Subgroups — C₅×#994 #92055

Order 480.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#41⋊C₃	C₂	1	3	yes	maximal, complemented
2	C₅×H(5,𝔽₂)	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₃×C₅×Q₈	—	4	1	no	maximal
4	C₅×SL(2,𝔽₃)	C₂²	1	1	yes	characteristic, complemented
5	#994	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×#41	—	3	1	no	—
7	C₅×#41	C₂×C₃	1	3	yes	—
8	C₂×C₅×D₄	—	3	3	no	—
9	C₃×C₄×C₅	—	4	3	no	—
10	#41⋊C₃	C₂×C₅	1	3	yes	complemented
11	C₂³×C₅	—	3	2	no	—
12	C₅×Q₈	A₄	1	1	yes	characteristic
13	C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
14	C₅×D₄	—	3	3	no	—
15	C₅×D₄	—	3	3	no	—
16	C₂×C₄×C₅	—	3	3	no	—
17	H(5,𝔽₂)	C₃×C₅	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₃×C₅	—	4	1	no	—
19	C₃×Q₈	—	4	1	no	—
20	SL(2,𝔽₃)	C₂²×C₅	1	1	yes	characteristic, complemented
21	C₂²×C₅	—	3	3	no	—
22	C₂²×C₅	—	12	2	no	—
23	C₄×C₅	—	3	1	no	—
24	C₄×C₅	C₂×A₄	1	3	yes	—
25	#41	—	3	1	no	—
26	#41	C₂×C₃×C₅	1	3	yes	—
27	C₂×D₄	—	3	3	no	—
28	C₃×C₅	—	4	1	no	Hall
29	C₃×C₄	—	4	3	no	—
30	C₂×C₅	—	6	3	no	—
31	C₂×C₅	C₂²×A₄	1	1	yes	characteristic
32	C₂³	—	3	2	no	—
33	Q₈	C₅×A₄	1	1	yes	characteristic
34	Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
35	D₄	—	3	3	no	—
36	D₄	—	3	3	no	—
37	C₂×C₄	—	3	3	no	—
38	C₂×C₃	—	4	1	no	—
39	C₅	#994	1	1	yes	characteristic, direct product factor, Sylow
40	C₂²	—	3	3	no	—
41	C₂²	—	12	2	no	—
42	C₄	—	3	1	no	—
43	C₄	C₂×C₅×A₄	1	3	yes	—
44	C₃	—	4	1	no	Sylow
45	C₂	—	6	3	no	—
46	C₂	C₂²×C₅×A₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅	C₂²×A₄
commutator, cosocle, hypocenter	Q₈	C₂²×C₃×C₅
Frattini	C₂	C₂²×C₅×A₄
Fitting	C₅×H(5,𝔽₂)	C₃
hypercenter	C₅×Q₈	A₄
LCS	G ▷ Q₈
UCS	C₁ ◁ C₂×C₅ ◁ C₅×Q₈

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.