Subgroups — C₅×Dic₁₁₇₃ #37553285

Order 23460.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₁₇×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₃₉₁	—	3	1	no	maximal, Hall
3	C₃×C₅×C₁₇×C₂₃	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₁₁₇₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₁₇×C₂₃	D₃	1	1	yes	characteristic
6	C₂×C₃×C₁₇×C₂₃	C₂×C₅	1	1	yes	characteristic
7	C₅×C₁₇×C₂₃	Dic₃	1	1	yes	characteristic, complemented, Hall
8	Dic₃₉₁	—	3	1	no	Hall
9	C₅×Dic₆₉	—	17	1	no	maximal, Hall
10	C₃×C₁₇×C₂₃	C₄×C₅	1	1	yes	characteristic, complemented, Hall
11	C₅×Dic₅₁	—	23	1	no	maximal, Hall
12	C₂×C₁₇×C₂₃	C₅×D₃	1	1	yes	characteristic
13	C₂×C₃×C₅×C₂₃	D₁₇	1	1	yes	characteristic
14	C₂×C₃×C₅×C₁₇	D₂₃	1	1	yes	characteristic
15	C₅×Dic₂₃	—	51	1	no	Hall
16	C₁₇×C₂₃	C₅×Dic₃	1	1	yes	characteristic, complemented, Hall
17	C₃×C₅×C₂₃	Dic₁₇	1	1	yes	characteristic, complemented, Hall
18	C₅×Dic₁₇	—	69	1	no	Hall
19	Dic₆₉	—	17	1	no	Hall
20	C₃×C₅×C₁₇	Dic₂₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅×C₂₃	D₅₁	1	1	yes	characteristic
22	Dic₅₁	—	23	1	no	Hall
23	C₂×C₅×C₁₇	D₆₉	1	1	yes	characteristic
24	C₂×C₃×C₂₃	C₅×D₁₇	1	1	yes	characteristic
25	C₅×C₂₃	Dic₅₁	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×C₁₇	C₅×D₂₃	1	1	yes	characteristic
27	Dic₂₃	—	51	1	no	Hall
28	C₅×C₁₇	Dic₆₉	1	1	yes	characteristic, complemented, Hall
29	C₃×C₂₃	C₅×Dic₁₇	1	1	yes	characteristic, complemented, Hall
30	Dic₁₇	—	69	1	no	Hall
31	C₅×Dic₃	—	391	1	no	Hall
32	C₃×C₁₇	C₅×Dic₂₃	1	1	yes	characteristic, complemented, Hall
33	C₂×C₂₃	C₅×D₅₁	1	1	yes	characteristic
34	C₂×C₁₇	C₅×D₆₉	1	1	yes	characteristic
35	C₂×C₃×C₅	D₃₉₁	1	1	yes	characteristic
36	C₂₃	C₅×Dic₅₁	1	1	yes	characteristic, complemented, Sylow
37	C₄×C₅	—	1173	1	no	Hall
38	C₁₇	C₅×Dic₆₉	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₅	Dic₃₉₁	1	1	yes	characteristic, complemented, Hall
40	Dic₃	—	391	1	no	Hall
41	C₂×C₅	D₁₁₇₃	1	1	yes	characteristic
42	C₂×C₃	C₅×D₃₉₁	1	1	yes	characteristic
43	C₅	Dic₁₁₇₃	1	1	yes	characteristic, direct product factor, Sylow
44	C₄	—	1173	1	no	Sylow
45	C₃	C₅×Dic₃₉₁	1	1	yes	characteristic, complemented, Sylow
46	C₂	C₅×D₁₁₇₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅	D₁₁₇₃
commutator, hypocenter	C₃×C₁₇×C₂₃	C₄×C₅
Frattini	C₂	C₅×D₁₁₇₃
Fitting, socle, prime radical	C₂×C₃×C₅×C₁₇×C₂₃	C₂
cosocle	C₂×C₃×C₁₇×C₂₃	C₂×C₅
LCS	G ▷ C₃×C₁₇×C₂₃
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₁₇×C₂₃	C₄	semidirect
4. Dic₁₁₇₃	C₅	direct (N × H)
7. C₅×C₁₇×C₂₃	Dic₃	semidirect
10. C₃×C₁₇×C₂₃	C₄×C₅	semidirect
16. C₁₇×C₂₃	C₅×Dic₃	semidirect
17. C₃×C₅×C₂₃	Dic₁₇	semidirect
20. C₃×C₅×C₁₇	Dic₂₃	semidirect
25. C₅×C₂₃	Dic₅₁	semidirect
28. C₅×C₁₇	Dic₆₉	semidirect
29. C₃×C₂₃	C₅×Dic₁₇	semidirect
32. C₃×C₁₇	C₅×Dic₂₃	semidirect
36. C₂₃	C₅×Dic₅₁	semidirect
38. C₁₇	C₅×Dic₆₉	semidirect
39. C₃×C₅	Dic₃₉₁	semidirect
43. C₅	Dic₁₁₇₃	direct (N × H)
45. C₃	C₅×Dic₃₉₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×C₁₇×C₂₃	2
C₅×Dic₃₉₁	3
Dic₁₁₇₃	5
C₅×Dic₆₉	17
C₅×Dic₅₁	23

Subgroups — C5×Dic1173 #37553285

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×Dic₁₁₇₃ #37553285