Subgroups — C₆₁×#18545 #29521978

Order 15616.

1316 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3151	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3112	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3109	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#1631	C₂	1	4	yes	maximal, complemented
6	C₆₁×#1621	C₂	1	4	yes	maximal, complemented
7	C₆₁×#1555	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1491	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1490	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₆₁	—	2	1	no	—
11	C₂×AGL(1,ℤ/8)×C₆₁	—	2	2	no	—
12	C₆₁×#550	—	2	2	no	—
13	C₆₁×#550	—	2	2	no	—
14	C₆₁×#550	—	2	2	no	—
15	C₆₁×#550	C₂²	1	4	yes	—
16	C₆₁×#532	C₂²	1	1	yes	characteristic
17	C₂×#127×C₆₁	—	2	1	no	—
18	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×#121×C₆₁	—	2	2	no	—
20	C₂×#121×C₆₁	—	2	1	no	—
21	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₆₁	—	2	1	no	—
23	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
24	C₆₁×#496	—	2	2	no	—
25	C₆₁×#493	C₂²	1	2	yes	complemented
26	C₆₁×#492	C₂²	1	2	yes	complemented
27	C₆₁×#481	—	2	1	no	—
28	C₆₁×#480	—	2	1	no	—
29	C₆₁×#477	C₂²	1	2	yes	complemented
30	C₆₁×#476	C₂²	1	2	yes	complemented
31	C₆₁×#460	C₂²	1	2	yes	complemented
32	C₆₁×#459	C₂²	1	2	yes	complemented
33	C₆₁×#448	—	2	1	no	—
34	C₆₁×#447	—	2	1	no	—
35	C₆₁×#442	—	2	2	no	—
36	C₆₁×#440	—	2	2	no	—
37	C₆₁×#432	C₂²	1	1	yes	characteristic
38	C₆₁×#432	C₂²	1	1	yes	characteristic
39	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
40	C₆₁×#331	C₂²	1	4	yes	complemented
41	C₆₁×Q₈⋊C₈	C₂²	1	4	yes	complemented
42	C₆₁×D₄⋊C₈	C₂²	1	4	yes	complemented
43	C₂×#41×C₆₁	—	2	4	no	—
44	C₂×#41×C₆₁	—	2	4	no	—
45	C₂×#41×C₆₁	—	2	1	no	—
46	C₂×#41×C₆₁	—	4	8	no	—
47	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
48	C₂²×D₄×C₆₁	—	2	2	no	—
49	C₂²×D₄×C₆₁	—	2	2	no	—
50	C₂²×D₄×C₆₁	—	2	1	no	—
51	C₂²×D₄×C₆₁	—	2	1	no	—
52	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
53	C₂²×D₄×C₆₁	D₄	1	2	yes	—
54	C₂³×C₄×C₆₁	—	2	2	no	—
55	C₂³×C₄×C₆₁	—	2	1	no	—
56	AGL(1,ℤ/8)×C₆₁	—	4	8	no	—
57	C₂×SD₁₆×C₆₁	—	2	2	no	—
58	C₂×SD₁₆×C₆₁	—	2	4	no	—
59	C₂×D₈×C₆₁	—	2	4	no	—
60	C₂×D₈×C₆₁	—	2	2	no	—
61	C₂×M₁₆×C₆₁	—	2	1	no	—
62	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
63	#127×C₆₁	—	2	4	no	—
64	#127×C₆₁	—	2	4	no	—
65	#127×C₆₁	—	2	1	no	—
66	#127×C₆₁	—	2	1	no	—
67	#127×C₆₁	D₄	1	2	yes	—
68	#127×C₆₁	C₂³	1	1	yes	characteristic
69	#127×C₆₁	C₂³	1	2	yes	—
70	#124×C₆₁	—	2	1	no	—
71	#121×C₆₁	—	2	4	no	—
72	#121×C₆₁	—	2	8	no	—
73	#121×C₆₁	—	2	8	no	—
74	#121×C₆₁	—	2	4	no	—
75	#121×C₆₁	—	2	1	no	—
76	#121×C₆₁	—	2	1	no	—
77	C₄×Q₈×C₆₁	—	2	1	no	—
78	C₄×Q₈×C₆₁	—	2	1	no	—
79	C₄×Q₈×C₆₁	D₄	1	2	yes	—
