Subgroups — #34087113

Order 19620.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×#11758281	C₂	1	1	yes	maximal, characteristic
2	#14546128⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₅×#11758281	C₄	1	1	yes	characteristic, complemented, Hall
4	#16840993	—	5	1	no	maximal, Hall
5	D₅×C₁₀₉⋊C₃	C₂×C₃	1	1	yes	characteristic
6	#14546128	C₉	1	1	yes	characteristic, complemented, Hall
7	C₂×#11758281	—	5	1	no	—
8	C₅×C₁₀₉⋊C₃	C₃×C₄	1	1	yes	characteristic
9	Dic₁₀₉⋊C₃	—	5	1	no	—
10	D₅×C₁₀₉	C₂×C₉	1	1	yes	characteristic
11	#11758281	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	C₂×C₁₀₉⋊C₃	—	5	1	no	—
13	C₅×C₁₀₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
14	Dic₁₀₉	—	5	1	no	Hall
15	C₁₀₉⋊C₃	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
16	C₂×C₁₀₉	—	5	1	no	—
17	C₉×AGL(1,𝔽₅)	—	109	1	no	maximal, Hall
18	C₁₀₉	C₉×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
19	C₉×D₅	—	109	1	no	—
20	C₃×AGL(1,𝔽₅)	—	109	1	no	—
21	C₅×C₉	—	109	1	no	Hall
22	C₄×C₉	—	545	1	no	Hall
23	C₃×D₅	—	109	1	no	—
24	AGL(1,𝔽₅)	—	981	1	no	Hall
25	C₂×C₉	—	545	1	no	—
26	C₃×C₅	—	109	1	no	—
27	C₃×C₄	—	545	1	no	—
28	D₅	#11758281⋊C₂	1	1	yes	characteristic
29	C₉	—	109	1	no	Sylow
30	C₂×C₃	—	545	1	no	—
31	C₅	#16840993	1	1	yes	characteristic, complemented, Sylow
32	C₄	—	4905	1	no	Sylow
33	C₃	—	109	1	no	—
34	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₀₉	C₄×C₉
prime radical, cosocle	D₅×C₁₀₉⋊C₃	C₂×C₃
LCS	G ▷ C₅×C₁₀₉
UCS	C₁

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

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