Subgroups — C₂×C₆₁×#1288 #29511404

Order 15616.

678 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#432	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×M₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₆₁×#383	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#1288	C₂	1	4	yes	maximal, direct product factor
5	C₂²×M₁₆×C₆₁	—	2	1	no	—
6	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
7	C₆₁×#432	—	2	1	no	—
8	C₆₁×#432	—	2	1	no	—
9	C₆₁×#432	C₄	1	2	yes	complemented
10	C₆₁×#432	C₂²	1	2	yes	—
11	C₂×C₄⋊C₈×C₆₁	—	2	1	no	—
12	C₂×C₂²⋊C₈×C₆₁	—	2	1	no	—
13	C₄×M₁₆×C₆₁	—	2	1	no	—
14	C₄×M₁₆×C₆₁	—	2	1	no	—
15	C₄×M₁₆×C₆₁	C₄	1	2	yes	complemented
16	C₄×M₁₆×C₆₁	C₂²	1	2	yes	—
17	C₂×#97×C₆₁	—	2	1	no	—
18	C₂×#97×C₆₁	C₄	1	2	yes	complemented
19	C₂×C₄×C₈×C₆₁	C₄	1	2	yes	complemented
20	C₆₁×#383	—	2	1	no	—
21	C₆₁×#383	—	2	1	no	—
22	C₆₁×#383	C₄	1	2	yes	—
23	C₆₁×#383	C₂²	1	2	yes	—
24	C₂×#95×C₆₁	—	2	1	no	—
25	C₂×#95×C₆₁	—	2	1	no	—
26	C₂×#95×C₆₁	C₄	1	2	yes	—
27	C₂³×C₄×C₆₁	—	2	2	no	—
28	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
31	C₂×M₁₆×C₆₁	—	2	8	no	—
32	C₂×M₁₆×C₆₁	—	2	2	no	—
33	C₂×M₁₆×C₆₁	—	2	2	no	—
34	C₂²×C₈×C₆₁	—	2	2	no	—
35	C₂²×C₈×C₆₁	—	2	2	no	—
36	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₆₁	Q₈	1	1	yes	characteristic
46	C₂×C₄²×C₆₁	Q₈	1	1	yes	characteristic
47	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
48	C₄⋊C₈×C₆₁	—	2	2	no	—
49	C₄⋊C₈×C₆₁	—	2	2	no	—
50	C₂²⋊C₈×C₆₁	—	2	2	no	—
51	C₂²⋊C₈×C₆₁	—	2	2	no	—
52	#97×C₆₁	—	2	2	no	—
53	#97×C₆₁	—	2	2	no	—
54	#97×C₆₁	—	2	2	no	—
55	#97×C₆₁	C₂×C₄	1	4	yes	complemented
56	C₄×C₈×C₆₁	—	2	2	no	—
57	C₄×C₈×C₆₁	C₂×C₄	1	4	yes	complemented
58	#95×C₆₁	—	2	2	no	—
59	#95×C₆₁	—	2	2	no	—
60	#95×C₆₁	—	2	2	no	—
61	#95×C₆₁	—	2	2	no	—
62	#95×C₆₁	—	2	2	no	—
63	#95×C₆₁	C₂×C₄	1	4	yes	—
64	C₂⁴×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₆₁	—	2	4	no	—
66	C₂²×C₄×C₆₁	—	2	4	no	—
67	C₂²×C₄×C₆₁	—	4	2	no	—
68	C₂²×C₄×C₆₁	—	4	2	no	—
69	C₂²×C₄×C₆₁	—	4	4	no	—
70	C₂²×C₄×C₆₁	—	4	4	no	—
71	C₂²×C₄×C₆₁	—	4	4	no	—
72	C₂²×C₄×C₆₁	C₄²	1	1	yes	characteristic
73	C₂²×C₄×C₆₁	C₄²	1	1	yes	characteristic
74	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
90	M₁₆×C₆₁	—	2	8	no	—
91	M₁₆×C₆₁	—	2	8	no	—
92	C₂×C₈×C₆₁	—	2	8	no	—
93	C₂×C₈×C₆₁	—	2	4	no	—
94	C₂×C₈×C₆₁	—	2	4	no	—
95	C₂×C₈×C₆₁	—	4	4	no	—
96	C₄²×C₆₁	C₄²	1	1	yes	characteristic
97	C₄²×C₆₁	C₄²	1	1	yes	characteristic
98	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
99	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
100	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
101	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
102	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
109	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
110	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₆₁	C₂×Q₈	1	1	yes	characteristic
112	C₂³×C₆₁	—	2	2	no	—
113	C₂³×C₆₁	—	2	2	no	—
114	C₂³×C₆₁	#95	1	1	yes	characteristic
115	C₂³×C₆₁	#95	1	1	yes	characteristic
