Subgroups — #39908212

Order 26100.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅⋊D₁₄₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅²×C₃⋊D₈₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×C₃⋊(C₃⋊(C₅⋊D₅))	C₂	1	1	yes	maximal, characteristic, complemented
4	D₈₇⋊(C₅⋊D₅)	—	3	4	no	maximal
5	C₃²×C₅²×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₄₅⋊(C₃⋊D₃)	—	5	6	no	maximal
7	C₂₉×C₃⋊(C₅⋊D₅)	—	3	4	no	—
8	C₅²×D₈₇	—	3	4	no	—
9	C₃×C₅⋊D₁₄₅	D₃	1	4	yes	complemented
10	C₅⋊D₅×D₂₉	—	9	1	no	Hall
11	C₂₉×C₃⋊D₁₅	—	5	6	no	—
12	C₅×C₃⋊D₈₇	D₅	1	6	yes	complemented
13	C₃²×D₁₄₅	—	5	6	no	—
14	C₃×C₅²×C₂₉	C₂×D₃	1	4	yes	complemented
15	D₁₅⋊D₂₉	—	15	24	no	—
16	C₅⋊D₁₄₅	C₃⋊D₃	1	1	yes	characteristic, complemented
17	C₂₉×C₅⋊D₅	—	9	1	no	—
18	C₅²×D₂₉	—	9	1	no	—
19	C₃²×C₅×C₂₉	C₂×D₅	1	6	yes	complemented
20	C₃⋊D₃×D₂₉	—	25	1	no	Hall
21	C₃⋊D₃×C₅⋊D₅	—	29	1	no	maximal, Hall
22	C₂₉×D₁₅	—	15	24	no	—
23	C₅×D₈₇	—	3	24	no	—
24	C₃×D₁₄₅	—	5	24	no	—
25	C₅²×C₂₉	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
26	D₅×D₂₉	—	45	6	no	—
27	C₃⋊D₈₇	C₅⋊D₅	1	1	yes	characteristic, complemented
28	C₃⋊D₃×C₂₉	—	25	1	no	—
29	C₃²×D₂₉	—	25	1	no	—
30	C₃⋊(C₃⋊(C₅⋊D₅))	D₂₉	1	1	yes	characteristic, complemented
31	C₅²×C₃⋊D₃	—	29	1	no	—
32	C₃²×C₅⋊D₅	—	29	1	no	—
33	C₃×C₅×C₂₉	D₃×D₅	1	24	yes	complemented
34	D₃×D₂₉	—	75	4	no	—
35	D₃×C₅⋊D₅	—	87	4	no	—
36	D₁₄₅	—	5	6	no	—
37	C₅×D₂₉	—	9	6	no	—
38	D₅×C₂₉	—	45	6	no	—
39	C₃²×C₂₉	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
40	C₃²×C₅²	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
41	D₅×C₃⋊D₃	—	145	6	no	—
42	D₈₇	—	3	4	no	—
43	C₃×D₂₉	—	25	4	no	—
44	D₃×C₂₉	—	75	4	no	—
45	C₃⋊(C₅⋊D₅)	—	3	4	no	—
46	C₅²×D₃	—	87	4	no	—
47	C₃×C₅⋊D₅	—	29	4	no	—
48	C₅×C₂₉	D₅×C₃⋊D₃	1	6	yes	complemented
49	C₂×D₂₉	—	225	1	no	Hall
50	C₂×C₅⋊D₅	—	261	1	no	Hall
51	C₃⋊D₁₅	—	5	6	no	—
52	C₅×C₃⋊D₃	—	29	6	no	—
53	C₃²×D₅	—	145	6	no	—
54	C₃×C₂₉	D₃×C₅⋊D₅	1	4	yes	complemented
55	C₃×C₅²	D₃×D₂₉	1	4	yes	complemented
