Subgroups — C₂×C₆₁×#2618 #29537990

Order 15616.

3718 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#123×C₆₁	C₂	1	2	yes	maximal, complemented
2	C₂²×#121×C₆₁	C₂	1	1	yes	maximal, characteristic
3	C₂³×C₄⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2618	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₆₁×#398	C₂	1	2	yes	maximal, complemented
6	C₂×C₆₁×#396	C₂	1	4	yes	maximal, complemented
7	C₂×C₆₁×#394	C₂	1	2	yes	maximal, complemented
8	C₂×C₆₁×#386	C₂	1	2	yes	maximal, complemented
9	C₂×C₆₁×#380	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₆₁	C₂²	1	2	yes	—
11	C₂³×D₄×C₆₁	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₆₁	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₆₁	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×#123×C₆₁	—	2	16	no	—
16	C₂×#123×C₆₁	C₂²	1	16	yes	complemented
17	C₂×#121×C₆₁	—	2	8	no	—
18	C₂×#121×C₆₁	C₂²	1	8	yes	—
19	C₂²×C₄⋊C₄×C₆₁	—	2	8	no	—
20	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
21	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
22	C₂²×C₄⋊C₄×C₆₁	C₂²	1	4	yes	—
23	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
25	C₂²×C₄⋊C₄×C₆₁	C₂²	1	8	yes	complemented
26	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
27	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	4	yes	—
28	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
29	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	4	yes	—
30	C₆₁×#398	C₂²	1	16	yes	complemented
31	C₆₁×#396	C₂²	1	32	yes	complemented
32	C₆₁×#394	C₂²	1	16	yes	complemented
33	C₆₁×#386	C₂²	1	16	yes	complemented
34	C₆₁×#380	C₂²	1	8	yes	complemented
35	C₂×#95×C₆₁	C₂²	1	2	yes	—
36	C₂×#95×C₆₁	C₂²	1	4	yes	—
37	C₂⁵×C₆₁	C₂³	1	2	yes	—
38	C₂⁵×C₆₁	C₂³	1	1	yes	characteristic
39	C₂²×D₄×C₆₁	—	2	8	no	—
40	C₂²×D₄×C₆₁	—	2	8	no	—
41	C₂²×D₄×C₆₁	—	2	8	no	—
42	C₂²×D₄×C₆₁	—	2	4	no	—
43	C₂²×D₄×C₆₁	—	4	4	no	—
44	C₂²×D₄×C₆₁	C₂³	1	8	yes	—
45	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
46	C₂³×C₄×C₆₁	—	2	4	no	—
47	C₂³×C₄×C₆₁	—	2	4	no	—
48	C₂³×C₄×C₆₁	—	2	4	no	—
49	C₂³×C₄×C₆₁	—	4	4	no	—
50	C₂³×C₄×C₆₁	—	4	4	no	—
51	C₂³×C₄×C₆₁	D₄	1	8	yes	—
52	C₂³×C₄×C₆₁	D₄	1	8	yes	complemented
53	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
54	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
55	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
56	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
58	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
60	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
61	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
62	#123×C₆₁	—	2	64	no	—
63	#121×C₆₁	—	2	32	no	—
64	C₂×C₄⋊C₄×C₆₁	—	2	8	no	—
65	C₂×C₄⋊C₄×C₆₁	—	2	8	no	—
66	C₂×C₄⋊C₄×C₆₁	—	2	32	no	—
67	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
68	C₂×C₄⋊C₄×C₆₁	—	2	16	no	—
69	C₂×C₄⋊C₄×C₆₁	—	4	4	no	—
70	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
