Subgroups — C₆₁×#61810 #29565243

Order 15616.

1724 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3548	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3356	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3343	C₂	1	4	yes	maximal, complemented
5	C₆₁×#3338	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3333	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3315	C₂	1	4	yes	maximal, complemented
8	C₆₁×#3304	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3237	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#3228	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3201	C₂	1	4	yes	maximal, complemented
12	C₆₁×#3112	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3104	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3098	C₂	1	4	yes	maximal, complemented
15	C₆₁×#2981	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#562	—	2	2	no	—
17	C₆₁×#559	—	2	1	no	—
18	C₆₁×#557	—	2	1	no	—
19	C₆₁×#556	—	2	2	no	—
20	C₆₁×#556	C₂²	1	2	yes	—
21	C₆₁×#554	—	2	1	no	—
22	C₆₁×#554	C₂²	1	2	yes	—
23	C₆₁×#554	C₂²	1	2	yes	—
24	C₆₁×#552	C₂²	1	4	yes	—
25	C₆₁×#550	—	2	1	no	—
26	C₆₁×#550	C₂²	1	2	yes	—
27	C₆₁×#547	C₂²	1	2	yes	—
28	C₆₁×#547	C₂²	1	2	yes	—
29	C₆₁×#540	—	2	2	no	—
30	C₆₁×#539	—	2	2	no	—
31	C₆₁×#537	—	2	2	no	—
32	C₆₁×#537	C₂²	1	4	yes	—
33	C₆₁×#536	C₂²	1	2	yes	—
34	C₆₁×#533	C₂²	1	1	yes	characteristic
35	C₆₁×#533	C₂²	1	1	yes	characteristic
36	C₆₁×#532	C₂²	1	1	yes	characteristic
37	C₆₁×#532	C₂²	1	1	yes	characteristic
38	C₆₁×#529	—	2	2	no	—
39	C₆₁×#520	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
41	C₆₁×#501	C₂²	1	2	yes	—
42	C₆₁×#500	C₂²	1	1	yes	characteristic
43	C₆₁×#498	C₂²	1	1	yes	characteristic
44	C₆₁×#491	C₂²	1	2	yes	—
45	C₆₁×#486	C₂²	1	1	yes	characteristic
46	C₆₁×#486	C₂²	1	1	yes	characteristic
47	C₆₁×#485	C₂²	1	4	yes	—
48	C₆₁×#485	C₂²	1	4	yes	—
49	C₆₁×#484	C₂²	1	4	yes	—
50	C₆₁×#484	C₂²	1	4	yes	—
51	C₆₁×#484	C₂²	1	2	yes	—
52	C₆₁×#483	C₂²	1	4	yes	—
53	C₆₁×#482	C₂²	1	4	yes	—
54	C₆₁×#482	C₂²	1	4	yes	—
55	C₆₁×#480	C₂²	1	4	yes	—
56	C₆₁×#480	C₂²	1	2	yes	—
57	C₆₁×#478	C₂²	1	4	yes	—
58	C₆₁×#477	C₂²	1	2	yes	—
59	C₆₁×#477	C₂²	1	2	yes	—
60	C₆₁×#477	C₂²	1	2	yes	—
61	C₆₁×#475	C₂²	1	2	yes	—
62	C₆₁×#470	C₂²	1	4	yes	—
63	C₆₁×#468	C₂²	1	4	yes	—
64	C₆₁×#467	C₂²	1	4	yes	—
65	C₆₁×#465	C₂²	1	4	yes	—
66	C₆₁×#462	C₂²	1	2	yes	—
67	C₆₁×#460	C₂²	1	2	yes	—
68	C₆₁×#452	C₂²	1	4	yes	—
69	C₆₁×#452	C₂²	1	4	yes	—
70	C₆₁×#451	C₂²	1	2	yes	—
71	C₆₁×#448	C₂²	1	2	yes	—
72	C₆₁×#440	C₂²	1	4	yes	—
73	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
74	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
75	C₆₁×#436	C₂²	1	2	yes	—
76	C₆₁×#435	C₂²	1	4	yes	—
77	C₈×D₄×C₆₁	C₂²	1	2	yes	—
78	C₆₁×#432	C₂²	1	1	yes	characteristic
79	C₆₁×#431	C₂²	1	1	yes	characteristic
80	C₆₁×#428	C₂²	1	4	yes	—
81	C₂×#107×C₆₁	C₂²	1	4	yes	—
82	C₆₁×#417	C₂²	1	4	yes	—
83	C₆₁×#416	C₂²	1	4	yes	—
84	C₆₁×#408	C₂²	1	4	yes	—
85	C₂×#41×C₆₁	—	2	2	no	—
86	C₂×#41×C₆₁	—	2	1	no	—
87	C₂×#41×C₆₁	C₂³	1	4	yes	—
88	C₂×#41×C₆₁	C₂³	1	2	yes	—
