Subgroups — D₁₆₉₀₅ #46798913

Order 33810.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₂₃×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₆₃₅	—	3	1	no	maximal, Hall
3	D₃₃₈₁	—	5	1	no	maximal, Hall
4	C₅×C₂₃×C₄₉	D₃	1	1	yes	characteristic, complemented, Hall
5	D₂₄₁₅	—	7	1	no	maximal
6	C₃×C₂₃×C₄₉	D₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₅×C₇×C₂₃	D₇	1	1	yes	characteristic
8	D₁₁₂₇	—	15	1	no	Hall
9	D₈₀₅	—	21	1	no	—
10	D₇₃₅	—	23	1	no	maximal, Hall
11	C₂₃×C₄₉	D₁₅	1	1	yes	characteristic, complemented, Hall
12	D₄₈₃	—	35	1	no	—
13	C₅×C₇×C₂₃	D₂₁	1	1	yes	characteristic
14	C₃×C₅×C₄₉	D₂₃	1	1	yes	characteristic, complemented, Hall
15	D₃₄₅	—	49	1	no	Hall
16	D₂₄₅	—	69	1	no	Hall
17	C₃×C₇×C₂₃	D₃₅	1	1	yes	characteristic
18	C₃×C₅×C₂₃	D₄₉	1	1	yes	characteristic, complemented, Hall
19	D₁₆₁	—	105	1	no	—
20	D₁₄₇	—	115	1	no	Hall
21	C₅×C₄₉	D₆₉	1	1	yes	characteristic, complemented, Hall
22	D₁₁₅	—	147	1	no	Hall
23	D₁₀₅	—	161	1	no	—
24	C₇×C₂₃	D₁₀₅	1	1	yes	characteristic
25	C₃×C₄₉	D₁₁₅	1	1	yes	characteristic, complemented, Hall
26	D₆₉	—	245	1	no	Hall
27	C₅×C₂₃	D₁₄₇	1	1	yes	characteristic, complemented, Hall
28	C₃×C₅×C₇	D₁₆₁	1	1	yes	characteristic
29	D₄₉	—	345	1	no	Hall
30	D₃₅	—	483	1	no	—
31	C₃×C₂₃	D₂₄₅	1	1	yes	characteristic, complemented, Hall
32	C₄₉	D₃₄₅	1	1	yes	characteristic, complemented, Sylow
33	D₂₃	—	735	1	no	Hall
34	D₂₁	—	805	1	no	—
35	C₅×C₇	D₄₈₃	1	1	yes	characteristic
36	D₁₅	—	1127	1	no	Hall
37	C₂₃	D₇₃₅	1	1	yes	characteristic, complemented, Sylow
38	C₃×C₇	D₈₀₅	1	1	yes	characteristic
39	C₃×C₅	D₁₁₂₇	1	1	yes	characteristic, complemented, Hall
40	D₇	—	2415	1	no	—
41	D₅	—	3381	1	no	Hall
42	C₇	D₂₄₁₅	1	1	yes	characteristic
43	D₃	—	5635	1	no	Hall
44	C₅	D₃₃₈₁	1	1	yes	characteristic, complemented, Sylow
45	C₃	D₅₆₃₅	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	16905	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃×C₅×C₂₃×C₄₉	C₂
Frattini	C₇	D₂₄₁₅
socle	C₃×C₅×C₇×C₂₃	D₇
LCS	G ▷ C₃×C₅×C₂₃×C₄₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₂₃×C₄₉	C₂	semidirect
4. C₅×C₂₃×C₄₉	D₃	semidirect
6. C₃×C₂₃×C₄₉	D₅	semidirect
11. C₂₃×C₄₉	D₁₅	semidirect
14. C₃×C₅×C₄₉	D₂₃	semidirect
18. C₃×C₅×C₂₃	D₄₉	semidirect
21. C₅×C₄₉	D₆₉	semidirect
25. C₃×C₄₉	D₁₁₅	semidirect
27. C₅×C₂₃	D₁₄₇	semidirect
31. C₃×C₂₃	D₂₄₅	semidirect
32. C₄₉	D₃₄₅	semidirect
37. C₂₃	D₇₃₅	semidirect
39. C₃×C₅	D₁₁₂₇	semidirect
44. C₅	D₃₃₈₁	semidirect
45. C₃	D₅₆₃₅	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₂₃×C₄₉	2
D₅₆₃₅	3
D₃₃₈₁	5
D₂₄₁₅	7
D₇₃₅	23

Subgroups — D16905 #46798913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₆₉₀₅ #46798913