Subgroups — C₂×D₅×#13183714 #47977708

Order 35340.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×#13183714	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×#13183714	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₅×C₁₉×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×#13183714	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂²×#13183714	—	5	1	no	maximal, Hall
6	D₅×C₁₉×C₃₁	C₂×C₃	1	2	yes	complemented
7	C₂×C₅×C₁₉×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×#13183714	—	5	2	no	—
9	C₂×#13183714	D₅	1	1	yes	characteristic, direct product factor
10	C₅×C₁₉×C₃₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂²×C₁₉×C₃₁	—	5	1	no	Hall
12	C₂×D₅×C₃₁⋊C₃	—	19	1	no	maximal, Hall
13	#13183714	C₂×D₅	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₁₉×C₃₁	—	5	2	no	—
15	C₂×C₁₉×C₃₁	C₃×D₅	1	1	yes	characteristic, complemented
16	C₂×D₅×C₁₉⋊C₃	—	31	1	no	maximal, Hall
17	C₂×C₅×C₃₁⋊C₃	—	19	1	no	—
18	D₅×C₃₁⋊C₃	—	19	2	no	—
19	C₂×D₅×C₃₁	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
20	C₁₉×C₃₁	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅×C₁₉⋊C₃	—	31	1	no	—
22	D₅×C₁₉⋊C₃	—	31	2	no	—
23	C₅×C₃₁⋊C₃	—	19	1	no	Hall
24	C₂×D₅×C₁₉	C₃₁⋊C₃	1	1	yes	characteristic, complemented, Hall
25	C₂²×C₃₁⋊C₃	—	95	1	no	Hall
26	C₂×C₅×C₃₁	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
27	D₅×C₃₁	C₂×C₁₉⋊C₃	1	2	yes	complemented
28	C₅×C₁₉⋊C₃	—	31	1	no	Hall
29	C₂²×C₁₉⋊C₃	—	155	1	no	Hall
30	C₂×C₅×C₁₉	C₂×C₃₁⋊C₃	1	1	yes	characteristic, complemented
31	D₅×C₁₉	C₂×C₃₁⋊C₃	1	2	yes	complemented
32	C₂×C₃₁⋊C₃	—	19	1	no	—
33	C₂×C₃₁⋊C₃	—	95	2	no	—
34	C₅×C₃₁	C₂²×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
35	C₂²×C₃₁	—	5	1	no	Hall
36	C₂×C₁₉⋊C₃	—	31	1	no	—
37	C₂×C₁₉⋊C₃	—	155	2	no	—
38	C₅×C₁₉	C₂²×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Hall
39	C₃₁⋊C₃	—	19	1	no	Hall
40	C₂²×C₁₉	—	5	1	no	Hall
41	C₂×C₃₁	—	5	2	no	—
42	C₂×C₃₁	D₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
43	C₂×C₃×D₅	—	589	1	no	Hall
44	C₁₉⋊C₃	—	31	1	no	Hall
45	C₂×C₁₉	—	5	2	no	—
46	C₂×C₁₉	D₅×C₃₁⋊C₃	1	1	yes	characteristic, complemented
47	C₃₁	C₂×D₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃×C₅	—	589	1	no	—
49	C₃×D₅	—	589	2	no	—
50	C₂×D₅	#13183714	1	1	yes	characteristic, direct product factor, Hall
51	C₁₉	C₂×D₅×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
52	C₃×C₅	—	589	1	no	Hall
53	C₂²×C₃	—	2945	1	no	Hall
54	C₂×C₅	C₂×#13183714	1	1	yes	characteristic, complemented
55	D₅	C₂×#13183714	1	2	yes	direct product factor
56	C₂×C₃	—	589	1	no	—
57	C₂×C₃	—	2945	2	no	—
58	C₅	C₂²×#13183714	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	5	1	no	Sylow
60	C₃	—	589	1	no	Sylow
61	C₂	—	5	2	no	—
62	C₂	D₅×#13183714	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₅×#13183714
commutator, cosocle, hypocenter	C₅×C₁₉×C₃₁	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₉×C₃₁	C₂×C₃
LCS	G ▷ C₅×C₁₉×C₃₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. D₅×#13183714	C₂	direct (N × H)
2. C₂×C₅×#13183714	C₂	semidirect
3. C₂×D₅×C₁₉×C₃₁	C₃	semidirect
4. C₅×#13183714	C₂²	semidirect
6. D₅×C₁₉×C₃₁	C₂×C₃	semidirect
7. C₂×C₅×C₁₉×C₃₁	C₂×C₃	semidirect
9. C₂×#13183714	D₅	direct (N × H)
10. C₅×C₁₉×C₃₁	C₂²×C₃	semidirect
13. #13183714	C₂×D₅	direct (N × H)
15. C₂×C₁₉×C₃₁	C₃×D₅	semidirect
19. C₂×D₅×C₃₁	C₁₉⋊C₃	semidirect
20. C₁₉×C₃₁	C₂×C₃×D₅	semidirect
24. C₂×D₅×C₁₉	C₃₁⋊C₃	semidirect
26. C₂×C₅×C₃₁	C₂×C₁₉⋊C₃	semidirect
27. D₅×C₃₁	C₂×C₁₉⋊C₃	semidirect
30. C₂×C₅×C₁₉	C₂×C₃₁⋊C₃	semidirect
31. D₅×C₁₉	C₂×C₃₁⋊C₃	semidirect
34. C₅×C₃₁	C₂²×C₁₉⋊C₃	semidirect
38. C₅×C₁₉	C₂²×C₃₁⋊C₃	semidirect
42. C₂×C₃₁	D₅×C₁₉⋊C₃	semidirect
46. C₂×C₁₉	D₅×C₃₁⋊C₃	semidirect
47. C₃₁	C₂×D₅×C₁₉⋊C₃	semidirect
50. C₂×D₅	#13183714	direct (N × H)
51. C₁₉	C₂×D₅×C₃₁⋊C₃	semidirect
54. C₂×C₅	C₂×#13183714	semidirect
55. D₅	C₂×#13183714	direct (N × H)
58. C₅	C₂²×#13183714	semidirect
62. C₂	D₅×#13183714	direct (N × H)

Maximal subgroups

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

subgroup	index
D₅×#13183714	2
C₂×C₅×#13183714	2
C₂×D₅×C₁₉×C₃₁	3
C₂²×#13183714	5
C₂×D₅×C₃₁⋊C₃	19
C₂×D₅×C₁₉⋊C₃	31

Subgroups — C2×D5×#13183714 #47977708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅×#13183714 #47977708