Subgroups — C₅⋊(#126⋊C₃) #91187

Order 480.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₄²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#4022	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	D₅×A₄	—	4	1	no	maximal
4	#126⋊C₃	—	5	1	no	maximal, Hall
5	C₄²×C₅	C₂×C₃	1	1	yes	characteristic, complemented
6	#685	—	3	1	no	—
7	#683	—	3	1	no	—
8	C₅×A₄	—	4	1	no	—
9	C₄²⋊C₃	D₅	1	1	yes	characteristic, complemented
10	C₂²×D₅	A₄	1	1	yes	characteristic
11	C₂×C₄×C₅	—	3	1	no	—
12	C₂×Dic₅	—	3	1	no	—
13	#126	—	5	1	no	Sylow
14	C₃×D₅	—	16	1	no	—
15	C₂×A₄	—	20	1	no	—
16	C₂²×C₅	C₂×A₄	1	1	yes	characteristic
17	C₂×D₅	—	6	1	no	—
18	C₄×C₅	—	6	1	no	—
19	Dic₅	—	6	1	no	—
20	C₄⋊C₄	—	15	1	no	—
21	C₂²⋊C₄	—	15	1	no	—
22	C₄²	C₃×D₅	1	1	yes	characteristic, complemented
23	C₃×C₅	—	16	1	no	Hall
24	A₄	—	4	1	no	—
25	C₂×C₅	—	3	1	no	—
26	D₅	—	4	1	no	—
27	C₂³	—	5	1	no	—
28	C₂×C₄	—	3	1	no	—
29	C₂×C₄	—	15	1	no	—
30	C₂×C₃	—	80	1	no	—
31	C₅	#126⋊C₃	1	1	yes	characteristic, complemented, Sylow
32	C₂²	—	30	1	no	—
33	C₂²	D₅×A₄	1	1	yes	characteristic
34	C₄	—	6	1	no	—
35	C₄	—	30	1	no	—
36	C₃	—	16	1	no	Sylow
37	C₂	—	3	1	no	—
38	C₂	—	20	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₄²×C₅	C₂×C₃
Frattini	C₂²	D₅×A₄
socle	C₂²×C₅	C₂×A₄
LCS	G ▷ C₄²×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.