Subgroups — C₂×C₆₁×#3365 #29564735

Order 15616.

1894 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#559	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#557	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3365	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₆₁×#488	C₂	1	2	yes	maximal, complemented
5	C₂×C₆₁×#486	C₂	1	1	yes	maximal, characteristic
6	C₂×C₆₁×#475	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₆₁×#478	C₂	1	2	yes	maximal, complemented
8	C₂×C₆₁×#464	C₂	1	2	yes	maximal, complemented
9	C₂×C₆₁×#460	C₂	1	1	yes	maximal, characteristic
10	C₂×C₈×Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×Q₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×SD₁₆×C₆₁	C₂	1	2	yes	maximal, complemented
13	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	—
15	C₆₁×#559	—	2	4	no	—
16	C₆₁×#559	C₂²	1	8	yes	—
17	C₆₁×#557	—	2	4	no	—
18	C₆₁×#557	C₂²	1	8	yes	complemented
19	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
20	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×#125×C₆₁	—	2	2	no	—
23	C₂×#125×C₆₁	C₂²	1	2	yes	—
24	C₂×#124×C₆₁	—	2	1	no	—
25	C₂×#124×C₆₁	C₂²	1	2	yes	—
26	C₂×#123×C₆₁	—	2	2	no	—
27	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
28	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
30	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₆₁	—	2	1	no	—
33	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
34	C₆₁×#488	C₂²	1	16	yes	complemented
35	C₆₁×#486	C₂²	1	8	yes	—
36	C₆₁×#478	C₂²	1	16	yes	complemented
37	C₆₁×#475	C₂²	1	8	yes	complemented
38	C₆₁×#464	C₂²	1	16	yes	complemented
39	C₆₁×#460	C₂²	1	8	yes	—
40	C₈×Q₈×C₆₁	C₂²	1	8	yes	complemented
41	C₄×Q₁₆×C₆₁	C₂²	1	8	yes	complemented
42	C₄×SD₁₆×C₆₁	C₂²	1	16	yes	complemented
43	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
44	C₂×#106×C₆₁	C₂²	1	2	yes	—
45	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
47	C₂×#103×C₆₁	C₂²	1	2	yes	—
48	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
49	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
50	C₂×#102×C₆₁	C₂²	1	2	yes	—
51	C₂×#102×C₆₁	C₂²	1	2	yes	—
52	C₂×#102×C₆₁	C₂²	1	2	yes	—
53	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
54	C₂×C₄×C₈×C₆₁	C₂²	1	2	yes	—
55	C₂²×Q₈×C₆₁	—	2	1	no	—
56	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
57	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
58	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
59	C₂²×D₄×C₆₁	—	2	1	no	—
60	C₂²×D₄×C₆₁	—	2	1	no	—
61	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
62	C₂³×C₄×C₆₁	—	2	2	no	—
63	C₂×Q₁₆×C₆₁	—	2	4	no	—
64	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
65	C₂×SD₁₆×C₆₁	—	2	8	no	—
66	C₂×SD₁₆×C₆₁	C₂³	1	8	yes	—
67	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
68	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
70	C₄⋊Q₈×C₆₁	—	2	8	no	—
71	C₄⋊Q₈×C₆₁	—	2	2	no	—
72	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
73	#127×C₆₁	—	2	2	no	—
74	#127×C₆₁	C₂³	1	4	yes	—
75	#125×C₆₁	—	2	16	no	—
76	#125×C₆₁	—	2	4	no	—
77	#125×C₆₁	C₂³	1	8	yes	—
78	#124×C₆₁	—	2	8	no	—
79	#124×C₆₁	—	2	4	no	—
80	#124×C₆₁	C₂³	1	8	yes	—
81	#123×C₆₁	—	2	16	no	—
82	C₄×Q₈×C₆₁	—	2	8	no	—
