Subgroups — C₆₁×#24540 #29527973

Order 15616.

940 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#451	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#419	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2499	C₂	1	1	yes	maximal, characteristic
4	Q₈×C₂²⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2074	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#2072	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#2056	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2056	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1894	C₂	1	1	yes	maximal, characteristic
10	C₆₁×#1878	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1878	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#1851	C₂	1	1	yes	maximal, characteristic
13	C₆₁×#1825	C₂	1	1	yes	maximal, characteristic
14	C₆₁×#1805	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#1803	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×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	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
24	C₆₁×#451	—	2	4	no	—
25	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
27	C₆₁×#419	—	2	4	no	—
28	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
33	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
34	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
35	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
37	C₆₁×#397	—	2	1	no	—
38	C₆₁×#397	—	2	1	no	—
39	C₆₁×#391	—	2	1	no	—
40	C₆₁×#391	—	2	1	no	—
41	C₆₁×#391	C₂²	1	1	yes	characteristic
42	C₆₁×#391	C₂²	1	1	yes	characteristic
43	C₆₁×#391	C₂²	1	1	yes	characteristic
44	C₆₁×#391	C₂²	1	1	yes	characteristic
45	C₆₁×#387	—	2	1	no	—
46	C₆₁×#387	—	2	1	no	—
47	C₆₁×#384	C₂²	1	1	yes	characteristic
48	C₆₁×#382	C₂²	1	1	yes	characteristic
49	C₆₁×#380	—	2	1	no	—
50	C₆₁×#380	C₂²	1	1	yes	characteristic
51	C₄×C₂²⋊C₄×C₆₁	—	2	1	no	—
52	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
53	C₆₁×#340	C₂²	1	1	yes	characteristic
54	C₆₁×#340	C₂²	1	1	yes	characteristic
55	C₆₁×#340	C₂²	1	1	yes	characteristic
56	C₆₁×#340	C₂²	1	1	yes	characteristic
57	C₆₁×#340	C₂²	1	1	yes	characteristic
58	C₆₁×#340	C₂²	1	1	yes	characteristic
59	C₆₁×#336	C₂²	1	1	yes	characteristic
60	C₆₁×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₆₁	—	2	1	no	—
62	C₂²×Q₈×C₆₁	—	2	2	no	—
63	C₂²×Q₈×C₆₁	—	2	2	no	—
64	C₂²×Q₈×C₆₁	—	2	2	no	—
65	C₂²×Q₈×C₆₁	—	4	1	no	—
66	C₂²×Q₈×C₆₁	—	4	1	no	—
67	C₂²×Q₈×C₆₁	D₄	1	4	yes	—
68	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
69	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
70	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₆₁	—	2	1	no	—
72	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
73	C₂×Q₁₆×C₆₁	—	2	2	no	—
74	C₂×Q₁₆×C₆₁	—	2	2	no	—
75	C₂×Q₁₆×C₆₁	—	2	2	no	—
76	C₂×Q₁₆×C₆₁	—	2	2	no	—
77	C₂×Q₁₆×C₆₁	—	4	1	no	—
78	C₂×Q₁₆×C₆₁	—	4	1	no	—
79	C₂×M₁₆×C₆₁	—	2	2	no	—
80	C₂×M₁₆×C₆₁	—	4	1	no	—
