Subgroups — C₂×C₁₇⋊#90646 #29505762

Order 15300.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×C₅²⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇⋊#90646	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅×D₂₅₅	—	3	1	no	maximal
4	C₁₇×C₅²⋊C₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₅×D₂₅₅	—	3	2	no	—
6	C₂×C₃×C₅²×C₁₇	D₃	1	1	yes	characteristic
7	C₂×C₅×D₈₅	—	9	1	no	Hall
8	C₃×C₅²×C₁₇	C₂×D₃	1	1	yes	characteristic
9	C₂×D₂₅₅	—	3	1	no	—
10	C₂×C₅×D₅₁	—	15	1	no	—
11	C₂×#90646	—	17	1	no	maximal, Hall
12	C₂×C₅²×C₁₇	D₉	1	1	yes	characteristic, complemented
13	C₅×D₈₅	—	9	2	no	—
14	C₂×D₁₅₃	—	25	1	no	maximal, Hall
15	C₂×C₃×C₅×C₁₇	—	3	1	no	—
16	C₂×C₃×C₅×C₁₇	—	6	1	no	—
17	D₂₅₅	—	3	2	no	—
18	C₅×D₅₁	—	15	2	no	—
19	C₂×C₅²⋊C₉	D₁₇	1	1	yes	characteristic, complemented
20	#90646	—	17	2	no	—
21	C₅²×C₁₇	C₂×D₉	1	1	yes	characteristic, complemented, Hall
22	C₂×D₈₅	—	9	1	no	—
23	C₂×C₅×D₁₇	—	45	1	no	—
24	C₂×C₉×C₁₇	—	50	1	no	—
25	D₁₅₃	—	25	2	no	—
26	C₂×C₅×D₁₅	—	51	1	no	—
27	C₃×C₅×C₁₇	—	3	1	no	—
28	C₃×C₅×C₁₇	—	6	1	no	—
29	C₅²⋊C₉	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
30	C₂×D₅₁	—	15	1	no	—
31	C₂×C₅×C₁₇	—	3	1	no	—
32	C₂×C₅×C₁₇	—	3	1	no	—
33	D₈₅	—	9	2	no	—
34	C₅×D₁₇	—	45	2	no	—
35	C₉×C₁₇	—	50	1	no	Hall
36	C₂×C₃×C₅²	D₅₁	1	1	yes	characteristic
37	C₅×D₁₅	—	51	2	no	—
38	C₂×C₃×C₁₇	#3874	1	1	yes	characteristic
39	D₅₁	—	15	2	no	—
40	C₂×C₅×D₅	—	153	1	no	Hall
41	C₅×C₁₇	—	3	1	no	—
42	C₅×C₁₇	—	3	1	no	—
43	C₃×C₅²	C₂×D₅₁	1	1	yes	characteristic
44	C₂×D₁₇	—	45	1	no	Hall
45	C₂×D₁₅	—	51	1	no	—
46	C₂×C₅×D₃	—	255	1	no	—
47	C₃×C₁₇	C₂×#3874	1	1	yes	characteristic
48	C₂×C₅²	D₁₅₃	1	1	yes	characteristic, complemented
49	C₅×D₅	—	153	2	no	—
50	C₂×D₉	—	425	1	no	Hall
51	C₂×C₁₇	#90646	1	1	yes	characteristic, complemented
52	D₁₇	—	45	2	no	—
53	C₂×C₃×C₅	—	3	1	no	—
54	C₂×C₃×C₅	—	6	1	no	—
55	D₁₅	—	51	2	no	—
56	C₅×D₃	—	255	2	no	—
57	C₅²	C₂×D₁₅₃	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₅	—	765	1	no	—
59	C₂×D₅	—	153	1	no	—
60	C₂×C₉	—	50	1	no	—
61	D₉	—	425	2	no	—
62	C₁₇	C₂×#90646	1	1	yes	characteristic, complemented, Sylow
63	C₃×C₅	—	3	1	no	—
64	C₃×C₅	—	6	1	no	—
65	C₂×D₃	—	255	1	no	—
66	C₂×C₅	—	3	1	no	—
67	C₂×C₅	—	6	1	no	—
68	C₂×C₅	—	765	2	no	—
69	D₅	—	153	2	no	—
70	C₉	—	50	1	no	Sylow
71	C₂×C₃	C₁₇⋊#3874	1	1	yes	characteristic
72	D₃	—	255	2	no	—
73	C₅	—	3	1	no	—
74	C₅	—	6	1	no	—
75	C₂²	—	765	1	no	Sylow
76	C₃	C₂×C₁₇⋊#3874	1	1	yes	characteristic
77	C₂	—	765	2	no	—
78	C₂	C₁₇⋊#90646	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₁₇⋊#90646
commutator, cosocle, hypocenter	C₁₇×C₅²⋊C₉	C₂²
Frattini	C₃	C₂×C₁₇⋊#3874
Fitting, socle	C₂×C₃×C₅²×C₁₇	D₃
LCS	G ▷ C₁₇×C₅²⋊C₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₇×C₅²⋊C₉	C₂	semidirect
2. C₁₇⋊#90646	C₂	direct (N × H)
4. C₁₇×C₅²⋊C₉	C₂²	semidirect
12. C₂×C₅²×C₁₇	D₉	semidirect
19. C₂×C₅²⋊C₉	D₁₇	semidirect
21. C₅²×C₁₇	C₂×D₉	semidirect
29. C₅²⋊C₉	C₂×D₁₇	semidirect
48. C₂×C₅²	D₁₅₃	semidirect
51. C₂×C₁₇	#90646	semidirect
57. C₅²	C₂×D₁₅₃	semidirect
62. C₁₇	C₂×#90646	semidirect
78. C₂	C₁₇⋊#90646	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₇×C₅²⋊C₉	2
C₁₇⋊#90646	2
C₂×C₅×D₂₅₅	3
C₂×#90646	17
C₂×D₁₅₃	25

Subgroups — C2×C17⋊#90646 #29505762

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇⋊#90646 #29505762