Subgroups — C₂×#16812976⋊C₅ #47977607

Order 35340.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812976⋊C₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×#13183714⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉⋊(D₃₁⋊C₅)	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	#13183714⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×#16812976	C₅	1	1	yes	maximal, characteristic, complemented, Hall
6	C₁₉⋊(D₃₁⋊C₅)	C₂×C₃	1	2	yes	complemented
7	C₂×C₁₉×ΓL(1,𝔽₃₂)	C₂×C₃	1	1	yes	characteristic, complemented
8	#16812976	C₂×C₅	1	2	yes	complemented
9	C₂×#13183714	C₂×C₅	1	1	yes	characteristic, complemented
10	C₁₉×ΓL(1,𝔽₃₂)	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×D₅₈₉	C₃×C₅	1	1	yes	characteristic, complemented, Hall
12	C₂×AGL(1,𝔽₃₁)	—	19	1	no	maximal, Hall
13	#13183714	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₉×C₃₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented
15	D₅₈₉	C₂×C₃×C₅	1	2	yes	complemented
16	C₂×C₅×D₁₉⋊C₃	—	31	1	no	maximal, Hall
17	C₂×(C₃₁⋊C₃)⋊C₅	—	19	1	no	—
18	AGL(1,𝔽₃₁)	—	19	2	no	—
19	C₂×D₃₁⋊C₅	—	19	1	no	Hall
20	C₁₉×C₃₁	C₂²×C₃×C₅	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅×C₁₉⋊C₃	—	31	1	no	—
22	C₅×D₁₉⋊C₃	—	31	2	no	—
23	(C₃₁⋊C₃)⋊C₅	—	19	1	no	Hall
24	C₂×C₅×D₁₉	—	31	1	no	Hall
25	C₂×D₃₁⋊C₃	—	19	1	no	Hall
26	C₂×ΓL(1,𝔽₃₂)	D₁₉⋊C₃	1	1	yes	characteristic, complemented
27	D₃₁⋊C₅	—	19	2	no	—
28	C₅×C₁₉⋊C₃	—	31	1	no	Hall
29	C₂×D₁₉⋊C₃	—	31	1	no	Hall
30	C₂×C₅×C₁₉	—	31	1	no	—
31	C₅×D₁₉	—	31	2	no	—
32	C₂×C₃₁⋊C₃	—	19	1	no	—
33	D₃₁⋊C₃	—	19	2	no	—
34	ΓL(1,𝔽₃₂)	C₂×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
35	C₂×D₃₁	—	19	1	no	Hall
36	C₂×C₁₉⋊C₃	—	31	1	no	—
37	D₁₉⋊C₃	—	31	2	no	—
38	C₅×C₁₉	—	31	1	no	Hall
39	C₃₁⋊C₃	—	19	1	no	Hall
40	C₂×D₁₉	—	31	1	no	Hall
41	C₂×C₃₁	C₅×D₁₉⋊C₃	1	1	yes	characteristic, complemented
42	D₃₁	—	19	2	no	—
43	C₂²×C₃×C₅	—	589	1	no	Hall
44	C₁₉⋊C₃	—	31	1	no	Hall
45	C₂×C₁₉	AGL(1,𝔽₃₁)	1	1	yes	characteristic, complemented
46	D₁₉	—	31	2	no	—
47	C₃₁	C₂×C₅×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃×C₅	—	589	1	no	—
49	C₂×C₃×C₅	—	589	2	no	—
50	C₂²×C₅	—	589	1	no	Hall
51	C₁₉	C₂×AGL(1,𝔽₃₁)	1	1	yes	characteristic, complemented, Sylow
52	C₃×C₅	—	589	1	no	Hall
53	C₂²×C₃	—	589	1	no	Hall
54	C₂×C₅	—	31	1	no	—
55	C₂×C₅	—	589	2	no	—
56	C₂×C₃	—	589	2	no	—
57	C₂×C₃	—	589	1	no	—
58	C₅	—	31	1	no	Sylow
59	C₂²	—	589	1	no	Sylow
60	C₃	—	589	1	no	Sylow
61	C₂	—	589	2	no	—
62	C₂	#16812976⋊C₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#16812976⋊C₅
commutator, cosocle, hypocenter	C₁₉×C₃₁	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₁₉×C₃₁	C₂×C₃×C₅
LCS	G ▷ C₁₉×C₃₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. #16812976⋊C₅	C₂	direct (N × H)
2. C₂×#13183714⋊C₅	C₂	semidirect
3. C₂×C₁₉⋊(D₃₁⋊C₅)	C₃	semidirect
4. #13183714⋊C₅	C₂²	semidirect
5. C₂×#16812976	C₅	semidirect
6. C₁₉⋊(D₃₁⋊C₅)	C₂×C₃	semidirect
7. C₂×C₁₉×ΓL(1,𝔽₃₂)	C₂×C₃	semidirect
8. #16812976	C₂×C₅	semidirect
9. C₂×#13183714	C₂×C₅	semidirect
10. C₁₉×ΓL(1,𝔽₃₂)	C₂²×C₃	semidirect
11. C₂×D₅₈₉	C₃×C₅	semidirect
13. #13183714	C₂²×C₅	semidirect
14. C₂×C₁₉×C₃₁	C₂×C₃×C₅	semidirect
15. D₅₈₉	C₂×C₃×C₅	semidirect
20. C₁₉×C₃₁	C₂²×C₃×C₅	semidirect
26. C₂×ΓL(1,𝔽₃₂)	D₁₉⋊C₃	semidirect
34. ΓL(1,𝔽₃₂)	C₂×D₁₉⋊C₃	semidirect
41. C₂×C₃₁	C₅×D₁₉⋊C₃	semidirect
45. C₂×C₁₉	AGL(1,𝔽₃₁)	semidirect
47. C₃₁	C₂×C₅×D₁₉⋊C₃	semidirect
51. C₁₉	C₂×AGL(1,𝔽₃₁)	semidirect
62. C₂	#16812976⋊C₅	direct (N × H)

Maximal subgroups

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

subgroup	index
#16812976⋊C₅	2
C₂×#13183714⋊C₅	2
C₂×C₁₉⋊(D₃₁⋊C₅)	3
C₂×#16812976	5
C₂×AGL(1,𝔽₃₁)	19
C₂×C₅×D₁₉⋊C₃	31

Subgroups — C2×#16812976⋊C5 #47977607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#16812976⋊C₅ #47977607