Subgroups — C₆₁×#61927 #29565360

Order 15616.

1718 conjugacy classes of subgroups.

The subgroup lattice has 1130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3401	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3398	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3397	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3394	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3393	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3392	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#3371	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3369	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3366	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3365	C₂	1	2	yes	maximal, complemented
13	C₆₁×#3362	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3360	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3224	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3222	C₂	1	2	yes	maximal, complemented
17	C₆₁×#3212	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#3125	C₂	1	2	yes	maximal, complemented
20	C₆₁×#3120	C₂	1	2	yes	maximal, complemented
21	C₆₁×#3105	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₁×#3101	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₁×#2986	C₂	1	1	yes	maximal, characteristic, complemented
24	C₆₁×#563	—	2	2	no	—
25	C₆₁×#559	C₂²	1	2	yes	—
26	C₆₁×#559	C₂²	1	2	yes	—
27	Q₈²×C₆₁	C₂²	1	1	yes	characteristic, complemented
28	C₆₁×#557	C₂²	1	1	yes	characteristic, complemented
29	C₆₁×#557	C₂²	1	2	yes	complemented
30	C₆₁×#556	—	2	1	no	—
31	C₆₁×#556	C₂²	1	1	yes	characteristic
32	C₆₁×#556	C₂²	1	1	yes	characteristic
33	C₆₁×#556	C₂²	1	1	yes	characteristic, complemented
34	C₆₁×#556	C₂²	1	2	yes	complemented
35	C₆₁×#555	—	2	1	no	—
36	C₆₁×#554	C₂²	1	1	yes	characteristic, complemented
37	C₆₁×#553	—	2	2	no	—
38	C₆₁×#552	—	2	1	no	—
39	C₆₁×#550	C₂²	1	1	yes	characteristic
40	C₆₁×#550	C₂²	1	1	yes	characteristic
41	C₆₁×#547	—	2	1	no	—
42	C₆₁×#544	—	2	1	no	—
43	C₆₁×#542	C₂²	1	2	yes	—
44	C₆₁×#541	—	2	1	no	—
45	C₆₁×#541	—	2	2	no	—
46	C₆₁×#541	C₂²	1	2	yes	—
47	C₆₁×#538	—	2	2	no	—
48	C₆₁×#535	C₂²	1	2	yes	—
49	C₆₁×#533	C₂²	1	1	yes	characteristic
50	C₆₁×#533	C₂²	1	1	yes	characteristic
51	C₆₁×#532	C₂²	1	1	yes	characteristic
52	C₆₁×#529	C₂²	1	1	yes	characteristic
53	C₆₁×#525	—	2	1	no	—
54	C₆₁×#525	—	2	1	no	—
55	C₆₁×#520	C₂²	1	2	yes	—
56	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
57	C₆₁×#497	C₂²	1	2	yes	—
58	C₆₁×#496	C₂²	1	2	yes	—
59	C₆₁×#495	C₂²	1	2	yes	—
60	C₆₁×#495	C₂²	1	2	yes	complemented
61	C₆₁×#494	C₂²	1	1	yes	characteristic, complemented
62	C₆₁×#492	C₂²	1	2	yes	—
63	C₆₁×#492	C₂²	1	1	yes	characteristic, complemented
64	C₆₁×#490	C₂²	1	2	yes	—
65	C₆₁×#489	C₂²	1	2	yes	—
66	C₆₁×#488	C₂²	1	2	yes	—
67	C₆₁×#488	C₂²	1	2	yes	complemented
68	C₆₁×#487	C₂²	1	1	yes	characteristic, complemented
69	C₆₁×#486	C₂²	1	2	yes	—
70	C₆₁×#486	C₂²	1	1	yes	characteristic, complemented
71	C₆₁×#484	C₂²	1	1	yes	characteristic
72	C₆₁×#483	C₂²	1	2	yes	—
73	C₆₁×#481	C₂²	1	1	yes	characteristic
74	C₆₁×#479	C₂²	1	2	yes	complemented
75	C₆₁×#478	C₂²	1	1	yes	characteristic
76	C₆₁×#478	C₂²	1	1	yes	characteristic
77	C₆₁×#478	C₂²	1	2	yes	complemented
78	C₆₁×#476	C₂²	1	1	yes	characteristic
79	C₆₁×#476	C₂²	1	1	yes	characteristic
80	C₆₁×#476	C₂²	1	2	yes	complemented
81	C₆₁×#475	C₂²	1	2	yes	complemented
82	C₆₁×#464	C₂²	1	2	yes	—
83	C₆₁×#464	C₂²	1	2	yes	—
84	C₆₁×#464	C₂²	1	2	yes	—
85	C₆₁×#464	C₂²	1	2	yes	complemented
86	C₆₁×#464	C₂²	1	2	yes	complemented
87	C₆₁×#464	C₂²	1	2	yes	complemented
88	C₆₁×#463	C₂²	1	2	yes	—
89	C₆₁×#463	C₂²	1	1	yes	characteristic
90	C₆₁×#463	C₂²	1	1	yes	characteristic
91	C₆₁×#463	C₂²	1	2	yes	complemented
92	C₆₁×#462	C₂²	1	1	yes	characteristic, complemented
93	C₆₁×#462	C₂²	1	2	yes	complemented
94	C₆₁×#461	C₂²	1	1	yes	characteristic
95	C₆₁×#461	C₂²	1	1	yes	characteristic
96	C₆₁×#461	C₂²	1	1	yes	characteristic, complemented
97	C₆₁×#461	C₂²	1	2	yes	complemented
98	C₆₁×#460	C₂²	1	2	yes	—
99	C₆₁×#460	C₂²	1	2	yes	—
100	C₆₁×#460	C₂²	1	2	yes	—
101	C₆₁×#460	C₂²	1	1	yes	characteristic, complemented
102	C₆₁×#459	C₂²	1	2	yes	—
103	C₆₁×#459	C₂²	1	1	yes	characteristic, complemented
104	C₆₁×#452	C₂²	1	2	yes	—
105	C₆₁×#452	C₂²	1	2	yes	—
106	C₆₁×#452	C₂²	1	2	yes	—
107	C₆₁×#450	C₂²	1	2	yes	—
108	C₆₁×#450	C₂²	1	1	yes	characteristic
109	C₆₁×#449	C₂²	1	2	yes	—
110	C₆₁×#447	C₂²	1	1	yes	characteristic
111	C₆₁×#446	C₂²	1	1	yes	characteristic, complemented
112	C₆₁×#446	C₂²	1	1	yes	characteristic, complemented
113	C₆₁×#446	C₂²	1	2	yes	complemented
114	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
116	C₈×Q₈×C₆₁	C₂²	1	2	yes	complemented
117	C₆₁×#442	C₂²	1	2	yes	complemented
118	C₆₁×#441	C₂²	1	2	yes	complemented
119	C₆₁×#441	C₂²	1	2	yes	complemented
120	C₆₁×#440	C₂²	1	2	yes	complemented
121	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	complemented
122	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
