Subgroups — D₃₉×C₄₃⋊C₇ #37553451

Order 23478.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₄₃⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₃×C₄₃⋊C₇	—	3	1	no	maximal, Hall
3	C₁₃×C₄₃⋊C₇	D₃	1	1	yes	characteristic, complemented, Hall
4	C₄₃×D₃₉	C₇	1	1	yes	maximal, characteristic, complemented, Hall
5	D₃×C₄₃⋊C₇	—	13	1	no	maximal, Hall
6	C₃×C₁₃×C₄₃	C₂×C₇	1	1	yes	characteristic, complemented, Hall
7	D₁₃×C₄₃	—	3	1	no	Hall
8	C₃×C₄₃⋊C₇	D₁₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₄₃⋊C₇	—	39	1	no	Hall
10	C₁₃×C₄₃	D₃×C₇	1	1	yes	characteristic, complemented, Hall
11	C₇×D₃₉	—	43	1	no	maximal, Hall
12	C₄₃⋊C₇	D₃₉	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₇×C₁₃	—	43	1	no	Hall
14	D₃×C₄₃	—	13	1	no	Hall
15	C₇×D₁₃	—	129	1	no	Hall
16	C₃×C₄₃	C₇×D₁₃	1	1	yes	characteristic, complemented, Hall
17	C₇×C₁₃	—	43	1	no	Hall
18	C₂×C₄₃	—	39	1	no	Hall
19	D₃₉	C₄₃⋊C₇	1	1	yes	characteristic, direct product factor, Hall
20	C₄₃	C₇×D₃₉	1	1	yes	characteristic, complemented, Sylow
21	D₃×C₇	—	559	1	no	Hall
22	C₃×C₁₃	C₂×C₄₃⋊C₇	1	1	yes	characteristic, complemented, Hall
23	D₁₃	—	3	1	no	Hall
24	C₃×C₇	—	43	1	no	Hall
25	C₂×C₇	—	1677	1	no	Hall
26	C₁₃	D₃×C₄₃⋊C₇	1	1	yes	characteristic, complemented, Sylow
27	C₇	—	43	1	no	Sylow
28	D₃	—	13	1	no	Hall
29	C₃	D₁₃×C₄₃⋊C₇	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	39	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₃×C₄₃	C₂×C₇
LCS	G ▷ C₃×C₁₃×C₄₃
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.