Subgroups — D₂₉×C₃⋊D₈₇ #44475671

Order 30276.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₉×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×C₃⋊D₈₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊(C₃⋊(C₂₉⋊D₂₉))	C₂	1	1	yes	maximal, characteristic, complemented
4	D₂₉×D₈₇	—	3	4	no	maximal
5	C₃²×C₂₉²	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃⋊(C₂₉⋊D₂₉)	—	3	4	no	—
7	C₂₉×D₈₇	—	3	4	no	—
8	C₃×C₂₉×D₂₉	D₃	1	4	yes	complemented
9	D₂₉²	—	9	1	no	Hall
10	C₃×C₂₉²	C₂×D₃	1	4	yes	complemented
11	C₂₉⋊D₂₉	—	9	1	no	—
12	C₂₉×D₂₉	—	9	1	no	—
13	C₂₉×D₂₉	C₃⋊D₃	1	1	yes	characteristic, complemented
14	C₂×C₃⋊D₈₇	—	29	1	no	maximal
15	C₃⋊D₃×D₂₉	—	29	1	no	maximal
16	C₂₉²	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₃²×C₂₉	—	29	1	no	—
18	C₃⋊D₈₇	—	29	1	no	—
19	C₃⋊D₈₇	—	29	1	no	—
20	C₃⋊D₈₇	—	58	14	no	—
21	C₃⋊D₈₇	D₂₉	1	1	yes	characteristic, direct product factor
22	C₃⋊D₃×C₂₉	—	29	1	no	—
23	C₃²×D₂₉	D₂₉	1	1	yes	characteristic, complemented
24	C₂×D₈₇	—	87	4	no	—
25	D₃×D₂₉	—	87	4	no	—
26	C₃²×C₂₉	—	2	14	no	—
27	C₃²×C₂₉	C₂×D₂₉	1	1	yes	characteristic, complemented
28	C₃²×C₂₉	C₂×D₂₉	1	1	yes	characteristic, complemented
29	C₂×C₃×C₂₉	—	29	4	no	—
30	D₈₇	—	3	4	no	—
31	D₈₇	—	87	4	no	—
32	D₈₇	—	87	4	no	—
33	D₈₇	—	174	56	no	—
34	C₃×D₂₉	D₈₇	1	4	yes	complemented
35	D₃×C₂₉	—	87	4	no	—
36	C₂×D₂₉	—	261	1	no	—
37	C₂×D₂₉	—	261	1	no	—
38	C₃×C₂₉	—	2	56	no	—
39	C₃×C₂₉	D₃×D₂₉	1	4	yes	complemented
40	C₃×C₂₉	C₂×D₈₇	1	4	yes	complemented
41	C₂×C₂₉	—	261	1	no	—
42	C₂×C₂₉	—	29	1	no	—
43	D₂₉	—	261	1	no	—
44	D₂₉	—	261	1	no	—
45	D₂₉	—	9	1	no	—
46	D₂₉	—	522	14	no	—
47	D₂₉	C₃⋊D₈₇	1	1	yes	characteristic, direct product factor
48	C₂×C₃⋊D₃	—	841	1	no	Hall
49	C₂₉	—	2	14	no	—
50	C₂₉	C₃⋊D₃×D₂₉	1	1	yes	characteristic, complemented
51	C₂₉	C₂×C₃⋊D₈₇	1	1	yes	characteristic, complemented
52	C₂×C₃²	—	29	1	no	—
53	C₃⋊D₃	—	29	1	no	—
54	C₃⋊D₃	—	841	1	no	—
55	C₂×D₃	—	2523	4	no	—
56	C₃²	D₂₉²	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₃	—	29	4	no	—
58	D₃	—	87	4	no	—
59	D₃	—	2523	4	no	—
60	C₂²	—	7569	1	no	Sylow
61	C₃	D₂₉×D₈₇	1	4	yes	complemented
62	C₂	—	261	1	no	—
63	C₂	—	29	1	no	—
64	C₂	—	7569	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₂₉²	C₂²
LCS	G ▷ C₃²×C₂₉²
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₂₉×D₂₉	C₂	semidirect
2. C₂₉×C₃⋊D₈₇	C₂	semidirect
3. C₃⋊(C₃⋊(C₂₉⋊D₂₉))	C₂	semidirect
5. C₃²×C₂₉²	C₂²	semidirect
8. C₃×C₂₉×D₂₉	D₃	semidirect
10. C₃×C₂₉²	C₂×D₃	semidirect
13. C₂₉×D₂₉	C₃⋊D₃	semidirect
16. C₂₉²	C₂×C₃⋊D₃	semidirect
21. C₃⋊D₈₇	D₂₉	direct (N × H)
23. C₃²×D₂₉	D₂₉	semidirect
27. C₃²×C₂₉	C₂×D₂₉	semidirect
28. C₃²×C₂₉	C₂×D₂₉	semidirect
34. C₃×D₂₉	D₈₇	semidirect
39. C₃×C₂₉	D₃×D₂₉	semidirect
40. C₃×C₂₉	C₂×D₈₇	semidirect
47. D₂₉	C₃⋊D₈₇	direct (N × H)
50. C₂₉	C₃⋊D₃×D₂₉	semidirect
51. C₂₉	C₂×C₃⋊D₈₇	semidirect
56. C₃²	D₂₉²	semidirect
61. C₃	D₂₉×D₈₇	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₂₉×D₂₉	2
C₂₉×C₃⋊D₈₇	2
C₃⋊(C₃⋊(C₂₉⋊D₂₉))	2
D₂₉×D₈₇	3
C₂×C₃⋊D₈₇	29
C₃⋊D₃×D₂₉	29

Subgroups — D29×C3⋊D87 #44475671

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₉×C₃⋊D₈₇ #44475671