Subgroups — C₆₁×#34256 #29537689

Order 15616.

5898 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×H(5,𝔽₂)×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2339	C₂	1	8	yes	maximal, complemented
5	D₄×C₂²⋊C₄×C₆₁	C₂	1	8	yes	maximal, complemented
6	C₆₁×#2311	C₂	1	2	yes	maximal, complemented
7	C₆₁×#2308	C₂	1	4	yes	maximal, complemented
8	C₆₁×#2297	C₂	1	2	yes	maximal, complemented
9	C₂×C₆₁×#386	C₂	1	4	yes	maximal, complemented
10	C₂×H(5,𝔽₂)×C₆₁	—	2	8	no	—
11	C₂×H(5,𝔽₂)×C₆₁	—	2	8	no	—
12	C₂×H(5,𝔽₂)×C₆₁	C₄	1	16	yes	complemented
13	C₂²×#41×C₆₁	C₂²	1	2	yes	—
14	C₂²×#41×C₆₁	C₂²	1	4	yes	—
15	C₂³×D₄×C₆₁	C₂²	1	4	yes	—
16	C₂³×D₄×C₆₁	C₂²	1	4	yes	—
17	C₂³×D₄×C₆₁	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₆₁	C₂²	1	2	yes	complemented
19	C₆₁×#518	—	2	8	no	—
20	C₂×C₄×D₄×C₆₁	—	2	8	no	—
21	C₂×C₄×D₄×C₆₁	C₂²	1	8	yes	complemented
22	C₂×C₄×D₄×C₆₁	C₂²	1	8	yes	complemented
23	C₂×#117×C₆₁	C₂²	1	2	yes	complemented
24	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	4	yes	complemented
26	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	complemented
27	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	8	yes	complemented
28	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic, complemented
29	C₆₁×#391	C₂²	1	4	yes	complemented
30	C₆₁×#391	C₂²	1	4	yes	complemented
31	C₆₁×#390	C₂²	1	4	yes	complemented
32	C₆₁×#390	C₂²	1	4	yes	complemented
33	C₆₁×#386	C₂²	1	4	yes	complemented
34	C₆₁×#386	C₂²	1	8	yes	complemented
35	C₆₁×#386	C₂²	1	16	yes	complemented
36	C₆₁×#386	C₂²	1	4	yes	complemented
37	C₆₁×#386	C₂²	1	16	yes	complemented
38	C₆₁×#381	C₂²	1	8	yes	complemented
39	C₆₁×#380	C₂²	1	8	yes	complemented
40	C₆₁×#379	C₂²	1	8	yes	complemented
41	C₄×C₂²⋊C₄×C₆₁	C₂²	1	8	yes	complemented
42	C₂×#95×C₆₁	C₂²	1	8	yes	complemented
43	C₂⁵×C₆₁	C₂³	1	4	yes	—
44	C₂⁵×C₆₁	C₂³	1	2	yes	—
45	H(5,𝔽₂)×C₆₁	—	2	128	no	—
46	C₂×#41×C₆₁	—	2	16	no	—
47	C₂×#41×C₆₁	—	2	16	no	—
48	C₂×#41×C₆₁	—	2	8	no	—
49	C₂×#41×C₆₁	—	2	8	no	—
50	C₂×#41×C₆₁	C₂×C₄	1	16	yes	complemented
51	C₂×#41×C₆₁	C₂×C₄	1	32	yes	complemented
52	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
53	C₂²×D₄×C₆₁	—	2	16	no	—
54	C₂²×D₄×C₆₁	—	2	16	no	—
55	C₂²×D₄×C₆₁	—	2	16	no	—
56	C₂²×D₄×C₆₁	—	2	16	no	—
57	C₂²×D₄×C₆₁	C₂×C₄	1	8	yes	—
58	C₂²×D₄×C₆₁	C₂×C₄	1	32	yes	complemented
59	C₂²×D₄×C₆₁	C₂×C₄	1	32	yes	complemented
60	C₂²×D₄×C₆₁	D₄	1	8	yes	—
61	C₂²×D₄×C₆₁	D₄	1	8	yes	—
62	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
63	C₂²×D₄×C₆₁	C₂³	1	8	yes	—
64	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
65	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
66	C₂³×C₄×C₆₁	—	2	8	no	—
67	C₂³×C₄×C₆₁	—	4	8	no	—
