Subgroups — #11724924

Order 880.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₂₀	C₂	1	1	yes	maximal, characteristic
2	Dic₁₁₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₅₅	—	2	1	no	—
5	C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic
6	Dic₅₅	—	2	1	no	—
7	#4314	—	5	1	no	maximal, Hall
8	C₂×C₅×C₁₁	D₄	1	1	yes	characteristic
9	D₅₅	—	4	1	no	—
10	D₄₄	—	5	1	no	—
11	Dic₂₂	—	5	1	no	—
12	C₈×C₁₁	D₅	1	1	yes	characteristic, complemented
13	#677	—	11	1	no	maximal, Hall
14	C₅×C₁₁	SD₁₆	1	1	yes	characteristic, complemented, Hall
15	C₂×D₁₁	—	10	1	no	—
16	C₄×C₁₁	C₂×D₅	1	1	yes	characteristic
17	Dic₁₁	—	10	1	no	—
18	D₂₀	—	11	1	no	—
19	Dic₁₀	—	11	1	no	—
20	C₅×C₈	D₁₁	1	1	yes	characteristic, complemented
21	C₂×C₁₁	D₂₀	1	1	yes	characteristic
22	D₁₁	—	20	1	no	—
23	C₂×D₅	—	22	1	no	—
24	C₄×C₅	C₂×D₁₁	1	1	yes	characteristic
25	Dic₅	—	22	1	no	—
26	SD₁₆	—	55	1	no	Sylow
27	C₁₁	#677	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₅	D₄₄	1	1	yes	characteristic
29	D₅	—	44	1	no	—
30	Q₈	—	55	1	no	—
31	D₄	—	55	1	no	—
32	C₈	D₅₅	1	1	yes	characteristic, complemented
33	C₅	#4314	1	1	yes	characteristic, complemented, Sylow
34	C₂²	—	110	1	no	—
35	C₄	—	110	1	no	—
36	C₄	C₂×D₅₅	1	1	yes	characteristic
37	C₂	—	220	1	no	—
38	C₂	D₂₂₀	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.