Subgroups — C₆₁×#60453 #29563886

Order 15616.

2722 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#575	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#131×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3449	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3063	C₂	1	8	yes	maximal, complemented
5	C₆₁×#3062	C₂	1	8	yes	maximal, complemented
6	C₆₁×#3054	C₂	1	4	yes	maximal, complemented
7	C₆₁×#3050	C₂	1	4	yes	maximal, complemented
8	C₆₁×#2911	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₆₁×#416	C₂	1	2	yes	maximal, complemented
10	C₂²×#41×C₆₁	C₂²	1	2	yes	—
11	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
12	C₆₁×#575	—	2	8	no	—
13	C₂×#137×C₆₁	C₂²	1	4	yes	complemented
14	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	4	yes	complemented
15	C₂×#135×C₆₁	C₂²	1	4	yes	—
16	C₂×#131×C₆₁	—	2	8	no	—
17	C₂×#131×C₆₁	C₂²	1	8	yes	complemented
18	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₆₁	C₂²	1	2	yes	complemented
20	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₂³×C₈×C₆₁	C₂²	1	2	yes	complemented
22	C₆₁×#537	C₂²	1	8	yes	—
23	C₆₁×#536	—	2	2	no	—
24	C₆₁×#536	C₂²	1	4	yes	complemented
25	C₆₁×#535	—	2	2	no	—
26	C₆₁×#535	C₂²	1	4	yes	complemented
27	C₆₁×#534	—	2	4	no	—
28	C₆₁×#532	—	2	4	no	—
29	C₆₁×#525	—	2	4	no	—
30	C₆₁×#525	C₂²	1	8	yes	complemented
31	C₂×#117×C₆₁	C₂²	1	2	yes	—
32	C₆₁×#470	C₂²	1	8	yes	complemented
33	C₆₁×#469	C₂²	1	8	yes	complemented
34	C₆₁×#468	C₂²	1	16	yes	complemented
35	C₆₁×#467	C₂²	1	8	yes	complemented
36	C₆₁×#466	C₂²	1	8	yes	complemented
37	C₆₁×#465	C₂²	1	16	yes	complemented
38	C₆₁×#428	C₂²	1	8	yes	complemented
39	C₆₁×#427	C₂²	1	4	yes	complemented
40	C₆₁×#416	C₂²	1	4	yes	complemented
41	C₆₁×#416	C₂²	1	4	yes	complemented
42	C₆₁×#416	C₂²	1	8	yes	complemented
43	C₂×#103×C₆₁	C₂²	1	4	yes	complemented
44	C₂×#102×C₆₁	C₂²	1	4	yes	complemented
45	C₂×#41×C₆₁	—	2	4	no	—
46	C₂×#41×C₆₁	—	2	2	no	—
47	C₂×#41×C₆₁	—	2	2	no	—
48	C₂×#41×C₆₁	—	2	4	no	—
49	C₂×#41×C₆₁	—	2	8	no	—
50	C₂×#41×C₆₁	—	2	8	no	—
51	C₂×#41×C₆₁	D₄	1	4	yes	—
52	C₂×#41×C₆₁	C₂³	1	4	yes	—
53	C₂×#41×C₆₁	C₂³	1	4	yes	—
54	C₂×#41×C₆₁	C₂³	1	4	yes	—
55	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
56	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
57	C₂²×D₄×C₆₁	—	2	2	no	—
58	C₂²×D₄×C₆₁	D₄	1	2	yes	—
59	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
60	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
61	C₂³×C₄×C₆₁	—	2	2	no	—
62	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
63	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
64	#137×C₆₁	—	2	16	no	—
65	AGL(1,ℤ/8)×C₆₁	—	2	16	no	—