80	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
81	C₄×D₄×C₆₁	—	2	4	no	—
82	C₄×D₄×C₆₁	—	2	4	no	—
83	C₄×D₄×C₆₁	—	2	1	no	—
84	C₄×D₄×C₆₁	—	2	1	no	—
85	C₄×D₄×C₆₁	—	2	1	no	—
86	C₄×D₄×C₆₁	—	2	1	no	—
87	C₄×D₄×C₆₁	D₄	1	2	yes	—
88	C₄×D₄×C₆₁	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
90	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
92	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
94	C₂×C₄²×C₆₁	—	2	1	no	—
95	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
96	#107×C₆₁	—	2	2	no	—
97	#106×C₆₁	—	2	2	no	—
98	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
99	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
100	#103×C₆₁	—	2	2	no	—
101	#102×C₆₁	—	2	2	no	—
102	#102×C₆₁	—	2	2	no	—
103	#102×C₆₁	—	2	2	no	—
104	C₂²⋊C₈×C₆₁	—	2	1	no	—
105	C₂²⋊C₈×C₆₁	—	2	1	no	—
106	#97×C₆₁	—	2	1	no	—
107	#97×C₆₁	—	2	1	no	—
108	#97×C₆₁	—	2	1	no	—
109	C₄×C₈×C₆₁	C₂³	1	2	yes	—
110	C₂⁴×C₆₁	—	2	2	no	—
111	C₂⁴×C₆₁	—	2	1	no	—
112	#41×C₆₁	—	4	4	no	—
113	#41×C₆₁	—	4	16	no	—
114	#41×C₆₁	—	4	8	no	—
115	#41×C₆₁	—	4	8	no	—
116	C₂×Q₈×C₆₁	—	2	4	no	—
117	C₂×Q₈×C₆₁	—	2	1	no	—
118	C₂×Q₈×C₆₁	—	2	1	no	—
119	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
120	C₂×D₄×C₆₁	—	2	8	no	—
121	C₂×D₄×C₆₁	—	2	8	no	—
122	C₂×D₄×C₆₁	—	2	1	no	—
123	C₂×D₄×C₆₁	—	2	2	no	—
124	C₂×D₄×C₆₁	—	2	2	no	—
125	C₂×D₄×C₆₁	—	2	2	no	—
126	C₂×D₄×C₆₁	—	2	2	no	—
127	C₂×D₄×C₆₁	—	2	2	no	—
128	C₂×D₄×C₆₁	—	2	1	no	—
129	C₂×D₄×C₆₁	—	2	1	no	—
130	C₂×D₄×C₆₁	—	2	1	no	—
131	C₂×D₄×C₆₁	—	4	2	no	—
132	C₂×D₄×C₆₁	—	4	4	no	—
133	C₂×D₄×C₆₁	—	4	8	no	—
134	C₂×D₄×C₆₁	—	4	4	no	—
135	C₂×D₄×C₆₁	—	4	4	no	—
136	C₂×D₄×C₆₁	—	4	1	no	—
137	C₂×D₄×C₆₁	—	8	4	no	—
138	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
139	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
140	C₂²×C₄×C₆₁	—	2	1	no	—
141	C₂²×C₄×C₆₁	—	2	8	no	—
142	C₂²×C₄×C₆₁	—	2	1	no	—
143	C₂²×C₄×C₆₁	—	2	1	no	—
144	C₂²×C₄×C₆₁	—	2	2	no	—
145	C₂²×C₄×C₆₁	—	2	2	no	—
146	C₂²×C₄×C₆₁	—	4	8	no	—
147	C₂²×C₄×C₆₁	—	4	4	no	—
148	C₂²×C₄×C₆₁	—	4	1	no	—
149	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
152	SD₁₆×C₆₁	—	4	8	no	—
153	SD₁₆×C₆₁	—	4	4	no	—
154	D₈×C₆₁	—	4	8	no	—
155	D₈×C₆₁	—	4	4	no	—
156	M₁₆×C₆₁	—	2	4	no	—
157	C₂×C₈×C₆₁	—	2	2	no	—
158	C₂×C₈×C₆₁	—	2	2	no	—
159	C₂×C₈×C₆₁	—	2	2	no	—
160	C₄⋊C₄×C₆₁	—	2	2	no	—
161	C₄⋊C₄×C₆₁	—	2	1	no	—
162	C₄⋊C₄×C₆₁	—	2	1	no	—
163	C₄⋊C₄×C₆₁	—	2	2	no	—
164	C₄⋊C₄×C₆₁	—	2	1	no	—
165	C₄⋊C₄×C₆₁	—	2	1	no	—
166	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
167	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
168	C₂²⋊C₄×C₆₁	—	2	8	no	—
169	C₂²⋊C₄×C₆₁	—	2	2	no	—
170	C₂²⋊C₄×C₆₁	—	2	2	no	—
171	C₂²⋊C₄×C₆₁	—	4	1	no	—
172	C₂²⋊C₄×C₆₁	—	4	1	no	—
173	C₄²×C₆₁	—	2	2	no	—
174	C₄²×C₆₁	—	2	2	no	—
