Subgroups — C₆₁×#21514 #29524947

Order 15616.

1008 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#461	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#440	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×SD₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2327	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2275	C₂	1	1	yes	maximal, characteristic
6	C₆₁×#1981	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1949	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1928	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1927	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1877	C₂	1	1	yes	maximal, characteristic
11	C₆₁×#1877	C₂	1	1	yes	maximal, characteristic
12	C₆₁×#1804	C₂	1	1	yes	maximal, characteristic
13	C₆₁×#1768	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#1763	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#103×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
24	C₆₁×#461	C₄	1	8	yes	complemented
25	C₆₁×#440	—	2	4	no	—
26	C₄×SD₁₆×C₆₁	—	2	4	no	—
27	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
33	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
34	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
35	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
36	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
37	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
38	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
39	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
41	C₆₁×#391	C₂²	1	1	yes	characteristic
42	C₆₁×#391	C₂²	1	1	yes	characteristic
43	C₆₁×#387	—	2	1	no	—
44	C₆₁×#387	—	2	1	no	—
45	C₆₁×#387	—	2	1	no	—
46	C₆₁×#387	—	2	1	no	—
47	C₆₁×#382	C₂²	1	1	yes	characteristic
48	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
49	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
50	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
51	C₄×C₂²⋊C₄×C₆₁	—	2	1	no	—
52	C₄×C₂²⋊C₄×C₆₁	—	2	1	no	—
53	C₄×C₂²⋊C₄×C₆₁	—	2	1	no	—
54	C₆₁×#376	C₂²	1	1	yes	characteristic
55	C₂×#95×C₆₁	—	2	1	no	—
56	C₆₁×#340	C₂²	1	1	yes	characteristic
57	C₆₁×#340	C₂²	1	1	yes	characteristic
58	C₆₁×#340	C₂²	1	1	yes	characteristic
59	C₆₁×#340	C₂²	1	1	yes	characteristic
60	C₆₁×#336	C₂²	1	1	yes	characteristic
61	C₆₁×#336	C₂²	1	1	yes	characteristic
62	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
63	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₆₁	—	2	1	no	—
66	C₂³×C₄×C₆₁	—	2	1	no	—
67	C₂³×C₄×C₆₁	—	2	1	no	—
68	C₂×SD₁₆×C₆₁	—	2	2	no	—
69	C₂×SD₁₆×C₆₁	—	2	2	no	—
70	C₂×SD₁₆×C₆₁	—	2	2	no	—
71	C₂×SD₁₆×C₆₁	—	2	2	no	—
72	C₂×SD₁₆×C₆₁	C₂×C₄	1	4	yes	—
73	C₂×SD₁₆×C₆₁	C₂×C₄	1	4	yes	—
74	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
78	C₄⋊Q₈×C₆₁	—	2	2	no	—
79	C₄⋊Q₈×C₆₁	C₂×C₄	1	4	yes	complemented
80	C₄×Q₈×C₆₁	—	2	2	no	—
81	C₄×Q₈×C₆₁	—	2	2	no	—
82	C₄×Q₈×C₆₁	—	2	2	no	—
83	C₄×Q₈×C₆₁	—	2	2	no	—
84	C₄×D₄×C₆₁	—	2	2	no	—
85	C₄×D₄×C₆₁	—	2	2	no	—
86	C₄×D₄×C₆₁	—	2	2	no	—
87	C₄×D₄×C₆₁	—	2	2	no	—
88	C₄×D₄×C₆₁	C₂×C₄	1	4	yes	—
