Subgroups — C₆₁×#60939 #29564372

Order 15616.

1758 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3495	C₂	1	2	yes	maximal, complemented
2	C₆₁×#3263	C₂	1	2	yes	maximal, complemented
3	C₆₁×#3261	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3258	C₂	1	4	yes	maximal, complemented
5	C₆₁×#3256	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3255	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3252	C₂	1	4	yes	maximal, complemented
8	C₆₁×#3084	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3082	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3056	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3054	C₂	1	1	yes	maximal, characteristic
12	C₂×C₆₁×#470	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3046	C₂	1	2	yes	maximal, complemented
14	C₆₁×#3044	C₂	1	2	yes	maximal, complemented
15	C₆₁×#2905	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#137×C₆₁	C₂²	1	2	yes	—
17	C₂×#135×C₆₁	C₂²	1	1	yes	characteristic
18	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
21	C₆₁×#556	—	2	2	no	—
22	C₆₁×#554	—	2	2	no	—
23	C₆₁×#552	—	2	4	no	—
24	C₆₁×#552	—	2	2	no	—
25	C₆₁×#552	—	2	2	no	—
26	C₆₁×#551	—	2	4	no	—
27	C₆₁×#544	C₂²	1	2	yes	—
28	C₆₁×#542	C₂²	1	4	yes	—
29	C₆₁×#541	C₂²	1	4	yes	—
30	C₆₁×#536	C₂²	1	2	yes	—
31	C₆₁×#533	C₂²	1	4	yes	—
32	C₆₁×#529	C₂²	1	4	yes	—
33	C₆₁×#525	C₂²	1	2	yes	—
34	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
35	C₆₁×#520	C₂²	1	2	yes	—
36	C₆₁×#519	C₂²	1	2	yes	—
37	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
38	C₆₁×#479	C₂²	1	4	yes	complemented
39	C₆₁×#479	C₂²	1	4	yes	complemented
40	C₆₁×#479	C₂²	1	4	yes	complemented
41	C₆₁×#478	C₂²	1	4	yes	complemented
42	C₆₁×#477	C₂²	1	4	yes	complemented
43	C₆₁×#476	C₂²	1	4	yes	complemented
44	C₆₁×#475	C₂²	1	4	yes	complemented
45	C₆₁×#475	C₂²	1	4	yes	complemented
46	C₆₁×#470	C₂²	1	2	yes	—
47	C₆₁×#470	C₂²	1	2	yes	—
48	C₆₁×#470	C₂²	1	2	yes	—
49	C₆₁×#470	C₂²	1	2	yes	—
50	C₆₁×#470	C₂²	1	1	yes	characteristic
51	C₆₁×#470	C₂²	1	1	yes	characteristic
52	C₆₁×#470	C₂²	1	4	yes	—
53	C₆₁×#469	C₂²	1	1	yes	characteristic
54	C₆₁×#469	C₂²	1	1	yes	characteristic
55	C₆₁×#468	C₂²	1	2	yes	—
56	C₆₁×#468	C₂²	1	2	yes	—
57	C₆₁×#468	C₂²	1	4	yes	—
58	C₆₁×#467	C₂²	1	4	yes	—
59	C₆₁×#465	C₂²	1	4	yes	—
60	C₆₁×#464	C₂²	1	4	yes	complemented
61	C₆₁×#464	C₂²	1	4	yes	complemented
62	C₆₁×#464	C₂²	1	4	yes	complemented
63	C₆₁×#463	C₂²	1	4	yes	complemented
64	C₆₁×#462	C₂²	1	4	yes	complemented
65	C₆₁×#462	C₂²	1	4	yes	complemented
66	C₆₁×#462	C₂²	1	4	yes	complemented
67	C₆₁×#461	C₂²	1	4	yes	complemented
68	C₆₁×#428	C₂²	1	2	yes	—
69	C₆₁×#427	C₂²	1	1	yes	characteristic
70	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
71	C₆₁×#424	C₂²	1	2	yes	—
72	C₆₁×#424	C₂²	1	2	yes	—
73	C₆₁×#424	C₂²	1	2	yes	—
74	C₆₁×#424	C₂²	1	2	yes	—
75	C₆₁×#423	C₂²	1	2	yes	—
76	C₆₁×#423	C₂²	1	2	yes	—
77	C₆₁×#419	C₂²	1	2	yes	—
78	C₆₁×#417	C₂²	1	2	yes	—
79	C₆₁×#416	C₂²	1	2	yes	—
80	C₂×#103×C₆₁	C₂²	1	2	yes	—
81	C₂×#41×C₆₁	C₂³	1	2	yes	—
82	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
83	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
84	#137×C₆₁	—	4	4	no	—
85	#135×C₆₁	—	4	2	no	—