71	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
72	C₂×C₄⋊C₄×C₆₁	C₂³	1	16	yes	—
73	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
74	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
75	C₂×C₂²⋊C₄×C₆₁	—	2	8	no	—
76	C₂×C₂²⋊C₄×C₆₁	—	2	8	no	—
77	C₂×C₂²⋊C₄×C₆₁	—	2	16	no	—
78	C₂×C₂²⋊C₄×C₆₁	—	4	8	no	—
79	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
80	C₂×C₂²⋊C₄×C₆₁	C₂³	1	16	yes	—
81	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
82	C₂×C₂²⋊C₄×C₆₁	C₂³	1	16	yes	—
83	#95×C₆₁	C₂³	1	8	yes	—
84	#95×C₆₁	C₂³	1	16	yes	—
85	C₂⁴×C₆₁	—	2	4	no	—
86	C₂⁴×C₆₁	—	2	4	no	—
87	C₂⁴×C₆₁	—	2	4	no	—
88	C₂⁴×C₆₁	—	2	4	no	—
89	C₂⁴×C₆₁	—	2	4	no	—
90	C₂⁴×C₆₁	—	2	8	no	—
91	C₂⁴×C₆₁	—	2	8	no	—
92	C₂⁴×C₆₁	C₂×D₄	1	4	yes	—
93	C₂⁴×C₆₁	C₂×D₄	1	4	yes	—
94	C₂⁴×C₆₁	#41	1	4	yes	—
95	C₂⁴×C₆₁	C₂⁴	1	4	yes	—
96	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
97	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
98	C₂×D₄×C₆₁	—	2	16	no	—
99	C₂×D₄×C₆₁	—	2	16	no	—
100	C₂×D₄×C₆₁	—	2	16	no	—
101	C₂×D₄×C₆₁	—	2	8	no	—
102	C₂×D₄×C₆₁	—	4	8	no	—
103	C₂×D₄×C₆₁	—	4	16	no	—
104	C₂×D₄×C₆₁	—	4	32	no	—
105	C₂²×C₄×C₆₁	—	2	32	no	—
106	C₂²×C₄×C₆₁	—	2	4	no	—
107	C₂²×C₄×C₆₁	—	2	8	no	—
108	C₂²×C₄×C₆₁	—	2	4	no	—
109	C₂²×C₄×C₆₁	—	2	8	no	—
110	C₂²×C₄×C₆₁	—	2	4	no	—
111	C₂²×C₄×C₆₁	—	2	4	no	—
112	C₂²×C₄×C₆₁	—	2	8	no	—
113	C₂²×C₄×C₆₁	—	2	4	no	—
114	C₂²×C₄×C₆₁	—	2	8	no	—
115	C₂²×C₄×C₆₁	—	2	4	no	—
116	C₂²×C₄×C₆₁	—	2	4	no	—
117	C₂²×C₄×C₆₁	—	2	4	no	—
118	C₂²×C₄×C₆₁	—	2	8	no	—
119	C₂²×C₄×C₆₁	—	2	8	no	—
120	C₂²×C₄×C₆₁	—	2	8	no	—
121	C₂²×C₄×C₆₁	—	4	16	no	—
122	C₂²×C₄×C₆₁	—	4	8	no	—
123	C₂²×C₄×C₆₁	—	4	8	no	—
124	C₂²×C₄×C₆₁	—	4	16	no	—
125	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
126	C₂²×C₄×C₆₁	C₂×D₄	1	8	yes	—
127	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
128	C₂²×C₄×C₆₁	C₂×D₄	1	16	yes	—
129	C₂²×C₄×C₆₁	C₂×D₄	1	16	yes	complemented
130	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
131	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
132	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
133	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
134	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
136	C₄⋊C₄×C₆₁	—	2	16	no	—
137	C₄⋊C₄×C₆₁	—	2	16	no	—
138	C₄⋊C₄×C₆₁	—	2	8	no	—
139	C₄⋊C₄×C₆₁	—	2	32	no	—
140	C₄⋊C₄×C₆₁	—	4	8	no	—
141	C₂²⋊C₄×C₆₁	—	2	16	no	—
142	C₂²⋊C₄×C₆₁	—	2	16	no	—
143	C₂²⋊C₄×C₆₁	—	2	32	no	—
144	C₂²⋊C₄×C₆₁	—	4	16	no	—
145	C₂³×C₆₁	—	2	8	no	—
146	C₂³×C₆₁	—	2	8	no	—
147	C₂³×C₆₁	—	2	16	no	—
148	C₂³×C₆₁	—	2	16	no	—
149	C₂³×C₆₁	—	2	4	no	—
150	C₂³×C₆₁	—	2	4	no	—
151	C₂³×C₆₁	—	2	4	no	—
152	C₂³×C₆₁	—	2	4	no	—
153	C₂³×C₆₁	—	2	4	no	—
154	C₂³×C₆₁	—	2	8	no	—
155	C₂³×C₆₁	—	2	8	no	—
156	C₂³×C₆₁	—	4	8	no	—
157	C₂³×C₆₁	—	4	8	no	—
158	C₂³×C₆₁	—	4	8	no	—
159	C₂³×C₆₁	—	4	16	no	—
160	C₂³×C₆₁	—	4	16	no	—
161	C₂³×C₆₁	#121	1	16	yes	—
