Finite Group Databasebeta

← C₇²×C₁₃×C₄₉ #44530133

Subgroups — C₇²×C₁₃×C₄₉ #44530133

Order 31213.

444 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇³×C₁₃	C₇	1	1	yes	maximal, characteristic
2	C₇×C₁₃×C₄₉	C₇	1	56	yes	maximal, direct product factor
3	C₇²×C₄₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₇²×C₁₃	C₄₉	1	49	yes	direct product factor
5	C₇²×C₁₃	C₇²	1	8	yes	—
6	C₁₃×C₄₉	C₇²	1	49	yes	direct product factor
7	C₇³	C₇×C₁₃	1	1	yes	characteristic
8	C₇×C₄₉	C₇×C₁₃	1	56	yes	direct product factor
9	C₇×C₁₃	C₇×C₄₉	1	56	yes	direct product factor
10	C₇×C₁₃	C₇³	1	1	yes	characteristic
11	C₇²	C₁₃×C₄₉	1	49	yes	direct product factor
12	C₇²	C₇²×C₁₃	1	8	yes	—
13	C₄₉	C₇²×C₁₃	1	49	yes	direct product factor
14	C₁₃	C₇²×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
15	C₇	C₇×C₁₃×C₄₉	1	56	yes	direct product factor
16	C₇	C₇³×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₇	C₇³×C₁₃
socle, prime radical	C₇³×C₁₃	C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×C₁₃×C₄₉	C₇	direct (N × H)
3. C₇²×C₄₉	C₁₃	direct (N × H)
4. C₇²×C₁₃	C₄₉	direct (N × H)
6. C₁₃×C₄₉	C₇²	direct (N × H)
8. C₇×C₄₉	C₇×C₁₃	direct (N × H)
9. C₇×C₁₃	C₇×C₄₉	direct (N × H)
11. C₇²	C₁₃×C₄₉	direct (N × H)
13. C₄₉	C₇²×C₁₃	direct (N × H)
14. C₁₃	C₇²×C₄₉	direct (N × H)
15. C₇	C₇×C₁₃×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
C₇³×C₁₃	7
C₇×C₁₃×C₄₉	7
C₇²×C₄₉	13