89	C₄×D₄×C₆₁	D₄	1	4	yes	—
90	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
91	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
92	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
93	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
94	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
102	C₂×C₄²×C₆₁	—	2	1	no	—
103	C₂×C₄²×C₆₁	—	2	1	no	—
104	C₂×C₄²×C₆₁	—	2	1	no	—
105	C₂×C₄²×C₆₁	—	2	1	no	—
106	C₂×C₄²×C₆₁	—	2	1	no	—
107	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
110	#107×C₆₁	—	2	2	no	—
111	#106×C₆₁	—	2	2	no	—
112	C₄⋊C₈×C₆₁	—	2	2	no	—
113	C₄⋊C₈×C₆₁	C₂×C₄	1	4	yes	complemented
114	#103×C₆₁	—	2	2	no	—
115	#103×C₆₁	—	2	2	no	—
116	#103×C₆₁	—	2	2	no	—
117	#103×C₆₁	—	2	2	no	—
118	#103×C₆₁	C₂×C₄	1	4	yes	complemented
119	#103×C₆₁	C₂×C₄	1	4	yes	complemented
120	#102×C₆₁	—	2	2	no	—
121	#102×C₆₁	—	2	2	no	—
122	#97×C₆₁	—	2	2	no	—
123	C₄×C₈×C₆₁	—	2	2	no	—
124	#95×C₆₁	—	2	1	no	—
125	#95×C₆₁	—	2	1	no	—
126	#95×C₆₁	—	2	1	no	—
127	#95×C₆₁	—	2	1	no	—
128	#95×C₆₁	—	2	1	no	—
129	#95×C₆₁	—	2	1	no	—
130	#95×C₆₁	—	2	1	no	—
131	#95×C₆₁	—	2	1	no	—
132	#95×C₆₁	—	2	1	no	—
133	#95×C₆₁	D₄	1	1	yes	characteristic
134	#95×C₆₁	D₄	1	1	yes	characteristic
135	#95×C₆₁	D₄	1	1	yes	characteristic
136	#95×C₆₁	D₄	1	1	yes	characteristic
137	C₂⁴×C₆₁	—	2	1	no	—
138	C₂×Q₈×C₆₁	—	2	1	no	—
139	C₂×Q₈×C₆₁	—	2	1	no	—
140	C₂×Q₈×C₆₁	—	2	1	no	—
141	C₂×Q₈×C₆₁	—	2	1	no	—
142	C₂×Q₈×C₆₁	—	2	1	no	—
143	C₂×Q₈×C₆₁	—	2	1	no	—
144	C₂×Q₈×C₆₁	—	2	1	no	—
145	C₂×Q₈×C₆₁	—	2	1	no	—
146	C₂×Q₈×C₆₁	—	2	1	no	—
147	C₂×Q₈×C₆₁	—	2	1	no	—
148	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
149	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
150	C₂×D₄×C₆₁	—	2	1	no	—
151	C₂×D₄×C₆₁	—	2	1	no	—
152	C₂×D₄×C₆₁	—	2	1	no	—
153	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
154	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
155	C₂×D₄×C₆₁	#41	1	2	yes	—
156	C₂²×C₄×C₆₁	—	2	1	no	—
157	C₂²×C₄×C₆₁	—	2	1	no	—
158	C₂²×C₄×C₆₁	—	2	1	no	—
159	C₂²×C₄×C₆₁	—	2	1	no	—
160	C₂²×C₄×C₆₁	—	2	1	no	—
161	C₂²×C₄×C₆₁	—	2	4	no	—
162	C₂²×C₄×C₆₁	—	2	4	no	—
163	C₂²×C₄×C₆₁	—	2	4	no	—
164	C₂²×C₄×C₆₁	—	2	1	no	—
165	C₂²×C₄×C₆₁	—	2	1	no	—
166	C₂²×C₄×C₆₁	—	8	1	no	—
167	C₂²×C₄×C₆₁	—	8	1	no	—
168	C₂²×C₄×C₆₁	—	8	1	no	—
169	C₂²×C₄×C₆₁	—	8	1	no	—
170	C₂²×C₄×C₆₁	—	8	1	no	—
171	C₂²×C₄×C₆₁	—	8	1	no	—
172	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
179	SD₁₆×C₆₁	—	2	8	no	—
180	SD₁₆×C₆₁	—	2	8	no	—
181	C₂×C₈×C₆₁	—	2	1	no	—
182	C₂×C₈×C₆₁	—	2	1	no	—
183	C₂×C₈×C₆₁	—	2	1	no	—
184	C₂×C₈×C₆₁	—	2	1	no	—
185	C₂×C₈×C₆₁	—	2	1	no	—
186	C₂×C₈×C₆₁	—	2	1	no	—
187	C₂×C₈×C₆₁	—	2	1	no	—
188	C₂×C₈×C₆₁	—	2	1	no	—
189	C₂×C₈×C₆₁	—	2	1	no	—
190	C₂×C₈×C₆₁	—	2	1	no	—
191	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
192	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
193	C₄⋊C₄×C₆₁	—	2	4	no	—
194	C₄⋊C₄×C₆₁	—	2	4	no	—
195	C₄⋊C₄×C₆₁	—	2	1	no	—
196	C₄⋊C₄×C₆₁	—	2	1	no	—
197	C₄⋊C₄×C₆₁	—	2	1	no	—
198	C₄⋊C₄×C₆₁	—	2	1	no	—
199	C₄⋊C₄×C₆₁	—	2	1	no	—
