Subgroups — D₅⋊#108 #65724

Order 320.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅⋊M₁₆	C₂	1	2	yes	maximal
2	C₂×C₈×D₅	C₂	1	1	yes	maximal, characteristic
3	#3996	C₂	1	2	yes	maximal, complemented
4	#3995	C₂	1	2	yes	maximal, complemented
5	C₂×C₄×D₅	C₂²	1	1	yes	characteristic
6	#704	—	2	2	no	—
7	#700	C₂²	1	4	yes	—
8	D₅⋊C₈	—	2	2	no	—
9	C₂×C₅×C₈	C₄	1	1	yes	characteristic
10	C₂×#168	C₄	1	1	yes	characteristic
11	C₈×D₅	C₄	1	1	yes	characteristic
12	C₈×D₅	C₄	1	1	yes	characteristic
13	C₈×D₅	C₂²	1	1	yes	characteristic
14	C₈×D₅	C₂²	1	1	yes	characteristic
15	C₂×#108	—	5	1	no	maximal, Sylow
16	C₂²×D₅	Q₈	1	1	yes	characteristic
17	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₅	D₄	1	1	yes	characteristic
19	C₄×D₅	C₂×C₄	1	1	yes	characteristic
20	C₄×D₅	D₄	1	1	yes	characteristic
21	C₄×D₅	Q₈	1	1	yes	characteristic
22	C₄×D₅	C₂³	1	1	yes	characteristic
23	#170	—	2	4	no	—
24	C₅×C₈	C₂×C₄	1	1	yes	characteristic
25	C₅×C₈	C₂×C₄	1	1	yes	characteristic
26	#168	C₂×C₄	1	1	yes	characteristic
27	#168	C₂×C₄	1	1	yes	characteristic
28	C₂×M₁₆	—	5	2	no	—
29	C₂²×C₈	—	5	1	no	—
30	#108	—	5	2	no	—
31	#108	—	5	2	no	—
32	C₂²×C₅	C₄⋊C₄	1	1	yes	characteristic
33	C₂×D₅	—	2	2	no	—
34	C₂×D₅	C₄⋊C₄	1	1	yes	characteristic
35	C₂×D₅	C₂×Q₈	1	1	yes	characteristic
36	C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
37	C₄×C₅	C₂²×C₄	1	1	yes	characteristic
38	Dic₅	C₄⋊C₄	1	1	yes	characteristic
39	Dic₅	C₂×D₄	1	1	yes	characteristic
40	C₂²×C₄	—	5	1	no	—
41	M₁₆	—	5	4	no	—
42	M₁₆	—	10	2	no	—
43	C₂×C₈	—	5	1	no	—
44	C₂×C₈	—	5	1	no	—
45	C₂×C₈	—	5	1	no	—
46	C₂×C₈	—	5	1	no	—
47	C₂×C₈	—	5	1	no	—
48	C₂×C₈	—	10	2	no	—
49	C₂×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
50	C₂×C₅	—	2	1	no	—
51	C₂×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
52	D₅	—	2	1	no	—
53	D₅	#108	1	2	yes	complemented
54	C₂³	—	5	1	no	—
55	C₂×C₄	—	5	1	no	—
56	C₂×C₄	—	5	1	no	—
57	C₂×C₄	—	5	1	no	—
58	C₂×C₄	—	5	1	no	—
59	C₂×C₄	—	5	1	no	—
60	C₂×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
61	C₈	—	5	1	no	—
62	C₈	—	5	1	no	—
63	C₈	—	10	4	no	—
64	C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
65	C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
66	C₅	C₂×#108	1	1	yes	characteristic, complemented, Sylow
67	C₂²	—	5	1	no	—
68	C₂²	—	5	1	no	—
69	C₂²	—	10	2	no	—
70	C₂²	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
71	C₄	—	5	1	no	—
72	C₄	—	5	1	no	—
73	C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
74	C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
75	C₂	—	2	1	no	—
76	C₂	—	5	2	no	—
77	C₂	—	10	1	no	—
78	C₂	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄⋊AGL(1,𝔽₅)
commutator	C₄×C₅	C₂²×C₄
Frattini	C₄	C₂²×AGL(1,𝔽₅)
Fitting	C₂×C₅×C₈	C₄
socle	C₂×C₅	C₂×C₄⋊C₄
prime radical	C₂²×D₅	Q₈
cosocle	C₄×D₅	C₂³
hypercenter	C₂×C₈	AGL(1,𝔽₅)
hypocenter	C₅	C₂×#108
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
3. #3996	C₂	semidirect
4. #3995	C₂	semidirect
53. D₅	#108	semidirect
66. C₅	C₂×#108	semidirect

Maximal subgroups

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

subgroup	index
D₅⋊M₁₆	2
C₂×C₈×D₅	2
#3996	2
#3995	2
C₂×#108	5

Subgroups — D5⋊#108 #65724

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅⋊#108 #65724