175	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
179	C₂³×C₆₁	—	2	2	no	—
180	C₂³×C₆₁	—	2	4	no	—
181	C₂³×C₆₁	—	4	4	no	—
182	C₂³×C₆₁	—	4	2	no	—
183	C₂³×C₆₁	—	4	2	no	—
184	C₂³×C₆₁	—	4	4	no	—
185	C₂³×C₆₁	—	4	4	no	—
186	C₂³×C₆₁	—	4	2	no	—
187	C₂³×C₆₁	—	4	1	no	—
188	C₂³×C₆₁	#120	1	1	yes	characteristic
189	Q₈×C₆₁	—	2	4	no	—
190	Q₈×C₆₁	—	2	2	no	—
191	Q₈×C₆₁	—	4	2	no	—
192	Q₈×C₆₁	AGL(1,ℤ/8)	1	4	yes	complemented
193	D₄×C₆₁	—	2	2	no	—
194	D₄×C₆₁	—	2	2	no	—
195	D₄×C₆₁	—	4	4	no	—
196	D₄×C₆₁	—	4	2	no	—
197	D₄×C₆₁	—	4	4	no	—
198	D₄×C₆₁	—	4	16	no	—
199	D₄×C₆₁	—	4	4	no	—
200	D₄×C₆₁	—	4	2	no	—
201	D₄×C₆₁	—	4	4	no	—
202	D₄×C₆₁	—	4	2	no	—
203	D₄×C₆₁	—	4	4	no	—
204	D₄×C₆₁	—	4	2	no	—
205	D₄×C₆₁	—	8	2	no	—
206	D₄×C₆₁	—	8	8	no	—
207	D₄×C₆₁	—	8	2	no	—
208	C₂×C₄×C₆₁	—	2	4	no	—
209	C₂×C₄×C₆₁	—	2	2	no	—
210	C₂×C₄×C₆₁	—	2	2	no	—
211	C₂×C₄×C₆₁	—	2	2	no	—
212	C₂×C₄×C₆₁	—	2	2	no	—
213	C₂×C₄×C₆₁	—	2	2	no	—
214	C₂×C₄×C₆₁	—	2	2	no	—
215	C₂×C₄×C₆₁	—	4	16	no	—
216	C₂×C₄×C₆₁	—	4	4	no	—
217	C₂×C₄×C₆₁	—	4	2	no	—
218	C₂×C₄×C₆₁	—	4	2	no	—
219	C₂×C₄×C₆₁	—	4	4	no	—
220	C₂×C₄×C₆₁	—	4	1	no	—
221	C₂×C₄×C₆₁	—	8	2	no	—
222	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
223	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
224	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
225	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
228	C₈×C₆₁	—	2	4	no	—
229	C₈×C₆₁	—	4	2	no	—
230	C₈×C₆₁	—	4	2	no	—
231	#18545	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂²×C₆₁	—	2	1	no	—
233	C₂²×C₆₁	—	2	1	no	—
234	C₂²×C₆₁	—	4	4	no	—
235	C₂²×C₆₁	—	4	2	no	—
236	C₂²×C₆₁	—	4	2	no	—
237	C₂²×C₆₁	—	4	4	no	—
238	C₂²×C₆₁	—	4	4	no	—
239	C₂²×C₆₁	—	4	2	no	—
240	C₂²×C₆₁	—	8	8	no	—
241	C₂²×C₆₁	—	8	4	no	—
242	C₂²×C₆₁	—	8	1	no	—
243	C₂²×C₆₁	—	8	1	no	—
244	C₂²×C₆₁	—	8	1	no	—
245	C₂²×C₆₁	#453	1	2	yes	—
246	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
247	C₄×C₆₁	—	2	4	no	—
248	C₄×C₆₁	—	2	1	no	—
249	C₄×C₆₁	—	2	1	no	—
250	C₄×C₆₁	—	2	1	no	—
251	C₄×C₆₁	—	2	1	no	—
252	C₄×C₆₁	—	4	2	no	—
253	C₄×C₆₁	—	4	2	no	—
254	C₄×C₆₁	—	8	1	no	—
255	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
256	C₄×C₆₁	#575	1	2	yes	—
257	C₂×#550	C₂×C₆₁	1	1	yes	characteristic, complemented
258	#3151	C₂×C₆₁	1	1	yes	characteristic, complemented
259	#3112	C₂×C₆₁	1	1	yes	characteristic, complemented
260	#3109	C₂×C₆₁	1	1	yes	characteristic, complemented
261	#1631	C₂×C₆₁	1	4	yes	complemented
262	#1621	C₂×C₆₁	1	4	yes	complemented
263	#1555	C₂×C₆₁	1	1	yes	characteristic, complemented
264	#1491	C₂×C₆₁	1	1	yes	characteristic, complemented
265	#1490	C₂×C₆₁	1	1	yes	characteristic, complemented
266	C₂×C₆₁	—	2	2	no	—
267	C₂×C₆₁	—	8	2	no	—
268	C₂×C₆₁	—	8	4	no	—
269	C₂×C₆₁	—	16	1	no	—
270	C₂×C₆₁	#3003	1	1	yes	characteristic
