Subgroups — C₆₁×#24494 #29527927

Order 15616.

1198 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#482	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#418	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2433	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2346	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2065	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2041	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1982	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1925	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1895	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1851	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1786	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₆₁	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×#127×C₆₁	C₂²	1	2	yes	—
15	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×#120×C₆₁	—	2	2	no	—
17	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
18	C₆₁×#482	—	2	4	no	—
19	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic, complemented
20	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	complemented
22	C₆₁×#418	—	2	4	no	—
23	C₂×#102×C₆₁	C₂²	1	2	yes	—
24	C₂×#102×C₆₁	C₂²	1	2	yes	—
25	C₂×#102×C₆₁	C₂²	1	2	yes	—
26	C₂×#102×C₆₁	C₂²	1	2	yes	—
27	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic, complemented
28	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic, complemented
29	C₂×#102×C₆₁	C₂²	1	2	yes	complemented
30	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
31	C₆₁×#392	—	2	1	no	—
32	C₆₁×#392	—	2	1	no	—
33	C₆₁×#390	C₂²	1	2	yes	—
34	C₆₁×#389	C₂²	1	2	yes	complemented
35	C₆₁×#388	—	2	2	no	—
36	C₆₁×#382	—	2	1	no	—
37	C₆₁×#380	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	complemented
39	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
40	C₆₁×#376	—	2	1	no	—
41	C₆₁×#340	C₂²	1	2	yes	complemented
42	C₆₁×#336	C₂²	1	2	yes	complemented
43	C₂⁵×C₆₁	—	2	1	no	—
44	C₂²×D₄×C₆₁	—	2	4	no	—
45	C₂²×D₄×C₆₁	—	2	1	no	—
46	C₂²×D₄×C₆₁	—	2	2	no	—
47	C₂²×D₄×C₆₁	—	2	1	no	—
48	C₂²×D₄×C₆₁	—	2	2	no	—
49	C₂²×D₄×C₆₁	—	2	2	no	—
50	C₂²×D₄×C₆₁	—	2	2	no	—
51	C₂²×D₄×C₆₁	—	4	2	no	—
52	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
54	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
55	C₂×M₁₆×C₆₁	—	2	2	no	—
56	C₂×M₁₆×C₆₁	—	4	2	no	—
57	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
58	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
60	#127×C₆₁	—	2	4	no	—
61	#127×C₆₁	—	4	2	no	—
62	#121×C₆₁	—	2	2	no	—
63	#121×C₆₁	—	2	2	no	—
64	#120×C₆₁	—	4	8	no	—
65	#117×C₆₁	—	2	2	no	—
66	#117×C₆₁	D₄	1	4	yes	complemented
67	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
68	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
78	C₂×C₄²×C₆₁	—	2	1	no	—
79	C₂×C₄²×C₆₁	—	2	2	no	—
