Subgroups — C₆₁×#19641 #29523074

Order 15616.

806 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3228	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3207	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3184	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3182	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3167	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3147	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1723	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1721	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1720	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1717	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1708	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#1706	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#1706	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#1705	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×M₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#135×C₆₁	—	2	2	no	—
17	C₆₁×#533	C₂²	1	1	yes	characteristic
18	C₆₁×#532	C₂²	1	1	yes	characteristic
19	C₆₁×#532	C₂²	1	1	yes	characteristic
20	C₆₁×#532	C₂²	1	1	yes	characteristic
21	C₆₁×#500	C₂²	1	1	yes	characteristic
22	C₆₁×#500	C₂²	1	1	yes	characteristic
23	C₆₁×#498	C₂²	1	1	yes	characteristic
24	C₆₁×#498	C₂²	1	1	yes	characteristic
25	C₆₁×#498	C₂²	1	1	yes	characteristic
26	C₆₁×#495	—	2	2	no	—
27	C₆₁×#494	C₂²	1	1	yes	characteristic
28	C₆₁×#493	C₂²	1	1	yes	characteristic
29	C₆₁×#493	C₂²	1	1	yes	characteristic
30	C₆₁×#493	C₂²	1	1	yes	characteristic
31	C₆₁×#492	C₂²	1	1	yes	characteristic
32	C₆₁×#492	C₂²	1	1	yes	characteristic
33	C₆₁×#492	C₂²	1	1	yes	characteristic
34	C₆₁×#492	C₂²	1	1	yes	characteristic
35	C₆₁×#492	C₂²	1	1	yes	characteristic
36	C₆₁×#487	C₂²	1	1	yes	characteristic
37	C₆₁×#487	C₂²	1	1	yes	characteristic
38	C₆₁×#487	C₂²	1	1	yes	characteristic
39	C₆₁×#486	C₂²	1	1	yes	characteristic
40	C₆₁×#486	C₂²	1	1	yes	characteristic
41	C₆₁×#486	C₂²	1	1	yes	characteristic
42	C₆₁×#486	C₂²	1	1	yes	characteristic
43	C₆₁×#486	C₂²	1	1	yes	characteristic
44	C₆₁×#486	C₂²	1	1	yes	characteristic
45	C₆₁×#486	C₂²	1	1	yes	characteristic
46	C₆₁×#482	—	2	2	no	—
47	C₆₁×#478	—	2	2	no	—
48	C₆₁×#469	—	2	2	no	—
49	C₆₁×#468	—	2	2	no	—
50	C₆₁×#465	—	2	2	no	—
51	C₆₁×#463	—	2	2	no	—
52	C₆₁×#449	—	2	2	no	—
53	C₆₁×#442	—	2	2	no	—
54	C₆₁×#440	—	2	2	no	—
55	C₄×SD₁₆×C₆₁	—	2	2	no	—
56	C₆₁×#431	C₂²	1	1	yes	characteristic
57	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
58	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
59	C₆₁×#322	C₂²	1	1	yes	characteristic
60	C₆₁×#322	C₂²	1	1	yes	characteristic
