Subgroups — C₆₁×#24476 #29527909

Order 15616.

1260 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#480	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#102×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2433	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2344	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2067	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×#1893	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1850	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	C₂³×C₈×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	1	no	—
17	C₂×#120×C₆₁	—	2	1	no	—
18	C₂×#117×C₆₁	—	2	1	no	—
19	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
20	C₆₁×#480	—	2	4	no	—
21	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic, complemented
22	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	complemented
24	C₂×#102×C₆₁	—	2	4	no	—
25	C₂×#102×C₆₁	C₂²	1	2	yes	—
26	C₂×#102×C₆₁	C₂²	1	2	yes	—
27	C₂×#102×C₆₁	C₂²	1	2	yes	—
28	C₂×#102×C₆₁	C₂²	1	2	yes	—
29	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic, complemented
30	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic, complemented
31	C₂×#102×C₆₁	C₂²	1	2	yes	complemented
32	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
33	C₆₁×#392	—	2	2	no	—
34	C₆₁×#390	C₂²	1	2	yes	—
35	C₆₁×#389	C₂²	1	2	yes	complemented
36	C₆₁×#387	—	2	2	no	—
37	C₆₁×#381	—	2	1	no	—
38	C₆₁×#380	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	complemented
40	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
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	—	2	1	no	—
55	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₆₁	—	2	2	no	—
57	C₂²×C₈×C₆₁	—	4	2	no	—
58	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
59	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
61	#127×C₆₁	—	2	4	no	—
62	#127×C₆₁	—	4	2	no	—
63	#121×C₆₁	—	2	2	no	—
64	#121×C₆₁	—	2	2	no	—
65	#120×C₆₁	—	4	4	no	—
66	#120×C₆₁	—	4	4	no	—
67	#117×C₆₁	—	4	4	no	—
68	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
69	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
70	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
71	C₂×C₄⋊C₄×C₆₁	D₄	1	4	yes	complemented
72	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
76	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₆₁	—	2	2	no	—
83	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
84	#107×C₆₁	—	2	2	no	—
85	#107×C₆₁	—	2	2	no	—
86	C₄⋊C₈×C₆₁	—	4	2	no	—
87	#102×C₆₁	—	2	4	no	—
88	#102×C₆₁	—	2	4	no	—
89	#102×C₆₁	—	2	4	no	—
90	#102×C₆₁	—	2	2	no	—
91	#102×C₆₁	—	2	2	no	—
92	#102×C₆₁	—	4	2	no	—
93	#102×C₆₁	—	4	2	no	—
94	C₂²⋊C₈×C₆₁	—	2	2	no	—
95	#95×C₆₁	—	2	2	no	—
96	#95×C₆₁	—	2	1	no	—
97	#95×C₆₁	—	2	2	no	—
98	#95×C₆₁	D₄	1	2	yes	—
99	C₂⁴×C₆₁	—	2	2	no	—
