Subgroups — D₁₅×#3862 #17984393

Order 4410.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#3862	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇²×D₁₅	C₃	1	1	yes	maximal, characteristic, complemented
3	D₅×#3862	—	3	1	no	maximal
4	D₃×#3862	—	5	1	no	maximal, Hall
5	C₃×C₅×C₇²	C₂×C₃	1	1	yes	characteristic, complemented
6	C₅×#3862	—	2	1	no	—
7	C₅×#3862	D₃	1	1	yes	characteristic, complemented
8	ΓL(1,𝔽₈)×D₁₅	—	7	2	no	maximal
9	C₇²×D₅	—	3	1	no	Hall
10	C₃×#3862	D₅	1	1	yes	characteristic, complemented, Hall
11	C₃×C₅×ΓL(1,𝔽₈)	—	7	2	no	—
12	D₃×C₇²	—	5	1	no	—
13	C₂×#3862	—	15	1	no	—
14	C₅×C₇²	C₃×D₃	1	1	yes	characteristic, complemented, Hall
15	C₇×D₁₅	—	3	2	no	—
16	C₇×D₁₅	ΓL(1,𝔽₈)	1	2	yes	complemented
17	D₅×ΓL(1,𝔽₈)	—	21	2	no	—
18	C₃×C₇²	C₃×D₅	1	1	yes	characteristic, complemented
19	#3862	—	2	1	no	—
20	#3862	D₁₅	1	1	yes	characteristic, direct product factor
21	D₃×ΓL(1,𝔽₈)	—	35	2	no	—
22	C₃×C₅×C₇	—	3	2	no	—
23	C₃×C₅×C₇	C₂×ΓL(1,𝔽₈)	1	2	yes	complemented
24	C₅×ΓL(1,𝔽₈)	—	7	2	no	—
25	C₅×ΓL(1,𝔽₈)	—	14	2	no	—
26	C₂×C₇²	—	15	1	no	Hall
27	C₃×D₁₅	—	49	1	no	Hall
28	C₇×D₅	—	3	2	no	—
29	C₇×D₅	—	9	2	no	—
30	C₃×ΓL(1,𝔽₈)	—	7	2	no	—
31	C₇²	C₃×D₁₅	1	1	yes	characteristic, complemented, Sylow
32	C₃²×C₅	—	49	1	no	Hall
33	D₃×C₇	—	5	2	no	—
34	D₃×C₇	—	15	2	no	—
35	C₂×ΓL(1,𝔽₈)	—	105	2	no	—
36	C₅×C₇	—	3	2	no	—
37	C₅×C₇	D₃×ΓL(1,𝔽₈)	1	2	yes	complemented
38	D₁₅	#3862	1	1	yes	characteristic, direct product factor
39	C₃×D₅	—	147	1	no	—
40	C₃×C₇	—	3	2	no	—
41	C₃×C₇	D₅×ΓL(1,𝔽₈)	1	2	yes	complemented
42	ΓL(1,𝔽₈)	—	7	2	no	—
43	ΓL(1,𝔽₈)	—	14	2	no	—
44	C₃×D₃	—	245	1	no	Hall
45	C₃×C₅	—	49	1	no	—
46	C₃×C₅	—	98	1	no	—
47	C₃×C₅	C₂×#3862	1	1	yes	characteristic, complemented
48	C₂×C₇	—	15	2	no	—
49	C₂×C₇	—	45	2	no	—
50	D₅	—	3	1	no	Hall
51	C₃²	—	49	1	no	Sylow
52	C₇	—	3	2	no	—
53	C₇	ΓL(1,𝔽₈)×D₁₅	1	2	yes	complemented
54	C₂×C₃	—	735	1	no	—
55	D₃	—	5	1	no	—
56	C₅	D₃×#3862	1	1	yes	characteristic, complemented, Sylow
57	C₃	—	49	1	no	—
58	C₃	—	98	1	no	—
59	C₃	D₅×#3862	1	1	yes	characteristic, complemented
60	C₂	—	15	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₇²	C₂×C₃
LCS	G ▷ C₃×C₅×C₇²
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#3862	C₂	semidirect
2. C₇²×D₁₅	C₃	semidirect
5. C₃×C₅×C₇²	C₂×C₃	semidirect
7. C₅×#3862	D₃	semidirect
10. C₃×#3862	D₅	semidirect
14. C₅×C₇²	C₃×D₃	semidirect
16. C₇×D₁₅	ΓL(1,𝔽₈)	semidirect
18. C₃×C₇²	C₃×D₅	semidirect
20. #3862	D₁₅	direct (N × H)
23. C₃×C₅×C₇	C₂×ΓL(1,𝔽₈)	semidirect
31. C₇²	C₃×D₁₅	semidirect
37. C₅×C₇	D₃×ΓL(1,𝔽₈)	semidirect
38. D₁₅	#3862	direct (N × H)
41. C₃×C₇	D₅×ΓL(1,𝔽₈)	semidirect
47. C₃×C₅	C₂×#3862	semidirect
53. C₇	ΓL(1,𝔽₈)×D₁₅	semidirect
56. C₅	D₃×#3862	semidirect
59. C₃	D₅×#3862	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#3862	2
C₇²×D₁₅	3
D₅×#3862	3
D₃×#3862	5
ΓL(1,𝔽₈)×D₁₅	7

Subgroups — D15×#3862 #17984393

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₅×#3862 #17984393