Subgroups — C₇×C₁₃×C₂²⋊(C₅²⋊C₃) #41032073

Order 27300.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅²×C₇×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₁₃×C₅²⋊C₃	—	4	1	no	maximal, Hall
3	C₂×C₅²×C₇×C₁₃	—	3	1	no	—
4	C₁₃×C₂²⋊(C₅²⋊C₃)	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅²×C₇×C₁₃	A₄	1	1	yes	characteristic, complemented, Hall
6	C₇×C₂²⋊(C₅²⋊C₃)	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₅×C₇×C₁₃	—	3	2	no	—
8	C₂²×C₅²×C₁₃	C₃×C₇	1	1	yes	characteristic, complemented, Hall
9	C₇×A₄×C₁₃	—	25	1	no	maximal, Hall
10	C₁₃×C₅²⋊C₃	—	4	1	no	Hall
11	C₂×C₅×C₇×C₁₃	—	3	6	no	—
12	C₂²×C₅²×C₇	C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅²×C₁₃	—	3	1	no	—
14	C₇×C₅²⋊C₃	—	4	1	no	Hall
15	C₅×C₇×C₁₃	—	3	2	no	—
16	C₂²×C₇×C₁₃	C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₅²×C₇	—	3	1	no	—
18	C₅²×C₁₃	C₇×A₄	1	1	yes	characteristic, complemented, Hall
19	C₂²⋊(C₅²⋊C₃)	C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
20	C₃×C₇×C₁₃	—	100	1	no	Hall
21	C₂²×C₅×C₁₃	—	3	2	no	—
22	C₂×C₇×C₁₃	—	3	1	no	—
23	C₅²×C₇	A₄×C₁₃	1	1	yes	characteristic, complemented, Hall
24	A₄×C₁₃	—	25	1	no	Hall
25	C₂²×C₅×C₇	—	3	2	no	—
26	C₂×C₅×C₁₃	—	3	6	no	—
27	C₂²×C₅²	C₃×C₇×C₁₃	1	1	yes	characteristic, complemented, Hall
28	C₇×C₁₃	C₂²⋊(C₅²⋊C₃)	1	1	yes	characteristic, direct product factor, Hall
29	C₇×A₄	—	25	1	no	Hall
30	C₅²⋊C₃	—	4	1	no	Hall
31	C₂×C₅×C₇	—	3	6	no	—
32	C₅×C₁₃	—	3	2	no	—
33	C₂²×C₁₃	C₇×C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
34	C₂×C₅²	—	3	1	no	—
35	C₃×C₁₃	—	100	1	no	Hall
36	C₅×C₇	—	3	2	no	—
37	C₂²×C₇	C₁₃×C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
38	C₂×C₁₃	—	3	1	no	—
39	C₅²	C₇×A₄×C₁₃	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₇	—	100	1	no	Hall
41	C₂²×C₅	—	3	2	no	—
42	C₂×C₇	—	3	1	no	—
43	C₁₃	C₇×C₂²⋊(C₅²⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
44	A₄	—	25	1	no	Hall
45	C₂×C₅	—	3	6	no	—
46	C₇	C₁₃×C₂²⋊(C₅²⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
47	C₅	—	3	2	no	—
48	C₂²	C₇×C₁₃×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
49	C₃	—	100	1	no	Sylow
50	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₇×C₁₃	C₂²⋊(C₅²⋊C₃)
commutator, cosocle, hypocenter	C₂²×C₅²	C₃×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₂²×C₅²×C₇×C₁₃	C₃
LCS	G ▷ C₂²×C₅²
UCS	C₁ ◁ C₇×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅²×C₇×C₁₃	C₃	semidirect
4. C₁₃×C₂²⋊(C₅²⋊C₃)	C₇	direct (N × H)
5. C₅²×C₇×C₁₃	A₄	semidirect
6. C₇×C₂²⋊(C₅²⋊C₃)	C₁₃	direct (N × H)
8. C₂²×C₅²×C₁₃	C₃×C₇	semidirect
12. C₂²×C₅²×C₇	C₃×C₁₃	semidirect
16. C₂²×C₇×C₁₃	C₅²⋊C₃	semidirect
18. C₅²×C₁₃	C₇×A₄	semidirect
19. C₂²⋊(C₅²⋊C₃)	C₇×C₁₃	direct (N × H)
23. C₅²×C₇	A₄×C₁₃	semidirect
27. C₂²×C₅²	C₃×C₇×C₁₃	semidirect
28. C₇×C₁₃	C₂²⋊(C₅²⋊C₃)	direct (N × H)
33. C₂²×C₁₃	C₇×C₅²⋊C₃	semidirect
37. C₂²×C₇	C₁₃×C₅²⋊C₃	semidirect
39. C₅²	C₇×A₄×C₁₃	semidirect
43. C₁₃	C₇×C₂²⋊(C₅²⋊C₃)	direct (N × H)
46. C₇	C₁₃×C₂²⋊(C₅²⋊C₃)	direct (N × H)
48. C₂²	C₇×C₁₃×C₅²⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅²×C₇×C₁₃	3
C₇×C₁₃×C₅²⋊C₃	4
C₁₃×C₂²⋊(C₅²⋊C₃)	7
C₇×C₂²⋊(C₅²⋊C₃)	13
C₇×A₄×C₁₃	25

Subgroups — C7×C13×C22⋊(C52⋊C3) #41032073

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₁₃×C₂²⋊(C₅²⋊C₃) #41032073