66	#135×C₆₁	—	2	16	no	—
67	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
68	C₂×SD₁₆×C₆₁	C₂³	1	8	yes	—
69	C₂×D₈×C₆₁	C₂³	1	4	yes	—
70	#131×C₆₁	—	2	32	no	—
71	C₂×M₁₆×C₆₁	—	2	8	no	—
72	C₂×M₁₆×C₆₁	D₄	1	8	yes	complemented
73	C₂×M₁₆×C₆₁	C₂³	1	8	yes	—
74	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
75	C₂²×C₈×C₆₁	—	2	4	no	—
76	C₂²×C₈×C₆₁	—	2	8	no	—
77	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
80	C₂²×C₈×C₆₁	C₂³	1	8	yes	—
81	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
82	C₄⋊Q₈×C₆₁	—	2	4	no	—
83	#127×C₆₁	—	2	4	no	—
84	#124×C₆₁	—	2	4	no	—
85	#124×C₆₁	—	2	4	no	—
86	#123×C₆₁	—	2	8	no	—
87	#123×C₆₁	—	2	8	no	—
88	C₂²⋊Q₈×C₆₁	—	2	8	no	—
89	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
90	#121×C₆₁	—	2	16	no	—
91	#121×C₆₁	—	2	8	no	—
92	#121×C₆₁	C₂³	1	16	yes	—
93	#120×C₆₁	—	2	8	no	—
94	#120×C₆₁	—	2	8	no	—
95	C₄×D₄×C₆₁	—	2	16	no	—
96	#117×C₆₁	—	2	2	no	—
97	#117×C₆₁	—	2	2	no	—
98	#117×C₆₁	C₂³	1	4	yes	—
99	#117×C₆₁	C₂³	1	4	yes	—
100	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
101	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
102	C₂×C₄²×C₆₁	—	2	2	no	—
103	#107×C₆₁	C₂³	1	8	yes	—
104	#106×C₆₁	C₂³	1	8	yes	—
105	#103×C₆₁	C₂³	1	8	yes	—
106	#103×C₆₁	C₂³	1	8	yes	—
107	#102×C₆₁	C₂³	1	8	yes	—
108	#102×C₆₁	C₂³	1	8	yes	—
109	C₂⁴×C₆₁	—	2	2	no	—
110	C₂⁴×C₆₁	C₂×D₄	1	2	yes	—
111	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
112	#41×C₆₁	—	2	16	no	—
113	#41×C₆₁	—	2	8	no	—
114	#41×C₆₁	—	2	8	no	—
115	#41×C₆₁	—	2	8	no	—
116	#41×C₆₁	—	2	8	no	—
117	#41×C₆₁	—	2	8	no	—
118	#41×C₆₁	—	2	8	no	—
119	#41×C₆₁	—	4	8	no	—
120	#41×C₆₁	—	4	8	no	—
121	C₂×Q₈×C₆₁	—	2	4	no	—
122	C₂×Q₈×C₆₁	—	2	2	no	—
123	C₂×Q₈×C₆₁	—	2	4	no	—
124	C₂×Q₈×C₆₁	—	2	4	no	—
125	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	—
126	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
127	C₂×D₄×C₆₁	—	2	8	no	—
128	C₂×D₄×C₆₁	—	2	4	no	—
129	C₂×D₄×C₆₁	—	2	4	no	—
130	C₂×D₄×C₆₁	—	2	16	no	—
131	C₂×D₄×C₆₁	—	2	4	no	—
132	C₂×D₄×C₆₁	—	2	4	no	—
133	C₂×D₄×C₆₁	—	2	2	no	—
134	C₂×D₄×C₆₁	—	2	4	no	—
135	C₂×D₄×C₆₁	—	4	8	no	—
136	C₂×D₄×C₆₁	C₂×D₄	1	8	yes	—
137	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
138	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
139	C₂²×C₄×C₆₁	—	2	4	no	—
140	C₂²×C₄×C₆₁	—	2	4	no	—
141	C₂²×C₄×C₆₁	—	2	2	no	—
142	C₂²×C₄×C₆₁	—	2	4	no	—
143	C₂²×C₄×C₆₁	—	2	4	no	—
144	C₂²×C₄×C₆₁	—	2	4	no	—
145	C₂²×C₄×C₆₁	—	4	8	no	—
146	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
148	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
151	C₂²×C₄×C₆₁	#41	1	4	yes	—
152	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
