Subgroups — C₂×C₆₁×#3059 #29563880

Order 15616.

2678 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Q₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#131×C₆₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₆₁×#536	C₂	1	2	yes	maximal
4	C₆₁×#3059	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₆₁×#470	C₂	1	4	yes	maximal, complemented
6	C₂×C₆₁×#467	C₂	1	4	yes	maximal, complemented
7	C₂×C₆₁×#427	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₆₁×#419	C₂	1	2	yes	maximal, complemented
9	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
10	C₂³×Q₈×C₆₁	C₂²	1	2	yes	—
11	C₂²×Q₁₆×C₆₁	—	2	8	no	—
12	C₂²×Q₁₆×C₆₁	C₂²	1	2	yes	—
13	C₂²×Q₁₆×C₆₁	C₂²	1	2	yes	—
14	C₂²×Q₁₆×C₆₁	C₂²	1	8	yes	complemented
15	C₂×#131×C₆₁	—	2	8	no	—
16	C₂×#131×C₆₁	C₂²	1	8	yes	—
17	C₂²×M₁₆×C₆₁	C₂²	1	2	yes	—
18	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₆₁	C₂²	1	2	yes	—
20	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₆₁×#536	—	2	8	no	—
22	C₆₁×#536	C₂²	1	16	yes	—
23	C₂×C₄⋊Q₈×C₆₁	—	2	2	no	—
24	C₂×#124×C₆₁	—	2	2	no	—
25	C₂×#123×C₆₁	—	2	4	no	—
26	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	8	yes	—
27	C₂×#117×C₆₁	C₂²	1	2	yes	—
28	C₆₁×#470	C₂²	1	32	yes	complemented
29	C₆₁×#467	C₂²	1	32	yes	complemented
30	C₆₁×#427	C₂²	1	8	yes	complemented
31	C₂×#107×C₆₁	C₂²	1	2	yes	—
32	C₂×#106×C₆₁	C₂²	1	2	yes	—
33	C₆₁×#419	C₂²	1	16	yes	complemented
34	C₂×#103×C₆₁	C₂²	1	8	yes	—
35	C₂×#41×C₆₁	—	2	4	no	—
36	C₂×#41×C₆₁	—	2	4	no	—
37	C₂×#41×C₆₁	D₄	1	4	yes	—
38	C₂×#41×C₆₁	C₂³	1	4	yes	—
39	C₂²×Q₈×C₆₁	—	2	2	no	—
40	C₂²×Q₈×C₆₁	—	2	4	no	—
41	C₂²×Q₈×C₆₁	—	2	8	no	—
42	C₂²×Q₈×C₆₁	—	2	8	no	—
43	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
44	C₂²×Q₈×C₆₁	C₂³	1	8	yes	—
45	C₂²×Q₈×C₆₁	C₂³	1	4	yes	—
46	C₂²×D₄×C₆₁	D₄	1	2	yes	—
47	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₆₁	—	2	2	no	—
49	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
50	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
51	C₂×Q₁₆×C₆₁	—	2	8	no	—
52	C₂×Q₁₆×C₆₁	—	2	8	no	—
53	C₂×Q₁₆×C₆₁	—	2	32	no	—
54	C₂×Q₁₆×C₆₁	C₂³	1	8	yes	—
55	C₂×Q₁₆×C₆₁	C₂³	1	8	yes	—
56	#131×C₆₁	—	2	32	no	—
57	C₂×M₁₆×C₆₁	—	2	4	no	—
58	C₂×M₁₆×C₆₁	—	2	8	no	—
59	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
60	C₂×M₁₆×C₆₁	C₂³	1	8	yes	—
61	C₂²×C₈×C₆₁	—	2	8	no	—
62	C₂²×C₈×C₆₁	D₄	1	8	yes	—
63	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
64	C₂²×C₈×C₆₁	C₂³	1	8	yes	—
65	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
68	C₄⋊Q₈×C₆₁	—	2	16	no	—
69	#124×C₆₁	—	2	16	no	—
70	#123×C₆₁	—	2	32	no	—
71	C₂²⋊Q₈×C₆₁	—	2	16	no	—
72	C₂²⋊Q₈×C₆₁	C₂³	1	32	yes	—
73	#117×C₆₁	—	2	4	no	—
74	#117×C₆₁	C₂³	1	8	yes	—
75	C₂×C₄⋊C₄×C₆₁	—	2	8	no	—
76	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
77	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₆₁	—	2	8	no	—
