Subgroups — C₂×C₆₁×#3256 #29564339

Order 15616.

1930 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#529	C₂	1	2	yes	maximal, complemented
2	C₆₁×#3256	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₆₁×#479	C₂	1	2	yes	maximal, complemented
4	C₂×C₆₁×#478	C₂	1	2	yes	maximal, complemented
5	C₂×C₆₁×#470	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₆₁×#469	C₂	1	1	yes	maximal, characteristic
7	C₂×C₆₁×#468	C₂	1	2	yes	maximal, complemented
8	C₂×C₆₁×#464	C₂	1	2	yes	maximal, complemented
9	C₂×C₆₁×#463	C₂	1	2	yes	maximal, complemented
10	C₂×C₆₁×#423	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
12	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	—
13	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
15	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
16	C₆₁×#529	—	2	8	no	—
17	C₆₁×#529	C₂²	1	16	yes	complemented
18	C₂×#126×C₆₁	—	2	2	no	—
19	C₂×#125×C₆₁	C₂²	1	2	yes	—
20	C₂×#124×C₆₁	C₂²	1	2	yes	—
21	C₂×#123×C₆₁	—	2	2	no	—
22	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
23	C₂×#121×C₆₁	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₆₁	—	2	2	no	—
26	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
27	C₂×#117×C₆₁	—	2	2	no	—
28	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
29	C₆₁×#479	C₂²	1	16	yes	complemented
30	C₆₁×#478	C₂²	1	16	yes	complemented
31	C₆₁×#470	C₂²	1	8	yes	complemented
32	C₆₁×#469	C₂²	1	8	yes	—
33	C₆₁×#468	C₂²	1	16	yes	complemented
34	C₆₁×#464	C₂²	1	16	yes	complemented
35	C₆₁×#463	C₂²	1	16	yes	complemented
36	C₂×#107×C₆₁	C₂²	1	2	yes	—
37	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
38	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
39	C₆₁×#423	C₂²	1	8	yes	complemented
40	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
41	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
42	C₂×#103×C₆₁	C₂²	1	2	yes	—
43	C₂×#103×C₆₁	C₂²	1	2	yes	—
44	C₂×#102×C₆₁	C₂²	1	2	yes	—
45	C₂×#102×C₆₁	C₂²	1	2	yes	—
46	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
47	C₂²×D₄×C₆₁	—	2	2	no	—
48	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
49	C₂³×C₄×C₆₁	—	2	2	no	—
50	C₂³×C₄×C₆₁	D₄	1	2	yes	—
51	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
52	C₂×Q₁₆×C₆₁	—	4	2	no	—
53	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
54	C₂×SD₁₆×C₆₁	—	4	4	no	—
55	C₂×SD₁₆×C₆₁	C₂³	1	8	yes	—
56	C₂×D₈×C₆₁	—	4	2	no	—
57	C₂×D₈×C₆₁	C₂³	1	4	yes	—
58	C₂×M₁₆×C₆₁	—	4	2	no	—
59	C₂×M₁₆×C₆₁	—	4	2	no	—
60	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
61	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
62	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
64	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
65	#126×C₆₁	—	2	16	no	—
66	#125×C₆₁	—	2	4	no	—
67	#125×C₆₁	C₂³	1	8	yes	—
68	#124×C₆₁	—	2	4	no	—
69	#124×C₆₁	C₂³	1	8	yes	—
70	#123×C₆₁	—	2	16	no	—
71	C₂²⋊Q₈×C₆₁	—	2	4	no	—
72	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
73	#121×C₆₁	—	2	4	no	—
74	#121×C₆₁	C₂³	1	8	yes	—
75	C₄×Q₈×C₆₁	—	2	4	no	—
76	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
77	C₄×D₄×C₆₁	—	2	16	no	—
78	C₄×D₄×C₆₁	—	2	4	no	—
79	C₄×D₄×C₆₁	C₂³	1	8	yes	—
80	#117×C₆₁	—	2	16	no	—
81	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
82	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
83	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