153	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
155	Q₁₆×C₆₁	—	2	8	no	—
156	SD₁₆×C₆₁	—	2	16	no	—
157	D₈×C₆₁	—	2	8	no	—
158	M₁₆×C₆₁	—	2	16	no	—
159	M₁₆×C₆₁	C₂×D₄	1	16	yes	—
160	C₂×C₈×C₆₁	—	2	2	no	—
161	C₂×C₈×C₆₁	—	2	2	no	—
162	C₂×C₈×C₆₁	—	2	8	no	—
163	C₂×C₈×C₆₁	—	2	16	no	—
164	C₂×C₈×C₆₁	C₂×D₄	1	8	yes	—
165	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
166	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
167	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
168	C₄⋊C₄×C₆₁	—	2	4	no	—
169	C₄⋊C₄×C₆₁	—	2	16	no	—
170	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
171	C₂²⋊C₄×C₆₁	—	2	4	no	—
172	C₂²⋊C₄×C₆₁	—	2	4	no	—
173	C₂²⋊C₄×C₆₁	—	2	16	no	—
174	C₂²⋊C₄×C₆₁	—	2	16	no	—
175	C₄²×C₆₁	—	2	4	no	—
176	C₄²×C₆₁	—	2	4	no	—
177	C₂³×C₆₁	—	2	4	no	—
178	C₂³×C₆₁	—	2	4	no	—
179	C₂³×C₆₁	—	4	2	no	—
180	C₂³×C₆₁	—	4	4	no	—
181	C₂³×C₆₁	—	4	4	no	—
182	C₂³×C₆₁	—	8	4	no	—
183	C₂³×C₆₁	#121	1	4	yes	—
184	C₂³×C₆₁	C₂²×D₄	1	4	yes	—
185	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
186	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
187	Q₈×C₆₁	—	2	8	no	—
188	Q₈×C₆₁	—	2	4	no	—
189	Q₈×C₆₁	—	2	4	no	—
190	Q₈×C₆₁	—	4	4	no	—
191	D₄×C₆₁	—	2	16	no	—
192	D₄×C₆₁	—	2	8	no	—
193	D₄×C₆₁	—	2	4	no	—
194	D₄×C₆₁	—	2	4	no	—
195	D₄×C₆₁	—	4	8	no	—
196	D₄×C₆₁	—	4	8	no	—
197	D₄×C₆₁	—	4	4	no	—
198	D₄×C₆₁	—	8	16	no	—
199	C₂×C₄×C₆₁	—	2	4	no	—
200	C₂×C₄×C₆₁	—	2	8	no	—
201	C₂×C₄×C₆₁	—	2	4	no	—
202	C₂×C₄×C₆₁	—	2	4	no	—
203	C₂×C₄×C₆₁	—	2	8	no	—
204	C₂×C₄×C₆₁	—	2	4	no	—
205	C₂×C₄×C₆₁	—	4	4	no	—
206	C₂×C₄×C₆₁	—	4	8	no	—
207	C₂×C₄×C₆₁	—	4	8	no	—
208	C₂×C₄×C₆₁	—	8	4	no	—
209	C₂×C₄×C₆₁	#121	1	8	yes	—
210	C₂×C₄×C₆₁	#121	1	4	yes	—
211	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
212	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
213	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
214	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
215	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
217	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
218	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
219	C₈×C₆₁	—	2	2	no	—
220	C₈×C₆₁	—	2	2	no	—
221	C₈×C₆₁	C₂²×D₄	1	8	yes	—
222	#60453	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
223	C₂²×C₆₁	—	2	4	no	—
224	C₂²×C₆₁	—	2	2	no	—
225	C₂²×C₆₁	—	2	8	no	—
226	C₂²×C₆₁	—	2	4	no	—
227	C₂²×C₆₁	—	4	4	no	—
228	C₂²×C₆₁	—	4	8	no	—
229	C₂²×C₆₁	—	4	8	no	—
230	C₂²×C₆₁	—	4	4	no	—
231	C₂²×C₆₁	—	8	8	no	—
232	C₂²×C₆₁	C₂×#121	1	2	yes	—
233	C₂²×C₆₁	C₂×#121	1	4	yes	—
234	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
235	C₄×C₆₁	—	2	4	no	—
236	C₄×C₆₁	—	4	8	no	—
237	C₄×C₆₁	—	4	4	no	—