79	C₂×C₄²×C₆₁	—	2	2	no	—
80	#107×C₆₁	C₂³	1	8	yes	—
81	#106×C₆₁	C₂³	1	8	yes	—
82	#103×C₆₁	C₂³	1	32	yes	—
83	C₂⁴×C₆₁	C₂×D₄	1	2	yes	—
84	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
85	#41×C₆₁	—	2	16	no	—
86	#41×C₆₁	—	2	8	no	—
87	#41×C₆₁	—	2	8	no	—
88	C₂×Q₈×C₆₁	—	2	4	no	—
89	C₂×Q₈×C₆₁	—	2	4	no	—
90	C₂×Q₈×C₆₁	—	2	8	no	—
91	C₂×Q₈×C₆₁	—	2	8	no	—
92	C₂×Q₈×C₆₁	—	2	16	no	—
93	C₂×Q₈×C₆₁	—	2	8	no	—
94	C₂×Q₈×C₆₁	—	2	16	no	—
95	C₂×Q₈×C₆₁	—	4	8	no	—
96	C₂×Q₈×C₆₁	—	4	16	no	—
97	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	—
98	C₂×Q₈×C₆₁	C₂⁴	1	8	yes	—
99	C₂×D₄×C₆₁	—	2	8	no	—
100	C₂×D₄×C₆₁	—	2	4	no	—
101	C₂×D₄×C₆₁	C₂×D₄	1	8	yes	—
102	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
103	C₂²×C₄×C₆₁	—	2	4	no	—
104	C₂²×C₄×C₆₁	—	2	4	no	—
105	C₂²×C₄×C₆₁	—	2	8	no	—
106	C₂²×C₄×C₆₁	—	2	4	no	—
107	C₂²×C₄×C₆₁	—	2	4	no	—
108	C₂²×C₄×C₆₁	—	4	8	no	—
109	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
110	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
114	C₂²×C₄×C₆₁	#41	1	4	yes	—
115	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
116	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
117	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
118	Q₁₆×C₆₁	—	2	16	no	—
119	Q₁₆×C₆₁	—	2	16	no	—
120	M₁₆×C₆₁	—	2	8	no	—
121	M₁₆×C₆₁	—	2	16	no	—
122	C₂×C₈×C₆₁	—	2	4	no	—
123	C₂×C₈×C₆₁	—	2	16	no	—
124	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
125	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
126	C₂×C₈×C₆₁	C₂×D₄	1	16	yes	—
127	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
128	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
129	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
130	C₄⋊C₄×C₆₁	—	2	32	no	—
131	C₄⋊C₄×C₆₁	—	2	4	no	—
132	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
133	C₂²⋊C₄×C₆₁	—	2	8	no	—
134	C₂²⋊C₄×C₆₁	—	2	32	no	—
135	C₄²×C₆₁	—	2	8	no	—
136	C₂³×C₆₁	—	2	4	no	—
137	C₂³×C₆₁	—	2	4	no	—
138	C₂³×C₆₁	—	2	8	no	—
139	C₂³×C₆₁	#121	1	4	yes	—
140	C₂³×C₆₁	C₂²×D₄	1	4	yes	—
141	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
142	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
143	Q₈×C₆₁	—	2	8	no	—
144	Q₈×C₆₁	—	2	8	no	—
145	Q₈×C₆₁	—	2	8	no	—
146	Q₈×C₆₁	—	4	8	no	—
147	Q₈×C₆₁	—	4	16	no	—
148	D₄×C₆₁	—	2	16	no	—
149	D₄×C₆₁	—	2	8	no	—
150	C₂×C₄×C₆₁	—	2	4	no	—
151	C₂×C₄×C₆₁	—	2	8	no	—
152	C₂×C₄×C₆₁	—	2	4	no	—
153	C₂×C₄×C₆₁	—	2	4	no	—
154	C₂×C₄×C₆₁	—	2	8	no	—
155	C₂×C₄×C₆₁	—	2	8	no	—
156	C₂×C₄×C₆₁	—	4	16	no	—
157	C₂×C₄×C₆₁	—	4	8	no	—
158	C₂×C₄×C₆₁	—	4	8	no	—
159	C₂×C₄×C₆₁	#121	1	4	yes	—
160	C₂×C₄×C₆₁	#121	1	8	yes	—
161	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
162	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
163	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
165	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
