Subgroups — #6821

Order 240.

80 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	3	yes	maximal, complemented
3	C₄×D₁₅	C₂	1	3	yes	maximal, complemented
4	#713	—	3	1	no	maximal, Hall
5	C₂×D₁₅	C₂²	1	3	yes	—
6	C₃×C₄×C₅	C₂²	1	3	yes	—
7	Dic₁₅	C₂²	1	1	yes	characteristic
8	#239	—	5	1	no	maximal, Hall
9	C₅×Q₈	D₃	1	1	yes	characteristic, complemented
10	D₂₀	—	3	3	no	—
11	C₄×D₅	—	3	3	no	—
12	C₂×C₃×C₅	C₂³	1	1	yes	characteristic
13	D₁₅	—	2	3	no	—
14	C₃×Q₈	D₅	1	1	yes	characteristic, complemented
15	D₁₂	—	5	3	no	—
16	C₄×D₃	—	5	3	no	—
17	C₂×D₅	—	3	3	no	—
18	C₄×C₅	C₂×D₃	1	3	yes	—
19	Dic₅	—	3	1	no	—
20	#41	—	15	1	no	Sylow
21	C₃×C₅	#41	1	1	yes	characteristic, complemented, Hall
22	C₂×D₃	—	5	3	no	—
23	C₃×C₄	C₂×D₅	1	3	yes	—
24	Dic₃	—	5	1	no	—
25	C₂×C₅	C₂²×D₃	1	1	yes	characteristic
26	D₅	—	6	3	no	—
27	Q₈	D₁₅	1	1	yes	characteristic, complemented
28	D₄	—	15	3	no	—
29	C₂×C₄	—	15	3	no	—
30	C₂×C₃	C₂²×D₅	1	1	yes	characteristic
31	D₃	—	10	3	no	—
32	C₅	#239	1	1	yes	characteristic, complemented, Sylow
33	C₂²	—	15	3	no	—
34	C₄	—	15	1	no	—
35	C₄	C₂×D₁₅	1	3	yes	—
36	C₃	#713	1	1	yes	characteristic, complemented, Sylow
37	C₂	—	30	3	no	—
38	C₂	C₂²×D₁₅	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.