Subgroups — C₂×C₆₁×#1512 #29520986

Order 15616.

1098 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	C₂×C₆₁×#529	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#382	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#1512	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₆₁×#328	C₂	1	2	yes	maximal, complemented
6	C₂×C₆₁×#327	C₂	1	2	yes	maximal
7	C₆₁×#529	—	2	2	no	—
8	C₆₁×#529	—	2	2	no	—
9	C₆₁×#529	C₄	1	4	yes	complemented
10	C₆₁×#529	C₂²	1	4	yes	—
11	C₂×#126×C₆₁	—	2	1	no	—
12	C₂×#125×C₆₁	C₄	1	1	yes	characteristic, complemented
13	C₂×#124×C₆₁	C₄	1	1	yes	characteristic, complemented
14	C₂×#123×C₆₁	—	2	1	no	—
15	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₆₁	C₄	1	1	yes	characteristic, complemented
18	C₂×C₄×D₄×C₆₁	—	2	1	no	—
19	C₂×C₄×D₄×C₆₁	C₄	1	1	yes	characteristic, complemented
20	C₂×#117×C₆₁	—	2	1	no	—
21	C₂²×C₄⋊C₄×C₆₁	—	2	1	no	—
22	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
23	C₆₁×#432	—	2	2	no	—
24	C₆₁×#432	C₂²	1	4	yes	complemented
25	C₂×C₄⋊C₈×C₆₁	—	2	1	no	—
26	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
27	C₂×#97×C₆₁	—	2	1	no	—
28	C₆₁×#382	—	2	2	no	—
29	C₆₁×#382	C₂²	1	4	yes	complemented
30	C₂×#95×C₆₁	—	2	1	no	—
31	C₂×#95×C₆₁	C₂²	1	2	yes	—
32	C₆₁×#328	C₂²	1	8	yes	complemented
33	C₆₁×#327	C₂²	1	8	yes	—
34	C₂²×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₄×C₆₁	—	2	1	no	—
36	C₂²×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₆₁	—	2	1	no	—
38	C₂³×C₄×C₆₁	—	2	2	no	—
39	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₆₁	—	2	2	no	—
43	#126×C₆₁	—	2	4	no	—
44	#126×C₆₁	—	2	4	no	—
45	#125×C₆₁	—	2	2	no	—
46	#125×C₆₁	C₂×C₄	1	4	yes	complemented
47	#124×C₆₁	—	2	2	no	—
48	#124×C₆₁	C₂×C₄	1	4	yes	complemented
49	#123×C₆₁	—	2	4	no	—
50	#123×C₆₁	—	2	4	no	—
51	C₂²⋊Q₈×C₆₁	—	2	1	no	—
52	C₂²⋊Q₈×C₆₁	—	2	1	no	—
53	C₂²⋊Q₈×C₆₁	C₂×C₄	1	2	yes	—
54	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
55	#121×C₆₁	—	2	1	no	—
56	#121×C₆₁	—	2	1	no	—
57	#121×C₆₁	C₂×C₄	1	2	yes	—
58	#121×C₆₁	C₂³	1	2	yes	—
59	C₄×Q₈×C₆₁	—	2	2	no	—
60	C₄×Q₈×C₆₁	C₂×C₄	1	4	yes	complemented
61	C₄×D₄×C₆₁	—	2	4	no	—
62	C₄×D₄×C₆₁	—	2	4	no	—
63	C₄×D₄×C₆₁	—	2	2	no	—
64	C₄×D₄×C₆₁	C₂×C₄	1	4	yes	complemented
65	#117×C₆₁	—	2	4	no	—
66	#117×C₆₁	—	2	4	no	—
67	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
68	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
69	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
70	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
71	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
72	C₂×C₄⋊C₄×C₆₁	—	4	4	no	—
73	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
80	C₂×C₄²×C₆₁	—	2	1	no	—
81	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄²×C₆₁	C₂×C₄	1	2	yes	—
84	C₂×C₄²×C₆₁	D₄	1	2	yes	—
