Subgroups — C₂×C₆₁×#2409 #29538115

Order 15616.

5566 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	C₂⁴×Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂²⋊Q₈×C₆₁	C₂	1	2	yes	maximal, complemented
3	C₂²×C₄×D₄×C₆₁	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2409	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₆₁×#395	C₂	1	2	yes	maximal, complemented
6	C₂×C₆₁×#393	C₂	1	2	yes	maximal, complemented
7	C₂×C₆₁×#391	C₂	1	2	yes	maximal, complemented
8	C₂×C₆₁×#386	C₂	1	2	yes	maximal
9	C₂×C₆₁×#385	C₂	1	2	yes	maximal, complemented
10	C₂×C₆₁×#380	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×Q₈×C₆₁	—	2	16	no	—
12	C₂³×Q₈×C₆₁	—	2	8	no	—
13	C₂³×Q₈×C₆₁	C₂²	1	2	yes	—
14	C₂³×Q₈×C₆₁	C₂²	1	2	yes	—
15	C₂³×Q₈×C₆₁	C₂²	1	8	yes	complemented
16	C₂³×D₄×C₆₁	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₆₁	C₂²	1	2	yes	—
18	C₂⁴×C₄×C₆₁	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊Q₈×C₆₁	—	2	16	no	—
21	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	16	yes	complemented
22	C₂×C₄×D₄×C₆₁	—	2	8	no	—
23	C₂×C₄×D₄×C₆₁	C₂²	1	8	yes	—
24	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
25	C₂²×C₄⋊C₄×C₆₁	C₂²	1	4	yes	—
26	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
27	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
28	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	4	yes	—
30	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
32	C₆₁×#395	C₂²	1	16	yes	complemented
33	C₆₁×#393	C₂²	1	16	yes	complemented
34	C₆₁×#391	C₂²	1	16	yes	complemented
35	C₆₁×#386	C₂²	1	16	yes	—
36	C₆₁×#385	C₂²	1	16	yes	complemented
37	C₆₁×#380	C₂²	1	8	yes	complemented
38	C₂×#95×C₆₁	C₂²	1	2	yes	—
39	C₂×#95×C₆₁	C₂²	1	4	yes	—
40	C₂×#95×C₆₁	C₂²	1	4	yes	—
41	C₂⁵×C₆₁	C₂³	1	1	yes	characteristic
42	C₂⁵×C₆₁	C₂³	1	1	yes	characteristic
43	C₂²×Q₈×C₆₁	—	2	128	no	—
44	C₂²×Q₈×C₆₁	—	2	64	no	—
45	C₂²×Q₈×C₆₁	—	2	16	no	—
46	C₂²×Q₈×C₆₁	—	2	8	no	—
47	C₂²×Q₈×C₆₁	—	2	8	no	—
48	C₂²×Q₈×C₆₁	—	2	8	no	—
49	C₂²×Q₈×C₆₁	—	2	32	no	—
50	C₂²×Q₈×C₆₁	D₄	1	16	yes	complemented
51	C₂²×Q₈×C₆₁	C₂³	1	8	yes	—
52	C₂²×Q₈×C₆₁	C₂³	1	8	yes	—
53	C₂²×D₄×C₆₁	—	2	4	no	—
54	C₂²×D₄×C₆₁	—	2	4	no	—
55	C₂²×D₄×C₆₁	Q₈	1	8	yes	complemented
56	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
57	C₂³×C₄×C₆₁	—	2	8	no	—
58	C₂³×C₄×C₆₁	—	2	16	no	—
59	C₂³×C₄×C₆₁	—	2	8	no	—
60	C₂³×C₄×C₆₁	—	2	4	no	—
