Subgroups — C₄×C₁₇×C₁₆₉⋊C₃ #46828124

Order 34476.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×C₁₆₉⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₇×C₁₆₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₇×C₁₆₉⋊C₃	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₁₇×C₁₆₉	C₂×C₃	1	1	yes	characteristic
5	C₁₇×C₁₆₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₄×C₁₇×C₁₃⋊C₃	—	13	1	no	maximal
7	C₄×C₁₆₉⋊C₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₁₇×C₁₃⋊C₃	—	13	1	no	—
9	C₂×C₁₆₉⋊C₃	C₂×C₁₇	1	1	yes	characteristic
10	C₄×C₁₃×C₁₇	C₁₃⋊C₃	1	1	yes	characteristic
11	C₄×C₁₆₉	C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
12	C₁₇×C₁₃⋊C₃	—	13	1	no	—
13	C₁₆₉⋊C₃	C₄×C₁₇	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₁₃×C₁₇	C₂×C₁₃⋊C₃	1	1	yes	characteristic
15	C₂×C₁₆₉	C₂×C₃×C₁₇	1	1	yes	characteristic
16	C₁₃×C₁₇	C₄×C₁₃⋊C₃	1	1	yes	characteristic
17	C₃×C₄×C₁₇	—	169	1	no	Hall
18	C₁₆₉	C₃×C₄×C₁₇	1	1	yes	characteristic, complemented, Sylow
19	C₄×C₁₃⋊C₃	—	13	1	no	—
20	C₂×C₃×C₁₇	—	169	1	no	—
21	C₂×C₁₃⋊C₃	—	13	1	no	—
22	C₄×C₁₇	C₁₆₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
23	C₄×C₁₃	C₁₇×C₁₃⋊C₃	1	1	yes	characteristic
24	C₃×C₁₇	—	169	1	no	Hall
25	C₁₃⋊C₃	—	13	1	no	—
26	C₂×C₁₇	C₂×C₁₆₉⋊C₃	1	1	yes	characteristic
27	C₂×C₁₃	C₂×C₁₇×C₁₃⋊C₃	1	1	yes	characteristic
28	C₁₇	C₄×C₁₆₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₁₃	C₄×C₁₇×C₁₃⋊C₃	1	1	yes	characteristic
30	C₃×C₄	—	169	1	no	Hall
31	C₂×C₃	—	169	1	no	—
32	C₄	C₁₇×C₁₆₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	—	169	1	no	Sylow
34	C₂	C₂×C₁₇×C₁₆₉⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₁₇	C₁₆₉⋊C₃
commutator, hypocenter	C₁₆₉	C₃×C₄×C₁₇
Frattini	C₂×C₁₃	C₂×C₁₇×C₁₃⋊C₃
Fitting	C₄×C₁₇×C₁₆₉	C₃
socle	C₂×C₁₃×C₁₇	C₂×C₁₃⋊C₃
prime radical	C₂×C₁₇×C₁₆₉⋊C₃	C₂
cosocle	C₂×C₁₆₉	C₂×C₃×C₁₇
LCS	G ▷ C₁₆₉
UCS	C₁ ◁ C₄×C₁₇

Complements

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

N	H ≅ G/N	type
2. C₄×C₁₇×C₁₆₉	C₃	semidirect
3. C₁₇×C₁₆₉⋊C₃	C₄	direct (N × H)
5. C₁₇×C₁₆₉	C₃×C₄	semidirect
7. C₄×C₁₆₉⋊C₃	C₁₇	direct (N × H)
11. C₄×C₁₆₉	C₃×C₁₇	semidirect
13. C₁₆₉⋊C₃	C₄×C₁₇	direct (N × H)
18. C₁₆₉	C₃×C₄×C₁₇	semidirect
22. C₄×C₁₇	C₁₆₉⋊C₃	direct (N × H)
28. C₁₇	C₄×C₁₆₉⋊C₃	direct (N × H)
32. C₄	C₁₇×C₁₆₉⋊C₃	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×C₁₇×C₁₆₉⋊C₃	2
C₄×C₁₇×C₁₆₉	3
C₄×C₁₇×C₁₃⋊C₃	13
C₄×C₁₆₉⋊C₃	17

Subgroups — C4×C17×C169⋊C3 #46828124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₇×C₁₆₉⋊C₃ #46828124