271	C₂×C₆₁	#3005	1	1	yes	characteristic
272	C₂×C₆₁	C₂×#453	1	1	yes	characteristic
273	C₂²×#41	—	2	1	no	—
274	C₂×AGL(1,ℤ/8)	—	2	2	no	—
275	#550	—	2	2	no	—
276	#550	—	2	2	no	—
277	#550	—	2	2	no	—
278	#550	C₂²×C₆₁	1	4	yes	—
279	#532	C₂²×C₆₁	1	1	yes	characteristic
280	C₂×#127	—	2	1	no	—
281	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
282	C₂×#121	—	2	2	no	—
283	C₂×#121	—	2	1	no	—
284	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
285	C₂×C₄×D₄	—	2	1	no	—
286	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
287	#496	—	2	2	no	—
288	#493	C₂²×C₆₁	1	2	yes	complemented
289	#492	C₂²×C₆₁	1	2	yes	complemented
290	#481	—	2	1	no	—
291	#480	—	2	1	no	—
292	#477	C₂²×C₆₁	1	2	yes	complemented
293	#476	C₂²×C₆₁	1	2	yes	complemented
294	#460	C₂²×C₆₁	1	2	yes	complemented
295	#459	C₂²×C₆₁	1	2	yes	complemented
296	#448	—	2	1	no	—
297	#447	—	2	1	no	—
298	#442	—	2	2	no	—
299	#440	—	2	2	no	—
300	#432	C₂²×C₆₁	1	1	yes	characteristic
301	#432	C₂²×C₆₁	1	1	yes	characteristic
302	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
303	#331	C₂²×C₆₁	1	4	yes	complemented
304	Q₈⋊C₈	C₂²×C₆₁	1	4	yes	complemented
305	D₄⋊C₈	C₂²×C₆₁	1	4	yes	complemented
306	C₆₁	#18545	1	1	yes	characteristic, direct product factor, Sylow
307	C₂×#41	—	2	4	no	—
308	C₂×#41	—	2	4	no	—
309	C₂×#41	—	2	1	no	—
310	C₂×#41	—	4	8	no	—
311	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
312	C₂²×D₄	—	2	2	no	—
313	C₂²×D₄	—	2	2	no	—
314	C₂²×D₄	—	2	1	no	—
315	C₂²×D₄	—	2	1	no	—
316	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
317	C₂²×D₄	D₄×C₆₁	1	2	yes	—
318	C₂³×C₄	—	2	2	no	—
319	C₂³×C₄	—	2	1	no	—
320	AGL(1,ℤ/8)	—	4	8	no	—
321	C₂×SD₁₆	—	2	2	no	—
322	C₂×SD₁₆	—	2	4	no	—
323	C₂×D₈	—	2	4	no	—
324	C₂×D₈	—	2	2	no	—
325	C₂×M₁₆	—	2	1	no	—
326	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
327	#127	—	2	4	no	—
328	#127	—	2	4	no	—
329	#127	—	2	1	no	—
330	#127	—	2	1	no	—
331	#127	D₄×C₆₁	1	2	yes	—
332	#127	C₂³×C₆₁	1	1	yes	characteristic
333	#127	C₂³×C₆₁	1	2	yes	—
334	#124	—	2	1	no	—
335	#121	—	2	4	no	—
336	#121	—	2	8	no	—
337	#121	—	2	8	no	—
338	#121	—	2	4	no	—
339	#121	—	2	1	no	—
340	#121	—	2	1	no	—
341	C₄×Q₈	—	2	1	no	—
342	C₄×Q₈	—	2	1	no	—
343	C₄×Q₈	D₄×C₆₁	1	2	yes	—
344	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
345	C₄×D₄	—	2	4	no	—
346	C₄×D₄	—	2	4	no	—
347	C₄×D₄	—	2	1	no	—
348	C₄×D₄	—	2	1	no	—
349	C₄×D₄	—	2	1	no	—
350	C₄×D₄	—	2	1	no	—
351	C₄×D₄	D₄×C₆₁	1	2	yes	—
352	C₄×D₄	C₂³×C₆₁	1	2	yes	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
355	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
356	C₂×C₂²⋊C₄	—	2	2	no	—
357	C₂×C₂²⋊C₄	—	2	1	no	—
358	C₂×C₄²	—	2	1	no	—
359	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
360	#107	—	2	2	no	—
