Subgroups — #13129856

Order 1664.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718725	C₂	1	1	yes	maximal, characteristic
2	#11718233	C₂	1	1	yes	maximal, characteristic
3	#11718233	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#125	C₄	1	1	yes	characteristic
5	#88124	C₄	1	1	yes	characteristic
6	#88106	—	2	1	no	—
7	#88106	—	2	1	no	—
8	#88048	—	2	1	no	—
9	#88047	—	2	1	no	—
10	C₄×#1055	C₂²	1	1	yes	characteristic
11	C₁₃×C₄⋊C₄	—	2	1	no	—
12	C₁₃×C₄⋊C₄	—	4	1	no	—
13	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
14	C₄⋊Dic₁₃	—	2	1	no	—
15	#6101	—	4	1	no	—
16	C₂×#1055	D₄	1	1	yes	characteristic
17	C₂×#1055	D₄	1	1	yes	characteristic
18	#6092	—	4	1	no	—
19	#6092	—	4	1	no	—
20	#1366	—	13	1	no	maximal, Sylow
21	C₂×C₄×C₁₃	—	2	1	no	—
22	C₂×C₄×C₁₃	—	4	1	no	—
23	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×Dic₁₃	—	4	1	no	—
25	#1055	SD₁₆	1	1	yes	characteristic
26	#1055	SD₁₆	1	1	yes	characteristic
27	#1055	Q₁₆	1	1	yes	characteristic
28	#1055	Q₁₆	1	1	yes	characteristic
29	#499	—	13	1	no	—
30	#364	—	13	1	no	—
31	#364	—	13	1	no	—
32	C₂²×C₁₃	#100	1	1	yes	characteristic
33	C₄×C₁₃	—	4	1	no	—
34	C₄×C₁₃	—	8	1	no	—
35	C₄×C₁₃	#103	1	1	yes	characteristic
36	C₄×C₁₃	#103	1	1	yes	characteristic
37	Dic₁₃	—	8	1	no	—
38	#125	—	13	1	no	—
39	#125	#261	1	1	yes	characteristic
40	M₃₂	—	26	1	no	—
41	M₃₂	—	26	1	no	—
42	#107	—	26	1	no	—
43	#106	—	26	1	no	—
44	C₄×C₈	—	13	1	no	—
45	C₂×C₁₃	—	2	1	no	—
46	C₂×C₁₃	#333	1	1	yes	characteristic
47	C₂×C₈	—	13	1	no	—
48	C₂×C₈	—	13	1	no	—
49	C₄⋊C₄	—	2	1	no	—
50	C₄⋊C₄	—	4	1	no	—
51	C₄⋊C₄	—	26	1	no	—
52	C₄⋊C₄	—	52	1	no	—
53	C₄²	C₂×#261	1	1	yes	characteristic
54	C₁₆	—	52	1	no	—
55	C₁₆	—	52	1	no	—
56	C₁₃	#1366	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₄	—	2	1	no	—
58	C₂×C₄	—	4	1	no	—
59	C₂×C₄	—	52	1	no	—
60	C₂×C₄	C₂²⋊#261	1	1	yes	characteristic
61	C₈	—	13	1	no	—
62	C₈	—	13	1	no	—
63	C₈	—	13	1	no	—
64	C₈	—	13	1	no	—
65	C₂²	#88121	1	1	yes	characteristic
66	C₄	—	4	1	no	—
67	C₄	—	8	1	no	—
68	C₄	—	104	1	no	—
69	C₄	#88117	1	1	yes	characteristic
70	C₄	#88117	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	#11718303	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11718303
commutator	C₄²×C₁₃	C₂×C₄
Frattini	C₄²	C₂×#261
Fitting	C₁₃×#125	C₄
socle	C₂×C₁₃	#333
prime radical	C₂²×C₁₃	#100
cosocle	C₄×#1055	C₂²
hypercenter	#125	#261
hypocenter	C₁₃	#1366
LCS	G ▷ C₄²×C₁₃ ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
56. C₁₃	#1366	semidirect

Maximal subgroups

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

subgroup	index
#11718725	2
#11718233	2
#1366	13