Subgroups — C₂×C₆₁×#2550 #29538321

Order 15616.

2574 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×#125×C₆₁	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2550	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₆₁×#398	C₂	1	2	yes	maximal
5	C₂×C₆₁×#395	C₂	1	2	yes	maximal
6	C₂×C₆₁×#391	C₂	1	2	yes	maximal
7	C₂×C₆₁×#389	C₂	1	2	yes	maximal
8	C₂×C₆₁×#389	C₂	1	1	yes	maximal, characteristic
9	C₂×C₆₁×#389	C₂	1	1	yes	maximal, characteristic
10	C₂×C₆₁×#382	C₂	1	1	yes	maximal, characteristic
11	C₂×C₄×C₄⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×C₄⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic
13	C₂³×Q₈×C₆₁	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₆₁	—	2	8	no	—
15	C₂×C₄⋊Q₈×C₆₁	C₂²	1	8	yes	—
16	C₂×#125×C₆₁	—	2	8	no	—
17	C₂×#125×C₆₁	C₂²	1	8	yes	—
18	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
23	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
24	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
25	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
26	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
27	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₆₁	C₂²	1	2	yes	—
32	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
33	C₆₁×#398	C₂²	1	16	yes	—
34	C₆₁×#395	C₂²	1	16	yes	—
35	C₆₁×#391	C₂²	1	16	yes	—
36	C₆₁×#389	C₂²	1	16	yes	—
37	C₆₁×#389	C₂²	1	8	yes	—
38	C₆₁×#389	C₂²	1	8	yes	—
39	C₆₁×#382	C₂²	1	8	yes	—
40	C₄×C₄⋊C₄×C₆₁	C₂²	1	8	yes	—
41	C₄×C₄⋊C₄×C₆₁	C₂²	1	8	yes	—
42	C₂×#95×C₆₁	C₂²	1	1	yes	characteristic
43	C₂×#95×C₆₁	C₂²	1	1	yes	characteristic
44	C₂×#95×C₆₁	C₂²	1	2	yes	—
45	C₂×#95×C₆₁	C₂²	1	2	yes	—
46	C₂×#95×C₆₁	C₂²	1	2	yes	—
47	C₂×#95×C₆₁	C₂²	1	2	yes	—
48	C₂×#95×C₆₁	C₂²	1	2	yes	—
49	C₂²×Q₈×C₆₁	—	2	8	no	—
50	C₂²×Q₈×C₆₁	—	2	8	no	—
51	C₂²×Q₈×C₆₁	—	4	4	no	—
52	C₂²×Q₈×C₆₁	C₂³	1	8	yes	—
53	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
54	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₆₁	C₂³	1	2	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	1	yes	characteristic
60	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
61	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
64	C₄⋊Q₈×C₆₁	—	2	32	no	—
65	#125×C₆₁	—	2	32	no	—
66	C₂×C₄⋊C₄×C₆₁	—	2	8	no	—
67	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
68	C₂×C₄⋊C₄×C₆₁	—	2	8	no	—
69	C₂×C₄⋊C₄×C₆₁	—	2	8	no	—
70	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
71	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
72	C₂×C₄⋊C₄×C₆₁	—	2	8	no	—
73	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
74	C₂×C₄⋊C₄×C₆₁	—	4	4	no	—
75	C₂×C₄⋊C₄×C₆₁	D₄	1	8	yes	—
76	C₂×C₄⋊C₄×C₆₁	Q₈	1	8	yes	complemented
77	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
78	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
79	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
80	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
81	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
