Subgroups — #64736

Order 320.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄₀	C₂	1	1	yes	maximal, characteristic
2	C₅×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#3951	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₀	—	2	1	no	—
5	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
6	#681	—	2	1	no	—
7	D₄₀	—	2	1	no	—
8	D₄₀	C₄	1	2	yes	—
9	C₅×C₁₆	—	2	1	no	—
10	#361	—	5	1	no	maximal, Sylow
11	C₂²×D₅	—	4	1	no	—
12	C₂×C₄×C₅	D₄	1	1	yes	characteristic
13	D₂₀	—	2	2	no	—
14	D₂₀	—	4	1	no	—
15	C₅×C₈	C₂×C₄	1	1	yes	characteristic
16	C₅×C₈	D₄	1	1	yes	characteristic
17	#168	—	4	1	no	—
18	C₂×D₈	—	5	1	no	—
19	M₃₂	D₅	1	1	yes	characteristic, complemented
20	#108	—	5	1	no	—
21	C₂²×C₅	SD₁₆	1	1	yes	characteristic
22	C₂×D₅	—	4	2	no	—
23	C₂×D₅	—	8	2	no	—
24	C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
25	C₄×C₅	D₈	1	1	yes	characteristic
26	C₂×D₄	—	10	1	no	—
27	D₈	—	5	2	no	—
28	D₈	—	10	1	no	—
29	M₁₆	—	10	1	no	—
30	C₂×C₈	C₂×D₅	1	1	yes	characteristic
31	C₁₆	—	2	1	no	—
32	C₂×C₅	—	2	1	no	—
33	C₂×C₅	#102	1	1	yes	characteristic
34	D₅	—	8	2	no	—
35	C₂³	—	20	1	no	—
36	D₄	—	10	2	no	—
37	D₄	—	20	1	no	—
38	C₂×C₄	D₂₀	1	1	yes	characteristic
39	C₈	—	20	1	no	—
40	C₈	C₄×D₅	1	1	yes	characteristic
41	C₈	C₂²⋊D₅	1	1	yes	characteristic
42	C₅	#361	1	1	yes	characteristic, complemented, Sylow
43	C₂²	—	20	2	no	—
44	C₂²	—	40	2	no	—
45	C₂²	#677	1	1	yes	characteristic
46	C₄	D₄₀	1	1	yes	characteristic
47	C₄	#685	1	1	yes	characteristic
48	C₂	—	2	1	no	—
49	C₂	—	40	2	no	—
50	C₂	#3953	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.