Subgroups — C₂⁵×C₁₃⋊C₃ #11929340

Order 1248.

1496 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₁₃⋊C₃	C₂	1	31	yes	maximal, direct product factor
2	C₂⁵×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂³×C₁₃⋊C₃	C₂²	1	155	yes	direct product factor
4	C₂⁴×C₁₃	C₂×C₃	1	31	yes	complemented
5	C₂²×C₁₃⋊C₃	C₂³	1	155	yes	direct product factor
6	C₂³×C₁₃	C₂²×C₃	1	155	yes	complemented
7	C₂⁵×C₃	—	13	1	no	maximal, Hall
8	C₂×C₁₃⋊C₃	C₂⁴	1	31	yes	direct product factor
9	C₂²×C₁₃	C₂³×C₃	1	155	yes	complemented
10	C₂⁴×C₃	—	13	31	no	—
11	C₁₃⋊C₃	C₂⁵	1	1	yes	characteristic, direct product factor, Hall
12	C₂⁵	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₂×C₁₃	C₂⁴×C₃	1	31	yes	complemented
14	C₂³×C₃	—	13	155	no	—
15	C₂⁴	C₂×C₁₃⋊C₃	1	31	yes	direct product factor
16	C₁₃	C₂⁵×C₃	1	1	yes	characteristic, complemented, Sylow
17	C₂²×C₃	—	13	155	no	—
18	C₂³	C₂²×C₁₃⋊C₃	1	155	yes	direct product factor
19	C₂×C₃	—	13	31	no	—
20	C₂²	C₂³×C₁₃⋊C₃	1	155	yes	direct product factor
21	C₃	—	13	1	no	Sylow
22	C₂	C₂⁴×C₁₃⋊C₃	1	31	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁵	C₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₂⁵×C₃
Frattini	C₁	G
Fitting, socle	C₂⁵×C₁₃	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂⁵

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.