Subgroups — C₂×C₁₃×C₂₇² #72196705

Order 18954.

304 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₁₃×C₂₇	C₃	1	4	yes	maximal
2	C₂×C₉²×C₁₃	C₃²	1	1	yes	characteristic
3	C₂×C₃×C₁₃×C₂₇	C₉	1	12	yes	—
4	C₁₃×C₂₇²	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₉×C₁₃×C₂₇	C₂×C₃	1	4	yes	—
6	C₂×C₂₇²	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₁₃×C₂₇	C₂×C₉	1	12	yes	—
8	C₉²×C₁₃	C₂×C₃²	1	1	yes	characteristic
9	C₂₇²	C₂×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
10	C₂×C₃×C₉×C₁₃	C₃×C₉	1	4	yes	—
11	C₂×C₁₃×C₂₇	C₂₇	1	36	yes	direct product factor
12	C₂×C₉×C₂₇	C₃×C₁₃	1	4	yes	—
13	C₃×C₉×C₁₃	C₂×C₃×C₉	1	4	yes	—
14	C₁₃×C₂₇	C₂×C₂₇	1	36	yes	direct product factor
15	C₉×C₂₇	C₂×C₃×C₁₃	1	4	yes	—
16	C₂×C₃²×C₁₃	C₉²	1	1	yes	characteristic
17	C₂×C₉×C₁₃	C₃×C₂₇	1	12	yes	—
18	C₂×C₃×C₂₇	C₉×C₁₃	1	12	yes	—
19	C₂×C₉²	C₃²×C₁₃	1	1	yes	characteristic
20	C₃²×C₁₃	C₂×C₉²	1	1	yes	characteristic
21	C₉×C₁₃	C₂×C₃×C₂₇	1	12	yes	—
22	C₃×C₂₇	C₂×C₉×C₁₃	1	12	yes	—
23	C₉²	C₂×C₃²×C₁₃	1	1	yes	characteristic
24	C₂×C₃×C₁₃	C₉×C₂₇	1	4	yes	—
25	C₂×C₃×C₉	C₃×C₉×C₁₃	1	4	yes	—
26	C₂×C₂₇	C₁₃×C₂₇	1	36	yes	direct product factor
27	C₃×C₁₃	C₂×C₉×C₂₇	1	4	yes	—
28	C₃×C₉	C₂×C₃×C₉×C₁₃	1	4	yes	—
29	C₂₇	C₂×C₁₃×C₂₇	1	36	yes	direct product factor
30	C₂×C₁₃	C₂₇²	1	1	yes	characteristic, direct product factor, Hall
31	C₂×C₃²	C₉²×C₁₃	1	1	yes	characteristic
32	C₂×C₉	C₃×C₁₃×C₂₇	1	12	yes	—
33	C₁₃	C₂×C₂₇²	1	1	yes	characteristic, direct product factor, Sylow
34	C₃²	C₂×C₉²×C₁₃	1	1	yes	characteristic
35	C₉	C₂×C₃×C₁₃×C₂₇	1	12	yes	—
36	C₂×C₃	C₉×C₁₃×C₂₇	1	4	yes	—
37	C₃	C₂×C₉×C₁₃×C₂₇	1	4	yes	—
38	C₂	C₁₃×C₂₇²	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₉²	C₂×C₃²×C₁₃
socle, prime radical	C₂×C₃²×C₁₃	C₉²
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₃×C₂₇²	C₂	direct (N × H)
6. C₂×C₂₇²	C₁₃	direct (N × H)
9. C₂₇²	C₂×C₁₃	direct (N × H)
11. C₂×C₁₃×C₂₇	C₂₇	direct (N × H)
14. C₁₃×C₂₇	C₂×C₂₇	direct (N × H)
26. C₂×C₂₇	C₁₃×C₂₇	direct (N × H)
29. C₂₇	C₂×C₁₃×C₂₇	direct (N × H)
30. C₂×C₁₃	C₂₇²	direct (N × H)
33. C₁₃	C₂×C₂₇²	direct (N × H)
38. C₂	C₁₃×C₂₇²	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×C₉×C₁₃×C₂₇	3
C₁₃×C₂₇²	2
C₂×C₂₇²	13

Subgroups — C2×C13×C272 #72196705

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×C₂₇² #72196705