Subgroups — #64856

Order 320.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#4021	C₂	1	1	yes	maximal, characteristic
2	#4005	C₂	1	2	yes	maximal, complemented
3	C₂×D₂₀	C₄	1	1	yes	characteristic
4	C₂×Dic₁₀	C₂²	1	1	yes	characteristic
5	#704	—	2	2	no	—
6	C₄²×C₅	C₄	1	1	yes	characteristic
7	#685	—	2	2	no	—
8	#355	—	5	1	no	maximal, Sylow
9	C₂²×D₅	—	2	1	no	—
10	C₂×C₄×C₅	—	2	1	no	—
11	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
12	C₂×Dic₅	D₄	1	2	yes	—
13	D₂₀	—	4	1	no	—
14	Dic₁₀	—	4	1	no	—
15	#170	—	4	2	no	—
16	#124	—	5	1	no	—
17	#101	—	5	2	no	—
18	C₂²×C₅	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×D₅	—	4	2	no	—
20	C₂×D₅	—	4	1	no	—
21	C₄×C₅	—	2	1	no	—
22	C₄×C₅	—	4	1	no	—
23	Dic₅	—	2	2	no	—
24	C₂×Q₈	—	5	1	no	—
25	C₂×D₄	—	5	1	no	—
26	M₁₆	—	10	2	no	—
27	C₂²⋊C₄	—	10	2	no	—
28	C₄²	AGL(1,𝔽₅)	1	1	yes	characteristic
29	C₂×C₅	—	2	1	no	—
30	C₂×C₅	#99	1	1	yes	characteristic
31	D₅	—	8	1	no	—
32	C₂³	—	10	1	no	—
33	Q₈	—	20	1	no	—
34	D₄	—	20	1	no	—
35	C₂×C₄	—	2	1	no	—
36	C₂×C₄	—	5	2	no	—
37	C₂×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
38	C₈	—	20	2	no	—
39	C₅	#355	1	1	yes	characteristic, complemented, Sylow
40	C₂²	—	20	2	no	—
41	C₂²	—	20	1	no	—
42	C₂²	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	—	4	1	no	—
45	C₄	—	10	2	no	—
46	C₂	—	2	1	no	—
47	C₂	—	40	1	no	—
48	C₂	#3999	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #4005	C₂	semidirect
39. C₅	#355	semidirect

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