Subgroups — #44527609

Order 31122.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#11717942	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₁₃×D₁₃₃	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic
4	D₁₉×C₁₃⋊C₉	—	7	1	no	maximal, Hall
5	C₁₃×D₁₃₃	C₉	1	1	yes	characteristic, complemented, Hall
6	(C₇⋊C₉)⋊D₁₉	—	13	1	no	maximal, Hall
7	C₁₉×C₁₃⋊C₉	—	7	1	no	Hall
8	C₇×C₁₃×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	#13109901	—	19	1	no	maximal, Hall
10	C₃×C₁₃×D₁₉	—	7	1	no	—
11	C₁₉×C₇⋊C₉	—	13	1	no	Hall
12	#11717942	D₁₉	1	1	yes	characteristic, complemented, Hall
13	C₃×D₁₃₃	C₁₃⋊C₃	1	1	yes	characteristic
14	C₃×C₁₃×C₁₉	AGL(1,𝔽₇)	1	1	yes	characteristic
15	C₃×C₁₃×D₇	—	19	1	no	—
16	C₁₃×D₁₉	—	7	1	no	Hall
17	C₃×C₇×C₁₉	C₂×C₁₃⋊C₃	1	1	yes	characteristic
18	C₉×D₁₉	—	91	1	no	Hall
19	C₃×C₇×C₁₃	C₃×D₁₉	1	1	yes	characteristic
20	D₁₃₃	C₁₃⋊C₉	1	1	yes	characteristic, complemented, Hall
21	C₁₃×C₁₉	D₇⋊C₉	1	1	yes	characteristic, complemented, Hall
22	C₂×C₁₃⋊C₉	—	133	1	no	Hall
23	C₁₃×D₇	—	19	1	no	Hall
24	C₉×C₁₉	—	91	1	no	Hall
25	C₇×C₁₉	C₂×C₁₃⋊C₉	1	1	yes	characteristic, complemented, Hall
26	D₇⋊C₉	—	247	1	no	Hall
27	C₁₃⋊C₉	—	7	1	no	Hall
28	C₃×D₁₉	—	7	1	no	—
29	C₇×C₁₃	C₉×D₁₉	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₁₃	—	133	1	no	—
31	C₇⋊C₉	—	13	1	no	Hall
32	C₃×C₁₉	#10587721	1	1	yes	characteristic
33	C₃×D₇	—	19	1	no	—
34	C₃×C₁₃	ΓL(1,𝔽₈)⋊D₁₉	1	1	yes	characteristic
35	D₁₉	—	7	1	no	Hall
36	C₂×C₁₃	—	133	1	no	Hall
37	C₃×C₇	D₁₉×C₁₃⋊C₃	1	1	yes	characteristic
38	C₁₉	#13109901	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₉	—	1729	1	no	Hall
40	D₇	—	19	1	no	Hall
41	C₁₃	(C₇⋊C₉)⋊D₁₉	1	1	yes	characteristic, complemented, Sylow
42	C₉	—	91	1	no	Sylow
43	C₇	D₁₉×C₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₃	—	133	1	no	—
45	C₃	#23780601	1	1	yes	characteristic
46	C₂	—	133	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	#23780601
commutator, hypocenter	C₇×C₁₃×C₁₉	C₂×C₉
Fitting, socle, cosocle	C₃×C₇×C₁₃×C₁₉	C₂×C₃
prime radical	C₃×C₁₃×D₁₃₃	C₃
LCS	G ▷ C₇×C₁₃×C₁₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₁₉×#11717942	C₂	semidirect
5. C₁₃×D₁₃₃	C₉	semidirect
8. C₇×C₁₃×C₁₉	C₂×C₉	semidirect
12. #11717942	D₁₉	semidirect
20. D₁₃₃	C₁₃⋊C₉	semidirect
21. C₁₃×C₁₉	D₇⋊C₉	semidirect
25. C₇×C₁₉	C₂×C₁₃⋊C₉	semidirect
29. C₇×C₁₃	C₉×D₁₉	semidirect
38. C₁₉	#13109901	semidirect
41. C₁₃	(C₇⋊C₉)⋊D₁₉	semidirect
43. C₇	D₁₉×C₁₃⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#11717942	2
C₃×C₁₃×D₁₃₃	3
D₁₉×C₁₃⋊C₉	7
(C₇⋊C₉)⋊D₁₉	13
#13109901	19