Subgroups — C₂×C₆₁×#3060 #29563881

Order 15616.

2806 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#135×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#131×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#537	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3060	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₆₁×#470	C₂	1	2	yes	maximal, complemented
6	C₂×C₆₁×#469	C₂	1	2	yes	maximal, complemented
7	C₂×C₆₁×#465	C₂	1	4	yes	maximal, complemented
8	C₂²×#106×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₆₁×#417	C₂	1	2	yes	maximal, complemented
10	C₂²×#41×C₆₁	C₂²	1	2	yes	—
11	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
12	C₂×#135×C₆₁	—	2	8	no	—
13	C₂×#135×C₆₁	C₂²	1	8	yes	complemented
14	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
15	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	—
16	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×#131×C₆₁	—	2	8	no	—
18	C₂×#131×C₆₁	C₂²	1	8	yes	complemented
19	C₂²×M₁₆×C₆₁	C₂²	1	2	yes	—
20	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
21	C₂³×C₈×C₆₁	C₂²	1	2	yes	—
22	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
23	C₆₁×#537	—	2	8	no	—
24	C₆₁×#537	C₂²	1	16	yes	complemented
25	C₂×C₂²⋊Q₈×C₆₁	—	2	2	no	—
26	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	4	yes	—
27	C₂×#121×C₆₁	—	2	2	no	—
28	C₂×#121×C₆₁	—	2	4	no	—
29	C₂×#121×C₆₁	C₂²	1	4	yes	—
30	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
31	C₆₁×#470	C₂²	1	16	yes	complemented
32	C₆₁×#469	C₂²	1	16	yes	complemented
33	C₆₁×#465	C₂²	1	32	yes	complemented
34	C₂×#106×C₆₁	C₂²	1	2	yes	—
35	C₂×#106×C₆₁	C₂²	1	2	yes	—
36	C₂×#106×C₆₁	C₂²	1	8	yes	complemented
37	C₆₁×#417	C₂²	1	16	yes	complemented
38	C₂×#103×C₆₁	C₂²	1	4	yes	—
39	C₂×#102×C₆₁	C₂²	1	4	yes	—
40	C₂×#41×C₆₁	—	2	4	no	—
41	C₂×#41×C₆₁	—	2	4	no	—
42	C₂×#41×C₆₁	—	2	4	no	—
43	C₂×#41×C₆₁	—	2	8	no	—
44	C₂×#41×C₆₁	—	2	8	no	—
45	C₂×#41×C₆₁	D₄	1	4	yes	—
46	C₂×#41×C₆₁	C₂³	1	8	yes	—
47	C₂×#41×C₆₁	C₂³	1	4	yes	—
48	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
49	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
50	C₂²×D₄×C₆₁	—	2	2	no	—
51	C₂²×D₄×C₆₁	—	2	4	no	—
52	C₂²×D₄×C₆₁	D₄	1	2	yes	—
53	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
54	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
55	C₂³×C₄×C₆₁	—	2	2	no	—
56	C₂³×C₄×C₆₁	—	2	2	no	—
57	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
58	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
59	#135×C₆₁	—	2	32	no	—
60	C₂×Q₁₆×C₆₁	—	2	4	no	—
61	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
62	C₂×SD₁₆×C₆₁	—	2	8	no	—
63	C₂×SD₁₆×C₆₁	C₂³	1	8	yes	—
64	C₂×D₈×C₆₁	—	2	4	no	—
65	C₂×D₈×C₆₁	C₂³	1	4	yes	—
66	#131×C₆₁	—	2	32	no	—
67	C₂×M₁₆×C₆₁	—	2	4	no	—
68	C₂×M₁₆×C₆₁	—	2	8	no	—
69	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
70	C₂×M₁₆×C₆₁	C₂³	1	8	yes	—
71	C₂²×C₈×C₆₁	—	2	8	no	—
72	C₂²×C₈×C₆₁	D₄	1	8	yes	complemented
