Subgroups — C₂×C₆₁×#3339 #29564663

Order 15616.

1994 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#553	C₂	1	2	yes	maximal, complemented
2	C₆₁×#3339	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₆₁×#499	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₆₁×#481	C₂	1	2	yes	maximal, complemented
5	C₂×C₆₁×#482	C₂	1	2	yes	maximal, complemented
6	C₂×C₆₁×#478	C₂	1	2	yes	maximal, complemented
7	C₂×C₆₁×#466	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₆₁×#466	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×D₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₈×D₄×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₆₁×#427	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#107×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
16	C₆₁×#553	—	2	8	no	—
17	C₆₁×#553	C₂²	1	16	yes	complemented
18	C₂×#126×C₆₁	—	2	2	no	—
19	C₂×#125×C₆₁	C₂²	1	2	yes	—
20	C₂×#123×C₆₁	—	2	2	no	—
21	C₂×#121×C₆₁	—	2	2	no	—
22	C₂×#121×C₆₁	C₂²	1	2	yes	—
23	C₂×#121×C₆₁	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₆₁	—	2	2	no	—
25	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×#117×C₆₁	C₂²	1	2	yes	—
28	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
29	C₆₁×#499	C₂²	1	8	yes	complemented
30	C₆₁×#482	C₂²	1	16	yes	complemented
31	C₆₁×#481	C₂²	1	16	yes	complemented
32	C₆₁×#478	C₂²	1	16	yes	complemented
33	C₆₁×#466	C₂²	1	8	yes	complemented
34	C₆₁×#466	C₂²	1	8	yes	complemented
35	C₄×D₈×C₆₁	C₂²	1	8	yes	complemented
36	C₈×D₄×C₆₁	C₂²	1	8	yes	complemented
37	C₆₁×#427	C₂²	1	8	yes	complemented
38	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
39	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
40	C₂×#107×C₆₁	C₂²	1	2	yes	—
41	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
42	C₂×#107×C₆₁	C₂²	1	8	yes	complemented
43	C₂×#106×C₆₁	C₂²	1	2	yes	—
44	C₂×#106×C₆₁	C₂²	1	2	yes	—
45	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
46	C₂×#102×C₆₁	C₂²	1	2	yes	—
47	C₂×#102×C₆₁	C₂²	1	2	yes	—
48	C₂×#102×C₆₁	C₂²	1	2	yes	—
49	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
50	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
52	C₂²×D₄×C₆₁	—	2	2	no	—
53	C₂²×D₄×C₆₁	—	2	2	no	—
54	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
55	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
56	C₂³×C₄×C₆₁	—	2	2	no	—
57	C₂³×C₄×C₆₁	—	2	2	no	—
58	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
60	C₂×D₈×C₆₁	—	2	4	no	—
61	C₂×D₈×C₆₁	C₂³	1	4	yes	—
62	C₂²×C₈×C₆₁	—	2	4	no	—
63	C₂²×C₈×C₆₁	—	2	4	no	—
64	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
67	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
68	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
70	#126×C₆₁	—	2	16	no	—
71	#125×C₆₁	—	2	4	no	—
72	#125×C₆₁	C₂³	1	8	yes	—
73	#123×C₆₁	—	2	16	no	—
74	#121×C₆₁	—	2	16	no	—
75	#121×C₆₁	—	2	4	no	—
76	#121×C₆₁	—	2	4	no	—
77	#121×C₆₁	C₂³	1	8	yes	—
78	#121×C₆₁	C₂³	1	8	yes	—
79	C₄×D₄×C₆₁	—	2	16	no	—
80	C₄×D₄×C₆₁	—	2	4	no	—
81	C₄×D₄×C₆₁	D₄	1	4	yes	—
82	C₄×D₄×C₆₁	C₂³	1	8	yes	—
83	C₄×D₄×C₆₁	C₂³	1	4	yes	—
84	#117×C₆₁	—	2	4	no	—
85	#117×C₆₁	C₂³	1	8	yes	—
86	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
