Subgroups — C₁₃×#131⋊C₃ #11928749

Order 1248.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#41⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#131	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃×SL(2,𝔽₃)	C₄	1	1	yes	characteristic
4	C₃×C₈×C₁₃	—	4	1	no	maximal
5	C₁₃×#41	C₂×C₃	1	1	yes	characteristic
6	C₁₃×M₁₆	—	3	1	no	—
7	C₂×C₈×C₁₃	—	3	1	no	—
8	C₃×C₄×C₁₃	—	4	1	no	—
9	Q₈×C₁₃	C₃×C₄	1	1	yes	characteristic
10	D₄×C₁₃	—	3	1	no	—
11	C₂×C₄×C₁₃	—	3	1	no	—
12	C₈×C₁₃	—	3	1	no	—
13	C₈×C₁₃	A₄	1	1	yes	characteristic
14	#131⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₃×C₁₃	—	4	1	no	—
16	C₂²×C₁₃	—	3	1	no	—
17	C₄×C₁₃	—	3	1	no	—
18	C₄×C₁₃	C₂×A₄	1	1	yes	characteristic
19	#41⋊C₃	C₂×C₁₃	1	1	yes	characteristic
20	C₃×C₁₃	—	4	1	no	Hall
21	#131	C₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₁₃	—	6	1	no	—
23	C₂×C₁₃	C₄×A₄	1	1	yes	characteristic
24	SL(2,𝔽₃)	C₄×C₁₃	1	1	yes	characteristic
25	C₃×C₈	—	4	1	no	—
26	#41	C₂×C₃×C₁₃	1	1	yes	characteristic
27	M₁₆	—	3	1	no	—
28	C₂×C₈	—	3	1	no	—
29	C₁₃	#131⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
30	C₃×C₄	—	4	1	no	—
31	Q₈	C₃×C₄×C₁₃	1	1	yes	characteristic
32	D₄	—	3	1	no	—
33	C₂×C₄	—	3	1	no	—
34	C₈	—	3	1	no	—
35	C₈	A₄×C₁₃	1	1	yes	characteristic
36	C₂×C₃	—	4	1	no	—
37	C₂²	—	3	1	no	—
38	C₄	—	3	1	no	—
39	C₄	C₂×A₄×C₁₃	1	1	yes	characteristic
40	C₃	—	4	1	no	Sylow
41	C₂	—	6	1	no	—
42	C₂	C₄×A₄×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₈×C₁₃	A₄
commutator, hypocenter	Q₈	C₃×C₄×C₁₃
Frattini	C₄	C₂×A₄×C₁₃
Fitting	C₁₃×#131	C₃
socle	C₂×C₁₃	C₄×A₄
prime radical	C₁₃×#41⋊C₃	C₂
cosocle	#41	C₂×C₃×C₁₃
LCS	G ▷ Q₈
UCS	C₁ ◁ C₈×C₁₃

Complements

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

N	H ≅ G/N	type
2. C₁₃×#131	C₃	semidirect
14. #131⋊C₃	C₁₃	direct (N × H)
21. #131	C₃×C₁₃	semidirect
29. C₁₃	#131⋊C₃	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×#41⋊C₃	2
C₁₃×#131	3
C₃×C₈×C₁₃	4
#131⋊C₃	13

Subgroups — C13×#131⋊C3 #11928749

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#131⋊C₃ #11928749