Subgroups — C₂×C₃⋊(D₄₃₉⋊C₃) #30628996

Order 15804.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄₃₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊(D₄₃₉⋊C₃)	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₁₃₁₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄₃₉⋊C₃	—	3	1	no	maximal
5	C₃×C₄₃₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₄₃₉	C₂×C₃	1	1	yes	characteristic, complemented
7	D₁₃₁₇	C₂×C₃	1	2	yes	complemented
8	C₂×C₄₃₉⋊C₃	—	2	1	no	—
9	C₂×C₄₃₉⋊C₃	D₃	1	1	yes	characteristic, complemented
10	D₄₃₉⋊C₃	—	3	2	no	—
11	C₂×D₄₃₉	—	3	1	no	Hall
12	C₃×C₄₃₉	C₂²×C₃	1	1	yes	characteristic, complemented
13	C₄₃₉⋊C₃	—	2	1	no	—
14	C₄₃₉⋊C₃	C₂×D₃	1	1	yes	characteristic, complemented
15	C₂×C₄₃₉	C₃×D₃	1	1	yes	characteristic, complemented
16	D₄₃₉	—	3	2	no	—
17	C₄₃₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₃×D₃	—	439	1	no	maximal, Hall
19	C₂×C₃²	—	878	1	no	—
20	C₃×D₃	—	439	2	no	—
21	C₂²×C₃	—	1317	1	no	—
22	C₂×D₃	—	439	1	no	—
23	C₃²	—	878	1	no	Sylow
24	C₂×C₃	—	1317	2	no	—
25	C₂×C₃	—	878	1	no	—
26	C₂×C₃	—	878	1	no	—
27	C₂×C₃	D₄₃₉⋊C₃	1	1	yes	characteristic, complemented
28	D₃	—	439	2	no	—
29	C₂²	—	1317	1	no	Sylow
30	C₃	—	878	1	no	—
31	C₃	—	878	1	no	—
32	C₃	C₂×D₄₃₉⋊C₃	1	1	yes	characteristic, complemented
33	C₂	—	1317	2	no	—
34	C₂	C₃⋊(D₄₃₉⋊C₃)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊(D₄₃₉⋊C₃)
commutator, cosocle, hypocenter	C₃×C₄₃₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₄₃₉	C₂×C₃
LCS	G ▷ C₃×C₄₃₉
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.