Subgroups — C₆₁×#19676 #29523109

Order 15616.

956 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3208	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3205	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3167	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3151	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₆₁×#493	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3138	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1721	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1721	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1717	C₂	1	2	yes	maximal, complemented
10	C₆₁×#1715	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×D₈×C₆₁	—	2	2	no	—
14	C₆₁×#533	C₂²	1	1	yes	characteristic
15	C₆₁×#532	C₂²	1	1	yes	characteristic
16	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
18	C₆₁×#498	C₂²	1	1	yes	characteristic, complemented
19	C₆₁×#496	—	2	2	no	—
20	C₆₁×#493	—	2	2	no	—
21	C₆₁×#493	C₂²	1	2	yes	—
22	C₆₁×#493	C₂²	1	2	yes	—
23	C₆₁×#493	C₂²	1	2	yes	complemented
24	C₆₁×#493	C₂²	1	2	yes	complemented
25	C₆₁×#492	C₂²	1	2	yes	complemented
26	C₆₁×#492	C₂²	1	1	yes	characteristic, complemented
27	C₆₁×#492	C₂²	1	2	yes	complemented
28	C₆₁×#490	—	2	2	no	—
29	C₆₁×#487	C₂²	1	1	yes	characteristic, complemented
30	C₆₁×#486	C₂²	1	2	yes	complemented
31	C₆₁×#486	C₂²	1	2	yes	complemented
32	C₆₁×#486	C₂²	1	1	yes	characteristic, complemented
33	C₆₁×#486	C₂²	1	2	yes	complemented
34	C₆₁×#486	C₂²	1	2	yes	complemented
35	C₆₁×#465	—	2	2	no	—
36	C₆₁×#460	—	2	2	no	—
37	C₆₁×#459	—	2	2	no	—
38	C₆₁×#450	—	2	2	no	—
39	C₆₁×#447	—	2	2	no	—
40	C₄×SD₁₆×C₆₁	—	2	2	no	—
41	C₆₁×#431	C₂²	1	1	yes	characteristic
42	C₆₁×#418	—	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	C₂²×D₄×C₆₁	—	2	1	no	—
49	C₂²×D₄×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	C₂²×D₄×C₆₁	—	2	1	no	—
54	AGL(1,ℤ/8)×C₆₁	—	4	8	no	—
55	C₂×SD₁₆×C₆₁	—	2	4	no	—
56	C₂×SD₁₆×C₆₁	—	2	2	no	—
57	C₂×SD₁₆×C₆₁	—	2	4	no	—
58	C₂×D₈×C₆₁	—	2	4	no	—
59	C₂×D₈×C₆₁	—	2	4	no	—
60	C₂×D₈×C₆₁	—	2	4	no	—
61	C₂×D₈×C₆₁	—	2	4	no	—
62	C₂×D₈×C₆₁	—	4	8	no	—
63	C₂×M₁₆×C₆₁	D₄	1	2	yes	—
64	C₂²×C₈×C₆₁	D₄	1	2	yes	—
65	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
66	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
67	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
68	#127×C₆₁	—	2	1	no	—
69	#127×C₆₁	—	2	1	no	—
70	#127×C₆₁	—	2	1	no	—
71	#127×C₆₁	—	2	1	no	—
72	#127×C₆₁	—	2	1	no	—
73	#127×C₆₁	—	2	1	no	—
74	#127×C₆₁	C₂³	1	2	yes	—
