Subgroups — C₆₁×#61342 #29564775

Order 15616.

1724 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3509	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3377	C₂	1	4	yes	maximal, complemented
4	C₆₁×#3374	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3374	C₂	1	4	yes	maximal, complemented
6	C₆₁×#3369	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3364	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3363	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3139	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#3137	C₂	1	2	yes	maximal
11	C₆₁×#3082	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3076	C₂	1	1	yes	maximal, characteristic
13	C₆₁×#3044	C₂	1	2	yes	maximal
14	C₂×C₆₁×#462	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#2950	C₂	1	2	yes	maximal, complemented
17	C₄×#137×C₆₁	C₂	1	1	yes	maximal, characteristic
18	C₂×#137×C₆₁	C₂²	1	1	yes	characteristic
19	C₂²×Q₁₆×C₆₁	C₂²	1	2	yes	—
20	Q₈²×C₆₁	—	2	1	no	—
21	Q₈²×C₆₁	C₂²	1	2	yes	—
22	C₆₁×#557	—	2	1	no	—
23	C₆₁×#557	—	2	2	no	—
24	C₆₁×#557	C₂²	1	2	yes	—
25	C₆₁×#557	C₂²	1	2	yes	—
26	C₆₁×#557	C₂²	1	2	yes	—
27	C₆₁×#557	C₂²	1	4	yes	—
28	C₆₁×#556	C₂²	1	2	yes	—
29	C₆₁×#556	C₂²	1	2	yes	—
30	C₆₁×#552	—	2	2	no	—
31	C₆₁×#552	—	2	2	no	—
32	C₆₁×#544	—	2	2	no	—
33	C₆₁×#544	C₂²	1	2	yes	—
34	C₆₁×#541	—	2	2	no	—
35	C₆₁×#536	C₂²	1	2	yes	—
36	C₆₁×#533	—	2	1	no	—
37	C₆₁×#533	—	2	1	no	—
38	C₆₁×#533	—	2	2	no	—
39	C₆₁×#533	C₂²	1	1	yes	characteristic
40	C₆₁×#533	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
42	C₆₁×#519	C₂²	1	2	yes	—
43	C₆₁×#519	C₂²	1	2	yes	—
44	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
46	C₆₁×#491	C₂²	1	4	yes	—
47	C₆₁×#491	C₂²	1	4	yes	—
48	C₆₁×#489	C₂²	1	4	yes	—
49	C₆₁×#488	C₂²	1	4	yes	—
50	C₆₁×#487	C₂²	1	2	yes	—
51	C₆₁×#487	C₂²	1	4	yes	—
52	C₆₁×#487	C₂²	1	2	yes	—
53	C₆₁×#479	C₂²	1	2	yes	—
54	C₆₁×#479	C₂²	1	4	yes	—
55	C₆₁×#479	C₂²	1	4	yes	—
56	C₆₁×#478	C₂²	1	2	yes	—
57	C₆₁×#477	C₂²	1	1	yes	characteristic
58	C₆₁×#477	C₂²	1	4	yes	—
59	C₆₁×#476	C₂²	1	1	yes	characteristic
60	C₆₁×#475	C₂²	1	1	yes	characteristic
61	C₆₁×#475	C₂²	1	4	yes	—
62	C₆₁×#474	C₂²	1	1	yes	characteristic
63	C₆₁×#464	C₂²	1	4	yes	—
64	C₆₁×#464	C₂²	1	4	yes	—
65	C₆₁×#462	C₂²	1	2	yes	—
66	C₆₁×#462	C₂²	1	2	yes	—
67	C₆₁×#462	C₂²	1	4	yes	—
68	C₆₁×#462	C₂²	1	4	yes	—
69	C₆₁×#462	C₂²	1	4	yes	—
70	C₆₁×#446	C₂²	1	2	yes	—
71	C₆₁×#446	C₂²	1	4	yes	—
72	C₈×Q₈×C₆₁	C₂²	1	2	yes	—
73	C₆₁×#441	C₂²	1	4	yes	—
74	C₆₁×#441	C₂²	1	2	yes	—
75	C₆₁×#441	C₂²	1	4	yes	—
76	C₆₁×#440	C₂²	1	2	yes	—
77	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
78	C₄×Q₁₆×C₆₁	C₂²	1	4	yes	—
79	C₄×Q₁₆×C₆₁	C₂²	1	4	yes	—
80	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
81	C₆₁×#428	C₂²	1	1	yes	characteristic
82	C₆₁×#427	C₂²	1	2	yes	—
83	C₆₁×#424	C₂²	1	2	yes	—
84	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
85	C₆₁×#419	C₂²	1	2	yes	—
86	C₆₁×#419	C₂²	1	2	yes	—
87	C₆₁×#419	C₂²	1	1	yes	characteristic
88	C₆₁×#417	C₂²	1	1	yes	characteristic
89	C₆₁×#416	C₂²	1	2	yes	—
90	C₂×#103×C₆₁	C₂²	1	2	yes	—
91	C₆₁×#405	C₂²	1	2	yes	—
92	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
93	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
94	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
