Subgroups — C₆₁×#11121 #29514554

Order 15616.

1254 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#106×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#102×C₆₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×#102×C₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₆₁×#390	C₂	1	1	yes	maximal, characteristic
5	C₂×C₆₁×#340	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₆₁×#336	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×C₄⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₆₁	C₂²	1	1	yes	characteristic
9	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
14	C₂²×C₂²⋊C₄×C₆₁	—	2	2	no	—
15	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×#106×C₆₁	—	2	2	no	—
17	C₂×#106×C₆₁	—	2	2	no	—
18	C₂×#106×C₆₁	—	2	2	no	—
19	C₂×#102×C₆₁	—	2	2	no	—
20	C₂×#102×C₆₁	—	2	2	no	—
21	C₂×#102×C₆₁	—	2	2	no	—
22	C₂×#102×C₆₁	—	2	2	no	—
23	C₂×#102×C₆₁	—	2	2	no	—
24	C₂×#102×C₆₁	C₄	1	4	yes	complemented
25	C₆₁×#390	—	2	2	no	—
26	C₆₁×#390	—	2	2	no	—
27	C₂×#95×C₆₁	—	2	2	no	—
28	C₆₁×#340	—	2	2	no	—
29	C₆₁×#336	—	2	2	no	—
30	C₂⁵×C₆₁	—	2	1	no	—
31	C₂²×D₄×C₆₁	—	2	1	no	—
32	C₂²×D₄×C₆₁	—	2	1	no	—
33	C₂²×D₄×C₆₁	—	2	1	no	—
34	C₂²×D₄×C₆₁	—	2	1	no	—
35	C₂²×D₄×C₆₁	—	2	1	no	—
36	C₂²×D₄×C₆₁	—	2	1	no	—
37	C₂²×D₄×C₆₁	—	2	1	no	—
38	C₂²×D₄×C₆₁	—	2	1	no	—
39	C₂²×D₄×C₆₁	—	2	1	no	—
40	C₂²×D₄×C₆₁	—	2	1	no	—
41	C₂²×D₄×C₆₁	—	2	1	no	—
42	C₂²×D₄×C₆₁	C₂×C₄	1	2	yes	—
43	C₂²×D₄×C₆₁	D₄	1	2	yes	—
44	C₂²×D₄×C₆₁	Q₈	1	2	yes	—
45	C₂³×C₄×C₆₁	—	2	1	no	—
46	C₂³×C₄×C₆₁	—	2	1	no	—
47	C₂³×C₄×C₆₁	—	2	1	no	—
48	C₂³×C₄×C₆₁	D₄	1	2	yes	—
49	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₆₁	—	2	1	no	—
51	C₂²×C₈×C₆₁	—	2	1	no	—
52	C₂²×C₈×C₆₁	—	2	1	no	—
53	C₂²×C₈×C₆₁	—	2	1	no	—
54	C₂²×C₈×C₆₁	—	2	1	no	—
55	C₂²×C₈×C₆₁	—	2	1	no	—
56	C₂²×C₈×C₆₁	—	2	1	no	—
57	C₂²×C₈×C₆₁	—	2	1	no	—
58	C₂²×C₈×C₆₁	—	2	1	no	—
59	C₂²×C₈×C₆₁	—	2	1	no	—
60	C₂²×C₈×C₆₁	C₂×C₄	1	2	yes	—
61	C₂²×C₈×C₆₁	D₄	1	2	yes	—
62	C₂²×C₈×C₆₁	D₄	1	2	yes	—
63	C₂²×C₈×C₆₁	D₄	1	2	yes	—
64	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
66	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
67	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
68	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
69	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
70	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
71	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
72	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
73	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
74	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
75	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
76	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
77	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
78	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
79	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
