊C₄×C₆₁	—	2	2	no	—
396	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
397	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
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	1	yes	characteristic
403	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
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	1	no	—
413	C₂²⋊C₄×C₆₁	—	2	2	no	—
414	C₂²⋊C₄×C₆₁	—	2	2	no	—
415	C₂²⋊C₄×C₆₁	—	2	2	no	—
416	C₂²⋊C₄×C₆₁	—	2	2	no	—
417	C₂²⋊C₄×C₆₁	—	2	2	no	—
418	C₂²⋊C₄×C₆₁	—	2	1	no	—
419	C₂²⋊C₄×C₆₁	—	2	1	no	—
420	C₂²⋊C₄×C₆₁	—	2	1	no	—
421	C₂²⋊C₄×C₆₁	—	2	1	no	—
422	C₂²⋊C₄×C₆₁	—	2	2	no	—
423	C₂²⋊C₄×C₆₁	—	2	2	no	—
424	C₂²⋊C₄×C₆₁	—	2	2	no	—
425	C₂²⋊C₄×C₆₁	—	2	2	no	—
426	C₂²⋊C₄×C₆₁	—	2	1	no	—
427	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
428	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
429	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
430	C₄²×C₆₁	—	2	1	no	—
431	C₄²×C₆₁	—	2	1	no	—
432	C₄²×C₆₁	—	2	1	no	—
433	C₄²×C₆₁	—	2	2	no	—
434	C₄²×C₆₁	—	2	2	no	—
435	C₄²×C₆₁	—	2	1	no	—
436	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
437	C₄²×C₆₁	C₂×D₄	1	2	yes	—
438	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
439	C₄²×C₆₁	C₂×D₄	1	2	yes	—
440	C₄²×C₆₁	C₂⁴	1	2	yes	—
441	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
442	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
443	C₂³×C₆₁	—	2	1	no	—
444	C₂³×C₆₁	—	2	1	no	—
445	C₂³×C₆₁	—	2	2	no	—
446	C₂³×C₆₁	—	4	4	no	—
447	C₂³×C₆₁	—	4	4	no	—
448	C₂³×C₆₁	—	8	2	no	—
449	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
450	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
451	Q₈×C₆₁	—	2	2	no	—
452	Q₈×C₆₁	—	2	1	no	—
453	Q₈×C₆₁	—	2	1	no	—
454	Q₈×C₆₁	—	2	1	no	—
455	Q₈×C₆₁	—	2	1	no	—
456	Q₈×C₆₁	—	4	2	no	—
457	Q₈×C₆₁	—	8	1	no	—
458	Q₈×C₆₁	—	8	1	no	—
459	D₄×C₆₁	—	2	4	no	—
460	D₄×C₆₁	—	2	1	no	—
461	D₄×C₆₁	—	2	2	no	—
462	D₄×C₆₁	—	2	1	no	—
463	D₄×C₆₁	—	2	1	no	—
464	D₄×C₆₁	—	2	2	no	—
465	D₄×C₆₁	—	4	4	no	—
466	D₄×C₆₁	—	4	2	no	—
467	D₄×C₆₁	—	4	4	no	—
468	D₄×C₆₁	—	4	4	no	—
469	D₄×C₆₁	—	4	2	no	—
470	D₄×C₆₁	—	8	1	no	—
471	D₄×C₆₁	—	8	1	no	—
472	D₄×C₆₁	—	8	2	no	—
473	D₄×C₆₁	#135	1	4	yes	—
474	D₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
475	C₂×C₄×C₆₁	—	2	4	no	—
476	C₂×C₄×C₆₁	—	2	2	no	—
477	C₂×C₄×C₆₁	—	2	2	no	—
478	C₂×C₄×C₆₁	—	2	1	no	—
479	C₂×C₄×C₆₁	—	2	2	no	—
480	C₂×C₄×C₆₁	—	2	1	no	—
481	C₂×C₄×C₆₁	—	2	1	no	—
482	C₂×C₄×C₆₁	—	2	1	no	—
483	C₂×C₄×C₆₁	—	2	1	no	—
484	C₂×C₄×C₆₁	—	2	1	no	—
485	C₂×C₄×C₆₁	—	2	2	no	—
486	C₂×C₄×C₆₁	—	2	2	no	—
487	C₂×C₄×C₆₁	—	2	1	no	—
488	C₂×C₄×C₆₁	—	2	2	no	—
489	C₂×C₄×C₆₁	—	2	1	no	—
490	C₂×C₄×C₆₁	—	4	2	no	—
491	C₂×C₄×C₆₁	—	4	1	no	—
492	C₂×C₄×C₆₁	—	4	2	no	—
493	C₂×C₄×C₆₁	—	4	2	no	—
494	C₂×C₄×C₆₁	—	4	4	no	—
495	C₂×C₄×C₆₁	—	4	4	no	—
496	C₂×C₄×C₆₁	—	4	2	no	—
497	C₂×C₄×C₆₁	—	4	2	no	—
498	C₂×C₄×C₆₁	—	8	2	no	—
499	C₂×C₄×C₆₁	—	8	2	no	—
500	C₂×C₄×C₆₁	—	8	2	no	—
501	C₂×C₄×C₆₁	—	8	2	no	—
502	C₂×C₄×C₆₁	—	8	2	no	—
503	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
506	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
508	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
509	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
512	C₈×C₆₁	—	2	1	no	—
513	C₈×C₆₁	—	2	1	no	—
514	C₈×C₆₁	—	2	2	no	—
515	C₈×C₆₁	—	2	2	no	—
516	C₈×C₆₁	—	2	1	no	—
517	C₈×C₆₁	—	2	1	no	—
518	#62103	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
519	C₂²×C₆₁	—	2	2	no	—
520	C₂²×C₆₁	—	2	2	no	—
521	C₂²×C₆₁	—	2	1	no	—
522	C₂²×C₆₁	—	2	1	no	—
523	C₂²×C₆₁	—	2	2	no	—
