Subgroups — C₁₃×#12895 #15699234

Order 3328.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#1726	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1374	C₂	1	6	yes	maximal
3	C₂²×C₁₃×C₁₆	C₂²	1	4	yes	—
4	C₂×C₁₃×#97	C₄	1	3	yes	—
5	C₂×C₄×C₈×C₁₃	C₂²	1	3	yes	—
6	C₁₃×#376	C₄	1	1	yes	characteristic
7	C₂²×C₈×C₁₃	C₂×C₄	1	3	yes	—
8	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
9	C₂×C₄²×C₁₃	C₂×C₄	1	3	yes	—
10	C₂×C₁₃×C₁₆	—	2	12	no	—
11	C₁₃×#97	—	2	6	no	—
12	C₄×C₈×C₁₃	—	2	6	no	—
13	C₁₃×#95	C₈	1	4	yes	—
14	#12895	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂²×C₄×C₁₃	C₂×C₈	1	6	yes	—
16	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
17	C₂×C₈×C₁₃	—	2	3	no	—
18	C₂×C₈×C₁₃	—	2	3	no	—
19	C₂×C₈×C₁₃	M₁₆	1	6	yes	—
20	C₂×C₈×C₁₃	#41	1	6	yes	—
21	C₄²×C₁₃	—	2	3	no	—
22	C₄²×C₁₃	—	2	3	no	—
23	C₁₃×C₁₆	—	4	4	no	—
24	#1726	C₂×C₁₃	1	1	yes	characteristic
25	#1374	C₂×C₁₃	1	6	yes	—
26	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
27	C₂×C₄×C₁₃	—	2	6	no	—
28	C₂×C₄×C₁₃	—	2	12	no	—
29	C₂×C₄×C₁₃	#117	1	3	yes	—
30	C₂×C₄×C₁₃	C₂×M₁₆	1	3	yes	—
31	C₈×C₁₃	—	2	6	no	—
32	C₈×C₁₃	#126	1	4	yes	—
33	C₂²×C₁₆	C₂²×C₁₃	1	4	yes	—
34	C₂×#97	C₄×C₁₃	1	3	yes	—
35	C₂×C₄×C₈	C₂²×C₁₃	1	3	yes	—
36	#376	C₄×C₁₃	1	1	yes	characteristic
37	C₂²×C₁₃	#431	1	3	yes	—
38	C₂²×C₁₃	#504	1	4	yes	—
39	C₄×C₁₃	—	4	6	no	—
40	C₄×C₁₃	#383	1	1	yes	characteristic
41	C₄×C₁₃	#432	1	3	yes	—
42	C₂²×C₈	C₂×C₄×C₁₃	1	3	yes	—
43	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
44	C₂×C₄²	C₂×C₄×C₁₃	1	3	yes	—
45	C₂×C₁₆	—	2	12	no	—
46	#97	—	2	6	no	—
47	C₄×C₈	—	2	6	no	—
48	#95	C₈×C₁₃	1	4	yes	—
49	C₂×C₁₃	#1839	1	1	yes	characteristic
50	C₂×C₁₃	#2164	1	6	yes	—
51	C₂²×C₄	C₂×C₈×C₁₃	1	6	yes	—
52	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
53	C₂×C₈	—	2	3	no	—
54	C₂×C₈	—	2	3	no	—
55	C₂×C₈	C₁₃×M₁₆	1	6	yes	—
56	C₂×C₈	C₁₃×#41	1	6	yes	—
57	C₄²	—	2	3	no	—
58	C₄²	—	2	3	no	—
59	C₁₆	—	4	4	no	—
60	C₁₃	#12895	1	1	yes	characteristic, direct product factor, Sylow
61	C₂³	C₂²×C₈×C₁₃	1	1	yes	characteristic
62	C₂×C₄	—	2	6	no	—
63	C₂×C₄	—	2	12	no	—
64	C₂×C₄	C₁₃×#117	1	3	yes	—
65	C₂×C₄	C₂×C₁₃×M₁₆	1	3	yes	—
66	C₈	—	2	6	no	—
67	C₈	C₁₃×#126	1	4	yes	—
68	C₂²	C₁₃×#431	1	3	yes	—
69	C₂²	C₁₃×#504	1	4	yes	—
70	C₄	—	4	6	no	—
71	C₄	C₁₃×#383	1	1	yes	characteristic
72	C₄	C₁₃×#432	1	3	yes	—
73	C₂	C₁₃×#1839	1	1	yes	characteristic
74	C₂	C₁₃×#2164	1	6	yes	—

	subgroup	G/H
center	C₂²×C₈×C₁₃	C₂³
commutator	C₂³	C₂²×C₈×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle, prime radical	C₂³×C₁₃	C₂²×C₈
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
14. #12895	C₁₃	direct (N × H)
60. C₁₃	#12895	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×#1726	2
C₁₃×#1374	2
#12895	13

Subgroups — C13×#12895 #15699234

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#12895 #15699234