61	C₈²×C₆₁	C₂²	1	1	yes	characteristic
62	C₈²×C₆₁	C₂²	1	1	yes	characteristic
63	C₂×#41×C₆₁	—	2	1	no	—
64	C₂×#41×C₆₁	—	2	1	no	—
65	C₂×#41×C₆₁	—	2	1	no	—
66	#135×C₆₁	—	4	8	no	—
67	C₂×Q₁₆×C₆₁	—	2	2	no	—
68	C₂×SD₁₆×C₆₁	—	2	2	no	—
69	C₂×SD₁₆×C₆₁	—	2	2	no	—
70	C₂×SD₁₆×C₆₁	—	2	2	no	—
71	C₂×SD₁₆×C₆₁	—	2	2	no	—
72	C₂×SD₁₆×C₆₁	—	2	2	no	—
73	C₂×D₈×C₆₁	—	2	2	no	—
74	C₂×D₈×C₆₁	—	2	2	no	—
75	C₂×D₈×C₆₁	—	2	2	no	—
76	C₂×M₁₆×C₆₁	D₄	1	2	yes	—
77	C₂²×C₈×C₆₁	D₄	1	2	yes	—
78	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
79	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
80	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
81	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
82	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
83	#127×C₆₁	C₂³	1	1	yes	characteristic
84	#127×C₆₁	C₂³	1	1	yes	characteristic
85	#127×C₆₁	C₂³	1	1	yes	characteristic
86	#125×C₆₁	—	2	1	no	—
87	#124×C₆₁	—	2	1	no	—
88	#124×C₆₁	—	2	1	no	—
89	#124×C₆₁	—	2	1	no	—
90	C₂²⋊Q₈×C₆₁	—	2	1	no	—
91	C₂²⋊Q₈×C₆₁	—	2	1	no	—
92	#121×C₆₁	—	2	1	no	—
93	#121×C₆₁	—	2	1	no	—
94	#121×C₆₁	—	2	1	no	—
95	#121×C₆₁	—	2	1	no	—
96	#121×C₆₁	—	2	1	no	—
97	#121×C₆₁	—	2	1	no	—
98	C₄×Q₈×C₆₁	—	2	1	no	—
99	C₄×Q₈×C₆₁	—	2	1	no	—
100	C₄×D₄×C₆₁	—	2	1	no	—
101	C₄×D₄×C₆₁	—	2	1	no	—
102	C₄×D₄×C₆₁	—	2	1	no	—
103	C₄×D₄×C₆₁	—	2	1	no	—
104	C₄×D₄×C₆₁	—	2	1	no	—
105	C₄×D₄×C₆₁	—	2	1	no	—
106	#117×C₆₁	—	2	1	no	—
107	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
108	#107×C₆₁	—	2	2	no	—
109	#107×C₆₁	—	2	2	no	—
110	#106×C₆₁	—	2	2	no	—
111	#106×C₆₁	—	2	2	no	—
112	#106×C₆₁	—	2	2	no	—
113	C₄⋊C₈×C₆₁	D₄	1	2	yes	—
114	#103×C₆₁	—	2	2	no	—
115	#103×C₆₁	—	2	2	no	—
116	#103×C₆₁	—	2	2	no	—
117	#102×C₆₁	—	2	2	no	—
118	#102×C₆₁	—	2	2	no	—
119	#102×C₆₁	—	2	2	no	—
120	#102×C₆₁	—	2	2	no	—
121	#102×C₆₁	—	2	2	no	—
122	#102×C₆₁	—	2	2	no	—
123	#102×C₆₁	—	2	2	no	—
124	C₂²⋊C₈×C₆₁	D₄	1	2	yes	—
125	#97×C₆₁	D₄	1	2	yes	—
126	C₄×C₈×C₆₁	D₄	1	2	yes	—
127	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
128	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
129	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
130	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
131	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
132	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
133	#41×C₆₁	—	4	4	no	—
134	#41×C₆₁	—	4	4	no	—
135	#41×C₆₁	—	8	2	no	—
136	C₂×Q₈×C₆₁	—	2	1	no	—
137	C₂×Q₈×C₆₁	—	2	1	no	—
138	C₂×Q₈×C₆₁	—	2	1	no	—
139	C₂×Q₈×C₆₁	—	2	1	no	—
140	C₂×Q₈×C₆₁	—	2	1	no	—
141	C₂×D₄×C₆₁	—	2	1	no	—
142	C₂×D₄×C₆₁	—	2	1	no	—
143	C₂×D₄×C₆₁	—	2	1	no	—
144	C₂×D₄×C₆₁	—	2	1	no	—
145	C₂×D₄×C₆₁	—	2	1	no	—
146	C₂×D₄×C₆₁	—	2	1	no	—
