Subgroups — D₁₃×D₆₉₇ #49136175

Order 36244.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₉₀₆₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×D₁₃×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×D₆₉₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×C₁₇×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₆₉₇	—	13	1	no	maximal, Hall
6	D₁₃×D₄₁	—	17	1	no	maximal, Hall
7	C₂×C₁₇×C₄₁	—	13	1	no	—
8	D₆₉₇	—	13	1	no	—
9	D₆₉₇	D₁₃	1	1	yes	characteristic, direct product factor
10	D₅₃₃	—	17	1	no	—
11	C₁₃×D₄₁	—	17	1	no	—
12	D₁₃×C₄₁	D₁₇	1	1	yes	characteristic, complemented
13	D₁₃×D₁₇	—	41	1	no	maximal, Hall
14	C₁₇×C₄₁	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
15	C₁₃×C₄₁	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
16	D₂₂₁	—	41	1	no	—
17	C₁₃×D₁₇	—	41	1	no	—
18	C₁₇×D₁₃	D₄₁	1	1	yes	characteristic, complemented
19	C₁₃×C₁₇	C₂×D₄₁	1	1	yes	characteristic, complemented, Hall
20	C₂×D₄₁	—	221	1	no	Hall
21	C₂×C₄₁	—	13	1	no	—
22	D₄₁	—	17	1	no	—
23	D₄₁	—	221	1	no	—
24	C₂×D₁₇	—	533	1	no	Hall
25	C₂×D₁₃	—	697	1	no	Hall
26	C₄₁	D₁₃×D₁₇	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₁₇	—	13	1	no	—
28	D₁₇	—	533	1	no	—
29	D₁₇	—	41	1	no	—
30	C₂×C₁₃	—	697	1	no	—
31	D₁₃	—	697	1	no	—
32	D₁₃	D₆₉₇	1	1	yes	characteristic, direct product factor
33	C₁₇	D₁₃×D₄₁	1	1	yes	characteristic, complemented, Sylow
34	C₁₃	C₂×D₆₉₇	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	9061	1	no	Sylow
36	C₂	—	13	1	no	—
37	C₂	—	9061	1	no	—
38	C₂	—	697	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃×C₁₇×C₄₁	C₂²
LCS	G ▷ C₁₃×C₁₇×C₄₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₉₀₆₁	C₂	semidirect
2. C₁₇×D₁₃×C₄₁	C₂	semidirect
3. C₁₃×D₆₉₇	C₂	semidirect
4. C₁₃×C₁₇×C₄₁	C₂²	semidirect
9. D₆₉₇	D₁₃	direct (N × H)
12. D₁₃×C₄₁	D₁₇	semidirect
14. C₁₇×C₄₁	C₂×D₁₃	semidirect
15. C₁₃×C₄₁	C₂×D₁₇	semidirect
18. C₁₇×D₁₃	D₄₁	semidirect
19. C₁₃×C₁₇	C₂×D₄₁	semidirect
26. C₄₁	D₁₃×D₁₇	semidirect
32. D₁₃	D₆₉₇	direct (N × H)
33. C₁₇	D₁₃×D₄₁	semidirect
34. C₁₃	C₂×D₆₉₇	semidirect

Maximal subgroups

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

subgroup	index
D₉₀₆₁	2
C₁₇×D₁₃×C₄₁	2
C₁₃×D₆₉₇	2
C₂×D₆₉₇	13
D₁₃×D₄₁	17
D₁₃×D₁₇	41

Subgroups — D13×D697 #49136175

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×D₆₉₇ #49136175