Subgroups — C₆₁×#19671 #29523104

Order 15616.

914 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3227	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3205	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3169	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3151	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₆₁×#492	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3141	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1721	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1717	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1715	C₂	1	2	yes	maximal, complemented
10	C₆₁×#1714	C₂	1	2	yes	maximal, complemented
11	C₆₁×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₆₁	—	2	2	no	—
13	C₂²×SD₁₆×C₆₁	—	2	2	no	—
14	C₆₁×#532	C₂²	1	1	yes	characteristic
15	C₆₁×#532	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
18	C₆₁×#500	C₂²	1	1	yes	characteristic, complemented
19	C₆₁×#498	C₂²	1	2	yes	complemented
20	C₆₁×#496	—	2	2	no	—
21	C₆₁×#493	C₂²	1	2	yes	—
22	C₆₁×#493	C₂²	1	2	yes	—
23	C₆₁×#493	C₂²	1	1	yes	characteristic, complemented
24	C₆₁×#492	—	2	2	no	—
25	C₆₁×#492	C₂²	1	2	yes	—
26	C₆₁×#492	C₂²	1	2	yes	—
27	C₆₁×#492	C₂²	1	2	yes	—
28	C₆₁×#489	—	2	2	no	—
29	C₆₁×#487	C₂²	1	2	yes	complemented
30	C₆₁×#486	C₂²	1	2	yes	—
31	C₆₁×#486	C₂²	1	2	yes	complemented
32	C₆₁×#486	C₂²	1	1	yes	characteristic, complemented
33	C₆₁×#486	C₂²	1	1	yes	characteristic, complemented
34	C₆₁×#486	C₂²	1	2	yes	complemented
35	C₆₁×#481	—	2	2	no	—
36	C₆₁×#476	—	2	2	no	—
37	C₆₁×#466	—	2	2	no	—
38	C₆₁×#459	—	2	2	no	—
39	C₆₁×#447	—	2	2	no	—
40	C₄×D₈×C₆₁	—	2	2	no	—
41	C₆₁×#431	C₂²	1	1	yes	characteristic
42	C₆₁×#417	—	2	2	no	—
43	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
45	C₆₁×#322	C₂²	1	2	yes	complemented
46	C₆₁×#322	C₂²	1	2	yes	complemented
47	C₂×#41×C₆₁	—	2	1	no	—
48	C₂×#41×C₆₁	—	2	1	no	—
49	C₂²×Q₈×C₆₁	—	2	1	no	—
50	C₂²×D₄×C₆₁	—	2	1	no	—
51	C₂²×D₄×C₆₁	—	2	1	no	—
52	C₂²×D₄×C₆₁	—	2	1	no	—
53	AGL(1,ℤ/8)×C₆₁	—	4	8	no	—
54	C₂×SD₁₆×C₆₁	—	2	4	no	—
55	C₂×SD₁₆×C₆₁	—	2	4	no	—
56	C₂×SD₁₆×C₆₁	—	2	4	no	—
57	C₂×SD₁₆×C₆₁	—	4	8	no	—
58	C₂×D₈×C₆₁	—	2	4	no	—
59	C₂×D₈×C₆₁	—	2	2	no	—
60	C₂×D₈×C₆₁	—	2	4	no	—
61	C₂×M₁₆×C₆₁	D₄	1	2	yes	—
62	C₂²×C₈×C₆₁	D₄	1	2	yes	—
63	C₄⋊Q₈×C₆₁	—	2	1	no	—
64	C₄⋊Q₈×C₆₁	—	2	1	no	—
65	C₄⋊Q₈×C₆₁	—	2	1	no	—
66	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
67	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
68	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
69	#127×C₆₁	—	2	1	no	—
70	#127×C₆₁	—	2	1	no	—
