Subgroups — C₂×C₇₁×D₉₅ #41008708

Order 26980.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×D₉₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₁₉×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₉×C₇₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₉×C₇₁	—	5	1	no	maximal, Hall
5	C₂×C₁₉×C₇₁	D₅	1	1	yes	characteristic, complemented
6	D₁₉×C₇₁	—	5	2	no	—
7	C₂×D₅×C₇₁	—	19	1	no	maximal, Hall
8	C₁₉×C₇₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
9	C₂×C₅×C₇₁	D₁₉	1	1	yes	characteristic, complemented
10	D₅×C₇₁	—	19	2	no	—
11	C₂×D₉₅	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₅×C₇₁	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
13	C₂²×C₇₁	—	95	1	no	Hall
14	C₂×C₅×C₁₉	C₂×C₇₁	1	1	yes	characteristic, complemented
15	D₉₅	C₂×C₇₁	1	2	yes	direct product factor
16	C₂×C₇₁	—	95	2	no	—
17	C₂×C₇₁	D₉₅	1	1	yes	characteristic, direct product factor
18	C₅×C₁₉	C₂²×C₇₁	1	1	yes	characteristic, complemented, Hall
19	C₂×D₁₉	—	5	1	no	Hall
20	C₇₁	C₂×D₉₅	1	1	yes	characteristic, direct product factor, Sylow
21	C₂×C₁₉	D₅×C₇₁	1	1	yes	characteristic, complemented
22	D₁₉	—	5	2	no	—
23	C₂×D₅	—	19	1	no	Hall
24	C₁₉	C₂×D₅×C₇₁	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₅	D₁₉×C₇₁	1	1	yes	characteristic, complemented
26	D₅	—	19	2	no	—
27	C₅	C₂×D₁₉×C₇₁	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	95	1	no	Sylow
29	C₂	—	95	2	no	—
30	C₂	C₇₁×D₉₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇₁	D₉₅
commutator, cosocle, hypocenter	C₅×C₁₉	C₂²×C₇₁
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₉×C₇₁	C₂
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₂×C₇₁

Complements

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

N	H ≅ G/N	type
1. C₇₁×D₉₅	C₂	direct (N × H)
2. C₂×C₅×C₁₉×C₇₁	C₂	semidirect
3. C₅×C₁₉×C₇₁	C₂²	semidirect
5. C₂×C₁₉×C₇₁	D₅	semidirect
8. C₁₉×C₇₁	C₂×D₅	semidirect
9. C₂×C₅×C₇₁	D₁₉	semidirect
11. C₂×D₉₅	C₇₁	direct (N × H)
12. C₅×C₇₁	C₂×D₁₉	semidirect
14. C₂×C₅×C₁₉	C₂×C₇₁	semidirect
15. D₉₅	C₂×C₇₁	direct (N × H)
17. C₂×C₇₁	D₉₅	direct (N × H)
18. C₅×C₁₉	C₂²×C₇₁	semidirect
20. C₇₁	C₂×D₉₅	direct (N × H)
21. C₂×C₁₉	D₅×C₇₁	semidirect
24. C₁₉	C₂×D₅×C₇₁	semidirect
25. C₂×C₅	D₁₉×C₇₁	semidirect
27. C₅	C₂×D₁₉×C₇₁	semidirect
30. C₂	C₇₁×D₉₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇₁×D₉₅	2
C₂×C₅×C₁₉×C₇₁	2
C₂×D₁₉×C₇₁	5
C₂×D₅×C₇₁	19
C₂×D₉₅	71

Subgroups — C2×C71×D95 #41008708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₁×D₉₅ #41008708