84	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
85	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
87	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
89	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
91	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
92	C₂×C₄²×C₆₁	—	2	2	no	—
93	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₆₁	D₄	1	4	yes	—
96	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
97	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
98	#107×C₆₁	C₂³	1	8	yes	—
99	#106×C₆₁	C₂³	1	4	yes	—
100	#106×C₆₁	C₂³	1	4	yes	—
101	C₄⋊C₈×C₆₁	C₂³	1	8	yes	—
102	C₄⋊C₈×C₆₁	C₂³	1	8	yes	—
103	#103×C₆₁	C₂³	1	8	yes	—
104	#103×C₆₁	C₂³	1	8	yes	—
105	#102×C₆₁	C₂³	1	8	yes	—
106	#102×C₆₁	C₂³	1	8	yes	—
107	C₂⁴×C₆₁	—	2	2	no	—
108	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
109	C₂×Q₈×C₆₁	—	2	2	no	—
110	C₂×Q₈×C₆₁	—	2	4	no	—
111	C₂×Q₈×C₆₁	—	2	4	no	—
112	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
113	C₂×D₄×C₆₁	—	2	8	no	—
114	C₂×D₄×C₆₁	—	2	2	no	—
115	C₂×D₄×C₆₁	—	2	4	no	—
116	C₂×D₄×C₆₁	—	2	4	no	—
117	C₂×D₄×C₆₁	—	4	8	no	—
118	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
119	C₂²×C₄×C₆₁	—	2	2	no	—
120	C₂²×C₄×C₆₁	—	2	2	no	—
121	C₂²×C₄×C₆₁	—	2	2	no	—
122	C₂²×C₄×C₆₁	—	2	2	no	—
123	C₂²×C₄×C₆₁	—	2	2	no	—
124	C₂²×C₄×C₆₁	—	2	8	no	—
125	C₂²×C₄×C₆₁	—	4	4	no	—
126	C₂²×C₄×C₆₁	—	4	8	no	—
127	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₆₁	C₂×D₄	1	8	yes	—
132	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
133	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
134	Q₁₆×C₆₁	—	4	4	no	—
135	SD₁₆×C₆₁	—	4	8	no	—
136	D₈×C₆₁	—	4	4	no	—
137	M₁₆×C₆₁	—	4	4	no	—
138	M₁₆×C₆₁	—	4	4	no	—
139	C₂×C₈×C₆₁	—	2	2	no	—
140	C₂×C₈×C₆₁	—	2	4	no	—
141	C₂×C₈×C₆₁	—	2	2	no	—
142	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
143	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
144	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
145	C₄⋊C₄×C₆₁	—	2	8	no	—
146	C₄⋊C₄×C₆₁	—	2	8	no	—
147	C₄⋊C₄×C₆₁	—	2	8	no	—
148	C₄⋊C₄×C₆₁	—	2	8	no	—
149	C₄⋊C₄×C₆₁	—	2	2	no	—
150	C₄⋊C₄×C₆₁	—	2	2	no	—
151	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
152	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
153	C₂²⋊C₄×C₆₁	—	2	8	no	—
154	C₂²⋊C₄×C₆₁	—	2	8	no	—
155	C₂²⋊C₄×C₆₁	—	2	8	no	—
156	C₂²⋊C₄×C₆₁	—	2	8	no	—
157	C₂²⋊C₄×C₆₁	—	2	8	no	—
158	C₄²×C₆₁	—	2	8	no	—
159	C₄²×C₆₁	C₂×D₄	1	4	yes	—
160	C₄²×C₆₁	C₂×D₄	1	4	yes	—
161	C₄²×C₆₁	C₂×D₄	1	4	yes	—
162	C₄²×C₆₁	C₂⁴	1	4	yes	—
163	C₂³×C₆₁	—	2	2	no	—
164	C₂³×C₆₁	—	2	4	no	—
165	C₂³×C₆₁	—	2	4	no	—
166	C₂³×C₆₁	—	4	4	no	—
167	C₂³×C₆₁	—	4	4	no	—
168	C₂³×C₆₁	—	4	4	no	—
169	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
170	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
171	Q₈×C₆₁	—	2	4	no	—
172	Q₈×C₆₁	—	2	4	no	—
173	Q₈×C₆₁	—	4	4	no	—
174	D₄×C₆₁	—	2	4	no	—
175	D₄×C₆₁	—	2	4	no	—
176	D₄×C₆₁	—	4	16	no	—
177	D₄×C₆₁	—	4	4	no	—
178	C₂×C₄×C₆₁	—	2	2	no	—
179	C₂×C₄×C₆₁	—	2	4	no	—
180	C₂×C₄×C₆₁	—	2	4	no	—
181	C₂×C₄×C₆₁	—	2	4	no	—
182	C₂×C₄×C₆₁	—	2	2	no	—
183	C₂×C₄×C₆₁	—	2	2	no	—
184	C₂×C₄×C₆₁	—	2	4	no	—
185	C₂×C₄×C₆₁	—	2	4	no	—
186	C₂×C₄×C₆₁	—	2	4	no	—
187	C₂×C₄×C₆₁	—	4	8	no	—
188	C₂×C₄×C₆₁	—	4	16	no	—
189	C₂×C₄×C₆₁	—	4	4	no	—
190	C₂×C₄×C₆₁	—	4	4	no	—
191	C₂×C₄×C₆₁	—	4	4	no	—
