Subgroups — C₁₃×#876 #11928852

Order 1248.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×(C₂×D₃)⋊C₄	C₂	1	3	yes	maximal
3	C₁₃×Dic₃⋊C₄	C₂	1	3	yes	maximal, complemented
4	C₁₃×#126	—	3	1	no	maximal, Hall
5	C₂²×D₃×C₁₃	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₄×C₁₃	C₂²	1	3	yes	—
7	C₂×Dic₃×C₁₃	C₂²	1	3	yes	—
8	C₁₃×C₄⋊C₄	—	3	3	no	—
9	C₁₃×C₂²⋊C₄	—	3	3	no	—
10	C₄²×C₁₃	D₃	1	1	yes	characteristic, complemented
11	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
12	C₂×D₃×C₁₃	—	2	3	no	—
13	C₃×C₄×C₁₃	—	2	3	no	—
14	Dic₃×C₁₃	—	2	3	no	—
15	C₂³×C₁₃	—	3	1	no	—
16	C₂×C₄×C₁₃	—	3	3	no	—
17	C₂×C₄×C₁₃	C₂×D₃	1	3	yes	—
18	#876	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₃×C₁₃	#41	1	3	yes	—
20	D₃×C₁₃	—	4	1	no	—
21	C₂²×C₁₃	—	6	3	no	—
22	C₂²×C₁₃	C₂²×D₃	1	1	yes	characteristic
23	C₄×C₁₃	—	2	3	no	—
24	C₄×C₁₃	—	6	3	no	—
25	C₃×C₄²	C₂×C₁₃	1	1	yes	characteristic, complemented
26	(C₂×D₃)⋊C₄	C₂×C₁₃	1	3	yes	—
27	Dic₃⋊C₄	C₂×C₁₃	1	3	yes	complemented
28	C₃×C₁₃	#126	1	1	yes	characteristic, complemented, Hall
29	#126	—	3	1	no	Sylow
30	C₂×C₁₃	—	12	1	no	—
31	C₂×C₁₃	#235	1	3	yes	—
32	C₂²×D₃	C₂²×C₁₃	1	1	yes	characteristic
33	C₂×C₃×C₄	C₂²×C₁₃	1	3	yes	—
34	C₂×Dic₃	C₂²×C₁₃	1	3	yes	—
35	C₄⋊C₄	—	3	3	no	—
36	C₂²⋊C₄	—	3	3	no	—
37	C₄²	D₃×C₁₃	1	1	yes	characteristic, complemented
38	C₁₃	#876	1	1	yes	characteristic, direct product factor, Sylow
39	C₂²×C₃	C₂³×C₁₃	1	1	yes	characteristic
40	C₂×D₃	—	2	3	no	—
41	C₃×C₄	—	2	3	no	—
42	Dic₃	—	2	3	no	—
43	C₂³	—	3	1	no	—
44	C₂×C₄	—	3	3	no	—
45	C₂×C₄	C₂×D₃×C₁₃	1	3	yes	—
46	C₂×C₃	C₁₃×#41	1	3	yes	—
47	D₃	—	4	1	no	—
48	C₂²	—	6	3	no	—
49	C₂²	C₂²×D₃×C₁₃	1	1	yes	characteristic
50	C₄	—	2	3	no	—
51	C₄	—	6	3	no	—
52	C₃	C₁₃×#126	1	1	yes	characteristic, complemented, Sylow
53	C₂	—	12	1	no	—
54	C₂	C₁₃×#235	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
prime radical	C₂²×D₃×C₁₃	C₂²
hypercenter	C₄²×C₁₃	D₃
hypocenter	C₃	C₁₃×#126
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. C₃×C₄²×C₁₃	C₂	semidirect
3. C₁₃×Dic₃⋊C₄	C₂	semidirect
10. C₄²×C₁₃	D₃	semidirect
18. #876	C₁₃	direct (N × H)
25. C₃×C₄²	C₂×C₁₃	semidirect
27. Dic₃⋊C₄	C₂×C₁₃	semidirect
28. C₃×C₁₃	#126	semidirect
37. C₄²	D₃×C₁₃	semidirect
38. C₁₃	#876	direct (N × H)
52. C₃	C₁₃×#126	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄²×C₁₃	2
C₁₃×(C₂×D₃)⋊C₄	2
C₁₃×Dic₃⋊C₄	2
C₁₃×#126	3
#876	13

Subgroups — C13×#876 #11928852

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#876 #11928852