Subgroups — C₂×C₇×D₁₂₁₉ #46802434

Order 34132.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₁₂₁₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₂₃×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₂₃×C₅₃	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₂₁₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₂₃×C₅₃	C₂×C₇	1	1	yes	characteristic, complemented
6	D₁₂₁₉	C₂×C₇	1	2	yes	direct product factor
7	C₂×C₇×D₅₃	—	23	1	no	maximal, Hall
8	C₂₃×C₅₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
9	C₂×C₇×C₅₃	D₂₃	1	1	yes	characteristic, complemented
10	C₇×D₅₃	—	23	2	no	—
11	C₂×C₇×D₂₃	—	53	1	no	maximal, Hall
12	C₇×C₅₃	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₇×C₂₃	D₅₃	1	1	yes	characteristic, complemented
14	C₇×D₂₃	—	53	2	no	—
15	C₂×D₅₃	—	23	1	no	Hall
16	C₇×C₂₃	C₂×D₅₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₅₃	C₇×D₂₃	1	1	yes	characteristic, complemented
18	D₅₃	—	23	2	no	—
19	C₂×D₂₃	—	53	1	no	Hall
20	C₅₃	C₂×C₇×D₂₃	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₂₃	C₇×D₅₃	1	1	yes	characteristic, complemented
22	D₂₃	—	53	2	no	—
23	C₂²×C₇	—	1219	1	no	Hall
24	C₂₃	C₂×C₇×D₅₃	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₇	—	1219	2	no	—
26	C₂×C₇	D₁₂₁₉	1	1	yes	characteristic, direct product factor
27	C₇	C₂×D₁₂₁₉	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²	—	1219	1	no	Sylow
29	C₂	—	1219	2	no	—
30	C₂	C₇×D₁₂₁₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇	D₁₂₁₉
commutator, cosocle, hypocenter	C₂₃×C₅₃	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₂₃×C₅₃	C₂
LCS	G ▷ C₂₃×C₅₃
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
1. C₇×D₁₂₁₉	C₂	direct (N × H)
2. C₂×C₇×C₂₃×C₅₃	C₂	semidirect
3. C₇×C₂₃×C₅₃	C₂²	semidirect
4. C₂×D₁₂₁₉	C₇	direct (N × H)
5. C₂×C₂₃×C₅₃	C₂×C₇	semidirect
6. D₁₂₁₉	C₂×C₇	direct (N × H)
8. C₂₃×C₅₃	C₂²×C₇	semidirect
9. C₂×C₇×C₅₃	D₂₃	semidirect
12. C₇×C₅₃	C₂×D₂₃	semidirect
13. C₂×C₇×C₂₃	D₅₃	semidirect
16. C₇×C₂₃	C₂×D₅₃	semidirect
17. C₂×C₅₃	C₇×D₂₃	semidirect
20. C₅₃	C₂×C₇×D₂₃	semidirect
21. C₂×C₂₃	C₇×D₅₃	semidirect
24. C₂₃	C₂×C₇×D₅₃	semidirect
26. C₂×C₇	D₁₂₁₉	direct (N × H)
27. C₇	C₂×D₁₂₁₉	direct (N × H)
30. C₂	C₇×D₁₂₁₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×D₁₂₁₉	2
C₂×C₇×C₂₃×C₅₃	2
C₂×D₁₂₁₉	7
C₂×C₇×D₅₃	23
C₂×C₇×D₂₃	53

Subgroups — C2×C7×D1219 #46802434

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×D₁₂₁₉ #46802434