162	C₂³×C₆₁	C₂²×D₄	1	4	yes	—
163	C₂³×C₆₁	C₂²×D₄	1	4	yes	—
164	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
165	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
166	C₂³×C₆₁	C₂×#41	1	4	yes	—
167	C₂³×C₆₁	C₂×#41	1	2	yes	—
168	C₂³×C₆₁	H(5,𝔽₂)	1	4	yes	—
169	C₂³×C₆₁	2₋¹⁺⁴	1	4	yes	—
170	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
171	D₄×C₆₁	—	4	16	no	—
172	D₄×C₆₁	—	4	32	no	—
173	C₂×C₄×C₆₁	—	2	16	no	—
174	C₂×C₄×C₆₁	—	2	32	no	—
175	C₂×C₄×C₆₁	—	2	8	no	—
176	C₂×C₄×C₆₁	—	2	8	no	—
177	C₂×C₄×C₆₁	—	2	4	no	—
178	C₂×C₄×C₆₁	—	2	4	no	—
179	C₂×C₄×C₆₁	—	2	4	no	—
180	C₂×C₄×C₆₁	—	2	4	no	—
181	C₂×C₄×C₆₁	—	2	8	no	—
182	C₂×C₄×C₆₁	—	2	4	no	—
183	C₂×C₄×C₆₁	—	2	4	no	—
184	C₂×C₄×C₆₁	—	2	4	no	—
185	C₂×C₄×C₆₁	—	2	4	no	—
186	C₂×C₄×C₆₁	—	2	8	no	—
187	C₂×C₄×C₆₁	—	2	8	no	—
188	C₂×C₄×C₆₁	—	2	8	no	—
189	C₂×C₄×C₆₁	—	4	16	no	—
190	C₂×C₄×C₆₁	—	4	16	no	—
191	C₂×C₄×C₆₁	—	4	8	no	—
192	C₂×C₄×C₆₁	—	4	8	no	—
193	C₂×C₄×C₆₁	—	4	16	no	—
194	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
195	C₂×C₄×C₆₁	C₂²×D₄	1	8	yes	—
196	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
197	C₂×#2618	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₂²×C₆₁	—	2	32	no	—
199	C₂²×C₆₁	—	2	4	no	—
200	C₂²×C₆₁	—	2	4	no	—
201	C₂²×C₆₁	—	2	8	no	—
202	C₂²×C₆₁	—	2	8	no	—
203	C₂²×C₆₁	—	4	4	no	—
204	C₂²×C₆₁	—	4	4	no	—
205	C₂²×C₆₁	—	4	4	no	—
206	C₂²×C₆₁	—	4	8	no	—
207	C₂²×C₆₁	—	4	8	no	—
208	C₂²×C₆₁	—	8	16	no	—
209	C₂²×C₆₁	C₂×#121	1	8	yes	—
210	C₂²×C₆₁	C₂×#121	1	4	yes	—
211	C₂²×C₆₁	#534	1	4	yes	—
212	C₂²×C₆₁	#536	1	4	yes	—
213	C₂²×C₆₁	#537	1	8	yes	—
214	C₂²×C₆₁	#539	1	8	yes	—
215	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
216	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
217	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
218	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	2	yes	—
219	C₂²×C₆₁	C₂×2₋¹⁺⁴	1	2	yes	—
220	C₄×C₆₁	—	2	8	no	—
221	C₄×C₆₁	—	2	4	no	—
222	C₄×C₆₁	—	2	4	no	—
223	C₄×C₆₁	—	4	4	no	—
224	C₄×C₆₁	—	4	4	no	—
225	C₄×C₆₁	—	4	8	no	—
226	C₂²×#123	C₂×C₆₁	1	2	yes	complemented
227	C₂²×#121	C₂×C₆₁	1	1	yes	characteristic
228	C₂³×C₄⋊C₄	C₂×C₆₁	1	1	yes	characteristic, complemented
229	#2618	C₂×C₆₁	1	16	yes	direct product factor
230	C₂×#398	C₂×C₆₁	1	2	yes	complemented
231	C₂×#396	C₂×C₆₁	1	4	yes	complemented
232	C₂×#394	C₂×C₆₁	1	2	yes	complemented
233	C₂×#386	C₂×C₆₁	1	2	yes	complemented
234	C₂×#380	C₂×C₆₁	1	1	yes	characteristic, complemented
235	C₂×C₆₁	—	2	8	no	—
236	C₂×C₆₁	—	8	4	no	—
237	C₂×C₆₁	#2618	1	8	yes	direct product factor
238	C₂×C₆₁	C₂²×#121	1	1	yes	characteristic
239	C₂×C₆₁	C₂×#534	1	1	yes	characteristic
240	C₂×C₆₁	C₂×#536	1	1	yes	characteristic
241	C₂×C₆₁	C₂×#537	1	2	yes	—
242	C₂×C₆₁	C₂×#539	1	2	yes	—
243	C₂³×D₄	C₂²×C₆₁	1	2	yes	—
244	C₂³×D₄	C₂²×C₆₁	1	1	yes	characteristic
245	C₂⁴×C₄	C₂²×C₆₁	1	1	yes	characteristic
246	C₂⁴×C₄	C₂²×C₆₁	1	1	yes	characteristic
