Subgroups — C₁₃×#8817 #15695156

Order 3328.

390 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#1834	C₂	1	6	yes	maximal
2	C₂×C₈²×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₈×C₁₃	C₂²	1	3	yes	—
4	C₁₃×#384	C₂²	1	4	yes	—
5	C₁₃×#340	—	2	12	no	—
6	C₈²×C₁₃	C₄	1	4	yes	complemented
7	C₂²×C₈×C₁₃	D₄	1	6	yes	—
8	C₂×C₁₃×C₄⋊C₄	—	2	12	no	—
9	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
10	C₄×C₈×C₁₃	C₂×C₄	1	6	yes	—
11	C₄×C₈×C₁₃	Q₈	1	6	yes	—
12	#8817	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂²×C₄×C₁₃	—	4	4	no	—
14	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
15	C₂×C₈×C₁₃	—	2	12	no	—
16	C₂×C₈×C₁₃	C₄⋊C₄	1	12	yes	—
17	C₁₃×C₄⋊C₄	—	4	24	no	—
18	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
19	C₄²×C₁₃	C₂×Q₈	1	3	yes	—
20	#1834	C₂×C₁₃	1	6	yes	—
21	C₂×C₈²	C₂×C₁₃	1	1	yes	characteristic
22	C₂³×C₁₃	#127	1	1	yes	characteristic
23	C₂×C₄×C₁₃	—	8	12	no	—
24	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	3	yes	—
25	C₂×C₄×C₁₃	C₄⋊Q₈	1	3	yes	—
26	C₂×C₄×C₁₃	#135	1	12	yes	—
27	C₈×C₁₃	—	2	12	no	—
28	C₂×C₄×C₈	C₂²×C₁₃	1	3	yes	—
29	#384	C₂²×C₁₃	1	4	yes	—
30	#340	—	2	12	no	—
31	C₈²	C₄×C₁₃	1	4	yes	complemented
32	C₂²×C₁₃	#384	1	1	yes	characteristic
33	C₂²×C₁₃	#495	1	6	yes	—
34	C₄×C₁₃	—	16	4	no	—
35	C₄×C₁₃	#427	1	6	yes	—
36	C₄×C₁₃	#499	1	6	yes	—
37	C₂²×C₈	D₄×C₁₃	1	6	yes	—
38	C₂×C₄⋊C₄	—	2	12	no	—
39	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
40	C₄×C₈	C₂×C₄×C₁₃	1	6	yes	—
41	C₄×C₈	Q₈×C₁₃	1	6	yes	—
42	C₂×C₁₃	#1711	1	4	yes	—
43	C₂×C₁₃	#1846	1	3	yes	—
44	C₂²×C₄	—	4	4	no	—
45	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
46	C₂×C₈	—	2	12	no	—
47	C₂×C₈	C₁₃×C₄⋊C₄	1	12	yes	—
48	C₄⋊C₄	—	4	24	no	—
49	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
50	C₄²	C₂×Q₈×C₁₃	1	3	yes	—
51	C₁₃	#8817	1	1	yes	characteristic, direct product factor, Sylow
52	C₂³	C₁₃×#127	1	1	yes	characteristic
53	C₂×C₄	—	8	12	no	—
54	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	3	yes	—
55	C₂×C₄	C₁₃×C₄⋊Q₈	1	3	yes	—
56	C₂×C₄	C₁₃×#135	1	12	yes	—
57	C₈	—	2	12	no	—
58	C₂²	C₁₃×#384	1	1	yes	characteristic
59	C₂²	C₁₃×#495	1	6	yes	—
60	C₄	—	16	4	no	—
61	C₄	C₁₃×#427	1	6	yes	—
62	C₄	C₁₃×#499	1	6	yes	—
63	C₂	C₁₃×#1711	1	4	yes	—
64	C₂	C₁₃×#1846	1	3	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	#127
commutator	C₄²	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₈²×C₁₃	C₄	semidirect
12. #8817	C₁₃	direct (N × H)
31. C₈²	C₄×C₁₃	semidirect
51. C₁₃	#8817	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#1834	2
C₂×C₈²×C₁₃	2
#8817	13

Subgroups — C13×#8817 #15695156

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#8817 #15695156