89	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
90	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
91	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
92	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
93	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
94	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
95	C₄⋊Q₈×C₆₁	—	2	2	no	—
96	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
97	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
98	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
99	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
100	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
101	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
102	#127×C₆₁	—	2	2	no	—
103	#127×C₆₁	D₄	1	1	yes	characteristic
104	#127×C₆₁	C₂³	1	1	yes	characteristic
105	#126×C₆₁	—	2	4	no	—
106	#126×C₆₁	—	2	4	no	—
107	#125×C₆₁	—	2	4	no	—
108	#125×C₆₁	—	2	2	no	—
109	#125×C₆₁	—	2	2	no	—
110	#125×C₆₁	—	2	1	no	—
111	#125×C₆₁	C₂³	1	2	yes	—
112	#124×C₆₁	—	2	2	no	—
113	#124×C₆₁	—	2	2	no	—
114	#124×C₆₁	—	2	1	no	—
115	#124×C₆₁	D₄	1	2	yes	—
116	#123×C₆₁	—	2	4	no	—
117	#123×C₆₁	—	2	4	no	—
118	#123×C₆₁	—	2	4	no	—
119	#123×C₆₁	—	2	4	no	—
120	C₂²⋊Q₈×C₆₁	—	2	4	no	—
121	C₂²⋊Q₈×C₆₁	—	2	1	no	—
122	C₂²⋊Q₈×C₆₁	—	2	1	no	—
123	C₂²⋊Q₈×C₆₁	—	2	1	no	—
124	C₂²⋊Q₈×C₆₁	—	2	2	no	—
125	C₂²⋊Q₈×C₆₁	—	2	4	no	—
126	C₂²⋊Q₈×C₆₁	—	2	4	no	—
127	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
128	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
129	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
130	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
131	#121×C₆₁	—	2	4	no	—
132	#121×C₆₁	—	2	4	no	—
133	#121×C₆₁	—	2	2	no	—
134	#121×C₆₁	—	2	4	no	—
135	#121×C₆₁	—	2	1	no	—
136	#121×C₆₁	—	2	4	no	—
137	#121×C₆₁	D₄	1	2	yes	—
138	#121×C₆₁	D₄	1	2	yes	—
139	#121×C₆₁	C₂³	1	2	yes	—
140	#121×C₆₁	C₂³	1	4	yes	—
141	C₄×Q₈×C₆₁	—	2	2	no	—
142	C₄×Q₈×C₆₁	—	2	2	no	—
143	C₄×Q₈×C₆₁	—	2	1	no	—
144	C₄×Q₈×C₆₁	—	2	1	no	—
145	C₄×Q₈×C₆₁	—	2	1	no	—
146	C₄×Q₈×C₆₁	—	2	1	no	—
147	C₄×Q₈×C₆₁	—	2	1	no	—
148	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
149	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
150	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
151	C₄×D₄×C₆₁	—	2	4	no	—
152	C₄×D₄×C₆₁	—	2	2	no	—
153	C₄×D₄×C₆₁	—	2	2	no	—
154	C₄×D₄×C₆₁	—	2	2	no	—
155	C₄×D₄×C₆₁	—	2	2	no	—
156	C₄×D₄×C₆₁	—	2	1	no	—
157	C₄×D₄×C₆₁	C₂³	1	2	yes	—
158	C₄×D₄×C₆₁	C₂³	1	2	yes	—
159	C₄×D₄×C₆₁	C₂³	1	2	yes	—
160	#117×C₆₁	—	2	1	no	—
161	#117×C₆₁	—	2	4	no	—
162	#117×C₆₁	C₂³	1	2	yes	—
163	#117×C₆₁	C₂³	1	4	yes	—
164	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
165	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
166	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
167	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
168	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₆₁	—	2	1	no	—
170	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
171	#107×C₆₁	C₂³	1	2	yes	—
172	#107×C₆₁	C₂³	1	4	yes	—
