Subgroups — C₁₃×#123 #88217

Order 416.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
4	C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
6	C₂³×C₁₃	C₂²	1	1	yes	characteristic
7	C₂³×C₁₃	C₂²	1	1	yes	characteristic
8	D₄×C₁₃	—	2	2	no	—
9	C₂×C₄×C₁₃	—	2	2	no	—
10	C₂×C₄×C₁₃	C₂²	1	2	yes	—
11	C₂×C₄×C₁₃	C₂²	1	2	yes	—
12	C₂×C₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃	—	2	2	no	—
14	C₂²×C₁₃	—	2	1	no	—
15	C₂²×C₁₃	—	2	2	no	—
16	C₂²×C₁₃	D₄	1	2	yes	—
17	C₂²×C₁₃	C₂³	1	1	yes	characteristic
18	C₄×C₁₃	—	2	2	no	—
19	C₄×C₁₃	—	2	1	no	—
20	C₄×C₁₃	—	2	2	no	—
21	#123	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₂×C₁₃	—	2	2	no	—
23	C₂×C₁₃	—	4	1	no	—
24	C₂×C₁₃	C₂×D₄	1	1	yes	characteristic
25	C₂×C₁₃	#41	1	2	yes	—
26	C₂×D₄	C₂×C₁₃	1	1	yes	characteristic
27	C₂²×C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
28	C₄⋊C₄	C₂×C₁₃	1	2	yes	complemented
29	C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
30	C₂²⋊C₄	C₂×C₁₃	1	2	yes	complemented
31	C₁₃	#123	1	1	yes	characteristic, direct product factor, Sylow
32	C₂³	C₂²×C₁₃	1	1	yes	characteristic
33	C₂³	C₂²×C₁₃	1	1	yes	characteristic
34	D₄	—	2	2	no	—
35	C₂×C₄	—	2	2	no	—
36	C₂×C₄	C₂²×C₁₃	1	2	yes	—
37	C₂×C₄	C₂²×C₁₃	1	2	yes	—
38	C₂×C₄	C₂²×C₁₃	1	1	yes	characteristic
39	C₂²	—	2	2	no	—
40	C₂²	—	2	1	no	—
41	C₂²	—	2	2	no	—
42	C₂²	D₄×C₁₃	1	2	yes	—
43	C₂²	C₂³×C₁₃	1	1	yes	characteristic
44	C₄	—	2	2	no	—
45	C₄	—	2	1	no	—
46	C₄	—	2	2	no	—
47	C₂	—	2	2	no	—
48	C₂	—	4	1	no	—
49	C₂	C₂×D₄×C₁₃	1	1	yes	characteristic
50	C₂	C₁₃×#41	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³
commutator, Frattini, cosocle	C₂²	C₂³×C₁₃
prime radical	C₂×D₄×C₁₃	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×C₁₃	C₂	semidirect
3. C₁₃×C₄⋊C₄	C₂	semidirect
4. C₁₃×C₂²⋊C₄	C₂	semidirect
5. C₁₃×C₂²⋊C₄	C₂	semidirect
21. #123	C₁₃	direct (N × H)
27. C₂²×C₄	C₂×C₁₃	semidirect
28. C₄⋊C₄	C₂×C₁₃	semidirect
29. C₂²⋊C₄	C₂×C₁₃	semidirect
30. C₂²⋊C₄	C₂×C₁₃	semidirect
31. C₁₃	#123	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×D₄×C₁₃	2
C₂²×C₄×C₁₃	2
C₁₃×C₄⋊C₄	2
C₁₃×C₂²⋊C₄	2
#123	13

Subgroups — C13×#123 #88217

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#123 #88217