73	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
74	C₂²×C₈×C₆₁	C₂³	1	8	yes	—
75	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
78	C₂²⋊Q₈×C₆₁	—	2	16	no	—
79	C₂²⋊Q₈×C₆₁	—	2	8	no	—
80	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
81	#121×C₆₁	—	2	16	no	—
82	#121×C₆₁	—	2	32	no	—
83	#121×C₆₁	—	2	8	no	—
84	#121×C₆₁	C₂³	1	16	yes	—
85	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
86	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
87	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
88	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
89	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
90	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
91	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
92	#106×C₆₁	C₂³	1	8	yes	—
93	#106×C₆₁	C₂³	1	8	yes	—
94	#103×C₆₁	C₂³	1	16	yes	—
95	#102×C₆₁	C₂³	1	16	yes	—
96	C₂⁴×C₆₁	—	2	2	no	—
97	C₂⁴×C₆₁	C₂×D₄	1	2	yes	—
98	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
99	#41×C₆₁	—	2	16	no	—
100	#41×C₆₁	—	2	8	no	—
101	#41×C₆₁	—	2	8	no	—
102	#41×C₆₁	—	2	16	no	—
103	#41×C₆₁	—	2	16	no	—
104	#41×C₆₁	—	4	16	no	—
105	C₂×Q₈×C₆₁	—	2	4	no	—
106	C₂×Q₈×C₆₁	—	2	2	no	—
107	C₂×Q₈×C₆₁	—	2	4	no	—
108	C₂×Q₈×C₆₁	—	2	4	no	—
109	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	—
110	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
111	C₂×D₄×C₆₁	—	2	8	no	—
112	C₂×D₄×C₆₁	—	2	8	no	—
113	C₂×D₄×C₆₁	—	2	16	no	—
114	C₂×D₄×C₆₁	—	2	4	no	—
115	C₂×D₄×C₆₁	—	2	4	no	—
116	C₂×D₄×C₆₁	—	2	2	no	—
117	C₂×D₄×C₆₁	—	2	4	no	—
118	C₂×D₄×C₆₁	—	4	8	no	—
119	C₂×D₄×C₆₁	—	8	8	no	—
120	C₂×D₄×C₆₁	C₂×D₄	1	8	yes	—
121	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
122	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
123	C₂²×C₄×C₆₁	—	2	4	no	—
124	C₂²×C₄×C₆₁	—	2	4	no	—
125	C₂²×C₄×C₆₁	—	2	4	no	—
126	C₂²×C₄×C₆₁	—	2	2	no	—
127	C₂²×C₄×C₆₁	—	2	8	no	—
128	C₂²×C₄×C₆₁	—	2	8	no	—
129	C₂²×C₄×C₆₁	—	4	8	no	—
130	C₂²×C₄×C₆₁	—	8	4	no	—
131	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
132	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
136	C₂²×C₄×C₆₁	#41	1	4	yes	—
137	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
138	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
139	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
140	Q₁₆×C₆₁	—	2	8	no	—
141	SD₁₆×C₆₁	—	2	16	no	—
142	D₈×C₆₁	—	2	8	no	—
143	M₁₆×C₆₁	—	2	8	no	—
144	M₁₆×C₆₁	—	2	16	no	—
145	C₂×C₈×C₆₁	—	2	4	no	—
146	C₂×C₈×C₆₁	—	2	16	no	—
147	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
148	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
149	C₂×C₈×C₆₁	C₂×D₄	1	16	yes	complemented
150	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
151	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
152	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
153	C₄⋊C₄×C₆₁	—	2	8	no	—
154	C₄⋊C₄×C₆₁	—	2	4	no	—
155	C₄⋊C₄×C₆₁	—	2	16	no	—
