Subgroups — C₅×C₇×3₋¹⁺² #11745708

Order 945.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₇	C₃	1	1	yes	maximal, characteristic
2	C₅×C₇×C₉	C₃	1	3	yes	maximal, complemented
3	C₇×3₋¹⁺²	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×3₋¹⁺²	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₇	—	3	1	no	—
6	C₃×C₅×C₇	C₃²	1	1	yes	characteristic
7	C₃²×C₇	C₃×C₅	1	1	yes	characteristic
8	C₇×C₉	C₃×C₅	1	3	yes	complemented
9	C₃²×C₅	C₃×C₇	1	1	yes	characteristic
10	C₅×C₉	C₃×C₇	1	3	yes	complemented
11	C₅×C₇	3₋¹⁺²	1	1	yes	characteristic, direct product factor, Hall
12	3₋¹⁺²	C₅×C₇	1	1	yes	characteristic, direct product factor, Sylow
13	C₃×C₇	—	3	1	no	—
14	C₃×C₇	C₃²×C₅	1	1	yes	characteristic
15	C₃×C₅	—	3	1	no	—
16	C₃×C₅	C₃²×C₇	1	1	yes	characteristic
17	C₃²	C₃×C₅×C₇	1	1	yes	characteristic
18	C₉	C₃×C₅×C₇	1	3	yes	complemented
19	C₇	C₅×3₋¹⁺²	1	1	yes	characteristic, direct product factor, Sylow
20	C₅	C₇×3₋¹⁺²	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	—	3	1	no	—
22	C₃	C₃²×C₅×C₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃×C₅×C₇	C₃²
commutator, Frattini, cosocle	C₃	C₃²×C₅×C₇
prime radical	C₃²×C₅×C₇	C₃
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₅×C₇ ◁ G

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.