Subgroups — C₅×C₃⋊D₇₃₅ #36347711

Order 22050.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅²×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₇₃₅	—	3	4	no	maximal
3	C₃⋊D₇₃₅	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×C₃⋊D₁₄₇	—	5	1	no	maximal
5	C₃×C₅²×C₄₉	D₃	1	4	yes	complemented
6	C₅×C₃⋊D₁₀₅	—	7	1	no	maximal
7	C₅×D₂₄₅	—	9	1	no	Hall
8	C₃²×C₅×C₄₉	—	2	2	no	—
9	C₃²×C₅×C₄₉	D₅	1	1	yes	characteristic, complemented
10	C₃²×C₅×C₄₉	C₂×C₅	1	1	yes	characteristic, complemented
11	C₃²×C₅²×C₇	D₇	1	1	yes	characteristic
12	D₇₃₅	—	3	4	no	—
13	C₅×D₁₄₇	—	15	4	no	—
14	C₅²×C₄₉	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
15	C₅×D₁₀₅	—	21	4	no	—
16	C₃⋊D₁₄₇	—	5	1	no	Hall
17	C₃×C₅×C₄₉	—	2	8	no	—
18	C₃×C₅×C₄₉	C₅×D₃	1	4	yes	complemented
19	C₃×C₅×C₄₉	D₁₅	1	4	yes	complemented
20	C₃⋊D₁₀₅	—	7	1	no	—
21	C₅×C₃⋊D₂₁	—	35	1	no	—
22	C₃×C₅²×C₇	D₂₁	1	4	yes	—
23	D₂₄₅	—	9	1	no	—
24	C₅×D₄₉	—	45	1	no	—
25	C₅×C₃⋊D₁₅	—	49	1	no	Hall
26	C₃²×C₄₉	C₅×D₅	1	1	yes	characteristic, complemented, Hall
27	C₅×D₃₅	—	63	1	no	—
28	C₃²×C₅×C₇	—	2	2	no	—
29	C₃²×C₅×C₇	C₅×D₇	1	1	yes	characteristic
30	C₃²×C₅×C₇	D₃₅	1	1	yes	characteristic
31	D₁₄₇	—	15	4	no	—
32	C₅×C₄₉	—	2	2	no	—
33	C₅×C₄₉	C₅×C₃⋊D₃	1	1	yes	characteristic, complemented
34	C₅×C₄₉	C₃⋊D₁₅	1	1	yes	characteristic, complemented
35	C₃²×C₅²	D₄₉	1	1	yes	characteristic, complemented, Hall
36	D₁₀₅	—	21	4	no	—
37	C₅×D₂₁	—	105	4	no	—
38	C₅²×C₇	C₃⋊D₂₁	1	1	yes	characteristic
39	C₅×D₁₅	—	147	4	no	—
40	C₃×C₄₉	C₅×D₁₅	1	4	yes	complemented
41	C₃⋊D₂₁	—	35	1	no	—
42	C₃×C₅×C₇	—	2	8	no	—
43	C₃×C₅×C₇	C₅×D₂₁	1	4	yes	—
44	C₃×C₅×C₇	D₁₀₅	1	4	yes	—
45	D₄₉	—	45	1	no	Hall
46	C₃⋊D₁₅	—	49	1	no	—
47	C₅×C₃⋊D₃	—	245	1	no	—
48	C₃×C₅²	D₁₄₇	1	4	yes	complemented
49	D₃₅	—	63	1	no	—
50	C₅×D₇	—	315	1	no	—
51	C₃²×C₇	C₅×D₃₅	1	1	yes	characteristic
52	C₅×D₅	—	441	1	no	Hall
53	C₄₉	C₅×C₃⋊D₁₅	1	1	yes	characteristic, complemented, Sylow
54	C₃²×C₅	—	2	2	no	—
55	C₃²×C₅	C₅×D₄₉	1	1	yes	characteristic, complemented
