Subgroups — C₆₁×#20679 #29524112

Order 15616.

1330 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#568	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#430	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#428	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2896	C₂	1	1	yes	maximal, characteristic
5	C₂×C₆₁×#417	C₂	1	1	yes	maximal, characteristic
6	C₆₁×#1816	C₂	1	4	yes	maximal, complemented
7	C₆₁×#1815	C₂	1	4	yes	maximal, complemented
8	C₆₁×#1742	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₆₁×#343	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
11	C₆₁×#568	—	2	4	no	—
12	C₆₁×#568	C₄	1	8	yes	complemented
13	C₂×#131×C₆₁	—	2	2	no	—
14	C₂×#131×C₆₁	C₂²	1	4	yes	—
15	C₂²×M₁₆×C₆₁	—	2	2	no	—
16	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
22	C₆₁×#430	—	2	4	no	—
23	C₂×#108×C₆₁	C₂²	1	4	yes	complemented
24	C₆₁×#428	—	2	2	no	—
25	C₆₁×#428	—	2	2	no	—
26	C₂×#107×C₆₁	C₂²	1	2	yes	complemented
27	C₂×#106×C₆₁	C₂²	1	2	yes	complemented
28	C₆₁×#419	—	2	1	no	—
29	C₆₁×#418	—	2	1	no	—
30	C₆₁×#417	—	2	2	no	—
31	C₆₁×#417	C₂²	1	2	yes	—
32	C₆₁×#417	C₂²	1	4	yes	—
33	C₆₁×#417	C₂²	1	2	yes	—
34	C₆₁×#416	—	2	2	no	—
35	C₂×#103×C₆₁	—	2	1	no	—
36	C₂×#102×C₆₁	—	2	1	no	—
37	C₆₁×#343	C₂²	1	2	yes	complemented
38	C₆₁×#343	C₂²	1	4	yes	complemented
39	C₆₁×#343	C₂²	1	2	yes	complemented
40	C₂×#41×C₆₁	—	2	1	no	—
41	C₂×#41×C₆₁	—	2	2	no	—
42	C₂×#41×C₆₁	—	2	1	no	—
43	C₂×#41×C₆₁	—	2	2	no	—
44	C₂×#41×C₆₁	C₂×C₄	1	4	yes	—
45	C₂×#41×C₆₁	D₄	1	2	yes	—
46	C₂×#41×C₆₁	Q₈	1	4	yes	—
47	C₂×#41×C₆₁	C₂³	1	2	yes	—
48	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
49	C₂²×D₄×C₆₁	—	2	1	no	—
50	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₆₁	—	2	1	no	—
52	C₂³×C₄×C₆₁	—	2	1	no	—
53	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
54	#131×C₆₁	—	2	16	no	—
55	#131×C₆₁	—	2	8	no	—
56	#131×C₆₁	C₂×C₄	1	16	yes	complemented
57	C₂×M₁₆×C₆₁	—	2	1	no	—
58	C₂×M₁₆×C₆₁	—	2	2	no	—
59	C₂×M₁₆×C₆₁	—	2	16	no	—
60	C₂×M₁₆×C₆₁	—	2	1	no	—
61	C₂×M₁₆×C₆₁	—	2	1	no	—
62	C₂×M₁₆×C₆₁	—	2	4	no	—
63	C₂×M₁₆×C₆₁	—	2	2	no	—
64	C₂×M₁₆×C₆₁	—	2	2	no	—
65	C₂×M₁₆×C₆₁	—	2	2	no	—
66	C₂×M₁₆×C₆₁	—	2	2	no	—
67	C₂×M₁₆×C₆₁	C₂×C₄	1	4	yes	—
68	C₂×M₁₆×C₆₁	C₂×C₄	1	4	yes	—
69	C₂×M₁₆×C₆₁	D₄	1	2	yes	—
70	C₂×M₁₆×C₆₁	D₄	1	2	yes	—
71	C₂×M₁₆×C₆₁	D₄	1	4	yes	—
72	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
73	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
74	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
75	C₂²×C₈×C₆₁	—	2	1	no	—
76	C₂²×C₈×C₆₁	—	2	4	no	—
77	C₂²×C₈×C₆₁	—	2	1	no	—
78	C₂²×C₈×C₆₁	—	2	1	no	—
79	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
80	#117×C₆₁	—	2	1	no	—
81	#117×C₆₁	—	2	1	no	—
82	#117×C₆₁	—	2	1	no	—
83	#117×C₆₁	—	2	1	no	—
84	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
85	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
86	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
