Subgroups — C₆₁×#17449 #29520882

Order 15616.

1214 conjugacy classes of subgroups.

The subgroup lattice has 534 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	C₆₁×#2920	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2920	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#1491	C₂	1	4	yes	maximal, complemented
5	C₆₁×#1487	C₂	1	4	yes	maximal, complemented
6	C₆₁×#1479	C₂	1	4	yes	maximal, complemented
7	C₂³×Q₈×C₆₁	C₄	1	1	yes	characteristic
8	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
9	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
10	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
11	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
12	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
13	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
14	C₂×C₄×Q₈×C₆₁	C₄	1	2	yes	—
15	C₂×C₄×Q₈×C₆₁	C₄	1	2	yes	—
16	C₂×C₄×Q₈×C₆₁	C₄	1	2	yes	—
17	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
18	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
20	C₂²×C₄⋊C₄×C₆₁	—	2	1	no	—
21	C₂²×C₄⋊C₄×C₆₁	C₄	1	1	yes	characteristic
22	C₂²×C₄²×C₆₁	—	2	1	no	—
23	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
24	C₆₁×#432	—	2	1	no	—
25	C₆₁×#432	—	2	1	no	—
26	C₆₁×#432	—	2	1	no	—
27	C₆₁×#432	C₂²	1	2	yes	—
28	C₆₁×#431	—	2	1	no	—
29	C₆₁×#431	C₂²	1	2	yes	—
30	C₆₁×#431	C₂²	1	2	yes	—
31	C₆₁×#431	C₂²	1	2	yes	—
32	C₆₁×#423	—	2	1	no	—
33	C₆₁×#423	C₂²	1	2	yes	—
34	C₆₁×#407	—	2	1	no	—
35	C₆₁×#407	—	2	1	no	—
36	C₄×M₁₆×C₆₁	—	2	1	no	—
37	C₄×M₁₆×C₆₁	C₂²	1	2	yes	—
38	C₆₁×Q₈⋊C₈	C₂²	1	16	yes	complemented
39	C₂²×Q₈×C₆₁	—	2	8	no	—
40	C₂²×Q₈×C₆₁	—	2	1	no	—
41	C₂²×Q₈×C₆₁	—	2	1	no	—
42	C₂²×Q₈×C₆₁	—	2	1	no	—
43	C₂²×Q₈×C₆₁	C₂×C₄	1	2	yes	—
44	C₂²×Q₈×C₆₁	C₂×C₄	1	2	yes	—
45	C₂²×Q₈×C₆₁	C₂×C₄	1	2	yes	—
46	C₂³×C₄×C₆₁	—	2	1	no	—
47	C₂³×C₄×C₆₁	—	2	1	no	—
48	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
51	C₂×M₁₆×C₆₁	—	2	2	no	—
52	C₂×M₁₆×C₆₁	—	2	2	no	—
53	C₄×Q₈×C₆₁	—	2	2	no	—
54	C₄×Q₈×C₆₁	—	2	2	no	—
55	C₄×Q₈×C₆₁	—	2	2	no	—
56	C₄×Q₈×C₆₁	—	2	2	no	—
57	C₄×Q₈×C₆₁	—	2	2	no	—
58	C₄×Q₈×C₆₁	—	2	2	no	—
59	C₄×Q₈×C₆₁	—	2	2	no	—
60	C₄×Q₈×C₆₁	—	2	2	no	—
61	C₄×Q₈×C₆₁	—	2	2	no	—
62	C₄×Q₈×C₆₁	—	2	2	no	—
63	C₄×Q₈×C₆₁	—	2	2	no	—
64	C₄×Q₈×C₆₁	—	2	2	no	—
65	C₄×Q₈×C₆₁	C₂×C₄	1	4	yes	—
66	C₄×Q₈×C₆₁	C₂×C₄	1	4	yes	—
67	C₄×Q₈×C₆₁	C₂×C₄	1	4	yes	—
68	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
69	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
70	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
71	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
72	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
73	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
74	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
75	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
76	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
77	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
78	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
79	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
80	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
81	C₂×C₄²×C₆₁	—	2	2	no	—
82	C₂×C₄²×C₆₁	—	2	2	no	—
83	C₂×C₄²×C₆₁	—	2	2	no	—
84	C₂×C₄²×C₆₁	—	2	2	no	—
85	C₂×C₄²×C₆₁	—	2	2	no	—
86	C₂×C₄²×C₆₁	—	2	2	no	—
87	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
91	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
92	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₆₁	—	2	2	no	—
100	C₄⋊C₈×C₆₁	—	2	2	no	—
101	C₄⋊C₈×C₆₁	—	2	2	no	—
