Subgroups — D₂₄₀ #91083

Order 480.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₂₀	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈₀	—	3	1	no	maximal, Hall
4	D₆₀	—	2	2	no	—
5	C₃×C₅×C₈	C₂²	1	1	yes	characteristic
6	D₄₈	—	5	1	no	maximal, Hall
7	D₄₀	—	3	2	no	—
8	C₅×C₁₆	D₃	1	1	yes	characteristic, complemented
9	C₂×D₁₅	—	4	2	no	—
10	C₃×C₄×C₅	D₄	1	1	yes	characteristic
11	D₂₄	—	5	2	no	—
12	C₃×C₁₆	D₅	1	1	yes	characteristic, complemented
13	D₂₀	—	6	2	no	—
14	C₅×C₈	C₂×D₃	1	1	yes	characteristic
15	D₁₆	—	15	1	no	Sylow
16	C₂×C₃×C₅	D₈	1	1	yes	characteristic
17	D₁₅	—	8	2	no	—
18	D₁₂	—	10	2	no	—
19	C₃×C₈	C₂×D₅	1	1	yes	characteristic
20	C₂×D₅	—	12	2	no	—
21	C₄×C₅	D₁₂	1	1	yes	characteristic
22	D₈	—	15	2	no	—
23	C₁₆	D₁₅	1	1	yes	characteristic, complemented
24	C₃×C₅	D₁₆	1	1	yes	characteristic, complemented, Hall
25	C₂×D₃	—	20	2	no	—
26	C₃×C₄	D₂₀	1	1	yes	characteristic
27	C₂×C₅	D₂₄	1	1	yes	characteristic
28	D₅	—	24	2	no	—
29	D₄	—	30	2	no	—
30	C₈	C₂×D₁₅	1	1	yes	characteristic
31	C₂×C₃	D₄₀	1	1	yes	characteristic
32	D₃	—	40	2	no	—
33	C₅	D₄₈	1	1	yes	characteristic, complemented, Sylow
34	C₂²	—	60	2	no	—
35	C₄	D₆₀	1	1	yes	characteristic
36	C₃	D₈₀	1	1	yes	characteristic, complemented, Sylow
37	C₂	—	120	2	no	—
38	C₂	D₁₂₀	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.