Subgroups — D₁₅×C₁₇⋊D₁₇ #31773309

Order 17340.

400 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₅⋊(C₁₇⋊D₁₇))	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇²×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×C₁₇⋊D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×C₁₇⋊D₁₇	—	3	1	no	maximal, Hall
5	C₃×C₅×C₁₇²	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×C₁₇⋊D₁₇	—	5	1	no	maximal, Hall
7	C₅⋊(C₁₇⋊D₁₇)	—	3	1	no	—
8	D₅×C₁₇²	—	3	1	no	—
9	C₅×C₁₇⋊D₁₇	D₃	1	1	yes	characteristic, complemented
10	C₃×C₁₇⋊D₁₇	D₅	1	1	yes	characteristic, complemented
11	D₃×C₁₇²	—	5	1	no	—
12	C₃⋊(C₁₇⋊D₁₇)	—	5	1	no	—
13	C₅×C₁₇²	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₇⋊D₁₇	—	15	1	no	Hall
15	D₁₅×D₁₇	—	17	18	no	maximal
16	C₃×C₁₇²	C₂×D₅	1	1	yes	characteristic, complemented, Hall
17	C₂×C₁₇²	—	15	1	no	—
18	C₁₇⋊D₁₇	—	15	1	no	—
19	C₁₇⋊D₁₇	D₁₅	1	1	yes	characteristic, direct product factor
20	D₂₅₅	—	17	18	no	—
21	C₁₇×D₁₅	D₁₇	1	18	yes	complemented
22	C₃×C₅×D₁₇	—	17	18	no	—
23	D₅×D₁₇	—	51	18	no	—
24	C₁₇²	C₂×D₁₅	1	1	yes	characteristic, complemented, Sylow
25	C₃×C₅×C₁₇	C₂×D₁₇	1	18	yes	complemented
26	D₃×D₁₇	—	85	18	no	—
27	D₈₅	—	51	18	no	—
28	C₅×D₁₇	—	17	18	no	—
29	D₅×C₁₇	—	3	18	no	—
30	D₅₁	—	85	18	no	—
31	C₃×D₁₇	—	17	18	no	—
32	D₃×C₁₇	—	5	18	no	—
33	C₅×C₁₇	D₃×D₁₇	1	18	yes	complemented
34	C₂×D₁₇	—	255	18	no	—
35	C₂×D₁₅	—	289	1	no	Hall
36	C₃×C₁₇	D₅×D₁₇	1	18	yes	complemented
37	C₂×C₁₇	—	15	18	no	—
38	D₁₇	—	17	18	no	—
39	D₁₇	—	255	18	no	—
40	C₂×C₃×C₅	—	289	1	no	—
41	D₁₅	—	289	1	no	—
42	D₁₅	C₁₇⋊D₁₇	1	1	yes	characteristic, direct product factor
43	C₂×D₅	—	867	1	no	Hall
44	C₁₇	D₁₅×D₁₇	1	18	yes	complemented
45	C₃×C₅	C₂×C₁₇⋊D₁₇	1	1	yes	characteristic, complemented, Hall
46	C₂×D₃	—	1445	1	no	Hall
47	C₂×C₅	—	289	1	no	—
48	D₅	—	3	1	no	—
49	D₅	—	867	1	no	—
50	C₂×C₃	—	289	1	no	—
51	D₃	—	5	1	no	—
52	D₃	—	1445	1	no	—
53	C₅	D₃×C₁₇⋊D₁₇	1	1	yes	characteristic, complemented, Sylow
54	C₂²	—	4335	1	no	Sylow
55	C₃	D₅×C₁₇⋊D₁₇	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	15	1	no	—
57	C₂	—	289	1	no	—
58	C₂	—	4335	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₁₇²	C₂²
LCS	G ▷ C₃×C₅×C₁₇²
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊(C₅⋊(C₁₇⋊D₁₇))	C₂	semidirect
2. C₁₇²×D₁₅	C₂	semidirect
3. C₃×C₅×C₁₇⋊D₁₇	C₂	semidirect
5. C₃×C₅×C₁₇²	C₂²	semidirect
9. C₅×C₁₇⋊D₁₇	D₃	semidirect
10. C₃×C₁₇⋊D₁₇	D₅	semidirect
13. C₅×C₁₇²	C₂×D₃	semidirect
16. C₃×C₁₇²	C₂×D₅	semidirect
19. C₁₇⋊D₁₇	D₁₅	direct (N × H)
21. C₁₇×D₁₅	D₁₇	semidirect
24. C₁₇²	C₂×D₁₅	semidirect
25. C₃×C₅×C₁₇	C₂×D₁₇	semidirect
33. C₅×C₁₇	D₃×D₁₇	semidirect
36. C₃×C₁₇	D₅×D₁₇	semidirect
42. D₁₅	C₁₇⋊D₁₇	direct (N × H)
44. C₁₇	D₁₅×D₁₇	semidirect
45. C₃×C₅	C₂×C₁₇⋊D₁₇	semidirect
53. C₅	D₃×C₁₇⋊D₁₇	semidirect
55. C₃	D₅×C₁₇⋊D₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊(C₅⋊(C₁₇⋊D₁₇))	2
C₁₇²×D₁₅	2
C₃×C₅×C₁₇⋊D₁₇	2
D₅×C₁₇⋊D₁₇	3
D₃×C₁₇⋊D₁₇	5
D₁₅×D₁₇	17

Subgroups — D15×C17⋊D17 #31773309

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₅×C₁₇⋊D₁₇ #31773309