173	#107×C₆₁	C₂³	1	4	yes	—
174	#107×C₆₁	C₂³	1	4	yes	—
175	#107×C₆₁	C₂³	1	2	yes	—
176	#106×C₆₁	C₂³	1	4	yes	—
177	#106×C₆₁	C₂³	1	4	yes	—
178	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
179	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
180	#103×C₆₁	C₂³	1	2	yes	—
181	#103×C₆₁	C₂³	1	4	yes	—
182	#103×C₆₁	C₂³	1	2	yes	—
183	#103×C₆₁	C₂³	1	4	yes	—
184	#103×C₆₁	C₂³	1	2	yes	—
185	#103×C₆₁	C₂³	1	2	yes	—
186	#103×C₆₁	C₂³	1	4	yes	—
187	#102×C₆₁	C₂³	1	4	yes	—
188	#102×C₆₁	C₂³	1	4	yes	—
189	#102×C₆₁	C₂³	1	4	yes	—
190	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
191	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
192	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
193	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
194	#97×C₆₁	C₂³	1	2	yes	—
195	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
197	#41×C₆₁	—	4	4	no	—
198	#41×C₆₁	—	4	4	no	—
199	#41×C₆₁	—	4	4	no	—
200	#41×C₆₁	—	8	2	no	—
201	#41×C₆₁	—	8	4	no	—
202	C₂×Q₈×C₆₁	—	2	1	no	—
203	C₂×Q₈×C₆₁	—	2	1	no	—
204	C₂×Q₈×C₆₁	—	2	1	no	—
205	C₂×Q₈×C₆₁	—	2	1	no	—
206	C₂×Q₈×C₆₁	—	2	1	no	—
207	C₂×Q₈×C₆₁	—	4	2	no	—
208	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
209	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
210	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
211	C₂×D₄×C₆₁	—	2	2	no	—
212	C₂×D₄×C₆₁	—	2	4	no	—
213	C₂×D₄×C₆₁	—	2	4	no	—
214	C₂×D₄×C₆₁	—	2	1	no	—
215	C₂×D₄×C₆₁	—	2	1	no	—
216	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
217	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
218	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
219	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
220	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₆₁	—	2	1	no	—
222	C₂²×C₄×C₆₁	—	2	1	no	—
223	C₂²×C₄×C₆₁	—	2	4	no	—
224	C₂²×C₄×C₆₁	—	2	4	no	—
225	C₂²×C₄×C₆₁	—	2	2	no	—
226	C₂²×C₄×C₆₁	—	2	4	no	—
227	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
231	Q₁₆×C₆₁	—	4	2	no	—
232	Q₁₆×C₆₁	—	4	2	no	—
233	SD₁₆×C₆₁	—	4	4	no	—
234	M₁₆×C₆₁	—	4	4	no	—
235	C₂×C₈×C₆₁	—	4	4	no	—
236	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
237	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
238	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
239	C₄⋊C₄×C₆₁	—	2	1	no	—
240	C₄⋊C₄×C₆₁	—	2	2	no	—
241	C₄⋊C₄×C₆₁	—	2	2	no	—
242	C₄⋊C₄×C₆₁	—	2	4	no	—
243	C₄⋊C₄×C₆₁	—	2	1	no	—
244	C₄⋊C₄×C₆₁	—	2	4	no	—
245	C₄⋊C₄×C₆₁	—	2	4	no	—
246	C₄⋊C₄×C₆₁	—	2	2	no	—
247	C₄⋊C₄×C₆₁	—	2	4	no	—
248	C₄⋊C₄×C₆₁	—	2	1	no	—
249	C₄⋊C₄×C₆₁	—	2	1	no	—
250	C₄⋊C₄×C₆₁	—	2	1	no	—
251	C₄⋊C₄×C₆₁	—	2	1	no	—
252	C₄⋊C₄×C₆₁	—	2	2	no	—
253	C₄⋊C₄×C₆₁	—	2	2	no	—
254	C₄⋊C₄×C₆₁	—	2	1	no	—
255	C₄⋊C₄×C₆₁	—	2	4	no	—
256	C₄⋊C₄×C₆₁	—	2	2	no	—
257	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
258	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
259	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
260	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
263	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
264	C₂²⋊C₄×C₆₁	—	2	2	no	—