80	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
81	#107×C₆₁	—	2	2	no	—
82	#106×C₆₁	—	2	2	no	—
83	C₄⋊C₈×C₆₁	—	4	2	no	—
84	#102×C₆₁	—	2	4	no	—
85	#102×C₆₁	—	2	4	no	—
86	#102×C₆₁	—	2	4	no	—
87	#102×C₆₁	—	2	2	no	—
88	#102×C₆₁	—	2	2	no	—
89	#102×C₆₁	—	4	2	no	—
90	#102×C₆₁	—	4	2	no	—
91	C₂²⋊C₈×C₆₁	—	2	2	no	—
92	#95×C₆₁	—	2	1	no	—
93	#95×C₆₁	—	2	2	no	—
94	#95×C₆₁	—	2	2	no	—
95	#95×C₆₁	D₄	1	1	yes	characteristic
96	#95×C₆₁	D₄	1	1	yes	characteristic
97	C₂⁴×C₆₁	—	2	2	no	—
98	C₂⁴×C₆₁	—	2	1	no	—
99	C₂⁴×C₆₁	—	4	4	no	—
100	C₂⁴×C₆₁	—	4	4	no	—
101	C₂⁴×C₆₁	—	4	2	no	—
102	C₂⁴×C₆₁	—	8	1	no	—
103	C₂⁴×C₆₁	—	8	1	no	—
104	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
105	C₂×D₄×C₆₁	—	2	8	no	—
106	C₂×D₄×C₆₁	—	2	2	no	—
107	C₂×D₄×C₆₁	—	2	1	no	—
108	C₂×D₄×C₆₁	—	2	2	no	—
109	C₂×D₄×C₆₁	—	2	2	no	—
110	C₂×D₄×C₆₁	—	2	1	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	—	4	8	no	—
116	C₂×D₄×C₆₁	—	4	4	no	—
117	C₂×D₄×C₆₁	—	4	4	no	—
118	C₂×D₄×C₆₁	—	4	4	no	—
119	C₂×D₄×C₆₁	—	4	4	no	—
120	C₂×D₄×C₆₁	—	4	4	no	—
121	C₂×D₄×C₆₁	—	4	4	no	—
122	C₂×D₄×C₆₁	—	4	2	no	—
123	C₂×D₄×C₆₁	—	4	2	no	—
124	C₂×D₄×C₆₁	—	4	4	no	—
125	C₂×D₄×C₆₁	—	8	2	no	—
126	C₂×D₄×C₆₁	—	8	2	no	—
127	C₂×D₄×C₆₁	#41	1	4	yes	—
128	C₂²×C₄×C₆₁	—	2	2	no	—
129	C₂²×C₄×C₆₁	—	2	2	no	—
130	C₂²×C₄×C₆₁	—	2	1	no	—
131	C₂²×C₄×C₆₁	—	2	1	no	—
132	C₂²×C₄×C₆₁	—	2	2	no	—
133	C₂²×C₄×C₆₁	—	2	1	no	—
134	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₆₁	#41	1	2	yes	—
139	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
140	M₁₆×C₆₁	—	4	4	no	—
141	C₂×C₈×C₆₁	—	2	1	no	—
142	C₂×C₈×C₆₁	—	2	1	no	—
143	C₂×C₈×C₆₁	—	2	2	no	—
144	C₂×C₈×C₆₁	—	2	2	no	—
145	C₂×C₈×C₆₁	—	2	2	no	—
146	C₂×C₈×C₆₁	—	2	2	no	—
147	C₂×C₈×C₆₁	—	2	2	no	—
148	C₄⋊C₄×C₆₁	—	2	1	no	—
149	C₄⋊C₄×C₆₁	—	2	1	no	—
150	C₄⋊C₄×C₆₁	—	2	1	no	—
151	C₄⋊C₄×C₆₁	—	2	2	no	—
152	C₄⋊C₄×C₆₁	—	2	1	no	—
153	C₄⋊C₄×C₆₁	—	2	2	no	—
154	C₄⋊C₄×C₆₁	—	8	2	no	—
155	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
156	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
157	C₂²⋊C₄×C₆₁	—	2	4	no	—
158	C₂²⋊C₄×C₆₁	—	2	4	no	—
159	C₂²⋊C₄×C₆₁	—	4	4	no	—
160	C₂²⋊C₄×C₆₁	—	4	2	no	—
161	C₂²⋊C₄×C₆₁	—	4	4	no	—
162	C₂²⋊C₄×C₆₁	—	8	1	no	—
163	C₄²×C₆₁	—	2	4	no	—
164	C₄²×C₆₁	—	2	2	no	—
165	C₄²×C₆₁	—	2	2	no	—
166	C₄²×C₆₁	—	4	4	no	—
167	C₂³×C₆₁	—	2	2	no	—
168	C₂³×C₆₁	—	2	2	no	—
169	C₂³×C₆₁	—	2	1	no	—
170	C₂³×C₆₁	—	2	1	no	—
171	C₂³×C₆₁	—	2	4	no	—
172	C₂³×C₆₁	—	4	8	no	—
173	C₂³×C₆₁	—	4	2	no	—
174	C₂³×C₆₁	—	4	2	no	—
175	C₂³×C₆₁	—	4	2	no	—
176	C₂³×C₆₁	—	4	2	no	—
177	C₂³×C₆₁	—	4	2	no	—
178	C₂³×C₆₁	—	4	2	no	—
179	C₂³×C₆₁	—	4	1	no	—
180	C₂³×C₆₁	—	4	2	no	—
181	C₂³×C₆₁	—	4	2	no	—
182	C₂³×C₆₁	—	4	1	no	—
183	C₂³×C₆₁	—	4	1	no	—
184	C₂³×C₆₁	—	8	4	no	—
185	C₂³×C₆₁	—	8	4	no	—
186	C₂³×C₆₁	—	8	8	no	—
187	C₂³×C₆₁	—	8	8	no	—
188	C₂³×C₆₁	#121	1	2	yes	—