68	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₆₁	C₂³	1	8	yes	—
70	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
71	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
72	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
73	C₂³×C₄×C₆₁	C₂³	1	8	yes	—
74	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
76	C₄×D₄×C₆₁	—	2	32	no	—
77	C₄×D₄×C₆₁	—	2	32	no	—
78	#117×C₆₁	—	2	8	no	—
79	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
80	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
81	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
82	C₂×C₂²⋊C₄×C₆₁	—	2	8	no	—
83	C₂×C₂²⋊C₄×C₆₁	—	2	16	no	—
84	C₂×C₂²⋊C₄×C₆₁	—	4	16	no	—
85	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
86	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
87	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
88	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
89	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
90	C₂×C₂²⋊C₄×C₆₁	C₂³	1	16	yes	—
91	C₂×C₄²×C₆₁	—	2	4	no	—
92	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
93	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
94	#95×C₆₁	C₂³	1	8	yes	—
95	#95×C₆₁	C₂³	1	16	yes	—
96	#95×C₆₁	C₂³	1	8	yes	—
97	C₂⁴×C₆₁	—	2	8	no	—
98	C₂⁴×C₆₁	—	2	8	no	—
99	C₂⁴×C₆₁	—	4	4	no	—
100	C₂⁴×C₆₁	—	4	4	no	—
101	C₂⁴×C₆₁	—	4	8	no	—
102	C₂⁴×C₆₁	—	4	8	no	—
103	C₂⁴×C₆₁	C₂²×C₄	1	8	yes	—
104	C₂⁴×C₆₁	C₂²×C₄	1	16	yes	complemented
105	C₂⁴×C₆₁	C₂×D₄	1	8	yes	—
106	C₂⁴×C₆₁	C₂×D₄	1	8	yes	—
107	C₂⁴×C₆₁	C₂⁴	1	4	yes	—
108	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
109	C₂⁴×C₆₁	C₂⁴	1	4	yes	—
110	#41×C₆₁	—	2	128	no	—
111	#41×C₆₁	—	2	64	no	—
112	C₂×Q₈×C₆₁	—	2	4	no	—
113	C₂×Q₈×C₆₁	—	2	4	no	—
114	C₂×Q₈×C₆₁	C₂²×C₄	1	8	yes	complemented
115	C₂×D₄×C₆₁	—	2	128	no	—
116	C₂×D₄×C₆₁	—	2	8	no	—
117	C₂×D₄×C₆₁	—	2	8	no	—
118	C₂×D₄×C₆₁	—	2	16	no	—
119	C₂×D₄×C₆₁	—	2	16	no	—
120	C₂×D₄×C₆₁	—	2	128	no	—
121	C₂×D₄×C₆₁	—	2	4	no	—
122	C₂×D₄×C₆₁	—	2	4	no	—
123	C₂×D₄×C₆₁	C₂²⋊C₄	1	64	yes	complemented
124	C₂×D₄×C₆₁	C₂²×C₄	1	16	yes	—
125	C₂×D₄×C₆₁	C₂²×C₄	1	16	yes	—
126	C₂×D₄×C₆₁	C₂²×C₄	1	32	yes	complemented
127	C₂×D₄×C₆₁	C₂²×C₄	1	8	yes	complemented
128	C₂×D₄×C₆₁	C₂×D₄	1	16	yes	—
129	C₂×D₄×C₆₁	C₂×D₄	1	16	yes	—
130	C₂²×C₄×C₆₁	—	2	2	no	—
131	C₂²×C₄×C₆₁	—	2	8	no	—
132	C₂²×C₄×C₆₁	—	2	8	no	—
133	C₂²×C₄×C₆₁	—	2	8	no	—
134	C₂²×C₄×C₆₁	—	2	8	no	—
135	C₂²×C₄×C₆₁	—	2	4	no	—
136	C₂²×C₄×C₆₁	—	2	2	no	—
137	C₂²×C₄×C₆₁	—	2	4	no	—
138	C₂²×C₄×C₆₁	—	2	16	no	—
139	C₂²×C₄×C₆₁	—	2	16	no	—
140	C₂²×C₄×C₆₁	—	2	16	no	—
141	C₂²×C₄×C₆₁	—	4	8	no	—
142	C₂²×C₄×C₆₁	—	4	4	no	—
143	C₂²×C₄×C₆₁	—	4	2	no	—
144	C₂²×C₄×C₆₁	—	4	8	no	—
145	C₂²×C₄×C₆₁	—	4	8	no	—
