Subgroups — C₆₁×#61789 #29565222

Order 15616.

1718 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3511	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#3356	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3353	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3342	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3340	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3329	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3328	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3299	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3298	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3230	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3229	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3201	C₂	1	4	yes	maximal, complemented
14	C₆₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#3097	C₂	1	4	yes	maximal, complemented
17	C₆₁×#2979	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#563	—	2	2	no	—
19	C₆₁×#559	—	2	1	no	—
20	Q₈²×C₆₁	—	2	1	no	—
21	C₆₁×#556	C₂²	1	2	yes	—
22	C₆₁×#556	C₂²	1	2	yes	—
23	C₆₁×#556	C₂²	1	2	yes	—
24	C₆₁×#555	C₂²	1	2	yes	—
25	C₆₁×#554	C₂²	1	2	yes	—
26	C₆₁×#553	—	2	2	no	—
27	D₄×Q₈×C₆₁	C₂²	1	2	yes	—
28	D₄×Q₈×C₆₁	C₂²	1	2	yes	—
29	C₆₁×#548	—	2	2	no	—
30	C₆₁×#547	C₂²	1	2	yes	—
31	C₆₁×#542	—	2	2	no	—
32	C₆₁×#542	—	2	2	no	—
33	C₆₁×#542	—	2	2	no	—
34	C₆₁×#537	C₂²	1	2	yes	—
35	C₆₁×#536	C₂²	1	4	yes	—
36	C₆₁×#533	—	2	1	no	—
37	C₆₁×#533	C₂²	1	1	yes	characteristic
38	C₆₁×#533	C₂²	1	1	yes	characteristic
39	C₆₁×#532	—	2	1	no	—
40	C₆₁×#532	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
42	C₆₁×#520	C₂²	1	2	yes	—
43	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
44	C₆₁×#500	C₂²	1	2	yes	—
45	C₆₁×#498	C₂²	1	2	yes	—
46	C₆₁×#487	C₂²	1	2	yes	—
47	C₆₁×#487	C₂²	1	2	yes	—
48	C₆₁×#485	C₂²	1	4	yes	—
49	C₆₁×#485	C₂²	1	4	yes	—
50	C₆₁×#485	C₂²	1	4	yes	—
51	C₆₁×#485	C₂²	1	2	yes	—
52	C₆₁×#485	C₂²	1	2	yes	—
53	C₆₁×#484	C₂²	1	4	yes	—
54	C₆₁×#484	C₂²	1	4	yes	—
55	C₆₁×#483	C₂²	1	4	yes	—
56	C₆₁×#483	C₂²	1	4	yes	—
57	C₆₁×#482	C₂²	1	4	yes	—
58	C₆₁×#477	C₂²	1	2	yes	—
59	C₆₁×#477	C₂²	1	2	yes	—
60	C₆₁×#475	C₂²	1	2	yes	—
61	C₆₁×#475	C₂²	1	2	yes	—
62	C₆₁×#475	C₂²	1	1	yes	characteristic
63	C₆₁×#475	C₂²	1	1	yes	characteristic
64	C₆₁×#474	C₂²	1	1	yes	characteristic
65	C₆₁×#474	C₂²	1	1	yes	characteristic
66	C₆₁×#470	C₂²	1	4	yes	—
67	C₆₁×#468	C₂²	1	4	yes	—
68	C₆₁×#467	C₂²	1	4	yes	—
69	C₆₁×#465	C₂²	1	4	yes	—
70	C₆₁×#462	C₂²	1	1	yes	characteristic
71	C₆₁×#462	C₂²	1	1	yes	characteristic
72	C₆₁×#461	C₂²	1	1	yes	characteristic
73	C₆₁×#461	C₂²	1	1	yes	characteristic
74	C₆₁×#452	C₂²	1	2	yes	—
75	C₆₁×#452	C₂²	1	2	yes	—
76	C₆₁×#451	C₂²	1	4	yes	—
77	C₆₁×#448	C₂²	1	4	yes	—
78	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
79	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
80	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
81	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
82	C₆₁×#436	C₂²	1	2	yes	—
83	C₆₁×#436	C₂²	1	2	yes	—
84	C₈×D₄×C₆₁	C₂²	1	2	yes	—
85	C₈×D₄×C₆₁	C₂²	1	2	yes	—
86	C₆₁×#431	C₂²	1	1	yes	characteristic
87	C₆₁×#431	C₂²	1	1	yes	characteristic
88	C₆₁×#428	C₂²	1	4	yes	—
89	C₆₁×#427	C₂²	1	4	yes	—
90	C₆₁×#419	C₂²	1	4	yes	—
91	C₂×#103×C₆₁	C₂²	1	4	yes	—
92	C₆₁×#408	C₂²	1	4	yes	—
93	C₂×#41×C₆₁	—	2	2	no	—