86	C₂×Q₁₆×C₆₁	—	4	2	no	—
87	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
88	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
89	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
90	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
91	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
92	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
93	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
94	C₂×M₁₆×C₆₁	—	4	2	no	—
95	C₂×M₁₆×C₆₁	—	4	2	no	—
96	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
97	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
98	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
99	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
100	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
101	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
105	C₄⋊Q₈×C₆₁	—	2	2	no	—
106	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
107	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
108	#126×C₆₁	—	2	4	no	—
109	#126×C₆₁	—	2	4	no	—
110	#126×C₆₁	—	2	4	no	—
111	#126×C₆₁	—	2	4	no	—
112	#125×C₆₁	—	2	4	no	—
113	#125×C₆₁	—	2	4	no	—
114	#125×C₆₁	—	2	2	no	—
115	#125×C₆₁	—	2	4	no	—
116	#125×C₆₁	C₂³	1	4	yes	—
117	#124×C₆₁	—	2	4	no	—
118	#124×C₆₁	C₂³	1	4	yes	—
119	#123×C₆₁	—	2	4	no	—
120	#123×C₆₁	—	2	2	no	—
121	#123×C₆₁	—	2	4	no	—
122	#123×C₆₁	—	2	4	no	—
123	C₂²⋊Q₈×C₆₁	—	2	4	no	—
124	C₂²⋊Q₈×C₆₁	—	2	2	no	—
125	C₂²⋊Q₈×C₆₁	—	2	2	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	C₂³	1	2	yes	—
131	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
132	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
133	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
134	#121×C₆₁	C₂³	1	2	yes	—
135	#121×C₆₁	C₂³	1	2	yes	—
136	#120×C₆₁	—	2	2	no	—
137	C₄×Q₈×C₆₁	—	2	2	no	—
138	C₄×Q₈×C₆₁	—	2	2	no	—
139	C₄×Q₈×C₆₁	—	2	4	no	—
140	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
141	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
142	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
143	C₄×D₄×C₆₁	—	2	4	no	—
144	C₄×D₄×C₆₁	—	2	2	no	—
145	C₄×D₄×C₆₁	—	2	2	no	—
146	C₄×D₄×C₆₁	—	2	4	no	—
147	C₄×D₄×C₆₁	C₂³	1	4	yes	—
148	#117×C₆₁	—	2	4	no	—
149	#117×C₆₁	—	2	2	no	—
150	#117×C₆₁	—	2	4	no	—
151	#117×C₆₁	—	2	4	no	—
152	#117×C₆₁	D₄	1	1	yes	characteristic
153	#117×C₆₁	D₄	1	2	yes	—
154	#117×C₆₁	D₄	1	1	yes	characteristic
155	#117×C₆₁	C₂³	1	2	yes	—
156	#117×C₆₁	C₂³	1	2	yes	—
157	#117×C₆₁	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
159	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
160	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
161	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
163	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
164	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
165	#107×C₆₁	C₂³	1	2	yes	—
166	#107×C₆₁	C₂³	1	4	yes	—
167	#106×C₆₁	C₂³	1	2	yes	—
168	#106×C₆₁	C₂³	1	2	yes	—
169	#106×C₆₁	C₂³	1	1	yes	characteristic
170	#106×C₆₁	C₂³	1	1	yes	characteristic
171	#106×C₆₁	C₂³	1	4	yes	—
172	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
173	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
174	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