146	C₂²×C₄×C₆₁	—	4	32	no	—
147	C₂²×C₄×C₆₁	C₂²×C₄	1	4	yes	—
148	C₂²×C₄×C₆₁	C₂²×C₄	1	16	yes	complemented
149	C₂²×C₄×C₆₁	C₂²×C₄	1	16	yes	complemented
150	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
151	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
152	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
153	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
154	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
155	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
156	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
158	C₄⋊C₄×C₆₁	—	2	8	no	—
159	C₄⋊C₄×C₆₁	—	2	8	no	—
160	C₂²⋊C₄×C₆₁	—	2	8	no	—
161	C₂²⋊C₄×C₆₁	—	2	16	no	—
162	C₂²⋊C₄×C₆₁	—	2	16	no	—
163	C₂²⋊C₄×C₆₁	—	2	16	no	—
164	C₂²⋊C₄×C₆₁	—	4	16	no	—
165	C₂²⋊C₄×C₆₁	—	4	8	no	—
166	C₄²×C₆₁	—	2	8	no	—
167	C₄²×C₆₁	—	2	8	no	—
168	C₂³×C₆₁	—	2	2	no	—
169	C₂³×C₆₁	—	2	8	no	—
170	C₂³×C₆₁	—	2	2	no	—
171	C₂³×C₆₁	—	2	8	no	—
172	C₂³×C₆₁	—	2	4	no	—
173	C₂³×C₆₁	—	2	4	no	—
174	C₂³×C₆₁	—	2	8	no	—
175	C₂³×C₆₁	—	2	8	no	—
176	C₂³×C₆₁	—	2	32	no	—
177	C₂³×C₆₁	—	4	8	no	—
178	C₂³×C₆₁	—	4	16	no	—
179	C₂³×C₆₁	—	4	8	no	—
180	C₂³×C₆₁	—	4	16	no	—
181	C₂³×C₆₁	—	4	32	no	—
182	C₂³×C₆₁	—	8	8	no	—
183	C₂³×C₆₁	—	8	8	no	—
184	C₂³×C₆₁	—	8	16	no	—
185	C₂³×C₆₁	C₂×C₂²⋊C₄	1	32	yes	complemented
186	C₂³×C₆₁	C₂³×C₄	1	8	yes	—
187	C₂³×C₆₁	C₂³×C₄	1	2	yes	—
188	C₂³×C₆₁	C₂³×C₄	1	8	yes	—
189	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
190	C₂³×C₆₁	C₂²×D₄	1	8	yes	—
191	C₂³×C₆₁	C₂²×D₄	1	8	yes	—
192	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
193	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
194	Q₈×C₆₁	—	2	16	no	—
195	D₄×C₆₁	—	2	32	no	—
196	D₄×C₆₁	—	2	64	no	—
197	D₄×C₆₁	—	2	16	no	—
198	D₄×C₆₁	C₂×C₂²⋊C₄	1	64	yes	complemented
199	C₂×C₄×C₆₁	—	2	8	no	—
200	C₂×C₄×C₆₁	—	2	32	no	—
201	C₂×C₄×C₆₁	—	2	2	no	—
202	C₂×C₄×C₆₁	—	2	4	no	—
203	C₂×C₄×C₆₁	—	2	4	no	—
204	C₂×C₄×C₆₁	—	2	2	no	—
205	C₂×C₄×C₆₁	—	2	32	no	—
206	C₂×C₄×C₆₁	—	2	2	no	—
207	C₂×C₄×C₆₁	—	2	8	no	—
208	C₂×C₄×C₆₁	—	2	4	no	—
209	C₂×C₄×C₆₁	—	2	8	no	—
210	C₂×C₄×C₆₁	—	2	8	no	—
211	C₂×C₄×C₆₁	—	2	4	no	—
212	C₂×C₄×C₆₁	—	2	8	no	—
213	C₂×C₄×C₆₁	—	4	32	no	—
214	C₂×C₄×C₆₁	—	4	4	no	—
215	C₂×C₄×C₆₁	—	4	8	no	—
216	C₂×C₄×C₆₁	—	8	16	no	—
217	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	16	yes	complemented
218	C₂×C₄×C₆₁	C₂³×C₄	1	8	yes	—
219	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
220	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
221	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
222	C₂×C₄×C₆₁	H(5,𝔽₂)	1	4	yes	complemented
223	#34256	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
224	C₂²×C₆₁	—	2	4	no	—
225	C₂²×C₆₁	—	2	16	no	—