156	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
157	C₂²⋊C₄×C₆₁	—	2	16	no	—
158	C₂²⋊C₄×C₆₁	—	2	16	no	—
159	C₂³×C₆₁	—	2	4	no	—
160	C₂³×C₆₁	—	2	4	no	—
161	C₂³×C₆₁	—	2	8	no	—
162	C₂³×C₆₁	—	2	4	no	—
163	C₂³×C₆₁	—	4	4	no	—
164	C₂³×C₆₁	—	4	4	no	—
165	C₂³×C₆₁	—	4	4	no	—
166	C₂³×C₆₁	#121	1	4	yes	—
167	C₂³×C₆₁	C₂²×D₄	1	4	yes	—
168	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
169	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
170	Q₈×C₆₁	—	2	8	no	—
171	Q₈×C₆₁	—	2	4	no	—
172	Q₈×C₆₁	—	2	4	no	—
173	Q₈×C₆₁	—	4	4	no	—
174	D₄×C₆₁	—	2	16	no	—
175	D₄×C₆₁	—	2	8	no	—
176	D₄×C₆₁	—	2	4	no	—
177	D₄×C₆₁	—	2	4	no	—
178	D₄×C₆₁	—	4	16	no	—
179	D₄×C₆₁	—	4	4	no	—
180	D₄×C₆₁	—	8	16	no	—
181	C₂×C₄×C₆₁	—	2	4	no	—
182	C₂×C₄×C₆₁	—	2	8	no	—
183	C₂×C₄×C₆₁	—	2	4	no	—
184	C₂×C₄×C₆₁	—	2	4	no	—
185	C₂×C₄×C₆₁	—	2	8	no	—
186	C₂×C₄×C₆₁	—	2	4	no	—
187	C₂×C₄×C₆₁	—	4	4	no	—
188	C₂×C₄×C₆₁	—	4	8	no	—
189	C₂×C₄×C₆₁	—	4	16	no	—
190	C₂×C₄×C₆₁	—	8	8	no	—
191	C₂×C₄×C₆₁	#121	1	4	yes	—
192	C₂×C₄×C₆₁	#121	1	8	yes	—
193	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
194	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
195	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
198	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
199	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
200	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
201	C₈×C₆₁	—	2	4	no	—
202	C₈×C₆₁	C₂²×D₄	1	4	yes	—
203	C₈×C₆₁	C₂²×D₄	1	4	yes	—
204	C₂×#3060	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂²×C₆₁	—	2	8	no	—
206	C₂²×C₆₁	—	2	4	no	—
207	C₂²×C₆₁	—	2	4	no	—
208	C₂²×C₆₁	—	2	8	no	—
209	C₂²×C₆₁	—	4	8	no	—
210	C₂²×C₆₁	—	4	4	no	—
211	C₂²×C₆₁	—	4	4	no	—
212	C₂²×C₆₁	—	4	4	no	—
213	C₂²×C₆₁	—	8	8	no	—
214	C₂²×C₆₁	C₂×#121	1	4	yes	—
215	C₂²×C₆₁	C₂×#121	1	2	yes	—
216	C₂²×C₆₁	#577	1	4	yes	—
217	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
218	C₄×C₆₁	—	2	4	no	—
219	C₄×C₆₁	—	4	4	no	—
220	C₄×C₆₁	—	4	8	no	—
221	C₄×C₆₁	C₂×#121	1	2	yes	—
222	C₄×C₆₁	C₂×#121	1	4	yes	—
223	C₄×C₆₁	C₂³×D₄	1	1	yes	characteristic
224	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
225	C₂²×#135	C₂×C₆₁	1	1	yes	characteristic, complemented
226	C₂²×#131	C₂×C₆₁	1	1	yes	characteristic, complemented
227	C₂×#537	C₂×C₆₁	1	2	yes	complemented
228	#3060	C₂×C₆₁	1	16	yes	direct product factor
229	C₂×#470	C₂×C₆₁	1	2	yes	complemented
230	C₂×#469	C₂×C₆₁	1	2	yes	complemented
231	C₂×#465	C₂×C₆₁	1	4	yes	complemented
232	C₂²×#106	C₂×C₆₁	1	1	yes	characteristic, complemented
233	C₂×#417	C₂×C₆₁	1	2	yes	complemented
234	C₂×C₆₁	—	2	4	no	—
235	C₂×C₆₁	—	4	4	no	—
236	C₂×C₆₁	—	8	4	no	—
237	C₂×C₆₁	#3060	1	4	yes	direct product factor
238	C₂×C₆₁	C₂²×#121	1	1	yes	characteristic
239	C₂×C₆₁	C₂×#577	1	2	yes	—
240	C₂²×#41	C₂²×C₆₁	1	2	yes	—
241	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
242	C₂×#135	—	2	8	no	—
243	C₂×#135	C₂²×C₆₁	1	8	yes	complemented
244	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