361	#106	—	2	2	no	—
362	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
363	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
364	#103	—	2	2	no	—
365	#102	—	2	2	no	—
366	#102	—	2	2	no	—
367	#102	—	2	2	no	—
368	C₂²⋊C₈	—	2	1	no	—
369	C₂²⋊C₈	—	2	1	no	—
370	#97	—	2	1	no	—
371	#97	—	2	1	no	—
372	#97	—	2	1	no	—
373	C₄×C₈	C₂³×C₆₁	1	2	yes	—
374	C₂⁴	—	2	2	no	—
375	C₂⁴	—	2	1	no	—
376	#41	—	4	4	no	—
377	#41	—	4	16	no	—
378	#41	—	4	8	no	—
379	#41	—	4	8	no	—
380	C₂×Q₈	—	2	4	no	—
381	C₂×Q₈	—	2	1	no	—
382	C₂×Q₈	—	2	1	no	—
383	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
384	C₂×D₄	—	2	8	no	—
385	C₂×D₄	—	2	8	no	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	1	no	—
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	—	4	2	no	—
396	C₂×D₄	—	4	8	no	—
397	C₂×D₄	—	4	4	no	—
398	C₂×D₄	—	4	4	no	—
399	C₂×D₄	—	4	4	no	—
400	C₂×D₄	—	4	1	no	—
401	C₂×D₄	—	8	4	no	—
402	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
403	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	8	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	4	8	no	—
411	C₂²×C₄	—	4	4	no	—
412	C₂²×C₄	—	4	1	no	—
413	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
414	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
415	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
416	SD₁₆	—	4	8	no	—
417	SD₁₆	—	4	4	no	—
418	D₈	—	4	8	no	—
419	D₈	—	4	4	no	—
420	M₁₆	—	2	4	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
431	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
432	C₂²⋊C₄	—	2	8	no	—
433	C₂²⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	4	1	no	—
436	C₂²⋊C₄	—	4	1	no	—
437	C₄²	—	2	2	no	—
438	C₄²	—	2	2	no	—
439	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
440	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
441	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
442	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
443	C₂³	—	2	2	no	—
444	C₂³	—	2	4	no	—
445	C₂³	—	4	4	no	—
446	C₂³	—	4	2	no	—
447	C₂³	—	4	2	no	—
448	C₂³	—	4	4	no	—
449	C₂³	—	4	4	no	—
450	C₂³	—	4	2	no	—
451	C₂³	—	4	1	no	—
452	C₂³	#120×C₆₁	1	1	yes	characteristic
453	Q₈	—	2	4	no	—
454	Q₈	—	2	2	no	—
455	Q₈	—	4	2	no	—
456	Q₈	AGL(1,ℤ/8)×C₆₁	1	4	yes	complemented
457	D₄	—	2	2	no	—
458	D₄	—	2	2	no	—
459	D₄	—	4	4	no	—
460	D₄	—	4	2	no	—
461	D₄	—	4	4	no	—
462	D₄	—	4	16	no	—
463	D₄	—	4	4	no	—
464	D₄	—	4	2	no	—
465	D₄	—	4	4	no	—
466	D₄	—	4	2	no	—
467	D₄	—	4	4	no	—
468	D₄	—	4	2	no	—
469	D₄	—	8	2	no	—
470	D₄	—	8	8	no	—
471	D₄	—	8	2	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	4	16	no	—
480	C₂×C₄	—	4	4	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	4	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	8	2	no	—
486	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