123	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
124	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
125	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
126	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
127	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
128	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
129	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
130	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
131	C₆₁×#433	C₂²	1	2	yes	—
132	C₆₁×#433	C₂²	1	2	yes	—
133	C₆₁×#431	C₂²	1	1	yes	characteristic
134	C₆₁×#431	C₂²	1	1	yes	characteristic
135	C₂×#41×C₆₁	—	2	1	no	—
136	C₂×#41×C₆₁	—	2	1	no	—
137	C₂×#41×C₆₁	C₂³	1	2	yes	—
138	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₆₁	—	2	1	no	—
140	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
141	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
143	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
151	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
152	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
153	C₂×D₈×C₆₁	C₂³	1	2	yes	—
154	C₄⋊Q₈×C₆₁	—	2	2	no	—
155	C₄⋊Q₈×C₆₁	—	2	2	no	—
156	C₄⋊Q₈×C₆₁	—	2	1	no	—
157	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
158	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
159	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
162	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
164	#127×C₆₁	C₂³	1	1	yes	characteristic
165	#127×C₆₁	C₂³	1	2	yes	—
166	#127×C₆₁	C₂³	1	2	yes	—
167	#126×C₆₁	—	2	2	no	—
168	#126×C₆₁	—	2	2	no	—
169	#126×C₆₁	—	2	2	no	—
170	#126×C₆₁	—	2	2	no	—
171	#126×C₆₁	—	2	2	no	—
172	#126×C₆₁	—	2	2	no	—
173	#126×C₆₁	—	2	2	no	—
174	#126×C₆₁	—	2	2	no	—
175	#126×C₆₁	—	2	1	no	—
176	#125×C₆₁	—	2	2	no	—
177	#125×C₆₁	—	2	2	no	—
178	#125×C₆₁	—	2	2	no	—
179	#125×C₆₁	—	2	2	no	—
180	#125×C₆₁	—	2	2	no	—
181	#125×C₆₁	—	2	1	no	—
182	#125×C₆₁	—	2	1	no	—
183	#125×C₆₁	D₄	1	2	yes	—
184	#125×C₆₁	C₂³	1	2	yes	—
185	#125×C₆₁	C₂³	1	1	yes	characteristic
186	#124×C₆₁	—	2	2	no	—
187	#124×C₆₁	—	2	2	no	—
188	#124×C₆₁	—	2	2	no	—
189	#124×C₆₁	C₂³	1	2	yes	—
190	#124×C₆₁	C₂³	1	2	yes	—
191	#124×C₆₁	C₂³	1	2	yes	—
192	#124×C₆₁	C₂³	1	2	yes	—
193	#124×C₆₁	C₂³	1	1	yes	characteristic
194	#123×C₆₁	—	2	1	no	—
195	#123×C₆₁	—	2	2	no	—
196	#123×C₆₁	—	2	2	no	—
197	#123×C₆₁	—	2	2	no	—
198	#123×C₆₁	—	2	2	no	—
199	#123×C₆₁	—	2	2	no	—
200	C₂²⋊Q₈×C₆₁	—	2	1	no	—
201	C₂²⋊Q₈×C₆₁	—	2	1	no	—
202	C₂²⋊Q₈×C₆₁	—	2	2	no	—
203	C₂²⋊Q₈×C₆₁	—	2	1	no	—
204	C₂²⋊Q₈×C₆₁	—	2	1	no	—
205	C₂²⋊Q₈×C₆₁	—	2	1	no	—
206	C₂²⋊Q₈×C₆₁	—	2	2	no	—
207	C₂²⋊Q₈×C₆₁	—	2	2	no	—
208	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
209	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
210	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
211	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
212	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
213	#121×C₆₁	—	2	1	no	—
214	#121×C₆₁	—	2	1	no	—
215	#121×C₆₁	—	2	2	no	—
216	#121×C₆₁	—	2	2	no	—
217	#121×C₆₁	—	2	2	no	—
218	#121×C₆₁	—	2	2	no	—
219	#121×C₆₁	—	2	1	no	—
220	#121×C₆₁	—	2	1	no	—
221	#121×C₆₁	C₂³	1	1	yes	characteristic
222	#120×C₆₁	—	2	2	no	—
223	#120×C₆₁	—	2	2	no	—
224	C₄×Q₈×C₆₁	—	2	1	no	—
225	C₄×Q₈×C₆₁	—	2	1	no	—
226	C₄×Q₈×C₆₁	—	2	2	no	—
227	C₄×Q₈×C₆₁	—	2	1	no	—
228	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
229	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
230	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
231	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
232	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
233	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
234	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
235	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
238	C₄×D₄×C₆₁	—	2	1	no	—
239	C₄×D₄×C₆₁	—	2	2	no	—
240	C₄×D₄×C₆₁	—	2	2	no	—
241	C₄×D₄×C₆₁	—	2	2	no	—
242	C₄×D₄×C₆₁	—	2	2	no	—
243	C₄×D₄×C₆₁	—	2	1	no	—
244	C₄×D₄×C₆₁	—	2	1	no	—
245	C₄×D₄×C₆₁	—	2	1	no	—
246	C₄×D₄×C₆₁	—	2	1	no	—
247	C₄×D₄×C₆₁	C₂³	1	2	yes	—
248	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₆₁	C₂³	1	2	yes	—
251	C₄×D₄×C₆₁	C₂³	1	2	yes	—
252	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
255	#117×C₆₁	—	2	1	no	—
256	#117×C₆₁	—	2	2	no	—
257	#117×C₆₁	—	2	1	no	—
258	#117×C₆₁	—	2	2	no	—
259	#117×C₆₁	—	2	1	no	—
260	#117×C₆₁	—	2	1	no	—
261	#117×C₆₁	—	2	1	no	—
262	#117×C₆₁	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
264	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
265	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
267	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
268	#107×C₆₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
273	#106×C₆₁	C₂³	1	2	yes	—
274	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
275	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
276	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
277	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