102	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
103	C₂²⋊C₈×C₆₁	—	2	2	no	—
104	C₂²⋊C₈×C₆₁	—	2	2	no	—
105	C₂²⋊C₈×C₆₁	—	2	2	no	—
106	C₂²⋊C₈×C₆₁	—	2	2	no	—
107	#97×C₆₁	—	2	2	no	—
108	#97×C₆₁	—	2	2	no	—
109	C₄×C₈×C₆₁	—	2	2	no	—
110	C₄×C₈×C₆₁	C₂³	1	4	yes	—
111	C₂⁴×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
112	C₂×Q₈×C₆₁	—	2	8	no	—
113	C₂×Q₈×C₆₁	—	2	8	no	—
114	C₂×Q₈×C₆₁	—	2	8	no	—
115	C₂×Q₈×C₆₁	—	2	8	no	—
116	C₂×Q₈×C₆₁	—	2	8	no	—
117	C₂×Q₈×C₆₁	—	2	2	no	—
118	C₂×Q₈×C₆₁	—	2	2	no	—
119	C₂×Q₈×C₆₁	—	2	2	no	—
120	C₂×Q₈×C₆₁	—	2	4	no	—
121	C₂×Q₈×C₆₁	M₁₆	1	8	yes	complemented
122	C₂×Q₈×C₆₁	C₂²×C₄	1	4	yes	—
123	C₂²×C₄×C₆₁	—	2	8	no	—
124	C₂²×C₄×C₆₁	—	2	2	no	—
125	C₂²×C₄×C₆₁	—	2	2	no	—
126	C₂²×C₄×C₆₁	—	2	2	no	—
127	C₂²×C₄×C₆₁	—	2	4	no	—
128	C₂²×C₄×C₆₁	—	2	4	no	—
129	C₂²×C₄×C₆₁	—	2	2	no	—
130	C₂²×C₄×C₆₁	—	2	2	no	—
131	C₂²×C₄×C₆₁	—	2	2	no	—
132	C₂²×C₄×C₆₁	—	4	2	no	—
133	C₂²×C₄×C₆₁	—	4	4	no	—
134	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
135	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
136	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
137	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
138	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
139	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
140	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
141	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
142	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
143	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
152	M₁₆×C₆₁	—	4	4	no	—
153	M₁₆×C₆₁	—	4	4	no	—
154	C₂×C₈×C₆₁	—	2	4	no	—
155	C₂×C₈×C₆₁	—	2	4	no	—
156	C₄⋊C₄×C₆₁	—	2	4	no	—
157	C₄⋊C₄×C₆₁	—	2	4	no	—
158	C₄⋊C₄×C₆₁	—	2	4	no	—
159	C₄⋊C₄×C₆₁	—	2	2	no	—
160	C₄⋊C₄×C₆₁	—	2	2	no	—
161	C₄⋊C₄×C₆₁	—	2	2	no	—
162	C₄⋊C₄×C₆₁	—	2	4	no	—
163	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
164	C₄²×C₆₁	—	2	4	no	—
165	C₄²×C₆₁	—	2	4	no	—
166	C₄²×C₆₁	—	2	4	no	—
167	C₄²×C₆₁	—	2	4	no	—
168	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
169	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
170	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
171	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
172	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
173	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
174	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
175	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
176	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
177	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
184	C₂³×C₆₁	—	2	2	no	—
185	C₂³×C₆₁	—	2	2	no	—
186	C₂³×C₆₁	—	2	2	no	—
187	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
188	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	Q₈×C₆₁	—	2	8	no	—
191	Q₈×C₆₁	—	2	8	no	—
192	Q₈×C₆₁	—	2	4	no	—
193	Q₈×C₆₁	—	2	8	no	—
194	Q₈×C₆₁	C₂×M₁₆	1	8	yes	—
195	C₂×C₄×C₆₁	—	2	8	no	—
196	C₂×C₄×C₆₁	—	2	8	no	—
197	C₂×C₄×C₆₁	—	2	4	no	—
198	C₂×C₄×C₆₁	—	2	8	no	—
199	C₂×C₄×C₆₁	—	2	2	no	—
200	C₂×C₄×C₆₁	—	2	2	no	—
201	C₂×C₄×C₆₁	—	2	2	no	—
202	C₂×C₄×C₆₁	—	2	2	no	—
203	C₂×C₄×C₆₁	—	2	2	no	—
204	C₂×C₄×C₆₁	—	2	2	no	—
205	C₂×C₄×C₆₁	—	2	2	no	—
206	C₂×C₄×C₆₁	—	2	2	no	—
207	C₂×C₄×C₆₁	—	2	2	no	—
208	C₂×C₄×C₆₁	—	2	2	no	—
209	C₂×C₄×C₆₁	—	2	2	no	—
210	C₂×C₄×C₆₁	—	2	2	no	—
211	C₂×C₄×C₆₁	—	2	4	no	—
212	C₂×C₄×C₆₁	—	4	1	no	—
213	C₂×C₄×C₆₁	—	4	1	no	—
214	C₂×C₄×C₆₁	—	4	1	no	—
215	C₂×C₄×C₆₁	—	4	1	no	—
216	C₂×C₄×C₆₁	—	4	4	no	—
217	C₂×C₄×C₆₁	—	4	4	no	—
218	C₂×C₄×C₆₁	—	4	4	no	—
