Subgroups — C₂×C₆₁×#1509 #29520969

Order 15616.

1206 conjugacy classes of subgroups.

The subgroup lattice has 512 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×C₄×C₄⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#1509	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	—	2	1	no	—
23	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
24	C₆₁×#432	—	2	2	no	—
25	C₆₁×#432	C₂²	1	4	yes	complemented
26	C₂×C₄⋊C₈×C₆₁	—	2	1	no	—
27	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
28	C₂×#97×C₆₁	—	2	1	no	—
29	C₄×C₄⋊C₄×C₆₁	—	2	2	no	—
30	C₄×C₄⋊C₄×C₆₁	C₂²	1	4	yes	complemented
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	2	no	—
38	C₂³×C₄×C₆₁	—	2	1	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	8	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	—	2	1	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	—	2	4	no	—
82	C₂×C₄²×C₆₁	—	4	4	no	—
83	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₆₁	C₂×C₄	1	2	yes	—
86	C₂×C₄²×C₆₁	D₄	1	2	yes	—
87	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₆₁	D₄	1	2	yes	—
90	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
91	C₄⋊C₈×C₆₁	—	2	4	no	—
92	C₂²⋊C₈×C₆₁	—	2	2	no	—
93	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
94	#97×C₆₁	—	2	4	no	—
95	#95×C₆₁	—	2	2	no	—
96	#95×C₆₁	C₂³	1	4	yes	—
97	C₂⁴×C₆₁	—	2	1	no	—
98	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
99	C₂×Q₈×C₆₁	—	2	1	no	—
100	C₂×Q₈×C₆₁	—	4	2	no	—
101	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
102	C₂×D₄×C₆₁	—	2	2	no	—
103	C₂×D₄×C₆₁	—	2	2	no	—
104	C₂×D₄×C₆₁	—	2	1	no	—
105	C₂×D₄×C₆₁	—	4	2	no	—
106	C₂×D₄×C₆₁	—	4	2	no	—
107	C₂×D₄×C₆₁	—	4	2	no	—
108	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₆₁	—	2	2	no	—
110	C₂²×C₄×C₆₁	—	2	2	no	—
111	C₂²×C₄×C₆₁	—	2	4	no	—
112	C₂²×C₄×C₆₁	—	2	8	no	—
113	C₂²×C₄×C₆₁	—	2	1	no	—
114	C₂²×C₄×C₆₁	—	2	1	no	—
115	C₂²×C₄×C₆₁	—	2	1	no	—
116	C₂²×C₄×C₆₁	—	2	4	no	—
117	C₂²×C₄×C₆₁	—	2	4	no	—
118	C₂²×C₄×C₆₁	—	4	2	no	—
119	C₂²×C₄×C₆₁	—	4	4	no	—
120	C₂²×C₄×C₆₁	—	4	4	no	—
121	C₂²×C₄×C₆₁	—	4	4	no	—
122	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
123	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
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	1	yes	characteristic
127	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
128	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
136	C₂×C₈×C₆₁	—	2	4	no	—
137	C₂×C₈×C₆₁	—	4	4	no	—
138	C₄⋊C₄×C₆₁	—	2	16	no	—
139	C₄⋊C₄×C₆₁	—	2	2	no	—
140	C₄⋊C₄×C₆₁	—	2	4	no	—
141	C₄⋊C₄×C₆₁	—	2	4	no	—
142	C₄⋊C₄×C₆₁	—	2	4	no	—
143	C₄⋊C₄×C₆₁	—	2	1	no	—
144	C₄⋊C₄×C₆₁	—	2	1	no	—
145	C₄⋊C₄×C₆₁	—	2	2	no	—
146	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
147	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
148	C₂²⋊C₄×C₆₁	—	2	2	no	—
149	C₂²⋊C₄×C₆₁	—	2	2	no	—
150	C₂²⋊C₄×C₆₁	—	2	2	no	—