189	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
190	D₄×C₆₁	—	2	4	no	—
191	D₄×C₆₁	—	2	4	no	—
192	D₄×C₆₁	—	4	8	no	—
193	D₄×C₆₁	—	4	1	no	—
194	D₄×C₆₁	—	4	2	no	—
195	D₄×C₆₁	—	4	1	no	—
196	D₄×C₆₁	—	4	2	no	—
197	D₄×C₆₁	—	4	2	no	—
198	D₄×C₆₁	—	8	8	no	—
199	D₄×C₆₁	—	8	8	no	—
200	D₄×C₆₁	—	8	4	no	—
201	C₂×C₄×C₆₁	—	2	2	no	—
202	C₂×C₄×C₆₁	—	2	2	no	—
203	C₂×C₄×C₆₁	—	2	2	no	—
204	C₂×C₄×C₆₁	—	2	2	no	—
205	C₂×C₄×C₆₁	—	2	2	no	—
206	C₂×C₄×C₆₁	—	2	4	no	—
207	C₂×C₄×C₆₁	—	2	2	no	—
208	C₂×C₄×C₆₁	—	2	2	no	—
209	C₂×C₄×C₆₁	—	2	2	no	—
210	C₂×C₄×C₆₁	—	2	2	no	—
211	C₂×C₄×C₆₁	—	2	2	no	—
212	C₂×C₄×C₆₁	—	4	2	no	—
213	C₂×C₄×C₆₁	—	4	1	no	—
214	C₂×C₄×C₆₁	—	4	1	no	—
215	C₂×C₄×C₆₁	—	4	1	no	—
216	C₂×C₄×C₆₁	—	4	2	no	—
217	C₂×C₄×C₆₁	—	4	2	no	—
218	C₂×C₄×C₆₁	—	4	2	no	—
219	C₂×C₄×C₆₁	—	4	2	no	—
220	C₂×C₄×C₆₁	#121	1	2	yes	—
221	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	4	yes	—
222	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
224	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
226	C₈×C₆₁	—	4	1	no	—
227	C₈×C₆₁	—	4	1	no	—
228	C₈×C₆₁	—	4	2	no	—
229	#24494	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₂²×C₆₁	—	2	2	no	—
231	C₂²×C₆₁	—	2	2	no	—
232	C₂²×C₆₁	—	2	2	no	—
233	C₂²×C₆₁	—	4	2	no	—
234	C₂²×C₆₁	—	4	2	no	—
235	C₂²×C₆₁	—	4	4	no	—
236	C₂²×C₆₁	—	4	4	no	—
237	C₂²×C₆₁	—	4	4	no	—
238	C₂²×C₆₁	—	8	16	no	—
239	C₂²×C₆₁	—	8	2	no	—
240	C₂²×C₆₁	—	8	2	no	—
241	C₂²×C₆₁	—	8	2	no	—
242	C₂²×C₆₁	—	8	2	no	—
243	C₂²×C₆₁	—	8	1	no	—
244	C₂²×C₆₁	—	8	1	no	—
245	C₂²×C₆₁	—	8	1	no	—
246	C₂²×C₆₁	—	8	2	no	—
247	C₂²×C₆₁	—	8	2	no	—
248	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
249	C₂²×C₆₁	#546	1	2	yes	—
250	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
251	C₂²×C₆₁	#576	1	1	yes	characteristic
252	C₂²×C₆₁	#577	1	1	yes	characteristic
253	C₄×C₆₁	—	2	2	no	—
254	C₄×C₆₁	—	2	4	no	—
255	C₄×C₆₁	—	4	2	no	—
256	C₄×C₆₁	—	4	2	no	—
257	C₄×C₆₁	—	4	2	no	—
258	C₄×C₆₁	—	8	1	no	—
259	C₄×C₆₁	—	8	2	no	—
260	C₄×C₆₁	#525	1	1	yes	characteristic
261	C₄×C₆₁	#535	1	1	yes	characteristic
262	C₄×C₆₁	#551	1	2	yes	—
263	C₂×#482	C₂×C₆₁	1	1	yes	characteristic, complemented
264	C₂×#418	C₂×C₆₁	1	1	yes	characteristic, complemented
265	#2433	C₂×C₆₁	1	1	yes	characteristic
266	#2346	C₂×C₆₁	1	1	yes	characteristic, complemented
267	#2065	C₂×C₆₁	1	2	yes	complemented
268	#2041	C₂×C₆₁	1	2	yes	complemented
269	#1982	C₂×C₆₁	1	2	yes	complemented
270	#1925	C₂×C₆₁	1	2	yes	complemented
271	#1895	C₂×C₆₁	1	1	yes	characteristic, complemented
272	#1851	C₂×C₆₁	1	1	yes	characteristic, complemented
273	#1786	C₂×C₆₁	1	1	yes	characteristic, complemented
274	C₂×C₆₁	—	4	2	no	—
275	C₂×C₆₁	—	8	4	no	—
276	C₂×C₆₁	—	16	1	no	—
277	C₂×C₆₁	#2411	1	1	yes	characteristic
278	C₂×C₆₁	#3038	1	1	yes	characteristic
279	C₂×C₆₁	#3045	1	1	yes	characteristic
280	C₂×C₆₁	#3310	1	2	yes	—