226	C₂²×C₆₁	—	2	2	no	—
227	C₂²×C₆₁	—	2	8	no	—
228	C₂²×C₆₁	—	2	2	no	—
229	C₂²×C₆₁	—	2	8	no	—
230	C₂²×C₆₁	—	2	16	no	—
231	C₂²×C₆₁	—	2	4	no	—
232	C₂²×C₆₁	—	2	8	no	—
233	C₂²×C₆₁	—	2	16	no	—
234	C₂²×C₆₁	—	4	32	no	—
235	C₂²×C₆₁	—	4	4	no	—
236	C₂²×C₆₁	—	4	4	no	—
237	C₂²×C₆₁	—	4	8	no	—
238	C₂²×C₆₁	—	8	32	no	—
239	C₂²×C₆₁	C₂²×C₂²⋊C₄	1	16	yes	—
240	C₂²×C₆₁	C₂²×C₂²⋊C₄	1	4	yes	—
241	C₂²×C₆₁	C₂⁴×C₄	1	1	yes	characteristic
242	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
243	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
244	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	2	yes	—
245	C₂²×C₆₁	#585	1	2	yes	—
246	C₄×C₆₁	—	2	8	no	—
247	C₄×C₆₁	—	2	4	no	—
248	C₄×C₆₁	—	4	4	no	—
249	C₄×C₆₁	—	4	2	no	—
250	C₄×C₆₁	—	4	8	no	—
251	C₄×C₆₁	C₂²×C₂²⋊C₄	1	8	yes	—
252	C₂²×H(5,𝔽₂)	C₂×C₆₁	1	1	yes	characteristic
253	C₂×#518	C₂×C₆₁	1	1	yes	characteristic, complemented
254	C₂²×C₄×D₄	C₂×C₆₁	1	1	yes	characteristic, complemented
255	#2339	C₂×C₆₁	1	8	yes	complemented
256	D₄×C₂²⋊C₄	C₂×C₆₁	1	8	yes	complemented
257	#2311	C₂×C₆₁	1	2	yes	complemented
258	#2308	C₂×C₆₁	1	4	yes	complemented
259	#2297	C₂×C₆₁	1	2	yes	complemented
260	C₂×#386	C₂×C₆₁	1	4	yes	complemented
261	C₂×C₆₁	—	2	4	no	—
262	C₂×C₆₁	—	2	16	no	—
263	C₂×C₆₁	—	4	8	no	—
264	C₂×C₆₁	C₂³×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₆₁	C₄×H(5,𝔽₂)	1	2	yes	—
266	C₂×C₆₁	#3484	1	1	yes	characteristic
267	C₂×C₆₁	#3485	1	1	yes	characteristic
268	C₂×C₆₁	#3496	1	2	yes	—
269	C₂×H(5,𝔽₂)	—	2	8	no	—
270	C₂×H(5,𝔽₂)	—	2	8	no	—
271	C₂×H(5,𝔽₂)	C₄×C₆₁	1	16	yes	complemented
272	C₂²×#41	C₂²×C₆₁	1	2	yes	—
273	C₂²×#41	C₂²×C₆₁	1	4	yes	—
274	C₂³×D₄	C₂²×C₆₁	1	4	yes	—
275	C₂³×D₄	C₂²×C₆₁	1	4	yes	—
276	C₂³×D₄	C₂²×C₆₁	1	1	yes	characteristic
277	C₂⁴×C₄	C₂²×C₆₁	1	2	yes	complemented
278	#518	—	2	8	no	—
279	C₂×C₄×D₄	—	2	8	no	—
280	C₂×C₄×D₄	C₂²×C₆₁	1	8	yes	complemented
281	C₂×C₄×D₄	C₂²×C₆₁	1	8	yes	complemented
282	C₂×#117	C₂²×C₆₁	1	2	yes	complemented
283	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
284	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	complemented
285	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	4	yes	complemented
286	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	8	yes	complemented
287	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic, complemented
288	#391	C₂²×C₆₁	1	4	yes	complemented
289	#391	C₂²×C₆₁	1	4	yes	complemented
290	#390	C₂²×C₆₁	1	4	yes	complemented
291	#390	C₂²×C₆₁	1	4	yes	complemented
292	#386	C₂²×C₆₁	1	4	yes	complemented
293	#386	C₂²×C₆₁	1	8	yes	complemented
294	#386	C₂²×C₆₁	1	16	yes	complemented
295	#386	C₂²×C₆₁	1	16	yes	complemented
296	#386	C₂²×C₆₁	1	4	yes	complemented