116	C₂³×C₆₁	#104	1	4	yes	—
117	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
118	C₂×C₄×C₆₁	—	2	2	no	—
119	C₂×C₄×C₆₁	—	2	2	no	—
120	C₂×C₄×C₆₁	—	2	2	no	—
121	C₂×C₄×C₆₁	—	2	2	no	—
122	C₂×C₄×C₆₁	—	2	2	no	—
123	C₂×C₄×C₆₁	—	2	2	no	—
124	C₂×C₄×C₆₁	—	2	2	no	—
125	C₂×C₄×C₆₁	—	2	2	no	—
126	C₂×C₄×C₆₁	—	2	2	no	—
127	C₂×C₄×C₆₁	—	2	2	no	—
128	C₂×C₄×C₆₁	—	4	1	no	—
129	C₂×C₄×C₆₁	—	4	1	no	—
130	C₂×C₄×C₆₁	—	4	1	no	—
131	C₂×C₄×C₆₁	—	4	1	no	—
132	C₂×C₄×C₆₁	—	4	1	no	—
133	C₂×C₄×C₆₁	—	4	1	no	—
134	C₂×C₄×C₆₁	—	4	1	no	—
135	C₂×C₄×C₆₁	—	4	1	no	—
136	C₂×C₄×C₆₁	—	4	4	no	—
137	C₂×C₄×C₆₁	—	4	4	no	—
138	C₂×C₄×C₆₁	—	4	4	no	—
139	C₂×C₄×C₆₁	—	8	8	no	—
140	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
141	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
142	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
143	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
144	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
145	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
146	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
147	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₈×C₆₁	—	2	8	no	—
153	C₈×C₆₁	—	4	4	no	—
154	C₂×#1288	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂²×C₆₁	—	2	8	no	—
156	C₂²×C₆₁	—	2	1	no	—
157	C₂²×C₆₁	—	2	1	no	—
158	C₂²×C₆₁	—	2	1	no	—
159	C₂²×C₆₁	—	2	1	no	—
160	C₂²×C₆₁	H(3,ℤ/4)	1	2	yes	—
161	C₂²×C₆₁	#339	1	2	yes	—
162	C₂²×C₆₁	#339	1	2	yes	—
163	C₂²×C₆₁	#344	1	2	yes	—
164	C₂²×C₆₁	C₂×#95	1	1	yes	characteristic
165	C₂²×C₆₁	C₂×#104	1	2	yes	—
166	C₄×C₆₁	—	2	1	no	—
167	C₄×C₆₁	—	2	1	no	—
168	C₄×C₆₁	—	2	1	no	—
169	C₄×C₆₁	—	2	1	no	—
170	C₄×C₆₁	—	2	1	no	—
171	C₄×C₆₁	—	2	1	no	—
172	C₄×C₆₁	—	2	1	no	—
173	C₄×C₆₁	—	2	1	no	—
174	C₄×C₆₁	—	2	1	no	—
175	C₄×C₆₁	—	2	1	no	—
176	C₄×C₆₁	—	2	1	no	—
177	C₄×C₆₁	—	2	1	no	—
178	C₄×C₆₁	—	8	4	no	—
179	C₂×#432	C₂×C₆₁	1	1	yes	characteristic
180	C₂×C₄×M₁₆	C₂×C₆₁	1	1	yes	characteristic
181	C₂×#383	C₂×C₆₁	1	1	yes	characteristic
182	#1288	C₂×C₆₁	1	4	yes	direct product factor
183	C₂×C₆₁	—	2	2	no	—
184	C₂×C₆₁	—	2	2	no	—
185	C₂×C₆₁	#1288	1	4	yes	direct product factor
186	C₂×C₆₁	C₂×H(3,ℤ/4)	1	1	yes	characteristic
187	C₂×C₆₁	C₂×#339	1	1	yes	characteristic
188	C₂×C₆₁	C₂×#344	1	1	yes	characteristic
189	C₂²×M₁₆	—	2	1	no	—
190	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
191	#432	—	2	1	no	—
192	#432	—	2	1	no	—
193	#432	C₄×C₆₁	1	2	yes	complemented
194	#432	C₂²×C₆₁	1	2	yes	—
195	C₂×C₄⋊C₈	—	2	1	no	—
196	C₂×C₂²⋊C₈	—	2	1	no	—
197	C₄×M₁₆	—	2	1	no	—
198	C₄×M₁₆	—	2	1	no	—
199	C₄×M₁₆	C₄×C₆₁	1	2	yes	complemented
200	C₄×M₁₆	C₂²×C₆₁	1	2	yes	—
201	C₂×#97	—	2	1	no	—
202	C₂×#97	C₄×C₆₁	1	2	yes	complemented
203	C₂×C₄×C₈	C₄×C₆₁	1	2	yes	complemented
204	#383	—	2	1	no	—
205	#383	—	2	1	no	—
206	#383	C₄×C₆₁	1	2	yes	—
207	#383	C₂²×C₆₁	1	2	yes	—
208	C₂×#95	—	2	1	no	—
209	C₂×#95	—	2	1	no	—
210	C₂×#95	C₄×C₆₁	1	2	yes	—
211	C₆₁	C₂×#1288	1	1	yes	characteristic, direct product factor, Sylow
212	C₂³×C₄	—	2	2	no	—
