Subgroups — D₅×D₇₇₉ #29510013

Order 15580.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₈₉₅	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅×C₁₉×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₇₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₁₉×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₇₇₉	—	5	1	no	maximal, Hall
6	C₂×C₁₉×C₄₁	—	5	1	no	—
7	D₇₇₉	—	5	1	no	—
8	D₇₇₉	D₅	1	1	yes	characteristic, direct product factor
9	D₅×D₄₁	—	19	1	no	maximal, Hall
10	C₁₉×C₄₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
11	D₂₀₅	—	19	1	no	—
12	C₅×D₄₁	—	19	1	no	—
13	D₅×C₄₁	D₁₉	1	1	yes	characteristic, complemented
14	D₅×D₁₉	—	41	1	no	maximal, Hall
15	C₅×C₄₁	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
16	D₉₅	—	41	1	no	—
17	C₅×D₁₉	—	41	1	no	—
18	D₅×C₁₉	D₄₁	1	1	yes	characteristic, complemented
19	C₂×D₄₁	—	95	1	no	Hall
20	C₅×C₁₉	C₂×D₄₁	1	1	yes	characteristic, complemented, Hall
21	C₂×C₄₁	—	5	1	no	—
22	D₄₁	—	19	1	no	—
23	D₄₁	—	95	1	no	—
24	C₂×D₁₉	—	205	1	no	Hall
25	C₄₁	D₅×D₁₉	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₁₉	—	5	1	no	—
27	D₁₉	—	41	1	no	—
28	D₁₉	—	205	1	no	—
29	C₂×D₅	—	779	1	no	Hall
30	C₁₉	D₅×D₄₁	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅	—	779	1	no	—
32	D₅	—	779	1	no	—
33	D₅	D₇₇₉	1	1	yes	characteristic, direct product factor
34	C₅	C₂×D₇₇₉	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	3895	1	no	Sylow
36	C₂	—	5	1	no	—
37	C₂	—	779	1	no	—
38	C₂	—	3895	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₉×C₄₁	C₂²
LCS	G ▷ C₅×C₁₉×C₄₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₃₈₉₅	C₂	semidirect
2. D₅×C₁₉×C₄₁	C₂	semidirect
3. C₅×D₇₇₉	C₂	semidirect
4. C₅×C₁₉×C₄₁	C₂²	semidirect
8. D₇₇₉	D₅	direct (N × H)
10. C₁₉×C₄₁	C₂×D₅	semidirect
13. D₅×C₄₁	D₁₉	semidirect
15. C₅×C₄₁	C₂×D₁₉	semidirect
18. D₅×C₁₉	D₄₁	semidirect
20. C₅×C₁₉	C₂×D₄₁	semidirect
25. C₄₁	D₅×D₁₉	semidirect
30. C₁₉	D₅×D₄₁	semidirect
33. D₅	D₇₇₉	direct (N × H)
34. C₅	C₂×D₇₇₉	semidirect

Maximal subgroups

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

subgroup	index
D₃₈₉₅	2
D₅×C₁₉×C₄₁	2
C₅×D₇₇₉	2
C₂×D₇₇₉	5
D₅×D₄₁	19
D₅×D₁₉	41

Subgroups — D5×D779 #29510013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×D₇₇₉ #29510013