Subgroups — C₁₃×#1020 #11929330

Order 1248.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₂²⋊A₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#120	—	3	1	no	maximal, Hall
3	C₁₃×S₄	—	4	3	no	maximal
4	C₂⁴×C₁₃	D₃	1	1	yes	characteristic, complemented
5	C₂×D₄×C₁₃	—	3	3	no	—
6	C₁₃×C₂²⋊C₄	—	3	3	no	—
7	A₄×C₁₃	—	4	3	no	—
8	A₄×C₁₃	—	8	1	no	—
9	C₂³×C₁₃	—	3	3	no	—
10	C₂³×C₁₃	—	3	1	no	—
11	C₂³×C₁₃	—	6	1	no	—
12	D₄×C₁₃	—	6	3	no	—
13	D₄×C₁₃	—	6	3	no	—
14	C₂×C₄×C₁₃	—	3	3	no	—
15	#1020	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
16	D₃×C₁₃	—	16	1	no	—
17	C₂²×C₁₃	—	2	1	no	—
18	C₂²×C₁₃	—	3	1	no	—
19	C₂²×C₁₃	—	3	3	no	—
20	C₂²×C₁₃	—	6	3	no	—
21	C₂²×C₁₃	—	6	3	no	—
22	C₂²×C₁₃	S₄	1	3	yes	complemented
23	C₄×C₁₃	—	6	3	no	—
24	C₂²⋊A₄	C₂×C₁₃	1	1	yes	characteristic, complemented
25	C₃×C₁₃	—	16	1	no	Hall
26	#120	—	3	1	no	Sylow
27	C₂×C₁₃	—	3	3	no	—
28	C₂×C₁₃	—	6	1	no	—
29	C₂×C₁₃	—	12	1	no	—
30	S₄	—	4	3	no	—
31	C₂⁴	D₃×C₁₃	1	1	yes	characteristic, complemented
32	C₂×D₄	—	3	3	no	—
33	C₂²⋊C₄	—	3	3	no	—
34	C₁₃	#1020	1	1	yes	characteristic, direct product factor, Sylow
35	A₄	—	4	3	no	—
36	A₄	—	8	1	no	—
37	C₂³	—	3	3	no	—
38	C₂³	—	3	1	no	—
39	C₂³	—	6	1	no	—
40	D₄	—	6	3	no	—
41	D₄	—	6	3	no	—
42	C₂×C₄	—	3	3	no	—
43	D₃	—	16	1	no	—
44	C₂²	—	2	1	no	—
45	C₂²	—	3	1	no	—
46	C₂²	—	3	3	no	—
47	C₂²	—	6	3	no	—
48	C₂²	—	6	3	no	—
49	C₂²	C₁₃×S₄	1	3	yes	complemented
50	C₄	—	6	3	no	—
51	C₃	—	16	1	no	Sylow
52	C₂	—	3	3	no	—
53	C₂	—	6	1	no	—
54	C₂	—	12	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	#1020
commutator, cosocle, hypocenter	C₂²⋊A₄	C₂×C₁₃
Frattini	C₁	G
Fitting, socle	C₂⁴×C₁₃	D₃
LCS	G ▷ C₂²⋊A₄
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₂²⋊A₄	C₂	semidirect
4. C₂⁴×C₁₃	D₃	semidirect
15. #1020	C₁₃	direct (N × H)
22. C₂²×C₁₃	S₄	semidirect
24. C₂²⋊A₄	C₂×C₁₃	semidirect
31. C₂⁴	D₃×C₁₃	semidirect
34. C₁₃	#1020	direct (N × H)
49. C₂²	C₁₃×S₄	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×C₂²⋊A₄	2
C₁₃×#120	3
C₁₃×S₄	4
#1020	13

Subgroups — C13×#1020 #11929330

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#1020 #11929330