Subgroups — C₆₁×#61914 #29565347

Order 15616.

1752 conjugacy classes of subgroups.

The subgroup lattice has 748 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, complemented
2	C₆₁×#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3399	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3397	C₂	1	4	yes	maximal, complemented
5	C₆₁×#3392	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3376	C₂	1	4	yes	maximal, complemented
7	C₆₁×#3372	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3361	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3221	C₂	1	4	yes	maximal, complemented
10	C₆₁×#3214	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3207	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3119	C₂	1	4	yes	maximal, complemented
13	C₆₁×#3112	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3103	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#2985	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#562	—	2	2	no	—
17	C₆₁×#559	C₂²	1	2	yes	—
18	C₆₁×#557	C₂²	1	2	yes	—
19	C₆₁×#556	—	2	1	no	—
20	C₆₁×#556	C₂²	1	4	yes	—
21	C₆₁×#554	—	2	1	no	—
22	C₆₁×#554	C₂²	1	2	yes	—
23	C₆₁×#554	C₂²	1	2	yes	—
24	C₆₁×#552	—	2	2	no	—
25	C₆₁×#550	C₂²	1	2	yes	—
26	C₆₁×#550	C₂²	1	2	yes	—
27	C₆₁×#547	—	2	1	no	—
28	C₆₁×#547	—	2	1	no	—
29	C₆₁×#540	C₂²	1	4	yes	—
30	C₆₁×#539	—	2	2	no	—
31	C₆₁×#537	—	2	2	no	—
32	C₆₁×#537	—	2	2	no	—
33	C₆₁×#536	C₂²	1	2	yes	—
34	C₆₁×#533	C₂²	1	1	yes	characteristic
35	C₆₁×#532	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×#496	C₂²	1	2	yes	—
42	C₆₁×#496	C₂²	1	4	yes	—
43	C₆₁×#493	C₂²	1	1	yes	characteristic
44	C₆₁×#492	C₂²	1	1	yes	characteristic
45	C₆₁×#492	C₂²	1	4	yes	—
46	C₆₁×#491	C₂²	1	4	yes	—
47	C₆₁×#489	C₂²	1	2	yes	—
48	C₆₁×#488	C₂²	1	4	yes	—
49	C₆₁×#487	C₂²	1	1	yes	characteristic
50	C₆₁×#486	C₂²	1	1	yes	characteristic
51	C₆₁×#481	C₂²	1	2	yes	—
52	C₆₁×#480	C₂²	1	2	yes	—
53	C₆₁×#479	C₂²	1	4	yes	—
54	C₆₁×#478	C₂²	1	4	yes	—
55	C₆₁×#477	C₂²	1	2	yes	—
56	C₆₁×#475	C₂²	1	2	yes	—
57	C₆₁×#463	C₂²	1	4	yes	—
58	C₆₁×#463	C₂²	1	4	yes	—
59	C₆₁×#463	C₂²	1	4	yes	—
60	C₆₁×#461	C₂²	1	2	yes	—
61	C₆₁×#461	C₂²	1	4	yes	—
62	C₆₁×#461	C₂²	1	4	yes	—
63	C₆₁×#460	C₂²	1	2	yes	—
64	C₆₁×#460	C₂²	1	2	yes	—
65	C₆₁×#460	C₂²	1	4	yes	—
66	C₆₁×#459	C₂²	1	2	yes	—
67	C₆₁×#459	C₂²	1	4	yes	—
68	C₆₁×#449	C₂²	1	4	yes	—
69	C₆₁×#449	C₂²	1	4	yes	—
70	C₆₁×#448	C₂²	1	2	yes	—
71	C₆₁×#448	C₂²	1	2	yes	—
72	C₆₁×#446	C₂²	1	2	yes	—
73	C₆₁×#446	C₂²	1	4	yes	—
74	C₈×Q₈×C₆₁	C₂²	1	2	yes	—
75	C₆₁×#442	C₂²	1	4	yes	—
76	C₆₁×#440	C₂²	1	4	yes	—
77	C₆₁×#440	C₂²	1	4	yes	—
78	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
79	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
80	C₄×SD₁₆×C₆₁	C₂²	1	4	yes	—
81	C₄×D₈×C₆₁	C₂²	1	4	yes	—
82	C₆₁×#433	C₂²	1	4	yes	—
83	C₆₁×#432	C₂²	1	1	yes	characteristic
84	C₆₁×#431	C₂²	1	1	yes	characteristic
85	C₂×#41×C₆₁	—	2	2	no	—
86	C₂×#41×C₆₁	—	2	2	no	—
87	C₂×#41×C₆₁	—	2	1	no	—
88	C₂×#41×C₆₁	—	2	1	no	—
89	C₂×#41×C₆₁	C₂³	1	2	yes	—
