Subgroups — C₇×#19104887 #49141524

Order 36540.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂₉×C₃⋊D₁₅	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅×C₇×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇×#11760330	—	5	1	no	maximal, Hall
4	C₇×C₂₉×D₁₅	—	6	2	no	—
5	#19104887	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×#10596816	—	9	1	no	maximal, Hall
7	C₇×C₃⋊D₃×C₂₉	—	5	1	no	—
8	C₃×C₅×C₇×C₂₉	—	2	2	no	—
9	C₂₉×C₃⋊D₁₅	C₂×C₇	1	1	yes	characteristic
10	C₇×D₅×C₂₉	—	9	1	no	—
11	C₃²×C₇×C₂₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	C₃²×C₅×C₂₉	C₄×C₇	1	1	yes	characteristic, complemented, Hall
13	C₇×#4380	—	29	1	no	maximal, Hall
14	D₃×C₇×C₂₉	—	30	2	no	—
15	#11760330	—	5	1	no	Hall
16	C₅×C₇×C₂₉	#157	1	1	yes	characteristic, complemented, Hall
17	C₂₉×D₁₅	—	6	2	no	—
18	C₇×Dic₂₉	—	45	1	no	Hall
19	C₇×C₃⋊D₁₅	D₂₉	1	1	yes	characteristic
20	C₃×C₇×C₂₉	—	2	2	no	—
21	#10596816	—	9	1	no	Hall
22	C₃⋊D₃×C₂₉	—	5	1	no	—
23	C₃×C₅×C₂₉	—	2	2	no	—
24	C₂×C₇×C₂₉	—	45	1	no	—
25	C₃²×C₅×C₇	Dic₂₉	1	1	yes	characteristic, complemented, Hall
26	D₅×C₂₉	—	9	1	no	—
27	C₃²×C₂₉	C₇×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
28	C₇×#157	—	145	1	no	Hall
29	C₇×D₁₅	—	6	2	no	—
30	C₇×C₂₉	#4380	1	1	yes	characteristic, complemented, Hall
31	#4380	—	29	1	no	Hall
32	D₃×C₂₉	—	30	2	no	—
33	C₅×C₂₉	C₇×#157	1	1	yes	characteristic, complemented, Hall
34	C₇×AGL(1,𝔽₅)	—	261	1	no	Hall
35	C₇×C₃⋊D₃	—	5	1	no	—
36	Dic₂₉	—	45	1	no	Hall
37	C₃×C₅×C₇	—	2	2	no	—
38	C₃⋊D₁₅	C₇×D₂₉	1	1	yes	characteristic
39	C₃×C₂₉	—	2	2	no	—
40	C₇×D₅	—	9	1	no	—
41	C₃²×C₇	#10596816	1	1	yes	characteristic, complemented, Hall
42	C₂×C₂₉	—	45	1	no	—
43	C₃²×C₅	C₇×Dic₂₉	1	1	yes	characteristic, complemented, Hall
44	D₃×C₇	—	30	2	no	—
45	#157	—	145	1	no	Hall
46	C₅×C₇	#11760330	1	1	yes	characteristic, complemented, Hall
47	D₁₅	—	6	2	no	—
48	C₂₉	C₇×#4380	1	1	yes	characteristic, complemented, Sylow
49	C₄×C₇	—	1305	1	no	Hall
50	C₃×C₇	—	2	2	no	—
51	AGL(1,𝔽₅)	—	261	1	no	Hall
52	C₃⋊D₃	—	5	1	no	—
53	C₃×C₅	—	2	2	no	—
54	C₂×C₇	—	45	1	no	—
55	D₅	—	9	1	no	—
56	C₃²	C₇×#10596816	1	1	yes	characteristic, complemented, Sylow
57	C₇	#19104887	1	1	yes	characteristic, direct product factor, Sylow
58	D₃	—	30	2	no	—
59	C₅	C₇×#11760330	1	1	yes	characteristic, complemented, Sylow
60	C₄	—	1305	1	no	Sylow
61	C₃	—	2	2	no	—
62	C₂	—	45	1	no	—

	subgroup	G/H
center, hypercenter	C₇	#19104887
commutator, hypocenter	C₃²×C₅×C₂₉	C₄×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₂₉	C₄
prime radical	C₇×C₂₉×C₃⋊D₁₅	C₂
cosocle	C₂₉×C₃⋊D₁₅	C₂×C₇
LCS	G ▷ C₃²×C₅×C₂₉
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅×C₇×C₂₉	C₄	semidirect
5. #19104887	C₇	direct (N × H)
11. C₃²×C₇×C₂₉	AGL(1,𝔽₅)	semidirect
12. C₃²×C₅×C₂₉	C₄×C₇	semidirect
16. C₅×C₇×C₂₉	#157	semidirect
25. C₃²×C₅×C₇	Dic₂₉	semidirect
27. C₃²×C₂₉	C₇×AGL(1,𝔽₅)	semidirect
30. C₇×C₂₉	#4380	semidirect
33. C₅×C₂₉	C₇×#157	semidirect
41. C₃²×C₇	#10596816	semidirect
43. C₃²×C₅	C₇×Dic₂₉	semidirect
46. C₅×C₇	#11760330	semidirect
48. C₂₉	C₇×#4380	semidirect
56. C₃²	C₇×#10596816	semidirect
57. C₇	#19104887	direct (N × H)
59. C₅	C₇×#11760330	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₂₉×C₃⋊D₁₅	2
C₇×#11760330	5
#19104887	7
C₇×#10596816	9
C₇×#4380	29

Subgroups — C7×#19104887 #49141524

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19104887 #49141524