87	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
88	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
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	1	yes	characteristic
92	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
93	C₂×C₄²×C₆₁	—	2	1	no	—
94	#108×C₆₁	—	2	8	no	—
95	#107×C₆₁	—	2	4	no	—
96	#106×C₆₁	—	2	4	no	—
97	#103×C₆₁	—	2	4	no	—
98	#103×C₆₁	—	2	2	no	—
99	#103×C₆₁	—	2	2	no	—
100	#102×C₆₁	—	2	4	no	—
101	#102×C₆₁	—	2	2	no	—
102	#102×C₆₁	—	2	2	no	—
103	C₂⁴×C₆₁	—	2	1	no	—
104	C₂⁴×C₆₁	#41	1	1	yes	characteristic
105	#41×C₆₁	—	2	4	no	—
106	#41×C₆₁	—	2	4	no	—
107	#41×C₆₁	—	2	4	no	—
108	#41×C₆₁	—	2	4	no	—
109	#41×C₆₁	—	2	4	no	—
110	#41×C₆₁	—	2	2	no	—
111	#41×C₆₁	—	2	2	no	—
112	#41×C₆₁	C₄⋊C₄	1	8	yes	—
113	#41×C₆₁	C₂²×C₄	1	4	yes	—
114	#41×C₆₁	C₂×Q₈	1	4	yes	—
115	C₂×Q₈×C₆₁	—	2	1	no	—
116	C₂×Q₈×C₆₁	—	2	2	no	—
117	C₂×Q₈×C₆₁	C₄⋊C₄	1	4	yes	—
118	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
119	C₂×D₄×C₆₁	—	2	4	no	—
120	C₂×D₄×C₆₁	—	2	2	no	—
121	C₂×D₄×C₆₁	—	2	4	no	—
122	C₂×D₄×C₆₁	—	2	2	no	—
123	C₂×D₄×C₆₁	—	2	2	no	—
124	C₂×D₄×C₆₁	—	2	1	no	—
125	C₂×D₄×C₆₁	C₄⋊C₄	1	4	yes	—
126	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₆₁	—	2	1	no	—
128	C₂²×C₄×C₆₁	—	2	4	no	—
129	C₂²×C₄×C₆₁	—	2	2	no	—
130	C₂²×C₄×C₆₁	—	2	4	no	—
131	C₂²×C₄×C₆₁	—	2	2	no	—
132	C₂²×C₄×C₆₁	—	2	1	no	—
133	C₂²×C₄×C₆₁	—	2	1	no	—
134	C₂²×C₄×C₆₁	—	2	2	no	—
135	C₂²×C₄×C₆₁	—	4	1	no	—
136	C₂²×C₄×C₆₁	—	4	1	no	—
137	C₂²×C₄×C₆₁	—	8	2	no	—
138	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
139	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
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×Q₈	1	2	yes	—
145	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
146	C₂²×C₄×C₆₁	#41	1	2	yes	—
147	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
148	M₁₆×C₆₁	—	2	4	no	—
149	M₁₆×C₆₁	—	2	2	no	—
150	M₁₆×C₆₁	—	2	16	no	—
151	M₁₆×C₆₁	—	2	2	no	—
152	M₁₆×C₆₁	—	2	2	no	—
153	M₁₆×C₆₁	—	2	2	no	—
154	M₁₆×C₆₁	—	2	2	no	—
155	M₁₆×C₆₁	—	4	2	no	—
156	M₁₆×C₆₁	—	4	2	no	—
157	M₁₆×C₆₁	C₂²⋊C₄	1	8	yes	—
158	M₁₆×C₆₁	C₂²⋊C₄	1	8	yes	—
159	M₁₆×C₆₁	C₂²×C₄	1	4	yes	—
160	C₂×C₈×C₆₁	—	2	4	no	—
161	C₂×C₈×C₆₁	—	2	2	no	—
162	C₂×C₈×C₆₁	—	2	16	no	—
163	C₂×C₈×C₆₁	—	2	2	no	—
164	C₂×C₈×C₆₁	—	2	2	no	—
165	C₂×C₈×C₆₁	—	4	2	no	—
166	C₂×C₈×C₆₁	—	4	2	no	—
167	C₂×C₈×C₆₁	C₂²×C₄	1	4	yes	—
168	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
169	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
170	C₄⋊C₄×C₆₁	—	2	2	no	—
171	C₄⋊C₄×C₆₁	—	2	1	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	—	2	1	no	—
176	C₄⋊C₄×C₆₁	—	4	1	no	—
177	C₄⋊C₄×C₆₁	—	4	1	no	—
178	C₂²⋊C₄×C₆₁	—	4	1	no	—
179	C₂²⋊C₄×C₆₁	—	4	1	no	—
180	C₄²×C₆₁	—	4	1	no	—
181	C₄²×C₆₁	—	4	1	no	—
182	C₂³×C₆₁	—	2	2	no	—
183	C₂³×C₆₁	—	2	4	no	—
184	C₂³×C₆₁	—	4	1	no	—
185	C₂³×C₆₁	—	4	1	no	—
186	C₂³×C₆₁	—	8	1	no	—
187	C₂³×C₆₁	—	8	1	no	—
188	C₂³×C₆₁	#117	1	2	yes	—