524	C₂²×C₆₁	—	2	1	no	—
525	C₂²×C₆₁	—	4	1	no	—
526	C₂²×C₆₁	—	4	1	no	—
527	C₂²×C₆₁	—	4	2	no	—
528	C₂²×C₆₁	—	4	1	no	—
529	C₂²×C₆₁	—	4	2	no	—
530	C₂²×C₆₁	—	4	1	no	—
531	C₂²×C₆₁	—	4	1	no	—
532	C₂²×C₆₁	—	4	2	no	—
533	C₂²×C₆₁	—	8	8	no	—
534	C₂²×C₆₁	C₂×#135	1	4	yes	—
535	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
536	C₄×C₆₁	—	2	1	no	—
537	C₄×C₆₁	—	2	2	no	—
538	C₄×C₆₁	—	2	1	no	—
539	C₄×C₆₁	—	2	1	no	—
540	C₄×C₆₁	—	2	2	no	—
541	C₄×C₆₁	—	2	1	no	—
542	C₄×C₆₁	—	2	2	no	—
543	C₄×C₆₁	—	4	1	no	—
544	C₄×C₆₁	—	4	2	no	—
545	C₄×C₆₁	—	4	1	no	—
546	C₄×C₆₁	—	4	2	no	—
547	C₄×C₆₁	—	4	1	no	—
548	C₄×C₆₁	—	4	1	no	—
549	C₄×C₆₁	—	4	1	no	—
550	C₄×C₆₁	—	4	1	no	—
551	C₄×C₆₁	—	4	2	no	—
552	C₄×C₆₁	C₂×#135	1	2	yes	—
553	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
554	C₄×C₆₁	#585	1	1	yes	characteristic
555	#3515	C₂×C₆₁	1	1	yes	characteristic, complemented
556	#3481	C₂×C₆₁	1	1	yes	characteristic, complemented
557	#3381	C₂×C₆₁	1	1	yes	characteristic, complemented
558	#3380	C₂×C₆₁	1	1	yes	characteristic, complemented
559	#3365	C₂×C₆₁	1	1	yes	characteristic, complemented
560	#3361	C₂×C₆₁	1	1	yes	characteristic, complemented
561	#3339	C₂×C₆₁	1	2	yes	complemented
562	#3338	C₂×C₆₁	1	1	yes	characteristic, complemented
563	#3337	C₂×C₆₁	1	2	yes	complemented
564	#3335	C₂×C₆₁	1	1	yes	characteristic, complemented
565	#3297	C₂×C₆₁	1	2	yes	complemented
566	#3296	C₂×C₆₁	1	2	yes	complemented
567	#3295	C₂×C₆₁	1	1	yes	characteristic, complemented
568	#3294	C₂×C₆₁	1	1	yes	characteristic, complemented
569	#3250	C₂×C₆₁	1	2	yes	complemented
570	#3247	C₂×C₆₁	1	1	yes	characteristic, complemented
571	#3232	C₂×C₆₁	1	2	yes	complemented
572	#3228	C₂×C₆₁	1	1	yes	characteristic, complemented
573	#3105	C₂×C₆₁	1	2	yes	complemented
574	#3102	C₂×C₆₁	1	1	yes	characteristic, complemented
575	#3076	C₂×C₆₁	1	1	yes	characteristic, complemented
576	C₂×#478	C₂×C₆₁	1	2	yes	complemented
577	#2988	C₂×C₆₁	1	1	yes	characteristic, complemented
578	C₂×C₆₁	—	2	4	no	—
579	C₂×C₆₁	—	4	1	no	—
580	C₂×C₆₁	—	4	2	no	—
581	C₂×C₆₁	—	8	1	no	—
582	C₂×C₆₁	—	8	2	no	—
583	C₂×C₆₁	#3489	1	1	yes	characteristic
584	C₂×C₆₁	C₂²×#135	1	1	yes	characteristic
585	C₂×C₆₁	#3585	1	1	yes	characteristic
586	#559	C₂²×C₆₁	1	1	yes	characteristic
587	#557	C₂²×C₆₁	1	1	yes	characteristic, complemented
588	#554	C₂²×C₆₁	1	1	yes	characteristic
589	#554	C₂²×C₆₁	1	1	yes	characteristic
590	#554	C₂²×C₆₁	1	1	yes	characteristic
591	#554	C₂²×C₆₁	1	1	yes	characteristic, complemented
592	#553	—	2	1	no	—
593	#553	C₂²×C₆₁	1	2	yes	—
594	#553	C₂²×C₆₁	1	2	yes	complemented
595	#552	—	2	2	no	—
596	#552	—	2	1	no	—
597	#552	C₂²×C₆₁	1	2	yes	complemented
598	#551	—	2	2	no	—
599	#547	—	2	1	no	—
600	#547	C₂²×C₆₁	1	1	yes	characteristic
601	#546	—	2	1	no	—
602	#546	C₂²×C₆₁	1	2	yes	—
603	D₄²	C₂²×C₆₁	1	1	yes	characteristic
604	#541	—	2	1	no	—
605	#539	—	2	2	no	—
606	#533	C₂²×C₆₁	1	1	yes	characteristic, complemented
607	#532	C₂²×C₆₁	1	1	yes	characteristic
608	#529	—	2	1	no	—
609	#529	C₂²×C₆₁	1	2	yes	—
610	#529	C₂²×C₆₁	1	1	yes	characteristic, complemented
611	#529	C₂²×C₆₁	1	2	yes	complemented
612	C₂×#125	C₂²×C₆₁	1	2	yes	complemented
613	#525	—	2	2	no	—
614	#520	—	2	1	no	—
615	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
616	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
617	C₂×C₄×D₄	—	2	1	no	—
618	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
619	#500	C₂²×C₆₁	1	1	yes	characteristic, complemented
620	#499	C₂²×C₆₁	1	2	yes	complemented
621	#499	C₂²×C₆₁	1	2	yes	complemented