61	C₂³×C₄×C₆₁	—	2	8	no	—
62	C₂³×C₄×C₆₁	D₄	1	8	yes	—
63	C₂³×C₄×C₆₁	C₂³	1	8	yes	—
64	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
65	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
68	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
69	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
70	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
73	C₂²⋊Q₈×C₆₁	—	2	64	no	—
74	C₄×D₄×C₆₁	—	2	32	no	—
75	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
76	C₂×C₄⋊C₄×C₆₁	—	2	8	no	—
77	C₂×C₄⋊C₄×C₆₁	—	2	16	no	—
78	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
79	C₂×C₄⋊C₄×C₆₁	C₂³	1	16	yes	—
80	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
81	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
82	C₂×C₂²⋊C₄×C₆₁	—	2	8	no	—
83	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
84	C₂×C₂²⋊C₄×C₆₁	—	2	16	no	—
85	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
86	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
87	C₂×C₂²⋊C₄×C₆₁	C₂³	1	16	yes	—
88	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
89	C₂×C₄²×C₆₁	—	2	4	no	—
90	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
91	#95×C₆₁	C₂³	1	8	yes	—
92	#95×C₆₁	C₂³	1	16	yes	—
93	#95×C₆₁	C₂³	1	16	yes	—
94	C₂⁴×C₆₁	—	2	4	no	—
95	C₂⁴×C₆₁	—	2	4	no	—
96	C₂⁴×C₆₁	—	2	4	no	—
97	C₂⁴×C₆₁	—	2	2	no	—
98	C₂⁴×C₆₁	—	2	2	no	—
99	C₂⁴×C₆₁	—	2	4	no	—
100	C₂⁴×C₆₁	C₂×D₄	1	4	yes	—
101	C₂⁴×C₆₁	C₂×Q₈	1	4	yes	—
102	C₂⁴×C₆₁	C₂×Q₈	1	4	yes	complemented
103	C₂⁴×C₆₁	#41	1	4	yes	—
104	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
105	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
106	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
107	C₂×Q₈×C₆₁	—	2	256	no	—
108	C₂×Q₈×C₆₁	—	2	64	no	—
109	C₂×Q₈×C₆₁	—	2	64	no	—
110	C₂×Q₈×C₆₁	—	2	32	no	—
111	C₂×Q₈×C₆₁	—	2	16	no	—
112	C₂×Q₈×C₆₁	—	2	16	no	—
113	C₂×Q₈×C₆₁	—	2	16	no	—
114	C₂×Q₈×C₆₁	C₂×D₄	1	32	yes	complemented
115	C₂×D₄×C₆₁	—	2	32	no	—
116	C₂×D₄×C₆₁	—	2	8	no	—
117	C₂×D₄×C₆₁	—	2	8	no	—
118	C₂×D₄×C₆₁	C₂×Q₈	1	16	yes	complemented
119	C₂²×C₄×C₆₁	—	2	64	no	—
120	C₂²×C₄×C₆₁	—	2	2	no	—
121	C₂²×C₄×C₆₁	—	2	16	no	—
122	C₂²×C₄×C₆₁	—	2	8	no	—
123	C₂²×C₄×C₆₁	—	2	8	no	—
124	C₂²×C₄×C₆₁	—	2	4	no	—
125	C₂²×C₄×C₆₁	—	2	2	no	—
126	C₂²×C₄×C₆₁	—	2	32	no	—
127	C₂²×C₄×C₆₁	—	2	32	no	—
128	C₂²×C₄×C₆₁	—	2	16	no	—
129	C₂²×C₄×C₆₁	—	2	2	no	—
130	C₂²×C₄×C₆₁	—	2	8	no	—
131	C₂²×C₄×C₆₁	—	2	2	no	—
