Subgroups — C₂⁵×D₁₆₇ #24924107

Order 10688.

5650 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₁₆₇	C₂	1	62	yes	maximal, direct product factor
2	C₂⁵×C₁₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×D₁₆₇	C₂²	1	620	yes	direct product factor
4	C₂⁴×C₁₆₇	C₂²	1	31	yes	complemented
5	C₂²×D₁₆₇	C₂³	1	1240	yes	direct product factor
6	C₂³×C₁₆₇	C₂³	1	155	yes	complemented
7	C₂²×C₁₆₇	C₂⁴	1	155	yes	complemented
8	C₂×D₁₆₇	C₂⁴	1	496	yes	direct product factor
9	C₂×C₁₆₇	C₂⁵	1	31	yes	complemented
10	D₁₆₇	C₂⁵	1	32	yes	direct product factor
11	C₁₆₇	C₂⁶	1	1	yes	characteristic, complemented, Sylow
12	C₂⁶	—	167	1	no	maximal, Sylow
13	C₂⁵	—	167	62	no	—
14	C₂⁵	D₁₆₇	1	1	yes	characteristic, direct product factor
15	C₂⁴	—	167	620	no	—
16	C₂⁴	C₂×D₁₆₇	1	31	yes	direct product factor
17	C₂³	—	167	1240	no	—
18	C₂³	C₂²×D₁₆₇	1	155	yes	direct product factor
19	C₂²	—	167	496	no	—
20	C₂²	C₂³×D₁₆₇	1	155	yes	direct product factor
21	C₂	—	167	32	no	—
22	C₂	C₂⁴×D₁₆₇	1	31	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁵	D₁₆₇
commutator, cosocle, hypocenter	C₁₆₇	C₂⁶
Frattini	C₁	G
Fitting, socle	C₂⁵×C₁₆₇	C₂
LCS	G ▷ C₁₆₇
UCS	C₁ ◁ C₂⁵

Splittings G = N ⋊ H with N normal; H ≅ G/N.