278	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
279	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
280	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
281	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
282	#103×C₆₁	C₂³	1	1	yes	characteristic
283	#103×C₆₁	C₂³	1	2	yes	—
284	#103×C₆₁	C₂³	1	2	yes	—
285	#103×C₆₁	C₂³	1	1	yes	characteristic
286	#103×C₆₁	C₂³	1	2	yes	—
287	#103×C₆₁	C₂³	1	2	yes	—
288	#103×C₆₁	C₂³	1	2	yes	—
289	#103×C₆₁	C₂³	1	2	yes	—
290	#102×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	1	yes	characteristic
294	#102×C₆₁	C₂³	1	1	yes	characteristic
295	#102×C₆₁	C₂³	1	1	yes	characteristic
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	2	yes	—
301	#102×C₆₁	C₂³	1	2	yes	—
302	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
303	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
305	#97×C₆₁	C₂³	1	2	yes	—
306	#97×C₆₁	C₂³	1	2	yes	—
307	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
308	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₆₁	C₂³	1	2	yes	—
310	C₄×C₈×C₆₁	C₂³	1	2	yes	—
311	C₄×C₈×C₆₁	C₂³	1	2	yes	—
312	C₂⁴×C₆₁	—	2	1	no	—
313	#41×C₆₁	—	4	2	no	—
314	#41×C₆₁	—	4	2	no	—
315	#41×C₆₁	—	8	2	no	—
316	#41×C₆₁	—	8	2	no	—
317	C₂×Q₈×C₆₁	—	2	1	no	—
318	C₂×Q₈×C₆₁	—	2	2	no	—
319	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
320	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
321	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
322	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
323	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
324	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
325	C₂×D₄×C₆₁	—	2	2	no	—
326	C₂×D₄×C₆₁	—	2	1	no	—
327	C₂×D₄×C₆₁	—	2	1	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	2	no	—
333	C₂×D₄×C₆₁	—	2	2	no	—
334	C₂×D₄×C₆₁	—	4	1	no	—
335	C₂×D₄×C₆₁	—	4	1	no	—
336	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
337	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
338	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
339	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₆₁	—	2	1	no	—
341	C₂²×C₄×C₆₁	—	2	1	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	2	no	—
346	C₂²×C₄×C₆₁	—	2	2	no	—
347	C₂²×C₄×C₆₁	—	2	2	no	—
348	C₂²×C₄×C₆₁	—	2	1	no	—
349	C₂²×C₄×C₆₁	—	2	1	no	—
350	C₂²×C₄×C₆₁	—	8	2	no	—
351	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
352	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
353	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
354	Q₁₆×C₆₁	—	4	2	no	—
355	Q₁₆×C₆₁	—	4	2	no	—
356	Q₁₆×C₆₁	—	4	2	no	—
357	SD₁₆×C₆₁	—	4	2	no	—
358	SD₁₆×C₆₁	—	4	2	no	—
359	SD₁₆×C₆₁	—	4	2	no	—
360	SD₁₆×C₆₁	—	4	1	no	—
361	SD₁₆×C₆₁	—	4	2	no	—
362	SD₁₆×C₆₁	—	4	2	no	—
363	SD₁₆×C₆₁	—	4	2	no	—
364	SD₁₆×C₆₁	—	4	1	no	—
365	D₈×C₆₁	—	4	1	no	—
366	D₈×C₆₁	—	4	2	no	—
367	D₈×C₆₁	—	4	1	no	—
368	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
371	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
373	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
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	2	no	—
378	C₄⋊C₄×C₆₁	—	2	2	no	—
379	C₄⋊C₄×C₆₁	—	2	1	no	—
380	C₄⋊C₄×C₆₁	—	2	1	no	—
381	C₄⋊C₄×C₆₁	—	2	2	no	—
382	C₄⋊C₄×C₆₁	—	2	1	no	—
383	C₄⋊C₄×C₆₁	—	2	1	no	—
384	C₄⋊C₄×C₆₁	—	2	1	no	—
385	C₄⋊C₄×C₆₁	—	2	1	no	—
386	C₄⋊C₄×C₆₁	—	2	2	no	—
387	C₄⋊C₄×C₆₁	—	2	2	no	—
388	C₄⋊C₄×C₆₁	—	2	1	no	—
389	C₄⋊C₄×C₆₁	—	2	2	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	2	no	—
394	C₄⋊C₄×C₆₁	—	2	2	no	—
395	C₄⋊C₄×C₆₁	—	2	1	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	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
405	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
406	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
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	1	no	—
414	C₂²⋊C₄×C₆₁	—	2	1	no	—
415	C₂²⋊C₄×C₆₁	—	2	1	no	—
416	C₂²⋊C₄×C₆₁	—	2	1	no	—
417	C₂²⋊C₄×C₆₁	—	2	2	no	—
418	C₂²⋊C₄×C₆₁	—	2	2	no	—
419	C₂²⋊C₄×C₆₁	—	2	2	no	—
420	C₂²⋊C₄×C₆₁	—	2	2	no	—
421	C₂²⋊C₄×C₆₁	—	2	1	no	—
422	C₂²⋊C₄×C₆₁	—	2	1	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	2	no	—
427	C₂²⋊C₄×C₆₁	—	2	2	no	—
428	C₂²⋊C₄×C₆₁	—	2	2	no	—
429	C₂²⋊C₄×C₆₁	—	2	1	no	—
430	C₂²⋊C₄×C₆₁	—	2	2	no	—
431	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
433	C₄²×C₆₁	—	2	2	no	—
434	C₄²×C₆₁	—	2	2	no	—
435	C₄²×C₆₁	—	2	2	no	—
436	C₄²×C₆₁	—	2	1	no	—
437	C₄²×C₆₁	—	2	2	no	—
438	C₄²×C₆₁	—	2	2	no	—
439	C₄²×C₆₁	—	2	2	no	—
440	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
441	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
442	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
443	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
444	C₄²×C₆₁	C₂⁴	1	2	yes	—
445	C₄²×C₆₁	C₂⁴	1	2	yes	—
446	C₂³×C₆₁	—	2	1	no	—
447	C₂³×C₆₁	—	2	1	no	—
448	C₂³×C₆₁	—	2	1	no	—
449	C₂³×C₆₁	—	2	2	no	—
450	C₂³×C₆₁	—	4	2	no	—
451	C₂³×C₆₁	—	8	1	no	—
452	C₂³×C₆₁	—	8	1	no	—
453	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