87	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
88	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
89	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
90	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
92	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
95	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
96	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
98	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
99	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₆₁	—	2	2	no	—
102	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
103	#107×C₆₁	C₂³	1	4	yes	—
104	#107×C₆₁	C₂³	1	4	yes	—
105	#107×C₆₁	C₂³	1	8	yes	—
106	#107×C₆₁	C₂³	1	4	yes	—
107	#106×C₆₁	C₂³	1	8	yes	—
108	#106×C₆₁	C₂³	1	8	yes	—
109	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
110	#102×C₆₁	C₂³	1	8	yes	—
111	#102×C₆₁	C₂³	1	8	yes	—
112	#102×C₆₁	C₂³	1	8	yes	—
113	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
114	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
115	C₄×C₈×C₆₁	C₂³	1	4	yes	—
116	C₂⁴×C₆₁	—	2	2	no	—
117	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
118	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
119	C₂×D₄×C₆₁	—	2	4	no	—
120	C₂×D₄×C₆₁	—	2	8	no	—
121	C₂×D₄×C₆₁	—	2	8	no	—
122	C₂×D₄×C₆₁	—	2	2	no	—
123	C₂×D₄×C₆₁	—	2	4	no	—
124	C₂×D₄×C₆₁	—	2	4	no	—
125	C₂×D₄×C₆₁	—	4	8	no	—
126	C₂×D₄×C₆₁	—	8	4	no	—
127	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
128	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
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	—	2	2	no	—
133	C₂²×C₄×C₆₁	—	2	2	no	—
134	C₂²×C₄×C₆₁	—	2	2	no	—
135	C₂²×C₄×C₆₁	—	2	2	no	—
136	C₂²×C₄×C₆₁	—	2	8	no	—
137	C₂²×C₄×C₆₁	—	2	8	no	—
138	C₂²×C₄×C₆₁	—	8	4	no	—
139	C₂²×C₄×C₆₁	—	8	4	no	—
140	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
147	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
149	D₈×C₆₁	—	2	8	no	—
150	C₂×C₈×C₆₁	—	2	2	no	—
151	C₂×C₈×C₆₁	—	2	2	no	—
152	C₂×C₈×C₆₁	—	2	2	no	—
153	C₂×C₈×C₆₁	—	2	8	no	—
154	C₂×C₈×C₆₁	—	2	8	no	—
155	C₂×C₈×C₆₁	#41	1	4	yes	—
156	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
157	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
158	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
159	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
160	C₄⋊C₄×C₆₁	—	2	2	no	—
161	C₄⋊C₄×C₆₁	—	2	2	no	—
162	C₄⋊C₄×C₆₁	—	2	8	no	—
163	C₄⋊C₄×C₆₁	—	2	8	no	—
164	C₄⋊C₄×C₆₁	—	2	8	no	—
165	C₄⋊C₄×C₆₁	—	2	2	no	—
166	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
167	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
168	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
169	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
170	C₂²⋊C₄×C₆₁	—	2	8	no	—
171	C₂²⋊C₄×C₆₁	—	2	8	no	—
172	C₂²⋊C₄×C₆₁	—	2	8	no	—
173	C₂²⋊C₄×C₆₁	—	2	8	no	—
174	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
175	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
176	C₄²×C₆₁	—	2	8	no	—
177	C₄²×C₆₁	C₂×D₄	1	2	yes	—
178	C₄²×C₆₁	C₂⁴	1	2	yes	—
179	C₂³×C₆₁	—	2	2	no	—
180	C₂³×C₆₁	—	2	2	no	—
181	C₂³×C₆₁	—	2	2	no	—
182	C₂³×C₆₁	—	2	2	no	—
183	C₂³×C₆₁	—	2	2	no	—
184	C₂³×C₆₁	—	2	4	no	—
185	C₂³×C₆₁	—	4	4	no	—
186	C₂³×C₆₁	—	4	4	no	—