71	#127×C₆₁	—	2	1	no	—
72	#127×C₆₁	C₂³	1	2	yes	—
73	#127×C₆₁	C₂³	1	1	yes	characteristic
74	#127×C₆₁	C₂³	1	1	yes	characteristic
75	#124×C₆₁	—	2	1	no	—
76	#124×C₆₁	—	2	1	no	—
77	#121×C₆₁	—	2	1	no	—
78	#121×C₆₁	—	2	1	no	—
79	#121×C₆₁	—	2	1	no	—
80	#121×C₆₁	—	2	1	no	—
81	C₄×D₄×C₆₁	—	2	1	no	—
82	C₄×D₄×C₆₁	—	2	1	no	—
83	C₄×D₄×C₆₁	—	2	1	no	—
84	C₄×D₄×C₆₁	—	2	1	no	—
85	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
86	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
87	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
88	#107×C₆₁	—	2	2	no	—
89	#106×C₆₁	—	2	4	no	—
90	C₄⋊C₈×C₆₁	D₄	1	2	yes	—
91	#103×C₆₁	—	2	4	no	—
92	#102×C₆₁	—	2	4	no	—
93	#102×C₆₁	—	2	2	no	—
94	#102×C₆₁	—	2	2	no	—
95	#102×C₆₁	—	2	4	no	—
96	#102×C₆₁	—	2	4	no	—
97	C₂²⋊C₈×C₆₁	D₄	1	2	yes	—
98	#97×C₆₁	D₄	1	2	yes	—
99	C₄×C₈×C₆₁	D₄	1	2	yes	—
100	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
102	C₄×C₈×C₆₁	C₂³	1	2	yes	—
103	C₄×C₈×C₆₁	C₂³	1	2	yes	—
104	C₂⁴×C₆₁	—	4	1	no	—
105	#41×C₆₁	—	4	4	no	—
106	#41×C₆₁	—	4	4	no	—
107	C₂×Q₈×C₆₁	—	2	1	no	—
108	C₂×Q₈×C₆₁	—	2	1	no	—
109	C₂×Q₈×C₆₁	—	2	2	no	—
110	C₂×Q₈×C₆₁	—	4	4	no	—
111	C₂×Q₈×C₆₁	—	4	1	no	—
112	C₂×D₄×C₆₁	—	2	1	no	—
113	C₂×D₄×C₆₁	—	2	1	no	—
114	C₂×D₄×C₆₁	—	2	1	no	—
115	C₂×D₄×C₆₁	—	2	1	no	—
116	C₂×D₄×C₆₁	—	2	2	no	—
117	C₂×D₄×C₆₁	—	2	1	no	—
118	C₂×D₄×C₆₁	—	2	1	no	—
119	C₂×D₄×C₆₁	—	2	2	no	—
120	C₂×D₄×C₆₁	—	2	2	no	—
121	C₂×D₄×C₆₁	—	4	4	no	—
122	C₂×D₄×C₆₁	—	4	1	no	—
123	C₂×D₄×C₆₁	—	4	1	no	—
124	C₂×D₄×C₆₁	—	4	1	no	—
125	C₂×D₄×C₆₁	—	4	1	no	—
126	C₂×D₄×C₆₁	—	4	1	no	—
127	C₂×D₄×C₆₁	—	4	4	no	—
128	C₂×D₄×C₆₁	—	8	2	no	—
129	C₂²×C₄×C₆₁	—	4	1	no	—
130	C₂²×C₄×C₆₁	—	4	1	no	—
131	C₂²×C₄×C₆₁	—	4	1	no	—
132	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
135	SD₁₆×C₆₁	—	4	8	no	—
136	SD₁₆×C₆₁	—	4	8	no	—
137	SD₁₆×C₆₁	—	4	8	no	—
138	D₈×C₆₁	—	4	8	no	—
139	D₈×C₆₁	—	4	4	no	—
140	D₈×C₆₁	—	8	4	no	—
141	M₁₆×C₆₁	—	2	4	no	—
142	C₂×C₈×C₆₁	—	2	4	no	—
143	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
144	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
145	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
146	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
147	C₄⋊C₄×C₆₁	—	2	1	no	—
148	C₄⋊C₄×C₆₁	—	2	2	no	—
149	C₄⋊C₄×C₆₁	—	2	2	no	—
150	C₄⋊C₄×C₆₁	—	2	1	no	—
151	C₄⋊C₄×C₆₁	—	2	1	no	—
152	C₄⋊C₄×C₆₁	—	2	1	no	—
153	C₄⋊C₄×C₆₁	—	4	1	no	—
154	C₄⋊C₄×C₆₁	—	4	1	no	—
155	C₂²⋊C₄×C₆₁	—	4	1	no	—
156	C₂²⋊C₄×C₆₁	—	4	1	no	—
157	C₂²⋊C₄×C₆₁	—	4	1	no	—
158	C₂²⋊C₄×C₆₁	—	4	1	no	—
159	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
163	C₂³×C₆₁	—	4	1	no	—