75	#127×C₆₁	C₂³	1	2	yes	—
76	#127×C₆₁	C₂³	1	1	yes	characteristic
77	#125×C₆₁	—	2	1	no	—
78	#124×C₆₁	—	2	1	no	—
79	C₂²⋊Q₈×C₆₁	—	2	1	no	—
80	C₂²⋊Q₈×C₆₁	—	2	1	no	—
81	#121×C₆₁	—	2	1	no	—
82	#121×C₆₁	—	2	1	no	—
83	C₄×Q₈×C₆₁	—	2	1	no	—
84	C₄×Q₈×C₆₁	—	2	1	no	—
85	C₄×D₄×C₆₁	—	2	1	no	—
86	C₄×D₄×C₆₁	—	2	1	no	—
87	#117×C₆₁	—	2	1	no	—
88	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
89	#106×C₆₁	—	2	2	no	—
90	C₄⋊C₈×C₆₁	D₄	1	2	yes	—
91	#103×C₆₁	—	2	2	no	—
92	#102×C₆₁	—	2	4	no	—
93	#102×C₆₁	—	2	4	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	C₂⁴×C₆₁	—	4	1	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	1	no	—
110	C₂×D₄×C₆₁	—	2	2	no	—
111	C₂×D₄×C₆₁	—	2	1	no	—
112	C₂×D₄×C₆₁	—	2	2	no	—
113	C₂×D₄×C₆₁	—	2	2	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	2	no	—
118	C₂×D₄×C₆₁	—	2	2	no	—
119	C₂×D₄×C₆₁	—	4	4	no	—
120	C₂×D₄×C₆₁	—	4	4	no	—
121	C₂×D₄×C₆₁	—	4	1	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	1	no	—
128	C₂×D₄×C₆₁	—	4	4	no	—
129	C₂×D₄×C₆₁	—	4	4	no	—
130	C₂×D₄×C₆₁	—	8	2	no	—
131	C₂×D₄×C₆₁	—	8	2	no	—
132	C₂²×C₄×C₆₁	—	4	1	no	—
133	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
136	SD₁₆×C₆₁	—	4	8	no	—
137	SD₁₆×C₆₁	—	4	4	no	—
138	SD₁₆×C₆₁	—	8	4	no	—
139	D₈×C₆₁	—	4	8	no	—
140	D₈×C₆₁	—	4	8	no	—
141	D₈×C₆₁	—	4	8	no	—
142	D₈×C₆₁	—	8	4	no	—
143	M₁₆×C₆₁	—	2	4	no	—
144	C₂×C₈×C₆₁	—	2	4	no	—
145	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
146	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
147	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
148	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
149	C₄⋊C₄×C₆₁	—	2	1	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	—	2	1	no	—
154	C₄⋊C₄×C₆₁	—	2	1	no	—
155	C₄⋊C₄×C₆₁	—	4	1	no	—
156	C₄⋊C₄×C₆₁	—	4	1	no	—
157	C₂²⋊C₄×C₆₁	—	4	1	no	—
158	C₂²⋊C₄×C₆₁	—	4	1	no	—
159	C₂²⋊C₄×C₆₁	—	4	1	no	—
160	C₄²×C₆₁	—	4	1	no	—
161	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
165	C₂³×C₆₁	—	4	1	no	—
166	C₂³×C₆₁	—	4	2	no	—
167	C₂³×C₆₁	—	4	2	no	—
168	C₂³×C₆₁	—	8	2	no	—
169	C₂³×C₆₁	—	8	2	no	—
170	C₂³×C₆₁	—	8	2	no	—
171	C₂³×C₆₁	—	8	2	no	—
172	C₂³×C₆₁	—	8	2	no	—
173	C₂³×C₆₁	—	8	2	no	—
174	C₂³×C₆₁	#127	1	1	yes	characteristic
175	Q₈×C₆₁	—	4	2	no	—
176	Q₈×C₆₁	—	4	2	no	—
177	Q₈×C₆₁	—	4	2	no	—
178	D₄×C₆₁	—	4	4	no	—
179	D₄×C₆₁	—	4	4	no	—
180	D₄×C₆₁	—	4	2	no	—
181	D₄×C₆₁	—	4	4	no	—
182	D₄×C₆₁	—	4	2	no	—
183	D₄×C₆₁	—	4	4	no	—
184	D₄×C₆₁	—	4	2	no	—
185	D₄×C₆₁	—	4	4	no	—
186	D₄×C₆₁	—	4	4	no	—
187	D₄×C₆₁	—	8	2	no	—
188	D₄×C₆₁	—	8	2	no	—
189	D₄×C₆₁	—	8	2	no	—
