Subgroups — C₇×#19104885 #49141522

Order 36540.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃⋊D₄₃₅	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅×C₇×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇×#11760329	—	5	1	no	maximal, Hall
4	C₇×D₄₃₅	—	6	2	no	—
5	#19104885	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×#10596814	—	9	1	no	maximal, Hall
7	C₇×C₃⋊D₈₇	—	5	1	no	—
8	C₃×C₅×C₇×C₂₉	—	2	2	no	—
9	C₃⋊D₄₃₅	C₂×C₇	1	1	yes	characteristic
10	C₇×D₁₄₅	—	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	C₇×D₈₇	—	30	2	no	—
15	#11760329	—	5	1	no	Hall
16	C₅×C₇×C₂₉	#157	1	1	yes	characteristic, complemented, Hall
17	D₄₃₅	—	6	2	no	—
18	C₇×#1181	—	45	1	no	Hall
19	C₇×C₃⋊D₁₅	—	29	1	no	—
20	C₃×C₇×C₂₉	—	2	2	no	—
21	#10596814	—	9	1	no	Hall
22	C₃⋊D₈₇	—	5	1	no	—
23	C₃×C₅×C₂₉	—	2	2	no	—
24	C₇×D₂₉	—	45	1	no	—
25	C₃²×C₅×C₇	#1181	1	1	yes	characteristic, complemented, Hall
26	D₁₄₅	—	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	—	174	2	no	—
30	C₇×C₂₉	#4380	1	1	yes	characteristic, complemented, Hall
31	#4380	—	29	1	no	Hall
32	D₈₇	—	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	—	145	1	no	—
36	#1181	—	45	1	no	Hall
37	C₃×C₅×C₇	—	2	2	no	—
38	C₃⋊D₁₅	—	29	1	no	—
39	C₃×C₂₉	—	2	2	no	—
40	C₇×D₅	—	261	1	no	—
41	C₃²×C₇	#10596814	1	1	yes	characteristic, complemented, Hall
42	D₂₉	—	45	1	no	—
43	C₃²×C₅	C₇×#1181	1	1	yes	characteristic, complemented, Hall
44	D₃×C₇	—	870	2	no	—
45	#157	—	145	1	no	Hall
46	C₅×C₇	#11760329	1	1	yes	characteristic, complemented, Hall
47	D₁₅	—	174	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	—	145	1	no	—
53	C₃×C₅	—	2	2	no	—
54	C₂×C₇	—	1305	1	no	—
55	D₅	—	261	1	no	—
56	C₃²	C₇×#10596814	1	1	yes	characteristic, complemented, Sylow
57	C₇	#19104885	1	1	yes	characteristic, direct product factor, Sylow
58	D₃	—	870	2	no	—
59	C₅	C₇×#11760329	1	1	yes	characteristic, complemented, Sylow
60	C₄	—	1305	1	no	Sylow
61	C₃	—	2	2	no	—
62	C₂	—	1305	1	no	—

	subgroup	G/H
center, hypercenter	C₇	#19104885
commutator, hypocenter	C₃²×C₅×C₂₉	C₄×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₂₉	C₄
prime radical	C₇×C₃⋊D₄₃₅	C₂
cosocle	C₃⋊D₄₃₅	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. #19104885	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	#1181	semidirect
27. C₃²×C₂₉	C₇×AGL(1,𝔽₅)	semidirect
30. C₇×C₂₉	#4380	semidirect
33. C₅×C₂₉	C₇×#157	semidirect
41. C₃²×C₇	#10596814	semidirect
43. C₃²×C₅	C₇×#1181	semidirect
46. C₅×C₇	#11760329	semidirect
48. C₂₉	C₇×#4380	semidirect
56. C₃²	C₇×#10596814	semidirect
57. C₇	#19104885	direct (N × H)
59. C₅	C₇×#11760329	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₃⋊D₄₃₅	2
C₇×#11760329	5
#19104885	7
C₇×#10596814	9
C₇×#4380	29

Subgroups — C7×#19104885 #49141522

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19104885 #49141522