Subgroups — C₁₃×#8960 #15695299

Order 3328.

566 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2982	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₁₃×#124	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1478	C₂	1	2	yes	maximal
4	C₁₃×#1461	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1276	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#124	C₄	1	1	yes	characteristic
7	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
9	C₈×Q₈×C₁₃	—	2	4	no	—
10	C₁₃×#431	—	2	2	no	—
11	C₁₃×#431	C₂²	1	2	yes	—
12	C₁₃×#431	C₂²	1	2	yes	—
13	C₁₃×#391	C₄	1	1	yes	characteristic
14	C₁₃×#390	C₄	1	1	yes	characteristic
15	C₁₃×#388	—	2	2	no	—
16	C₁₃×#382	C₄	1	1	yes	characteristic
17	C₄×C₁₃×C₂²⋊C₄	—	2	2	no	—
18	C₄³×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×D₄⋊C₈	—	2	4	no	—
20	C₁₃×#324	—	2	2	no	—
21	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₃	—	2	1	no	—
24	C₁₃×#124	—	2	2	no	—
25	C₁₃×#124	C₈	1	4	yes	complemented
26	C₄×Q₈×C₁₃	—	2	2	no	—
27	C₄×Q₈×C₁₃	—	2	2	no	—
28	C₄×D₄×C₁₃	—	2	2	no	—
29	C₄×D₄×C₁₃	—	2	2	no	—
30	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
31	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
32	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
33	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
34	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
35	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
36	C₂×C₄²×C₁₃	—	2	1	no	—
37	C₂×C₄²×C₁₃	—	2	1	no	—
38	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₃	D₄	1	2	yes	—
41	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
42	C₁₃×C₄⋊C₈	—	2	4	no	—
43	C₁₃×C₄⋊C₈	—	2	2	no	—
44	C₁₃×C₄⋊C₈	D₄	1	4	yes	—
45	C₁₃×C₂²⋊C₈	—	2	2	no	—
46	C₁₃×C₂²⋊C₈	—	2	2	no	—
47	C₄×C₈×C₁₃	—	2	4	no	—
48	C₄×C₈×C₁₃	—	2	2	no	—
49	C₄×C₈×C₁₃	—	2	2	no	—
50	C₁₃×#95	—	2	2	no	—
51	C₁₃×#95	—	2	2	no	—
52	#8960	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
53	C₂⁴×C₁₃	—	2	1	no	—
54	C₂×Q₈×C₁₃	—	2	2	no	—
55	C₂×Q₈×C₁₃	—	2	2	no	—
56	C₂×Q₈×C₁₃	C₂×C₈	1	2	yes	—
57	C₂×Q₈×C₁₃	M₁₆	1	2	yes	—
58	C₂×D₄×C₁₃	—	2	2	no	—
59	C₂×D₄×C₁₃	—	2	1	no	—
60	C₂×D₄×C₁₃	—	2	2	no	—
61	C₂×D₄×C₁₃	C₂×C₈	1	2	yes	—
62	C₂²×C₄×C₁₃	—	2	1	no	—
63	C₂²×C₄×C₁₃	—	2	1	no	—
64	C₂²×C₄×C₁₃	—	2	1	no	—
65	C₂²×C₄×C₁₃	—	4	4	no	—
66	C₂²×C₄×C₁₃	—	4	1	no	—
67	C₂²×C₄×C₁₃	—	4	1	no	—
68	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
69	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
70	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