132	C₂²×C₄×C₆₁	—	2	4	no	—
133	C₂²×C₄×C₆₁	—	2	8	no	—
134	C₂²×C₄×C₆₁	—	2	4	no	—
135	C₂²×C₄×C₆₁	—	2	8	no	—
136	C₂²×C₄×C₆₁	—	2	8	no	—
137	C₂²×C₄×C₆₁	—	2	16	no	—
138	C₂²×C₄×C₆₁	—	4	16	no	—
139	C₂²×C₄×C₆₁	C₂×D₄	1	16	yes	—
140	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₆₁	C₂×D₄	1	16	yes	—
142	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
143	C₂²×C₄×C₆₁	C₂×D₄	1	8	yes	—
144	C₂²×C₄×C₆₁	C₂×Q₈	1	4	yes	complemented
145	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
146	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
147	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₆₁	C₂⁴	1	8	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	8	no	—
153	C₄⋊C₄×C₆₁	—	2	16	no	—
154	C₄⋊C₄×C₆₁	—	2	32	no	—
155	C₂²⋊C₄×C₆₁	—	2	8	no	—
156	C₂²⋊C₄×C₆₁	—	2	16	no	—
157	C₂²⋊C₄×C₆₁	—	2	8	no	—
158	C₂²⋊C₄×C₆₁	—	2	32	no	—
159	C₄²×C₆₁	—	2	8	no	—
160	C₂³×C₆₁	—	2	8	no	—
161	C₂³×C₆₁	—	2	8	no	—
162	C₂³×C₆₁	—	2	16	no	—
163	C₂³×C₆₁	—	2	16	no	—
164	C₂³×C₆₁	—	2	4	no	—
165	C₂³×C₆₁	—	2	4	no	—
166	C₂³×C₆₁	—	2	8	no	—
167	C₂³×C₆₁	—	2	16	no	—
168	C₂³×C₆₁	—	2	4	no	—
169	C₂³×C₆₁	—	2	2	no	—
170	C₂³×C₆₁	—	2	2	no	—
171	C₂³×C₆₁	—	2	4	no	—
172	C₂³×C₆₁	—	4	4	no	—
173	C₂³×C₆₁	—	4	4	no	—
174	C₂³×C₆₁	—	4	8	no	—
175	C₂³×C₆₁	C₂²⋊Q₈	1	16	yes	complemented
176	C₂³×C₆₁	C₂²×D₄	1	4	yes	—
177	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
178	C₂³×C₆₁	C₂²×D₄	1	4	yes	—
179	C₂³×C₆₁	C₂²×Q₈	1	4	yes	—
180	C₂³×C₆₁	C₂²×Q₈	1	2	yes	—
181	C₂³×C₆₁	C₂²×Q₈	1	4	yes	complemented
182	C₂³×C₆₁	C₂×#41	1	4	yes	—
183	C₂³×C₆₁	C₂×#41	1	2	yes	—
184	C₂³×C₆₁	2₋¹⁺⁴	1	4	yes	—
185	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
186	Q₈×C₆₁	—	2	64	no	—
187	Q₈×C₆₁	—	2	64	no	—
188	D₄×C₆₁	—	2	32	no	—
189	C₂×C₄×C₆₁	—	2	64	no	—
190	C₂×C₄×C₆₁	—	2	32	no	—
191	C₂×C₄×C₆₁	—	2	8	no	—
192	C₂×C₄×C₆₁	—	2	8	no	—
193	C₂×C₄×C₆₁	—	2	2	no	—
194	C₂×C₄×C₆₁	—	2	8	no	—
195	C₂×C₄×C₆₁	—	2	8	no	—
196	C₂×C₄×C₆₁	—	2	4	no	—
197	C₂×C₄×C₆₁	—	2	2	no	—
198	C₂×C₄×C₆₁	—	2	32	no	—
199	C₂×C₄×C₆₁	—	2	2	no	—
200	C₂×C₄×C₆₁	—	2	8	no	—
201	C₂×C₄×C₆₁	—	2	2	no	—
202	C₂×C₄×C₆₁	—	2	4	no	—
203	C₂×C₄×C₆₁	—	2	8	no	—
204	C₂×C₄×C₆₁	—	2	4	no	—
205	C₂×C₄×C₆₁	—	2	8	no	—
206	C₂×C₄×C₆₁	—	4	4	no	—
207	C₂×C₄×C₆₁	—	4	4	no	—
208	C₂×C₄×C₆₁	—	4	16	no	—
209	C₂×C₄×C₆₁	—	4	16	no	—
210	C₂×C₄×C₆₁	#120	1	16	yes	—
211	C₂×C₄×C₆₁	C₂²×D₄	1	16	yes	—
