Subgroups — C₅×#829 #91072

Order 480.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₁₂	C₂	1	1	yes	maximal, characteristic
3	C₅×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₅×Q₃₂	—	3	1	no	maximal, Hall
5	C₃×C₅×Q₈	—	2	1	no	—
6	C₅×Dic₆	—	2	1	no	—
7	C₃×C₅×C₈	C₂²	1	1	yes	characteristic
8	#829	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×Q₁₆	—	3	1	no	—
10	C₅×Q₁₆	D₃	1	1	yes	characteristic
11	C₅×C₁₆	—	3	1	no	—
12	C₃×C₄×C₅	—	4	1	no	—
13	C₃×C₄×C₅	D₄	1	1	yes	characteristic
14	C₅×Dic₃	—	4	1	no	—
15	C₃×Q₁₆	C₂×C₅	1	1	yes	characteristic
16	Dic₁₂	C₂×C₅	1	1	yes	characteristic
17	C₃⋊C₁₆	C₂×C₅	1	1	yes	characteristic
18	C₅×Q₈	—	2	1	no	—
19	C₅×Q₈	—	6	1	no	—
20	C₅×C₈	C₂×D₃	1	1	yes	characteristic
21	Q₃₂	—	3	1	no	Sylow
22	C₂×C₃×C₅	D₈	1	1	yes	characteristic
23	C₃×Q₈	—	2	1	no	—
24	Dic₆	—	2	1	no	—
25	C₃×C₈	C₂²×C₅	1	1	yes	characteristic
26	C₄×C₅	—	4	1	no	—
27	C₄×C₅	—	12	1	no	—
28	C₄×C₅	#67	1	1	yes	characteristic
29	Q₁₆	—	3	1	no	—
30	Q₁₆	C₅×D₃	1	1	yes	characteristic
31	C₁₆	—	3	1	no	—
32	C₃×C₅	Q₃₂	1	1	yes	characteristic, complemented, Hall
33	C₃×C₄	—	4	1	no	—
34	C₃×C₄	C₅×D₄	1	1	yes	characteristic
35	Dic₃	—	4	1	no	—
36	C₂×C₅	#213	1	1	yes	characteristic
37	Q₈	—	2	1	no	—
38	Q₈	—	6	1	no	—
39	C₈	C₂×C₅×D₃	1	1	yes	characteristic
40	C₂×C₃	C₅×D₈	1	1	yes	characteristic
41	C₅	#829	1	1	yes	characteristic, direct product factor, Sylow
42	C₄	—	4	1	no	—
43	C₄	—	12	1	no	—
44	C₄	C₅×#67	1	1	yes	characteristic
45	C₃	C₅×Q₃₂	1	1	yes	characteristic, complemented, Sylow
46	C₂	C₅×#213	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	#213
commutator, cosocle	C₃×C₈	C₂²×C₅
Frattini	C₈	C₂×C₅×D₃
Fitting	C₃×C₅×Q₁₆	C₂
socle, prime radical	C₂×C₃×C₅	D₈
hypercenter	C₅×Q₁₆	D₃
hypocenter	C₃	C₅×Q₃₂
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×C₈ ◁ C₅×Q₁₆

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
8. #829	C₅	direct (N × H)
32. C₃×C₅	Q₃₂	semidirect
41. C₅	#829	direct (N × H)
45. C₃	C₅×Q₃₂	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅×Q₁₆	2
C₅×Dic₁₂	2
C₅×C₃⋊C₁₆	2
C₅×Q₃₂	3
#829	5

Subgroups — C5×#829 #91072

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#829 #91072