Subgroups — C₂×C₁₇×C₃⋊#3874 #29505919

Order 15300.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₇×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×C₃⋊#3874	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅×C₁₇×D₁₅	—	3	1	no	maximal
4	C₂×C₁₇×#3874	—	3	3	no	maximal
5	C₃×C₁₇×C₅²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₅×C₁₇×D₁₅	—	3	2	no	—
7	C₂×C₁₇×C₅²⋊C₃	D₃	1	3	yes	complemented
8	C₁₇×#3874	—	3	6	no	—
9	C₂×C₃×C₅²×C₁₇	D₃	1	1	yes	characteristic, complemented
10	C₂×C₅×D₅×C₁₇	—	9	1	no	Hall
11	C₃×C₅²×C₁₇	C₂×D₃	1	1	yes	characteristic, complemented
12	C₁₇×C₅²⋊C₃	C₂×D₃	1	3	yes	complemented
13	C₂×C₁₇×D₁₅	—	3	1	no	—
14	C₂×C₅×D₃×C₁₇	—	15	1	no	—
15	C₂×C₃⋊#3874	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₅²×C₁₇	C₃⋊D₃	1	1	yes	characteristic, complemented
17	C₅×D₅×C₁₇	—	9	2	no	—
18	C₂×C₁₇×C₃⋊D₃	—	25	1	no	maximal, Hall
19	C₂×C₃×C₅×C₁₇	—	3	1	no	—
20	C₂×C₃×C₅×C₁₇	—	3	1	no	—
21	C₁₇×D₁₅	—	3	2	no	—
22	C₅×D₃×C₁₇	—	15	2	no	—
23	C₂×C₃×C₅²⋊C₃	C₂×C₁₇	1	1	yes	characteristic, complemented
24	C₃⋊#3874	C₂×C₁₇	1	2	yes	direct product factor
25	C₅²×C₁₇	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
26	C₂²×C₅×C₁₇	—	45	1	no	—
27	C₂×D₅×C₁₇	—	9	1	no	—
28	C₂×C₃²×C₁₇	—	25	1	no	—
29	C₁₇×C₃⋊D₃	—	25	2	no	—
30	C₂×C₅×D₁₅	—	3	1	no	—
31	C₂×#3874	—	3	3	no	—
32	C₃×C₅×C₁₇	—	3	1	no	—
33	C₃×C₅×C₁₇	—	3	1	no	—
34	C₃×C₅²⋊C₃	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
35	C₂×D₃×C₁₇	—	15	1	no	—
36	C₂×D₃×C₁₇	—	75	3	no	—
37	C₂×C₅×C₁₇	—	3	1	no	—
38	C₂×C₅×C₁₇	—	3	1	no	—
39	C₂×C₅×C₁₇	—	45	2	no	—
40	D₅×C₁₇	—	9	2	no	—
41	C₃²×C₁₇	—	25	1	no	Hall
42	C₂×C₃×C₅²	D₃×C₁₇	1	1	yes	characteristic, complemented
43	C₅×D₁₅	—	3	2	no	—
44	C₂×C₅²⋊C₃	D₃×C₁₇	1	3	yes	complemented
45	#3874	—	3	6	no	—
46	C₂×C₃×C₁₇	—	25	3	no	—
47	C₂×C₃×C₁₇	#3874	1	1	yes	characteristic, complemented
48	D₃×C₁₇	—	15	2	no	—
49	D₃×C₁₇	—	75	6	no	—
50	C₂×C₅×D₅	—	9	1	no	Hall
51	C₅×C₁₇	—	3	1	no	—
52	C₅×C₁₇	—	3	1	no	—
53	C₃×C₅²	C₂×D₃×C₁₇	1	1	yes	characteristic, complemented
54	C₅²⋊C₃	C₂×D₃×C₁₇	1	3	yes	complemented
55	C₂²×C₁₇	—	45	1	no	Hall
56	C₂×D₁₅	—	3	1	no	—
57	C₂×C₅×D₃	—	15	1	no	—
58	C₃×C₁₇	—	25	3	no	—
59	C₃×C₁₇	C₂×#3874	1	1	yes	characteristic, complemented
60	C₂×C₅²	C₁₇×C₃⋊D₃	1	1	yes	characteristic, complemented
61	C₅×D₅	—	9	2	no	—
62	C₂×C₃⋊D₃	—	25	1	no	Hall
63	C₂×C₁₇	—	45	2	no	—
64	C₂×C₁₇	C₃⋊#3874	1	1	yes	characteristic, direct product factor
65	C₂×C₃×C₅	—	3	1	no	—
66	C₂×C₃×C₅	—	3	1	no	—
67	D₁₅	—	3	2	no	—
68	C₅×D₃	—	15	2	no	—
69	C₅²	C₂×C₁₇×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
70	C₂²×C₅	—	45	1	no	—
71	C₂×D₅	—	9	1	no	—
72	C₂×C₃²	—	25	1	no	—
73	C₃⋊D₃	—	25	2	no	—
74	C₁₇	C₂×C₃⋊#3874	1	1	yes	characteristic, direct product factor, Sylow
75	C₃×C₅	—	3	1	no	—
76	C₃×C₅	—	3	1	no	—
77	C₂×D₃	—	15	1	no	—
78	C₂×D₃	—	75	3	no	—
79	C₂×C₅	—	3	1	no	—
80	C₂×C₅	—	3	1	no	—
81	C₂×C₅	—	45	2	no	—
82	D₅	—	9	2	no	—
83	C₃²	—	25	1	no	Sylow
84	C₂×C₃	—	25	3	no	—
85	C₂×C₃	C₁₇×#3874	1	1	yes	characteristic, complemented
86	D₃	—	15	2	no	—
87	D₃	—	75	6	no	—
88	C₅	—	3	1	no	—
89	C₅	—	3	1	no	—
90	C₂²	—	45	1	no	Sylow
91	C₃	—	25	3	no	—
92	C₃	C₂×C₁₇×#3874	1	1	yes	characteristic, complemented
93	C₂	—	45	2	no	—
94	C₂	C₁₇×C₃⋊#3874	1	1	yes	characteristic, direct product factor

