Subgroups — C₂³×D₅₅ #11725052

Order 880.

268 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₅₅	C₂	1	14	yes	maximal, direct product factor
3	C₂²×C₅×C₁₁	C₂²	1	7	yes	complemented
4	C₂×D₅₅	C₂²	1	28	yes	direct product factor
5	C₂³×D₁₁	—	5	1	no	maximal, Hall
6	C₂×C₅×C₁₁	C₂³	1	7	yes	complemented
7	D₅₅	C₂³	1	8	yes	direct product factor
8	C₂³×C₁₁	D₅	1	1	yes	characteristic, complemented
9	C₂²×D₁₁	—	5	14	no	—
10	C₂³×D₅	—	11	1	no	maximal, Hall
11	C₅×C₁₁	C₂⁴	1	1	yes	characteristic, complemented, Hall
12	C₂²×C₁₁	C₂×D₅	1	7	yes	complemented
13	C₂×D₁₁	—	5	28	no	—
14	C₂³×C₅	D₁₁	1	1	yes	characteristic, complemented
15	C₂²×D₅	—	11	14	no	—
16	C₂×C₁₁	C₂²×D₅	1	7	yes	complemented
17	D₁₁	—	5	8	no	—
18	C₂²×C₅	C₂×D₁₁	1	7	yes	complemented
19	C₂×D₅	—	11	28	no	—
20	C₂⁴	—	55	1	no	Sylow
21	C₁₁	C₂³×D₅	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₅	C₂²×D₁₁	1	7	yes	complemented
23	D₅	—	11	8	no	—
24	C₂³	—	55	14	no	—
25	C₂³	D₅₅	1	1	yes	characteristic, direct product factor
26	C₅	C₂³×D₁₁	1	1	yes	characteristic, complemented, Sylow
27	C₂²	—	55	28	no	—
28	C₂²	C₂×D₅₅	1	7	yes	direct product factor
29	C₂	—	55	8	no	—
30	C₂	C₂²×D₅₅	1	7	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂³	D₅₅
commutator, cosocle, hypocenter	C₅×C₁₁	C₂⁴
Frattini	C₁	G
Fitting, socle	C₂³×C₅×C₁₁	C₂
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₂³

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.