147	C₂×D₄×C₆₁	—	2	1	no	—
148	C₂×D₄×C₆₁	—	2	1	no	—
149	C₂×D₄×C₆₁	—	2	1	no	—
150	C₂×D₄×C₆₁	—	4	1	no	—
151	C₂×D₄×C₆₁	—	4	1	no	—
152	C₂×D₄×C₆₁	—	4	1	no	—
153	C₂²×C₄×C₆₁	—	4	1	no	—
154	C₂²×C₄×C₆₁	—	4	1	no	—
155	C₂²×C₄×C₆₁	—	4	1	no	—
156	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
159	Q₁₆×C₆₁	—	4	4	no	—
160	SD₁₆×C₆₁	—	4	4	no	—
161	SD₁₆×C₆₁	—	4	4	no	—
162	SD₁₆×C₆₁	—	4	4	no	—
163	SD₁₆×C₆₁	—	4	4	no	—
164	SD₁₆×C₆₁	—	8	2	no	—
165	D₈×C₆₁	—	4	4	no	—
166	D₈×C₆₁	—	4	4	no	—
167	D₈×C₆₁	—	8	2	no	—
168	M₁₆×C₆₁	—	2	4	no	—
169	C₂×C₈×C₆₁	—	2	4	no	—
170	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
171	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
172	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
173	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
174	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
175	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
176	C₄⋊C₄×C₆₁	—	2	1	no	—
177	C₄⋊C₄×C₆₁	—	2	1	no	—
178	C₄⋊C₄×C₆₁	—	2	1	no	—
179	C₄⋊C₄×C₆₁	—	2	1	no	—
180	C₄⋊C₄×C₆₁	—	2	1	no	—
181	C₄⋊C₄×C₆₁	—	2	1	no	—
182	C₄⋊C₄×C₆₁	—	2	1	no	—
183	C₄⋊C₄×C₆₁	—	2	1	no	—
184	C₄⋊C₄×C₆₁	—	2	1	no	—
185	C₄⋊C₄×C₆₁	—	2	1	no	—
186	C₄⋊C₄×C₆₁	—	4	1	no	—
187	C₄⋊C₄×C₆₁	—	4	1	no	—
188	C₂²⋊C₄×C₆₁	—	4	1	no	—
189	C₂²⋊C₄×C₆₁	—	4	1	no	—
190	C₂²⋊C₄×C₆₁	—	4	1	no	—
191	C₂²⋊C₄×C₆₁	—	4	1	no	—
192	C₂²⋊C₄×C₆₁	—	4	1	no	—
193	C₂²⋊C₄×C₆₁	—	4	1	no	—
194	C₂²⋊C₄×C₆₁	—	4	1	no	—
195	C₄²×C₆₁	—	4	1	no	—
196	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
197	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
198	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
199	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
200	C₂³×C₆₁	—	4	1	no	—
201	C₂³×C₆₁	—	4	1	no	—
202	C₂³×C₆₁	—	4	1	no	—
203	C₂³×C₆₁	#127	1	1	yes	characteristic
204	Q₈×C₆₁	—	4	2	no	—
205	Q₈×C₆₁	—	4	2	no	—
206	Q₈×C₆₁	—	4	2	no	—
207	Q₈×C₆₁	—	4	2	no	—
208	Q₈×C₆₁	—	4	2	no	—
209	D₄×C₆₁	—	4	2	no	—
210	D₄×C₆₁	—	4	2	no	—
211	D₄×C₆₁	—	4	2	no	—
212	D₄×C₆₁	—	4	2	no	—
213	D₄×C₆₁	—	4	2	no	—
214	D₄×C₆₁	—	4	2	no	—
215	D₄×C₆₁	—	4	2	no	—
216	D₄×C₆₁	—	4	2	no	—
217	D₄×C₆₁	—	4	2	no	—
218	D₄×C₆₁	—	8	2	no	—
219	D₄×C₆₁	—	8	2	no	—
220	D₄×C₆₁	—	8	2	no	—
221	C₂×C₄×C₆₁	—	2	2	no	—
222	C₂×C₄×C₆₁	—	2	2	no	—
223	C₂×C₄×C₆₁	—	2	2	no	—
224	C₂×C₄×C₆₁	—	4	1	no	—
225	C₂×C₄×C₆₁	—	4	1	no	—
226	C₂×C₄×C₆₁	—	4	1	no	—
227	C₂×C₄×C₆₁	—	4	1	no	—
228	C₂×C₄×C₆₁	—	4	1	no	—
229	C₂×C₄×C₆₁	—	8	2	no	—
230	C₂×C₄×C₆₁	—	8	2	no	—
231	C₂×C₄×C₆₁	—	8	2	no	—
232	C₂×C₄×C₆₁	#127	1	1	yes	characteristic
233	C₂×C₄×C₆₁	#127	1	1	yes	characteristic
234	C₂×C₄×C₆₁	#127	1	1	yes	characteristic
235	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
238	C₈×C₆₁	—	2	2	no	—