94	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
95	C₂×#41×C₆₁	C₂³	1	2	yes	—
96	C₂²×Q₈×C₆₁	—	2	1	no	—
97	C₂²×Q₈×C₆₁	C₂³	1	4	yes	—
98	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
99	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
100	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
101	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
102	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
103	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
104	C₄⋊Q₈×C₆₁	—	2	4	no	—
105	C₄⋊Q₈×C₆₁	—	2	2	no	—
106	C₄⋊Q₈×C₆₁	—	2	2	no	—
107	C₄⋊Q₈×C₆₁	—	2	1	no	—
108	C₄⋊Q₈×C₆₁	—	2	1	no	—
109	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
110	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
111	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
112	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
113	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
114	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
115	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
116	#127×C₆₁	D₄	1	1	yes	characteristic
117	#126×C₆₁	—	2	4	no	—
118	#126×C₆₁	—	2	4	no	—
119	#126×C₆₁	—	2	4	no	—
120	#125×C₆₁	—	2	2	no	—
121	#125×C₆₁	—	2	1	no	—
122	#125×C₆₁	—	2	1	no	—
123	#124×C₆₁	—	2	2	no	—
124	#124×C₆₁	—	2	4	no	—
125	#124×C₆₁	—	2	2	no	—
126	#124×C₆₁	—	2	2	no	—
127	#124×C₆₁	—	2	4	no	—
128	#124×C₆₁	D₄	1	2	yes	—
129	#123×C₆₁	—	2	4	no	—
130	#123×C₆₁	—	2	4	no	—
131	#123×C₆₁	—	2	4	no	—
132	C₂²⋊Q₈×C₆₁	—	2	2	no	—
133	C₂²⋊Q₈×C₆₁	—	2	1	no	—
134	C₂²⋊Q₈×C₆₁	—	2	1	no	—
135	C₂²⋊Q₈×C₆₁	—	2	2	no	—
136	C₂²⋊Q₈×C₆₁	—	2	4	no	—
137	C₂²⋊Q₈×C₆₁	—	2	4	no	—
138	C₂²⋊Q₈×C₆₁	—	2	4	no	—
139	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
140	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
141	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
142	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
143	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
144	#121×C₆₁	—	2	2	no	—
145	#121×C₆₁	—	2	2	no	—
146	#121×C₆₁	—	2	4	no	—
147	#121×C₆₁	D₄	1	2	yes	—
148	#121×C₆₁	D₄	1	2	yes	—
149	#121×C₆₁	C₂³	1	4	yes	—
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	2	no	—
154	C₄×Q₈×C₆₁	—	2	1	no	—
155	C₄×Q₈×C₆₁	—	2	1	no	—
156	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
157	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
158	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
159	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
160	C₄×D₄×C₆₁	—	2	2	no	—
161	C₄×D₄×C₆₁	—	2	2	no	—
162	C₄×D₄×C₆₁	—	2	2	no	—
163	C₄×D₄×C₆₁	—	2	2	no	—
164	C₄×D₄×C₆₁	—	2	4	no	—
165	C₄×D₄×C₆₁	—	2	1	no	—
166	C₄×D₄×C₆₁	—	2	1	no	—
167	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
168	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
169	C₄×D₄×C₆₁	C₂³	1	2	yes	—
170	C₄×D₄×C₆₁	C₂³	1	2	yes	—
171	#117×C₆₁	—	2	1	no	—
172	#117×C₆₁	—	2	1	no	—
173	#117×C₆₁	—	2	2	no	—
174	#117×C₆₁	—	2	1	no	—
175	#117×C₆₁	C₂³	1	4	yes	—
176	#117×C₆₁	C₂³	1	4	yes	—
177	#117×C₆₁	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
179	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
181	C₂×C₄²×C₆₁	—	2	1	no	—
182	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
183	#107×C₆₁	C₂³	1	2	yes	—
184	#107×C₆₁	C₂³	1	4	yes	—
185	#107×C₆₁	C₂³	1	2	yes	—
186	#107×C₆₁	C₂³	1	4	yes	—
187	#106×C₆₁	C₂³	1	2	yes	—
188	#106×C₆₁	C₂³	1	4	yes	—
