Subgroups — C₆₁×#34123 #29537556

Order 15616.

2598 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#2356	C₂	1	2	yes	maximal, complemented
3	C₆₁×#2353	C₂	1	4	yes	maximal, complemented
4	C₆₁×#2349	C₂	1	2	yes	maximal, complemented
5	C₆₁×#2346	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2343	C₂	1	4	yes	maximal, complemented
7	C₆₁×#2339	C₂	1	2	yes	maximal
8	C₆₁×#2295	C₂	1	2	yes	maximal, complemented
9	C₆₁×#2290	C₂	1	4	yes	maximal, complemented
10	C₆₁×#2283	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#2283	C₂	1	2	yes	maximal, complemented
12	C₄²×D₄×C₆₁	C₂	1	2	yes	maximal, complemented
13	C₄×#117×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₆₁×#376	C₂	1	2	yes	maximal, complemented
15	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
16	C₄×#41×C₆₁	C₄	1	16	yes	complemented
17	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₆₁	C₂²	1	4	yes	—
20	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
24	C₂×#117×C₆₁	C₂²	1	2	yes	—
25	C₂×#117×C₆₁	C₂²	1	2	yes	—
26	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₆₁	C₂²	1	4	yes	—
28	C₂²×C₄²×C₆₁	C₂²	1	2	yes	—
29	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
30	C₆₁×#391	C₂²	1	4	yes	—
31	C₆₁×#389	C₂²	1	4	yes	—
32	C₆₁×#388	C₂²	1	8	yes	—
33	C₆₁×#387	C₂²	1	8	yes	—
34	C₆₁×#387	C₂²	1	8	yes	—
35	C₆₁×#386	C₂²	1	8	yes	—
36	C₆₁×#385	C₂²	1	8	yes	—
37	C₆₁×#383	C₂²	1	2	yes	—
38	C₆₁×#383	C₂²	1	4	yes	—
39	C₆₁×#382	C₂²	1	4	yes	—
40	C₆₁×#382	C₂²	1	2	yes	—
41	C₆₁×#381	C₂²	1	4	yes	—
42	C₆₁×#381	C₂²	1	2	yes	—
43	C₆₁×#380	C₂²	1	2	yes	—
44	C₆₁×#380	C₂²	1	4	yes	—
45	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
46	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
47	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
48	C₄×C₄⋊C₄×C₆₁	C₂²	1	4	yes	—
49	C₄×C₄⋊C₄×C₆₁	C₂²	1	4	yes	—
50	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
51	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
52	C₄×C₂²⋊C₄×C₆₁	C₂²	1	4	yes	—
53	C₄×C₂²⋊C₄×C₆₁	C₂²	1	8	yes	—
54	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
55	C₆₁×#376	C₂²	1	1	yes	characteristic
56	C₆₁×#376	C₂²	1	2	yes	—
57	C₆₁×#376	C₂²	1	4	yes	—
58	C₆₁×#376	C₂²	1	4	yes	—
59	C₆₁×#376	C₂²	1	4	yes	—
60	C₆₁×#376	C₂²	1	1	yes	characteristic
61	C₂×#95×C₆₁	C₂²	1	4	yes	—
62	C₂×#95×C₆₁	C₂²	1	4	yes	—
63	C₄³×C₆₁	C₂²	1	2	yes	—
64	C₂×#41×C₆₁	—	2	8	no	—
65	C₂×#41×C₆₁	C₂×C₄	1	8	yes	—
66	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
68	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₆₁	C₂³	1	8	yes	—
70	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
71	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
73	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
75	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
76	C₄×Q₈×C₆₁	C₂×C₄	1	8	yes	complemented
77	C₄×Q₈×C₆₁	C₂×C₄	1	8	yes	complemented
78	C₄×D₄×C₆₁	—	2	16	no	—
79	C₄×D₄×C₆₁	C₂×C₄	1	8	yes	—
80	C₄×D₄×C₆₁	C₂×C₄	1	8	yes	—
81	C₄×D₄×C₆₁	C₂×C₄	1	16	yes	complemented
82	C₄×D₄×C₆₁	C₂×C₄	1	16	yes	complemented
83	#117×C₆₁	—	2	8	no	—