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₁₇×C₅²⋊C₃	C₂	semidirect
2. C₁₇×C₃⋊#3874	C₂	direct (N × H)
5. C₃×C₁₇×C₅²⋊C₃	C₂²	semidirect
7. C₂×C₁₇×C₅²⋊C₃	D₃	semidirect
9. C₂×C₃×C₅²×C₁₇	D₃	semidirect
11. C₃×C₅²×C₁₇	C₂×D₃	semidirect
12. C₁₇×C₅²⋊C₃	C₂×D₃	semidirect
15. C₂×C₃⋊#3874	C₁₇	direct (N × H)
16. C₂×C₅²×C₁₇	C₃⋊D₃	semidirect
23. C₂×C₃×C₅²⋊C₃	C₂×C₁₇	semidirect
24. C₃⋊#3874	C₂×C₁₇	direct (N × H)
25. C₅²×C₁₇	C₂×C₃⋊D₃	semidirect
34. C₃×C₅²⋊C₃	C₂²×C₁₇	semidirect
42. C₂×C₃×C₅²	D₃×C₁₇	semidirect
44. C₂×C₅²⋊C₃	D₃×C₁₇	semidirect
47. C₂×C₃×C₁₇	#3874	semidirect
53. C₃×C₅²	C₂×D₃×C₁₇	semidirect
54. C₅²⋊C₃	C₂×D₃×C₁₇	semidirect
59. C₃×C₁₇	C₂×#3874	semidirect
60. C₂×C₅²	C₁₇×C₃⋊D₃	semidirect
64. C₂×C₁₇	C₃⋊#3874	direct (N × H)
69. C₅²	C₂×C₁₇×C₃⋊D₃	semidirect
74. C₁₇	C₂×C₃⋊#3874	direct (N × H)
85. C₂×C₃	C₁₇×#3874	semidirect
92. C₃	C₂×C₁₇×#3874	semidirect
94. C₂	C₁₇×C₃⋊#3874	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×C₃×C₁₇×C₅²⋊C₃	2
C₁₇×C₃⋊#3874	2
C₂×C₅×C₁₇×D₁₅	3
C₂×C₁₇×#3874	3
C₂×C₃⋊#3874	17
C₂×C₁₇×C₃⋊D₃	25

Subgroups — C2×C17×C3⋊#3874 #29505919

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×C₃⋊#3874 #29505919