Subgroups — C₇×#17984465 #44525901

Order 30940.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₃×D₈₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇×C₁₃×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇×#11725133	—	5	1	no	maximal, Hall
4	#17984465	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×C₁₃×D₁₇	—	5	1	no	—
6	C₇×#66776	—	13	1	no	maximal, Hall
7	C₁₃×D₈₅	C₂×C₇	1	1	yes	characteristic
8	C₇×#63120	—	17	1	no	maximal, Hall
9	C₇×C₁₃×C₁₇	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
10	C₇×D₈₅	D₁₃	1	1	yes	characteristic
11	C₅×C₁₃×C₁₇	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	C₇×D₅×C₁₃	—	17	1	no	—
13	#11725133	—	5	1	no	Hall
14	C₅×C₇×C₁₇	Dic₁₃	1	1	yes	characteristic, complemented, Hall
15	C₇×#595	—	65	1	no	Hall
16	C₅×C₇×C₁₃	#595	1	1	yes	characteristic, complemented, Hall
17	C₁₃×D₁₇	—	5	1	no	—
18	C₇×Dic₁₃	—	85	1	no	Hall
19	#66776	—	13	1	no	Hall
20	#63120	—	17	1	no	Hall
21	C₇×D₁₇	—	5	1	no	—
22	C₁₃×C₁₇	C₇×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
23	C₂×C₇×C₁₃	—	85	1	no	—
24	D₈₅	C₇×D₁₃	1	1	yes	characteristic
25	C₇×AGL(1,𝔽₅)	—	221	1	no	Hall
26	D₅×C₁₃	—	17	1	no	—
27	C₇×C₁₇	#63120	1	1	yes	characteristic, complemented, Hall
28	C₇×C₁₃	#66776	1	1	yes	characteristic, complemented, Hall
29	C₅×C₁₇	C₇×Dic₁₃	1	1	yes	characteristic, complemented, Hall
30	C₇×D₅	—	17	1	no	—
31	#595	—	65	1	no	Hall
32	C₅×C₁₃	C₇×#595	1	1	yes	characteristic, complemented, Hall
33	Dic₁₃	—	85	1	no	Hall
34	C₅×C₇	#11725133	1	1	yes	characteristic, complemented, Hall
35	D₁₇	—	5	1	no	—
36	C₄×C₇	—	1105	1	no	Hall
37	C₂×C₁₃	—	85	1	no	—
38	AGL(1,𝔽₅)	—	221	1	no	Hall
39	C₁₇	C₇×#63120	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₇	—	85	1	no	—
41	C₁₃	C₇×#66776	1	1	yes	characteristic, complemented, Sylow
42	D₅	—	17	1	no	—
43	C₇	#17984465	1	1	yes	characteristic, direct product factor, Sylow
44	C₅	C₇×#11725133	1	1	yes	characteristic, complemented, Sylow
45	C₄	—	1105	1	no	Sylow
46	C₂	—	85	1	no	—

	subgroup	G/H
center, hypercenter	C₇	#17984465
commutator, hypocenter	C₅×C₁₃×C₁₇	C₄×C₇
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₃×C₁₇	C₄
prime radical	C₇×C₁₃×D₈₅	C₂
cosocle	C₁₃×D₈₅	C₂×C₇
LCS	G ▷ C₅×C₁₃×C₁₇
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
2. C₅×C₇×C₁₃×C₁₇	C₄	semidirect
4. #17984465	C₇	direct (N × H)
9. C₇×C₁₃×C₁₇	AGL(1,𝔽₅)	semidirect
11. C₅×C₁₃×C₁₇	C₄×C₇	semidirect
14. C₅×C₇×C₁₇	Dic₁₃	semidirect
16. C₅×C₇×C₁₃	#595	semidirect
22. C₁₃×C₁₇	C₇×AGL(1,𝔽₅)	semidirect
27. C₇×C₁₇	#63120	semidirect
28. C₇×C₁₃	#66776	semidirect
29. C₅×C₁₇	C₇×Dic₁₃	semidirect
32. C₅×C₁₃	C₇×#595	semidirect
34. C₅×C₇	#11725133	semidirect
39. C₁₇	C₇×#63120	semidirect
41. C₁₃	C₇×#66776	semidirect
43. C₇	#17984465	direct (N × H)
44. C₅	C₇×#11725133	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₁₃×D₈₅	2
C₇×#11725133	5
#17984465	7
C₇×#66776	13
C₇×#63120	17

Subgroups — C7×#17984465 #44525901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#17984465 #44525901