175	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
176	#103×C₆₁	C₂³	1	4	yes	—
177	#103×C₆₁	C₂³	1	4	yes	—
178	#103×C₆₁	C₂³	1	2	yes	—
179	#103×C₆₁	C₂³	1	2	yes	—
180	#103×C₆₁	C₂³	1	4	yes	—
181	#103×C₆₁	C₂³	1	4	yes	—
182	#103×C₆₁	C₂³	1	4	yes	—
183	#102×C₆₁	C₂³	1	2	yes	—
184	#102×C₆₁	C₂³	1	2	yes	—
185	#102×C₆₁	C₂³	1	4	yes	—
186	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
187	#41×C₆₁	—	2	4	no	—
188	#41×C₆₁	—	2	4	no	—
189	C₂×Q₈×C₆₁	—	2	2	no	—
190	C₂×Q₈×C₆₁	—	2	4	no	—
191	C₂×Q₈×C₆₁	—	2	4	no	—
192	C₂×Q₈×C₆₁	—	2	4	no	—
193	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
194	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
195	C₂×D₄×C₆₁	—	2	2	no	—
196	C₂×D₄×C₆₁	—	2	2	no	—
197	C₂×D₄×C₆₁	—	2	2	no	—
198	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₆₁	—	2	2	no	—
200	C₂²×C₄×C₆₁	—	2	2	no	—
201	C₂²×C₄×C₆₁	—	2	2	no	—
202	C₂²×C₄×C₆₁	—	2	2	no	—
203	C₂²×C₄×C₆₁	—	2	2	no	—
204	C₂²×C₄×C₆₁	—	2	4	no	—
205	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
209	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
212	Q₁₆×C₆₁	—	4	2	no	—
213	Q₁₆×C₆₁	—	4	2	no	—
214	Q₁₆×C₆₁	—	4	1	no	—
215	Q₁₆×C₆₁	—	4	4	no	—
216	SD₁₆×C₆₁	—	4	2	no	—
217	SD₁₆×C₆₁	—	4	4	no	—
218	D₈×C₆₁	—	4	1	no	—
219	M₁₆×C₆₁	—	2	4	no	—
220	M₁₆×C₆₁	—	4	1	no	—
221	M₁₆×C₆₁	—	4	1	no	—
222	M₁₆×C₆₁	—	4	1	no	—
223	M₁₆×C₆₁	—	4	1	no	—
224	M₁₆×C₆₁	—	4	2	no	—
225	C₂×C₈×C₆₁	—	2	2	no	—
226	C₂×C₈×C₆₁	—	2	2	no	—
227	C₂×C₈×C₆₁	—	4	2	no	—
228	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
229	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
230	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
231	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
232	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
233	C₄⋊C₄×C₆₁	—	2	2	no	—
234	C₄⋊C₄×C₆₁	—	2	4	no	—
235	C₄⋊C₄×C₆₁	—	2	4	no	—
236	C₄⋊C₄×C₆₁	—	2	4	no	—
237	C₄⋊C₄×C₆₁	—	2	4	no	—
238	C₄⋊C₄×C₆₁	—	2	4	no	—
239	C₄⋊C₄×C₆₁	—	2	4	no	—
240	C₄⋊C₄×C₆₁	—	2	4	no	—
241	C₄⋊C₄×C₆₁	—	2	4	no	—
242	C₄⋊C₄×C₆₁	—	2	2	no	—
243	C₄⋊C₄×C₆₁	—	2	4	no	—
244	C₄⋊C₄×C₆₁	—	2	2	no	—
245	C₄⋊C₄×C₆₁	—	2	4	no	—
246	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
247	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
248	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
249	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
250	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
251	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
252	C₂²⋊C₄×C₆₁	—	2	4	no	—
253	C₂²⋊C₄×C₆₁	—	2	4	no	—
254	C₂²⋊C₄×C₆₁	—	2	2	no	—
255	C₂²⋊C₄×C₆₁	—	2	2	no	—
256	C₂²⋊C₄×C₆₁	—	2	2	no	—
257	C₂²⋊C₄×C₆₁	—	2	2	no	—
258	C₂²⋊C₄×C₆₁	—	2	4	no	—
259	C₂²⋊C₄×C₆₁	—	2	4	no	—
260	C₂²⋊C₄×C₆₁	—	2	2	no	—
261	C₂²⋊C₄×C₆₁	—	2	4	no	—
262	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
263	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
264	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
265	C₄²×C₆₁	—	2	4	no	—
266	C₄²×C₆₁	—	2	4	no	—
267	C₄²×C₆₁	—	2	4	no	—
268	C₄²×C₆₁	—	2	2	no	—
269	C₄²×C₆₁	C₂×D₄	1	2	yes	—
270	C₄²×C₆₁	C₂×D₄	1	2	yes	—
271	C₄²×C₆₁	C₂⁴	1	4	yes	—
272	C₂³×C₆₁	—	2	2	no	—
273	C₂³×C₆₁	—	2	2	no	—
274	C₂³×C₆₁	—	4	2	no	—
275	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