84	#117×C₆₁	C₂×C₄	1	16	yes	complemented
85	#117×C₆₁	C₂×C₄	1	8	yes	complemented
86	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
87	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
88	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
89	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
93	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
94	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
95	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
96	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
97	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
98	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
99	C₂×C₄²×C₆₁	—	2	16	no	—
100	C₂×C₄²×C₆₁	C₂×C₄	1	8	yes	complemented
101	C₂×C₄²×C₆₁	C₂×C₄	1	16	yes	complemented
102	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
103	C₂×C₄²×C₆₁	C₂³	1	8	yes	—
104	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
105	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
106	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
107	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
108	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
109	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
114	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
115	#95×C₆₁	C₂³	1	2	yes	—
116	#95×C₆₁	C₂³	1	2	yes	—
117	#95×C₆₁	C₂³	1	4	yes	—
118	#95×C₆₁	C₂³	1	4	yes	—
119	#95×C₆₁	C₂³	1	8	yes	—
120	#95×C₆₁	C₂³	1	8	yes	—
121	#95×C₆₁	C₂³	1	2	yes	—
122	#95×C₆₁	C₂³	1	2	yes	—
123	#95×C₆₁	C₂³	1	4	yes	—
124	#95×C₆₁	C₂³	1	8	yes	—
125	#95×C₆₁	C₂³	1	4	yes	—
126	#95×C₆₁	C₂³	1	8	yes	—
127	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
128	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
129	#41×C₆₁	—	2	32	no	—
130	C₂×Q₈×C₆₁	—	2	4	no	—
131	C₂×Q₈×C₆₁	C₂²×C₄	1	4	yes	—
132	C₂×D₄×C₆₁	—	2	8	no	—
133	C₂×D₄×C₆₁	C₂²×C₄	1	8	yes	—
134	C₂×D₄×C₆₁	C₂²×C₄	1	4	yes	—
135	C₂×D₄×C₆₁	#41	1	8	yes	—
136	C₂²×C₄×C₆₁	—	2	8	no	—
137	C₂²×C₄×C₆₁	—	2	8	no	—
138	C₂²×C₄×C₆₁	—	2	4	no	—
139	C₂²×C₄×C₆₁	—	2	4	no	—
140	C₂²×C₄×C₆₁	—	2	16	no	—
141	C₂²×C₄×C₆₁	—	2	16	no	—
142	C₂²×C₄×C₆₁	—	4	2	no	—
143	C₂²×C₄×C₆₁	—	4	8	no	—
144	C₂²×C₄×C₆₁	—	4	4	no	—
145	C₂²×C₄×C₆₁	C₂²×C₄	1	8	yes	—
146	C₂²×C₄×C₆₁	C₂²×C₄	1	4	yes	—
147	C₂²×C₄×C₆₁	C₂²×C₄	1	8	yes	—
148	C₂²×C₄×C₆₁	C₂²×C₄	1	4	yes	—
149	C₂²×C₄×C₆₁	C₂²×C₄	1	8	yes	—
150	C₂²×C₄×C₆₁	C₂²×C₄	1	4	yes	—
151	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
152	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
153	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
154	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
155	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
156	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
158	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
159	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
160	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
161	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
162	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