265	C₂²⋊C₄×C₆₁	—	2	4	no	—
266	C₂²⋊C₄×C₆₁	—	2	2	no	—
267	C₂²⋊C₄×C₆₁	—	2	4	no	—
268	C₂²⋊C₄×C₆₁	—	2	4	no	—
269	C₂²⋊C₄×C₆₁	—	2	4	no	—
270	C₂²⋊C₄×C₆₁	—	2	4	no	—
271	C₂²⋊C₄×C₆₁	—	2	2	no	—
272	C₂²⋊C₄×C₆₁	—	2	2	no	—
273	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
274	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
275	C₄²×C₆₁	—	2	2	no	—
276	C₄²×C₆₁	—	2	2	no	—
277	C₄²×C₆₁	—	2	4	no	—
278	C₄²×C₆₁	—	2	2	no	—
279	C₄²×C₆₁	—	2	2	no	—
280	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
281	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
282	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
283	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
284	C₂³×C₆₁	—	2	2	no	—
285	C₂³×C₆₁	C₂²×D₄	1	4	yes	—
286	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
287	Q₈×C₆₁	—	2	2	no	—
288	Q₈×C₆₁	—	2	2	no	—
289	Q₈×C₆₁	—	2	2	no	—
290	Q₈×C₆₁	—	2	2	no	—
291	Q₈×C₆₁	—	4	2	no	—
292	Q₈×C₆₁	—	4	2	no	—
293	Q₈×C₆₁	—	4	2	no	—
294	Q₈×C₆₁	—	4	2	no	—
295	Q₈×C₆₁	—	8	1	no	—
296	Q₈×C₆₁	—	8	1	no	—
297	D₄×C₆₁	—	2	4	no	—
298	D₄×C₆₁	—	2	4	no	—
299	D₄×C₆₁	—	4	4	no	—
300	D₄×C₆₁	—	4	2	no	—
301	D₄×C₆₁	—	4	2	no	—
302	D₄×C₆₁	—	4	2	no	—
303	D₄×C₆₁	—	8	1	no	—
304	D₄×C₆₁	—	8	4	no	—
305	D₄×C₆₁	—	8	2	no	—
306	D₄×C₆₁	—	8	4	no	—
307	C₂×C₄×C₆₁	—	2	2	no	—
308	C₂×C₄×C₆₁	—	2	4	no	—
309	C₂×C₄×C₆₁	—	2	4	no	—
310	C₂×C₄×C₆₁	—	2	2	no	—
311	C₂×C₄×C₆₁	—	2	2	no	—
312	C₂×C₄×C₆₁	—	2	2	no	—
313	C₂×C₄×C₆₁	—	2	2	no	—
314	C₂×C₄×C₆₁	—	2	2	no	—
315	C₂×C₄×C₆₁	—	2	2	no	—
316	C₂×C₄×C₆₁	—	2	2	no	—
317	C₂×C₄×C₆₁	—	2	2	no	—
318	C₂×C₄×C₆₁	—	4	1	no	—
319	C₂×C₄×C₆₁	—	4	4	no	—
320	C₂×C₄×C₆₁	—	4	2	no	—
321	C₂×C₄×C₆₁	—	8	4	no	—
322	C₂×C₄×C₆₁	—	8	1	no	—
323	C₂×C₄×C₆₁	—	8	4	no	—
324	C₂×C₄×C₆₁	—	8	4	no	—
325	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
328	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
332	C₈×C₆₁	—	2	2	no	—
333	C₈×C₆₁	—	2	4	no	—
334	C₈×C₆₁	—	2	2	no	—
335	#61810	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
336	C₂²×C₆₁	—	2	1	no	—
337	C₂²×C₆₁	—	2	4	no	—
338	C₂²×C₆₁	—	2	1	no	—
339	C₂²×C₆₁	—	2	4	no	—
340	C₂²×C₆₁	—	2	1	no	—
341	C₂²×C₆₁	—	2	4	no	—
342	C₂²×C₆₁	—	4	2	no	—
343	C₂²×C₆₁	—	4	2	no	—
344	C₂²×C₆₁	—	4	2	no	—
345	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
346	C₄×C₆₁	—	2	1	no	—
347	C₄×C₆₁	—	2	1	no	—
348	C₄×C₆₁	—	2	4	no	—
349	C₄×C₆₁	—	2	1	no	—
350	C₄×C₆₁	—	2	1	no	—
351	C₄×C₆₁	—	4	2	no	—
352	C₄×C₆₁	—	4	2	no	—
353	C₄×C₆₁	—	4	2	no	—
354	C₄×C₆₁	—	4	2	no	—
355	C₄×C₆₁	—	4	2	no	—
356	C₄×C₆₁	—	4	2	no	—
357	C₄×C₆₁	—	4	2	no	—
358	C₄×C₆₁	#578	1	2	yes	—
359	C₄×C₆₁	#585	1	2	yes	—
360	#3548	C₂×C₆₁	1	1	yes	characteristic
361	#3507	C₂×C₆₁	1	1	yes	characteristic, complemented
362	#3356	C₂×C₆₁	1	2	yes	complemented
363	#3343	C₂×C₆₁	1	4	yes	complemented
364	#3338	C₂×C₆₁	1	2	yes	complemented
365	#3333	C₂×C₆₁	1	2	yes	complemented
366	#3315	C₂×C₆₁	1	4	yes	complemented
367	#3304	C₂×C₆₁	1	2	yes	complemented
368	#3237	C₂×C₆₁	1	1	yes	characteristic, complemented
369	#3228	C₂×C₆₁	1	1	yes	characteristic, complemented