73	C₂×C₈×C₁₃	—	2	4	no	—
74	C₂×C₈×C₁₃	—	4	2	no	—
75	C₁₃×C₄⋊C₄	—	2	2	no	—
76	C₁₃×C₄⋊C₄	—	2	4	no	—
77	C₁₃×C₄⋊C₄	—	2	2	no	—
78	C₁₃×C₂²⋊C₄	—	2	8	no	—
79	C₁₃×C₂²⋊C₄	—	4	4	no	—
80	C₁₃×C₂²⋊C₄	—	4	2	no	—
81	C₄²×C₁₃	—	2	2	no	—
82	C₄²×C₁₃	—	2	2	no	—
83	C₄²×C₁₃	—	2	1	no	—
84	C₄²×C₁₃	—	2	2	no	—
85	C₄²×C₁₃	—	4	2	no	—
86	C₄²×C₁₃	—	4	2	no	—
87	C₄²×C₁₃	C₂×C₈	1	2	yes	—
88	C₄²×C₁₃	C₂×D₄	1	2	yes	—
89	C₄²×C₁₃	#41	1	2	yes	—
90	#2982	C₂×C₁₃	1	1	yes	characteristic, complemented
91	C₄×#124	C₂×C₁₃	1	1	yes	characteristic
92	#1478	C₂×C₁₃	1	2	yes	—
93	#1461	C₂×C₁₃	1	1	yes	characteristic, complemented
94	#1276	C₂×C₁₃	1	2	yes	complemented
95	C₂³×C₁₃	—	2	2	no	—
96	C₂³×C₁₃	—	4	2	no	—
97	C₂³×C₁₃	—	4	2	no	—
98	C₂³×C₁₃	—	4	1	no	—
99	C₂³×C₁₃	—	4	1	no	—
100	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
101	Q₈×C₁₃	—	2	4	no	—
102	Q₈×C₁₃	—	2	4	no	—
103	D₄×C₁₃	—	2	4	no	—
104	D₄×C₁₃	—	4	2	no	—
105	C₂×C₄×C₁₃	—	2	2	no	—
106	C₂×C₄×C₁₃	—	2	2	no	—
107	C₂×C₄×C₁₃	—	2	2	no	—
108	C₂×C₄×C₁₃	—	2	2	no	—
109	C₂×C₄×C₁₃	—	2	2	no	—
110	C₂×C₄×C₁₃	—	2	2	no	—
111	C₂×C₄×C₁₃	—	4	1	no	—
112	C₂×C₄×C₁₃	—	4	1	no	—
113	C₂×C₄×C₁₃	—	4	1	no	—
114	C₂×C₄×C₁₃	—	4	1	no	—
115	C₂×C₄×C₁₃	—	4	1	no	—
116	C₂×C₄×C₁₃	—	4	2	no	—
117	C₂×C₄×C₁₃	—	4	2	no	—
118	C₂×C₄×C₁₃	—	4	1	no	—
119	C₂×C₄×C₁₃	—	8	2	no	—
120	C₂×C₄×C₁₃	—	8	2	no	—
121	C₂×C₄×C₁₃	C₂²⋊C₈	1	4	yes	—
122	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
123	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
124	C₂×C₄×C₁₃	#121	1	2	yes	—
125	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
126	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
127	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
128	C₂×C₄×C₁₃	#131	1	2	yes	—
129	C₈×C₁₃	—	4	4	no	—
130	C₈×C₁₃	—	8	2	no	—
131	C₂×#124	C₄×C₁₃	1	1	yes	characteristic
132	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
133	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
134	C₈×Q₈	—	2	4	no	—
135	#431	—	2	2	no	—
136	#431	C₂²×C₁₃	1	2	yes	—
137	#431	C₂²×C₁₃	1	2	yes	—
138	#391	C₄×C₁₃	1	1	yes	characteristic
139	#390	C₄×C₁₃	1	1	yes	characteristic
140	#388	—	2	2	no	—
141	#382	C₄×C₁₃	1	1	yes	characteristic
142	C₄×C₂²⋊C₄	—	2	2	no	—
143	C₄³	C₂²×C₁₃	1	1	yes	characteristic
144	D₄⋊C₈	—	2	4	no	—
145	#324	—	2	2	no	—
146	C₂²×C₁₃	—	2	1	no	—
147	C₂²×C₁₃	—	2	1	no	—
148	C₂²×C₁₃	—	4	4	no	—
149	C₂²×C₁₃	—	4	2	no	—
150	C₂²×C₁₃	—	8	2	no	—
151	C₂²×C₁₃	—	8	1	no	—
152	C₂²×C₁₃	—	8	1	no	—
153	C₂²×C₁₃	#386	1	1	yes	characteristic