454	Q₈×C₆₁	—	2	2	no	—
455	Q₈×C₆₁	—	2	2	no	—
456	Q₈×C₆₁	—	2	1	no	—
457	Q₈×C₆₁	—	2	2	no	—
458	Q₈×C₆₁	—	2	2	no	—
459	Q₈×C₆₁	—	2	1	no	—
460	Q₈×C₆₁	—	2	2	no	—
461	Q₈×C₆₁	—	2	2	no	—
462	Q₈×C₆₁	—	4	2	no	—
463	Q₈×C₆₁	—	8	1	no	—
464	Q₈×C₆₁	—	8	2	no	—
465	D₄×C₆₁	—	2	1	no	—
466	D₄×C₆₁	—	2	1	no	—
467	D₄×C₆₁	—	2	1	no	—
468	D₄×C₆₁	—	2	1	no	—
469	D₄×C₆₁	—	2	2	no	—
470	D₄×C₆₁	—	2	1	no	—
471	D₄×C₆₁	—	2	1	no	—
472	D₄×C₆₁	—	2	2	no	—
473	D₄×C₆₁	—	4	2	no	—
474	D₄×C₆₁	—	4	4	no	—
475	D₄×C₆₁	—	4	2	no	—
476	D₄×C₆₁	—	8	1	no	—
477	D₄×C₆₁	—	8	2	no	—
478	D₄×C₆₁	—	8	2	no	—
479	D₄×C₆₁	—	8	2	no	—
480	D₄×C₆₁	—	8	2	no	—
481	D₄×C₆₁	—	8	1	no	—
482	C₂×C₄×C₆₁	—	2	2	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	1	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	—	2	1	no	—
491	C₂×C₄×C₆₁	—	2	1	no	—
492	C₂×C₄×C₆₁	—	2	2	no	—
493	C₂×C₄×C₆₁	—	4	1	no	—
494	C₂×C₄×C₆₁	—	4	4	no	—
495	C₂×C₄×C₆₁	—	4	2	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	1	no	—
500	C₂×C₄×C₆₁	—	8	1	no	—
501	C₂×C₄×C₆₁	—	8	2	no	—
502	C₂×C₄×C₆₁	—	8	2	no	—
503	C₂×C₄×C₆₁	—	8	1	no	—
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	2	yes	—
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	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
514	C₈×C₆₁	—	2	1	no	—
515	C₈×C₆₁	—	2	2	no	—
516	C₈×C₆₁	—	2	1	no	—
517	C₈×C₆₁	—	2	2	no	—
518	C₈×C₆₁	—	2	1	no	—
519	C₈×C₆₁	—	2	1	no	—
520	#61927	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
521	C₂²×C₆₁	—	2	1	no	—
522	C₂²×C₆₁	—	2	1	no	—
523	C₂²×C₆₁	—	2	1	no	—
524	C₂²×C₆₁	—	4	1	no	—
525	C₂²×C₆₁	—	4	2	no	—
526	C₂²×C₆₁	—	4	1	no	—
527	C₂²×C₆₁	—	4	1	no	—
528	C₂²×C₆₁	—	4	2	no	—
529	C₂²×C₆₁	—	4	1	no	—
530	C₂²×C₆₁	—	4	1	no	—
531	C₂²×C₆₁	—	4	1	no	—
532	C₂²×C₆₁	—	4	1	no	—
533	C₂²×C₆₁	—	4	1	no	—
534	C₂²×C₆₁	—	4	1	no	—
535	C₂²×C₆₁	—	4	2	no	—
536	C₂²×C₆₁	—	8	4	no	—
537	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
538	C₄×C₆₁	—	2	1	no	—
539	C₄×C₆₁	—	2	1	no	—
540	C₄×C₆₁	—	2	2	no	—
541	C₄×C₆₁	—	2	2	no	—
542	C₄×C₆₁	—	2	1	no	—
543	C₄×C₆₁	—	2	1	no	—
544	C₄×C₆₁	—	2	2	no	—
545	C₄×C₆₁	—	2	2	no	—
546	C₄×C₆₁	—	4	2	no	—
547	C₄×C₆₁	—	4	1	no	—
548	C₄×C₆₁	—	4	2	no	—
549	C₄×C₆₁	—	4	1	no	—
550	C₄×C₆₁	—	4	2	no	—
551	C₄×C₆₁	—	4	1	no	—
552	C₄×C₆₁	—	4	1	no	—
553	C₄×C₆₁	—	4	1	no	—
554	C₄×C₆₁	#577	1	2	yes	—
555	C₄×C₆₁	#585	1	1	yes	characteristic
556	C₄×C₆₁	#585	1	1	yes	characteristic
557	#3555	C₂×C₆₁	1	1	yes	characteristic, complemented
558	#3506	C₂×C₆₁	1	1	yes	characteristic, complemented
559	#3401	C₂×C₆₁	1	2	yes	complemented
560	#3398	C₂×C₆₁	1	1	yes	characteristic, complemented
561	#3397	C₂×C₆₁	1	1	yes	characteristic, complemented
562	#3394	C₂×C₆₁	1	2	yes	complemented
563	#3393	C₂×C₆₁	1	1	yes	characteristic, complemented
564	#3392	C₂×C₆₁	1	1	yes	characteristic, complemented
565	#3371	C₂×C₆₁	1	2	yes	complemented
566	#3369	C₂×C₆₁	1	1	yes	characteristic, complemented
567	#3366	C₂×C₆₁	1	1	yes	characteristic, complemented
568	#3365	C₂×C₆₁	1	2	yes	complemented
569	#3362	C₂×C₆₁	1	1	yes	characteristic, complemented
570	#3360	C₂×C₆₁	1	1	yes	characteristic, complemented
571	#3224	C₂×C₆₁	1	2	yes	complemented
572	#3222	C₂×C₆₁	1	2	yes	complemented
573	#3212	C₂×C₆₁	1	1	yes	characteristic, complemented
574	#3210	C₂×C₆₁	1	1	yes	characteristic, complemented
575	#3125	C₂×C₆₁	1	2	yes	complemented
576	#3120	C₂×C₆₁	1	2	yes	complemented
577	#3105	C₂×C₆₁	1	1	yes	characteristic, complemented
578	#3101	C₂×C₆₁	1	1	yes	characteristic, complemented
579	#2986	C₂×C₆₁	1	1	yes	characteristic, complemented
580	C₂×C₆₁	—	4	1	no	—
581	C₂×C₆₁	—	8	1	no	—
582	C₂×C₆₁	—	8	2	no	—
583	C₂×C₆₁	—	8	1	no	—
584	C₂×C₆₁	—	8	1	no	—
585	C₂×C₆₁	#3487	1	1	yes	characteristic
586	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
587	C₂×C₆₁	#3584	1	1	yes	characteristic
588	#563	—	2	2	no	—
589	#559	C₂²×C₆₁	1	2	yes	—
590	#559	C₂²×C₆₁	1	2	yes	—
591	Q₈²	C₂²×C₆₁	1	1	yes	characteristic, complemented
592	#557	C₂²×C₆₁	1	1	yes	characteristic, complemented
593	#557	C₂²×C₆₁	1	2	yes	complemented
594	#556	—	2	1	no	—
595	#556	C₂²×C₆₁	1	1	yes	characteristic
596	#556	C₂²×C₆₁	1	1	yes	characteristic
597	#556	C₂²×C₆₁	1	1	yes	characteristic, complemented
598	#556	C₂²×C₆₁	1	2	yes	complemented
599	#555	—	2	1	no	—
600	#554	C₂²×C₆₁	1	1	yes	characteristic, complemented
601	#553	—	2	2	no	—
602	#552	—	2	1	no	—
603	#550	C₂²×C₆₁	1	1	yes	characteristic
604	#550	C₂²×C₆₁	1	1	yes	characteristic
605	#547	—	2	1	no	—
606	#544	—	2	1	no	—
607	#542	C₂²×C₆₁	1	2	yes	—
608	#541	—	2	1	no	—
609	#541	—	2	2	no	—
610	#541	C₂²×C₆₁	1	2	yes	—
611	#538	—	2	2	no	—
612	#535	C₂²×C₆₁	1	2	yes	—
613	#533	C₂²×C₆₁	1	1	yes	characteristic
614	#533	C₂²×C₆₁	1	1	yes	characteristic
615	#532	C₂²×C₆₁	1	1	yes	characteristic
616	#529	C₂²×C₆₁	1	1	yes	characteristic
617	#525	—	2	1	no	—
618	#525	—	2	1	no	—
619	#520	C₂²×C₆₁	1	2	yes	—
620	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
621	#497	C₂²×C₆₁	1	2	yes	—
622	#496	C₂²×C₆₁	1	2	yes	—
623	#495	C₂²×C₆₁	1	2	yes	—