81	C₂×M₁₆×C₆₁	—	4	1	no	—
82	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
86	C₂²⋊Q₈×C₆₁	—	2	2	no	—
87	C₂²⋊Q₈×C₆₁	—	2	2	no	—
88	C₄×Q₈×C₆₁	—	2	2	no	—
89	C₄×Q₈×C₆₁	—	2	2	no	—
90	C₄×Q₈×C₆₁	—	4	1	no	—
91	C₄×Q₈×C₆₁	—	4	1	no	—
92	#117×C₆₁	—	2	2	no	—
93	#117×C₆₁	—	2	2	no	—
94	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
95	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
96	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
97	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
98	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
99	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₆₁	—	2	1	no	—
110	C₂×C₄²×C₆₁	—	2	1	no	—
111	C₂×C₄²×C₆₁	—	2	1	no	—
112	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
114	C₄⋊C₈×C₆₁	—	4	1	no	—
115	C₄⋊C₈×C₆₁	—	4	1	no	—
116	#103×C₆₁	—	2	2	no	—
117	#103×C₆₁	—	2	2	no	—
118	#103×C₆₁	—	2	2	no	—
119	#103×C₆₁	—	2	2	no	—
120	#103×C₆₁	—	2	2	no	—
121	#103×C₆₁	—	2	2	no	—
122	#103×C₆₁	—	4	1	no	—
123	#103×C₆₁	—	4	1	no	—
124	C₂²⋊C₈×C₆₁	—	2	2	no	—
125	#95×C₆₁	—	2	1	no	—
126	#95×C₆₁	—	2	1	no	—
127	#95×C₆₁	—	2	1	no	—
128	#95×C₆₁	—	2	1	no	—
129	#95×C₆₁	—	2	1	no	—
130	#95×C₆₁	—	2	1	no	—
131	#95×C₆₁	—	2	1	no	—
132	#95×C₆₁	—	2	1	no	—
133	#95×C₆₁	—	2	1	no	—
134	#95×C₆₁	—	2	1	no	—
135	#95×C₆₁	—	2	1	no	—
136	#95×C₆₁	D₄	1	1	yes	characteristic
137	#95×C₆₁	D₄	1	1	yes	characteristic
138	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
139	C₂×Q₈×C₆₁	—	2	4	no	—
140	C₂×Q₈×C₆₁	—	2	1	no	—
141	C₂×Q₈×C₆₁	—	2	1	no	—
142	C₂×Q₈×C₆₁	—	2	1	no	—
143	C₂×Q₈×C₆₁	—	2	1	no	—
144	C₂×Q₈×C₆₁	—	2	8	no	—
145	C₂×Q₈×C₆₁	—	2	1	no	—
146	C₂×Q₈×C₆₁	—	2	1	no	—
147	C₂×Q₈×C₆₁	—	2	1	no	—
148	C₂×Q₈×C₆₁	—	2	1	no	—
149	C₂×Q₈×C₆₁	—	2	1	no	—
150	C₂×Q₈×C₆₁	—	2	1	no	—
151	C₂×Q₈×C₆₁	—	2	1	no	—
152	C₂×Q₈×C₆₁	—	2	1	no	—
153	C₂×Q₈×C₆₁	—	2	1	no	—
154	C₂×Q₈×C₆₁	—	2	1	no	—
155	C₂×Q₈×C₆₁	—	4	2	no	—
156	C₂×Q₈×C₆₁	—	4	2	no	—
157	C₂×Q₈×C₆₁	—	4	4	no	—
158	C₂×Q₈×C₆₁	—	4	4	no	—
159	C₂×Q₈×C₆₁	—	4	4	no	—
160	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
161	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
162	C₂×Q₈×C₆₁	#41	1	2	yes	—
163	C₂×Q₈×C₆₁	#41	1	2	yes	—
164	C₂²×C₄×C₆₁	—	2	1	no	—
165	C₂²×C₄×C₆₁	—	2	1	no	—
166	C₂²×C₄×C₆₁	—	2	1	no	—
167	C₂²×C₄×C₆₁	—	2	1	no	—
168	C₂²×C₄×C₆₁	—	2	1	no	—
169	C₂²×C₄×C₆₁	—	2	4	no	—
170	C₂²×C₄×C₆₁	—	2	1	no	—
171	C₂²×C₄×C₆₁	—	2	1	no	—
172	C₂²×C₄×C₆₁	—	2	1	no	—
173	C₂²×C₄×C₆₁	—	2	1	no	—
174	C₂²×C₄×C₆₁	—	2	1	no	—
175	C₂²×C₄×C₆₁	—	2	1	no	—
176	C₂²×C₄×C₆₁	—	2	1	no	—
177	C₂²×C₄×C₆₁	—	4	2	no	—
178	C₂²×C₄×C₆₁	—	4	2	no	—
179	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
184	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₆₁	#41	1	2	yes	—
186	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
187	Q₁₆×C₆₁	—	4	4	no	—
188	Q₁₆×C₆₁	—	4	4	no	—
189	M₁₆×C₆₁	—	4	4	no	—
190	C₂×C₈×C₆₁	—	2	1	no	—
191	C₂×C₈×C₆₁	—	2	1	no	—
192	C₂×C₈×C₆₁	—	2	1	no	—
193	C₂×C₈×C₆₁	—	2	1	no	—
