Subgroups — C₁₃×#7450 #15693789

Order 3328.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2252	C₂	1	1	yes	maximal, characteristic
2	C₁₃×C₄⋊C₃₂	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1371	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#500	—	2	1	no	—
5	C₂×C₁₃×C₃₂	—	2	1	no	—
6	C₁₃×#366	—	2	1	no	—
7	C₁₃×#366	C₄	1	2	yes	—
8	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
9	C₁₃×#335	—	2	1	no	—
10	C₁₃×C₄⋊Q₈	—	4	1	no	—
11	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
12	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
13	C₁₃×#107	—	2	2	no	—
14	C₁₃×#107	—	4	1	no	—
15	C₁₃×C₄⋊C₈	—	4	1	no	—
16	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
17	C₁₃×C₃₂	—	4	1	no	—
18	#7450	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂×Q₈×C₁₃	—	8	1	no	—
20	C₂×C₈×C₁₃	—	8	1	no	—
21	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₈×C₁₃	SD₁₆	1	1	yes	characteristic
23	C₁₃×C₄⋊C₄	—	4	2	no	—
24	C₁₃×C₄⋊C₄	—	8	1	no	—
25	C₄²×C₁₃	D₈	1	1	yes	characteristic
26	C₁₃×C₁₆	—	2	1	no	—
27	C₁₃×C₁₆	SD₁₆	1	1	yes	characteristic
28	C₁₃×C₁₆	Q₁₆	1	1	yes	characteristic
29	#2252	C₂×C₁₃	1	1	yes	characteristic
30	C₄⋊C₃₂	C₂×C₁₃	1	1	yes	characteristic
31	#1371	C₂×C₁₃	1	1	yes	characteristic
32	Q₈×C₁₃	—	16	1	no	—
33	Q₈×C₁₃	—	16	1	no	—
34	C₂×C₄×C₁₃	—	8	2	no	—
35	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
36	C₂×C₄×C₁₃	D₁₆	1	1	yes	characteristic
37	C₂×C₄×C₁₃	SD₃₂	1	1	yes	characteristic
38	C₈×C₁₃	—	2	1	no	—
39	C₈×C₁₃	—	16	1	no	—
40	C₈×C₁₃	#101	1	1	yes	characteristic
41	C₈×C₁₃	#103	1	1	yes	characteristic
42	#500	—	2	1	no	—
43	C₂×C₃₂	—	2	1	no	—
44	#366	—	2	1	no	—
45	#366	C₄×C₁₃	1	2	yes	—
46	C₄×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
47	#335	—	2	1	no	—
48	C₂²×C₁₃	#357	1	1	yes	characteristic
49	C₄×C₁₃	—	2	1	no	—
50	C₄×C₁₃	—	16	2	no	—
51	C₄×C₁₃	#332	1	1	yes	characteristic
52	C₄×C₁₃	#362	1	1	yes	characteristic
53	C₄×C₁₃	D₃₂	1	1	yes	characteristic
54	C₄×C₁₃	SD₆₄	1	1	yes	characteristic
55	C₄⋊Q₈	—	4	1	no	—
56	C₂×C₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
57	C₂×C₁₆	D₄×C₁₃	1	1	yes	characteristic
58	#107	—	2	2	no	—
59	#107	—	4	1	no	—
60	C₄⋊C₈	—	4	1	no	—
61	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
62	C₃₂	—	4	1	no	—
63	C₂×C₁₃	#1364	1	1	yes	characteristic
64	C₂×C₁₃	#1415	1	1	yes	characteristic
65	C₂×C₁₃	#1420	1	1	yes	characteristic
66	C₂×Q₈	—	8	1	no	—
67	C₂×C₈	—	8	1	no	—
68	C₂×C₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₈	C₁₃×SD₁₆	1	1	yes	characteristic
70	C₄⋊C₄	—	4	2	no	—
71	C₄⋊C₄	—	8	1	no	—
72	C₄²	C₁₃×D₈	1	1	yes	characteristic
73	C₁₆	—	2	1	no	—
74	C₁₆	C₁₃×SD₁₆	1	1	yes	characteristic
75	C₁₆	C₁₃×Q₁₆	1	1	yes	characteristic
76	C₁₃	#7450	1	1	yes	characteristic, direct product factor, Sylow
77	Q₈	—	16	1	no	—
78	Q₈	—	16	1	no	—
79	C₂×C₄	—	8	2	no	—
80	C₂×C₄	C₁₃×#102	1	1	yes	characteristic
81	C₂×C₄	C₁₃×D₁₆	1	1	yes	characteristic
82	C₂×C₄	C₁₃×SD₃₂	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	16	1	no	—
85	C₈	C₁₃×#101	1	1	yes	characteristic
86	C₈	C₁₃×#103	1	1	yes	characteristic
87	C₂²	C₁₃×#357	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	16	2	no	—
90	C₄	C₁₃×#332	1	1	yes	characteristic
91	C₄	C₁₃×#362	1	1	yes	characteristic
92	C₄	C₁₃×D₃₂	1	1	yes	characteristic
93	C₄	C₁₃×SD₆₄	1	1	yes	characteristic
94	C₂	C₁₃×#1364	1	1	yes	characteristic
95	C₂	C₁₃×#1415	1	1	yes	characteristic
96	C₂	C₁₃×#1420	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₃	#357
commutator	C₂×C₁₆	C₂×C₄×C₁₃
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₃
LCS	G ▷ C₂×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄²×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. #7450	C₁₃	direct (N × H)
76. C₁₃	#7450	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×#2252	2
C₁₃×C₄⋊C₃₂	2
C₁₃×#1371	2
#7450	13

Subgroups — C13×#7450 #15693789

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#7450 #15693789