189	#106×C₆₁	C₂³	1	2	yes	—
190	#106×C₆₁	C₂³	1	4	yes	—
191	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
192	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
193	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
194	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
195	#103×C₆₁	C₂³	1	2	yes	—
196	#103×C₆₁	C₂³	1	2	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	4	yes	—
202	#103×C₆₁	C₂³	1	4	yes	—
203	#103×C₆₁	C₂³	1	2	yes	—
204	#103×C₆₁	C₂³	1	2	yes	—
205	#102×C₆₁	C₂³	1	2	yes	—
206	#102×C₆₁	C₂³	1	2	yes	—
207	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
208	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
209	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
210	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
211	C₄×C₈×C₆₁	C₂³	1	2	yes	—
212	C₄×C₈×C₆₁	C₂³	1	2	yes	—
213	#41×C₆₁	—	4	2	no	—
214	#41×C₆₁	—	4	2	no	—
215	#41×C₆₁	—	4	1	no	—
216	#41×C₆₁	—	4	1	no	—
217	#41×C₆₁	—	8	4	no	—
218	C₂×Q₈×C₆₁	—	2	1	no	—
219	C₂×Q₈×C₆₁	—	2	1	no	—
220	C₂×Q₈×C₆₁	—	2	2	no	—
221	C₂×Q₈×C₆₁	—	2	2	no	—
222	C₂×Q₈×C₆₁	—	2	4	no	—
223	C₂×Q₈×C₆₁	—	4	4	no	—
224	C₂×Q₈×C₆₁	—	4	4	no	—
225	C₂×Q₈×C₆₁	—	8	2	no	—
226	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
227	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
228	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
229	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
230	C₂×D₄×C₆₁	—	2	1	no	—
231	C₂×D₄×C₆₁	—	2	4	no	—
232	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
233	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
234	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
235	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
236	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
237	C₂²×C₄×C₆₁	—	2	2	no	—
238	C₂²×C₄×C₆₁	—	2	4	no	—
239	C₂²×C₄×C₆₁	—	2	4	no	—
240	C₂²×C₄×C₆₁	—	2	1	no	—
241	C₂²×C₄×C₆₁	—	2	1	no	—
242	C₂²×C₄×C₆₁	—	2	1	no	—
243	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
247	Q₁₆×C₆₁	—	4	2	no	—
248	Q₁₆×C₆₁	—	4	2	no	—
249	SD₁₆×C₆₁	—	4	2	no	—
250	SD₁₆×C₆₁	—	4	2	no	—
251	M₁₆×C₆₁	—	4	4	no	—
252	C₂×C₈×C₆₁	—	4	4	no	—
253	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
254	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
255	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
256	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
257	C₄⋊C₄×C₆₁	—	2	2	no	—
258	C₄⋊C₄×C₆₁	—	2	2	no	—
259	C₄⋊C₄×C₆₁	—	2	2	no	—
260	C₄⋊C₄×C₆₁	—	2	4	no	—
261	C₄⋊C₄×C₆₁	—	2	1	no	—
262	C₄⋊C₄×C₆₁	—	2	1	no	—
263	C₄⋊C₄×C₆₁	—	2	1	no	—
264	C₄⋊C₄×C₆₁	—	2	1	no	—
265	C₄⋊C₄×C₆₁	—	2	1	no	—
266	C₄⋊C₄×C₆₁	—	2	1	no	—
267	C₄⋊C₄×C₆₁	—	2	1	no	—
268	C₄⋊C₄×C₆₁	—	2	1	no	—
269	C₄⋊C₄×C₆₁	—	2	4	no	—
270	C₄⋊C₄×C₆₁	—	2	4	no	—
271	C₄⋊C₄×C₆₁	—	2	4	no	—
272	C₄⋊C₄×C₆₁	—	2	2	no	—
273	C₄⋊C₄×C₆₁	—	2	2	no	—
274	C₄⋊C₄×C₆₁	—	2	2	no	—
275	C₄⋊C₄×C₆₁	—	2	2	no	—
276	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
277	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
279	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
280	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
281	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
282	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
283	C₂²⋊C₄×C₆₁	—	2	2	no	—
284	C₂²⋊C₄×C₆₁	—	2	2	no	—
285	C₂²⋊C₄×C₆₁	—	2	1	no	—
286	C₂²⋊C₄×C₆₁	—	2	4	no	—
287	C₂²⋊C₄×C₆₁	—	2	4	no	—