80	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
81	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
82	C₂×C₂²⋊C₄×C₆₁	—	2	8	no	—
83	C₂×C₂²⋊C₄×C₆₁	—	4	4	no	—
84	C₂×C₂²⋊C₄×C₆₁	—	4	4	no	—
85	C₂×C₄²×C₆₁	—	2	1	no	—
86	C₂×C₄²×C₆₁	—	2	1	no	—
87	C₂×C₄²×C₆₁	—	2	1	no	—
88	C₂×C₄²×C₆₁	—	2	1	no	—
89	C₂×C₄²×C₆₁	—	2	1	no	—
90	C₂×C₄²×C₆₁	—	2	1	no	—
91	#106×C₆₁	—	2	8	no	—
92	#102×C₆₁	—	2	8	no	—
93	#102×C₆₁	—	2	8	no	—
94	#95×C₆₁	—	4	4	no	—
95	C₂⁴×C₆₁	—	2	2	no	—
96	C₂⁴×C₆₁	—	2	2	no	—
97	C₂⁴×C₆₁	—	2	2	no	—
98	C₂⁴×C₆₁	—	4	1	no	—
99	C₂⁴×C₆₁	—	4	1	no	—
100	C₂⁴×C₆₁	—	4	1	no	—
101	C₂⁴×C₆₁	—	4	1	no	—
102	C₂⁴×C₆₁	—	4	2	no	—
103	C₂⁴×C₆₁	—	4	2	no	—
104	C₂⁴×C₆₁	—	4	2	no	—
105	C₂⁴×C₆₁	—	4	2	no	—
106	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
107	C₂×D₄×C₆₁	—	2	2	no	—
108	C₂×D₄×C₆₁	—	2	2	no	—
109	C₂×D₄×C₆₁	—	2	2	no	—
110	C₂×D₄×C₆₁	—	2	2	no	—
111	C₂×D₄×C₆₁	—	2	2	no	—
112	C₂×D₄×C₆₁	—	2	2	no	—
113	C₂×D₄×C₆₁	—	2	2	no	—
114	C₂×D₄×C₆₁	—	2	2	no	—
115	C₂×D₄×C₆₁	—	2	2	no	—
116	C₂×D₄×C₆₁	—	2	2	no	—
117	C₂×D₄×C₆₁	—	2	2	no	—
118	C₂×D₄×C₆₁	—	2	2	no	—
119	C₂×D₄×C₆₁	—	2	2	no	—
120	C₂×D₄×C₆₁	—	2	2	no	—
121	C₂×D₄×C₆₁	—	2	2	no	—
122	C₂×D₄×C₆₁	—	4	1	no	—
123	C₂×D₄×C₆₁	—	4	1	no	—
124	C₂×D₄×C₆₁	—	4	1	no	—
125	C₂×D₄×C₆₁	—	4	1	no	—
126	C₂×D₄×C₆₁	—	4	1	no	—
127	C₂×D₄×C₆₁	—	4	1	no	—
128	C₂×D₄×C₆₁	—	4	1	no	—
129	C₂×D₄×C₆₁	—	4	1	no	—
130	C₂×D₄×C₆₁	—	4	1	no	—
131	C₂×D₄×C₆₁	—	4	1	no	—
132	C₂×D₄×C₆₁	—	4	1	no	—
133	C₂×D₄×C₆₁	—	4	1	no	—
134	C₂×D₄×C₆₁	C₄⋊C₄	1	4	yes	—
135	C₂²×C₄×C₆₁	—	2	2	no	—
136	C₂²×C₄×C₆₁	—	2	2	no	—
137	C₂²×C₄×C₆₁	—	2	2	no	—
138	C₂²×C₄×C₆₁	—	2	2	no	—
139	C₂²×C₄×C₆₁	—	2	2	no	—
140	C₂²×C₄×C₆₁	—	2	2	no	—
141	C₂²×C₄×C₆₁	—	2	2	no	—
142	C₂²×C₄×C₆₁	—	2	2	no	—
143	C₂²×C₄×C₆₁	—	2	2	no	—
144	C₂²×C₄×C₆₁	—	4	1	no	—
145	C₂²×C₄×C₆₁	—	4	1	no	—
146	C₂²×C₄×C₆₁	—	4	1	no	—
147	C₂²×C₄×C₆₁	—	4	1	no	—
148	C₂²×C₄×C₆₁	—	4	1	no	—
149	C₂²×C₄×C₆₁	—	4	1	no	—
150	C₂²×C₄×C₆₁	—	4	2	no	—
151	C₂²×C₄×C₆₁	—	4	2	no	—
152	C₂²×C₄×C₆₁	—	4	2	no	—
153	C₂²×C₄×C₆₁	—	4	2	no	—
154	C₂²×C₄×C₆₁	—	4	2	no	—
155	C₂²×C₄×C₆₁	—	4	2	no	—
156	C₂²×C₄×C₆₁	SD₁₆	1	4	yes	—
157	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
165	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
166	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
167	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
168	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
169	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
170	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
171	C₂×C₈×C₆₁	—	2	2	no	—
172	C₂×C₈×C₆₁	—	2	2	no	—
173	C₂×C₈×C₆₁	—	2	2	no	—
174	C₂×C₈×C₆₁	—	2	2	no	—
175	C₂×C₈×C₆₁	—	2	2	no	—
176	C₂×C₈×C₆₁	—	2	2	no	—
177	C₂×C₈×C₆₁	—	2	2	no	—
178	C₂×C₈×C₆₁	—	2	2	no	—
179	C₂×C₈×C₆₁	—	2	2	no	—
180	C₂×C₈×C₆₁	—	4	1	no	—
181	C₂×C₈×C₆₁	—	4	1	no	—
182	C₂×C₈×C₆₁	—	4	1	no	—
183	C₂×C₈×C₆₁	—	4	1	no	—
184	C₂×C₈×C₆₁	C₂²⋊C₄	1	4	yes	complemented
185	C₄⋊C₄×C₆₁	—	2	2	no	—
