Subgroups — C₂×C₃⋊(C₁₇⋊#3874) #29505920

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	C₃⋊(C₁₇⋊#3874)	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅×D₂₅₅	—	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×D₂₅₅	—	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×D₈₅	—	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×D₂₅₅	—	3	1	no	—
14	C₂×C₅×D₅₁	—	15	1	no	—
15	C₂×C₃⋊#3874	—	17	1	no	maximal, Hall
16	C₂×C₅²×C₁₇	C₃⋊D₃	1	1	yes	characteristic, complemented
17	C₅×D₈₅	—	9	2	no	—
18	C₂×C₃⋊D₅₁	—	25	1	no	maximal, Hall
19	C₂×C₃×C₅×C₁₇	—	6	1	no	—
20	C₂×C₃×C₅×C₁₇	—	6	1	no	—
21	D₂₅₅	—	3	2	no	—
22	C₅×D₅₁	—	15	2	no	—
23	C₂×C₃×C₅²⋊C₃	D₁₇	1	1	yes	characteristic, complemented
24	C₃⋊#3874	—	17	2	no	—
25	C₅²×C₁₇	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
26	C₂×D₈₅	—	9	1	no	—
27	C₂×C₅×D₁₇	—	45	1	no	—
28	C₂×C₃²×C₁₇	—	25	1	no	—
29	C₃⋊D₅₁	—	25	2	no	—
30	C₂×C₅×D₁₅	—	51	1	no	—
31	C₂×#3874	—	51	3	no	—
32	C₃×C₅×C₁₇	—	6	1	no	—
33	C₃×C₅×C₁₇	—	6	1	no	—
34	C₃×C₅²⋊C₃	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
35	C₂×D₅₁	—	15	1	no	—
36	C₂×D₅₁	—	75	3	no	—
37	C₂×C₅×C₁₇	—	3	1	no	—
38	C₂×C₅×C₁₇	—	6	1	no	—
39	D₈₅	—	9	2	no	—
40	C₅×D₁₇	—	45	2	no	—
41	C₃²×C₁₇	—	25	1	no	Hall
42	C₂×C₃×C₅²	D₅₁	1	1	yes	characteristic, complemented
43	C₅×D₁₅	—	51	2	no	—
44	C₂×C₅²⋊C₃	D₅₁	1	3	yes	complemented
45	#3874	—	51	6	no	—
46	C₂×C₃×C₁₇	—	50	3	no	—
47	C₂×C₃×C₁₇	#3874	1	1	yes	characteristic, complemented
48	D₅₁	—	15	2	no	—
49	D₅₁	—	75	6	no	—
50	C₂×C₅×D₅	—	153	1	no	Hall
51	C₅×C₁₇	—	3	1	no	—
52	C₅×C₁₇	—	6	1	no	—
53	C₃×C₅²	C₂×D₅₁	1	1	yes	characteristic, complemented
54	C₅²⋊C₃	C₂×D₅₁	1	3	yes	complemented
55	C₂×D₁₇	—	45	1	no	Hall
56	C₂×D₁₅	—	51	1	no	—
57	C₂×C₅×D₃	—	255	1	no	—
58	C₃×C₁₇	—	50	3	no	—
59	C₃×C₁₇	C₂×#3874	1	1	yes	characteristic, complemented
60	C₂×C₅²	C₃⋊D₅₁	1	1	yes	characteristic, complemented
61	C₅×D₅	—	153	2	no	—
62	C₂×C₃⋊D₃	—	425	1	no	Hall
63	C₂×C₁₇	C₃⋊#3874	1	1	yes	characteristic, complemented
64	D₁₇	—	45	2	no	—
65	C₂×C₃×C₅	—	6	1	no	—
66	C₂×C₃×C₅	—	6	1	no	—
67	D₁₅	—	51	2	no	—
68	C₅×D₃	—	255	2	no	—
69	C₅²	C₂×C₃⋊D₅₁	1	1	yes	characteristic, complemented, Sylow
70	C₂²×C₅	—	765	1	no	—
71	C₂×D₅	—	153	1	no	—
72	C₂×C₃²	—	50	1	no	—
73	C₃⋊D₃	—	425	2	no	—
74	C₁₇	C₂×C₃⋊#3874	1	1	yes	characteristic, complemented, Sylow
75	C₃×C₅	—	6	1	no	—
76	C₃×C₅	—	6	1	no	—
77	C₂×D₃	—	1275	3	no	—
78	C₂×D₃	—	255	1	no	—
79	C₂×C₅	—	6	1	no	—
80	C₂×C₅	—	6	1	no	—
81	C₂×C₅	—	765	2	no	—
82	D₅	—	153	2	no	—
83	C₃²	—	50	1	no	Sylow
84	C₂×C₃	—	50	3	no	—
85	C₂×C₃	C₁₇⋊#3874	1	1	yes	characteristic, complemented
86	D₃	—	1275	6	no	—
87	D₃	—	255	2	no	—
88	C₅	—	6	1	no	—
89	C₅	—	6	1	no	—
90	C₂²	—	765	1	no	Sylow
91	C₃	—	50	3	no	—
92	C₃	C₂×C₁₇⋊#3874	1	1	yes	characteristic, complemented
93	C₂	—	765	2	no	—
94	C₂	C₃⋊(C₁₇⋊#3874)	1	1	yes	characteristic, direct product factor

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

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. C₃⋊(C₁₇⋊#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
16. C₂×C₅²×C₁₇	C₃⋊D₃	semidirect
23. C₂×C₃×C₅²⋊C₃	D₁₇	semidirect
25. C₅²×C₁₇	C₂×C₃⋊D₃	semidirect
34. C₃×C₅²⋊C₃	C₂×D₁₇	semidirect
42. C₂×C₃×C₅²	D₅₁	semidirect
44. C₂×C₅²⋊C₃	D₅₁	semidirect
47. C₂×C₃×C₁₇	#3874	semidirect
53. C₃×C₅²	C₂×D₅₁	semidirect
54. C₅²⋊C₃	C₂×D₅₁	semidirect
59. C₃×C₁₇	C₂×#3874	semidirect
60. C₂×C₅²	C₃⋊D₅₁	semidirect
63. C₂×C₁₇	C₃⋊#3874	semidirect
69. C₅²	C₂×C₃⋊D₅₁	semidirect
74. C₁₇	C₂×C₃⋊#3874	semidirect
85. C₂×C₃	C₁₇⋊#3874	semidirect
92. C₃	C₂×C₁₇⋊#3874	semidirect
94. C₂	C₃⋊(C₁₇⋊#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
C₃⋊(C₁₇⋊#3874)	2
C₂×C₅×D₂₅₅	3
C₂×C₁₇⋊#3874	3
C₂×C₃⋊#3874	17
C₂×C₃⋊D₅₁	25

Subgroups — C2×C3⋊(C17⋊#3874) #29505920

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊(C₁₇⋊#3874) #29505920