151	C₂²⋊C₄×C₆₁	—	2	4	no	—
152	C₂²⋊C₄×C₆₁	—	2	4	no	—
153	C₂²⋊C₄×C₆₁	—	2	4	no	—
154	C₂²⋊C₄×C₆₁	—	2	2	no	—
155	C₄²×C₆₁	—	2	4	no	—
156	C₄²×C₆₁	—	4	8	no	—
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	C₂²×C₄	1	2	yes	—
162	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
163	C₄²×C₆₁	C₂×D₄	1	2	yes	—
164	C₄²×C₆₁	C₂×D₄	1	2	yes	—
165	C₂³×C₆₁	—	2	2	no	—
166	C₂³×C₆₁	—	2	2	no	—
167	C₂³×C₆₁	—	2	2	no	—
168	C₂³×C₆₁	—	4	2	no	—
169	C₂³×C₆₁	—	4	2	no	—
170	C₂³×C₆₁	—	4	2	no	—
171	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	C₂³×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
174	C₂³×C₆₁	#137	1	2	yes	—
175	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
176	Q₈×C₆₁	—	4	2	no	—
177	Q₈×C₆₁	—	4	2	no	—
178	D₄×C₆₁	—	4	2	no	—
179	D₄×C₆₁	—	4	2	no	—
180	D₄×C₆₁	—	4	2	no	—
181	D₄×C₆₁	—	4	2	no	—
182	D₄×C₆₁	—	4	4	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	2	no	—
187	C₂×C₄×C₆₁	—	2	4	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	4	no	—
192	C₂×C₄×C₆₁	—	2	4	no	—
193	C₂×C₄×C₆₁	—	2	8	no	—
194	C₂×C₄×C₆₁	—	2	2	no	—
195	C₂×C₄×C₆₁	—	2	2	no	—
196	C₂×C₄×C₆₁	—	2	2	no	—
197	C₂×C₄×C₆₁	—	4	1	no	—
198	C₂×C₄×C₆₁	—	4	1	no	—
199	C₂×C₄×C₆₁	—	4	1	no	—
200	C₂×C₄×C₆₁	—	4	1	no	—
201	C₂×C₄×C₆₁	—	4	4	no	—
202	C₂×C₄×C₆₁	—	4	16	no	—
203	C₂×C₄×C₆₁	—	4	4	no	—
204	C₂×C₄×C₆₁	—	4	2	no	—
205	C₂×C₄×C₆₁	—	4	2	no	—
206	C₂×C₄×C₆₁	—	4	2	no	—
207	C₂×C₄×C₆₁	—	4	8	no	—
208	C₂×C₄×C₆₁	#104	1	4	yes	—
209	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
210	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
212	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
213	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
214	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
215	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
216	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
217	C₈×C₆₁	—	4	4	no	—
218	C₂×#1509	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂²×C₆₁	—	2	1	no	—
220	C₂²×C₆₁	—	2	1	no	—
221	C₂²×C₆₁	—	2	1	no	—
222	C₂²×C₆₁	—	2	1	no	—
223	C₂²×C₆₁	—	2	4	no	—
224	C₂²×C₆₁	—	2	4	no	—
225	C₂²×C₆₁	—	4	2	no	—
226	C₂²×C₆₁	—	4	2	no	—
227	C₂²×C₆₁	—	4	2	no	—
228	C₂²×C₆₁	—	8	4	no	—
229	C₂²×C₆₁	#410	1	2	yes	—
230	C₂²×C₆₁	#417	1	2	yes	—
231	C₂²×C₆₁	#417	1	2	yes	—
232	C₂²×C₆₁	C₂×#104	1	2	yes	—
233	C₂²×C₆₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
234	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
235	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
236	C₄×C₆₁	—	2	1	no	—
237	C₄×C₆₁	—	2	1	no	—
238	C₄×C₆₁	—	2	1	no	—
239	C₄×C₆₁	—	2	1	no	—
240	C₄×C₆₁	—	2	2	no	—
241	C₄×C₆₁	—	2	2	no	—
242	C₄×C₆₁	—	2	2	no	—
243	C₄×C₆₁	—	4	8	no	—
244	C₄×C₆₁	—	4	2	no	—
245	C₄×C₆₁	—	4	2	no	—
246	C₄×C₆₁	—	4	2	no	—
247	C₄×C₆₁	C₂×#104	1	4	yes	—
248	C₂×#529	C₂×C₆₁	1	1	yes	characteristic
