Subgroups — C₁₃×Dic₉×C₆₇ #44535573

Order 31356.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₁₃×C₆₇	C₂	1	1	yes	maximal, characteristic
2	Dic₃×C₁₃×C₆₇	—	3	1	no	maximal
3	C₉×C₁₃×C₆₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₃×C₆₇	D₃	1	1	yes	characteristic
5	C₄×C₁₃×C₆₇	—	9	1	no	Hall
6	C₃×C₁₃×C₆₇	Dic₃	1	1	yes	characteristic
7	Dic₉×C₆₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₁₃×C₆₇	D₉	1	1	yes	characteristic
9	C₂×C₉×C₆₇	C₂×C₁₃	1	1	yes	characteristic
10	C₁₃×C₆₇	Dic₉	1	1	yes	characteristic, direct product factor, Hall
11	Dic₃×C₆₇	—	3	1	no	—
12	C₉×C₆₇	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
13	C₁₃×Dic₉	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₃×C₆₇	D₃×C₁₃	1	1	yes	characteristic
15	C₄×C₆₇	—	9	1	no	Hall
16	C₂×C₉×C₁₃	C₂×C₆₇	1	1	yes	characteristic
17	C₃×C₆₇	Dic₃×C₁₃	1	1	yes	characteristic
18	Dic₃×C₁₃	—	3	1	no	—
19	C₂×C₆₇	C₁₃×D₉	1	1	yes	characteristic
20	C₉×C₁₃	C₄×C₆₇	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₁₃	D₃×C₆₇	1	1	yes	characteristic
22	C₆₇	C₁₃×Dic₉	1	1	yes	characteristic, direct product factor, Sylow
23	C₄×C₁₃	—	9	1	no	Hall
24	C₃×C₁₃	Dic₃×C₆₇	1	1	yes	characteristic
25	Dic₉	C₁₃×C₆₇	1	1	yes	characteristic, direct product factor, Hall
26	C₂×C₁₃	D₉×C₆₇	1	1	yes	characteristic
27	C₂×C₉	C₂×C₁₃×C₆₇	1	1	yes	characteristic
28	C₁₃	Dic₉×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
29	Dic₃	—	3	1	no	—
30	C₉	C₄×C₁₃×C₆₇	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	D₃×C₁₃×C₆₇	1	1	yes	characteristic
32	C₄	—	9	1	no	Sylow
33	C₃	Dic₃×C₁₃×C₆₇	1	1	yes	characteristic
34	C₂	C₁₃×D₉×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₃×C₆₇	D₉
commutator, hypocenter	C₉	C₄×C₁₃×C₆₇
Frattini	C₂×C₃	D₃×C₁₃×C₆₇
Fitting	C₂×C₉×C₁₃×C₆₇	C₂
socle, prime radical	C₂×C₃×C₁₃×C₆₇	D₃
cosocle	C₂×C₉	C₂×C₁₃×C₆₇
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₁₃×C₆₇

Complements

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

N	H ≅ G/N	type
3. C₉×C₁₃×C₆₇	C₄	semidirect
7. Dic₉×C₆₇	C₁₃	direct (N × H)
10. C₁₃×C₆₇	Dic₉	direct (N × H)
12. C₉×C₆₇	C₄×C₁₃	semidirect
13. C₁₃×Dic₉	C₆₇	direct (N × H)
20. C₉×C₁₃	C₄×C₆₇	semidirect
22. C₆₇	C₁₃×Dic₉	direct (N × H)
25. Dic₉	C₁₃×C₆₇	direct (N × H)
28. C₁₃	Dic₉×C₆₇	direct (N × H)
30. C₉	C₄×C₁₃×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×C₁₃×C₆₇	2
Dic₃×C₁₃×C₆₇	3
Dic₉×C₆₇	13
C₁₃×Dic₉	67

Subgroups — C13×Dic9×C67 #44535573

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×Dic₉×C₆₇ #44535573