Subgroups — C₅×C₃⋊Dic₄₃₅ #39908006

Order 26100.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₅²×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₄₃₅	—	3	4	no	maximal
3	C₃²×C₅²×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊Dic₄₃₅	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₅×C₃⋊Dic₈₇	—	5	1	no	maximal
6	C₂×C₃×C₅²×C₂₉	D₃	1	4	yes	—
7	C₅×Dic₁₄₅	—	9	1	no	Hall
8	C₂×C₃²×C₅×C₂₉	—	2	2	no	—
9	C₂×C₃²×C₅×C₂₉	D₅	1	1	yes	characteristic
10	C₂×C₃²×C₅×C₂₉	C₂×C₅	1	1	yes	characteristic
11	C₃×C₅²×C₂₉	Dic₃	1	4	yes	complemented
12	Dic₄₃₅	—	3	4	no	—
13	C₅×Dic₈₇	—	15	4	no	—
14	C₂×C₅²×C₂₉	C₃⋊D₃	1	1	yes	characteristic
15	C₃²×C₅×C₂₉	—	2	2	no	—
16	C₃²×C₅×C₂₉	Dic₅	1	1	yes	characteristic, complemented
17	C₃²×C₅×C₂₉	C₄×C₅	1	1	yes	characteristic, complemented
18	C₃⋊Dic₈₇	—	5	1	no	Hall
19	C₅×C₃⋊Dic₁₅	—	29	1	no	maximal, Hall
20	C₂×C₃×C₅×C₂₉	—	2	8	no	—
21	C₂×C₃×C₅×C₂₉	C₅×D₃	1	4	yes	—
22	C₂×C₃×C₅×C₂₉	D₁₅	1	4	yes	—
23	C₅²×C₂₉	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
24	Dic₁₄₅	—	9	1	no	—
25	C₅×Dic₂₉	—	45	1	no	—
26	C₂×C₃²×C₂₉	C₅×D₅	1	1	yes	characteristic
27	C₂×C₃²×C₅²	D₂₉	1	1	yes	characteristic
28	C₃×C₅×C₂₉	—	2	8	no	—
29	C₃×C₅×C₂₉	C₅×Dic₃	1	4	yes	complemented
30	C₃×C₅×C₂₉	Dic₁₅	1	4	yes	complemented
31	Dic₈₇	—	15	4	no	—
32	C₅×Dic₁₅	—	87	4	no	—
33	C₂×C₅×C₂₉	—	2	2	no	—
34	C₂×C₅×C₂₉	C₅×C₃⋊D₃	1	1	yes	characteristic
35	C₂×C₅×C₂₉	C₃⋊D₁₅	1	1	yes	characteristic
36	C₃²×C₂₉	C₅×Dic₅	1	1	yes	characteristic, complemented, Hall
37	C₃²×C₅²	Dic₂₉	1	1	yes	characteristic, complemented, Hall
38	C₃⋊Dic₁₅	—	29	1	no	—
39	C₅×C₃⋊Dic₃	—	145	1	no	—
40	C₂×C₃×C₂₉	C₅×D₁₅	1	4	yes	—
41	C₂×C₃×C₅²	D₈₇	1	4	yes	—
42	C₅×C₂₉	—	2	2	no	—
43	C₅×C₂₉	C₅×C₃⋊Dic₃	1	1	yes	characteristic, complemented
44	C₅×C₂₉	C₃⋊Dic₁₅	1	1	yes	characteristic, complemented
45	Dic₂₉	—	45	1	no	Hall
46	C₅×Dic₅	—	261	1	no	Hall
47	C₂×C₃²×C₅	—	2	2	no	—
48	C₂×C₃²×C₅	C₅×D₂₉	1	1	yes	characteristic
49	C₂×C₃²×C₅	D₁₄₅	1	1	yes	characteristic
50	C₃×C₂₉	C₅×Dic₁₅	1	4	yes	complemented
51	C₃×C₅²	Dic₈₇	1	4	yes	complemented
52	Dic₁₅	—	87	4	no	—
53	C₅×Dic₃	—	435	4	no	—
54	C₂×C₂₉	C₅×C₃⋊D₁₅	1	1	yes	characteristic
55	C₂×C₅²	C₃⋊D₈₇	1	1	yes	characteristic
56	C₃²×C₅	—	2	2	no	—
