Subgroups — D₁₇×C₃⋊D₇₅ #29505708

Order 15300.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₁₂₇₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×C₃⋊D₇₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₂₅×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₇×D₇₅	—	3	4	no	maximal
5	C₃²×C₁₇×C₂₅	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₇×C₃⋊D₁₅	—	5	1	no	maximal
7	D₁₂₇₅	—	3	4	no	—
8	C₁₇×D₇₅	—	3	4	no	—
9	C₃×C₂₅×D₁₇	D₃	1	4	yes	complemented
10	D₁₇×D₂₅	—	9	1	no	Hall
11	C₃⋊D₂₅₅	—	5	1	no	—
12	C₁₇×C₃⋊D₁₅	—	5	1	no	—
13	C₃²×C₅×D₁₇	D₅	1	1	yes	characteristic
14	C₃×C₁₇×C₂₅	C₂×D₃	1	4	yes	complemented
15	D₁₅×D₁₇	—	15	4	no	—
16	C₂×C₃⋊D₇₅	—	17	1	no	maximal, Hall
17	D₄₂₅	—	9	1	no	—
18	C₂₅×D₁₇	C₃⋊D₃	1	1	yes	characteristic, complemented
19	C₁₇×D₂₅	—	9	1	no	—
20	C₃²×C₅×C₁₇	C₂×D₅	1	1	yes	characteristic
21	C₃⋊D₃×D₁₇	—	25	1	no	Hall
22	D₂₅₅	—	15	4	no	—
23	C₁₇×D₁₅	—	15	4	no	—
24	C₃×C₅×D₁₇	D₁₅	1	4	yes	—
25	C₂×C₃²×C₂₅	—	17	1	no	—
26	C₃⋊D₇₅	—	17	1	no	—
27	C₃⋊D₇₅	D₁₇	1	1	yes	characteristic, direct product factor
28	C₁₇×C₂₅	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
29	D₅×D₁₇	—	45	1	no	—
30	C₃⋊D₅₁	—	25	1	no	—
31	C₁₇×C₃⋊D₃	—	25	1	no	—
32	C₃²×D₁₇	D₂₅	1	1	yes	characteristic, complemented
33	C₂×D₇₅	—	51	4	no	—
34	C₃×C₅×C₁₇	C₂×D₁₅	1	4	yes	—
35	C₃²×C₂₅	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
36	D₃×D₁₇	—	75	4	no	—
37	C₂×C₃⋊D₁₅	—	85	1	no	—
38	D₈₅	—	45	1	no	—
39	C₅×D₁₇	C₃⋊D₁₅	1	1	yes	characteristic
40	D₅×C₁₇	—	45	1	no	—
41	C₃²×C₁₇	C₂×D₂₅	1	1	yes	characteristic, complemented, Hall
42	C₂×C₃×C₂₅	—	17	4	no	—
43	D₇₅	—	3	4	no	—
44	D₇₅	—	51	4	no	—
45	D₅₁	—	75	4	no	—
46	C₃×D₁₇	D₇₅	1	4	yes	complemented
47	D₃×C₁₇	—	75	4	no	—
48	C₂×D₂₅	—	153	1	no	Hall
49	C₂×C₃²×C₅	—	17	1	no	—
50	C₃⋊D₁₅	—	5	1	no	—
51	C₃⋊D₁₅	—	85	1	no	—
52	C₅×C₁₇	C₂×C₃⋊D₁₅	1	1	yes	characteristic
53	C₃×C₂₅	D₃×D₁₇	1	4	yes	complemented
54	C₂×D₁₇	—	225	1	no	Hall
55	C₂×D₁₅	—	255	4	no	—
56	C₃×C₁₇	C₂×D₇₅	1	4	yes	complemented
57	C₂×C₂₅	—	17	1	no	—
58	D₂₅	—	9	1	no	—
59	D₂₅	—	153	1	no	—
60	C₃²×C₅	D₅×D₁₇	1	1	yes	characteristic
61	C₂×C₃⋊D₃	—	425	1	no	Hall
62	C₂×C₁₇	—	225	1	no	—
63	D₁₇	—	225	1	no	—
64	D₁₇	C₃⋊D₇₅	1	1	yes	characteristic, direct product factor
65	C₂×C₃×C₅	—	17	4	no	—
66	D₁₅	—	15	4	no	—
67	D₁₅	—	255	4	no	—
68	C₂₅	C₃⋊D₃×D₁₇	1	1	yes	characteristic, complemented, Sylow
69	C₂×D₅	—	765	1	no	—
70	C₂×C₃²	—	17	1	no	—
71	C₃⋊D₃	—	25	1	no	—
72	C₃⋊D₃	—	425	1	no	—
73	C₁₇	C₂×C₃⋊D₇₅	1	1	yes	characteristic, complemented, Sylow
74	C₃×C₅	D₁₅×D₁₇	1	4	yes	—
75	C₂×D₃	—	1275	4	no	—
76	C₂×C₅	—	17	1	no	—
77	D₅	—	45	1	no	—
78	D₅	—	765	1	no	—
79	C₃²	D₁₇×D₂₅	1	1	yes	characteristic, complemented, Sylow
80	C₂×C₃	—	17	4	no	—
81	D₃	—	75	4	no	—
82	D₃	—	1275	4	no	—
83	C₅	D₁₇×C₃⋊D₁₅	1	1	yes	characteristic
84	C₂²	—	3825	1	no	Sylow
85	C₃	D₁₇×D₇₅	1	4	yes	complemented
86	C₂	—	17	1	no	—
87	C₂	—	225	1	no	—
88	C₂	—	3825	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃²×C₁₇×C₂₅	C₂²
Frattini	C₅	D₁₇×C₃⋊D₁₅
socle	C₃²×C₅×C₁₇	C₂×D₅
LCS	G ▷ C₃²×C₁₇×C₂₅
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₁₂₇₅	C₂	semidirect
2. C₁₇×C₃⋊D₇₅	C₂	semidirect
3. C₃²×C₂₅×D₁₇	C₂	semidirect
5. C₃²×C₁₇×C₂₅	C₂²	semidirect
9. C₃×C₂₅×D₁₇	D₃	semidirect
14. C₃×C₁₇×C₂₅	C₂×D₃	semidirect
18. C₂₅×D₁₇	C₃⋊D₃	semidirect
27. C₃⋊D₇₅	D₁₇	direct (N × H)
28. C₁₇×C₂₅	C₂×C₃⋊D₃	semidirect
32. C₃²×D₁₇	D₂₅	semidirect
35. C₃²×C₂₅	C₂×D₁₇	semidirect
41. C₃²×C₁₇	C₂×D₂₅	semidirect
46. C₃×D₁₇	D₇₅	semidirect
53. C₃×C₂₅	D₃×D₁₇	semidirect
56. C₃×C₁₇	C₂×D₇₅	semidirect
64. D₁₇	C₃⋊D₇₅	direct (N × H)
68. C₂₅	C₃⋊D₃×D₁₇	semidirect
73. C₁₇	C₂×C₃⋊D₇₅	semidirect
79. C₃²	D₁₇×D₂₅	semidirect
85. C₃	D₁₇×D₇₅	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊D₁₂₇₅	2
C₁₇×C₃⋊D₇₅	2
C₃²×C₂₅×D₁₇	2
D₁₇×D₇₅	3
D₁₇×C₃⋊D₁₅	5
C₂×C₃⋊D₇₅	17

Subgroups — D17×C3⋊D75 #29505708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₇×C₃⋊D₇₅ #29505708