Subgroups — C₃×C₂₉⋊(D₃₁⋊C₃) #30633650

Order 16182.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₉×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₉⋊(D₃₁⋊C₃)	C₃	1	3	yes	maximal, direct product factor
3	C₃×D₈₉₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₂₉×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
5	C₂₉×C₃₁⋊C₃	C₂×C₃	1	3	yes	complemented
6	D₈₉₉	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₂₉×C₃₁	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×D₃₁⋊C₃	—	29	1	no	maximal, Hall
9	C₃²×D₂₉	—	31	1	no	maximal, Hall
10	C₃×C₃₁⋊C₃	D₂₉	1	1	yes	characteristic, complemented, Hall
11	C₃²×C₂₉	—	31	1	no	Hall
12	C₃×D₃₁	—	29	1	no	—
13	D₃₁⋊C₃	—	29	3	no	—
14	C₃×D₂₉	—	31	3	no	—
15	C₃×D₂₉	—	93	1	no	—
16	C₃×C₃₁	C₃×D₂₉	1	1	yes	characteristic, complemented
17	C₃₁⋊C₃	C₃×D₂₉	1	3	yes	complemented
18	C₃×C₂₉	—	31	3	no	—
19	C₃×C₂₉	D₃₁⋊C₃	1	1	yes	characteristic, complemented
20	D₃₁	—	29	1	no	Hall
21	D₂₉	—	93	1	no	Hall
22	C₃₁	C₃²×D₂₉	1	1	yes	characteristic, complemented, Sylow
23	C₂₉	C₃×D₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃²	—	899	1	no	Hall
25	C₃²	—	31	1	no	Sylow
26	C₂×C₃	—	899	3	no	—
27	C₂×C₃	—	2697	1	no	—
28	C₃	—	31	3	no	—
29	C₃	C₂₉⋊(D₃₁⋊C₃)	1	1	yes	characteristic, direct product factor
30	C₂	—	2697	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	C₂₉⋊(D₃₁⋊C₃)
commutator, cosocle, hypocenter	C₂₉×C₃₁	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₂₉×C₃₁	C₂×C₃
LCS	G ▷ C₂₉×C₃₁
UCS	C₁ ◁ C₃

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.