Subgroups — C₁₃×#1373 #13110431

Order 1664.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#364	C₂	1	2	yes	maximal
2	C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₁₃×M₃₂	—	2	2	no	—
4	C₂×C₁₃×C₁₆	C₄	1	1	yes	characteristic
5	C₂×C₁₃×C₁₆	C₄	1	1	yes	characteristic
6	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
8	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
9	C₄²×C₁₃	Q₈	1	1	yes	characteristic
10	C₁₃×C₁₆	—	2	1	no	—
11	C₁₃×C₁₆	—	4	2	no	—
12	C₁₃×C₁₆	C₈	1	2	yes	—
13	#1373	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₂×C₄×C₁₃	—	2	1	no	—
15	C₂×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
16	C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
17	C₈×C₁₃	M₁₆	1	1	yes	characteristic
18	C₈×C₁₃	D₈	1	1	yes	characteristic
19	C₈×C₁₃	Q₁₆	1	1	yes	characteristic
20	#364	C₂×C₁₃	1	2	yes	—
21	C₄×C₁₆	C₂×C₁₃	1	1	yes	characteristic
22	C₂²×C₁₃	#108	1	1	yes	characteristic
23	C₄×C₁₃	—	2	2	no	—
24	C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
25	C₄×C₁₃	#107	1	1	yes	characteristic
26	M₃₂	—	2	2	no	—
27	C₂×C₁₆	C₄×C₁₃	1	1	yes	characteristic
28	C₂×C₁₆	C₄×C₁₃	1	1	yes	characteristic
29	C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
30	C₂×C₁₃	—	2	1	no	—
31	C₂×C₁₃	#335	1	1	yes	characteristic
32	C₂×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
33	C₂×C₈	D₄×C₁₃	1	1	yes	characteristic
34	C₄²	Q₈×C₁₃	1	1	yes	characteristic
35	C₁₆	—	2	1	no	—
36	C₁₆	—	4	2	no	—
37	C₁₆	C₈×C₁₃	1	2	yes	—
38	C₁₃	#1373	1	1	yes	characteristic, direct product factor, Sylow
39	C₂×C₄	—	2	1	no	—
40	C₂×C₄	C₁₃×C₄⋊C₄	1	1	yes	characteristic
41	C₈	C₂×C₈×C₁₃	1	1	yes	characteristic
42	C₈	C₁₃×M₁₆	1	1	yes	characteristic
43	C₈	C₁₃×D₈	1	1	yes	characteristic
44	C₈	C₁₃×Q₁₆	1	1	yes	characteristic
45	C₂²	C₁₃×#108	1	1	yes	characteristic
46	C₄	—	2	2	no	—
47	C₄	C₁₃×C₄⋊C₈	1	1	yes	characteristic
48	C₄	C₁₃×#107	1	1	yes	characteristic
49	C₂	—	2	1	no	—
50	C₂	C₁₃×#335	1	1	yes	characteristic

	subgroup	G/H
center	C₈×C₁₃	D₈
commutator	C₈	C₂×C₈×C₁₃
Frattini, cosocle	C₄×C₈	C₂²×C₁₃
socle	C₂×C₁₃	#335
prime radical	C₂²×C₁₃	#108
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₃ ◁ C₂×C₈×C₁₃ ◁ C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
13. #1373	C₁₃	direct (N × H)
38. C₁₃	#1373	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×#364	2
C₄×C₁₃×C₁₆	2
#1373	13

Subgroups — C13×#1373 #13110431

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#1373 #13110431