Subgroups — C₂³×C₅×C₃₄₃ #72191925

Order 13720.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×C₃₄₃	C₂	1	7	yes	maximal, direct product factor
2	C₂×C₅×C₃₄₃	C₂²	1	7	yes	direct product factor
3	C₂³×C₃₄₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂³×C₅×C₄₉	C₇	1	1	yes	maximal, characteristic
5	C₅×C₃₄₃	C₂³	1	1	yes	characteristic, direct product factor, Hall
6	C₂²×C₃₄₃	C₂×C₅	1	7	yes	direct product factor
7	C₂²×C₅×C₄₉	C₂×C₇	1	7	yes	—
8	C₂×C₃₄₃	C₂²×C₅	1	7	yes	direct product factor
9	C₂×C₅×C₄₉	C₂²×C₇	1	7	yes	—
10	C₂³×C₄₉	C₅×C₇	1	1	yes	characteristic
11	C₃₄₃	C₂³×C₅	1	1	yes	characteristic, direct product factor, Sylow
12	C₂³×C₅×C₇	C₄₉	1	1	yes	characteristic
13	C₅×C₄₉	C₂³×C₇	1	1	yes	characteristic
14	C₂²×C₄₉	C₂×C₅×C₇	1	7	yes	—
15	C₂²×C₅×C₇	C₂×C₄₉	1	7	yes	—
16	C₂×C₄₉	C₂²×C₅×C₇	1	7	yes	—
17	C₂×C₅×C₇	C₂²×C₄₉	1	7	yes	—
18	C₂³×C₇	C₅×C₄₉	1	1	yes	characteristic
19	C₄₉	C₂³×C₅×C₇	1	1	yes	characteristic
20	C₂³×C₅	C₃₄₃	1	1	yes	characteristic, direct product factor, Hall
21	C₅×C₇	C₂³×C₄₉	1	1	yes	characteristic
22	C₂²×C₇	C₂×C₅×C₄₉	1	7	yes	—
23	C₂²×C₅	C₂×C₃₄₃	1	7	yes	direct product factor
24	C₂×C₇	C₂²×C₅×C₄₉	1	7	yes	—
25	C₂×C₅	C₂²×C₃₄₃	1	7	yes	direct product factor
26	C₂³	C₅×C₃₄₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₇	C₂³×C₅×C₄₉	1	1	yes	characteristic
28	C₅	C₂³×C₃₄₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₂²	C₂×C₅×C₃₄₃	1	7	yes	direct product factor
30	C₂	C₂²×C₅×C₃₄₃	1	7	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄₉	C₂³×C₅×C₇
socle, prime radical	C₂³×C₅×C₇	C₄₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×C₃₄₃	C₂	direct (N × H)
2. C₂×C₅×C₃₄₃	C₂²	direct (N × H)
3. C₂³×C₃₄₃	C₅	direct (N × H)
5. C₅×C₃₄₃	C₂³	direct (N × H)
6. C₂²×C₃₄₃	C₂×C₅	direct (N × H)
8. C₂×C₃₄₃	C₂²×C₅	direct (N × H)
11. C₃₄₃	C₂³×C₅	direct (N × H)
20. C₂³×C₅	C₃₄₃	direct (N × H)
23. C₂²×C₅	C₂×C₃₄₃	direct (N × H)
25. C₂×C₅	C₂²×C₃₄₃	direct (N × H)
26. C₂³	C₅×C₃₄₃	direct (N × H)
28. C₅	C₂³×C₃₄₃	direct (N × H)
29. C₂²	C₂×C₅×C₃₄₃	direct (N × H)
30. C₂	C₂²×C₅×C₃₄₃	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×C₅×C₃₄₃	2
C₂³×C₃₄₃	5
C₂³×C₅×C₄₉	7

Subgroups — C23×C5×C343 #72191925

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₅×C₃₄₃ #72191925