100	C₂⁴×C₆₁	—	2	1	no	—
101	C₂⁴×C₆₁	—	4	4	no	—
102	C₂⁴×C₆₁	—	4	2	no	—
103	C₂⁴×C₆₁	—	4	2	no	—
104	C₂⁴×C₆₁	—	4	2	no	—
105	C₂⁴×C₆₁	—	8	2	no	—
106	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
107	C₂×D₄×C₆₁	—	2	8	no	—
108	C₂×D₄×C₆₁	—	2	2	no	—
109	C₂×D₄×C₆₁	—	2	1	no	—
110	C₂×D₄×C₆₁	—	2	2	no	—
111	C₂×D₄×C₆₁	—	2	2	no	—
112	C₂×D₄×C₆₁	—	2	1	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	—	4	8	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	4	no	—
123	C₂×D₄×C₆₁	—	4	2	no	—
124	C₂×D₄×C₆₁	—	4	2	no	—
125	C₂×D₄×C₆₁	—	4	2	no	—
126	C₂×D₄×C₆₁	—	4	2	no	—
127	C₂×D₄×C₆₁	—	4	4	no	—
128	C₂×D₄×C₆₁	—	8	2	no	—
129	C₂×D₄×C₆₁	—	8	2	no	—
130	C₂×D₄×C₆₁	#41	1	4	yes	—
131	C₂²×C₄×C₆₁	—	2	2	no	—
132	C₂²×C₄×C₆₁	—	2	2	no	—
133	C₂²×C₄×C₆₁	—	2	4	no	—
134	C₂²×C₄×C₆₁	—	2	1	no	—
135	C₂²×C₄×C₆₁	—	2	1	no	—
136	C₂²×C₄×C₆₁	—	2	2	no	—
137	C₂²×C₄×C₆₁	—	2	1	no	—
138	C₂²×C₄×C₆₁	—	4	2	no	—
139	C₂²×C₄×C₆₁	—	4	2	no	—
140	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₆₁	#41	1	2	yes	—
145	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
146	C₂×C₈×C₆₁	—	2	1	no	—
147	C₂×C₈×C₆₁	—	2	1	no	—
148	C₂×C₈×C₆₁	—	2	2	no	—
149	C₂×C₈×C₆₁	—	2	2	no	—
150	C₂×C₈×C₆₁	—	2	2	no	—
151	C₂×C₈×C₆₁	—	2	2	no	—
152	C₂×C₈×C₆₁	—	2	2	no	—
153	C₂×C₈×C₆₁	—	4	4	no	—
154	C₄⋊C₄×C₆₁	—	2	4	no	—
155	C₄⋊C₄×C₆₁	—	2	1	no	—
156	C₄⋊C₄×C₆₁	—	2	1	no	—
157	C₄⋊C₄×C₆₁	—	2	1	no	—
158	C₄⋊C₄×C₆₁	—	2	2	no	—
159	C₄⋊C₄×C₆₁	—	2	1	no	—
160	C₄⋊C₄×C₆₁	—	2	2	no	—
161	C₄⋊C₄×C₆₁	—	4	4	no	—
162	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
163	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
164	C₂²⋊C₄×C₆₁	—	2	2	no	—
165	C₂²⋊C₄×C₆₁	—	4	4	no	—
166	C₂²⋊C₄×C₆₁	—	4	2	no	—
167	C₂²⋊C₄×C₆₁	—	4	2	no	—
168	C₂²⋊C₄×C₆₁	—	4	4	no	—
169	C₂²⋊C₄×C₆₁	D₈	1	4	yes	—
170	C₄²×C₆₁	—	2	2	no	—
171	C₄²×C₆₁	—	2	2	no	—
172	C₄²×C₆₁	—	4	4	no	—
173	C₂³×C₆₁	—	2	2	no	—
174	C₂³×C₆₁	—	2	2	no	—
175	C₂³×C₆₁	—	2	4	no	—
176	C₂³×C₆₁	—	4	8	no	—
177	C₂³×C₆₁	—	4	2	no	—
178	C₂³×C₆₁	—	4	2	no	—
179	C₂³×C₆₁	—	4	2	no	—
180	C₂³×C₆₁	—	4	2	no	—
181	C₂³×C₆₁	—	4	2	no	—
182	C₂³×C₆₁	—	4	2	no	—
183	C₂³×C₆₁	—	4	1	no	—
184	C₂³×C₆₁	—	4	2	no	—
185	C₂³×C₆₁	—	4	1	no	—
186	C₂³×C₆₁	—	4	1	no	—
187	C₂³×C₆₁	—	4	2	no	—
188	C₂³×C₆₁	—	8	8	no	—
189	C₂³×C₆₁	—	8	8	no	—
190	C₂³×C₆₁	—	8	4	no	—
191	C₂³×C₆₁	—	8	4	no	—
192	C₂³×C₆₁	#121	1	2	yes	—
193	C₂³×C₆₁	C₂×D₈	1	2	yes	—
194	C₂³×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
195	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
196	D₄×C₆₁	—	2	4	no	—
197	D₄×C₆₁	—	2	4	no	—
198	D₄×C₆₁	—	4	8	no	—
199	D₄×C₆₁	—	4	1	no	—
200	D₄×C₆₁	—	4	2	no	—
201	D₄×C₆₁	—	4	1	no	—
202	D₄×C₆₁	—	4	2	no	—
203	D₄×C₆₁	—	4	2	no	—
204	D₄×C₆₁	—	8	8	no	—
205	D₄×C₆₁	—	8	8	no	—
206	D₄×C₆₁	—	8	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	—	2	4	no	—
