Subgroups — C₅×D₁₃×D₉₇ #38759727

Order 25220.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₂₆₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₁₃×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₃×D₉₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₁₃×C₉₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₃×D₉₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	D₁₂₆₁	C₂×C₅	1	1	yes	characteristic, complemented
7	C₁₃×D₉₇	C₂×C₅	1	1	yes	characteristic, complemented
8	D₁₃×C₉₇	C₂×C₅	1	1	yes	characteristic, complemented
9	C₂×C₅×D₉₇	—	13	1	no	maximal, Hall
10	C₁₃×C₉₇	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅×C₉₇	—	13	1	no	—
12	C₅×D₉₇	—	13	1	no	—
13	C₅×D₉₇	D₁₃	1	1	yes	characteristic, direct product factor
14	C₅×C₉₇	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
15	C₂×D₉₇	—	13	1	no	Hall
16	C₂×C₅×D₁₃	—	97	1	no	maximal, Hall
17	C₂×C₉₇	—	13	1	no	—
18	D₉₇	—	13	1	no	—
19	D₉₇	C₅×D₁₃	1	1	yes	characteristic, direct product factor
20	C₂×C₅×C₁₃	—	97	1	no	—
21	C₅×D₁₃	—	97	1	no	—
22	C₅×D₁₃	D₉₇	1	1	yes	characteristic, direct product factor
23	C₉₇	C₂×C₅×D₁₃	1	1	yes	characteristic, complemented, Sylow
24	C₅×C₁₃	C₂×D₉₇	1	1	yes	characteristic, complemented, Hall
25	C₂×D₁₃	—	97	1	no	Hall
26	C₂×C₁₃	—	97	1	no	—
27	D₁₃	—	97	1	no	—
28	D₁₃	C₅×D₉₇	1	1	yes	characteristic, direct product factor
29	C₂²×C₅	—	1261	1	no	Hall
30	C₁₃	C₂×C₅×D₉₇	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅	—	13	1	no	—
32	C₂×C₅	—	97	1	no	—
33	C₂×C₅	—	1261	1	no	—
34	C₅	D₁₃×D₉₇	1	1	yes	characteristic, direct product factor, Sylow
35	C₂²	—	1261	1	no	Sylow
36	C₂	—	13	1	no	—
37	C₂	—	97	1	no	—
38	C₂	—	1261	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₁₃×D₉₇
commutator, cosocle, hypocenter	C₁₃×C₉₇	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₁₃×C₉₇	C₂²
LCS	G ▷ C₁₃×C₉₇
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₁₂₆₁	C₂	semidirect
2. C₅×D₁₃×C₉₇	C₂	semidirect
3. C₅×C₁₃×D₉₇	C₂	semidirect
4. C₅×C₁₃×C₉₇	C₂²	semidirect
5. D₁₃×D₉₇	C₅	direct (N × H)
6. D₁₂₆₁	C₂×C₅	semidirect
7. C₁₃×D₉₇	C₂×C₅	semidirect
8. D₁₃×C₉₇	C₂×C₅	semidirect
10. C₁₃×C₉₇	C₂²×C₅	semidirect
13. C₅×D₉₇	D₁₃	direct (N × H)
14. C₅×C₉₇	C₂×D₁₃	semidirect
19. D₉₇	C₅×D₁₃	direct (N × H)
22. C₅×D₁₃	D₉₇	direct (N × H)
23. C₉₇	C₂×C₅×D₁₃	semidirect
24. C₅×C₁₃	C₂×D₉₇	semidirect
28. D₁₃	C₅×D₉₇	direct (N × H)
30. C₁₃	C₂×C₅×D₉₇	semidirect
34. C₅	D₁₃×D₉₇	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×D₁₂₆₁	2
C₅×D₁₃×C₉₇	2
C₅×C₁₃×D₉₇	2
D₁₃×D₉₇	5
C₂×C₅×D₉₇	13
C₂×C₅×D₁₃	97

Subgroups — C5×D13×D97 #38759727

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₁₃×D₉₇ #38759727