Subgroups — C₁₃×#2868 #13111926

Order 1664.

648 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×C₄⋊Q₈	C₂	1	6	yes	maximal
2	C₁₃×#384	C₂	1	8	yes	maximal
3	C₄³×C₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×Q₈×C₁₃	C₂²	1	4	yes	—
5	C₁₃×C₄⋊Q₈	—	2	24	no	—
6	C₂×C₁₃×C₄⋊C₄	C₂²	1	24	yes	—
7	C₂×C₄²×C₁₃	C₂²	1	3	yes	—
8	C₂×C₄²×C₁₃	C₂²	1	4	yes	—
9	C₂×Q₈×C₁₃	—	2	24	no	—
10	C₂²×C₄×C₁₃	C₂³	1	8	yes	—
11	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
12	C₂²×C₄×C₁₃	C₂³	1	6	yes	—
13	C₁₃×C₄⋊C₄	—	2	48	no	—
14	C₄²×C₁₃	D₄	1	12	yes	—
15	C₄²×C₁₃	Q₈	1	16	yes	complemented
16	#2868	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
18	Q₈×C₁₃	—	4	16	no	—
19	C₂×C₄×C₁₃	—	2	24	no	—
20	C₂×C₄×C₁₃	C₂×D₄	1	6	yes	—
21	C₂×C₄×C₁₃	C₂×D₄	1	12	yes	—
22	C₂×C₄×C₁₃	C₂×Q₈	1	24	yes	—
23	C₂×C₄⋊Q₈	C₂×C₁₃	1	6	yes	—
24	#384	C₂×C₁₃	1	8	yes	—
25	C₄³	C₂×C₁₃	1	1	yes	characteristic
26	C₂²×C₁₃	C₂²×D₄	1	3	yes	—
27	C₂²×C₁₃	C₂²×Q₈	1	4	yes	—
28	C₄×C₁₃	—	4	8	no	—
29	C₄×C₁₃	#127	1	4	yes	—
30	C₄×C₁₃	C₄⋊Q₈	1	24	yes	complemented
31	C₂²×Q₈	C₂²×C₁₃	1	4	yes	—
32	C₄⋊Q₈	—	2	24	no	—
33	C₂×C₄⋊C₄	C₂²×C₁₃	1	24	yes	—
34	C₂×C₄²	C₂²×C₁₃	1	3	yes	—
35	C₂×C₄²	C₂²×C₁₃	1	4	yes	—
36	C₂×C₁₃	C₂×#127	1	1	yes	characteristic
37	C₂×C₁₃	C₂×C₄⋊Q₈	1	6	yes	—
38	C₂×Q₈	—	2	24	no	—
39	C₂²×C₄	C₂³×C₁₃	1	8	yes	—
40	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
41	C₂²×C₄	C₂³×C₁₃	1	6	yes	—
42	C₄⋊C₄	—	2	48	no	—
43	C₄²	D₄×C₁₃	1	12	yes	—
44	C₄²	Q₈×C₁₃	1	16	yes	complemented
45	C₁₃	#2868	1	1	yes	characteristic, direct product factor, Sylow
46	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
47	Q₈	—	4	16	no	—
48	C₂×C₄	—	2	24	no	—
49	C₂×C₄	C₂×D₄×C₁₃	1	6	yes	—
50	C₂×C₄	C₂×D₄×C₁₃	1	12	yes	—
51	C₂×C₄	C₂×Q₈×C₁₃	1	24	yes	—
52	C₂²	C₂²×D₄×C₁₃	1	3	yes	—
53	C₂²	C₂²×Q₈×C₁₃	1	4	yes	—
54	C₄	—	4	8	no	—
55	C₄	C₁₃×#127	1	4	yes	—
56	C₄	C₁₃×C₄⋊Q₈	1	24	yes	complemented
57	C₂	C₂×C₁₃×#127	1	1	yes	characteristic
58	C₂	C₂×C₁₃×C₄⋊Q₈	1	6	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
15. C₄²×C₁₃	Q₈	semidirect
16. #2868	C₁₃	direct (N × H)
30. C₄×C₁₃	C₄⋊Q₈	semidirect
44. C₄²	Q₈×C₁₃	semidirect
45. C₁₃	#2868	direct (N × H)
56. C₄	C₁₃×C₄⋊Q₈	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×C₄⋊Q₈	2
C₁₃×#384	2
C₄³×C₁₃	2
#2868	13

Subgroups — C13×#2868 #13111926

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2868 #13111926