212	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
213	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
214	C₂×C₄×C₆₁	C₂²×D₄	1	8	yes	—
215	C₂×C₄×C₆₁	C₂²×Q₈	1	4	yes	complemented
216	C₂×#2409	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
217	C₂²×C₆₁	—	2	4	no	—
218	C₂²×C₆₁	—	2	32	no	—
219	C₂²×C₆₁	—	2	4	no	—
220	C₂²×C₆₁	—	2	8	no	—
221	C₂²×C₆₁	—	2	8	no	—
222	C₂²×C₆₁	—	2	4	no	—
223	C₂²×C₆₁	—	2	8	no	—
224	C₂²×C₆₁	—	4	2	no	—
225	C₂²×C₆₁	—	4	16	no	—
226	C₂²×C₆₁	—	4	2	no	—
227	C₂²×C₆₁	—	4	4	no	—
228	C₂²×C₆₁	C₂×#120	1	4	yes	—
229	C₂²×C₆₁	C₂×C₂²⋊Q₈	1	4	yes	—
230	C₂²×C₆₁	C₂×C₂²⋊Q₈	1	8	yes	complemented
231	C₂²×C₆₁	#536	1	4	yes	—
232	C₂²×C₆₁	#548	1	8	yes	—
233	C₂²×C₆₁	D₄×Q₈	1	8	yes	—
234	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
235	C₂²×C₆₁	C₂³×D₄	1	2	yes	—
236	C₂²×C₆₁	C₂³×Q₈	1	1	yes	characteristic
237	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
238	C₂²×C₆₁	C₂×2₋¹⁺⁴	1	2	yes	—
239	C₄×C₆₁	—	2	16	no	—
240	C₄×C₆₁	—	2	4	no	—
241	C₄×C₆₁	—	2	4	no	—
242	C₄×C₆₁	—	4	2	no	—
243	C₄×C₆₁	—	4	2	no	—
244	C₄×C₆₁	—	4	8	no	—
245	C₄×C₆₁	C₂×#120	1	8	yes	—
246	C₂⁴×Q₈	C₂×C₆₁	1	1	yes	characteristic, complemented
247	C₂²×C₂²⋊Q₈	C₂×C₆₁	1	2	yes	complemented
248	C₂²×C₄×D₄	C₂×C₆₁	1	1	yes	characteristic
249	#2409	C₂×C₆₁	1	16	yes	direct product factor
250	C₂×#395	C₂×C₆₁	1	2	yes	complemented
251	C₂×#393	C₂×C₆₁	1	2	yes	complemented
252	C₂×#391	C₂×C₆₁	1	2	yes	complemented
253	C₂×#386	C₂×C₆₁	1	2	yes	—
254	C₂×#385	C₂×C₆₁	1	2	yes	complemented
255	C₂×#380	C₂×C₆₁	1	1	yes	characteristic, complemented
256	C₂×C₆₁	—	2	8	no	—
257	C₂×C₆₁	—	4	4	no	—
258	C₂×C₆₁	#2409	1	8	yes	direct product factor
259	C₂×C₆₁	C₂²×#120	1	1	yes	characteristic
260	C₂×C₆₁	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
261	C₂×C₆₁	C₂×#536	1	1	yes	characteristic
262	C₂×C₆₁	C₂×#548	1	2	yes	—
263	C₂×C₆₁	C₂×D₄×Q₈	1	2	yes	—
264	C₂³×Q₈	—	2	16	no	—
265	C₂³×Q₈	—	2	8	no	—
266	C₂³×Q₈	C₂²×C₆₁	1	2	yes	—
267	C₂³×Q₈	C₂²×C₆₁	1	2	yes	—
268	C₂³×Q₈	C₂²×C₆₁	1	8	yes	complemented
269	C₂³×D₄	C₂²×C₆₁	1	1	yes	characteristic
270	C₂⁴×C₄	C₂²×C₆₁	1	2	yes	—
271	C₂⁴×C₄	C₂²×C₆₁	1	1	yes	characteristic
272	C₂⁴×C₄	C₂²×C₆₁	1	1	yes	characteristic
273	C₂×C₂²⋊Q₈	—	2	16	no	—
274	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	16	yes	complemented
275	C₂×C₄×D₄	—	2	8	no	—
276	C₂×C₄×D₄	C₂²×C₆₁	1	8	yes	—
277	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