239	C₈×C₆₁	—	2	2	no	—
240	C₈×C₆₁	—	2	2	no	—
241	C₈×C₆₁	—	2	2	no	—
242	C₈×C₆₁	#135	1	4	yes	complemented
243	C₈×C₆₁	AGL(1,ℤ/8)	1	4	yes	—
244	#19641	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
245	C₂²×C₆₁	—	2	1	no	—
246	C₂²×C₆₁	—	2	1	no	—
247	C₂²×C₆₁	—	2	1	no	—
248	C₂²×C₆₁	—	8	1	no	—
249	C₂²×C₆₁	—	8	1	no	—
250	C₂²×C₆₁	—	8	1	no	—
251	C₂²×C₆₁	—	8	1	no	—
252	C₂²×C₆₁	—	8	1	no	—
253	C₂²×C₆₁	—	8	1	no	—
254	C₂²×C₆₁	—	8	1	no	—
255	C₂²×C₆₁	—	8	1	no	—
256	C₂²×C₆₁	—	8	1	no	—
257	C₂²×C₆₁	C₂×#127	1	1	yes	characteristic
258	C₄×C₆₁	—	2	1	no	—
259	C₄×C₆₁	—	2	1	no	—
260	C₄×C₆₁	—	2	1	no	—
261	C₄×C₆₁	—	8	1	no	—
262	C₄×C₆₁	—	8	1	no	—
263	C₄×C₆₁	—	8	1	no	—
264	C₄×C₆₁	—	8	1	no	—
265	C₄×C₆₁	—	8	1	no	—
266	C₄×C₆₁	C₂×#135	1	2	yes	—
267	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
268	C₄×C₆₁	#577	1	2	yes	—
269	#3228	C₂×C₆₁	1	1	yes	characteristic, complemented
270	#3207	C₂×C₆₁	1	1	yes	characteristic, complemented
271	#3184	C₂×C₆₁	1	1	yes	characteristic, complemented
272	#3182	C₂×C₆₁	1	1	yes	characteristic, complemented
273	#3167	C₂×C₆₁	1	1	yes	characteristic, complemented
274	#3147	C₂×C₆₁	1	1	yes	characteristic, complemented
275	#1723	C₂×C₆₁	1	1	yes	characteristic, complemented
276	#1721	C₂×C₆₁	1	1	yes	characteristic, complemented
277	#1720	C₂×C₆₁	1	1	yes	characteristic, complemented
278	#1717	C₂×C₆₁	1	1	yes	characteristic, complemented
279	#1708	C₂×C₆₁	1	1	yes	characteristic, complemented
280	#1706	C₂×C₆₁	1	1	yes	characteristic, complemented
281	#1706	C₂×C₆₁	1	1	yes	characteristic, complemented
282	#1705	C₂×C₆₁	1	1	yes	characteristic, complemented
283	C₈×M₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
284	C₂×C₆₁	—	4	1	no	—
285	C₂×C₆₁	—	16	1	no	—
286	C₂×C₆₁	—	16	1	no	—
287	C₂×C₆₁	—	16	1	no	—
288	C₂×C₆₁	#3147	1	1	yes	characteristic
289	C₂×C₆₁	#3151	1	1	yes	characteristic
290	C₂×C₆₁	#3154	1	1	yes	characteristic
291	C₂×#135	—	2	2	no	—
292	#533	C₂²×C₆₁	1	1	yes	characteristic
293	#532	C₂²×C₆₁	1	1	yes	characteristic
294	#532	C₂²×C₆₁	1	1	yes	characteristic
295	#532	C₂²×C₆₁	1	1	yes	characteristic
296	#500	C₂²×C₆₁	1	1	yes	characteristic
297	#500	C₂²×C₆₁	1	1	yes	characteristic
298	#498	C₂²×C₆₁	1	1	yes	characteristic
299	#498	C₂²×C₆₁	1	1	yes	characteristic
300	#498	C₂²×C₆₁	1	1	yes	characteristic
301	#495	—	2	2	no	—
302	#494	C₂²×C₆₁	1	1	yes	characteristic
303	#493	C₂²×C₆₁	1	1	yes	characteristic
304	#493	C₂²×C₆₁	1	1	yes	characteristic
305	#493	C₂²×C₆₁	1	1	yes	characteristic
306	#492	C₂²×C₆₁	1	1	yes	characteristic
307	#492	C₂²×C₆₁	1	1	yes	characteristic
308	#492	C₂²×C₆₁	1	1	yes	characteristic
309	#492	C₂²×C₆₁	1	1	yes	characteristic