95	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
96	#137×C₆₁	—	2	4	no	—
97	C₂×Q₁₆×C₆₁	—	2	8	no	—
98	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
99	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
100	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
101	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
102	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
103	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
105	C₄⋊Q₈×C₆₁	—	2	2	no	—
106	C₄⋊Q₈×C₆₁	—	2	4	no	—
107	C₄⋊Q₈×C₆₁	—	2	2	no	—
108	C₄⋊Q₈×C₆₁	—	2	4	no	—
109	C₄⋊Q₈×C₆₁	—	2	2	no	—
110	C₄⋊Q₈×C₆₁	—	2	1	no	—
111	C₄⋊Q₈×C₆₁	—	2	1	no	—
112	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
113	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
114	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
115	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
116	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
117	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
118	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
119	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
120	#126×C₆₁	—	2	4	no	—
121	#126×C₆₁	—	2	4	no	—
122	#125×C₆₁	—	2	2	no	—
123	#125×C₆₁	—	2	2	no	—
124	#125×C₆₁	—	2	4	no	—
125	#125×C₆₁	—	2	4	no	—
126	#125×C₆₁	—	2	4	no	—
127	#125×C₆₁	—	2	4	no	—
128	#125×C₆₁	—	2	4	no	—
129	#125×C₆₁	—	2	2	no	—
130	#125×C₆₁	D₄	1	2	yes	—
131	#125×C₆₁	C₂³	1	2	yes	—
132	#125×C₆₁	C₂³	1	4	yes	—
133	#124×C₆₁	C₂³	1	4	yes	—
134	#123×C₆₁	—	2	4	no	—
135	C₂²⋊Q₈×C₆₁	—	2	2	no	—
136	C₂²⋊Q₈×C₆₁	—	2	2	no	—
137	C₂²⋊Q₈×C₆₁	—	2	1	no	—
138	C₂²⋊Q₈×C₆₁	—	2	1	no	—
139	C₂²⋊Q₈×C₆₁	—	2	2	no	—
140	C₂²⋊Q₈×C₆₁	—	2	2	no	—
141	C₂²⋊Q₈×C₆₁	—	2	4	no	—
142	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
143	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
144	C₄×Q₈×C₆₁	—	2	2	no	—
145	C₄×Q₈×C₆₁	—	2	2	no	—
146	C₄×Q₈×C₆₁	—	2	2	no	—
147	C₄×Q₈×C₆₁	—	2	2	no	—
148	C₄×Q₈×C₆₁	—	2	2	no	—
149	C₄×Q₈×C₆₁	—	2	4	no	—
150	C₄×Q₈×C₆₁	—	2	2	no	—
151	C₄×Q₈×C₆₁	—	2	2	no	—
152	C₄×Q₈×C₆₁	—	2	2	no	—
153	C₄×Q₈×C₆₁	—	2	1	no	—
154	C₄×Q₈×C₆₁	—	2	1	no	—
155	C₄×Q₈×C₆₁	—	2	1	no	—
156	C₄×Q₈×C₆₁	—	2	1	no	—
157	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
158	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
159	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
160	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
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	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
165	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
166	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
167	C₄×D₄×C₆₁	—	2	1	no	—
168	C₄×D₄×C₆₁	—	2	1	no	—
169	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
170	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
171	#117×C₆₁	—	2	2	no	—
172	#117×C₆₁	—	2	2	no	—
173	#117×C₆₁	—	2	4	no	—
174	#117×C₆₁	—	2	4	no	—
175	#117×C₆₁	—	2	1	no	—
176	#117×C₆₁	C₂³	1	2	yes	—
177	#117×C₆₁	C₂³	1	1	yes	characteristic
178	#117×C₆₁	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
180	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
181	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
182	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₆₁	—	2	1	no	—
