Subgroups — C₁₃×#578 #11719613

Order 832.

248 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×2₋¹⁺⁴	C₂	1	2	yes	maximal, complemented
2	C₁₃×#137	C₂	1	6	yes	maximal, complemented
3	C₁₃×#135	C₂	1	3	yes	maximal, complemented
4	C₂×C₁₃×Q₁₆	C₂	1	3	yes	maximal, complemented
5	C₁₃×#131	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#41	—	2	6	no	—
7	C₁₃×#41	C₂²	1	6	yes	—
8	C₁₃×#41	C₂²	1	1	yes	characteristic
9	C₂×Q₈×C₁₃	—	2	2	no	—
10	C₂×Q₈×C₁₃	C₂²	1	6	yes	—
11	C₁₃×Q₁₆	C₂²	1	3	yes	—
12	C₁₃×Q₁₆	C₂²	1	6	yes	—
13	C₁₃×SD₁₆	C₂²	1	6	yes	—
14	C₁₃×D₈	C₂²	1	1	yes	characteristic
15	C₁₃×M₁₆	C₂²	1	3	yes	—
16	C₂×C₈×C₁₃	C₂²	1	3	yes	—
17	Q₈×C₁₃	—	2	6	no	—
18	Q₈×C₁₃	D₄	1	1	yes	characteristic
19	Q₈×C₁₃	C₂³	1	6	yes	—
20	D₄×C₁₃	—	2	6	no	—
21	D₄×C₁₃	D₄	1	3	yes	—
22	D₄×C₁₃	C₂³	1	2	yes	—
23	C₂×C₄×C₁₃	—	2	6	no	—
24	C₂×C₄×C₁₃	—	2	6	no	—
25	C₂×C₄×C₁₃	C₂³	1	3	yes	—
26	C₈×C₁₃	C₂³	1	1	yes	characteristic
27	C₈×C₁₃	C₂³	1	3	yes	—
28	#578	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
29	C₂²×C₁₃	—	2	2	no	—
30	C₂²×C₁₃	C₂×D₄	1	3	yes	—
31	C₄×C₁₃	—	2	6	no	—
32	C₄×C₁₃	C₂×D₄	1	3	yes	—
33	C₄×C₁₃	C₂⁴	1	1	yes	characteristic
34	2₋¹⁺⁴	C₂×C₁₃	1	2	yes	complemented
35	#137	C₂×C₁₃	1	6	yes	complemented
36	#135	C₂×C₁₃	1	3	yes	complemented
37	C₂×Q₁₆	C₂×C₁₃	1	3	yes	complemented
38	#131	C₂×C₁₃	1	1	yes	characteristic, complemented
39	C₂×C₁₃	—	2	3	no	—
40	C₂×C₁₃	—	4	2	no	—
41	C₂×C₁₃	C₂²×D₄	1	1	yes	characteristic
42	#41	—	2	6	no	—
43	#41	C₂²×C₁₃	1	6	yes	—
44	#41	C₂²×C₁₃	1	1	yes	characteristic
45	C₂×Q₈	—	2	2	no	—
46	C₂×Q₈	C₂²×C₁₃	1	6	yes	—
47	Q₁₆	C₂²×C₁₃	1	3	yes	—
48	Q₁₆	C₂²×C₁₃	1	6	yes	—
49	SD₁₆	C₂²×C₁₃	1	6	yes	—
50	D₈	C₂²×C₁₃	1	1	yes	characteristic
51	M₁₆	C₂²×C₁₃	1	3	yes	—
52	C₂×C₈	C₂²×C₁₃	1	3	yes	—
53	C₁₃	#578	1	1	yes	characteristic, direct product factor, Sylow
54	Q₈	—	2	6	no	—
55	Q₈	D₄×C₁₃	1	1	yes	characteristic
56	Q₈	C₂³×C₁₃	1	6	yes	—
57	D₄	—	2	6	no	—
58	D₄	D₄×C₁₃	1	3	yes	—
59	D₄	C₂³×C₁₃	1	2	yes	—
60	C₂×C₄	—	2	6	no	—
61	C₂×C₄	—	2	6	no	—
62	C₂×C₄	C₂³×C₁₃	1	3	yes	—
63	C₈	C₂³×C₁₃	1	1	yes	characteristic
64	C₈	C₂³×C₁₃	1	3	yes	—
65	C₂²	—	2	2	no	—
66	C₂²	C₂×D₄×C₁₃	1	3	yes	—
67	C₄	—	2	6	no	—
68	C₄	C₂×D₄×C₁₃	1	3	yes	—
69	C₄	C₂⁴×C₁₃	1	1	yes	characteristic
70	C₂	—	2	3	no	—
71	C₂	—	4	2	no	—
72	C₂	C₂²×D₄×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₄	C₂⁴×C₁₃
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×2₋¹⁺⁴	C₂	semidirect
2. C₁₃×#137	C₂	semidirect
3. C₁₃×#135	C₂	semidirect
4. C₂×C₁₃×Q₁₆	C₂	semidirect
5. C₁₃×#131	C₂	semidirect
28. #578	C₁₃	direct (N × H)
34. 2₋¹⁺⁴	C₂×C₁₃	semidirect
35. #137	C₂×C₁₃	semidirect
36. #135	C₂×C₁₃	semidirect
37. C₂×Q₁₆	C₂×C₁₃	semidirect
38. #131	C₂×C₁₃	semidirect
53. C₁₃	#578	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×2₋¹⁺⁴	2
C₁₃×#137	2
C₁₃×#135	2
C₂×C₁₃×Q₁₆	2
C₁₃×#131	2
#578	13

Subgroups — C13×#578 #11719613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#578 #11719613