85	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₆₁	D₄	1	2	yes	—
88	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
89	C₄⋊C₈×C₆₁	—	2	4	no	—
90	C₂²⋊C₈×C₆₁	—	2	2	no	—
91	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
92	#97×C₆₁	—	2	4	no	—
93	#95×C₆₁	—	2	4	no	—
94	#95×C₆₁	—	2	2	no	—
95	#95×C₆₁	C₂³	1	4	yes	—
96	C₂⁴×C₆₁	—	2	1	no	—
97	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
98	C₂×Q₈×C₆₁	—	2	1	no	—
99	C₂×Q₈×C₆₁	—	4	2	no	—
100	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
101	C₂×D₄×C₆₁	—	2	2	no	—
102	C₂×D₄×C₆₁	—	2	2	no	—
103	C₂×D₄×C₆₁	—	2	1	no	—
104	C₂×D₄×C₆₁	—	4	2	no	—
105	C₂×D₄×C₆₁	—	4	2	no	—
106	C₂×D₄×C₆₁	—	4	2	no	—
107	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₆₁	—	2	2	no	—
109	C₂²×C₄×C₆₁	—	2	2	no	—
110	C₂²×C₄×C₆₁	—	2	1	no	—
111	C₂²×C₄×C₆₁	—	2	1	no	—
112	C₂²×C₄×C₆₁	—	2	1	no	—
113	C₂²×C₄×C₆₁	—	2	4	no	—
114	C₂²×C₄×C₆₁	—	2	4	no	—
115	C₂²×C₄×C₆₁	—	4	2	no	—
116	C₂²×C₄×C₆₁	—	4	2	no	—
117	C₂²×C₄×C₆₁	—	4	4	no	—
118	C₂²×C₄×C₆₁	—	4	4	no	—
119	C₂²×C₄×C₆₁	—	4	4	no	—
120	C₂²×C₄×C₆₁	—	4	4	no	—
121	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
122	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
123	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
126	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
127	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
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	1	yes	characteristic
134	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
135	C₂×C₈×C₆₁	—	2	4	no	—
136	C₂×C₈×C₆₁	—	4	4	no	—
137	C₄⋊C₄×C₆₁	—	2	2	no	—
138	C₄⋊C₄×C₆₁	—	2	4	no	—
139	C₄⋊C₄×C₆₁	—	2	4	no	—
140	C₄⋊C₄×C₆₁	—	2	4	no	—
141	C₄⋊C₄×C₆₁	—	2	1	no	—
142	C₄⋊C₄×C₆₁	—	2	1	no	—
143	C₄⋊C₄×C₆₁	—	2	2	no	—
144	C₄⋊C₄×C₆₁	—	4	8	no	—
145	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
146	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
147	C₂²⋊C₄×C₆₁	—	2	2	no	—
148	C₂²⋊C₄×C₆₁	—	2	2	no	—
149	C₂²⋊C₄×C₆₁	—	2	2	no	—
150	C₂²⋊C₄×C₆₁	—	2	4	no	—
151	C₂²⋊C₄×C₆₁	—	2	4	no	—
152	C₂²⋊C₄×C₆₁	—	2	4	no	—
153	C₂²⋊C₄×C₆₁	—	2	2	no	—
154	C₄²×C₆₁	—	2	4	no	—
155	C₄²×C₆₁	C₂²⋊C₄	1	2	yes	—
156	C₄²×C₆₁	C₂²⋊C₄	1	2	yes	—
157	C₄²×C₆₁	C₂²⋊C₄	1	2	yes	—
158	C₄²×C₆₁	C₂²⋊C₄	1	2	yes	—
159	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
160	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
161	C₄²×C₆₁	C₂×D₄	1	2	yes	—
162	C₄²×C₆₁	C₂×D₄	1	2	yes	—
163	C₂³×C₆₁	—	2	2	no	—
164	C₂³×C₆₁	—	2	2	no	—
165	C₂³×C₆₁	—	2	2	no	—
166	C₂³×C₆₁	—	4	2	no	—
167	C₂³×C₆₁	—	4	2	no	—
168	C₂³×C₆₁	—	4	2	no	—
169	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
170	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂³×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
172	C₂³×C₆₁	#137	1	2	yes	—
173	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