622	#498	C₂²×C₆₁	1	1	yes	characteristic, complemented
623	#488	C₂²×C₆₁	1	2	yes	complemented
624	#488	C₂²×C₆₁	1	2	yes	complemented
625	#486	C₂²×C₆₁	1	1	yes	characteristic
626	#486	C₂²×C₆₁	1	1	yes	characteristic
627	#485	C₂²×C₆₁	1	1	yes	characteristic, complemented
628	#484	C₂²×C₆₁	1	2	yes	complemented
629	#484	C₂²×C₆₁	1	2	yes	complemented
630	#483	C₂²×C₆₁	1	2	yes	complemented
631	#482	C₂²×C₆₁	1	2	yes	complemented
632	#482	C₂²×C₆₁	1	1	yes	characteristic, complemented
633	#482	C₂²×C₆₁	1	2	yes	complemented
634	#481	C₂²×C₆₁	1	2	yes	—
635	#481	C₂²×C₆₁	1	2	yes	complemented
636	#480	C₂²×C₆₁	1	2	yes	—
637	#479	C₂²×C₆₁	1	2	yes	complemented
638	#479	C₂²×C₆₁	1	2	yes	complemented
639	#479	C₂²×C₆₁	1	1	yes	characteristic, complemented
640	#478	C₂²×C₆₁	1	1	yes	characteristic
641	#478	C₂²×C₆₁	1	2	yes	—
642	#478	C₂²×C₆₁	1	2	yes	—
643	#478	C₂²×C₆₁	1	2	yes	—
644	#478	C₂²×C₆₁	1	2	yes	complemented
645	#478	C₂²×C₆₁	1	2	yes	complemented
646	#478	C₂²×C₆₁	1	2	yes	complemented
647	#478	C₂²×C₆₁	1	2	yes	complemented
648	#478	C₂²×C₆₁	1	2	yes	complemented
649	#478	C₂²×C₆₁	1	2	yes	complemented
650	#477	C₂²×C₆₁	1	1	yes	characteristic, complemented
651	#477	C₂²×C₆₁	1	1	yes	characteristic, complemented
652	#476	C₂²×C₆₁	1	1	yes	characteristic
653	#476	C₂²×C₆₁	1	1	yes	characteristic, complemented
654	#475	C₂²×C₆₁	1	1	yes	characteristic, complemented
655	#474	C₂²×C₆₁	1	1	yes	characteristic
656	#467	C₂²×C₆₁	1	2	yes	complemented
657	#466	C₂²×C₆₁	1	2	yes	—
658	#466	C₂²×C₆₁	1	2	yes	complemented
659	#465	C₂²×C₆₁	1	2	yes	—
660	#465	C₂²×C₆₁	1	2	yes	complemented
661	#465	C₂²×C₆₁	1	2	yes	complemented
662	#464	C₂²×C₆₁	1	1	yes	characteristic, complemented
663	#464	C₂²×C₆₁	1	2	yes	complemented
664	#463	C₂²×C₆₁	1	1	yes	characteristic
665	#463	C₂²×C₆₁	1	2	yes	complemented
666	#463	C₂²×C₆₁	1	2	yes	complemented
667	#460	C₂²×C₆₁	1	1	yes	characteristic
668	#459	C₂²×C₆₁	1	1	yes	characteristic
669	#452	C₂²×C₆₁	1	1	yes	characteristic
670	#450	C₂²×C₆₁	1	2	yes	—
671	#449	C₂²×C₆₁	1	1	yes	characteristic
672	#447	C₂²×C₆₁	1	2	yes	—
673	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
674	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
675	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
676	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
677	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
678	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
679	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
680	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
681	C₄×D₈	C₂²×C₆₁	1	2	yes	—
682	C₄×D₈	C₂²×C₆₁	1	2	yes	complemented
683	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic
684	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic
685	C₈×D₄	C₂²×C₆₁	1	2	yes	complemented
686	C₈×D₄	C₂²×C₆₁	1	2	yes	complemented
687	#431	C₂²×C₆₁	1	1	yes	characteristic, complemented
688	#431	C₂²×C₆₁	1	2	yes	complemented
689	#427	C₂²×C₆₁	1	2	yes	complemented
690	C₂×#107	C₂²×C₆₁	1	2	yes	complemented
691	C₂×#106	C₂²×C₆₁	1	2	yes	complemented
692	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	complemented
693	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
694	#416	C₂²×C₆₁	1	2	yes	—
695	C₂×#102	C₂²×C₆₁	1	2	yes	—
696	C₂×#102	C₂²×C₆₁	1	2	yes	—
697	C₆₁	#62103	1	1	yes	characteristic, direct product factor, Sylow
698	C₂×#41	—	2	1	no	—
699	C₂×#41	—	2	1	no	—
700	C₂×#41	D₄×C₆₁	1	1	yes	characteristic
701	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