166	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
167	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
168	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
169	C₈×C₆₁	—	2	4	no	—
170	C₈×C₆₁	C₂²×D₄	1	4	yes	—
171	C₈×C₆₁	C₂²×D₄	1	4	yes	—
172	C₂×#3059	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂²×C₆₁	—	2	8	no	—
174	C₂²×C₆₁	—	2	4	no	—
175	C₂²×C₆₁	—	2	4	no	—
176	C₂²×C₆₁	—	2	8	no	—
177	C₂²×C₆₁	—	4	8	no	—
178	C₂²×C₆₁	C₂×#121	1	4	yes	—
179	C₂²×C₆₁	C₂×#121	1	2	yes	—
180	C₂²×C₆₁	#578	1	4	yes	—
181	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
182	C₄×C₆₁	—	2	4	no	—
183	C₄×C₆₁	—	4	8	no	—
184	C₄×C₆₁	—	4	8	no	—
185	C₄×C₆₁	C₂×#121	1	2	yes	—
186	C₄×C₆₁	C₂×#121	1	4	yes	—
187	C₄×C₆₁	C₂³×D₄	1	1	yes	characteristic
188	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
189	C₂³×Q₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
190	C₂²×#131	C₂×C₆₁	1	1	yes	characteristic
191	C₂×#536	C₂×C₆₁	1	2	yes	—
192	#3059	C₂×C₆₁	1	16	yes	direct product factor
193	C₂×#470	C₂×C₆₁	1	4	yes	complemented
194	C₂×#467	C₂×C₆₁	1	4	yes	complemented
195	C₂×#427	C₂×C₆₁	1	1	yes	characteristic, complemented
196	C₂×#419	C₂×C₆₁	1	2	yes	complemented
197	C₂×C₆₁	—	2	4	no	—
198	C₂×C₆₁	—	4	4	no	—
199	C₂×C₆₁	#3059	1	4	yes	direct product factor
200	C₂×C₆₁	C₂²×#121	1	1	yes	characteristic
201	C₂×C₆₁	C₂×#578	1	2	yes	—
202	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
203	C₂³×Q₈	C₂²×C₆₁	1	2	yes	—
204	C₂²×Q₁₆	—	2	8	no	—
205	C₂²×Q₁₆	C₂²×C₆₁	1	2	yes	—
206	C₂²×Q₁₆	C₂²×C₆₁	1	2	yes	—
207	C₂²×Q₁₆	C₂²×C₆₁	1	8	yes	complemented
208	C₂×#131	—	2	8	no	—
209	C₂×#131	C₂²×C₆₁	1	8	yes	—
210	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
211	C₂²×M₁₆	C₂²×C₆₁	1	2	yes	—
212	C₂³×C₈	C₂²×C₆₁	1	2	yes	—
213	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
214	#536	—	2	8	no	—
215	#536	C₂²×C₆₁	1	16	yes	—
216	C₂×C₄⋊Q₈	—	2	2	no	—
217	C₂×#124	—	2	2	no	—
218	C₂×#123	—	2	4	no	—
219	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	8	yes	—
220	C₂×#117	C₂²×C₆₁	1	2	yes	—
221	#470	C₂²×C₆₁	1	32	yes	complemented
222	#467	C₂²×C₆₁	1	32	yes	complemented
223	#427	C₂²×C₆₁	1	8	yes	complemented
224	C₂×#107	C₂²×C₆₁	1	2	yes	—
225	C₂×#106	C₂²×C₆₁	1	2	yes	—
226	#419	C₂²×C₆₁	1	16	yes	complemented
227	C₂×#103	C₂²×C₆₁	1	8	yes	—
228	C₆₁	C₂×#3059	1	1	yes	characteristic, direct product factor, Sylow
229	C₂×#41	—	2	4	no	—
230	C₂×#41	—	2	4	no	—
231	C₂×#41	D₄×C₆₁	1	4	yes	—
232	C₂×#41	C₂³×C₆₁	1	4	yes	—
233	C₂²×Q₈	—	2	2	no	—
234	C₂²×Q₈	—	2	4	no	—
235	C₂²×Q₈	—	2	8	no	—
236	C₂²×Q₈	—	2	8	no	—
237	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
238	C₂²×Q₈	C₂³×C₆₁	1	4	yes	—
239	C₂²×Q₈	C₂³×C₆₁	1	8	yes	—
240	C₂²×D₄	D₄×C₆₁	1	2	yes	—
241	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
242	C₂³×C₄	—	2	2	no	—
243	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