624	#495	C₂²×C₆₁	1	2	yes	complemented
625	#494	C₂²×C₆₁	1	1	yes	characteristic, complemented
626	#492	C₂²×C₆₁	1	2	yes	—
627	#492	C₂²×C₆₁	1	1	yes	characteristic, complemented
628	#490	C₂²×C₆₁	1	2	yes	—
629	#489	C₂²×C₆₁	1	2	yes	—
630	#488	C₂²×C₆₁	1	2	yes	—
631	#488	C₂²×C₆₁	1	2	yes	complemented
632	#487	C₂²×C₆₁	1	1	yes	characteristic, complemented
633	#486	C₂²×C₆₁	1	2	yes	—
634	#486	C₂²×C₆₁	1	1	yes	characteristic, complemented
635	#484	C₂²×C₆₁	1	1	yes	characteristic
636	#483	C₂²×C₆₁	1	2	yes	—
637	#481	C₂²×C₆₁	1	1	yes	characteristic
638	#479	C₂²×C₆₁	1	2	yes	complemented
639	#478	C₂²×C₆₁	1	1	yes	characteristic
640	#478	C₂²×C₆₁	1	1	yes	characteristic
641	#478	C₂²×C₆₁	1	2	yes	complemented
642	#476	C₂²×C₆₁	1	1	yes	characteristic
643	#476	C₂²×C₆₁	1	1	yes	characteristic
644	#476	C₂²×C₆₁	1	2	yes	complemented
645	#475	C₂²×C₆₁	1	2	yes	complemented
646	#464	C₂²×C₆₁	1	2	yes	—
647	#464	C₂²×C₆₁	1	2	yes	—
648	#464	C₂²×C₆₁	1	2	yes	—
649	#464	C₂²×C₆₁	1	2	yes	complemented
650	#464	C₂²×C₆₁	1	2	yes	complemented
651	#464	C₂²×C₆₁	1	2	yes	complemented
652	#463	C₂²×C₆₁	1	2	yes	—
653	#463	C₂²×C₆₁	1	1	yes	characteristic
654	#463	C₂²×C₆₁	1	1	yes	characteristic
655	#463	C₂²×C₆₁	1	2	yes	complemented
656	#462	C₂²×C₆₁	1	1	yes	characteristic, complemented
657	#462	C₂²×C₆₁	1	2	yes	complemented
658	#461	C₂²×C₆₁	1	1	yes	characteristic
659	#461	C₂²×C₆₁	1	1	yes	characteristic
660	#461	C₂²×C₆₁	1	1	yes	characteristic, complemented
661	#461	C₂²×C₆₁	1	2	yes	complemented
662	#460	C₂²×C₆₁	1	2	yes	—
663	#460	C₂²×C₆₁	1	2	yes	—
664	#460	C₂²×C₆₁	1	2	yes	—
665	#460	C₂²×C₆₁	1	1	yes	characteristic, complemented
666	#459	C₂²×C₆₁	1	2	yes	—
667	#459	C₂²×C₆₁	1	1	yes	characteristic, complemented
668	#452	C₂²×C₆₁	1	2	yes	—
669	#452	C₂²×C₆₁	1	2	yes	—
670	#452	C₂²×C₆₁	1	2	yes	—
671	#450	C₂²×C₆₁	1	2	yes	—
672	#450	C₂²×C₆₁	1	1	yes	characteristic
673	#449	C₂²×C₆₁	1	2	yes	—
674	#447	C₂²×C₆₁	1	1	yes	characteristic
675	#446	C₂²×C₆₁	1	1	yes	characteristic, complemented
676	#446	C₂²×C₆₁	1	1	yes	characteristic, complemented
677	#446	C₂²×C₆₁	1	2	yes	complemented
678	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
679	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
680	C₈×Q₈	C₂²×C₆₁	1	2	yes	complemented
681	#442	C₂²×C₆₁	1	2	yes	complemented
682	#441	C₂²×C₆₁	1	2	yes	complemented
683	#441	C₂²×C₆₁	1	2	yes	complemented
684	#440	C₂²×C₆₁	1	2	yes	complemented
685	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	complemented
686	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
687	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
688	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
689	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
690	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
691	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
692	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
693	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
694	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
695	#433	C₂²×C₆₁	1	2	yes	—
696	#433	C₂²×C₆₁	1	2	yes	—
697	#431	C₂²×C₆₁	1	1	yes	characteristic
698	#431	C₂²×C₆₁	1	1	yes	characteristic
699	C₆₁	#61927	1	1	yes	characteristic, direct product factor, Sylow
700	C₂×#41	—	2	1	no	—
701	C₂×#41	—	2	1	no	—
702	C₂×#41	C₂³×C₆₁	1	2	yes	—
703	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
704	C₂³×C₄	—	2	1	no	—
705	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
706	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
707	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
708	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
709	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
710	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
711	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
712	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
713	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
714	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
715	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
716	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
717	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
718	C₂×D₈	C₂³×C₆₁	1	2	yes	—
719	C₄⋊Q₈	—	2	2	no	—
720	C₄⋊Q₈	—	2	2	no	—
721	C₄⋊Q₈	—	2	1	no	—
722	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
723	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
724	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
725	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
726	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
727	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
728	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
729	#127	C₂³×C₆₁	1	1	yes	characteristic
730	#127	C₂³×C₆₁	1	2	yes	—
731	#127	C₂³×C₆₁	1	2	yes	—
732	#126	—	2	2	no	—
733	#126	—	2	2	no	—
734	#126	—	2	2	no	—
735	#126	—	2	2	no	—
736	#126	—	2	2	no	—
737	#126	—	2	2	no	—
738	#126	—	2	2	no	—
739	#126	—	2	2	no	—
