Subgroups — C₁₃×#874 #11928850

Order 1248.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×D₁₂	C₂	1	6	yes	maximal, complemented
2	C₃×C₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#127	—	3	1	no	maximal, Hall
4	C₂²×D₃×C₁₃	C₂²	1	4	yes	—
5	C₂×C₃×C₄×C₁₃	C₂²	1	3	yes	—
6	C₁₃×D₁₂	—	2	12	no	—
7	C₂×D₄×C₁₃	—	3	6	no	—
8	C₄²×C₁₃	D₃	1	1	yes	characteristic, complemented
9	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
10	C₂×D₃×C₁₃	—	2	12	no	—
11	C₃×C₄×C₁₃	D₄	1	6	yes	complemented
12	C₂³×C₁₃	—	3	4	no	—
13	D₄×C₁₃	—	6	12	no	—
14	C₂×C₄×C₁₃	C₂×D₃	1	3	yes	—
15	#874	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₃×C₁₃	C₂×D₄	1	3	yes	—
17	D₃×C₁₃	—	4	4	no	—
18	C₂²×C₁₃	—	6	12	no	—
19	C₂²×C₁₃	C₂²×D₃	1	1	yes	characteristic
20	C₄×C₁₃	D₁₂	1	6	yes	complemented
21	C₂×D₁₂	C₂×C₁₃	1	6	yes	complemented
22	C₃×C₄²	C₂×C₁₃	1	1	yes	characteristic, complemented
23	C₃×C₁₃	#127	1	1	yes	characteristic, complemented, Hall
24	#127	—	3	1	no	Sylow
25	C₂×C₁₃	—	12	4	no	—
26	C₂×C₁₃	C₂×D₁₂	1	3	yes	—
27	C₂²×D₃	C₂²×C₁₃	1	4	yes	—
28	C₂×C₃×C₄	C₂²×C₁₃	1	3	yes	—
29	D₁₂	—	2	12	no	—
30	C₂×D₄	—	3	6	no	—
31	C₄²	D₃×C₁₃	1	1	yes	characteristic, complemented
32	C₁₃	#874	1	1	yes	characteristic, direct product factor, Sylow
33	C₂²×C₃	C₂³×C₁₃	1	1	yes	characteristic
34	C₂×D₃	—	2	12	no	—
35	C₃×C₄	D₄×C₁₃	1	6	yes	complemented
36	C₂³	—	3	4	no	—
37	D₄	—	6	12	no	—
38	C₂×C₄	C₂×D₃×C₁₃	1	3	yes	—
39	C₂×C₃	C₂×D₄×C₁₃	1	3	yes	—
40	D₃	—	4	4	no	—
41	C₂²	—	6	12	no	—
42	C₂²	C₂²×D₃×C₁₃	1	1	yes	characteristic
43	C₄	C₁₃×D₁₂	1	6	yes	complemented
44	C₃	C₁₃×#127	1	1	yes	characteristic, complemented, Sylow
45	C₂	—	12	4	no	—
46	C₂	C₂×C₁₃×D₁₂	1	3	yes	—

	subgroup	G/H
center	C₂²×C₁₃	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂³×C₁₃
Frattini	C₂²	C₂²×D₃×C₁₃
Fitting	C₃×C₄²×C₁₃	C₂
socle	C₂²×C₃×C₁₃	C₂³
hypercenter	C₄²×C₁₃	D₃
hypocenter	C₃	C₁₃×#127
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄²×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×D₁₂	C₂	semidirect
2. C₃×C₄²×C₁₃	C₂	semidirect
8. C₄²×C₁₃	D₃	semidirect
11. C₃×C₄×C₁₃	D₄	semidirect
15. #874	C₁₃	direct (N × H)
20. C₄×C₁₃	D₁₂	semidirect
21. C₂×D₁₂	C₂×C₁₃	semidirect
22. C₃×C₄²	C₂×C₁₃	semidirect
23. C₃×C₁₃	#127	semidirect
31. C₄²	D₃×C₁₃	semidirect
32. C₁₃	#874	direct (N × H)
35. C₃×C₄	D₄×C₁₃	semidirect
43. C₄	C₁₃×D₁₂	semidirect
44. C₃	C₁₃×#127	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×D₁₂	2
C₃×C₄²×C₁₃	2
C₁₃×#127	3
#874	13

Subgroups — C13×#874 #11928850

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#874 #11928850