Subgroups — C₂×C₄×C₅²×C₄₇ #72188162

Order 9400.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅²×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅²×C₄₇	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅²×C₄₇	C₄	1	2	yes	direct product factor
4	C₂×C₅²×C₄₇	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₅×C₄₇	C₅	1	6	yes	maximal, direct product factor
6	C₅²×C₄₇	C₂×C₄	1	1	yes	characteristic, direct product factor, Hall
7	C₂²×C₅×C₄₇	C₂×C₅	1	6	yes	—
8	C₄×C₅×C₄₇	C₂×C₅	1	12	yes	direct product factor
9	C₂×C₅×C₄₇	C₄×C₅	1	12	yes	direct product factor
10	C₂×C₅×C₄₇	C₂²×C₅	1	6	yes	—
11	C₂×C₄×C₄₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
12	C₅×C₄₇	C₂×C₄×C₅	1	6	yes	direct product factor
13	C₂×C₄×C₅²	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂²×C₄₇	C₂×C₅²	1	1	yes	characteristic
15	C₄×C₄₇	C₂×C₅²	1	2	yes	direct product factor
16	C₂²×C₅²	C₂×C₄₇	1	1	yes	characteristic
17	C₄×C₅²	C₂×C₄₇	1	2	yes	direct product factor
18	C₂×C₄₇	C₄×C₅²	1	2	yes	direct product factor
19	C₂×C₄₇	C₂²×C₅²	1	1	yes	characteristic
20	C₂×C₅²	C₄×C₄₇	1	2	yes	direct product factor
21	C₂×C₅²	C₂²×C₄₇	1	1	yes	characteristic
22	C₄₇	C₂×C₄×C₅²	1	1	yes	characteristic, direct product factor, Sylow
23	C₂×C₄×C₅	C₅×C₄₇	1	6	yes	direct product factor
24	C₅²	C₂×C₄×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
25	C₂²×C₅	C₂×C₅×C₄₇	1	6	yes	—
26	C₄×C₅	C₂×C₅×C₄₇	1	12	yes	direct product factor
27	C₂×C₅	C₄×C₅×C₄₇	1	12	yes	direct product factor
28	C₂×C₅	C₂²×C₅×C₄₇	1	6	yes	—
29	C₂×C₄	C₅²×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₅	C₂×C₄×C₅×C₄₇	1	6	yes	direct product factor
31	C₂²	C₂×C₅²×C₄₇	1	1	yes	characteristic
32	C₄	C₂×C₅²×C₄₇	1	2	yes	direct product factor
33	C₂	C₄×C₅²×C₄₇	1	2	yes	direct product factor
34	C₂	C₂²×C₅²×C₄₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂²×C₅²×C₄₇
socle, prime radical	C₂²×C₅²×C₄₇	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₅²×C₄₇	C₂	direct (N × H)
3. C₂×C₅²×C₄₇	C₄	direct (N × H)
5. C₂×C₄×C₅×C₄₇	C₅	direct (N × H)
6. C₅²×C₄₇	C₂×C₄	direct (N × H)
8. C₄×C₅×C₄₇	C₂×C₅	direct (N × H)
9. C₂×C₅×C₄₇	C₄×C₅	direct (N × H)
11. C₂×C₄×C₄₇	C₅²	direct (N × H)
12. C₅×C₄₇	C₂×C₄×C₅	direct (N × H)
13. C₂×C₄×C₅²	C₄₇	direct (N × H)
15. C₄×C₄₇	C₂×C₅²	direct (N × H)
17. C₄×C₅²	C₂×C₄₇	direct (N × H)
18. C₂×C₄₇	C₄×C₅²	direct (N × H)
20. C₂×C₅²	C₄×C₄₇	direct (N × H)
22. C₄₇	C₂×C₄×C₅²	direct (N × H)
23. C₂×C₄×C₅	C₅×C₄₇	direct (N × H)
24. C₅²	C₂×C₄×C₄₇	direct (N × H)
26. C₄×C₅	C₂×C₅×C₄₇	direct (N × H)
27. C₂×C₅	C₄×C₅×C₄₇	direct (N × H)
29. C₂×C₄	C₅²×C₄₇	direct (N × H)
30. C₅	C₂×C₄×C₅×C₄₇	direct (N × H)
32. C₄	C₂×C₅²×C₄₇	direct (N × H)
33. C₂	C₄×C₅²×C₄₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅²×C₄₇	2
C₄×C₅²×C₄₇	2
C₂×C₄×C₅×C₄₇	5
C₂×C₄×C₅²	47

Subgroups — C2×C4×C52×C47 #72188162

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₅²×C₄₇ #72188162