83	C₄×Q₈×C₆₁	—	2	4	no	—
84	C₄×Q₈×C₆₁	—	2	2	no	—
85	C₄×Q₈×C₆₁	—	2	2	no	—
86	C₄×Q₈×C₆₁	D₄	1	4	yes	—
87	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
88	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
89	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
90	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
91	C₄×D₄×C₆₁	—	2	8	no	—
92	C₄×D₄×C₆₁	—	2	4	no	—
93	C₄×D₄×C₆₁	C₂³	1	8	yes	—
94	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
95	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
96	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
97	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
98	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
99	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
100	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
102	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
103	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
106	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
107	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
108	C₂×C₄²×C₆₁	—	2	1	no	—
109	C₂×C₄²×C₆₁	—	2	1	no	—
110	C₂×C₄²×C₆₁	—	2	2	no	—
111	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
113	#107×C₆₁	C₂³	1	4	yes	—
114	#106×C₆₁	C₂³	1	8	yes	—
115	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
116	C₄⋊C₈×C₆₁	C₂³	1	8	yes	—
117	#103×C₆₁	C₂³	1	4	yes	—
118	#103×C₆₁	C₂³	1	4	yes	—
119	#103×C₆₁	C₂³	1	8	yes	—
120	#102×C₆₁	C₂³	1	8	yes	—
121	#102×C₆₁	C₂³	1	8	yes	—
122	#102×C₆₁	C₂³	1	8	yes	—
123	C₄×C₈×C₆₁	C₂³	1	8	yes	—
124	C₄×C₈×C₆₁	C₂³	1	4	yes	—
125	C₂⁴×C₆₁	—	2	2	no	—
126	C₂×Q₈×C₆₁	—	2	4	no	—
127	C₂×Q₈×C₆₁	—	2	1	no	—
128	C₂×Q₈×C₆₁	—	2	1	no	—
129	C₂×Q₈×C₆₁	—	2	4	no	—
130	C₂×Q₈×C₆₁	—	2	2	no	—
131	C₂×Q₈×C₆₁	—	2	2	no	—
132	C₂×Q₈×C₆₁	—	2	2	no	—
133	C₂×Q₈×C₆₁	—	4	4	no	—
134	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	—
135	C₂×Q₈×C₆₁	#41	1	4	yes	—
136	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
137	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
138	C₂×D₄×C₆₁	—	2	2	no	—
139	C₂×D₄×C₆₁	—	2	4	no	—
140	C₂×D₄×C₆₁	—	2	4	no	—
141	C₂×D₄×C₆₁	—	2	4	no	—
142	C₂×D₄×C₆₁	—	2	4	no	—
143	C₂×D₄×C₆₁	—	4	4	no	—
144	C₂×D₄×C₆₁	—	8	2	no	—
145	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
146	C₂²×C₄×C₆₁	—	2	1	no	—
147	C₂²×C₄×C₆₁	—	2	1	no	—
148	C₂²×C₄×C₆₁	—	2	1	no	—
149	C₂²×C₄×C₆₁	—	2	1	no	—
150	C₂²×C₄×C₆₁	—	2	2	no	—
151	C₂²×C₄×C₆₁	—	2	8	no	—
152	C₂²×C₄×C₆₁	—	8	4	no	—
153	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
158	Q₁₆×C₆₁	—	2	8	no	—
159	SD₁₆×C₆₁	—	2	16	no	—
160	C₂×C₈×C₆₁	—	2	4	no	—
161	C₂×C₈×C₆₁	—	2	2	no	—
162	C₂×C₈×C₆₁	—	2	2	no	—
163	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
164	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
165	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
166	C₄⋊C₄×C₆₁	—	2	8	no	—
167	C₄⋊C₄×C₆₁	—	2	4	no	—
168	C₄⋊C₄×C₆₁	—	2	4	no	—
169	C₄⋊C₄×C₆₁	—	2	8	no	—
170	C₄⋊C₄×C₆₁	—	2	4	no	—
171	C₄⋊C₄×C₆₁	—	2	8	no	—
172	C₄⋊C₄×C₆₁	—	2	1	no	—
173	C₄⋊C₄×C₆₁	—	2	1	no	—
174	C₄⋊C₄×C₆₁	—	2	2	no	—
175	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
176	C₄⋊C₄×C₆₁	C₂×D₄	1	8	yes	—
177	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
