Subgroups — C₂×C₃×Dic₁₀ #6794

Order 240.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×Dic₅	C₂	1	2	yes	maximal
3	C₃×Dic₁₀	C₂	1	4	yes	maximal, direct product factor
4	C₂×Dic₁₀	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₃×C₅	C₂²	1	1	yes	characteristic
6	C₃×C₄×C₅	C₂²	1	2	yes	—
7	C₃×Dic₅	C₂²	1	4	yes	—
8	C₂×C₃×Q₈	—	5	1	no	maximal, Hall
9	C₂×C₄×C₅	C₂×C₃	1	1	yes	characteristic
10	C₂×Dic₅	C₂×C₃	1	2	yes	—
11	Dic₁₀	C₂×C₃	1	4	yes	direct product factor
12	C₂×C₃×C₅	Q₈	1	2	yes	complemented
13	C₂×C₃×C₅	C₂³	1	1	yes	characteristic
14	C₃×Q₈	—	5	4	no	—
15	C₂×C₃×C₄	—	5	2	no	—
16	C₂×C₃×C₄	D₅	1	1	yes	characteristic
17	C₂²×C₅	C₂²×C₃	1	1	yes	characteristic
18	C₄×C₅	C₂²×C₃	1	2	yes	—
19	Dic₅	C₂²×C₃	1	4	yes	—
20	C₂×Q₈	—	5	1	no	Sylow
21	C₃×C₅	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
22	C₂²×C₃	C₂×D₅	1	1	yes	characteristic
23	C₃×C₄	—	5	4	no	—
24	C₃×C₄	C₂×D₅	1	2	yes	—
25	C₂×C₅	C₃×Q₈	1	2	yes	complemented
26	C₂×C₅	C₂³×C₃	1	1	yes	characteristic
27	Q₈	—	5	4	no	—
28	C₂×C₄	—	5	2	no	—
29	C₂×C₄	C₃×D₅	1	1	yes	characteristic
30	C₂×C₃	Dic₁₀	1	2	yes	direct product factor
31	C₂×C₃	C₂²×D₅	1	1	yes	characteristic
32	C₅	C₂×C₃×Q₈	1	1	yes	characteristic, complemented, Sylow
33	C₂²	C₂×C₃×D₅	1	1	yes	characteristic
34	C₄	—	5	4	no	—
35	C₄	C₂×C₃×D₅	1	2	yes	—
36	C₃	C₂×Dic₁₀	1	1	yes	characteristic, direct product factor, Sylow
37	C₂	C₃×Dic₁₀	1	2	yes	direct product factor
38	C₂	C₂²×C₃×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₅
commutator, cosocle	C₂×C₅	C₂³×C₃
Frattini	C₂	C₂²×C₃×D₅
Fitting	C₂×C₃×C₄×C₅	C₂
socle, prime radical	C₂²×C₃×C₅	C₂²
hypercenter	C₂×C₃×C₄	D₅
hypocenter	C₅	C₂×C₃×Q₈
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄

Complements

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

N	H ≅ G/N	type
3. C₃×Dic₁₀	C₂	direct (N × H)
4. C₂×Dic₁₀	C₃	direct (N × H)
11. Dic₁₀	C₂×C₃	direct (N × H)
12. C₂×C₃×C₅	Q₈	semidirect
21. C₃×C₅	C₂×Q₈	semidirect
25. C₂×C₅	C₃×Q₈	semidirect
30. C₂×C₃	Dic₁₀	direct (N × H)
32. C₅	C₂×C₃×Q₈	semidirect
36. C₃	C₂×Dic₁₀	direct (N × H)
37. C₂	C₃×Dic₁₀	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×C₄×C₅	2
C₂×C₃×Dic₅	2
C₃×Dic₁₀	2
C₂×Dic₁₀	3
C₂×C₃×Q₈	5

Subgroups — C2×C3×Dic10 #6794

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×Dic₁₀ #6794