Subgroups — (C₃⋊D₃)⋊D₄₇₅ #30685512

Order 17100.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₃×C₁₉×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₁₄₂₅	C₂	1	2	yes	maximal, complemented
3	D₃×D₄₇₅	—	3	2	no	maximal
4	C₃²×C₁₉×C₂₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	(C₃⋊D₃)⋊D₉₅	—	5	1	no	maximal
6	D₁₄₂₅	D₃	1	2	yes	complemented
7	D₃×C₁₉×C₂₅	—	3	2	no	—
8	D₃×C₁₉×C₂₅	—	6	1	no	—
9	C₃×D₄₇₅	—	3	2	no	—
10	C₂×D₄₇₅	—	9	1	no	Hall
11	C₅×C₃⋊D₃×C₁₉	D₅	1	1	yes	characteristic
12	C₃×D₂₈₅	—	5	2	no	—
13	C₃×C₁₉×C₂₅	—	2	1	no	—
14	C₃×C₁₉×C₂₅	C₂×D₃	1	2	yes	complemented
15	D₃×D₉₅	—	15	2	no	—
16	C₂×C₁₉×C₂₅	—	9	1	no	—
17	D₄₇₅	—	3	2	no	—
18	(C₃⋊D₃)⋊D₂₅	—	19	1	no	maximal, Hall
19	C₃²×C₅×C₁₉	C₂×D₅	1	1	yes	characteristic
20	(C₃⋊D₃)⋊D₁₉	—	25	1	no	Hall
21	D₂₈₅	—	5	2	no	—
22	C₅×D₃×C₁₉	—	3	2	no	—
23	C₅×D₃×C₁₉	—	6	1	no	—
24	C₃×D₉₅	—	15	2	no	—
25	C₁₉×C₂₅	D₃²	1	1	yes	characteristic, complemented, Hall
26	C₃⋊D₃×C₂₅	D₁₉	1	1	yes	characteristic, complemented
27	C₃×D₇₅	—	19	2	no	—
28	C₂×D₉₅	—	45	1	no	—
29	C₃⋊D₃×C₁₉	D₂₅	1	1	yes	characteristic, complemented
30	C₃×D₅₇	—	25	2	no	—
31	D₃×D₂₅	—	57	2	no	—
32	C₃×C₅×C₁₉	—	2	1	no	—
33	C₃×C₅×C₁₉	D₃×D₅	1	2	yes	—
34	D₃×D₁₉	—	75	2	no	—
35	C₃²×C₂₅	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
36	C₂×C₅×C₁₉	—	9	1	no	—
37	D₉₅	—	15	2	no	—
38	(C₃⋊D₃)⋊D₅	—	95	1	no	—
39	C₃²×C₁₉	C₂×D₂₅	1	1	yes	characteristic, complemented, Hall
40	D₇₅	—	19	2	no	—
41	C₃×D₂₅	—	57	2	no	—
42	D₃×C₂₅	—	3	2	no	—
43	D₃×C₂₅	—	6	1	no	—
44	D₅₇	—	25	2	no	—
45	C₃×D₁₉	—	75	2	no	—
46	D₃×C₁₉	—	3	2	no	—
47	D₃×C₁₉	—	6	1	no	—
48	C₂×D₂₅	—	171	1	no	Hall
49	C₅×C₁₉	(C₃⋊D₃)⋊D₅	1	1	yes	characteristic
50	C₅×C₃⋊D₃	D₉₅	1	1	yes	characteristic
51	C₃×D₁₅	—	95	2	no	—
52	C₂×D₁₉	—	225	1	no	Hall
53	C₃×C₂₅	—	2	1	no	—
54	C₃×C₂₅	D₃×D₁₉	1	2	yes	complemented
55	D₃×D₅	—	285	2	no	—
56	C₃×C₁₉	—	2	1	no	—
57	C₃×C₁₉	D₃×D₂₅	1	2	yes	complemented
58	C₂×C₂₅	—	9	1	no	—
59	D₂₅	—	57	2	no	—
60	C₃²×C₅	C₂×D₉₅	1	1	yes	characteristic
61	C₂×C₁₉	—	9	1	no	—
62	D₁₉	—	75	2	no	—
63	D₃²	—	475	1	no	Hall
64	D₁₅	—	95	2	no	—
65	C₃×D₅	—	285	2	no	—
66	C₅×D₃	—	3	2	no	—
67	C₅×D₃	—	6	1	no	—
68	C₂₅	(C₃⋊D₃)⋊D₁₉	1	1	yes	characteristic, complemented, Sylow
69	C₂×D₅	—	855	1	no	—
70	C₁₉	(C₃⋊D₃)⋊D₂₅	1	1	yes	characteristic, complemented, Sylow
71	C₃⋊D₃	D₄₇₅	1	1	yes	characteristic, complemented
72	C₃×D₃	—	475	2	no	—
73	C₃×C₅	—	2	1	no	—
74	C₃×C₅	D₃×D₉₅	1	2	yes	—
75	C₂×D₃	—	1425	2	no	—
76	C₂×C₅	—	9	1	no	—
77	D₅	—	285	2	no	—
78	C₃²	C₂×D₄₇₅	1	1	yes	characteristic, complemented, Sylow
79	C₂×C₃	—	1425	2	no	—
80	D₃	—	3	2	no	—
81	D₃	—	6	1	no	—
82	D₃	—	475	2	no	—
83	C₅	(C₃⋊D₃)⋊D₉₅	1	1	yes	characteristic
84	C₂²	—	4275	1	no	Sylow
85	C₃	—	2	1	no	—
86	C₃	D₃×D₄₇₅	1	2	yes	complemented
87	C₂	—	9	1	no	—
88	C₂	—	1425	2	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃²×C₁₉×C₂₅	C₂²
Frattini	C₅	(C₃⋊D₃)⋊D₉₅
socle	C₃²×C₅×C₁₉	C₂×D₅
LCS	G ▷ C₃²×C₁₉×C₂₅
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₃×C₁₉×C₂₅	C₂	semidirect
2. C₃×D₁₄₂₅	C₂	semidirect
4. C₃²×C₁₉×C₂₅	C₂²	semidirect
6. D₁₄₂₅	D₃	semidirect
14. C₃×C₁₉×C₂₅	C₂×D₃	semidirect
25. C₁₉×C₂₅	D₃²	semidirect
26. C₃⋊D₃×C₂₅	D₁₉	semidirect
29. C₃⋊D₃×C₁₉	D₂₅	semidirect
35. C₃²×C₂₅	C₂×D₁₉	semidirect
39. C₃²×C₁₉	C₂×D₂₅	semidirect
54. C₃×C₂₅	D₃×D₁₉	semidirect
57. C₃×C₁₉	D₃×D₂₅	semidirect
68. C₂₅	(C₃⋊D₃)⋊D₁₉	semidirect
70. C₁₉	(C₃⋊D₃)⋊D₂₅	semidirect
71. C₃⋊D₃	D₄₇₅	semidirect
78. C₃²	C₂×D₄₇₅	semidirect
86. C₃	D₃×D₄₇₅	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊D₃×C₁₉×C₂₅	2
C₃×D₁₄₂₅	2
D₃×D₄₇₅	3
(C₃⋊D₃)⋊D₉₅	5
(C₃⋊D₃)⋊D₂₅	19

Subgroups — (C3⋊D3)⋊D475 #30685512

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₃⋊D₃)⋊D₄₇₅ #30685512