Subgroups — D₇×D₉₅₉ #41001660

Order 26852.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₇×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₉₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇⋊D₉₅₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇²×C₁₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₉₅₉	—	7	1	no	maximal
6	D₇×D₁₃₇	—	7	1	no	maximal
7	C₂×C₇×C₁₃₇	—	7	1	no	—
8	D₉₅₉	—	7	1	no	—
9	D₉₅₉	—	7	1	no	—
10	D₉₅₉	—	14	3	no	—
11	D₉₅₉	D₇	1	1	yes	characteristic, direct product factor
12	C₇×D₁₃₇	—	7	1	no	—
13	D₇×C₁₃₇	D₇	1	1	yes	characteristic, complemented
14	C₇×C₁₃₇	—	2	3	no	—
15	C₇×C₁₃₇	C₂×D₇	1	1	yes	characteristic, complemented
16	C₇×C₁₃₇	C₂×D₇	1	1	yes	characteristic, complemented
17	C₂×D₁₃₇	—	49	1	no	Hall
18	C₂×C₁₃₇	—	7	1	no	—
19	D₁₃₇	—	7	1	no	—
20	D₁₃₇	—	49	1	no	—
21	D₇²	—	137	1	no	maximal, Hall
22	C₁₃₇	D₇²	1	1	yes	characteristic, complemented, Sylow
23	C₇⋊D₇	—	137	1	no	—
24	C₇×D₇	—	137	1	no	—
25	C₇×D₇	D₁₃₇	1	1	yes	characteristic, complemented
26	C₇²	C₂×D₁₃₇	1	1	yes	characteristic, complemented, Sylow
27	C₂×D₇	—	959	1	no	—
28	C₂×D₇	—	959	1	no	—
29	C₂×C₇	—	7	1	no	—
30	C₂×C₇	—	959	1	no	—
31	D₇	—	1918	3	no	—
32	D₇	—	137	1	no	—
33	D₇	—	959	1	no	—
34	D₇	—	959	1	no	—
35	D₇	D₉₅₉	1	1	yes	characteristic, direct product factor
36	C₇	—	2	3	no	—
37	C₇	D₇×D₁₃₇	1	1	yes	characteristic, complemented
38	C₇	C₂×D₉₅₉	1	1	yes	characteristic, complemented
39	C₂²	—	6713	1	no	Sylow
40	C₂	—	7	1	no	—
41	C₂	—	6713	1	no	—
42	C₂	—	959	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇²×C₁₃₇	C₂²
LCS	G ▷ C₇²×C₁₃₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₇×D₇×C₁₃₇	C₂	semidirect
2. C₇×D₉₅₉	C₂	semidirect
3. C₇⋊D₉₅₉	C₂	semidirect
4. C₇²×C₁₃₇	C₂²	semidirect
11. D₉₅₉	D₇	direct (N × H)
13. D₇×C₁₃₇	D₇	semidirect
15. C₇×C₁₃₇	C₂×D₇	semidirect
16. C₇×C₁₃₇	C₂×D₇	semidirect
22. C₁₃₇	D₇²	semidirect
25. C₇×D₇	D₁₃₇	semidirect
26. C₇²	C₂×D₁₃₇	semidirect
35. D₇	D₉₅₉	direct (N × H)
37. C₇	D₇×D₁₃₇	semidirect
38. C₇	C₂×D₉₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₇×D₇×C₁₃₇	2
C₇×D₉₅₉	2
C₇⋊D₉₅₉	2
C₂×D₉₅₉	7
D₇×D₁₃₇	7
D₇²	137

Subgroups — D7×D959 #41001660

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×D₉₅₉ #41001660