Subgroups — C₇×C₇⋊#10596816 #43249346

Order 28420.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×D₅×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇²×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇×Dic₂₀₃	—	5	1	no	maximal, Hall
4	C₇⋊#10596816	C₇	1	1	yes	maximal, characteristic, direct product factor
5	C₇×#10596816	—	7	1	no	maximal
6	C₂×C₇²×C₂₉	—	5	1	no	—
7	C₇×D₅×C₂₉	—	2	3	no	—
8	C₇×D₅×C₂₉	D₇	1	1	yes	characteristic
9	C₇×D₅×C₂₉	C₂×C₇	1	1	yes	characteristic
10	C₇²×C₂₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
11	C₅×C₇×C₂₉	—	2	3	no	—
12	C₅×C₇×C₂₉	Dic₇	1	1	yes	characteristic, complemented
13	C₅×C₇×C₂₉	C₄×C₇	1	1	yes	characteristic, complemented
14	C₇×C₇⋊AGL(1,𝔽₅)	—	29	1	no	maximal, Hall
15	Dic₂₀₃	—	5	1	no	—
16	C₇×Dic₂₉	—	35	1	no	—
17	#10596816	—	7	1	no	Hall
18	C₇²×D₅	D₂₉	1	1	yes	characteristic
19	C₂×C₇×C₂₉	—	5	1	no	—
20	C₂×C₇×C₂₉	—	5	1	no	—
21	C₂×C₇×C₂₉	—	10	3	no	—
22	D₅×C₂₉	C₇×D₇	1	1	yes	characteristic
23	C₅×C₇²	Dic₂₉	1	1	yes	characteristic, complemented, Hall
24	C₇×C₂₉	—	2	3	no	—
25	C₇×C₂₉	C₇×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
26	C₇×C₂₉	C₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
27	C₇×Dic₇	—	145	1	no	Hall
28	C₅×C₂₉	C₇×Dic₇	1	1	yes	characteristic, complemented, Hall
29	C₇⋊AGL(1,𝔽₅)	—	29	1	no	—
30	C₇×AGL(1,𝔽₅)	—	203	1	no	—
31	Dic₂₉	—	35	1	no	Hall
32	C₂×C₇²	—	5	1	no	—
33	C₇×D₅	—	2	3	no	—
34	C₇×D₅	C₇×D₂₉	1	1	yes	characteristic
35	C₇×D₅	D₂₀₃	1	1	yes	characteristic
36	C₂×C₂₉	—	5	1	no	—
37	C₇²	#10596816	1	1	yes	characteristic, complemented, Sylow
38	C₅×C₇	—	2	3	no	—
39	C₅×C₇	C₇×Dic₂₉	1	1	yes	characteristic, complemented
40	C₅×C₇	Dic₂₀₃	1	1	yes	characteristic, complemented
41	C₂₉	C₇×C₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
42	C₄×C₇	—	1015	1	no	—
43	Dic₇	—	145	1	no	—
44	AGL(1,𝔽₅)	—	203	1	no	Hall
45	C₂×C₇	—	5	1	no	—
46	C₂×C₇	—	5	1	no	—
47	C₂×C₇	—	10	3	no	—
48	D₅	C₇×D₂₀₃	1	1	yes	characteristic
49	C₇	—	2	3	no	—
50	C₇	C₇×#10596816	1	1	yes	characteristic, complemented
51	C₇	C₇⋊#10596816	1	1	yes	characteristic, direct product factor
52	C₅	C₇×Dic₂₀₃	1	1	yes	characteristic, complemented, Sylow
53	C₄	—	1015	1	no	Sylow
54	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₇	C₇⋊#10596816
commutator, hypocenter	C₅×C₇×C₂₉	C₄×C₇
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₂₉	C₄
prime radical	C₇²×D₅×C₂₉	C₂
cosocle	C₇×D₅×C₂₉	C₂×C₇
LCS	G ▷ C₅×C₇×C₂₉
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
2. C₅×C₇²×C₂₉	C₄	semidirect
4. C₇⋊#10596816	C₇	direct (N × H)
10. C₇²×C₂₉	AGL(1,𝔽₅)	semidirect
12. C₅×C₇×C₂₉	Dic₇	semidirect
13. C₅×C₇×C₂₉	C₄×C₇	semidirect
23. C₅×C₇²	Dic₂₉	semidirect
25. C₇×C₂₉	C₇×AGL(1,𝔽₅)	semidirect
26. C₇×C₂₉	C₇⋊AGL(1,𝔽₅)	semidirect
28. C₅×C₂₉	C₇×Dic₇	semidirect
37. C₇²	#10596816	semidirect
39. C₅×C₇	C₇×Dic₂₉	semidirect
40. C₅×C₇	Dic₂₀₃	semidirect
41. C₂₉	C₇×C₇⋊AGL(1,𝔽₅)	semidirect
50. C₇	C₇×#10596816	semidirect
51. C₇	C₇⋊#10596816	direct (N × H)
52. C₅	C₇×Dic₂₀₃	semidirect

Maximal subgroups

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

subgroup	index
C₇²×D₅×C₂₉	2
C₇×Dic₂₀₃	5
C₇⋊#10596816	7
C₇×#10596816	7
C₇×C₇⋊AGL(1,𝔽₅)	29

Subgroups — C7×C7⋊#10596816 #43249346

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₇⋊#10596816 #43249346