213	C₂×C₄×C₆₁	—	2	2	no	—
214	C₂×C₄×C₆₁	—	2	2	no	—
215	C₂×C₄×C₆₁	—	2	2	no	—
216	C₂×C₄×C₆₁	—	2	2	no	—
217	C₂×C₄×C₆₁	—	2	2	no	—
218	C₂×C₄×C₆₁	—	4	1	no	—
219	C₂×C₄×C₆₁	—	4	1	no	—
220	C₂×C₄×C₆₁	—	4	1	no	—
221	C₂×C₄×C₆₁	—	4	1	no	—
222	C₂×C₄×C₆₁	—	4	8	no	—
223	C₂×C₄×C₆₁	—	4	1	no	—
224	C₂×C₄×C₆₁	—	4	2	no	—
225	C₂×C₄×C₆₁	—	4	2	no	—
226	C₂×C₄×C₆₁	—	4	1	no	—
227	C₂×C₄×C₆₁	—	4	1	no	—
228	C₂×C₄×C₆₁	—	4	2	no	—
229	C₂×C₄×C₆₁	#121	1	2	yes	—
230	C₂×C₄×C₆₁	C₂×D₈	1	4	yes	—
231	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
233	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
235	C₈×C₆₁	—	4	1	no	—
236	C₈×C₆₁	—	4	1	no	—
237	C₈×C₆₁	—	4	2	no	—
238	#24476	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₂²×C₆₁	—	2	2	no	—
240	C₂²×C₆₁	—	2	4	no	—
241	C₂²×C₆₁	—	2	2	no	—
242	C₂²×C₆₁	—	2	4	no	—
243	C₂²×C₆₁	—	4	4	no	—
244	C₂²×C₆₁	—	4	4	no	—
245	C₂²×C₆₁	—	4	4	no	—
246	C₂²×C₆₁	—	8	16	no	—
247	C₂²×C₆₁	—	8	2	no	—
248	C₂²×C₆₁	—	8	2	no	—
249	C₂²×C₆₁	—	8	2	no	—
250	C₂²×C₆₁	—	8	2	no	—
251	C₂²×C₆₁	—	8	1	no	—
252	C₂²×C₆₁	—	8	1	no	—
253	C₂²×C₆₁	—	8	2	no	—
254	C₂²×C₆₁	—	8	1	no	—
255	C₂²×C₆₁	—	8	2	no	—
256	C₂²×C₆₁	#459	1	4	yes	—
257	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
258	C₂²×C₆₁	#546	1	2	yes	—
259	C₂²×C₆₁	C₂²×D₈	1	1	yes	characteristic
260	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
261	C₂²×C₆₁	#577	1	2	yes	—
262	C₄×C₆₁	—	2	2	no	—
263	C₄×C₆₁	—	2	4	no	—
264	C₄×C₆₁	—	4	2	no	—
265	C₄×C₆₁	—	4	2	no	—
266	C₄×C₆₁	—	4	2	no	—
267	C₄×C₆₁	—	8	1	no	—
268	C₄×C₆₁	—	8	2	no	—
269	C₄×C₆₁	#525	1	1	yes	characteristic
270	C₄×C₆₁	#535	1	1	yes	characteristic
271	C₄×C₆₁	#551	1	2	yes	—
272	C₂×#480	C₂×C₆₁	1	1	yes	characteristic, complemented
273	C₂²×#102	C₂×C₆₁	1	1	yes	characteristic, complemented
274	#2433	C₂×C₆₁	1	1	yes	characteristic
275	#2344	C₂×C₆₁	1	1	yes	characteristic, complemented
276	#2067	C₂×C₆₁	1	2	yes	complemented
277	#2041	C₂×C₆₁	1	2	yes	complemented
278	#1982	C₂×C₆₁	1	2	yes	complemented
279	#1925	C₂×C₆₁	1	2	yes	complemented
280	#1893	C₂×C₆₁	1	1	yes	characteristic, complemented
281	#1850	C₂×C₆₁	1	1	yes	characteristic, complemented
282	#1786	C₂×C₆₁	1	1	yes	characteristic, complemented
283	C₂×C₆₁	—	2	4	no	—
284	C₂×C₆₁	—	8	4	no	—
285	C₂×C₆₁	—	16	1	no	—
286	C₂×C₆₁	#2411	1	1	yes	characteristic
287	C₂×C₆₁	C₂×#459	1	1	yes	characteristic
288	C₂×C₆₁	#3043	1	1	yes	characteristic
289	C₂×C₆₁	#3294	1	2	yes	—
290	C₂×C₆₁	#3310	1	2	yes	—
291	C₂³×D₄	C₂²×C₆₁	1	1	yes	characteristic
292	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
293	C₂×#127	C₂²×C₆₁	1	2	yes	—
294	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
295	C₂×#120	—	2	1	no	—
296	C₂×#120	—	2	1	no	—
297	C₂×#117	—	2	1	no	—
298	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
299	#480	—	2	4	no	—