56	C₃²×C₅	D₂₄₅	1	1	yes	characteristic, complemented
57	D₂₁	—	105	4	no	—
58	C₅×C₇	—	2	2	no	—
59	C₅×C₇	C₅×C₃⋊D₂₁	1	1	yes	characteristic
60	C₅×C₇	C₃⋊D₁₀₅	1	1	yes	characteristic
61	D₁₅	—	147	4	no	—
62	C₅×D₃	—	735	4	no	—
63	C₅²	C₃⋊D₁₄₇	1	1	yes	characteristic, complemented, Sylow
64	C₃×C₇	C₅×D₁₀₅	1	4	yes	—
65	C₃⋊D₃	—	245	1	no	Hall
66	C₃×C₅	—	2	8	no	—
67	C₃×C₅	C₅×D₁₄₇	1	4	yes	complemented
68	C₃×C₅	D₇₃₅	1	4	yes	complemented
69	D₇	—	315	1	no	—
70	C₂×C₅	—	2205	1	no	—
71	D₅	—	441	1	no	—
72	C₃²	C₅×D₂₄₅	1	1	yes	characteristic, complemented, Sylow
73	C₇	C₅×C₃⋊D₁₀₅	1	1	yes	characteristic
74	D₃	—	735	4	no	—
75	C₅	—	2	2	no	—
76	C₅	C₅×C₃⋊D₁₄₇	1	1	yes	characteristic, complemented
77	C₅	C₃⋊D₇₃₅	1	1	yes	characteristic, direct product factor
78	C₃	C₅×D₇₃₅	1	4	yes	complemented
79	C₂	—	2205	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	C₃⋊D₇₃₅
commutator, cosocle, hypocenter	C₃²×C₅×C₄₉	C₂×C₅
Frattini	C₇	C₅×C₃⋊D₁₀₅
Fitting	C₃²×C₅²×C₄₉	C₂
socle	C₃²×C₅²×C₇	D₇
LCS	G ▷ C₃²×C₅×C₄₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅²×C₄₉	C₂	semidirect
3. C₃⋊D₇₃₅	C₅	direct (N × H)
5. C₃×C₅²×C₄₉	D₃	semidirect
9. C₃²×C₅×C₄₉	D₅	semidirect
10. C₃²×C₅×C₄₉	C₂×C₅	semidirect
14. C₅²×C₄₉	C₃⋊D₃	semidirect
18. C₃×C₅×C₄₉	C₅×D₃	semidirect
19. C₃×C₅×C₄₉	D₁₅	semidirect
26. C₃²×C₄₉	C₅×D₅	semidirect
33. C₅×C₄₉	C₅×C₃⋊D₃	semidirect
34. C₅×C₄₉	C₃⋊D₁₅	semidirect
35. C₃²×C₅²	D₄₉	semidirect
40. C₃×C₄₉	C₅×D₁₅	semidirect
48. C₃×C₅²	D₁₄₇	semidirect
53. C₄₉	C₅×C₃⋊D₁₅	semidirect
55. C₃²×C₅	C₅×D₄₉	semidirect
56. C₃²×C₅	D₂₄₅	semidirect
63. C₅²	C₃⋊D₁₄₇	semidirect
67. C₃×C₅	C₅×D₁₄₇	semidirect
68. C₃×C₅	D₇₃₅	semidirect
72. C₃²	C₅×D₂₄₅	semidirect
76. C₅	C₅×C₃⋊D₁₄₇	semidirect
77. C₅	C₃⋊D₇₃₅	direct (N × H)
78. C₃	C₅×D₇₃₅	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅²×C₄₉	2
C₅×D₇₃₅	3
C₃⋊D₇₃₅	5
C₅×C₃⋊D₁₄₇	5
C₅×C₃⋊D₁₀₅	7

Subgroups — C5×C3⋊D735 #36347711

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₃⋊D₇₃₅ #36347711