238	C₄×C₆₁	C₂×#121	1	2	yes	—
239	C₄×C₆₁	C₂×#121	1	4	yes	—
240	C₄×C₆₁	C₂³×D₄	1	1	yes	characteristic
241	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
242	C₂×#575	C₂×C₆₁	1	1	yes	characteristic, complemented
243	C₂²×#131	C₂×C₆₁	1	1	yes	characteristic, complemented
244	#3449	C₂×C₆₁	1	2	yes	complemented
245	#3063	C₂×C₆₁	1	8	yes	complemented
246	#3062	C₂×C₆₁	1	8	yes	complemented
247	#3054	C₂×C₆₁	1	4	yes	complemented
248	#3050	C₂×C₆₁	1	4	yes	complemented
249	#2911	C₂×C₆₁	1	1	yes	characteristic, complemented
250	C₂×#416	C₂×C₆₁	1	2	yes	complemented
251	C₂×C₆₁	—	2	2	no	—
252	C₂×C₆₁	—	2	4	no	—
253	C₂×C₆₁	—	4	4	no	—
254	C₂×C₆₁	—	8	4	no	—
255	C₂×C₆₁	C₂²×#121	1	1	yes	characteristic
256	C₂×C₆₁	#3584	1	2	yes	—
257	C₂²×#41	C₂²×C₆₁	1	2	yes	—
258	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
259	#575	—	2	8	no	—
260	C₂×#137	C₂²×C₆₁	1	4	yes	complemented
261	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	4	yes	complemented
262	C₂×#135	C₂²×C₆₁	1	4	yes	—
263	C₂×#131	—	2	8	no	—
264	C₂×#131	C₂²×C₆₁	1	8	yes	complemented
265	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
266	C₂²×M₁₆	C₂²×C₆₁	1	2	yes	complemented
267	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
268	C₂³×C₈	C₂²×C₆₁	1	2	yes	complemented
269	#537	C₂²×C₆₁	1	8	yes	—
270	#536	—	2	2	no	—
271	#536	C₂²×C₆₁	1	4	yes	complemented
272	#535	—	2	2	no	—
273	#535	C₂²×C₆₁	1	4	yes	complemented
274	#534	—	2	4	no	—
275	#532	—	2	4	no	—
276	#525	—	2	4	no	—
277	#525	C₂²×C₆₁	1	8	yes	complemented
278	C₂×#117	C₂²×C₆₁	1	2	yes	—
279	#470	C₂²×C₆₁	1	8	yes	complemented
280	#469	C₂²×C₆₁	1	8	yes	complemented
281	#468	C₂²×C₆₁	1	16	yes	complemented
282	#467	C₂²×C₆₁	1	8	yes	complemented
283	#466	C₂²×C₆₁	1	8	yes	complemented
284	#465	C₂²×C₆₁	1	16	yes	complemented
285	#428	C₂²×C₆₁	1	8	yes	complemented
286	#427	C₂²×C₆₁	1	4	yes	complemented
287	#416	C₂²×C₆₁	1	4	yes	complemented
288	#416	C₂²×C₆₁	1	4	yes	complemented
289	#416	C₂²×C₆₁	1	8	yes	complemented
290	C₂×#103	C₂²×C₆₁	1	4	yes	complemented
291	C₂×#102	C₂²×C₆₁	1	4	yes	complemented
292	C₆₁	#60453	1	1	yes	characteristic, direct product factor, Sylow
293	C₂×#41	—	2	4	no	—
294	C₂×#41	—	2	2	no	—
295	C₂×#41	—	2	2	no	—
296	C₂×#41	—	2	4	no	—
297	C₂×#41	—	2	8	no	—
298	C₂×#41	—	2	8	no	—
299	C₂×#41	D₄×C₆₁	1	4	yes	—
300	C₂×#41	C₂³×C₆₁	1	4	yes	—
301	C₂×#41	C₂³×C₆₁	1	4	yes	—
302	C₂×#41	C₂³×C₆₁	1	4	yes	—
303	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
304	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
305	C₂²×D₄	—	2	2	no	—
306	C₂²×D₄	D₄×C₆₁	1	2	yes	—
307	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
308	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