244	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
245	C₂×Q₁₆	—	2	8	no	—
246	C₂×Q₁₆	—	2	8	no	—
247	C₂×Q₁₆	—	2	32	no	—
248	C₂×Q₁₆	C₂³×C₆₁	1	8	yes	—
249	C₂×Q₁₆	C₂³×C₆₁	1	8	yes	—
250	#131	—	2	32	no	—
251	C₂×M₁₆	—	2	4	no	—
252	C₂×M₁₆	—	2	8	no	—
253	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
254	C₂×M₁₆	C₂³×C₆₁	1	8	yes	—
255	C₂²×C₈	—	2	8	no	—
256	C₂²×C₈	D₄×C₆₁	1	8	yes	—
257	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
258	C₂²×C₈	C₂³×C₆₁	1	8	yes	—
259	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
260	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
261	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
262	C₄⋊Q₈	—	2	16	no	—
263	#124	—	2	16	no	—
264	#123	—	2	32	no	—
265	C₂²⋊Q₈	—	2	16	no	—
266	C₂²⋊Q₈	C₂³×C₆₁	1	32	yes	—
267	#117	—	2	4	no	—
268	#117	C₂³×C₆₁	1	8	yes	—
269	C₂×C₄⋊C₄	—	2	8	no	—
270	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₂²⋊C₄	—	2	8	no	—
273	C₂×C₄²	—	2	2	no	—
274	#107	C₂³×C₆₁	1	8	yes	—
275	#106	C₂³×C₆₁	1	8	yes	—
276	#103	C₂³×C₆₁	1	32	yes	—
277	C₂⁴	C₂×D₄×C₆₁	1	2	yes	—
278	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
279	#41	—	2	16	no	—
280	#41	—	2	8	no	—
281	#41	—	2	8	no	—
282	C₂×Q₈	—	2	4	no	—
283	C₂×Q₈	—	2	4	no	—
284	C₂×Q₈	—	2	8	no	—
285	C₂×Q₈	—	2	8	no	—
286	C₂×Q₈	—	2	16	no	—
287	C₂×Q₈	—	2	8	no	—
288	C₂×Q₈	—	2	16	no	—
289	C₂×Q₈	—	4	8	no	—
290	C₂×Q₈	—	4	16	no	—
291	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	—
292	C₂×Q₈	C₂⁴×C₆₁	1	8	yes	—
293	C₂×D₄	—	2	8	no	—
294	C₂×D₄	—	2	4	no	—
295	C₂×D₄	C₂×D₄×C₆₁	1	8	yes	—
296	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	8	no	—
302	C₂²×C₄	—	4	8	no	—
303	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
305	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
307	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
308	C₂²×C₄	#41×C₆₁	1	4	yes	—
309	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
310	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
311	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
312	Q₁₆	—	2	16	no	—
313	Q₁₆	—	2	16	no	—
314	M₁₆	—	2	8	no	—
315	M₁₆	—	2	16	no	—
316	C₂×C₈	—	2	4	no	—
317	C₂×C₈	—	2	16	no	—
318	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
319	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
320	C₂×C₈	C₂×D₄×C₆₁	1	16	yes	—
321	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
322	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
323	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
324	C₄⋊C₄	—	2	32	no	—
325	C₄⋊C₄	—	2	4	no	—
326	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
327	C₂²⋊C₄	—	2	8	no	—
328	C₂²⋊C₄	—	2	32	no	—
329	C₄²	—	2	8	no	—
330	C₂³	—	2	4	no	—
331	C₂³	—	2	8	no	—
332	C₂³	—	2	4	no	—
333	C₂³	#121×C₆₁	1	4	yes	—
334	C₂³	C₂²×D₄×C₆₁	1	4	yes	—
