Subgroups — #90948

Order 480.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₆₀	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₁₂	C₂	1	1	yes	maximal, characteristic
3	C₃×#672	C₂	1	1	yes	maximal, characteristic
4	#3961	—	3	1	no	maximal, Hall
5	Dic₃₀	—	2	1	no	—
6	C₅×Dic₆	—	2	1	no	—
7	C₃×C₅×C₈	C₂²	1	1	yes	characteristic
8	Dic₂₄	—	5	1	no	maximal, Hall
9	C₅×Q₁₆	—	3	1	no	—
10	Dic₂₀	—	3	1	no	—
11	#672	D₃	1	1	yes	characteristic
12	C₃×C₄×C₅	D₄	1	1	yes	characteristic
13	Dic₁₅	—	4	1	no	—
14	C₅×Dic₃	—	4	1	no	—
15	Dic₁₂	—	5	1	no	—
16	Dic₁₂	D₅	1	1	yes	characteristic
17	C₃×C₁₆	—	5	1	no	—
18	C₅×Q₈	—	6	1	no	—
19	Dic₁₀	—	6	1	no	—
20	C₅×C₈	C₂×D₃	1	1	yes	characteristic
21	Q₃₂	—	15	1	no	Sylow
22	C₂×C₃×C₅	D₈	1	1	yes	characteristic
23	Dic₆	—	2	1	no	—
24	Dic₆	—	10	1	no	—
25	C₃×C₈	C₂×D₅	1	1	yes	characteristic
26	C₄×C₅	—	12	1	no	—
27	C₄×C₅	D₁₂	1	1	yes	characteristic
28	Dic₅	—	12	1	no	—
29	Q₁₆	—	3	1	no	—
30	Q₁₆	—	15	1	no	—
31	C₁₆	—	5	1	no	—
32	C₃×C₅	Q₃₂	1	1	yes	characteristic, complemented, Hall
33	C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
34	Dic₃	—	4	1	no	—
35	Dic₃	—	20	1	no	—
36	C₂×C₅	D₂₄	1	1	yes	characteristic
37	Q₈	—	6	1	no	—
38	Q₈	—	30	1	no	—
39	C₈	D₃×D₅	1	1	yes	characteristic
40	C₂×C₃	#686	1	1	yes	characteristic
41	C₅	Dic₂₄	1	1	yes	characteristic, complemented, Sylow
42	C₄	—	12	1	no	—
43	C₄	—	60	1	no	—
44	C₄	#1203	1	1	yes	characteristic
45	C₃	#3961	1	1	yes	characteristic, complemented, Sylow
46	C₂	#6654	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.