163	C₄⋊C₄×C₆₁	—	2	8	no	—
164	C₄⋊C₄×C₆₁	—	2	8	no	—
165	C₄⋊C₄×C₆₁	—	4	8	no	—
166	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
167	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
168	C₄⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
169	C₄⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
170	C₂²⋊C₄×C₆₁	—	2	16	no	—
171	C₂²⋊C₄×C₆₁	—	2	8	no	—
172	C₂²⋊C₄×C₆₁	—	4	4	no	—
173	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
174	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
175	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
176	C₄²×C₆₁	—	2	16	no	—
177	C₄²×C₆₁	—	2	8	no	—
178	C₄²×C₆₁	—	2	4	no	—
179	C₄²×C₆₁	—	2	8	no	—
180	C₄²×C₆₁	—	4	4	no	—
181	C₄²×C₆₁	C₂²×C₄	1	4	yes	—
182	C₄²×C₆₁	C₂²×C₄	1	8	yes	—
183	C₄²×C₆₁	C₂²×C₄	1	4	yes	—
184	C₄²×C₆₁	C₂²×C₄	1	4	yes	—
185	C₄²×C₆₁	C₂²×C₄	1	4	yes	—
186	C₄²×C₆₁	C₂²×C₄	1	8	yes	—
187	C₄²×C₆₁	C₂²×C₄	1	8	yes	—
188	C₄²×C₆₁	#41	1	8	yes	complemented
189	C₂³×C₆₁	—	2	4	no	—
190	C₂³×C₆₁	—	2	4	no	—
191	C₂³×C₆₁	—	2	2	no	—
192	C₂³×C₆₁	—	2	2	no	—
193	C₂³×C₆₁	—	2	2	no	—
194	C₂³×C₆₁	C₂³×C₄	1	2	yes	—
195	C₂³×C₆₁	C₂³×C₄	1	4	yes	—
196	C₂³×C₆₁	C₂×#41	1	8	yes	—
197	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
198	Q₈×C₆₁	—	2	8	no	—
199	D₄×C₆₁	—	2	16	no	—
200	D₄×C₆₁	#117	1	16	yes	complemented
201	C₂×C₄×C₆₁	—	2	16	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	4	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	2	no	—
211	C₂×C₄×C₆₁	—	2	8	no	—
212	C₂×C₄×C₆₁	—	2	16	no	—
213	C₂×C₄×C₆₁	—	2	8	no	—
214	C₂×C₄×C₆₁	—	2	8	no	—
215	C₂×C₄×C₆₁	—	2	4	no	—
216	C₂×C₄×C₆₁	—	2	4	no	—
217	C₂×C₄×C₆₁	—	2	8	no	—
218	C₂×C₄×C₆₁	—	2	4	no	—
219	C₂×C₄×C₆₁	—	2	8	no	—
220	C₂×C₄×C₆₁	—	4	8	no	—
221	C₂×C₄×C₆₁	—	4	4	no	—
222	C₂×C₄×C₆₁	—	4	32	no	—
223	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
224	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
225	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
226	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
227	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
228	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
229	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
230	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
231	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
232	C₂×C₄×C₆₁	C₂×#41	1	8	yes	—
233	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
234	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
235	#34123	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
236	C₂²×C₆₁	—	2	4	no	—
237	C₂²×C₆₁	—	2	4	no	—
238	C₂²×C₆₁	—	2	16	no	—
239	C₂²×C₆₁	—	2	2	no	—
240	C₂²×C₆₁	—	2	2	no	—
241	C₂²×C₆₁	—	2	2	no	—
242	C₂²×C₆₁	—	4	4	no	—
243	C₂²×C₆₁	C₂×#117	1	8	yes	—
244	C₂²×C₆₁	C₂⁴×C₄	1	1	yes	characteristic
245	C₂²×C₆₁	C₂²×#41	1	2	yes	—
246	C₂²×C₆₁	C₂²×#41	1	2	yes	—
247	C₂²×C₆₁	#585	1	2	yes	—
248	C₄×C₆₁	—	2	2	no	—
249	C₄×C₆₁	—	2	4	no	—
250	C₄×C₆₁	—	2	4	no	—
251	C₄×C₆₁	—	2	2	no	—
252	C₄×C₆₁	—	2	2	no	—
253	C₄×C₆₁	—	2	2	no	—
254	C₄×C₆₁	—	2	4	no	—
255	C₄×C₆₁	—	2	8	no	—
256	C₄×C₆₁	—	4	4	no	—