370	#3201	C₂×C₆₁	1	4	yes	complemented
371	#3112	C₂×C₆₁	1	1	yes	characteristic, complemented
372	#3104	C₂×C₆₁	1	1	yes	characteristic, complemented
373	#3098	C₂×C₆₁	1	4	yes	complemented
374	#2981	C₂×C₆₁	1	1	yes	characteristic, complemented
375	C₂×C₆₁	—	4	1	no	—
376	C₂×C₆₁	—	4	4	no	—
377	C₂×C₆₁	—	8	2	no	—
378	C₂×C₆₁	#3485	1	1	yes	characteristic
379	C₂×C₆₁	C₂×#578	1	1	yes	characteristic
380	C₂×C₆₁	#3585	1	1	yes	characteristic
381	#562	—	2	2	no	—
382	#559	—	2	1	no	—
383	#557	—	2	1	no	—
384	#556	—	2	2	no	—
385	#556	C₂²×C₆₁	1	2	yes	—
386	#554	—	2	1	no	—
387	#554	C₂²×C₆₁	1	2	yes	—
388	#554	C₂²×C₆₁	1	2	yes	—
389	#552	C₂²×C₆₁	1	4	yes	—
390	#550	—	2	1	no	—
391	#550	C₂²×C₆₁	1	2	yes	—
392	#547	C₂²×C₆₁	1	2	yes	—
393	#547	C₂²×C₆₁	1	2	yes	—
394	#540	—	2	2	no	—
395	#539	—	2	2	no	—
396	#537	—	2	2	no	—
397	#537	C₂²×C₆₁	1	4	yes	—
398	#536	C₂²×C₆₁	1	2	yes	—
399	#533	C₂²×C₆₁	1	1	yes	characteristic
400	#533	C₂²×C₆₁	1	1	yes	characteristic
401	#532	C₂²×C₆₁	1	1	yes	characteristic
402	#532	C₂²×C₆₁	1	1	yes	characteristic
403	#529	—	2	2	no	—
404	#520	C₂²×C₆₁	1	2	yes	—
405	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
406	#501	C₂²×C₆₁	1	2	yes	—
407	#500	C₂²×C₆₁	1	1	yes	characteristic
408	#498	C₂²×C₆₁	1	1	yes	characteristic
409	#491	C₂²×C₆₁	1	2	yes	—
410	#486	C₂²×C₆₁	1	1	yes	characteristic
411	#486	C₂²×C₆₁	1	1	yes	characteristic
412	#485	C₂²×C₆₁	1	4	yes	—
413	#485	C₂²×C₆₁	1	4	yes	—
414	#484	C₂²×C₆₁	1	4	yes	—
415	#484	C₂²×C₆₁	1	4	yes	—
416	#484	C₂²×C₆₁	1	2	yes	—
417	#483	C₂²×C₆₁	1	4	yes	—
418	#482	C₂²×C₆₁	1	4	yes	—
419	#482	C₂²×C₆₁	1	4	yes	—
420	#480	C₂²×C₆₁	1	4	yes	—
421	#480	C₂²×C₆₁	1	2	yes	—
422	#478	C₂²×C₆₁	1	4	yes	—
423	#477	C₂²×C₆₁	1	2	yes	—
424	#477	C₂²×C₆₁	1	2	yes	—
425	#477	C₂²×C₆₁	1	2	yes	—
426	#475	C₂²×C₆₁	1	2	yes	—
427	#470	C₂²×C₆₁	1	4	yes	—
428	#468	C₂²×C₆₁	1	4	yes	—
429	#467	C₂²×C₆₁	1	4	yes	—
430	#465	C₂²×C₆₁	1	4	yes	—
431	#462	C₂²×C₆₁	1	2	yes	—
432	#460	C₂²×C₆₁	1	2	yes	—
433	#452	C₂²×C₆₁	1	4	yes	—
434	#452	C₂²×C₆₁	1	4	yes	—
435	#451	C₂²×C₆₁	1	2	yes	—
436	#448	C₂²×C₆₁	1	2	yes	—
437	#440	C₂²×C₆₁	1	4	yes	—
438	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
439	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
440	#436	C₂²×C₆₁	1	2	yes	—
441	#435	C₂²×C₆₁	1	4	yes	—
442	C₈×D₄	C₂²×C₆₁	1	2	yes	—
443	#432	C₂²×C₆₁	1	1	yes	characteristic
444	#431	C₂²×C₆₁	1	1	yes	characteristic
445	#428	C₂²×C₆₁	1	4	yes	—
446	C₂×#107	C₂²×C₆₁	1	4	yes	—
447	#417	C₂²×C₆₁	1	4	yes	—
448	#416	C₂²×C₆₁	1	4	yes	—
449	#408	C₂²×C₆₁	1	4	yes	—
450	C₆₁	#61810	1	1	yes	characteristic, direct product factor, Sylow
451	C₂×#41	—	2	2	no	—
452	C₂×#41	—	2	1	no	—
453	C₂×#41	C₂³×C₆₁	1	4	yes	—
454	C₂×#41	C₂³×C₆₁	1	2	yes	—
455	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
456	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
457	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
458	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
459	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
460	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