90	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
91	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
92	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
93	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
94	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
95	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
96	C₂×D₈×C₆₁	C₂³	1	4	yes	—
97	C₂×D₈×C₆₁	C₂³	1	4	yes	—
98	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
99	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
100	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
101	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
102	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
103	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
104	#127×C₆₁	C₂³	1	1	yes	characteristic
105	#127×C₆₁	C₂³	1	1	yes	characteristic
106	#127×C₆₁	C₂³	1	1	yes	characteristic
107	#127×C₆₁	C₂³	1	4	yes	—
108	#126×C₆₁	—	2	4	no	—
109	#126×C₆₁	—	2	4	no	—
110	#125×C₆₁	—	2	4	no	—
111	#125×C₆₁	—	2	2	no	—
112	#125×C₆₁	D₄	1	2	yes	—
113	#125×C₆₁	C₂³	1	4	yes	—
114	#124×C₆₁	—	2	2	no	—
115	#124×C₆₁	—	2	1	no	—
116	#124×C₆₁	—	2	1	no	—
117	#124×C₆₁	C₂³	1	2	yes	—
118	#124×C₆₁	C₂³	1	4	yes	—
119	#123×C₆₁	—	2	4	no	—
120	#123×C₆₁	—	2	4	no	—
121	#123×C₆₁	—	2	4	no	—
122	#123×C₆₁	—	2	4	no	—
123	C₂²⋊Q₈×C₆₁	—	2	2	no	—
124	C₂²⋊Q₈×C₆₁	—	2	2	no	—
125	C₂²⋊Q₈×C₆₁	—	2	4	no	—
126	C₂²⋊Q₈×C₆₁	—	2	2	no	—
127	C₂²⋊Q₈×C₆₁	—	2	2	no	—
128	C₂²⋊Q₈×C₆₁	—	2	4	no	—
129	C₂²⋊Q₈×C₆₁	—	2	4	no	—
130	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
131	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
132	#121×C₆₁	—	2	1	no	—
133	#121×C₆₁	—	2	1	no	—
134	#121×C₆₁	—	2	1	no	—
135	#121×C₆₁	—	2	1	no	—
136	#121×C₆₁	—	2	2	no	—
137	#121×C₆₁	—	2	2	no	—
138	#121×C₆₁	—	2	4	no	—
139	#121×C₆₁	—	2	4	no	—
140	#121×C₆₁	—	2	4	no	—
141	#121×C₆₁	—	2	4	no	—
142	#121×C₆₁	C₂³	1	2	yes	—
143	#121×C₆₁	C₂³	1	2	yes	—
144	C₄×Q₈×C₆₁	—	2	2	no	—
145	C₄×Q₈×C₆₁	—	2	1	no	—
146	C₄×Q₈×C₆₁	—	2	1	no	—
147	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
148	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
149	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
150	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
151	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
152	C₄×D₄×C₆₁	—	2	2	no	—
153	C₄×D₄×C₆₁	—	2	4	no	—
154	C₄×D₄×C₆₁	—	2	1	no	—
155	C₄×D₄×C₆₁	—	2	1	no	—
156	C₄×D₄×C₆₁	—	2	1	no	—
157	C₄×D₄×C₆₁	—	2	1	no	—
158	C₄×D₄×C₆₁	C₂³	1	2	yes	—
159	C₄×D₄×C₆₁	C₂³	1	2	yes	—
160	C₄×D₄×C₆₁	C₂³	1	4	yes	—
161	C₄×D₄×C₆₁	C₂³	1	4	yes	—
162	C₄×D₄×C₆₁	C₂³	1	4	yes	—
163	#117×C₆₁	—	2	2	no	—
164	#117×C₆₁	—	2	4	no	—
165	#117×C₆₁	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
167	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
168	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
169	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
170	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₆₁	—	2	1	no	—
172	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
