Subgroups — C₇⋊#17984466 #44525918

Order 30940.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₅×C₁₃×C₁₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇×C₁₃×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₅₄₇	—	5	1	no	maximal, Hall
4	#17984466	—	7	1	no	maximal, Hall
5	C₂×C₇×C₁₃×C₁₇	—	5	1	no	—
6	C₇⋊#66774	—	13	1	no	maximal, Hall
7	D₅×C₁₃×C₁₇	D₇	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×D₅×C₁₇	D₁₃	1	1	yes	characteristic
11	C₅×C₁₃×C₁₇	Dic₇	1	1	yes	characteristic, complemented, Hall
12	C₇×D₅×C₁₃	D₁₇	1	1	yes	characteristic
13	Dic₂₂₁	—	35	1	no	Hall
14	C₅×C₇×C₁₇	Dic₁₃	1	1	yes	characteristic, complemented, Hall
15	Dic₁₁₉	—	65	1	no	Hall
16	C₅×C₇×C₁₃	Dic₁₇	1	1	yes	characteristic, complemented, Hall
17	C₂×C₁₃×C₁₇	—	5	1	no	—
18	Dic₉₁	—	85	1	no	Hall
19	#66774	—	91	1	no	Hall
20	#63120	—	119	1	no	Hall
21	C₂×C₇×C₁₇	—	5	1	no	—
22	C₁₃×C₁₇	C₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
23	C₂×C₇×C₁₃	—	5	1	no	—
24	D₅×C₁₇	D₉₁	1	1	yes	characteristic
25	C₇⋊AGL(1,𝔽₅)	—	221	1	no	Hall
26	D₅×C₁₃	D₁₁₉	1	1	yes	characteristic
27	C₇×C₁₇	#63120	1	1	yes	characteristic, complemented, Hall
28	C₇×C₁₃	#66774	1	1	yes	characteristic, complemented, Hall
29	C₅×C₁₇	Dic₉₁	1	1	yes	characteristic, complemented, Hall
30	C₇×D₅	D₂₂₁	1	1	yes	characteristic
31	Dic₁₇	—	455	1	no	Hall
32	C₅×C₁₃	Dic₁₁₉	1	1	yes	characteristic, complemented, Hall
33	Dic₁₃	—	595	1	no	Hall
34	C₅×C₇	Dic₂₂₁	1	1	yes	characteristic, complemented, Hall
35	C₂×C₁₇	—	5	1	no	—
36	Dic₇	—	1105	1	no	Hall
37	C₂×C₁₃	—	5	1	no	—
38	AGL(1,𝔽₅)	—	1547	1	no	Hall
39	C₁₇	C₇⋊#63120	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₇	—	5	1	no	—
41	C₁₃	C₇⋊#66774	1	1	yes	characteristic, complemented, Sylow
42	D₅	D₁₅₄₇	1	1	yes	characteristic
43	C₇	#17984466	1	1	yes	characteristic, complemented, Sylow
44	C₅	Dic₁₅₄₇	1	1	yes	characteristic, complemented, Sylow
45	C₄	—	7735	1	no	Sylow
46	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₇×C₁₃×C₁₇	C₄
prime radical, cosocle	C₇×D₅×C₁₃×C₁₇	C₂
LCS	G ▷ C₅×C₇×C₁₃×C₁₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₅×C₇×C₁₃×C₁₇	C₄	semidirect
9. C₇×C₁₃×C₁₇	AGL(1,𝔽₅)	semidirect
11. C₅×C₁₃×C₁₇	Dic₇	semidirect
14. C₅×C₇×C₁₇	Dic₁₃	semidirect
16. C₅×C₇×C₁₃	Dic₁₇	semidirect
22. C₁₃×C₁₇	C₇⋊AGL(1,𝔽₅)	semidirect
27. C₇×C₁₇	#63120	semidirect
28. C₇×C₁₃	#66774	semidirect
29. C₅×C₁₇	Dic₉₁	semidirect
32. C₅×C₁₃	Dic₁₁₉	semidirect
34. C₅×C₇	Dic₂₂₁	semidirect
39. C₁₇	C₇⋊#63120	semidirect
41. C₁₃	C₇⋊#66774	semidirect
43. C₇	#17984466	semidirect
44. C₅	Dic₁₅₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₇×D₅×C₁₃×C₁₇	2
Dic₁₅₄₇	5
#17984466	7
C₇⋊#66774	13
C₇⋊#63120	17

Subgroups — C7⋊#17984466 #44525918

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇⋊#17984466 #44525918