Subgroups — C₁₃⋊C₃×#63120 #23778484

Order 10140.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₁₃×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#63120	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×C₁₃×C₁₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₃⋊C₃×Dic₁₃	—	5	1	no	maximal, Hall
5	D₅×C₁₃²	C₂×C₃	1	1	yes	characteristic
6	C₂×C₁₃×C₁₃⋊C₃	—	5	1	no	—
7	C₅×C₁₃²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₃×#63120	—	13	1	no	maximal
9	AGL(1,𝔽₅)×C₁₃⋊C₃	—	13	1	no	maximal
10	C₁₃×Dic₁₃	—	5	1	no	Hall
11	C₁₃×C₁₃⋊C₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	C₃×D₅×C₁₃	—	13	1	no	—
13	D₅×C₁₃⋊C₃	D₁₃	1	1	yes	characteristic
14	C₂×C₁₃²	—	5	1	no	—
15	#63120	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
16	C₁₃×AGL(1,𝔽₅)	—	13	1	no	—
17	C₃×C₅×C₁₃	—	13	1	no	—
18	C₅×C₁₃⋊C₃	Dic₁₃	1	1	yes	characteristic, complemented
19	C₁₃²	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
20	C₃×Dic₁₃	—	65	1	no	—
21	C₄×C₁₃⋊C₃	—	65	1	no	—
22	D₅×C₁₃	—	6	2	no	—
23	D₅×C₁₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic
24	D₅×C₁₃	C₃×D₁₃	1	1	yes	characteristic
25	C₂×C₃×C₁₃	—	65	1	no	—
26	C₂×C₁₃⋊C₃	—	5	1	no	—
27	C₅×C₁₃	—	6	2	no	—
28	C₅×C₁₃	C₄×C₁₃⋊C₃	1	1	yes	characteristic, complemented
29	C₅×C₁₃	C₃×Dic₁₃	1	1	yes	characteristic, complemented
30	C₃×AGL(1,𝔽₅)	—	169	1	no	Hall
31	C₄×C₁₃	—	65	1	no	—
32	Dic₁₃	—	5	1	no	—
33	C₃×C₁₃	—	13	1	no	—
34	C₁₃⋊C₃	#63120	1	1	yes	characteristic, direct product factor
35	C₃×D₅	—	13	1	no	—
36	C₂×C₁₃	—	5	1	no	—
37	C₂×C₁₃	—	5	1	no	—
38	C₂×C₁₃	—	30	2	no	—
39	AGL(1,𝔽₅)	—	13	1	no	Hall
40	C₃×C₅	—	13	1	no	Hall
41	C₁₃	—	6	2	no	—
42	C₁₃	AGL(1,𝔽₅)×C₁₃⋊C₃	1	1	yes	characteristic, complemented
43	C₁₃	C₃×#63120	1	1	yes	characteristic, complemented
44	C₃×C₄	—	845	1	no	Hall
45	D₅	D₁₃×C₁₃⋊C₃	1	1	yes	characteristic
46	C₂×C₃	—	65	1	no	—
47	C₅	C₁₃⋊C₃×Dic₁₃	1	1	yes	characteristic, complemented, Sylow
48	C₄	—	65	1	no	Sylow
49	C₃	—	13	1	no	Sylow
50	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₃²	C₃×C₄
prime radical	D₅×C₁₃×C₁₃⋊C₃	C₂
cosocle	D₅×C₁₃²	C₂×C₃
LCS	G ▷ C₅×C₁₃²
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₁₃×#63120	C₃	semidirect
3. C₅×C₁₃×C₁₃⋊C₃	C₄	semidirect
7. C₅×C₁₃²	C₃×C₄	semidirect
11. C₁₃×C₁₃⋊C₃	AGL(1,𝔽₅)	semidirect
15. #63120	C₁₃⋊C₃	direct (N × H)
18. C₅×C₁₃⋊C₃	Dic₁₃	semidirect
19. C₁₃²	C₃×AGL(1,𝔽₅)	semidirect
28. C₅×C₁₃	C₄×C₁₃⋊C₃	semidirect
29. C₅×C₁₃	C₃×Dic₁₃	semidirect
34. C₁₃⋊C₃	#63120	direct (N × H)
42. C₁₃	AGL(1,𝔽₅)×C₁₃⋊C₃	semidirect
43. C₁₃	C₃×#63120	semidirect
47. C₅	C₁₃⋊C₃×Dic₁₃	semidirect

Subgroups — C13⋊C3×#63120 #23778484

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃⋊C₃×#63120 #23778484