Subgroups — D₄₉×(C₅⋊D₅)⋊C₃ #28412949

Order 14700.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20301201	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₉×(C₅⋊D₅)⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²⋊C₃×D₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅⋊D₅×D₄₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₄₉×C₅²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₅⋊D₂₄₅	C₂×C₃	1	1	yes	characteristic, complemented
7	C₄₉×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅²×D₄₉	C₂×C₃	1	1	yes	characteristic, complemented
9	D₇×(C₅⋊D₅)⋊C₃	—	7	1	no	maximal
10	C₅²×C₄₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	#11760384	—	7	1	no	—
12	C₇×(C₅⋊D₅)⋊C₃	D₇	1	1	yes	characteristic
13	D₇×C₅²⋊C₃	—	7	1	no	—
14	D₅×D₄₉	—	15	2	no	—
15	D₇×C₅⋊D₅	—	7	1	no	—
16	C₂×C₃×D₄₉	—	25	1	no	maximal, Hall
17	C₇×C₅²⋊C₃	C₂×D₇	1	1	yes	characteristic
18	D₂₄₅	—	15	2	no	—
19	C₅×D₄₉	—	3	2	no	—
20	D₅×C₄₉	—	15	2	no	—
21	C₅⋊D₃₅	—	7	1	no	—
22	C₇×C₅⋊D₅	C₃×D₇	1	1	yes	characteristic
23	C₅²×D₇	—	7	1	no	—
24	C₂×(C₅⋊D₅)⋊C₃	—	49	1	no	Hall
25	C₂×C₃×C₄₉	—	25	1	no	—
26	C₃×D₄₉	—	25	1	no	—
27	C₃×D₄₉	—	25	1	no	—
28	C₅×C₄₉	—	3	2	no	—
29	C₂×D₄₉	—	25	1	no	Hall
30	C₅²×C₇	C₂×C₃×D₇	1	1	yes	characteristic
31	C₂×C₅²⋊C₃	—	49	1	no	—
32	(C₅⋊D₅)⋊C₃	—	49	1	no	—
33	(C₅⋊D₅)⋊C₃	D₄₉	1	1	yes	characteristic, direct product factor
34	C₃×C₄₉	—	25	1	no	Hall
35	D₅×D₇	—	105	2	no	—
36	C₂×C₅⋊D₅	—	49	1	no	Hall
37	C₂×C₄₉	—	25	1	no	—
38	D₄₉	—	25	1	no	—
39	D₄₉	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, direct product factor
40	C₂×C₃×D₇	—	175	1	no	—
41	C₅²⋊C₃	C₂×D₄₉	1	1	yes	characteristic, complemented, Hall
42	D₃₅	—	105	2	no	—
43	C₅×D₇	—	21	2	no	—
44	C₇×D₅	—	15	2	no	—
45	C₂×C₅²	—	49	1	no	—
46	C₅⋊D₅	—	49	1	no	—
47	C₅⋊D₅	C₃×D₄₉	1	1	yes	characteristic, complemented
48	C₄₉	C₂×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₃×C₇	—	25	1	no	—
50	C₃×D₇	—	175	1	no	—
51	C₃×D₇	—	175	1	no	—
52	C₅×C₇	—	3	2	no	—
53	C₂×D₇	—	175	1	no	—
54	C₅²	C₂×C₃×D₄₉	1	1	yes	characteristic, complemented, Sylow
55	C₃×C₇	—	25	1	no	—
56	C₂×D₅	—	735	2	no	—
57	C₂×C₇	—	25	1	no	—
58	D₇	—	7	1	no	—
59	D₇	—	175	1	no	—
60	C₂²×C₃	—	1225	1	no	Hall
61	C₂×C₅	—	147	2	no	—
62	D₅	—	15	2	no	—
63	D₅	—	735	2	no	—
64	C₇	D₇×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic
65	C₂×C₃	—	25	1	no	—
66	C₂×C₃	—	1225	1	no	—
67	C₂×C₃	—	1225	1	no	—
68	C₅	—	3	2	no	—
69	C₂²	—	1225	1	no	Sylow
70	C₃	—	25	1	no	Sylow
71	C₂	—	25	1	no	—
72	C₂	—	49	1	no	—
73	C₂	—	1225	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅²×C₄₉	C₂²×C₃
Frattini	C₇	D₇×(C₅⋊D₅)⋊C₃
socle	C₅²×C₇	C₂×C₃×D₇
LCS	G ▷ C₅²×C₄₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. #20301201	C₂	semidirect
2. C₄₉×(C₅⋊D₅)⋊C₃	C₂	semidirect
3. C₅²⋊C₃×D₄₉	C₂	semidirect
4. C₅⋊D₅×D₄₉	C₃	semidirect
5. C₄₉×C₅²⋊C₃	C₂²	semidirect
6. C₅⋊D₂₄₅	C₂×C₃	semidirect
7. C₄₉×C₅⋊D₅	C₂×C₃	semidirect
8. C₅²×D₄₉	C₂×C₃	semidirect
10. C₅²×C₄₉	C₂²×C₃	semidirect
33. (C₅⋊D₅)⋊C₃	D₄₉	direct (N × H)
39. D₄₉	(C₅⋊D₅)⋊C₃	direct (N × H)
41. C₅²⋊C₃	C₂×D₄₉	semidirect
47. C₅⋊D₅	C₃×D₄₉	semidirect
48. C₄₉	C₂×(C₅⋊D₅)⋊C₃	semidirect
54. C₅²	C₂×C₃×D₄₉	semidirect

Maximal subgroups

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

subgroup	index
#20301201	2
C₄₉×(C₅⋊D₅)⋊C₃	2
C₅²⋊C₃×D₄₉	2
C₅⋊D₅×D₄₉	3
D₇×(C₅⋊D₅)⋊C₃	7
C₂×C₃×D₄₉	25

Subgroups — D49×(C5⋊D5)⋊C3 #28412949

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₉×(C₅⋊D₅)⋊C₃ #28412949