335	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
336	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
337	Q₈	—	2	8	no	—
338	Q₈	—	2	8	no	—
339	Q₈	—	2	8	no	—
340	Q₈	—	4	8	no	—
341	Q₈	—	4	16	no	—
342	D₄	—	2	16	no	—
343	D₄	—	2	8	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	8	no	—
348	C₂×C₄	—	2	8	no	—
349	C₂×C₄	—	2	8	no	—
350	C₂×C₄	—	4	8	no	—
351	C₂×C₄	—	4	16	no	—
352	C₂×C₄	—	4	8	no	—
353	C₂×C₄	#121×C₆₁	1	4	yes	—
354	C₂×C₄	#121×C₆₁	1	8	yes	—
355	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
356	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
357	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
358	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
359	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
360	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
361	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
362	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
363	C₈	—	2	4	no	—
364	C₈	C₂²×D₄×C₆₁	1	4	yes	—
365	C₈	C₂²×D₄×C₆₁	1	4	yes	—
366	C₂²	—	2	8	no	—
367	C₂²	—	2	4	no	—
368	C₂²	—	2	8	no	—
369	C₂²	—	2	4	no	—
370	C₂²	—	4	8	no	—
371	C₂²	C₂×#121×C₆₁	1	4	yes	—
372	C₂²	C₂×#121×C₆₁	1	2	yes	—
373	C₂²	C₆₁×#578	1	4	yes	—
374	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
375	C₄	—	2	4	no	—
376	C₄	—	4	8	no	—
377	C₄	—	4	8	no	—
378	C₄	C₂×#121×C₆₁	1	2	yes	—
379	C₄	C₂×#121×C₆₁	1	4	yes	—
380	C₄	C₂³×D₄×C₆₁	1	1	yes	characteristic
381	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
382	C₂	—	2	4	no	—
383	C₂	—	4	4	no	—
384	C₂	C₆₁×#3059	1	4	yes	direct product factor
385	C₂	C₂²×#121×C₆₁	1	1	yes	characteristic
386	C₂	C₂×C₆₁×#578	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₂²×#41×C₆₁	C₂²
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. C₂³×Q₁₆×C₆₁	C₂	semidirect
4. C₆₁×#3059	C₂	direct (N × H)
5. C₂×C₆₁×#470	C₂	semidirect
6. C₂×C₆₁×#467	C₂	semidirect
7. C₂×C₆₁×#427	C₂	semidirect
8. C₂×C₆₁×#419	C₂	semidirect
14. C₂²×Q₁₆×C₆₁	C₂²	semidirect
28. C₆₁×#470	C₂²	semidirect
29. C₆₁×#467	C₂²	semidirect
30. C₆₁×#427	C₂²	semidirect
33. C₆₁×#419	C₂²	semidirect
172. C₂×#3059	C₆₁	direct (N × H)
189. C₂³×Q₁₆	C₂×C₆₁	semidirect
192. #3059	C₂×C₆₁	direct (N × H)
193. C₂×#470	C₂×C₆₁	semidirect
194. C₂×#467	C₂×C₆₁	semidirect
195. C₂×#427	C₂×C₆₁	semidirect
196. C₂×#419	C₂×C₆₁	semidirect
199. C₂×C₆₁	#3059	direct (N × H)
207. C₂²×Q₁₆	C₂²×C₆₁	semidirect
221. #470	C₂²×C₆₁	semidirect
222. #467	C₂²×C₆₁	semidirect
223. #427	C₂²×C₆₁	semidirect
226. #419	C₂²×C₆₁	semidirect
228. C₆₁	C₂×#3059	direct (N × H)
384. C₂	C₆₁×#3059	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×Q₁₆×C₆₁	2
C₂²×#131×C₆₁	2
C₂×C₆₁×#536	2
C₆₁×#3059	2
C₂×C₆₁×#470	2
C₂×C₆₁×#467	2
C₂×C₆₁×#427	2
C₂×C₆₁×#419	2
C₂×#3059	61

Subgroups — C2×C61×#3059 #29563880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#3059 #29563880