Subgroups — C₂×C₅×C₂₅×C₄₉ #72190604

Order 12250.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂₅×C₄₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅²×C₄₉	C₅	1	1	yes	maximal, characteristic
3	C₂×C₂₅×C₄₉	C₅	1	5	yes	maximal, direct product factor
4	C₂×C₅×C₇×C₂₅	C₇	1	1	yes	maximal, characteristic
5	C₅²×C₄₉	C₂×C₅	1	1	yes	characteristic
6	C₂₅×C₄₉	C₂×C₅	1	5	yes	direct product factor
7	C₅×C₇×C₂₅	C₂×C₇	1	1	yes	characteristic
8	C₂×C₅×C₄₉	C₂₅	1	5	yes	direct product factor
9	C₂×C₅×C₄₉	C₅²	1	1	yes	characteristic
10	C₂×C₅²×C₇	C₅×C₇	1	1	yes	characteristic
11	C₂×C₇×C₂₅	C₅×C₇	1	5	yes	—
12	C₂×C₅×C₂₅	C₄₉	1	1	yes	characteristic, direct product factor, Hall
13	C₅×C₄₉	C₂×C₂₅	1	5	yes	direct product factor
14	C₅×C₄₉	C₂×C₅²	1	1	yes	characteristic
15	C₅²×C₇	C₂×C₅×C₇	1	1	yes	characteristic
16	C₇×C₂₅	C₂×C₅×C₇	1	5	yes	—
17	C₅×C₂₅	C₂×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₄₉	C₅×C₂₅	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₅×C₇	C₇×C₂₅	1	5	yes	—
20	C₂×C₅×C₇	C₅²×C₇	1	1	yes	characteristic
21	C₂×C₅²	C₅×C₄₉	1	1	yes	characteristic
22	C₂×C₂₅	C₅×C₄₉	1	5	yes	direct product factor
23	C₄₉	C₂×C₅×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
24	C₅×C₇	C₂×C₇×C₂₅	1	5	yes	—
25	C₅×C₇	C₂×C₅²×C₇	1	1	yes	characteristic
26	C₅²	C₂×C₅×C₄₉	1	1	yes	characteristic
27	C₂₅	C₂×C₅×C₄₉	1	5	yes	direct product factor
28	C₂×C₇	C₅×C₇×C₂₅	1	1	yes	characteristic
29	C₂×C₅	C₂₅×C₄₉	1	5	yes	direct product factor
30	C₂×C₅	C₅²×C₄₉	1	1	yes	characteristic
31	C₇	C₂×C₅×C₇×C₂₅	1	1	yes	characteristic
32	C₅	C₂×C₂₅×C₄₉	1	5	yes	direct product factor
33	C₅	C₂×C₅²×C₄₉	1	1	yes	characteristic
34	C₂	C₅×C₂₅×C₄₉	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅×C₇	C₂×C₅²×C₇
socle, prime radical	C₂×C₅²×C₇	C₅×C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×C₂₅×C₄₉	C₂	direct (N × H)
3. C₂×C₂₅×C₄₉	C₅	direct (N × H)
6. C₂₅×C₄₉	C₂×C₅	direct (N × H)
8. C₂×C₅×C₄₉	C₂₅	direct (N × H)
12. C₂×C₅×C₂₅	C₄₉	direct (N × H)
13. C₅×C₄₉	C₂×C₂₅	direct (N × H)
17. C₅×C₂₅	C₂×C₄₉	direct (N × H)
18. C₂×C₄₉	C₅×C₂₅	direct (N × H)
22. C₂×C₂₅	C₅×C₄₉	direct (N × H)
23. C₄₉	C₂×C₅×C₂₅	direct (N × H)
27. C₂₅	C₂×C₅×C₄₉	direct (N × H)
29. C₂×C₅	C₂₅×C₄₉	direct (N × H)
32. C₅	C₂×C₂₅×C₄₉	direct (N × H)
34. C₂	C₅×C₂₅×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
C₅×C₂₅×C₄₉	2
C₂×C₅²×C₄₉	5
C₂×C₂₅×C₄₉	5
C₂×C₅×C₇×C₂₅	7

Subgroups — C2×C5×C25×C49 #72190604

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₂₅×C₄₉ #72190604