257	C₄×C₆₁	—	4	8	no	—
258	C₄×C₆₁	C₂×#117	1	4	yes	—
259	C₄×C₆₁	C₄×#41	1	4	yes	—
260	C₂×C₄×#41	C₂×C₆₁	1	1	yes	characteristic
261	#2356	C₂×C₆₁	1	2	yes	complemented
262	#2353	C₂×C₆₁	1	4	yes	complemented
263	#2349	C₂×C₆₁	1	2	yes	complemented
264	#2346	C₂×C₆₁	1	2	yes	complemented
265	#2343	C₂×C₆₁	1	4	yes	complemented
266	#2339	C₂×C₆₁	1	2	yes	—
267	#2295	C₂×C₆₁	1	2	yes	complemented
268	#2290	C₂×C₆₁	1	4	yes	complemented
269	#2283	C₂×C₆₁	1	1	yes	characteristic, complemented
270	#2283	C₂×C₆₁	1	2	yes	complemented
271	C₄²×D₄	C₂×C₆₁	1	2	yes	complemented
272	C₄×#117	C₂×C₆₁	1	1	yes	characteristic, complemented
273	C₂×#376	C₂×C₆₁	1	2	yes	complemented
274	C₂×C₆₁	—	2	8	no	—
275	C₂×C₆₁	—	4	2	no	—
276	C₂×C₆₁	C₂²×#117	1	1	yes	characteristic
277	C₂×C₆₁	C₂×C₄×#41	1	1	yes	characteristic
278	C₂×C₆₁	#3428	1	1	yes	characteristic
279	C₂×C₆₁	#3475	1	4	yes	—
280	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
281	C₄×#41	C₄×C₆₁	1	16	yes	complemented
282	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
283	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
284	C₂×C₄×D₄	C₂²×C₆₁	1	4	yes	—
285	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
286	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
287	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
288	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
289	C₂×#117	C₂²×C₆₁	1	2	yes	—
290	C₂×#117	C₂²×C₆₁	1	2	yes	—
291	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
292	C₂²×C₄²	C₂²×C₆₁	1	4	yes	—
293	C₂²×C₄²	C₂²×C₆₁	1	2	yes	—
294	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
295	#391	C₂²×C₆₁	1	4	yes	—
296	#389	C₂²×C₆₁	1	4	yes	—
297	#388	C₂²×C₆₁	1	8	yes	—
298	#387	C₂²×C₆₁	1	8	yes	—
299	#387	C₂²×C₆₁	1	8	yes	—
300	#386	C₂²×C₆₁	1	8	yes	—
301	#385	C₂²×C₆₁	1	8	yes	—
302	#383	C₂²×C₆₁	1	2	yes	—
303	#383	C₂²×C₆₁	1	4	yes	—
304	#382	C₂²×C₆₁	1	4	yes	—
305	#382	C₂²×C₆₁	1	2	yes	—
306	#381	C₂²×C₆₁	1	4	yes	—
307	#381	C₂²×C₆₁	1	2	yes	—
308	#380	C₂²×C₆₁	1	2	yes	—
309	#380	C₂²×C₆₁	1	4	yes	—
310	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
311	C₄×C₄⋊C₄	C₂²×C₆₁	1	4	yes	—
312	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
313	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
314	C₄×C₄⋊C₄	C₂²×C₆₁	1	4	yes	—
315	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
316	C₄×C₂²⋊C₄	C₂²×C₆₁	1	8	yes	—
317	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
318	C₄×C₂²⋊C₄	C₂²×C₆₁	1	4	yes	—
319	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
320	#376	C₂²×C₆₁	1	4	yes	—
321	#376	C₂²×C₆₁	1	4	yes	—
322	#376	C₂²×C₆₁	1	1	yes	characteristic
323	#376	C₂²×C₆₁	1	2	yes	—
324	#376	C₂²×C₆₁	1	4	yes	—
325	#376	C₂²×C₆₁	1	1	yes	characteristic
326	C₂×#95	C₂²×C₆₁	1	4	yes	—
327	C₂×#95	C₂²×C₆₁	1	4	yes	—
328	C₄³	C₂²×C₆₁	1	2	yes	—
329	C₆₁	#34123	1	1	yes	characteristic, direct product factor, Sylow
330	C₂×#41	—	2	8	no	—
331	C₂×#41	C₂×C₄×C₆₁	1	8	yes	—
332	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
333	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