184	C₂×C₄²×C₆₁	—	2	1	no	—
185	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
186	#107×C₆₁	C₂³	1	2	yes	—
187	#107×C₆₁	C₂³	1	2	yes	—
188	#107×C₆₁	C₂³	1	2	yes	—
189	#106×C₆₁	C₂³	1	2	yes	—
190	#106×C₆₁	C₂³	1	2	yes	—
191	#106×C₆₁	C₂³	1	2	yes	—
192	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
193	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
194	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
195	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
196	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
197	#103×C₆₁	C₂³	1	4	yes	—
198	#103×C₆₁	C₂³	1	4	yes	—
199	#103×C₆₁	C₂³	1	2	yes	—
200	#103×C₆₁	C₂³	1	2	yes	—
201	#103×C₆₁	C₂³	1	2	yes	—
202	#103×C₆₁	C₂³	1	2	yes	—
203	#103×C₆₁	C₂³	1	2	yes	—
204	#103×C₆₁	C₂³	1	4	yes	—
205	#103×C₆₁	C₂³	1	4	yes	—
206	#103×C₆₁	C₂³	1	4	yes	—
207	#103×C₆₁	C₂³	1	4	yes	—
208	#102×C₆₁	C₂³	1	2	yes	—
209	#102×C₆₁	C₂³	1	2	yes	—
210	#102×C₆₁	C₂³	1	2	yes	—
211	#97×C₆₁	C₂³	1	2	yes	—
212	#97×C₆₁	C₂³	1	4	yes	—
213	C₄×C₈×C₆₁	C₂³	1	2	yes	—
214	C₄×C₈×C₆₁	C₂³	1	4	yes	—
215	#41×C₆₁	—	2	2	no	—
216	#41×C₆₁	—	2	2	no	—
217	C₂×Q₈×C₆₁	—	2	1	no	—
218	C₂×Q₈×C₆₁	—	2	1	no	—
219	C₂×Q₈×C₆₁	—	2	2	no	—
220	C₂×Q₈×C₆₁	—	2	1	no	—
221	C₂×Q₈×C₆₁	—	2	4	no	—
222	C₂×Q₈×C₆₁	—	2	2	no	—
223	C₂×Q₈×C₆₁	—	2	4	no	—
224	C₂×Q₈×C₆₁	—	2	4	no	—
225	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
226	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
227	C₂×Q₈×C₆₁	#41	1	4	yes	—
228	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
229	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
230	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
231	C₂×D₄×C₆₁	—	2	1	no	—
232	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₆₁	—	2	1	no	—
234	C₂²×C₄×C₆₁	—	2	2	no	—
235	C₂²×C₄×C₆₁	—	2	1	no	—
236	C₂²×C₄×C₆₁	—	2	1	no	—
237	C₂²×C₄×C₆₁	—	2	1	no	—
238	C₂²×C₄×C₆₁	—	2	1	no	—
239	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
242	Q₁₆×C₆₁	—	2	8	no	—
243	Q₁₆×C₆₁	—	2	8	no	—
244	Q₁₆×C₆₁	—	2	4	no	—
245	SD₁₆×C₆₁	—	2	4	no	—
246	M₁₆×C₆₁	—	2	2	no	—
247	M₁₆×C₆₁	—	2	2	no	—
248	C₂×C₈×C₆₁	—	2	4	no	—
249	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
250	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
251	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
252	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
253	C₄⋊C₄×C₆₁	—	2	2	no	—
254	C₄⋊C₄×C₆₁	—	2	2	no	—
255	C₄⋊C₄×C₆₁	—	2	2	no	—
256	C₄⋊C₄×C₆₁	—	2	2	no	—
257	C₄⋊C₄×C₆₁	—	2	2	no	—
258	C₄⋊C₄×C₆₁	—	2	2	no	—
259	C₄⋊C₄×C₆₁	—	2	1	no	—
260	C₄⋊C₄×C₆₁	—	2	1	no	—
261	C₄⋊C₄×C₆₁	—	2	1	no	—
262	C₄⋊C₄×C₆₁	—	2	4	no	—
263	C₄⋊C₄×C₆₁	—	2	4	no	—
264	C₄⋊C₄×C₆₁	—	2	4	no	—
265	C₄⋊C₄×C₆₁	—	2	4	no	—
266	C₄⋊C₄×C₆₁	—	2	2	no	—
267	C₄⋊C₄×C₆₁	—	2	1	no	—
268	C₄⋊C₄×C₆₁	—	2	4	no	—
269	C₄⋊C₄×C₆₁	—	2	4	no	—
270	C₄⋊C₄×C₆₁	—	2	1	no	—
271	C₄⋊C₄×C₆₁	—	2	4	no	—
272	C₄⋊C₄×C₆₁	—	2	4	no	—
273	C₄⋊C₄×C₆₁	—	2	2	no	—
274	C₄⋊C₄×C₆₁	—	2	4	no	—
275	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
276	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
277	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
279	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
280	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
