Subgroups — C₂×C₆₁×#1289 #29511412

Order 15616.

1130 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊C₈×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#380	C₂	1	2	yes	maximal
3	C₆₁×#1289	C₂	1	4	yes	maximal, direct product factor
4	C₂⁴×C₄×C₆₁	C₂²	1	1	yes	characteristic
5	C₂³×C₈×C₆₁	C₄	1	2	yes	complemented
6	C₂²×C₄⋊C₄×C₆₁	—	2	2	no	—
7	C₂²×C₂²⋊C₄×C₆₁	—	2	2	no	—
8	C₂×C₂²⋊C₈×C₆₁	—	2	2	no	—
9	C₂×C₂²⋊C₈×C₆₁	—	2	2	no	—
10	C₂×C₂²⋊C₈×C₆₁	C₄	1	2	yes	complemented
11	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
12	C₆₁×#380	—	2	2	no	—
13	C₆₁×#380	—	2	2	no	—
14	C₆₁×#380	C₄	1	4	yes	complemented
15	C₆₁×#380	C₂²	1	4	yes	—
16	C₂×#95×C₆₁	C₄	1	4	yes	complemented
17	C₂⁵×C₆₁	D₄	1	1	yes	characteristic
18	C₂³×C₄×C₆₁	—	2	4	no	—
19	C₂³×C₄×C₆₁	—	4	4	no	—
20	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
21	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₆₁	C₂×C₄	1	2	yes	—
23	C₂³×C₄×C₆₁	C₂×C₄	1	2	yes	—
24	C₂³×C₄×C₆₁	D₄	1	2	yes	—
25	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
26	C₂³×C₄×C₆₁	D₄	1	2	yes	—
27	C₂³×C₄×C₆₁	Q₈	1	1	yes	characteristic
28	C₂³×C₄×C₆₁	Q₈	1	1	yes	characteristic
29	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
30	C₂²×C₈×C₆₁	—	2	2	no	—
31	C₂²×C₈×C₆₁	—	2	2	no	—
32	C₂²×C₈×C₆₁	—	4	4	no	—
33	C₂²×C₈×C₆₁	C₂×C₄	1	4	yes	complemented
34	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
35	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
36	C₂×C₄⋊C₄×C₆₁	—	4	8	no	—
37	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
38	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
39	C₂×C₂²⋊C₄×C₆₁	—	4	4	no	—
40	C₂×C₂²⋊C₄×C₆₁	—	4	4	no	—
41	C₂²⋊C₈×C₆₁	—	2	4	no	—
42	C₂²⋊C₈×C₆₁	—	2	4	no	—
43	#95×C₆₁	—	2	4	no	—
44	#95×C₆₁	C₂×C₄	1	8	yes	complemented
45	C₂⁴×C₆₁	—	4	2	no	—
46	C₂⁴×C₆₁	—	4	2	no	—
47	C₂⁴×C₆₁	C₂²⋊C₄	1	2	yes	—
48	C₂⁴×C₆₁	C₂²⋊C₄	1	2	yes	—
49	C₂⁴×C₆₁	C₄⋊C₄	1	1	yes	characteristic
50	C₂⁴×C₆₁	C₄⋊C₄	1	1	yes	characteristic
51	C₂⁴×C₆₁	D₈	1	2	yes	—
52	C₂⁴×C₆₁	SD₁₆	1	4	yes	—
53	C₂⁴×C₆₁	Q₁₆	1	2	yes	—
54	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₆₁	—	2	8	no	—
56	C₂²×C₄×C₆₁	—	2	4	no	—
57	C₂²×C₄×C₆₁	—	2	8	no	—
