Subgroups — C₃×C₅×#106 #91133

Order 480.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×C₄⋊C₄	C₂	1	2	yes	maximal
3	C₅×#106	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₄×C₅	—	2	2	no	—
5	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
6	C₃×C₅×C₈	C₄	1	2	yes	complemented
7	C₃×#106	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₅×C₈	C₂×C₃	1	1	yes	characteristic
9	C₅×C₄⋊C₄	C₂×C₃	1	2	yes	—
10	C₂²×C₃×C₅	D₄	1	1	yes	characteristic
11	C₃×C₄×C₅	—	4	2	no	—
12	C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
13	C₃×C₄×C₅	Q₈	1	1	yes	characteristic
14	C₂×C₃×C₈	C₂×C₅	1	1	yes	characteristic
15	C₃×C₄⋊C₄	C₂×C₅	1	2	yes	—
16	C₂×C₄×C₅	—	2	2	no	—
17	C₂×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
18	C₅×C₈	C₃×C₄	1	2	yes	complemented
19	#106	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃×C₅	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₃×C₅	SD₁₆	1	2	yes	—
22	C₂×C₃×C₄	—	2	2	no	—
23	C₂×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
24	C₃×C₈	C₄×C₅	1	2	yes	complemented
25	C₂²×C₅	C₃×D₄	1	1	yes	characteristic
26	C₄×C₅	—	4	2	no	—
27	C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
28	C₄×C₅	C₃×Q₈	1	1	yes	characteristic
29	C₂×C₈	C₂×C₃×C₅	1	1	yes	characteristic
30	C₄⋊C₄	C₂×C₃×C₅	1	2	yes	—
31	C₃×C₅	#106	1	1	yes	characteristic, direct product factor, Hall
32	C₂²×C₃	C₅×D₄	1	1	yes	characteristic
33	C₃×C₄	—	4	2	no	—
34	C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
35	C₃×C₄	C₅×Q₈	1	1	yes	characteristic
36	C₂×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₅	C₃×SD₁₆	1	2	yes	—
38	C₂×C₄	—	2	2	no	—
39	C₂×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
40	C₈	C₃×C₄×C₅	1	2	yes	complemented
41	C₂×C₃	C₅×C₄⋊C₄	1	1	yes	characteristic
42	C₂×C₃	C₅×SD₁₆	1	2	yes	—
43	C₅	C₃×#106	1	1	yes	characteristic, direct product factor, Sylow
44	C₂²	C₃×C₅×D₄	1	1	yes	characteristic
45	C₄	—	4	2	no	—
46	C₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
47	C₄	C₃×C₅×Q₈	1	1	yes	characteristic
48	C₃	C₅×#106	1	1	yes	characteristic, direct product factor, Sylow
49	C₂	C₃×C₅×C₄⋊C₄	1	1	yes	characteristic
50	C₂	C₃×C₅×SD₁₆	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₃×C₅	D₄
commutator	C₄	C₂×C₃×C₄×C₅
Frattini, cosocle	C₂×C₄	C₂²×C₃×C₅
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅×#106	C₃	direct (N × H)
6. C₃×C₅×C₈	C₄	semidirect
7. C₃×#106	C₅	direct (N × H)
18. C₅×C₈	C₃×C₄	semidirect
19. #106	C₃×C₅	direct (N × H)
24. C₃×C₈	C₄×C₅	semidirect
31. C₃×C₅	#106	direct (N × H)
40. C₈	C₃×C₄×C₅	semidirect
43. C₅	C₃×#106	direct (N × H)
48. C₃	C₅×#106	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×C₈	2
C₃×C₅×C₄⋊C₄	2
C₅×#106	3
C₃×#106	5

Subgroups — C3×C5×#106 #91133

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#106 #91133