194	C₂×C₈×C₆₁	—	2	1	no	—
195	C₂×C₈×C₆₁	—	2	1	no	—
196	C₂×C₈×C₆₁	—	2	1	no	—
197	C₂×C₈×C₆₁	—	2	1	no	—
198	C₂×C₈×C₆₁	—	2	1	no	—
199	C₂×C₈×C₆₁	—	2	1	no	—
200	C₂×C₈×C₆₁	—	2	1	no	—
201	C₂×C₈×C₆₁	—	2	1	no	—
202	C₄⋊C₄×C₆₁	—	2	1	no	—
203	C₄⋊C₄×C₆₁	—	2	1	no	—
204	C₄⋊C₄×C₆₁	—	2	1	no	—
205	C₄⋊C₄×C₆₁	—	2	1	no	—
206	C₄⋊C₄×C₆₁	—	2	1	no	—
207	C₄⋊C₄×C₆₁	—	2	1	no	—
208	C₄⋊C₄×C₆₁	—	2	1	no	—
209	C₄⋊C₄×C₆₁	—	2	1	no	—
210	C₄⋊C₄×C₆₁	—	2	1	no	—
211	C₄⋊C₄×C₆₁	—	2	1	no	—
212	C₄⋊C₄×C₆₁	—	4	2	no	—
213	C₄⋊C₄×C₆₁	—	4	2	no	—
214	C₄⋊C₄×C₆₁	—	4	2	no	—
215	C₄⋊C₄×C₆₁	—	4	2	no	—
216	C₄⋊C₄×C₆₁	—	4	2	no	—
217	C₂²⋊C₄×C₆₁	—	2	2	no	—
218	C₂²⋊C₄×C₆₁	—	4	1	no	—
219	C₂²⋊C₄×C₆₁	—	4	2	no	—
220	C₂²⋊C₄×C₆₁	—	4	2	no	—
221	C₂²⋊C₄×C₆₁	—	4	2	no	—
222	C₄²×C₆₁	—	2	1	no	—
223	C₄²×C₆₁	—	2	1	no	—
224	C₄²×C₆₁	—	2	1	no	—
225	C₄²×C₆₁	—	2	1	no	—
226	C₄²×C₆₁	—	4	2	no	—
227	C₄²×C₆₁	—	4	2	no	—
228	C₄²×C₆₁	—	4	2	no	—
229	C₂³×C₆₁	—	2	1	no	—
230	C₂³×C₆₁	—	2	1	no	—
231	C₂³×C₆₁	—	2	1	no	—
232	C₂³×C₆₁	—	2	1	no	—
233	C₂³×C₆₁	—	2	1	no	—
234	C₂³×C₆₁	—	2	1	no	—
235	C₂³×C₆₁	#121	1	2	yes	—
236	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
237	Q₈×C₆₁	—	2	2	no	—
238	Q₈×C₆₁	—	2	2	no	—
239	Q₈×C₆₁	—	2	2	no	—
240	Q₈×C₆₁	—	2	2	no	—
241	Q₈×C₆₁	—	2	2	no	—
242	Q₈×C₆₁	—	4	8	no	—
243	Q₈×C₆₁	—	4	1	no	—
244	Q₈×C₆₁	—	4	1	no	—
245	Q₈×C₆₁	—	4	1	no	—
246	Q₈×C₆₁	—	4	1	no	—
247	Q₈×C₆₁	—	4	1	no	—
248	Q₈×C₆₁	—	4	1	no	—
249	Q₈×C₆₁	#123	1	4	yes	—
250	C₂×C₄×C₆₁	—	2	2	no	—
251	C₂×C₄×C₆₁	—	2	1	no	—
252	C₂×C₄×C₆₁	—	2	2	no	—
253	C₂×C₄×C₆₁	—	2	2	no	—
254	C₂×C₄×C₆₁	—	2	1	no	—
255	C₂×C₄×C₆₁	—	2	1	no	—
256	C₂×C₄×C₆₁	—	2	1	no	—
257	C₂×C₄×C₆₁	—	2	2	no	—
258	C₂×C₄×C₆₁	—	2	2	no	—
259	C₂×C₄×C₆₁	—	2	2	no	—
260	C₂×C₄×C₆₁	—	2	2	no	—
261	C₂×C₄×C₆₁	—	2	2	no	—
262	C₂×C₄×C₆₁	—	2	1	no	—
263	C₂×C₄×C₆₁	—	2	1	no	—
264	C₂×C₄×C₆₁	—	2	1	no	—
265	C₂×C₄×C₆₁	—	2	1	no	—
266	C₂×C₄×C₆₁	—	2	1	no	—
267	C₂×C₄×C₆₁	—	2	1	no	—
268	C₂×C₄×C₆₁	—	2	1	no	—
269	C₂×C₄×C₆₁	—	2	1	no	—
270	C₂×C₄×C₆₁	—	2	1	no	—
271	C₂×C₄×C₆₁	—	4	8	no	—
272	C₂×C₄×C₆₁	—	4	1	no	—
273	C₂×C₄×C₆₁	—	4	1	no	—
274	C₂×C₄×C₆₁	—	4	1	no	—
275	C₂×C₄×C₆₁	—	4	1	no	—
276	C₂×C₄×C₆₁	—	4	1	no	—
277	C₂×C₄×C₆₁	—	4	1	no	—
278	C₂×C₄×C₆₁	—	4	1	no	—
279	C₂×C₄×C₆₁	—	4	1	no	—
280	C₂×C₄×C₆₁	—	4	1	no	—
281	C₂×C₄×C₆₁	—	4	1	no	—
282	C₂×C₄×C₆₁	—	4	1	no	—
283	C₂×C₄×C₆₁	—	4	1	no	—
284	C₂×C₄×C₆₁	—	4	1	no	—
285	C₂×C₄×C₆₁	—	4	1	no	—
286	C₂×C₄×C₆₁	—	4	1	no	—
287	C₂×C₄×C₆₁	—	4	1	no	—
288	C₂×C₄×C₆₁	—	4	1	no	—
289	C₂×C₄×C₆₁	—	4	1	no	—
290	C₂×C₄×C₆₁	—	4	1	no	—
291	C₂×C₄×C₆₁	—	4	1	no	—
292	C₂×C₄×C₆₁	#121	1	2	yes	—
293	C₂×C₄×C₆₁	#137	1	2	yes	—
294	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
295	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
296	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
297	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
298	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
299	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
300	C₈×C₆₁	—	4	1	no	—