190	D₄×C₆₁	—	8	2	no	—
191	D₄×C₆₁	—	8	2	no	—
192	D₄×C₆₁	—	8	2	no	—
193	D₄×C₆₁	—	8	2	no	—
194	C₂×C₄×C₆₁	—	2	2	no	—
195	C₂×C₄×C₆₁	—	2	2	no	—
196	C₂×C₄×C₆₁	—	4	1	no	—
197	C₂×C₄×C₆₁	—	4	1	no	—
198	C₂×C₄×C₆₁	—	4	1	no	—
199	C₂×C₄×C₆₁	—	8	2	no	—
200	C₂×C₄×C₆₁	#127	1	1	yes	characteristic
201	C₂×C₄×C₆₁	#127	1	1	yes	characteristic
202	C₂×C₄×C₆₁	#127	1	1	yes	characteristic
203	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	4	yes	—
204	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
207	C₈×C₆₁	—	2	2	no	—
208	C₈×C₆₁	—	2	4	no	—
209	C₈×C₆₁	—	2	4	no	—
210	C₈×C₆₁	AGL(1,ℤ/8)	1	4	yes	complemented
211	#19676	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
212	C₂²×C₆₁	—	2	1	no	—
213	C₂²×C₆₁	—	2	1	no	—
214	C₂²×C₆₁	—	8	1	no	—
215	C₂²×C₆₁	—	8	2	no	—
216	C₂²×C₆₁	—	8	2	no	—
217	C₂²×C₆₁	—	8	2	no	—
218	C₂²×C₆₁	—	8	2	no	—
219	C₂²×C₆₁	—	8	1	no	—
220	C₂²×C₆₁	—	8	2	no	—
221	C₂²×C₆₁	—	8	2	no	—
222	C₂²×C₆₁	—	8	1	no	—
223	C₂²×C₆₁	—	16	4	no	—
224	C₂²×C₆₁	—	16	4	no	—
225	C₂²×C₆₁	#496	1	2	yes	—
226	C₂²×C₆₁	C₂×#127	1	1	yes	characteristic
227	C₄×C₆₁	—	2	1	no	—
228	C₄×C₆₁	—	2	1	no	—
229	C₄×C₆₁	—	8	1	no	—
230	C₄×C₆₁	—	8	1	no	—
231	C₄×C₆₁	—	8	1	no	—
232	C₄×C₆₁	#496	1	2	yes	—
233	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
234	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
235	C₄×C₆₁	#576	1	2	yes	—
236	#3208	C₂×C₆₁	1	1	yes	characteristic, complemented
237	#3205	C₂×C₆₁	1	1	yes	characteristic, complemented
238	#3167	C₂×C₆₁	1	1	yes	characteristic, complemented
239	#3151	C₂×C₆₁	1	1	yes	characteristic, complemented
240	C₂×#493	C₂×C₆₁	1	1	yes	characteristic, complemented
241	#3138	C₂×C₆₁	1	1	yes	characteristic, complemented
242	#1721	C₂×C₆₁	1	2	yes	complemented
243	#1721	C₂×C₆₁	1	2	yes	complemented
244	#1717	C₂×C₆₁	1	2	yes	complemented
245	#1715	C₂×C₆₁	1	2	yes	complemented
246	#1451	C₂×C₆₁	1	1	yes	characteristic, complemented
247	C₂×C₆₁	—	2	2	no	—
248	C₂×C₆₁	—	16	1	no	—
249	C₂×C₆₁	—	16	2	no	—
250	C₂×C₆₁	—	16	2	no	—
251	C₂×C₆₁	C₂×#496	1	1	yes	characteristic
252	C₂×C₆₁	#3151	1	1	yes	characteristic
253	C₂×C₆₁	#3155	1	1	yes	characteristic
254	C₂×AGL(1,ℤ/8)	—	2	2	no	—
255	C₂²×D₈	—	2	2	no	—
256	#533	C₂²×C₆₁	1	1	yes	characteristic
257	#532	C₂²×C₆₁	1	1	yes	characteristic
258	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
259	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
260	#498	C₂²×C₆₁	1	1	yes	characteristic, complemented
261	#496	—	2	2	no	—
262	#493	—	2	2	no	—
263	#493	C₂²×C₆₁	1	2	yes	—
