Subgroups — D₁₅⋊D₄₉₇ #44447270

Order 29820.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₁₅×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₁₄₉₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₂₄₈₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₄₉₇	—	3	1	no	maximal, Hall
5	C₃×C₅×C₇×C₇₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×D₄₉₇	—	5	1	no	maximal, Hall
7	D₂₄₈₅	D₃	1	1	yes	characteristic, complemented
8	C₇×D₅×C₇₁	—	3	1	no	—
9	C₅×D₄₉₇	—	3	1	no	—
10	D₁₅⋊D₇₁	—	7	1	no	maximal, Hall
11	D₁₄₉₁	D₅	1	1	yes	characteristic, complemented
12	D₃×C₇×C₇₁	—	5	1	no	—
13	C₃×D₄₉₇	—	5	1	no	—
14	C₅×C₇×C₇₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
15	D₁₅×C₇₁	D₇	1	1	yes	characteristic, complemented
16	C₅×D₂₁₃	—	7	1	no	—
17	C₃×D₃₅₅	—	7	1	no	—
18	C₂×D₄₉₇	—	15	1	no	Hall
19	C₃×C₇×C₇₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	D₅×D₇₁	—	21	1	no	Hall
21	C₃×C₅×C₇₁	C₂×D₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₇×C₇₁	—	15	1	no	—
23	D₄₉₇	—	3	1	no	—
24	D₄₉₇	—	5	1	no	—
25	D₃×D₇₁	—	35	1	no	Hall
26	D₃₅₅	—	7	1	no	—
27	C₅×D₇₁	—	21	1	no	—
28	D₅×C₇₁	—	3	1	no	—
29	C₇×C₇₁	D₃×D₅	1	1	yes	characteristic, complemented, Hall
30	D₂₁₃	—	7	1	no	—
31	C₃×D₇₁	—	35	1	no	—
32	D₃×C₇₁	—	5	1	no	—
33	D₁₅⋊D₇	—	71	1	no	maximal, Hall
34	C₅×C₇₁	D₃×D₇	1	1	yes	characteristic, complemented, Hall
35	C₂×D₇₁	—	105	1	no	Hall
36	C₃×C₇₁	D₅×D₇	1	1	yes	characteristic, complemented, Hall
37	C₇×D₁₅	D₇₁	1	1	yes	characteristic, complemented
38	C₅×D₂₁	—	71	1	no	—
39	C₃×D₃₅	—	71	1	no	—
40	C₂×C₇₁	—	15	1	no	—
41	D₇₁	—	21	1	no	—
42	D₇₁	—	35	1	no	—
43	D₅×D₇	—	213	1	no	Hall
44	C₃×C₅×C₇	C₂×D₇₁	1	1	yes	characteristic, complemented, Hall
45	D₃×D₇	—	355	1	no	Hall
46	C₇₁	D₁₅⋊D₇	1	1	yes	characteristic, complemented, Sylow
47	D₃₅	—	71	1	no	—
48	C₅×D₇	—	213	1	no	—
49	C₇×D₅	—	3	1	no	—
50	D₃×D₅	—	497	1	no	Hall
51	D₂₁	—	71	1	no	—
52	C₃×D₇	—	355	1	no	—
53	D₃×C₇	—	5	1	no	—
54	C₅×C₇	D₃×D₇₁	1	1	yes	characteristic, complemented, Hall
55	D₁₅	D₄₉₇	1	1	yes	characteristic, complemented
56	C₃×D₅	—	497	1	no	—
57	C₅×D₃	—	497	1	no	—
58	C₂×D₇	—	1065	1	no	Hall
59	C₃×C₇	D₅×D₇₁	1	1	yes	characteristic, complemented, Hall
60	C₂×D₅	—	1491	1	no	Hall
61	C₃×C₅	C₂×D₄₉₇	1	1	yes	characteristic, complemented, Hall
62	C₂×C₇	—	15	1	no	—
63	D₇	—	355	1	no	—
64	D₇	—	213	1	no	—
65	C₂×D₃	—	2485	1	no	Hall
66	C₂×C₅	—	1491	1	no	—
67	D₅	—	3	1	no	—
68	D₅	—	497	1	no	—
69	C₇	D₁₅⋊D₇₁	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₃	—	2485	1	no	—
71	D₃	—	5	1	no	—
72	D₃	—	497	1	no	—
73	C₅	D₃×D₄₉₇	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	7455	1	no	Sylow
75	C₃	D₅×D₄₉₇	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	15	1	no	—
77	C₂	—	2485	1	no	—
78	C₂	—	1491	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₇×C₇₁	C₂²
LCS	G ▷ C₃×C₅×C₇×C₇₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₇×D₁₅×C₇₁	C₂	semidirect
2. C₅×D₁₄₉₁	C₂	semidirect
3. C₃×D₂₄₈₅	C₂	semidirect
5. C₃×C₅×C₇×C₇₁	C₂²	semidirect
7. D₂₄₈₅	D₃	semidirect
11. D₁₄₉₁	D₅	semidirect
14. C₅×C₇×C₇₁	C₂×D₃	semidirect
15. D₁₅×C₇₁	D₇	semidirect
19. C₃×C₇×C₇₁	C₂×D₅	semidirect
21. C₃×C₅×C₇₁	C₂×D₇	semidirect
29. C₇×C₇₁	D₃×D₅	semidirect
34. C₅×C₇₁	D₃×D₇	semidirect
36. C₃×C₇₁	D₅×D₇	semidirect
37. C₇×D₁₅	D₇₁	semidirect
44. C₃×C₅×C₇	C₂×D₇₁	semidirect
46. C₇₁	D₁₅⋊D₇	semidirect
54. C₅×C₇	D₃×D₇₁	semidirect
55. D₁₅	D₄₉₇	semidirect
59. C₃×C₇	D₅×D₇₁	semidirect
61. C₃×C₅	C₂×D₄₉₇	semidirect
69. C₇	D₁₅⋊D₇₁	semidirect
73. C₅	D₃×D₄₉₇	semidirect
75. C₃	D₅×D₄₉₇	semidirect

Maximal subgroups

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

subgroup	index
C₇×D₁₅×C₇₁	2
C₅×D₁₄₉₁	2
C₃×D₂₄₈₅	2
D₅×D₄₉₇	3
D₃×D₄₉₇	5
D₁₅⋊D₇₁	7
D₁₅⋊D₇	71

Subgroups — D15⋊D497 #44447270

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₅⋊D₄₉₇ #44447270