Subgroups — C₃×C₅²×C₇⋊Dic₇ #28413196

Order 14700.

480 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	C₅²×C₇⋊Dic₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅²×C₇²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₅×C₇⋊Dic₇	C₅	1	6	yes	maximal, direct product factor
5	C₂×C₅²×C₇²	C₂×C₃	1	1	yes	characteristic
6	C₃×C₅²×Dic₇	—	7	8	no	maximal
7	C₂×C₃×C₅×C₇²	C₂×C₅	1	6	yes	—
8	C₅²×C₇²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₅²×C₇	D₇	1	8	yes	—
10	C₅×C₇⋊Dic₇	C₃×C₅	1	6	yes	direct product factor
11	C₃×C₅×C₇²	C₄×C₅	1	6	yes	complemented
12	C₅²×Dic₇	—	7	8	no	—
13	C₃×C₇⋊Dic₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₅²×C₇	Dic₇	1	8	yes	complemented
15	C₂×C₅×C₇²	C₂×C₃×C₅	1	6	yes	—
16	C₃×C₅×Dic₇	—	7	48	no	—
17	C₂×C₅²×C₇	C₃×D₇	1	8	yes	—
18	C₃×C₄×C₅²	—	49	1	no	Hall
19	C₂×C₃×C₇²	C₂×C₅²	1	1	yes	characteristic
20	C₅×C₇²	C₃×C₄×C₅	1	6	yes	complemented
21	C₂×C₃×C₅×C₇	C₅×D₇	1	48	yes	—
22	C₇⋊Dic₇	C₃×C₅²	1	1	yes	characteristic, direct product factor, Hall
23	C₅²×C₇	C₃×Dic₇	1	8	yes	complemented
24	C₂×C₃×C₅²	C₇⋊D₇	1	1	yes	characteristic
25	C₃×C₇²	C₄×C₅²	1	1	yes	characteristic, complemented, Hall
26	C₅×Dic₇	—	7	48	no	—
27	C₃×C₅×C₇	C₅×Dic₇	1	48	yes	complemented
28	C₄×C₅²	—	49	1	no	Hall
29	C₂×C₇²	C₂×C₃×C₅²	1	1	yes	characteristic
30	C₃×Dic₇	—	7	8	no	—
31	C₃×C₅²	C₇⋊Dic₇	1	1	yes	characteristic, direct product factor, Hall
32	C₂×C₅×C₇	C₃×C₅×D₇	1	48	yes	—
33	C₃×C₄×C₅	—	49	6	no	—
34	C₂×C₅²	C₃×C₇⋊D₇	1	1	yes	characteristic
35	C₇²	C₃×C₄×C₅²	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃×C₇	C₅²×D₇	1	8	yes	—
37	C₅×C₇	C₃×C₅×Dic₇	1	48	yes	complemented
38	C₂×C₃×C₅	C₅×C₇⋊D₇	1	6	yes	—
39	Dic₇	—	7	8	no	—
40	C₅²	C₃×C₇⋊Dic₇	1	1	yes	characteristic, direct product factor, Sylow
41	C₃×C₇	C₅²×Dic₇	1	8	yes	complemented
42	C₄×C₅	—	49	6	no	—
43	C₃×C₅	C₅×C₇⋊Dic₇	1	6	yes	direct product factor
44	C₂×C₇	C₃×C₅²×D₇	1	8	yes	—
45	C₃×C₄	—	49	1	no	Hall
46	C₂×C₅	C₃×C₅×C₇⋊D₇	1	6	yes	—
47	C₇	C₃×C₅²×Dic₇	1	8	yes	complemented
48	C₂×C₃	C₅²×C₇⋊D₇	1	1	yes	characteristic
49	C₅	C₃×C₅×C₇⋊Dic₇	1	6	yes	direct product factor
50	C₄	—	49	1	no	Sylow
51	C₃	C₅²×C₇⋊Dic₇	1	1	yes	characteristic, direct product factor, Sylow
52	C₂	C₃×C₅²×C₇⋊D₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅²	C₇⋊D₇
commutator, hypocenter	C₇²	C₃×C₄×C₅²
Frattini	C₂	C₃×C₅²×C₇⋊D₇
Fitting, socle, prime radical	C₂×C₃×C₅²×C₇²	C₂
cosocle	C₂×C₇²	C₂×C₃×C₅²
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂×C₃×C₅²

Complements

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

N	H ≅ G/N	type
2. C₅²×C₇⋊Dic₇	C₃	direct (N × H)
3. C₃×C₅²×C₇²	C₄	semidirect
4. C₃×C₅×C₇⋊Dic₇	C₅	direct (N × H)
8. C₅²×C₇²	C₃×C₄	semidirect
10. C₅×C₇⋊Dic₇	C₃×C₅	direct (N × H)
11. C₃×C₅×C₇²	C₄×C₅	semidirect
13. C₃×C₇⋊Dic₇	C₅²	direct (N × H)
14. C₃×C₅²×C₇	Dic₇	semidirect
20. C₅×C₇²	C₃×C₄×C₅	semidirect
22. C₇⋊Dic₇	C₃×C₅²	direct (N × H)
23. C₅²×C₇	C₃×Dic₇	semidirect
25. C₃×C₇²	C₄×C₅²	semidirect
27. C₃×C₅×C₇	C₅×Dic₇	semidirect
31. C₃×C₅²	C₇⋊Dic₇	direct (N × H)
35. C₇²	C₃×C₄×C₅²	semidirect
37. C₅×C₇	C₃×C₅×Dic₇	semidirect
40. C₅²	C₃×C₇⋊Dic₇	direct (N × H)
41. C₃×C₇	C₅²×Dic₇	semidirect
43. C₃×C₅	C₅×C₇⋊Dic₇	direct (N × H)
47. C₇	C₃×C₅²×Dic₇	semidirect
49. C₅	C₃×C₅×C₇⋊Dic₇	direct (N × H)
51. C₃	C₅²×C₇⋊Dic₇	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
C₅²×C₇⋊Dic₇	3
C₃×C₅×C₇⋊Dic₇	5
C₃×C₅²×Dic₇	7

Subgroups — C3×C52×C7⋊Dic7 #28413196

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅²×C₇⋊Dic₇ #28413196