189	C₂³×C₆₁	#121	1	1	yes	characteristic
190	C₂³×C₆₁	#121	1	1	yes	characteristic
191	C₂³×C₆₁	C₂²⋊Q₈	1	2	yes	—
192	C₂³×C₆₁	C₂×#41	1	1	yes	characteristic
193	Q₈×C₆₁	—	2	2	no	—
194	Q₈×C₆₁	—	2	4	no	—
195	Q₈×C₆₁	C₂×C₄⋊C₄	1	4	yes	—
196	D₄×C₆₁	—	2	4	no	—
197	D₄×C₆₁	—	2	4	no	—
198	D₄×C₆₁	—	2	8	no	—
199	D₄×C₆₁	—	2	2	no	—
200	D₄×C₆₁	—	2	4	no	—
201	D₄×C₆₁	C₂×C₄⋊C₄	1	4	yes	—
202	C₂×C₄×C₆₁	—	2	2	no	—
203	C₂×C₄×C₆₁	—	2	4	no	—
204	C₂×C₄×C₆₁	—	2	4	no	—
205	C₂×C₄×C₆₁	—	2	4	no	—
206	C₂×C₄×C₆₁	—	2	8	no	—
207	C₂×C₄×C₆₁	—	4	1	no	—
208	C₂×C₄×C₆₁	—	4	1	no	—
209	C₂×C₄×C₆₁	—	4	2	no	—
210	C₂×C₄×C₆₁	—	8	2	no	—
211	C₂×C₄×C₆₁	—	8	2	no	—
212	C₂×C₄×C₆₁	—	8	1	no	—
213	C₂×C₄×C₆₁	—	8	1	no	—
214	C₂×C₄×C₆₁	—	8	2	no	—
215	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
216	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
217	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
218	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
219	C₂×C₄×C₆₁	#117	1	2	yes	—
220	C₂×C₄×C₆₁	#121	1	2	yes	—
221	C₂×C₄×C₆₁	#121	1	2	yes	—
222	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
223	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
224	C₂×C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
225	C₂×C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
226	C₂×C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
227	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
228	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
232	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
233	C₈×C₆₁	—	2	4	no	—
234	C₈×C₆₁	—	4	2	no	—
235	C₈×C₆₁	—	4	2	no	—
236	C₈×C₆₁	C₂×C₂²⋊C₄	1	8	yes	—
237	#20679	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	—	2	1	no	—
244	C₂²×C₆₁	—	2	4	no	—
245	C₂²×C₆₁	—	4	2	no	—
246	C₂²×C₆₁	—	4	2	no	—
247	C₂²×C₆₁	—	4	2	no	—
248	C₂²×C₆₁	—	4	2	no	—
249	C₂²×C₆₁	—	8	4	no	—
250	C₂²×C₆₁	#380	1	2	yes	—
251	C₂²×C₆₁	#380	1	2	yes	—
252	C₂²×C₆₁	C₂×#117	1	1	yes	characteristic
253	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
254	C₂²×C₆₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
255	C₄×C₆₁	—	2	4	no	—
256	C₄×C₆₁	—	8	1	no	—
257	C₄×C₆₁	—	8	2	no	—
258	C₄×C₆₁	—	8	1	no	—
259	C₄×C₆₁	#380	1	2	yes	—
260	C₄×C₆₁	#380	1	2	yes	—
261	C₄×C₆₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
262	C₄×C₆₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
263	C₄×C₆₁	C₂×#121	1	1	yes	characteristic
264	C₄×C₆₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
265	C₂×#568	C₂×C₆₁	1	1	yes	characteristic
266	C₂×#430	C₂×C₆₁	1	1	yes	characteristic, complemented
267	C₂×#428	C₂×C₆₁	1	1	yes	characteristic, complemented
268	#2896	C₂×C₆₁	1	1	yes	characteristic
269	C₂×#417	C₂×C₆₁	1	1	yes	characteristic
270	#1816	C₂×C₆₁	1	4	yes	complemented
271	#1815	C₂×C₆₁	1	4	yes	complemented
272	#1742	C₂×C₆₁	1	1	yes	characteristic, complemented
273	C₂×#343	C₂×C₆₁	1	1	yes	characteristic, complemented
274	C₂×C₆₁	—	2	2	no	—