461	C₄⋊Q₈	—	2	2	no	—
462	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
463	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
464	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
465	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
466	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
467	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
468	#127	—	2	2	no	—
469	#127	D₄×C₆₁	1	1	yes	characteristic
470	#127	C₂³×C₆₁	1	1	yes	characteristic
471	#126	—	2	4	no	—
472	#126	—	2	4	no	—
473	#125	—	2	2	no	—
474	#125	—	2	4	no	—
475	#125	—	2	2	no	—
476	#125	—	2	1	no	—
477	#125	C₂³×C₆₁	1	2	yes	—
478	#124	—	2	2	no	—
479	#124	—	2	2	no	—
480	#124	—	2	1	no	—
481	#124	D₄×C₆₁	1	2	yes	—
482	#123	—	2	4	no	—
483	#123	—	2	4	no	—
484	#123	—	2	4	no	—
485	#123	—	2	4	no	—
486	C₂²⋊Q₈	—	2	4	no	—
487	C₂²⋊Q₈	—	2	1	no	—
488	C₂²⋊Q₈	—	2	1	no	—
489	C₂²⋊Q₈	—	2	1	no	—
490	C₂²⋊Q₈	—	2	2	no	—
491	C₂²⋊Q₈	—	2	4	no	—
492	C₂²⋊Q₈	—	2	4	no	—
493	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
494	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
495	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
496	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
497	#121	—	2	4	no	—
498	#121	—	2	4	no	—
499	#121	—	2	2	no	—
500	#121	—	2	4	no	—
501	#121	—	2	1	no	—
502	#121	—	2	4	no	—
503	#121	D₄×C₆₁	1	2	yes	—
504	#121	D₄×C₆₁	1	2	yes	—
505	#121	C₂³×C₆₁	1	2	yes	—
506	#121	C₂³×C₆₁	1	4	yes	—
507	C₄×Q₈	—	2	2	no	—
508	C₄×Q₈	—	2	2	no	—
509	C₄×Q₈	—	2	1	no	—
510	C₄×Q₈	—	2	1	no	—
511	C₄×Q₈	—	2	1	no	—
512	C₄×Q₈	—	2	1	no	—
513	C₄×Q₈	—	2	1	no	—
514	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
515	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
516	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
517	C₄×D₄	—	2	4	no	—
518	C₄×D₄	—	2	2	no	—
519	C₄×D₄	—	2	2	no	—
520	C₄×D₄	—	2	2	no	—
521	C₄×D₄	—	2	2	no	—
522	C₄×D₄	—	2	1	no	—
523	C₄×D₄	C₂³×C₆₁	1	2	yes	—
524	C₄×D₄	C₂³×C₆₁	1	2	yes	—
525	C₄×D₄	C₂³×C₆₁	1	2	yes	—
526	#117	—	2	1	no	—
527	#117	—	2	4	no	—
528	#117	C₂³×C₆₁	1	2	yes	—
529	#117	C₂³×C₆₁	1	4	yes	—
530	C₂×C₄⋊C₄	—	2	1	no	—
531	C₂×C₄⋊C₄	—	2	2	no	—
532	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
533	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
534	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
535	C₂×C₄²	—	2	1	no	—
536	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
537	#107	C₂³×C₆₁	1	2	yes	—
538	#107	C₂³×C₆₁	1	4	yes	—
539	#107	C₂³×C₆₁	1	4	yes	—
540	#107	C₂³×C₆₁	1	4	yes	—
541	#107	C₂³×C₆₁	1	2	yes	—
542	#106	C₂³×C₆₁	1	4	yes	—
543	#106	C₂³×C₆₁	1	4	yes	—
544	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
545	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
546	#103	C₂³×C₆₁	1	2	yes	—
547	#103	C₂³×C₆₁	1	4	yes	—
548	#103	C₂³×C₆₁	1	2	yes	—
549	#103	C₂³×C₆₁	1	4	yes	—
550	#103	C₂³×C₆₁	1	2	yes	—
551	#103	C₂³×C₆₁	1	2	yes	—
552	#103	C₂³×C₆₁	1	4	yes	—
553	#102	C₂³×C₆₁	1	4	yes	—
554	#102	C₂³×C₆₁	1	4	yes	—
555	#102	C₂³×C₆₁	1	4	yes	—
556	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
