Subgroups — #39908205

Order 26100.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₉×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₃⋊D₄₃₅	C₂	1	2	yes	maximal, complemented
3	#22576491	—	3	4	no	maximal
4	C₃²×C₅²×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₅×C₃⋊D₈₇	—	5	2	no	maximal
6	C₅×D₄₃₅	—	3	8	no	—
7	C₃×C₂₉×C₅⋊D₅	D₃	1	4	yes	complemented
8	(C₅⋊D₅)⋊D₂₉	—	9	1	no	Hall
9	C₃⋊D₄₃₅	D₅	1	2	yes	complemented
10	C₅×C₃⋊D₈₇	—	5	2	no	—
11	C₃²×D₅×C₂₉	—	5	2	no	—
12	C₃²×D₅×C₂₉	—	10	2	no	—
13	C₃×C₅²×C₂₉	C₂×D₃	1	4	yes	complemented
14	D₅×D₈₇	—	15	8	no	—
15	C₂₉×C₅⋊D₅	C₃⋊D₃	1	1	yes	characteristic, complemented
16	C₅×D₁₄₅	—	9	2	no	—
17	C₃²×C₅×C₂₉	—	2	2	no	—
18	C₃²×C₅×C₂₉	C₂×D₅	1	2	yes	complemented
19	C₂×C₃⋊D₈₇	—	25	1	no	Hall
20	#11744719	—	29	1	no	maximal, Hall
21	D₄₃₅	—	3	8	no	—
22	C₅×D₈₇	—	15	8	no	—
23	C₃×D₅×C₂₉	—	5	8	no	—
24	C₃×D₅×C₂₉	—	10	8	no	—
25	C₅²×C₂₉	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
26	D₅×D₂₉	—	45	2	no	—
27	C₂×C₃²×C₂₉	—	25	1	no	—
28	C₃⋊D₈₇	—	5	2	no	—
29	C₅×C₃⋊D₁₅	—	29	2	no	—
30	C₃²×C₅⋊D₅	D₂₉	1	1	yes	characteristic, complemented
31	C₃×C₅×C₂₉	—	2	8	no	—
32	C₃×C₅×C₂₉	D₃×D₅	1	8	yes	complemented
33	C₂×D₈₇	—	75	4	no	—
34	D₁₅⋊D₅	—	87	4	no	—
35	D₁₄₅	—	9	2	no	—
36	C₅×D₂₉	—	45	2	no	—
37	D₅×C₂₉	—	5	2	no	—
38	D₅×C₂₉	—	10	2	no	—
39	C₃²×C₂₉	D₅²	1	1	yes	characteristic, complemented, Hall
40	C₃²×C₅²	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
41	D₅×C₃⋊D₃	—	145	2	no	—
42	C₂×C₃×C₂₉	—	25	4	no	—
43	D₈₇	—	15	8	no	—
44	C₅×D₁₅	—	87	8	no	—
45	C₃×C₅⋊D₅	D₈₇	1	4	yes	complemented
46	C₅×C₂₉	—	2	2	no	—
47	C₅×C₂₉	D₅×C₃⋊D₃	1	2	yes	complemented
48	C₂×D₂₉	—	225	1	no	Hall
49	D₅²	—	261	1	no	Hall
50	C₃⋊D₁₅	—	29	2	no	—
51	C₅×C₃⋊D₃	—	145	2	no	—
52	C₃²×D₅	—	5	2	no	—
53	C₃²×D₅	—	10	2	no	—
54	C₃×C₂₉	D₁₅⋊D₅	1	4	yes	complemented
55	C₃×C₅²	C₂×D₈₇	1	4	yes	complemented
56	D₃×D₅	—	435	8	no	—
57	C₂×C₂₉	—	25	1	no	—
58	D₂₉	—	45	2	no	—
59	C₅⋊D₅	C₃⋊D₈₇	1	1	yes	characteristic, complemented
60	C₅×D₅	—	261	2	no	—
61	C₃²×C₅	—	2	2	no	—
62	C₃²×C₅	D₅×D₂₉	1	2	yes	complemented
63	C₂×C₃⋊D₃	—	725	1	no	Hall
64	D₁₅	—	87	8	no	—
65	C₃×D₅	—	5	8	no	—
66	C₃×D₅	—	10	8	no	—
67	C₅×D₃	—	435	8	no	—
68	C₂₉	#11744719	1	1	yes	characteristic, complemented, Sylow
69	C₅²	C₂×C₃⋊D₈₇	1	1	yes	characteristic, complemented, Sylow
70	C₂×D₅	—	1305	2	no	—
71	C₂×C₃²	—	25	1	no	—
72	C₃⋊D₃	—	145	2	no	—
73	C₃×C₅	—	2	8	no	—
74	C₃×C₅	D₅×D₈₇	1	8	yes	complemented
75	C₂×D₃	—	2175	4	no	—
76	C₂×C₅	—	1305	2	no	—
77	D₅	—	5	2	no	—
78	D₅	—	261	2	no	—
79	D₅	—	10	2	no	—
80	C₃²	(C₅⋊D₅)⋊D₂₉	1	1	yes	characteristic, complemented, Sylow
81	C₂×C₃	—	25	4	no	—
82	D₃	—	435	8	no	—
83	C₅	—	2	2	no	—
84	C₅	D₅×C₃⋊D₈₇	1	2	yes	complemented
85	C₂²	—	6525	1	no	Sylow
86	C₃	#22576491	1	4	yes	complemented
87	C₂	—	25	1	no	—
88	C₂	—	1305	2	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×C₂₉×C₅⋊D₅	C₂	semidirect
2. C₅×C₃⋊D₄₃₅	C₂	semidirect
4. C₃²×C₅²×C₂₉	C₂²	semidirect
7. C₃×C₂₉×C₅⋊D₅	D₃	semidirect
9. C₃⋊D₄₃₅	D₅	semidirect
13. C₃×C₅²×C₂₉	C₂×D₃	semidirect
15. C₂₉×C₅⋊D₅	C₃⋊D₃	semidirect
18. C₃²×C₅×C₂₉	C₂×D₅	semidirect
25. C₅²×C₂₉	C₂×C₃⋊D₃	semidirect
30. C₃²×C₅⋊D₅	D₂₉	semidirect
32. C₃×C₅×C₂₉	D₃×D₅	semidirect
39. C₃²×C₂₉	D₅²	semidirect
40. C₃²×C₅²	C₂×D₂₉	semidirect
45. C₃×C₅⋊D₅	D₈₇	semidirect
47. C₅×C₂₉	D₅×C₃⋊D₃	semidirect
54. C₃×C₂₉	D₁₅⋊D₅	semidirect
55. C₃×C₅²	C₂×D₈₇	semidirect
59. C₅⋊D₅	C₃⋊D₈₇	semidirect
62. C₃²×C₅	D₅×D₂₉	semidirect
68. C₂₉	#11744719	semidirect
69. C₅²	C₂×C₃⋊D₈₇	semidirect
74. C₃×C₅	D₅×D₈₇	semidirect
80. C₃²	(C₅⋊D₅)⋊D₂₉	semidirect
84. C₅	D₅×C₃⋊D₈₇	semidirect
86. C₃	#22576491	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₂₉×C₅⋊D₅	2
C₅×C₃⋊D₄₃₅	2
#22576491	3
D₅×C₃⋊D₈₇	5
#11744719	29