178	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
179	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
180	C₂²⋊C₄×C₆₁	—	2	8	no	—
181	C₂²⋊C₄×C₆₁	—	2	8	no	—
182	C₂²⋊C₄×C₆₁	—	2	8	no	—
183	C₄²×C₆₁	—	2	4	no	—
184	C₄²×C₆₁	—	2	8	no	—
185	C₄²×C₆₁	—	2	4	no	—
186	C₄²×C₆₁	C₂×D₄	1	4	yes	—
187	C₄²×C₆₁	C₂×D₄	1	2	yes	—
188	C₄²×C₆₁	C₂⁴	1	4	yes	—
189	C₄²×C₆₁	C₂⁴	1	2	yes	—
190	C₂³×C₆₁	—	2	4	no	—
191	C₂³×C₆₁	—	4	4	no	—
192	C₂³×C₆₁	—	4	4	no	—
193	C₂³×C₆₁	—	4	4	no	—
194	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
195	Q₈×C₆₁	—	2	4	no	—
196	Q₈×C₆₁	—	2	8	no	—
197	Q₈×C₆₁	—	2	2	no	—
198	Q₈×C₆₁	—	2	2	no	—
199	Q₈×C₆₁	—	2	2	no	—
200	Q₈×C₆₁	—	4	2	no	—
201	Q₈×C₆₁	—	4	8	no	—
202	Q₈×C₆₁	C₂×#41	1	4	yes	—
203	D₄×C₆₁	—	2	4	no	—
204	D₄×C₆₁	—	2	4	no	—
205	D₄×C₆₁	—	4	4	no	—
206	D₄×C₆₁	—	4	8	no	—
207	D₄×C₆₁	—	8	4	no	—
208	C₂×C₄×C₆₁	—	2	4	no	—
209	C₂×C₄×C₆₁	—	2	4	no	—
210	C₂×C₄×C₆₁	—	2	4	no	—
211	C₂×C₄×C₆₁	—	2	2	no	—
212	C₂×C₄×C₆₁	—	2	2	no	—
213	C₂×C₄×C₆₁	—	2	2	no	—
214	C₂×C₄×C₆₁	—	2	2	no	—
215	C₂×C₄×C₆₁	—	2	2	no	—
216	C₂×C₄×C₆₁	—	2	4	no	—
217	C₂×C₄×C₆₁	—	4	2	no	—
218	C₂×C₄×C₆₁	—	4	4	no	—
219	C₂×C₄×C₆₁	—	4	2	no	—
220	C₂×C₄×C₆₁	—	4	2	no	—
221	C₂×C₄×C₆₁	—	8	8	no	—
222	C₂×C₄×C₆₁	#135	1	4	yes	—
223	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
224	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
225	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
226	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
228	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
229	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
230	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
231	C₈×C₆₁	—	2	4	no	—
232	C₈×C₆₁	—	2	2	no	—
233	C₈×C₆₁	—	2	2	no	—
234	C₂×#3365	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂²×C₆₁	—	4	4	no	—
236	C₂²×C₆₁	—	4	4	no	—
237	C₂²×C₆₁	—	4	4	no	—
238	C₂²×C₆₁	—	8	8	no	—
239	C₂²×C₆₁	#548	1	2	yes	—
240	C₂²×C₆₁	C₂×#135	1	2	yes	—
241	C₂²×C₆₁	#577	1	2	yes	—
242	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
243	C₄×C₆₁	—	2	4	no	—
244	C₄×C₆₁	—	2	4	no	—
245	C₄×C₆₁	—	2	4	no	—
246	C₄×C₆₁	—	2	2	no	—
247	C₄×C₆₁	—	4	2	no	—
248	C₄×C₆₁	—	4	4	no	—
249	C₄×C₆₁	—	4	2	no	—
250	C₄×C₆₁	—	4	2	no	—
251	C₄×C₆₁	#548	1	2	yes	—
252	C₄×C₆₁	C₂×#135	1	4	yes	—
253	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
254	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
255	C₂×#559	C₂×C₆₁	1	1	yes	characteristic
256	C₂×#557	C₂×C₆₁	1	1	yes	characteristic, complemented
257	#3365	C₂×C₆₁	1	16	yes	direct product factor
258	C₂×#488	C₂×C₆₁	1	2	yes	complemented
259	C₂×#486	C₂×C₆₁	1	1	yes	characteristic
260	C₂×#475	C₂×C₆₁	1	1	yes	characteristic, complemented
261	C₂×#478	C₂×C₆₁	1	2	yes	complemented
262	C₂×#464	C₂×C₆₁	1	2	yes	complemented
263	C₂×#460	C₂×C₆₁	1	1	yes	characteristic
264	C₂×C₈×Q₈	C₂×C₆₁	1	1	yes	characteristic, complemented
265	C₂×C₄×Q₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
266	C₂×C₄×SD₁₆	C₂×C₆₁	1	2	yes	complemented
267	C₂×C₆₁	—	8	4	no	—
268	C₂×C₆₁	#3365	1	4	yes	direct product factor
269	C₂×C₆₁	C₂×#548	1	1	yes	characteristic
270	C₂×C₆₁	C₂²×#135	1	1	yes	characteristic
271	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
