Subgroups — C₂×C₄₇×C₁₃⋊D₁₃ #44540975

Order 31772.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×C₁₃⋊D₁₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₃²×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃²×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₃×C₄₇	—	13	14	no	maximal
5	C₂×C₁₃×C₄₇	D₁₃	1	14	yes	complemented
6	D₁₃×C₄₇	—	13	28	no	—
7	C₂×C₁₃⋊D₁₃	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₃×C₄₇	C₂×D₁₃	1	14	yes	complemented
9	C₂×C₁₃²	C₂×C₄₇	1	1	yes	characteristic, complemented
10	C₁₃⋊D₁₃	C₂×C₄₇	1	2	yes	direct product factor
11	C₂²×C₄₇	—	169	1	no	Hall
12	C₁₃²	C₂²×C₄₇	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₄₇	—	169	2	no	—
14	C₂×C₄₇	C₁₃⋊D₁₃	1	1	yes	characteristic, direct product factor
15	C₂×D₁₃	—	13	14	no	—
16	C₄₇	C₂×C₁₃⋊D₁₃	1	1	yes	characteristic, direct product factor, Sylow
17	C₂×C₁₃	D₁₃×C₄₇	1	14	yes	complemented
18	D₁₃	—	13	28	no	—
19	C₁₃	C₂×D₁₃×C₄₇	1	14	yes	complemented
20	C₂²	—	169	1	no	Sylow
21	C₂	—	169	2	no	—
22	C₂	C₄₇×C₁₃⋊D₁₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₄₇	C₁₃⋊D₁₃
commutator, cosocle, hypocenter	C₁₃²	C₂²×C₄₇
Frattini	C₁	G
Fitting, socle	C₂×C₁₃²×C₄₇	C₂
LCS	G ▷ C₁₃²
UCS	C₁ ◁ C₂×C₄₇

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.