Subgroups — C₆₁×#21556 #29524989

Order 15616.

874 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#473	C₂	1	1	yes	maximal, characteristic
2	C₄×#137×C₆₁	C₂	1	2	yes	maximal
3	C₂×C₆₁×#441	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2875	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#1979	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#1951	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1930	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1908	C₂	1	2	yes	maximal
9	C₆₁×#1815	C₂	1	1	yes	maximal, characteristic
10	C₆₁×#1778	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#101×C₆₁	C₂	1	2	yes	maximal, complemented
12	C₂×#137×C₆₁	C₂²	1	2	yes	—
13	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
16	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
18	C₆₁×#473	C₄	1	8	yes	complemented
19	C₆₁×#441	—	2	2	no	—
20	C₆₁×#441	—	2	1	no	—
21	C₆₁×#441	—	2	1	no	—
22	C₆₁×#441	—	2	1	no	—
23	C₆₁×#441	—	2	1	no	—
24	C₆₁×#440	—	2	2	no	—
25	C₄×Q₁₆×C₆₁	—	2	2	no	—
26	C₄×SD₁₆×C₆₁	—	2	2	no	—
27	C₂×#108×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×#108×C₆₁	C₂²	1	1	yes	characteristic
29	C₆₁×#428	C₂²	1	2	yes	—
30	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
31	C₆₁×#419	C₂²	1	2	yes	—
32	C₆₁×#417	C₂²	1	2	yes	—
33	C₂×#103×C₆₁	C₂²	1	2	yes	—
34	C₂×#101×C₆₁	C₂²	1	2	yes	—
35	C₂×#101×C₆₁	C₂²	1	2	yes	—
36	C₆₁×#405	—	2	1	no	—
37	C₆₁×#405	—	2	1	no	—
38	C₆₁×#405	C₂²	1	1	yes	characteristic
39	C₆₁×#405	C₂²	1	1	yes	characteristic
40	C₄×M₁₆×C₆₁	—	2	1	no	—
41	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
42	C₄×M₁₆×C₆₁	C₂²	1	2	yes	—
43	C₂×#97×C₆₁	—	2	1	no	—
44	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
45	C₆₁×#343	C₂²	1	2	yes	—
46	C₆₁×#343	C₂²	1	2	yes	—
47	C₆₁×#341	C₂²	1	2	yes	—
48	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
49	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
50	#137×C₆₁	—	2	4	no	—
51	#137×C₆₁	C₂×C₄	1	8	yes	—
52	C₂×Q₁₆×C₆₁	—	2	2	no	—
53	C₂×Q₁₆×C₆₁	—	2	1	no	—
54	C₂×Q₁₆×C₆₁	—	2	1	no	—
55	C₂×Q₁₆×C₆₁	—	2	2	no	—
56	C₂×Q₁₆×C₆₁	C₂×C₄	1	4	yes	complemented
57	C₂×SD₁₆×C₆₁	—	2	2	no	—
58	#131×C₆₁	—	2	2	no	—
59	#131×C₆₁	—	2	2	no	—
60	#131×C₆₁	—	2	2	no	—
61	#131×C₆₁	C₂×C₄	1	4	yes	—
62	C₂×M₁₆×C₆₁	—	2	1	no	—
63	C₂×M₁₆×C₆₁	—	2	1	no	—
64	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
65	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
66	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
67	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₆₁	—	2	1	no	—
69	C₂²×C₈×C₆₁	—	2	1	no	—
70	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
72	C₄×Q₈×C₆₁	—	2	2	no	—
73	C₄×Q₈×C₆₁	—	2	2	no	—
74	C₄×Q₈×C₆₁	—	2	2	no	—
75	C₄×Q₈×C₆₁	—	2	2	no	—
76	C₄×Q₈×C₆₁	D₄	1	2	yes	—
77	C₄×D₄×C₆₁	—	2	2	no	—
78	C₄×D₄×C₆₁	D₄	1	2	yes	—
79	#117×C₆₁	—	2	1	no	—
80	#117×C₆₁	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
82	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
83	C₂×C₄²×C₆₁	—	2	1	no	—
84	C₂×C₄²×C₆₁	—	2	2	no	—
