Subgroups — D₅×#13093361 #28414833

Order 14820.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊#13093361	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅×#10625203	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#13093361	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×C₁₃×D₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₅×#10625203	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×#13093361	—	5	1	no	maximal, Hall
7	C₁₃×D₉₅	C₂×C₃	1	1	yes	characteristic, complemented
8	D₅×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×C₁₃×D₁₉	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×#10625203	—	5	1	no	—
11	#13093361	—	5	1	no	—
12	#13093361	D₅	1	1	yes	characteristic, direct product factor
13	C₅×C₁₃×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
14	D₅×D₁₉⋊C₃	—	13	1	no	maximal, Hall
15	C₂×C₁₃×D₁₉	—	5	1	no	Hall
16	C₂×D₅×C₁₃⋊C₃	—	19	1	no	maximal, Hall
17	#10625203	C₂×D₅	1	1	yes	characteristic, complemented, Hall
18	C₅⋊(D₁₉⋊C₃)	—	13	1	no	—
19	D₅×C₁₉⋊C₃	—	13	1	no	—
20	C₅×D₁₉⋊C₃	—	13	1	no	—
21	C₂×C₁₃×C₁₉	—	5	1	no	—
22	C₁₃×D₁₉	—	5	1	no	—
23	C₁₃×D₁₉	C₃×D₅	1	1	yes	characteristic, complemented
24	C₂×C₅×C₁₃⋊C₃	—	19	1	no	—
25	D₅×C₁₃⋊C₃	—	19	1	no	—
26	D₅×C₁₃⋊C₃	—	38	1	no	—
27	D₅×D₁₉	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
28	C₅×C₁₉⋊C₃	—	13	1	no	Hall
29	C₂×D₅×C₁₃	—	19	1	no	Hall
30	C₁₃×C₁₉	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
31	C₂×D₁₉⋊C₃	—	65	1	no	Hall
32	C₅×C₁₃⋊C₃	—	38	1	no	Hall
33	D₉₅	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
34	C₅×D₁₉	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
35	D₅×C₁₉	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
36	C₂²×C₁₃⋊C₃	—	95	1	no	Hall
37	C₂×C₅×C₁₃	—	19	1	no	—
38	D₅×C₁₃	—	19	1	no	—
39	D₅×C₁₃	D₁₉⋊C₃	1	1	yes	characteristic, complemented
40	C₂×C₁₉⋊C₃	—	65	1	no	—
41	D₁₉⋊C₃	—	13	1	no	—
42	D₁₉⋊C₃	—	65	1	no	—
43	C₅×C₁₉	C₂²×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
44	C₂×C₁₃⋊C₃	—	19	1	no	—
45	C₂×C₁₃⋊C₃	—	95	1	no	—
46	C₂×C₁₃⋊C₃	—	190	1	no	—
47	C₂×D₁₉	—	5	1	no	Hall
48	C₅×C₁₃	C₂×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
49	C₂×C₃×D₅	—	247	1	no	Hall
50	C₁₉⋊C₃	—	13	1	no	Hall
51	C₂²×C₁₃	—	95	1	no	Hall
52	C₁₃⋊C₃	—	38	1	no	Hall
53	C₂×C₁₉	—	5	1	no	—
54	D₁₉	—	5	1	no	—
55	D₁₉	D₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented
56	C₂×C₃×C₅	—	247	1	no	—
57	C₃×D₅	—	494	1	no	—
58	C₃×D₅	—	247	1	no	—
59	C₂×C₁₃	—	5	1	no	—
60	C₂×C₁₃	—	19	1	no	—
61	C₂×C₁₃	—	95	1	no	—
62	C₂×D₅	—	19	1	no	Hall
63	C₁₉	C₂×D₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
64	C₃×C₅	—	494	1	no	Hall
65	C₁₃	D₅×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
66	C₂²×C₃	—	1235	1	no	Hall
67	C₂×C₅	—	19	1	no	—
68	D₅	—	19	1	no	—
69	D₅	#13093361	1	1	yes	characteristic, direct product factor
70	C₂×C₃	—	2470	1	no	—
71	C₂×C₃	—	1235	1	no	—
72	C₂×C₃	—	247	1	no	—
73	C₅	C₂×#13093361	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	95	1	no	Sylow
75	C₃	—	494	1	no	Sylow
76	C₂	—	5	1	no	—
77	C₂	—	19	1	no	—
78	C₂	—	95	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₃×C₁₉	C₂²×C₃
LCS	G ▷ C₅×C₁₃×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅⋊#13093361	C₂	semidirect
2. D₅×#10625203	C₂	semidirect
3. C₅×#13093361	C₂	semidirect
4. D₅×C₁₃×D₁₉	C₃	semidirect
5. C₅×#10625203	C₂²	semidirect
7. C₁₃×D₉₅	C₂×C₃	semidirect
8. D₅×C₁₃×C₁₉	C₂×C₃	semidirect
9. C₅×C₁₃×D₁₉	C₂×C₃	semidirect
12. #13093361	D₅	direct (N × H)
13. C₅×C₁₃×C₁₉	C₂²×C₃	semidirect
17. #10625203	C₂×D₅	semidirect
23. C₁₃×D₁₉	C₃×D₅	semidirect
27. D₅×D₁₉	C₁₃⋊C₃	semidirect
30. C₁₃×C₁₉	C₂×C₃×D₅	semidirect
33. D₉₅	C₂×C₁₃⋊C₃	semidirect
34. C₅×D₁₉	C₂×C₁₃⋊C₃	semidirect
35. D₅×C₁₉	C₂×C₁₃⋊C₃	semidirect
39. D₅×C₁₃	D₁₉⋊C₃	semidirect
43. C₅×C₁₉	C₂²×C₁₃⋊C₃	semidirect
48. C₅×C₁₃	C₂×D₁₉⋊C₃	semidirect
55. D₁₉	D₅×C₁₃⋊C₃	semidirect
63. C₁₉	C₂×D₅×C₁₃⋊C₃	semidirect
65. C₁₃	D₅×D₁₉⋊C₃	semidirect
69. D₅	#13093361	direct (N × H)
73. C₅	C₂×#13093361	semidirect

Maximal subgroups

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

subgroup	index
C₅⋊#13093361	2
D₅×#10625203	2
C₅×#13093361	2
D₅×C₁₃×D₁₉	3
C₂×#13093361	5
D₅×D₁₉⋊C₃	13
C₂×D₅×C₁₃⋊C₃	19

Subgroups — D5×#13093361 #28414833

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#13093361 #28414833