219	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₆₁	C₂×M₁₆	1	4	yes	—
229	C₂×C₄×C₆₁	#137	1	4	yes	—
230	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
231	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
233	C₈×C₆₁	—	4	4	no	—
234	C₈×C₆₁	—	4	4	no	—
235	#17449	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
236	C₂²×C₆₁	—	2	8	no	—
237	C₂²×C₆₁	—	2	1	no	—
238	C₂²×C₆₁	—	2	1	no	—
239	C₂²×C₆₁	—	2	1	no	—
240	C₂²×C₆₁	—	2	1	no	—
241	C₂²×C₆₁	—	2	1	no	—
242	C₂²×C₆₁	—	2	1	no	—
243	C₂²×C₆₁	#407	1	2	yes	—
244	C₂²×C₆₁	#419	1	2	yes	—
245	C₂²×C₆₁	#421	1	2	yes	—
246	C₂²×C₆₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
247	C₄×C₆₁	—	2	8	no	—
248	C₄×C₆₁	—	2	1	no	—
249	C₄×C₆₁	—	2	1	no	—
250	C₄×C₆₁	—	2	1	no	—
251	C₄×C₆₁	—	2	1	no	—
252	C₄×C₆₁	—	2	1	no	—
253	C₄×C₆₁	—	2	1	no	—
254	C₄×C₆₁	—	2	1	no	—
255	C₄×C₆₁	—	2	1	no	—
256	C₄×C₆₁	—	4	4	no	—
257	C₄×C₆₁	#407	1	2	yes	—
258	C₄×C₆₁	#419	1	2	yes	—
259	C₄×C₆₁	C₂²×M₁₆	1	2	yes	—
260	C₄×C₆₁	C₂×#137	1	2	yes	—
261	C₂²×C₄×Q₈	C₂×C₆₁	1	1	yes	characteristic
262	#2920	C₂×C₆₁	1	1	yes	characteristic
263	#2920	C₂×C₆₁	1	1	yes	characteristic
264	#1491	C₂×C₆₁	1	4	yes	complemented
265	#1487	C₂×C₆₁	1	4	yes	complemented
266	#1479	C₂×C₆₁	1	4	yes	complemented
267	C₂×C₆₁	—	2	2	no	—
268	C₂×C₆₁	—	2	2	no	—
269	C₂×C₆₁	—	2	2	no	—
270	C₂×C₆₁	C₂×#407	1	1	yes	characteristic
271	C₂×C₆₁	C₂×#419	1	1	yes	characteristic
272	C₂×C₆₁	C₂×#421	1	1	yes	characteristic
273	C₂³×Q₈	C₄×C₆₁	1	1	yes	characteristic
274	C₂×C₄×Q₈	—	2	1	no	—
275	C₂×C₄×Q₈	—	2	1	no	—
276	C₂×C₄×Q₈	—	2	1	no	—
277	C₂×C₄×Q₈	—	2	1	no	—
278	C₂×C₄×Q₈	—	2	1	no	—
279	C₂×C₄×Q₈	—	2	1	no	—
280	C₂×C₄×Q₈	C₄×C₆₁	1	2	yes	—
281	C₂×C₄×Q₈	C₄×C₆₁	1	2	yes	—
282	C₂×C₄×Q₈	C₄×C₆₁	1	2	yes	—
283	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
284	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
285	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
286	C₂²×C₄⋊C₄	—	2	1	no	—
287	C₂²×C₄⋊C₄	C₄×C₆₁	1	1	yes	characteristic
288	C₂²×C₄²	—	2	1	no	—
289	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
290	#432	—	2	1	no	—
291	#432	—	2	1	no	—
292	#432	—	2	1	no	—
293	#432	C₂²×C₆₁	1	2	yes	—
294	#431	—	2	1	no	—
295	#431	C₂²×C₆₁	1	2	yes	—
296	#431	C₂²×C₆₁	1	2	yes	—
297	#431	C₂²×C₆₁	1	2	yes	—
298	#423	—	2	1	no	—
299	#423	C₂²×C₆₁	1	2	yes	—
300	#407	—	2	1	no	—
301	#407	—	2	1	no	—
302	C₄×M₁₆	—	2	1	no	—
303	C₄×M₁₆	C₂²×C₆₁	1	2	yes	—
304	Q₈⋊C₈	C₂²×C₆₁	1	16	yes	complemented
305	C₆₁	#17449	1	1	yes	characteristic, direct product factor, Sylow
306	C₂²×Q₈	—	2	8	no	—
307	C₂²×Q₈	—	2	1	no	—
308	C₂²×Q₈	—	2	1	no	—
309	C₂²×Q₈	—	2	1	no	—
310	C₂²×Q₈	C₂×C₄×C₆₁	1	2	yes	—
311	C₂²×Q₈	C₂×C₄×C₆₁	1	2	yes	—
312	C₂²×Q₈	C₂×C₄×C₆₁	1	2	yes	—
313	C₂³×C₄	—	2	1	no	—
314	C₂³×C₄	—	2	1	no	—
315	C₂³×C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
316	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
317	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
318	C₂×M₁₆	—	2	2	no	—
319	C₂×M₁₆	—	2	2	no	—
320	C₄×Q₈	—	2	2	no	—
321	C₄×Q₈	—	2	2	no	—
322	C₄×Q₈	—	2	2	no	—
323	C₄×Q₈	—	2	2	no	—
324	C₄×Q₈	—	2	2	no	—
325	C₄×Q₈	—	2	2	no	—
326	C₄×Q₈	—	2	2	no	—
327	C₄×Q₈	—	2	2	no	—
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	—	2	2	no	—
330	C₄×Q₈	—	2	2	no	—
331	C₄×Q₈	—	2	2	no	—
332	C₄×Q₈	C₂×C₄×C₆₁	1	4	yes	—
333	C₄×Q₈	C₂×C₄×C₆₁	1	4	yes	—
334	C₄×Q₈	C₂×C₄×C₆₁	1	4	yes	—
335	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	2	no	—
338	C₂×C₄⋊C₄	—	2	2	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	—	2	2	no	—
343	C₂×C₄⋊C₄	—	2	2	no	—
344	C₂×C₄⋊C₄	—	2	2	no	—
