Subgroups — C₃×#87756 #11924977

Order 1200.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₈	C₂	1	1	yes	maximal, characteristic
2	#87756	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₄×C₅²	C₄	1	1	yes	characteristic
4	C₃×#672	—	5	6	no	maximal
5	C₅²×C₈	C₂×C₃	1	1	yes	characteristic
6	C₂×C₃×C₅²	C₈	1	1	yes	characteristic
7	C₃×C₅×C₈	D₅	1	6	yes	—
8	C₄×C₅²	C₃×C₄	1	1	yes	characteristic
9	#672	—	5	6	no	—
10	C₃×C₅²	C₁₆	1	1	yes	characteristic, complemented, Hall
11	C₃×C₄×C₅	Dic₅	1	6	yes	—
12	C₂×C₅²	C₃×C₈	1	1	yes	characteristic
13	C₃×C₁₆	—	25	1	no	Hall
14	C₅×C₈	C₃×D₅	1	6	yes	—
15	C₂×C₃×C₅	#168	1	6	yes	—
16	C₅²	C₃×C₁₆	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₈	C₅⋊D₅	1	1	yes	characteristic
18	C₄×C₅	C₃×Dic₅	1	6	yes	—
19	C₁₆	—	25	1	no	Sylow
20	C₃×C₅	#672	1	6	yes	complemented
21	C₃×C₄	#1039	1	1	yes	characteristic
22	C₂×C₅	C₃×#168	1	6	yes	—
23	C₈	C₃×C₅⋊D₅	1	1	yes	characteristic
24	C₂×C₃	#6029	1	1	yes	characteristic
25	C₅	C₃×#672	1	6	yes	complemented
26	C₄	C₃×#1039	1	1	yes	characteristic
27	C₃	#87756	1	1	yes	characteristic, direct product factor, Sylow
28	C₂	C₃×#6029	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.