Subgroups — #23778474

Order 10140.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×#92789	C₂	1	1	yes	maximal, characteristic
2	#16810007	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×#92789	C₄	1	1	yes	characteristic, complemented, Hall
4	#14523129	—	5	1	no	maximal, Hall
5	D₅×C₁₃²	C₂×C₃	1	1	yes	characteristic
6	C₂×#92789	—	5	1	no	—
7	C₅×C₁₃²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	#63120⋊C₃	—	13	2	no	maximal
9	#10621725	—	5	1	no	Hall
10	#92789	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
11	D₅×C₁₃⋊C₃	—	13	2	no	—
12	C₂×C₁₃²	—	5	1	no	—
13	#63120	—	13	2	no	—
14	#63120	—	39	4	no	—
15	C₅×C₁₃⋊C₃	—	13	2	no	—
16	C₁₃²	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
17	Dic₁₃⋊C₃	—	65	2	no	—
18	D₅×C₁₃	—	3	4	no	—
19	D₅×C₁₃	D₁₃⋊C₃	1	2	yes	—
20	C₂×C₁₃⋊C₃	—	65	2	no	—
21	C₅×C₁₃	—	3	4	no	—
22	C₅×C₁₃	Dic₁₃⋊C₃	1	2	yes	complemented
23	C₃×AGL(1,𝔽₅)	—	169	1	no	Hall
24	Dic₁₃	—	65	2	no	—
25	Dic₁₃	—	195	4	no	—
26	C₁₃⋊C₃	—	13	2	no	—
27	C₃×D₅	—	169	1	no	—
28	C₂×C₁₃	—	5	2	no	—
29	C₂×C₁₃	—	15	4	no	—
30	AGL(1,𝔽₅)	—	169	1	no	Hall
31	C₃×C₅	—	169	1	no	Hall
32	C₁₃	—	3	4	no	—
33	C₁₃	#63120⋊C₃	1	2	yes	complemented
34	C₃×C₄	—	845	1	no	Hall
35	D₅	#11759816	1	1	yes	characteristic
36	C₂×C₃	—	845	1	no	—
37	C₅	#14523129	1	1	yes	characteristic, complemented, Sylow
38	C₄	—	845	1	no	Sylow
39	C₃	—	169	1	no	Sylow
40	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₃²	C₃×C₄
prime radical	D₅×#92789	C₂
cosocle	D₅×C₁₃²	C₂×C₃
LCS	G ▷ C₅×C₁₃²
UCS	C₁

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