Subgroups — ((C₂⁴⋊C₅)⋊C₂)⋊C₃ #92112

Order 480.

31 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	AGL(1,𝔽₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
2	(C₂⁴⋊C₅)⋊C₂	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#120⋊C₃	—	5	1	no	maximal, Hall
4	C₂⁴⋊C₅	C₂×C₃	1	1	yes	characteristic, complemented
5	C₂²⋊A₄	D₅	1	1	yes	characteristic, complemented
6	#120	—	5	1	no	Sylow
7	C₃×D₅	—	16	1	no	maximal
8	C₂×A₄	—	20	1	no	—
9	C₂⁴	C₃×D₅	1	1	yes	characteristic, complemented
10	C₂×D₄	—	15	1	no	—
11	C₂²⋊C₄	—	15	1	no	—
12	C₃×C₅	—	16	1	no	Hall
13	A₄	—	20	1	no	—
14	D₅	—	16	1	no	—
15	C₂³	—	5	1	no	—
16	C₂³	—	15	1	no	—
17	D₄	—	30	2	no	—
18	C₂×C₄	—	15	1	no	—
19	C₂×C₃	—	80	1	no	—
20	C₅	—	16	1	no	Sylow
21	C₂²	—	5	1	no	—
22	C₂²	—	15	2	no	—
23	C₂²	—	30	1	no	—
24	C₄	—	30	1	no	—
25	C₃	—	16	1	no	Sylow
26	C₂	—	15	1	no	—
27	C₂	—	20	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₂⁴⋊C₅	C₂×C₃
Fitting, socle	C₂⁴	C₃×D₅
LCS	G ▷ C₂⁴⋊C₅
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.