58	C₂²×C₄×C₆₁	—	4	4	no	—
59	C₂²×C₄×C₆₁	—	4	2	no	—
60	C₂²×C₄×C₆₁	—	4	2	no	—
61	C₂²×C₄×C₆₁	—	4	4	no	—
62	C₂²×C₄×C₆₁	—	4	2	no	—
63	C₂²×C₄×C₆₁	—	4	2	no	—
64	C₂²×C₄×C₆₁	—	4	4	no	—
65	C₂²×C₄×C₆₁	—	4	2	no	—
66	C₂²×C₄×C₆₁	—	4	8	no	—
67	C₂²×C₄×C₆₁	—	4	8	no	—
68	C₂²×C₄×C₆₁	—	4	8	no	—
69	C₂²×C₄×C₆₁	C₄²	1	1	yes	characteristic
70	C₂²×C₄×C₆₁	C₄²	1	1	yes	characteristic
71	C₂²×C₄×C₆₁	C₄²	1	2	yes	—
72	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
73	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
74	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
76	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
79	C₂²×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
80	C₂²×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
82	C₂²×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
83	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
86	C₂²×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
87	C₂×C₈×C₆₁	—	2	4	no	—
88	C₂×C₈×C₆₁	—	4	4	no	—
89	C₂×C₈×C₆₁	—	4	4	no	—
90	C₂×C₈×C₆₁	—	4	4	no	—
91	C₄⋊C₄×C₆₁	—	4	8	no	—
92	C₄⋊C₄×C₆₁	—	4	8	no	—
93	C₂²⋊C₄×C₆₁	—	4	8	no	—
94	C₂²⋊C₄×C₆₁	—	4	4	no	—
95	C₂²⋊C₄×C₆₁	—	4	4	no	—
96	C₂³×C₆₁	—	2	4	no	—
97	C₂³×C₆₁	—	2	2	no	—
98	C₂³×C₆₁	—	2	4	no	—
99	C₂³×C₆₁	—	2	2	no	—
100	C₂³×C₆₁	—	4	2	no	—
101	C₂³×C₆₁	—	4	1	no	—
102	C₂³×C₆₁	—	4	1	no	—
103	C₂³×C₆₁	—	4	2	no	—
104	C₂³×C₆₁	—	4	1	no	—
105	C₂³×C₆₁	—	4	4	no	—
106	C₂³×C₆₁	—	4	8	no	—
107	C₂³×C₆₁	—	4	4	no	—
108	C₂³×C₆₁	—	4	1	no	—
109	C₂³×C₆₁	#95	1	1	yes	characteristic
110	C₂³×C₆₁	#95	1	2	yes	—
111	C₂³×C₆₁	#95	1	1	yes	characteristic
112	C₂³×C₆₁	#102	1	4	yes	—
113	C₂³×C₆₁	#102	1	4	yes	—
114	C₂³×C₆₁	#103	1	4	yes	—
115	C₂³×C₆₁	#103	1	4	yes	—
116	C₂³×C₆₁	#106	1	2	yes	—
117	C₂³×C₆₁	#106	1	2	yes	—
118	C₂³×C₆₁	#107	1	2	yes	—
119	C₂³×C₆₁	#107	1	2	yes	—
120	C₂³×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
121	C₂³×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
122	C₂³×C₆₁	C₂×D₈	1	1	yes	characteristic
123	C₂³×C₆₁	C₂×SD₁₆	1	2	yes	—
124	C₂³×C₆₁	C₂×Q₁₆	1	1	yes	characteristic
125	C₂×C₄×C₆₁	—	2	2	no	—
126	C₂×C₄×C₆₁	—	2	4	no	—
127	C₂×C₄×C₆₁	—	2	4	no	—
128	C₂×C₄×C₆₁	—	2	2	no	—
