Subgroups — #64764

Order 320.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#127	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#168	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×D₄	—	2	2	no	—
4	C₂×C₅×D₄	C₄	1	2	yes	—
5	C₄²×C₅	C₂²	1	1	yes	characteristic
6	C₂×#168	—	2	2	no	—
7	#331	—	5	1	no	maximal, Sylow
8	C₂³×C₅	—	2	2	no	—
9	C₅×D₄	—	4	2	no	—
10	C₅×D₄	—	4	2	no	—
11	C₅×D₄	—	4	2	no	—
12	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₅	D₄	1	2	yes	—
14	#168	—	4	2	no	—
15	#127	D₅	1	1	yes	characteristic
16	C₄⋊C₈	—	5	2	no	—
17	C₂²×C₅	—	4	2	no	—
18	C₂²×C₅	—	4	4	no	—
19	C₂²×C₅	C₂²⋊C₄	1	1	yes	characteristic
20	C₄×C₅	—	2	1	no	—
21	C₄×C₅	D₈	1	2	yes	—
22	C₄×C₅	SD₁₆	1	2	yes	—
23	C₂×D₄	—	2	2	no	—
24	C₂×D₄	Dic₅	1	2	yes	—
25	C₂×C₈	—	10	2	no	—
26	C₄²	C₂×D₅	1	1	yes	characteristic
27	C₂×C₅	—	8	2	no	—
28	C₂×C₅	#100	1	1	yes	characteristic
29	C₂×C₅	#102	1	2	yes	—
30	C₂³	—	2	2	no	—
31	D₄	—	4	2	no	—
32	D₄	—	4	2	no	—
33	D₄	—	4	2	no	—
34	C₂×C₄	C₂×Dic₅	1	1	yes	characteristic
35	C₂×C₄	C₂²⋊D₅	1	2	yes	—
36	C₈	—	20	2	no	—
37	C₅	#331	1	1	yes	characteristic, complemented, Sylow
38	C₂²	—	4	4	no	—
39	C₂²	—	4	2	no	—
40	C₂²	C₂²⋊Dic₅	1	1	yes	characteristic
41	C₄	—	2	1	no	—
42	C₄	#686	1	2	yes	—
43	C₄	#687	1	2	yes	—
44	C₂	—	8	2	no	—
45	C₂	#3964	1	2	yes	—
46	C₂	#3965	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. C₄⋊#168	C₂	semidirect
37. C₅	#331	semidirect

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