Subgroups — C₁₆×C₅⋊D₅ #11716664

Order 800.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#87756	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₅⋊D₅	C₄	1	1	yes	characteristic
5	C₅²×C₈	C₂²	1	1	yes	characteristic
6	#6029	C₄	1	1	yes	characteristic
7	D₅×C₁₆	—	5	6	no	maximal
8	C₂×C₅⋊D₅	C₈	1	1	yes	characteristic
9	C₄×C₅²	C₂×C₄	1	1	yes	characteristic
10	#1039	C₈	1	1	yes	characteristic
11	C₈×D₅	—	5	6	no	—
12	C₅×C₁₆	D₅	1	6	yes	complemented
13	#672	—	5	6	no	—
14	C₂×C₅²	C₂×C₈	1	1	yes	characteristic
15	C₅⋊D₅	C₁₆	1	2	yes	direct product factor
16	C₄×D₅	—	5	6	no	—
17	C₅×C₈	C₂×D₅	1	6	yes	—
18	#168	—	5	6	no	—
19	C₂×C₁₆	—	25	1	no	Sylow
20	C₅²	C₂×C₁₆	1	1	yes	characteristic, complemented, Sylow
21	C₂×D₅	—	5	6	no	—
22	C₄×C₅	C₄×D₅	1	6	yes	—
23	Dic₅	—	5	6	no	—
24	C₂×C₈	—	25	1	no	—
25	C₁₆	—	25	1	no	—
26	C₁₆	C₅⋊D₅	1	1	yes	characteristic, direct product factor
27	C₂×C₅	C₈×D₅	1	6	yes	—
28	D₅	—	5	12	no	—
29	C₂×C₄	—	25	1	no	—
30	C₈	—	25	1	no	—
31	C₈	C₂×C₅⋊D₅	1	1	yes	characteristic
32	C₅	D₅×C₁₆	1	6	yes	complemented
33	C₂²	—	25	1	no	—
34	C₄	—	25	1	no	—
35	C₄	C₄×C₅⋊D₅	1	1	yes	characteristic
36	C₂	—	25	2	no	—
37	C₂	C₈×C₅⋊D₅	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.