Subgroups — C₅×#127⋊C₃ #91582

Order 480.

56 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	C₅×#127	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×C₅×A₄	—	4	1	no	maximal
4	#127⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×D₄	—	3	1	no	—
6	C₂×C₅×D₄	—	3	1	no	—
7	C₄²×C₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅×A₄	—	4	1	no	—
9	C₄²⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented
10	C₂³×C₅	—	3	1	no	—
11	C₂³×C₅	A₄	1	1	yes	characteristic
12	C₅×D₄	—	6	2	no	—
13	C₅×D₄	—	6	2	no	—
14	C₂×C₄×C₅	—	3	1	no	—
15	#127	C₃×C₅	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃×C₅	—	16	1	no	—
17	C₂×A₄	—	4	1	no	—
18	C₂²×C₅	—	6	1	no	—
19	C₂²×C₅	—	6	1	no	—
20	C₂²×C₅	—	6	2	no	—
21	C₂²×C₅	C₂×A₄	1	1	yes	characteristic
22	C₄×C₅	—	3	2	no	—
23	C₂×D₄	—	3	1	no	—
24	C₂×D₄	—	3	1	no	—
25	C₄²	C₂×C₃×C₅	1	1	yes	characteristic, complemented
26	C₃×C₅	—	16	1	no	Hall
27	A₄	—	4	1	no	—
28	C₂×C₅	—	3	1	no	—
29	C₂×C₅	—	4	1	no	—
30	C₂×C₅	—	12	1	no	—
31	C₂³	—	3	1	no	—
32	C₂³	C₅×A₄	1	1	yes	characteristic
33	D₄	—	6	2	no	—
34	D₄	—	6	2	no	—
35	C₂×C₄	—	3	1	no	—
36	C₂×C₃	—	16	1	no	—
37	C₅	#127⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
38	C₂²	—	6	1	no	—
39	C₂²	—	6	1	no	—
40	C₂²	—	6	2	no	—
41	C₂²	C₂×C₅×A₄	1	1	yes	characteristic
42	C₄	—	3	2	no	—
43	C₃	—	16	1	no	Sylow
44	C₂	—	3	1	no	—
45	C₂	—	4	1	no	—
46	C₂	—	12	1	no	—

	subgroup	G/H
center, hypercenter	C₅	#127⋊C₃
commutator, cosocle, hypocenter	C₄²	C₂×C₃×C₅
Frattini	C₂²	C₂×C₅×A₄
Fitting	C₅×#127	C₃
socle	C₂²×C₅	C₂×A₄
LCS	G ▷ C₄²
UCS	C₁ ◁ C₅

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.