281	C₂×C₆₁	#3325	1	2	yes	—
282	C₂³×D₄	C₂²×C₆₁	1	1	yes	characteristic
283	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
284	C₂×#127	C₂²×C₆₁	1	2	yes	—
285	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
286	C₂×#120	—	2	2	no	—
287	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
288	#482	—	2	4	no	—
289	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic, complemented
290	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic, complemented
291	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	complemented
292	#418	—	2	4	no	—
293	C₂×#102	C₂²×C₆₁	1	2	yes	—
294	C₂×#102	C₂²×C₆₁	1	2	yes	—
295	C₂×#102	C₂²×C₆₁	1	2	yes	—
296	C₂×#102	C₂²×C₆₁	1	2	yes	—
297	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic, complemented
298	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic, complemented
299	C₂×#102	C₂²×C₆₁	1	2	yes	complemented
300	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
301	#392	—	2	1	no	—
302	#392	—	2	1	no	—
303	#390	C₂²×C₆₁	1	2	yes	—
304	#389	C₂²×C₆₁	1	2	yes	complemented
305	#388	—	2	2	no	—
306	#382	—	2	1	no	—
307	#380	C₂²×C₆₁	1	1	yes	characteristic
308	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	complemented
309	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
310	#376	—	2	1	no	—
311	#340	C₂²×C₆₁	1	2	yes	complemented
312	#336	C₂²×C₆₁	1	2	yes	complemented
313	C₆₁	#24494	1	1	yes	characteristic, direct product factor, Sylow
314	C₂⁵	—	2	1	no	—
315	C₂²×D₄	—	2	4	no	—
316	C₂²×D₄	—	2	1	no	—
317	C₂²×D₄	—	2	2	no	—
318	C₂²×D₄	—	2	1	no	—
319	C₂²×D₄	—	2	2	no	—
320	C₂²×D₄	—	2	2	no	—
321	C₂²×D₄	—	2	2	no	—
322	C₂²×D₄	—	4	2	no	—
323	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
324	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
325	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
326	C₂×M₁₆	—	2	2	no	—
327	C₂×M₁₆	—	4	2	no	—
328	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
329	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
330	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
331	#127	—	2	4	no	—
332	#127	—	4	2	no	—
333	#121	—	2	2	no	—
334	#121	—	2	2	no	—
335	#120	—	4	8	no	—
336	#117	—	2	2	no	—
337	#117	D₄×C₆₁	1	4	yes	complemented
338	C₂×C₄⋊C₄	—	2	2	no	—
339	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
340	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
341	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
342	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
343	C₂×C₂²⋊C₄	—	2	1	no	—
344	C₂×C₂²⋊C₄	—	2	2	no	—
345	C₂×C₂²⋊C₄	—	2	2	no	—
346	C₂×C₂²⋊C₄	—	2	1	no	—
347	C₂×C₂²⋊C₄	—	2	1	no	—
348	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
349	C₂×C₄²	—	2	1	no	—
350	C₂×C₄²	—	2	2	no	—
351	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
352	#107	—	2	2	no	—
353	#106	—	2	2	no	—