276	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
277	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
278	Q₈×C₆₁	—	2	4	no	—
279	Q₈×C₆₁	—	2	2	no	—
280	Q₈×C₆₁	—	2	4	no	—
281	Q₈×C₆₁	—	2	2	no	—
282	Q₈×C₆₁	—	4	4	no	—
283	Q₈×C₆₁	—	8	4	no	—
284	D₄×C₆₁	—	2	2	no	—
285	D₄×C₆₁	—	2	2	no	—
286	D₄×C₆₁	—	4	4	no	—
287	D₄×C₆₁	—	4	4	no	—
288	D₄×C₆₁	—	8	2	no	—
289	C₂×C₄×C₆₁	—	2	2	no	—
290	C₂×C₄×C₆₁	—	2	2	no	—
291	C₂×C₄×C₆₁	—	2	2	no	—
292	C₂×C₄×C₆₁	—	2	1	no	—
293	C₂×C₄×C₆₁	—	2	1	no	—
294	C₂×C₄×C₆₁	—	2	1	no	—
295	C₂×C₄×C₆₁	—	2	1	no	—
296	C₂×C₄×C₆₁	—	2	2	no	—
297	C₂×C₄×C₆₁	—	2	2	no	—
298	C₂×C₄×C₆₁	—	2	4	no	—
299	C₂×C₄×C₆₁	—	2	2	no	—
300	C₂×C₄×C₆₁	—	2	4	no	—
301	C₂×C₄×C₆₁	—	4	4	no	—
302	C₂×C₄×C₆₁	—	4	4	no	—
303	C₂×C₄×C₆₁	—	4	4	no	—
304	C₂×C₄×C₆₁	—	8	4	no	—
305	C₂×C₄×C₆₁	—	8	2	no	—
306	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
307	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
308	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
309	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
310	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
311	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
312	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
313	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
314	C₈×C₆₁	—	2	1	no	—
315	C₈×C₆₁	—	2	1	no	—
316	C₈×C₆₁	—	2	1	no	—
317	C₈×C₆₁	—	2	1	no	—
318	C₈×C₆₁	—	2	4	no	—
319	#60939	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
320	C₂²×C₆₁	—	2	2	no	—
321	C₂²×C₆₁	—	2	2	no	—
322	C₂²×C₆₁	—	2	2	no	—
323	C₂²×C₆₁	—	2	1	no	—
324	C₂²×C₆₁	—	2	1	no	—
325	C₂²×C₆₁	—	4	2	no	—
326	C₂²×C₆₁	—	4	2	no	—
327	C₂²×C₆₁	—	4	2	no	—
328	C₂²×C₆₁	—	8	2	no	—
329	C₂²×C₆₁	#537	1	2	yes	—
330	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
331	C₄×C₆₁	—	2	4	no	—
332	C₄×C₆₁	—	2	4	no	—
333	C₄×C₆₁	—	2	1	no	—
334	C₄×C₆₁	—	2	1	no	—
335	C₄×C₆₁	—	4	4	no	—
336	C₄×C₆₁	—	4	2	no	—
337	C₄×C₆₁	—	4	2	no	—
338	C₄×C₆₁	—	4	2	no	—
339	C₄×C₆₁	—	4	4	no	—
340	C₄×C₆₁	#537	1	2	yes	—
341	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
342	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
343	#3495	C₂×C₆₁	1	2	yes	complemented
344	#3263	C₂×C₆₁	1	2	yes	complemented
345	#3261	C₂×C₆₁	1	2	yes	complemented
346	#3258	C₂×C₆₁	1	4	yes	complemented
347	#3256	C₂×C₆₁	1	2	yes	complemented
348	#3255	C₂×C₆₁	1	2	yes	complemented
349	#3252	C₂×C₆₁	1	4	yes	complemented
350	#3084	C₂×C₆₁	1	2	yes	complemented
351	#3082	C₂×C₆₁	1	2	yes	complemented
352	#3056	C₂×C₆₁	1	2	yes	complemented
353	#3054	C₂×C₆₁	1	1	yes	characteristic
354	C₂×#470	C₂×C₆₁	1	1	yes	characteristic, complemented
355	#3046	C₂×C₆₁	1	2	yes	complemented
356	#3044	C₂×C₆₁	1	2	yes	complemented
357	#2905	C₂×C₆₁	1	1	yes	characteristic, complemented
358	C₂×C₆₁	—	2	2	no	—
359	C₂×C₆₁	—	4	1	no	—
360	C₂×C₆₁	—	4	1	no	—
361	C₂×C₆₁	—	8	2	no	—
362	C₂×C₆₁	C₂×#537	1	1	yes	characteristic
363	C₂×C₆₁	#3586	1	2	yes	—
364	C₂×#137	C₂²×C₆₁	1	2	yes	—
365	C₂×#135	C₂²×C₆₁	1	1	yes	characteristic
366	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
367	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
368	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
369	#556	—	2	2	no	—