264	#493	C₂²×C₆₁	1	2	yes	—
265	#493	C₂²×C₆₁	1	2	yes	complemented
266	#493	C₂²×C₆₁	1	2	yes	complemented
267	#492	C₂²×C₆₁	1	2	yes	complemented
268	#492	C₂²×C₆₁	1	1	yes	characteristic, complemented
269	#492	C₂²×C₆₁	1	2	yes	complemented
270	#490	—	2	2	no	—
271	#487	C₂²×C₆₁	1	1	yes	characteristic, complemented
272	#486	C₂²×C₆₁	1	2	yes	complemented
273	#486	C₂²×C₆₁	1	2	yes	complemented
274	#486	C₂²×C₆₁	1	1	yes	characteristic, complemented
275	#486	C₂²×C₆₁	1	2	yes	complemented
276	#486	C₂²×C₆₁	1	2	yes	complemented
277	#465	—	2	2	no	—
278	#460	—	2	2	no	—
279	#459	—	2	2	no	—
280	#450	—	2	2	no	—
281	#447	—	2	2	no	—
282	C₄×SD₁₆	—	2	2	no	—
283	#431	C₂²×C₆₁	1	1	yes	characteristic
284	#418	—	2	2	no	—
285	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
286	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
287	#322	C₂²×C₆₁	1	2	yes	complemented
288	#322	C₂²×C₆₁	1	2	yes	complemented
289	C₆₁	#19676	1	1	yes	characteristic, direct product factor, Sylow
290	C₂×#41	—	2	1	no	—
291	C₂²×D₄	—	2	1	no	—
292	C₂²×D₄	—	2	1	no	—
293	C₂²×D₄	—	2	1	no	—
294	C₂²×D₄	—	2	1	no	—
295	C₂²×D₄	—	2	1	no	—
296	C₂²×D₄	—	2	1	no	—
297	AGL(1,ℤ/8)	—	4	8	no	—
298	C₂×SD₁₆	—	2	4	no	—
299	C₂×SD₁₆	—	2	2	no	—
300	C₂×SD₁₆	—	2	4	no	—
301	C₂×D₈	—	2	4	no	—
302	C₂×D₈	—	2	4	no	—
303	C₂×D₈	—	2	4	no	—
304	C₂×D₈	—	2	4	no	—
305	C₂×D₈	—	4	8	no	—
306	C₂×M₁₆	D₄×C₆₁	1	2	yes	—
307	C₂²×C₈	D₄×C₆₁	1	2	yes	—
308	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
309	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
310	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
311	#127	—	2	1	no	—
312	#127	—	2	1	no	—
313	#127	—	2	1	no	—
314	#127	—	2	1	no	—
315	#127	—	2	1	no	—
316	#127	—	2	1	no	—
317	#127	C₂³×C₆₁	1	2	yes	—
318	#127	C₂³×C₆₁	1	2	yes	—
319	#127	C₂³×C₆₁	1	1	yes	characteristic
320	#125	—	2	1	no	—
321	#124	—	2	1	no	—
322	C₂²⋊Q₈	—	2	1	no	—
323	C₂²⋊Q₈	—	2	1	no	—
324	#121	—	2	1	no	—
325	#121	—	2	1	no	—
326	C₄×Q₈	—	2	1	no	—
327	C₄×Q₈	—	2	1	no	—
328	C₄×D₄	—	2	1	no	—
329	C₄×D₄	—	2	1	no	—
330	#117	—	2	1	no	—
331	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
332	#106	—	2	2	no	—
333	C₄⋊C₈	D₄×C₆₁	1	2	yes	—
334	#103	—	2	2	no	—
335	#102	—	2	4	no	—
336	#102	—	2	4	no	—
337	#102	—	2	2	no	—
338	#102	—	2	4	no	—
339	#102	—	2	4	no	—
340	C₂²⋊C₈	D₄×C₆₁	1	2	yes	—
341	#97	D₄×C₆₁	1	2	yes	—
342	C₄×C₈	D₄×C₆₁	1	2	yes	—
343	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
344	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
345	C₄×C₈	C₂³×C₆₁	1	2	yes	—
346	C₄×C₈	C₂³×C₆₁	1	2	yes	—