173	#107×C₆₁	C₂³	1	4	yes	—
174	#106×C₆₁	C₂³	1	2	yes	—
175	#106×C₆₁	C₂³	1	2	yes	—
176	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
177	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
178	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
179	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
180	#103×C₆₁	C₂³	1	2	yes	—
181	#103×C₆₁	C₂³	1	2	yes	—
182	#103×C₆₁	C₂³	1	4	yes	—
183	#103×C₆₁	C₂³	1	4	yes	—
184	#103×C₆₁	C₂³	1	4	yes	—
185	#102×C₆₁	C₂³	1	2	yes	—
186	#102×C₆₁	C₂³	1	4	yes	—
187	#102×C₆₁	C₂³	1	2	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	#97×C₆₁	C₂³	1	2	yes	—
193	#97×C₆₁	C₂³	1	4	yes	—
194	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₆₁	C₂³	1	4	yes	—
197	#41×C₆₁	—	4	4	no	—
198	#41×C₆₁	—	8	2	no	—
199	#41×C₆₁	—	8	2	no	—
200	#41×C₆₁	—	8	4	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	—	4	2	no	—
206	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
207	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
208	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
209	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
210	C₂×D₄×C₆₁	—	2	2	no	—
211	C₂×D₄×C₆₁	—	2	2	no	—
212	C₂×D₄×C₆₁	—	2	2	no	—
213	C₂×D₄×C₆₁	—	2	1	no	—
214	C₂×D₄×C₆₁	—	2	1	no	—
215	C₂×D₄×C₆₁	—	2	1	no	—
216	C₂×D₄×C₆₁	—	2	1	no	—
217	C₂×D₄×C₆₁	—	2	4	no	—
218	C₂×D₄×C₆₁	—	2	4	no	—
219	C₂×D₄×C₆₁	—	2	1	no	—
220	C₂×D₄×C₆₁	—	2	1	no	—
221	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
222	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
223	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₆₁	—	2	1	no	—
225	C₂²×C₄×C₆₁	—	2	1	no	—
226	C₂²×C₄×C₆₁	—	2	2	no	—
227	C₂²×C₄×C₆₁	—	2	2	no	—
228	C₂²×C₄×C₆₁	—	2	2	no	—
229	C₂²×C₄×C₆₁	—	2	4	no	—
230	C₂²×C₄×C₆₁	—	2	4	no	—
231	C₂²×C₄×C₆₁	—	2	4	no	—
232	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
235	SD₁₆×C₆₁	—	4	2	no	—
236	SD₁₆×C₆₁	—	4	4	no	—
237	SD₁₆×C₆₁	—	4	4	no	—
238	SD₁₆×C₆₁	—	4	2	no	—
239	SD₁₆×C₆₁	—	4	4	no	—
240	D₈×C₆₁	—	4	4	no	—
241	D₈×C₆₁	—	4	4	no	—
242	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
243	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
244	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
245	C₄⋊C₄×C₆₁	—	2	1	no	—
246	C₄⋊C₄×C₆₁	—	2	1	no	—
247	C₄⋊C₄×C₆₁	—	2	1	no	—
248	C₄⋊C₄×C₆₁	—	2	4	no	—
249	C₄⋊C₄×C₆₁	—	2	2	no	—
250	C₄⋊C₄×C₆₁	—	2	2	no	—
251	C₄⋊C₄×C₆₁	—	2	4	no	—
252	C₄⋊C₄×C₆₁	—	2	4	no	—
253	C₄⋊C₄×C₆₁	—	2	4	no	—
254	C₄⋊C₄×C₆₁	—	2	1	no	—
255	C₄⋊C₄×C₆₁	—	2	1	no	—
256	C₄⋊C₄×C₆₁	—	2	4	no	—
257	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
258	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
259	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
260	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
261	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
262	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
263	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
264	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