186	C₄⋊C₄×C₆₁	—	2	2	no	—
187	C₄⋊C₄×C₆₁	—	2	2	no	—
188	C₄⋊C₄×C₆₁	—	2	2	no	—
189	C₄⋊C₄×C₆₁	—	2	2	no	—
190	C₄⋊C₄×C₆₁	—	2	2	no	—
191	C₄⋊C₄×C₆₁	—	4	1	no	—
192	C₄⋊C₄×C₆₁	—	4	1	no	—
193	C₄⋊C₄×C₆₁	—	4	1	no	—
194	C₄⋊C₄×C₆₁	—	4	1	no	—
195	C₄⋊C₄×C₆₁	—	4	1	no	—
196	C₄⋊C₄×C₆₁	—	4	1	no	—
197	C₂²⋊C₄×C₆₁	—	4	16	no	—
198	C₄²×C₆₁	—	4	1	no	—
199	C₄²×C₆₁	—	4	1	no	—
200	C₄²×C₆₁	—	4	1	no	—
201	C₄²×C₆₁	—	4	1	no	—
202	C₂³×C₆₁	—	2	4	no	—
203	C₂³×C₆₁	—	4	2	no	—
204	C₂³×C₆₁	—	4	2	no	—
205	C₂³×C₆₁	—	4	2	no	—
206	C₂³×C₆₁	—	4	2	no	—
207	C₂³×C₆₁	—	4	2	no	—
208	C₂³×C₆₁	—	4	2	no	—
209	C₂³×C₆₁	—	4	4	no	—
210	C₂³×C₆₁	—	4	4	no	—
211	C₂³×C₆₁	—	4	4	no	—
212	C₂³×C₆₁	—	4	4	no	—
213	C₂³×C₆₁	—	4	4	no	—
214	C₂³×C₆₁	—	4	4	no	—
215	C₂³×C₆₁	—	8	2	no	—
216	C₂³×C₆₁	—	8	2	no	—
217	C₂³×C₆₁	—	8	2	no	—
218	C₂³×C₆₁	—	8	2	no	—
219	C₂³×C₆₁	—	8	2	no	—
220	C₂³×C₆₁	—	8	2	no	—
221	C₂³×C₆₁	—	8	1	no	—
222	C₂³×C₆₁	—	8	1	no	—
223	C₂³×C₆₁	—	8	1	no	—
224	C₂³×C₆₁	—	8	1	no	—
225	C₂³×C₆₁	C₄×D₄	1	1	yes	characteristic
226	C₂³×C₆₁	#120	1	1	yes	characteristic
227	C₂³×C₆₁	#121	1	1	yes	characteristic
228	C₂³×C₆₁	#121	1	1	yes	characteristic
229	C₂³×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
230	C₂³×C₆₁	#123	1	1	yes	characteristic
231	C₂³×C₆₁	#127	1	1	yes	characteristic
232	C₂³×C₆₁	C₂×SD₁₆	1	2	yes	—
233	C₂³×C₆₁	#135	1	2	yes	—
234	C₂³×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
235	C₂³×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
236	D₄×C₆₁	—	2	4	no	—
237	D₄×C₆₁	—	2	4	no	—
238	D₄×C₆₁	—	4	2	no	—
239	D₄×C₆₁	—	4	2	no	—
240	D₄×C₆₁	—	4	2	no	—
241	D₄×C₆₁	—	4	2	no	—
242	D₄×C₆₁	—	4	2	no	—
243	D₄×C₆₁	—	4	2	no	—
244	C₂×C₄×C₆₁	—	2	4	no	—
245	C₂×C₄×C₆₁	—	2	4	no	—
246	C₂×C₄×C₆₁	—	2	4	no	—
247	C₂×C₄×C₆₁	—	4	2	no	—
248	C₂×C₄×C₆₁	—	4	2	no	—
249	C₂×C₄×C₆₁	—	4	2	no	—
250	C₂×C₄×C₆₁	—	4	2	no	—
251	C₂×C₄×C₆₁	—	4	2	no	—
252	C₂×C₄×C₆₁	—	4	2	no	—
253	C₂×C₄×C₆₁	—	4	2	no	—
254	C₂×C₄×C₆₁	—	4	4	no	—
255	C₂×C₄×C₆₁	—	4	4	no	—
256	C₂×C₄×C₆₁	—	4	4	no	—
257	C₂×C₄×C₆₁	—	8	2	no	—
258	C₂×C₄×C₆₁	—	8	2	no	—
259	C₂×C₄×C₆₁	—	8	2	no	—
260	C₂×C₄×C₆₁	—	8	1	no	—
261	C₂×C₄×C₆₁	—	8	1	no	—
262	C₂×C₄×C₆₁	—	8	1	no	—
263	C₂×C₄×C₆₁	—	8	1	no	—
264	C₂×C₄×C₆₁	—	8	1	no	—
265	C₂×C₄×C₆₁	—	8	1	no	—
266	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
268	C₂×C₄×C₆₁	#117	1	1	yes	characteristic
269	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
270	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
271	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
272	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
273	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
274	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
275	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
276	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
277	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
278	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