370	#554	—	2	2	no	—
371	#552	—	2	4	no	—
372	#552	—	2	2	no	—
373	#552	—	2	2	no	—
374	#551	—	2	4	no	—
375	#544	C₂²×C₆₁	1	2	yes	—
376	#542	C₂²×C₆₁	1	4	yes	—
377	#541	C₂²×C₆₁	1	4	yes	—
378	#536	C₂²×C₆₁	1	2	yes	—
379	#533	C₂²×C₆₁	1	4	yes	—
380	#529	C₂²×C₆₁	1	4	yes	—
381	#525	C₂²×C₆₁	1	2	yes	—
382	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
383	#520	C₂²×C₆₁	1	2	yes	—
384	#519	C₂²×C₆₁	1	2	yes	—
385	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
386	#479	C₂²×C₆₁	1	4	yes	complemented
387	#479	C₂²×C₆₁	1	4	yes	complemented
388	#479	C₂²×C₆₁	1	4	yes	complemented
389	#478	C₂²×C₆₁	1	4	yes	complemented
390	#477	C₂²×C₆₁	1	4	yes	complemented
391	#476	C₂²×C₆₁	1	4	yes	complemented
392	#475	C₂²×C₆₁	1	4	yes	complemented
393	#475	C₂²×C₆₁	1	4	yes	complemented
394	#470	C₂²×C₆₁	1	2	yes	—
395	#470	C₂²×C₆₁	1	4	yes	—
396	#470	C₂²×C₆₁	1	1	yes	characteristic
397	#470	C₂²×C₆₁	1	2	yes	—
398	#470	C₂²×C₆₁	1	2	yes	—
399	#470	C₂²×C₆₁	1	1	yes	characteristic
400	#470	C₂²×C₆₁	1	2	yes	—
401	#469	C₂²×C₆₁	1	1	yes	characteristic
402	#469	C₂²×C₆₁	1	1	yes	characteristic
403	#468	C₂²×C₆₁	1	2	yes	—
404	#468	C₂²×C₆₁	1	4	yes	—
405	#468	C₂²×C₆₁	1	2	yes	—
406	#467	C₂²×C₆₁	1	4	yes	—
407	#465	C₂²×C₆₁	1	4	yes	—
408	#464	C₂²×C₆₁	1	4	yes	complemented
409	#464	C₂²×C₆₁	1	4	yes	complemented
410	#464	C₂²×C₆₁	1	4	yes	complemented
411	#463	C₂²×C₆₁	1	4	yes	complemented
412	#462	C₂²×C₆₁	1	4	yes	complemented
413	#462	C₂²×C₆₁	1	4	yes	complemented
414	#462	C₂²×C₆₁	1	4	yes	complemented
415	#461	C₂²×C₆₁	1	4	yes	complemented
416	#428	C₂²×C₆₁	1	2	yes	—
417	#427	C₂²×C₆₁	1	1	yes	characteristic
418	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
419	#424	C₂²×C₆₁	1	2	yes	—
420	#424	C₂²×C₆₁	1	2	yes	—
421	#424	C₂²×C₆₁	1	2	yes	—
422	#424	C₂²×C₆₁	1	2	yes	—
423	#423	C₂²×C₆₁	1	2	yes	—
424	#423	C₂²×C₆₁	1	2	yes	—
425	#419	C₂²×C₆₁	1	2	yes	—
426	#417	C₂²×C₆₁	1	2	yes	—
427	#416	C₂²×C₆₁	1	2	yes	—
428	C₂×#103	C₂²×C₆₁	1	2	yes	—
429	C₆₁	#60939	1	1	yes	characteristic, direct product factor, Sylow
430	C₂×#41	C₂³×C₆₁	1	2	yes	—
431	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
432	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
433	#137	—	4	4	no	—
434	#135	—	4	2	no	—
435	C₂×Q₁₆	—	4	2	no	—
436	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
437	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
438	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
439	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
440	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
441	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
442	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
443	C₂×M₁₆	—	4	2	no	—
444	C₂×M₁₆	—	4	2	no	—
445	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
446	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
447	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
448	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
449	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
450	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
451	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
452	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
