Subgroups — D₅×D₁₃×C₉₇ #38759752

Order 25220.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉₇×D₆₅	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅×C₁₃×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₁₃×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₁₃×C₉₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₁₃×C₉₇	—	5	1	no	maximal, Hall
6	C₂×C₁₃×C₉₇	—	5	1	no	—
7	D₁₃×C₉₇	—	5	1	no	—
8	D₁₃×C₉₇	D₅	1	1	yes	characteristic, direct product factor
9	C₂×D₅×C₉₇	—	13	1	no	maximal, Hall
10	C₁₃×C₉₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅×C₉₇	—	13	1	no	—
12	D₅×C₉₇	—	13	1	no	—
13	D₅×C₉₇	D₁₃	1	1	yes	characteristic, direct product factor
14	C₅×C₉₇	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
15	C₂²×C₉₇	—	65	1	no	Hall
16	D₅×D₁₃	C₉₇	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₉₇	—	5	1	no	—
18	C₂×C₉₇	—	13	1	no	—
19	C₂×C₉₇	—	65	1	no	—
20	D₆₅	C₂×C₉₇	1	1	yes	characteristic, complemented
21	C₅×D₁₃	C₂×C₉₇	1	1	yes	characteristic, complemented
22	D₅×C₁₃	C₂×C₉₇	1	1	yes	characteristic, complemented
23	C₉₇	D₅×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
24	C₅×C₁₃	C₂²×C₉₇	1	1	yes	characteristic, complemented, Hall
25	C₂×D₁₃	—	5	1	no	Hall
26	C₂×C₁₃	—	5	1	no	—
27	D₁₃	—	5	1	no	—
28	D₁₃	D₅×C₉₇	1	1	yes	characteristic, direct product factor
29	C₂×D₅	—	13	1	no	Hall
30	C₁₃	C₂×D₅×C₉₇	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅	—	13	1	no	—
32	D₅	—	13	1	no	—
33	D₅	D₁₃×C₉₇	1	1	yes	characteristic, direct product factor
34	C₅	C₂×D₁₃×C₉₇	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	65	1	no	Sylow
36	C₂	—	5	1	no	—
37	C₂	—	13	1	no	—
38	C₂	—	65	1	no	—

	subgroup	G/H
center, hypercenter	C₉₇	D₅×D₁₃
commutator, cosocle, hypocenter	C₅×C₁₃	C₂²×C₉₇
Frattini	C₁	G
Fitting, socle	C₅×C₁₃×C₉₇	C₂²
LCS	G ▷ C₅×C₁₃
UCS	C₁ ◁ C₉₇

Complements

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

N	H ≅ G/N	type
1. C₉₇×D₆₅	C₂	semidirect
2. D₅×C₁₃×C₉₇	C₂	semidirect
3. C₅×D₁₃×C₉₇	C₂	semidirect
4. C₅×C₁₃×C₉₇	C₂²	semidirect
8. D₁₃×C₉₇	D₅	direct (N × H)
10. C₁₃×C₉₇	C₂×D₅	semidirect
13. D₅×C₉₇	D₁₃	direct (N × H)
14. C₅×C₉₇	C₂×D₁₃	semidirect
16. D₅×D₁₃	C₉₇	direct (N × H)
20. D₆₅	C₂×C₉₇	semidirect
21. C₅×D₁₃	C₂×C₉₇	semidirect
22. D₅×C₁₃	C₂×C₉₇	semidirect
23. C₉₇	D₅×D₁₃	direct (N × H)
24. C₅×C₁₃	C₂²×C₉₇	semidirect
28. D₁₃	D₅×C₉₇	direct (N × H)
30. C₁₃	C₂×D₅×C₉₇	semidirect
33. D₅	D₁₃×C₉₇	direct (N × H)
34. C₅	C₂×D₁₃×C₉₇	semidirect

Maximal subgroups

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

subgroup	index
C₉₇×D₆₅	2
D₅×C₁₃×C₉₇	2
C₅×D₁₃×C₉₇	2
C₂×D₁₃×C₉₇	5
C₂×D₅×C₉₇	13
D₅×D₁₃	97

Subgroups — D5×D13×C97 #38759752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×D₁₃×C₉₇ #38759752