249	C₂×#432	C₂×C₆₁	1	1	yes	characteristic, complemented
250	C₂×C₄×C₄⋊C₄	C₂×C₆₁	1	1	yes	characteristic, complemented
251	#1509	C₂×C₆₁	1	8	yes	direct product factor
252	C₂×#328	C₂×C₆₁	1	2	yes	complemented
253	C₂×#327	C₂×C₆₁	1	2	yes	—
254	C₂×C₆₁	—	2	1	no	—
255	C₂×C₆₁	—	2	1	no	—
256	C₂×C₆₁	—	2	2	no	—
257	C₂×C₆₁	—	8	2	no	—
258	C₂×C₆₁	#1509	1	4	yes	direct product factor
259	C₂×C₆₁	C₂×#410	1	1	yes	characteristic
260	C₂×C₆₁	C₂×#417	1	1	yes	characteristic
261	C₂×C₆₁	C₂²×#104	1	1	yes	characteristic
262	#529	—	2	2	no	—
263	#529	—	2	2	no	—
264	#529	C₄×C₆₁	1	4	yes	complemented
265	#529	C₂²×C₆₁	1	4	yes	—
266	C₂×#126	—	2	1	no	—
267	C₂×#125	C₄×C₆₁	1	1	yes	characteristic, complemented
268	C₂×#124	C₄×C₆₁	1	1	yes	characteristic, complemented
269	C₂×#123	—	2	1	no	—
270	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
271	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
272	C₂×C₄×Q₈	C₄×C₆₁	1	1	yes	characteristic, complemented
273	C₂×C₄×D₄	—	2	1	no	—
274	C₂×C₄×D₄	C₄×C₆₁	1	1	yes	characteristic, complemented
275	C₂×#117	—	2	1	no	—
276	C₂²×C₄⋊C₄	—	2	1	no	—
277	C₂²×C₄²	—	2	1	no	—
278	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
279	#432	—	2	2	no	—
280	#432	C₂²×C₆₁	1	4	yes	complemented
281	C₂×C₄⋊C₈	—	2	1	no	—
282	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
283	C₂×#97	—	2	1	no	—
284	C₄×C₄⋊C₄	—	2	2	no	—
285	C₄×C₄⋊C₄	C₂²×C₆₁	1	4	yes	complemented
286	C₂×#95	C₂²×C₆₁	1	2	yes	—
287	#328	C₂²×C₆₁	1	8	yes	complemented
288	#327	C₂²×C₆₁	1	8	yes	—
289	C₆₁	C₂×#1509	1	1	yes	characteristic, direct product factor, Sylow
290	C₂²×Q₈	C₂×C₄×C₆₁	1	1	yes	characteristic
291	C₂²×D₄	—	2	1	no	—
292	C₂²×D₄	C₂×C₄×C₆₁	1	1	yes	characteristic
293	C₂³×C₄	—	2	2	no	—
294	C₂³×C₄	—	2	1	no	—
295	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
296	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
297	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
298	C₂²×C₈	—	2	2	no	—
299	#126	—	2	4	no	—
300	#126	—	2	4	no	—
301	#125	—	2	2	no	—
302	#125	C₂×C₄×C₆₁	1	4	yes	complemented
303	#124	—	2	2	no	—
304	#124	C₂×C₄×C₆₁	1	4	yes	complemented
305	#123	—	2	4	no	—
306	#123	—	2	4	no	—
307	C₂²⋊Q₈	—	2	1	no	—
308	C₂²⋊Q₈	—	2	1	no	—
309	C₂²⋊Q₈	C₂×C₄×C₆₁	1	2	yes	—
310	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
311	#121	—	2	1	no	—
312	#121	—	2	1	no	—
313	#121	C₂×C₄×C₆₁	1	2	yes	—
314	#121	C₂³×C₆₁	1	2	yes	—
315	C₄×Q₈	—	2	2	no	—
316	C₄×Q₈	C₂×C₄×C₆₁	1	4	yes	complemented
317	C₄×D₄	—	2	4	no	—
318	C₄×D₄	—	2	4	no	—
319	C₄×D₄	—	2	2	no	—
320	C₄×D₄	C₂×C₄×C₆₁	1	4	yes	complemented
321	#117	—	2	4	no	—
322	#117	—	2	4	no	—
323	C₂×C₄⋊C₄	—	2	8	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	4	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
330	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
331	C₂×C₂²⋊C₄	—	2	1	no	—
332	C₂×C₂²⋊C₄	—	2	1	no	—
333	C₂×C₂²⋊C₄	—	2	1	no	—