309	C₂³×C₄	—	2	2	no	—
310	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
311	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
312	#137	—	2	16	no	—
313	AGL(1,ℤ/8)	—	2	16	no	—
314	#135	—	2	16	no	—
315	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
316	C₂×SD₁₆	C₂³×C₆₁	1	8	yes	—
317	C₂×D₈	C₂³×C₆₁	1	4	yes	—
318	#131	—	2	32	no	—
319	C₂×M₁₆	—	2	8	no	—
320	C₂×M₁₆	D₄×C₆₁	1	8	yes	complemented
321	C₂×M₁₆	C₂³×C₆₁	1	8	yes	—
322	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
323	C₂²×C₈	—	2	4	no	—
324	C₂²×C₈	—	2	8	no	—
325	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
326	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
327	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
328	C₂²×C₈	C₂³×C₆₁	1	8	yes	—
329	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
330	C₄⋊Q₈	—	2	4	no	—
331	#127	—	2	4	no	—
332	#124	—	2	4	no	—
333	#124	—	2	4	no	—
334	#123	—	2	8	no	—
335	#123	—	2	8	no	—
336	C₂²⋊Q₈	—	2	8	no	—
337	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
338	#121	—	2	8	no	—
339	#121	—	2	16	no	—
340	#121	C₂³×C₆₁	1	16	yes	—
341	#120	—	2	8	no	—
342	#120	—	2	8	no	—
343	C₄×D₄	—	2	16	no	—
344	#117	—	2	2	no	—
345	#117	—	2	2	no	—
346	#117	C₂³×C₆₁	1	4	yes	—
347	#117	C₂³×C₆₁	1	4	yes	—
348	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
349	C₂×C₂²⋊C₄	—	2	2	no	—
350	C₂×C₄²	—	2	2	no	—
351	#107	C₂³×C₆₁	1	8	yes	—
352	#106	C₂³×C₆₁	1	8	yes	—
353	#103	C₂³×C₆₁	1	8	yes	—
354	#103	C₂³×C₆₁	1	8	yes	—
355	#102	C₂³×C₆₁	1	8	yes	—
356	#102	C₂³×C₆₁	1	8	yes	—
357	C₂⁴	—	2	2	no	—
358	C₂⁴	C₂×D₄×C₆₁	1	2	yes	—
359	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
360	#41	—	2	16	no	—
361	#41	—	2	8	no	—
362	#41	—	2	8	no	—
363	#41	—	2	8	no	—
364	#41	—	2	8	no	—
365	#41	—	2	8	no	—
366	#41	—	2	8	no	—
367	#41	—	4	8	no	—
368	#41	—	4	8	no	—
369	C₂×Q₈	—	2	4	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	2	4	no	—
372	C₂×Q₈	—	2	4	no	—
373	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	—
374	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
375	C₂×D₄	—	2	8	no	—
376	C₂×D₄	—	2	4	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	—	2	16	no	—
379	C₂×D₄	—	2	4	no	—
380	C₂×D₄	—	2	4	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	2	4	no	—
383	C₂×D₄	—	4	8	no	—
384	C₂×D₄	C₂×D₄×C₆₁	1	8	yes	—
385	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
386	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	4	8	no	—
394	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
395	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
396	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