354	C₄⋊C₈	—	4	2	no	—
355	#102	—	2	4	no	—
356	#102	—	2	4	no	—
357	#102	—	2	4	no	—
358	#102	—	2	2	no	—
359	#102	—	2	2	no	—
360	#102	—	4	2	no	—
361	#102	—	4	2	no	—
362	C₂²⋊C₈	—	2	2	no	—
363	#95	—	2	1	no	—
364	#95	—	2	2	no	—
365	#95	—	2	2	no	—
366	#95	D₄×C₆₁	1	1	yes	characteristic
367	#95	D₄×C₆₁	1	1	yes	characteristic
368	C₂⁴	—	2	2	no	—
369	C₂⁴	—	2	1	no	—
370	C₂⁴	—	4	4	no	—
371	C₂⁴	—	4	4	no	—
372	C₂⁴	—	4	2	no	—
373	C₂⁴	—	8	1	no	—
374	C₂⁴	—	8	1	no	—
375	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
376	C₂×D₄	—	2	8	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	4	8	no	—
387	C₂×D₄	—	4	4	no	—
388	C₂×D₄	—	4	4	no	—
389	C₂×D₄	—	4	4	no	—
390	C₂×D₄	—	4	4	no	—
391	C₂×D₄	—	4	4	no	—
392	C₂×D₄	—	4	4	no	—
393	C₂×D₄	—	4	2	no	—
394	C₂×D₄	—	4	2	no	—
395	C₂×D₄	—	4	4	no	—
396	C₂×D₄	—	8	2	no	—
397	C₂×D₄	—	8	2	no	—
398	C₂×D₄	#41×C₆₁	1	4	yes	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
406	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
407	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
408	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
409	C₂²×C₄	#41×C₆₁	1	2	yes	—
410	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
411	M₁₆	—	4	4	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	2	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	8	2	no	—
426	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
427	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
428	C₂²⋊C₄	—	2	4	no	—
429	C₂²⋊C₄	—	2	4	no	—
430	C₂²⋊C₄	—	4	4	no	—
431	C₂²⋊C₄	—	4	2	no	—
432	C₂²⋊C₄	—	4	4	no	—
433	C₂²⋊C₄	—	8	1	no	—
434	C₄²	—	2	4	no	—
435	C₄²	—	2	2	no	—
436	C₄²	—	2	2	no	—
437	C₄²	—	4	4	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	1	no	—
441	C₂³	—	2	1	no	—
442	C₂³	—	2	4	no	—
443	C₂³	—	4	8	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	—	4	2	no	—
448	C₂³	—	4	2	no	—
449	C₂³	—	4	2	no	—
450	C₂³	—	4	2	no	—
451	C₂³	—	4	2	no	—
452	C₂³	—	4	1	no	—
453	C₂³	—	4	1	no	—
454	C₂³	—	4	1	no	—
455	C₂³	—	8	4	no	—
456	C₂³	—	8	4	no	—
457	C₂³	—	8	8	no	—
458	C₂³	—	8	8	no	—
459	C₂³	#121×C₆₁	1	2	yes	—
460	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
461	D₄	—	2	4	no	—
462	D₄	—	2	4	no	—
463	D₄	—	4	8	no	—
464	D₄	—	4	2	no	—
465	D₄	—	4	1	no	—
466	D₄	—	4	2	no	—
467	D₄	—	4	2	no	—
468	D₄	—	4	1	no	—
469	D₄	—	8	8	no	—
470	D₄	—	8	8	no	—
471	D₄	—	8	4	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	#121×C₆₁	1	2	yes	—
492	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	4	yes	—
493	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
494	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
495	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
496	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
497	C₈	—	4	1	no	—
498	C₈	—	4	2	no	—
499	C₈	—	4	1	no	—
500	C₂²	—	2	2	no	—
501	C₂²	—	2	2	no	—