192	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
193	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
194	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
195	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
197	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
198	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
199	C₈×C₆₁	—	2	2	no	—
200	C₈×C₆₁	—	2	4	no	—
201	C₈×C₆₁	—	2	2	no	—
202	C₂×#3256	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₂²×C₆₁	—	2	2	no	—
204	C₂²×C₆₁	—	2	4	no	—
205	C₂²×C₆₁	—	4	4	no	—
206	C₂²×C₆₁	—	4	4	no	—
207	C₂²×C₆₁	—	4	4	no	—
208	C₂²×C₆₁	—	4	4	no	—
209	C₂²×C₆₁	—	8	8	no	—
210	C₂²×C₆₁	#537	1	2	yes	—
211	C₂²×C₆₁	#575	1	4	yes	—
212	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
213	C₄×C₆₁	—	2	2	no	—
214	C₄×C₆₁	—	2	4	no	—
215	C₄×C₆₁	—	2	4	no	—
216	C₄×C₆₁	—	4	4	no	—
217	C₄×C₆₁	—	4	4	no	—
218	C₄×C₆₁	—	4	4	no	—
219	C₄×C₆₁	#537	1	2	yes	—
220	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
221	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
222	C₂×#529	C₂×C₆₁	1	2	yes	complemented
223	#3256	C₂×C₆₁	1	16	yes	direct product factor
224	C₂×#479	C₂×C₆₁	1	2	yes	complemented
225	C₂×#478	C₂×C₆₁	1	2	yes	complemented
226	C₂×#470	C₂×C₆₁	1	1	yes	characteristic, complemented
227	C₂×#469	C₂×C₆₁	1	1	yes	characteristic
228	C₂×#468	C₂×C₆₁	1	2	yes	complemented
229	C₂×#464	C₂×C₆₁	1	2	yes	complemented
230	C₂×#463	C₂×C₆₁	1	2	yes	complemented
231	C₂×#423	C₂×C₆₁	1	1	yes	characteristic, complemented
232	C₂×C₆₁	—	4	2	no	—
233	C₂×C₆₁	—	8	4	no	—
234	C₂×C₆₁	#3256	1	4	yes	direct product factor
235	C₂×C₆₁	C₂×#537	1	1	yes	characteristic
236	C₂×C₆₁	C₂×#575	1	2	yes	—
237	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
238	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	—
239	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
240	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
241	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
242	#529	—	2	8	no	—
243	#529	C₂²×C₆₁	1	16	yes	complemented
244	C₂×#126	—	2	2	no	—
245	C₂×#125	C₂²×C₆₁	1	2	yes	—
246	C₂×#124	C₂²×C₆₁	1	2	yes	—
247	C₂×#123	—	2	2	no	—
248	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
249	C₂×#121	C₂²×C₆₁	1	2	yes	—
250	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
251	C₂×C₄×D₄	—	2	2	no	—
252	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
253	C₂×#117	—	2	2	no	—
254	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
255	#479	C₂²×C₆₁	1	16	yes	complemented
256	#478	C₂²×C₆₁	1	16	yes	complemented
257	#470	C₂²×C₆₁	1	8	yes	complemented
258	#469	C₂²×C₆₁	1	8	yes	—
259	#468	C₂²×C₆₁	1	16	yes	complemented
260	#464	C₂²×C₆₁	1	16	yes	complemented
261	#463	C₂²×C₆₁	1	16	yes	complemented
262	C₂×#107	C₂²×C₆₁	1	2	yes	—
263	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
264	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
265	#423	C₂²×C₆₁	1	8	yes	complemented
266	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
267	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
268	C₂×#103	C₂²×C₆₁	1	2	yes	—
269	C₂×#103	C₂²×C₆₁	1	2	yes	—
270	C₂×#102	C₂²×C₆₁	1	2	yes	—
271	C₂×#102	C₂²×C₆₁	1	2	yes	—
272	C₆₁	C₂×#3256	1	1	yes	characteristic, direct product factor, Sylow
273	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
274	C₂²×D₄	—	2	2	no	—
