Subgroups — C₃×#676 #6673

Order 240.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×D₅	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#168	C₂	1	1	yes	maximal, characteristic, complemented
4	#676	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×D₅	C₄	1	1	yes	characteristic
6	C₃×C₄×C₅	C₂²	1	1	yes	characteristic
7	C₃×Dic₅	C₄	1	1	yes	characteristic
8	C₃×M₁₆	—	5	1	no	maximal, Hall
9	C₄×D₅	C₂×C₃	1	1	yes	characteristic
10	C₅×C₈	C₂×C₃	1	1	yes	characteristic, complemented
11	#168	C₂×C₃	1	1	yes	characteristic, complemented
12	C₂×C₃×C₅	C₂×C₄	1	1	yes	characteristic
13	C₃×D₅	—	2	1	no	—
14	C₂×C₃×C₄	—	5	1	no	—
15	C₃×C₈	—	5	1	no	—
16	C₃×C₈	D₅	1	1	yes	characteristic, complemented
17	C₂×D₅	C₃×C₄	1	1	yes	characteristic
18	C₄×C₅	C₂²×C₃	1	1	yes	characteristic
19	Dic₅	C₃×C₄	1	1	yes	characteristic
20	M₁₆	—	5	1	no	Sylow
21	C₃×C₅	M₁₆	1	1	yes	characteristic, complemented, Hall
22	C₂²×C₃	—	5	1	no	—
23	C₃×C₄	—	5	1	no	—
24	C₃×C₄	C₂×D₅	1	1	yes	characteristic
25	C₂×C₅	C₂×C₃×C₄	1	1	yes	characteristic
26	D₅	—	2	1	no	—
27	C₂×C₄	—	5	1	no	—
28	C₈	—	5	1	no	—
29	C₈	C₃×D₅	1	1	yes	characteristic, complemented
30	C₂×C₃	—	10	1	no	—
31	C₂×C₃	C₄×D₅	1	1	yes	characteristic
32	C₅	C₃×M₁₆	1	1	yes	characteristic, complemented, Sylow
33	C₂²	—	5	1	no	—
34	C₄	—	5	1	no	—
35	C₄	C₂×C₃×D₅	1	1	yes	characteristic
36	C₃	#676	1	1	yes	characteristic, direct product factor, Sylow
37	C₂	—	10	1	no	—
38	C₂	C₃×C₄×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂×D₅
commutator	C₂×C₅	C₂×C₃×C₄
Frattini	C₄	C₂×C₃×D₅
Fitting	C₃×C₅×C₈	C₂
socle	C₂×C₃×C₅	C₂×C₄
prime radical	C₂×C₃×D₅	C₄
cosocle	C₄×C₅	C₂²×C₃
hypercenter	C₃×C₈	D₅
hypocenter	C₅	C₃×M₁₆
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄ ◁ C₃×C₈

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×C₈	C₂	semidirect
3. C₃×#168	C₂	semidirect
4. #676	C₃	direct (N × H)
10. C₅×C₈	C₂×C₃	semidirect
11. #168	C₂×C₃	semidirect
16. C₃×C₈	D₅	semidirect
21. C₃×C₅	M₁₆	semidirect
29. C₈	C₃×D₅	semidirect
32. C₅	C₃×M₁₆	semidirect
36. C₃	#676	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×C₄×D₅	2
C₃×C₅×C₈	2
C₃×#168	2
#676	3
C₃×M₁₆	5

Subgroups — C3×#676 #6673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#676 #6673