187	C₂³×C₆₁	—	4	4	no	—
188	C₂³×C₆₁	#135	1	4	yes	—
189	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
190	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
191	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
192	D₄×C₆₁	—	2	8	no	—
193	D₄×C₆₁	—	2	4	no	—
194	D₄×C₆₁	—	2	4	no	—
195	D₄×C₆₁	—	4	16	no	—
196	D₄×C₆₁	—	4	4	no	—
197	D₄×C₆₁	—	8	8	no	—
198	C₂×C₄×C₆₁	—	2	2	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	4	no	—
203	C₂×C₄×C₆₁	—	2	4	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	4	no	—
209	C₂×C₄×C₆₁	—	2	4	no	—
210	C₂×C₄×C₆₁	—	2	4	no	—
211	C₂×C₄×C₆₁	—	4	4	no	—
212	C₂×C₄×C₆₁	—	4	4	no	—
213	C₂×C₄×C₆₁	—	4	4	no	—
214	C₂×C₄×C₆₁	—	8	8	no	—
215	C₂×C₄×C₆₁	—	8	8	no	—
216	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
217	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
218	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
219	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
220	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
222	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
223	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
224	C₈×C₆₁	—	2	2	no	—
225	C₈×C₆₁	—	2	2	no	—
226	C₈×C₆₁	—	2	2	no	—
227	C₈×C₆₁	C₂×#41	1	4	yes	—
228	C₂×#3339	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂²×C₆₁	—	2	8	no	—
230	C₂²×C₆₁	—	2	2	no	—
231	C₂²×C₆₁	—	2	2	no	—
232	C₂²×C₆₁	—	2	2	no	—
233	C₂²×C₆₁	—	2	2	no	—
234	C₂²×C₆₁	—	2	2	no	—
235	C₂²×C₆₁	—	4	4	no	—
236	C₂²×C₆₁	—	4	4	no	—
237	C₂²×C₆₁	—	4	4	no	—
238	C₂²×C₆₁	—	4	4	no	—
239	C₂²×C₆₁	—	8	8	no	—
240	C₂²×C₆₁	#547	1	2	yes	—
241	C₂²×C₆₁	C₂×#135	1	4	yes	—
242	C₂²×C₆₁	C₂×#135	1	2	yes	—
243	C₂²×C₆₁	#576	1	2	yes	—
244	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
245	C₄×C₆₁	—	2	2	no	—
246	C₄×C₆₁	—	2	2	no	—
247	C₄×C₆₁	—	2	2	no	—
248	C₄×C₆₁	—	2	2	no	—
249	C₄×C₆₁	—	4	4	no	—
250	C₄×C₆₁	—	4	4	no	—
251	C₄×C₆₁	—	4	4	no	—
252	C₄×C₆₁	#547	1	2	yes	—
253	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
254	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
255	C₂×#553	C₂×C₆₁	1	2	yes	complemented
256	#3339	C₂×C₆₁	1	16	yes	direct product factor
257	C₂×#499	C₂×C₆₁	1	1	yes	characteristic, complemented
258	C₂×#481	C₂×C₆₁	1	2	yes	complemented
259	C₂×#482	C₂×C₆₁	1	2	yes	complemented
260	C₂×#478	C₂×C₆₁	1	2	yes	complemented
261	C₂×#466	C₂×C₆₁	1	1	yes	characteristic, complemented
262	C₂×#466	C₂×C₆₁	1	1	yes	characteristic, complemented
263	C₂×C₄×D₈	C₂×C₆₁	1	1	yes	characteristic, complemented
264	C₂×C₈×D₄	C₂×C₆₁	1	1	yes	characteristic, complemented
265	C₂×#427	C₂×C₆₁	1	1	yes	characteristic, complemented
266	C₂²×#107	C₂×C₆₁	1	1	yes	characteristic, complemented
267	C₂×C₆₁	—	2	4	no	—
268	C₂×C₆₁	—	4	2	no	—
269	C₂×C₆₁	—	8	4	no	—
270	C₂×C₆₁	#3339	1	4	yes	direct product factor
271	C₂×C₆₁	C₂×#547	1	1	yes	characteristic
272	C₂×C₆₁	C₂²×#135	1	1	yes	characteristic
273	C₂×C₆₁	C₂×#576	1	1	yes	characteristic
274	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
275	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
276	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
277	#553	—	2	8	no	—
278	#553	C₂²×C₆₁	1	16	yes	complemented
279	C₂×#126	—	2	2	no	—
280	C₂×#125	C₂²×C₆₁	1	2	yes	—