278	C₂²×C₄⋊C₄	C₂²×C₆₁	1	4	yes	—
279	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
280	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
281	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	4	yes	—
282	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
283	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
284	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
285	#395	C₂²×C₆₁	1	16	yes	complemented
286	#393	C₂²×C₆₁	1	16	yes	complemented
287	#391	C₂²×C₆₁	1	16	yes	complemented
288	#386	C₂²×C₆₁	1	16	yes	—
289	#385	C₂²×C₆₁	1	16	yes	complemented
290	#380	C₂²×C₆₁	1	8	yes	complemented
291	C₂×#95	C₂²×C₆₁	1	2	yes	—
292	C₂×#95	C₂²×C₆₁	1	4	yes	—
293	C₂×#95	C₂²×C₆₁	1	4	yes	—
294	C₆₁	C₂×#2409	1	1	yes	characteristic, direct product factor, Sylow
295	C₂⁵	C₂³×C₆₁	1	1	yes	characteristic
296	C₂⁵	C₂³×C₆₁	1	1	yes	characteristic
297	C₂²×Q₈	—	2	128	no	—
298	C₂²×Q₈	—	2	64	no	—
299	C₂²×Q₈	—	2	16	no	—
300	C₂²×Q₈	—	2	8	no	—
301	C₂²×Q₈	—	2	8	no	—
302	C₂²×Q₈	—	2	8	no	—
303	C₂²×Q₈	—	2	32	no	—
304	C₂²×Q₈	D₄×C₆₁	1	16	yes	complemented
305	C₂²×Q₈	C₂³×C₆₁	1	8	yes	—
306	C₂²×Q₈	C₂³×C₆₁	1	8	yes	—
307	C₂²×D₄	—	2	4	no	—
308	C₂²×D₄	—	2	4	no	—
309	C₂²×D₄	Q₈×C₆₁	1	8	yes	complemented
310	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
311	C₂³×C₄	—	2	8	no	—
312	C₂³×C₄	—	2	16	no	—
313	C₂³×C₄	—	2	8	no	—
314	C₂³×C₄	—	2	4	no	—
315	C₂³×C₄	—	2	8	no	—
316	C₂³×C₄	D₄×C₆₁	1	8	yes	—
317	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
318	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
319	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
320	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
321	C₂³×C₄	C₂³×C₆₁	1	8	yes	—
322	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
323	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
324	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
325	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
326	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
327	C₂²⋊Q₈	—	2	64	no	—
328	C₄×D₄	—	2	32	no	—
329	C₂×C₄⋊C₄	—	2	4	no	—
330	C₂×C₄⋊C₄	—	2	8	no	—
331	C₂×C₄⋊C₄	—	2	16	no	—
332	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
333	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
334	C₂×C₄⋊C₄	C₂³×C₆₁	1	16	yes	—
335	C₂×C₂²⋊C₄	—	2	4	no	—
336	C₂×C₂²⋊C₄	—	2	8	no	—
337	C₂×C₂²⋊C₄	—	2	4	no	—
338	C₂×C₂²⋊C₄	—	2	16	no	—
