Subgroups — #30629293⋊C₂ #44540089

Order 31692.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30629301	C₂	1	1	yes	maximal, characteristic, complemented
2	#30629297	C₂	1	1	yes	maximal, characteristic, complemented
3	#30629293	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₉×D₁₃₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	#21463701	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₆₄₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₉×D₁₃₉	C₂×C₃	1	1	yes	characteristic, complemented
8	D₁₉×C₁₃₉	C₂×C₃	1	1	yes	characteristic, complemented
9	C₁₉×C₁₃₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×D₁₃₉⋊C₃	—	19	1	no	maximal, Hall
11	C₂×C₁₃₉⋊C₃	—	19	1	no	—
12	D₁₃₉⋊C₃	—	19	1	no	—
13	D₁₃₉⋊C₃	—	19	1	no	—
14	C₂×D₁₃₉	—	19	1	no	Hall
15	C₁₃₉⋊C₃	—	19	1	no	Hall
16	C₂×C₁₃₉	—	19	1	no	—
17	D₁₃₉	—	19	1	no	—
18	D₁₃₉	D₁₉⋊C₃	1	1	yes	characteristic, complemented
19	C₂×D₁₉⋊C₃	—	139	1	no	maximal, Hall
20	C₁₃₉	C₂×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₁₉⋊C₃	—	139	1	no	—
22	D₁₉⋊C₃	—	139	1	no	—
23	D₁₉⋊C₃	—	139	1	no	—
24	C₂×D₁₉	—	139	1	no	Hall
25	C₁₉⋊C₃	—	139	1	no	Hall
26	C₂×C₁₉	—	139	1	no	—
27	D₁₉	—	139	1	no	—
28	D₁₉	D₁₃₉⋊C₃	1	1	yes	characteristic, complemented
29	C₁₉	C₂×D₁₃₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
30	C₂²×C₃	—	2641	1	no	Hall
31	C₂×C₃	—	2641	1	no	—
32	C₂×C₃	—	2641	1	no	—
33	C₂×C₃	—	2641	1	no	—
34	C₂²	—	2641	1	no	Sylow
35	C₃	—	2641	1	no	Sylow
36	C₂	—	19	1	no	—
37	C₂	—	2641	1	no	—
38	C₂	—	139	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₉×C₁₃₉	C₂²×C₃
LCS	G ▷ C₁₉×C₁₃₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. #30629301	C₂	semidirect
2. #30629297	C₂	semidirect
3. #30629293	C₂	semidirect
4. D₁₉×D₁₃₉	C₃	semidirect
5. #21463701	C₂²	semidirect
6. D₂₆₄₁	C₂×C₃	semidirect
7. C₁₉×D₁₃₉	C₂×C₃	semidirect
8. D₁₉×C₁₃₉	C₂×C₃	semidirect
9. C₁₉×C₁₃₉	C₂²×C₃	semidirect
18. D₁₃₉	D₁₉⋊C₃	semidirect
20. C₁₃₉	C₂×D₁₉⋊C₃	semidirect
28. D₁₉	D₁₃₉⋊C₃	semidirect
29. C₁₉	C₂×D₁₃₉⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
#30629301	2
#30629297	2
#30629293	2
D₁₉×D₁₃₉	3
C₂×D₁₃₉⋊C₃	19
C₂×D₁₉⋊C₃	139

Subgroups — #30629293⋊C2 #44540089

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #30629293⋊C₂ #44540089