82	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
83	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
84	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
85	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
86	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
87	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
88	C₂×C₄²×C₆₁	—	2	4	no	—
89	C₂×C₄²×C₆₁	—	2	4	no	—
90	C₂×C₄²×C₆₁	—	4	4	no	—
91	C₂×C₄²×C₆₁	Q₈	1	8	yes	complemented
92	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
93	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
94	C₂×C₄²×C₆₁	C₂³	1	8	yes	—
95	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
96	#95×C₆₁	C₂³	1	4	yes	—
97	#95×C₆₁	C₂³	1	4	yes	—
98	#95×C₆₁	C₂³	1	8	yes	—
99	#95×C₆₁	C₂³	1	8	yes	—
100	#95×C₆₁	C₂³	1	8	yes	—
101	#95×C₆₁	C₂³	1	8	yes	—
102	#95×C₆₁	C₂³	1	8	yes	—
103	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
104	C₂×Q₈×C₆₁	—	2	16	no	—
105	C₂×Q₈×C₆₁	—	2	16	no	—
106	C₂×Q₈×C₆₁	—	4	8	no	—
107	C₂×Q₈×C₆₁	—	4	32	no	—
108	C₂²×C₄×C₆₁	—	2	2	no	—
109	C₂²×C₄×C₆₁	—	2	2	no	—
110	C₂²×C₄×C₆₁	—	2	2	no	—
111	C₂²×C₄×C₆₁	—	2	2	no	—
112	C₂²×C₄×C₆₁	—	2	4	no	—
113	C₂²×C₄×C₆₁	—	2	4	no	—
114	C₂²×C₄×C₆₁	—	2	2	no	—
115	C₂²×C₄×C₆₁	—	2	4	no	—
116	C₂²×C₄×C₆₁	—	2	4	no	—
117	C₂²×C₄×C₆₁	—	2	2	no	—
118	C₂²×C₄×C₆₁	—	2	2	no	—
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	4	no	—
123	C₂²×C₄×C₆₁	—	2	4	no	—
124	C₂²×C₄×C₆₁	—	2	2	no	—
125	C₂²×C₄×C₆₁	—	2	2	no	—
126	C₂²×C₄×C₆₁	—	2	4	no	—
127	C₂²×C₄×C₆₁	—	2	4	no	—
128	C₂²×C₄×C₆₁	—	2	2	no	—
129	C₂²×C₄×C₆₁	—	2	4	no	—
130	C₂²×C₄×C₆₁	—	2	2	no	—
131	C₂²×C₄×C₆₁	—	2	4	no	—
132	C₂²×C₄×C₆₁	C₂×D₄	1	8	yes	—
133	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
134	C₂²×C₄×C₆₁	C₂×Q₈	1	4	yes	—
135	C₂²×C₄×C₆₁	C₂×Q₈	1	4	yes	—
136	C₂²×C₄×C₆₁	C₂×Q₈	1	8	yes	—
137	C₂²×C₄×C₆₁	C₂×Q₈	1	4	yes	—
138	C₂²×C₄×C₆₁	C₂×Q₈	1	4	yes	—
139	C₂²×C₄×C₆₁	#41	1	4	yes	—
140	C₂²×C₄×C₆₁	#41	1	4	yes	—
141	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
142	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
143	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
144	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
145	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
146	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
147	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
150	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
151	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
152	C₄⋊C₄×C₆₁	—	2	16	no	—
153	C₄⋊C₄×C₆₁	—	2	16	no	—
154	C₄⋊C₄×C₆₁	—	2	8	no	—
155	C₄⋊C₄×C₆₁	—	2	16	no	—
156	C₄⋊C₄×C₆₁	—	2	8	no	—
157	C₄⋊C₄×C₆₁	—	2	8	no	—
158	C₄⋊C₄×C₆₁	—	2	16	no	—
159	C₄⋊C₄×C₆₁	—	2	8	no	—
160	C₄⋊C₄×C₆₁	—	4	8	no	—
161	C₄⋊C₄×C₆₁	C₂×D₄	1	16	yes	—
162	C₄⋊C₄×C₆₁	C₂×Q₈	1	16	yes	complemented
163	C₄²×C₆₁	—	2	8	no	—
164	C₄²×C₆₁	—	2	8	no	—
165	C₄²×C₆₁	—	4	8	no	—
166	C₄²×C₆₁	C₂×Q₈	1	16	yes	complemented
167	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