174	Q₈×C₆₁	—	4	2	no	—
175	Q₈×C₆₁	—	4	2	no	—
176	D₄×C₆₁	—	4	2	no	—
177	D₄×C₆₁	—	4	2	no	—
178	D₄×C₆₁	—	4	2	no	—
179	D₄×C₆₁	—	4	2	no	—
180	D₄×C₆₁	—	4	4	no	—
181	C₂×C₄×C₆₁	—	2	2	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	4	no	—
186	C₂×C₄×C₆₁	—	2	2	no	—
187	C₂×C₄×C₆₁	—	2	2	no	—
188	C₂×C₄×C₆₁	—	2	2	no	—
189	C₂×C₄×C₆₁	—	2	2	no	—
190	C₂×C₄×C₆₁	—	2	2	no	—
191	C₂×C₄×C₆₁	—	2	2	no	—
192	C₂×C₄×C₆₁	—	2	2	no	—
193	C₂×C₄×C₆₁	—	4	2	no	—
194	C₂×C₄×C₆₁	—	4	1	no	—
195	C₂×C₄×C₆₁	—	4	1	no	—
196	C₂×C₄×C₆₁	—	4	1	no	—
197	C₂×C₄×C₆₁	—	4	2	no	—
198	C₂×C₄×C₆₁	—	4	1	no	—
199	C₂×C₄×C₆₁	—	4	8	no	—
200	C₂×C₄×C₆₁	—	4	2	no	—
201	C₂×C₄×C₆₁	—	4	2	no	—
202	C₂×C₄×C₆₁	—	4	2	no	—
203	C₂×C₄×C₆₁	—	4	4	no	—
204	C₂×C₄×C₆₁	—	4	4	no	—
205	C₂×C₄×C₆₁	—	4	4	no	—
206	C₂×C₄×C₆₁	—	8	8	no	—
207	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
208	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
210	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
211	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
212	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
213	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
214	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
215	C₈×C₆₁	—	4	4	no	—
216	C₂×#1512	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
217	C₂²×C₆₁	—	2	1	no	—
218	C₂²×C₆₁	—	2	1	no	—
219	C₂²×C₆₁	—	2	1	no	—
220	C₂²×C₆₁	—	2	1	no	—
221	C₂²×C₆₁	—	2	4	no	—
222	C₂²×C₆₁	—	2	4	no	—
223	C₂²×C₆₁	—	4	2	no	—
224	C₂²×C₆₁	—	4	2	no	—
225	C₂²×C₆₁	—	4	2	no	—
226	C₂²×C₆₁	—	8	4	no	—
227	C₂²×C₆₁	#410	1	2	yes	—
228	C₂²×C₆₁	#417	1	2	yes	—
229	C₂²×C₆₁	#417	1	2	yes	—
230	C₂²×C₆₁	#421	1	2	yes	—
231	C₂²×C₆₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
232	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
233	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
234	C₄×C₆₁	—	2	1	no	—
235	C₄×C₆₁	—	2	1	no	—
236	C₄×C₆₁	—	2	1	no	—
237	C₄×C₆₁	—	2	1	no	—
238	C₄×C₆₁	—	2	2	no	—
239	C₄×C₆₁	—	2	2	no	—
240	C₄×C₆₁	—	2	2	no	—
241	C₄×C₆₁	—	2	2	no	—
242	C₄×C₆₁	—	4	2	no	—
243	C₄×C₆₁	—	4	2	no	—
244	C₄×C₆₁	—	4	2	no	—
245	C₄×C₆₁	—	8	4	no	—
246	C₂×#529	C₂×C₆₁	1	1	yes	characteristic
247	C₂×#432	C₂×C₆₁	1	1	yes	characteristic, complemented
248	C₂×#382	C₂×C₆₁	1	1	yes	characteristic, complemented
249	#1512	C₂×C₆₁	1	8	yes	direct product factor
250	C₂×#328	C₂×C₆₁	1	2	yes	complemented
251	C₂×#327	C₂×C₆₁	1	2	yes	—
252	C₂×C₆₁	—	2	1	no	—
253	C₂×C₆₁	—	2	1	no	—
254	C₂×C₆₁	—	2	2	no	—
255	C₂×C₆₁	—	8	2	no	—
256	C₂×C₆₁	#1512	1	4	yes	direct product factor
257	C₂×C₆₁	C₂×#410	1	1	yes	characteristic
258	C₂×C₆₁	C₂×#417	1	1	yes	characteristic
259	C₂×C₆₁	C₂×#421	1	1	yes	characteristic
260	#529	—	2	2	no	—
261	#529	—	2	2	no	—
262	#529	C₄×C₆₁	1	4	yes	complemented
263	#529	C₂²×C₆₁	1	4	yes	—