347	C₂⁴	—	4	1	no	—
348	C₂⁴	—	4	1	no	—
349	#41	—	4	4	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	4	4	no	—
363	C₂×D₄	—	4	4	no	—
364	C₂×D₄	—	4	1	no	—
365	C₂×D₄	—	4	1	no	—
366	C₂×D₄	—	4	1	no	—
367	C₂×D₄	—	4	1	no	—
368	C₂×D₄	—	4	1	no	—
369	C₂×D₄	—	4	1	no	—
370	C₂×D₄	—	4	1	no	—
371	C₂×D₄	—	4	4	no	—
372	C₂×D₄	—	4	4	no	—
373	C₂×D₄	—	8	2	no	—
374	C₂×D₄	—	8	2	no	—
375	C₂²×C₄	—	4	1	no	—
376	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
378	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
379	SD₁₆	—	4	8	no	—
380	SD₁₆	—	4	4	no	—
381	SD₁₆	—	8	4	no	—
382	D₈	—	4	8	no	—
383	D₈	—	4	8	no	—
384	D₈	—	4	8	no	—
385	D₈	—	8	4	no	—
386	M₁₆	—	2	4	no	—
387	C₂×C₈	—	2	4	no	—
388	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
389	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
390	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
391	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	4	1	no	—
399	C₄⋊C₄	—	4	1	no	—
400	C₂²⋊C₄	—	4	1	no	—
401	C₂²⋊C₄	—	4	1	no	—
402	C₂²⋊C₄	—	4	1	no	—
403	C₄²	—	4	1	no	—
404	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
405	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
406	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
407	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
408	C₂³	—	4	1	no	—
409	C₂³	—	4	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	8	2	no	—
412	C₂³	—	8	2	no	—
413	C₂³	—	8	2	no	—
414	C₂³	—	8	2	no	—
415	C₂³	—	8	2	no	—
416	C₂³	—	8	2	no	—
417	C₂³	#127×C₆₁	1	1	yes	characteristic
418	Q₈	—	4	2	no	—
419	Q₈	—	4	2	no	—
420	Q₈	—	4	2	no	—
421	D₄	—	4	4	no	—
422	D₄	—	4	4	no	—
423	D₄	—	4	2	no	—
424	D₄	—	4	4	no	—
425	D₄	—	4	2	no	—
426	D₄	—	4	4	no	—
427	D₄	—	4	2	no	—
428	D₄	—	4	4	no	—
429	D₄	—	4	4	no	—
430	D₄	—	8	2	no	—
431	D₄	—	8	2	no	—
432	D₄	—	8	2	no	—
433	D₄	—	8	2	no	—
434	D₄	—	8	2	no	—
435	D₄	—	8	2	no	—
436	D₄	—	8	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	8	2	no	—
443	C₂×C₄	#127×C₆₁	1	1	yes	characteristic
444	C₂×C₄	#127×C₆₁	1	1	yes	characteristic
445	C₂×C₄	#127×C₆₁	1	1	yes	characteristic
446	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	4	yes	—
447	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
448	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
449	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
450	C₈	—	2	2	no	—
451	C₈	—	2	4	no	—
452	C₈	—	2	4	no	—
453	C₈	AGL(1,ℤ/8)×C₆₁	1	4	yes	complemented
454	C₂²	—	2	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	8	1	no	—