702	C₂²×D₄	—	2	1	no	—
703	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
704	C₂³×C₄	—	2	2	no	—
705	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
706	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
707	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
708	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
709	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
710	C₂×D₈	C₂³×C₆₁	1	2	yes	—
711	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
712	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
713	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
714	C₄⋊Q₈	—	2	1	no	—
715	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
716	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
717	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
718	#127	C₂³×C₆₁	1	1	yes	characteristic
719	#126	—	2	2	no	—
720	#126	—	2	2	no	—
721	#126	—	2	2	no	—
722	#126	—	2	2	no	—
723	#126	—	2	2	no	—
724	#126	—	2	1	no	—
725	#125	—	2	1	no	—
726	#125	—	2	2	no	—
727	#125	—	2	2	no	—
728	#125	—	2	1	no	—
729	#125	—	2	2	no	—
730	#125	—	2	2	no	—
731	#125	C₂³×C₆₁	1	1	yes	characteristic
732	#125	C₂³×C₆₁	1	2	yes	—
733	#125	C₂³×C₆₁	1	2	yes	—
734	#125	C₂³×C₆₁	1	2	yes	—
735	#125	C₂³×C₆₁	1	2	yes	—
736	#124	—	2	1	no	—
737	#124	—	2	1	no	—
738	#124	C₂³×C₆₁	1	2	yes	—
739	#124	C₂³×C₆₁	1	1	yes	characteristic
740	#123	—	2	2	no	—
741	#123	—	2	2	no	—
742	#123	—	2	1	no	—
743	#123	—	2	2	no	—
744	#123	—	2	2	no	—
745	#123	—	2	2	no	—
746	#123	—	2	2	no	—
747	#123	—	2	2	no	—
748	#123	—	2	2	no	—
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	2	1	no	—
752	C₂²⋊Q₈	—	2	1	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	1	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
759	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
760	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
761	#121	—	2	2	no	—
762	#121	—	2	2	no	—
763	#121	—	2	1	no	—
764	#121	—	2	1	no	—
765	#121	—	2	2	no	—
766	#121	C₂³×C₆₁	1	2	yes	—
767	#121	C₂³×C₆₁	1	2	yes	—
768	#121	C₂³×C₆₁	1	1	yes	characteristic
769	#121	C₂³×C₆₁	1	2	yes	—
770	#120	—	2	2	no	—
771	#120	—	2	2	no	—
772	C₄×Q₈	—	2	1	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
776	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
777	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
778	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
779	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
780	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
781	C₄×D₄	—	2	1	no	—
782	C₄×D₄	—	2	1	no	—
783	C₄×D₄	—	2	2	no	—
784	C₄×D₄	—	2	1	no	—
785	C₄×D₄	—	2	1	no	—
786	C₄×D₄	—	2	2	no	—
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	—	2	1	no	—
789	C₄×D₄	—	2	2	no	—
790	C₄×D₄	—	2	2	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	2	no	—
793	C₄×D₄	—	2	2	no	—
794	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
795	C₄×D₄	D₄×C₆₁	1	2	yes	—
796	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
797	C₄×D₄	C₂³×C₆₁	1	2	yes	—
798	C₄×D₄	C₂³×C₆₁	1	2	yes	—
799	C₄×D₄	C₂³×C₆₁	1	2	yes	—
800	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
801	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
802	C₄×D₄	C₂³×C₆₁	1	2	yes	—
803	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
804	C₄×D₄	C₂³×C₆₁	1	2	yes	—
805	#117	—	2	2	no	—
806	#117	—	2	1	no	—
807	#117	—	2	1	no	—
808	#117	—	2	2	no	—
809	#117	—	2	2	no	—
810	#117	D₄×C₆₁	1	2	yes	—
811	#117	D₄×C₆₁	1	1	yes	characteristic
812	#117	C₂³×C₆₁	1	1	yes	characteristic