264	C₂×#126	—	2	1	no	—
265	C₂×#125	C₄×C₆₁	1	1	yes	characteristic, complemented
266	C₂×#124	C₄×C₆₁	1	1	yes	characteristic, complemented
267	C₂×#123	—	2	1	no	—
268	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
269	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
270	C₂×C₄×Q₈	C₄×C₆₁	1	1	yes	characteristic, complemented
271	C₂×C₄×D₄	—	2	1	no	—
272	C₂×C₄×D₄	C₄×C₆₁	1	1	yes	characteristic, complemented
273	C₂×#117	—	2	1	no	—
274	C₂²×C₄⋊C₄	—	2	1	no	—
275	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
276	#432	—	2	2	no	—
277	#432	C₂²×C₆₁	1	4	yes	complemented
278	C₂×C₄⋊C₈	—	2	1	no	—
279	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
280	C₂×#97	—	2	1	no	—
281	#382	—	2	2	no	—
282	#382	C₂²×C₆₁	1	4	yes	complemented
283	C₂×#95	—	2	1	no	—
284	C₂×#95	C₂²×C₆₁	1	2	yes	—
285	#328	C₂²×C₆₁	1	8	yes	complemented
286	#327	C₂²×C₆₁	1	8	yes	—
287	C₆₁	C₂×#1512	1	1	yes	characteristic, direct product factor, Sylow
288	C₂²×Q₈	C₂×C₄×C₆₁	1	1	yes	characteristic
289	C₂²×D₄	—	2	1	no	—
290	C₂²×D₄	C₂×C₄×C₆₁	1	1	yes	characteristic
291	C₂³×C₄	—	2	1	no	—
292	C₂³×C₄	—	2	2	no	—
293	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
294	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
295	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
296	C₂²×C₈	—	2	2	no	—
297	#126	—	2	4	no	—
298	#126	—	2	4	no	—
299	#125	—	2	2	no	—
300	#125	C₂×C₄×C₆₁	1	4	yes	complemented
301	#124	—	2	2	no	—
302	#124	C₂×C₄×C₆₁	1	4	yes	complemented
303	#123	—	2	4	no	—
304	#123	—	2	4	no	—
305	C₂²⋊Q₈	—	2	1	no	—
306	C₂²⋊Q₈	—	2	1	no	—
307	C₂²⋊Q₈	C₂×C₄×C₆₁	1	2	yes	—
308	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
309	#121	—	2	1	no	—
310	#121	—	2	1	no	—
311	#121	C₂×C₄×C₆₁	1	2	yes	—
312	#121	C₂³×C₆₁	1	2	yes	—
313	C₄×Q₈	—	2	2	no	—
314	C₄×Q₈	C₂×C₄×C₆₁	1	4	yes	complemented
315	C₄×D₄	—	2	4	no	—
316	C₄×D₄	—	2	4	no	—
317	C₄×D₄	—	2	2	no	—
318	C₄×D₄	C₂×C₄×C₆₁	1	4	yes	complemented
319	#117	—	2	4	no	—
320	#117	—	2	4	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	—	2	4	no	—
326	C₂×C₄⋊C₄	—	4	4	no	—
327	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
329	C₂×C₂²⋊C₄	—	2	1	no	—
330	C₂×C₂²⋊C₄	—	2	1	no	—
331	C₂×C₂²⋊C₄	—	2	1	no	—
332	C₂×C₂²⋊C₄	—	2	1	no	—
333	C₂×C₂²⋊C₄	—	2	1	no	—
334	C₂×C₄²	—	2	1	no	—
335	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
336	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
337	C₂×C₄²	C₂×C₄×C₆₁	1	2	yes	—
338	C₂×C₄²	D₄×C₆₁	1	2	yes	—
339	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
340	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
341	C₂×C₄²	D₄×C₆₁	1	2	yes	—
342	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
343	C₄⋊C₈	—	2	4	no	—
344	C₂²⋊C₈	—	2	2	no	—
345	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
346	#97	—	2	4	no	—
