Subgroups — #44474635

Order 30150.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×C₅²⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅⋊D₃₃₅	C₃	1	1	yes	maximal, characteristic
3	C₃×C₅²×C₆₇	C₂×C₃	1	1	yes	characteristic
4	C₅⋊D₃₃₅	C₉	1	1	yes	characteristic, complemented, Hall
5	C₃×D₃₃₅	—	15	2	no	—
6	C₅²×C₆₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
7	C₉×D₆₇	—	25	1	no	maximal, Hall
8	C₃×C₅×C₆₇	—	3	2	no	—
9	D₃₃₅	—	15	2	no	—
10	C₉×C₆₇	—	25	1	no	Hall
11	(C₅⋊D₅)⋊C₉	—	67	1	no	maximal, Hall
12	C₃×D₆₇	—	75	1	no	—
13	C₅×C₆₇	—	3	2	no	—
14	C₅²⋊C₉	D₆₇	1	1	yes	characteristic, complemented, Hall
15	C₃×C₆₇	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic
16	C₃×C₅⋊D₅	—	67	1	no	—
17	D₆₇	—	75	1	no	Hall
18	C₃×C₅²	C₃×D₆₇	1	1	yes	characteristic
19	C₆₇	(C₅⋊D₅)⋊C₉	1	1	yes	characteristic, complemented, Sylow
20	C₅⋊D₅	—	67	1	no	Hall
21	C₃×D₅	—	1005	2	no	—
22	C₅²	C₉×D₆₇	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₉	—	1675	1	no	Hall
24	C₃×C₅	—	3	2	no	—
25	D₅	—	1005	2	no	—
26	C₉	—	25	1	no	Sylow
27	C₂×C₃	—	5025	1	no	—
28	C₅	—	3	2	no	—
29	C₃	#23758379	1	1	yes	characteristic
30	C₂	—	5025	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	#23758379
commutator, hypocenter	C₅²×C₆₇	C₂×C₉
Fitting, socle, cosocle	C₃×C₅²×C₆₇	C₂×C₃
prime radical	C₃×C₅⋊D₃₃₅	C₃
LCS	G ▷ C₅²×C₆₇
UCS	C₁ ◁ C₃

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.