Subgroups — C₄×C₅³×C₄₉ #72201760

Order 24500.

576 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅³×C₄₉	C₂	1	1	yes	maximal, characteristic
2	C₅³×C₄₉	C₄	1	1	yes	characteristic, direct product factor, Hall
3	C₄×C₅³×C₇	C₇	1	1	yes	maximal, characteristic
4	C₄×C₅²×C₄₉	C₅	1	31	yes	maximal, direct product factor
5	C₂×C₅²×C₄₉	C₂×C₅	1	31	yes	—
6	C₂×C₅³×C₇	C₂×C₇	1	1	yes	characteristic
7	C₅²×C₄₉	C₄×C₅	1	31	yes	direct product factor
8	C₄×C₅×C₄₉	C₅²	1	31	yes	direct product factor
9	C₅³×C₇	C₄×C₇	1	1	yes	characteristic
10	C₄×C₅²×C₇	C₅×C₇	1	31	yes	—
11	C₄×C₅³	C₄₉	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₅×C₄₉	C₂×C₅²	1	31	yes	—
13	C₂×C₅²×C₇	C₂×C₅×C₇	1	31	yes	—
14	C₂×C₅³	C₂×C₄₉	1	1	yes	characteristic
15	C₅×C₄₉	C₄×C₅²	1	31	yes	direct product factor
16	C₄×C₄₉	C₅³	1	1	yes	characteristic, direct product factor, Hall
17	C₅²×C₇	C₄×C₅×C₇	1	31	yes	—
18	C₄×C₅×C₇	C₅²×C₇	1	31	yes	—
19	C₅³	C₄×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
20	C₄×C₅²	C₅×C₄₉	1	31	yes	direct product factor
21	C₂×C₄₉	C₂×C₅³	1	1	yes	characteristic
22	C₂×C₅×C₇	C₂×C₅²×C₇	1	31	yes	—
23	C₂×C₅²	C₂×C₅×C₄₉	1	31	yes	—
24	C₄₉	C₄×C₅³	1	1	yes	characteristic, direct product factor, Sylow
25	C₅×C₇	C₄×C₅²×C₇	1	31	yes	—
26	C₄×C₇	C₅³×C₇	1	1	yes	characteristic
27	C₅²	C₄×C₅×C₄₉	1	31	yes	direct product factor
28	C₄×C₅	C₅²×C₄₉	1	31	yes	direct product factor
29	C₂×C₇	C₂×C₅³×C₇	1	1	yes	characteristic
30	C₂×C₅	C₂×C₅²×C₄₉	1	31	yes	—
31	C₇	C₄×C₅³×C₇	1	1	yes	characteristic
32	C₅	C₄×C₅²×C₄₉	1	31	yes	direct product factor
33	C₄	C₅³×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₂×C₅³×C₄₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₇	C₂×C₅³×C₇
socle, prime radical	C₂×C₅³×C₇	C₂×C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅³×C₄₉	C₄	direct (N × H)
4. C₄×C₅²×C₄₉	C₅	direct (N × H)
7. C₅²×C₄₉	C₄×C₅	direct (N × H)
8. C₄×C₅×C₄₉	C₅²	direct (N × H)
11. C₄×C₅³	C₄₉	direct (N × H)
15. C₅×C₄₉	C₄×C₅²	direct (N × H)
16. C₄×C₄₉	C₅³	direct (N × H)
19. C₅³	C₄×C₄₉	direct (N × H)
20. C₄×C₅²	C₅×C₄₉	direct (N × H)
24. C₄₉	C₄×C₅³	direct (N × H)
27. C₅²	C₄×C₅×C₄₉	direct (N × H)
28. C₄×C₅	C₅²×C₄₉	direct (N × H)
32. C₅	C₄×C₅²×C₄₉	direct (N × H)
33. C₄	C₅³×C₄₉	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×C₅³×C₄₉	2
C₄×C₅³×C₇	7
C₄×C₅²×C₄₉	5

Subgroups — C4×C53×C49 #72201760

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅³×C₄₉ #72201760