813	#117	C₂³×C₆₁	1	2	yes	—
814	C₂×C₄⋊C₄	—	2	2	no	—
815	C₂×C₄⋊C₄	—	2	2	no	—
816	C₂×C₄⋊C₄	—	2	1	no	—
817	C₂×C₄⋊C₄	—	2	1	no	—
818	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
819	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
820	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
821	C₂×C₂²⋊C₄	—	2	2	no	—
822	C₂×C₂²⋊C₄	—	2	2	no	—
823	C₂×C₄²	—	2	1	no	—
824	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
825	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
826	#107	C₂³×C₆₁	1	1	yes	characteristic
827	#107	C₂³×C₆₁	1	2	yes	—
828	#107	C₂³×C₆₁	1	2	yes	—
829	#107	C₂³×C₆₁	1	2	yes	—
830	#107	C₂³×C₆₁	1	2	yes	—
831	#107	C₂³×C₆₁	1	2	yes	—
832	#107	C₂³×C₆₁	1	1	yes	characteristic
833	#106	C₂³×C₆₁	1	1	yes	characteristic
834	#106	C₂³×C₆₁	1	2	yes	—
835	#106	C₂³×C₆₁	1	2	yes	—
836	#106	C₂³×C₆₁	1	2	yes	—
837	#106	C₂³×C₆₁	1	2	yes	—
838	#106	C₂³×C₆₁	1	2	yes	—
839	#106	C₂³×C₆₁	1	1	yes	characteristic
840	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
841	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
842	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
843	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
844	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
845	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
846	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
847	#103	C₂³×C₆₁	1	2	yes	—
848	#103	C₂³×C₆₁	1	2	yes	—
849	#103	C₂³×C₆₁	1	2	yes	—
850	#103	C₂³×C₆₁	1	1	yes	characteristic
851	#103	C₂³×C₆₁	1	1	yes	characteristic
852	#103	C₂³×C₆₁	1	1	yes	characteristic
853	#103	C₂³×C₆₁	1	1	yes	characteristic
854	#102	C₂³×C₆₁	1	1	yes	characteristic
855	#102	C₂³×C₆₁	1	1	yes	characteristic
856	#102	C₂³×C₆₁	1	2	yes	—
857	#102	C₂³×C₆₁	1	2	yes	—
858	#102	C₂³×C₆₁	1	2	yes	—
859	#102	C₂³×C₆₁	1	2	yes	—
860	#102	C₂³×C₆₁	1	2	yes	—
861	#102	C₂³×C₆₁	1	2	yes	—
862	#102	C₂³×C₆₁	1	2	yes	—
863	#102	C₂³×C₆₁	1	1	yes	characteristic
864	#102	C₂³×C₆₁	1	1	yes	characteristic
865	#102	C₂³×C₆₁	1	2	yes	—
866	#102	C₂³×C₆₁	1	2	yes	—
867	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
868	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
869	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
870	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
871	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
872	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
873	C₄×C₈	C₂³×C₆₁	1	2	yes	—
874	C₄×C₈	C₂³×C₆₁	1	2	yes	—
875	C₂⁴	—	2	2	no	—
876	#41	—	2	4	no	—
877	#41	—	2	2	no	—
878	#41	—	4	1	no	—
879	#41	—	4	4	no	—
880	#41	—	8	2	no	—
881	C₂×Q₈	—	2	1	no	—
882	C₂×Q₈	—	2	1	no	—
883	C₂×Q₈	—	2	1	no	—
884	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
885	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
886	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
887	C₂×D₄	—	2	4	no	—
888	C₂×D₄	—	2	1	no	—
889	C₂×D₄	—	2	2	no	—
890	C₂×D₄	—	2	2	no	—
891	C₂×D₄	—	2	1	no	—
892	C₂×D₄	—	2	2	no	—
893	C₂×D₄	—	2	2	no	—
894	C₂×D₄	—	2	1	no	—
895	C₂×D₄	—	2	1	no	—
896	C₂×D₄	—	4	2	no	—
897	C₂×D₄	—	4	4	no	—
898	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
899	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
900	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
901	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
902	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
903	C₂²×C₄	—	2	2	no	—
904	C₂²×C₄	—	2	2	no	—
905	C₂²×C₄	—	2	2	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	2	1	no	—
908	C₂²×C₄	—	2	1	no	—
