Subgroups — #64910

Order 320.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	#3995	C₂	1	1	yes	maximal, characteristic
3	#3990	C₂	1	1	yes	maximal, characteristic
4	Q₈×D₅	—	2	1	no	—
5	#700	—	2	1	no	—
6	C₅×Q₁₆	C₄	1	1	yes	characteristic
7	#689	—	2	1	no	—
8	Dic₂₀	C₄	1	1	yes	characteristic
9	C₈×D₅	C₂²	1	1	yes	characteristic
10	#674	—	2	1	no	—
11	#362	—	5	1	no	maximal, Sylow
12	C₅×Q₈	—	2	1	no	—
13	C₄×D₅	—	4	1	no	—
14	C₄×D₅	D₄	1	1	yes	characteristic
15	Dic₁₀	—	2	1	no	—
16	Dic₁₀	—	4	1	no	—
17	#170	—	4	1	no	—
18	C₅×C₈	C₂×C₄	1	1	yes	characteristic
19	#168	D₄	1	1	yes	characteristic
20	C₂×Q₁₆	—	5	1	no	—
21	M₃₂	—	5	1	no	—
22	#108	—	5	1	no	—
23	C₂×D₅	SD₁₆	1	1	yes	characteristic
24	C₄×C₅	—	4	1	no	—
25	C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
26	Dic₅	—	4	1	no	—
27	Dic₅	D₈	1	1	yes	characteristic
28	C₂×Q₈	—	10	1	no	—
29	Q₁₆	—	5	1	no	—
30	Q₁₆	—	10	1	no	—
31	Q₁₆	AGL(1,𝔽₅)	1	1	yes	characteristic
32	M₁₆	—	10	1	no	—
33	C₂×C₈	—	5	1	no	—
34	C₁₆	—	10	1	no	—
35	C₂×C₅	#102	1	1	yes	characteristic
36	D₅	—	2	1	no	—
37	Q₈	—	2	1	no	—
38	Q₈	—	10	1	no	—
39	Q₈	—	20	1	no	—
40	C₂×C₄	—	5	1	no	—
41	C₂×C₄	—	20	1	no	—
42	C₈	—	5	1	no	—
43	C₈	—	20	1	no	—
44	C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
45	C₅	#362	1	1	yes	characteristic, complemented, Sylow
46	C₂²	—	5	1	no	—
47	C₄	—	4	1	no	—
48	C₄	—	5	1	no	—
49	C₄	—	20	1	no	—
50	C₄	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
51	C₂	—	10	1	no	—
52	C₂	#4007	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
45. C₅	#362	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.