301	C₈×C₆₁	—	4	1	no	—
302	C₈×C₆₁	—	4	1	no	—
303	C₈×C₆₁	—	4	1	no	—
304	#24540	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
305	C₂²×C₆₁	—	2	2	no	—
306	C₂²×C₆₁	—	2	2	no	—
307	C₂²×C₆₁	—	2	2	no	—
308	C₂²×C₆₁	—	4	1	no	—
309	C₂²×C₆₁	—	4	1	no	—
310	C₂²×C₆₁	—	4	1	no	—
311	C₂²×C₆₁	—	4	1	no	—
312	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
313	C₂²×C₆₁	#546	1	1	yes	characteristic
314	C₂²×C₆₁	#546	1	1	yes	characteristic
315	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
316	C₂²×C₆₁	#575	1	1	yes	characteristic
317	C₂²×C₆₁	#578	1	1	yes	characteristic
318	C₂²×C₆₁	#578	1	1	yes	characteristic
319	C₄×C₆₁	—	2	2	no	—
320	C₄×C₆₁	—	2	4	no	—
321	C₄×C₆₁	—	2	2	no	—
322	C₄×C₆₁	—	4	1	no	—
323	C₄×C₆₁	—	4	2	no	—
324	C₄×C₆₁	—	4	1	no	—
325	C₄×C₆₁	—	4	1	no	—
326	C₄×C₆₁	—	8	1	no	—
327	C₄×C₆₁	—	8	1	no	—
328	C₄×C₆₁	—	8	1	no	—
329	C₄×C₆₁	—	8	1	no	—
330	C₄×C₆₁	—	8	1	no	—
331	C₄×C₆₁	—	8	1	no	—
332	C₄×C₆₁	C₂×#123	1	1	yes	characteristic
333	C₄×C₆₁	#534	1	1	yes	characteristic
334	C₄×C₆₁	#551	1	1	yes	characteristic
335	C₄×C₆₁	#551	1	1	yes	characteristic
336	C₂×#451	C₂×C₆₁	1	1	yes	characteristic
337	C₂×#419	C₂×C₆₁	1	1	yes	characteristic
338	#2499	C₂×C₆₁	1	1	yes	characteristic
339	Q₈×C₂²⋊C₄	C₂×C₆₁	1	1	yes	characteristic
340	#2074	C₂×C₆₁	1	1	yes	characteristic, complemented
341	#2072	C₂×C₆₁	1	1	yes	characteristic, complemented
342	#2056	C₂×C₆₁	1	1	yes	characteristic, complemented
343	#2056	C₂×C₆₁	1	1	yes	characteristic, complemented
344	#1894	C₂×C₆₁	1	1	yes	characteristic
345	#1878	C₂×C₆₁	1	1	yes	characteristic, complemented
346	#1878	C₂×C₆₁	1	1	yes	characteristic, complemented
347	#1851	C₂×C₆₁	1	1	yes	characteristic
348	#1825	C₂×C₆₁	1	1	yes	characteristic
349	#1805	C₂×C₆₁	1	1	yes	characteristic, complemented
350	#1803	C₂×C₆₁	1	1	yes	characteristic, complemented
351	C₂×C₆₁	—	4	2	no	—
352	C₂×C₆₁	#2412	1	1	yes	characteristic
353	C₂×C₆₁	#3037	1	1	yes	characteristic
354	C₂×C₆₁	#3044	1	1	yes	characteristic
355	C₂×C₆₁	#3312	1	1	yes	characteristic
356	C₂×C₆₁	#3313	1	1	yes	characteristic
357	C₂×C₆₁	#3327	1	1	yes	characteristic
358	C₂×C₆₁	#3328	1	1	yes	characteristic
359	C₂³×Q₈	C₂²×C₆₁	1	1	yes	characteristic
360	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
361	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
362	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
363	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
364	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
365	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
366	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
367	#451	—	2	4	no	—
368	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
369	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
370	#419	—	2	4	no	—
371	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
372	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
373	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