334	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
335	C₂³×C₄	C₂³×C₆₁	1	8	yes	—
336	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
337	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
338	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
339	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
340	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
341	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
342	C₄×Q₈	C₂×C₄×C₆₁	1	8	yes	complemented
343	C₄×Q₈	C₂×C₄×C₆₁	1	8	yes	complemented
344	C₄×D₄	—	2	16	no	—
345	C₄×D₄	C₂×C₄×C₆₁	1	8	yes	—
346	C₄×D₄	C₂×C₄×C₆₁	1	8	yes	—
347	C₄×D₄	C₂×C₄×C₆₁	1	16	yes	complemented
348	C₄×D₄	C₂×C₄×C₆₁	1	16	yes	complemented
349	#117	—	2	8	no	—
350	#117	C₂×C₄×C₆₁	1	16	yes	complemented
351	#117	C₂×C₄×C₆₁	1	8	yes	complemented
352	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
353	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
354	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
355	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
357	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
358	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
359	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
360	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
361	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
362	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
363	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
364	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
365	C₂×C₄²	—	2	16	no	—
366	C₂×C₄²	C₂×C₄×C₆₁	1	8	yes	complemented
367	C₂×C₄²	C₂×C₄×C₆₁	1	16	yes	complemented
368	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
369	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
370	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
371	C₂×C₄²	C₂³×C₆₁	1	8	yes	—
372	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
373	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
374	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
375	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
376	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
377	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
378	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
379	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
380	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
381	#95	C₂³×C₆₁	1	2	yes	—
382	#95	C₂³×C₆₁	1	2	yes	—
383	#95	C₂³×C₆₁	1	4	yes	—
384	#95	C₂³×C₆₁	1	4	yes	—
385	#95	C₂³×C₆₁	1	8	yes	—
386	#95	C₂³×C₆₁	1	8	yes	—
387	#95	C₂³×C₆₁	1	2	yes	—
388	#95	C₂³×C₆₁	1	2	yes	—
389	#95	C₂³×C₆₁	1	4	yes	—
390	#95	C₂³×C₆₁	1	8	yes	—
391	#95	C₂³×C₆₁	1	4	yes	—
392	#95	C₂³×C₆₁	1	8	yes	—
393	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
394	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
395	#41	—	2	32	no	—
396	C₂×Q₈	—	2	4	no	—
397	C₂×Q₈	C₂²×C₄×C₆₁	1	4	yes	—
398	C₂×D₄	—	2	8	no	—
399	C₂×D₄	C₂²×C₄×C₆₁	1	8	yes	—
400	C₂×D₄	C₂²×C₄×C₆₁	1	4	yes	—
401	C₂×D₄	#41×C₆₁	1	8	yes	—
402	C₂²×C₄	—	2	8	no	—