297	#381	C₂²×C₆₁	1	8	yes	complemented
298	#380	C₂²×C₆₁	1	8	yes	complemented
299	#379	C₂²×C₆₁	1	8	yes	complemented
300	C₄×C₂²⋊C₄	C₂²×C₆₁	1	8	yes	complemented
301	C₂×#95	C₂²×C₆₁	1	8	yes	complemented
302	C₆₁	#34256	1	1	yes	characteristic, direct product factor, Sylow
303	C₂⁵	C₂³×C₆₁	1	4	yes	—
304	C₂⁵	C₂³×C₆₁	1	2	yes	—
305	H(5,𝔽₂)	—	2	128	no	—
306	C₂×#41	—	2	16	no	—
307	C₂×#41	—	2	16	no	—
308	C₂×#41	—	2	8	no	—
309	C₂×#41	—	2	8	no	—
310	C₂×#41	C₂×C₄×C₆₁	1	16	yes	complemented
311	C₂×#41	C₂×C₄×C₆₁	1	32	yes	complemented
312	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
313	C₂²×D₄	—	2	16	no	—
314	C₂²×D₄	—	2	16	no	—
315	C₂²×D₄	—	2	16	no	—
316	C₂²×D₄	—	2	16	no	—
317	C₂²×D₄	C₂×C₄×C₆₁	1	8	yes	—
318	C₂²×D₄	C₂×C₄×C₆₁	1	32	yes	complemented
319	C₂²×D₄	C₂×C₄×C₆₁	1	32	yes	complemented
320	C₂²×D₄	D₄×C₆₁	1	8	yes	—
321	C₂²×D₄	D₄×C₆₁	1	8	yes	—
322	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
323	C₂²×D₄	C₂³×C₆₁	1	8	yes	—
324	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
325	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
326	C₂³×C₄	—	2	8	no	—
327	C₂³×C₄	—	4	8	no	—
328	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
329	C₂³×C₄	C₂³×C₆₁	1	8	yes	—
330	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
331	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
332	C₂³×C₄	C₂³×C₆₁	1	8	yes	—
333	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
334	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
335	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
336	C₄×D₄	—	2	32	no	—
337	C₄×D₄	—	2	32	no	—
338	#117	—	2	8	no	—
339	C₂×C₄⋊C₄	—	2	4	no	—
340	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
341	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
342	C₂×C₂²⋊C₄	—	2	8	no	—
343	C₂×C₂²⋊C₄	—	2	16	no	—
344	C₂×C₂²⋊C₄	—	4	16	no	—
345	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
346	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
347	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
348	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₆₁	1	16	yes	—
350	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
351	C₂×C₄²	—	2	4	no	—
352	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
353	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
354	#95	C₂³×C₆₁	1	8	yes	—
355	#95	C₂³×C₆₁	1	16	yes	—
356	#95	C₂³×C₆₁	1	8	yes	—
357	C₂⁴	—	2	8	no	—
358	C₂⁴	—	2	8	no	—
359	C₂⁴	—	4	4	no	—
360	C₂⁴	—	4	4	no	—
361	C₂⁴	—	4	8	no	—
362	C₂⁴	—	4	8	no	—
363	C₂⁴	C₂²×C₄×C₆₁	1	8	yes	—
364	C₂⁴	C₂²×C₄×C₆₁	1	16	yes	complemented
365	C₂⁴	C₂×D₄×C₆₁	1	8	yes	—
366	C₂⁴	C₂×D₄×C₆₁	1	8	yes	—
367	C₂⁴	C₂⁴×C₆₁	1	4	yes	—