168	C₂³×C₆₁	C₂²×Q₈	1	2	yes	—
169	C₂³×C₆₁	C₂²×Q₈	1	2	yes	—
170	C₂³×C₆₁	C₂×#41	1	2	yes	—
171	C₂³×C₆₁	C₂×#41	1	2	yes	—
172	C₂³×C₆₁	H(5,𝔽₂)	1	2	yes	—
173	C₂³×C₆₁	2₋¹⁺⁴	1	2	yes	—
174	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
175	Q₈×C₆₁	—	4	32	no	—
176	C₂×C₄×C₆₁	—	2	8	no	—
177	C₂×C₄×C₆₁	—	2	8	no	—
178	C₂×C₄×C₆₁	—	2	16	no	—
179	C₂×C₄×C₆₁	—	2	8	no	—
180	C₂×C₄×C₆₁	—	2	8	no	—
181	C₂×C₄×C₆₁	—	2	16	no	—
182	C₂×C₄×C₆₁	—	2	2	no	—
183	C₂×C₄×C₆₁	—	2	2	no	—
184	C₂×C₄×C₆₁	—	2	2	no	—
185	C₂×C₄×C₆₁	—	2	2	no	—
186	C₂×C₄×C₆₁	—	2	4	no	—
187	C₂×C₄×C₆₁	—	2	4	no	—
188	C₂×C₄×C₆₁	—	2	2	no	—
189	C₂×C₄×C₆₁	—	2	4	no	—
190	C₂×C₄×C₆₁	—	2	4	no	—
191	C₂×C₄×C₆₁	—	2	2	no	—
192	C₂×C₄×C₆₁	—	2	2	no	—
193	C₂×C₄×C₆₁	—	2	2	no	—
194	C₂×C₄×C₆₁	—	2	2	no	—
195	C₂×C₄×C₆₁	—	2	2	no	—
196	C₂×C₄×C₆₁	—	2	4	no	—
197	C₂×C₄×C₆₁	—	2	4	no	—
198	C₂×C₄×C₆₁	—	2	2	no	—
199	C₂×C₄×C₆₁	—	2	2	no	—
200	C₂×C₄×C₆₁	—	2	4	no	—
201	C₂×C₄×C₆₁	—	2	4	no	—
202	C₂×C₄×C₆₁	—	2	2	no	—
203	C₂×C₄×C₆₁	—	2	4	no	—
204	C₂×C₄×C₆₁	—	2	2	no	—
205	C₂×C₄×C₆₁	—	2	4	no	—
206	C₂×C₄×C₆₁	—	4	4	no	—
207	C₂×C₄×C₆₁	—	4	8	no	—
208	C₂×C₄×C₆₁	—	4	4	no	—
209	C₂×C₄×C₆₁	—	4	8	no	—
210	C₂×C₄×C₆₁	C₄⋊Q₈	1	16	yes	—
211	C₂×C₄×C₆₁	C₂²×D₄	1	8	yes	—
212	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
213	C₂×C₄×C₆₁	C₂²×Q₈	1	4	yes	—
214	C₂×C₄×C₆₁	C₂²×Q₈	1	4	yes	—
215	C₂×C₄×C₆₁	C₂²×Q₈	1	8	yes	—
216	C₂×C₄×C₆₁	C₂²×Q₈	1	4	yes	—
217	C₂×C₄×C₆₁	C₂²×Q₈	1	4	yes	—
218	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
219	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
220	C₂×#2550	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
221	C₂²×C₆₁	C₂×C₄⋊Q₈	1	4	yes	—
222	C₂²×C₆₁	#533	1	4	yes	—
223	C₂²×C₆₁	#544	1	4	yes	—
224	C₂²×C₆₁	#546	1	4	yes	—
225	C₂²×C₆₁	#548	1	4	yes	—
226	C₂²×C₆₁	#554	1	4	yes	—
227	C₂²×C₆₁	#557	1	4	yes	—
228	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
229	C₂²×C₆₁	C₂³×Q₈	1	1	yes	characteristic
230	C₂²×C₆₁	C₂³×Q₈	1	1	yes	characteristic
231	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
232	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
233	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
234	C₂²×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
235	C₄×C₆₁	—	2	4	no	—
236	C₄×C₆₁	—	2	4	no	—
237	C₄×C₆₁	—	2	8	no	—
238	C₄×C₆₁	—	2	4	no	—
239	C₄×C₆₁	—	2	4	no	—
240	C₄×C₆₁	—	2	8	no	—
241	C₄×C₆₁	—	4	2	no	—
242	C₄×C₆₁	—	4	4	no	—
243	C₄×C₆₁	—	4	2	no	—
244	C₄×C₆₁	—	4	4	no	—
245	C₄×C₆₁	C₂×C₄⋊Q₈	1	8	yes	—
246	C₂²×C₄⋊Q₈	C₂×C₆₁	1	1	yes	characteristic
247	C₂²×#125	C₂×C₆₁	1	1	yes	characteristic
248	#2550	C₂×C₆₁	1	16	yes	direct product factor
249	C₂×#398	C₂×C₆₁	1	2	yes	—
250	C₂×#395	C₂×C₆₁	1	2	yes	—
251	C₂×#391	C₂×C₆₁	1	2	yes	—
252	C₂×#389	C₂×C₆₁	1	2	yes	—
253	C₂×#389	C₂×C₆₁	1	1	yes	characteristic
254	C₂×#389	C₂×C₆₁	1	1	yes	characteristic
255	C₂×#382	C₂×C₆₁	1	1	yes	characteristic
256	C₂×C₄×C₄⋊C₄	C₂×C₆₁	1	1	yes	characteristic
257	C₂×C₄×C₄⋊C₄	C₂×C₆₁	1	1	yes	characteristic
