Subgroups — C₁₃×#2381 #13111439

Order 1664.

424 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#391	C₂	1	4	yes	maximal
3	C₁₃×#387	C₂	1	8	yes	maximal
4	C₁₃×#383	C₂	1	2	yes	maximal
5	C₂²×Q₈×C₁₃	C₂²	1	2	yes	—
6	C₁₃×C₄⋊Q₈	C₄	1	8	yes	complemented
7	C₂×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
8	C₂×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
9	C₂×C₄²×C₁₃	C₂²	1	4	yes	—
10	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
11	C₁₃×#95	C₂²	1	8	yes	—
12	C₁₃×#95	C₂²	1	4	yes	—
13	C₁₃×#95	C₂²	1	8	yes	—
14	C₂×Q₈×C₁₃	—	4	2	no	—
15	C₂×Q₈×C₁₃	—	4	2	no	—
16	C₂×Q₈×C₁₃	C₂×C₄	1	8	yes	—
17	C₂²×C₄×C₁₃	C₂³	1	8	yes	—
18	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
19	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
20	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
21	C₁₃×C₄⋊C₄	—	4	4	no	—
22	C₁₃×C₄⋊C₄	C₂×C₄	1	16	yes	—
23	C₄²×C₁₃	—	4	4	no	—
24	C₄²×C₁₃	C₂×C₄	1	4	yes	—
25	#2381	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
26	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
27	Q₈×C₁₃	—	4	8	no	—
28	C₂×C₄×C₁₃	—	2	4	no	—
29	C₂×C₄×C₁₃	—	2	4	no	—
30	C₂×C₄×C₁₃	—	2	2	no	—
31	C₂×C₄×C₁₃	—	2	4	no	—
32	C₂×C₄×C₁₃	—	2	8	no	—
33	C₂×C₄×C₁₃	—	2	16	no	—
34	C₂×C₄×C₁₃	C₂²×C₄	1	4	yes	—
35	C₂×C₄×C₁₃	C₂²×C₄	1	2	yes	—
36	C₂×C₄×C₁₃	C₂²×C₄	1	8	yes	—
37	C₂×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
38	#391	C₂×C₁₃	1	4	yes	—
39	#387	C₂×C₁₃	1	8	yes	—
40	#383	C₂×C₁₃	1	2	yes	—
41	C₂²×C₁₃	C₂³×C₄	1	1	yes	characteristic
42	C₂²×C₁₃	H(5,𝔽₂)	1	2	yes	—
43	C₂²×C₁₃	2₋¹⁺⁴	1	4	yes	—
44	C₄×C₁₃	—	2	8	no	—
45	C₄×C₁₃	—	2	2	no	—
46	C₄×C₁₃	—	2	4	no	—
47	C₄×C₁₃	—	4	8	no	—
48	C₂²×Q₈	C₂²×C₁₃	1	2	yes	—
49	C₄⋊Q₈	C₄×C₁₃	1	8	yes	complemented
50	C₂×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
51	C₂×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
52	C₂×C₄²	C₂²×C₁₃	1	4	yes	—
53	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
54	#95	C₂²×C₁₃	1	8	yes	—
55	#95	C₂²×C₁₃	1	4	yes	—
56	#95	C₂²×C₁₃	1	8	yes	—
57	C₂×C₁₃	#518	1	1	yes	characteristic
58	C₂×C₁₃	#519	1	2	yes	—
59	C₂×C₁₃	#563	1	4	yes	—
60	C₂×Q₈	—	4	2	no	—
61	C₂×Q₈	—	4	2	no	—
62	C₂×Q₈	C₂×C₄×C₁₃	1	8	yes	—
63	C₂²×C₄	C₂³×C₁₃	1	8	yes	—
64	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
65	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
66	C₂²×C₄	C₂³×C₁₃	1	4	yes	—
67	C₄⋊C₄	—	4	4	no	—
68	C₄⋊C₄	C₂×C₄×C₁₃	1	16	yes	—
69	C₄²	—	4	4	no	—
70	C₄²	C₂×C₄×C₁₃	1	4	yes	—
71	C₁₃	#2381	1	1	yes	characteristic, direct product factor, Sylow
72	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
73	Q₈	—	4	8	no	—
74	C₂×C₄	—	2	4	no	—
75	C₂×C₄	—	2	4	no	—
76	C₂×C₄	—	2	2	no	—
77	C₂×C₄	—	2	4	no	—
78	C₂×C₄	—	2	8	no	—
79	C₂×C₄	—	2	16	no	—
80	C₂×C₄	C₂²×C₄×C₁₃	1	4	yes	—
81	C₂×C₄	C₂²×C₄×C₁₃	1	2	yes	—
82	C₂×C₄	C₂²×C₄×C₁₃	1	8	yes	—
83	C₂²	C₂³×C₄×C₁₃	1	1	yes	characteristic
84	C₂²	C₁₃×H(5,𝔽₂)	1	2	yes	—
85	C₂²	C₁₃×2₋¹⁺⁴	1	4	yes	—
86	C₄	—	2	8	no	—
87	C₄	—	2	2	no	—
88	C₄	—	2	4	no	—
89	C₄	—	4	8	no	—
90	C₂	C₁₃×#518	1	1	yes	characteristic
91	C₂	C₁₃×#519	1	2	yes	—
92	C₂	C₁₃×#563	1	4	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂⁴
commutator	C₂²	C₂³×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁴×C₁₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₁₃×C₄⋊Q₈	C₄	semidirect
25. #2381	C₁₃	direct (N × H)
49. C₄⋊Q₈	C₄×C₁₃	semidirect
71. C₁₃	#2381	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×C₁₃×C₄⋊Q₈	2
C₁₃×#391	2
C₁₃×#387	2
C₁₃×#383	2
#2381	13

Subgroups — C13×#2381 #13111439

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2381 #13111439