164	C₂³×C₆₁	—	4	1	no	—
165	C₂³×C₆₁	—	4	2	no	—
166	C₂³×C₆₁	—	8	2	no	—
167	C₂³×C₆₁	—	8	2	no	—
168	C₂³×C₆₁	—	8	2	no	—
169	C₂³×C₆₁	#127	1	1	yes	characteristic
170	Q₈×C₆₁	—	4	4	no	—
171	Q₈×C₆₁	—	4	2	no	—
172	Q₈×C₆₁	—	4	2	no	—
173	Q₈×C₆₁	—	8	2	no	—
174	D₄×C₆₁	—	4	2	no	—
175	D₄×C₆₁	—	4	4	no	—
176	D₄×C₆₁	—	4	2	no	—
177	D₄×C₆₁	—	4	2	no	—
178	D₄×C₆₁	—	4	4	no	—
179	D₄×C₆₁	—	4	2	no	—
180	D₄×C₆₁	—	4	2	no	—
181	D₄×C₆₁	—	4	4	no	—
182	D₄×C₆₁	—	4	2	no	—
183	D₄×C₆₁	—	8	2	no	—
184	D₄×C₆₁	—	8	2	no	—
185	D₄×C₆₁	—	8	2	no	—
186	D₄×C₆₁	—	8	2	no	—
187	D₄×C₆₁	—	8	2	no	—
188	C₂×C₄×C₆₁	—	2	2	no	—
189	C₂×C₄×C₆₁	—	2	2	no	—
190	C₂×C₄×C₆₁	—	4	1	no	—
191	C₂×C₄×C₆₁	—	4	1	no	—
192	C₂×C₄×C₆₁	—	4	2	no	—
193	C₂×C₄×C₆₁	—	8	2	no	—
194	C₂×C₄×C₆₁	—	8	2	no	—
195	C₂×C₄×C₆₁	—	8	2	no	—
196	C₂×C₄×C₆₁	#127	1	1	yes	characteristic
197	C₂×C₄×C₆₁	#127	1	1	yes	characteristic
198	C₂×C₄×C₆₁	#127	1	1	yes	characteristic
199	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	4	yes	—
200	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
203	C₈×C₆₁	—	2	2	no	—
204	C₈×C₆₁	—	2	4	no	—
205	C₈×C₆₁	—	2	4	no	—
206	C₈×C₆₁	AGL(1,ℤ/8)	1	4	yes	complemented
207	#19671	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂²×C₆₁	—	2	1	no	—
209	C₂²×C₆₁	—	2	1	no	—
210	C₂²×C₆₁	—	8	1	no	—
211	C₂²×C₆₁	—	8	1	no	—
212	C₂²×C₆₁	—	8	2	no	—
213	C₂²×C₆₁	—	8	2	no	—
214	C₂²×C₆₁	—	8	1	no	—
215	C₂²×C₆₁	—	8	1	no	—
216	C₂²×C₆₁	—	8	2	no	—
217	C₂²×C₆₁	—	8	1	no	—
218	C₂²×C₆₁	—	8	1	no	—
219	C₂²×C₆₁	—	16	4	no	—
220	C₂²×C₆₁	#496	1	2	yes	—
221	C₂²×C₆₁	C₂×#127	1	1	yes	characteristic
222	C₄×C₆₁	—	2	1	no	—
223	C₄×C₆₁	—	2	1	no	—
224	C₄×C₆₁	—	8	1	no	—
225	C₄×C₆₁	—	8	1	no	—
226	C₄×C₆₁	—	8	2	no	—
227	C₄×C₆₁	#496	1	2	yes	—
228	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
229	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
230	C₄×C₆₁	#577	1	2	yes	—
231	#3227	C₂×C₆₁	1	1	yes	characteristic, complemented
232	#3205	C₂×C₆₁	1	1	yes	characteristic, complemented
233	#3169	C₂×C₆₁	1	1	yes	characteristic, complemented
234	#3151	C₂×C₆₁	1	1	yes	characteristic, complemented
235	C₂×#492	C₂×C₆₁	1	1	yes	characteristic, complemented
236	#3141	C₂×C₆₁	1	1	yes	characteristic, complemented
237	#1721	C₂×C₆₁	1	2	yes	complemented
238	#1717	C₂×C₆₁	1	2	yes	complemented
239	#1715	C₂×C₆₁	1	2	yes	complemented
240	#1714	C₂×C₆₁	1	2	yes	complemented
241	#1451	C₂×C₆₁	1	1	yes	characteristic, complemented
242	C₂×C₆₁	—	2	2	no	—
243	C₂×C₆₁	—	16	1	no	—
244	C₂×C₆₁	—	16	1	no	—
245	C₂×C₆₁	—	16	2	no	—
246	C₂×C₆₁	C₂×#496	1	1	yes	characteristic
247	C₂×C₆₁	#3151	1	1	yes	characteristic