85	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
86	#108×C₆₁	—	2	2	no	—
87	#108×C₆₁	C₂×C₄	1	4	yes	complemented
88	#107×C₆₁	—	2	2	no	—
89	#106×C₆₁	—	2	1	no	—
90	#106×C₆₁	—	2	1	no	—
91	#106×C₆₁	—	2	2	no	—
92	#103×C₆₁	—	2	2	no	—
93	#103×C₆₁	—	2	2	no	—
94	#103×C₆₁	—	2	2	no	—
95	#103×C₆₁	—	2	2	no	—
96	#103×C₆₁	—	2	2	no	—
97	#102×C₆₁	—	2	2	no	—
98	#101×C₆₁	—	2	4	no	—
99	#101×C₆₁	C₂×C₄	1	8	yes	complemented
100	#97×C₆₁	—	2	1	no	—
101	#97×C₆₁	—	2	1	no	—
102	#97×C₆₁	—	2	1	no	—
103	#97×C₆₁	—	2	2	no	—
104	#97×C₆₁	D₄	1	1	yes	characteristic
105	#97×C₆₁	D₄	1	1	yes	characteristic
106	#97×C₆₁	D₄	1	1	yes	characteristic
107	#97×C₆₁	D₄	1	1	yes	characteristic
108	C₄×C₈×C₆₁	—	2	1	no	—
109	C₄×C₈×C₆₁	—	2	1	no	—
110	C₄×C₈×C₆₁	—	2	1	no	—
111	C₄×C₈×C₆₁	—	2	2	no	—
112	#41×C₆₁	—	2	1	no	—
113	#41×C₆₁	—	2	1	no	—
114	#41×C₆₁	C₂²×C₄	1	2	yes	—
115	#41×C₆₁	#41	1	2	yes	—
116	C₂×Q₈×C₆₁	—	2	2	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	2	no	—
121	C₂×Q₈×C₆₁	C₂²×C₄	1	4	yes	—
122	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
123	C₂×D₄×C₆₁	—	2	1	no	—
124	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₆₁	—	2	1	no	—
126	C₂²×C₄×C₆₁	—	2	2	no	—
127	C₂²×C₄×C₆₁	—	2	2	no	—
128	C₂²×C₄×C₆₁	—	2	2	no	—
129	C₂²×C₄×C₆₁	#41	1	2	yes	—
130	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
131	Q₁₆×C₆₁	—	2	8	no	—
132	Q₁₆×C₆₁	—	2	4	no	—
133	Q₁₆×C₆₁	—	2	4	no	—
134	SD₁₆×C₆₁	—	2	8	no	—
135	M₁₆×C₆₁	—	2	4	no	—
136	M₁₆×C₆₁	—	2	1	no	—
137	M₁₆×C₆₁	—	2	1	no	—
138	M₁₆×C₆₁	—	2	2	no	—
139	M₁₆×C₆₁	—	2	4	no	—
140	M₁₆×C₆₁	—	2	2	no	—
141	M₁₆×C₆₁	—	2	2	no	—
142	M₁₆×C₆₁	C₂²×C₄	1	2	yes	—
143	M₁₆×C₆₁	C₂²×C₄	1	4	yes	—
144	M₁₆×C₆₁	#41	1	2	yes	—
145	C₂×C₈×C₆₁	—	2	4	no	—
146	C₂×C₈×C₆₁	—	2	1	no	—
147	C₂×C₈×C₆₁	—	2	1	no	—
148	C₂×C₈×C₆₁	—	2	2	no	—
149	C₂×C₈×C₆₁	—	2	1	no	—
150	C₂×C₈×C₆₁	—	2	1	no	—
151	C₂×C₈×C₆₁	—	2	4	no	—
152	C₂×C₈×C₆₁	—	2	2	no	—
153	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
154	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
156	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
157	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
158	C₂×C₈×C₆₁	#41	1	2	yes	—
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	—	4	2	no	—
163	C₄⋊C₄×C₆₁	—	4	2	no	—
164	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
165	C₂²⋊C₄×C₆₁	—	2	1	no	—
166	C₂²⋊C₄×C₆₁	—	2	2	no	—
167	C₄²×C₆₁	—	2	2	no	—
168	C₄²×C₆₁	—	2	1	no	—
169	C₄²×C₆₁	—	4	2	no	—
170	C₄²×C₆₁	—	4	2	no	—
171	C₄²×C₆₁	C₂×D₄	1	2	yes	—
172	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
174	C₂³×C₆₁	—	2	1	no	—
175	C₂³×C₆₁	C₂×#41	1	1	yes	characteristic
176	Q₈×C₆₁	—	2	1	no	—
177	Q₈×C₆₁	—	2	4	no	—
178	Q₈×C₆₁	—	2	4	no	—
179	Q₈×C₆₁	—	4	2	no	—
180	Q₈×C₆₁	—	4	2	no	—
181	Q₈×C₆₁	C₄×D₄	1	2	yes	—
182	D₄×C₆₁	—	2	2	no	—
183	D₄×C₆₁	—	2	2	no	—
184	D₄×C₆₁	—	2	1	no	—
185	D₄×C₆₁	C₄×D₄	1	2	yes	—
186	C₂×C₄×C₆₁	—	2	1	no	—
187	C₂×C₄×C₆₁	—	2	2	no	—
188	C₂×C₄×C₆₁	—	2	2	no	—
189	C₂×C₄×C₆₁	—	2	4	no	—
190	C₂×C₄×C₆₁	—	2	2	no	—
191	C₂×C₄×C₆₁	—	4	2	no	—
192	C₂×C₄×C₆₁	—	4	2	no	—
