Subgroups — C₁₃×#127⋊C₃ #11928747

Order 1248.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₄²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#127	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×A₄×C₁₃	—	4	1	no	maximal
4	C₂×D₄×C₁₃	—	3	1	no	—
5	C₂×D₄×C₁₃	—	3	1	no	—
6	C₄²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
7	A₄×C₁₃	—	4	1	no	—
8	C₂³×C₁₃	—	3	1	no	—
9	C₂³×C₁₃	A₄	1	1	yes	characteristic
10	D₄×C₁₃	—	6	2	no	—
11	D₄×C₁₃	—	6	2	no	—
12	C₂×C₄×C₁₃	—	3	1	no	—
13	#127⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₃×C₁₃	—	16	1	no	—
15	C₂²×C₁₃	—	6	1	no	—
16	C₂²×C₁₃	—	6	1	no	—
17	C₂²×C₁₃	—	6	2	no	—
18	C₂²×C₁₃	C₂×A₄	1	1	yes	characteristic
19	C₄×C₁₃	—	3	2	no	—
20	C₄²⋊C₃	C₂×C₁₃	1	1	yes	characteristic, complemented
21	C₃×C₁₃	—	16	1	no	Hall
22	#127	C₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₁₃	—	3	1	no	—
24	C₂×C₁₃	—	4	1	no	—
25	C₂×C₁₃	—	12	1	no	—
26	C₂×A₄	—	4	1	no	—
27	C₂×D₄	—	3	1	no	—
28	C₂×D₄	—	3	1	no	—
29	C₄²	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
30	C₁₃	#127⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
31	A₄	—	4	1	no	—
32	C₂³	—	3	1	no	—
33	C₂³	A₄×C₁₃	1	1	yes	characteristic
34	D₄	—	6	2	no	—
35	D₄	—	6	2	no	—
36	C₂×C₄	—	3	1	no	—
37	C₂×C₃	—	16	1	no	—
38	C₂²	—	6	1	no	—
39	C₂²	—	6	1	no	—
40	C₂²	—	6	2	no	—
41	C₂²	C₂×A₄×C₁₃	1	1	yes	characteristic
42	C₄	—	3	2	no	—
43	C₃	—	16	1	no	Sylow
44	C₂	—	3	1	no	—
45	C₂	—	4	1	no	—
46	C₂	—	12	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	#127⋊C₃
commutator, cosocle, hypocenter	C₄²	C₂×C₃×C₁₃
Frattini	C₂²	C₂×A₄×C₁₃
Fitting	C₁₃×#127	C₃
socle	C₂²×C₁₃	C₂×A₄
LCS	G ▷ C₄²
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₄²⋊C₃	C₂	semidirect
2. C₁₃×#127	C₃	semidirect
6. C₄²×C₁₃	C₂×C₃	semidirect
13. #127⋊C₃	C₁₃	direct (N × H)
20. C₄²⋊C₃	C₂×C₁₃	semidirect
22. #127	C₃×C₁₃	semidirect
29. C₄²	C₂×C₃×C₁₃	semidirect
30. C₁₃	#127⋊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×C₄²⋊C₃	2
C₁₃×#127	3
C₂×A₄×C₁₃	4
#127⋊C₃	13

Subgroups — C13×#127⋊C3 #11928747

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#127⋊C₃ #11928747