245	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	—
246	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
247	C₂×#131	—	2	8	no	—
248	C₂×#131	C₂²×C₆₁	1	8	yes	complemented
249	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
250	C₂²×M₁₆	C₂²×C₆₁	1	2	yes	—
251	C₂³×C₈	C₂²×C₆₁	1	2	yes	—
252	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
253	#537	—	2	8	no	—
254	#537	C₂²×C₆₁	1	16	yes	complemented
255	C₂×C₂²⋊Q₈	—	2	2	no	—
256	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	4	yes	—
257	C₂×#121	—	2	2	no	—
258	C₂×#121	—	2	4	no	—
259	C₂×#121	C₂²×C₆₁	1	4	yes	—
260	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
261	#470	C₂²×C₆₁	1	16	yes	complemented
262	#469	C₂²×C₆₁	1	16	yes	complemented
263	#465	C₂²×C₆₁	1	32	yes	complemented
264	C₂×#106	C₂²×C₆₁	1	2	yes	—
265	C₂×#106	C₂²×C₆₁	1	2	yes	—
266	C₂×#106	C₂²×C₆₁	1	8	yes	complemented
267	#417	C₂²×C₆₁	1	16	yes	complemented
268	C₂×#103	C₂²×C₆₁	1	4	yes	—
269	C₂×#102	C₂²×C₆₁	1	4	yes	—
270	C₆₁	C₂×#3060	1	1	yes	characteristic, direct product factor, Sylow
271	C₂×#41	—	2	4	no	—
272	C₂×#41	—	2	4	no	—
273	C₂×#41	—	2	4	no	—
274	C₂×#41	—	2	8	no	—
275	C₂×#41	—	2	8	no	—
276	C₂×#41	D₄×C₆₁	1	4	yes	—
277	C₂×#41	C₂³×C₆₁	1	8	yes	—
278	C₂×#41	C₂³×C₆₁	1	4	yes	—
279	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
280	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
281	C₂²×D₄	—	2	2	no	—
282	C₂²×D₄	—	2	4	no	—
283	C₂²×D₄	D₄×C₆₁	1	2	yes	—
284	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
285	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
286	C₂³×C₄	—	2	2	no	—
287	C₂³×C₄	—	2	2	no	—
288	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
289	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
290	#135	—	2	32	no	—
291	C₂×Q₁₆	—	2	4	no	—
292	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
293	C₂×SD₁₆	—	2	8	no	—
294	C₂×SD₁₆	C₂³×C₆₁	1	8	yes	—
295	C₂×D₈	—	2	4	no	—
296	C₂×D₈	C₂³×C₆₁	1	4	yes	—
297	#131	—	2	32	no	—
298	C₂×M₁₆	—	2	4	no	—
299	C₂×M₁₆	—	2	8	no	—
300	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
301	C₂×M₁₆	C₂³×C₆₁	1	8	yes	—
302	C₂²×C₈	—	2	8	no	—
303	C₂²×C₈	D₄×C₆₁	1	8	yes	complemented
304	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
305	C₂²×C₈	C₂³×C₆₁	1	8	yes	—
306	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
307	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
308	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
309	C₂²⋊Q₈	—	2	16	no	—
310	C₂²⋊Q₈	—	2	8	no	—
311	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
312	#121	—	2	16	no	—
313	#121	—	2	32	no	—
314	#121	—	2	8	no	—
315	#121	C₂³×C₆₁	1	16	yes	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	—	2	4	no	—
318	C₂×C₄⋊C₄	—	2	4	no	—
319	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
320	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
321	C₂×C₂²⋊C₄	—	2	4	no	—
322	C₂×C₂²⋊C₄	—	2	4	no	—
