Subgroups — C₂×C₅×D₁₃₄₃ #41001721

Order 26860.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₃₄₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₁₇×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₇×C₇₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₃₄₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₇×C₇₉	C₂×C₅	1	1	yes	characteristic, complemented
6	D₁₃₄₃	C₂×C₅	1	2	yes	direct product factor
7	C₂×C₅×D₇₉	—	17	1	no	maximal, Hall
8	C₁₇×C₇₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
9	C₂×C₅×C₇₉	D₁₇	1	1	yes	characteristic, complemented
10	C₅×D₇₉	—	17	2	no	—
11	C₅×C₇₉	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
12	C₂×C₅×D₁₇	—	79	1	no	maximal, Hall
13	C₂×D₇₉	—	17	1	no	Hall
14	C₂×C₅×C₁₇	D₇₉	1	1	yes	characteristic, complemented
15	C₅×D₁₇	—	79	2	no	—
16	C₂×C₇₉	C₅×D₁₇	1	1	yes	characteristic, complemented
17	D₇₉	—	17	2	no	—
18	C₅×C₁₇	C₂×D₇₉	1	1	yes	characteristic, complemented, Hall
19	C₇₉	C₂×C₅×D₁₇	1	1	yes	characteristic, complemented, Sylow
20	C₂×D₁₇	—	79	1	no	Hall
21	C₂×C₁₇	C₅×D₇₉	1	1	yes	characteristic, complemented
22	D₁₇	—	79	2	no	—
23	C₂²×C₅	—	1343	1	no	Hall
24	C₁₇	C₂×C₅×D₇₉	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₅	—	1343	2	no	—
26	C₂×C₅	D₁₃₄₃	1	1	yes	characteristic, direct product factor
27	C₅	C₂×D₁₃₄₃	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²	—	1343	1	no	Sylow
29	C₂	—	1343	2	no	—
30	C₂	C₅×D₁₃₄₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	D₁₃₄₃
commutator, cosocle, hypocenter	C₁₇×C₇₉	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₇×C₇₉	C₂
LCS	G ▷ C₁₇×C₇₉
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₁₃₄₃	C₂	direct (N × H)
2. C₂×C₅×C₁₇×C₇₉	C₂	semidirect
3. C₅×C₁₇×C₇₉	C₂²	semidirect
4. C₂×D₁₃₄₃	C₅	direct (N × H)
5. C₂×C₁₇×C₇₉	C₂×C₅	semidirect
6. D₁₃₄₃	C₂×C₅	direct (N × H)
8. C₁₇×C₇₉	C₂²×C₅	semidirect
9. C₂×C₅×C₇₉	D₁₇	semidirect
11. C₅×C₇₉	C₂×D₁₇	semidirect
14. C₂×C₅×C₁₇	D₇₉	semidirect
16. C₂×C₇₉	C₅×D₁₇	semidirect
18. C₅×C₁₇	C₂×D₇₉	semidirect
19. C₇₉	C₂×C₅×D₁₇	semidirect
21. C₂×C₁₇	C₅×D₇₉	semidirect
24. C₁₇	C₂×C₅×D₇₉	semidirect
26. C₂×C₅	D₁₃₄₃	direct (N × H)
27. C₅	C₂×D₁₃₄₃	direct (N × H)
30. C₂	C₅×D₁₃₄₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×D₁₃₄₃	2
C₂×C₅×C₁₇×C₇₉	2
C₂×D₁₃₄₃	5
C₂×C₅×D₇₉	17
C₂×C₅×D₁₇	79

Subgroups — C2×C5×D1343 #41001721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₁₃₄₃ #41001721