213	C₂³×C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
214	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
215	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
216	C₂×M₁₆	—	2	8	no	—
217	C₂×M₁₆	—	2	2	no	—
218	C₂×M₁₆	—	2	2	no	—
219	C₂²×C₈	—	2	2	no	—
220	C₂²×C₈	—	2	2	no	—
221	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
222	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
223	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
224	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
225	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
226	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
227	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
228	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
229	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
230	C₂×C₄²	Q₈×C₆₁	1	1	yes	characteristic
231	C₂×C₄²	Q₈×C₆₁	1	1	yes	characteristic
232	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
233	C₄⋊C₈	—	2	2	no	—
234	C₄⋊C₈	—	2	2	no	—
235	C₂²⋊C₈	—	2	2	no	—
236	C₂²⋊C₈	—	2	2	no	—
237	#97	—	2	2	no	—
238	#97	—	2	2	no	—
239	#97	—	2	2	no	—
240	#97	C₂×C₄×C₆₁	1	4	yes	complemented
241	C₄×C₈	—	2	2	no	—
242	C₄×C₈	C₂×C₄×C₆₁	1	4	yes	complemented
243	#95	—	2	2	no	—
244	#95	—	2	2	no	—
245	#95	—	2	2	no	—
246	#95	—	2	2	no	—
247	#95	—	2	2	no	—
248	#95	C₂×C₄×C₆₁	1	4	yes	—
249	C₂⁴	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	4	2	no	—
253	C₂²×C₄	—	4	2	no	—
254	C₂²×C₄	—	4	4	no	—
255	C₂²×C₄	—	4	4	no	—
256	C₂²×C₄	—	4	4	no	—
257	C₂²×C₄	C₄²×C₆₁	1	1	yes	characteristic
258	C₂²×C₄	C₄²×C₆₁	1	1	yes	characteristic
259	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
260	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
261	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
262	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
263	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
264	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
265	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
266	C₂²×C₄	C₄⋊C₄×C₆₁	1	1	yes	characteristic
267	C₂²×C₄	C₄⋊C₄×C₆₁	1	1	yes	characteristic
268	C₂²×C₄	C₄⋊C₄×C₆₁	1	1	yes	characteristic
269	C₂²×C₄	C₄⋊C₄×C₆₁	1	1	yes	characteristic
270	C₂²×C₄	C₄⋊C₄×C₆₁	1	1	yes	characteristic
271	C₂²×C₄	C₄⋊C₄×C₆₁	1	1	yes	characteristic
272	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
274	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
275	M₁₆	—	2	8	no	—
276	M₁₆	—	2	8	no	—
277	C₂×C₈	—	2	8	no	—
278	C₂×C₈	—	2	4	no	—
279	C₂×C₈	—	2	4	no	—
280	C₂×C₈	—	4	4	no	—
281	C₄²	C₄²×C₆₁	1	1	yes	characteristic
282	C₄²	C₄²×C₆₁	1	1	yes	characteristic
283	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
284	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
285	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
286	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
287	C₄²	C₄⋊C₄×C₆₁	1	1	yes	characteristic
288	C₄²	C₄⋊C₄×C₆₁	1	1	yes	characteristic