347	#95	—	2	4	no	—
348	#95	—	2	2	no	—
349	#95	C₂³×C₆₁	1	4	yes	—
350	C₂⁴	—	2	1	no	—
351	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	4	2	no	—
354	C₂×Q₈	C₂²×C₄×C₆₁	1	2	yes	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	4	2	no	—
359	C₂×D₄	—	4	2	no	—
360	C₂×D₄	—	4	2	no	—
361	C₂×D₄	C₂²×C₄×C₆₁	1	2	yes	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	4	2	no	—
370	C₂²×C₄	—	4	2	no	—
371	C₂²×C₄	—	4	4	no	—
372	C₂²×C₄	—	4	4	no	—
373	C₂²×C₄	—	4	4	no	—
374	C₂²×C₄	—	4	4	no	—
375	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
376	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
377	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
378	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
379	C₂²×C₄	C₂²⋊C₄×C₆₁	1	2	yes	—
380	C₂²×C₄	C₂²⋊C₄×C₆₁	1	2	yes	—
381	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
382	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
384	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
385	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
387	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
388	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
389	C₂×C₈	—	2	4	no	—
390	C₂×C₈	—	4	4	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	4	no	—
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	4	8	no	—
399	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
400	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
401	C₂²⋊C₄	—	2	2	no	—
402	C₂²⋊C₄	—	2	2	no	—
403	C₂²⋊C₄	—	2	2	no	—
404	C₂²⋊C₄	—	2	4	no	—
405	C₂²⋊C₄	—	2	4	no	—
406	C₂²⋊C₄	—	2	4	no	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₄²	—	2	4	no	—
409	C₄²	C₂²⋊C₄×C₆₁	1	2	yes	—
410	C₄²	C₂²⋊C₄×C₆₁	1	2	yes	—
411	C₄²	C₂²⋊C₄×C₆₁	1	2	yes	—
412	C₄²	C₂²⋊C₄×C₆₁	1	2	yes	—
413	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
414	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
415	C₄²	C₂×D₄×C₆₁	1	2	yes	—
416	C₄²	C₂×D₄×C₆₁	1	2	yes	—
417	C₂³	—	2	2	no	—
418	C₂³	—	2	2	no	—
419	C₂³	—	2	2	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
424	C₂³	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
425	C₂³	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
426	C₂³	#137×C₆₁	1	2	yes	—
427	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
428	Q₈	—	4	2	no	—
429	Q₈	—	4	2	no	—
430	D₄	—	4	2	no	—
431	D₄	—	4	2	no	—
432	D₄	—	4	2	no	—
433	D₄	—	4	2	no	—
434	D₄	—	4	4	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	8	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	4	no	—
458	C₂×C₄	—	4	4	no	—
459	C₂×C₄	—	4	4	no	—
460	C₂×C₄	—	8	8	no	—
461	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
462	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
463	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
