Subgroups — C₃×(C₂⁴⋊C₅)⋊C₂ #92118

Order 480.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

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.