289	C₄²	C₄⋊C₄×C₆₁	1	1	yes	characteristic
290	C₄²	C₄⋊C₄×C₆₁	1	1	yes	characteristic
291	C₄²	C₄⋊C₄×C₆₁	1	1	yes	characteristic
292	C₄²	C₄⋊C₄×C₆₁	1	1	yes	characteristic
293	C₄²	C₂²×C₄×C₆₁	1	1	yes	characteristic
294	C₄²	C₂²×C₄×C₆₁	1	1	yes	characteristic
295	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
296	C₄²	C₂×Q₈×C₆₁	1	1	yes	characteristic
297	C₂³	—	2	2	no	—
298	C₂³	—	2	2	no	—
299	C₂³	#95×C₆₁	1	1	yes	characteristic
300	C₂³	#95×C₆₁	1	1	yes	characteristic
301	C₂³	#104×C₆₁	1	4	yes	—
302	C₂³	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	4	1	no	—
314	C₂×C₄	—	4	1	no	—
315	C₂×C₄	—	4	1	no	—
316	C₂×C₄	—	4	1	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	1	no	—
319	C₂×C₄	—	4	1	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	—	4	4	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	—	8	8	no	—
325	C₂×C₄	#95×C₆₁	1	1	yes	characteristic
326	C₂×C₄	#95×C₆₁	1	1	yes	characteristic
327	C₂×C₄	#95×C₆₁	1	1	yes	characteristic
328	C₂×C₄	#95×C₆₁	1	1	yes	characteristic
329	C₂×C₄	#95×C₆₁	1	1	yes	characteristic
330	C₂×C₄	#95×C₆₁	1	1	yes	characteristic
331	C₂×C₄	C₂×C₄²×C₆₁	1	1	yes	characteristic
332	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
333	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
334	C₂×C₄	C₂×C₄⋊C₄×C₆₁	1	1	yes	characteristic
335	C₂×C₄	C₂×C₄⋊C₄×C₆₁	1	1	yes	characteristic
336	C₂×C₄	C₂×C₄⋊C₄×C₆₁	1	1	yes	characteristic
337	C₈	—	2	8	no	—
338	C₈	—	4	4	no	—
339	C₂²	—	2	8	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	C₆₁×H(3,ℤ/4)	1	2	yes	—
345	C₂²	C₆₁×#339	1	2	yes	—
346	C₂²	C₆₁×#339	1	2	yes	—
347	C₂²	C₆₁×#344	1	2	yes	—
348	C₂²	C₂×#95×C₆₁	1	1	yes	characteristic
349	C₂²	C₂×#104×C₆₁	1	2	yes	—
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	8	4	no	—
363	C₂	—	2	2	no	—
364	C₂	—	2	2	no	—
365	C₂	C₆₁×#1288	1	4	yes	direct product factor
366	C₂	C₂×C₆₁×H(3,ℤ/4)	1	1	yes	characteristic
367	C₂	C₂×C₆₁×#339	1	1	yes	characteristic
368	C₂	C₂×C₆₁×#344	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	#95
commutator	C₂×C₄	C₂×C₄²×C₆₁
Frattini, cosocle	C₂×C₄²	C₂³×C₆₁
prime radical	C₂⁴×C₆₁	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂²×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₆₁×#1288	C₂	direct (N × H)
9. C₆₁×#432	C₄	semidirect
15. C₄×M₁₆×C₆₁	C₄	semidirect
18. C₂×#97×C₆₁	C₄	semidirect
19. C₂×C₄×C₈×C₆₁	C₄	semidirect
55. #97×C₆₁	C₂×C₄	semidirect
57. C₄×C₈×C₆₁	C₂×C₄	semidirect
154. C₂×#1288	C₆₁	direct (N × H)
182. #1288	C₂×C₆₁	direct (N × H)
185. C₂×C₆₁	#1288	direct (N × H)
193. #432	C₄×C₆₁	semidirect
199. C₄×M₁₆	C₄×C₆₁	semidirect
202. C₂×#97	C₄×C₆₁	semidirect
203. C₂×C₄×C₈	C₄×C₆₁	semidirect
211. C₆₁	C₂×#1288	direct (N × H)
240. #97	C₂×C₄×C₆₁	semidirect
242. C₄×C₈	C₂×C₄×C₆₁	semidirect
365. C₂	C₆₁×#1288	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#432	2
C₂×C₄×M₁₆×C₆₁	2
C₂×C₆₁×#383	2
C₆₁×#1288	2
C₂×#1288	61

Subgroups — C2×C61×#1288 #29511404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#1288 #29511404