310	#492	C₂²×C₆₁	1	1	yes	characteristic
311	#487	C₂²×C₆₁	1	1	yes	characteristic
312	#487	C₂²×C₆₁	1	1	yes	characteristic
313	#487	C₂²×C₆₁	1	1	yes	characteristic
314	#486	C₂²×C₆₁	1	1	yes	characteristic
315	#486	C₂²×C₆₁	1	1	yes	characteristic
316	#486	C₂²×C₆₁	1	1	yes	characteristic
317	#486	C₂²×C₆₁	1	1	yes	characteristic
318	#486	C₂²×C₆₁	1	1	yes	characteristic
319	#486	C₂²×C₆₁	1	1	yes	characteristic
320	#486	C₂²×C₆₁	1	1	yes	characteristic
321	#482	—	2	2	no	—
322	#478	—	2	2	no	—
323	#469	—	2	2	no	—
324	#468	—	2	2	no	—
325	#465	—	2	2	no	—
326	#463	—	2	2	no	—
327	#449	—	2	2	no	—
328	#442	—	2	2	no	—
329	#440	—	2	2	no	—
330	C₄×SD₁₆	—	2	2	no	—
331	#431	C₂²×C₆₁	1	1	yes	characteristic
332	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
333	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
334	#322	C₂²×C₆₁	1	1	yes	characteristic
335	#322	C₂²×C₆₁	1	1	yes	characteristic
336	C₈²	C₂²×C₆₁	1	1	yes	characteristic
337	C₈²	C₂²×C₆₁	1	1	yes	characteristic
338	C₆₁	#19641	1	1	yes	characteristic, direct product factor, Sylow
339	C₂×#41	—	2	1	no	—
340	C₂×#41	—	2	1	no	—
341	C₂×#41	—	2	1	no	—
342	#135	—	4	8	no	—
343	C₂×Q₁₆	—	2	2	no	—
344	C₂×SD₁₆	—	2	2	no	—
345	C₂×SD₁₆	—	2	2	no	—
346	C₂×SD₁₆	—	2	2	no	—
347	C₂×SD₁₆	—	2	2	no	—
348	C₂×SD₁₆	—	2	2	no	—
349	C₂×D₈	—	2	2	no	—
350	C₂×D₈	—	2	2	no	—
351	C₂×D₈	—	2	2	no	—
352	C₂×M₁₆	D₄×C₆₁	1	2	yes	—
353	C₂²×C₈	D₄×C₆₁	1	2	yes	—
354	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
355	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
356	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
357	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
358	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
359	#127	C₂³×C₆₁	1	1	yes	characteristic
360	#127	C₂³×C₆₁	1	1	yes	characteristic
361	#127	C₂³×C₆₁	1	1	yes	characteristic
362	#125	—	2	1	no	—
363	#124	—	2	1	no	—
364	#124	—	2	1	no	—
365	#124	—	2	1	no	—
366	C₂²⋊Q₈	—	2	1	no	—
367	C₂²⋊Q₈	—	2	1	no	—
368	#121	—	2	1	no	—
369	#121	—	2	1	no	—
370	#121	—	2	1	no	—
371	#121	—	2	1	no	—
372	#121	—	2	1	no	—
373	#121	—	2	1	no	—
374	C₄×Q₈	—	2	1	no	—
375	C₄×Q₈	—	2	1	no	—
376	C₄×D₄	—	2	1	no	—
377	C₄×D₄	—	2	1	no	—
378	C₄×D₄	—	2	1	no	—
379	C₄×D₄	—	2	1	no	—
380	C₄×D₄	—	2	1	no	—
381	C₄×D₄	—	2	1	no	—
382	#117	—	2	1	no	—
383	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
384	#107	—	2	2	no	—
385	#107	—	2	2	no	—
386	#106	—	2	2	no	—
387	#106	—	2	2	no	—
388	#106	—	2	2	no	—
389	C₄⋊C₈	D₄×C₆₁	1	2	yes	—
390	#103	—	2	2	no	—
391	#103	—	2	2	no	—
392	#103	—	2	2	no	—
393	#102	—	2	2	no	—
394	#102	—	2	2	no	—
395	#102	—	2	2	no	—
396	#102	—	2	2	no	—
397	#102	—	2	2	no	—
398	#102	—	2	2	no	—
