Subgroups — #34093071

Order 19950.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²⋊#87705	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₅⋊D₉₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₇×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	#15668133	—	7	1	no	maximal, Hall
5	C₁₉⋊(C₅²⋊C₃)	—	7	1	no	Hall
6	C₇×D₉₅	—	15	2	no	—
7	(C₅⋊D₅)⋊ΓL(1,𝔽₈)	—	19	1	no	maximal, Hall
8	C₅⋊D₉₅	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
9	#11716322	—	25	1	no	maximal, Hall
10	C₅×C₇×C₁₉	—	3	2	no	—
11	C₇⋊(C₅²⋊C₃)	—	19	1	no	Hall
12	C₅²×C₁₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
13	#87705	—	25	1	no	Hall
14	C₇×C₅⋊D₅	—	57	1	no	Hall
15	C₇×D₁₉	—	75	1	no	Hall
16	D₉₅	—	15	2	no	—
17	C₅²×C₇	D₁₉⋊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	D₁₉⋊C₃	—	175	1	no	Hall
21	C₅×C₁₉	—	3	2	no	—
22	C₅²⋊C₃	—	133	1	no	Hall
23	C₇×D₅	—	285	2	no	—
24	C₁₉⋊C₃	—	175	1	no	Hall
25	C₅⋊D₅	—	19	1	no	Hall
26	C₂×ΓL(1,𝔽₈)	—	475	1	no	Hall
27	D₁₉	—	75	1	no	Hall
28	C₅×C₇	—	3	2	no	—
29	C₅²	#11716322	1	1	yes	characteristic, complemented, Sylow
30	ΓL(1,𝔽₈)	—	475	1	no	Hall
31	C₁₉	(C₅⋊D₅)⋊ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₇	—	1425	1	no	Hall
33	D₅	—	285	2	no	—
34	C₇	#15668133	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	—	1425	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⋊#87705	C₂	semidirect
2. C₇×C₅⋊D₉₅	C₃	semidirect
3. C₅²×C₇×C₁₉	C₂×C₃	semidirect
8. C₅⋊D₉₅	ΓL(1,𝔽₈)	semidirect
12. C₅²×C₁₉	C₂×ΓL(1,𝔽₈)	semidirect
17. C₅²×C₇	D₁₉⋊C₃	semidirect
19. C₇×C₁₉	(C₅⋊D₅)⋊C₃	semidirect
29. C₅²	#11716322	semidirect
31. C₁₉	(C₅⋊D₅)⋊ΓL(1,𝔽₈)	semidirect
34. C₇	#15668133	semidirect

Maximal subgroups

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

subgroup	index
C₅²⋊#87705	2
C₇×C₅⋊D₉₅	3
#15668133	7
(C₅⋊D₅)⋊ΓL(1,𝔽₈)	19
#11716322	25