200	C₄⋊C₄×C₆₁	—	2	1	no	—
201	C₄⋊C₄×C₆₁	—	2	1	no	—
202	C₄⋊C₄×C₆₁	—	4	2	no	—
203	C₄⋊C₄×C₆₁	—	4	2	no	—
204	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
205	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
206	C₄⋊C₄×C₆₁	#41	1	2	yes	—
207	C₂²⋊C₄×C₆₁	—	2	4	no	—
208	C₂²⋊C₄×C₆₁	—	2	4	no	—
209	C₂²⋊C₄×C₆₁	—	2	4	no	—
210	C₄²×C₆₁	—	2	1	no	—
211	C₄²×C₆₁	—	2	1	no	—
212	C₄²×C₆₁	—	4	2	no	—
213	C₄²×C₆₁	—	4	2	no	—
214	C₄²×C₆₁	—	8	1	no	—
215	C₄²×C₆₁	—	8	1	no	—
216	C₄²×C₆₁	—	8	1	no	—
217	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
218	C₄²×C₆₁	C₂×D₄	1	2	yes	—
219	C₄²×C₆₁	#41	1	2	yes	—
220	C₄²×C₆₁	#41	1	2	yes	—
221	C₂³×C₆₁	—	2	2	no	—
222	C₂³×C₆₁	—	2	2	no	—
223	C₂³×C₆₁	—	2	2	no	—
224	C₂³×C₆₁	—	4	1	no	—
225	C₂³×C₆₁	—	4	1	no	—
226	C₂³×C₆₁	—	4	1	no	—
227	C₂³×C₆₁	—	4	1	no	—
228	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
229	Q₈×C₆₁	—	2	2	no	—
230	Q₈×C₆₁	—	2	2	no	—
231	Q₈×C₆₁	—	2	2	no	—
232	Q₈×C₆₁	—	2	2	no	—
233	Q₈×C₆₁	—	4	1	no	—
234	Q₈×C₆₁	—	4	1	no	—
235	Q₈×C₆₁	—	4	1	no	—
236	Q₈×C₆₁	—	4	1	no	—
237	D₄×C₆₁	—	2	2	no	—
238	D₄×C₆₁	—	2	2	no	—
239	D₄×C₆₁	—	2	2	no	—
240	D₄×C₆₁	C₄×D₄	1	4	yes	—
241	C₂×C₄×C₆₁	—	2	1	no	—
242	C₂×C₄×C₆₁	—	2	1	no	—
243	C₂×C₄×C₆₁	—	2	1	no	—
244	C₂×C₄×C₆₁	—	2	1	no	—
245	C₂×C₄×C₆₁	—	2	1	no	—
246	C₂×C₄×C₆₁	—	2	1	no	—
247	C₂×C₄×C₆₁	—	2	1	no	—
248	C₂×C₄×C₆₁	—	2	1	no	—
249	C₂×C₄×C₆₁	—	2	2	no	—
250	C₂×C₄×C₆₁	—	2	2	no	—
251	C₂×C₄×C₆₁	—	2	2	no	—
252	C₂×C₄×C₆₁	—	2	2	no	—
253	C₂×C₄×C₆₁	—	2	1	no	—
254	C₂×C₄×C₆₁	—	2	1	no	—
255	C₂×C₄×C₆₁	—	2	2	no	—
256	C₂×C₄×C₆₁	—	2	1	no	—
257	C₂×C₄×C₆₁	—	2	1	no	—
258	C₂×C₄×C₆₁	—	2	1	no	—
259	C₂×C₄×C₆₁	—	2	1	no	—
260	C₂×C₄×C₆₁	—	4	1	no	—
261	C₂×C₄×C₆₁	—	4	1	no	—
262	C₂×C₄×C₆₁	—	4	1	no	—
263	C₂×C₄×C₆₁	—	4	1	no	—
264	C₂×C₄×C₆₁	—	4	1	no	—
265	C₂×C₄×C₆₁	—	4	1	no	—
266	C₂×C₄×C₆₁	—	4	1	no	—
267	C₂×C₄×C₆₁	—	4	1	no	—
268	C₂×C₄×C₆₁	—	4	1	no	—
269	C₂×C₄×C₆₁	—	4	1	no	—
270	C₂×C₄×C₆₁	—	4	1	no	—
271	C₂×C₄×C₆₁	—	4	1	no	—
272	C₂×C₄×C₆₁	—	4	1	no	—
273	C₂×C₄×C₆₁	—	4	1	no	—
274	C₂×C₄×C₆₁	—	4	1	no	—
275	C₂×C₄×C₆₁	—	4	1	no	—
276	C₂×C₄×C₆₁	—	8	4	no	—
277	C₂×C₄×C₆₁	—	8	4	no	—
278	C₂×C₄×C₆₁	—	8	4	no	—
279	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
280	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
281	C₂×C₄×C₆₁	#121	1	2	yes	—
282	C₂×C₄×C₆₁	#121	1	2	yes	—
283	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
284	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
285	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
286	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
287	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
288	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
289	C₈×C₆₁	—	2	2	no	—
290	C₈×C₆₁	—	2	2	no	—
291	C₈×C₆₁	—	4	1	no	—
292	C₈×C₆₁	—	4	1	no	—
293	#21514	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
294	C₂²×C₆₁	—	2	4	no	—
295	C₂²×C₆₁	—	4	2	no	—
296	C₂²×C₆₁	—	4	2	no	—
297	C₂²×C₆₁	—	4	2	no	—
298	C₂²×C₆₁	—	4	2	no	—
299	C₂²×C₆₁	—	4	2	no	—
300	C₂²×C₆₁	—	4	2	no	—
301	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