502	C₂²	—	2	2	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	4	no	—
506	C₂²	—	4	4	no	—
507	C₂²	—	4	4	no	—
508	C₂²	—	8	16	no	—
509	C₂²	—	8	2	no	—
510	C₂²	—	8	2	no	—
511	C₂²	—	8	2	no	—
512	C₂²	—	8	2	no	—
513	C₂²	—	8	1	no	—
514	C₂²	—	8	1	no	—
515	C₂²	—	8	2	no	—
516	C₂²	—	8	2	no	—
517	C₂²	—	8	1	no	—
518	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
519	C₂²	C₆₁×#546	1	2	yes	—
520	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	2	yes	—
521	C₂²	C₆₁×#576	1	1	yes	characteristic
522	C₂²	C₆₁×#577	1	1	yes	characteristic
523	C₄	—	2	4	no	—
524	C₄	—	2	2	no	—
525	C₄	—	4	2	no	—
526	C₄	—	4	2	no	—
527	C₄	—	4	2	no	—
528	C₄	—	8	1	no	—
529	C₄	—	8	2	no	—
530	C₄	C₆₁×#525	1	1	yes	characteristic
531	C₄	C₆₁×#535	1	1	yes	characteristic
532	C₄	C₆₁×#551	1	2	yes	—
533	C₂	—	4	2	no	—
534	C₂	—	8	4	no	—
535	C₂	—	16	1	no	—
536	C₂	C₆₁×#2411	1	1	yes	characteristic
537	C₂	C₆₁×#3038	1	1	yes	characteristic
538	C₂	C₆₁×#3045	1	1	yes	characteristic
539	C₂	C₆₁×#3310	1	2	yes	—
540	C₂	C₆₁×#3325	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₆₁×#2433	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₄×C₂²⋊C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#482	C₂	semidirect
2. C₂×C₆₁×#418	C₂	semidirect
4. C₆₁×#2346	C₂	semidirect
5. C₆₁×#2065	C₂	semidirect
6. C₆₁×#2041	C₂	semidirect
7. C₆₁×#1982	C₂	semidirect
8. C₆₁×#1925	C₂	semidirect
9. C₆₁×#1895	C₂	semidirect
10. C₆₁×#1851	C₂	semidirect
11. C₆₁×#1786	C₂	semidirect
19. C₂×#107×C₆₁	C₂²	semidirect
20. C₂×#106×C₆₁	C₂²	semidirect
21. C₂×C₄⋊C₈×C₆₁	C₂²	semidirect
27. C₂×#102×C₆₁	C₂²	semidirect
28. C₂×#102×C₆₁	C₂²	semidirect
29. C₂×#102×C₆₁	C₂²	semidirect
34. C₆₁×#389	C₂²	semidirect
38. C₄×C₄⋊C₄×C₆₁	C₂²	semidirect
41. C₆₁×#340	C₂²	semidirect
42. C₆₁×#336	C₂²	semidirect
66. #117×C₆₁	D₄	semidirect
229. #24494	C₆₁	direct (N × H)
263. C₂×#482	C₂×C₆₁	semidirect
264. C₂×#418	C₂×C₆₁	semidirect
266. #2346	C₂×C₆₁	semidirect
267. #2065	C₂×C₆₁	semidirect
268. #2041	C₂×C₆₁	semidirect
269. #1982	C₂×C₆₁	semidirect
270. #1925	C₂×C₆₁	semidirect
271. #1895	C₂×C₆₁	semidirect
272. #1851	C₂×C₆₁	semidirect
273. #1786	C₂×C₆₁	semidirect
289. C₂×#107	C₂²×C₆₁	semidirect
290. C₂×#106	C₂²×C₆₁	semidirect
291. C₂×C₄⋊C₈	C₂²×C₆₁	semidirect
297. C₂×#102	C₂²×C₆₁	semidirect
298. C₂×#102	C₂²×C₆₁	semidirect
299. C₂×#102	C₂²×C₆₁	semidirect
304. #389	C₂²×C₆₁	semidirect
308. C₄×C₄⋊C₄	C₂²×C₆₁	semidirect
311. #340	C₂²×C₆₁	semidirect
312. #336	C₂²×C₆₁	semidirect
313. C₆₁	#24494	direct (N × H)
337. #117	D₄×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×#482	2
C₂×C₆₁×#418	2
C₆₁×#2433	2
C₆₁×#2346	2
C₆₁×#2065	2
C₆₁×#2041	2
C₆₁×#1982	2
C₆₁×#1925	2
C₆₁×#1895	2
C₆₁×#1851	2
C₆₁×#1786	2
#24494	61

Subgroups — C61×#24494 #29527927

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24494 #29527927