Subgroups — #30659271

Order 16650.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²⋊#66526	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅⋊(C₅⋊(D₃₇⋊C₃))	C₃	1	1	yes	maximal, characteristic
3	C₅²×C₃₇⋊C₃	C₂×C₃	1	1	yes	characteristic
4	C₅⋊D₁₈₅	C₉	1	1	yes	characteristic, complemented, Hall
5	C₅⋊(D₃₇⋊C₃)	—	15	2	no	—
6	C₅²×C₃₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
7	#66526⋊C₂	—	25	1	no	maximal, Hall
8	C₅×C₃₇⋊C₃	—	3	2	no	—
9	(C₅⋊D₅)⋊C₉	—	37	1	no	maximal, Hall
10	D₁₈₅	—	15	2	no	—
11	#66526	—	25	1	no	Hall
12	C₅²⋊C₉	—	37	1	no	Hall
13	D₃₇⋊C₃	—	75	1	no	—
14	C₅×C₃₇	—	3	2	no	—
15	C₃×C₅⋊D₅	—	37	1	no	—
16	C₃₇⋊C₃	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic
17	C₃×C₅²	—	37	1	no	—
18	D₃₇	—	75	1	no	Hall
19	C₅⋊D₅	—	333	1	no	Hall
20	C₃₇	(C₅⋊D₅)⋊C₉	1	1	yes	characteristic, complemented, Sylow
21	C₃×D₅	—	555	2	no	—
22	C₅²	#66526⋊C₂	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₉	—	925	1	no	Hall
24	C₃×C₅	—	111	2	no	—
25	D₅	—	1665	2	no	—
26	C₉	—	925	1	no	Sylow
27	C₂×C₃	—	2775	1	no	—
28	C₅	—	3	2	no	—
29	C₃	—	37	1	no	—
30	C₂	—	8325	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₃₇	C₂×C₉
prime radical	C₅⋊(C₅⋊(D₃₇⋊C₃))	C₃
cosocle	C₅²×C₃₇⋊C₃	C₂×C₃
LCS	G ▷ C₅²×C₃₇
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.