281	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
283	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
284	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
285	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
286	C₂²⋊C₄×C₆₁	—	2	1	no	—
287	C₂²⋊C₄×C₆₁	—	2	2	no	—
288	C₂²⋊C₄×C₆₁	—	2	1	no	—
289	C₂²⋊C₄×C₆₁	—	2	1	no	—
290	C₂²⋊C₄×C₆₁	—	2	4	no	—
291	C₂²⋊C₄×C₆₁	—	2	4	no	—
292	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
293	C₄²×C₆₁	—	2	1	no	—
294	C₄²×C₆₁	—	2	1	no	—
295	C₄²×C₆₁	—	2	1	no	—
296	C₄²×C₆₁	—	2	2	no	—
297	C₄²×C₆₁	—	2	2	no	—
298	C₄²×C₆₁	—	2	4	no	—
299	C₄²×C₆₁	—	2	4	no	—
300	C₄²×C₆₁	—	2	4	no	—
301	C₄²×C₆₁	—	2	4	no	—
302	C₄²×C₆₁	—	2	2	no	—
303	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
306	C₄²×C₆₁	C₂⁴	1	4	yes	—
307	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
308	C₂³×C₆₁	—	2	1	no	—
309	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
310	Q₈×C₆₁	—	2	4	no	—
311	Q₈×C₆₁	—	2	4	no	—
312	Q₈×C₆₁	—	2	2	no	—
313	Q₈×C₆₁	—	2	4	no	—
314	Q₈×C₆₁	—	2	1	no	—
315	Q₈×C₆₁	—	2	4	no	—
316	Q₈×C₆₁	—	2	1	no	—
317	Q₈×C₆₁	—	4	2	no	—
318	Q₈×C₆₁	—	4	4	no	—
319	Q₈×C₆₁	—	4	2	no	—
320	Q₈×C₆₁	—	8	1	no	—
321	Q₈×C₆₁	—	8	4	no	—
322	Q₈×C₆₁	C₂×#41	1	4	yes	—
323	D₄×C₆₁	—	2	1	no	—
324	D₄×C₆₁	—	2	1	no	—
325	D₄×C₆₁	—	4	2	no	—
326	C₂×C₄×C₆₁	—	2	4	no	—
327	C₂×C₄×C₆₁	—	2	2	no	—
328	C₂×C₄×C₆₁	—	2	2	no	—
329	C₂×C₄×C₆₁	—	2	1	no	—
330	C₂×C₄×C₆₁	—	2	1	no	—
331	C₂×C₄×C₆₁	—	2	2	no	—
332	C₂×C₄×C₆₁	—	2	2	no	—
333	C₂×C₄×C₆₁	—	2	4	no	—
334	C₂×C₄×C₆₁	—	2	1	no	—
335	C₂×C₄×C₆₁	—	2	2	no	—
336	C₂×C₄×C₆₁	—	4	1	no	—
337	C₂×C₄×C₆₁	—	4	2	no	—
338	C₂×C₄×C₆₁	—	4	4	no	—
339	C₂×C₄×C₆₁	—	4	2	no	—
340	C₂×C₄×C₆₁	—	4	2	no	—
341	C₂×C₄×C₆₁	—	8	1	no	—
342	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
344	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
345	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
350	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
351	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
352	C₈×C₆₁	—	2	2	no	—
353	C₈×C₆₁	—	2	2	no	—
354	C₈×C₆₁	—	2	2	no	—
355	C₈×C₆₁	—	2	2	no	—
356	#61342	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
357	C₂²×C₆₁	—	2	1	no	—
358	C₂²×C₆₁	—	2	1	no	—
359	C₂²×C₆₁	—	4	1	no	—
360	C₂²×C₆₁	—	4	1	no	—
361	C₂²×C₆₁	—	4	1	no	—
362	C₂²×C₆₁	#548	1	2	yes	—
363	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
364	C₄×C₆₁	—	2	1	no	—
365	C₄×C₆₁	—	2	1	no	—
366	C₄×C₆₁	—	2	4	no	—
367	C₄×C₆₁	—	2	4	no	—
368	C₄×C₆₁	—	2	1	no	—
369	C₄×C₆₁	—	2	4	no	—
370	C₄×C₆₁	—	4	1	no	—
371	C₄×C₆₁	—	4	2	no	—
372	C₄×C₆₁	—	4	2	no	—
373	C₄×C₆₁	—	4	1	no	—
374	C₄×C₆₁	—	4	4	no	—
375	C₄×C₆₁	—	4	1	no	—
376	C₄×C₆₁	—	4	2	no	—
377	C₄×C₆₁	#548	1	2	yes	—
378	C₄×C₆₁	#578	1	2	yes	—
379	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
380	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
381	#3509	C₂×C₆₁	1	1	yes	characteristic
382	#3502	C₂×C₆₁	1	1	yes	characteristic, complemented
383	#3377	C₂×C₆₁	1	4	yes	complemented
384	#3374	C₂×C₆₁	1	2	yes	complemented
385	#3374	C₂×C₆₁	1	4	yes	complemented
386	#3369	C₂×C₆₁	1	2	yes	complemented
387	#3364	C₂×C₆₁	1	2	yes	complemented
388	#3363	C₂×C₆₁	1	2	yes	complemented
389	#3139	C₂×C₆₁	1	1	yes	characteristic, complemented
390	#3137	C₂×C₆₁	1	2	yes	—
