Subgroups — Dic₂₄₀ #11746271

Order 960.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₂₀	C₂	1	2	yes	maximal
2	C₃×C₅×C₃₂	C₂	1	1	yes	maximal, characteristic
3	Dic₈₀	—	3	1	no	maximal, Hall
4	Dic₆₀	—	2	2	no	—
5	C₃×C₅×C₁₆	C₂²	1	1	yes	characteristic
6	Dic₄₈	—	5	1	no	maximal, Hall
7	Dic₄₀	—	3	2	no	—
8	C₅×C₃₂	D₃	1	1	yes	characteristic
9	Dic₃₀	—	4	2	no	—
10	C₃×C₅×C₈	D₄	1	1	yes	characteristic
11	Dic₂₄	—	5	2	no	—
12	C₃×C₃₂	D₅	1	1	yes	characteristic
13	Dic₂₀	—	6	2	no	—
14	C₅×C₁₆	C₂×D₃	1	1	yes	characteristic
15	Q₆₄	—	15	1	no	Sylow
16	C₃×C₄×C₅	D₈	1	1	yes	characteristic
17	Dic₁₅	—	8	2	no	—
18	Dic₁₂	—	10	2	no	—
19	C₃×C₁₆	C₂×D₅	1	1	yes	characteristic
20	Dic₁₀	—	12	2	no	—
21	C₅×C₈	D₁₂	1	1	yes	characteristic
22	Q₃₂	—	15	2	no	—
23	C₃₂	D₁₅	1	1	yes	characteristic
24	C₂×C₃×C₅	D₁₆	1	1	yes	characteristic
25	Dic₆	—	20	2	no	—
26	C₃×C₈	D₂₀	1	1	yes	characteristic
27	C₄×C₅	D₂₄	1	1	yes	characteristic
28	Dic₅	—	24	2	no	—
29	Q₁₆	—	30	2	no	—
30	C₁₆	C₂×D₁₅	1	1	yes	characteristic
31	C₃×C₅	Q₆₄	1	1	yes	characteristic, complemented, Hall
32	C₃×C₄	D₄₀	1	1	yes	characteristic
33	Dic₃	—	40	2	no	—
34	C₂×C₅	D₄₈	1	1	yes	characteristic
35	Q₈	—	60	2	no	—
36	C₈	D₆₀	1	1	yes	characteristic
37	C₂×C₃	D₈₀	1	1	yes	characteristic
38	C₅	Dic₄₈	1	1	yes	characteristic, complemented, Sylow
39	C₄	—	120	2	no	—
40	C₄	D₁₂₀	1	1	yes	characteristic
41	C₃	Dic₈₀	1	1	yes	characteristic, complemented, Sylow
42	C₂	D₂₄₀	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.