248	C₂×C₆₁	#3154	1	1	yes	characteristic
249	C₂×AGL(1,ℤ/8)	—	2	2	no	—
250	C₂²×SD₁₆	—	2	2	no	—
251	#532	C₂²×C₆₁	1	1	yes	characteristic
252	#532	C₂²×C₆₁	1	1	yes	characteristic
253	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
254	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
255	#500	C₂²×C₆₁	1	1	yes	characteristic, complemented
256	#498	C₂²×C₆₁	1	2	yes	complemented
257	#496	—	2	2	no	—
258	#493	C₂²×C₆₁	1	2	yes	—
259	#493	C₂²×C₆₁	1	2	yes	—
260	#493	C₂²×C₆₁	1	1	yes	characteristic, complemented
261	#492	—	2	2	no	—
262	#492	C₂²×C₆₁	1	2	yes	—
263	#492	C₂²×C₆₁	1	2	yes	—
264	#492	C₂²×C₆₁	1	2	yes	—
265	#489	—	2	2	no	—
266	#487	C₂²×C₆₁	1	2	yes	complemented
267	#486	C₂²×C₆₁	1	2	yes	—
268	#486	C₂²×C₆₁	1	2	yes	complemented
269	#486	C₂²×C₆₁	1	1	yes	characteristic, complemented
270	#486	C₂²×C₆₁	1	1	yes	characteristic, complemented
271	#486	C₂²×C₆₁	1	2	yes	complemented
272	#481	—	2	2	no	—
273	#476	—	2	2	no	—
274	#466	—	2	2	no	—
275	#459	—	2	2	no	—
276	#447	—	2	2	no	—
277	C₄×D₈	—	2	2	no	—
278	#431	C₂²×C₆₁	1	1	yes	characteristic
279	#417	—	2	2	no	—
280	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
281	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
282	#322	C₂²×C₆₁	1	2	yes	complemented
283	#322	C₂²×C₆₁	1	2	yes	complemented
284	C₆₁	#19671	1	1	yes	characteristic, direct product factor, Sylow
285	C₂×#41	—	2	1	no	—
286	C₂×#41	—	2	1	no	—
287	C₂²×Q₈	—	2	1	no	—
288	C₂²×D₄	—	2	1	no	—
289	C₂²×D₄	—	2	1	no	—
290	C₂²×D₄	—	2	1	no	—
291	AGL(1,ℤ/8)	—	4	8	no	—
292	C₂×SD₁₆	—	2	4	no	—
293	C₂×SD₁₆	—	2	4	no	—
294	C₂×SD₁₆	—	2	4	no	—
295	C₂×SD₁₆	—	4	8	no	—
296	C₂×D₈	—	2	4	no	—
297	C₂×D₈	—	2	2	no	—
298	C₂×D₈	—	2	4	no	—
299	C₂×M₁₆	D₄×C₆₁	1	2	yes	—
300	C₂²×C₈	D₄×C₆₁	1	2	yes	—
301	C₄⋊Q₈	—	2	1	no	—
302	C₄⋊Q₈	—	2	1	no	—
303	C₄⋊Q₈	—	2	1	no	—
304	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
305	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
306	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
307	#127	—	2	1	no	—
308	#127	—	2	1	no	—
309	#127	—	2	1	no	—
310	#127	C₂³×C₆₁	1	2	yes	—
311	#127	C₂³×C₆₁	1	1	yes	characteristic
312	#127	C₂³×C₆₁	1	1	yes	characteristic
313	#124	—	2	1	no	—
314	#124	—	2	1	no	—
315	#121	—	2	1	no	—
316	#121	—	2	1	no	—
317	#121	—	2	1	no	—
318	#121	—	2	1	no	—
319	C₄×D₄	—	2	1	no	—
320	C₄×D₄	—	2	1	no	—
321	C₄×D₄	—	2	1	no	—
322	C₄×D₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
326	#107	—	2	2	no	—
327	#106	—	2	4	no	—
328	C₄⋊C₈	D₄×C₆₁	1	2	yes	—
329	#103	—	2	4	no	—
330	#102	—	2	4	no	—
331	#102	—	2	2	no	—
