Subgroups — D₁₃²×C₄₇ #44540964

Order 31772.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×D₁₃×C₄₇	C₂	1	2	yes	maximal, complemented
2	C₄₇×C₁₃⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃²×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₃×C₄₇	—	13	2	no	maximal
5	C₂×C₁₃×C₄₇	—	13	2	no	—
6	D₁₃×C₄₇	—	13	2	no	—
7	D₁₃×C₄₇	—	26	6	no	—
8	D₁₃×C₄₇	D₁₃	1	2	yes	direct product factor
9	D₁₃²	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₁₃×C₄₇	—	2	6	no	—
11	C₁₃×C₄₇	C₂×D₁₃	1	2	yes	complemented
12	C₁₃⋊D₁₃	C₂×C₄₇	1	1	yes	characteristic, complemented
13	C₁₃×D₁₃	C₂×C₄₇	1	2	yes	complemented
14	C₂²×C₄₇	—	169	1	no	Hall
15	C₁₃²	C₂²×C₄₇	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₄₇	—	13	2	no	—
17	C₂×C₄₇	—	169	1	no	—
18	C₂×D₁₃	—	13	2	no	—
19	C₄₇	D₁₃²	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₁₃	—	13	2	no	—
21	D₁₃	—	13	2	no	—
22	D₁₃	—	26	6	no	—
23	D₁₃	D₁₃×C₄₇	1	2	yes	direct product factor
24	C₁₃	—	2	6	no	—
25	C₁₃	C₂×D₁₃×C₄₇	1	2	yes	complemented
26	C₂²	—	169	1	no	Sylow
27	C₂	—	13	2	no	—
28	C₂	—	169	1	no	—

	subgroup	G/H
center, hypercenter	C₄₇	D₁₃²
commutator, cosocle, hypocenter	C₁₃²	C₂²×C₄₇
Frattini	C₁	G
Fitting, socle	C₁₃²×C₄₇	C₂²
LCS	G ▷ C₁₃²
UCS	C₁ ◁ 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.