Subgroups — C₂⁵×D₃ #5983

Order 192.

5650 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×D₃	C₂	1	62	yes	maximal, direct product factor
3	C₂⁶	—	3	1	no	maximal, Sylow
4	C₂⁴×C₃	C₂²	1	31	yes	complemented
5	C₂³×D₃	C₂²	1	620	yes	direct product factor
6	C₂⁵	—	3	62	no	—
7	C₂⁵	D₃	1	1	yes	characteristic, direct product factor
8	C₂³×C₃	C₂³	1	155	yes	complemented
9	C₂²×D₃	C₂³	1	1240	yes	direct product factor
10	C₂⁴	—	3	620	no	—
11	C₂⁴	C₂×D₃	1	31	yes	direct product factor
12	C₂²×C₃	C₂⁴	1	155	yes	complemented
13	C₂×D₃	C₂⁴	1	496	yes	direct product factor
14	C₂³	—	3	1240	no	—
15	C₂³	C₂²×D₃	1	155	yes	direct product factor
16	C₂×C₃	C₂⁵	1	31	yes	complemented
17	D₃	C₂⁵	1	32	yes	direct product factor
18	C₂²	—	3	496	no	—
19	C₂²	C₂³×D₃	1	155	yes	direct product factor
20	C₃	C₂⁶	1	1	yes	characteristic, complemented, Sylow
21	C₂	—	3	32	no	—
22	C₂	C₂⁴×D₃	1	31	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁵	D₃
commutator, cosocle, hypocenter	C₃	C₂⁶
Frattini	C₁	G
Fitting, socle	C₂⁵×C₃	C₂
LCS	G ▷ C₃
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.