332	#102	—	2	2	no	—
333	#102	—	2	4	no	—
334	#102	—	2	4	no	—
335	C₂²⋊C₈	D₄×C₆₁	1	2	yes	—
336	#97	D₄×C₆₁	1	2	yes	—
337	C₄×C₈	D₄×C₆₁	1	2	yes	—
338	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
339	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
340	C₄×C₈	C₂³×C₆₁	1	2	yes	—
341	C₄×C₈	C₂³×C₆₁	1	2	yes	—
342	C₂⁴	—	4	1	no	—
343	#41	—	4	4	no	—
344	#41	—	4	4	no	—
345	C₂×Q₈	—	2	1	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	—	4	4	no	—
349	C₂×Q₈	—	4	1	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	4	4	no	—
360	C₂×D₄	—	4	1	no	—
361	C₂×D₄	—	4	1	no	—
362	C₂×D₄	—	4	1	no	—
363	C₂×D₄	—	4	1	no	—
364	C₂×D₄	—	4	1	no	—
365	C₂×D₄	—	4	4	no	—
366	C₂×D₄	—	8	2	no	—
367	C₂²×C₄	—	4	1	no	—
368	C₂²×C₄	—	4	1	no	—
369	C₂²×C₄	—	4	1	no	—
370	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
373	SD₁₆	—	4	8	no	—
374	SD₁₆	—	4	8	no	—
375	SD₁₆	—	4	8	no	—
376	D₈	—	4	8	no	—
377	D₈	—	4	4	no	—
378	D₈	—	8	4	no	—
379	M₁₆	—	2	4	no	—
380	C₂×C₈	—	2	4	no	—
381	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
382	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
383	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
384	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	4	1	no	—
392	C₄⋊C₄	—	4	1	no	—
393	C₂²⋊C₄	—	4	1	no	—
394	C₂²⋊C₄	—	4	1	no	—
395	C₂²⋊C₄	—	4	1	no	—
396	C₂²⋊C₄	—	4	1	no	—
397	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
398	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
399	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
400	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
401	C₂³	—	4	1	no	—
402	C₂³	—	4	1	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	8	2	no	—
405	C₂³	—	8	2	no	—
406	C₂³	—	8	2	no	—
407	C₂³	#127×C₆₁	1	1	yes	characteristic
408	Q₈	—	4	4	no	—
409	Q₈	—	4	2	no	—
410	Q₈	—	4	2	no	—
411	Q₈	—	8	2	no	—
412	D₄	—	4	2	no	—
413	D₄	—	4	4	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	4	no	—
417	D₄	—	4	2	no	—
418	D₄	—	4	2	no	—
419	D₄	—	4	4	no	—
420	D₄	—	4	2	no	—
421	D₄	—	8	2	no	—
422	D₄	—	8	2	no	—
423	D₄	—	8	2	no	—
424	D₄	—	8	2	no	—
425	D₄	—	8	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	8	2	no	—
432	C₂×C₄	—	8	2	no	—
433	C₂×C₄	—	8	2	no	—
434	C₂×C₄	#127×C₆₁	1	1	yes	characteristic
435	C₂×C₄	#127×C₆₁	1	1	yes	characteristic
436	C₂×C₄	#127×C₆₁	1	1	yes	characteristic
437	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	4	yes	—
438	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
439	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
440	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