391	#3082	C₂×C₆₁	1	2	yes	complemented
392	#3076	C₂×C₆₁	1	1	yes	characteristic
393	#3044	C₂×C₆₁	1	2	yes	—
394	C₂×#462	C₂×C₆₁	1	1	yes	characteristic, complemented
395	#2962	C₂×C₆₁	1	1	yes	characteristic, complemented
396	#2950	C₂×C₆₁	1	2	yes	complemented
397	C₄×#137	C₂×C₆₁	1	1	yes	characteristic
398	C₂×C₆₁	—	2	2	no	—
399	C₂×C₆₁	—	8	1	no	—
400	C₂×C₆₁	C₂×#548	1	1	yes	characteristic
401	C₂×C₆₁	C₂×#578	1	1	yes	characteristic
402	C₂×C₆₁	#3586	1	1	yes	characteristic
403	C₂×#137	C₂²×C₆₁	1	1	yes	characteristic
404	C₂²×Q₁₆	C₂²×C₆₁	1	2	yes	—
405	Q₈²	—	2	1	no	—
406	Q₈²	C₂²×C₆₁	1	2	yes	—
407	#557	—	2	1	no	—
408	#557	—	2	2	no	—
409	#557	C₂²×C₆₁	1	2	yes	—
410	#557	C₂²×C₆₁	1	2	yes	—
411	#557	C₂²×C₆₁	1	2	yes	—
412	#557	C₂²×C₆₁	1	4	yes	—
413	#556	C₂²×C₆₁	1	2	yes	—
414	#556	C₂²×C₆₁	1	2	yes	—
415	#552	—	2	2	no	—
416	#552	—	2	2	no	—
417	#544	—	2	2	no	—
418	#544	C₂²×C₆₁	1	2	yes	—
419	#541	—	2	2	no	—
420	#536	C₂²×C₆₁	1	2	yes	—
421	#533	—	2	1	no	—
422	#533	—	2	1	no	—
423	#533	—	2	2	no	—
424	#533	C₂²×C₆₁	1	1	yes	characteristic
425	#533	C₂²×C₆₁	1	1	yes	characteristic
426	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
427	#519	C₂²×C₆₁	1	2	yes	—
428	#519	C₂²×C₆₁	1	2	yes	—
429	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
430	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
431	#491	C₂²×C₆₁	1	4	yes	—
432	#491	C₂²×C₆₁	1	4	yes	—
433	#489	C₂²×C₆₁	1	4	yes	—
434	#488	C₂²×C₆₁	1	4	yes	—
435	#487	C₂²×C₆₁	1	2	yes	—
436	#487	C₂²×C₆₁	1	4	yes	—
437	#487	C₂²×C₆₁	1	2	yes	—
438	#479	C₂²×C₆₁	1	2	yes	—
439	#479	C₂²×C₆₁	1	4	yes	—
440	#479	C₂²×C₆₁	1	4	yes	—
441	#478	C₂²×C₆₁	1	2	yes	—
442	#477	C₂²×C₆₁	1	1	yes	characteristic
443	#477	C₂²×C₆₁	1	4	yes	—
444	#476	C₂²×C₆₁	1	1	yes	characteristic
445	#475	C₂²×C₆₁	1	1	yes	characteristic
446	#475	C₂²×C₆₁	1	4	yes	—
447	#474	C₂²×C₆₁	1	1	yes	characteristic
448	#464	C₂²×C₆₁	1	4	yes	—
449	#464	C₂²×C₆₁	1	4	yes	—
450	#462	C₂²×C₆₁	1	2	yes	—
451	#462	C₂²×C₆₁	1	4	yes	—
452	#462	C₂²×C₆₁	1	2	yes	—
453	#462	C₂²×C₆₁	1	4	yes	—
454	#462	C₂²×C₆₁	1	4	yes	—
455	#446	C₂²×C₆₁	1	2	yes	—
456	#446	C₂²×C₆₁	1	4	yes	—
457	C₈×Q₈	C₂²×C₆₁	1	2	yes	—
458	#441	C₂²×C₆₁	1	4	yes	—
459	#441	C₂²×C₆₁	1	2	yes	—
460	#441	C₂²×C₆₁	1	4	yes	—
461	#440	C₂²×C₆₁	1	2	yes	—
462	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
463	C₄×Q₁₆	C₂²×C₆₁	1	4	yes	—
464	C₄×Q₁₆	C₂²×C₆₁	1	4	yes	—
465	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
466	#428	C₂²×C₆₁	1	1	yes	characteristic
467	#427	C₂²×C₆₁	1	2	yes	—
468	#424	C₂²×C₆₁	1	2	yes	—
469	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
470	#419	C₂²×C₆₁	1	2	yes	—
471	#419	C₂²×C₆₁	1	2	yes	—
472	#419	C₂²×C₆₁	1	1	yes	characteristic
473	#417	C₂²×C₆₁	1	1	yes	characteristic
474	#416	C₂²×C₆₁	1	2	yes	—
475	C₂×#103	C₂²×C₆₁	1	2	yes	—
476	#405	C₂²×C₆₁	1	2	yes	—
477	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
478	C₆₁	#61342	1	1	yes	characteristic, direct product factor, Sylow
479	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
480	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
481	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
482	#137	—	2	4	no	—
483	C₂×Q₁₆	—	2	8	no	—
484	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
485	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
