Subgroups — #6717

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	D₆₀	C₂	1	1	yes	maximal, characteristic
3	C₃⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
4	#688	—	3	1	no	maximal, Hall
5	C₂×D₁₅	—	2	1	no	—
6	C₃×C₄×C₅	—	2	1	no	—
7	C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	#215	—	5	1	no	maximal, Hall
9	C₅×Q₈	D₃	1	1	yes	characteristic, complemented
10	D₂₀	—	3	1	no	—
11	#168	—	3	1	no	—
12	C₂×C₃×C₅	D₄	1	1	yes	characteristic
13	D₁₅	—	4	1	no	—
14	C₃×Q₈	D₅	1	1	yes	characteristic, complemented
15	D₁₂	—	5	1	no	—
16	C₃⋊C₈	—	5	1	no	—
17	C₂×D₅	—	6	1	no	—
18	C₄×C₅	—	2	1	no	—
19	C₄×C₅	C₂×D₃	1	1	yes	characteristic
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	—	2	1	no	—
24	C₃×C₄	C₂×D₅	1	1	yes	characteristic
25	C₂×C₅	#67	1	1	yes	characteristic
26	D₅	—	12	1	no	—
27	Q₈	D₁₅	1	1	yes	characteristic, complemented
28	D₄	—	15	1	no	—
29	C₈	—	15	1	no	—
30	C₂×C₃	C₂²⋊D₅	1	1	yes	characteristic
31	D₃	—	20	1	no	—
32	C₅	#215	1	1	yes	characteristic, complemented, Sylow
33	C₂²	—	30	1	no	—
34	C₄	—	2	1	no	—
35	C₄	C₂×D₁₅	1	1	yes	characteristic
36	C₃	#688	1	1	yes	characteristic, complemented, Sylow
37	C₂	—	60	1	no	—
38	C₂	#1220	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.