Subgroups — #6648

Order 240.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₁₅	C₂	1	1	yes	maximal, characteristic
2	C₃×#168	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×D₅	—	3	1	no	maximal, Hall
5	C₂×D₁₅	C₄	1	1	yes	characteristic
6	C₃×C₄×C₅	C₂²	1	1	yes	characteristic
7	Dic₁₅	C₄	1	1	yes	characteristic
8	D₃×C₈	—	5	1	no	maximal, Hall
9	C₄×D₅	—	3	1	no	—
10	C₅×C₈	—	3	1	no	—
11	#168	D₃	1	1	yes	characteristic, complemented
12	C₂×C₃×C₅	C₂×C₄	1	1	yes	characteristic
13	D₁₅	C₈	1	2	yes	complemented
14	C₄×D₃	—	5	1	no	—
15	C₃×C₈	—	5	1	no	—
16	C₃⋊C₈	D₅	1	1	yes	characteristic, complemented
17	C₂×D₅	—	3	1	no	—
18	C₄×C₅	C₂×D₃	1	1	yes	characteristic
19	Dic₅	—	3	1	no	—
20	C₂×C₈	—	15	1	no	Sylow
21	C₃×C₅	C₂×C₈	1	1	yes	characteristic, complemented, Hall
22	C₂×D₃	—	5	1	no	—
23	C₃×C₄	C₂×D₅	1	1	yes	characteristic
24	Dic₃	—	5	1	no	—
25	C₂×C₅	C₄×D₃	1	1	yes	characteristic
26	D₅	—	3	2	no	—
27	C₂×C₄	—	15	1	no	—
28	C₈	—	3	1	no	—
29	C₈	—	5	1	no	—
30	C₂×C₃	C₄×D₅	1	1	yes	characteristic
31	D₃	—	5	2	no	—
32	C₅	D₃×C₈	1	1	yes	characteristic, complemented, Sylow
33	C₂²	—	15	1	no	—
34	C₄	—	15	1	no	—
35	C₄	D₃×D₅	1	1	yes	characteristic
36	C₃	C₈×D₅	1	1	yes	characteristic, complemented, Sylow
37	C₂	—	15	2	no	—
38	C₂	#1200	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₄	D₃×D₅
commutator, hypocenter	C₃×C₅	C₂×C₈
Fitting, cosocle	C₃×C₄×C₅	C₂²
socle	C₂×C₃×C₅	C₂×C₄
prime radical	C₂×D₁₅	C₄
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₄

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

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