Subgroups — C₁₃×#7454 #15693793

Order 3328.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2253	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1422	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1373	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#499	—	2	1	no	—
5	C₁₃×M₆₄	—	2	1	no	—
6	C₁₃×#367	C₄	1	2	yes	—
7	C₁₃×#366	—	2	1	no	—
8	C₁₃×#364	—	2	1	no	—
9	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
10	C₁₃×#125	—	4	1	no	—
11	C₁₃×M₃₂	—	4	1	no	—
12	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
13	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
14	C₁₃×#107	—	2	2	no	—
15	C₁₃×#106	—	4	1	no	—
16	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
17	C₁₃×C₃₂	—	4	1	no	—
18	#7454	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
20	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
21	C₁₃×C₄⋊C₄	—	4	2	no	—
22	C₁₃×C₄⋊C₄	—	8	2	no	—
23	C₄²×C₁₃	SD₁₆	1	1	yes	characteristic
24	C₁₃×C₁₆	—	2	1	no	—
25	C₁₃×C₁₆	—	8	1	no	—
26	C₁₃×C₁₆	SD₁₆	1	1	yes	characteristic
27	C₁₃×C₁₆	Q₁₆	1	1	yes	characteristic
28	#2253	C₂×C₁₃	1	1	yes	characteristic
29	#1422	C₂×C₁₃	1	1	yes	characteristic
30	#1373	C₂×C₁₃	1	1	yes	characteristic
31	C₂×C₄×C₁₃	—	2	1	no	—
32	C₂×C₄×C₁₃	—	8	2	no	—
33	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
34	C₈×C₁₃	#101	1	1	yes	characteristic
35	C₈×C₁₃	#103	1	1	yes	characteristic
36	C₈×C₁₃	SD₃₂	1	1	yes	characteristic
37	C₈×C₁₃	Q₃₂	1	1	yes	characteristic
38	#499	—	2	1	no	—
39	M₆₄	—	2	1	no	—
40	#367	C₄×C₁₃	1	2	yes	—
41	#366	—	2	1	no	—
42	#364	—	2	1	no	—
43	C₄×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
44	C₂²×C₁₃	#361	1	1	yes	characteristic
45	C₄×C₁₃	—	4	1	no	—
46	C₄×C₁₃	—	16	2	no	—
47	C₄×C₁₃	#332	1	1	yes	characteristic
48	C₄×C₁₃	#358	1	1	yes	characteristic
49	#125	—	4	1	no	—
50	M₃₂	—	4	1	no	—
51	C₂×C₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
52	C₂×C₁₆	D₄×C₁₃	1	1	yes	characteristic
53	#107	—	2	2	no	—
54	#106	—	4	1	no	—
55	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
56	C₃₂	—	4	1	no	—
57	C₂×C₁₃	—	2	1	no	—
58	C₂×C₁₃	#1365	1	1	yes	characteristic
59	C₂×C₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
60	C₂×C₈	C₁₃×D₈	1	1	yes	characteristic
61	C₄⋊C₄	—	4	2	no	—
62	C₄⋊C₄	—	8	2	no	—
63	C₄²	C₁₃×SD₁₆	1	1	yes	characteristic
64	C₁₆	—	2	1	no	—
65	C₁₆	—	8	1	no	—
66	C₁₆	C₁₃×SD₁₆	1	1	yes	characteristic
67	C₁₆	C₁₃×Q₁₆	1	1	yes	characteristic
68	C₁₃	#7454	1	1	yes	characteristic, direct product factor, Sylow
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	8	2	no	—
71	C₂×C₄	C₁₃×#102	1	1	yes	characteristic
72	C₈	C₁₃×#101	1	1	yes	characteristic
73	C₈	C₁₃×#103	1	1	yes	characteristic
74	C₈	C₁₃×SD₃₂	1	1	yes	characteristic
75	C₈	C₁₃×Q₃₂	1	1	yes	characteristic
76	C₂²	C₁₃×#361	1	1	yes	characteristic
77	C₄	—	4	1	no	—
78	C₄	—	16	2	no	—
79	C₄	C₁₃×#332	1	1	yes	characteristic
80	C₄	C₁₃×#358	1	1	yes	characteristic
81	C₂	—	2	1	no	—
82	C₂	C₁₃×#1365	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	#1365
commutator	C₂×C₁₆	C₂×C₄×C₁₃
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₃
prime radical	C₂²×C₁₃	#361
LCS	G ▷ C₂×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₄×C₈×C₁₃ ◁ C₄×C₁₃×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
18. #7454	C₁₃	direct (N × H)
68. C₁₃	#7454	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×#2253	2
C₁₃×#1422	2
C₁₃×#1373	2
#7454	13

Subgroups — C13×#7454 #15693793

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#7454 #15693793