374	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
375	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
376	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
377	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
378	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
379	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
380	#397	—	2	1	no	—
381	#397	—	2	1	no	—
382	#391	—	2	1	no	—
383	#391	—	2	1	no	—
384	#391	C₂²×C₆₁	1	1	yes	characteristic
385	#391	C₂²×C₆₁	1	1	yes	characteristic
386	#391	C₂²×C₆₁	1	1	yes	characteristic
387	#391	C₂²×C₆₁	1	1	yes	characteristic
388	#387	—	2	1	no	—
389	#387	—	2	1	no	—
390	#384	C₂²×C₆₁	1	1	yes	characteristic
391	#382	C₂²×C₆₁	1	1	yes	characteristic
392	#380	—	2	1	no	—
393	#380	C₂²×C₆₁	1	1	yes	characteristic
394	C₄×C₂²⋊C₄	—	2	1	no	—
395	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
396	#340	C₂²×C₆₁	1	1	yes	characteristic
397	#340	C₂²×C₆₁	1	1	yes	characteristic
398	#340	C₂²×C₆₁	1	1	yes	characteristic
399	#340	C₂²×C₆₁	1	1	yes	characteristic
400	#340	C₂²×C₆₁	1	1	yes	characteristic
401	#340	C₂²×C₆₁	1	1	yes	characteristic
402	#336	C₂²×C₆₁	1	1	yes	characteristic
403	#336	C₂²×C₆₁	1	1	yes	characteristic
404	C₆₁	#24540	1	1	yes	characteristic, direct product factor, Sylow
405	C₂²×Q₈	—	2	1	no	—
406	C₂²×Q₈	—	2	2	no	—
407	C₂²×Q₈	—	2	2	no	—
408	C₂²×Q₈	—	2	2	no	—
409	C₂²×Q₈	—	4	1	no	—
410	C₂²×Q₈	—	4	1	no	—
411	C₂²×Q₈	D₄×C₆₁	1	4	yes	—
412	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
413	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
414	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
415	C₂³×C₄	—	2	1	no	—
416	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
417	C₂×Q₁₆	—	2	2	no	—
418	C₂×Q₁₆	—	2	2	no	—
419	C₂×Q₁₆	—	2	2	no	—
420	C₂×Q₁₆	—	2	2	no	—
421	C₂×Q₁₆	—	4	1	no	—
422	C₂×Q₁₆	—	4	1	no	—
423	C₂×M₁₆	—	2	2	no	—
424	C₂×M₁₆	—	4	1	no	—
425	C₂×M₁₆	—	4	1	no	—
426	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
427	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
428	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
429	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
430	C₂²⋊Q₈	—	2	2	no	—
431	C₂²⋊Q₈	—	2	2	no	—
432	C₄×Q₈	—	2	2	no	—
433	C₄×Q₈	—	2	2	no	—
434	C₄×Q₈	—	4	1	no	—
435	C₄×Q₈	—	4	1	no	—
436	#117	—	2	2	no	—
437	#117	—	2	2	no	—
438	C₂×C₄⋊C₄	—	2	1	no	—
439	C₂×C₄⋊C₄	—	2	1	no	—
440	C₂×C₄⋊C₄	—	2	1	no	—
441	C₂×C₄⋊C₄	—	2	1	no	—
442	C₂×C₄⋊C₄	—	2	1	no	—
443	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
444	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
445	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
446	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
448	C₂×C₂²⋊C₄	—	2	1	no	—
449	C₂×C₂²⋊C₄	—	2	1	no	—
450	C₂×C₂²⋊C₄	—	2	1	no	—
451	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
452	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
453	C₂×C₄²	—	2	1	no	—