323	#106	C₂³×C₆₁	1	8	yes	—
324	#106	C₂³×C₆₁	1	8	yes	—
325	#103	C₂³×C₆₁	1	16	yes	—
326	#102	C₂³×C₆₁	1	16	yes	—
327	C₂⁴	—	2	2	no	—
328	C₂⁴	C₂×D₄×C₆₁	1	2	yes	—
329	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
330	#41	—	2	16	no	—
331	#41	—	2	8	no	—
332	#41	—	2	8	no	—
333	#41	—	2	16	no	—
334	#41	—	2	16	no	—
335	#41	—	4	16	no	—
336	C₂×Q₈	—	2	4	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	4	no	—
339	C₂×Q₈	—	2	4	no	—
340	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	—
341	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
342	C₂×D₄	—	2	8	no	—
343	C₂×D₄	—	2	8	no	—
344	C₂×D₄	—	2	16	no	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	2	4	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	4	no	—
349	C₂×D₄	—	4	8	no	—
350	C₂×D₄	—	8	8	no	—
351	C₂×D₄	C₂×D₄×C₆₁	1	8	yes	—
352	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
353	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	8	no	—
359	C₂²×C₄	—	2	8	no	—
360	C₂²×C₄	—	4	8	no	—
361	C₂²×C₄	—	8	4	no	—
362	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
363	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
364	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
366	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
367	C₂²×C₄	#41×C₆₁	1	4	yes	—
368	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
369	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
370	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
371	Q₁₆	—	2	8	no	—
372	SD₁₆	—	2	16	no	—
373	D₈	—	2	8	no	—
374	M₁₆	—	2	8	no	—
375	M₁₆	—	2	16	no	—
376	C₂×C₈	—	2	4	no	—
377	C₂×C₈	—	2	16	no	—
378	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
379	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
380	C₂×C₈	C₂×D₄×C₆₁	1	16	yes	complemented
381	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
382	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
383	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
384	C₄⋊C₄	—	2	8	no	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	16	no	—
387	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
388	C₂²⋊C₄	—	2	16	no	—
389	C₂²⋊C₄	—	2	16	no	—
390	C₂³	—	2	4	no	—
391	C₂³	—	2	8	no	—
392	C₂³	—	2	4	no	—
393	C₂³	—	2	4	no	—
394	C₂³	—	4	4	no	—
395	C₂³	—	4	4	no	—
396	C₂³	—	4	4	no	—
397	C₂³	#121×C₆₁	1	4	yes	—
398	C₂³	C₂²×D₄×C₆₁	1	4	yes	—
399	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
400	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
401	Q₈	—	2	8	no	—
402	Q₈	—	2	4	no	—
403	Q₈	—	2	4	no	—
404	Q₈	—	4	4	no	—
405	D₄	—	2	16	no	—
406	D₄	—	2	4	no	—
407	D₄	—	2	4	no	—
408	D₄	—	2	8	no	—
409	D₄	—	4	16	no	—
410	D₄	—	4	4	no	—
411	D₄	—	8	16	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	8	no	—
416	C₂×C₄	—	2	8	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	4	8	no	—
419	C₂×C₄	—	4	4	no	—
420	C₂×C₄	—	4	16	no	—
421	C₂×C₄	—	8	8	no	—
422	C₂×C₄	#121×C₆₁	1	4	yes	—
423	C₂×C₄	#121×C₆₁	1	8	yes	—
