Subgroups — D₁₁₅₇₁ #37529013

Order 23142.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₉×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₈₅₇	—	3	1	no	maximal, Hall
3	C₇×C₁₉×C₂₉	D₃	1	1	yes	characteristic, complemented, Hall
4	D₁₆₅₃	—	7	1	no	maximal, Hall
5	C₃×C₁₉×C₂₉	D₇	1	1	yes	characteristic, complemented, Hall
6	D₆₀₉	—	19	1	no	maximal, Hall
7	D₅₅₁	—	21	1	no	Hall
8	D₃₉₉	—	29	1	no	maximal, Hall
9	C₃×C₇×C₂₉	D₁₉	1	1	yes	characteristic, complemented, Hall
10	C₁₉×C₂₉	D₂₁	1	1	yes	characteristic, complemented, Hall
11	D₂₀₃	—	57	1	no	Hall
12	C₃×C₇×C₁₉	D₂₉	1	1	yes	characteristic, complemented, Hall
13	D₁₃₃	—	87	1	no	Hall
14	C₇×C₂₉	D₅₇	1	1	yes	characteristic, complemented, Hall
15	D₈₇	—	133	1	no	Hall
16	C₇×C₁₉	D₈₇	1	1	yes	characteristic, complemented, Hall
17	D₅₇	—	203	1	no	Hall
18	C₃×C₂₉	D₁₃₃	1	1	yes	characteristic, complemented, Hall
19	D₂₉	—	399	1	no	Hall
20	C₃×C₁₉	D₂₀₃	1	1	yes	characteristic, complemented, Hall
21	D₂₁	—	551	1	no	Hall
22	D₁₉	—	609	1	no	Hall
23	C₂₉	D₃₉₉	1	1	yes	characteristic, complemented, Sylow
24	C₃×C₇	D₅₅₁	1	1	yes	characteristic, complemented, Hall
25	C₁₉	D₆₀₉	1	1	yes	characteristic, complemented, Sylow
26	D₇	—	1653	1	no	Hall
27	C₇	D₁₆₅₃	1	1	yes	characteristic, complemented, Sylow
28	D₃	—	3857	1	no	Hall
29	C₃	D₃₈₅₇	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	11571	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₁₉×C₂₉	C₂
LCS	G ▷ C₃×C₇×C₁₉×C₂₉
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.