453	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
454	C₄⋊Q₈	—	2	2	no	—
455	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
456	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
457	#126	—	2	4	no	—
458	#126	—	2	4	no	—
459	#126	—	2	4	no	—
460	#126	—	2	4	no	—
461	#125	—	2	4	no	—
462	#125	—	2	4	no	—
463	#125	—	2	2	no	—
464	#125	—	2	4	no	—
465	#125	C₂³×C₆₁	1	4	yes	—
466	#124	—	2	4	no	—
467	#124	C₂³×C₆₁	1	4	yes	—
468	#123	—	2	2	no	—
469	#123	—	2	4	no	—
470	#123	—	2	4	no	—
471	#123	—	2	4	no	—
472	C₂²⋊Q₈	—	2	2	no	—
473	C₂²⋊Q₈	—	2	2	no	—
474	C₂²⋊Q₈	—	2	4	no	—
475	C₂²⋊Q₈	—	2	2	no	—
476	C₂²⋊Q₈	—	2	2	no	—
477	C₂²⋊Q₈	—	2	4	no	—
478	C₂²⋊Q₈	—	2	4	no	—
479	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
480	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
481	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
482	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
483	#121	C₂³×C₆₁	1	2	yes	—
484	#121	C₂³×C₆₁	1	2	yes	—
485	#120	—	2	2	no	—
486	C₄×Q₈	—	2	2	no	—
487	C₄×Q₈	—	2	2	no	—
488	C₄×Q₈	—	2	4	no	—
489	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
490	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
491	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
492	C₄×D₄	—	2	2	no	—
493	C₄×D₄	—	2	2	no	—
494	C₄×D₄	—	2	4	no	—
495	C₄×D₄	—	2	4	no	—
496	C₄×D₄	C₂³×C₆₁	1	4	yes	—
497	#117	—	2	4	no	—
498	#117	—	2	2	no	—
499	#117	—	2	4	no	—
500	#117	—	2	4	no	—
501	#117	D₄×C₆₁	1	1	yes	characteristic
502	#117	D₄×C₆₁	1	2	yes	—
503	#117	D₄×C₆₁	1	1	yes	characteristic
504	#117	C₂³×C₆₁	1	2	yes	—
505	#117	C₂³×C₆₁	1	2	yes	—
506	#117	C₂³×C₆₁	1	2	yes	—
507	C₂×C₄⋊C₄	—	2	2	no	—
508	C₂×C₄⋊C₄	—	2	2	no	—
509	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
511	C₂×C₂²⋊C₄	—	2	2	no	—
512	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
513	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
514	#107	C₂³×C₆₁	1	2	yes	—
515	#107	C₂³×C₆₁	1	4	yes	—
516	#106	C₂³×C₆₁	1	2	yes	—
517	#106	C₂³×C₆₁	1	2	yes	—
518	#106	C₂³×C₆₁	1	1	yes	characteristic
519	#106	C₂³×C₆₁	1	1	yes	characteristic
520	#106	C₂³×C₆₁	1	4	yes	—
521	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
522	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
523	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
524	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
525	#103	C₂³×C₆₁	1	4	yes	—
526	#103	C₂³×C₆₁	1	4	yes	—
527	#103	C₂³×C₆₁	1	2	yes	—
528	#103	C₂³×C₆₁	1	2	yes	—
529	#103	C₂³×C₆₁	1	4	yes	—
530	#103	C₂³×C₆₁	1	4	yes	—
531	#103	C₂³×C₆₁	1	4	yes	—
532	#102	C₂³×C₆₁	1	2	yes	—
533	#102	C₂³×C₆₁	1	2	yes	—
534	#102	C₂³×C₆₁	1	4	yes	—
535	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
536	#41	—	2	4	no	—
537	#41	—	2	4	no	—
538	C₂×Q₈	—	2	2	no	—
539	C₂×Q₈	—	2	4	no	—
540	C₂×Q₈	—	2	4	no	—
541	C₂×Q₈	—	2	4	no	—
542	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
543	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
544	C₂×D₄	—	2	2	no	—
545	C₂×D₄	—	2	2	no	—
546	C₂×D₄	—	2	2	no	—
547	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	2	2	no	—
553	C₂²×C₄	—	2	4	no	—
554	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
555	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