399	#102	—	2	2	no	—
400	C₂²⋊C₈	D₄×C₆₁	1	2	yes	—
401	#97	D₄×C₆₁	1	2	yes	—
402	C₄×C₈	D₄×C₆₁	1	2	yes	—
403	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
404	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
405	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
406	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
407	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
408	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
409	#41	—	4	4	no	—
410	#41	—	4	4	no	—
411	#41	—	8	2	no	—
412	C₂×Q₈	—	2	1	no	—
413	C₂×Q₈	—	2	1	no	—
414	C₂×Q₈	—	2	1	no	—
415	C₂×Q₈	—	2	1	no	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×D₄	—	2	1	no	—
418	C₂×D₄	—	2	1	no	—
419	C₂×D₄	—	2	1	no	—
420	C₂×D₄	—	2	1	no	—
421	C₂×D₄	—	2	1	no	—
422	C₂×D₄	—	2	1	no	—
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	—	4	1	no	—
427	C₂×D₄	—	4	1	no	—
428	C₂×D₄	—	4	1	no	—
429	C₂²×C₄	—	4	1	no	—
430	C₂²×C₄	—	4	1	no	—
431	C₂²×C₄	—	4	1	no	—
432	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
433	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
434	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
435	Q₁₆	—	4	4	no	—
436	SD₁₆	—	4	4	no	—
437	SD₁₆	—	4	4	no	—
438	SD₁₆	—	4	4	no	—
439	SD₁₆	—	4	4	no	—
440	SD₁₆	—	8	2	no	—
441	D₈	—	4	4	no	—
442	D₈	—	4	4	no	—
443	D₈	—	8	2	no	—
444	M₁₆	—	2	4	no	—
445	C₂×C₈	—	2	4	no	—
446	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
447	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
448	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
449	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
450	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
451	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	4	1	no	—
463	C₄⋊C₄	—	4	1	no	—
464	C₂²⋊C₄	—	4	1	no	—
465	C₂²⋊C₄	—	4	1	no	—
466	C₂²⋊C₄	—	4	1	no	—
467	C₂²⋊C₄	—	4	1	no	—
468	C₂²⋊C₄	—	4	1	no	—
469	C₂²⋊C₄	—	4	1	no	—
470	C₂²⋊C₄	—	4	1	no	—
471	C₄²	—	4	1	no	—
472	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
473	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
474	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
475	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
476	C₂³	—	4	1	no	—
477	C₂³	—	4	1	no	—
478	C₂³	—	4	1	no	—
479	C₂³	#127×C₆₁	1	1	yes	characteristic
480	Q₈	—	4	2	no	—
481	Q₈	—	4	2	no	—
482	Q₈	—	4	2	no	—
483	Q₈	—	4	2	no	—
484	Q₈	—	4	2	no	—
485	D₄	—	4	2	no	—
486	D₄	—	4	2	no	—
487	D₄	—	4	2	no	—
488	D₄	—	4	2	no	—
489	D₄	—	4	2	no	—
490	D₄	—	4	2	no	—
491	D₄	—	4	2	no	—
492	D₄	—	4	2	no	—
493	D₄	—	4	2	no	—
494	D₄	—	8	2	no	—
495	D₄	—	8	2	no	—
496	D₄	—	8	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	8	2	no	—
506	C₂×C₄	—	8	2	no	—
