Subgroups — #34093066

Order 19950.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²⋊#87704	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×C₅⋊D₃₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₇×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	(C₅⋊D₅)⋊(C₁₉⋊C₃)	—	7	1	no	maximal, Hall
5	C₁₉⋊(C₅²⋊C₃)	—	7	1	no	Hall
6	C₁₉×D₃₅	—	15	2	no	—
7	#11760386	—	19	1	no	maximal, Hall
8	C₁₉×C₅⋊D₅	—	21	1	no	Hall
9	#11716325	—	25	1	no	maximal, Hall
10	C₅×C₇×C₁₉	—	3	2	no	—
11	C₇⋊(C₅²⋊C₃)	—	19	1	no	Hall
12	C₅²×C₁₉	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
13	#87704	—	25	1	no	Hall
14	C₅⋊D₃₅	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
15	D₇×C₁₉	—	75	1	no	Hall
16	D₅×C₁₉	—	105	2	no	—
17	C₅²×C₇	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
18	(C₅⋊D₅)⋊C₃	—	133	1	no	Hall
19	C₇×C₁₉	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented, Hall
20	C₂×C₁₉⋊C₃	—	175	1	no	Hall
21	C₅×C₁₉	—	3	2	no	—
22	C₅²⋊C₃	—	133	1	no	Hall
23	D₃₅	—	15	2	no	—
24	C₁₉⋊C₃	—	175	1	no	Hall
25	C₅⋊D₅	—	21	1	no	Hall
26	AGL(1,𝔽₇)	—	475	1	no	Hall
27	C₂×C₁₉	—	525	1	no	Hall
28	C₅×C₇	—	3	2	no	—
29	C₅²	#11716325	1	1	yes	characteristic, complemented, Sylow
30	ΓL(1,𝔽₈)	—	475	1	no	Hall
31	C₁₉	#11760386	1	1	yes	characteristic, complemented, Sylow
32	D₇	—	75	1	no	Hall
33	D₅	—	105	2	no	—
34	C₇	(C₅⋊D₅)⋊(C₁₉⋊C₃)	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₃	—	3325	1	no	Hall
36	C₅	—	3	2	no	—
37	C₃	—	3325	1	no	Sylow
38	C₂	—	525	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅²×C₇×C₁₉	C₂×C₃
LCS	G ▷ C₅²×C₇×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅²⋊#87704	C₂	semidirect
2. C₁₉×C₅⋊D₃₅	C₃	semidirect
3. C₅²×C₇×C₁₉	C₂×C₃	semidirect
12. C₅²×C₁₉	AGL(1,𝔽₇)	semidirect
14. C₅⋊D₃₅	C₁₉⋊C₃	semidirect
17. C₅²×C₇	C₂×C₁₉⋊C₃	semidirect
19. C₇×C₁₉	(C₅⋊D₅)⋊C₃	semidirect
29. C₅²	#11716325	semidirect
31. C₁₉	#11760386	semidirect
34. C₇	(C₅⋊D₅)⋊(C₁₉⋊C₃)	semidirect

Maximal subgroups

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

subgroup	index
C₅²⋊#87704	2
C₁₉×C₅⋊D₃₅	3
(C₅⋊D₅)⋊(C₁₉⋊C₃)	7
#11760386	19
#11716325	25