272	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
273	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	—
274	#559	—	2	4	no	—
275	#559	C₂²×C₆₁	1	8	yes	—
276	#557	—	2	4	no	—
277	#557	C₂²×C₆₁	1	8	yes	complemented
278	C₂×C₄⋊Q₈	—	2	1	no	—
279	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
280	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
281	C₂×#125	—	2	2	no	—
282	C₂×#125	C₂²×C₆₁	1	2	yes	—
283	C₂×#124	—	2	1	no	—
284	C₂×#124	C₂²×C₆₁	1	2	yes	—
285	C₂×#123	—	2	2	no	—
286	C₂×C₄×Q₈	—	2	1	no	—
287	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
288	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
289	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
290	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
291	C₂×C₄×D₄	—	2	1	no	—
292	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
293	#488	C₂²×C₆₁	1	16	yes	complemented
294	#486	C₂²×C₆₁	1	8	yes	—
295	#478	C₂²×C₆₁	1	16	yes	complemented
296	#475	C₂²×C₆₁	1	8	yes	complemented
297	#464	C₂²×C₆₁	1	16	yes	complemented
298	#460	C₂²×C₆₁	1	8	yes	—
299	C₈×Q₈	C₂²×C₆₁	1	8	yes	complemented
300	C₄×Q₁₆	C₂²×C₆₁	1	8	yes	complemented
301	C₄×SD₁₆	C₂²×C₆₁	1	16	yes	complemented
302	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
303	C₂×#106	C₂²×C₆₁	1	2	yes	—
304	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
305	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
306	C₂×#103	C₂²×C₆₁	1	2	yes	—
307	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
308	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
309	C₂×#102	C₂²×C₆₁	1	2	yes	—
310	C₂×#102	C₂²×C₆₁	1	2	yes	—
311	C₂×#102	C₂²×C₆₁	1	2	yes	—
312	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
313	C₂×C₄×C₈	C₂²×C₆₁	1	2	yes	—
314	C₆₁	C₂×#3365	1	1	yes	characteristic, direct product factor, Sylow
315	C₂²×Q₈	—	2	1	no	—
316	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
317	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
318	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
319	C₂²×D₄	—	2	1	no	—
320	C₂²×D₄	—	2	1	no	—
321	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
322	C₂³×C₄	—	2	2	no	—
323	C₂×Q₁₆	—	2	4	no	—
324	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
325	C₂×SD₁₆	—	2	8	no	—
326	C₂×SD₁₆	C₂³×C₆₁	1	8	yes	—
327	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
328	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
329	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
330	C₄⋊Q₈	—	2	8	no	—
331	C₄⋊Q₈	—	2	2	no	—
332	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
333	#127	—	2	2	no	—
334	#127	C₂³×C₆₁	1	4	yes	—
335	#125	—	2	16	no	—
336	#125	—	2	4	no	—
337	#125	C₂³×C₆₁	1	8	yes	—
338	#124	—	2	8	no	—
339	#124	—	2	4	no	—
340	#124	C₂³×C₆₁	1	8	yes	—
341	#123	—	2	16	no	—
342	C₄×Q₈	—	2	8	no	—
343	C₄×Q₈	—	2	4	no	—
344	C₄×Q₈	—	2	2	no	—
345	C₄×Q₈	—	2	2	no	—
346	C₄×Q₈	D₄×C₆₁	1	4	yes	—
347	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
348	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
349	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
350	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
351	C₄×D₄	—	2	8	no	—
352	C₄×D₄	—	2	4	no	—
