Subgroups — C₃²×C₅⋊D₃₅ #15691305

Order 3150.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅²×C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅⋊D₃₅	C₃	1	4	yes	maximal, direct product factor
3	C₃²×D₃₅	—	5	6	no	maximal
4	C₃×C₅²×C₇	C₂×C₃	1	4	yes	complemented
5	C₃²×C₅⋊D₅	—	7	1	no	maximal, Hall
6	C₅⋊D₃₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×C₅×C₇	D₅	1	6	yes	complemented
8	C₃²×C₅²	D₇	1	1	yes	characteristic, complemented, Hall
9	C₃×D₃₅	—	5	24	no	—
10	C₅²×C₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
11	C₃×C₅⋊D₅	—	7	4	no	—
12	C₃²×D₇	—	25	1	no	Hall
13	C₃×C₅×C₇	C₃×D₅	1	24	yes	complemented
14	C₃²×D₅	—	35	6	no	—
15	C₃×C₅²	C₃×D₇	1	4	yes	complemented
16	D₃₅	—	5	6	no	—
17	C₃²×C₇	C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
18	C₅⋊D₅	—	7	1	no	Hall
19	C₃²×C₅	D₃₅	1	6	yes	complemented
20	C₃×D₇	—	25	4	no	—
21	C₅×C₇	C₃²×D₅	1	6	yes	complemented
22	C₃×D₅	—	35	24	no	—
23	C₅²	C₃²×D₇	1	1	yes	characteristic, complemented, Sylow
24	C₃×C₇	C₃×C₅⋊D₅	1	4	yes	complemented
25	C₂×C₃²	—	175	1	no	Hall
26	C₃×C₅	C₃×D₃₅	1	24	yes	complemented
27	D₇	—	25	1	no	Hall
28	D₅	—	35	6	no	—
29	C₃²	C₅⋊D₃₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₇	C₃²×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	175	4	no	—
32	C₅	C₃²×D₃₅	1	6	yes	complemented
33	C₃	C₃×C₅⋊D₃₅	1	4	yes	direct product factor
34	C₂	—	175	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²	C₅⋊D₃₅
commutator, cosocle, hypocenter	C₅²×C₇	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₇	C₂
LCS	G ▷ C₅²×C₇
UCS	C₁ ◁ C₃²

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.