265	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
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	2	no	—
270	C₂²⋊C₄×C₆₁	—	2	2	no	—
271	C₂²⋊C₄×C₆₁	—	2	2	no	—
272	C₂²⋊C₄×C₆₁	—	2	4	no	—
273	C₂²⋊C₄×C₆₁	—	2	4	no	—
274	C₂²⋊C₄×C₆₁	—	2	4	no	—
275	C₂²⋊C₄×C₆₁	—	2	2	no	—
276	C₂²⋊C₄×C₆₁	—	2	2	no	—
277	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
278	C₄²×C₆₁	—	2	2	no	—
279	C₄²×C₆₁	—	2	2	no	—
280	C₄²×C₆₁	—	2	4	no	—
281	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
282	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
284	C₄²×C₆₁	C₂⁴	1	4	yes	—
285	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
286	C₂³×C₆₁	—	2	2	no	—
287	C₂³×C₆₁	—	2	2	no	—
288	C₂³×C₆₁	—	2	2	no	—
289	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
290	Q₈×C₆₁	—	2	4	no	—
291	Q₈×C₆₁	—	2	2	no	—
292	Q₈×C₆₁	—	2	2	no	—
293	Q₈×C₆₁	—	2	4	no	—
294	Q₈×C₆₁	—	4	2	no	—
295	Q₈×C₆₁	—	4	2	no	—
296	Q₈×C₆₁	—	8	1	no	—
297	Q₈×C₆₁	—	8	1	no	—
298	D₄×C₆₁	—	2	2	no	—
299	D₄×C₆₁	—	2	4	no	—
300	D₄×C₆₁	—	2	4	no	—
301	D₄×C₆₁	—	2	2	no	—
302	D₄×C₆₁	—	4	2	no	—
303	D₄×C₆₁	—	4	4	no	—
304	D₄×C₆₁	—	4	2	no	—
305	D₄×C₆₁	—	4	2	no	—
306	D₄×C₆₁	—	8	1	no	—
307	D₄×C₆₁	—	8	1	no	—
308	D₄×C₆₁	—	8	4	no	—
309	D₄×C₆₁	—	8	1	no	—
310	D₄×C₆₁	—	8	4	no	—
311	D₄×C₆₁	—	8	2	no	—
312	D₄×C₆₁	—	8	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	—	2	2	no	—
319	C₂×C₄×C₆₁	—	2	2	no	—
320	C₂×C₄×C₆₁	—	4	1	no	—
321	C₂×C₄×C₆₁	—	4	4	no	—
322	C₂×C₄×C₆₁	—	4	4	no	—
323	C₂×C₄×C₆₁	—	4	2	no	—
324	C₂×C₄×C₆₁	—	4	4	no	—
325	C₂×C₄×C₆₁	—	8	4	no	—
326	C₂×C₄×C₆₁	—	8	4	no	—
327	C₂×C₄×C₆₁	—	8	4	no	—
328	C₂×C₄×C₆₁	—	8	1	no	—
329	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
331	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
335	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
337	C₈×C₆₁	—	2	2	no	—
338	C₈×C₆₁	—	2	4	no	—
339	C₈×C₆₁	—	2	2	no	—
340	#61914	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
341	C₂²×C₆₁	—	2	1	no	—
342	C₂²×C₆₁	—	2	1	no	—
343	C₂²×C₆₁	—	2	1	no	—
344	C₂²×C₆₁	—	4	2	no	—
345	C₂²×C₆₁	—	4	2	no	—
346	C₂²×C₆₁	—	4	2	no	—
347	C₂²×C₆₁	—	4	2	no	—
348	C₂²×C₆₁	—	4	2	no	—
349	C₂²×C₆₁	—	4	2	no	—
350	C₂²×C₆₁	—	4	2	no	—
351	C₂²×C₆₁	—	4	2	no	—
352	C₂²×C₆₁	—	4	2	no	—
353	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
354	C₄×C₆₁	—	2	1	no	—
355	C₄×C₆₁	—	2	1	no	—
356	C₄×C₆₁	—	2	4	no	—
357	C₄×C₆₁	—	2	1	no	—
358	C₄×C₆₁	—	2	1	no	—
359	C₄×C₆₁	—	2	4	no	—
360	C₄×C₆₁	—	4	2	no	—
361	C₄×C₆₁	—	4	2	no	—
362	C₄×C₆₁	—	4	2	no	—
363	C₄×C₆₁	—	4	2	no	—
364	C₄×C₆₁	—	4	2	no	—
365	C₄×C₆₁	#577	1	2	yes	—
366	C₄×C₆₁	#585	1	2	yes	—
367	#3548	C₂×C₆₁	1	1	yes	characteristic, complemented
368	#3507	C₂×C₆₁	1	1	yes	characteristic, complemented
369	#3399	C₂×C₆₁	1	2	yes	complemented
370	#3397	C₂×C₆₁	1	4	yes	complemented
371	#3392	C₂×C₆₁	1	2	yes	complemented
372	#3376	C₂×C₆₁	1	4	yes	complemented
373	#3372	C₂×C₆₁	1	2	yes	complemented
374	#3361	C₂×C₆₁	1	2	yes	complemented
375	#3221	C₂×C₆₁	1	4	yes	complemented
376	#3214	C₂×C₆₁	1	1	yes	characteristic, complemented