129	C₂×C₄×C₆₁	—	2	2	no	—
130	C₂×C₄×C₆₁	—	2	4	no	—
131	C₂×C₄×C₆₁	—	2	4	no	—
132	C₂×C₄×C₆₁	—	2	2	no	—
133	C₂×C₄×C₆₁	—	2	2	no	—
134	C₂×C₄×C₆₁	—	2	4	no	—
135	C₂×C₄×C₆₁	—	4	2	no	—
136	C₂×C₄×C₆₁	—	4	2	no	—
137	C₂×C₄×C₆₁	—	4	1	no	—
138	C₂×C₄×C₆₁	—	4	2	no	—
139	C₂×C₄×C₆₁	—	4	2	no	—
140	C₂×C₄×C₆₁	—	4	2	no	—
141	C₂×C₄×C₆₁	—	4	1	no	—
142	C₂×C₄×C₆₁	—	4	8	no	—
143	C₂×C₄×C₆₁	—	4	8	no	—
144	C₂×C₄×C₆₁	—	4	8	no	—
145	C₂×C₄×C₆₁	—	8	16	no	—
146	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
147	C₂×C₄×C₆₁	#95	1	2	yes	—
148	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
149	C₂×C₄×C₆₁	#99	1	4	yes	—
150	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
151	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
153	C₈×C₆₁	—	4	4	no	—
154	C₂×#1289	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂²×C₆₁	—	2	8	no	—
156	C₂²×C₆₁	—	2	8	no	—
157	C₂²×C₆₁	—	2	4	no	—
158	C₂²×C₆₁	—	2	4	no	—
159	C₂²×C₆₁	—	2	2	no	—
160	C₂²×C₆₁	—	2	2	no	—
161	C₂²×C₆₁	—	2	1	no	—
162	C₂²×C₆₁	—	2	1	no	—
163	C₂²×C₆₁	—	2	2	no	—
164	C₂²×C₆₁	—	2	1	no	—
165	C₂²×C₆₁	—	2	2	no	—
166	C₂²×C₆₁	—	2	1	no	—
167	C₂²×C₆₁	—	4	4	no	—
168	C₂²×C₆₁	—	4	4	no	—
169	C₂²×C₆₁	—	4	2	no	—
170	C₂²×C₆₁	—	4	2	no	—
171	C₂²×C₆₁	—	4	1	no	—
172	C₂²×C₆₁	—	4	2	no	—
173	C₂²×C₆₁	—	4	1	no	—
174	C₂²×C₆₁	H(3,ℤ/4)	1	2	yes	—
175	C₂²×C₆₁	#340	1	4	yes	—
176	C₂²×C₆₁	#340	1	2	yes	—
177	C₂²×C₆₁	#340	1	2	yes	—
178	C₂²×C₆₁	#342	1	2	yes	—
179	C₂²×C₆₁	C₂×#95	1	1	yes	characteristic
180	C₂²×C₆₁	C₂×#102	1	2	yes	—
181	C₂²×C₆₁	C₂×#103	1	2	yes	—
182	C₂²×C₆₁	C₂×#106	1	1	yes	characteristic
183	C₂²×C₆₁	C₂×#107	1	1	yes	characteristic
184	C₄×C₆₁	—	2	1	no	—
185	C₄×C₆₁	—	2	2	no	—
186	C₄×C₆₁	—	2	1	no	—
187	C₄×C₆₁	—	2	2	no	—
188	C₄×C₆₁	—	8	8	no	—
189	C₄×C₆₁	#342	1	2	yes	—
190	C₄×C₆₁	C₂×#99	1	2	yes	—
191	C₂²×C₂²⋊C₈	C₂×C₆₁	1	1	yes	characteristic
192	C₂×#380	C₂×C₆₁	1	2	yes	—
193	#1289	C₂×C₆₁	1	4	yes	direct product factor
194	C₂×C₆₁	—	2	2	no	—
195	C₂×C₆₁	—	2	4	no	—
196	C₂×C₆₁	—	2	2	no	—
197	C₂×C₆₁	—	2	2	no	—
198	C₂×C₆₁	—	2	1	no	—
199	C₂×C₆₁	—	2	1	no	—
200	C₂×C₆₁	#1289	1	4	yes	direct product factor
201	C₂×C₆₁	C₂×H(3,ℤ/4)	1	1	yes	characteristic
202	C₂×C₆₁	C₂×#340	1	1	yes	characteristic
