Subgroups — #64709

Order 320.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#107	C₂	1	1	yes	maximal, characteristic
2	#3950	C₂	1	1	yes	maximal, characteristic
3	C₂×#672	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
5	C₅×C₄⋊C₄	—	2	1	no	—
6	C₄⋊Dic₅	—	2	1	no	—
7	#672	C₄	1	2	yes	complemented
8	#366	—	5	1	no	maximal, Sylow
9	C₂×C₄×C₅	—	4	1	no	—
10	C₂×C₄×C₅	D₄	1	1	yes	characteristic
11	C₂×Dic₅	—	4	1	no	—
12	C₅×C₈	C₂×C₄	1	1	yes	characteristic
13	C₅×C₈	Q₈	1	1	yes	characteristic
14	C₂×C₁₆	—	5	1	no	—
15	#107	—	5	1	no	—
16	#107	D₅	1	1	yes	characteristic
17	C₂²×C₅	D₈	1	1	yes	characteristic
18	C₄×C₅	—	8	1	no	—
19	C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
20	C₄×C₅	Q₁₆	1	1	yes	characteristic
21	Dic₅	—	8	1	no	—
22	C₂×C₈	C₂×D₅	1	1	yes	characteristic
23	C₄⋊C₄	—	2	1	no	—
24	C₄⋊C₄	—	10	1	no	—
25	C₁₆	—	5	2	no	—
26	C₂×C₅	#107	1	1	yes	characteristic
27	C₂×C₅	D₁₆	1	1	yes	characteristic
28	C₂×C₅	Q₃₂	1	1	yes	characteristic
29	C₂×C₄	—	4	1	no	—
30	C₂×C₄	—	20	1	no	—
31	C₂×C₄	C₂²⋊D₅	1	1	yes	characteristic
32	C₈	Dic₁₀	1	1	yes	characteristic
33	C₈	C₄×D₅	1	1	yes	characteristic
34	C₅	#366	1	1	yes	characteristic, complemented, Sylow
35	C₂²	#686	1	1	yes	characteristic
36	C₄	—	8	1	no	—
37	C₄	—	40	1	no	—
38	C₄	#683	1	1	yes	characteristic
39	C₄	#689	1	1	yes	characteristic
40	C₂	#3939	1	1	yes	characteristic
41	C₂	#3958	1	1	yes	characteristic
42	C₂	#3961	1	1	yes	characteristic

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

N	H ≅ G/N	type
7. #672	C₄	semidirect
34. C₅	#366	semidirect

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