Subgroups — #6653

Order 240.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₀	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄₀	—	3	1	no	maximal, Hall
5	C₂×D₁₅	—	2	1	no	—
6	C₂×C₃×D₅	—	2	1	no	—
7	C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	#213	—	5	1	no	maximal, Hall
9	D₂₀	—	3	1	no	—
10	D₂₀	D₃	1	1	yes	characteristic, complemented
11	C₅×C₈	—	3	1	no	—
12	C₂×C₃×C₅	D₄	1	1	yes	characteristic
13	D₁₅	—	4	1	no	—
14	C₃×D₅	—	4	1	no	—
15	C₃×D₄	—	5	1	no	—
16	D₁₂	—	5	1	no	—
17	C₃⋊C₈	D₅	1	1	yes	characteristic, complemented
18	C₂×D₅	—	2	1	no	—
19	C₂×D₅	—	6	1	no	—
20	C₄×C₅	C₂×D₃	1	1	yes	characteristic
21	D₈	—	15	1	no	Sylow
22	C₃×C₅	D₈	1	1	yes	characteristic, complemented, Hall
23	C₂²×C₃	—	10	1	no	—
24	C₂×D₃	—	10	1	no	—
25	C₃×C₄	C₂×D₅	1	1	yes	characteristic
26	C₂×C₅	#67	1	1	yes	characteristic
27	D₅	—	4	1	no	—
28	D₅	—	12	1	no	—
29	D₄	—	5	1	no	—
30	D₄	—	15	1	no	—
31	C₈	—	3	1	no	—
32	C₂×C₃	—	20	1	no	—
33	C₂×C₃	D₂₀	1	1	yes	characteristic
34	D₃	—	20	1	no	—
35	C₅	#213	1	1	yes	characteristic, complemented, Sylow
36	C₂²	—	10	1	no	—
37	C₂²	—	30	1	no	—
38	C₄	D₃×D₅	1	1	yes	characteristic
39	C₃	D₄₀	1	1	yes	characteristic, complemented, Sylow
40	C₂	—	20	1	no	—
41	C₂	—	60	1	no	—
42	C₂	#1202	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.