Subgroups — C₂×#700 #4126

Order 160.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₅	C₂	1	1	yes	maximal, characteristic
2	C₂×#170	C₂	1	2	yes	maximal, complemented
3	#700	C₂	1	4	yes	maximal, direct product factor
4	C₂²×D₅	C₄	1	1	yes	characteristic
5	C₂×C₄×C₅	C₄	1	1	yes	characteristic
6	C₂×Dic₅	C₂²	1	1	yes	characteristic
7	C₄×D₅	C₄	1	2	yes	—
8	C₄×D₅	C₂²	1	2	yes	—
9	#170	C₂²	1	4	yes	complemented
10	C₂×M₁₆	—	5	1	no	maximal, Sylow
11	C₂²×C₅	C₂×C₄	1	1	yes	characteristic
12	C₂×D₅	—	2	2	no	—
13	C₂×D₅	C₂×C₄	1	2	yes	—
14	C₄×C₅	C₂×C₄	1	2	yes	—
15	Dic₅	C₂×C₄	1	1	yes	characteristic
16	Dic₅	C₂³	1	1	yes	characteristic
17	C₂²×C₄	—	5	1	no	—
18	M₁₆	—	5	4	no	—
19	C₂×C₈	—	5	2	no	—
20	C₂×C₅	M₁₆	1	2	yes	complemented
21	C₂×C₅	C₂²×C₄	1	1	yes	characteristic
22	D₅	—	2	2	no	—
23	C₂³	—	5	1	no	—
24	C₂×C₄	—	5	1	no	—
25	C₂×C₄	—	5	2	no	—
26	C₂×C₄	—	5	2	no	—
27	C₂×C₄	AGL(1,𝔽₅)	1	1	yes	characteristic
28	C₈	—	5	4	no	—
29	C₅	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
30	C₂²	—	5	2	no	—
31	C₂²	—	10	2	no	—
32	C₂²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
33	C₄	—	5	1	no	—
34	C₄	—	5	1	no	—
35	C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
36	C₂	—	10	2	no	—
37	C₂	#700	1	2	yes	direct product factor
38	C₂	C₂²×AGL(1,𝔽₅)	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.