258	C₂×C₆₁	#2550	1	8	yes	direct product factor
259	C₂×C₆₁	C₂²×C₄⋊Q₈	1	1	yes	characteristic
260	C₂×C₆₁	C₂×#533	1	1	yes	characteristic
261	C₂×C₆₁	C₂×#544	1	1	yes	characteristic
262	C₂×C₆₁	C₂×#546	1	1	yes	characteristic
263	C₂×C₆₁	C₂×#548	1	1	yes	characteristic
264	C₂×C₆₁	C₂×#554	1	1	yes	characteristic
265	C₂×C₆₁	C₂×#557	1	1	yes	characteristic
266	C₂³×Q₈	C₂²×C₆₁	1	2	yes	—
267	C₂×C₄⋊Q₈	—	2	8	no	—
268	C₂×C₄⋊Q₈	C₂²×C₆₁	1	8	yes	—
269	C₂×#125	—	2	8	no	—
270	C₂×#125	C₂²×C₆₁	1	8	yes	—
271	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
272	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
273	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
274	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
275	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
276	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
277	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
278	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
279	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
280	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
281	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
282	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
283	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
284	C₂²×C₄²	C₂²×C₆₁	1	2	yes	—
285	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
286	#398	C₂²×C₆₁	1	16	yes	—
287	#395	C₂²×C₆₁	1	16	yes	—
288	#391	C₂²×C₆₁	1	16	yes	—
289	#389	C₂²×C₆₁	1	16	yes	—
290	#389	C₂²×C₆₁	1	8	yes	—
291	#389	C₂²×C₆₁	1	8	yes	—
292	#382	C₂²×C₆₁	1	8	yes	—
293	C₄×C₄⋊C₄	C₂²×C₆₁	1	8	yes	—
294	C₄×C₄⋊C₄	C₂²×C₆₁	1	8	yes	—
295	C₂×#95	C₂²×C₆₁	1	2	yes	—
296	C₂×#95	C₂²×C₆₁	1	2	yes	—
297	C₂×#95	C₂²×C₆₁	1	2	yes	—
298	C₂×#95	C₂²×C₆₁	1	2	yes	—
299	C₂×#95	C₂²×C₆₁	1	1	yes	characteristic
300	C₂×#95	C₂²×C₆₁	1	1	yes	characteristic
301	C₂×#95	C₂²×C₆₁	1	2	yes	—
302	C₆₁	C₂×#2550	1	1	yes	characteristic, direct product factor, Sylow
303	C₂²×Q₈	—	2	8	no	—
304	C₂²×Q₈	—	2	8	no	—
305	C₂²×Q₈	—	4	4	no	—
306	C₂²×Q₈	C₂³×C₆₁	1	8	yes	—
307	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
308	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
309	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
310	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
311	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
312	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
313	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
314	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
315	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
316	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
317	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
318	C₄⋊Q₈	—	2	32	no	—
319	#125	—	2	32	no	—
320	C₂×C₄⋊C₄	—	2	8	no	—
321	C₂×C₄⋊C₄	—	2	8	no	—
322	C₂×C₄⋊C₄	—	2	4	no	—
323	C₂×C₄⋊C₄	—	2	8	no	—
324	C₂×C₄⋊C₄	—	2	4	no	—
325	C₂×C₄⋊C₄	—	2	4	no	—
326	C₂×C₄⋊C₄	—	2	8	no	—
327	C₂×C₄⋊C₄	—	2	4	no	—
