Subgroups — D₁₉×D₂₈₇ #36345577

Order 21812.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₄₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×D₂₈₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×D₁₉×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×C₁₉×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₉×D₄₁	—	7	1	no	maximal, Hall
6	D₇₇₉	—	7	1	no	—
7	C₁₉×D₄₁	—	7	1	no	—
8	D₁₉×C₄₁	D₇	1	1	yes	characteristic, complemented
9	C₂×D₂₈₇	—	19	1	no	maximal, Hall
10	C₁₉×C₄₁	C₂×D₇	1	1	yes	characteristic, complemented, Hall
11	C₂×C₇×C₄₁	—	19	1	no	—
12	D₂₈₇	—	19	1	no	—
13	D₂₈₇	D₁₉	1	1	yes	characteristic, direct product factor
14	D₇×D₁₉	—	41	1	no	maximal, Hall
15	C₇×C₄₁	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
16	D₁₃₃	—	41	1	no	—
17	C₇×D₁₉	D₄₁	1	1	yes	characteristic, complemented
18	D₇×C₁₉	—	41	1	no	—
19	C₂×D₄₁	—	133	1	no	Hall
20	C₇×C₁₉	C₂×D₄₁	1	1	yes	characteristic, complemented, Hall
21	C₂×C₄₁	—	19	1	no	—
22	D₄₁	—	7	1	no	—
23	D₄₁	—	133	1	no	—
24	C₂×D₁₉	—	287	1	no	Hall
25	C₄₁	D₇×D₁₉	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₁₉	—	287	1	no	—
27	D₁₉	—	287	1	no	—
28	D₁₉	D₂₈₇	1	1	yes	characteristic, direct product factor
29	C₂×D₇	—	779	1	no	Hall
30	C₁₉	C₂×D₂₈₇	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₇	—	19	1	no	—
32	D₇	—	779	1	no	—
33	D₇	—	41	1	no	—
34	C₇	D₁₉×D₄₁	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	5453	1	no	Sylow
36	C₂	—	19	1	no	—
37	C₂	—	287	1	no	—
38	C₂	—	5453	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₉×C₄₁	C₂²
LCS	G ▷ C₇×C₁₉×C₄₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₅₄₅₃	C₂	semidirect
2. C₁₉×D₂₈₇	C₂	semidirect
3. C₇×D₁₉×C₄₁	C₂	semidirect
4. C₇×C₁₉×C₄₁	C₂²	semidirect
8. D₁₉×C₄₁	D₇	semidirect
10. C₁₉×C₄₁	C₂×D₇	semidirect
13. D₂₈₇	D₁₉	direct (N × H)
15. C₇×C₄₁	C₂×D₁₉	semidirect
17. C₇×D₁₉	D₄₁	semidirect
20. C₇×C₁₉	C₂×D₄₁	semidirect
25. C₄₁	D₇×D₁₉	semidirect
28. D₁₉	D₂₈₇	direct (N × H)
30. C₁₉	C₂×D₂₈₇	semidirect
34. C₇	D₁₉×D₄₁	semidirect

Maximal subgroups

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

subgroup	index
D₅₄₅₃	2
C₁₉×D₂₈₇	2
C₇×D₁₉×C₄₁	2
D₁₉×D₄₁	7
C₂×D₂₈₇	19
D₇×D₁₉	41

Subgroups — D19×D287 #36345577

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₉×D₂₈₇ #36345577