454	C₂×C₄²	—	2	1	no	—
455	C₂×C₄²	—	2	1	no	—
456	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
457	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
458	C₄⋊C₈	—	4	1	no	—
459	C₄⋊C₈	—	4	1	no	—
460	#103	—	2	2	no	—
461	#103	—	2	2	no	—
462	#103	—	2	2	no	—
463	#103	—	2	2	no	—
464	#103	—	2	2	no	—
465	#103	—	2	2	no	—
466	#103	—	4	1	no	—
467	#103	—	4	1	no	—
468	C₂²⋊C₈	—	2	2	no	—
469	#95	—	2	1	no	—
470	#95	—	2	1	no	—
471	#95	—	2	1	no	—
472	#95	—	2	1	no	—
473	#95	—	2	1	no	—
474	#95	—	2	1	no	—
475	#95	—	2	1	no	—
476	#95	—	2	1	no	—
477	#95	—	2	1	no	—
478	#95	—	2	1	no	—
479	#95	—	2	1	no	—
480	#95	D₄×C₆₁	1	1	yes	characteristic
481	#95	D₄×C₆₁	1	1	yes	characteristic
482	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
483	C₂×Q₈	—	2	4	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	2	1	no	—
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	—	2	1	no	—
488	C₂×Q₈	—	2	8	no	—
489	C₂×Q₈	—	2	1	no	—
490	C₂×Q₈	—	2	1	no	—
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	—	2	1	no	—
494	C₂×Q₈	—	2	1	no	—
495	C₂×Q₈	—	2	1	no	—
496	C₂×Q₈	—	2	1	no	—
497	C₂×Q₈	—	2	1	no	—
498	C₂×Q₈	—	2	1	no	—
499	C₂×Q₈	—	4	2	no	—
500	C₂×Q₈	—	4	2	no	—
501	C₂×Q₈	—	4	4	no	—
502	C₂×Q₈	—	4	4	no	—
503	C₂×Q₈	—	4	4	no	—
504	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
505	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
506	C₂×Q₈	#41×C₆₁	1	2	yes	—
507	C₂×Q₈	#41×C₆₁	1	2	yes	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	4	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	4	2	no	—
522	C₂²×C₄	—	4	2	no	—
523	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
524	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
525	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
526	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
527	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
528	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
529	C₂²×C₄	#41×C₆₁	1	2	yes	—
530	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
531	Q₁₆	—	4	4	no	—
532	Q₁₆	—	4	4	no	—
533	M₁₆	—	4	4	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	2	1	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	—	2	1	no	—
548	C₄⋊C₄	—	2	1	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	—	2	1	no	—
556	C₄⋊C₄	—	4	2	no	—
557	C₄⋊C₄	—	4	2	no	—
558	C₄⋊C₄	—	4	2	no	—
559	C₄⋊C₄	—	4	2	no	—
560	C₄⋊C₄	—	4	2	no	—
561	C₂²⋊C₄	—	2	2	no	—
562	C₂²⋊C₄	—	4	1	no	—
563	C₂²⋊C₄	—	4	2	no	—
564	C₂²⋊C₄	—	4	2	no	—
565	C₂²⋊C₄	—	4	2	no	—
566	C₄²	—	2	1	no	—
567	C₄²	—	2	1	no	—
568	C₄²	—	2	1	no	—
569	C₄²	—	2	1	no	—
570	C₄²	—	4	2	no	—
571	C₄²	—	4	2	no	—
572	C₄²	—	4	2	no	—
573	C₂³	—	2	1	no	—
574	C₂³	—	2	1	no	—
575	C₂³	—	2	1	no	—
576	C₂³	—	2	1	no	—
577	C₂³	—	2	1	no	—
578	C₂³	—	2	1	no	—
579	C₂³	#121×C₆₁	1	2	yes	—
580	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
581	Q₈	—	2	2	no	—
582	Q₈	—	2	2	no	—
583	Q₈	—	2	2	no	—
584	Q₈	—	2	2	no	—
585	Q₈	—	2	2	no	—