507	C₂×C₄	—	8	2	no	—
508	C₂×C₄	#127×C₆₁	1	1	yes	characteristic
509	C₂×C₄	#127×C₆₁	1	1	yes	characteristic
510	C₂×C₄	#127×C₆₁	1	1	yes	characteristic
511	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
512	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
513	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
514	C₈	—	2	2	no	—
515	C₈	—	2	2	no	—
516	C₈	—	2	2	no	—
517	C₈	—	2	2	no	—
518	C₈	#135×C₆₁	1	4	yes	complemented
519	C₈	AGL(1,ℤ/8)×C₆₁	1	4	yes	—
520	C₂²	—	2	1	no	—
521	C₂²	—	2	1	no	—
522	C₂²	—	2	1	no	—
523	C₂²	—	8	1	no	—
524	C₂²	—	8	1	no	—
525	C₂²	—	8	1	no	—
526	C₂²	—	8	1	no	—
527	C₂²	—	8	1	no	—
528	C₂²	—	8	1	no	—
529	C₂²	—	8	1	no	—
530	C₂²	—	8	1	no	—
531	C₂²	—	8	1	no	—
532	C₂²	C₂×#127×C₆₁	1	1	yes	characteristic
533	C₄	—	2	1	no	—
534	C₄	—	2	1	no	—
535	C₄	—	2	1	no	—
536	C₄	—	8	1	no	—
537	C₄	—	8	1	no	—
538	C₄	—	8	1	no	—
539	C₄	—	8	1	no	—
540	C₄	—	8	1	no	—
541	C₄	C₂×#135×C₆₁	1	2	yes	—
542	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	2	yes	—
543	C₄	C₆₁×#577	1	2	yes	—
544	C₂	—	4	1	no	—
545	C₂	—	16	1	no	—
546	C₂	—	16	1	no	—
547	C₂	—	16	1	no	—
548	C₂	C₆₁×#3147	1	1	yes	characteristic
549	C₂	C₆₁×#3151	1	1	yes	characteristic
550	C₂	C₆₁×#3154	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₁
LCS	G ▷ C₄² ▷ C₂² ▷ 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
1. C₆₁×#3228	C₂	semidirect
2. C₆₁×#3207	C₂	semidirect
3. C₆₁×#3184	C₂	semidirect
4. C₆₁×#3182	C₂	semidirect
5. C₆₁×#3167	C₂	semidirect
6. C₆₁×#3147	C₂	semidirect
7. C₆₁×#1723	C₂	semidirect
8. C₆₁×#1721	C₂	semidirect
9. C₆₁×#1720	C₂	semidirect
10. C₆₁×#1717	C₂	semidirect
11. C₆₁×#1708	C₂	semidirect
12. C₆₁×#1706	C₂	semidirect
13. C₆₁×#1706	C₂	semidirect
14. C₆₁×#1705	C₂	semidirect
15. C₈×M₁₆×C₆₁	C₂	semidirect
242. C₈×C₆₁	#135	semidirect
244. #19641	C₆₁	direct (N × H)
269. #3228	C₂×C₆₁	semidirect
270. #3207	C₂×C₆₁	semidirect
271. #3184	C₂×C₆₁	semidirect
272. #3182	C₂×C₆₁	semidirect
273. #3167	C₂×C₆₁	semidirect
274. #3147	C₂×C₆₁	semidirect
275. #1723	C₂×C₆₁	semidirect
276. #1721	C₂×C₆₁	semidirect
277. #1720	C₂×C₆₁	semidirect
278. #1717	C₂×C₆₁	semidirect
279. #1708	C₂×C₆₁	semidirect
280. #1706	C₂×C₆₁	semidirect
281. #1706	C₂×C₆₁	semidirect
282. #1705	C₂×C₆₁	semidirect
283. C₈×M₁₆	C₂×C₆₁	semidirect
338. C₆₁	#19641	direct (N × H)
518. C₈	#135×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3228	2
C₆₁×#3207	2
C₆₁×#3184	2
C₆₁×#3182	2
C₆₁×#3167	2
C₆₁×#3147	2
C₆₁×#1723	2
C₆₁×#1721	2
C₆₁×#1720	2
C₆₁×#1717	2
C₆₁×#1708	2
C₆₁×#1706	2
C₆₁×#1705	2
C₈×M₁₆×C₆₁	2
#19641	61

Subgroups — C61×#19641 #29523074

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#19641 #29523074