275	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
276	C₂³×C₄	—	2	2	no	—
277	C₂³×C₄	D₄×C₆₁	1	2	yes	—
278	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
279	C₂×Q₁₆	—	4	2	no	—
280	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
281	C₂×SD₁₆	—	4	4	no	—
282	C₂×SD₁₆	C₂³×C₆₁	1	8	yes	—
283	C₂×D₈	—	4	2	no	—
284	C₂×D₈	C₂³×C₆₁	1	4	yes	—
285	C₂×M₁₆	—	4	2	no	—
286	C₂×M₁₆	—	4	2	no	—
287	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
288	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
289	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
290	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
291	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
292	#126	—	2	16	no	—
293	#125	—	2	4	no	—
294	#125	C₂³×C₆₁	1	8	yes	—
295	#124	—	2	4	no	—
296	#124	C₂³×C₆₁	1	8	yes	—
297	#123	—	2	16	no	—
298	C₂²⋊Q₈	—	2	4	no	—
299	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
300	#121	—	2	4	no	—
301	#121	C₂³×C₆₁	1	8	yes	—
302	C₄×Q₈	—	2	4	no	—
303	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
304	C₄×D₄	—	2	16	no	—
305	C₄×D₄	—	2	4	no	—
306	C₄×D₄	C₂³×C₆₁	1	8	yes	—
307	#117	—	2	16	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
313	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₂²⋊C₄	—	2	2	no	—
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₄²	—	2	2	no	—
320	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
321	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
322	C₂×C₄²	D₄×C₆₁	1	4	yes	—
323	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
324	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
325	#107	C₂³×C₆₁	1	8	yes	—
326	#106	C₂³×C₆₁	1	4	yes	—
327	#106	C₂³×C₆₁	1	4	yes	—
328	C₄⋊C₈	C₂³×C₆₁	1	8	yes	—
329	C₄⋊C₈	C₂³×C₆₁	1	8	yes	—
330	#103	C₂³×C₆₁	1	8	yes	—
331	#103	C₂³×C₆₁	1	8	yes	—
332	#102	C₂³×C₆₁	1	8	yes	—
333	#102	C₂³×C₆₁	1	8	yes	—
334	C₂⁴	—	2	2	no	—
335	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	2	4	no	—
338	C₂×Q₈	—	2	4	no	—
339	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
340	C₂×D₄	—	2	8	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	4	no	—
343	C₂×D₄	—	2	4	no	—
344	C₂×D₄	—	4	8	no	—
345	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	8	no	—
352	C₂²×C₄	—	4	4	no	—
353	C₂²×C₄	—	4	8	no	—
354	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
355	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
357	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
358	C₂²×C₄	C₂×D₄×C₆₁	1	8	yes	—
359	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
360	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
361	Q₁₆	—	4	4	no	—
362	SD₁₆	—	4	8	no	—
363	D₈	—	4	4	no	—
364	M₁₆	—	4	4	no	—
365	M₁₆	—	4	4	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	4	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
370	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
371	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
372	C₄⋊C₄	—	2	8	no	—
373	C₄⋊C₄	—	2	8	no	—
374	C₄⋊C₄	—	2	8	no	—
375	C₄⋊C₄	—	2	8	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
379	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
380	C₂²⋊C₄	—	2	8	no	—
381	C₂²⋊C₄	—	2	8	no	—
382	C₂²⋊C₄	—	2	8	no	—
383	C₂²⋊C₄	—	2	8	no	—
384	C₂²⋊C₄	—	2	8	no	—
385	C₄²	—	2	8	no	—
386	C₄²	C₂×D₄×C₆₁	1	4	yes	—
387	C₄²	C₂×D₄×C₆₁	1	4	yes	—