424	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
425	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
426	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
427	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
428	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
429	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
430	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
431	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
432	C₈	—	2	4	no	—
433	C₈	C₂²×D₄×C₆₁	1	4	yes	—
434	C₈	C₂²×D₄×C₆₁	1	4	yes	—
435	C₂²	—	2	8	no	—
436	C₂²	—	2	4	no	—
437	C₂²	—	2	8	no	—
438	C₂²	—	2	4	no	—
439	C₂²	—	4	8	no	—
440	C₂²	—	4	4	no	—
441	C₂²	—	4	4	no	—
442	C₂²	—	4	4	no	—
443	C₂²	—	8	8	no	—
444	C₂²	C₂×#121×C₆₁	1	4	yes	—
445	C₂²	C₂×#121×C₆₁	1	2	yes	—
446	C₂²	C₆₁×#577	1	4	yes	—
447	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
448	C₄	—	2	4	no	—
449	C₄	—	4	8	no	—
450	C₄	—	4	4	no	—
451	C₄	C₂×#121×C₆₁	1	2	yes	—
452	C₄	C₂×#121×C₆₁	1	4	yes	—
453	C₄	C₂³×D₄×C₆₁	1	1	yes	characteristic
454	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
455	C₂	—	2	4	no	—
456	C₂	—	4	4	no	—
457	C₂	—	8	4	no	—
458	C₂	C₆₁×#3060	1	4	yes	direct product factor
459	C₂	C₂²×#121×C₆₁	1	1	yes	characteristic
460	C₂	C₂×C₆₁×#577	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂²×#135×C₆₁	C₂	semidirect
2. C₂²×#131×C₆₁	C₂	semidirect
3. C₂×C₆₁×#537	C₂	semidirect
4. C₆₁×#3060	C₂	direct (N × H)
5. C₂×C₆₁×#470	C₂	semidirect
6. C₂×C₆₁×#469	C₂	semidirect
7. C₂×C₆₁×#465	C₂	semidirect
8. C₂²×#106×C₆₁	C₂	semidirect
9. C₂×C₆₁×#417	C₂	semidirect
13. C₂×#135×C₆₁	C₂²	semidirect
18. C₂×#131×C₆₁	C₂²	semidirect
24. C₆₁×#537	C₂²	semidirect
31. C₆₁×#470	C₂²	semidirect
32. C₆₁×#469	C₂²	semidirect
33. C₆₁×#465	C₂²	semidirect
36. C₂×#106×C₆₁	C₂²	semidirect
37. C₆₁×#417	C₂²	semidirect
72. C₂²×C₈×C₆₁	D₄	semidirect
149. C₂×C₈×C₆₁	C₂×D₄	semidirect
204. C₂×#3060	C₆₁	direct (N × H)
225. C₂²×#135	C₂×C₆₁	semidirect
226. C₂²×#131	C₂×C₆₁	semidirect
227. C₂×#537	C₂×C₆₁	semidirect
228. #3060	C₂×C₆₁	direct (N × H)
229. C₂×#470	C₂×C₆₁	semidirect
230. C₂×#469	C₂×C₆₁	semidirect
231. C₂×#465	C₂×C₆₁	semidirect
232. C₂²×#106	C₂×C₆₁	semidirect
233. C₂×#417	C₂×C₆₁	semidirect
237. C₂×C₆₁	#3060	direct (N × H)
243. C₂×#135	C₂²×C₆₁	semidirect
248. C₂×#131	C₂²×C₆₁	semidirect
254. #537	C₂²×C₆₁	semidirect
261. #470	C₂²×C₆₁	semidirect
262. #469	C₂²×C₆₁	semidirect
263. #465	C₂²×C₆₁	semidirect
266. C₂×#106	C₂²×C₆₁	semidirect
267. #417	C₂²×C₆₁	semidirect
270. C₆₁	C₂×#3060	direct (N × H)
303. C₂²×C₈	D₄×C₆₁	semidirect
380. C₂×C₈	C₂×D₄×C₆₁	semidirect
458. C₂	C₆₁×#3060	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#135×C₆₁	2
C₂²×#131×C₆₁	2
C₂×C₆₁×#537	2
C₆₁×#3060	2
C₂×C₆₁×#470	2
C₂×C₆₁×#469	2
C₂×C₆₁×#465	2
C₂²×#106×C₆₁	2
C₂×C₆₁×#417	2
C₂×#3060	61

Subgroups — C2×C61×#3060 #29563881

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#3060 #29563881