487	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
488	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
489	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
490	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
491	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
492	C₈	—	2	4	no	—
493	C₈	—	4	2	no	—
494	C₈	—	4	2	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	4	4	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	4	no	—
501	C₂²	—	4	4	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	8	8	no	—
504	C₂²	—	8	4	no	—
505	C₂²	—	8	1	no	—
506	C₂²	—	8	1	no	—
507	C₂²	—	8	1	no	—
508	C₂²	C₆₁×#453	1	2	yes	—
509	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
510	C₄	—	2	4	no	—
511	C₄	—	2	1	no	—
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	2	1	no	—
515	C₄	—	4	2	no	—
516	C₄	—	4	2	no	—
517	C₄	—	8	1	no	—
518	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	2	yes	—
519	C₄	C₆₁×#575	1	2	yes	—
520	C₂	—	2	2	no	—
521	C₂	—	8	2	no	—
522	C₂	—	8	4	no	—
523	C₂	—	16	1	no	—
524	C₂	C₆₁×#3003	1	1	yes	characteristic
525	C₂	C₆₁×#3005	1	1	yes	characteristic
526	C₂	C₂×C₆₁×#453	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#120
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. C₂×C₆₁×#550	C₂	semidirect
2. C₆₁×#3151	C₂	semidirect
3. C₆₁×#3112	C₂	semidirect
4. C₆₁×#3109	C₂	semidirect
5. C₆₁×#1631	C₂	semidirect
6. C₆₁×#1621	C₂	semidirect
7. C₆₁×#1555	C₂	semidirect
8. C₆₁×#1491	C₂	semidirect
9. C₆₁×#1490	C₂	semidirect
25. C₆₁×#493	C₂²	semidirect
26. C₆₁×#492	C₂²	semidirect
29. C₆₁×#477	C₂²	semidirect
30. C₆₁×#476	C₂²	semidirect
31. C₆₁×#460	C₂²	semidirect
32. C₆₁×#459	C₂²	semidirect
40. C₆₁×#331	C₂²	semidirect
41. C₆₁×Q₈⋊C₈	C₂²	semidirect
42. C₆₁×D₄⋊C₈	C₂²	semidirect
192. Q₈×C₆₁	AGL(1,ℤ/8)	semidirect
231. #18545	C₆₁	direct (N × H)
257. C₂×#550	C₂×C₆₁	semidirect
258. #3151	C₂×C₆₁	semidirect
259. #3112	C₂×C₆₁	semidirect
260. #3109	C₂×C₆₁	semidirect
261. #1631	C₂×C₆₁	semidirect
262. #1621	C₂×C₆₁	semidirect
263. #1555	C₂×C₆₁	semidirect
264. #1491	C₂×C₆₁	semidirect
265. #1490	C₂×C₆₁	semidirect
288. #493	C₂²×C₆₁	semidirect
289. #492	C₂²×C₆₁	semidirect
292. #477	C₂²×C₆₁	semidirect
293. #476	C₂²×C₆₁	semidirect
294. #460	C₂²×C₆₁	semidirect
295. #459	C₂²×C₆₁	semidirect
303. #331	C₂²×C₆₁	semidirect
304. Q₈⋊C₈	C₂²×C₆₁	semidirect
305. D₄⋊C₈	C₂²×C₆₁	semidirect
306. C₆₁	#18545	direct (N × H)
456. Q₈	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
C₂×C₆₁×#550	2
C₆₁×#3151	2
C₆₁×#3112	2
C₆₁×#3109	2
C₆₁×#1631	2
C₆₁×#1621	2
C₆₁×#1555	2
C₆₁×#1491	2
C₆₁×#1490	2
#18545	61

Subgroups — C61×#18545 #29521978

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#18545 #29521978