377	#3207	C₂×C₆₁	1	1	yes	characteristic, complemented
378	#3119	C₂×C₆₁	1	4	yes	complemented
379	#3112	C₂×C₆₁	1	1	yes	characteristic, complemented
380	#3103	C₂×C₆₁	1	1	yes	characteristic, complemented
381	#2985	C₂×C₆₁	1	1	yes	characteristic, complemented
382	C₂×C₆₁	—	4	1	no	—
383	C₂×C₆₁	—	8	2	no	—
384	C₂×C₆₁	—	8	2	no	—
385	C₂×C₆₁	—	8	2	no	—
386	C₂×C₆₁	#3487	1	1	yes	characteristic
387	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
388	C₂×C₆₁	#3585	1	1	yes	characteristic
389	#562	—	2	2	no	—
390	#559	C₂²×C₆₁	1	2	yes	—
391	#557	C₂²×C₆₁	1	2	yes	—
392	#556	—	2	1	no	—
393	#556	C₂²×C₆₁	1	4	yes	—
394	#554	—	2	1	no	—
395	#554	C₂²×C₆₁	1	2	yes	—
396	#554	C₂²×C₆₁	1	2	yes	—
397	#552	—	2	2	no	—
398	#550	C₂²×C₆₁	1	2	yes	—
399	#550	C₂²×C₆₁	1	2	yes	—
400	#547	—	2	1	no	—
401	#547	—	2	1	no	—
402	#540	C₂²×C₆₁	1	4	yes	—
403	#539	—	2	2	no	—
404	#537	—	2	2	no	—
405	#537	—	2	2	no	—
406	#536	C₂²×C₆₁	1	2	yes	—
407	#533	C₂²×C₆₁	1	1	yes	characteristic
408	#532	C₂²×C₆₁	1	1	yes	characteristic
409	#532	C₂²×C₆₁	1	1	yes	characteristic
410	#532	C₂²×C₆₁	1	1	yes	characteristic
411	#529	—	2	2	no	—
412	#520	C₂²×C₆₁	1	2	yes	—
413	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
414	#496	C₂²×C₆₁	1	2	yes	—
415	#496	C₂²×C₆₁	1	4	yes	—
416	#493	C₂²×C₆₁	1	1	yes	characteristic
417	#492	C₂²×C₆₁	1	1	yes	characteristic
418	#492	C₂²×C₆₁	1	4	yes	—
419	#491	C₂²×C₆₁	1	4	yes	—
420	#489	C₂²×C₆₁	1	2	yes	—
421	#488	C₂²×C₆₁	1	4	yes	—
422	#487	C₂²×C₆₁	1	1	yes	characteristic
423	#486	C₂²×C₆₁	1	1	yes	characteristic
424	#481	C₂²×C₆₁	1	2	yes	—
425	#480	C₂²×C₆₁	1	2	yes	—
426	#479	C₂²×C₆₁	1	4	yes	—
427	#478	C₂²×C₆₁	1	4	yes	—
428	#477	C₂²×C₆₁	1	2	yes	—
429	#475	C₂²×C₆₁	1	2	yes	—
430	#463	C₂²×C₆₁	1	4	yes	—
431	#463	C₂²×C₆₁	1	4	yes	—
432	#463	C₂²×C₆₁	1	4	yes	—
433	#461	C₂²×C₆₁	1	2	yes	—
434	#461	C₂²×C₆₁	1	4	yes	—
435	#461	C₂²×C₆₁	1	4	yes	—
436	#460	C₂²×C₆₁	1	2	yes	—
437	#460	C₂²×C₆₁	1	2	yes	—
438	#460	C₂²×C₆₁	1	4	yes	—
439	#459	C₂²×C₆₁	1	2	yes	—
440	#459	C₂²×C₆₁	1	4	yes	—
441	#449	C₂²×C₆₁	1	4	yes	—
442	#449	C₂²×C₆₁	1	4	yes	—
443	#448	C₂²×C₆₁	1	2	yes	—
444	#448	C₂²×C₆₁	1	2	yes	—
445	#446	C₂²×C₆₁	1	2	yes	—
446	#446	C₂²×C₆₁	1	4	yes	—
447	C₈×Q₈	C₂²×C₆₁	1	2	yes	—
448	#442	C₂²×C₆₁	1	4	yes	—
449	#440	C₂²×C₆₁	1	4	yes	—
450	#440	C₂²×C₆₁	1	4	yes	—
451	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
452	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
453	C₄×SD₁₆	C₂²×C₆₁	1	4	yes	—
454	C₄×D₈	C₂²×C₆₁	1	4	yes	—
455	#433	C₂²×C₆₁	1	4	yes	—
456	#432	C₂²×C₆₁	1	1	yes	characteristic
457	#431	C₂²×C₆₁	1	1	yes	characteristic
458	C₆₁	#61914	1	1	yes	characteristic, direct product factor, Sylow
459	C₂×#41	—	2	2	no	—
460	C₂×#41	—	2	2	no	—
461	C₂×#41	—	2	1	no	—
462	C₂×#41	—	2	1	no	—
463	C₂×#41	C₂³×C₆₁	1	2	yes	—
464	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
465	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
466	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
467	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