300	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic, complemented
301	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic, complemented
302	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	complemented
303	C₂×#102	—	2	4	no	—
304	C₂×#102	C₂²×C₆₁	1	2	yes	—
305	C₂×#102	C₂²×C₆₁	1	2	yes	—
306	C₂×#102	C₂²×C₆₁	1	2	yes	—
307	C₂×#102	C₂²×C₆₁	1	2	yes	—
308	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic, complemented
309	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic, complemented
310	C₂×#102	C₂²×C₆₁	1	2	yes	complemented
311	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
312	#392	—	2	2	no	—
313	#390	C₂²×C₆₁	1	2	yes	—
314	#389	C₂²×C₆₁	1	2	yes	complemented
315	#387	—	2	2	no	—
316	#381	—	2	1	no	—
317	#380	C₂²×C₆₁	1	1	yes	characteristic
318	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	complemented
319	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
320	#340	C₂²×C₆₁	1	2	yes	complemented
321	#336	C₂²×C₆₁	1	2	yes	complemented
322	C₆₁	#24476	1	1	yes	characteristic, direct product factor, Sylow
323	C₂⁵	—	2	1	no	—
324	C₂²×D₄	—	2	4	no	—
325	C₂²×D₄	—	2	1	no	—
326	C₂²×D₄	—	2	2	no	—
327	C₂²×D₄	—	2	1	no	—
328	C₂²×D₄	—	2	2	no	—
329	C₂²×D₄	—	2	2	no	—
330	C₂²×D₄	—	2	2	no	—
331	C₂²×D₄	—	4	2	no	—
332	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
333	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
334	C₂³×C₄	—	2	1	no	—
335	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
336	C₂²×C₈	—	2	2	no	—
337	C₂²×C₈	—	4	2	no	—
338	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
339	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
340	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
341	#127	—	2	4	no	—
342	#127	—	4	2	no	—
343	#121	—	2	2	no	—
344	#121	—	2	2	no	—
345	#120	—	4	4	no	—
346	#120	—	4	4	no	—
347	#117	—	4	4	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	2	no	—
350	C₂×C₄⋊C₄	—	2	2	no	—
351	C₂×C₄⋊C₄	D₄×C₆₁	1	4	yes	complemented
352	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
354	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
355	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
356	C₂×C₂²⋊C₄	—	2	1	no	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₂²⋊C₄	—	2	2	no	—
359	C₂×C₂²⋊C₄	—	2	1	no	—
360	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
361	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
362	C₂×C₄²	—	2	2	no	—
363	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
364	#107	—	2	2	no	—
365	#107	—	2	2	no	—
366	C₄⋊C₈	—	4	2	no	—
367	#102	—	2	4	no	—
368	#102	—	2	4	no	—
369	#102	—	2	4	no	—
370	#102	—	2	2	no	—
371	#102	—	2	2	no	—
372	#102	—	4	2	no	—
373	#102	—	4	2	no	—
374	C₂²⋊C₈	—	2	2	no	—
375	#95	—	2	2	no	—
376	#95	—	2	1	no	—
377	#95	—	2	2	no	—
378	#95	D₄×C₆₁	1	2	yes	—
