Subgroups — C₂×C₆₁×#3250 #29564332

Order 15616.

1962 conjugacy classes of subgroups.

The subgroup lattice has 466 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×#3250	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×#467	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₆₁×#466	C₂	1	1	yes	maximal, characteristic
7	C₂×C₆₁×#465	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	C₂²×C₄⋊C₈×C₆₁	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	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂³×C₈×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×#467	C₂²	1	8	yes	complemented
32	C₆₁×#466	C₂²	1	8	yes	—
33	C₆₁×#465	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	1	yes	characteristic
37	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
38	C₂×#106×C₆₁	C₂²	1	2	yes	—
39	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
40	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
41	C₂×C₄⋊C₈×C₆₁	C₂²	1	8	yes	complemented
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	1	yes	characteristic
51	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
53	C₂×Q₁₆×C₆₁	—	4	2	no	—
54	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
55	C₂×SD₁₆×C₆₁	—	4	4	no	—
56	C₂×SD₁₆×C₆₁	C₂³	1	8	yes	—
57	C₂×D₈×C₆₁	—	4	2	no	—
58	C₂×D₈×C₆₁	C₂³	1	4	yes	—
59	C₂²×C₈×C₆₁	—	4	2	no	—
60	C₂²×C₈×C₆₁	—	4	2	no	—
61	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
63	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
65	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
66	#126×C₆₁	—	2	16	no	—
67	#125×C₆₁	—	2	4	no	—
68	#125×C₆₁	C₂³	1	8	yes	—
69	#124×C₆₁	—	2	4	no	—
70	#124×C₆₁	C₂³	1	8	yes	—
71	#123×C₆₁	—	2	16	no	—
72	C₂²⋊Q₈×C₆₁	—	2	4	no	—
73	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
74	#121×C₆₁	—	2	4	no	—
75	#121×C₆₁	C₂³	1	8	yes	—
76	C₄×Q₈×C₆₁	—	2	4	no	—
77	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
78	C₄×D₄×C₆₁	—	2	16	no	—
79	C₄×D₄×C₆₁	—	2	4	no	—
80	C₄×D₄×C₆₁	C₂³	1	8	yes	—
81	#117×C₆₁	—	2	16	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	—	2	2	no	—
86	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
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×C₂²⋊C₄×C₆₁	—	2	2	no	—
93	C₂×C₄²×C₆₁	—	2	2	no	—
94	C₂×C₄²×C₆₁	D₄	1	2	yes	—
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	4	yes	—
99	#107×C₆₁	C₂³	1	4	yes	—
100	#106×C₆₁	C₂³	1	8	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	4	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	2	no	—
125	C₂²×C₄×C₆₁	—	2	8	no	—
126	C₂²×C₄×C₆₁	—	4	2	no	—
127	C₂²×C₄×C₆₁	—	4	8	no	—
128	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
130	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
134	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
135	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
136	Q₁₆×C₆₁	—	4	4	no	—
137	SD₁₆×C₆₁	—	4	8	no	—
138	D₈×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	—	4	4	no	—
143	C₂×C₈×C₆₁	—	4	4	no	—
144	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
145	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
146	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
147	C₄⋊C₄×C₆₁	—	2	8	no	—
148	C₄⋊C₄×C₆₁	—	2	8	no	—
149	C₄⋊C₄×C₆₁	—	2	8	no	—
150	C₄⋊C₄×C₆₁	—	2	8	no	—
151	C₄⋊C₄×C₆₁	—	2	2	no	—
152	C₄⋊C₄×C₆₁	—	2	2	no	—
153	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
154	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
155	C₂²⋊C₄×C₆₁	—	2	8	no	—
156	C₂²⋊C₄×C₆₁	—	2	8	no	—
157	C₂²⋊C₄×C₆₁	—	2	8	no	—
158	C₂²⋊C₄×C₆₁	—	2	8	no	—
159	C₂²⋊C₄×C₆₁	—	2	8	no	—
160	C₄²×C₆₁	—	2	8	no	—
161	C₄²×C₆₁	C₂×D₄	1	8	yes	—
162	C₄²×C₆₁	C₂×D₄	1	4	yes	—
163	C₄²×C₆₁	C₂⁴	1	4	yes	—
164	C₂³×C₆₁	—	2	2	no	—