556	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
557	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
558	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
559	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
560	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
561	Q₁₆	—	4	2	no	—
562	Q₁₆	—	4	2	no	—
563	Q₁₆	—	4	1	no	—
564	Q₁₆	—	4	4	no	—
565	SD₁₆	—	4	2	no	—
566	SD₁₆	—	4	4	no	—
567	D₈	—	4	1	no	—
568	M₁₆	—	2	4	no	—
569	M₁₆	—	4	1	no	—
570	M₁₆	—	4	1	no	—
571	M₁₆	—	4	1	no	—
572	M₁₆	—	4	1	no	—
573	M₁₆	—	4	2	no	—
574	C₂×C₈	—	2	2	no	—
575	C₂×C₈	—	2	2	no	—
576	C₂×C₈	—	4	2	no	—
577	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
578	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
579	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
580	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
581	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
582	C₄⋊C₄	—	2	2	no	—
583	C₄⋊C₄	—	2	4	no	—
584	C₄⋊C₄	—	2	4	no	—
585	C₄⋊C₄	—	2	4	no	—
586	C₄⋊C₄	—	2	4	no	—
587	C₄⋊C₄	—	2	4	no	—
588	C₄⋊C₄	—	2	4	no	—
589	C₄⋊C₄	—	2	4	no	—
590	C₄⋊C₄	—	2	4	no	—
591	C₄⋊C₄	—	2	2	no	—
592	C₄⋊C₄	—	2	4	no	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
596	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
597	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
598	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
599	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
600	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
601	C₂²⋊C₄	—	2	4	no	—
602	C₂²⋊C₄	—	2	4	no	—
603	C₂²⋊C₄	—	2	2	no	—
604	C₂²⋊C₄	—	2	2	no	—
605	C₂²⋊C₄	—	2	2	no	—
606	C₂²⋊C₄	—	2	2	no	—
607	C₂²⋊C₄	—	2	4	no	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	2	no	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
612	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
613	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
614	C₄²	—	2	4	no	—
615	C₄²	—	2	4	no	—
616	C₄²	—	2	4	no	—
617	C₄²	—	2	2	no	—
618	C₄²	C₂×D₄×C₆₁	1	2	yes	—
619	C₄²	C₂×D₄×C₆₁	1	2	yes	—
620	C₄²	C₂⁴×C₆₁	1	4	yes	—
621	C₂³	—	2	2	no	—
622	C₂³	—	2	2	no	—
623	C₂³	—	4	2	no	—
624	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
625	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
626	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
627	Q₈	—	2	4	no	—
628	Q₈	—	2	2	no	—
629	Q₈	—	2	4	no	—
630	Q₈	—	2	2	no	—
631	Q₈	—	4	4	no	—
632	Q₈	—	8	4	no	—
633	D₄	—	2	2	no	—
634	D₄	—	2	2	no	—
635	D₄	—	4	4	no	—
636	D₄	—	4	4	no	—
637	D₄	—	8	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	4	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	4	no	—
650	C₂×C₄	—	4	4	no	—
651	C₂×C₄	—	4	4	no	—
652	C₂×C₄	—	4	4	no	—
653	C₂×C₄	—	8	4	no	—
654	C₂×C₄	—	8	2	no	—
655	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
656	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
657	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
658	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
659	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
660	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
661	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
662	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
