Subgroups — #23778486

Order 10140.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊#11759816	C₂	1	1	yes	maximal, characteristic
2	#16810004	—	3	1	no	maximal, Hall
3	C₅×#92789	C₄	1	1	yes	characteristic, complemented, Hall
4	#14523161	—	5	1	no	maximal, Hall
5	C₅⋊(C₁₃⋊D₁₃)	D₃	1	1	yes	characteristic
6	#11759816	—	5	1	no	—
7	C₅×C₁₃²	Dic₃	1	1	yes	characteristic, complemented, Hall
8	#10621729	—	15	1	no	Hall
9	#92789	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
10	C₅⋊(D₁₃⋊C₃)	—	26	1	no	—
11	C₁₃⋊D₁₃	—	5	1	no	—
12	#63122	—	39	1	no	—
13	#63121	—	39	1	no	—
14	C₅×C₁₃⋊C₃	—	26	1	no	—
15	C₁₃²	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented, Sylow
16	D₆₅	—	26	1	no	—
17	D₆₅	—	39	1	no	—
18	D₆₅	—	39	1	no	—
19	D₆₅	—	78	1	no	—
20	D₁₃⋊C₃	—	130	1	no	—
21	C₅×C₁₃	—	2	1	no	—
22	C₅×C₁₃	—	3	1	no	—
23	C₅×C₁₃	—	3	1	no	—
24	C₅×C₁₃	—	6	1	no	—
25	ΓL(1,𝔽₁₆)	—	169	1	no	maximal, Hall
26	#261	—	195	1	no	—
27	#261	—	195	1	no	—
28	C₁₃⋊C₃	—	26	1	no	—
29	C₃×D₅	—	169	1	no	—
30	D₁₃	—	130	1	no	—
31	D₁₃	—	390	1	no	—
32	D₁₃	—	195	1	no	—
33	D₁₃	—	195	1	no	—
34	AGL(1,𝔽₅)	—	507	1	no	Hall
35	C₃×C₅	—	169	1	no	Hall
36	C₁₃	—	2	1	no	—
37	C₁₃	—	3	1	no	—
38	C₁₃	—	3	1	no	—
39	C₁₃	—	6	1	no	—
40	Dic₃	—	845	1	no	Hall
41	D₅	—	169	1	no	—
42	C₂×C₃	—	845	1	no	—
43	C₅	#14523161	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	2535	1	no	Sylow
45	C₃	—	169	1	no	Sylow
46	C₂	—	845	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, hypocenter	C₅×#92789	C₄
Fitting, socle	C₅×C₁₃²	Dic₃
prime radical, cosocle	C₅⋊#11759816	C₂
LCS	G ▷ C₅×#92789
UCS	C₁

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