279	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
280	C₂×C₄×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
281	C₂×C₄×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
282	C₂×C₄×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
283	C₂×C₄×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
284	C₂×C₄×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
285	C₂×C₄×C₆₁	#123	1	1	yes	characteristic
286	C₂×C₄×C₆₁	#123	1	1	yes	characteristic
287	C₂×C₄×C₆₁	#123	1	1	yes	characteristic
288	C₂×C₄×C₆₁	#123	1	1	yes	characteristic
289	C₂×C₄×C₆₁	#124	1	1	yes	characteristic
290	C₂×C₄×C₆₁	#124	1	1	yes	characteristic
291	C₂×C₄×C₆₁	#124	1	1	yes	characteristic
292	C₂×C₄×C₆₁	#126	1	1	yes	characteristic
293	C₂×C₄×C₆₁	#126	1	1	yes	characteristic
294	C₈×C₆₁	—	2	4	no	—
295	C₈×C₆₁	—	4	2	no	—
296	#11121	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
297	C₂²×C₆₁	—	4	8	no	—
298	C₂²×C₆₁	—	4	4	no	—
299	C₂²×C₆₁	—	8	4	no	—
300	C₂²×C₆₁	—	8	2	no	—
301	C₂²×C₆₁	—	8	2	no	—
302	C₂²×C₆₁	—	8	4	no	—
303	C₂²×C₆₁	—	8	2	no	—
304	C₂²×C₆₁	—	8	2	no	—
305	C₂²×C₆₁	—	8	2	no	—
306	C₂²×C₆₁	—	8	2	no	—
307	C₂²×C₆₁	—	8	4	no	—
308	C₂²×C₆₁	#385	1	1	yes	characteristic
309	C₂²×C₆₁	#388	1	1	yes	characteristic
310	C₂²×C₆₁	#390	1	1	yes	characteristic
311	C₂²×C₆₁	#392	1	1	yes	characteristic
312	C₂²×C₆₁	#394	1	1	yes	characteristic
313	C₂²×C₆₁	#396	1	1	yes	characteristic
314	C₂²×C₆₁	#399	1	1	yes	characteristic
315	C₂²×C₆₁	C₄×SD₁₆	1	2	yes	—
316	C₂²×C₆₁	#442	1	2	yes	—
317	C₂²×C₆₁	#449	1	2	yes	—
318	C₂²×C₆₁	#450	1	2	yes	—
319	C₂²×C₆₁	#460	1	2	yes	—
320	C₂²×C₆₁	#463	1	2	yes	—
321	C₂²×C₆₁	#465	1	2	yes	—
322	C₂²×C₆₁	#469	1	2	yes	—
323	C₂²×C₆₁	#476	1	2	yes	—
324	C₂²×C₆₁	#478	1	2	yes	—
325	C₂²×C₆₁	#481	1	2	yes	—
326	C₂²×C₆₁	#482	1	2	yes	—
327	C₂²×C₆₁	#492	1	1	yes	characteristic
328	C₂²×C₆₁	#495	1	1	yes	characteristic
329	C₂²×C₆₁	#496	1	1	yes	characteristic
330	C₂²×C₆₁	#496	1	1	yes	characteristic
331	C₄×C₆₁	—	4	4	no	—
332	C₄×C₆₁	—	8	2	no	—
333	C₄×C₆₁	—	8	2	no	—
334	C₄×C₆₁	—	8	2	no	—
335	C₄×C₆₁	#380	1	1	yes	characteristic
336	C₄×C₆₁	#385	1	1	yes	characteristic
337	C₄×C₆₁	#386	1	1	yes	characteristic
338	C₄×C₆₁	#388	1	1	yes	characteristic
339	C₄×C₆₁	#393	1	1	yes	characteristic
340	C₄×C₆₁	#394	1	1	yes	characteristic
341	C₄×C₆₁	#396	1	1	yes	characteristic
342	C₄×C₆₁	#397	1	1	yes	characteristic
343	C₂²×#106	C₂×C₆₁	1	1	yes	characteristic, complemented
344	C₂²×#102	C₂×C₆₁	1	1	yes	characteristic
345	C₂²×#102	C₂×C₆₁	1	1	yes	characteristic
346	C₂×#390	C₂×C₆₁	1	1	yes	characteristic
347	C₂×#340	C₂×C₆₁	1	1	yes	characteristic, complemented
348	C₂×#336	C₂×C₆₁	1	1	yes	characteristic, complemented
349	C₄⋊#95	C₂×C₆₁	1	1	yes	characteristic, complemented
350	C₂×C₆₁	—	8	4	no	—
351	C₂×C₆₁	#1439	1	1	yes	characteristic
352	C₂×C₆₁	#1864	1	2	yes	—
353	C₂×C₆₁	#1926	1	2	yes	—
354	C₂×C₆₁	#1968	1	1	yes	characteristic