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	—	8	4	no	—
915	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
916	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
917	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
918	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
919	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
920	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
921	Q₁₆	—	4	1	no	—
922	SD₁₆	—	2	2	no	—
923	SD₁₆	—	4	1	no	—
924	SD₁₆	—	4	2	no	—
925	D₈	—	2	2	no	—
926	D₈	—	4	2	no	—
927	C₂×C₈	—	4	2	no	—
928	C₂×C₈	—	4	2	no	—
929	C₂×C₈	—	4	2	no	—
930	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
931	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
932	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
933	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
934	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
935	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
960	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
961	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
962	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
963	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
964	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
965	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
966	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
967	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
968	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
969	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	1	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	1	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
991	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
992	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
993	C₄²	—	2	1	no	—
994	C₄²	—	2	1	no	—
995	C₄²	—	2	1	no	—
996	C₄²	—	2	2	no	—
997	C₄²	—	2	2	no	—
998	C₄²	—	2	1	no	—
999	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1000	C₄²	C₂×D₄×C₆₁	1	2	yes	—
1001	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1002	C₄²	C₂×D₄×C₆₁	1	2	yes	—
1003	C₄²	C₂⁴×C₆₁	1	2	yes	—
1004	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1005	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1006	C₂³	—	2	1	no	—
1007	C₂³	—	2	1	no	—
1008	C₂³	—	2	2	no	—
1009	C₂³	—	4	4	no	—
1010	C₂³	—	4	4	no	—
1011	C₂³	—	8	2	no	—
1012	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1013	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1014	Q₈	—	2	2	no	—
1015	Q₈	—	2	1	no	—
1016	Q₈	—	2	1	no	—
1017	Q₈	—	2	1	no	—
1018	Q₈	—	2	1	no	—
1019	Q₈	—	4	2	no	—
1020	Q₈	—	8	1	no	—
1021	Q₈	—	8	1	no	—
1022	D₄	—	2	4	no	—
1023	D₄	—	2	1	no	—
1024	D₄	—	2	2	no	—
1025	D₄	—	2	1	no	—
1026	D₄	—	2	1	no	—
1027	D₄	—	2	2	no	—
1028	D₄	—	4	4	no	—
1029	D₄	—	4	2	no	—
1030	D₄	—	4	4	no	—
1031	D₄	—	4	4	no	—
1032	D₄	—	4	2	no	—
1033	D₄	—	8	1	no	—
1034	D₄	—	8	1	no	—
1035	D₄	—	8	2	no	—
1036	D₄	#135×C₆₁	1	4	yes	—
1037	D₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
1038	C₂×C₄	—	2	4	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	4	2	no	—
1054	C₂×C₄	—	4	1	no	—
1055	C₂×C₄	—	4	2	no	—
1056	C₂×C₄	—	4	2	no	—
1057	C₂×C₄	—	4	4	no	—
1058	C₂×C₄	—	4	4	no	—
1059	C₂×C₄	—	4	2	no	—
1060	C₂×C₄	—	4	2	no	—
1061	C₂×C₄	—	8	2	no	—
1062	C₂×C₄	—	8	2	no	—
1063	C₂×C₄	—	8	2	no	—
1064	C₂×C₄	—	8	2	no	—
1065	C₂×C₄	—	8	2	no	—
