Subgroups — #65358

Order 320.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#125	C₂	1	1	yes	maximal, characteristic
2	#4015	C₂	1	1	yes	maximal, characteristic
3	#3942	C₂	1	4	yes	maximal
4	#3935	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₁₀	C₂²	1	2	yes	—
6	C₅×C₄⋊C₄	—	2	2	no	—
7	C₅×C₄⋊C₄	C₂²	1	2	yes	—
8	C₄²×C₅	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₅	—	2	2	no	—
10	C₂×#168	C₂²	1	2	yes	—
11	#491	—	5	1	no	maximal, Sylow
12	C₂×C₄×C₅	—	2	2	no	—
13	C₂×C₄×C₅	D₄	1	2	yes	—
14	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
15	C₂×Dic₅	—	2	2	no	—
16	Dic₁₀	—	2	4	no	—
17	#168	—	2	2	no	—
18	C₄⋊Q₈	—	5	1	no	—
19	#125	D₅	1	1	yes	characteristic
20	#103	—	5	4	no	—
21	#97	—	5	1	no	—
22	C₂²×C₅	C₂×D₄	1	1	yes	characteristic
23	C₄×C₅	—	2	2	no	—
24	C₄×C₅	—	4	2	no	—
25	C₄×C₅	#41	1	2	yes	—
26	Dic₅	—	4	2	no	—
27	C₂×Q₈	—	5	2	no	—
28	C₂×C₈	—	5	2	no	—
29	C₄⋊C₄	—	2	2	no	—
30	C₄⋊C₄	—	10	2	no	—
31	C₄⋊C₄	C₂×D₅	1	2	yes	—
32	C₄²	C₂×D₅	1	1	yes	characteristic
33	C₂×C₅	#124	1	1	yes	characteristic
34	C₂×C₅	#137	1	2	yes	—
35	Q₈	—	10	4	no	—
36	C₂×C₄	—	2	2	no	—
37	C₂×C₄	—	10	2	no	—
38	C₂×C₄	C₂²⋊D₅	1	2	yes	—
39	C₂×C₄	C₂²×D₅	1	1	yes	characteristic
40	C₈	—	10	2	no	—
41	C₅	#491	1	1	yes	characteristic, complemented, Sylow
42	C₂²	C₂×C₂²⋊D₅	1	1	yes	characteristic
43	C₄	—	2	2	no	—
44	C₄	—	4	2	no	—
45	C₄	—	20	2	no	—
46	C₄	#713	1	2	yes	—
47	C₂	#4093	1	1	yes	characteristic
48	C₂	#4097	1	2	yes	—

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

N	H ≅ G/N	type
41. C₅	#491	semidirect

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