353	C₄×D₄	C₂³×C₆₁	1	8	yes	—
354	C₂×C₄⋊C₄	—	2	2	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	2	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	2	no	—
360	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
361	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
362	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
365	C₂×C₂²⋊C₄	—	2	2	no	—
366	C₂×C₂²⋊C₄	—	2	2	no	—
367	C₂×C₂²⋊C₄	—	2	2	no	—
368	C₂×C₄²	—	2	1	no	—
369	C₂×C₄²	—	2	2	no	—
370	C₂×C₄²	—	2	1	no	—
371	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
372	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
373	#107	C₂³×C₆₁	1	4	yes	—
374	#106	C₂³×C₆₁	1	8	yes	—
375	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
376	C₄⋊C₈	C₂³×C₆₁	1	8	yes	—
377	#103	C₂³×C₆₁	1	4	yes	—
378	#103	C₂³×C₆₁	1	4	yes	—
379	#103	C₂³×C₆₁	1	8	yes	—
380	#102	C₂³×C₆₁	1	8	yes	—
381	#102	C₂³×C₆₁	1	8	yes	—
382	#102	C₂³×C₆₁	1	8	yes	—
383	C₄×C₈	C₂³×C₆₁	1	8	yes	—
384	C₄×C₈	C₂³×C₆₁	1	4	yes	—
385	C₂⁴	—	2	2	no	—
386	C₂×Q₈	—	2	4	no	—
387	C₂×Q₈	—	2	1	no	—
388	C₂×Q₈	—	2	1	no	—
389	C₂×Q₈	—	2	4	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	2	no	—
392	C₂×Q₈	—	2	2	no	—
393	C₂×Q₈	—	4	4	no	—
394	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	—
395	C₂×Q₈	#41×C₆₁	1	4	yes	—
396	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
397	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	4	no	—
400	C₂×D₄	—	2	4	no	—
401	C₂×D₄	—	2	4	no	—
402	C₂×D₄	—	2	4	no	—
403	C₂×D₄	—	4	4	no	—
404	C₂×D₄	—	8	2	no	—
405	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	8	no	—
412	C₂²×C₄	—	8	4	no	—
413	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
414	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
415	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
416	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
417	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
418	Q₁₆	—	2	8	no	—
419	SD₁₆	—	2	16	no	—
420	C₂×C₈	—	2	4	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
424	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
425	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
426	C₄⋊C₄	—	2	8	no	—
427	C₄⋊C₄	—	2	4	no	—
428	C₄⋊C₄	—	2	4	no	—
429	C₄⋊C₄	—	2	8	no	—
430	C₄⋊C₄	—	2	4	no	—
431	C₄⋊C₄	—	2	8	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
436	C₄⋊C₄	C₂×D₄×C₆₁	1	8	yes	—
437	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
438	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
439	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
440	C₂²⋊C₄	—	2	8	no	—
441	C₂²⋊C₄	—	2	8	no	—
442	C₂²⋊C₄	—	2	8	no	—
443	C₄²	—	2	4	no	—
444	C₄²	—	2	8	no	—
445	C₄²	—	2	4	no	—
446	C₄²	C₂×D₄×C₆₁	1	4	yes	—
447	C₄²	C₂×D₄×C₆₁	1	2	yes	—
448	C₄²	C₂⁴×C₆₁	1	4	yes	—
449	C₄²	C₂⁴×C₆₁	1	2	yes	—
450	C₂³	—	2	4	no	—
451	C₂³	—	4	4	no	—
452	C₂³	—	4	4	no	—
453	C₂³	—	4	4	no	—
454	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
455	Q₈	—	2	4	no	—
456	Q₈	—	2	8	no	—
457	Q₈	—	2	2	no	—
458	Q₈	—	2	2	no	—
459	Q₈	—	2	2	no	—
460	Q₈	—	4	2	no	—
461	Q₈	—	4	8	no	—
462	Q₈	C₂×#41×C₆₁	1	4	yes	—
463	D₄	—	2	4	no	—
464	D₄	—	2	4	no	—
465	D₄	—	4	4	no	—
466	D₄	—	4	8	no	—