203	C₂×C₆₁	C₂×#342	1	1	yes	characteristic
204	C₂⁴×C₄	C₂²×C₆₁	1	1	yes	characteristic
205	C₂³×C₈	C₄×C₆₁	1	2	yes	complemented
206	C₂²×C₄⋊C₄	—	2	2	no	—
207	C₂²×C₂²⋊C₄	—	2	2	no	—
208	C₂×C₂²⋊C₈	—	2	2	no	—
209	C₂×C₂²⋊C₈	—	2	2	no	—
210	C₂×C₂²⋊C₈	C₄×C₆₁	1	2	yes	complemented
211	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
212	#380	—	2	2	no	—
213	#380	—	2	2	no	—
214	#380	C₄×C₆₁	1	4	yes	complemented
215	#380	C₂²×C₆₁	1	4	yes	—
216	C₂×#95	C₄×C₆₁	1	4	yes	complemented
217	C₆₁	C₂×#1289	1	1	yes	characteristic, direct product factor, Sylow
218	C₂⁵	D₄×C₆₁	1	1	yes	characteristic
219	C₂³×C₄	—	2	4	no	—
220	C₂³×C₄	—	4	4	no	—
221	C₂³×C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
222	C₂³×C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
223	C₂³×C₄	C₂×C₄×C₆₁	1	2	yes	—
224	C₂³×C₄	C₂×C₄×C₆₁	1	2	yes	—
225	C₂³×C₄	D₄×C₆₁	1	2	yes	—
226	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
227	C₂³×C₄	D₄×C₆₁	1	2	yes	—
228	C₂³×C₄	Q₈×C₆₁	1	1	yes	characteristic
229	C₂³×C₄	Q₈×C₆₁	1	1	yes	characteristic
230	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
231	C₂²×C₈	—	2	2	no	—
232	C₂²×C₈	—	2	2	no	—
233	C₂²×C₈	—	4	4	no	—
234	C₂²×C₈	C₂×C₄×C₆₁	1	4	yes	complemented
235	C₂×C₄⋊C₄	—	2	4	no	—
236	C₂×C₄⋊C₄	—	2	4	no	—
237	C₂×C₄⋊C₄	—	4	8	no	—
238	C₂×C₂²⋊C₄	—	2	4	no	—
239	C₂×C₂²⋊C₄	—	2	4	no	—
240	C₂×C₂²⋊C₄	—	4	4	no	—
241	C₂×C₂²⋊C₄	—	4	4	no	—
242	C₂²⋊C₈	—	2	4	no	—
243	C₂²⋊C₈	—	2	4	no	—
244	#95	—	2	4	no	—
245	#95	C₂×C₄×C₆₁	1	8	yes	complemented
246	C₂⁴	—	4	2	no	—
247	C₂⁴	—	4	2	no	—
248	C₂⁴	C₂²⋊C₄×C₆₁	1	2	yes	—
249	C₂⁴	C₂²⋊C₄×C₆₁	1	2	yes	—
250	C₂⁴	C₄⋊C₄×C₆₁	1	1	yes	characteristic
251	C₂⁴	C₄⋊C₄×C₆₁	1	1	yes	characteristic
252	C₂⁴	D₈×C₆₁	1	2	yes	—
253	C₂⁴	SD₁₆×C₆₁	1	4	yes	—
254	C₂⁴	Q₁₆×C₆₁	1	2	yes	—
255	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
256	C₂²×C₄	—	2	8	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	2	8	no	—
259	C₂²×C₄	—	4	4	no	—
260	C₂²×C₄	—	4	2	no	—
261	C₂²×C₄	—	4	2	no	—
262	C₂²×C₄	—	4	4	no	—
263	C₂²×C₄	—	4	2	no	—
264	C₂²×C₄	—	4	2	no	—
265	C₂²×C₄	—	4	4	no	—
266	C₂²×C₄	—	4	2	no	—
267	C₂²×C₄	—	4	8	no	—
268	C₂²×C₄	—	4	8	no	—
269	C₂²×C₄	—	4	8	no	—