57	C₃²×C₅	C₅×Dic₂₉	1	1	yes	characteristic, complemented
58	C₃²×C₅	Dic₁₄₅	1	1	yes	characteristic, complemented
59	C₃⋊Dic₃	—	145	1	no	Hall
60	C₂×C₃×C₅	—	2	8	no	—
61	C₂×C₃×C₅	C₅×D₈₇	1	4	yes	—
62	C₂×C₃×C₅	D₄₃₅	1	4	yes	—
63	C₂₉	C₅×C₃⋊Dic₁₅	1	1	yes	characteristic, complemented, Sylow
64	C₅²	C₃⋊Dic₈₇	1	1	yes	characteristic, complemented, Sylow
65	C₄×C₅	—	1305	1	no	—
66	Dic₅	—	261	1	no	—
67	C₂×C₃²	C₅×D₁₄₅	1	1	yes	characteristic
68	C₃×C₅	—	2	8	no	—
69	C₃×C₅	C₅×Dic₈₇	1	4	yes	complemented
70	C₃×C₅	Dic₄₃₅	1	4	yes	complemented
71	Dic₃	—	435	4	no	—
72	C₂×C₅	—	2	2	no	—
73	C₂×C₅	C₅×C₃⋊D₈₇	1	1	yes	characteristic
74	C₂×C₅	C₃⋊D₄₃₅	1	1	yes	characteristic
75	C₃²	C₅×Dic₁₄₅	1	1	yes	characteristic, complemented, Sylow
76	C₂×C₃	C₅×D₄₃₅	1	4	yes	—
77	C₅	—	2	2	no	—
78	C₅	C₅×C₃⋊Dic₈₇	1	1	yes	characteristic, complemented
79	C₅	C₃⋊Dic₄₃₅	1	1	yes	characteristic, direct product factor
80	C₄	—	1305	1	no	Sylow
81	C₃	C₅×Dic₄₃₅	1	4	yes	complemented
82	C₂	C₅×C₃⋊D₄₃₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅	C₃⋊D₄₃₅
commutator, hypocenter	C₃²×C₅×C₂₉	C₄×C₅
Frattini	C₂	C₅×C₃⋊D₄₃₅
Fitting, socle, prime radical	C₂×C₃²×C₅²×C₂₉	C₂
cosocle	C₂×C₃²×C₅×C₂₉	C₂×C₅
LCS	G ▷ C₃²×C₅×C₂₉
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
3. C₃²×C₅²×C₂₉	C₄	semidirect
4. C₃⋊Dic₄₃₅	C₅	direct (N × H)
11. C₃×C₅²×C₂₉	Dic₃	semidirect
16. C₃²×C₅×C₂₉	Dic₅	semidirect
17. C₃²×C₅×C₂₉	C₄×C₅	semidirect
23. C₅²×C₂₉	C₃⋊Dic₃	semidirect
29. C₃×C₅×C₂₉	C₅×Dic₃	semidirect
30. C₃×C₅×C₂₉	Dic₁₅	semidirect
36. C₃²×C₂₉	C₅×Dic₅	semidirect
37. C₃²×C₅²	Dic₂₉	semidirect
43. C₅×C₂₉	C₅×C₃⋊Dic₃	semidirect
44. C₅×C₂₉	C₃⋊Dic₁₅	semidirect
50. C₃×C₂₉	C₅×Dic₁₅	semidirect
51. C₃×C₅²	Dic₈₇	semidirect
57. C₃²×C₅	C₅×Dic₂₉	semidirect
58. C₃²×C₅	Dic₁₄₅	semidirect
63. C₂₉	C₅×C₃⋊Dic₁₅	semidirect
64. C₅²	C₃⋊Dic₈₇	semidirect
69. C₃×C₅	C₅×Dic₈₇	semidirect
70. C₃×C₅	Dic₄₃₅	semidirect
75. C₃²	C₅×Dic₁₄₅	semidirect
78. C₅	C₅×C₃⋊Dic₈₇	semidirect
79. C₅	C₃⋊Dic₄₃₅	direct (N × H)
81. C₃	C₅×Dic₄₃₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₅²×C₂₉	2
C₅×Dic₄₃₅	3
C₃⋊Dic₄₃₅	5
C₅×C₃⋊Dic₈₇	5
C₅×C₃⋊Dic₁₅	29

Subgroups — C5×C3⋊Dic435 #39908006

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₃⋊Dic₄₃₅ #39908006