379	C₂⁴	—	2	2	no	—
380	C₂⁴	—	2	1	no	—
381	C₂⁴	—	4	4	no	—
382	C₂⁴	—	4	2	no	—
383	C₂⁴	—	4	2	no	—
384	C₂⁴	—	4	2	no	—
385	C₂⁴	—	8	2	no	—
386	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
387	C₂×D₄	—	2	8	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	1	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	4	8	no	—
398	C₂×D₄	—	4	4	no	—
399	C₂×D₄	—	4	4	no	—
400	C₂×D₄	—	4	4	no	—
401	C₂×D₄	—	4	4	no	—
402	C₂×D₄	—	4	4	no	—
403	C₂×D₄	—	4	2	no	—
404	C₂×D₄	—	4	2	no	—
405	C₂×D₄	—	4	2	no	—
406	C₂×D₄	—	4	2	no	—
407	C₂×D₄	—	4	4	no	—
408	C₂×D₄	—	8	2	no	—
409	C₂×D₄	—	8	2	no	—
410	C₂×D₄	#41×C₆₁	1	4	yes	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	4	2	no	—
419	C₂²×C₄	—	4	2	no	—
420	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
421	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
422	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
423	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
424	C₂²×C₄	#41×C₆₁	1	2	yes	—
425	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	1	no	—
428	C₂×C₈	—	2	2	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	4	4	no	—
434	C₄⋊C₄	—	2	4	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	4	4	no	—
442	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
443	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
444	C₂²⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	—	4	4	no	—
446	C₂²⋊C₄	—	4	2	no	—
447	C₂²⋊C₄	—	4	2	no	—
448	C₂²⋊C₄	—	4	4	no	—
449	C₂²⋊C₄	D₈×C₆₁	1	4	yes	—
450	C₄²	—	2	2	no	—
451	C₄²	—	2	2	no	—
452	C₄²	—	4	4	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	2	2	no	—
455	C₂³	—	2	4	no	—
456	C₂³	—	4	8	no	—
457	C₂³	—	4	2	no	—
458	C₂³	—	4	2	no	—
459	C₂³	—	4	2	no	—
460	C₂³	—	4	2	no	—
461	C₂³	—	4	2	no	—
462	C₂³	—	4	2	no	—
463	C₂³	—	4	2	no	—
464	C₂³	—	4	1	no	—
465	C₂³	—	4	1	no	—
466	C₂³	—	4	2	no	—
467	C₂³	—	4	1	no	—
468	C₂³	—	8	8	no	—
469	C₂³	—	8	8	no	—
470	C₂³	—	8	4	no	—
471	C₂³	—	8	4	no	—
472	C₂³	#121×C₆₁	1	2	yes	—
473	C₂³	C₂×D₈×C₆₁	1	2	yes	—
474	C₂³	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
475	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
476	D₄	—	2	4	no	—
477	D₄	—	2	4	no	—
478	D₄	—	4	8	no	—
479	D₄	—	4	2	no	—
480	D₄	—	4	1	no	—
481	D₄	—	4	2	no	—
482	D₄	—	4	2	no	—
483	D₄	—	4	1	no	—
484	D₄	—	8	8	no	—
485	D₄	—	8	8	no	—
486	D₄	—	8	4	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	8	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	#121×C₆₁	1	2	yes	—
510	C₂×C₄	C₂×D₈×C₆₁	1	4	yes	—
511	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
512	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
513	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
514	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
515	C₈	—	4	1	no	—
516	C₈	—	4	2	no	—
517	C₈	—	4	1	no	—