1066	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1067	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1068	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1069	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1070	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1071	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1072	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1073	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1074	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1075	C₈	—	2	1	no	—
1076	C₈	—	2	1	no	—
1077	C₈	—	2	2	no	—
1078	C₈	—	2	2	no	—
1079	C₈	—	2	1	no	—
1080	C₈	—	2	1	no	—
1081	C₂²	—	2	2	no	—
1082	C₂²	—	2	2	no	—
1083	C₂²	—	2	1	no	—
1084	C₂²	—	2	1	no	—
1085	C₂²	—	2	1	no	—
1086	C₂²	—	2	2	no	—
1087	C₂²	—	4	1	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	4	2	no	—
1091	C₂²	—	4	2	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	4	2	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	8	8	no	—
1096	C₂²	C₂×#135×C₆₁	1	4	yes	—
1097	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1098	C₄	—	2	1	no	—
1099	C₄	—	2	2	no	—
1100	C₄	—	2	1	no	—
1101	C₄	—	2	2	no	—
1102	C₄	—	2	1	no	—
1103	C₄	—	2	1	no	—
1104	C₄	—	2	2	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	2	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	2	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	2	no	—
1112	C₄	—	4	1	no	—
1113	C₄	—	4	1	no	—
1114	C₄	C₂×#135×C₆₁	1	2	yes	—
1115	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
1116	C₄	C₆₁×#585	1	1	yes	characteristic
1117	C₂	—	2	4	no	—
1118	C₂	—	4	1	no	—
1119	C₂	—	4	2	no	—
1120	C₂	—	8	2	no	—
1121	C₂	—	8	1	no	—
1122	C₂	C₆₁×#3489	1	1	yes	characteristic
1123	C₂	C₂²×#135×C₆₁	1	1	yes	characteristic
1124	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×#3515	C₂	semidirect
2. C₆₁×#3481	C₂	semidirect
3. C₆₁×#3381	C₂	semidirect
4. C₆₁×#3380	C₂	semidirect
5. C₆₁×#3365	C₂	semidirect
6. C₆₁×#3361	C₂	semidirect
7. C₆₁×#3339	C₂	semidirect
8. C₆₁×#3338	C₂	semidirect
9. C₆₁×#3337	C₂	semidirect
10. C₆₁×#3335	C₂	semidirect
11. C₆₁×#3297	C₂	semidirect
12. C₆₁×#3296	C₂	semidirect
13. C₆₁×#3295	C₂	semidirect
14. C₆₁×#3294	C₂	semidirect
15. C₆₁×#3250	C₂	semidirect
16. C₆₁×#3247	C₂	semidirect
17. C₆₁×#3232	C₂	semidirect
18. C₆₁×#3228	C₂	semidirect
19. C₆₁×#3105	C₂	semidirect
20. C₆₁×#3102	C₂	semidirect
21. C₆₁×#3076	C₂	semidirect
22. C₂×C₆₁×#478	C₂	semidirect
23. C₆₁×#2988	C₂	semidirect
25. C₆₁×#557	C₂²	semidirect
29. C₆₁×#554	C₂²	semidirect
32. C₆₁×#553	C₂²	semidirect
35. C₆₁×#552	C₂²	semidirect
44. C₆₁×#533	C₂²	semidirect
48. C₆₁×#529	C₂²	semidirect
49. C₆₁×#529	C₂²	semidirect
50. C₂×#125×C₆₁	C₂²	semidirect
57. C₆₁×#500	C₂²	semidirect
58. C₆₁×#499	C₂²	semidirect
59. C₆₁×#499	C₂²	semidirect
60. C₆₁×#498	C₂²	semidirect
61. C₆₁×#488	C₂²	semidirect
62. C₆₁×#488	C₂²	semidirect
65. C₆₁×#485	C₂²	semidirect
66. C₆₁×#484	C₂²	semidirect
67. C₆₁×#484	C₂²	semidirect
68. C₆₁×#483	C₂²	semidirect
69. C₆₁×#482	C₂²	semidirect
70. C₆₁×#482	C₂²	semidirect
71. C₆₁×#482	C₂²	semidirect
73. C₆₁×#481	C₂²	semidirect
75. C₆₁×#479	C₂²	semidirect
76. C₆₁×#479	C₂²	semidirect
77. C₆₁×#479	C₂²	semidirect
82. C₆₁×#478	C₂²	semidirect
83. C₆₁×#478	C₂²	semidirect
84. C₆₁×#478	C₂²	semidirect
85. C₆₁×#478	C₂²	semidirect
86. C₆₁×#478	C₂²	semidirect
87. C₆₁×#478	C₂²	semidirect
88. C₆₁×#477	C₂²	semidirect
89. C₆₁×#477	C₂²	semidirect
91. C₆₁×#476	C₂²	semidirect
92. C₆₁×#475	C₂²	semidirect
94. C₆₁×#467	C₂²	semidirect
96. C₆₁×#466	C₂²	semidirect
98. C₆₁×#465	C₂²	semidirect
99. C₆₁×#465	C₂²	semidirect
100. C₆₁×#464	C₂²	semidirect
101. C₆₁×#464	C₂²	semidirect