275	C₂×C₆₁	—	2	1	no	—
276	C₂×C₆₁	—	2	1	no	—
277	C₂×C₆₁	—	2	2	no	—
278	C₂×C₆₁	—	4	4	no	—
279	C₂×C₆₁	C₂×#380	1	1	yes	characteristic
280	C₂×C₆₁	#3068	1	1	yes	characteristic
281	C₂×C₆₁	#3069	1	1	yes	characteristic
282	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
283	#568	—	2	4	no	—
284	#568	C₄×C₆₁	1	8	yes	complemented
285	C₂×#131	—	2	2	no	—
286	C₂×#131	C₂²×C₆₁	1	4	yes	—
287	C₂²×M₁₆	—	2	2	no	—
288	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
289	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
290	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
291	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
292	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
293	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
294	#430	—	2	4	no	—
295	C₂×#108	C₂²×C₆₁	1	4	yes	complemented
296	#428	—	2	2	no	—
297	#428	—	2	2	no	—
298	C₂×#107	C₂²×C₆₁	1	2	yes	complemented
299	C₂×#106	C₂²×C₆₁	1	2	yes	complemented
300	#419	—	2	1	no	—
301	#418	—	2	1	no	—
302	#417	—	2	2	no	—
303	#417	C₂²×C₆₁	1	2	yes	—
304	#417	C₂²×C₆₁	1	4	yes	—
305	#417	C₂²×C₆₁	1	2	yes	—
306	#416	—	2	2	no	—
307	C₂×#103	—	2	1	no	—
308	C₂×#102	—	2	1	no	—
309	#343	C₂²×C₆₁	1	2	yes	complemented
310	#343	C₂²×C₆₁	1	4	yes	complemented
311	#343	C₂²×C₆₁	1	2	yes	complemented
312	C₆₁	#20679	1	1	yes	characteristic, direct product factor, Sylow
313	C₂×#41	—	2	1	no	—
314	C₂×#41	—	2	2	no	—
315	C₂×#41	—	2	1	no	—
316	C₂×#41	—	2	2	no	—
317	C₂×#41	C₂×C₄×C₆₁	1	4	yes	—
318	C₂×#41	D₄×C₆₁	1	2	yes	—
319	C₂×#41	Q₈×C₆₁	1	4	yes	—
320	C₂×#41	C₂³×C₆₁	1	2	yes	—
321	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
322	C₂²×D₄	—	2	1	no	—
323	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
324	C₂³×C₄	—	2	1	no	—
325	C₂³×C₄	—	2	1	no	—
326	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
327	#131	—	2	16	no	—
328	#131	—	2	8	no	—
329	#131	C₂×C₄×C₆₁	1	16	yes	complemented
330	C₂×M₁₆	—	2	1	no	—
331	C₂×M₁₆	—	2	2	no	—
332	C₂×M₁₆	—	2	16	no	—
333	C₂×M₁₆	—	2	1	no	—
334	C₂×M₁₆	—	2	1	no	—
335	C₂×M₁₆	—	2	4	no	—
336	C₂×M₁₆	—	2	2	no	—
337	C₂×M₁₆	—	2	2	no	—
338	C₂×M₁₆	—	2	2	no	—
339	C₂×M₁₆	—	2	2	no	—
340	C₂×M₁₆	C₂×C₄×C₆₁	1	4	yes	—
341	C₂×M₁₆	C₂×C₄×C₆₁	1	4	yes	—
342	C₂×M₁₆	D₄×C₆₁	1	2	yes	—
343	C₂×M₁₆	D₄×C₆₁	1	2	yes	—
344	C₂×M₁₆	D₄×C₆₁	1	4	yes	—
345	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
346	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
347	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
348	C₂²×C₈	—	2	1	no	—
349	C₂²×C₈	—	2	4	no	—
350	C₂²×C₈	—	2	1	no	—
351	C₂²×C₈	—	2	1	no	—
352	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
353	#117	—	2	1	no	—
354	#117	—	2	1	no	—
355	#117	—	2	1	no	—
356	#117	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
363	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₄²	—	2	1	no	—
367	#108	—	2	8	no	—
368	#107	—	2	4	no	—
369	#106	—	2	4	no	—
370	#103	—	2	4	no	—
371	#103	—	2	2	no	—
