Subgroups — C₇×C₇⋊#10596817 #43249356

Order 28420.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇²×D₂₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇²×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇×C₇⋊#1181	—	5	1	no	maximal, Hall
4	C₇⋊#10596817	C₇	1	1	yes	maximal, characteristic, direct product factor
5	C₇×#10596817	—	7	1	no	maximal
6	C₇²×D₂₉	D₅	1	1	yes	characteristic
7	C₅×C₇×D₂₉	—	2	3	no	—
8	C₅×C₇×D₂₉	D₇	1	1	yes	characteristic
9	C₅×C₇×D₂₉	C₂×C₇	1	1	yes	characteristic
10	C₇²×C₂₉	Dic₅	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×Dic₃₅	—	29	1	no	maximal, Hall
15	C₇⋊#1181	—	5	1	no	—
16	C₇×#1181	—	35	1	no	—
17	#10596817	—	7	1	no	Hall
18	C₂×C₅×C₇²	—	29	1	no	—
19	C₇×D₂₉	—	2	3	no	—
20	C₇×D₂₉	C₇×D₅	1	1	yes	characteristic
21	C₇×D₂₉	D₃₅	1	1	yes	characteristic
22	C₅×D₂₉	C₇×D₇	1	1	yes	characteristic
23	C₅×C₇²	#1181	1	1	yes	characteristic, complemented, Hall
24	C₇×C₂₉	—	2	3	no	—
25	C₇×C₂₉	C₇×Dic₅	1	1	yes	characteristic, complemented
26	C₇×C₂₉	Dic₃₅	1	1	yes	characteristic, complemented
27	C₇×Dic₇	—	145	1	no	Hall
28	C₅×C₂₉	C₇×Dic₇	1	1	yes	characteristic, complemented, Hall
29	Dic₃₅	—	29	1	no	—
30	C₇×Dic₅	—	203	1	no	—
31	#1181	—	35	1	no	Hall
32	C₂×C₇²	—	29	1	no	—
33	C₂×C₅×C₇	—	29	1	no	—
34	C₂×C₅×C₇	—	29	1	no	—
35	C₂×C₅×C₇	—	58	3	no	—
36	D₂₉	C₇×D₃₅	1	1	yes	characteristic
37	C₇²	#10596817	1	1	yes	characteristic, complemented, Sylow
38	C₅×C₇	—	2	3	no	—
39	C₅×C₇	C₇×#1181	1	1	yes	characteristic, complemented
40	C₅×C₇	C₇⋊#1181	1	1	yes	characteristic, complemented
41	C₂₉	C₇×Dic₃₅	1	1	yes	characteristic, complemented, Sylow
42	C₄×C₇	—	1015	1	no	—
43	Dic₇	—	145	1	no	—
44	Dic₅	—	203	1	no	Hall
45	C₂×C₇	—	29	1	no	—
46	C₂×C₇	—	29	1	no	—
47	C₂×C₇	—	58	3	no	—
48	C₂×C₅	—	29	1	no	—
49	C₇	—	2	3	no	—
50	C₇	C₇×#10596817	1	1	yes	characteristic, complemented
51	C₇	C₇⋊#10596817	1	1	yes	characteristic, direct product factor
52	C₅	C₇×C₇⋊#1181	1	1	yes	characteristic, complemented, Sylow
53	C₄	—	1015	1	no	Sylow
54	C₂	—	29	1	no	—

	subgroup	G/H
center, hypercenter	C₇	C₇⋊#10596817
commutator, hypocenter	C₅×C₇×C₂₉	C₄×C₇
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₂₉	C₄
prime radical	C₅×C₇²×D₂₉	C₂
cosocle	C₅×C₇×D₂₉	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⋊#10596817	C₇	direct (N × H)
10. C₇²×C₂₉	Dic₅	semidirect
12. C₅×C₇×C₂₉	Dic₇	semidirect
13. C₅×C₇×C₂₉	C₄×C₇	semidirect
23. C₅×C₇²	#1181	semidirect
25. C₇×C₂₉	C₇×Dic₅	semidirect
26. C₇×C₂₉	Dic₃₅	semidirect
28. C₅×C₂₉	C₇×Dic₇	semidirect
37. C₇²	#10596817	semidirect
39. C₅×C₇	C₇×#1181	semidirect
40. C₅×C₇	C₇⋊#1181	semidirect
41. C₂₉	C₇×Dic₃₅	semidirect
50. C₇	C₇×#10596817	semidirect
51. C₇	C₇⋊#10596817	direct (N × H)
52. C₅	C₇×C₇⋊#1181	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₇²×D₂₉	2
C₇×C₇⋊#1181	5
C₇⋊#10596817	7
C₇×#10596817	7
C₇×Dic₃₅	29

Subgroups — C7×C7⋊#10596817 #43249356

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₇⋊#10596817 #43249356