468	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
469	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
470	C₂×D₈	C₂³×C₆₁	1	4	yes	—
471	C₂×D₈	C₂³×C₆₁	1	4	yes	—
472	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
473	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
474	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
475	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
476	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
477	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
478	#127	C₂³×C₆₁	1	1	yes	characteristic
479	#127	C₂³×C₆₁	1	1	yes	characteristic
480	#127	C₂³×C₆₁	1	1	yes	characteristic
481	#127	C₂³×C₆₁	1	4	yes	—
482	#126	—	2	4	no	—
483	#126	—	2	4	no	—
484	#125	—	2	2	no	—
485	#125	—	2	4	no	—
486	#125	D₄×C₆₁	1	2	yes	—
487	#125	C₂³×C₆₁	1	4	yes	—
488	#124	—	2	2	no	—
489	#124	—	2	1	no	—
490	#124	—	2	1	no	—
491	#124	C₂³×C₆₁	1	2	yes	—
492	#124	C₂³×C₆₁	1	4	yes	—
493	#123	—	2	4	no	—
494	#123	—	2	4	no	—
495	#123	—	2	4	no	—
496	#123	—	2	4	no	—
497	C₂²⋊Q₈	—	2	2	no	—
498	C₂²⋊Q₈	—	2	2	no	—
499	C₂²⋊Q₈	—	2	4	no	—
500	C₂²⋊Q₈	—	2	2	no	—
501	C₂²⋊Q₈	—	2	2	no	—
502	C₂²⋊Q₈	—	2	4	no	—
503	C₂²⋊Q₈	—	2	4	no	—
504	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
505	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
506	#121	—	2	1	no	—
507	#121	—	2	1	no	—
508	#121	—	2	1	no	—
509	#121	—	2	1	no	—
510	#121	—	2	2	no	—
511	#121	—	2	2	no	—
512	#121	—	2	4	no	—
513	#121	—	2	4	no	—
514	#121	—	2	4	no	—
515	#121	—	2	4	no	—
516	#121	C₂³×C₆₁	1	2	yes	—
517	#121	C₂³×C₆₁	1	2	yes	—
518	C₄×Q₈	—	2	2	no	—
519	C₄×Q₈	—	2	1	no	—
520	C₄×Q₈	—	2	1	no	—
521	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
522	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
523	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
524	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
525	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
526	C₄×D₄	—	2	2	no	—
527	C₄×D₄	—	2	4	no	—
528	C₄×D₄	—	2	1	no	—
529	C₄×D₄	—	2	1	no	—
530	C₄×D₄	—	2	1	no	—
531	C₄×D₄	—	2	1	no	—
532	C₄×D₄	C₂³×C₆₁	1	4	yes	—
533	C₄×D₄	C₂³×C₆₁	1	2	yes	—
534	C₄×D₄	C₂³×C₆₁	1	2	yes	—
535	C₄×D₄	C₂³×C₆₁	1	4	yes	—
536	C₄×D₄	C₂³×C₆₁	1	4	yes	—
537	#117	—	2	2	no	—
538	#117	—	2	4	no	—
539	#117	C₂³×C₆₁	1	2	yes	—
540	C₂×C₄⋊C₄	—	2	1	no	—
541	C₂×C₄⋊C₄	—	2	2	no	—
542	C₂×C₄⋊C₄	—	2	2	no	—
543	C₂×C₄⋊C₄	—	2	2	no	—
544	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
545	C₂×C₄²	—	2	1	no	—
546	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
547	#107	C₂³×C₆₁	1	4	yes	—
548	#106	C₂³×C₆₁	1	2	yes	—
549	#106	C₂³×C₆₁	1	2	yes	—
550	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
551	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
552	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
553	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
554	#103	C₂³×C₆₁	1	2	yes	—
555	#103	C₂³×C₆₁	1	2	yes	—
556	#103	C₂³×C₆₁	1	4	yes	—
557	#103	C₂³×C₆₁	1	4	yes	—
558	#103	C₂³×C₆₁	1	4	yes	—
