Subgroups — C₂×C₄×C₅²×C₉₇ #72197064

Order 19400.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×C₉₇	C₅	1	6	yes	maximal, direct product factor
2	C₂²×C₅²×C₉₇	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅²×C₉₇	C₂	1	2	yes	maximal, direct product factor
4	C₂×C₅²×C₉₇	C₄	1	2	yes	direct product factor
5	C₂×C₅²×C₉₇	C₂²	1	1	yes	characteristic
6	C₅²×C₉₇	C₂×C₄	1	1	yes	characteristic, direct product factor, Hall
7	C₂²×C₅×C₉₇	C₂×C₅	1	6	yes	—
8	C₄×C₅×C₉₇	C₂×C₅	1	12	yes	direct product factor
9	C₂×C₅×C₉₇	C₄×C₅	1	12	yes	direct product factor
10	C₂×C₅×C₉₇	C₂²×C₅	1	6	yes	—
11	C₂×C₄×C₉₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
12	C₅×C₉₇	C₂×C₄×C₅	1	6	yes	direct product factor
13	C₂²×C₉₇	C₂×C₅²	1	1	yes	characteristic
14	C₄×C₉₇	C₂×C₅²	1	2	yes	direct product factor
15	C₂×C₄×C₅²	C₉₇	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₉₇	C₄×C₅²	1	2	yes	direct product factor
17	C₂×C₉₇	C₂²×C₅²	1	1	yes	characteristic
18	C₂²×C₅²	C₂×C₉₇	1	1	yes	characteristic
19	C₄×C₅²	C₂×C₉₇	1	2	yes	direct product factor
20	C₉₇	C₂×C₄×C₅²	1	1	yes	characteristic, direct product factor, Sylow
21	C₂×C₅²	C₄×C₉₇	1	2	yes	direct product factor
22	C₂×C₅²	C₂²×C₉₇	1	1	yes	characteristic
23	C₂×C₄×C₅	C₅×C₉₇	1	6	yes	direct product factor
24	C₅²	C₂×C₄×C₉₇	1	1	yes	characteristic, direct product factor, Sylow
25	C₂²×C₅	C₂×C₅×C₉₇	1	6	yes	—
26	C₄×C₅	C₂×C₅×C₉₇	1	12	yes	direct product factor
27	C₂×C₅	C₄×C₅×C₉₇	1	12	yes	direct product factor
28	C₂×C₅	C₂²×C₅×C₉₇	1	6	yes	—
29	C₂×C₄	C₅²×C₉₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₅	C₂×C₄×C₅×C₉₇	1	6	yes	direct product factor
31	C₂²	C₂×C₅²×C₉₇	1	1	yes	characteristic
32	C₄	C₂×C₅²×C₉₇	1	2	yes	direct product factor
33	C₂	C₄×C₅²×C₉₇	1	2	yes	direct product factor
34	C₂	C₂²×C₅²×C₉₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂²×C₅²×C₉₇
socle, prime radical	C₂²×C₅²×C₉₇	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×C₅×C₉₇	C₅	direct (N × H)
3. C₄×C₅²×C₉₇	C₂	direct (N × H)
4. C₂×C₅²×C₉₇	C₄	direct (N × H)
6. C₅²×C₉₇	C₂×C₄	direct (N × H)
8. C₄×C₅×C₉₇	C₂×C₅	direct (N × H)
9. C₂×C₅×C₉₇	C₄×C₅	direct (N × H)
11. C₂×C₄×C₉₇	C₅²	direct (N × H)
12. C₅×C₉₇	C₂×C₄×C₅	direct (N × H)
14. C₄×C₉₇	C₂×C₅²	direct (N × H)
15. C₂×C₄×C₅²	C₉₇	direct (N × H)
16. C₂×C₉₇	C₄×C₅²	direct (N × H)
19. C₄×C₅²	C₂×C₉₇	direct (N × H)
20. C₉₇	C₂×C₄×C₅²	direct (N × H)
21. C₂×C₅²	C₄×C₉₇	direct (N × H)
23. C₂×C₄×C₅	C₅×C₉₇	direct (N × H)
24. C₅²	C₂×C₄×C₉₇	direct (N × H)
26. C₄×C₅	C₂×C₅×C₉₇	direct (N × H)
27. C₂×C₅	C₄×C₅×C₉₇	direct (N × H)
29. C₂×C₄	C₅²×C₉₇	direct (N × H)
30. C₅	C₂×C₄×C₅×C₉₇	direct (N × H)
32. C₄	C₂×C₅²×C₉₇	direct (N × H)
33. C₂	C₄×C₅²×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
C₂×C₄×C₅×C₉₇	5
C₂²×C₅²×C₉₇	2
C₄×C₅²×C₉₇	2
C₂×C₄×C₅²	97

Subgroups — C2×C4×C52×C97 #72197064

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₅²×C₉₇ #72197064