518	C₂²	—	2	4	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	2	4	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	4	4	no	—
523	C₂²	—	4	4	no	—
524	C₂²	—	4	4	no	—
525	C₂²	—	8	16	no	—
526	C₂²	—	8	2	no	—
527	C₂²	—	8	2	no	—
528	C₂²	—	8	2	no	—
529	C₂²	—	8	2	no	—
530	C₂²	—	8	2	no	—
531	C₂²	—	8	1	no	—
532	C₂²	—	8	2	no	—
533	C₂²	—	8	1	no	—
534	C₂²	—	8	1	no	—
535	C₂²	C₆₁×#459	1	4	yes	—
536	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
537	C₂²	C₆₁×#546	1	2	yes	—
538	C₂²	C₂²×D₈×C₆₁	1	1	yes	characteristic
539	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
540	C₂²	C₆₁×#577	1	2	yes	—
541	C₄	—	2	4	no	—
542	C₄	—	2	2	no	—
543	C₄	—	4	2	no	—
544	C₄	—	4	2	no	—
545	C₄	—	4	2	no	—
546	C₄	—	8	2	no	—
547	C₄	—	8	1	no	—
548	C₄	C₆₁×#525	1	1	yes	characteristic
549	C₄	C₆₁×#535	1	1	yes	characteristic
550	C₄	C₆₁×#551	1	2	yes	—
551	C₂	—	2	4	no	—
552	C₂	—	8	4	no	—
553	C₂	—	16	1	no	—
554	C₂	C₆₁×#2411	1	1	yes	characteristic
555	C₂	C₂×C₆₁×#459	1	1	yes	characteristic
556	C₂	C₆₁×#3043	1	1	yes	characteristic
557	C₂	C₆₁×#3294	1	2	yes	—
558	C₂	C₆₁×#3310	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×#480	C₂	semidirect
2. C₂²×#102×C₆₁	C₂	semidirect
4. C₆₁×#2344	C₂	semidirect
5. C₆₁×#2067	C₂	semidirect
6. C₆₁×#2041	C₂	semidirect
7. C₆₁×#1982	C₂	semidirect
8. C₆₁×#1925	C₂	semidirect
9. C₆₁×#1893	C₂	semidirect
10. C₆₁×#1850	C₂	semidirect
11. C₆₁×#1786	C₂	semidirect
21. C₂×#107×C₆₁	C₂²	semidirect
22. C₂×#107×C₆₁	C₂²	semidirect
23. C₂×C₄⋊C₈×C₆₁	C₂²	semidirect
29. C₂×#102×C₆₁	C₂²	semidirect
30. C₂×#102×C₆₁	C₂²	semidirect
31. C₂×#102×C₆₁	C₂²	semidirect
35. C₆₁×#389	C₂²	semidirect
39. C₄×C₄⋊C₄×C₆₁	C₂²	semidirect
41. C₆₁×#340	C₂²	semidirect
42. C₆₁×#336	C₂²	semidirect
71. C₂×C₄⋊C₄×C₆₁	D₄	semidirect
238. #24476	C₆₁	direct (N × H)
272. C₂×#480	C₂×C₆₁	semidirect
273. C₂²×#102	C₂×C₆₁	semidirect
275. #2344	C₂×C₆₁	semidirect
276. #2067	C₂×C₆₁	semidirect
277. #2041	C₂×C₆₁	semidirect
278. #1982	C₂×C₆₁	semidirect
279. #1925	C₂×C₆₁	semidirect
280. #1893	C₂×C₆₁	semidirect
281. #1850	C₂×C₆₁	semidirect
282. #1786	C₂×C₆₁	semidirect
300. C₂×#107	C₂²×C₆₁	semidirect
301. C₂×#107	C₂²×C₆₁	semidirect
302. C₂×C₄⋊C₈	C₂²×C₆₁	semidirect
308. C₂×#102	C₂²×C₆₁	semidirect
309. C₂×#102	C₂²×C₆₁	semidirect
310. C₂×#102	C₂²×C₆₁	semidirect
314. #389	C₂²×C₆₁	semidirect
318. C₄×C₄⋊C₄	C₂²×C₆₁	semidirect
320. #340	C₂²×C₆₁	semidirect
321. #336	C₂²×C₆₁	semidirect
322. C₆₁	#24476	direct (N × H)
351. C₂×C₄⋊C₄	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×#480	2
C₂²×#102×C₆₁	2
C₆₁×#2433	2
C₆₁×#2344	2
C₆₁×#2067	2
C₆₁×#2041	2
C₆₁×#1982	2
C₆₁×#1925	2
C₆₁×#1893	2
C₆₁×#1850	2
C₆₁×#1786	2
#24476	61

Subgroups — C61×#24476 #29527909

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24476 #29527909