165	C₂³×C₆₁	—	2	2	no	—
166	C₂³×C₆₁	—	2	4	no	—
167	C₂³×C₆₁	—	4	4	no	—
168	C₂³×C₆₁	—	4	4	no	—
169	C₂³×C₆₁	—	4	4	no	—
170	C₂³×C₆₁	#135	1	4	yes	—
171	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
172	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
173	Q₈×C₆₁	—	2	4	no	—
174	Q₈×C₆₁	—	2	4	no	—
175	Q₈×C₆₁	—	4	4	no	—
176	D₄×C₆₁	—	2	4	no	—
177	D₄×C₆₁	—	2	4	no	—
178	D₄×C₆₁	—	4	16	no	—
179	D₄×C₆₁	—	4	4	no	—
180	C₂×C₄×C₆₁	—	2	2	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	2	no	—
186	C₂×C₄×C₆₁	—	2	2	no	—
187	C₂×C₄×C₆₁	—	2	4	no	—
188	C₂×C₄×C₆₁	—	2	4	no	—
189	C₂×C₄×C₆₁	—	2	4	no	—
190	C₂×C₄×C₆₁	—	4	4	no	—
191	C₂×C₄×C₆₁	—	4	16	no	—
192	C₂×C₄×C₆₁	—	4	4	no	—
193	C₂×C₄×C₆₁	—	4	4	no	—
194	C₂×C₄×C₆₁	—	4	4	no	—
195	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
196	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
198	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
200	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
201	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
202	C₈×C₆₁	—	2	2	no	—
203	C₈×C₆₁	—	2	4	no	—
204	C₈×C₆₁	—	2	2	no	—
205	C₂×#3250	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₂²×C₆₁	—	2	2	no	—
207	C₂²×C₆₁	—	2	8	no	—
208	C₂²×C₆₁	—	2	2	no	—
209	C₂²×C₆₁	—	4	4	no	—
210	C₂²×C₆₁	—	4	4	no	—
211	C₂²×C₆₁	—	4	4	no	—
212	C₂²×C₆₁	—	8	8	no	—
213	C₂²×C₆₁	#537	1	2	yes	—
214	C₂²×C₆₁	C₂×#135	1	4	yes	—
215	C₂²×C₆₁	C₂×#135	1	2	yes	—
216	C₂²×C₆₁	#575	1	2	yes	—
217	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
218	C₄×C₆₁	—	2	2	no	—
219	C₄×C₆₁	—	2	4	no	—
220	C₄×C₆₁	—	2	4	no	—
221	C₄×C₆₁	—	4	4	no	—
222	C₄×C₆₁	—	4	4	no	—
223	C₄×C₆₁	—	4	4	no	—
224	C₄×C₆₁	#537	1	2	yes	—
225	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
226	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
227	C₂×#529	C₂×C₆₁	1	2	yes	complemented
228	#3250	C₂×C₆₁	1	16	yes	direct product factor
229	C₂×#479	C₂×C₆₁	1	2	yes	complemented
230	C₂×#478	C₂×C₆₁	1	2	yes	complemented
231	C₂×#467	C₂×C₆₁	1	1	yes	characteristic, complemented
232	C₂×#466	C₂×C₆₁	1	1	yes	characteristic
233	C₂×#465	C₂×C₆₁	1	2	yes	complemented
234	C₂×#464	C₂×C₆₁	1	2	yes	complemented
235	C₂×#463	C₂×C₆₁	1	2	yes	complemented
236	C₂²×C₄⋊C₈	C₂×C₆₁	1	1	yes	characteristic, complemented
237	C₂×C₆₁	—	2	4	no	—
238	C₂×C₆₁	—	8	4	no	—
239	C₂×C₆₁	#3250	1	4	yes	direct product factor
240	C₂×C₆₁	C₂×#537	1	1	yes	characteristic
241	C₂×C₆₁	C₂²×#135	1	1	yes	characteristic
242	C₂×C₆₁	C₂×#575	1	1	yes	characteristic
243	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
244	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	—
245	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
246	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
247	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
248	#529	—	2	8	no	—
249	#529	C₂²×C₆₁	1	16	yes	complemented
250	C₂×#126	—	2	2	no	—
251	C₂×#125	C₂²×C₆₁	1	2	yes	—
252	C₂×#124	C₂²×C₆₁	1	2	yes	—
253	C₂×#123	—	2	2	no	—
254	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
255	C₂×#121	C₂²×C₆₁	1	2	yes	—
256	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
257	C₂×C₄×D₄	—	2	2	no	—
258	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
259	C₂×#117	—	2	2	no	—
260	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
261	#479	C₂²×C₆₁	1	16	yes	complemented
262	#478	C₂²×C₆₁	1	16	yes	complemented
263	#467	C₂²×C₆₁	1	8	yes	complemented
264	#466	C₂²×C₆₁	1	8	yes	—
265	#465	C₂²×C₆₁	1	16	yes	complemented
266	#464	C₂²×C₆₁	1	16	yes	complemented
267	#463	C₂²×C₆₁	1	16	yes	complemented
268	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
269	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
270	C₂×#106	C₂²×C₆₁	1	2	yes	—
271	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