368	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
369	C₂⁴	C₂⁴×C₆₁	1	4	yes	—
370	#41	—	2	128	no	—
371	#41	—	2	64	no	—
372	C₂×Q₈	—	2	4	no	—
373	C₂×Q₈	—	2	4	no	—
374	C₂×Q₈	C₂²×C₄×C₆₁	1	8	yes	complemented
375	C₂×D₄	—	2	128	no	—
376	C₂×D₄	—	2	8	no	—
377	C₂×D₄	—	2	8	no	—
378	C₂×D₄	—	2	16	no	—
379	C₂×D₄	—	2	16	no	—
380	C₂×D₄	—	2	128	no	—
381	C₂×D₄	—	2	4	no	—
382	C₂×D₄	—	2	4	no	—
383	C₂×D₄	C₂²⋊C₄×C₆₁	1	64	yes	complemented
384	C₂×D₄	C₂²×C₄×C₆₁	1	16	yes	—
385	C₂×D₄	C₂²×C₄×C₆₁	1	16	yes	—
386	C₂×D₄	C₂²×C₄×C₆₁	1	32	yes	complemented
387	C₂×D₄	C₂²×C₄×C₆₁	1	8	yes	complemented
388	C₂×D₄	C₂×D₄×C₆₁	1	16	yes	—
389	C₂×D₄	C₂×D₄×C₆₁	1	16	yes	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	8	no	—
392	C₂²×C₄	—	2	8	no	—
393	C₂²×C₄	—	2	8	no	—
394	C₂²×C₄	—	2	8	no	—
395	C₂²×C₄	—	2	4	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	16	no	—
399	C₂²×C₄	—	2	16	no	—
400	C₂²×C₄	—	2	16	no	—
401	C₂²×C₄	—	4	8	no	—
402	C₂²×C₄	—	4	4	no	—
403	C₂²×C₄	—	4	2	no	—
404	C₂²×C₄	—	4	8	no	—
405	C₂²×C₄	—	4	8	no	—
406	C₂²×C₄	—	4	32	no	—
407	C₂²×C₄	C₂²×C₄×C₆₁	1	4	yes	—
408	C₂²×C₄	C₂²×C₄×C₆₁	1	16	yes	complemented
409	C₂²×C₄	C₂²×C₄×C₆₁	1	16	yes	complemented
410	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
411	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
412	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
413	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
414	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
415	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
416	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
417	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
418	C₄⋊C₄	—	2	8	no	—
419	C₄⋊C₄	—	2	8	no	—
420	C₂²⋊C₄	—	2	8	no	—
421	C₂²⋊C₄	—	2	16	no	—
422	C₂²⋊C₄	—	2	16	no	—
423	C₂²⋊C₄	—	2	16	no	—
424	C₂²⋊C₄	—	4	16	no	—
425	C₂²⋊C₄	—	4	8	no	—
426	C₄²	—	2	8	no	—
427	C₄²	—	2	8	no	—
428	C₂³	—	2	2	no	—
429	C₂³	—	2	8	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	2	8	no	—
432	C₂³	—	2	4	no	—
433	C₂³	—	2	4	no	—
434	C₂³	—	2	8	no	—
435	C₂³	—	2	8	no	—
436	C₂³	—	2	32	no	—
437	C₂³	—	4	8	no	—
438	C₂³	—	4	16	no	—
439	C₂³	—	4	8	no	—
440	C₂³	—	4	16	no	—
441	C₂³	—	4	32	no	—
442	C₂³	—	8	8	no	—
443	C₂³	—	8	8	no	—
444	C₂³	—	8	16	no	—
445	C₂³	C₂×C₂²⋊C₄×C₆₁	1	32	yes	complemented
446	C₂³	C₂³×C₄×C₆₁	1	8	yes	—
447	C₂³	C₂³×C₄×C₆₁	1	2	yes	—
448	C₂³	C₂³×C₄×C₆₁	1	8	yes	—
449	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
450	C₂³	C₂²×D₄×C₆₁	1	8	yes	—
451	C₂³	C₂²×D₄×C₆₁	1	8	yes	—
452	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
453	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
454	Q₈	—	2	16	no	—
455	D₄	—	2	32	no	—
456	D₄	—	2	64	no	—
457	D₄	—	2	16	no	—