486	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
487	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
488	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
489	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
490	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
491	C₄⋊Q₈	—	2	2	no	—
492	C₄⋊Q₈	—	2	4	no	—
493	C₄⋊Q₈	—	2	2	no	—
494	C₄⋊Q₈	—	2	4	no	—
495	C₄⋊Q₈	—	2	2	no	—
496	C₄⋊Q₈	—	2	1	no	—
497	C₄⋊Q₈	—	2	1	no	—
498	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
499	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
500	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
501	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
502	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
503	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
504	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
505	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
506	#126	—	2	4	no	—
507	#126	—	2	4	no	—
508	#125	—	2	2	no	—
509	#125	—	2	2	no	—
510	#125	—	2	4	no	—
511	#125	—	2	4	no	—
512	#125	—	2	4	no	—
513	#125	—	2	4	no	—
514	#125	—	2	4	no	—
515	#125	—	2	2	no	—
516	#125	D₄×C₆₁	1	2	yes	—
517	#125	C₂³×C₆₁	1	2	yes	—
518	#125	C₂³×C₆₁	1	4	yes	—
519	#124	C₂³×C₆₁	1	4	yes	—
520	#123	—	2	4	no	—
521	C₂²⋊Q₈	—	2	2	no	—
522	C₂²⋊Q₈	—	2	2	no	—
523	C₂²⋊Q₈	—	2	1	no	—
524	C₂²⋊Q₈	—	2	1	no	—
525	C₂²⋊Q₈	—	2	2	no	—
526	C₂²⋊Q₈	—	2	2	no	—
527	C₂²⋊Q₈	—	2	4	no	—
528	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
529	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
530	C₄×Q₈	—	2	2	no	—
531	C₄×Q₈	—	2	2	no	—
532	C₄×Q₈	—	2	2	no	—
533	C₄×Q₈	—	2	2	no	—
534	C₄×Q₈	—	2	2	no	—
535	C₄×Q₈	—	2	2	no	—
536	C₄×Q₈	—	2	2	no	—
537	C₄×Q₈	—	2	4	no	—
538	C₄×Q₈	—	2	2	no	—
539	C₄×Q₈	—	2	1	no	—
540	C₄×Q₈	—	2	1	no	—
541	C₄×Q₈	—	2	1	no	—
542	C₄×Q₈	—	2	1	no	—
543	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
544	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
545	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
546	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
547	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
548	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
549	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
550	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
551	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
552	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
553	C₄×D₄	—	2	1	no	—
554	C₄×D₄	—	2	1	no	—
555	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
556	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
557	#117	—	2	2	no	—
558	#117	—	2	2	no	—
559	#117	—	2	4	no	—
560	#117	—	2	4	no	—
561	#117	—	2	1	no	—
562	#117	C₂³×C₆₁	1	1	yes	characteristic
563	#117	C₂³×C₆₁	1	2	yes	—
564	#117	C₂³×C₆₁	1	2	yes	—
565	C₂×C₄⋊C₄	—	2	1	no	—
566	C₂×C₄⋊C₄	—	2	1	no	—
567	C₂×C₄⋊C₄	—	2	1	no	—
568	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
569	C₂×C₄²	—	2	1	no	—
570	C₂×C₄²	—	2	1	no	—
571	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
572	#107	C₂³×C₆₁	1	2	yes	—
573	#107	C₂³×C₆₁	1	2	yes	—
574	#107	C₂³×C₆₁	1	2	yes	—
575	#106	C₂³×C₆₁	1	2	yes	—
576	#106	C₂³×C₆₁	1	2	yes	—
577	#106	C₂³×C₆₁	1	2	yes	—
578	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
