Subgroups — #34093065

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	C₅⋊D₆₆₅	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	D₆₆₅	—	15	2	no	—
7	#11760386	—	19	1	no	maximal, Hall
8	C₅⋊D₉₅	—	7	1	no	Hall
9	#11716328	—	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	#87705	—	25	1	no	Hall
14	C₅⋊D₃₅	—	19	1	no	Hall
15	D₁₃₃	—	25	1	no	Hall
16	D₉₅	—	105	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	D₃₅	—	285	2	no	—
24	C₁₉⋊C₃	—	175	1	no	Hall
25	C₅⋊D₅	—	133	1	no	Hall
26	AGL(1,𝔽₇)	—	475	1	no	Hall
27	D₁₉	—	175	1	no	Hall
28	C₅×C₇	—	3	2	no	—
29	C₅²	#11716328	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	—	475	1	no	Hall
33	D₅	—	1995	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	—	3325	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

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

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