Subgroups — C₂⁵×D₁₉₉ #27164856

Order 12736.

5650 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₁₉₉	C₂	1	62	yes	maximal, direct product factor
2	C₂⁵×C₁₉₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×D₁₉₉	C₂²	1	620	yes	direct product factor
4	C₂⁴×C₁₉₉	C₂²	1	31	yes	complemented
5	C₂²×D₁₉₉	C₂³	1	1240	yes	direct product factor
6	C₂³×C₁₉₉	C₂³	1	155	yes	complemented
7	C₂²×C₁₉₉	C₂⁴	1	155	yes	complemented
8	C₂×D₁₉₉	C₂⁴	1	496	yes	direct product factor
9	C₂×C₁₉₉	C₂⁵	1	31	yes	complemented
10	D₁₉₉	C₂⁵	1	32	yes	direct product factor
11	C₁₉₉	C₂⁶	1	1	yes	characteristic, complemented, Sylow
12	C₂⁶	—	199	1	no	maximal, Sylow
13	C₂⁵	—	199	62	no	—
14	C₂⁵	D₁₉₉	1	1	yes	characteristic, direct product factor
15	C₂⁴	—	199	620	no	—
16	C₂⁴	C₂×D₁₉₉	1	31	yes	direct product factor
17	C₂³	—	199	1240	no	—
18	C₂³	C₂²×D₁₉₉	1	155	yes	direct product factor
19	C₂²	—	199	496	no	—
20	C₂²	C₂³×D₁₉₉	1	155	yes	direct product factor
21	C₂	—	199	32	no	—
22	C₂	C₂⁴×D₁₉₉	1	31	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁵	D₁₉₉
commutator, cosocle, hypocenter	C₁₉₉	C₂⁶
Frattini	C₁	G
Fitting, socle	C₂⁵×C₁₉₉	C₂
LCS	G ▷ C₁₉₉
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.