288	C₂²⋊C₄×C₆₁	—	2	4	no	—
289	C₂²⋊C₄×C₆₁	—	2	4	no	—
290	C₂²⋊C₄×C₆₁	—	2	4	no	—
291	C₂²⋊C₄×C₆₁	—	2	1	no	—
292	C₂²⋊C₄×C₆₁	—	2	1	no	—
293	C₂²⋊C₄×C₆₁	—	2	4	no	—
294	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
295	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
296	C₄²×C₆₁	—	2	1	no	—
297	C₄²×C₆₁	—	2	1	no	—
298	C₄²×C₆₁	—	2	1	no	—
299	C₄²×C₆₁	—	2	4	no	—
300	C₄²×C₆₁	—	2	2	no	—
301	C₄²×C₆₁	—	2	2	no	—
302	C₄²×C₆₁	—	2	4	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	1	yes	characteristic
307	C₂³×C₆₁	—	2	1	no	—
308	C₂³×C₆₁	C₂²×D₄	1	4	yes	—
309	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
310	Q₈×C₆₁	—	2	2	no	—
311	Q₈×C₆₁	—	2	2	no	—
312	Q₈×C₆₁	—	2	1	no	—
313	Q₈×C₆₁	—	2	1	no	—
314	Q₈×C₆₁	—	2	2	no	—
315	Q₈×C₆₁	—	2	2	no	—
316	Q₈×C₆₁	—	4	2	no	—
317	Q₈×C₆₁	—	4	2	no	—
318	Q₈×C₆₁	—	4	4	no	—
319	Q₈×C₆₁	—	4	2	no	—
320	Q₈×C₆₁	—	8	4	no	—
321	Q₈×C₆₁	—	8	2	no	—
322	D₄×C₆₁	—	2	4	no	—
323	D₄×C₆₁	—	2	4	no	—
324	D₄×C₆₁	—	2	1	no	—
325	D₄×C₆₁	—	2	1	no	—
326	D₄×C₆₁	—	4	2	no	—
327	D₄×C₆₁	—	4	4	no	—
328	D₄×C₆₁	—	4	2	no	—
329	D₄×C₆₁	—	8	4	no	—
330	C₂×C₄×C₆₁	—	2	2	no	—
331	C₂×C₄×C₆₁	—	2	2	no	—
332	C₂×C₄×C₆₁	—	2	4	no	—
333	C₂×C₄×C₆₁	—	2	4	no	—
334	C₂×C₄×C₆₁	—	2	1	no	—
335	C₂×C₄×C₆₁	—	2	1	no	—
336	C₂×C₄×C₆₁	—	2	1	no	—
337	C₂×C₄×C₆₁	—	2	2	no	—
338	C₂×C₄×C₆₁	—	2	2	no	—
339	C₂×C₄×C₆₁	—	2	1	no	—
340	C₂×C₄×C₆₁	—	2	1	no	—
341	C₂×C₄×C₆₁	—	2	2	no	—
342	C₂×C₄×C₆₁	—	2	2	no	—
343	C₂×C₄×C₆₁	—	2	4	no	—
344	C₂×C₄×C₆₁	—	4	2	no	—
345	C₂×C₄×C₆₁	—	4	2	no	—
346	C₂×C₄×C₆₁	—	4	2	no	—
347	C₂×C₄×C₆₁	—	8	4	no	—
348	C₂×C₄×C₆₁	—	8	2	no	—
349	C₂×C₄×C₆₁	—	8	4	no	—
350	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
351	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
355	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
357	C₈×C₆₁	—	2	2	no	—
358	C₈×C₆₁	—	2	2	no	—
359	C₈×C₆₁	—	2	2	no	—
360	C₈×C₆₁	—	2	2	no	—
361	#61789	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
362	C₂²×C₆₁	—	2	4	no	—
363	C₂²×C₆₁	—	2	1	no	—
364	C₂²×C₆₁	—	2	1	no	—
365	C₂²×C₆₁	—	2	4	no	—
366	C₂²×C₆₁	—	2	1	no	—
367	C₂²×C₆₁	—	2	4	no	—
368	C₂²×C₆₁	—	4	1	no	—
369	C₂²×C₆₁	—	4	1	no	—
370	C₂²×C₆₁	—	4	1	no	—
371	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
372	C₄×C₆₁	—	2	1	no	—
373	C₄×C₆₁	—	2	4	no	—
374	C₄×C₆₁	—	2	1	no	—
375	C₄×C₆₁	—	2	1	no	—
376	C₄×C₆₁	—	4	1	no	—
377	C₄×C₆₁	—	4	2	no	—
378	C₄×C₆₁	—	4	2	no	—
379	C₄×C₆₁	—	4	1	no	—
380	C₄×C₆₁	—	4	4	no	—
381	C₄×C₆₁	—	4	2	no	—
382	C₄×C₆₁	—	4	1	no	—
383	C₄×C₆₁	—	4	2	no	—
384	C₄×C₆₁	#577	1	2	yes	—
385	C₄×C₆₁	#578	1	2	yes	—
386	C₄×C₆₁	#585	1	1	yes	characteristic
387	C₄×C₆₁	#585	1	1	yes	characteristic
388	#3550	C₂×C₆₁	1	1	yes	characteristic, complemented
389	#3511	C₂×C₆₁	1	1	yes	characteristic
390	#3356	C₂×C₆₁	1	2	yes	complemented
391	#3353	C₂×C₆₁	1	2	yes	complemented
392	#3342	C₂×C₆₁	1	2	yes	complemented
393	#3340	C₂×C₆₁	1	2	yes	complemented
394	#3329	C₂×C₆₁	1	2	yes	complemented
395	#3328	C₂×C₆₁	1	2	yes	complemented
396	#3299	C₂×C₆₁	1	2	yes	complemented
397	#3298	C₂×C₆₁	1	2	yes	complemented
398	#3230	C₂×C₆₁	1	1	yes	characteristic, complemented
399	#3229	C₂×C₆₁	1	1	yes	characteristic, complemented
400	#3201	C₂×C₆₁	1	4	yes	complemented
401	#3107	C₂×C₆₁	1	1	yes	characteristic, complemented
402	#3107	C₂×C₆₁	1	1	yes	characteristic, complemented
403	#3097	C₂×C₆₁	1	4	yes	complemented