193	C₂×C₄×C₆₁	—	4	2	no	—
194	C₂×C₄×C₆₁	—	4	2	no	—
195	C₂×C₄×C₆₁	—	8	2	no	—
196	C₂×C₄×C₆₁	—	8	2	no	—
197	C₂×C₄×C₆₁	#121	1	2	yes	—
198	C₂×C₄×C₆₁	#121	1	2	yes	—
199	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
200	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
205	C₈×C₆₁	—	2	2	no	—
206	C₈×C₆₁	—	2	4	no	—
207	C₈×C₆₁	—	2	1	no	—
208	C₈×C₆₁	—	2	2	no	—
209	C₈×C₆₁	—	2	1	no	—
210	C₈×C₆₁	—	4	2	no	—
211	C₈×C₆₁	C₄×D₄	1	2	yes	—
212	C₈×C₆₁	C₄×D₄	1	2	yes	—
213	#21556	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂²×C₆₁	—	2	2	no	—
215	C₂²×C₆₁	—	2	2	no	—
216	C₂²×C₆₁	—	4	2	no	—
217	C₂²×C₆₁	C₄×#41	1	1	yes	characteristic
218	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
219	C₂²×C₆₁	#529	1	1	yes	characteristic
220	C₄×C₆₁	—	2	2	no	—
221	C₄×C₆₁	—	2	2	no	—
222	C₄×C₆₁	—	2	2	no	—
223	C₄×C₆₁	—	4	4	no	—
224	C₄×C₆₁	—	4	2	no	—
225	C₄×C₆₁	—	8	2	no	—
226	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
227	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
228	C₄×C₆₁	#525	1	1	yes	characteristic
229	C₄×C₆₁	#532	1	1	yes	characteristic
230	C₂×#473	C₂×C₆₁	1	1	yes	characteristic
231	C₄×#137	C₂×C₆₁	1	2	yes	—
232	C₂×#441	C₂×C₆₁	1	1	yes	characteristic, complemented
233	#2875	C₂×C₆₁	1	1	yes	characteristic
234	#1979	C₂×C₆₁	1	1	yes	characteristic, complemented
235	#1951	C₂×C₆₁	1	1	yes	characteristic, complemented
236	#1930	C₂×C₆₁	1	2	yes	complemented
237	#1908	C₂×C₆₁	1	2	yes	—
238	#1815	C₂×C₆₁	1	1	yes	characteristic
239	#1778	C₂×C₆₁	1	1	yes	characteristic, complemented
240	C₄×#101	C₂×C₆₁	1	2	yes	complemented
241	C₂×C₆₁	—	2	1	no	—
242	C₂×C₆₁	—	2	1	no	—
243	C₂×C₆₁	—	4	2	no	—
244	C₂×C₆₁	C₄×#121	1	1	yes	characteristic
245	C₂×C₆₁	#3069	1	2	yes	—
246	C₂×#137	C₂²×C₆₁	1	2	yes	—
247	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
248	C₂×#131	C₂²×C₆₁	1	1	yes	characteristic
249	C₂×#131	C₂²×C₆₁	1	1	yes	characteristic
250	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
251	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
252	#473	C₄×C₆₁	1	8	yes	complemented
253	#441	—	2	2	no	—
254	#441	—	2	1	no	—
255	#441	—	2	1	no	—
256	#441	—	2	1	no	—
257	#441	—	2	1	no	—
258	#440	—	2	2	no	—
259	C₄×Q₁₆	—	2	2	no	—
260	C₄×SD₁₆	—	2	2	no	—
261	C₂×#108	C₂²×C₆₁	1	1	yes	characteristic
262	C₂×#108	C₂²×C₆₁	1	1	yes	characteristic
263	#428	C₂²×C₆₁	1	2	yes	—
264	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
265	#419	C₂²×C₆₁	1	2	yes	—
266	#417	C₂²×C₆₁	1	2	yes	—
267	C₂×#103	C₂²×C₆₁	1	2	yes	—
268	C₂×#101	C₂²×C₆₁	1	2	yes	—
269	C₂×#101	C₂²×C₆₁	1	2	yes	—
270	#405	—	2	1	no	—
271	#405	—	2	1	no	—
272	#405	C₂²×C₆₁	1	1	yes	characteristic
273	#405	C₂²×C₆₁	1	1	yes	characteristic
274	C₄×M₁₆	—	2	1	no	—
275	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
276	C₄×M₁₆	C₂²×C₆₁	1	2	yes	—
277	C₂×#97	—	2	1	no	—
278	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
279	#343	C₂²×C₆₁	1	2	yes	—
280	#343	C₂²×C₆₁	1	2	yes	—
281	#341	C₂²×C₆₁	1	2	yes	—
282	C₆₁	#21556	1	1	yes	characteristic, direct product factor, Sylow
