Subgroups — C₅×C₁₇×#89205 #49154152

Order 37485.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇²×C₁₇	C₃	1	1	yes	maximal, characteristic
2	C₁₇×#89205	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×C₁₇×C₇⋊C₉	—	7	2	no	maximal
4	C₅×C₇²×C₁₇	C₉	1	1	yes	characteristic, complemented, Hall
5	C₃×C₇²×C₁₇	C₃×C₅	1	1	yes	characteristic
6	C₅×#89205	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₅×C₇×C₁₇	—	3	2	no	—
8	C₃×C₅×C₇×C₁₇	ΓL(1,𝔽₈)	1	2	yes	—
9	C₁₇×C₇⋊C₉	—	7	2	no	—
10	C₇²×C₁₇	C₅×C₉	1	1	yes	characteristic, complemented, Hall
11	C₅×C₉×C₁₇	—	49	1	no	Hall
12	C₃×C₅×C₇²	C₃×C₁₇	1	1	yes	characteristic
13	C₅×C₇×C₁₇	—	3	2	no	—
14	C₅×C₇×C₁₇	C₇⋊C₉	1	2	yes	complemented
15	#89205	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₇×C₁₇	—	3	2	no	—
17	C₃×C₇×C₁₇	C₅×ΓL(1,𝔽₈)	1	2	yes	—
18	C₅×C₇⋊C₉	—	7	2	no	—
19	C₃×C₅×C₁₇	#3862	1	1	yes	characteristic
20	C₅×C₇²	C₉×C₁₇	1	1	yes	characteristic, complemented, Hall
21	C₉×C₁₇	—	49	1	no	Hall
22	C₃×C₇²	C₃×C₅×C₁₇	1	1	yes	characteristic
23	C₇×C₁₇	—	3	2	no	—
24	C₇×C₁₇	C₅×C₇⋊C₉	1	2	yes	complemented
25	C₃×C₅×C₇	—	3	2	no	—
26	C₃×C₅×C₇	C₁₇×ΓL(1,𝔽₈)	1	2	yes	—
27	C₅×C₁₇	#89205	1	1	yes	characteristic, direct product factor, Hall
28	C₇⋊C₉	—	7	2	no	—
29	C₃×C₁₇	C₅×#3862	1	1	yes	characteristic
30	C₇²	C₅×C₉×C₁₇	1	1	yes	characteristic, complemented, Sylow
31	C₅×C₉	—	49	1	no	Hall
32	C₅×C₇	—	3	2	no	—
33	C₅×C₇	C₁₇×C₇⋊C₉	1	2	yes	complemented
34	C₃×C₇	—	3	2	no	—
35	C₃×C₇	C₅×C₁₇×ΓL(1,𝔽₈)	1	2	yes	—
36	C₁₇	C₅×#89205	1	1	yes	characteristic, direct product factor, Sylow
37	C₃×C₅	C₁₇×#3862	1	1	yes	characteristic
38	C₉	—	49	1	no	Sylow
39	C₇	—	3	2	no	—
40	C₇	C₅×C₁₇×C₇⋊C₉	1	2	yes	complemented
41	C₅	C₁₇×#89205	1	1	yes	characteristic, direct product factor, Sylow
42	C₃	C₅×C₁₇×#3862	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₅×C₁₇	#3862
commutator, hypocenter	C₇²	C₅×C₉×C₁₇
Frattini	C₃	C₅×C₁₇×#3862
Fitting, socle, prime radical	C₃×C₅×C₇²×C₁₇	C₃
cosocle	C₃×C₇²	C₃×C₅×C₁₇
LCS	G ▷ C₇²
UCS	C₁ ◁ C₃×C₅×C₁₇

Complements

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

N	H ≅ G/N	type
2. C₁₇×#89205	C₅	direct (N × H)
4. C₅×C₇²×C₁₇	C₉	semidirect
6. C₅×#89205	C₁₇	direct (N × H)
10. C₇²×C₁₇	C₅×C₉	semidirect
14. C₅×C₇×C₁₇	C₇⋊C₉	semidirect
15. #89205	C₅×C₁₇	direct (N × H)
20. C₅×C₇²	C₉×C₁₇	semidirect
24. C₇×C₁₇	C₅×C₇⋊C₉	semidirect
27. C₅×C₁₇	#89205	direct (N × H)
30. C₇²	C₅×C₉×C₁₇	semidirect
33. C₅×C₇	C₁₇×C₇⋊C₉	semidirect
36. C₁₇	C₅×#89205	direct (N × H)
40. C₇	C₅×C₁₇×C₇⋊C₉	semidirect
41. C₅	C₁₇×#89205	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×C₇²×C₁₇	3
C₁₇×#89205	5
C₅×C₁₇×C₇⋊C₉	7
C₅×#89205	17

Subgroups — C5×C17×#89205 #49154152

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₇×#89205 #49154152