302	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
303	C₂²×C₆₁	#525	1	1	yes	characteristic
304	C₂²×C₆₁	#577	1	1	yes	characteristic
305	C₂²×C₆₁	#577	1	1	yes	characteristic
306	C₂²×C₆₁	#577	1	1	yes	characteristic
307	C₂²×C₆₁	#578	1	1	yes	characteristic
308	C₄×C₆₁	—	2	2	no	—
309	C₄×C₆₁	—	2	2	no	—
310	C₄×C₆₁	—	2	2	no	—
311	C₄×C₆₁	—	2	2	no	—
312	C₄×C₆₁	—	4	1	no	—
313	C₄×C₆₁	—	4	1	no	—
314	C₄×C₆₁	—	4	2	no	—
315	C₄×C₆₁	—	4	2	no	—
316	C₄×C₆₁	—	4	2	no	—
317	C₄×C₆₁	—	4	2	no	—
318	C₄×C₆₁	—	4	2	no	—
319	C₄×C₆₁	—	8	1	no	—
320	C₄×C₆₁	—	8	1	no	—
321	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
322	C₄×C₆₁	C₄×#41	1	1	yes	characteristic
323	C₄×C₆₁	#529	1	1	yes	characteristic
324	C₄×C₆₁	#532	1	1	yes	characteristic
325	C₂×#461	C₂×C₆₁	1	1	yes	characteristic
326	C₂×#440	C₂×C₆₁	1	1	yes	characteristic
327	C₂×C₄×SD₁₆	C₂×C₆₁	1	1	yes	characteristic
328	#2327	C₂×C₆₁	1	1	yes	characteristic, complemented
329	#2275	C₂×C₆₁	1	1	yes	characteristic
330	#1981	C₂×C₆₁	1	1	yes	characteristic, complemented
331	#1949	C₂×C₆₁	1	1	yes	characteristic, complemented
332	#1928	C₂×C₆₁	1	1	yes	characteristic, complemented
333	#1927	C₂×C₆₁	1	1	yes	characteristic, complemented
334	#1877	C₂×C₆₁	1	1	yes	characteristic
335	#1877	C₂×C₆₁	1	1	yes	characteristic
336	#1804	C₂×C₆₁	1	1	yes	characteristic
337	#1768	C₂×C₆₁	1	1	yes	characteristic, complemented
338	#1763	C₂×C₆₁	1	1	yes	characteristic, complemented
339	C₄×#103	C₂×C₆₁	1	1	yes	characteristic, complemented
340	C₂×C₆₁	—	4	4	no	—
341	C₂×C₆₁	C₄×#121	1	1	yes	characteristic
342	C₂×C₆₁	#2947	1	1	yes	characteristic
343	C₂×C₆₁	#2949	1	1	yes	characteristic
344	C₂×C₆₁	#3042	1	1	yes	characteristic
345	C₂×C₆₁	#3046	1	1	yes	characteristic
346	C₂×C₆₁	#3120	1	1	yes	characteristic
347	C₂×C₆₁	#3123	1	1	yes	characteristic
348	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
349	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
350	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
351	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
352	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
353	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
354	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
355	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
356	#461	C₄×C₆₁	1	8	yes	complemented
357	#440	—	2	4	no	—
358	C₄×SD₁₆	—	2	4	no	—
359	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
360	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
361	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
362	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
363	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
364	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
365	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
366	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
367	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
368	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