403	C₂²×C₄	—	2	8	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	4	no	—
406	C₂²×C₄	—	2	16	no	—
407	C₂²×C₄	—	2	16	no	—
408	C₂²×C₄	—	4	2	no	—
409	C₂²×C₄	—	4	8	no	—
410	C₂²×C₄	—	4	4	no	—
411	C₂²×C₄	C₂²×C₄×C₆₁	1	8	yes	—
412	C₂²×C₄	C₂²×C₄×C₆₁	1	4	yes	—
413	C₂²×C₄	C₂²×C₄×C₆₁	1	8	yes	—
414	C₂²×C₄	C₂²×C₄×C₆₁	1	4	yes	—
415	C₂²×C₄	C₂²×C₄×C₆₁	1	8	yes	—
416	C₂²×C₄	C₂²×C₄×C₆₁	1	4	yes	—
417	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
418	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
419	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
420	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
421	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
422	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
423	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
424	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
425	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
426	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
427	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
428	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
429	C₄⋊C₄	—	2	8	no	—
430	C₄⋊C₄	—	2	8	no	—
431	C₄⋊C₄	—	4	8	no	—
432	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
433	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
434	C₄⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
435	C₄⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
436	C₂²⋊C₄	—	2	16	no	—
437	C₂²⋊C₄	—	2	8	no	—
438	C₂²⋊C₄	—	4	4	no	—
439	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
440	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
441	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
442	C₄²	—	2	16	no	—
443	C₄²	—	2	8	no	—
444	C₄²	—	2	4	no	—
445	C₄²	—	2	8	no	—
446	C₄²	—	4	4	no	—
447	C₄²	C₂²×C₄×C₆₁	1	4	yes	—
448	C₄²	C₂²×C₄×C₆₁	1	8	yes	—
449	C₄²	C₂²×C₄×C₆₁	1	4	yes	—
450	C₄²	C₂²×C₄×C₆₁	1	4	yes	—
451	C₄²	C₂²×C₄×C₆₁	1	4	yes	—
452	C₄²	C₂²×C₄×C₆₁	1	8	yes	—
453	C₄²	C₂²×C₄×C₆₁	1	8	yes	—
454	C₄²	#41×C₆₁	1	8	yes	complemented
455	C₂³	—	2	4	no	—
456	C₂³	—	2	4	no	—
457	C₂³	—	2	2	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	2	2	no	—
460	C₂³	C₂³×C₄×C₆₁	1	2	yes	—
461	C₂³	C₂³×C₄×C₆₁	1	4	yes	—
462	C₂³	C₂×#41×C₆₁	1	8	yes	—
463	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
464	Q₈	—	2	8	no	—
465	D₄	—	2	16	no	—
466	D₄	#117×C₆₁	1	16	yes	complemented
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	16	no	—
477	C₂×C₄	—	2	8	no	—
478	C₂×C₄	—	2	16	no	—
479	C₂×C₄	—	2	8	no	—
480	C₂×C₄	—	2	8	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	8	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	8	no	—
486	C₂×C₄	—	4	8	no	—
487	C₂×C₄	—	4	4	no	—
488	C₂×C₄	—	4	32	no	—
489	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
490	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
491	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
492	C₂×C₄	C₂³×C₄×C₆₁	1	4	yes	—
493	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
494	C₂×C₄	C₂³×C₄×C₆₁	1	4	yes	—
495	C₂×C₄	C₂³×C₄×C₆₁	1	4	yes	—