103. C₆₁×#463	C₂²	semidirect
104. C₆₁×#463	C₂²	semidirect
111. C₈×Q₈×C₆₁	C₂²	semidirect
112. C₈×Q₈×C₆₁	C₂²	semidirect
113. C₄×Q₁₆×C₆₁	C₂²	semidirect
116. C₄×SD₁₆×C₆₁	C₂²	semidirect
117. C₄×SD₁₆×C₆₁	C₂²	semidirect
120. C₄×D₈×C₆₁	C₂²	semidirect
123. C₈×D₄×C₆₁	C₂²	semidirect
124. C₈×D₄×C₆₁	C₂²	semidirect
125. C₆₁×#431	C₂²	semidirect
126. C₆₁×#431	C₂²	semidirect
127. C₆₁×#427	C₂²	semidirect
128. C₂×#107×C₆₁	C₂²	semidirect
129. C₂×#106×C₆₁	C₂²	semidirect
130. C₂×C₄⋊C₈×C₆₁	C₂²	semidirect
131. C₂×C₄⋊C₈×C₆₁	C₂²	semidirect
518. #62103	C₆₁	direct (N × H)
555. #3515	C₂×C₆₁	semidirect
556. #3481	C₂×C₆₁	semidirect
557. #3381	C₂×C₆₁	semidirect
558. #3380	C₂×C₆₁	semidirect
559. #3365	C₂×C₆₁	semidirect
560. #3361	C₂×C₆₁	semidirect
561. #3339	C₂×C₆₁	semidirect
562. #3338	C₂×C₆₁	semidirect
563. #3337	C₂×C₆₁	semidirect
564. #3335	C₂×C₆₁	semidirect
565. #3297	C₂×C₆₁	semidirect
566. #3296	C₂×C₆₁	semidirect
567. #3295	C₂×C₆₁	semidirect
568. #3294	C₂×C₆₁	semidirect
569. #3250	C₂×C₆₁	semidirect
570. #3247	C₂×C₆₁	semidirect
571. #3232	C₂×C₆₁	semidirect
572. #3228	C₂×C₆₁	semidirect
573. #3105	C₂×C₆₁	semidirect
574. #3102	C₂×C₆₁	semidirect
575. #3076	C₂×C₆₁	semidirect
576. C₂×#478	C₂×C₆₁	semidirect
577. #2988	C₂×C₆₁	semidirect
587. #557	C₂²×C₆₁	semidirect
591. #554	C₂²×C₆₁	semidirect
594. #553	C₂²×C₆₁	semidirect
597. #552	C₂²×C₆₁	semidirect
606. #533	C₂²×C₆₁	semidirect
610. #529	C₂²×C₆₁	semidirect
611. #529	C₂²×C₆₁	semidirect
612. C₂×#125	C₂²×C₆₁	semidirect
619. #500	C₂²×C₆₁	semidirect
620. #499	C₂²×C₆₁	semidirect
621. #499	C₂²×C₆₁	semidirect
622. #498	C₂²×C₆₁	semidirect
623. #488	C₂²×C₆₁	semidirect
624. #488	C₂²×C₆₁	semidirect
627. #485	C₂²×C₆₁	semidirect
628. #484	C₂²×C₆₁	semidirect
629. #484	C₂²×C₆₁	semidirect
630. #483	C₂²×C₆₁	semidirect
631. #482	C₂²×C₆₁	semidirect
632. #482	C₂²×C₆₁	semidirect
633. #482	C₂²×C₆₁	semidirect
635. #481	C₂²×C₆₁	semidirect
637. #479	C₂²×C₆₁	semidirect
638. #479	C₂²×C₆₁	semidirect
639. #479	C₂²×C₆₁	semidirect
644. #478	C₂²×C₆₁	semidirect
645. #478	C₂²×C₆₁	semidirect
646. #478	C₂²×C₆₁	semidirect
647. #478	C₂²×C₆₁	semidirect
648. #478	C₂²×C₆₁	semidirect
649. #478	C₂²×C₆₁	semidirect
650. #477	C₂²×C₆₁	semidirect
651. #477	C₂²×C₆₁	semidirect
653. #476	C₂²×C₆₁	semidirect
654. #475	C₂²×C₆₁	semidirect
656. #467	C₂²×C₆₁	semidirect
658. #466	C₂²×C₆₁	semidirect
660. #465	C₂²×C₆₁	semidirect
661. #465	C₂²×C₆₁	semidirect
662. #464	C₂²×C₆₁	semidirect
663. #464	C₂²×C₆₁	semidirect
665. #463	C₂²×C₆₁	semidirect
666. #463	C₂²×C₆₁	semidirect
673. C₈×Q₈	C₂²×C₆₁	semidirect
674. C₈×Q₈	C₂²×C₆₁	semidirect
675. C₄×Q₁₆	C₂²×C₆₁	semidirect
678. C₄×SD₁₆	C₂²×C₆₁	semidirect
679. C₄×SD₁₆	C₂²×C₆₁	semidirect
682. C₄×D₈	C₂²×C₆₁	semidirect
685. C₈×D₄	C₂²×C₆₁	semidirect
686. C₈×D₄	C₂²×C₆₁	semidirect
687. #431	C₂²×C₆₁	semidirect
688. #431	C₂²×C₆₁	semidirect
689. #427	C₂²×C₆₁	semidirect
690. C₂×#107	C₂²×C₆₁	semidirect
691. C₂×#106	C₂²×C₆₁	semidirect
692. C₂×C₄⋊C₈	C₂²×C₆₁	semidirect
693. C₂×C₄⋊C₈	C₂²×C₆₁	semidirect
697. C₆₁	#62103	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×#3515	2
C₆₁×#3481	2
C₆₁×#3381	2
C₆₁×#3380	2
C₆₁×#3365	2
C₆₁×#3361	2
C₆₁×#3339	2
C₆₁×#3338	2
C₆₁×#3337	2
C₆₁×#3335	2
C₆₁×#3297	2
C₆₁×#3296	2
C₆₁×#3295	2
C₆₁×#3294	2
C₆₁×#3250	2
C₆₁×#3247	2
C₆₁×#3232	2
C₆₁×#3228	2
C₆₁×#3105	2
C₆₁×#3102	2
C₆₁×#3076	2
C₂×C₆₁×#478	2
C₆₁×#2988	2
#62103	61

Subgroups — C61×#62103 #29565536

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62103 #29565536