Subgroups — C₂×C₉×C₁₉×C₉₇ #45684277

Order 33174.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₉×C₉₇	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₁₉×C₉₇	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₉×C₉₇	C₂×C₃	1	1	yes	characteristic
4	C₂×C₁₉×C₉₇	C₉	1	1	yes	characteristic, direct product factor, Hall
5	C₁₉×C₉₇	C₂×C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₉×C₉₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₉×C₉₇	C₂×C₁₉	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₃×C₉₇	C₃×C₁₉	1	1	yes	characteristic
9	C₂×C₉×C₁₉	C₉₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₉₇	C₂×C₃×C₁₉	1	1	yes	characteristic
11	C₂×C₉₇	C₉×C₁₉	1	1	yes	characteristic, direct product factor, Hall
12	C₉×C₁₉	C₂×C₉₇	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃×C₁₉	C₃×C₉₇	1	1	yes	characteristic
14	C₉₇	C₂×C₉×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
15	C₃×C₁₉	C₂×C₃×C₉₇	1	1	yes	characteristic
16	C₂×C₁₉	C₉×C₉₇	1	1	yes	characteristic, direct product factor, Hall
17	C₁₉	C₂×C₉×C₉₇	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₉	C₁₉×C₉₇	1	1	yes	characteristic, direct product factor, Hall
19	C₉	C₂×C₁₉×C₉₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	C₃×C₁₉×C₉₇	1	1	yes	characteristic
21	C₃	C₂×C₃×C₁₉×C₉₇	1	1	yes	characteristic
22	C₂	C₉×C₁₉×C₉₇	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂×C₃×C₁₉×C₉₇
socle, prime radical	C₂×C₃×C₁₉×C₉₇	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₉×C₁₉×C₉₇	C₂	direct (N × H)
4. C₂×C₁₉×C₉₇	C₉	direct (N × H)
5. C₁₉×C₉₇	C₂×C₉	direct (N × H)
6. C₂×C₉×C₉₇	C₁₉	direct (N × H)
7. C₉×C₉₇	C₂×C₁₉	direct (N × H)
9. C₂×C₉×C₁₉	C₉₇	direct (N × H)
11. C₂×C₉₇	C₉×C₁₉	direct (N × H)
12. C₉×C₁₉	C₂×C₉₇	direct (N × H)
14. C₉₇	C₂×C₉×C₁₉	direct (N × H)
16. C₂×C₁₉	C₉×C₉₇	direct (N × H)
17. C₁₉	C₂×C₉×C₉₇	direct (N × H)
18. C₂×C₉	C₁₉×C₉₇	direct (N × H)
19. C₉	C₂×C₁₉×C₉₇	direct (N × H)
22. C₂	C₉×C₁₉×C₉₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×C₁₉×C₉₇	2
C₂×C₃×C₁₉×C₉₇	3
C₂×C₉×C₉₇	19
C₂×C₉×C₁₉	97

Subgroups — C2×C9×C19×C97 #45684277

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×C₁₉×C₉₇ #45684277