270	C₂²×C₄	C₄²×C₆₁	1	1	yes	characteristic
271	C₂²×C₄	C₄²×C₆₁	1	1	yes	characteristic
272	C₂²×C₄	C₄²×C₆₁	1	2	yes	—
273	C₂²×C₄	C₂²⋊C₄×C₆₁	1	2	yes	—
274	C₂²×C₄	C₂²⋊C₄×C₆₁	1	2	yes	—
275	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
276	C₂²×C₄	C₂²⋊C₄×C₆₁	1	2	yes	—
277	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
278	C₂²×C₄	C₄⋊C₄×C₆₁	1	1	yes	characteristic
279	C₂²×C₄	C₄⋊C₄×C₆₁	1	2	yes	—
280	C₂²×C₄	C₄⋊C₄×C₆₁	1	2	yes	—
281	C₂²×C₄	C₄⋊C₄×C₆₁	1	1	yes	characteristic
282	C₂²×C₄	C₄⋊C₄×C₆₁	1	2	yes	—
283	C₂²×C₄	C₄⋊C₄×C₆₁	1	2	yes	—
284	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
285	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
286	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
287	C₂²×C₄	C₂×Q₈×C₆₁	1	1	yes	characteristic
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	4	4	no	—
290	C₂×C₈	—	4	4	no	—
291	C₂×C₈	—	4	4	no	—
292	C₄⋊C₄	—	4	8	no	—
293	C₄⋊C₄	—	4	8	no	—
294	C₂²⋊C₄	—	4	8	no	—
295	C₂²⋊C₄	—	4	4	no	—
296	C₂²⋊C₄	—	4	4	no	—
297	C₂³	—	2	4	no	—
298	C₂³	—	2	2	no	—
299	C₂³	—	2	4	no	—
300	C₂³	—	2	2	no	—
301	C₂³	—	4	2	no	—
302	C₂³	—	4	1	no	—
303	C₂³	—	4	1	no	—
304	C₂³	—	4	2	no	—
305	C₂³	—	4	1	no	—
306	C₂³	—	4	4	no	—
307	C₂³	—	4	8	no	—
308	C₂³	—	4	4	no	—
309	C₂³	—	4	1	no	—
310	C₂³	#95×C₆₁	1	1	yes	characteristic
311	C₂³	#95×C₆₁	1	2	yes	—
312	C₂³	#95×C₆₁	1	1	yes	characteristic
313	C₂³	#102×C₆₁	1	4	yes	—
314	C₂³	#102×C₆₁	1	4	yes	—
315	C₂³	#103×C₆₁	1	4	yes	—
316	C₂³	#103×C₆₁	1	4	yes	—
317	C₂³	#106×C₆₁	1	2	yes	—
318	C₂³	#106×C₆₁	1	2	yes	—
319	C₂³	#107×C₆₁	1	2	yes	—
320	C₂³	#107×C₆₁	1	2	yes	—
321	C₂³	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
322	C₂³	C₂×C₄⋊C₄×C₆₁	1	1	yes	characteristic
323	C₂³	C₂×D₈×C₆₁	1	1	yes	characteristic
324	C₂³	C₂×SD₁₆×C₆₁	1	2	yes	—
325	C₂³	C₂×Q₁₆×C₆₁	1	1	yes	characteristic
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	8	no	—
344	C₂×C₄	—	4	8	no	—
345	C₂×C₄	—	4	8	no	—
346	C₂×C₄	—	8	16	no	—
347	C₂×C₄	#95×C₆₁	1	1	yes	characteristic
348	C₂×C₄	#95×C₆₁	1	2	yes	—
349	C₂×C₄	#95×C₆₁	1	1	yes	characteristic
350	C₂×C₄	#99×C₆₁	1	4	yes	—
351	C₂×C₄	C₂×C₄²×C₆₁	1	1	yes	characteristic