283	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
284	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
285	#137	—	2	4	no	—
286	#137	C₂×C₄×C₆₁	1	8	yes	—
287	C₂×Q₁₆	—	2	2	no	—
288	C₂×Q₁₆	—	2	1	no	—
289	C₂×Q₁₆	—	2	1	no	—
290	C₂×Q₁₆	—	2	2	no	—
291	C₂×Q₁₆	C₂×C₄×C₆₁	1	4	yes	complemented
292	C₂×SD₁₆	—	2	2	no	—
293	#131	—	2	2	no	—
294	#131	—	2	2	no	—
295	#131	—	2	2	no	—
296	#131	C₂×C₄×C₆₁	1	4	yes	—
297	C₂×M₁₆	—	2	1	no	—
298	C₂×M₁₆	—	2	1	no	—
299	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
300	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
301	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
302	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
303	C₂²×C₈	—	2	1	no	—
304	C₂²×C₈	—	2	1	no	—
305	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
306	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
307	C₄×Q₈	—	2	2	no	—
308	C₄×Q₈	—	2	2	no	—
309	C₄×Q₈	—	2	2	no	—
310	C₄×Q₈	—	2	2	no	—
311	C₄×Q₈	D₄×C₆₁	1	2	yes	—
312	C₄×D₄	—	2	2	no	—
313	C₄×D₄	D₄×C₆₁	1	2	yes	—
314	#117	—	2	1	no	—
315	#117	C₂³×C₆₁	1	1	yes	characteristic
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
318	C₂×C₄²	—	2	1	no	—
319	C₂×C₄²	—	2	2	no	—
320	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
321	#108	—	2	2	no	—
322	#108	C₂×C₄×C₆₁	1	4	yes	complemented
323	#107	—	2	2	no	—
324	#106	—	2	1	no	—
325	#106	—	2	1	no	—
326	#106	—	2	2	no	—
327	#103	—	2	2	no	—
328	#103	—	2	2	no	—
329	#103	—	2	2	no	—
330	#103	—	2	2	no	—
331	#103	—	2	2	no	—
332	#102	—	2	2	no	—
333	#101	—	2	4	no	—
334	#101	C₂×C₄×C₆₁	1	8	yes	complemented
335	#97	—	2	1	no	—
336	#97	—	2	1	no	—
337	#97	—	2	1	no	—
338	#97	—	2	2	no	—
339	#97	D₄×C₆₁	1	1	yes	characteristic
340	#97	D₄×C₆₁	1	1	yes	characteristic
341	#97	D₄×C₆₁	1	1	yes	characteristic
342	#97	D₄×C₆₁	1	1	yes	characteristic
343	C₄×C₈	—	2	1	no	—
344	C₄×C₈	—	2	1	no	—
345	C₄×C₈	—	2	1	no	—
346	C₄×C₈	—	2	2	no	—
347	#41	—	2	1	no	—
348	#41	—	2	1	no	—
349	#41	C₂²×C₄×C₆₁	1	2	yes	—
350	#41	#41×C₆₁	1	2	yes	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	C₂²×C₄×C₆₁	1	4	yes	—
357	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	#41×C₆₁	1	2	yes	—
365	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
366	Q₁₆	—	2	8	no	—
367	Q₁₆	—	2	4	no	—
368	Q₁₆	—	2	4	no	—
369	SD₁₆	—	2	8	no	—
370	M₁₆	—	2	4	no	—
371	M₁₆	—	2	1	no	—
372	M₁₆	—	2	1	no	—
373	M₁₆	—	2	2	no	—
374	M₁₆	—	2	4	no	—
375	M₁₆	—	2	2	no	—
376	M₁₆	—	2	2	no	—
377	M₁₆	C₂²×C₄×C₆₁	1	2	yes	—
378	M₁₆	C₂²×C₄×C₆₁	1	4	yes	—
379	M₁₆	#41×C₆₁	1	2	yes	—
380	C₂×C₈	—	2	4	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	4	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
389	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
390	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
391	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
392	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
393	C₂×C₈	#41×C₆₁	1	2	yes	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	4	2	no	—
398	C₄⋊C₄	—	4	2	no	—