247	C₂⁴×C₄	C₂²×C₆₁	1	1	yes	characteristic
248	C₂×#123	—	2	16	no	—
249	C₂×#123	C₂²×C₆₁	1	16	yes	complemented
250	C₂×#121	—	2	8	no	—
251	C₂×#121	C₂²×C₆₁	1	8	yes	—
252	C₂²×C₄⋊C₄	—	2	8	no	—
253	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
254	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
255	C₂²×C₄⋊C₄	C₂²×C₆₁	1	4	yes	—
256	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
257	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
258	C₂²×C₄⋊C₄	C₂²×C₆₁	1	8	yes	complemented
259	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	4	yes	—
260	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
261	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
262	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	4	yes	—
263	#398	C₂²×C₆₁	1	16	yes	complemented
264	#396	C₂²×C₆₁	1	32	yes	complemented
265	#394	C₂²×C₆₁	1	16	yes	complemented
266	#386	C₂²×C₆₁	1	16	yes	complemented
267	#380	C₂²×C₆₁	1	8	yes	complemented
268	C₂×#95	C₂²×C₆₁	1	2	yes	—
269	C₂×#95	C₂²×C₆₁	1	4	yes	—
270	C₆₁	C₂×#2618	1	1	yes	characteristic, direct product factor, Sylow
271	C₂⁵	C₂³×C₆₁	1	2	yes	—
272	C₂⁵	C₂³×C₆₁	1	1	yes	characteristic
273	C₂²×D₄	—	2	8	no	—
274	C₂²×D₄	—	2	8	no	—
275	C₂²×D₄	—	2	8	no	—
276	C₂²×D₄	—	2	4	no	—
277	C₂²×D₄	—	4	4	no	—
278	C₂²×D₄	C₂³×C₆₁	1	8	yes	—
279	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
280	C₂³×C₄	—	2	4	no	—
281	C₂³×C₄	—	2	4	no	—
282	C₂³×C₄	—	2	4	no	—
283	C₂³×C₄	—	4	4	no	—
284	C₂³×C₄	—	4	4	no	—
285	C₂³×C₄	D₄×C₆₁	1	8	yes	—
286	C₂³×C₄	D₄×C₆₁	1	8	yes	complemented
287	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
288	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
289	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
290	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
291	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
292	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
293	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
294	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
295	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
296	#123	—	2	64	no	—
297	#121	—	2	32	no	—
298	C₂×C₄⋊C₄	—	2	8	no	—
299	C₂×C₄⋊C₄	—	2	8	no	—
300	C₂×C₄⋊C₄	—	2	32	no	—
301	C₂×C₄⋊C₄	—	2	4	no	—
302	C₂×C₄⋊C₄	—	2	16	no	—
303	C₂×C₄⋊C₄	—	4	4	no	—
304	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
305	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
306	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
307	C₂×C₄⋊C₄	C₂³×C₆₁	1	16	yes	—
308	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
309	C₂×C₂²⋊C₄	—	2	8	no	—
310	C₂×C₂²⋊C₄	—	2	8	no	—
311	C₂×C₂²⋊C₄	—	2	16	no	—
312	C₂×C₂²⋊C₄	—	4	8	no	—
313	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
314	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
315	C₂×C₂²⋊C₄	C₂³×C₆₁	1	16	yes	—
316	C₂×C₂²⋊C₄	C₂³×C₆₁	1	16	yes	—
317	#95	C₂³×C₆₁	1	8	yes	—
318	#95	C₂³×C₆₁	1	16	yes	—