355	C₂×C₆₁	#1972	1	1	yes	characteristic
356	C₂×C₆₁	#2012	1	1	yes	characteristic
357	C₂×C₆₁	#2014	1	1	yes	characteristic
358	C₂×C₆₁	#2034	1	2	yes	—
359	C₂×C₆₁	#2065	1	2	yes	—
360	C₂×C₆₁	#2092	1	1	yes	characteristic
361	C₂×C₆₁	#2094	1	1	yes	characteristic
362	C₂³×D₄	C₂²×C₆₁	1	1	yes	characteristic
363	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
364	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
365	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
366	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
367	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
368	C₂²×C₂²⋊C₄	—	2	2	no	—
369	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
370	C₂×#106	—	2	2	no	—
371	C₂×#106	—	2	2	no	—
372	C₂×#106	—	2	2	no	—
373	C₂×#102	—	2	2	no	—
374	C₂×#102	—	2	2	no	—
375	C₂×#102	—	2	2	no	—
376	C₂×#102	—	2	2	no	—
377	C₂×#102	—	2	2	no	—
378	C₂×#102	C₄×C₆₁	1	4	yes	complemented
379	#390	—	2	2	no	—
380	#390	—	2	2	no	—
381	C₂×#95	—	2	2	no	—
382	#340	—	2	2	no	—
383	#336	—	2	2	no	—
384	C₆₁	#11121	1	1	yes	characteristic, direct product factor, Sylow
385	C₂⁵	—	2	1	no	—
386	C₂²×D₄	—	2	1	no	—
387	C₂²×D₄	—	2	1	no	—
388	C₂²×D₄	—	2	1	no	—
389	C₂²×D₄	—	2	1	no	—
390	C₂²×D₄	—	2	1	no	—
391	C₂²×D₄	—	2	1	no	—
392	C₂²×D₄	—	2	1	no	—
393	C₂²×D₄	—	2	1	no	—
394	C₂²×D₄	—	2	1	no	—
395	C₂²×D₄	—	2	1	no	—
396	C₂²×D₄	—	2	1	no	—
397	C₂²×D₄	C₂×C₄×C₆₁	1	2	yes	—
398	C₂²×D₄	D₄×C₆₁	1	2	yes	—
399	C₂²×D₄	Q₈×C₆₁	1	2	yes	—
400	C₂³×C₄	—	2	1	no	—
401	C₂³×C₄	—	2	1	no	—
402	C₂³×C₄	—	2	1	no	—
403	C₂³×C₄	D₄×C₆₁	1	2	yes	—
404	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
405	C₂²×C₈	—	2	1	no	—
406	C₂²×C₈	—	2	1	no	—
407	C₂²×C₈	—	2	1	no	—
408	C₂²×C₈	—	2	1	no	—
409	C₂²×C₈	—	2	1	no	—
410	C₂²×C₈	—	2	1	no	—
411	C₂²×C₈	—	2	1	no	—
412	C₂²×C₈	—	2	1	no	—
413	C₂²×C₈	—	2	1	no	—
414	C₂²×C₈	—	2	1	no	—
415	C₂²×C₈	C₂×C₄×C₆₁	1	2	yes	—
416	C₂²×C₈	D₄×C₆₁	1	2	yes	—
417	C₂²×C₈	D₄×C₆₁	1	2	yes	—
418	C₂²×C₈	D₄×C₆₁	1	2	yes	—
419	C₂×C₄⋊C₄	—	2	1	no	—
420	C₂×C₄⋊C₄	—	2	1	no	—
421	C₂×C₄⋊C₄	—	2	1	no	—
422	C₂×C₄⋊C₄	—	2	1	no	—
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	—	2	1	no	—
428	C₂×C₄⋊C₄	—	2	1	no	—
429	C₂×C₄⋊C₄	—	2	1	no	—
430	C₂×C₄⋊C₄	—	2	1	no	—
431	C₂×C₄⋊C₄	—	2	1	no	—
432	C₂×C₄⋊C₄	—	2	1	no	—
433	C₂×C₄⋊C₄	—	2	1	no	—
434	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
435	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
436	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
437	C₂×C₂²⋊C₄	—	2	8	no	—
438	C₂×C₂²⋊C₄	—	4	4	no	—
439	C₂×C₂²⋊C₄	—	4	4	no	—
440	C₂×C₄²	—	2	1	no	—
441	C₂×C₄²	—	2	1	no	—
442	C₂×C₄²	—	2	1	no	—
443	C₂×C₄²	—	2	1	no	—
444	C₂×C₄²	—	2	1	no	—
445	C₂×C₄²	—	2	1	no	—
446	#106	—	2	8	no	—
447	#102	—	2	8	no	—
448	#102	—	2	8	no	—
449	#95	—	4	4	no	—
450	C₂⁴	—	2	2	no	—
451	C₂⁴	—	2	2	no	—
452	C₂⁴	—	2	2	no	—
453	C₂⁴	—	4	1	no	—
454	C₂⁴	—	4	1	no	—
455	C₂⁴	—	4	1	no	—
456	C₂⁴	—	4	1	no	—