281	C₂×#123	—	2	2	no	—
282	C₂×#121	—	2	2	no	—
283	C₂×#121	C₂²×C₆₁	1	2	yes	—
284	C₂×#121	C₂²×C₆₁	1	2	yes	—
285	C₂×C₄×D₄	—	2	2	no	—
286	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
287	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
288	C₂×#117	C₂²×C₆₁	1	2	yes	—
289	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
290	#499	C₂²×C₆₁	1	8	yes	complemented
291	#482	C₂²×C₆₁	1	16	yes	complemented
292	#481	C₂²×C₆₁	1	16	yes	complemented
293	#478	C₂²×C₆₁	1	16	yes	complemented
294	#466	C₂²×C₆₁	1	8	yes	complemented
295	#466	C₂²×C₆₁	1	8	yes	complemented
296	C₄×D₈	C₂²×C₆₁	1	8	yes	complemented
297	C₈×D₄	C₂²×C₆₁	1	8	yes	complemented
298	#427	C₂²×C₆₁	1	8	yes	complemented
299	C₂×#107	C₂²×C₆₁	1	2	yes	—
300	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
301	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
302	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
303	C₂×#107	C₂²×C₆₁	1	8	yes	complemented
304	C₂×#106	C₂²×C₆₁	1	2	yes	—
305	C₂×#106	C₂²×C₆₁	1	2	yes	—
306	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
307	C₂×#102	C₂²×C₆₁	1	2	yes	—
308	C₂×#102	C₂²×C₆₁	1	2	yes	—
309	C₂×#102	C₂²×C₆₁	1	2	yes	—
310	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
311	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
312	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
313	C₆₁	C₂×#3339	1	1	yes	characteristic, direct product factor, Sylow
314	C₂²×D₄	—	2	2	no	—
315	C₂²×D₄	—	2	2	no	—
316	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
317	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
318	C₂³×C₄	—	2	2	no	—
319	C₂³×C₄	—	2	2	no	—
320	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
321	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
322	C₂×D₈	—	2	4	no	—
323	C₂×D₈	C₂³×C₆₁	1	4	yes	—
324	C₂²×C₈	—	2	4	no	—
325	C₂²×C₈	—	2	4	no	—
326	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
327	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
328	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
329	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
330	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
331	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
332	#126	—	2	16	no	—
333	#125	—	2	4	no	—
334	#125	C₂³×C₆₁	1	8	yes	—
335	#123	—	2	16	no	—
336	#121	—	2	16	no	—
337	#121	—	2	4	no	—
338	#121	—	2	4	no	—
339	#121	C₂³×C₆₁	1	8	yes	—
340	#121	C₂³×C₆₁	1	8	yes	—
341	C₄×D₄	—	2	16	no	—
342	C₄×D₄	—	2	4	no	—
343	C₄×D₄	D₄×C₆₁	1	4	yes	—
344	C₄×D₄	C₂³×C₆₁	1	8	yes	—
345	C₄×D₄	C₂³×C₆₁	1	4	yes	—
346	#117	—	2	4	no	—
347	#117	C₂³×C₆₁	1	8	yes	—
348	C₂×C₄⋊C₄	—	2	2	no	—
349	C₂×C₄⋊C₄	—	2	4	no	—
350	C₂×C₄⋊C₄	—	2	2	no	—
351	C₂×C₄⋊C₄	—	2	2	no	—
352	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
354	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
355	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
356	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₂²⋊C₄	—	2	2	no	—
359	C₂×C₂²⋊C₄	—	2	2	no	—
360	C₂×C₂²⋊C₄	—	2	2	no	—
361	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
362	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
363	C₂×C₄²	—	2	2	no	—
364	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