56	D₃×D₅	—	435	24	no	—
57	C₂×C₂₉	—	225	1	no	—
58	D₂₉	—	9	1	no	—
59	D₂₉	—	25	1	no	—
60	C₂×C₅²	—	261	1	no	—
61	C₅⋊D₅	—	9	1	no	—
62	C₅⋊D₅	—	29	1	no	—
63	C₃²×C₅	D₅×D₂₉	1	6	yes	complemented
64	C₂×C₃⋊D₃	—	725	1	no	Hall
65	D₁₅	—	15	24	no	—
66	C₃×D₅	—	145	24	no	—
67	C₅×D₃	—	87	24	no	—
68	C₂₉	C₃⋊D₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
69	C₅²	C₃⋊D₃×D₂₉	1	1	yes	characteristic, complemented, Sylow
70	C₂×D₅	—	1305	6	no	—
71	C₂×C₃²	—	725	1	no	—
72	C₃⋊D₃	—	25	1	no	—
73	C₃⋊D₃	—	29	1	no	—
74	C₃×C₅	D₁₅⋊D₂₉	1	24	yes	complemented
75	C₂×D₃	—	2175	4	no	—
76	C₂×C₅	—	261	6	no	—
77	D₅	—	45	6	no	—
78	D₅	—	145	6	no	—
79	C₃²	C₅⋊D₅×D₂₉	1	1	yes	characteristic, complemented, Sylow
80	C₂×C₃	—	725	4	no	—
81	D₃	—	75	4	no	—
82	D₃	—	87	4	no	—
83	C₅	D₁₄₅⋊(C₃⋊D₃)	1	6	yes	complemented
84	C₂²	—	6525	1	no	Sylow
85	C₃	D₈₇⋊(C₅⋊D₅)	1	4	yes	complemented
86	C₂	—	261	1	no	—
87	C₂	—	725	1	no	—
88	C₂	—	225	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₅²×C₂₉	C₂²
LCS	G ▷ C₃²×C₅²×C₂₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅⋊D₁₄₅	C₂	semidirect
2. C₅²×C₃⋊D₈₇	C₂	semidirect
3. C₂₉×C₃⋊(C₃⋊(C₅⋊D₅))	C₂	semidirect
5. C₃²×C₅²×C₂₉	C₂²	semidirect
9. C₃×C₅⋊D₁₄₅	D₃	semidirect
12. C₅×C₃⋊D₈₇	D₅	semidirect
14. C₃×C₅²×C₂₉	C₂×D₃	semidirect
16. C₅⋊D₁₄₅	C₃⋊D₃	semidirect
19. C₃²×C₅×C₂₉	C₂×D₅	semidirect
25. C₅²×C₂₉	C₂×C₃⋊D₃	semidirect
27. C₃⋊D₈₇	C₅⋊D₅	semidirect
30. C₃⋊(C₃⋊(C₅⋊D₅))	D₂₉	semidirect
33. C₃×C₅×C₂₉	D₃×D₅	semidirect
39. C₃²×C₂₉	C₂×C₅⋊D₅	semidirect
40. C₃²×C₅²	C₂×D₂₉	semidirect
48. C₅×C₂₉	D₅×C₃⋊D₃	semidirect
54. C₃×C₂₉	D₃×C₅⋊D₅	semidirect
55. C₃×C₅²	D₃×D₂₉	semidirect
63. C₃²×C₅	D₅×D₂₉	semidirect
68. C₂₉	C₃⋊D₃×C₅⋊D₅	semidirect
69. C₅²	C₃⋊D₃×D₂₉	semidirect
74. C₃×C₅	D₁₅⋊D₂₉	semidirect
79. C₃²	C₅⋊D₅×D₂₉	semidirect
83. C₅	D₁₄₅⋊(C₃⋊D₃)	semidirect
85. C₃	D₈₇⋊(C₅⋊D₅)	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅⋊D₁₄₅	2
C₅²×C₃⋊D₈₇	2
C₂₉×C₃⋊(C₃⋊(C₅⋊D₅))	2
D₈₇⋊(C₅⋊D₅)	3
D₁₄₅⋊(C₃⋊D₃)	5
C₃⋊D₃×C₅⋊D₅	29