663	C₈	—	2	1	no	—
664	C₈	—	2	1	no	—
665	C₈	—	2	1	no	—
666	C₈	—	2	1	no	—
667	C₈	—	2	4	no	—
668	C₂²	—	2	2	no	—
669	C₂²	—	2	2	no	—
670	C₂²	—	2	2	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	2	1	no	—
673	C₂²	—	4	2	no	—
674	C₂²	—	4	2	no	—
675	C₂²	—	4	2	no	—
676	C₂²	—	8	2	no	—
677	C₂²	C₆₁×#537	1	2	yes	—
678	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
679	C₄	—	2	4	no	—
680	C₄	—	2	4	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	4	4	no	—
684	C₄	—	4	2	no	—
685	C₄	—	4	2	no	—
686	C₄	—	4	2	no	—
687	C₄	—	4	4	no	—
688	C₄	C₆₁×#537	1	2	yes	—
689	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
690	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
691	C₂	—	2	2	no	—
692	C₂	—	4	1	no	—
693	C₂	—	4	1	no	—
694	C₂	—	8	2	no	—
695	C₂	C₂×C₆₁×#537	1	1	yes	characteristic
696	C₂	C₆₁×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₆₁×#3054	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂×#117×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3495	C₂	semidirect
2. C₆₁×#3263	C₂	semidirect
3. C₆₁×#3261	C₂	semidirect
4. C₆₁×#3258	C₂	semidirect
5. C₆₁×#3256	C₂	semidirect
6. C₆₁×#3255	C₂	semidirect
7. C₆₁×#3252	C₂	semidirect
8. C₆₁×#3084	C₂	semidirect
9. C₆₁×#3082	C₂	semidirect
10. C₆₁×#3056	C₂	semidirect
12. C₂×C₆₁×#470	C₂	semidirect
13. C₆₁×#3046	C₂	semidirect
14. C₆₁×#3044	C₂	semidirect
15. C₆₁×#2905	C₂	semidirect
38. C₆₁×#479	C₂²	semidirect
39. C₆₁×#479	C₂²	semidirect
40. C₆₁×#479	C₂²	semidirect
41. C₆₁×#478	C₂²	semidirect
42. C₆₁×#477	C₂²	semidirect
43. C₆₁×#476	C₂²	semidirect
44. C₆₁×#475	C₂²	semidirect
45. C₆₁×#475	C₂²	semidirect
60. C₆₁×#464	C₂²	semidirect
61. C₆₁×#464	C₂²	semidirect
62. C₆₁×#464	C₂²	semidirect
63. C₆₁×#463	C₂²	semidirect
64. C₆₁×#462	C₂²	semidirect
65. C₆₁×#462	C₂²	semidirect
66. C₆₁×#462	C₂²	semidirect
67. C₆₁×#461	C₂²	semidirect
319. #60939	C₆₁	direct (N × H)
343. #3495	C₂×C₆₁	semidirect
344. #3263	C₂×C₆₁	semidirect
345. #3261	C₂×C₆₁	semidirect
346. #3258	C₂×C₆₁	semidirect
347. #3256	C₂×C₆₁	semidirect
348. #3255	C₂×C₆₁	semidirect
349. #3252	C₂×C₆₁	semidirect
350. #3084	C₂×C₆₁	semidirect
351. #3082	C₂×C₆₁	semidirect
352. #3056	C₂×C₆₁	semidirect
354. C₂×#470	C₂×C₆₁	semidirect
355. #3046	C₂×C₆₁	semidirect
356. #3044	C₂×C₆₁	semidirect
357. #2905	C₂×C₆₁	semidirect
386. #479	C₂²×C₆₁	semidirect
387. #479	C₂²×C₆₁	semidirect
388. #479	C₂²×C₆₁	semidirect
389. #478	C₂²×C₆₁	semidirect
390. #477	C₂²×C₆₁	semidirect
391. #476	C₂²×C₆₁	semidirect
392. #475	C₂²×C₆₁	semidirect
393. #475	C₂²×C₆₁	semidirect
408. #464	C₂²×C₆₁	semidirect
409. #464	C₂²×C₆₁	semidirect
410. #464	C₂²×C₆₁	semidirect
411. #463	C₂²×C₆₁	semidirect
412. #462	C₂²×C₆₁	semidirect
413. #462	C₂²×C₆₁	semidirect
414. #462	C₂²×C₆₁	semidirect
415. #461	C₂²×C₆₁	semidirect
429. C₆₁	#60939	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×#3495	2
C₆₁×#3263	2
C₆₁×#3261	2
C₆₁×#3258	2
C₆₁×#3256	2
C₆₁×#3255	2
C₆₁×#3252	2
C₆₁×#3084	2
C₆₁×#3082	2
C₆₁×#3056	2
C₆₁×#3054	2
C₂×C₆₁×#470	2
C₆₁×#3046	2
C₆₁×#3044	2
C₆₁×#2905	2
#60939	61

Subgroups — C61×#60939 #29564372

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#60939 #29564372