Subgroups — C₇²×C₃⋊D₁₅ #17984413

Order 4410.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₇²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇²×D₁₅	—	3	4	no	maximal
3	C₇²×C₃⋊D₃	—	5	1	no	maximal, Hall
4	C₃×C₅×C₇²	D₃	1	4	yes	complemented
5	C₇×C₃⋊D₁₅	C₇	1	8	yes	maximal, direct product factor
6	C₇²×D₅	—	9	1	no	Hall
7	C₃²×C₇²	D₅	1	1	yes	characteristic, complemented, Hall
8	C₃²×C₅×C₇	C₂×C₇	1	8	yes	complemented
9	D₃×C₇²	—	15	4	no	—
10	C₅×C₇²	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
11	C₇×D₁₅	—	3	32	no	—
12	C₃×C₇²	D₁₅	1	4	yes	complemented
13	C₇×C₃⋊D₃	—	5	8	no	—
14	C₃×C₅×C₇	D₃×C₇	1	32	yes	complemented
15	C₂×C₇²	—	45	1	no	Hall
16	C₃⋊D₁₅	C₇²	1	1	yes	characteristic, direct product factor, Hall
17	C₇×D₅	—	9	8	no	—
18	C₃²×C₇	C₇×D₅	1	8	yes	complemented
19	C₇²	C₃⋊D₁₅	1	1	yes	characteristic, direct product factor, Sylow
20	C₃²×C₅	C₂×C₇²	1	1	yes	characteristic, complemented, Hall
21	D₃×C₇	—	15	32	no	—
22	C₅×C₇	C₇×C₃⋊D₃	1	8	yes	complemented
23	D₁₅	—	3	4	no	—
24	C₃×C₇	C₇×D₁₅	1	32	yes	complemented
25	C₃⋊D₃	—	5	1	no	Hall
26	C₃×C₅	D₃×C₇²	1	4	yes	complemented
27	C₂×C₇	—	45	8	no	—
28	D₅	—	9	1	no	Hall
29	C₃²	C₇²×D₅	1	1	yes	characteristic, complemented, Sylow
30	C₇	C₇×C₃⋊D₁₅	1	8	yes	direct product factor
31	D₃	—	15	4	no	—
32	C₅	C₇²×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
33	C₃	C₇²×D₁₅	1	4	yes	complemented
34	C₂	—	45	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇²	C₃⋊D₁₅
commutator, cosocle, hypocenter	C₃²×C₅	C₂×C₇²
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇²	C₂
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₇²

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.