399	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
400	C₂²⋊C₄	—	2	1	no	—
401	C₂²⋊C₄	—	2	2	no	—
402	C₄²	—	2	2	no	—
403	C₄²	—	2	1	no	—
404	C₄²	—	4	2	no	—
405	C₄²	—	4	2	no	—
406	C₄²	C₂×D₄×C₆₁	1	2	yes	—
407	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
408	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
409	C₂³	—	2	1	no	—
410	C₂³	C₂×#41×C₆₁	1	1	yes	characteristic
411	Q₈	—	2	1	no	—
412	Q₈	—	2	4	no	—
413	Q₈	—	2	4	no	—
414	Q₈	—	4	2	no	—
415	Q₈	—	4	2	no	—
416	Q₈	C₄×D₄×C₆₁	1	2	yes	—
417	D₄	—	2	2	no	—
418	D₄	—	2	2	no	—
419	D₄	—	2	1	no	—
420	D₄	C₄×D₄×C₆₁	1	2	yes	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	8	2	no	—
431	C₂×C₄	—	8	2	no	—
432	C₂×C₄	#121×C₆₁	1	2	yes	—
433	C₂×C₄	#121×C₆₁	1	2	yes	—
434	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
435	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
436	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
437	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
438	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
439	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
440	C₈	—	2	2	no	—
441	C₈	—	2	4	no	—
442	C₈	—	2	1	no	—
443	C₈	—	2	2	no	—
444	C₈	—	2	1	no	—
445	C₈	—	4	2	no	—
446	C₈	C₄×D₄×C₆₁	1	2	yes	—
447	C₈	C₄×D₄×C₆₁	1	2	yes	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	4	2	no	—
451	C₂²	C₄×#41×C₆₁	1	1	yes	characteristic
452	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
453	C₂²	C₆₁×#529	1	1	yes	characteristic
454	C₄	—	2	2	no	—
455	C₄	—	2	2	no	—
456	C₄	—	2	2	no	—
457	C₄	—	4	4	no	—
458	C₄	—	4	2	no	—
459	C₄	—	8	2	no	—
460	C₄	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
461	C₄	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
462	C₄	C₆₁×#525	1	1	yes	characteristic
463	C₄	C₆₁×#532	1	1	yes	characteristic
464	C₂	—	2	1	no	—
465	C₂	—	2	1	no	—
466	C₂	—	4	2	no	—
467	C₂	C₄×#121×C₆₁	1	1	yes	characteristic
468	C₂	C₆₁×#3069	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#121
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂×#41×C₆₁	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₆₁×#441	C₂	semidirect
5. C₆₁×#1979	C₂	semidirect
6. C₆₁×#1951	C₂	semidirect
7. C₆₁×#1930	C₂	semidirect
10. C₆₁×#1778	C₂	semidirect
11. C₄×#101×C₆₁	C₂	semidirect
18. C₆₁×#473	C₄	semidirect
56. C₂×Q₁₆×C₆₁	C₂×C₄	semidirect
87. #108×C₆₁	C₂×C₄	semidirect
99. #101×C₆₁	C₂×C₄	semidirect
213. #21556	C₆₁	direct (N × H)
232. C₂×#441	C₂×C₆₁	semidirect
234. #1979	C₂×C₆₁	semidirect
235. #1951	C₂×C₆₁	semidirect
236. #1930	C₂×C₆₁	semidirect
239. #1778	C₂×C₆₁	semidirect
240. C₄×#101	C₂×C₆₁	semidirect
252. #473	C₄×C₆₁	semidirect
282. C₆₁	#21556	direct (N × H)
291. C₂×Q₁₆	C₂×C₄×C₆₁	semidirect
322. #108	C₂×C₄×C₆₁	semidirect
334. #101	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×#473	2
C₄×#137×C₆₁	2
C₂×C₆₁×#441	2
C₆₁×#2875	2
C₆₁×#1979	2
C₆₁×#1951	2
C₆₁×#1930	2
C₆₁×#1908	2
C₆₁×#1815	2
C₆₁×#1778	2
C₄×#101×C₆₁	2
#21556	61

Subgroups — C61×#21556 #29524989

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#21556 #29524989