339	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
340	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
341	C₂×C₂²⋊C₄	C₂³×C₆₁	1	16	yes	—
342	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
343	C₂×C₄²	—	2	4	no	—
344	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
345	#95	C₂³×C₆₁	1	8	yes	—
346	#95	C₂³×C₆₁	1	16	yes	—
347	#95	C₂³×C₆₁	1	16	yes	—
348	C₂⁴	—	2	4	no	—
349	C₂⁴	—	2	4	no	—
350	C₂⁴	—	2	4	no	—
351	C₂⁴	—	2	2	no	—
352	C₂⁴	—	2	2	no	—
353	C₂⁴	—	2	4	no	—
354	C₂⁴	C₂×D₄×C₆₁	1	4	yes	—
355	C₂⁴	C₂×Q₈×C₆₁	1	4	yes	—
356	C₂⁴	C₂×Q₈×C₆₁	1	4	yes	complemented
357	C₂⁴	#41×C₆₁	1	4	yes	—
358	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
359	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
360	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
361	C₂×Q₈	—	2	256	no	—
362	C₂×Q₈	—	2	64	no	—
363	C₂×Q₈	—	2	64	no	—
364	C₂×Q₈	—	2	32	no	—
365	C₂×Q₈	—	2	16	no	—
366	C₂×Q₈	—	2	16	no	—
367	C₂×Q₈	—	2	16	no	—
368	C₂×Q₈	C₂×D₄×C₆₁	1	32	yes	complemented
369	C₂×D₄	—	2	32	no	—
370	C₂×D₄	—	2	8	no	—
371	C₂×D₄	—	2	8	no	—
372	C₂×D₄	C₂×Q₈×C₆₁	1	16	yes	complemented
373	C₂²×C₄	—	2	64	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	16	no	—
376	C₂²×C₄	—	2	8	no	—
377	C₂²×C₄	—	2	8	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	32	no	—
381	C₂²×C₄	—	2	32	no	—
382	C₂²×C₄	—	2	16	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	8	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	2	8	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	8	no	—
390	C₂²×C₄	—	2	8	no	—
391	C₂²×C₄	—	2	16	no	—
392	C₂²×C₄	—	4	16	no	—
393	C₂²×C₄	C₂×D₄×C₆₁	1	16	yes	—
394	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
395	C₂²×C₄	C₂×D₄×C₆₁	1	16	yes	—
396	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
397	C₂²×C₄	C₂×D₄×C₆₁	1	8	yes	—
398	C₂²×C₄	C₂×Q₈×C₆₁	1	4	yes	complemented
399	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
400	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
401	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
402	C₂²×C₄	C₂⁴×C₆₁	1	8	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	8	no	—
407	C₄⋊C₄	—	2	16	no	—
408	C₄⋊C₄	—	2	32	no	—
409	C₂²⋊C₄	—	2	8	no	—
410	C₂²⋊C₄	—	2	16	no	—
411	C₂²⋊C₄	—	2	8	no	—
412	C₂²⋊C₄	—	2	32	no	—
413	C₄²	—	2	8	no	—
414	C₂³	—	2	8	no	—
415	C₂³	—	2	16	no	—
416	C₂³	—	2	16	no	—
417	C₂³	—	2	4	no	—