457	C₂⁴	—	4	2	no	—
458	C₂⁴	—	4	2	no	—
459	C₂⁴	—	4	2	no	—
460	C₂⁴	—	4	2	no	—
461	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
462	C₂×D₄	—	2	2	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	2	2	no	—
467	C₂×D₄	—	2	2	no	—
468	C₂×D₄	—	2	2	no	—
469	C₂×D₄	—	2	2	no	—
470	C₂×D₄	—	2	2	no	—
471	C₂×D₄	—	2	2	no	—
472	C₂×D₄	—	2	2	no	—
473	C₂×D₄	—	2	2	no	—
474	C₂×D₄	—	2	2	no	—
475	C₂×D₄	—	2	2	no	—
476	C₂×D₄	—	2	2	no	—
477	C₂×D₄	—	4	1	no	—
478	C₂×D₄	—	4	1	no	—
479	C₂×D₄	—	4	1	no	—
480	C₂×D₄	—	4	1	no	—
481	C₂×D₄	—	4	1	no	—
482	C₂×D₄	—	4	1	no	—
483	C₂×D₄	—	4	1	no	—
484	C₂×D₄	—	4	1	no	—
485	C₂×D₄	—	4	1	no	—
486	C₂×D₄	—	4	1	no	—
487	C₂×D₄	—	4	1	no	—
488	C₂×D₄	—	4	1	no	—
489	C₂×D₄	C₄⋊C₄×C₆₁	1	4	yes	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	2	no	—
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	—	2	2	no	—
495	C₂²×C₄	—	2	2	no	—
496	C₂²×C₄	—	2	2	no	—
497	C₂²×C₄	—	2	2	no	—
498	C₂²×C₄	—	2	2	no	—
499	C₂²×C₄	—	4	1	no	—
500	C₂²×C₄	—	4	1	no	—
501	C₂²×C₄	—	4	1	no	—
502	C₂²×C₄	—	4	1	no	—
503	C₂²×C₄	—	4	1	no	—
504	C₂²×C₄	—	4	1	no	—
505	C₂²×C₄	—	4	2	no	—
506	C₂²×C₄	—	4	2	no	—
507	C₂²×C₄	—	4	2	no	—
508	C₂²×C₄	—	4	2	no	—
509	C₂²×C₄	—	4	2	no	—
510	C₂²×C₄	—	4	2	no	—
511	C₂²×C₄	SD₁₆×C₆₁	1	4	yes	—
512	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
513	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
514	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
515	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
516	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
517	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
518	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
519	C₂²×C₄	C₂×Q₈×C₆₁	1	1	yes	characteristic
520	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
521	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
522	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
523	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
524	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
525	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
526	C₂×C₈	—	2	2	no	—
527	C₂×C₈	—	2	2	no	—
528	C₂×C₈	—	2	2	no	—
529	C₂×C₈	—	2	2	no	—
530	C₂×C₈	—	2	2	no	—
531	C₂×C₈	—	2	2	no	—
532	C₂×C₈	—	2	2	no	—
533	C₂×C₈	—	2	2	no	—
534	C₂×C₈	—	2	2	no	—
535	C₂×C₈	—	4	1	no	—
536	C₂×C₈	—	4	1	no	—
537	C₂×C₈	—	4	1	no	—
538	C₂×C₈	—	4	1	no	—
539	C₂×C₈	C₂²⋊C₄×C₆₁	1	4	yes	complemented
540	C₄⋊C₄	—	2	2	no	—
541	C₄⋊C₄	—	2	2	no	—
542	C₄⋊C₄	—	2	2	no	—
543	C₄⋊C₄	—	2	2	no	—
544	C₄⋊C₄	—	2	2	no	—
545	C₄⋊C₄	—	2	2	no	—
546	C₄⋊C₄	—	4	1	no	—
547	C₄⋊C₄	—	4	1	no	—
548	C₄⋊C₄	—	4	1	no	—
549	C₄⋊C₄	—	4	1	no	—
550	C₄⋊C₄	—	4	1	no	—
551	C₄⋊C₄	—	4	1	no	—
552	C₂²⋊C₄	—	4	16	no	—
553	C₄²	—	4	1	no	—
554	C₄²	—	4	1	no	—
555	C₄²	—	4	1	no	—
556	C₄²	—	4	1	no	—
557	C₂³	—	2	4	no	—
558	C₂³	—	4	2	no	—
559	C₂³	—	4	2	no	—
560	C₂³	—	4	2	no	—
561	C₂³	—	4	2	no	—
562	C₂³	—	4	2	no	—
563	C₂³	—	4	2	no	—