457	C₂²	—	8	2	no	—
458	C₂²	—	8	2	no	—
459	C₂²	—	8	2	no	—
460	C₂²	—	8	2	no	—
461	C₂²	—	8	1	no	—
462	C₂²	—	8	2	no	—
463	C₂²	—	8	2	no	—
464	C₂²	—	8	1	no	—
465	C₂²	—	16	4	no	—
466	C₂²	—	16	4	no	—
467	C₂²	C₆₁×#496	1	2	yes	—
468	C₂²	C₂×#127×C₆₁	1	1	yes	characteristic
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	8	1	no	—
472	C₄	—	8	1	no	—
473	C₄	—	8	1	no	—
474	C₄	C₆₁×#496	1	2	yes	—
475	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	2	yes	—
476	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	2	yes	—
477	C₄	C₆₁×#576	1	2	yes	—
478	C₂	—	2	2	no	—
479	C₂	—	16	2	no	—
480	C₂	—	16	2	no	—
481	C₂	—	16	1	no	—
482	C₂	C₂×C₆₁×#496	1	1	yes	characteristic
483	C₂	C₆₁×#3151	1	1	yes	characteristic
484	C₂	C₆₁×#3155	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×#3208	C₂	semidirect
2. C₆₁×#3205	C₂	semidirect
3. C₆₁×#3167	C₂	semidirect
4. C₆₁×#3151	C₂	semidirect
5. C₂×C₆₁×#493	C₂	semidirect
6. C₆₁×#3138	C₂	semidirect
7. C₆₁×#1721	C₂	semidirect
8. C₆₁×#1721	C₂	semidirect
9. C₆₁×#1717	C₂	semidirect
10. C₆₁×#1715	C₂	semidirect
11. C₆₁×#1451	C₂	semidirect
18. C₆₁×#498	C₂²	semidirect
23. C₆₁×#493	C₂²	semidirect
24. C₆₁×#493	C₂²	semidirect
25. C₆₁×#492	C₂²	semidirect
26. C₆₁×#492	C₂²	semidirect
27. C₆₁×#492	C₂²	semidirect
29. C₆₁×#487	C₂²	semidirect
30. C₆₁×#486	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
210. C₈×C₆₁	AGL(1,ℤ/8)	semidirect
211. #19676	C₆₁	direct (N × H)
236. #3208	C₂×C₆₁	semidirect
237. #3205	C₂×C₆₁	semidirect
238. #3167	C₂×C₆₁	semidirect
239. #3151	C₂×C₆₁	semidirect
240. C₂×#493	C₂×C₆₁	semidirect
241. #3138	C₂×C₆₁	semidirect
242. #1721	C₂×C₆₁	semidirect
243. #1721	C₂×C₆₁	semidirect
244. #1717	C₂×C₆₁	semidirect
245. #1715	C₂×C₆₁	semidirect
246. #1451	C₂×C₆₁	semidirect
260. #498	C₂²×C₆₁	semidirect
265. #493	C₂²×C₆₁	semidirect
266. #493	C₂²×C₆₁	semidirect
267. #492	C₂²×C₆₁	semidirect
268. #492	C₂²×C₆₁	semidirect
269. #492	C₂²×C₆₁	semidirect
271. #487	C₂²×C₆₁	semidirect
272. #486	C₂²×C₆₁	semidirect
273. #486	C₂²×C₆₁	semidirect
274. #486	C₂²×C₆₁	semidirect
275. #486	C₂²×C₆₁	semidirect
276. #486	C₂²×C₆₁	semidirect
287. #322	C₂²×C₆₁	semidirect
288. #322	C₂²×C₆₁	semidirect
289. C₆₁	#19676	direct (N × H)
453. 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×#3208	2
C₆₁×#3205	2
C₆₁×#3167	2
C₆₁×#3151	2
C₂×C₆₁×#493	2
C₆₁×#3138	2
C₆₁×#1721	2
C₆₁×#1717	2
C₆₁×#1715	2
C₆₁×#1451	2
#19676	61

Subgroups — C61×#19676 #29523109

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#19676 #29523109