372	#103	—	2	2	no	—
373	#102	—	2	4	no	—
374	#102	—	2	2	no	—
375	#102	—	2	2	no	—
376	C₂⁴	—	2	1	no	—
377	C₂⁴	#41×C₆₁	1	1	yes	characteristic
378	#41	—	2	4	no	—
379	#41	—	2	4	no	—
380	#41	—	2	4	no	—
381	#41	—	2	4	no	—
382	#41	—	2	4	no	—
383	#41	—	2	2	no	—
384	#41	—	2	2	no	—
385	#41	C₄⋊C₄×C₆₁	1	8	yes	—
386	#41	C₂²×C₄×C₆₁	1	4	yes	—
387	#41	C₂×Q₈×C₆₁	1	4	yes	—
388	C₂×Q₈	—	2	2	no	—
389	C₂×Q₈	—	2	1	no	—
390	C₂×Q₈	C₄⋊C₄×C₆₁	1	4	yes	—
391	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
392	C₂×D₄	—	2	4	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	C₄⋊C₄×C₆₁	1	4	yes	—
399	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	4	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	4	1	no	—
409	C₂²×C₄	—	4	1	no	—
410	C₂²×C₄	—	8	2	no	—
411	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
412	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
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×Q₈×C₆₁	1	2	yes	—
418	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
419	C₂²×C₄	#41×C₆₁	1	2	yes	—
420	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
421	M₁₆	—	2	4	no	—
422	M₁₆	—	2	2	no	—
423	M₁₆	—	2	16	no	—
424	M₁₆	—	2	2	no	—
425	M₁₆	—	2	2	no	—
426	M₁₆	—	2	2	no	—
427	M₁₆	—	2	2	no	—
428	M₁₆	—	4	2	no	—
429	M₁₆	—	4	2	no	—
430	M₁₆	C₂²⋊C₄×C₆₁	1	8	yes	—
431	M₁₆	C₂²⋊C₄×C₆₁	1	8	yes	—
432	M₁₆	C₂²×C₄×C₆₁	1	4	yes	—
433	C₂×C₈	—	2	4	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	16	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	4	2	no	—
439	C₂×C₈	—	4	2	no	—
440	C₂×C₈	C₂²×C₄×C₆₁	1	4	yes	—
441	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
442	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	4	1	no	—
450	C₄⋊C₄	—	4	1	no	—
451	C₂²⋊C₄	—	4	1	no	—
452	C₂²⋊C₄	—	4	1	no	—
453	C₄²	—	4	1	no	—
454	C₄²	—	4	1	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	4	no	—
457	C₂³	—	4	1	no	—
458	C₂³	—	4	1	no	—
459	C₂³	—	8	1	no	—
460	C₂³	—	8	1	no	—
461	C₂³	#117×C₆₁	1	2	yes	—
462	C₂³	#121×C₆₁	1	1	yes	characteristic
463	C₂³	#121×C₆₁	1	1	yes	characteristic
464	C₂³	C₂²⋊Q₈×C₆₁	1	2	yes	—
465	C₂³	C₂×#41×C₆₁	1	1	yes	characteristic
466	Q₈	—	2	4	no	—
467	Q₈	—	2	2	no	—
468	Q₈	C₂×C₄⋊C₄×C₆₁	1	4	yes	—
469	D₄	—	2	8	no	—
470	D₄	—	2	4	no	—
471	D₄	—	2	4	no	—
472	D₄	—	2	4	no	—
473	D₄	—	2	2	no	—
474	D₄	C₂×C₄⋊C₄×C₆₁	1	4	yes	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	8	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	8	2	no	—
484	C₂×C₄	—	8	2	no	—
485	C₂×C₄	—	8	1	no	—
486	C₂×C₄	—	8	1	no	—
487	C₂×C₄	—	8	2	no	—
488	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
489	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
490	C₂×C₄	C₂×C₄⋊C₄×C₆₁	1	2	yes	—
491	C₂×C₄	C₂×C₄⋊C₄×C₆₁	1	2	yes	—
492	C₂×C₄	#117×C₆₁	1	2	yes	—
493	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
494	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
495	C₂×C₄	#121×C₆₁	1	2	yes	—