441	C₈	—	2	2	no	—
442	C₈	—	2	4	no	—
443	C₈	—	2	4	no	—
444	C₈	AGL(1,ℤ/8)×C₆₁	1	4	yes	complemented
445	C₂²	—	2	1	no	—
446	C₂²	—	2	1	no	—
447	C₂²	—	8	1	no	—
448	C₂²	—	8	1	no	—
449	C₂²	—	8	2	no	—
450	C₂²	—	8	2	no	—
451	C₂²	—	8	1	no	—
452	C₂²	—	8	1	no	—
453	C₂²	—	8	2	no	—
454	C₂²	—	8	1	no	—
455	C₂²	—	8	1	no	—
456	C₂²	—	16	4	no	—
457	C₂²	C₆₁×#496	1	2	yes	—
458	C₂²	C₂×#127×C₆₁	1	1	yes	characteristic
459	C₄	—	2	1	no	—
460	C₄	—	2	1	no	—
461	C₄	—	8	1	no	—
462	C₄	—	8	1	no	—
463	C₄	—	8	2	no	—
464	C₄	C₆₁×#496	1	2	yes	—
465	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	2	yes	—
466	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	2	yes	—
467	C₄	C₆₁×#577	1	2	yes	—
468	C₂	—	2	2	no	—
469	C₂	—	16	2	no	—
470	C₂	—	16	1	no	—
471	C₂	—	16	1	no	—
472	C₂	C₂×C₆₁×#496	1	1	yes	characteristic
473	C₂	C₆₁×#3151	1	1	yes	characteristic
474	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×#3227	C₂	semidirect
2. C₆₁×#3205	C₂	semidirect
3. C₆₁×#3169	C₂	semidirect
4. C₆₁×#3151	C₂	semidirect
5. C₂×C₆₁×#492	C₂	semidirect
6. C₆₁×#3141	C₂	semidirect
7. C₆₁×#1721	C₂	semidirect
8. C₆₁×#1717	C₂	semidirect
9. C₆₁×#1715	C₂	semidirect
10. C₆₁×#1714	C₂	semidirect
11. C₆₁×#1451	C₂	semidirect
18. C₆₁×#500	C₂²	semidirect
19. C₆₁×#498	C₂²	semidirect
23. C₆₁×#493	C₂²	semidirect
29. C₆₁×#487	C₂²	semidirect
31. C₆₁×#486	C₂²	semidirect
32. C₆₁×#486	C₂²	semidirect
33. C₆₁×#486	C₂²	semidirect
34. C₆₁×#486	C₂²	semidirect
45. C₆₁×#322	C₂²	semidirect
46. C₆₁×#322	C₂²	semidirect
206. C₈×C₆₁	AGL(1,ℤ/8)	semidirect
207. #19671	C₆₁	direct (N × H)
231. #3227	C₂×C₆₁	semidirect
232. #3205	C₂×C₆₁	semidirect
233. #3169	C₂×C₆₁	semidirect
234. #3151	C₂×C₆₁	semidirect
235. C₂×#492	C₂×C₆₁	semidirect
236. #3141	C₂×C₆₁	semidirect
237. #1721	C₂×C₆₁	semidirect
238. #1717	C₂×C₆₁	semidirect
239. #1715	C₂×C₆₁	semidirect
240. #1714	C₂×C₆₁	semidirect
241. #1451	C₂×C₆₁	semidirect
255. #500	C₂²×C₆₁	semidirect
256. #498	C₂²×C₆₁	semidirect
260. #493	C₂²×C₆₁	semidirect
266. #487	C₂²×C₆₁	semidirect
268. #486	C₂²×C₆₁	semidirect
269. #486	C₂²×C₆₁	semidirect
270. #486	C₂²×C₆₁	semidirect
271. #486	C₂²×C₆₁	semidirect
282. #322	C₂²×C₆₁	semidirect
283. #322	C₂²×C₆₁	semidirect
284. C₆₁	#19671	direct (N × H)
444. C₈	AGL(1,ℤ/8)×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3227	2
C₆₁×#3205	2
C₆₁×#3169	2
C₆₁×#3151	2
C₂×C₆₁×#492	2
C₆₁×#3141	2
C₆₁×#1721	2
C₆₁×#1717	2
C₆₁×#1715	2
C₆₁×#1714	2
C₆₁×#1451	2
#19671	61

Subgroups — C61×#19671 #29523104

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#19671 #29523104