Subgroups — C₃²×C₄×C₁₉₁⋊C₅ #46805990

Order 34380.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₁₉₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₁₉₁⋊C₅	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₁₉₁⋊C₅	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₃²×C₄×C₁₉₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₃×C₁₉₁⋊C₅	C₂×C₃	1	4	yes	—
6	C₄×C₁₉₁⋊C₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃²×C₁₉₁	C₂×C₅	1	1	yes	characteristic
8	C₃×C₁₉₁⋊C₅	C₃×C₄	1	4	yes	direct product factor
9	C₃×C₄×C₁₉₁	C₃×C₅	1	4	yes	complemented
10	C₂×C₁₉₁⋊C₅	C₂×C₃²	1	1	yes	characteristic
11	C₃²×C₁₉₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₁₉₁	C₂×C₃×C₅	1	4	yes	—
13	C₁₉₁⋊C₅	C₃²×C₄	1	1	yes	characteristic, direct product factor, Hall
14	C₄×C₁₉₁	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
15	C₃×C₁₉₁	C₃×C₄×C₅	1	4	yes	complemented
16	C₂×C₁₉₁	C₂×C₃²×C₅	1	1	yes	characteristic
17	C₁₉₁	C₃²×C₄×C₅	1	1	yes	characteristic, complemented, Sylow
18	C₃²×C₄×C₅	—	191	1	no	maximal, Hall
19	C₂×C₃²×C₅	—	191	1	no	—
20	C₃×C₄×C₅	—	191	4	no	—
21	C₃²×C₅	—	191	1	no	Hall
22	C₃²×C₄	C₁₉₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₃×C₅	—	191	4	no	—
24	C₄×C₅	—	191	1	no	Hall
25	C₂×C₃²	C₂×C₁₉₁⋊C₅	1	1	yes	characteristic
26	C₃×C₅	—	191	4	no	—
27	C₃×C₄	C₃×C₁₉₁⋊C₅	1	4	yes	direct product factor
28	C₂×C₅	—	191	1	no	—
29	C₃²	C₄×C₁₉₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₃	C₂×C₃×C₁₉₁⋊C₅	1	4	yes	—
31	C₅	—	191	1	no	Sylow
32	C₄	C₃²×C₁₉₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₃×C₄×C₁₉₁⋊C₅	1	4	yes	direct product factor
34	C₂	C₂×C₃²×C₁₉₁⋊C₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃²×C₄	C₁₉₁⋊C₅
commutator, hypocenter	C₁₉₁	C₃²×C₄×C₅
Frattini	C₂	C₂×C₃²×C₁₉₁⋊C₅
Fitting	C₃²×C₄×C₁₉₁	C₅
socle	C₂×C₃²×C₁₉₁	C₂×C₅
prime radical	C₂×C₃²×C₁₉₁⋊C₅	C₂
cosocle	C₂×C₁₉₁	C₂×C₃²×C₅
LCS	G ▷ C₁₉₁
UCS	C₁ ◁ C₃²×C₄

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₁₉₁⋊C₅	C₃	direct (N × H)
3. C₃²×C₁₉₁⋊C₅	C₄	direct (N × H)
4. C₃²×C₄×C₁₉₁	C₅	semidirect
6. C₄×C₁₉₁⋊C₅	C₃²	direct (N × H)
8. C₃×C₁₉₁⋊C₅	C₃×C₄	direct (N × H)
9. C₃×C₄×C₁₉₁	C₃×C₅	semidirect
11. C₃²×C₁₉₁	C₄×C₅	semidirect
13. C₁₉₁⋊C₅	C₃²×C₄	direct (N × H)
14. C₄×C₁₉₁	C₃²×C₅	semidirect
15. C₃×C₁₉₁	C₃×C₄×C₅	semidirect
17. C₁₉₁	C₃²×C₄×C₅	semidirect
22. C₃²×C₄	C₁₉₁⋊C₅	direct (N × H)
27. C₃×C₄	C₃×C₁₉₁⋊C₅	direct (N × H)
29. C₃²	C₄×C₁₉₁⋊C₅	direct (N × H)
32. C₄	C₃²×C₁₉₁⋊C₅	direct (N × H)
33. C₃	C₃×C₄×C₁₉₁⋊C₅	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×C₃²×C₁₉₁⋊C₅	2
C₃×C₄×C₁₉₁⋊C₅	3
C₃²×C₄×C₁₉₁	5
C₃²×C₄×C₅	191

Subgroups — C32×C4×C191⋊C5 #46805990

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₄×C₁₉₁⋊C₅ #46805990