154	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
155	C₂²×C₁₃	#408	1	1	yes	characteristic
156	C₄×C₁₃	—	2	4	no	—
157	C₄×C₁₃	—	2	2	no	—
158	C₄×C₁₃	—	2	1	no	—
159	C₄×C₁₃	—	4	2	no	—
160	C₄×C₁₃	—	4	2	no	—
161	C₄×C₁₃	—	4	2	no	—
162	C₄×C₁₃	—	8	1	no	—
163	C₄×C₁₃	C₈×D₄	1	2	yes	—
164	C₄×C₁₃	#435	1	2	yes	—
165	C₄×C₁₃	#454	1	2	yes	—
166	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
167	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
168	C₂³×C₄	—	2	1	no	—
169	#124	—	2	2	no	—
170	#124	C₈×C₁₃	1	4	yes	complemented
171	C₄×Q₈	—	2	2	no	—
172	C₄×Q₈	—	2	2	no	—
173	C₄×D₄	—	2	2	no	—
174	C₄×D₄	—	2	2	no	—
175	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
176	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
177	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
178	C₂×C₂²⋊C₄	—	2	2	no	—
179	C₂×C₂²⋊C₄	—	2	2	no	—
180	C₂×C₂²⋊C₄	—	2	1	no	—
181	C₂×C₄²	—	2	1	no	—
182	C₂×C₄²	—	2	1	no	—
183	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
184	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
185	C₂×C₄²	D₄×C₁₃	1	2	yes	—
186	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
187	C₄⋊C₈	—	2	4	no	—
188	C₄⋊C₈	—	2	2	no	—
189	C₄⋊C₈	D₄×C₁₃	1	4	yes	—
190	C₂²⋊C₈	—	2	2	no	—
191	C₂²⋊C₈	—	2	2	no	—
192	C₄×C₈	—	2	4	no	—
193	C₄×C₈	—	2	2	no	—
194	C₄×C₈	—	2	2	no	—
195	#95	—	2	2	no	—
196	#95	—	2	2	no	—
197	C₂×C₁₃	—	2	1	no	—
198	C₂×C₁₃	—	2	1	no	—
199	C₂×C₁₃	—	8	2	no	—
200	C₂×C₁₃	#1869	1	1	yes	characteristic
201	C₂×C₁₃	#1884	1	1	yes	characteristic
202	C₂×C₁₃	#1888	1	1	yes	characteristic
203	C₂⁴	—	2	1	no	—
204	C₂×Q₈	—	2	2	no	—
205	C₂×Q₈	—	2	2	no	—
206	C₂×Q₈	C₂×C₈×C₁₃	1	2	yes	—
207	C₂×Q₈	C₁₃×M₁₆	1	2	yes	—
208	C₂×D₄	—	2	2	no	—
209	C₂×D₄	—	2	1	no	—
210	C₂×D₄	—	2	2	no	—
211	C₂×D₄	C₂×C₈×C₁₃	1	2	yes	—
212	C₂²×C₄	—	2	1	no	—
213	C₂²×C₄	—	2	1	no	—
214	C₂²×C₄	—	2	1	no	—
215	C₂²×C₄	—	4	4	no	—
216	C₂²×C₄	—	4	1	no	—
217	C₂²×C₄	—	4	1	no	—
218	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
219	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
220	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
221	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
222	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
223	C₂×C₈	—	2	4	no	—
224	C₂×C₈	—	4	2	no	—
225	C₄⋊C₄	—	2	2	no	—
226	C₄⋊C₄	—	2	4	no	—
227	C₄⋊C₄	—	2	2	no	—
228	C₂²⋊C₄	—	2	8	no	—
229	C₂²⋊C₄	—	4	4	no	—
230	C₂²⋊C₄	—	4	2	no	—
231	C₄²	—	2	2	no	—
232	C₄²	—	2	2	no	—
233	C₄²	—	2	1	no	—
234	C₄²	—	2	2	no	—
235	C₄²	—	4	2	no	—
236	C₄²	—	4	2	no	—
237	C₄²	C₂×C₈×C₁₃	1	2	yes	—