496	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
497	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
498	C₂×C₄	C₂×#41×C₆₁	1	8	yes	—
499	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
500	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
501	C₂²	—	2	4	no	—
502	C₂²	—	2	4	no	—
503	C₂²	—	2	16	no	—
504	C₂²	—	2	2	no	—
505	C₂²	—	2	2	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	4	4	no	—
508	C₂²	C₂×#117×C₆₁	1	8	yes	—
509	C₂²	C₂⁴×C₄×C₆₁	1	1	yes	characteristic
510	C₂²	C₂²×#41×C₆₁	1	2	yes	—
511	C₂²	C₂²×#41×C₆₁	1	2	yes	—
512	C₂²	C₆₁×#585	1	2	yes	—
513	C₄	—	2	2	no	—
514	C₄	—	2	4	no	—
515	C₄	—	2	4	no	—
516	C₄	—	2	2	no	—
517	C₄	—	2	2	no	—
518	C₄	—	2	2	no	—
519	C₄	—	2	4	no	—
520	C₄	—	2	8	no	—
521	C₄	—	4	4	no	—
522	C₄	—	4	8	no	—
523	C₄	C₂×#117×C₆₁	1	4	yes	—
524	C₄	C₄×#41×C₆₁	1	4	yes	—
525	C₂	—	2	8	no	—
526	C₂	—	4	2	no	—
527	C₂	C₂²×#117×C₆₁	1	1	yes	characteristic
528	C₂	C₂×C₄×#41×C₆₁	1	1	yes	characteristic
529	C₂	C₆₁×#3428	1	1	yes	characteristic
530	C₂	C₆₁×#3475	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₆₁	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₆₁
Frattini, cosocle	C₂³	C₂⁵×C₆₁
socle	C₂³×C₆₁	C₂⁵
prime radical	C₂²×#41×C₆₁	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₁×#2356	C₂	semidirect
3. C₆₁×#2353	C₂	semidirect
4. C₆₁×#2349	C₂	semidirect
5. C₆₁×#2346	C₂	semidirect
6. C₆₁×#2343	C₂	semidirect
8. C₆₁×#2295	C₂	semidirect
9. C₆₁×#2290	C₂	semidirect
10. C₆₁×#2283	C₂	semidirect
11. C₆₁×#2283	C₂	semidirect
12. C₄²×D₄×C₆₁	C₂	semidirect
13. C₄×#117×C₆₁	C₂	semidirect
14. C₂×C₆₁×#376	C₂	semidirect
16. C₄×#41×C₆₁	C₄	semidirect
76. C₄×Q₈×C₆₁	C₂×C₄	semidirect
77. C₄×Q₈×C₆₁	C₂×C₄	semidirect
81. C₄×D₄×C₆₁	C₂×C₄	semidirect
82. C₄×D₄×C₆₁	C₂×C₄	semidirect
84. #117×C₆₁	C₂×C₄	semidirect
85. #117×C₆₁	C₂×C₄	semidirect
100. C₂×C₄²×C₆₁	C₂×C₄	semidirect
101. C₂×C₄²×C₆₁	C₂×C₄	semidirect
188. C₄²×C₆₁	#41	semidirect
200. D₄×C₆₁	#117	semidirect
235. #34123	C₆₁	direct (N × H)
261. #2356	C₂×C₆₁	semidirect
262. #2353	C₂×C₆₁	semidirect
263. #2349	C₂×C₆₁	semidirect
264. #2346	C₂×C₆₁	semidirect
265. #2343	C₂×C₆₁	semidirect
267. #2295	C₂×C₆₁	semidirect
268. #2290	C₂×C₆₁	semidirect
269. #2283	C₂×C₆₁	semidirect
270. #2283	C₂×C₆₁	semidirect
271. C₄²×D₄	C₂×C₆₁	semidirect
272. C₄×#117	C₂×C₆₁	semidirect
273. C₂×#376	C₂×C₆₁	semidirect
281. C₄×#41	C₄×C₆₁	semidirect
329. C₆₁	#34123	direct (N × H)
342. C₄×Q₈	C₂×C₄×C₆₁	semidirect
343. C₄×Q₈	C₂×C₄×C₆₁	semidirect
347. C₄×D₄	C₂×C₄×C₆₁	semidirect
348. C₄×D₄	C₂×C₄×C₆₁	semidirect
350. #117	C₂×C₄×C₆₁	semidirect
351. #117	C₂×C₄×C₆₁	semidirect
366. C₂×C₄²	C₂×C₄×C₆₁	semidirect
367. C₂×C₄²	C₂×C₄×C₆₁	semidirect
454. C₄²	#41×C₆₁	semidirect
466. D₄	#117×C₆₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₄×#41×C₆₁	2
C₆₁×#2356	2
C₆₁×#2353	2
C₆₁×#2349	2
C₆₁×#2346	2
C₆₁×#2343	2
C₆₁×#2339	2
C₆₁×#2295	2
C₆₁×#2290	2
C₆₁×#2283	2
C₄²×D₄×C₆₁	2
C₄×#117×C₆₁	2
C₂×C₆₁×#376	2
#34123	61

Subgroups — C61×#34123 #29537556

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#34123 #29537556