365	#107	C₂³×C₆₁	1	4	yes	—
366	#107	C₂³×C₆₁	1	4	yes	—
367	#107	C₂³×C₆₁	1	8	yes	—
368	#107	C₂³×C₆₁	1	4	yes	—
369	#106	C₂³×C₆₁	1	8	yes	—
370	#106	C₂³×C₆₁	1	8	yes	—
371	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
372	#102	C₂³×C₆₁	1	8	yes	—
373	#102	C₂³×C₆₁	1	8	yes	—
374	#102	C₂³×C₆₁	1	8	yes	—
375	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
376	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
377	C₄×C₈	C₂³×C₆₁	1	4	yes	—
378	C₂⁴	—	2	2	no	—
379	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
380	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
381	C₂×D₄	—	2	4	no	—
382	C₂×D₄	—	2	8	no	—
383	C₂×D₄	—	2	8	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	2	4	no	—
386	C₂×D₄	—	2	4	no	—
387	C₂×D₄	—	4	8	no	—
388	C₂×D₄	—	8	4	no	—
389	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
390	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	8	no	—
399	C₂²×C₄	—	2	8	no	—
400	C₂²×C₄	—	8	4	no	—
401	C₂²×C₄	—	8	4	no	—
402	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
404	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
405	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
406	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
407	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
408	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
409	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
410	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
411	D₈	—	2	8	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	8	no	—
416	C₂×C₈	—	2	8	no	—
417	C₂×C₈	#41×C₆₁	1	4	yes	—
418	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
419	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
420	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
421	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	8	no	—
425	C₄⋊C₄	—	2	8	no	—
426	C₄⋊C₄	—	2	8	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
429	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
430	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
431	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
432	C₂²⋊C₄	—	2	8	no	—
433	C₂²⋊C₄	—	2	8	no	—
434	C₂²⋊C₄	—	2	8	no	—
435	C₂²⋊C₄	—	2	8	no	—
436	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
437	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
438	C₄²	—	2	8	no	—
439	C₄²	C₂×D₄×C₆₁	1	2	yes	—
440	C₄²	C₂⁴×C₆₁	1	2	yes	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	2	no	—
445	C₂³	—	2	2	no	—
446	C₂³	—	2	4	no	—
447	C₂³	—	4	4	no	—
448	C₂³	—	4	4	no	—
449	C₂³	—	4	4	no	—
450	C₂³	#135×C₆₁	1	4	yes	—
451	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
452	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
453	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
454	D₄	—	2	8	no	—
455	D₄	—	2	4	no	—
456	D₄	—	2	4	no	—
457	D₄	—	4	16	no	—
458	D₄	—	4	4	no	—
459	D₄	—	8	8	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	4	4	no	—
474	C₂×C₄	—	4	4	no	—
475	C₂×C₄	—	4	4	no	—
476	C₂×C₄	—	8	8	no	—
477	C₂×C₄	—	8	8	no	—
478	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
479	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
480	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