467	D₄	—	8	4	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	4	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	4	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	4	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	8	8	no	—
482	C₂×C₄	#135×C₆₁	1	4	yes	—
483	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
484	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
485	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
486	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
487	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
488	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
489	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
490	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
491	C₈	—	2	4	no	—
492	C₈	—	2	2	no	—
493	C₈	—	2	2	no	—
494	C₂²	—	4	4	no	—
495	C₂²	—	4	4	no	—
496	C₂²	—	4	4	no	—
497	C₂²	—	8	8	no	—
498	C₂²	C₆₁×#548	1	2	yes	—
499	C₂²	C₂×#135×C₆₁	1	2	yes	—
500	C₂²	C₆₁×#577	1	2	yes	—
501	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
502	C₄	—	2	4	no	—
503	C₄	—	2	4	no	—
504	C₄	—	2	2	no	—
505	C₄	—	2	4	no	—
506	C₄	—	4	4	no	—
507	C₄	—	4	2	no	—
508	C₄	—	4	2	no	—
509	C₄	—	4	2	no	—
510	C₄	C₆₁×#548	1	2	yes	—
511	C₄	C₂×#135×C₆₁	1	4	yes	—
512	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
513	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
514	C₂	—	8	4	no	—
515	C₂	C₆₁×#3365	1	4	yes	direct product factor
516	C₂	C₂×C₆₁×#548	1	1	yes	characteristic
517	C₂	C₂²×#135×C₆₁	1	1	yes	characteristic
518	C₂	C₂×C₆₁×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₂×#127×C₆₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂×C₄×Q₈×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₆₁×#557	C₂	semidirect
3. C₆₁×#3365	C₂	direct (N × H)
4. C₂×C₆₁×#488	C₂	semidirect
6. C₂×C₆₁×#475	C₂	semidirect
7. C₂×C₆₁×#478	C₂	semidirect
8. C₂×C₆₁×#464	C₂	semidirect
10. C₂×C₈×Q₈×C₆₁	C₂	semidirect
11. C₂×C₄×Q₁₆×C₆₁	C₂	semidirect
12. C₂×C₄×SD₁₆×C₆₁	C₂	semidirect
18. C₆₁×#557	C₂²	semidirect
34. C₆₁×#488	C₂²	semidirect
36. C₆₁×#478	C₂²	semidirect
37. C₆₁×#475	C₂²	semidirect
38. C₆₁×#464	C₂²	semidirect
40. C₈×Q₈×C₆₁	C₂²	semidirect
41. C₄×Q₁₆×C₆₁	C₂²	semidirect
42. C₄×SD₁₆×C₆₁	C₂²	semidirect
234. C₂×#3365	C₆₁	direct (N × H)
256. C₂×#557	C₂×C₆₁	semidirect
257. #3365	C₂×C₆₁	direct (N × H)
258. C₂×#488	C₂×C₆₁	semidirect
260. C₂×#475	C₂×C₆₁	semidirect
261. C₂×#478	C₂×C₆₁	semidirect
262. C₂×#464	C₂×C₆₁	semidirect
264. C₂×C₈×Q₈	C₂×C₆₁	semidirect
265. C₂×C₄×Q₁₆	C₂×C₆₁	semidirect
266. C₂×C₄×SD₁₆	C₂×C₆₁	semidirect
268. C₂×C₆₁	#3365	direct (N × H)
277. #557	C₂²×C₆₁	semidirect
293. #488	C₂²×C₆₁	semidirect
295. #478	C₂²×C₆₁	semidirect
296. #475	C₂²×C₆₁	semidirect
297. #464	C₂²×C₆₁	semidirect
299. C₈×Q₈	C₂²×C₆₁	semidirect
300. C₄×Q₁₆	C₂²×C₆₁	semidirect
301. C₄×SD₁₆	C₂²×C₆₁	semidirect
314. C₆₁	C₂×#3365	direct (N × H)
515. C₂	C₆₁×#3365	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×#559	2
C₂×C₆₁×#557	2
C₆₁×#3365	2
C₂×C₆₁×#488	2
C₂×C₆₁×#486	2
C₂×C₆₁×#475	2
C₂×C₆₁×#478	2
C₂×C₆₁×#464	2
C₂×C₆₁×#460	2
C₂×C₈×Q₈×C₆₁	2
C₂×C₄×Q₁₆×C₆₁	2
C₂×C₄×SD₁₆×C₆₁	2
C₂×#3365	61

Subgroups — C2×C61×#3365 #29564735

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#3365 #29564735