579	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
580	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
581	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
582	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
583	#103	C₂³×C₆₁	1	4	yes	—
584	#103	C₂³×C₆₁	1	4	yes	—
585	#103	C₂³×C₆₁	1	2	yes	—
586	#103	C₂³×C₆₁	1	2	yes	—
587	#103	C₂³×C₆₁	1	2	yes	—
588	#103	C₂³×C₆₁	1	2	yes	—
589	#103	C₂³×C₆₁	1	2	yes	—
590	#103	C₂³×C₆₁	1	4	yes	—
591	#103	C₂³×C₆₁	1	4	yes	—
592	#103	C₂³×C₆₁	1	4	yes	—
593	#103	C₂³×C₆₁	1	4	yes	—
594	#102	C₂³×C₆₁	1	2	yes	—
595	#102	C₂³×C₆₁	1	2	yes	—
596	#102	C₂³×C₆₁	1	2	yes	—
597	#97	C₂³×C₆₁	1	2	yes	—
598	#97	C₂³×C₆₁	1	4	yes	—
599	C₄×C₈	C₂³×C₆₁	1	2	yes	—
600	C₄×C₈	C₂³×C₆₁	1	4	yes	—
601	#41	—	2	2	no	—
602	#41	—	2	2	no	—
603	C₂×Q₈	—	2	1	no	—
604	C₂×Q₈	—	2	1	no	—
605	C₂×Q₈	—	2	2	no	—
606	C₂×Q₈	—	2	1	no	—
607	C₂×Q₈	—	2	4	no	—
608	C₂×Q₈	—	2	2	no	—
609	C₂×Q₈	—	2	4	no	—
610	C₂×Q₈	—	2	4	no	—
611	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
612	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
613	C₂×Q₈	#41×C₆₁	1	4	yes	—
614	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
615	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
616	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	1	no	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
626	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
627	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
628	Q₁₆	—	2	8	no	—
629	Q₁₆	—	2	8	no	—
630	Q₁₆	—	2	4	no	—
631	SD₁₆	—	2	4	no	—
632	M₁₆	—	2	2	no	—
633	M₁₆	—	2	2	no	—
634	C₂×C₈	—	2	4	no	—
635	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
636	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
637	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
638	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
639	C₄⋊C₄	—	2	2	no	—
640	C₄⋊C₄	—	2	2	no	—
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	2	no	—
644	C₄⋊C₄	—	2	2	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	—	2	1	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
662	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
663	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
664	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
665	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
666	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
667	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
668	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
669	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
670	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
671	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
672	C₂²⋊C₄	—	2	1	no	—
673	C₂²⋊C₄	—	2	2	no	—
674	C₂²⋊C₄	—	2	1	no	—
675	C₂²⋊C₄	—	2	1	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
679	C₄²	—	2	1	no	—
680	C₄²	—	2	1	no	—
681	C₄²	—	2	1	no	—
682	C₄²	—	2	2	no	—
683	C₄²	—	2	2	no	—
684	C₄²	—	2	4	no	—
685	C₄²	—	2	4	no	—
686	C₄²	—	2	4	no	—
687	C₄²	—	2	4	no	—
688	C₄²	—	2	2	no	—
689	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
690	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
691	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
692	C₄²	C₂⁴×C₆₁	1	4	yes	—