345	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
346	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
347	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
348	C₂×C₄²	—	2	2	no	—
349	C₂×C₄²	—	2	2	no	—
350	C₂×C₄²	—	2	2	no	—
351	C₂×C₄²	—	2	2	no	—
352	C₂×C₄²	—	2	2	no	—
353	C₂×C₄²	—	2	2	no	—
354	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
355	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
356	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
357	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
358	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
359	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
360	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
361	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
362	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
363	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
364	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
365	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
366	C₄⋊C₈	—	2	2	no	—
367	C₄⋊C₈	—	2	2	no	—
368	C₄⋊C₈	—	2	2	no	—
369	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
370	C₂²⋊C₈	—	2	2	no	—
371	C₂²⋊C₈	—	2	2	no	—
372	C₂²⋊C₈	—	2	2	no	—
373	C₂²⋊C₈	—	2	2	no	—
374	#97	—	2	2	no	—
375	#97	—	2	2	no	—
376	C₄×C₈	—	2	2	no	—
377	C₄×C₈	C₂³×C₆₁	1	4	yes	—
378	C₂⁴	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
379	C₂×Q₈	—	2	8	no	—
380	C₂×Q₈	—	2	8	no	—
381	C₂×Q₈	—	2	8	no	—
382	C₂×Q₈	—	2	8	no	—
383	C₂×Q₈	—	2	8	no	—
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	2	4	no	—
388	C₂×Q₈	M₁₆×C₆₁	1	8	yes	complemented
389	C₂×Q₈	C₂²×C₄×C₆₁	1	4	yes	—
390	C₂²×C₄	—	2	8	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	4	no	—
395	C₂²×C₄	—	2	4	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	4	2	no	—
400	C₂²×C₄	—	4	4	no	—
401	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
402	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
403	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
404	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
405	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
406	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
407	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
408	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
409	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
410	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
411	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
412	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
414	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
415	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
416	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
417	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
418	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
419	M₁₆	—	4	4	no	—
420	M₁₆	—	4	4	no	—
421	C₂×C₈	—	2	4	no	—
422	C₂×C₈	—	2	4	no	—
423	C₄⋊C₄	—	2	4	no	—
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	2	4	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	4	no	—
430	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
431	C₄²	—	2	4	no	—
432	C₄²	—	2	4	no	—
433	C₄²	—	2	4	no	—
434	C₄²	—	2	4	no	—
435	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
436	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
437	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
438	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
439	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