564	C₂³	—	4	4	no	—
565	C₂³	—	4	4	no	—
566	C₂³	—	4	4	no	—
567	C₂³	—	4	4	no	—
568	C₂³	—	4	4	no	—
569	C₂³	—	4	4	no	—
570	C₂³	—	8	2	no	—
571	C₂³	—	8	2	no	—
572	C₂³	—	8	2	no	—
573	C₂³	—	8	2	no	—
574	C₂³	—	8	2	no	—
575	C₂³	—	8	2	no	—
576	C₂³	—	8	1	no	—
577	C₂³	—	8	1	no	—
578	C₂³	—	8	1	no	—
579	C₂³	—	8	1	no	—
580	C₂³	C₄×D₄×C₆₁	1	1	yes	characteristic
581	C₂³	#120×C₆₁	1	1	yes	characteristic
582	C₂³	#121×C₆₁	1	1	yes	characteristic
583	C₂³	#121×C₆₁	1	1	yes	characteristic
584	C₂³	C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
585	C₂³	#123×C₆₁	1	1	yes	characteristic
586	C₂³	#127×C₆₁	1	1	yes	characteristic
587	C₂³	C₂×SD₁₆×C₆₁	1	2	yes	—
588	C₂³	#135×C₆₁	1	2	yes	—
589	C₂³	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
590	C₂³	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
591	D₄	—	2	4	no	—
592	D₄	—	2	4	no	—
593	D₄	—	4	2	no	—
594	D₄	—	4	2	no	—
595	D₄	—	4	2	no	—
596	D₄	—	4	2	no	—
597	D₄	—	4	2	no	—
598	D₄	—	4	2	no	—
599	C₂×C₄	—	2	4	no	—
600	C₂×C₄	—	2	4	no	—
601	C₂×C₄	—	2	4	no	—
602	C₂×C₄	—	4	2	no	—
603	C₂×C₄	—	4	2	no	—
604	C₂×C₄	—	4	2	no	—
605	C₂×C₄	—	4	2	no	—
606	C₂×C₄	—	4	2	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	—	4	4	no	—
610	C₂×C₄	—	4	4	no	—
611	C₂×C₄	—	4	4	no	—
612	C₂×C₄	—	8	2	no	—
613	C₂×C₄	—	8	2	no	—
614	C₂×C₄	—	8	2	no	—
615	C₂×C₄	—	8	1	no	—
616	C₂×C₄	—	8	1	no	—
617	C₂×C₄	—	8	1	no	—
618	C₂×C₄	—	8	1	no	—
619	C₂×C₄	—	8	1	no	—
620	C₂×C₄	—	8	1	no	—
621	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
622	C₂×C₄	C₂×C₄⋊C₄×C₆₁	1	1	yes	characteristic
623	C₂×C₄	#117×C₆₁	1	1	yes	characteristic
624	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
625	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
626	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
627	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
628	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
629	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
630	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
631	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
632	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
633	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
634	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
635	C₂×C₄	C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
636	C₂×C₄	C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
637	C₂×C₄	C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
638	C₂×C₄	C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
639	C₂×C₄	C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
640	C₂×C₄	#123×C₆₁	1	1	yes	characteristic
641	C₂×C₄	#123×C₆₁	1	1	yes	characteristic
642	C₂×C₄	#123×C₆₁	1	1	yes	characteristic
643	C₂×C₄	#123×C₆₁	1	1	yes	characteristic
644	C₂×C₄	#124×C₆₁	1	1	yes	characteristic
645	C₂×C₄	#124×C₆₁	1	1	yes	characteristic
646	C₂×C₄	#124×C₆₁	1	1	yes	characteristic