334	C₂×C₂²⋊C₄	—	2	1	no	—
335	C₂×C₂²⋊C₄	—	2	1	no	—
336	C₂×C₄²	—	2	1	no	—
337	C₂×C₄²	—	2	4	no	—
338	C₂×C₄²	—	4	4	no	—
339	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
340	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
341	C₂×C₄²	C₂×C₄×C₆₁	1	2	yes	—
342	C₂×C₄²	D₄×C₆₁	1	2	yes	—
343	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
344	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
345	C₂×C₄²	D₄×C₆₁	1	2	yes	—
346	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
347	C₄⋊C₈	—	2	4	no	—
348	C₂²⋊C₈	—	2	2	no	—
349	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
350	#97	—	2	4	no	—
351	#95	—	2	2	no	—
352	#95	C₂³×C₆₁	1	4	yes	—
353	C₂⁴	—	2	1	no	—
354	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	4	2	no	—
357	C₂×Q₈	C₂²×C₄×C₆₁	1	2	yes	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	4	2	no	—
362	C₂×D₄	—	4	2	no	—
363	C₂×D₄	—	4	2	no	—
364	C₂×D₄	C₂²×C₄×C₆₁	1	2	yes	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	2	8	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	—	2	4	no	—
374	C₂²×C₄	—	4	2	no	—
375	C₂²×C₄	—	4	4	no	—
376	C₂²×C₄	—	4	4	no	—
377	C₂²×C₄	—	4	4	no	—
378	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
379	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
380	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
381	C₂²×C₄	C₂²⋊C₄×C₆₁	1	2	yes	—
382	C₂²×C₄	C₂²⋊C₄×C₆₁	1	2	yes	—
383	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
384	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
385	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
387	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
388	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
391	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
392	C₂×C₈	—	2	4	no	—
393	C₂×C₈	—	4	4	no	—
394	C₄⋊C₄	—	2	16	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	4	no	—
397	C₄⋊C₄	—	2	4	no	—
398	C₄⋊C₄	—	2	4	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
403	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₂²⋊C₄	—	2	4	no	—
408	C₂²⋊C₄	—	2	4	no	—
409	C₂²⋊C₄	—	2	4	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₄²	—	2	4	no	—
412	C₄²	—	4	8	no	—
413	C₄²	C₂²⋊C₄×C₆₁	1	2	yes	—
414	C₄²	C₂²⋊C₄×C₆₁	1	2	yes	—
415	C₄²	C₂²⋊C₄×C₆₁	1	2	yes	—
416	C₄²	C₂²⋊C₄×C₆₁	1	2	yes	—
417	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
418	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
419	C₄²	C₂×D₄×C₆₁	1	2	yes	—
420	C₄²	C₂×D₄×C₆₁	1	2	yes	—
421	C₂³	—	2	2	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	4	2	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	4	2	no	—
427	C₂³	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
428	C₂³	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
429	C₂³	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
430	C₂³	#137×C₆₁	1	2	yes	—