559	#102	C₂³×C₆₁	1	2	yes	—
560	#102	C₂³×C₆₁	1	4	yes	—
561	#102	C₂³×C₆₁	1	2	yes	—
562	#102	C₂³×C₆₁	1	4	yes	—
563	#102	C₂³×C₆₁	1	4	yes	—
564	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
565	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
566	#97	C₂³×C₆₁	1	2	yes	—
567	#97	C₂³×C₆₁	1	4	yes	—
568	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
569	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
570	C₄×C₈	C₂³×C₆₁	1	4	yes	—
571	#41	—	4	4	no	—
572	#41	—	8	2	no	—
573	#41	—	8	2	no	—
574	#41	—	8	4	no	—
575	#41	—	8	4	no	—
576	C₂×Q₈	—	2	1	no	—
577	C₂×Q₈	—	2	1	no	—
578	C₂×Q₈	—	2	1	no	—
579	C₂×Q₈	—	4	2	no	—
580	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
581	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
582	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
583	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	2	2	no	—
587	C₂×D₄	—	2	1	no	—
588	C₂×D₄	—	2	1	no	—
589	C₂×D₄	—	2	1	no	—
590	C₂×D₄	—	2	1	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	4	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	—	2	1	no	—
595	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
596	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
597	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	4	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
607	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
609	SD₁₆	—	4	2	no	—
610	SD₁₆	—	4	4	no	—
611	SD₁₆	—	4	4	no	—
612	SD₁₆	—	4	2	no	—
613	SD₁₆	—	4	4	no	—
614	D₈	—	4	4	no	—
615	D₈	—	4	4	no	—
616	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
617	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
618	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	2	no	—
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
632	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
633	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
634	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
635	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
636	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
637	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
638	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
639	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
640	C₂²⋊C₄	—	2	2	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	2	no	—
650	C₂²⋊C₄	—	2	2	no	—
651	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
652	C₄²	—	2	2	no	—
653	C₄²	—	2	2	no	—
654	C₄²	—	2	4	no	—
655	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
656	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
657	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
658	C₄²	C₂⁴×C₆₁	1	4	yes	—
659	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
660	C₂³	—	2	2	no	—
661	C₂³	—	2	2	no	—
662	C₂³	—	2	2	no	—
663	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
664	Q₈	—	2	4	no	—
665	Q₈	—	2	2	no	—
666	Q₈	—	2	2	no	—
667	Q₈	—	2	4	no	—
668	Q₈	—	4	2	no	—
669	Q₈	—	4	2	no	—
670	Q₈	—	8	1	no	—
