Subgroups — C₇×C₁₃×D₁₅₃ #42123797

Order 27846.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₉×C₁₃×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₁₃×D₅₁	—	3	1	no	maximal
3	C₃×C₇×C₁₃×C₁₇	D₃	1	1	yes	characteristic
4	C₁₃×D₁₅₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×C₁₃×D₁₇	—	9	1	no	Hall
6	C₇×D₁₅₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₉×C₁₃×C₁₇	C₂×C₇	1	1	yes	characteristic, complemented, Hall
8	C₇×C₁₃×D₉	—	17	1	no	maximal, Hall
9	C₇×C₁₃×C₁₇	D₉	1	1	yes	characteristic, complemented, Hall
10	C₁₃×D₅₁	—	3	1	no	—
11	C₇×C₉×C₁₇	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
12	C₇×C₉×C₁₃	D₁₇	1	1	yes	characteristic, complemented, Hall
13	C₇×D₅₁	—	3	1	no	—
14	C₃×C₁₃×C₁₇	D₃×C₇	1	1	yes	characteristic
15	D₃×C₇×C₁₃	—	51	1	no	—
16	C₁₃×D₁₇	—	9	1	no	Hall
17	C₃×C₇×C₁₇	D₃×C₁₃	1	1	yes	characteristic
18	D₁₅₃	C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₇×C₁₃	D₅₁	1	1	yes	characteristic
20	C₇×D₁₇	—	9	1	no	Hall
21	C₁₃×D₉	—	17	1	no	Hall
22	C₁₃×C₁₇	C₇×D₉	1	1	yes	characteristic, complemented, Hall
23	C₂×C₇×C₁₃	—	153	1	no	Hall
24	C₉×C₁₇	C₂×C₇×C₁₃	1	1	yes	characteristic, complemented, Hall
25	C₇×D₉	—	17	1	no	Hall
26	C₇×C₁₇	C₁₃×D₉	1	1	yes	characteristic, complemented, Hall
27	C₉×C₁₃	C₇×D₁₇	1	1	yes	characteristic, complemented, Hall
28	D₅₁	—	3	1	no	—
29	C₇×C₁₃	D₁₅₃	1	1	yes	characteristic, direct product factor, Hall
30	D₃×C₁₃	—	51	1	no	—
31	C₇×C₉	C₁₃×D₁₇	1	1	yes	characteristic, complemented, Hall
32	C₃×C₁₇	D₃×C₇×C₁₃	1	1	yes	characteristic
33	D₃×C₇	—	51	1	no	—
34	C₃×C₁₃	C₇×D₅₁	1	1	yes	characteristic
35	D₁₇	—	9	1	no	Hall
36	C₂×C₁₃	—	153	1	no	Hall
37	C₃×C₇	C₁₃×D₅₁	1	1	yes	characteristic
38	D₉	—	17	1	no	Hall
39	C₁₇	C₇×C₁₃×D₉	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₇	—	153	1	no	Hall
41	C₁₃	C₇×D₁₅₃	1	1	yes	characteristic, direct product factor, Sylow
42	C₉	C₇×C₁₃×D₁₇	1	1	yes	characteristic, complemented, Sylow
43	C₇	C₁₃×D₁₅₃	1	1	yes	characteristic, direct product factor, Sylow
44	D₃	—	51	1	no	—
45	C₃	C₇×C₁₃×D₅₁	1	1	yes	characteristic
46	C₂	—	153	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₁₃	D₁₅₃
commutator, cosocle, hypocenter	C₉×C₁₇	C₂×C₇×C₁₃
Frattini	C₃	C₇×C₁₃×D₅₁
Fitting	C₇×C₉×C₁₃×C₁₇	C₂
socle	C₃×C₇×C₁₃×C₁₇	D₃
LCS	G ▷ C₉×C₁₇
UCS	C₁ ◁ C₇×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₇×C₉×C₁₃×C₁₇	C₂	semidirect
4. C₁₃×D₁₅₃	C₇	direct (N × H)
6. C₇×D₁₅₃	C₁₃	direct (N × H)
7. C₉×C₁₃×C₁₇	C₂×C₇	semidirect
9. C₇×C₁₃×C₁₇	D₉	semidirect
11. C₇×C₉×C₁₇	C₂×C₁₃	semidirect
12. C₇×C₉×C₁₃	D₁₇	semidirect
18. D₁₅₃	C₇×C₁₃	direct (N × H)
22. C₁₃×C₁₇	C₇×D₉	semidirect
24. C₉×C₁₇	C₂×C₇×C₁₃	semidirect
26. C₇×C₁₇	C₁₃×D₉	semidirect
27. C₉×C₁₃	C₇×D₁₇	semidirect
29. C₇×C₁₃	D₁₅₃	direct (N × H)
31. C₇×C₉	C₁₃×D₁₇	semidirect
39. C₁₇	C₇×C₁₃×D₉	semidirect
41. C₁₃	C₇×D₁₅₃	direct (N × H)
42. C₉	C₇×C₁₃×D₁₇	semidirect
43. C₇	C₁₃×D₁₅₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₉×C₁₃×C₁₇	2
C₇×C₁₃×D₅₁	3
C₁₃×D₁₅₃	7
C₇×D₁₅₃	13
C₇×C₁₃×D₉	17

Subgroups — C7×C13×D153 #42123797

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₁₃×D₁₅₃ #42123797