440	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
441	C₄²	C₂²×C₄×C₆₁	1	1	yes	characteristic
442	C₄²	C₂²×C₄×C₆₁	1	1	yes	characteristic
443	C₄²	C₂²×C₄×C₆₁	1	1	yes	characteristic
444	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
445	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
446	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
447	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
448	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
449	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
450	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
451	C₂³	—	2	2	no	—
452	C₂³	—	2	2	no	—
453	C₂³	—	2	2	no	—
454	C₂³	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
455	C₂³	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
456	C₂³	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
457	Q₈	—	2	8	no	—
458	Q₈	—	2	8	no	—
459	Q₈	—	2	4	no	—
460	Q₈	—	2	8	no	—
461	Q₈	C₂×M₁₆×C₆₁	1	8	yes	—
462	C₂×C₄	—	2	8	no	—
463	C₂×C₄	—	2	8	no	—
464	C₂×C₄	—	2	8	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	4	no	—
484	C₂×C₄	—	4	4	no	—
485	C₂×C₄	—	4	4	no	—
486	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
487	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
488	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
489	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
490	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
491	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
492	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
493	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
494	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
495	C₂×C₄	C₂×M₁₆×C₆₁	1	4	yes	—
496	C₂×C₄	#137×C₆₁	1	4	yes	—
497	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
498	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
499	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
500	C₈	—	4	4	no	—
501	C₈	—	4	4	no	—
502	C₂²	—	2	8	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	1	no	—
507	C₂²	—	2	1	no	—
508	C₂²	—	2	1	no	—
509	C₂²	C₆₁×#407	1	2	yes	—
510	C₂²	C₆₁×#419	1	2	yes	—
511	C₂²	C₆₁×#421	1	2	yes	—
512	C₂²	C₂²×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
513	C₄	—	2	8	no	—
514	C₄	—	2	1	no	—
515	C₄	—	2	1	no	—
516	C₄	—	2	1	no	—
517	C₄	—	2	1	no	—
518	C₄	—	2	1	no	—
519	C₄	—	2	1	no	—
520	C₄	—	2	1	no	—
521	C₄	—	2	1	no	—
522	C₄	—	4	4	no	—
523	C₄	C₆₁×#407	1	2	yes	—
524	C₄	C₆₁×#419	1	2	yes	—
525	C₄	C₂²×M₁₆×C₆₁	1	2	yes	—
526	C₄	C₂×#137×C₆₁	1	2	yes	—
527	C₂	—	2	2	no	—
528	C₂	—	2	2	no	—
529	C₂	—	2	2	no	—
530	C₂	C₂×C₆₁×#407	1	1	yes	characteristic
531	C₂	C₂×C₆₁×#419	1	1	yes	characteristic
532	C₂	C₂×C₆₁×#421	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₄²	C₂⁴×C₆₁
socle	C₂²×C₆₁	C₂²×C₂²⋊C₄
prime radical	C₂⁴×C₆₁	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₁ ◁ C₂²×C₄²×C₆₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. C₆₁×#1491	C₂	semidirect
5. C₆₁×#1487	C₂	semidirect
6. C₆₁×#1479	C₂	semidirect
38. C₆₁×Q₈⋊C₈	C₂²	semidirect
121. C₂×Q₈×C₆₁	M₁₆	semidirect
235. #17449	C₆₁	direct (N × H)
264. #1491	C₂×C₆₁	semidirect
265. #1487	C₂×C₆₁	semidirect
266. #1479	C₂×C₆₁	semidirect
304. Q₈⋊C₈	C₂²×C₆₁	semidirect
305. C₆₁	#17449	direct (N × H)
388. C₂×Q₈	M₁₆×C₆₁	semidirect

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
C₆₁×#2920	2
C₆₁×#1491	2
C₆₁×#1487	2
C₆₁×#1479	2
#17449	61

Subgroups — C61×#17449 #29520882

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#17449 #29520882