Subgroups — #3874×C₂₉⋊C₇ #44478552

Order 30450.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²⋊C₃×C₂₉⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₅×C₂₉⋊C₇	—	3	1	no	maximal, Hall
3	C₅²×C₂₉⋊C₇	D₃	1	1	yes	characteristic, complemented, Hall
4	C₂₉×#3874	C₇	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂₉×C₅²⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented, Hall
6	D₅×C₂₉⋊C₇	—	3	1	no	—
7	C₂×C₅×C₂₉⋊C₇	—	15	1	no	—
8	C₅×D₅×C₂₉	—	3	1	no	Hall
9	D₃×C₂₉⋊C₇	—	25	1	no	maximal, Hall
10	C₇×#3874	—	29	1	no	maximal, Hall
11	C₅×C₂₉⋊C₇	—	3	1	no	—
12	C₅×C₂₉⋊C₇	—	3	1	no	—
13	C₅²×C₂₉	D₃×C₇	1	1	yes	characteristic, complemented, Hall
14	C₃×C₂₉⋊C₇	—	25	1	no	Hall
15	C₇×C₅²⋊C₃	—	29	1	no	Hall
16	C₂×C₂₉⋊C₇	—	15	1	no	Hall
17	C₅×C₇×D₅	—	87	1	no	Hall
18	C₂×C₅×C₂₉	—	15	1	no	—
19	D₅×C₂₉	—	3	1	no	—
20	C₂₉⋊C₇	#3874	1	1	yes	characteristic, direct product factor, Hall
21	C₅²×C₇	—	29	1	no	Hall
22	D₃×C₂₉	—	25	1	no	Hall
23	#3874	C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Hall
24	C₅×C₂₉	—	3	1	no	—
25	C₅×C₂₉	—	3	1	no	—
26	C₃×C₂₉	—	25	1	no	Hall
27	C₅²⋊C₃	C₂×C₂₉⋊C₇	1	1	yes	characteristic, complemented, Hall
28	C₂×C₅×C₇	—	435	1	no	—
29	C₇×D₅	—	87	1	no	—
30	C₂×C₂₉	—	15	1	no	Hall
31	C₅×D₅	—	3	1	no	Hall
32	D₃×C₇	—	725	1	no	Hall
33	C₅×C₇	—	87	1	no	—
34	C₅×C₇	—	87	1	no	—
35	C₂₉	C₇×#3874	1	1	yes	characteristic, complemented, Sylow
36	C₅²	D₃×C₂₉⋊C₇	1	1	yes	characteristic, complemented, Sylow
37	C₃×C₇	—	725	1	no	Hall
38	C₂×C₇	—	435	1	no	Hall
39	C₂×C₅	—	15	1	no	—
40	D₅	—	3	1	no	—
41	C₇	—	29	1	no	Sylow
42	D₃	—	25	1	no	Hall
43	C₅	—	3	1	no	—
44	C₅	—	3	1	no	—
45	C₃	—	25	1	no	Sylow
46	C₂	—	15	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₂₉×C₅²⋊C₃	C₂×C₇
Fitting, socle	C₅²×C₂₉	D₃×C₇
LCS	G ▷ C₂₉×C₅²⋊C₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅²⋊C₃×C₂₉⋊C₇	C₂	semidirect
3. C₅²×C₂₉⋊C₇	D₃	semidirect
4. C₂₉×#3874	C₇	semidirect
5. C₂₉×C₅²⋊C₃	C₂×C₇	semidirect
13. C₅²×C₂₉	D₃×C₇	semidirect
20. C₂₉⋊C₇	#3874	direct (N × H)
23. #3874	C₂₉⋊C₇	direct (N × H)
27. C₅²⋊C₃	C₂×C₂₉⋊C₇	semidirect
35. C₂₉	C₇×#3874	semidirect
36. C₅²	D₃×C₂₉⋊C₇	semidirect

Maximal subgroups

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

subgroup	index
C₅²⋊C₃×C₂₉⋊C₇	2
C₅×D₅×C₂₉⋊C₇	3
C₂₉×#3874	7
D₃×C₂₉⋊C₇	25
C₇×#3874	29

Subgroups — #3874×C29⋊C7 #44478552

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3874×C₂₉⋊C₇ #44478552