Subgroups — C₁₃×#12902 #15699241

Order 3328.

278 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2153	C₂	1	3	yes	maximal
2	C₁₃×#2151	C₂	1	3	yes	maximal
3	C₁₃×#1747	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×M₃₂	C₂²	1	3	yes	—
5	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
6	C₁₃×#405	C₂²	1	3	yes	—
7	C₁₃×#364	—	2	6	no	—
8	C₁₃×C₄⋊C₁₆	—	2	6	no	—
9	C₁₃×#338	C₄	1	1	yes	characteristic
10	C₁₃×H(3,ℤ/4)	C₄	1	3	yes	—
11	C₂×C₁₃×M₁₆	C₂×C₄	1	3	yes	—
12	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
13	C₁₃×#117	C₂×C₄	1	3	yes	—
14	C₁₃×M₃₂	—	2	6	no	—
15	C₂×C₁₃×C₁₆	—	2	3	no	—
16	C₂×C₁₃×C₁₆	—	2	3	no	—
17	C₁₃×#97	Q₈	1	6	yes	—
18	C₄×C₈×C₁₃	D₄	1	6	yes	—
19	#12902	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
21	C₁₃×M₁₆	—	2	6	no	—
22	C₂×C₈×C₁₃	C₄⋊C₄	1	6	yes	—
23	C₂×C₈×C₁₃	C₂×D₄	1	3	yes	—
24	C₂×C₈×C₁₃	C₂×Q₈	1	3	yes	—
25	C₁₃×C₄⋊C₄	—	2	3	no	—
26	C₁₃×C₂²⋊C₄	—	2	3	no	—
27	C₄²×C₁₃	C₄⋊C₄	1	6	yes	—
28	C₁₃×C₁₆	—	4	1	no	—
29	C₁₃×C₁₆	—	4	3	no	—
30	#2153	C₂×C₁₃	1	3	yes	—
31	#2151	C₂×C₁₃	1	3	yes	—
32	#1747	C₂×C₁₃	1	1	yes	characteristic
33	C₂³×C₁₃	#131	1	1	yes	characteristic
34	C₂×C₄×C₁₃	—	2	6	no	—
35	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	3	yes	—
36	C₂×C₄×C₁₃	#131	1	3	yes	—
37	C₈×C₁₃	—	2	6	no	—
38	C₈×C₁₃	#127	1	1	yes	characteristic
39	C₈×C₁₃	C₄⋊Q₈	1	3	yes	—
40	C₂×M₃₂	C₂²×C₁₃	1	3	yes	—
41	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
42	#405	C₂²×C₁₃	1	3	yes	—
43	#364	—	2	6	no	—
44	C₄⋊C₁₆	—	2	6	no	—
45	#338	C₄×C₁₃	1	1	yes	characteristic
46	H(3,ℤ/4)	C₄×C₁₃	1	3	yes	—
47	C₂²×C₁₃	—	4	1	no	—
48	C₂²×C₁₃	#424	1	3	yes	—
49	C₄×C₁₃	—	4	6	no	—
50	C₄×C₁₃	#384	1	1	yes	characteristic
51	C₄×C₁₃	#424	1	3	yes	—
52	C₂×M₁₆	C₂×C₄×C₁₃	1	3	yes	—
53	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
54	#117	C₂×C₄×C₁₃	1	3	yes	—
55	M₃₂	—	2	6	no	—
56	C₂×C₁₆	—	2	3	no	—
57	C₂×C₁₆	—	2	3	no	—
58	#97	Q₈×C₁₃	1	6	yes	—
59	C₄×C₈	D₄×C₁₃	1	6	yes	—
60	C₂×C₁₃	—	2	3	no	—
61	C₂×C₁₃	#1843	1	1	yes	characteristic
62	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
63	M₁₆	—	2	6	no	—
64	C₂×C₈	C₁₃×C₄⋊C₄	1	6	yes	—
65	C₂×C₈	C₂×D₄×C₁₃	1	3	yes	—
66	C₂×C₈	C₂×Q₈×C₁₃	1	3	yes	—
67	C₄⋊C₄	—	2	3	no	—
68	C₂²⋊C₄	—	2	3	no	—
69	C₄²	C₁₃×C₄⋊C₄	1	6	yes	—
70	C₁₆	—	4	1	no	—
71	C₁₆	—	4	3	no	—
72	C₁₃	#12902	1	1	yes	characteristic, direct product factor, Sylow
73	C₂³	C₁₃×#131	1	1	yes	characteristic
74	C₂×C₄	—	2	6	no	—
75	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	3	yes	—
76	C₂×C₄	C₁₃×#131	1	3	yes	—
77	C₈	—	2	6	no	—
78	C₈	C₁₃×#127	1	1	yes	characteristic
79	C₈	C₁₃×C₄⋊Q₈	1	3	yes	—
80	C₂²	—	4	1	no	—
81	C₂²	C₁₃×#424	1	3	yes	—
82	C₄	—	4	6	no	—
83	C₄	C₁₃×#384	1	1	yes	characteristic
84	C₄	C₁₃×#424	1	3	yes	—
85	C₂	—	2	3	no	—
86	C₂	C₁₃×#1843	1	1	yes	characteristic

	subgroup	G/H
center	C₈×C₁₃	#127
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂×C₁₃	#1843
prime radical	C₂³×C₁₃	#131
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₃ ◁ C₂²×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
19. #12902	C₁₃	direct (N × H)
72. C₁₃	#12902	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×#2153	2
C₁₃×#2151	2
C₁₃×#1747	2
#12902	13

Subgroups — C13×#12902 #15699241

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#12902 #15699241