693	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
694	C₂³	—	2	1	no	—
695	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
696	Q₈	—	2	4	no	—
697	Q₈	—	2	4	no	—
698	Q₈	—	2	2	no	—
699	Q₈	—	2	4	no	—
700	Q₈	—	2	1	no	—
701	Q₈	—	2	4	no	—
702	Q₈	—	2	1	no	—
703	Q₈	—	4	2	no	—
704	Q₈	—	4	4	no	—
705	Q₈	—	4	2	no	—
706	Q₈	—	8	1	no	—
707	Q₈	—	8	4	no	—
708	Q₈	C₂×#41×C₆₁	1	4	yes	—
709	D₄	—	2	1	no	—
710	D₄	—	2	1	no	—
711	D₄	—	4	2	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	4	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	2	no	—
724	C₂×C₄	—	4	4	no	—
725	C₂×C₄	—	4	2	no	—
726	C₂×C₄	—	4	2	no	—
727	C₂×C₄	—	8	1	no	—
728	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
729	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
730	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
731	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
732	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
733	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
734	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
735	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
736	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
737	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
738	C₈	—	2	2	no	—
739	C₈	—	2	2	no	—
740	C₈	—	2	2	no	—
741	C₈	—	2	2	no	—
742	C₂²	—	2	1	no	—
743	C₂²	—	2	1	no	—
744	C₂²	—	4	1	no	—
745	C₂²	—	4	1	no	—
746	C₂²	—	4	1	no	—
747	C₂²	C₆₁×#548	1	2	yes	—
748	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
749	C₄	—	2	1	no	—
750	C₄	—	2	4	no	—
751	C₄	—	2	1	no	—
752	C₄	—	2	1	no	—
753	C₄	—	2	4	no	—
754	C₄	—	2	4	no	—
755	C₄	—	4	1	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	1	no	—
758	C₄	—	4	2	no	—
759	C₄	—	4	2	no	—
760	C₄	—	4	1	no	—
761	C₄	—	4	4	no	—
762	C₄	C₆₁×#548	1	2	yes	—
763	C₄	C₆₁×#578	1	2	yes	—
764	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
765	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
766	C₂	—	2	2	no	—
767	C₂	—	8	1	no	—
768	C₂	C₂×C₆₁×#548	1	1	yes	characteristic
769	C₂	C₂×C₆₁×#578	1	1	yes	characteristic
770	C₂	C₆₁×#3586	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₆₁×#3502	C₂	semidirect
3. C₆₁×#3377	C₂	semidirect
4. C₆₁×#3374	C₂	semidirect
5. C₆₁×#3374	C₂	semidirect
6. C₆₁×#3369	C₂	semidirect
7. C₆₁×#3364	C₂	semidirect
8. C₆₁×#3363	C₂	semidirect
9. C₆₁×#3139	C₂	semidirect
11. C₆₁×#3082	C₂	semidirect
14. C₂×C₆₁×#462	C₂	semidirect
15. C₆₁×#2962	C₂	semidirect
16. C₆₁×#2950	C₂	semidirect
356. #61342	C₆₁	direct (N × H)
382. #3502	C₂×C₆₁	semidirect
383. #3377	C₂×C₆₁	semidirect
384. #3374	C₂×C₆₁	semidirect
385. #3374	C₂×C₆₁	semidirect
386. #3369	C₂×C₆₁	semidirect
387. #3364	C₂×C₆₁	semidirect
388. #3363	C₂×C₆₁	semidirect
389. #3139	C₂×C₆₁	semidirect
391. #3082	C₂×C₆₁	semidirect
394. C₂×#462	C₂×C₆₁	semidirect
395. #2962	C₂×C₆₁	semidirect
396. #2950	C₂×C₆₁	semidirect
478. C₆₁	#61342	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×#3509	2
C₆₁×#3502	2
C₆₁×#3377	2
C₆₁×#3374	2
C₆₁×#3369	2
C₆₁×#3364	2
C₆₁×#3363	2
C₆₁×#3139	2
C₆₁×#3137	2
C₆₁×#3082	2
C₆₁×#3076	2
C₆₁×#3044	2
C₂×C₆₁×#462	2
C₆₁×#2962	2
C₆₁×#2950	2
C₄×#137×C₆₁	2
#61342	61

Subgroups — C61×#61342 #29564775

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61342 #29564775