404	#2979	C₂×C₆₁	1	1	yes	characteristic, complemented
405	C₂×C₆₁	—	4	4	no	—
406	C₂×C₆₁	—	4	1	no	—
407	C₂×C₆₁	—	8	1	no	—
408	C₂×C₆₁	#3485	1	1	yes	characteristic
409	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
410	C₂×C₆₁	C₂×#578	1	1	yes	characteristic
411	#563	—	2	2	no	—
412	#559	—	2	1	no	—
413	Q₈²	—	2	1	no	—
414	#556	C₂²×C₆₁	1	2	yes	—
415	#556	C₂²×C₆₁	1	2	yes	—
416	#556	C₂²×C₆₁	1	2	yes	—
417	#555	C₂²×C₆₁	1	2	yes	—
418	#554	C₂²×C₆₁	1	2	yes	—
419	#553	—	2	2	no	—
420	D₄×Q₈	C₂²×C₆₁	1	2	yes	—
421	D₄×Q₈	C₂²×C₆₁	1	2	yes	—
422	#548	—	2	2	no	—
423	#547	C₂²×C₆₁	1	2	yes	—
424	#542	—	2	2	no	—
425	#542	—	2	2	no	—
426	#542	—	2	2	no	—
427	#537	C₂²×C₆₁	1	2	yes	—
428	#536	C₂²×C₆₁	1	4	yes	—
429	#533	—	2	1	no	—
430	#533	C₂²×C₆₁	1	1	yes	characteristic
431	#533	C₂²×C₆₁	1	1	yes	characteristic
432	#532	—	2	1	no	—
433	#532	C₂²×C₆₁	1	1	yes	characteristic
434	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
435	#520	C₂²×C₆₁	1	2	yes	—
436	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
437	#500	C₂²×C₆₁	1	2	yes	—
438	#498	C₂²×C₆₁	1	2	yes	—
439	#487	C₂²×C₆₁	1	2	yes	—
440	#487	C₂²×C₆₁	1	2	yes	—
441	#485	C₂²×C₆₁	1	4	yes	—
442	#485	C₂²×C₆₁	1	4	yes	—
443	#485	C₂²×C₆₁	1	4	yes	—
444	#485	C₂²×C₆₁	1	2	yes	—
445	#485	C₂²×C₆₁	1	2	yes	—
446	#484	C₂²×C₆₁	1	4	yes	—
447	#484	C₂²×C₆₁	1	4	yes	—
448	#483	C₂²×C₆₁	1	4	yes	—
449	#483	C₂²×C₆₁	1	4	yes	—
450	#482	C₂²×C₆₁	1	4	yes	—
451	#477	C₂²×C₆₁	1	2	yes	—
452	#477	C₂²×C₆₁	1	2	yes	—
453	#475	C₂²×C₆₁	1	2	yes	—
454	#475	C₂²×C₆₁	1	1	yes	characteristic
455	#475	C₂²×C₆₁	1	2	yes	—
456	#475	C₂²×C₆₁	1	1	yes	characteristic
457	#474	C₂²×C₆₁	1	1	yes	characteristic
458	#474	C₂²×C₆₁	1	1	yes	characteristic
459	#470	C₂²×C₆₁	1	4	yes	—
460	#468	C₂²×C₆₁	1	4	yes	—
461	#467	C₂²×C₆₁	1	4	yes	—
462	#465	C₂²×C₆₁	1	4	yes	—
463	#462	C₂²×C₆₁	1	1	yes	characteristic
464	#462	C₂²×C₆₁	1	1	yes	characteristic
465	#461	C₂²×C₆₁	1	1	yes	characteristic
466	#461	C₂²×C₆₁	1	1	yes	characteristic
467	#452	C₂²×C₆₁	1	2	yes	—
468	#452	C₂²×C₆₁	1	2	yes	—
469	#451	C₂²×C₆₁	1	4	yes	—
470	#448	C₂²×C₆₁	1	4	yes	—
471	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
472	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
473	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
474	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
475	#436	C₂²×C₆₁	1	2	yes	—
476	#436	C₂²×C₆₁	1	2	yes	—
477	C₈×D₄	C₂²×C₆₁	1	2	yes	—
478	C₈×D₄	C₂²×C₆₁	1	2	yes	—
479	#431	C₂²×C₆₁	1	1	yes	characteristic
480	#431	C₂²×C₆₁	1	1	yes	characteristic
481	#428	C₂²×C₆₁	1	4	yes	—
482	#427	C₂²×C₆₁	1	4	yes	—
483	#419	C₂²×C₆₁	1	4	yes	—
484	C₂×#103	C₂²×C₆₁	1	4	yes	—
485	#408	C₂²×C₆₁	1	4	yes	—
486	C₆₁	#61789	1	1	yes	characteristic, direct product factor, Sylow
487	C₂×#41	—	2	2	no	—
488	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
489	C₂×#41	C₂³×C₆₁	1	2	yes	—
490	C₂²×Q₈	—	2	1	no	—
491	C₂²×Q₈	C₂³×C₆₁	1	4	yes	—
492	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
493	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
494	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
495	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
496	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
497	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
498	C₄⋊Q₈	—	2	4	no	—
499	C₄⋊Q₈	—	2	2	no	—
500	C₄⋊Q₈	—	2	2	no	—
501	C₄⋊Q₈	—	2	1	no	—