369	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
370	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
371	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
372	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
373	#391	C₂²×C₆₁	1	1	yes	characteristic
374	#391	C₂²×C₆₁	1	1	yes	characteristic
375	#387	—	2	1	no	—
376	#387	—	2	1	no	—
377	#387	—	2	1	no	—
378	#387	—	2	1	no	—
379	#382	C₂²×C₆₁	1	1	yes	characteristic
380	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
381	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
382	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
383	C₄×C₂²⋊C₄	—	2	1	no	—
384	C₄×C₂²⋊C₄	—	2	1	no	—
385	C₄×C₂²⋊C₄	—	2	1	no	—
386	#376	C₂²×C₆₁	1	1	yes	characteristic
387	C₂×#95	—	2	1	no	—
388	#340	C₂²×C₆₁	1	1	yes	characteristic
389	#340	C₂²×C₆₁	1	1	yes	characteristic
390	#340	C₂²×C₆₁	1	1	yes	characteristic
391	#340	C₂²×C₆₁	1	1	yes	characteristic
392	#336	C₂²×C₆₁	1	1	yes	characteristic
393	#336	C₂²×C₆₁	1	1	yes	characteristic
394	C₆₁	#21514	1	1	yes	characteristic, direct product factor, Sylow
395	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
396	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
397	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
398	C₂³×C₄	—	2	1	no	—
399	C₂³×C₄	—	2	1	no	—
400	C₂³×C₄	—	2	1	no	—
401	C₂×SD₁₆	—	2	2	no	—
402	C₂×SD₁₆	—	2	2	no	—
403	C₂×SD₁₆	—	2	2	no	—
404	C₂×SD₁₆	—	2	2	no	—
405	C₂×SD₁₆	C₂×C₄×C₆₁	1	4	yes	—
406	C₂×SD₁₆	C₂×C₄×C₆₁	1	4	yes	—
407	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
408	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
409	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
410	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
411	C₄⋊Q₈	—	2	2	no	—
412	C₄⋊Q₈	C₂×C₄×C₆₁	1	4	yes	complemented
413	C₄×Q₈	—	2	2	no	—
414	C₄×Q₈	—	2	2	no	—
415	C₄×Q₈	—	2	2	no	—
416	C₄×Q₈	—	2	2	no	—
417	C₄×D₄	—	2	2	no	—
418	C₄×D₄	—	2	2	no	—
419	C₄×D₄	—	2	2	no	—
420	C₄×D₄	—	2	2	no	—
421	C₄×D₄	C₂×C₄×C₆₁	1	4	yes	—
422	C₄×D₄	D₄×C₆₁	1	4	yes	—
423	C₂×C₄⋊C₄	—	2	1	no	—
424	C₂×C₄⋊C₄	—	2	1	no	—
425	C₂×C₄⋊C₄	—	2	1	no	—
426	C₂×C₄⋊C₄	—	2	1	no	—
427	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
430	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
431	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
432	C₂×C₂²⋊C₄	—	2	1	no	—
433	C₂×C₂²⋊C₄	—	2	1	no	—
434	C₂×C₂²⋊C₄	—	2	1	no	—
435	C₂×C₄²	—	2	1	no	—
436	C₂×C₄²	—	2	1	no	—
437	C₂×C₄²	—	2	1	no	—
438	C₂×C₄²	—	2	1	no	—
439	C₂×C₄²	—	2	1	no	—
440	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
441	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
442	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
443	#107	—	2	2	no	—
444	#106	—	2	2	no	—
445	C₄⋊C₈	—	2	2	no	—
446	C₄⋊C₈	C₂×C₄×C₆₁	1	4	yes	complemented
447	#103	—	2	2	no	—
448	#103	—	2	2	no	—
449	#103	—	2	2	no	—
450	#103	—	2	2	no	—
451	#103	C₂×C₄×C₆₁	1	4	yes	complemented
452	#103	C₂×C₄×C₆₁	1	4	yes	complemented
453	#102	—	2	2	no	—
454	#102	—	2	2	no	—
455	#97	—	2	2	no	—
456	C₄×C₈	—	2	2	no	—
457	#95	—	2	1	no	—
