Subgroups — C₃×C₇×C₇⋊#1039 #28413201

Order 14700.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅²×C₇²	C₂	1	1	yes	maximal, characteristic
2	C₇×C₇⋊#1039	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅²×C₇²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₇×Dic₃₅	—	5	6	no	maximal
5	C₂×C₅²×C₇²	C₂×C₃	1	1	yes	characteristic
6	C₃×C₇⋊#1039	C₇	1	1	yes	maximal, characteristic, direct product factor
7	C₃×C₇×#1039	—	7	1	no	maximal
8	C₂×C₃×C₅×C₇²	D₅	1	6	yes	—
9	C₅²×C₇²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₅²×C₇	—	2	3	no	—
11	C₂×C₃×C₅²×C₇	D₇	1	1	yes	characteristic
12	C₂×C₃×C₅²×C₇	C₂×C₇	1	1	yes	characteristic
13	C₇×Dic₃₅	—	5	6	no	—
14	C₃×C₅×C₇²	Dic₅	1	6	yes	complemented
15	C₇⋊#1039	C₃×C₇	1	1	yes	characteristic, direct product factor
16	C₇×#1039	—	7	1	no	—
17	C₃×C₇×Dic₇	—	25	1	no	Hall
18	C₃×C₅²×C₇	—	2	3	no	—
19	C₃×C₅²×C₇	Dic₇	1	1	yes	characteristic, complemented
20	C₃×C₅²×C₇	C₄×C₇	1	1	yes	characteristic, complemented
21	C₂×C₅×C₇²	C₃×D₅	1	6	yes	—
22	C₃×Dic₃₅	—	5	6	no	—
23	C₃×C₇×Dic₅	—	35	6	no	—
24	C₂×C₅²×C₇	—	2	3	no	—
25	C₂×C₅²×C₇	C₃×D₇	1	1	yes	characteristic
26	C₂×C₅²×C₇	C₂×C₃×C₇	1	1	yes	characteristic
27	C₃×#1039	—	7	1	no	Hall
28	C₂×C₃×C₇²	C₅⋊D₅	1	1	yes	characteristic
29	C₅×C₇²	C₃×Dic₅	1	6	yes	complemented
30	C₂×C₃×C₅×C₇	—	2	18	no	—
31	C₂×C₃×C₅×C₇	C₇×D₅	1	6	yes	—
32	C₂×C₃×C₅×C₇	D₃₅	1	6	yes	—
33	C₇×Dic₇	—	25	1	no	Hall
34	C₅²×C₇	—	2	3	no	—
35	C₅²×C₇	C₃×Dic₇	1	1	yes	characteristic, complemented
36	C₅²×C₇	C₃×C₄×C₇	1	1	yes	characteristic, complemented
37	C₂×C₃×C₅²	C₇×D₇	1	1	yes	characteristic
38	C₃×C₇²	#1039	1	1	yes	characteristic, complemented, Hall
39	Dic₃₅	—	5	6	no	—
40	C₇×Dic₅	—	35	6	no	—
41	C₃×C₅×C₇	—	2	18	no	—
42	C₃×C₅×C₇	C₇×Dic₅	1	6	yes	complemented
43	C₃×C₅×C₇	Dic₃₅	1	6	yes	complemented
44	#1039	—	7	1	no	Hall
45	C₂×C₇²	C₃×C₅⋊D₅	1	1	yes	characteristic
46	C₃×C₄×C₇	—	175	1	no	—
47	C₃×Dic₇	—	25	1	no	—
48	C₃×C₅²	C₇×Dic₇	1	1	yes	characteristic, complemented, Hall
49	C₂×C₅×C₇	—	2	18	no	—
50	C₂×C₅×C₇	C₃×C₇×D₅	1	6	yes	—
51	C₂×C₅×C₇	C₃×D₃₅	1	6	yes	—
52	C₃×Dic₅	—	35	6	no	—
53	C₂×C₅²	C₃×C₇×D₇	1	1	yes	characteristic
54	C₇²	C₃×#1039	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₃×C₇	—	2	3	no	—
56	C₂×C₃×C₇	C₇×C₅⋊D₅	1	1	yes	characteristic
57	C₂×C₃×C₇	C₅⋊D₃₅	1	1	yes	characteristic
58	C₅×C₇	—	2	18	no	—
59	C₅×C₇	C₃×C₇×Dic₅	1	6	yes	complemented
60	C₅×C₇	C₃×Dic₃₅	1	6	yes	complemented
61	C₂×C₃×C₅	C₇×D₃₅	1	6	yes	—
62	C₄×C₇	—	175	1	no	—
63	Dic₇	—	25	1	no	—
64	C₅²	C₃×C₇×Dic₇	1	1	yes	characteristic, complemented, Sylow
65	C₃×C₇	—	2	3	no	—
66	C₃×C₇	C₇×#1039	1	1	yes	characteristic, complemented
67	C₃×C₇	C₇⋊#1039	1	1	yes	characteristic, direct product factor
68	Dic₅	—	35	6	no	—
69	C₃×C₅	C₇×Dic₃₅	1	6	yes	complemented
70	C₂×C₇	—	2	3	no	—
71	C₂×C₇	C₃×C₇×C₅⋊D₅	1	1	yes	characteristic
72	C₂×C₇	C₃×C₅⋊D₃₅	1	1	yes	characteristic
73	C₃×C₄	—	175	1	no	Hall
74	C₂×C₅	C₃×C₇×D₃₅	1	6	yes	—
75	C₇	—	2	3	no	—
76	C₇	C₃×C₇×#1039	1	1	yes	characteristic, complemented
77	C₇	C₃×C₇⋊#1039	1	1	yes	characteristic, direct product factor
78	C₂×C₃	C₇×C₅⋊D₃₅	1	1	yes	characteristic
79	C₅	C₃×C₇×Dic₃₅	1	6	yes	complemented
80	C₄	—	175	1	no	Sylow
81	C₃	C₇×C₇⋊#1039	1	1	yes	characteristic, direct product factor, Sylow
82	C₂	C₃×C₇×C₅⋊D₃₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇	C₅⋊D₃₅
commutator, hypocenter	C₅²×C₇	C₃×C₄×C₇
Frattini	C₂	C₃×C₇×C₅⋊D₃₅
Fitting, socle, prime radical	C₂×C₃×C₅²×C₇²	C₂
cosocle	C₂×C₅²×C₇	C₂×C₃×C₇
LCS	G ▷ C₅²×C₇
UCS	C₁ ◁ C₂×C₃×C₇