431	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
432	Q₈	—	4	2	no	—
433	Q₈	—	4	2	no	—
434	D₄	—	4	2	no	—
435	D₄	—	4	2	no	—
436	D₄	—	4	2	no	—
437	D₄	—	4	2	no	—
438	D₄	—	4	4	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	8	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	16	no	—
458	C₂×C₄	—	4	4	no	—
459	C₂×C₄	—	4	4	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	8	no	—
464	C₂×C₄	#104×C₆₁	1	4	yes	—
465	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
466	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
467	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
468	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
469	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
470	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
471	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
472	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
473	C₈	—	4	4	no	—
474	C₂²	—	2	4	no	—
475	C₂²	—	2	4	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	8	4	no	—
484	C₂²	C₆₁×#410	1	2	yes	—
485	C₂²	C₆₁×#417	1	2	yes	—
486	C₂²	C₆₁×#417	1	2	yes	—
487	C₂²	C₂×#104×C₆₁	1	2	yes	—
488	C₂²	C₂²×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
489	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
490	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	2	2	no	—
496	C₄	—	2	2	no	—
497	C₄	—	2	2	no	—
498	C₄	—	4	8	no	—
499	C₄	—	4	2	no	—
500	C₄	—	4	2	no	—
501	C₄	—	4	2	no	—
502	C₄	C₂×#104×C₆₁	1	4	yes	—
503	C₂	—	2	1	no	—
504	C₂	—	2	1	no	—
505	C₂	—	2	2	no	—
506	C₂	—	8	2	no	—
507	C₂	C₆₁×#1509	1	4	yes	direct product factor
508	C₂	C₂×C₆₁×#410	1	1	yes	characteristic
509	C₂	C₂×C₆₁×#417	1	1	yes	characteristic
510	C₂	C₂²×#104×C₆₁	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×C₄×C₄⋊C₄×C₆₁	C₂	semidirect
4. C₆₁×#1509	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
25. C₆₁×#432	C₂²	semidirect
30. C₄×C₄⋊C₄×C₆₁	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
218. C₂×#1509	C₆₁	direct (N × H)
249. C₂×#432	C₂×C₆₁	semidirect
250. C₂×C₄×C₄⋊C₄	C₂×C₆₁	semidirect
251. #1509	C₂×C₆₁	direct (N × H)
252. C₂×#328	C₂×C₆₁	semidirect
258. C₂×C₆₁	#1509	direct (N × H)
264. #529	C₄×C₆₁	semidirect
267. C₂×#125	C₄×C₆₁	semidirect
268. C₂×#124	C₄×C₆₁	semidirect
272. C₂×C₄×Q₈	C₄×C₆₁	semidirect
274. C₂×C₄×D₄	C₄×C₆₁	semidirect
280. #432	C₂²×C₆₁	semidirect
285. C₄×C₄⋊C₄	C₂²×C₆₁	semidirect
287. #328	C₂²×C₆₁	semidirect
289. C₆₁	C₂×#1509	direct (N × H)
302. #125	C₂×C₄×C₆₁	semidirect
304. #124	C₂×C₄×C₆₁	semidirect
316. C₄×Q₈	C₂×C₄×C₆₁	semidirect
320. C₄×D₄	C₂×C₄×C₆₁	semidirect
507. C₂	C₆₁×#1509	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×C₄×C₄⋊C₄×C₆₁	2
C₆₁×#1509	2
C₂×C₆₁×#328	2
C₂×C₆₁×#327	2
C₂×#1509	61

Subgroups — C2×C61×#1509 #29520969

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#1509 #29520969