Subgroups — #13114588

Order 1664.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#376	C₂	1	1	yes	maximal, characteristic
2	C₂×#88043	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#1055	C₂	1	1	yes	maximal, characteristic
4	#11718116	C₂	1	4	yes	maximal
5	C₂×C₄²×C₁₃	C₂²	1	2	yes	—
6	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×#1055	C₂²	1	2	yes	—
8	C₂²×#1055	C₂²	1	2	yes	—
9	C₁₃×#95	C₄	1	4	yes	—
10	#88043	C₄	1	4	yes	complemented
11	C₄×#1055	C₄	1	4	yes	complemented
12	C₂²×C₄×C₁₃	C₂×C₄	1	4	yes	—
13	C₂²×C₄×C₁₃	C₂×C₄	1	2	yes	—
14	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
15	C₄²×C₁₃	—	2	4	no	—
16	C₄²×C₁₃	C₂×C₄	1	2	yes	—
17	C₄²×C₁₃	C₂×C₄	1	2	yes	—
18	C₂×#1055	—	2	4	no	—
19	C₂×#1055	—	2	4	no	—
20	C₂×#1055	C₂×C₄	1	4	yes	—
21	C₂×#1055	C₂×C₄	1	4	yes	—
22	#1746	—	13	1	no	maximal, Sylow
23	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
24	C₂×C₄×C₁₃	—	2	4	no	—
25	C₂×C₄×C₁₃	—	2	4	no	—
26	C₂×C₄×C₁₃	—	2	8	no	—
27	C₂×C₄×C₁₃	C₄²	1	4	yes	—
28	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₄×C₁₃	#41	1	4	yes	—
31	#1055	—	2	4	no	—
32	#1055	—	2	4	no	—
33	C₂×#97	—	13	1	no	—
34	C₂×C₄×C₈	—	13	1	no	—
35	#376	D₁₃	1	1	yes	characteristic
36	#336	—	13	4	no	—
37	C₂²×C₁₃	C₂×C₄²	1	1	yes	characteristic
38	C₂²×C₁₃	#117	1	2	yes	—
39	C₂²×C₁₃	#131	1	4	yes	—
40	C₄×C₁₃	—	2	4	no	—
41	C₄×C₁₃	—	4	4	no	—
42	C₄×C₁₃	#117	1	2	yes	—
43	C₄×C₁₃	#117	1	2	yes	—
44	C₂²×C₈	—	13	2	no	—
45	C₂²×C₈	—	13	2	no	—
46	C₂×C₄²	C₂×D₁₃	1	2	yes	—
47	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
48	#97	—	13	4	no	—
49	C₄×C₈	—	13	4	no	—
50	#95	Dic₁₃	1	4	yes	—
51	C₂×C₁₃	#376	1	1	yes	characteristic
52	C₂×C₁₃	#405	1	2	yes	—
53	C₂×C₁₃	#433	1	4	yes	—
54	C₂²×C₄	C₂×Dic₁₃	1	4	yes	—
55	C₂²×C₄	C₂×Dic₁₃	1	2	yes	—
56	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
57	C₂×C₈	—	13	4	no	—
58	C₂×C₈	—	13	4	no	—
59	C₂×C₈	—	26	4	no	—
60	C₂×C₈	—	26	4	no	—
61	C₄²	—	2	4	no	—
62	C₄²	C₄×D₁₃	1	2	yes	—
63	C₄²	C₄×D₁₃	1	2	yes	—
64	C₁₃	#1746	1	1	yes	characteristic, complemented, Sylow
65	C₂³	C₂²×Dic₁₃	1	1	yes	characteristic
66	C₂×C₄	—	2	4	no	—
67	C₂×C₄	—	2	4	no	—
68	C₂×C₄	—	2	8	no	—
69	C₂×C₄	C₄×Dic₁₃	1	4	yes	—
70	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
71	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
72	C₂×C₄	#6127	1	4	yes	—
73	C₈	—	26	4	no	—
74	C₈	—	26	4	no	—
75	C₂²	C₂×C₄×Dic₁₃	1	1	yes	characteristic
76	C₂²	#88180	1	2	yes	—
77	C₂²	#88202	1	4	yes	—
78	C₄	—	2	4	no	—
79	C₄	—	4	4	no	—
80	C₄	#88126	1	2	yes	—
81	C₄	#88126	1	2	yes	—
82	C₂	#11718593	1	1	yes	characteristic
83	C₂	#11718658	1	2	yes	—
84	C₂	#11718661	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₃
commutator	C₂²×C₁₃	C₂×C₄²
Fitting	C₁₃×#376	C₂
socle, prime radical	C₂³×C₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂³
hypercenter	#376	D₁₃
hypocenter	C₁₃	#1746
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #376

Complements

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

N	H ≅ G/N	type
10. #88043	C₄	semidirect
11. C₄×#1055	C₄	semidirect
64. C₁₃	#1746	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#376	2
C₂×#88043	2
C₂×C₄×#1055	2
#11718116	2
#1746	13