Complements

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

N	H ≅ G/N	type
2. C₇×C₇⋊#1039	C₃	direct (N × H)
3. C₃×C₅²×C₇²	C₄	semidirect
6. C₃×C₇⋊#1039	C₇	direct (N × H)
9. C₅²×C₇²	C₃×C₄	semidirect
14. C₃×C₅×C₇²	Dic₅	semidirect
15. C₇⋊#1039	C₃×C₇	direct (N × H)
19. C₃×C₅²×C₇	Dic₇	semidirect
20. C₃×C₅²×C₇	C₄×C₇	semidirect
29. C₅×C₇²	C₃×Dic₅	semidirect
35. C₅²×C₇	C₃×Dic₇	semidirect
36. C₅²×C₇	C₃×C₄×C₇	semidirect
38. C₃×C₇²	#1039	semidirect
42. C₃×C₅×C₇	C₇×Dic₅	semidirect
43. C₃×C₅×C₇	Dic₃₅	semidirect
48. C₃×C₅²	C₇×Dic₇	semidirect
54. C₇²	C₃×#1039	semidirect
59. C₅×C₇	C₃×C₇×Dic₅	semidirect
60. C₅×C₇	C₃×Dic₃₅	semidirect
64. C₅²	C₃×C₇×Dic₇	semidirect
66. C₃×C₇	C₇×#1039	semidirect
67. C₃×C₇	C₇⋊#1039	direct (N × H)
69. C₃×C₅	C₇×Dic₃₅	semidirect
76. C₇	C₃×C₇×#1039	semidirect
77. C₇	C₃×C₇⋊#1039	direct (N × H)
79. C₅	C₃×C₇×Dic₃₅	semidirect
81. C₃	C₇×C₇⋊#1039	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅²×C₇²	2
C₇×C₇⋊#1039	3
C₃×C₇×Dic₃₅	5
C₃×C₇⋊#1039	7
C₃×C₇×#1039	7

Subgroups — C3×C7×C7⋊#1039 #28413201

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×C₇⋊#1039 #28413201