Subgroups — #6706

Order 240.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₀	C₂	1	1	yes	maximal, characteristic
2	Dic₃₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#677	—	3	1	no	maximal, Hall
5	C₂×D₁₅	—	2	1	no	—
6	C₃×C₄×C₅	C₂²	1	1	yes	characteristic
7	Dic₁₅	—	2	1	no	—
8	#204	—	5	1	no	maximal, Hall
9	D₂₀	—	3	1	no	—
10	Dic₁₀	—	3	1	no	—
11	C₅×C₈	D₃	1	1	yes	characteristic, complemented
12	C₂×C₃×C₅	D₄	1	1	yes	characteristic
13	D₁₅	—	4	1	no	—
14	D₁₂	—	5	1	no	—
15	Dic₆	—	5	1	no	—
16	C₃×C₈	D₅	1	1	yes	characteristic, complemented
17	C₂×D₅	—	6	1	no	—
18	C₄×C₅	C₂×D₃	1	1	yes	characteristic
19	Dic₅	—	6	1	no	—
20	SD₁₆	—	15	1	no	Sylow
21	C₃×C₅	SD₁₆	1	1	yes	characteristic, complemented, Hall
22	C₂×D₃	—	10	1	no	—
23	C₃×C₄	C₂×D₅	1	1	yes	characteristic
24	Dic₃	—	10	1	no	—
25	C₂×C₅	D₁₂	1	1	yes	characteristic
26	D₅	—	12	1	no	—
27	Q₈	—	15	1	no	—
28	D₄	—	15	1	no	—
29	C₈	D₁₅	1	1	yes	characteristic, complemented
30	C₂×C₃	D₂₀	1	1	yes	characteristic
31	D₃	—	20	1	no	—
32	C₅	#204	1	1	yes	characteristic, complemented, Sylow
33	C₂²	—	30	1	no	—
34	C₄	—	30	1	no	—
35	C₄	C₂×D₁₅	1	1	yes	characteristic
36	C₃	#677	1	1	yes	characteristic, complemented, Sylow
37	C₂	—	60	1	no	—
38	C₂	D₆₀	1	1	yes	characteristic

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.