Subgroups — #44501329

Order 30660.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₅×C₇₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₇⋊#13091734	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×C₇×C₇₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	#20259490	—	5	1	no	maximal, Hall
5	C₇×D₅×C₇₃	C₂×C₃	1	1	yes	characteristic
6	#13091734⋊C₃	—	7	1	no	maximal, Hall
7	C₂×C₇×C₇₃⋊C₃	—	5	1	no	—
8	C₅×C₇×C₇₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
9	D₅×C₇₃⋊C₃	D₇	1	1	yes	characteristic
10	Dic₅₁₁	—	5	1	no	Hall
11	C₇×C₇₃⋊C₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	#13091734	—	7	1	no	Hall
13	C₅×C₇₃⋊C₃	Dic₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₇×C₇₃	—	5	1	no	—
15	Dic₇₃⋊C₃	—	35	1	no	Hall
16	D₅×C₇₃	C₃×D₇	1	1	yes	characteristic
17	C₇×C₇₃	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
18	C₂×C₇₃⋊C₃	—	5	1	no	—
19	C₃×C₇⋊AGL(1,𝔽₅)	—	73	1	no	maximal, Hall
20	C₅×C₇₃	C₃×Dic₇	1	1	yes	characteristic, complemented, Hall
21	Dic₇₃	—	35	1	no	Hall
22	C₇₃⋊C₃	C₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
23	C₃×C₇×D₅	—	73	1	no	—
24	C₂×C₇₃	—	5	1	no	—
25	C₇⋊AGL(1,𝔽₅)	—	73	1	no	Hall
26	C₃×C₅×C₇	—	73	1	no	Hall
27	C₃×Dic₇	—	365	1	no	Hall
28	C₇₃	C₃×C₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
29	C₇×D₅	D₇₃⋊C₃	1	1	yes	characteristic
30	C₃×AGL(1,𝔽₅)	—	511	1	no	Hall
31	C₂×C₃×C₇	—	365	1	no	—
32	C₅×C₇	Dic₇₃⋊C₃	1	1	yes	characteristic, complemented, Hall
33	C₃×D₅	—	73	1	no	—
34	Dic₇	—	365	1	no	Hall
35	C₃×C₇	—	73	1	no	Hall
36	AGL(1,𝔽₅)	—	511	1	no	Hall
37	C₃×C₅	—	73	1	no	Hall
38	C₂×C₇	—	5	1	no	—
39	C₃×C₄	—	2555	1	no	Hall
40	D₅	(C₇₃⋊C₃)⋊D₇	1	1	yes	characteristic
41	C₇	#13091734⋊C₃	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₃	—	365	1	no	—
43	C₅	#20259490	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	2555	1	no	Sylow
45	C₃	—	73	1	no	Sylow
46	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₇×C₇₃	C₃×C₄
prime radical	C₇×D₅×C₇₃⋊C₃	C₂
cosocle	C₇×D₅×C₇₃	C₂×C₃
LCS	G ▷ C₅×C₇×C₇₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₇⋊#13091734	C₃	semidirect
3. C₅×C₇×C₇₃⋊C₃	C₄	semidirect
8. C₅×C₇×C₇₃	C₃×C₄	semidirect
11. C₇×C₇₃⋊C₃	AGL(1,𝔽₅)	semidirect
13. C₅×C₇₃⋊C₃	Dic₇	semidirect
17. C₇×C₇₃	C₃×AGL(1,𝔽₅)	semidirect
20. C₅×C₇₃	C₃×Dic₇	semidirect
22. C₇₃⋊C₃	C₇⋊AGL(1,𝔽₅)	semidirect
28. C₇₃	C₃×C₇⋊AGL(1,𝔽₅)	semidirect
32. C₅×C₇	Dic₇₃⋊C₃	semidirect
41. C₇	#13091734⋊C₃	semidirect
43. C₅	#20259490	semidirect

Maximal subgroups

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

subgroup	index
C₇×D₅×C₇₃⋊C₃	2
C₇⋊#13091734	3
#20259490	5
#13091734⋊C₃	7
C₃×C₇⋊AGL(1,𝔽₅)	73