481	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
482	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
483	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
484	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
485	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
486	C₈	—	2	2	no	—
487	C₈	—	2	2	no	—
488	C₈	—	2	2	no	—
489	C₈	C₂×#41×C₆₁	1	4	yes	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	8	no	—
492	C₂²	—	2	2	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	2	2	no	—
496	C₂²	—	4	4	no	—
497	C₂²	—	4	4	no	—
498	C₂²	—	4	4	no	—
499	C₂²	—	4	4	no	—
500	C₂²	—	8	8	no	—
501	C₂²	C₆₁×#547	1	2	yes	—
502	C₂²	C₂×#135×C₆₁	1	4	yes	—
503	C₂²	C₂×#135×C₆₁	1	2	yes	—
504	C₂²	C₆₁×#576	1	2	yes	—
505	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
506	C₄	—	2	2	no	—
507	C₄	—	2	2	no	—
508	C₄	—	2	2	no	—
509	C₄	—	2	2	no	—
510	C₄	—	4	4	no	—
511	C₄	—	4	4	no	—
512	C₄	—	4	4	no	—
513	C₄	C₆₁×#547	1	2	yes	—
514	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
515	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
516	C₂	—	2	4	no	—
517	C₂	—	4	2	no	—
518	C₂	—	8	4	no	—
519	C₂	C₆₁×#3339	1	4	yes	direct product factor
520	C₂	C₂×C₆₁×#547	1	1	yes	characteristic
521	C₂	C₂²×#135×C₆₁	1	1	yes	characteristic
522	C₂	C₂×C₆₁×#576	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#553	C₂	semidirect
2. C₆₁×#3339	C₂	direct (N × H)
3. C₂×C₆₁×#499	C₂	semidirect
4. C₂×C₆₁×#481	C₂	semidirect
5. C₂×C₆₁×#482	C₂	semidirect
6. C₂×C₆₁×#478	C₂	semidirect
7. C₂×C₆₁×#466	C₂	semidirect
8. C₂×C₆₁×#466	C₂	semidirect
9. C₂×C₄×D₈×C₆₁	C₂	semidirect
10. C₂×C₈×D₄×C₆₁	C₂	semidirect
11. C₂×C₆₁×#427	C₂	semidirect
12. C₂²×#107×C₆₁	C₂	semidirect
17. C₆₁×#553	C₂²	semidirect
29. C₆₁×#499	C₂²	semidirect
30. C₆₁×#482	C₂²	semidirect
31. C₆₁×#481	C₂²	semidirect
32. C₆₁×#478	C₂²	semidirect
33. C₆₁×#466	C₂²	semidirect
34. C₆₁×#466	C₂²	semidirect
35. C₄×D₈×C₆₁	C₂²	semidirect
36. C₈×D₄×C₆₁	C₂²	semidirect
37. C₆₁×#427	C₂²	semidirect
42. C₂×#107×C₆₁	C₂²	semidirect
228. C₂×#3339	C₆₁	direct (N × H)
255. C₂×#553	C₂×C₆₁	semidirect
256. #3339	C₂×C₆₁	direct (N × H)
257. C₂×#499	C₂×C₆₁	semidirect
258. C₂×#481	C₂×C₆₁	semidirect
259. C₂×#482	C₂×C₆₁	semidirect
260. C₂×#478	C₂×C₆₁	semidirect
261. C₂×#466	C₂×C₆₁	semidirect
262. C₂×#466	C₂×C₆₁	semidirect
263. C₂×C₄×D₈	C₂×C₆₁	semidirect
264. C₂×C₈×D₄	C₂×C₆₁	semidirect
265. C₂×#427	C₂×C₆₁	semidirect
266. C₂²×#107	C₂×C₆₁	semidirect
270. C₂×C₆₁	#3339	direct (N × H)
278. #553	C₂²×C₆₁	semidirect
290. #499	C₂²×C₆₁	semidirect
291. #482	C₂²×C₆₁	semidirect
292. #481	C₂²×C₆₁	semidirect
293. #478	C₂²×C₆₁	semidirect
294. #466	C₂²×C₆₁	semidirect
295. #466	C₂²×C₆₁	semidirect
296. C₄×D₈	C₂²×C₆₁	semidirect
297. C₈×D₄	C₂²×C₆₁	semidirect
298. #427	C₂²×C₆₁	semidirect
303. C₂×#107	C₂²×C₆₁	semidirect
313. C₆₁	C₂×#3339	direct (N × H)
519. C₂	C₆₁×#3339	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×#553	2
C₆₁×#3339	2
C₂×C₆₁×#499	2
C₂×C₆₁×#481	2
C₂×C₆₁×#482	2
C₂×C₆₁×#478	2
C₂×C₆₁×#466	2
C₂×C₄×D₈×C₆₁	2
C₂×C₈×D₄×C₆₁	2
C₂×C₆₁×#427	2
C₂²×#107×C₆₁	2
C₂×#3339	61

Subgroups — C2×C61×#3339 #29564663

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#3339 #29564663