458	D₄	C₂×C₂²⋊C₄×C₆₁	1	64	yes	complemented
459	C₂×C₄	—	2	8	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	32	no	—
465	C₂×C₄	—	2	32	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	8	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	8	no	—
470	C₂×C₄	—	2	8	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	8	no	—
473	C₂×C₄	—	4	32	no	—
474	C₂×C₄	—	4	4	no	—
475	C₂×C₄	—	4	8	no	—
476	C₂×C₄	—	8	16	no	—
477	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	16	yes	complemented
478	C₂×C₄	C₂³×C₄×C₆₁	1	8	yes	—
479	C₂×C₄	C₂³×C₄×C₆₁	1	4	yes	—
480	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
481	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
482	C₂×C₄	H(5,𝔽₂)×C₆₁	1	4	yes	complemented
483	C₂²	—	2	4	no	—
484	C₂²	—	2	16	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	2	8	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	2	8	no	—
489	C₂²	—	2	16	no	—
490	C₂²	—	2	4	no	—
491	C₂²	—	2	8	no	—
492	C₂²	—	2	16	no	—
493	C₂²	—	4	32	no	—
494	C₂²	—	4	4	no	—
495	C₂²	—	4	4	no	—
496	C₂²	—	4	8	no	—
497	C₂²	—	8	32	no	—
498	C₂²	C₂²×C₂²⋊C₄×C₆₁	1	16	yes	—
499	C₂²	C₂²×C₂²⋊C₄×C₆₁	1	4	yes	—
500	C₂²	C₂⁴×C₄×C₆₁	1	1	yes	characteristic
501	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
502	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
503	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	2	yes	—
504	C₂²	C₆₁×#585	1	2	yes	—
505	C₄	—	2	8	no	—
506	C₄	—	2	4	no	—
507	C₄	—	4	4	no	—
508	C₄	—	4	2	no	—
509	C₄	—	4	8	no	—
510	C₄	C₂²×C₂²⋊C₄×C₆₁	1	8	yes	—
511	C₂	—	2	4	no	—
512	C₂	—	2	16	no	—
513	C₂	—	4	8	no	—
514	C₂	C₂³×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
515	C₂	C₄×H(5,𝔽₂)×C₆₁	1	2	yes	—
516	C₂	C₆₁×#3484	1	1	yes	characteristic
517	C₂	C₆₁×#3485	1	1	yes	characteristic
518	C₂	C₆₁×#3496	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₁
Frattini, cosocle	C₂³	C₂⁵×C₆₁
prime radical	C₂²×H(5,𝔽₂)×C₆₁	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₆₁×#518	C₂	semidirect
3. C₂²×C₄×D₄×C₆₁	C₂	semidirect
4. C₆₁×#2339	C₂	semidirect
5. D₄×C₂²⋊C₄×C₆₁	C₂	semidirect
6. C₆₁×#2311	C₂	semidirect
7. C₆₁×#2308	C₂	semidirect
8. C₆₁×#2297	C₂	semidirect
9. C₂×C₆₁×#386	C₂	semidirect
12. C₂×H(5,𝔽₂)×C₆₁	C₄	semidirect
18. C₂⁴×C₄×C₆₁	C₂²	semidirect
21. C₂×C₄×D₄×C₆₁	C₂²	semidirect
22. C₂×C₄×D₄×C₆₁	C₂²	semidirect
23. C₂×#117×C₆₁	C₂²	semidirect
24. C₂²×C₄⋊C₄×C₆₁	C₂²	semidirect
25. C₂²×C₂²⋊C₄×C₆₁	C₂²	semidirect
26. C₂²×C₂²⋊C₄×C₆₁	C₂²	semidirect
27. C₂²×C₂²⋊C₄×C₆₁	C₂²	semidirect
28. C₂²×C₄²×C₆₁	C₂²	semidirect
29. C₆₁×#391	C₂²	semidirect
30. C₆₁×#391	C₂²	semidirect
31. C₆₁×#390	C₂²	semidirect
32. C₆₁×#390	C₂²	semidirect
33. C₆₁×#386	C₂²	semidirect
