Subgroups — D₇×D₁₁₁₅ #44530243

Order 31220.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₈₀₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₁₁₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₇×C₂₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₇×C₂₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₇×D₂₂₃	—	5	1	no	maximal, Hall
6	C₂×D₁₁₁₅	—	7	1	no	maximal, Hall
7	D₁₅₆₁	—	5	1	no	—
8	C₇×D₂₂₃	—	5	1	no	—
9	D₇×C₂₂₃	D₅	1	1	yes	characteristic, complemented
10	C₂×C₅×C₂₂₃	—	7	1	no	—
11	D₁₁₁₅	—	7	1	no	—
12	D₁₁₁₅	D₇	1	1	yes	characteristic, direct product factor
13	C₇×C₂₂₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
14	C₅×C₂₂₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
15	C₂×D₂₂₃	—	35	1	no	Hall
16	C₂×C₂₂₃	—	7	1	no	—
17	D₂₂₃	—	5	1	no	—
18	D₂₂₃	—	35	1	no	—
19	C₂₂₃	D₅×D₇	1	1	yes	characteristic, complemented, Sylow
20	D₅×D₇	—	223	1	no	maximal, Hall
21	D₃₅	—	223	1	no	—
22	C₅×D₇	D₂₂₃	1	1	yes	characteristic, complemented
23	C₇×D₅	—	223	1	no	—
24	C₅×C₇	C₂×D₂₂₃	1	1	yes	characteristic, complemented, Hall
25	C₂×D₇	—	1115	1	no	Hall
26	C₂×D₅	—	1561	1	no	Hall
27	C₂×C₇	—	1115	1	no	—
28	D₇	—	1115	1	no	—
29	D₇	D₁₁₁₅	1	1	yes	characteristic, direct product factor
30	C₂×C₅	—	7	1	no	—
31	D₅	—	1561	1	no	—
32	D₅	—	223	1	no	—
33	C₇	C₂×D₁₁₁₅	1	1	yes	characteristic, complemented, Sylow
34	C₅	D₇×D₂₂₃	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	7805	1	no	Sylow
36	C₂	—	7	1	no	—
37	C₂	—	1115	1	no	—
38	C₂	—	7805	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₇×C₂₂₃	C₂²
LCS	G ▷ C₅×C₇×C₂₂₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₇₈₀₅	C₂	semidirect
2. C₇×D₁₁₁₅	C₂	semidirect
3. C₅×D₇×C₂₂₃	C₂	semidirect
4. C₅×C₇×C₂₂₃	C₂²	semidirect
9. D₇×C₂₂₃	D₅	semidirect
12. D₁₁₁₅	D₇	direct (N × H)
13. C₇×C₂₂₃	C₂×D₅	semidirect
14. C₅×C₂₂₃	C₂×D₇	semidirect
19. C₂₂₃	D₅×D₇	semidirect
22. C₅×D₇	D₂₂₃	semidirect
24. C₅×C₇	C₂×D₂₂₃	semidirect
29. D₇	D₁₁₁₅	direct (N × H)
33. C₇	C₂×D₁₁₁₅	semidirect
34. C₅	D₇×D₂₂₃	semidirect

Maximal subgroups

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

subgroup	index
D₇₈₀₅	2
C₇×D₁₁₁₅	2
C₅×D₇×C₂₂₃	2
D₇×D₂₂₃	5
C₂×D₁₁₁₅	7
D₅×D₇	223

Subgroups — D7×D1115 #44530243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×D₁₁₁₅ #44530243