Subgroups — D₅⋊#3708 #13085539

Order 1440.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₃⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	#10623725	C₂	1	2	yes	maximal, complemented
3	C₃²×C₄×D₅	C₄	1	1	yes	characteristic
4	C₃⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
5	C₅×C₃⋊(C₃⋊C₈)	C₄	1	1	yes	characteristic
6	C₂×#3708	—	5	1	no	maximal, Hall
7	D₅×C₃⋊C₈	—	6	2	no	—
8	C₂×C₃²×D₅	C₈	1	1	yes	characteristic
9	C₃²×C₄×C₅	C₂×C₄	1	1	yes	characteristic
10	C₃²×Dic₅	C₈	1	1	yes	characteristic
11	D₅⋊C₁₆	—	9	1	no	maximal, Hall
12	C₂×C₃⋊(C₃⋊C₈)	—	5	1	no	—
13	#3708	—	5	2	no	—
14	C₃×C₄×D₅	—	2	2	no	—
15	C₃⋊#168	—	6	2	no	—
16	C₅×C₃⋊C₈	—	6	2	no	—
17	C₂×C₃²×C₅	C₂×C₈	1	1	yes	characteristic
18	C₃²×D₅	C₁₆	1	2	yes	complemented
19	C₈×D₅	—	9	1	no	—
20	#674	—	9	2	no	—
21	C₂×C₃²×C₄	—	5	1	no	—
22	C₃⋊(C₃⋊C₈)	—	5	1	no	—
23	C₃⋊(C₃⋊C₈)	AGL(1,𝔽₅)	1	1	yes	characteristic
24	C₂×C₃×D₅	—	2	2	no	—
25	C₃×C₄×C₅	—	2	2	no	—
26	C₃×Dic₅	—	2	2	no	—
27	C₂×C₃⋊C₈	—	30	2	no	—
28	C₃²×C₅	C₂×C₁₆	1	1	yes	characteristic, complemented, Hall
29	C₄×D₅	#157	1	1	yes	characteristic
30	C₅×C₈	—	9	1	no	—
31	#168	—	9	1	no	—
32	C₂²×C₃²	—	5	1	no	—
33	C₃²×C₄	—	5	1	no	—
34	C₃²×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
35	C₂×C₁₆	—	45	1	no	Sylow
36	C₂×C₃×C₅	—	2	2	no	—
37	C₃×D₅	—	2	4	no	—
38	C₂×C₃×C₄	—	10	2	no	—
39	C₃⋊C₈	—	6	2	no	—
40	C₃⋊C₈	—	30	2	no	—
41	C₂×D₅	#622	1	1	yes	characteristic
42	C₄×C₅	C₂×#157	1	1	yes	characteristic
43	Dic₅	#622	1	1	yes	characteristic
44	C₂×C₃²	—	5	2	no	—
45	C₂×C₃²	D₅⋊C₈	1	1	yes	characteristic
46	C₂×C₈	—	45	1	no	—
47	C₁₆	—	45	2	no	—
48	C₃×C₅	—	2	2	no	—
49	C₂²×C₃	—	10	2	no	—
50	C₃×C₄	—	2	2	no	—
51	C₃×C₄	—	10	2	no	—
52	C₂×C₅	C₂×#622	1	1	yes	characteristic
53	D₅	#3708	1	2	yes	complemented
54	C₃²	D₅⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₄	—	5	1	no	—
56	C₈	—	9	1	no	—
57	C₈	—	45	1	no	—
58	C₂×C₃	—	2	2	no	—
59	C₂×C₃	—	10	4	no	—
60	C₅	C₂×#3708	1	1	yes	characteristic, complemented, Sylow
61	C₂²	—	5	1	no	—
62	C₄	—	5	1	no	—
63	C₄	D₅⋊#157	1	1	yes	characteristic
64	C₃	—	2	2	no	—
65	C₂	—	5	2	no	—
66	C₂	D₅⋊#622	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₄	D₅⋊#157
commutator, hypocenter	C₃²×C₅	C₂×C₁₆
Fitting	C₃²×C₄×C₅	C₂×C₄
socle	C₂×C₃²×C₅	C₂×C₈
prime radical	C₂×C₃²×D₅	C₈
cosocle	C₃⋊(C₃⋊#168)	C₂²
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₄

Complements

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

N	H ≅ G/N	type
2. #10623725	C₂	semidirect
18. C₃²×D₅	C₁₆	semidirect
28. C₃²×C₅	C₂×C₁₆	semidirect
53. D₅	#3708	semidirect
54. C₃²	D₅⋊C₁₆	semidirect
60. C₅	C₂×#3708	semidirect

Maximal subgroups

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

subgroup	index
D₅×C₃⋊(C₃⋊C₈)	2
#10623725	2
C₂×#3708	5
D₅⋊C₁₆	9

Subgroups — D5⋊#3708 #13085539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅⋊#3708 #13085539