Subgroups — C₂×D₁₃₁₇₉ #72289709

Order 52716.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃₁₇₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₂₃×C₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄₃₉₃	—	3	1	no	maximal, Hall
4	C₃×C₂₃×C₁₉₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₂₃×C₁₉₁	D₃	1	1	yes	characteristic, complemented
6	D₄₃₉₃	—	3	2	no	—
7	C₂₃×C₁₉₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₅₇₃	—	23	1	no	maximal, Hall
9	C₂×C₃×C₁₉₁	D₂₃	1	1	yes	characteristic, complemented
10	D₅₇₃	—	23	2	no	—
11	C₂×D₁₉₁	—	69	1	no	Hall
12	C₃×C₁₉₁	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₉₁	D₆₉	1	1	yes	characteristic, complemented
14	D₁₉₁	—	69	2	no	—
15	C₂×D₆₉	—	191	1	no	maximal, Hall
16	C₁₉₁	C₂×D₆₉	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₃×C₂₃	D₁₉₁	1	1	yes	characteristic, complemented
18	D₆₉	—	191	2	no	—
19	C₂×D₂₃	—	573	1	no	Hall
20	C₃×C₂₃	C₂×D₁₉₁	1	1	yes	characteristic, complemented, Hall
21	C₂×C₂₃	D₅₇₃	1	1	yes	characteristic, complemented
22	D₂₃	—	573	2	no	—
23	C₂₃	C₂×D₅₇₃	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₃	—	4393	1	no	Hall
25	C₂×C₃	D₄₃₉₃	1	1	yes	characteristic, complemented
26	D₃	—	4393	2	no	—
27	C₂²	—	13179	1	no	Sylow
28	C₃	C₂×D₄₃₉₃	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	13179	2	no	—
30	C₂	D₁₃₁₇₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₁₃₁₇₉
commutator, cosocle, hypocenter	C₃×C₂₃×C₁₉₁	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₂₃×C₁₉₁	C₂
LCS	G ▷ C₃×C₂₃×C₁₉₁
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.