272	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
273	C₂×C₄⋊C₈	C₂²×C₆₁	1	8	yes	complemented
274	C₂×#103	C₂²×C₆₁	1	2	yes	—
275	C₂×#103	C₂²×C₆₁	1	2	yes	—
276	C₂×#102	C₂²×C₆₁	1	2	yes	—
277	C₂×#102	C₂²×C₆₁	1	2	yes	—
278	C₆₁	C₂×#3250	1	1	yes	characteristic, direct product factor, Sylow
279	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
280	C₂²×D₄	—	2	2	no	—
281	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
282	C₂³×C₄	—	2	2	no	—
283	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
284	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
285	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
286	C₂×Q₁₆	—	4	2	no	—
287	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
288	C₂×SD₁₆	—	4	4	no	—
289	C₂×SD₁₆	C₂³×C₆₁	1	8	yes	—
290	C₂×D₈	—	4	2	no	—
291	C₂×D₈	C₂³×C₆₁	1	4	yes	—
292	C₂²×C₈	—	4	2	no	—
293	C₂²×C₈	—	4	2	no	—
294	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
295	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
296	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
297	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
298	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
299	#126	—	2	16	no	—
300	#125	—	2	4	no	—
301	#125	C₂³×C₆₁	1	8	yes	—
302	#124	—	2	4	no	—
303	#124	C₂³×C₆₁	1	8	yes	—
304	#123	—	2	16	no	—
305	C₂²⋊Q₈	—	2	4	no	—
306	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
307	#121	—	2	4	no	—
308	#121	C₂³×C₆₁	1	8	yes	—
309	C₄×Q₈	—	2	4	no	—
310	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
311	C₄×D₄	—	2	16	no	—
312	C₄×D₄	—	2	4	no	—
313	C₄×D₄	C₂³×C₆₁	1	8	yes	—
314	#117	—	2	16	no	—
315	C₂×C₄⋊C₄	—	2	2	no	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	2	no	—
319	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
320	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₂²⋊C₄	—	2	2	no	—
323	C₂×C₂²⋊C₄	—	2	2	no	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₂²⋊C₄	—	2	2	no	—
326	C₂×C₄²	—	2	2	no	—
327	C₂×C₄²	D₄×C₆₁	1	2	yes	—
328	C₂×C₄²	D₄×C₆₁	1	4	yes	—
329	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
330	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
331	#107	C₂³×C₆₁	1	4	yes	—
332	#107	C₂³×C₆₁	1	4	yes	—
333	#106	C₂³×C₆₁	1	8	yes	—
334	C₄⋊C₈	C₂³×C₆₁	1	8	yes	—
335	C₄⋊C₈	C₂³×C₆₁	1	8	yes	—
336	#103	C₂³×C₆₁	1	8	yes	—
337	#103	C₂³×C₆₁	1	8	yes	—
338	#102	C₂³×C₆₁	1	8	yes	—
339	#102	C₂³×C₆₁	1	8	yes	—
340	C₂⁴	—	2	2	no	—
341	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	4	no	—
344	C₂×Q₈	—	2	4	no	—
345	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
346	C₂×D₄	—	2	8	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	4	no	—
349	C₂×D₄	—	2	4	no	—
350	C₂×D₄	—	4	8	no	—
351	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	8	no	—
359	C₂²×C₄	—	4	2	no	—
360	C₂²×C₄	—	4	8	no	—
361	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
362	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
364	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
365	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
366	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
367	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
368	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
369	Q₁₆	—	4	4	no	—
370	SD₁₆	—	4	8	no	—
371	D₈	—	4	4	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	4	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	4	4	no	—
376	C₂×C₈	—	4	4	no	—
377	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
378	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
379	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
380	C₄⋊C₄	—	2	8	no	—
381	C₄⋊C₄	—	2	8	no	—
382	C₄⋊C₄	—	2	8	no	—