502	C₄⋊Q₈	—	2	1	no	—
503	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
504	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
505	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
506	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
507	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
508	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
509	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
510	#127	D₄×C₆₁	1	1	yes	characteristic
511	#126	—	2	4	no	—
512	#126	—	2	4	no	—
513	#126	—	2	4	no	—
514	#125	—	2	2	no	—
515	#125	—	2	1	no	—
516	#125	—	2	1	no	—
517	#124	—	2	2	no	—
518	#124	—	2	4	no	—
519	#124	—	2	2	no	—
520	#124	—	2	2	no	—
521	#124	—	2	4	no	—
522	#124	D₄×C₆₁	1	2	yes	—
523	#123	—	2	4	no	—
524	#123	—	2	4	no	—
525	#123	—	2	4	no	—
526	C₂²⋊Q₈	—	2	2	no	—
527	C₂²⋊Q₈	—	2	1	no	—
528	C₂²⋊Q₈	—	2	1	no	—
529	C₂²⋊Q₈	—	2	2	no	—
530	C₂²⋊Q₈	—	2	4	no	—
531	C₂²⋊Q₈	—	2	4	no	—
532	C₂²⋊Q₈	—	2	4	no	—
533	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
534	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
535	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
536	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
537	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
538	#121	—	2	2	no	—
539	#121	—	2	2	no	—
540	#121	—	2	4	no	—
541	#121	D₄×C₆₁	1	2	yes	—
542	#121	D₄×C₆₁	1	2	yes	—
543	#121	C₂³×C₆₁	1	4	yes	—
544	C₄×Q₈	—	2	2	no	—
545	C₄×Q₈	—	2	2	no	—
546	C₄×Q₈	—	2	2	no	—
547	C₄×Q₈	—	2	2	no	—
548	C₄×Q₈	—	2	1	no	—
549	C₄×Q₈	—	2	1	no	—
550	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
551	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
552	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
553	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
554	C₄×D₄	—	2	2	no	—
555	C₄×D₄	—	2	4	no	—
556	C₄×D₄	—	2	2	no	—
557	C₄×D₄	—	2	2	no	—
558	C₄×D₄	—	2	2	no	—
559	C₄×D₄	—	2	1	no	—
560	C₄×D₄	—	2	1	no	—
561	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
562	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
563	C₄×D₄	C₂³×C₆₁	1	2	yes	—
564	C₄×D₄	C₂³×C₆₁	1	2	yes	—
565	#117	—	2	1	no	—
566	#117	—	2	1	no	—
567	#117	—	2	2	no	—
568	#117	—	2	1	no	—
569	#117	C₂³×C₆₁	1	1	yes	characteristic
570	#117	C₂³×C₆₁	1	4	yes	—
571	#117	C₂³×C₆₁	1	4	yes	—
572	C₂×C₄⋊C₄	—	2	1	no	—
573	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
575	C₂×C₄²	—	2	1	no	—
576	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
577	#107	C₂³×C₆₁	1	2	yes	—
578	#107	C₂³×C₆₁	1	4	yes	—
579	#107	C₂³×C₆₁	1	2	yes	—
580	#107	C₂³×C₆₁	1	4	yes	—
581	#106	C₂³×C₆₁	1	2	yes	—
582	#106	C₂³×C₆₁	1	4	yes	—
583	#106	C₂³×C₆₁	1	2	yes	—
584	#106	C₂³×C₆₁	1	4	yes	—
585	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
586	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
587	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
588	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
589	#103	C₂³×C₆₁	1	2	yes	—
590	#103	C₂³×C₆₁	1	2	yes	—
591	#103	C₂³×C₆₁	1	4	yes	—
592	#103	C₂³×C₆₁	1	4	yes	—
593	#103	C₂³×C₆₁	1	2	yes	—
594	#103	C₂³×C₆₁	1	2	yes	—
595	#103	C₂³×C₆₁	1	4	yes	—
596	#103	C₂³×C₆₁	1	4	yes	—
597	#103	C₂³×C₆₁	1	2	yes	—
598	#103	C₂³×C₆₁	1	2	yes	—
599	#102	C₂³×C₆₁	1	2	yes	—
600	#102	C₂³×C₆₁	1	2	yes	—
601	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