496	C₂×C₄	#121×C₆₁	1	2	yes	—
497	C₂×C₄	C₂²⋊Q₈×C₆₁	1	2	yes	—
498	C₂×C₄	C₂²⋊Q₈×C₆₁	1	2	yes	—
499	C₂×C₄	C₂²⋊Q₈×C₆₁	1	2	yes	—
500	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
501	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
502	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
503	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
504	C₂×C₄	C₂²×Q₈×C₆₁	1	1	yes	characteristic
505	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
506	C₈	—	2	4	no	—
507	C₈	—	4	2	no	—
508	C₈	—	4	2	no	—
509	C₈	C₂×C₂²⋊C₄×C₆₁	1	8	yes	—
510	C₂²	—	2	1	no	—
511	C₂²	—	2	1	no	—
512	C₂²	—	2	1	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	2	4	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	8	4	no	—
522	C₂²	C₆₁×#380	1	2	yes	—
523	C₂²	C₆₁×#380	1	2	yes	—
524	C₂²	C₂×#117×C₆₁	1	1	yes	characteristic
525	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
526	C₂²	C₂×C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
527	C₄	—	2	4	no	—
528	C₄	—	8	1	no	—
529	C₄	—	8	2	no	—
530	C₄	—	8	1	no	—
531	C₄	C₆₁×#380	1	2	yes	—
532	C₄	C₆₁×#380	1	2	yes	—
533	C₄	C₂²×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
534	C₄	C₂²×C₄⋊C₄×C₆₁	1	1	yes	characteristic
535	C₄	C₂×#121×C₆₁	1	1	yes	characteristic
536	C₄	C₂×C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
537	C₂	—	2	2	no	—
538	C₂	—	2	2	no	—
539	C₂	—	2	1	no	—
540	C₂	—	2	1	no	—
541	C₂	—	4	4	no	—
542	C₂	C₂×C₆₁×#380	1	1	yes	characteristic
543	C₂	C₆₁×#3068	1	1	yes	characteristic
544	C₂	C₆₁×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#121
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂²×#41×C₆₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂³×C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₆₁×#430	C₂	semidirect
3. C₂×C₆₁×#428	C₂	semidirect
6. C₆₁×#1816	C₂	semidirect
7. C₆₁×#1815	C₂	semidirect
8. C₆₁×#1742	C₂	semidirect
9. C₂×C₆₁×#343	C₂	semidirect
12. C₆₁×#568	C₄	semidirect
23. C₂×#108×C₆₁	C₂²	semidirect
26. C₂×#107×C₆₁	C₂²	semidirect
27. C₂×#106×C₆₁	C₂²	semidirect
37. C₆₁×#343	C₂²	semidirect
38. C₆₁×#343	C₂²	semidirect
39. C₆₁×#343	C₂²	semidirect
56. #131×C₆₁	C₂×C₄	semidirect
237. #20679	C₆₁	direct (N × H)
266. C₂×#430	C₂×C₆₁	semidirect
267. C₂×#428	C₂×C₆₁	semidirect
270. #1816	C₂×C₆₁	semidirect
271. #1815	C₂×C₆₁	semidirect
272. #1742	C₂×C₆₁	semidirect
273. C₂×#343	C₂×C₆₁	semidirect
284. #568	C₄×C₆₁	semidirect
295. C₂×#108	C₂²×C₆₁	semidirect
298. C₂×#107	C₂²×C₆₁	semidirect
299. C₂×#106	C₂²×C₆₁	semidirect
309. #343	C₂²×C₆₁	semidirect
310. #343	C₂²×C₆₁	semidirect
311. #343	C₂²×C₆₁	semidirect
312. C₆₁	#20679	direct (N × H)
329. #131	C₂×C₄×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#568	2
C₂×C₆₁×#430	2
C₂×C₆₁×#428	2
C₆₁×#2896	2
C₂×C₆₁×#417	2
C₆₁×#1816	2
C₆₁×#1815	2
C₆₁×#1742	2
C₂×C₆₁×#343	2
#20679	61

Subgroups — C61×#20679 #29524112

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#20679 #29524112