464	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
465	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
466	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
467	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
468	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
469	C₈	—	4	4	no	—
470	C₂²	—	2	4	no	—
471	C₂²	—	2	4	no	—
472	C₂²	—	2	1	no	—
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	4	2	no	—
477	C₂²	—	4	2	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	8	4	no	—
480	C₂²	C₆₁×#410	1	2	yes	—
481	C₂²	C₆₁×#417	1	2	yes	—
482	C₂²	C₆₁×#417	1	2	yes	—
483	C₂²	C₆₁×#421	1	2	yes	—
484	C₂²	C₂²×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
485	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
486	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
487	C₄	—	2	1	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	2	no	—
492	C₄	—	2	2	no	—
493	C₄	—	2	2	no	—
494	C₄	—	2	2	no	—
495	C₄	—	4	2	no	—
496	C₄	—	4	2	no	—
497	C₄	—	4	2	no	—
498	C₄	—	8	4	no	—
499	C₂	—	2	1	no	—
500	C₂	—	2	1	no	—
501	C₂	—	2	2	no	—
502	C₂	—	8	2	no	—
503	C₂	C₆₁×#1512	1	4	yes	direct product factor
504	C₂	C₂×C₆₁×#410	1	1	yes	characteristic
505	C₂	C₂×C₆₁×#417	1	1	yes	characteristic
506	C₂	C₂×C₆₁×#421	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂×#121×C₆₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ 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
2. C₂×C₆₁×#432	C₂	semidirect
3. C₂×C₆₁×#382	C₂	semidirect
4. C₆₁×#1512	C₂	direct (N × H)
5. C₂×C₆₁×#328	C₂	semidirect
9. C₆₁×#529	C₄	semidirect
12. C₂×#125×C₆₁	C₄	semidirect
13. C₂×#124×C₆₁	C₄	semidirect
17. C₂×C₄×Q₈×C₆₁	C₄	semidirect
19. C₂×C₄×D₄×C₆₁	C₄	semidirect
24. C₆₁×#432	C₂²	semidirect
29. C₆₁×#382	C₂²	semidirect
32. C₆₁×#328	C₂²	semidirect
46. #125×C₆₁	C₂×C₄	semidirect
48. #124×C₆₁	C₂×C₄	semidirect
60. C₄×Q₈×C₆₁	C₂×C₄	semidirect
64. C₄×D₄×C₆₁	C₂×C₄	semidirect
216. C₂×#1512	C₆₁	direct (N × H)
247. C₂×#432	C₂×C₆₁	semidirect
248. C₂×#382	C₂×C₆₁	semidirect
249. #1512	C₂×C₆₁	direct (N × H)
250. C₂×#328	C₂×C₆₁	semidirect
256. C₂×C₆₁	#1512	direct (N × H)
262. #529	C₄×C₆₁	semidirect
265. C₂×#125	C₄×C₆₁	semidirect
266. C₂×#124	C₄×C₆₁	semidirect
270. C₂×C₄×Q₈	C₄×C₆₁	semidirect
272. C₂×C₄×D₄	C₄×C₆₁	semidirect
277. #432	C₂²×C₆₁	semidirect
282. #382	C₂²×C₆₁	semidirect
285. #328	C₂²×C₆₁	semidirect
287. C₆₁	C₂×#1512	direct (N × H)
300. #125	C₂×C₄×C₆₁	semidirect
302. #124	C₂×C₄×C₆₁	semidirect
314. C₄×Q₈	C₂×C₄×C₆₁	semidirect
318. C₄×D₄	C₂×C₄×C₆₁	semidirect
503. C₂	C₆₁×#1512	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
C₂×C₆₁×#432	2
C₂×C₆₁×#382	2
C₆₁×#1512	2
C₂×C₆₁×#328	2
C₂×C₆₁×#327	2
C₂×#1512	61

Subgroups — C2×C61×#1512 #29520986

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#1512 #29520986