Subgroups — C₂×C₇₉×D₉₉ #44530864

Order 31284.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×D₉₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₉×C₁₁×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃₃×C₇₉	—	3	1	no	maximal
4	C₉×C₁₁×C₇₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃₃×C₇₉	—	3	2	no	—
6	C₂×C₃×C₁₁×C₇₉	D₃	1	1	yes	characteristic
7	C₂×D₁₁×C₇₉	—	9	1	no	Hall
8	C₂×D₉×C₇₉	—	11	1	no	maximal, Hall
9	C₃×C₁₁×C₇₉	C₂×D₃	1	1	yes	characteristic
10	C₂×C₁₁×C₇₉	D₉	1	1	yes	characteristic, complemented
11	D₁₁×C₇₉	—	9	2	no	—
12	C₂×C₉×C₇₉	D₁₁	1	1	yes	characteristic, complemented
13	D₉×C₇₉	—	11	2	no	—
14	C₂×D₃×C₇₉	—	33	1	no	—
15	C₁₁×C₇₉	C₂×D₉	1	1	yes	characteristic, complemented, Hall
16	C₉×C₇₉	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₇₉	D₃₃	1	1	yes	characteristic
18	D₃×C₇₉	—	33	2	no	—
19	C₂×D₉₉	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂²×C₇₉	—	99	1	no	Hall
21	C₃×C₇₉	C₂×D₃₃	1	1	yes	characteristic
22	C₂×C₉×C₁₁	C₂×C₇₉	1	1	yes	characteristic, complemented
23	D₉₉	C₂×C₇₉	1	2	yes	direct product factor
24	C₂×C₇₉	—	99	2	no	—
25	C₂×C₇₉	D₉₉	1	1	yes	characteristic, direct product factor
26	C₂×D₃₃	—	3	1	no	—
27	C₉×C₁₁	C₂²×C₇₉	1	1	yes	characteristic, complemented, Hall
28	C₇₉	C₂×D₉₉	1	1	yes	characteristic, direct product factor, Sylow
29	C₂×C₃×C₁₁	D₃×C₇₉	1	1	yes	characteristic
30	D₃₃	—	3	2	no	—
31	C₂×D₁₁	—	9	1	no	Hall
32	C₂×D₉	—	11	1	no	Hall
33	C₃×C₁₁	C₂×D₃×C₇₉	1	1	yes	characteristic
34	C₂×C₁₁	D₉×C₇₉	1	1	yes	characteristic, complemented
35	D₁₁	—	9	2	no	—
36	C₂×C₉	D₁₁×C₇₉	1	1	yes	characteristic, complemented
37	D₉	—	11	2	no	—
38	C₂×D₃	—	33	1	no	—
39	C₁₁	C₂×D₉×C₇₉	1	1	yes	characteristic, complemented, Sylow
40	C₉	C₂×D₁₁×C₇₉	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	D₃₃×C₇₉	1	1	yes	characteristic
42	D₃	—	33	2	no	—
43	C₂²	—	99	1	no	Sylow
44	C₃	C₂×D₃₃×C₇₉	1	1	yes	characteristic
45	C₂	—	99	2	no	—
46	C₂	C₇₉×D₉₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇₉	D₉₉
commutator, cosocle, hypocenter	C₉×C₁₁	C₂²×C₇₉
Frattini	C₃	C₂×D₃₃×C₇₉
Fitting	C₂×C₉×C₁₁×C₇₉	C₂
socle	C₂×C₃×C₁₁×C₇₉	D₃
LCS	G ▷ C₉×C₁₁
UCS	C₁ ◁ C₂×C₇₉

Complements

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

N	H ≅ G/N	type
1. C₇₉×D₉₉	C₂	direct (N × H)
2. C₂×C₉×C₁₁×C₇₉	C₂	semidirect
4. C₉×C₁₁×C₇₉	C₂²	semidirect
10. C₂×C₁₁×C₇₉	D₉	semidirect
12. C₂×C₉×C₇₉	D₁₁	semidirect
15. C₁₁×C₇₉	C₂×D₉	semidirect
16. C₉×C₇₉	C₂×D₁₁	semidirect
19. C₂×D₉₉	C₇₉	direct (N × H)
22. C₂×C₉×C₁₁	C₂×C₇₉	semidirect
23. D₉₉	C₂×C₇₉	direct (N × H)
25. C₂×C₇₉	D₉₉	direct (N × H)
27. C₉×C₁₁	C₂²×C₇₉	semidirect
28. C₇₉	C₂×D₉₉	direct (N × H)
34. C₂×C₁₁	D₉×C₇₉	semidirect
36. C₂×C₉	D₁₁×C₇₉	semidirect
39. C₁₁	C₂×D₉×C₇₉	semidirect
40. C₉	C₂×D₁₁×C₇₉	semidirect
46. C₂	C₇₉×D₉₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇₉×D₉₉	2
C₂×C₉×C₁₁×C₇₉	2
C₂×D₃₃×C₇₉	3
C₂×D₉×C₇₉	11
C₂×D₉₉	79

Subgroups — C2×C79×D99 #44530864

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₉×D₉₉ #44530864