602	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
603	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
604	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
605	C₄×C₈	C₂³×C₆₁	1	2	yes	—
606	C₄×C₈	C₂³×C₆₁	1	2	yes	—
607	#41	—	4	2	no	—
608	#41	—	4	2	no	—
609	#41	—	4	1	no	—
610	#41	—	4	1	no	—
611	#41	—	8	4	no	—
612	C₂×Q₈	—	2	1	no	—
613	C₂×Q₈	—	2	1	no	—
614	C₂×Q₈	—	2	2	no	—
615	C₂×Q₈	—	2	2	no	—
616	C₂×Q₈	—	2	4	no	—
617	C₂×Q₈	—	4	4	no	—
618	C₂×Q₈	—	4	4	no	—
619	C₂×Q₈	—	8	2	no	—
620	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
621	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
622	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
623	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	—	2	4	no	—
626	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
627	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
628	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
629	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
630	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	2	4	no	—
633	C₂²×C₄	—	2	4	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
638	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
639	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
640	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
641	Q₁₆	—	4	2	no	—
642	Q₁₆	—	4	2	no	—
643	SD₁₆	—	4	2	no	—
644	SD₁₆	—	4	2	no	—
645	M₁₆	—	4	4	no	—
646	C₂×C₈	—	4	4	no	—
647	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
648	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
649	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
650	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
651	C₄⋊C₄	—	2	2	no	—
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	—	2	2	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	—	2	1	no	—
659	C₄⋊C₄	—	2	1	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	4	no	—
666	C₄⋊C₄	—	2	2	no	—
667	C₄⋊C₄	—	2	2	no	—
668	C₄⋊C₄	—	2	2	no	—
669	C₄⋊C₄	—	2	2	no	—
670	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
671	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
672	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
673	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
674	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
675	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
676	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
677	C₂²⋊C₄	—	2	2	no	—
678	C₂²⋊C₄	—	2	2	no	—
679	C₂²⋊C₄	—	2	1	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	4	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	4	no	—
684	C₂²⋊C₄	—	2	4	no	—
685	C₂²⋊C₄	—	2	1	no	—
686	C₂²⋊C₄	—	2	1	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
689	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
690	C₄²	—	2	1	no	—
691	C₄²	—	2	1	no	—
692	C₄²	—	2	1	no	—
693	C₄²	—	2	4	no	—
694	C₄²	—	2	2	no	—
695	C₄²	—	2	2	no	—
696	C₄²	—	2	4	no	—
697	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
698	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
699	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
700	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
701	C₂³	—	2	1	no	—
702	C₂³	C₂²×D₄×C₆₁	1	4	yes	—
703	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
704	Q₈	—	2	2	no	—
705	Q₈	—	2	2	no	—
706	Q₈	—	2	1	no	—
707	Q₈	—	2	1	no	—
708	Q₈	—	2	2	no	—
