Subgroups — C₂×#4223⋊C₅ #13110012

Order 1640.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	#4223⋊C₅	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₄₁⋊C₅	C₄	1	1	yes	characteristic, complemented
4	D₄₁⋊C₅	C₄	1	1	yes	characteristic, complemented
5	D₄₁⋊C₅	C₂²	1	1	yes	characteristic
6	C₂×#4223	C₅	1	1	yes	maximal, characteristic, complemented, Hall
7	C₄₁⋊C₅	C₂×C₄	1	1	yes	characteristic, complemented, Hall
8	C₂×D₄₁	C₂×C₅	1	1	yes	characteristic
9	#4223	C₂×C₅	1	2	yes	complemented
10	C₂×C₄₁	C₄×C₅	1	1	yes	characteristic, complemented
11	D₄₁	C₄×C₅	1	1	yes	characteristic, complemented
12	D₄₁	C₂²×C₅	1	1	yes	characteristic
13	C₄₁	C₂×C₄×C₅	1	1	yes	characteristic, complemented, Sylow
14	C₂×C₄×C₅	—	41	1	no	maximal, Hall
15	C₂²×C₅	—	41	1	no	—
16	C₄×C₅	—	41	2	no	—
17	C₂×C₅	—	41	1	no	—
18	C₂×C₅	—	41	1	no	—
19	C₂×C₅	—	41	1	no	—
20	C₂×C₄	—	41	1	no	Sylow
21	C₅	—	41	1	no	Sylow
22	C₂²	—	41	1	no	—
23	C₄	—	41	2	no	—
24	C₂	—	41	1	no	—
25	C₂	—	41	1	no	—
26	C₂	#4223⋊C₅	1	1	yes	characteristic, direct product factor

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.