740	#126	—	2	1	no	—
741	#125	—	2	2	no	—
742	#125	—	2	2	no	—
743	#125	—	2	2	no	—
744	#125	—	2	2	no	—
745	#125	—	2	2	no	—
746	#125	—	2	1	no	—
747	#125	—	2	1	no	—
748	#125	D₄×C₆₁	1	2	yes	—
749	#125	C₂³×C₆₁	1	1	yes	characteristic
750	#125	C₂³×C₆₁	1	2	yes	—
751	#124	—	2	2	no	—
752	#124	—	2	2	no	—
753	#124	—	2	2	no	—
754	#124	C₂³×C₆₁	1	1	yes	characteristic
755	#124	C₂³×C₆₁	1	2	yes	—
756	#124	C₂³×C₆₁	1	2	yes	—
757	#124	C₂³×C₆₁	1	2	yes	—
758	#124	C₂³×C₆₁	1	2	yes	—
759	#123	—	2	1	no	—
760	#123	—	2	2	no	—
761	#123	—	2	2	no	—
762	#123	—	2	2	no	—
763	#123	—	2	2	no	—
764	#123	—	2	2	no	—
765	C₂²⋊Q₈	—	2	1	no	—
766	C₂²⋊Q₈	—	2	1	no	—
767	C₂²⋊Q₈	—	2	1	no	—
768	C₂²⋊Q₈	—	2	1	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	2	1	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
774	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
775	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
776	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
777	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
778	#121	—	2	1	no	—
779	#121	—	2	1	no	—
780	#121	—	2	1	no	—
781	#121	—	2	1	no	—
782	#121	—	2	2	no	—
783	#121	—	2	2	no	—
784	#121	—	2	2	no	—
785	#121	—	2	2	no	—
786	#121	C₂³×C₆₁	1	1	yes	characteristic
787	#120	—	2	2	no	—
788	#120	—	2	2	no	—
789	C₄×Q₈	—	2	1	no	—
790	C₄×Q₈	—	2	1	no	—
791	C₄×Q₈	—	2	2	no	—
792	C₄×Q₈	—	2	1	no	—
793	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
794	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
795	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
796	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
797	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
798	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
799	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
800	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
801	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
802	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	2	no	—
806	C₄×D₄	—	2	2	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	1	no	—
809	C₄×D₄	—	2	1	no	—
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
813	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
814	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
815	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
816	C₄×D₄	C₂³×C₆₁	1	2	yes	—
817	C₄×D₄	C₂³×C₆₁	1	2	yes	—
818	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
819	C₄×D₄	C₂³×C₆₁	1	2	yes	—
820	#117	—	2	1	no	—
821	#117	—	2	2	no	—
822	#117	—	2	1	no	—
823	#117	—	2	1	no	—
824	#117	—	2	2	no	—
825	#117	—	2	1	no	—
826	#117	—	2	1	no	—
827	#117	C₂³×C₆₁	1	2	yes	—
828	C₂×C₄⋊C₄	—	2	2	no	—
829	C₂×C₄⋊C₄	—	2	1	no	—
830	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
831	C₂×C₂²⋊C₄	—	2	1	no	—
832	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
833	#107	C₂³×C₆₁	1	1	yes	characteristic
834	#107	C₂³×C₆₁	1	1	yes	characteristic
835	#106	C₂³×C₆₁	1	1	yes	characteristic
836	#106	C₂³×C₆₁	1	2	yes	—
837	#106	C₂³×C₆₁	1	1	yes	characteristic
838	#106	C₂³×C₆₁	1	2	yes	—
839	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
840	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
841	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
842	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
843	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
844	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
845	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
846	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
847	#103	C₂³×C₆₁	1	1	yes	characteristic
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	2	yes	—
852	#103	C₂³×C₆₁	1	2	yes	—
853	#103	C₂³×C₆₁	1	2	yes	—
854	#103	C₂³×C₆₁	1	2	yes	—
855	#102	C₂³×C₆₁	1	1	yes	characteristic
856	#102	C₂³×C₆₁	1	1	yes	characteristic
857	#102	C₂³×C₆₁	1	1	yes	characteristic
858	#102	C₂³×C₆₁	1	1	yes	characteristic
859	#102	C₂³×C₆₁	1	1	yes	characteristic
860	#102	C₂³×C₆₁	1	1	yes	characteristic
861	#102	C₂³×C₆₁	1	2	yes	—
862	#102	C₂³×C₆₁	1	2	yes	—
863	#102	C₂³×C₆₁	1	2	yes	—
864	#102	C₂³×C₆₁	1	2	yes	—
865	#102	C₂³×C₆₁	1	2	yes	—
866	#102	C₂³×C₆₁	1	2	yes	—
867	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
868	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
869	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
870	#97	C₂³×C₆₁	1	2	yes	—
871	#97	C₂³×C₆₁	1	2	yes	—
872	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
873	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
874	C₄×C₈	C₂³×C₆₁	1	2	yes	—
875	C₄×C₈	C₂³×C₆₁	1	2	yes	—
876	C₄×C₈	C₂³×C₆₁	1	2	yes	—
877	C₂⁴	—	2	1	no	—
878	#41	—	4	2	no	—
879	#41	—	4	2	no	—
880	#41	—	8	2	no	—
881	#41	—	8	2	no	—
882	C₂×Q₈	—	2	1	no	—
883	C₂×Q₈	—	2	2	no	—
884	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
885	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
886	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
887	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
