Subgroups — C₃⋊(C₃⋊(C₅⋊(C₇⋊D₇))) #17984415

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	C₃⋊(C₅⋊(C₇⋊D₇))	—	3	4	no	maximal
3	C₃⋊(C₃⋊(C₇⋊D₇))	—	5	1	no	maximal, Hall
4	C₃×C₅×C₇²	D₃	1	4	yes	complemented
5	C₃⋊D₁₀₅	—	7	8	no	maximal
6	C₅⋊(C₇⋊D₇)	—	9	1	no	Hall
7	C₃²×C₇²	D₅	1	1	yes	characteristic, complemented, Hall
8	C₃²×C₅×C₇	D₇	1	8	yes	complemented
9	C₃⋊(C₇⋊D₇)	—	15	4	no	—
10	C₅×C₇²	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
11	D₁₀₅	—	21	32	no	—
12	C₃×C₇²	D₁₅	1	4	yes	complemented
13	C₃⋊D₂₁	—	35	8	no	—
14	C₃×C₅×C₇	D₂₁	1	32	yes	complemented
15	C₇⋊D₇	—	45	1	no	Hall
16	C₃⋊D₁₅	—	49	1	no	Hall
17	D₃₅	—	63	8	no	—
18	C₃²×C₇	D₃₅	1	8	yes	complemented
19	C₇²	C₃⋊D₁₅	1	1	yes	characteristic, complemented, Sylow
20	C₃²×C₅	C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
21	D₂₁	—	105	32	no	—
22	C₅×C₇	C₃⋊D₂₁	1	8	yes	complemented
23	D₁₅	—	147	4	no	—
24	C₃×C₇	D₁₀₅	1	32	yes	complemented
25	C₃⋊D₃	—	245	1	no	Hall
26	C₃×C₅	C₃⋊(C₇⋊D₇)	1	4	yes	complemented
27	D₇	—	315	8	no	—
28	D₅	—	441	1	no	Hall
29	C₃²	C₅⋊(C₇⋊D₇)	1	1	yes	characteristic, complemented, Sylow
30	C₇	C₃⋊D₁₀₅	1	8	yes	complemented
31	D₃	—	735	4	no	—
32	C₅	C₃⋊(C₃⋊(C₇⋊D₇))	1	1	yes	characteristic, complemented, Sylow
33	C₃	C₃⋊(C₅⋊(C₇⋊D₇))	1	4	yes	complemented
34	C₂	—	2205	1	no	Sylow

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

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.