397	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
399	C₂²×C₄	#41×C₆₁	1	4	yes	—
400	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
401	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
402	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
403	Q₁₆	—	2	8	no	—
404	SD₁₆	—	2	16	no	—
405	D₈	—	2	8	no	—
406	M₁₆	—	2	16	no	—
407	M₁₆	C₂×D₄×C₆₁	1	16	yes	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	8	no	—
411	C₂×C₈	—	2	16	no	—
412	C₂×C₈	C₂×D₄×C₆₁	1	8	yes	—
413	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
414	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
415	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
416	C₄⋊C₄	—	2	4	no	—
417	C₄⋊C₄	—	2	16	no	—
418	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
419	C₂²⋊C₄	—	2	4	no	—
420	C₂²⋊C₄	—	2	4	no	—
421	C₂²⋊C₄	—	2	16	no	—
422	C₂²⋊C₄	—	2	16	no	—
423	C₄²	—	2	4	no	—
424	C₄²	—	2	4	no	—
425	C₂³	—	2	4	no	—
426	C₂³	—	2	4	no	—
427	C₂³	—	4	2	no	—
428	C₂³	—	4	4	no	—
429	C₂³	—	4	4	no	—
430	C₂³	—	8	4	no	—
431	C₂³	#121×C₆₁	1	4	yes	—
432	C₂³	C₂²×D₄×C₆₁	1	4	yes	—
433	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
434	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
435	Q₈	—	2	8	no	—
436	Q₈	—	2	4	no	—
437	Q₈	—	2	4	no	—
438	Q₈	—	4	4	no	—
439	D₄	—	2	16	no	—
440	D₄	—	2	4	no	—
441	D₄	—	2	4	no	—
442	D₄	—	2	8	no	—
443	D₄	—	4	8	no	—
444	D₄	—	4	8	no	—
445	D₄	—	4	4	no	—
446	D₄	—	8	16	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	8	no	—
451	C₂×C₄	—	2	8	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	—	4	8	no	—
455	C₂×C₄	—	4	8	no	—
456	C₂×C₄	—	8	4	no	—
457	C₂×C₄	#121×C₆₁	1	8	yes	—
458	C₂×C₄	#121×C₆₁	1	4	yes	—
459	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
460	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
461	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
462	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
463	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
464	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
465	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
466	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
467	C₈	—	2	2	no	—
468	C₈	—	2	2	no	—
469	C₈	C₂²×D₄×C₆₁	1	8	yes	—
470	C₂²	—	2	4	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	8	no	—
473	C₂²	—	2	4	no	—
474	C₂²	—	4	4	no	—
475	C₂²	—	4	8	no	—
476	C₂²	—	4	8	no	—
477	C₂²	—	4	4	no	—
478	C₂²	—	8	8	no	—
479	C₂²	C₂×#121×C₆₁	1	2	yes	—
480	C₂²	C₂×#121×C₆₁	1	4	yes	—
481	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
482	C₄	—	2	4	no	—
483	C₄	—	4	8	no	—
484	C₄	—	4	4	no	—
485	C₄	C₂×#121×C₆₁	1	2	yes	—
486	C₄	C₂×#121×C₆₁	1	4	yes	—
