Subgroups — C₃⋊#19150997 #30685010

Order 17052.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇⋊D₂₀₃	C₂	1	1	yes	maximal, characteristic
2	#19150997	—	3	1	no	maximal, Hall
3	C₃×C₇²×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇⋊D₂₀₃	D₃	1	1	yes	characteristic
5	C₇²×C₂₉	Dic₃	1	1	yes	characteristic, complemented, Hall
6	C₃×D₂₀₃	—	14	4	no	—
7	C₃×C₇×C₂₉	—	2	4	no	—
8	C₃⋊#5997	—	29	1	no	maximal, Hall
9	D₂₀₃	—	14	4	no	—
10	C₃⋊#1181	—	49	1	no	maximal, Hall
11	C₃×C₇⋊D₇	—	29	1	no	—
12	C₇×C₂₉	—	2	4	no	—
13	#5997	—	87	1	no	Hall
14	C₃×D₂₉	—	49	1	no	—
15	C₃×C₇²	#1181	1	1	yes	characteristic, complemented, Hall
16	#1181	—	147	1	no	Hall
17	C₇⋊D₇	—	29	1	no	—
18	C₃×C₂₉	#5997	1	1	yes	characteristic, complemented, Hall
19	D₂₉	—	49	1	no	—
20	C₇²	C₃⋊#1181	1	1	yes	characteristic, complemented, Sylow
21	C₃×D₇	—	406	4	no	—
22	C₂₉	C₃⋊#5997	1	1	yes	characteristic, complemented, Sylow
23	C₃×C₇	—	2	4	no	—
24	D₇	—	406	4	no	—
25	Dic₃	—	1421	1	no	Hall
26	C₇	—	2	4	no	—
27	C₂×C₃	—	1421	1	no	—
28	C₄	—	4263	1	no	Sylow
29	C₃	#19150997	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	1421	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₇²×C₂₉	C₄
prime radical, cosocle	C₃×C₇⋊D₂₀₃	C₂
LCS	G ▷ C₃×C₇²×C₂₉
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.