709	Q₈	—	2	2	no	—
710	Q₈	—	4	2	no	—
711	Q₈	—	4	2	no	—
712	Q₈	—	4	4	no	—
713	Q₈	—	4	2	no	—
714	Q₈	—	8	4	no	—
715	Q₈	—	8	2	no	—
716	D₄	—	2	4	no	—
717	D₄	—	2	4	no	—
718	D₄	—	2	1	no	—
719	D₄	—	2	1	no	—
720	D₄	—	4	2	no	—
721	D₄	—	4	4	no	—
722	D₄	—	4	2	no	—
723	D₄	—	8	4	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	4	no	—
727	C₂×C₄	—	2	4	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	4	no	—
738	C₂×C₄	—	4	2	no	—
739	C₂×C₄	—	4	2	no	—
740	C₂×C₄	—	4	2	no	—
741	C₂×C₄	—	8	4	no	—
742	C₂×C₄	—	8	2	no	—
743	C₂×C₄	—	8	4	no	—
744	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
745	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
746	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
747	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
748	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
749	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
750	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
751	C₈	—	2	2	no	—
752	C₈	—	2	2	no	—
753	C₈	—	2	2	no	—
754	C₈	—	2	2	no	—
755	C₂²	—	2	1	no	—
756	C₂²	—	2	4	no	—
757	C₂²	—	2	1	no	—
758	C₂²	—	2	4	no	—
759	C₂²	—	2	4	no	—
760	C₂²	—	2	1	no	—
761	C₂²	—	4	1	no	—
762	C₂²	—	4	1	no	—
763	C₂²	—	4	1	no	—
764	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
765	C₄	—	2	1	no	—
766	C₄	—	2	1	no	—
767	C₄	—	2	1	no	—
768	C₄	—	2	4	no	—
769	C₄	—	4	1	no	—
770	C₄	—	4	4	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	1	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	1	no	—
775	C₄	—	4	2	no	—
776	C₄	—	4	2	no	—
777	C₄	C₆₁×#577	1	2	yes	—
778	C₄	C₆₁×#578	1	2	yes	—
779	C₄	C₆₁×#585	1	1	yes	characteristic
780	C₄	C₆₁×#585	1	1	yes	characteristic
781	C₂	—	4	1	no	—
782	C₂	—	4	4	no	—
783	C₂	—	8	1	no	—
784	C₂	C₆₁×#3485	1	1	yes	characteristic
785	C₂	C₂×C₆₁×#577	1	1	yes	characteristic
786	C₂	C₂×C₆₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₆₁×#3511	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₆₁×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3550	C₂	semidirect
3. C₆₁×#3356	C₂	semidirect
4. C₆₁×#3353	C₂	semidirect
5. C₆₁×#3342	C₂	semidirect
6. C₆₁×#3340	C₂	semidirect
7. C₆₁×#3329	C₂	semidirect
8. C₆₁×#3328	C₂	semidirect
9. C₆₁×#3299	C₂	semidirect
10. C₆₁×#3298	C₂	semidirect
11. C₆₁×#3230	C₂	semidirect
12. C₆₁×#3229	C₂	semidirect
13. C₆₁×#3201	C₂	semidirect
14. C₆₁×#3107	C₂	semidirect
15. C₆₁×#3107	C₂	semidirect
16. C₆₁×#3097	C₂	semidirect
17. C₆₁×#2979	C₂	semidirect
361. #61789	C₆₁	direct (N × H)
388. #3550	C₂×C₆₁	semidirect
390. #3356	C₂×C₆₁	semidirect
391. #3353	C₂×C₆₁	semidirect
392. #3342	C₂×C₆₁	semidirect
393. #3340	C₂×C₆₁	semidirect
394. #3329	C₂×C₆₁	semidirect
395. #3328	C₂×C₆₁	semidirect
396. #3299	C₂×C₆₁	semidirect
397. #3298	C₂×C₆₁	semidirect
398. #3230	C₂×C₆₁	semidirect
399. #3229	C₂×C₆₁	semidirect
400. #3201	C₂×C₆₁	semidirect
401. #3107	C₂×C₆₁	semidirect
402. #3107	C₂×C₆₁	semidirect
403. #3097	C₂×C₆₁	semidirect
404. #2979	C₂×C₆₁	semidirect
486. C₆₁	#61789	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×#3550	2
C₆₁×#3511	2
C₆₁×#3356	2
C₆₁×#3353	2
C₆₁×#3342	2
C₆₁×#3340	2
C₆₁×#3329	2
C₆₁×#3328	2
C₆₁×#3299	2
C₆₁×#3298	2
C₆₁×#3230	2
C₆₁×#3229	2
C₆₁×#3201	2
C₆₁×#3107	2
C₆₁×#3097	2
C₆₁×#2979	2
#61789	61

Subgroups — C61×#61789 #29565222

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61789 #29565222