487	C₄	C₂³×D₄×C₆₁	1	1	yes	characteristic
488	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
489	C₂	—	2	2	no	—
490	C₂	—	2	4	no	—
491	C₂	—	4	4	no	—
492	C₂	—	8	4	no	—
493	C₂	C₂²×#121×C₆₁	1	1	yes	characteristic
494	C₂	C₆₁×#3584	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
socle	C₂²×C₆₁	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₁ ◁ C₂²×#41×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#575	C₂	semidirect
2. C₂²×#131×C₆₁	C₂	semidirect
3. C₆₁×#3449	C₂	semidirect
4. C₆₁×#3063	C₂	semidirect
5. C₆₁×#3062	C₂	semidirect
6. C₆₁×#3054	C₂	semidirect
7. C₆₁×#3050	C₂	semidirect
8. C₆₁×#2911	C₂	semidirect
9. C₂×C₆₁×#416	C₂	semidirect
13. C₂×#137×C₆₁	C₂²	semidirect
14. C₂×AGL(1,ℤ/8)×C₆₁	C₂²	semidirect
17. C₂×#131×C₆₁	C₂²	semidirect
19. C₂²×M₁₆×C₆₁	C₂²	semidirect
21. C₂³×C₈×C₆₁	C₂²	semidirect
24. C₆₁×#536	C₂²	semidirect
26. C₆₁×#535	C₂²	semidirect
30. C₆₁×#525	C₂²	semidirect
32. C₆₁×#470	C₂²	semidirect
33. C₆₁×#469	C₂²	semidirect
34. C₆₁×#468	C₂²	semidirect
35. C₆₁×#467	C₂²	semidirect
36. C₆₁×#466	C₂²	semidirect
37. C₆₁×#465	C₂²	semidirect
38. C₆₁×#428	C₂²	semidirect
39. C₆₁×#427	C₂²	semidirect
40. C₆₁×#416	C₂²	semidirect
41. C₆₁×#416	C₂²	semidirect
42. C₆₁×#416	C₂²	semidirect
43. C₂×#103×C₆₁	C₂²	semidirect
44. C₂×#102×C₆₁	C₂²	semidirect
72. C₂×M₁₆×C₆₁	D₄	semidirect
222. #60453	C₆₁	direct (N × H)
242. C₂×#575	C₂×C₆₁	semidirect
243. C₂²×#131	C₂×C₆₁	semidirect
244. #3449	C₂×C₆₁	semidirect
245. #3063	C₂×C₆₁	semidirect
246. #3062	C₂×C₆₁	semidirect
247. #3054	C₂×C₆₁	semidirect
248. #3050	C₂×C₆₁	semidirect
249. #2911	C₂×C₆₁	semidirect
250. C₂×#416	C₂×C₆₁	semidirect
260. C₂×#137	C₂²×C₆₁	semidirect
261. C₂×AGL(1,ℤ/8)	C₂²×C₆₁	semidirect
264. C₂×#131	C₂²×C₆₁	semidirect
266. C₂²×M₁₆	C₂²×C₆₁	semidirect
268. C₂³×C₈	C₂²×C₆₁	semidirect
271. #536	C₂²×C₆₁	semidirect
273. #535	C₂²×C₆₁	semidirect
277. #525	C₂²×C₆₁	semidirect
279. #470	C₂²×C₆₁	semidirect
280. #469	C₂²×C₆₁	semidirect
281. #468	C₂²×C₆₁	semidirect
282. #467	C₂²×C₆₁	semidirect
283. #466	C₂²×C₆₁	semidirect
284. #465	C₂²×C₆₁	semidirect
285. #428	C₂²×C₆₁	semidirect
286. #427	C₂²×C₆₁	semidirect
287. #416	C₂²×C₆₁	semidirect
288. #416	C₂²×C₆₁	semidirect
289. #416	C₂²×C₆₁	semidirect
290. C₂×#103	C₂²×C₆₁	semidirect
291. C₂×#102	C₂²×C₆₁	semidirect
292. C₆₁	#60453	direct (N × H)
320. C₂×M₁₆	D₄×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×#575	2
C₂²×#131×C₆₁	2
C₆₁×#3449	2
C₆₁×#3063	2
C₆₁×#3062	2
C₆₁×#3054	2
C₆₁×#3050	2
C₆₁×#2911	2
C₂×C₆₁×#416	2
#60453	61

Subgroups — C61×#60453 #29563886

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#60453 #29563886