647	C₂×C₄	#126×C₆₁	1	1	yes	characteristic
648	C₂×C₄	#126×C₆₁	1	1	yes	characteristic
649	C₈	—	2	4	no	—
650	C₈	—	4	2	no	—
651	C₂²	—	4	8	no	—
652	C₂²	—	4	4	no	—
653	C₂²	—	8	2	no	—
654	C₂²	—	8	2	no	—
655	C₂²	—	8	4	no	—
656	C₂²	—	8	4	no	—
657	C₂²	—	8	2	no	—
658	C₂²	—	8	2	no	—
659	C₂²	—	8	4	no	—
660	C₂²	—	8	2	no	—
661	C₂²	—	8	2	no	—
662	C₂²	C₆₁×#385	1	1	yes	characteristic
663	C₂²	C₆₁×#388	1	1	yes	characteristic
664	C₂²	C₆₁×#390	1	1	yes	characteristic
665	C₂²	C₆₁×#392	1	1	yes	characteristic
666	C₂²	C₆₁×#394	1	1	yes	characteristic
667	C₂²	C₆₁×#396	1	1	yes	characteristic
668	C₂²	C₆₁×#399	1	1	yes	characteristic
669	C₂²	C₄×SD₁₆×C₆₁	1	2	yes	—
670	C₂²	C₆₁×#442	1	2	yes	—
671	C₂²	C₆₁×#449	1	2	yes	—
672	C₂²	C₆₁×#450	1	2	yes	—
673	C₂²	C₆₁×#460	1	2	yes	—
674	C₂²	C₆₁×#463	1	2	yes	—
675	C₂²	C₆₁×#465	1	2	yes	—
676	C₂²	C₆₁×#469	1	2	yes	—
677	C₂²	C₆₁×#476	1	2	yes	—
678	C₂²	C₆₁×#478	1	2	yes	—
679	C₂²	C₆₁×#481	1	2	yes	—
680	C₂²	C₆₁×#482	1	2	yes	—
681	C₂²	C₆₁×#492	1	1	yes	characteristic
682	C₂²	C₆₁×#495	1	1	yes	characteristic
683	C₂²	C₆₁×#496	1	1	yes	characteristic
684	C₂²	C₆₁×#496	1	1	yes	characteristic
685	C₄	—	4	4	no	—
686	C₄	—	8	2	no	—
687	C₄	—	8	2	no	—
688	C₄	—	8	2	no	—
689	C₄	C₆₁×#380	1	1	yes	characteristic
690	C₄	C₆₁×#385	1	1	yes	characteristic
691	C₄	C₆₁×#386	1	1	yes	characteristic
692	C₄	C₆₁×#388	1	1	yes	characteristic
693	C₄	C₆₁×#393	1	1	yes	characteristic
694	C₄	C₆₁×#394	1	1	yes	characteristic
695	C₄	C₆₁×#396	1	1	yes	characteristic
696	C₄	C₆₁×#397	1	1	yes	characteristic
697	C₂	—	8	4	no	—
698	C₂	C₆₁×#1439	1	1	yes	characteristic
699	C₂	C₆₁×#1864	1	2	yes	—
700	C₂	C₆₁×#1926	1	2	yes	—
701	C₂	C₆₁×#1968	1	1	yes	characteristic
702	C₂	C₆₁×#1972	1	1	yes	characteristic
703	C₂	C₆₁×#2012	1	1	yes	characteristic
704	C₂	C₆₁×#2014	1	1	yes	characteristic
705	C₂	C₆₁×#2034	1	2	yes	—
706	C₂	C₆₁×#2065	1	2	yes	—
707	C₂	C₆₁×#2092	1	1	yes	characteristic
708	C₂	C₆₁×#2094	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₆₁	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₆₁
Frattini, cosocle	C₂³×C₄	C₂³×C₆₁
prime radical	C₂³×D₄×C₆₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₆₁ ◁ C₂²×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#106×C₆₁	C₂	semidirect
5. C₂×C₆₁×#340	C₂	semidirect
6. C₂×C₆₁×#336	C₂	semidirect
7. C₆₁×C₄⋊#95	C₂	semidirect
24. C₂×#102×C₆₁	C₄	semidirect
184. C₂×C₈×C₆₁	C₂²⋊C₄	semidirect
296. #11121	C₆₁	direct (N × H)
343. C₂²×#106	C₂×C₆₁	semidirect
347. C₂×#340	C₂×C₆₁	semidirect
348. C₂×#336	C₂×C₆₁	semidirect
349. C₄⋊#95	C₂×C₆₁	semidirect
378. C₂×#102	C₄×C₆₁	semidirect
384. C₆₁	#11121	direct (N × H)
539. C₂×C₈	C₂²⋊C₄×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#106×C₆₁	2
C₂²×#102×C₆₁	2
C₂×C₆₁×#390	2
C₂×C₆₁×#340	2
C₂×C₆₁×#336	2
C₆₁×C₄⋊#95	2
#11121	61

Subgroups — C61×#11121 #29514554

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#11121 #29514554