Subgroups — Dic₃×C₂₉²⋊C₃ #44475615

Order 30276.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₂₉²⋊C₃	C₂	1	1	yes	maximal, characteristic
2	Dic₃×C₂₉²	C₃	1	1	yes	maximal, characteristic, complemented
3	C₄×C₂₉²⋊C₃	—	3	1	no	maximal
4	C₃×C₂₉²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₂₉²⋊C₃	—	2	1	no	—
6	C₂×C₂₉²⋊C₃	D₃	1	1	yes	characteristic
7	C₂×C₃×C₂₉²	C₂×C₃	1	1	yes	characteristic
8	C₄×C₂₉²	—	3	1	no	Hall
9	C₃×C₂₉²	C₃×C₄	1	1	yes	characteristic, complemented
10	C₂₉²⋊C₃	—	2	1	no	—
11	C₂₉²⋊C₃	Dic₃	1	1	yes	characteristic, direct product factor
12	C₂×C₂₉²	C₃×D₃	1	1	yes	characteristic
13	C₂₉²	C₃×Dic₃	1	1	yes	characteristic, complemented, Sylow
14	Dic₃×C₂₉	—	3	10	no	—
15	C₂×C₃×C₂₉	—	3	10	no	—
16	C₄×C₂₉	—	9	10	no	—
17	C₃×C₂₉	—	3	10	no	—
18	C₂×C₂₉	—	3	10	no	—
19	C₃×Dic₃	—	841	1	no	maximal, Hall
20	C₂₉	—	3	10	no	—
21	C₂×C₃²	—	841	1	no	—
22	C₃×C₄	—	2523	1	no	—
23	Dic₃	C₂₉²⋊C₃	1	1	yes	characteristic, direct product factor
24	C₃²	—	841	1	no	Sylow
25	C₂×C₃	—	841	1	no	—
26	C₂×C₃	—	1682	1	no	—
27	C₂×C₃	C₂×C₂₉²⋊C₃	1	1	yes	characteristic
28	C₄	—	3	1	no	Sylow
29	C₃	—	841	1	no	—
30	C₃	—	1682	1	no	—
31	C₃	C₄×C₂₉²⋊C₃	1	1	yes	characteristic, complemented
32	C₂	D₃×C₂₉²⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×C₂₉²⋊C₃
commutator, hypocenter	C₃×C₂₉²	C₃×C₄
Fitting, socle, cosocle	C₂×C₃×C₂₉²	C₂×C₃
prime radical	C₂×C₃×C₂₉²⋊C₃	C₂
LCS	G ▷ C₃×C₂₉²
UCS	C₁ ◁ C₂

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.