888	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
889	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
890	C₂×D₄	—	2	2	no	—
891	C₂×D₄	—	2	1	no	—
892	C₂×D₄	—	2	1	no	—
893	C₂×D₄	—	2	1	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	2	1	no	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	—	4	1	no	—
900	C₂×D₄	—	4	1	no	—
901	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
902	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
903	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
904	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
905	C₂²×C₄	—	2	1	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	2	2	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	1	no	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	8	2	no	—
916	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
917	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
918	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
919	Q₁₆	—	4	2	no	—
920	Q₁₆	—	4	2	no	—
921	Q₁₆	—	4	2	no	—
922	SD₁₆	—	4	2	no	—
923	SD₁₆	—	4	2	no	—
924	SD₁₆	—	4	2	no	—
925	SD₁₆	—	4	1	no	—
926	SD₁₆	—	4	2	no	—
927	SD₁₆	—	4	2	no	—
928	SD₁₆	—	4	2	no	—
929	SD₁₆	—	4	1	no	—
930	D₈	—	4	1	no	—
931	D₈	—	4	2	no	—
932	D₈	—	4	1	no	—
933	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
934	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
935	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
936	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
937	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
938	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
962	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
963	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
964	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
965	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
966	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
967	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
968	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
969	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
970	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
971	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
972	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
973	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
974	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	—	2	1	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
997	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
998	C₄²	—	2	2	no	—
999	C₄²	—	2	2	no	—
1000	C₄²	—	2	2	no	—
1001	C₄²	—	2	1	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	—	2	2	no	—
1005	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1006	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1007	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1008	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1009	C₄²	C₂⁴×C₆₁	1	2	yes	—
1010	C₄²	C₂⁴×C₆₁	1	2	yes	—
1011	C₂³	—	2	1	no	—
1012	C₂³	—	2	1	no	—
1013	C₂³	—	2	1	no	—
1014	C₂³	—	2	2	no	—
1015	C₂³	—	4	2	no	—
1016	C₂³	—	8	1	no	—
1017	C₂³	—	8	1	no	—
1018	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1019	Q₈	—	2	2	no	—
1020	Q₈	—	2	2	no	—
1021	Q₈	—	2	1	no	—
1022	Q₈	—	2	2	no	—
1023	Q₈	—	2	2	no	—
1024	Q₈	—	2	1	no	—
1025	Q₈	—	2	2	no	—
1026	Q₈	—	2	2	no	—
1027	Q₈	—	4	2	no	—
1028	Q₈	—	8	1	no	—
1029	Q₈	—	8	2	no	—
1030	D₄	—	2	1	no	—
1031	D₄	—	2	1	no	—
1032	D₄	—	2	1	no	—
1033	D₄	—	2	1	no	—
1034	D₄	—	2	2	no	—
1035	D₄	—	2	1	no	—
1036	D₄	—	2	1	no	—
1037	D₄	—	2	2	no	—
1038	D₄	—	4	2	no	—
1039	D₄	—	4	4	no	—
1040	D₄	—	4	2	no	—
1041	D₄	—	8	1	no	—
1042	D₄	—	8	2	no	—
1043	D₄	—	8	2	no	—
1044	D₄	—	8	2	no	—
1045	D₄	—	8	2	no	—
1046	D₄	—	8	1	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	4	1	no	—
1059	C₂×C₄	—	4	4	no	—
1060	C₂×C₄	—	4	2	no	—
1061	C₂×C₄	—	4	2	no	—
1062	C₂×C₄	—	4	2	no	—
1063	C₂×C₄	—	8	2	no	—
1064	C₂×C₄	—	8	1	no	—
1065	C₂×C₄	—	8	1	no	—
1066	C₂×C₄	—	8	2	no	—
1067	C₂×C₄	—	8	2	no	—
1068	C₂×C₄	—	8	1	no	—
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	2	yes	—
1073	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1074	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1075	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1076	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1077	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1078	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1079	C₈	—	2	1	no	—
1080	C₈	—	2	2	no	—
1081	C₈	—	2	1	no	—
1082	C₈	—	2	2	no	—
1083	C₈	—	2	1	no	—
1084	C₈	—	2	1	no	—
1085	C₂²	—	2	1	no	—
1086	C₂²	—	2	1	no	—
1087	C₂²	—	2	1	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	4	1	no	—
1091	C₂²	—	4	2	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	4	2	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	4	1	no	—
1096	C₂²	—	4	2	no	—
1097	C₂²	—	4	1	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	1	no	—
1100	C₂²	—	8	4	no	—
1101	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1102	C₄	—	2	1	no	—