671	Q₈	—	8	1	no	—
672	D₄	—	2	2	no	—
673	D₄	—	2	4	no	—
674	D₄	—	2	4	no	—
675	D₄	—	2	2	no	—
676	D₄	—	4	2	no	—
677	D₄	—	4	4	no	—
678	D₄	—	4	2	no	—
679	D₄	—	4	2	no	—
680	D₄	—	8	1	no	—
681	D₄	—	8	1	no	—
682	D₄	—	8	4	no	—
683	D₄	—	8	1	no	—
684	D₄	—	8	4	no	—
685	D₄	—	8	2	no	—
686	D₄	—	8	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	4	no	—
696	C₂×C₄	—	4	4	no	—
697	C₂×C₄	—	4	2	no	—
698	C₂×C₄	—	4	4	no	—
699	C₂×C₄	—	8	4	no	—
700	C₂×C₄	—	8	4	no	—
701	C₂×C₄	—	8	4	no	—
702	C₂×C₄	—	8	1	no	—
703	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
704	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
705	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
706	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
707	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
708	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
709	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
710	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
711	C₈	—	2	2	no	—
712	C₈	—	2	4	no	—
713	C₈	—	2	2	no	—
714	C₂²	—	2	1	no	—
715	C₂²	—	2	1	no	—
716	C₂²	—	2	1	no	—
717	C₂²	—	4	2	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	2	no	—
726	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
727	C₄	—	2	1	no	—
728	C₄	—	2	4	no	—
729	C₄	—	2	1	no	—
730	C₄	—	2	1	no	—
731	C₄	—	2	4	no	—
732	C₄	—	2	1	no	—
733	C₄	—	4	2	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	2	no	—
738	C₄	C₆₁×#577	1	2	yes	—
739	C₄	C₆₁×#585	1	2	yes	—
740	C₂	—	4	1	no	—
741	C₂	—	8	2	no	—
742	C₂	—	8	2	no	—
743	C₂	—	8	2	no	—
744	C₂	C₆₁×#3487	1	1	yes	characteristic
745	C₂	C₂×C₆₁×#577	1	1	yes	characteristic
746	C₂	C₆₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₆₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3548	C₂	semidirect
2. C₆₁×#3507	C₂	semidirect
3. C₆₁×#3399	C₂	semidirect
4. C₆₁×#3397	C₂	semidirect
5. C₆₁×#3392	C₂	semidirect
6. C₆₁×#3376	C₂	semidirect
7. C₆₁×#3372	C₂	semidirect
8. C₆₁×#3361	C₂	semidirect
9. C₆₁×#3221	C₂	semidirect
10. C₆₁×#3214	C₂	semidirect
11. C₆₁×#3207	C₂	semidirect
12. C₆₁×#3119	C₂	semidirect
13. C₆₁×#3112	C₂	semidirect
14. C₆₁×#3103	C₂	semidirect
15. C₆₁×#2985	C₂	semidirect
340. #61914	C₆₁	direct (N × H)
367. #3548	C₂×C₆₁	semidirect
368. #3507	C₂×C₆₁	semidirect
369. #3399	C₂×C₆₁	semidirect
370. #3397	C₂×C₆₁	semidirect
371. #3392	C₂×C₆₁	semidirect
372. #3376	C₂×C₆₁	semidirect
373. #3372	C₂×C₆₁	semidirect
374. #3361	C₂×C₆₁	semidirect
375. #3221	C₂×C₆₁	semidirect
376. #3214	C₂×C₆₁	semidirect
377. #3207	C₂×C₆₁	semidirect
378. #3119	C₂×C₆₁	semidirect
379. #3112	C₂×C₆₁	semidirect
380. #3103	C₂×C₆₁	semidirect
381. #2985	C₂×C₆₁	semidirect
458. C₆₁	#61914	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×#3399	2
C₆₁×#3397	2
C₆₁×#3392	2
C₆₁×#3376	2
C₆₁×#3372	2
C₆₁×#3361	2
C₆₁×#3221	2
C₆₁×#3214	2
C₆₁×#3207	2
C₆₁×#3119	2
C₆₁×#3112	2
C₆₁×#3103	2
C₆₁×#2985	2
#61914	61

Subgroups — C61×#61914 #29565347

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61914 #29565347