418	C₂³	—	2	4	no	—
419	C₂³	—	2	8	no	—
420	C₂³	—	2	16	no	—
421	C₂³	—	2	4	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	4	no	—
425	C₂³	—	2	8	no	—
426	C₂³	—	4	4	no	—
427	C₂³	—	4	8	no	—
428	C₂³	—	4	4	no	—
429	C₂³	C₂²⋊Q₈×C₆₁	1	16	yes	complemented
430	C₂³	C₂²×D₄×C₆₁	1	4	yes	—
431	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
432	C₂³	C₂²×D₄×C₆₁	1	4	yes	—
433	C₂³	C₂²×Q₈×C₆₁	1	4	yes	—
434	C₂³	C₂²×Q₈×C₆₁	1	2	yes	—
435	C₂³	C₂²×Q₈×C₆₁	1	4	yes	complemented
436	C₂³	C₂×#41×C₆₁	1	4	yes	—
437	C₂³	C₂×#41×C₆₁	1	2	yes	—
438	C₂³	2₋¹⁺⁴×C₆₁	1	4	yes	—
439	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
440	Q₈	—	2	64	no	—
441	Q₈	—	2	64	no	—
442	D₄	—	2	32	no	—
443	C₂×C₄	—	2	64	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	8	no	—
446	C₂×C₄	—	2	8	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	32	no	—
450	C₂×C₄	—	2	8	no	—
451	C₂×C₄	—	2	8	no	—
452	C₂×C₄	—	2	32	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	8	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	8	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	8	no	—
460	C₂×C₄	—	4	4	no	—
461	C₂×C₄	—	4	16	no	—
462	C₂×C₄	—	4	4	no	—
463	C₂×C₄	—	4	16	no	—
464	C₂×C₄	#120×C₆₁	1	16	yes	—
465	C₂×C₄	C₂²×D₄×C₆₁	1	16	yes	—
466	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
467	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
468	C₂×C₄	C₂²×D₄×C₆₁	1	8	yes	—
469	C₂×C₄	C₂²×Q₈×C₆₁	1	4	yes	complemented
470	C₂²	—	2	4	no	—
471	C₂²	—	2	32	no	—
472	C₂²	—	2	4	no	—
473	C₂²	—	2	8	no	—
474	C₂²	—	2	8	no	—
475	C₂²	—	2	4	no	—
476	C₂²	—	2	8	no	—
477	C₂²	—	4	2	no	—
478	C₂²	—	4	16	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	4	4	no	—
481	C₂²	C₂×#120×C₆₁	1	4	yes	—
482	C₂²	C₂×C₂²⋊Q₈×C₆₁	1	4	yes	—
483	C₂²	C₂×C₂²⋊Q₈×C₆₁	1	8	yes	complemented
484	C₂²	C₆₁×#536	1	4	yes	—
485	C₂²	C₆₁×#548	1	8	yes	—
486	C₂²	D₄×Q₈×C₆₁	1	8	yes	—
487	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
488	C₂²	C₂³×D₄×C₆₁	1	2	yes	—
489	C₂²	C₂³×Q₈×C₆₁	1	1	yes	characteristic
490	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
491	C₂²	C₂×2₋¹⁺⁴×C₆₁	1	2	yes	—
492	C₄	—	2	16	no	—
493	C₄	—	2	4	no	—
494	C₄	—	2	4	no	—
495	C₄	—	4	2	no	—
496	C₄	—	4	2	no	—
497	C₄	—	4	8	no	—
498	C₄	C₂×#120×C₆₁	1	8	yes	—
499	C₂	—	2	8	no	—
500	C₂	—	4	4	no	—
501	C₂	C₆₁×#2409	1	8	yes	direct product factor
502	C₂	C₂²×#120×C₆₁	1	1	yes	characteristic
