Subgroups — #23778477

Order 10140.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×#92788	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#63120	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×#92788	C₄	1	1	yes	characteristic, complemented, Hall
4	#14523130	—	5	1	no	maximal, Hall
5	D₅×C₁₃²	C₂×C₃	1	1	yes	characteristic
6	C₂×#92788	—	5	1	no	—
7	C₅×C₁₃²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	#63120⋊C₃	—	13	1	no	maximal
9	AGL(1,𝔽₅)×C₁₃⋊C₃	—	13	1	no	maximal
10	C₁₃×Dic₁₃	—	5	1	no	Hall
11	#92788	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	D₅×C₁₃⋊C₃	—	13	1	no	—
13	D₅×C₁₃⋊C₃	—	13	1	no	—
14	D₅×C₁₃⋊C₃	—	26	6	no	—
15	C₂×C₁₃²	—	5	1	no	—
16	#63120	C₁₃⋊C₃	1	1	yes	characteristic, complemented
17	C₁₃×AGL(1,𝔽₅)	—	13	1	no	—
18	C₅×C₁₃⋊C₃	—	13	1	no	—
19	C₅×C₁₃⋊C₃	—	13	1	no	—
20	C₅×C₁₃⋊C₃	—	26	6	no	—
21	C₁₃²	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
22	C₄×C₁₃⋊C₃	—	65	1	no	—
23	Dic₁₃⋊C₃	—	65	1	no	—
24	D₅×C₁₃	—	2	6	no	—
25	D₅×C₁₃	D₁₃⋊C₃	1	1	yes	characteristic
26	D₅×C₁₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic
27	C₂×C₁₃⋊C₃	—	65	1	no	—
28	C₂×C₁₃⋊C₃	—	65	1	no	—
29	C₂×C₁₃⋊C₃	—	130	6	no	—
30	C₅×C₁₃	—	2	6	no	—
31	C₅×C₁₃	Dic₁₃⋊C₃	1	1	yes	characteristic, complemented
32	C₅×C₁₃	C₄×C₁₃⋊C₃	1	1	yes	characteristic, complemented
33	C₃×AGL(1,𝔽₅)	—	169	1	no	Hall
34	C₄×C₁₃	—	65	1	no	—
35	Dic₁₃	—	5	1	no	—
36	C₁₃⋊C₃	—	13	1	no	—
37	C₁₃⋊C₃	—	13	1	no	—
38	C₁₃⋊C₃	—	26	6	no	—
39	C₃×D₅	—	169	1	no	—
40	C₂×C₁₃	—	5	1	no	—
41	C₂×C₁₃	—	5	1	no	—
42	C₂×C₁₃	—	10	6	no	—
43	AGL(1,𝔽₅)	—	13	1	no	Hall
44	C₃×C₅	—	169	1	no	Hall
45	C₁₃	—	2	6	no	—
46	C₁₃	AGL(1,𝔽₅)×C₁₃⋊C₃	1	1	yes	characteristic, complemented
47	C₁₃	#63120⋊C₃	1	1	yes	characteristic, complemented
48	C₃×C₄	—	845	1	no	Hall
49	D₅	#11759817	1	1	yes	characteristic
50	C₂×C₃	—	845	1	no	—
51	C₅	#14523130	1	1	yes	characteristic, complemented, Sylow
52	C₄	—	65	1	no	Sylow
53	C₃	—	169	1	no	Sylow
54	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₃²	C₃×C₄
prime radical	D₅×#92788	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×#92788	C₄	semidirect
7. C₅×C₁₃²	C₃×C₄	semidirect
11. #92788	AGL(1,𝔽₅)	semidirect
16. #63120	C₁₃⋊C₃	semidirect
21. C₁₃²	C₃×AGL(1,𝔽₅)	semidirect
31. C₅×C₁₃	Dic₁₃⋊C₃	semidirect
32. C₅×C₁₃	C₄×C₁₃⋊C₃	semidirect
46. C₁₃	AGL(1,𝔽₅)×C₁₃⋊C₃	semidirect
47. C₁₃	#63120⋊C₃	semidirect
51. C₅	#14523130	semidirect