34. C₆₁×#386	C₂²	semidirect
35. C₆₁×#386	C₂²	semidirect
36. C₆₁×#386	C₂²	semidirect
37. C₆₁×#386	C₂²	semidirect
38. C₆₁×#381	C₂²	semidirect
39. C₆₁×#380	C₂²	semidirect
40. C₆₁×#379	C₂²	semidirect
41. C₄×C₂²⋊C₄×C₆₁	C₂²	semidirect
42. C₂×#95×C₆₁	C₂²	semidirect
50. C₂×#41×C₆₁	C₂×C₄	semidirect
51. C₂×#41×C₆₁	C₂×C₄	semidirect
58. C₂²×D₄×C₆₁	C₂×C₄	semidirect
59. C₂²×D₄×C₆₁	C₂×C₄	semidirect
104. C₂⁴×C₆₁	C₂²×C₄	semidirect
114. C₂×Q₈×C₆₁	C₂²×C₄	semidirect
123. C₂×D₄×C₆₁	C₂²⋊C₄	semidirect
126. C₂×D₄×C₆₁	C₂²×C₄	semidirect
127. C₂×D₄×C₆₁	C₂²×C₄	semidirect
148. C₂²×C₄×C₆₁	C₂²×C₄	semidirect
149. C₂²×C₄×C₆₁	C₂²×C₄	semidirect
185. C₂³×C₆₁	C₂×C₂²⋊C₄	semidirect
198. D₄×C₆₁	C₂×C₂²⋊C₄	semidirect
217. C₂×C₄×C₆₁	C₂×C₂²⋊C₄	semidirect
222. C₂×C₄×C₆₁	H(5,𝔽₂)	semidirect
223. #34256	C₆₁	direct (N × H)
253. C₂×#518	C₂×C₆₁	semidirect
254. C₂²×C₄×D₄	C₂×C₆₁	semidirect
255. #2339	C₂×C₆₁	semidirect
256. D₄×C₂²⋊C₄	C₂×C₆₁	semidirect
257. #2311	C₂×C₆₁	semidirect
258. #2308	C₂×C₆₁	semidirect
259. #2297	C₂×C₆₁	semidirect
260. C₂×#386	C₂×C₆₁	semidirect
271. C₂×H(5,𝔽₂)	C₄×C₆₁	semidirect
277. C₂⁴×C₄	C₂²×C₆₁	semidirect
280. C₂×C₄×D₄	C₂²×C₆₁	semidirect
281. C₂×C₄×D₄	C₂²×C₆₁	semidirect
282. C₂×#117	C₂²×C₆₁	semidirect
283. C₂²×C₄⋊C₄	C₂²×C₆₁	semidirect
284. C₂²×C₂²⋊C₄	C₂²×C₆₁	semidirect
285. C₂²×C₂²⋊C₄	C₂²×C₆₁	semidirect
286. C₂²×C₂²⋊C₄	C₂²×C₆₁	semidirect
287. C₂²×C₄²	C₂²×C₆₁	semidirect
288. #391	C₂²×C₆₁	semidirect
289. #391	C₂²×C₆₁	semidirect
290. #390	C₂²×C₆₁	semidirect
291. #390	C₂²×C₆₁	semidirect
292. #386	C₂²×C₆₁	semidirect
293. #386	C₂²×C₆₁	semidirect
294. #386	C₂²×C₆₁	semidirect
295. #386	C₂²×C₆₁	semidirect
296. #386	C₂²×C₆₁	semidirect
297. #381	C₂²×C₆₁	semidirect
298. #380	C₂²×C₆₁	semidirect
299. #379	C₂²×C₆₁	semidirect
300. C₄×C₂²⋊C₄	C₂²×C₆₁	semidirect
301. C₂×#95	C₂²×C₆₁	semidirect
302. C₆₁	#34256	direct (N × H)
310. C₂×#41	C₂×C₄×C₆₁	semidirect
311. C₂×#41	C₂×C₄×C₆₁	semidirect
318. C₂²×D₄	C₂×C₄×C₆₁	semidirect
319. C₂²×D₄	C₂×C₄×C₆₁	semidirect
364. C₂⁴	C₂²×C₄×C₆₁	semidirect
374. C₂×Q₈	C₂²×C₄×C₆₁	semidirect
383. C₂×D₄	C₂²⋊C₄×C₆₁	semidirect
386. C₂×D₄	C₂²×C₄×C₆₁	semidirect
387. C₂×D₄	C₂²×C₄×C₆₁	semidirect
408. C₂²×C₄	C₂²×C₄×C₆₁	semidirect
409. C₂²×C₄	C₂²×C₄×C₆₁	semidirect
445. C₂³	C₂×C₂²⋊C₄×C₆₁	semidirect
458. D₄	C₂×C₂²⋊C₄×C₆₁	semidirect
477. C₂×C₄	C₂×C₂²⋊C₄×C₆₁	semidirect
482. C₂×C₄	H(5,𝔽₂)×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×H(5,𝔽₂)×C₆₁	2
C₂×C₆₁×#518	2
C₂²×C₄×D₄×C₆₁	2
C₆₁×#2339	2
D₄×C₂²⋊C₄×C₆₁	2
C₆₁×#2311	2
C₆₁×#2308	2
C₆₁×#2297	2
C₂×C₆₁×#386	2
#34256	61

Subgroups — C61×#34256 #29537689

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#34256 #29537689