503	C₂	C₂²×C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
504	C₂	C₂×C₆₁×#536	1	1	yes	characteristic
505	C₂	C₂×C₆₁×#548	1	2	yes	—
506	C₂	C₂×D₄×Q₈×C₆₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₆₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₁
prime radical	C₂³×D₄×C₆₁	C₂²
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. C₂⁴×Q₈×C₆₁	C₂	semidirect
2. C₂²×C₂²⋊Q₈×C₆₁	C₂	semidirect
4. C₆₁×#2409	C₂	direct (N × H)
5. C₂×C₆₁×#395	C₂	semidirect
6. C₂×C₆₁×#393	C₂	semidirect
7. C₂×C₆₁×#391	C₂	semidirect
9. C₂×C₆₁×#385	C₂	semidirect
10. C₂×C₆₁×#380	C₂	semidirect
15. C₂³×Q₈×C₆₁	C₂²	semidirect
21. C₂×C₂²⋊Q₈×C₆₁	C₂²	semidirect
32. C₆₁×#395	C₂²	semidirect
33. C₆₁×#393	C₂²	semidirect
34. C₆₁×#391	C₂²	semidirect
36. C₆₁×#385	C₂²	semidirect
37. C₆₁×#380	C₂²	semidirect
50. C₂²×Q₈×C₆₁	D₄	semidirect
55. C₂²×D₄×C₆₁	Q₈	semidirect
102. C₂⁴×C₆₁	C₂×Q₈	semidirect
114. C₂×Q₈×C₆₁	C₂×D₄	semidirect
118. C₂×D₄×C₆₁	C₂×Q₈	semidirect
144. C₂²×C₄×C₆₁	C₂×Q₈	semidirect
175. C₂³×C₆₁	C₂²⋊Q₈	semidirect
181. C₂³×C₆₁	C₂²×Q₈	semidirect
215. C₂×C₄×C₆₁	C₂²×Q₈	semidirect
216. C₂×#2409	C₆₁	direct (N × H)
230. C₂²×C₆₁	C₂×C₂²⋊Q₈	semidirect
246. C₂⁴×Q₈	C₂×C₆₁	semidirect
247. C₂²×C₂²⋊Q₈	C₂×C₆₁	semidirect
249. #2409	C₂×C₆₁	direct (N × H)
250. C₂×#395	C₂×C₆₁	semidirect
251. C₂×#393	C₂×C₆₁	semidirect
252. C₂×#391	C₂×C₆₁	semidirect
254. C₂×#385	C₂×C₆₁	semidirect
255. C₂×#380	C₂×C₆₁	semidirect
258. C₂×C₆₁	#2409	direct (N × H)
268. C₂³×Q₈	C₂²×C₆₁	semidirect
274. C₂×C₂²⋊Q₈	C₂²×C₆₁	semidirect
285. #395	C₂²×C₆₁	semidirect
286. #393	C₂²×C₆₁	semidirect
287. #391	C₂²×C₆₁	semidirect
289. #385	C₂²×C₆₁	semidirect
290. #380	C₂²×C₆₁	semidirect
294. C₆₁	C₂×#2409	direct (N × H)
304. C₂²×Q₈	D₄×C₆₁	semidirect
309. C₂²×D₄	Q₈×C₆₁	semidirect
356. C₂⁴	C₂×Q₈×C₆₁	semidirect
368. C₂×Q₈	C₂×D₄×C₆₁	semidirect
372. C₂×D₄	C₂×Q₈×C₆₁	semidirect
398. C₂²×C₄	C₂×Q₈×C₆₁	semidirect
429. C₂³	C₂²⋊Q₈×C₆₁	semidirect
435. C₂³	C₂²×Q₈×C₆₁	semidirect
469. C₂×C₄	C₂²×Q₈×C₆₁	semidirect
483. C₂²	C₂×C₂²⋊Q₈×C₆₁	semidirect
501. C₂	C₆₁×#2409	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×Q₈×C₆₁	2
C₂²×C₂²⋊Q₈×C₆₁	2
C₂²×C₄×D₄×C₆₁	2
C₆₁×#2409	2
C₂×C₆₁×#395	2
C₂×C₆₁×#393	2
C₂×C₆₁×#391	2
C₂×C₆₁×#386	2
C₂×C₆₁×#385	2
C₂×C₆₁×#380	2
C₂×#2409	61

Subgroups — C2×C61×#2409 #29538115

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#2409 #29538115