352	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
353	C₂×C₄	C₂×C₄⋊C₄×C₆₁	1	2	yes	—
354	C₈	—	4	4	no	—
355	C₂²	—	2	8	no	—
356	C₂²	—	2	8	no	—
357	C₂²	—	2	4	no	—
358	C₂²	—	2	4	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	4	4	no	—
368	C₂²	—	4	4	no	—
369	C₂²	—	4	2	no	—
370	C₂²	—	4	2	no	—
371	C₂²	—	4	1	no	—
372	C₂²	—	4	2	no	—
373	C₂²	—	4	1	no	—
374	C₂²	C₆₁×H(3,ℤ/4)	1	2	yes	—
375	C₂²	C₆₁×#340	1	4	yes	—
376	C₂²	C₆₁×#340	1	2	yes	—
377	C₂²	C₆₁×#340	1	2	yes	—
378	C₂²	C₆₁×#342	1	2	yes	—
379	C₂²	C₂×#95×C₆₁	1	1	yes	characteristic
380	C₂²	C₂×#102×C₆₁	1	2	yes	—
381	C₂²	C₂×#103×C₆₁	1	2	yes	—
382	C₂²	C₂×#106×C₆₁	1	1	yes	characteristic
383	C₂²	C₂×#107×C₆₁	1	1	yes	characteristic
384	C₄	—	2	1	no	—
385	C₄	—	2	2	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	2	no	—
388	C₄	—	8	8	no	—
389	C₄	C₆₁×#342	1	2	yes	—
390	C₄	C₂×#99×C₆₁	1	2	yes	—
391	C₂	—	2	2	no	—
392	C₂	—	2	4	no	—
393	C₂	—	2	2	no	—
394	C₂	—	2	2	no	—
395	C₂	—	2	1	no	—
396	C₂	—	2	1	no	—
397	C₂	C₆₁×#1289	1	4	yes	direct product factor
398	C₂	C₂×C₆₁×H(3,ℤ/4)	1	1	yes	characteristic
399	C₂	C₂×C₆₁×#340	1	1	yes	characteristic
400	C₂	C₂×C₆₁×#342	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	#95
commutator	C₂×C₄	C₂×C₄²×C₆₁
Frattini, cosocle	C₂³×C₄	C₂³×C₆₁
prime radical	C₂⁵×C₆₁	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂⁴×C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₆₁×#1289	C₂	direct (N × H)
5. C₂³×C₈×C₆₁	C₄	semidirect
10. C₂×C₂²⋊C₈×C₆₁	C₄	semidirect
14. C₆₁×#380	C₄	semidirect
16. C₂×#95×C₆₁	C₄	semidirect
33. C₂²×C₈×C₆₁	C₂×C₄	semidirect
44. #95×C₆₁	C₂×C₄	semidirect
154. C₂×#1289	C₆₁	direct (N × H)
193. #1289	C₂×C₆₁	direct (N × H)
200. C₂×C₆₁	#1289	direct (N × H)
205. C₂³×C₈	C₄×C₆₁	semidirect
210. C₂×C₂²⋊C₈	C₄×C₆₁	semidirect
214. #380	C₄×C₆₁	semidirect
216. C₂×#95	C₄×C₆₁	semidirect
217. C₆₁	C₂×#1289	direct (N × H)
234. C₂²×C₈	C₂×C₄×C₆₁	semidirect
245. #95	C₂×C₄×C₆₁	semidirect
397. C₂	C₆₁×#1289	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×C₂²⋊C₈×C₆₁	2
C₂×C₆₁×#380	2
C₆₁×#1289	2
C₂×#1289	61

Subgroups — C2×C61×#1289 #29511412

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#1289 #29511412