557	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
558	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
559	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
560	#97	C₂³×C₆₁	1	2	yes	—
561	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
562	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
563	#41	—	4	4	no	—
564	#41	—	4	4	no	—
565	#41	—	4	4	no	—
566	#41	—	8	2	no	—
567	#41	—	8	4	no	—
568	C₂×Q₈	—	2	1	no	—
569	C₂×Q₈	—	2	1	no	—
570	C₂×Q₈	—	2	1	no	—
571	C₂×Q₈	—	2	1	no	—
572	C₂×Q₈	—	2	1	no	—
573	C₂×Q₈	—	4	2	no	—
574	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
575	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
576	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
577	C₂×D₄	—	2	2	no	—
578	C₂×D₄	—	2	4	no	—
579	C₂×D₄	—	2	4	no	—
580	C₂×D₄	—	2	1	no	—
581	C₂×D₄	—	2	1	no	—
582	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
583	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
584	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
585	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
586	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	4	no	—
593	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
594	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
595	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
597	Q₁₆	—	4	2	no	—
598	Q₁₆	—	4	2	no	—
599	SD₁₆	—	4	4	no	—
600	M₁₆	—	4	4	no	—
601	C₂×C₈	—	4	4	no	—
602	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
603	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
604	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	2	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	2	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	2	1	no	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
624	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
625	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
626	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
627	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
628	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
629	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
630	C₂²⋊C₄	—	2	2	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	2	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	2	no	—
638	C₂²⋊C₄	—	2	2	no	—
639	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
640	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
641	C₄²	—	2	2	no	—
642	C₄²	—	2	2	no	—
643	C₄²	—	2	4	no	—
644	C₄²	—	2	2	no	—
645	C₄²	—	2	2	no	—
646	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
647	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
648	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
649	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
650	C₂³	—	2	2	no	—
651	C₂³	C₂²×D₄×C₆₁	1	4	yes	—
652	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
653	Q₈	—	2	2	no	—
654	Q₈	—	2	2	no	—
655	Q₈	—	2	2	no	—
656	Q₈	—	2	2	no	—
657	Q₈	—	4	2	no	—
658	Q₈	—	4	2	no	—
659	Q₈	—	4	2	no	—
660	Q₈	—	4	2	no	—