388	C₄²	C₂×D₄×C₆₁	1	4	yes	—
389	C₄²	C₂⁴×C₆₁	1	4	yes	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	4	no	—
392	C₂³	—	2	4	no	—
393	C₂³	—	4	4	no	—
394	C₂³	—	4	4	no	—
395	C₂³	—	4	4	no	—
396	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
397	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
398	Q₈	—	2	4	no	—
399	Q₈	—	2	4	no	—
400	Q₈	—	4	4	no	—
401	D₄	—	2	4	no	—
402	D₄	—	2	4	no	—
403	D₄	—	4	16	no	—
404	D₄	—	4	4	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	4	8	no	—
415	C₂×C₄	—	4	16	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
420	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
421	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
422	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
423	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
424	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
425	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
426	C₈	—	2	2	no	—
427	C₈	—	2	4	no	—
428	C₈	—	2	2	no	—
429	C₂²	—	2	4	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	4	4	no	—
432	C₂²	—	4	4	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	4	4	no	—
435	C₂²	—	8	8	no	—
436	C₂²	C₆₁×#537	1	2	yes	—
437	C₂²	C₆₁×#575	1	4	yes	—
438	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
439	C₄	—	2	4	no	—
440	C₄	—	2	4	no	—
441	C₄	—	2	2	no	—
442	C₄	—	4	4	no	—
443	C₄	—	4	4	no	—
444	C₄	—	4	4	no	—
445	C₄	C₆₁×#537	1	2	yes	—
446	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
447	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
448	C₂	—	4	2	no	—
449	C₂	—	8	4	no	—
450	C₂	C₆₁×#3256	1	4	yes	direct product factor
451	C₂	C₂×C₆₁×#537	1	1	yes	characteristic
452	C₂	C₂×C₆₁×#575	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₂×C₆₁×#469	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂²×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#529	C₂	semidirect
2. C₆₁×#3256	C₂	direct (N × H)
3. C₂×C₆₁×#479	C₂	semidirect
4. C₂×C₆₁×#478	C₂	semidirect
5. C₂×C₆₁×#470	C₂	semidirect
7. C₂×C₆₁×#468	C₂	semidirect
8. C₂×C₆₁×#464	C₂	semidirect
9. C₂×C₆₁×#463	C₂	semidirect
10. C₂×C₆₁×#423	C₂	semidirect
17. C₆₁×#529	C₂²	semidirect
29. C₆₁×#479	C₂²	semidirect
30. C₆₁×#478	C₂²	semidirect
31. C₆₁×#470	C₂²	semidirect
33. C₆₁×#468	C₂²	semidirect
34. C₆₁×#464	C₂²	semidirect
35. C₆₁×#463	C₂²	semidirect
39. C₆₁×#423	C₂²	semidirect
202. C₂×#3256	C₆₁	direct (N × H)
222. C₂×#529	C₂×C₆₁	semidirect
223. #3256	C₂×C₆₁	direct (N × H)
224. C₂×#479	C₂×C₆₁	semidirect
225. C₂×#478	C₂×C₆₁	semidirect
226. C₂×#470	C₂×C₆₁	semidirect
228. C₂×#468	C₂×C₆₁	semidirect
229. C₂×#464	C₂×C₆₁	semidirect
230. C₂×#463	C₂×C₆₁	semidirect
231. C₂×#423	C₂×C₆₁	semidirect
234. C₂×C₆₁	#3256	direct (N × H)
243. #529	C₂²×C₆₁	semidirect
255. #479	C₂²×C₆₁	semidirect
256. #478	C₂²×C₆₁	semidirect
257. #470	C₂²×C₆₁	semidirect
259. #468	C₂²×C₆₁	semidirect
260. #464	C₂²×C₆₁	semidirect
261. #463	C₂²×C₆₁	semidirect
265. #423	C₂²×C₆₁	semidirect
272. C₆₁	C₂×#3256	direct (N × H)
450. C₂	C₆₁×#3256	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#529	2
C₆₁×#3256	2
C₂×C₆₁×#479	2
C₂×C₆₁×#478	2
C₂×C₆₁×#470	2
C₂×C₆₁×#469	2
C₂×C₆₁×#468	2
C₂×C₆₁×#464	2
C₂×C₆₁×#463	2
C₂×C₆₁×#423	2
C₂×#3256	61

Subgroups — C2×C61×#3256 #29564339

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#3256 #29564339