Subgroups — #6718

Order 240.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×Q₈	C₂	1	1	yes	maximal, characteristic
2	Dic₃₀	C₂	1	1	yes	maximal, characteristic
3	C₃⋊#168	C₂	1	1	yes	maximal, characteristic
4	#689	—	3	1	no	maximal, Hall
5	C₃×C₄×C₅	—	2	1	no	—
6	C₃×C₄×C₅	C₂²	1	1	yes	characteristic
7	Dic₁₅	—	2	1	no	—
8	#216	—	5	1	no	maximal, Hall
9	C₅×Q₈	D₃	1	1	yes	characteristic
10	Dic₁₀	—	3	1	no	—
11	#168	—	3	1	no	—
12	C₂×C₃×C₅	D₄	1	1	yes	characteristic
13	C₃×Q₈	D₅	1	1	yes	characteristic
14	Dic₆	—	5	1	no	—
15	C₃⋊C₈	—	5	1	no	—
16	C₄×C₅	—	2	1	no	—
17	C₄×C₅	C₂×D₃	1	1	yes	characteristic
18	Dic₅	—	6	1	no	—
19	Q₁₆	—	15	1	no	Sylow
20	C₃×C₅	Q₁₆	1	1	yes	characteristic, complemented, Hall
21	C₃×C₄	—	2	1	no	—
22	C₃×C₄	C₂×D₅	1	1	yes	characteristic
23	Dic₃	—	10	1	no	—
24	C₂×C₅	#67	1	1	yes	characteristic
25	Q₈	—	15	1	no	—
26	Q₈	D₁₅	1	1	yes	characteristic
27	C₈	—	15	1	no	—
28	C₂×C₃	C₂²⋊D₅	1	1	yes	characteristic
29	C₅	#216	1	1	yes	characteristic, complemented, Sylow
30	C₄	—	2	1	no	—
31	C₄	—	30	1	no	—
32	C₄	C₂×D₁₅	1	1	yes	characteristic
33	C₃	#689	1	1	yes	characteristic, complemented, Sylow
34	C₂	#1220	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.