Subgroups — C₂⁵×D₄ #63095

Order 256.

55599 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁷	C₂	1	2	yes	maximal, complemented
2	C₂⁴×D₄	C₂	1	124	yes	maximal, direct product factor
3	C₂⁵×C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂⁶	—	2	64	no	—
5	C₂⁶	C₂²	1	1	yes	characteristic
6	C₂⁶	C₂²	1	124	yes	complemented
7	C₂³×D₄	C₂²	1	2480	yes	direct product factor
8	C₂⁴×C₄	C₂²	1	62	yes	complemented
9	C₂⁵	—	2	1984	no	—
10	C₂⁵	D₄	1	32	yes	direct product factor
11	C₂⁵	C₂³	1	31	yes	—
12	C₂⁵	C₂³	1	1240	yes	complemented
13	C₂²×D₄	C₂³	1	9920	yes	direct product factor
14	C₂³×C₄	C₂³	1	620	yes	complemented
15	C₂⁴	—	2	9920	no	—
16	C₂⁴	C₂×D₄	1	496	yes	direct product factor
17	C₂⁴	C₂⁴	1	155	yes	—
18	C₂⁴	C₂⁴	1	2480	yes	complemented
19	C₂×D₄	C₂⁴	1	7936	yes	direct product factor
20	C₂²×C₄	C₂⁴	1	1240	yes	complemented
21	C₂³	—	2	9920	no	—
22	C₂³	C₂²×D₄	1	1240	yes	direct product factor
23	C₂³	C₂⁵	1	155	yes	—
24	C₂³	C₂⁵	1	992	yes	complemented
25	D₄	C₂⁵	1	1024	yes	direct product factor
26	C₂×C₄	C₂⁵	1	496	yes	complemented
27	C₂²	—	2	1984	no	—
28	C₂²	C₂³×D₄	1	620	yes	direct product factor
29	C₂²	C₂⁶	1	31	yes	—
30	C₂²	C₂⁶	1	64	yes	complemented
31	C₄	C₂⁶	1	32	yes	complemented
32	C₂	—	2	64	no	—
33	C₂	C₂⁴×D₄	1	62	yes	direct product factor
34	C₂	C₂⁷	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁶	C₂²
commutator, Frattini, cosocle	C₂	C₂⁷
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁶ ◁ G
LECS	G ▷ C₂ ▷ C₁

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.