328	C₂×C₄⋊C₄	—	4	4	no	—
329	C₂×C₄⋊C₄	D₄×C₆₁	1	8	yes	—
330	C₂×C₄⋊C₄	Q₈×C₆₁	1	8	yes	complemented
331	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
332	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
333	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
334	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
335	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
336	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
337	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
338	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
339	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
340	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
341	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
342	C₂×C₄²	—	2	4	no	—
343	C₂×C₄²	—	2	4	no	—
344	C₂×C₄²	—	4	4	no	—
345	C₂×C₄²	Q₈×C₆₁	1	8	yes	complemented
346	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
347	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
348	C₂×C₄²	C₂³×C₆₁	1	8	yes	—
349	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
350	#95	C₂³×C₆₁	1	4	yes	—
351	#95	C₂³×C₆₁	1	4	yes	—
352	#95	C₂³×C₆₁	1	8	yes	—
353	#95	C₂³×C₆₁	1	8	yes	—
354	#95	C₂³×C₆₁	1	8	yes	—
355	#95	C₂³×C₆₁	1	8	yes	—
356	#95	C₂³×C₆₁	1	8	yes	—
357	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
358	C₂×Q₈	—	2	16	no	—
359	C₂×Q₈	—	2	16	no	—
360	C₂×Q₈	—	4	8	no	—
361	C₂×Q₈	—	4	32	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	4	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	C₂×D₄×C₆₁	1	8	yes	—
387	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
388	C₂²×C₄	C₂×Q₈×C₆₁	1	4	yes	—
389	C₂²×C₄	C₂×Q₈×C₆₁	1	4	yes	—
390	C₂²×C₄	C₂×Q₈×C₆₁	1	8	yes	—
391	C₂²×C₄	C₂×Q₈×C₆₁	1	4	yes	—
392	C₂²×C₄	C₂×Q₈×C₆₁	1	4	yes	—
393	C₂²×C₄	#41×C₆₁	1	4	yes	—
394	C₂²×C₄	#41×C₆₁	1	4	yes	—
395	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
396	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
397	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
398	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
399	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
400	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
401	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
402	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
403	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
404	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
405	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
406	C₄⋊C₄	—	2	16	no	—
407	C₄⋊C₄	—	2	16	no	—
408	C₄⋊C₄	—	2	8	no	—
409	C₄⋊C₄	—	2	16	no	—
410	C₄⋊C₄	—	2	8	no	—
411	C₄⋊C₄	—	2	8	no	—
412	C₄⋊C₄	—	2	16	no	—
413	C₄⋊C₄	—	2	8	no	—
414	C₄⋊C₄	—	4	8	no	—
415	C₄⋊C₄	C₂×D₄×C₆₁	1	16	yes	—
416	C₄⋊C₄	C₂×Q₈×C₆₁	1	16	yes	complemented
417	C₄²	—	2	8	no	—
418	C₄²	—	2	8	no	—
419	C₄²	—	4	8	no	—
420	C₄²	C₂×Q₈×C₆₁	1	16	yes	complemented
421	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
422	C₂³	C₂²×Q₈×C₆₁	1	2	yes	—
