Subgroups — Q₈×D₅₅ #11725034

Order 880.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×D₅₅	C₂	1	3	yes	maximal
3	Dic₁₁₀	C₂	1	3	yes	maximal, complemented
4	C₂×D₅₅	C₂²	1	1	yes	characteristic
5	C₄×C₅×C₁₁	C₂²	1	3	yes	—
6	Dic₅₅	C₂²	1	3	yes	—
7	Q₈×D₁₁	—	5	1	no	maximal, Hall
8	C₂×C₅×C₁₁	C₂³	1	1	yes	characteristic
9	D₅₅	Q₈	1	2	yes	direct product factor
10	Q₈×C₁₁	D₅	1	1	yes	characteristic, complemented
11	C₄×D₁₁	—	5	3	no	—
12	Dic₂₂	—	5	3	no	—
13	Q₈×D₅	—	11	1	no	maximal, Hall
14	C₅×C₁₁	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
15	C₂×D₁₁	—	5	1	no	—
16	C₄×C₁₁	C₂×D₅	1	3	yes	—
17	Dic₁₁	—	5	3	no	—
18	C₅×Q₈	D₁₁	1	1	yes	characteristic, complemented
19	C₄×D₅	—	11	3	no	—
20	Dic₁₀	—	11	3	no	—
21	C₂×C₁₁	C₂²×D₅	1	1	yes	characteristic
22	D₁₁	—	5	2	no	—
23	C₂×D₅	—	11	1	no	—
24	C₄×C₅	C₂×D₁₁	1	3	yes	—
25	Dic₅	—	11	3	no	—
26	C₂×Q₈	—	55	1	no	Sylow
27	C₁₁	Q₈×D₅	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₅	C₂²×D₁₁	1	1	yes	characteristic
29	D₅	—	11	2	no	—
30	Q₈	—	55	3	no	—
31	Q₈	D₅₅	1	1	yes	characteristic, direct product factor
32	C₂×C₄	—	55	3	no	—
33	C₅	Q₈×D₁₁	1	1	yes	characteristic, complemented, Sylow
34	C₂²	—	55	1	no	—
35	C₄	—	55	3	no	—
36	C₄	C₂×D₅₅	1	3	yes	—
37	C₂	—	55	2	no	—
38	C₂	C₂²×D₅₅	1	1	yes	characteristic

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.