319	C₂⁴	—	2	4	no	—
320	C₂⁴	—	2	4	no	—
321	C₂⁴	—	2	4	no	—
322	C₂⁴	—	2	4	no	—
323	C₂⁴	—	2	4	no	—
324	C₂⁴	—	2	8	no	—
325	C₂⁴	—	2	8	no	—
326	C₂⁴	C₂×D₄×C₆₁	1	4	yes	—
327	C₂⁴	C₂×D₄×C₆₁	1	4	yes	—
328	C₂⁴	#41×C₆₁	1	4	yes	—
329	C₂⁴	C₂⁴×C₆₁	1	4	yes	—
330	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
331	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
332	C₂×D₄	—	2	16	no	—
333	C₂×D₄	—	2	16	no	—
334	C₂×D₄	—	2	16	no	—
335	C₂×D₄	—	2	8	no	—
336	C₂×D₄	—	4	8	no	—
337	C₂×D₄	—	4	16	no	—
338	C₂×D₄	—	4	32	no	—
339	C₂²×C₄	—	2	32	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	8	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	8	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	8	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	8	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	8	no	—
353	C₂²×C₄	—	2	8	no	—
354	C₂²×C₄	—	2	8	no	—
355	C₂²×C₄	—	4	16	no	—
356	C₂²×C₄	—	4	8	no	—
357	C₂²×C₄	—	4	8	no	—
358	C₂²×C₄	—	4	16	no	—
359	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
360	C₂²×C₄	C₂×D₄×C₆₁	1	8	yes	—
361	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
362	C₂²×C₄	C₂×D₄×C₆₁	1	16	yes	—
363	C₂²×C₄	C₂×D₄×C₆₁	1	16	yes	complemented
364	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
365	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
366	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
367	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
368	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
369	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
370	C₄⋊C₄	—	2	16	no	—
371	C₄⋊C₄	—	2	16	no	—
372	C₄⋊C₄	—	2	8	no	—
373	C₄⋊C₄	—	2	32	no	—
374	C₄⋊C₄	—	4	8	no	—
375	C₂²⋊C₄	—	2	16	no	—
376	C₂²⋊C₄	—	2	16	no	—
377	C₂²⋊C₄	—	2	32	no	—
378	C₂²⋊C₄	—	4	16	no	—
379	C₂³	—	2	8	no	—
380	C₂³	—	2	8	no	—
381	C₂³	—	2	16	no	—
382	C₂³	—	2	16	no	—
383	C₂³	—	2	4	no	—
384	C₂³	—	2	4	no	—
385	C₂³	—	2	4	no	—
386	C₂³	—	2	4	no	—
387	C₂³	—	2	4	no	—
388	C₂³	—	2	8	no	—
389	C₂³	—	2	8	no	—
390	C₂³	—	4	8	no	—
391	C₂³	—	4	8	no	—
392	C₂³	—	4	16	no	—
393	C₂³	—	4	16	no	—
394	C₂³	—	4	8	no	—
395	C₂³	#121×C₆₁	1	16	yes	—
396	C₂³	C₂²×D₄×C₆₁	1	4	yes	—
397	C₂³	C₂²×D₄×C₆₁	1	4	yes	—
398	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
399	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
400	C₂³	C₂×#41×C₆₁	1	4	yes	—
401	C₂³	C₂×#41×C₆₁	1	2	yes	—
402	C₂³	H(5,𝔽₂)×C₆₁	1	4	yes	—
403	C₂³	2₋¹⁺⁴×C₆₁	1	4	yes	—
404	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
405	D₄	—	4	16	no	—
406	D₄	—	4	32	no	—
407	C₂×C₄	—	2	8	no	—
408	C₂×C₄	—	2	8	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	16	no	—
414	C₂×C₄	—	2	32	no	—
415	C₂×C₄	—	2	8	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	8	no	—
421	C₂×C₄	—	2	8	no	—
422	C₂×C₄	—	2	8	no	—
423	C₂×C₄	—	4	16	no	—
424	C₂×C₄	—	4	16	no	—
425	C₂×C₄	—	4	8	no	—
426	C₂×C₄	—	4	16	no	—
427	C₂×C₄	—	4	8	no	—