423	C₂³	C₂²×Q₈×C₆₁	1	2	yes	—
424	C₂³	C₂×#41×C₆₁	1	2	yes	—
425	C₂³	C₂×#41×C₆₁	1	2	yes	—
426	C₂³	H(5,𝔽₂)×C₆₁	1	2	yes	—
427	C₂³	2₋¹⁺⁴×C₆₁	1	2	yes	—
428	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
429	Q₈	—	4	32	no	—
430	C₂×C₄	—	2	8	no	—
431	C₂×C₄	—	2	8	no	—
432	C₂×C₄	—	2	16	no	—
433	C₂×C₄	—	2	8	no	—
434	C₂×C₄	—	2	8	no	—
435	C₂×C₄	—	2	16	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	4	4	no	—
461	C₂×C₄	—	4	8	no	—
462	C₂×C₄	—	4	4	no	—
463	C₂×C₄	—	4	8	no	—
464	C₂×C₄	C₄⋊Q₈×C₆₁	1	16	yes	—
465	C₂×C₄	C₂²×D₄×C₆₁	1	8	yes	—
466	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
467	C₂×C₄	C₂²×Q₈×C₆₁	1	4	yes	—
468	C₂×C₄	C₂²×Q₈×C₆₁	1	4	yes	—
469	C₂×C₄	C₂²×Q₈×C₆₁	1	8	yes	—
470	C₂×C₄	C₂²×Q₈×C₆₁	1	4	yes	—
471	C₂×C₄	C₂²×Q₈×C₆₁	1	4	yes	—
472	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
473	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
474	C₂²	C₂×C₄⋊Q₈×C₆₁	1	4	yes	—
475	C₂²	C₆₁×#533	1	4	yes	—
476	C₂²	C₆₁×#544	1	4	yes	—
477	C₂²	C₆₁×#546	1	4	yes	—
478	C₂²	C₆₁×#548	1	4	yes	—
479	C₂²	C₆₁×#554	1	4	yes	—
480	C₂²	C₆₁×#557	1	4	yes	—
481	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
482	C₂²	C₂³×Q₈×C₆₁	1	1	yes	characteristic
483	C₂²	C₂³×Q₈×C₆₁	1	1	yes	characteristic
484	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
485	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
486	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
487	C₂²	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
488	C₄	—	2	4	no	—
489	C₄	—	2	4	no	—
490	C₄	—	2	8	no	—
491	C₄	—	2	4	no	—
492	C₄	—	2	4	no	—
493	C₄	—	2	8	no	—
494	C₄	—	4	2	no	—
495	C₄	—	4	4	no	—
496	C₄	—	4	2	no	—
497	C₄	—	4	4	no	—
498	C₄	C₂×C₄⋊Q₈×C₆₁	1	8	yes	—
499	C₂	C₆₁×#2550	1	8	yes	direct product factor
500	C₂	C₂²×C₄⋊Q₈×C₆₁	1	1	yes	characteristic
501	C₂	C₂×C₆₁×#533	1	1	yes	characteristic
502	C₂	C₂×C₆₁×#544	1	1	yes	characteristic
503	C₂	C₂×C₆₁×#546	1	1	yes	characteristic
504	C₂	C₂×C₆₁×#548	1	1	yes	characteristic
505	C₂	C₂×C₆₁×#554	1	1	yes	characteristic
506	C₂	C₂×C₆₁×#557	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₆₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₁
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
3. C₆₁×#2550	C₂	direct (N × H)
76. C₂×C₄⋊C₄×C₆₁	Q₈	semidirect
91. C₂×C₄²×C₆₁	Q₈	semidirect
162. C₄⋊C₄×C₆₁	C₂×Q₈	semidirect
166. C₄²×C₆₁	C₂×Q₈	semidirect
220. C₂×#2550	C₆₁	direct (N × H)
248. #2550	C₂×C₆₁	direct (N × H)
258. C₂×C₆₁	#2550	direct (N × H)
302. C₆₁	C₂×#2550	direct (N × H)
330. C₂×C₄⋊C₄	Q₈×C₆₁	semidirect
345. C₂×C₄²	Q₈×C₆₁	semidirect
416. C₄⋊C₄	C₂×Q₈×C₆₁	semidirect
420. C₄²	C₂×Q₈×C₆₁	semidirect
499. C₂	C₆₁×#2550	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×C₄⋊Q₈×C₆₁	2
C₂²×#125×C₆₁	2
C₆₁×#2550	2
C₂×C₆₁×#398	2
C₂×C₆₁×#395	2
C₂×C₆₁×#391	2
C₂×C₆₁×#389	2
C₂×C₆₁×#382	2
C₂×C₄×C₄⋊C₄×C₆₁	2
C₂×#2550	61

Subgroups — C2×C61×#2550 #29538321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#2550 #29538321