Subgroups — C₅×D₄₈ #91042

Order 480.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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