238	C₄²	C₂×D₄×C₁₃	1	2	yes	—
239	C₄²	C₁₃×#41	1	2	yes	—
240	C₁₃	#8960	1	1	yes	characteristic, direct product factor, Sylow
241	C₂³	—	2	2	no	—
242	C₂³	—	4	2	no	—
243	C₂³	—	4	2	no	—
244	C₂³	—	4	1	no	—
245	C₂³	—	4	1	no	—
246	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
247	Q₈	—	2	4	no	—
248	Q₈	—	2	4	no	—
249	D₄	—	2	4	no	—
250	D₄	—	4	2	no	—
251	C₂×C₄	—	2	2	no	—
252	C₂×C₄	—	2	2	no	—
253	C₂×C₄	—	2	2	no	—
254	C₂×C₄	—	2	2	no	—
255	C₂×C₄	—	2	2	no	—
256	C₂×C₄	—	2	2	no	—
257	C₂×C₄	—	4	1	no	—
258	C₂×C₄	—	4	1	no	—
259	C₂×C₄	—	4	1	no	—
260	C₂×C₄	—	4	1	no	—
261	C₂×C₄	—	4	1	no	—
262	C₂×C₄	—	4	2	no	—
263	C₂×C₄	—	4	2	no	—
264	C₂×C₄	—	4	1	no	—
265	C₂×C₄	—	8	2	no	—
266	C₂×C₄	—	8	2	no	—
267	C₂×C₄	C₁₃×C₂²⋊C₈	1	4	yes	—
268	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
269	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
270	C₂×C₄	C₁₃×#121	1	2	yes	—
271	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
272	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
273	C₂×C₄	C₂×C₁₃×M₁₆	1	1	yes	characteristic
274	C₂×C₄	C₁₃×#131	1	2	yes	—
275	C₈	—	4	4	no	—
276	C₈	—	8	2	no	—
277	C₂²	—	2	1	no	—
278	C₂²	—	2	1	no	—
279	C₂²	—	4	4	no	—
280	C₂²	—	4	2	no	—
281	C₂²	—	8	2	no	—
282	C₂²	—	8	1	no	—
283	C₂²	—	8	1	no	—
284	C₂²	C₁₃×#386	1	1	yes	characteristic
285	C₂²	C₂×C₁₃×C₂²⋊C₈	1	1	yes	characteristic
286	C₂²	C₁₃×#408	1	1	yes	characteristic
287	C₄	—	2	4	no	—
288	C₄	—	2	2	no	—
289	C₄	—	2	1	no	—
290	C₄	—	4	2	no	—
291	C₄	—	4	2	no	—
292	C₄	—	4	2	no	—
293	C₄	—	8	1	no	—
294	C₄	C₈×D₄×C₁₃	1	2	yes	—
295	C₄	C₁₃×#435	1	2	yes	—
296	C₄	C₁₃×#454	1	2	yes	—
297	C₂	—	2	1	no	—
298	C₂	—	2	1	no	—
299	C₂	—	8	2	no	—
300	C₂	C₁₃×#1869	1	1	yes	characteristic
301	C₂	C₁₃×#1884	1	1	yes	characteristic
302	C₂	C₁₃×#1888	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	#120
commutator	C₂×C₄	C₂²×C₈×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
socle	C₂²×C₁₃	#386
prime radical	C₂²×D₄×C₁₃	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2982	C₂	semidirect
4. C₁₃×#1461	C₂	semidirect
5. C₁₃×#1276	C₂	semidirect
25. C₁₃×#124	C₈	semidirect
52. #8960	C₁₃	direct (N × H)
90. #2982	C₂×C₁₃	semidirect
93. #1461	C₂×C₁₃	semidirect
94. #1276	C₂×C₁₃	semidirect
170. #124	C₈×C₁₃	semidirect
240. C₁₃	#8960	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2982	2
C₄×C₁₃×#124	2
C₁₃×#1478	2
C₁₃×#1461	2
C₁₃×#1276	2
#8960	13

Subgroups — C13×#8960 #15695299

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#8960 #15695299