586	Q₈	—	4	8	no	—
587	Q₈	—	4	1	no	—
588	Q₈	—	4	1	no	—
589	Q₈	—	4	1	no	—
590	Q₈	—	4	1	no	—
591	Q₈	—	4	1	no	—
592	Q₈	—	4	1	no	—
593	Q₈	#123×C₆₁	1	4	yes	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	4	8	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	#121×C₆₁	1	2	yes	—
637	C₂×C₄	#137×C₆₁	1	2	yes	—
638	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
639	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
640	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
641	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
642	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
643	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
644	C₈	—	4	1	no	—
645	C₈	—	4	1	no	—
646	C₈	—	4	1	no	—
647	C₈	—	4	1	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	4	1	no	—
652	C₂²	—	4	1	no	—
653	C₂²	—	4	1	no	—
654	C₂²	—	4	1	no	—
655	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
656	C₂²	C₆₁×#546	1	1	yes	characteristic
657	C₂²	C₆₁×#546	1	1	yes	characteristic
658	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
659	C₂²	C₆₁×#575	1	1	yes	characteristic
660	C₂²	C₆₁×#578	1	1	yes	characteristic
661	C₂²	C₆₁×#578	1	1	yes	characteristic
662	C₄	—	2	2	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	4	no	—
665	C₄	—	4	1	no	—
666	C₄	—	4	1	no	—
667	C₄	—	4	1	no	—
668	C₄	—	4	2	no	—
669	C₄	—	8	1	no	—
670	C₄	—	8	1	no	—
671	C₄	—	8	1	no	—
672	C₄	—	8	1	no	—
673	C₄	—	8	1	no	—
674	C₄	—	8	1	no	—
675	C₄	C₂×#123×C₆₁	1	1	yes	characteristic
676	C₄	C₆₁×#534	1	1	yes	characteristic
677	C₄	C₆₁×#551	1	1	yes	characteristic
678	C₄	C₆₁×#551	1	1	yes	characteristic
679	C₂	—	4	2	no	—
680	C₂	C₆₁×#2412	1	1	yes	characteristic
681	C₂	C₆₁×#3037	1	1	yes	characteristic
682	C₂	C₆₁×#3044	1	1	yes	characteristic
683	C₂	C₆₁×#3312	1	1	yes	characteristic
684	C₂	C₆₁×#3313	1	1	yes	characteristic
685	C₂	C₆₁×#3327	1	1	yes	characteristic
686	C₂	C₆₁×#3328	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂⁴×C₆₁	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₄×C₂²⋊C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₆₁×#2074	C₂	semidirect
6. C₆₁×#2072	C₂	semidirect
7. C₆₁×#2056	C₂	semidirect
8. C₆₁×#2056	C₂	semidirect
10. C₆₁×#1878	C₂	semidirect
11. C₆₁×#1878	C₂	semidirect
14. C₆₁×#1805	C₂	semidirect
15. C₆₁×#1803	C₂	semidirect
304. #24540	C₆₁	direct (N × H)
340. #2074	C₂×C₆₁	semidirect
341. #2072	C₂×C₆₁	semidirect
342. #2056	C₂×C₆₁	semidirect
343. #2056	C₂×C₆₁	semidirect
345. #1878	C₂×C₆₁	semidirect
346. #1878	C₂×C₆₁	semidirect
349. #1805	C₂×C₆₁	semidirect
350. #1803	C₂×C₆₁	semidirect
404. C₆₁	#24540	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#451	2
C₂×C₆₁×#419	2
C₆₁×#2499	2
Q₈×C₂²⋊C₄×C₆₁	2
C₆₁×#2074	2
C₆₁×#2072	2
C₆₁×#2056	2
C₆₁×#1894	2
C₆₁×#1878	2
C₆₁×#1851	2
C₆₁×#1825	2
C₆₁×#1805	2
C₆₁×#1803	2
#24540	61

Subgroups — C61×#24540 #29527973

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24540 #29527973