Subgroups — D₉×D₇₄₅ #41001241

Order 26820.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₇₀₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₉×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×D₇₄₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₇₄₅	—	3	1	no	maximal
5	C₅×C₉×C₁₄₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₉×D₁₄₉	—	5	1	no	maximal, Hall
7	D₂₂₃₅	—	3	1	no	—
8	C₅×D₃×C₁₄₉	—	3	1	no	—
9	C₃×D₇₄₅	D₃	1	1	yes	characteristic
10	C₂×D₇₄₅	—	9	1	no	Hall
11	D₁₃₄₁	—	5	1	no	—
12	C₉×D₁₄₉	—	5	1	no	—
13	D₉×C₁₄₉	D₅	1	1	yes	characteristic, complemented
14	C₃×C₅×C₁₄₉	C₂×D₃	1	1	yes	characteristic
15	D₃×D₁₄₉	—	15	1	no	—
16	C₂×C₅×C₁₄₉	—	9	1	no	—
17	D₇₄₅	—	9	1	no	—
18	D₇₄₅	D₉	1	1	yes	characteristic, direct product factor
19	C₉×C₁₄₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	D₄₄₇	—	15	1	no	—
21	C₃×D₁₄₉	—	5	1	no	—
22	D₃×C₁₄₉	—	3	1	no	—
23	C₅×C₁₄₉	C₂×D₉	1	1	yes	characteristic, complemented, Hall
24	C₂×D₁₄₉	—	45	1	no	Hall
25	C₃×C₁₄₉	D₃×D₅	1	1	yes	characteristic
26	C₂×C₁₄₉	—	9	1	no	—
27	D₁₄₉	—	5	1	no	—
28	D₁₄₉	—	45	1	no	—
29	D₅×D₉	—	149	1	no	maximal, Hall
30	C₁₄₉	D₅×D₉	1	1	yes	characteristic, complemented, Sylow
31	D₄₅	—	149	1	no	—
32	C₉×D₅	—	149	1	no	—
33	C₅×D₉	D₁₄₉	1	1	yes	characteristic, complemented
34	D₃×D₅	—	447	1	no	—
35	C₅×C₉	C₂×D₁₄₉	1	1	yes	characteristic, complemented, Hall
36	C₂×D₉	—	745	1	no	Hall
37	D₁₅	—	447	1	no	—
38	C₃×D₅	—	149	1	no	—
39	C₅×D₃	—	3	1	no	—
40	C₂×D₅	—	1341	1	no	Hall
41	C₂×C₉	—	745	1	no	—
42	D₉	—	745	1	no	—
43	D₉	D₇₄₅	1	1	yes	characteristic, direct product factor
44	C₃×C₅	D₃×D₁₄₉	1	1	yes	characteristic
45	C₂×D₃	—	2235	1	no	—
46	C₂×C₅	—	9	1	no	—
47	D₅	—	1341	1	no	—
48	D₅	—	149	1	no	—
49	C₉	C₂×D₇₄₅	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	745	1	no	—
51	D₃	—	3	1	no	—
52	D₃	—	2235	1	no	—
53	C₅	D₉×D₁₄₉	1	1	yes	characteristic, complemented, Sylow
54	C₂²	—	6705	1	no	Sylow
55	C₃	D₃×D₇₄₅	1	1	yes	characteristic
56	C₂	—	9	1	no	—
57	C₂	—	6705	1	no	—
58	C₂	—	745	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅×C₉×C₁₄₉	C₂²
Frattini	C₃	D₃×D₇₄₅
socle	C₃×C₅×C₁₄₉	C₂×D₃
LCS	G ▷ C₅×C₉×C₁₄₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₆₇₀₅	C₂	semidirect
2. C₅×D₉×C₁₄₉	C₂	semidirect
3. C₉×D₇₄₅	C₂	semidirect
5. C₅×C₉×C₁₄₉	C₂²	semidirect
13. D₉×C₁₄₉	D₅	semidirect
18. D₇₄₅	D₉	direct (N × H)
19. C₉×C₁₄₉	C₂×D₅	semidirect
23. C₅×C₁₄₉	C₂×D₉	semidirect
30. C₁₄₉	D₅×D₉	semidirect
33. C₅×D₉	D₁₄₉	semidirect
35. C₅×C₉	C₂×D₁₄₉	semidirect
43. D₉	D₇₄₅	direct (N × H)
49. C₉	C₂×D₇₄₅	semidirect
53. C₅	D₉×D₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
D₆₇₀₅	2
C₅×D₉×C₁₄₉	2
C₉×D₇₄₅	2
D₃×D₇₄₅	3
D₉×D₁₄₉	5
D₅×D₉	149

Subgroups — D9×D745 #41001241

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₉×D₇₄₅ #41001241