Subgroups — #44501281

Order 30660.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#13095276	C₂	1	1	yes	maximal, characteristic
2	C₇₃×Dic₃₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×#13095276	C₄	1	1	yes	characteristic, complemented, Hall
4	#20259489	—	5	1	no	maximal, Hall
5	C₂×C₅×C₇×C₇₃	C₂×C₃	1	1	yes	characteristic
6	Dic₅×C₇₃⋊C₃	—	7	1	no	maximal, Hall
7	C₂×#13095276	D₅	1	1	yes	characteristic
8	C₅×C₇×C₇₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
9	C₂×C₅×C₇₃⋊C₃	—	7	1	no	—
10	Dic₇×C₇₃	—	5	1	no	Hall
11	#13095276	Dic₅	1	1	yes	characteristic, complemented, Hall
12	Dic₅×C₇₃	—	7	1	no	Hall
13	C₅×C₇₃⋊C₃	—	7	1	no	Hall
14	C₂×C₇×C₇₃	C₃×D₅	1	1	yes	characteristic
15	C₄×C₇₃⋊C₃	—	35	1	no	Hall
16	C₂×C₅×C₇₃	AGL(1,𝔽₇)	1	1	yes	characteristic
17	C₇×C₇₃	C₃×Dic₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₇₃⋊C₃	—	7	1	no	—
19	ΓL(1,𝔽₈)⋊Dic₅	—	73	1	no	maximal, Hall
20	C₅×C₇₃	ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic, complemented, Hall
21	C₄×C₇₃	—	35	1	no	Hall
22	C₇₃⋊C₃	—	7	1	no	Hall
23	C₂×C₅×ΓL(1,𝔽₈)	—	73	1	no	—
24	C₂×C₇₃	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic
25	Dic₃₅	C₇₃⋊C₃	1	1	yes	characteristic, complemented, Hall
26	C₅×ΓL(1,𝔽₈)	—	73	1	no	Hall
27	ΓL(1,𝔽₈)⋊C₄	—	365	1	no	Hall
28	C₇₃	ΓL(1,𝔽₈)⋊Dic₅	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₅×C₇	C₂×C₇₃⋊C₃	1	1	yes	characteristic
30	C₃×Dic₅	—	511	1	no	Hall
31	C₂×ΓL(1,𝔽₈)	—	73	1	no	—
32	C₅×C₇	C₄×C₇₃⋊C₃	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×C₅	—	511	1	no	—
34	Dic₇	—	5	1	no	Hall
35	ΓL(1,𝔽₈)	—	73	1	no	Hall
36	Dic₅	—	7	1	no	Hall
37	C₃×C₅	—	511	1	no	Hall
38	C₂×C₇	D₅×C₇₃⋊C₃	1	1	yes	characteristic
39	C₃×C₄	—	2555	1	no	Hall
40	C₂×C₅	#15690446	1	1	yes	characteristic
41	C₇	Dic₅×C₇₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₃	—	511	1	no	—
43	C₅	#20259489	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	35	1	no	Sylow
45	C₃	—	511	1	no	Sylow
46	C₂	C₅⋊#15690446	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₅⋊#15690446
commutator, hypocenter	C₅×C₇×C₇₃	C₃×C₄
Fitting, socle, cosocle	C₂×C₅×C₇×C₇₃	C₂×C₃
prime radical	C₂×C₅×#13095276	C₂
LCS	G ▷ C₅×C₇×C₇₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. C₇₃×Dic₃₅	C₃	semidirect
3. C₅×#13095276	C₄	semidirect
8. C₅×C₇×C₇₃	C₃×C₄	semidirect
11. #13095276	Dic₅	semidirect
17. C₇×C₇₃	C₃×Dic₅	semidirect
20. C₅×C₇₃	ΓL(1,𝔽₈)⋊C₄	semidirect
25. Dic₃₅	C₇₃⋊C₃	semidirect
28. C₇₃	ΓL(1,𝔽₈)⋊Dic₅	semidirect
32. C₅×C₇	C₄×C₇₃⋊C₃	semidirect
41. C₇	Dic₅×C₇₃⋊C₃	semidirect
43. C₅	#20259489	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#13095276	2
C₇₃×Dic₃₅	3
#20259489	5
Dic₅×C₇₃⋊C₃	7
ΓL(1,𝔽₈)⋊Dic₅	73