428	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
429	C₂×C₄	C₂²×D₄×C₆₁	1	8	yes	—
430	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
431	C₂²	—	2	32	no	—
432	C₂²	—	2	4	no	—
433	C₂²	—	2	4	no	—
434	C₂²	—	2	8	no	—
435	C₂²	—	2	8	no	—
436	C₂²	—	4	4	no	—
437	C₂²	—	4	4	no	—
438	C₂²	—	4	4	no	—
439	C₂²	—	4	8	no	—
440	C₂²	—	4	8	no	—
441	C₂²	—	8	16	no	—
442	C₂²	C₂×#121×C₆₁	1	8	yes	—
443	C₂²	C₂×#121×C₆₁	1	4	yes	—
444	C₂²	C₆₁×#534	1	4	yes	—
445	C₂²	C₆₁×#536	1	4	yes	—
446	C₂²	C₆₁×#537	1	8	yes	—
447	C₂²	C₆₁×#539	1	8	yes	—
448	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
449	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
450	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
451	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	2	yes	—
452	C₂²	C₂×2₋¹⁺⁴×C₆₁	1	2	yes	—
453	C₄	—	2	8	no	—
454	C₄	—	2	4	no	—
455	C₄	—	2	4	no	—
456	C₄	—	4	4	no	—
457	C₄	—	4	4	no	—
458	C₄	—	4	8	no	—
459	C₂	—	2	8	no	—
460	C₂	—	8	4	no	—
461	C₂	C₆₁×#2618	1	8	yes	direct product factor
462	C₂	C₂²×#121×C₆₁	1	1	yes	characteristic
463	C₂	C₂×C₆₁×#534	1	1	yes	characteristic
464	C₂	C₂×C₆₁×#536	1	1	yes	characteristic
465	C₂	C₂×C₆₁×#537	1	2	yes	—
466	C₂	C₂×C₆₁×#539	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₆₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₁
prime radical	C₂²×#121×C₆₁	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#123×C₆₁	C₂	semidirect
3. C₂³×C₄⋊C₄×C₆₁	C₂	semidirect
4. C₆₁×#2618	C₂	direct (N × H)
5. C₂×C₆₁×#398	C₂	semidirect
6. C₂×C₆₁×#396	C₂	semidirect
7. C₂×C₆₁×#394	C₂	semidirect
8. C₂×C₆₁×#386	C₂	semidirect
9. C₂×C₆₁×#380	C₂	semidirect
16. C₂×#123×C₆₁	C₂²	semidirect
25. C₂²×C₄⋊C₄×C₆₁	C₂²	semidirect
30. C₆₁×#398	C₂²	semidirect
31. C₆₁×#396	C₂²	semidirect
32. C₆₁×#394	C₂²	semidirect
33. C₆₁×#386	C₂²	semidirect
34. C₆₁×#380	C₂²	semidirect
52. C₂³×C₄×C₆₁	D₄	semidirect
129. C₂²×C₄×C₆₁	C₂×D₄	semidirect
197. C₂×#2618	C₆₁	direct (N × H)
226. C₂²×#123	C₂×C₆₁	semidirect
228. C₂³×C₄⋊C₄	C₂×C₆₁	semidirect
229. #2618	C₂×C₆₁	direct (N × H)
230. C₂×#398	C₂×C₆₁	semidirect
231. C₂×#396	C₂×C₆₁	semidirect
232. C₂×#394	C₂×C₆₁	semidirect
233. C₂×#386	C₂×C₆₁	semidirect
234. C₂×#380	C₂×C₆₁	semidirect
237. C₂×C₆₁	#2618	direct (N × H)
249. C₂×#123	C₂²×C₆₁	semidirect
258. C₂²×C₄⋊C₄	C₂²×C₆₁	semidirect
263. #398	C₂²×C₆₁	semidirect
264. #396	C₂²×C₆₁	semidirect
265. #394	C₂²×C₆₁	semidirect
266. #386	C₂²×C₆₁	semidirect
267. #380	C₂²×C₆₁	semidirect
270. C₆₁	C₂×#2618	direct (N × H)
286. C₂³×C₄	D₄×C₆₁	semidirect
363. C₂²×C₄	C₂×D₄×C₆₁	semidirect
461. C₂	C₆₁×#2618	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#123×C₆₁	2
C₂²×#121×C₆₁	2
C₂³×C₄⋊C₄×C₆₁	2
C₆₁×#2618	2
C₂×C₆₁×#398	2
C₂×C₆₁×#396	2
C₂×C₆₁×#394	2
C₂×C₆₁×#386	2
C₂×C₆₁×#380	2
C₂×#2618	61

Subgroups — C2×C61×#2618 #29537990

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#2618 #29537990