458	#95	—	2	1	no	—
459	#95	—	2	1	no	—
460	#95	—	2	1	no	—
461	#95	—	2	1	no	—
462	#95	—	2	1	no	—
463	#95	—	2	1	no	—
464	#95	—	2	1	no	—
465	#95	—	2	1	no	—
466	#95	D₄×C₆₁	1	1	yes	characteristic
467	#95	D₄×C₆₁	1	1	yes	characteristic
468	#95	D₄×C₆₁	1	1	yes	characteristic
469	#95	D₄×C₆₁	1	1	yes	characteristic
470	C₂⁴	—	2	1	no	—
471	C₂×Q₈	—	2	1	no	—
472	C₂×Q₈	—	2	1	no	—
473	C₂×Q₈	—	2	1	no	—
474	C₂×Q₈	—	2	1	no	—
475	C₂×Q₈	—	2	1	no	—
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	2	1	no	—
479	C₂×Q₈	—	2	1	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	C₂²×C₄×C₆₁	1	2	yes	—
482	C₂×Q₈	C₂²×C₄×C₆₁	1	2	yes	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	2	1	no	—
486	C₂×D₄	C₂²×C₄×C₆₁	1	2	yes	—
487	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
488	C₂×D₄	#41×C₆₁	1	2	yes	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	4	no	—
495	C₂²×C₄	—	2	4	no	—
496	C₂²×C₄	—	2	4	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	8	1	no	—
500	C₂²×C₄	—	8	1	no	—
501	C₂²×C₄	—	8	1	no	—
502	C₂²×C₄	—	8	1	no	—
503	C₂²×C₄	—	8	1	no	—
504	C₂²×C₄	—	8	1	no	—
505	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
506	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
507	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
508	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
509	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
510	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
511	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
512	SD₁₆	—	2	8	no	—
513	SD₁₆	—	2	8	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
525	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
526	C₄⋊C₄	—	2	4	no	—
527	C₄⋊C₄	—	2	4	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	4	2	no	—
536	C₄⋊C₄	—	4	2	no	—
537	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
538	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
539	C₄⋊C₄	#41×C₆₁	1	2	yes	—
540	C₂²⋊C₄	—	2	4	no	—
541	C₂²⋊C₄	—	2	4	no	—
542	C₂²⋊C₄	—	2	4	no	—
543	C₄²	—	2	1	no	—
544	C₄²	—	2	1	no	—
545	C₄²	—	4	2	no	—
546	C₄²	—	4	2	no	—
547	C₄²	—	8	1	no	—
548	C₄²	—	8	1	no	—
549	C₄²	—	8	1	no	—
550	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
551	C₄²	C₂×D₄×C₆₁	1	2	yes	—
552	C₄²	#41×C₆₁	1	2	yes	—
553	C₄²	#41×C₆₁	1	2	yes	—
554	C₂³	—	2	2	no	—
555	C₂³	—	2	2	no	—
556	C₂³	—	2	2	no	—
557	C₂³	—	4	1	no	—
558	C₂³	—	4	1	no	—
559	C₂³	—	4	1	no	—
560	C₂³	—	4	1	no	—
561	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
562	Q₈	—	2	2	no	—
563	Q₈	—	2	2	no	—
564	Q₈	—	2	2	no	—
565	Q₈	—	2	2	no	—
566	Q₈	—	4	1	no	—
567	Q₈	—	4	1	no	—
568	Q₈	—	4	1	no	—
569	Q₈	—	4	1	no	—
570	D₄	—	2	2	no	—
571	D₄	—	2	2	no	—
572	D₄	—	2	2	no	—
573	D₄	C₄×D₄×C₆₁	1	4	yes	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	8	4	no	—
610	C₂×C₄	—	8	4	no	—
611	C₂×C₄	—	8	4	no	—
612	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
613	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
614	C₂×C₄	#121×C₆₁	1	2	yes	—
615	C₂×C₄	#121×C₆₁	1	2	yes	—