661	Q₈	—	8	1	no	—
662	Q₈	—	8	1	no	—
663	D₄	—	2	4	no	—
664	D₄	—	2	4	no	—
665	D₄	—	4	4	no	—
666	D₄	—	4	2	no	—
667	D₄	—	4	2	no	—
668	D₄	—	4	2	no	—
669	D₄	—	8	1	no	—
670	D₄	—	8	4	no	—
671	D₄	—	8	2	no	—
672	D₄	—	8	4	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	4	no	—
675	C₂×C₄	—	2	4	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	4	no	—
686	C₂×C₄	—	4	2	no	—
687	C₂×C₄	—	8	4	no	—
688	C₂×C₄	—	8	1	no	—
689	C₂×C₄	—	8	4	no	—
690	C₂×C₄	—	8	4	no	—
691	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
692	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
693	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
694	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
695	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
696	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
697	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
698	C₈	—	2	2	no	—
699	C₈	—	2	4	no	—
700	C₈	—	2	2	no	—
701	C₂²	—	2	1	no	—
702	C₂²	—	2	4	no	—
703	C₂²	—	2	1	no	—
704	C₂²	—	2	4	no	—
705	C₂²	—	2	1	no	—
706	C₂²	—	2	4	no	—
707	C₂²	—	4	2	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	4	2	no	—
710	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
711	C₄	—	2	1	no	—
712	C₄	—	2	1	no	—
713	C₄	—	2	1	no	—
714	C₄	—	2	4	no	—
715	C₄	—	2	1	no	—
716	C₄	—	4	2	no	—
717	C₄	—	4	2	no	—
718	C₄	—	4	2	no	—
719	C₄	—	4	2	no	—
720	C₄	—	4	2	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	2	no	—
723	C₄	C₆₁×#578	1	2	yes	—
724	C₄	C₆₁×#585	1	2	yes	—
725	C₂	—	4	1	no	—
726	C₂	—	4	4	no	—
727	C₂	—	8	2	no	—
728	C₂	C₆₁×#3485	1	1	yes	characteristic
729	C₂	C₂×C₆₁×#578	1	1	yes	characteristic
730	C₂	C₆₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₆₁×#3548	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₆₁×#532 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₁×#3507	C₂	semidirect
3. C₆₁×#3356	C₂	semidirect
4. C₆₁×#3343	C₂	semidirect
5. C₆₁×#3338	C₂	semidirect
6. C₆₁×#3333	C₂	semidirect
7. C₆₁×#3315	C₂	semidirect
8. C₆₁×#3304	C₂	semidirect
9. C₆₁×#3237	C₂	semidirect
10. C₆₁×#3228	C₂	semidirect
11. C₆₁×#3201	C₂	semidirect
12. C₆₁×#3112	C₂	semidirect
13. C₆₁×#3104	C₂	semidirect
14. C₆₁×#3098	C₂	semidirect
15. C₆₁×#2981	C₂	semidirect
335. #61810	C₆₁	direct (N × H)
361. #3507	C₂×C₆₁	semidirect
362. #3356	C₂×C₆₁	semidirect
363. #3343	C₂×C₆₁	semidirect
364. #3338	C₂×C₆₁	semidirect
365. #3333	C₂×C₆₁	semidirect
366. #3315	C₂×C₆₁	semidirect
367. #3304	C₂×C₆₁	semidirect
368. #3237	C₂×C₆₁	semidirect
369. #3228	C₂×C₆₁	semidirect
370. #3201	C₂×C₆₁	semidirect
371. #3112	C₂×C₆₁	semidirect
372. #3104	C₂×C₆₁	semidirect
373. #3098	C₂×C₆₁	semidirect
374. #2981	C₂×C₆₁	semidirect
450. C₆₁	#61810	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₁×#3548	2
C₆₁×#3507	2
C₆₁×#3356	2
C₆₁×#3343	2
C₆₁×#3338	2
C₆₁×#3333	2
C₆₁×#3315	2
C₆₁×#3304	2
C₆₁×#3237	2
C₆₁×#3228	2
C₆₁×#3201	2
C₆₁×#3112	2
C₆₁×#3104	2
C₆₁×#3098	2
C₆₁×#2981	2
#61810	61

Subgroups — C61×#61810 #29565243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61810 #29565243