Subgroups — C₃×C₅×SD₁₆ #6726

Order 240.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×Q₈	C₂	semidirect
3. C₃×C₅×C₈	C₂	semidirect
4. C₅×SD₁₆	C₃	direct (N × H)
8. C₃×SD₁₆	C₅	direct (N × H)
9. C₅×Q₈	C₂×C₃	semidirect
11. C₅×C₈	C₂×C₃	semidirect
14. C₃×Q₈	C₂×C₅	semidirect
16. C₃×C₈	C₂×C₅	semidirect
20. SD₁₆	C₃×C₅	direct (N × H)
21. C₃×C₅	SD₁₆	direct (N × H)
27. Q₈	C₂×C₃×C₅	semidirect
29. C₈	C₂×C₃×C₅	semidirect
32. C₅	C₃×SD₁₆	direct (N × H)
36. C₃	C₅×SD₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×Q₈	2
C₃×C₅×D₄	2
C₃×C₅×C₈	2
C₅×SD₁₆	3
C₃×SD₁₆	5

Subgroups — C3×C5×SD16 #6726

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×SD₁₆ #6726