616	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
617	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
618	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
619	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
620	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
621	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
622	C₈	—	2	2	no	—
623	C₈	—	2	2	no	—
624	C₈	—	4	1	no	—
625	C₈	—	4	1	no	—
626	C₂²	—	2	4	no	—
627	C₂²	—	4	2	no	—
628	C₂²	—	4	2	no	—
629	C₂²	—	4	2	no	—
630	C₂²	—	4	2	no	—
631	C₂²	—	4	2	no	—
632	C₂²	—	4	2	no	—
633	C₂²	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
634	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
635	C₂²	C₆₁×#525	1	1	yes	characteristic
636	C₂²	C₆₁×#577	1	1	yes	characteristic
637	C₂²	C₆₁×#577	1	1	yes	characteristic
638	C₂²	C₆₁×#577	1	1	yes	characteristic
639	C₂²	C₆₁×#578	1	1	yes	characteristic
640	C₄	—	2	2	no	—
641	C₄	—	2	2	no	—
642	C₄	—	2	2	no	—
643	C₄	—	2	2	no	—
644	C₄	—	4	2	no	—
645	C₄	—	4	2	no	—
646	C₄	—	4	2	no	—
647	C₄	—	4	1	no	—
648	C₄	—	4	1	no	—
649	C₄	—	4	2	no	—
650	C₄	—	4	2	no	—
651	C₄	—	8	1	no	—
652	C₄	—	8	1	no	—
653	C₄	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
654	C₄	C₄×#41×C₆₁	1	1	yes	characteristic
655	C₄	C₆₁×#529	1	1	yes	characteristic
656	C₄	C₆₁×#532	1	1	yes	characteristic
657	C₂	—	4	4	no	—
658	C₂	C₄×#121×C₆₁	1	1	yes	characteristic
659	C₂	C₆₁×#2947	1	1	yes	characteristic
660	C₂	C₆₁×#2949	1	1	yes	characteristic
661	C₂	C₆₁×#3042	1	1	yes	characteristic
662	C₂	C₆₁×#3046	1	1	yes	characteristic
663	C₂	C₆₁×#3120	1	1	yes	characteristic
664	C₂	C₆₁×#3123	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂²×D₄×C₆₁	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₆₁×#376 ◁ G

Complements

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

N	H ≅ G/N	type
4. C₆₁×#2327	C₂	semidirect
6. C₆₁×#1981	C₂	semidirect
7. C₆₁×#1949	C₂	semidirect
8. C₆₁×#1928	C₂	semidirect
9. C₆₁×#1927	C₂	semidirect
13. C₆₁×#1768	C₂	semidirect
14. C₆₁×#1763	C₂	semidirect
15. C₄×#103×C₆₁	C₂	semidirect
24. C₆₁×#461	C₄	semidirect
79. C₄⋊Q₈×C₆₁	C₂×C₄	semidirect
113. C₄⋊C₈×C₆₁	C₂×C₄	semidirect
118. #103×C₆₁	C₂×C₄	semidirect
119. #103×C₆₁	C₂×C₄	semidirect
293. #21514	C₆₁	direct (N × H)
328. #2327	C₂×C₆₁	semidirect
330. #1981	C₂×C₆₁	semidirect
331. #1949	C₂×C₆₁	semidirect
332. #1928	C₂×C₆₁	semidirect
333. #1927	C₂×C₆₁	semidirect
337. #1768	C₂×C₆₁	semidirect
338. #1763	C₂×C₆₁	semidirect
339. C₄×#103	C₂×C₆₁	semidirect
356. #461	C₄×C₆₁	semidirect
394. C₆₁	#21514	direct (N × H)
412. C₄⋊Q₈	C₂×C₄×C₆₁	semidirect
446. C₄⋊C₈	C₂×C₄×C₆₁	semidirect
451. #103	C₂×C₄×C₆₁	semidirect
452. #103	C₂×C₄×C₆₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₆₁×#461	2
C₂×C₆₁×#440	2
C₂×C₄×SD₁₆×C₆₁	2
C₆₁×#2327	2
C₆₁×#2275	2
C₆₁×#1981	2
C₆₁×#1949	2
C₆₁×#1928	2
C₆₁×#1927	2
C₆₁×#1877	2
C₆₁×#1804	2
C₆₁×#1768	2
C₆₁×#1763	2
C₄×#103×C₆₁	2
#21514	61

Subgroups — C61×#21514 #29524947

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#21514 #29524947