1103	C₄	—	2	2	no	—
1104	C₄	—	2	2	no	—
1105	C₄	—	2	1	no	—
1106	C₄	—	2	1	no	—
1107	C₄	—	2	2	no	—
1108	C₄	—	2	2	no	—
1109	C₄	—	2	1	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	1	no	—
1113	C₄	—	4	2	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	4	2	no	—
1116	C₄	—	4	1	no	—
1117	C₄	—	4	2	no	—
1118	C₄	C₆₁×#577	1	2	yes	—
1119	C₄	C₆₁×#585	1	1	yes	characteristic
1120	C₄	C₆₁×#585	1	1	yes	characteristic
1121	C₂	—	4	1	no	—
1122	C₂	—	8	1	no	—
1123	C₂	—	8	1	no	—
1124	C₂	—	8	1	no	—
1125	C₂	—	8	2	no	—
1126	C₂	C₆₁×#3487	1	1	yes	characteristic
1127	C₂	C₂×C₆₁×#577	1	1	yes	characteristic
1128	C₂	C₆₁×#3584	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3555	C₂	semidirect
2. C₆₁×#3506	C₂	semidirect
3. C₆₁×#3401	C₂	semidirect
4. C₆₁×#3398	C₂	semidirect
5. C₆₁×#3397	C₂	semidirect
6. C₆₁×#3394	C₂	semidirect
7. C₆₁×#3393	C₂	semidirect
8. C₆₁×#3392	C₂	semidirect
9. C₆₁×#3371	C₂	semidirect
10. C₆₁×#3369	C₂	semidirect
11. C₆₁×#3366	C₂	semidirect
12. C₆₁×#3365	C₂	semidirect
13. C₆₁×#3362	C₂	semidirect
14. C₆₁×#3360	C₂	semidirect
15. C₆₁×#3224	C₂	semidirect
16. C₆₁×#3222	C₂	semidirect
17. C₆₁×#3212	C₂	semidirect
18. C₆₁×#3210	C₂	semidirect
19. C₆₁×#3125	C₂	semidirect
20. C₆₁×#3120	C₂	semidirect
21. C₆₁×#3105	C₂	semidirect
22. C₆₁×#3101	C₂	semidirect
23. C₆₁×#2986	C₂	semidirect
27. Q₈²×C₆₁	C₂²	semidirect
28. C₆₁×#557	C₂²	semidirect
29. C₆₁×#557	C₂²	semidirect
33. C₆₁×#556	C₂²	semidirect
34. C₆₁×#556	C₂²	semidirect
36. C₆₁×#554	C₂²	semidirect
60. C₆₁×#495	C₂²	semidirect
61. C₆₁×#494	C₂²	semidirect
63. C₆₁×#492	C₂²	semidirect
67. C₆₁×#488	C₂²	semidirect
68. C₆₁×#487	C₂²	semidirect
70. C₆₁×#486	C₂²	semidirect
74. C₆₁×#479	C₂²	semidirect
77. C₆₁×#478	C₂²	semidirect
80. C₆₁×#476	C₂²	semidirect
81. C₆₁×#475	C₂²	semidirect
85. C₆₁×#464	C₂²	semidirect
86. C₆₁×#464	C₂²	semidirect
87. C₆₁×#464	C₂²	semidirect
91. C₆₁×#463	C₂²	semidirect
92. C₆₁×#462	C₂²	semidirect
93. C₆₁×#462	C₂²	semidirect
96. C₆₁×#461	C₂²	semidirect
97. C₆₁×#461	C₂²	semidirect
101. C₆₁×#460	C₂²	semidirect
103. C₆₁×#459	C₂²	semidirect
111. C₆₁×#446	C₂²	semidirect
112. C₆₁×#446	C₂²	semidirect
113. C₆₁×#446	C₂²	semidirect
114. C₈×Q₈×C₆₁	C₂²	semidirect
115. C₈×Q₈×C₆₁	C₂²	semidirect
116. C₈×Q₈×C₆₁	C₂²	semidirect
117. C₆₁×#442	C₂²	semidirect
118. C₆₁×#441	C₂²	semidirect
119. C₆₁×#441	C₂²	semidirect
120. C₆₁×#440	C₂²	semidirect
121. C₄×Q₁₆×C₆₁	C₂²	semidirect
126. C₄×SD₁₆×C₆₁	C₂²	semidirect
127. C₄×SD₁₆×C₆₁	C₂²	semidirect
128. C₄×SD₁₆×C₆₁	C₂²	semidirect
520. #61927	C₆₁	direct (N × H)
557. #3555	C₂×C₆₁	semidirect
558. #3506	C₂×C₆₁	semidirect
559. #3401	C₂×C₆₁	semidirect
560. #3398	C₂×C₆₁	semidirect
561. #3397	C₂×C₆₁	semidirect
562. #3394	C₂×C₆₁	semidirect
563. #3393	C₂×C₆₁	semidirect
564. #3392	C₂×C₆₁	semidirect
565. #3371	C₂×C₆₁	semidirect
566. #3369	C₂×C₆₁	semidirect
567. #3366	C₂×C₆₁	semidirect
568. #3365	C₂×C₆₁	semidirect
569. #3362	C₂×C₆₁	semidirect
570. #3360	C₂×C₆₁	semidirect
571. #3224	C₂×C₆₁	semidirect
572. #3222	C₂×C₆₁	semidirect
573. #3212	C₂×C₆₁	semidirect
574. #3210	C₂×C₆₁	semidirect
575. #3125	C₂×C₆₁	semidirect
576. #3120	C₂×C₆₁	semidirect
577. #3105	C₂×C₆₁	semidirect
578. #3101	C₂×C₆₁	semidirect
579. #2986	C₂×C₆₁	semidirect
591. Q₈²	C₂²×C₆₁	semidirect
592. #557	C₂²×C₆₁	semidirect
593. #557	C₂²×C₆₁	semidirect
597. #556	C₂²×C₆₁	semidirect
598. #556	C₂²×C₆₁	semidirect
600. #554	C₂²×C₆₁	semidirect
624. #495	C₂²×C₆₁	semidirect
625. #494	C₂²×C₆₁	semidirect
627. #492	C₂²×C₆₁	semidirect
631. #488	C₂²×C₆₁	semidirect
632. #487	C₂²×C₆₁	semidirect
634. #486	C₂²×C₆₁	semidirect
638. #479	C₂²×C₆₁	semidirect
641. #478	C₂²×C₆₁	semidirect
644. #476	C₂²×C₆₁	semidirect
645. #475	C₂²×C₆₁	semidirect
649. #464	C₂²×C₆₁	semidirect
650. #464	C₂²×C₆₁	semidirect
651. #464	C₂²×C₆₁	semidirect
655. #463	C₂²×C₆₁	semidirect
656. #462	C₂²×C₆₁	semidirect
657. #462	C₂²×C₆₁	semidirect
660. #461	C₂²×C₆₁	semidirect
661. #461	C₂²×C₆₁	semidirect
665. #460	C₂²×C₆₁	semidirect
667. #459	C₂²×C₆₁	semidirect
675. #446	C₂²×C₆₁	semidirect
676. #446	C₂²×C₆₁	semidirect
677. #446	C₂²×C₆₁	semidirect
678. C₈×Q₈	C₂²×C₆₁	semidirect
679. C₈×Q₈	C₂²×C₆₁	semidirect
680. C₈×Q₈	C₂²×C₆₁	semidirect
681. #442	C₂²×C₆₁	semidirect
682. #441	C₂²×C₆₁	semidirect
683. #441	C₂²×C₆₁	semidirect
684. #440	C₂²×C₆₁	semidirect
685. C₄×Q₁₆	C₂²×C₆₁	semidirect
690. C₄×SD₁₆	C₂²×C₆₁	semidirect
691. C₄×SD₁₆	C₂²×C₆₁	semidirect
692. C₄×SD₁₆	C₂²×C₆₁	semidirect
699. C₆₁	#61927	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×#3555	2
C₆₁×#3506	2
C₆₁×#3401	2
C₆₁×#3398	2
C₆₁×#3397	2
C₆₁×#3394	2
C₆₁×#3393	2
C₆₁×#3392	2
C₆₁×#3371	2
C₆₁×#3369	2
C₆₁×#3366	2
C₆₁×#3365	2
C₆₁×#3362	2
C₆₁×#3360	2
C₆₁×#3224	2
C₆₁×#3222	2
C₆₁×#3212	2
C₆₁×#3210	2
C₆₁×#3125	2
C₆₁×#3120	2
C₆₁×#3105	2
C₆₁×#3101	2
C₆₁×#2986	2
#61927	61

Subgroups — C61×#61927 #29565360

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61927 #29565360