Subgroups — C₃²×Dic₈₉₅ #44567351

Order 32220.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₅×C₁₇₉	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₈₉₅	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₅×C₁₇₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃²×Dic₁₇₉	—	5	1	no	maximal, Hall
5	C₂×C₃×C₅×C₁₇₉	C₂×C₃	1	4	yes	—
6	Dic₈₉₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃²×C₁₇₉	D₅	1	1	yes	characteristic
8	C₃×C₅×C₁₇₉	C₃×C₄	1	4	yes	complemented
9	C₃×Dic₁₇₉	—	5	4	no	—
10	C₂×C₅×C₁₇₉	C₂×C₃²	1	1	yes	characteristic
11	C₃²×C₁₇₉	Dic₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₁₇₉	C₃×D₅	1	4	yes	—
13	C₅×C₁₇₉	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
14	Dic₁₇₉	—	5	1	no	Hall
15	C₃×C₁₇₉	C₃×Dic₅	1	4	yes	complemented
16	C₂×C₁₇₉	C₃²×D₅	1	1	yes	characteristic
17	C₃²×Dic₅	—	179	1	no	maximal, Hall
18	C₁₇₉	C₃²×Dic₅	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃²×C₅	D₁₇₉	1	1	yes	characteristic
20	C₃×Dic₅	—	179	4	no	—
21	C₃²×C₅	Dic₁₇₉	1	1	yes	characteristic, complemented, Hall
22	C₃²×C₄	—	895	1	no	Hall
23	C₂×C₃×C₅	C₃×D₁₇₉	1	4	yes	—
24	Dic₅	—	179	1	no	Hall
25	C₂×C₃²	D₈₉₅	1	1	yes	characteristic
26	C₃×C₅	C₃×Dic₁₇₉	1	4	yes	complemented
27	C₃×C₄	—	895	4	no	—
28	C₂×C₅	C₃²×D₁₇₉	1	1	yes	characteristic
29	C₃²	Dic₈₉₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₃	C₃×D₈₉₅	1	4	yes	—
31	C₅	C₃²×Dic₁₇₉	1	1	yes	characteristic, complemented, Sylow
32	C₄	—	895	1	no	Sylow
33	C₃	C₃×Dic₈₉₅	1	4	yes	direct product factor
34	C₂	C₃²×D₈₉₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃²	D₈₉₅
commutator, hypocenter	C₅×C₁₇₉	C₃²×C₄
Frattini	C₂	C₃²×D₈₉₅
Fitting, socle, prime radical	C₂×C₃²×C₅×C₁₇₉	C₂
cosocle	C₂×C₅×C₁₇₉	C₂×C₃²
LCS	G ▷ C₅×C₁₇₉
UCS	C₁ ◁ C₂×C₃²

Complements

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

N	H ≅ G/N	type
2. C₃×Dic₈₉₅	C₃	direct (N × H)
3. C₃²×C₅×C₁₇₉	C₄	semidirect
6. Dic₈₉₅	C₃²	direct (N × H)
8. C₃×C₅×C₁₇₉	C₃×C₄	semidirect
11. C₃²×C₁₇₉	Dic₅	semidirect
13. C₅×C₁₇₉	C₃²×C₄	semidirect
15. C₃×C₁₇₉	C₃×Dic₅	semidirect
18. C₁₇₉	C₃²×Dic₅	semidirect
21. C₃²×C₅	Dic₁₇₉	semidirect
26. C₃×C₅	C₃×Dic₁₇₉	semidirect
29. C₃²	Dic₈₉₅	direct (N × H)
31. C₅	C₃²×Dic₁₇₉	semidirect
33. C₃	C₃×Dic₈₉₅	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×C₅×C₁₇₉	2
C₃×Dic₈₉₅	3
C₃²×Dic₁₇₉	5
C₃²×Dic₅	179

Subgroups — C32×Dic895 #44567351

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×Dic₈₉₅ #44567351