383	C₄⋊C₄	—	2	8	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
387	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
388	C₂²⋊C₄	—	2	8	no	—
389	C₂²⋊C₄	—	2	8	no	—
390	C₂²⋊C₄	—	2	8	no	—
391	C₂²⋊C₄	—	2	8	no	—
392	C₂²⋊C₄	—	2	8	no	—
393	C₄²	—	2	8	no	—
394	C₄²	C₂×D₄×C₆₁	1	8	yes	—
395	C₄²	C₂×D₄×C₆₁	1	4	yes	—
396	C₄²	C₂⁴×C₆₁	1	4	yes	—
397	C₂³	—	2	2	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	2	4	no	—
400	C₂³	—	4	4	no	—
401	C₂³	—	4	4	no	—
402	C₂³	—	4	4	no	—
403	C₂³	#135×C₆₁	1	4	yes	—
404	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
405	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
406	Q₈	—	2	4	no	—
407	Q₈	—	2	4	no	—
408	Q₈	—	4	4	no	—
409	D₄	—	2	4	no	—
410	D₄	—	2	4	no	—
411	D₄	—	4	16	no	—
412	D₄	—	4	4	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	8	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	4	16	no	—
425	C₂×C₄	—	4	4	no	—
426	C₂×C₄	—	4	4	no	—
427	C₂×C₄	—	4	4	no	—
428	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
429	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
430	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
431	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
432	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
433	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
434	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
435	C₈	—	2	2	no	—
436	C₈	—	2	4	no	—
437	C₈	—	2	2	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	8	no	—
441	C₂²	—	4	4	no	—
442	C₂²	—	4	4	no	—
443	C₂²	—	4	4	no	—
444	C₂²	—	8	8	no	—
445	C₂²	C₆₁×#537	1	2	yes	—
446	C₂²	C₂×#135×C₆₁	1	4	yes	—
447	C₂²	C₂×#135×C₆₁	1	2	yes	—
448	C₂²	C₆₁×#575	1	2	yes	—
449	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
450	C₄	—	2	4	no	—
451	C₄	—	2	4	no	—
452	C₄	—	2	2	no	—
453	C₄	—	4	4	no	—
454	C₄	—	4	4	no	—
455	C₄	—	4	4	no	—
456	C₄	C₆₁×#537	1	2	yes	—
457	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
458	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
459	C₂	—	2	4	no	—
460	C₂	—	8	4	no	—
461	C₂	C₆₁×#3250	1	4	yes	direct product factor
462	C₂	C₂×C₆₁×#537	1	1	yes	characteristic
463	C₂	C₂²×#135×C₆₁	1	1	yes	characteristic
464	C₂	C₂×C₆₁×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₂×C₆₁×#466	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×#3250	C₂	direct (N × H)
3. C₂×C₆₁×#479	C₂	semidirect
4. C₂×C₆₁×#478	C₂	semidirect
5. C₂×C₆₁×#467	C₂	semidirect
7. C₂×C₆₁×#465	C₂	semidirect
8. C₂×C₆₁×#464	C₂	semidirect
9. C₂×C₆₁×#463	C₂	semidirect
10. C₂²×C₄⋊C₈×C₆₁	C₂	semidirect
17. C₆₁×#529	C₂²	semidirect
29. C₆₁×#479	C₂²	semidirect
30. C₆₁×#478	C₂²	semidirect
31. C₆₁×#467	C₂²	semidirect
33. C₆₁×#465	C₂²	semidirect
34. C₆₁×#464	C₂²	semidirect
35. C₆₁×#463	C₂²	semidirect
41. C₂×C₄⋊C₈×C₆₁	C₂²	semidirect
205. C₂×#3250	C₆₁	direct (N × H)
227. C₂×#529	C₂×C₆₁	semidirect
228. #3250	C₂×C₆₁	direct (N × H)
229. C₂×#479	C₂×C₆₁	semidirect
230. C₂×#478	C₂×C₆₁	semidirect
231. C₂×#467	C₂×C₆₁	semidirect
233. C₂×#465	C₂×C₆₁	semidirect
234. C₂×#464	C₂×C₆₁	semidirect
235. C₂×#463	C₂×C₆₁	semidirect
236. C₂²×C₄⋊C₈	C₂×C₆₁	semidirect
239. C₂×C₆₁	#3250	direct (N × H)
249. #529	C₂²×C₆₁	semidirect
261. #479	C₂²×C₆₁	semidirect
262. #478	C₂²×C₆₁	semidirect
263. #467	C₂²×C₆₁	semidirect
265. #465	C₂²×C₆₁	semidirect
266. #464	C₂²×C₆₁	semidirect
267. #463	C₂²×C₆₁	semidirect
273. C₂×C₄⋊C₈	C₂²×C₆₁	semidirect
278. C₆₁	C₂×#3250	direct (N × H)
461. C₂	C₆₁×#3250	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×#3250	2
C₂×C₆₁×#479	2
C₂×C₆₁×#478	2
C₂×C₆₁×#467	2
C₂×C₆₁×#466	2
C₂×C₆₁×#465	2
C₂×C₆₁×#464	2
C₂×C₆₁×#463	2
C₂²×C₄⋊C₈×C₆₁	2
C₂×#3250	61

Subgroups — C2×C61×#3250 #29564332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#3250 #29564332