Subgroups — C₁₃×#1375 #13110433

Order 1664.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×M₃₂	C₂	1	2	yes	maximal
2	C₂×C₁₃×#97	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×C₁₃	C₄	1	1	yes	characteristic
4	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
5	C₂×C₄²×C₁₃	C₄	1	1	yes	characteristic
6	C₁₃×M₃₂	—	2	2	no	—
7	C₁₃×M₃₂	—	2	2	no	—
8	C₂×C₁₃×C₁₆	C₄	1	4	yes	complemented
9	C₁₃×#97	—	2	2	no	—
10	C₂²×C₄×C₁₃	—	2	1	no	—
11	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈×C₁₃	—	2	1	no	—
13	C₂×C₈×C₁₃	—	2	1	no	—
14	C₂×C₈×C₁₃	C₈	1	2	yes	—
15	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
16	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
17	C₂×C₈×C₁₃	D₄	1	2	yes	—
18	C₂×C₈×C₁₃	Q₈	1	1	yes	characteristic
19	C₄²×C₁₃	—	2	1	no	—
20	C₄²×C₁₃	C₈	1	2	yes	—
21	C₁₃×C₁₆	—	2	4	no	—
22	#1375	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
23	C₂³×C₁₃	M₁₆	1	1	yes	characteristic
24	C₂×C₄×C₁₃	—	2	2	no	—
25	C₂×C₄×C₁₃	—	4	2	no	—
26	C₂×C₄×C₁₃	C₄²	1	1	yes	characteristic
27	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₁₃	M₁₆	1	1	yes	characteristic
32	C₈×C₁₃	—	2	2	no	—
33	C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
34	C₈×C₁₃	C₄⋊C₄	1	2	yes	—
35	C₂×M₃₂	C₂×C₁₃	1	2	yes	—
36	C₂×#97	C₂×C₁₃	1	1	yes	characteristic
37	C₂²×C₁₃	—	2	2	no	—
38	C₂²×C₁₃	#97	1	1	yes	characteristic
39	C₂²×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
40	C₂²×C₁₃	C₄⋊C₈	1	1	yes	characteristic
41	C₄×C₁₃	—	4	2	no	—
42	C₄×C₁₃	#95	1	1	yes	characteristic
43	C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
44	C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
45	C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
46	C₂²×C₈	C₄×C₁₃	1	1	yes	characteristic
47	C₂²×C₈	C₂²×C₁₃	1	1	yes	characteristic
48	C₂×C₄²	C₄×C₁₃	1	1	yes	characteristic
49	M₃₂	—	2	2	no	—
50	M₃₂	—	2	2	no	—
51	C₂×C₁₆	C₄×C₁₃	1	4	yes	complemented
52	#97	—	2	2	no	—
53	C₂×C₁₃	—	2	1	no	—
54	C₂×C₁₃	—	2	1	no	—
55	C₂×C₁₃	#336	1	1	yes	characteristic
56	C₂×C₁₃	#347	1	2	yes	—
57	C₂²×C₄	—	2	1	no	—
58	C₂²×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
59	C₂×C₈	—	2	1	no	—
60	C₂×C₈	—	2	1	no	—
61	C₂×C₈	C₈×C₁₃	1	2	yes	—
62	C₂×C₈	C₂×C₄×C₁₃	1	2	yes	—
63	C₂×C₈	D₄×C₁₃	1	1	yes	characteristic
64	C₂×C₈	D₄×C₁₃	1	2	yes	—
65	C₂×C₈	Q₈×C₁₃	1	1	yes	characteristic
66	C₄²	—	2	1	no	—
67	C₄²	C₈×C₁₃	1	2	yes	—
68	C₁₆	—	2	4	no	—
69	C₁₃	#1375	1	1	yes	characteristic, direct product factor, Sylow
70	C₂³	C₁₃×M₁₆	1	1	yes	characteristic
71	C₂×C₄	—	2	2	no	—
72	C₂×C₄	—	4	2	no	—
73	C₂×C₄	C₄²×C₁₃	1	1	yes	characteristic
74	C₂×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
75	C₂×C₄	C₁₃×C₄⋊C₄	1	1	yes	characteristic
76	C₂×C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
77	C₂×C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
78	C₂×C₄	C₁₃×M₁₆	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₈	C₁₃×C₂²⋊C₄	1	2	yes	—
81	C₈	C₁₃×C₄⋊C₄	1	2	yes	—
82	C₂²	—	2	2	no	—
83	C₂²	C₁₃×#97	1	1	yes	characteristic
84	C₂²	C₁₃×C₂²⋊C₈	1	1	yes	characteristic
85	C₂²	C₁₃×C₄⋊C₈	1	1	yes	characteristic
86	C₄	—	4	2	no	—
87	C₄	C₁₃×#95	1	1	yes	characteristic
88	C₄	C₄×C₈×C₁₃	1	1	yes	characteristic
89	C₄	C₁₃×C₂²⋊C₈	1	1	yes	characteristic
90	C₄	C₁₃×C₄⋊C₈	1	1	yes	characteristic
91	C₂	—	2	1	no	—
92	C₂	—	2	1	no	—
93	C₂	C₁₃×#336	1	1	yes	characteristic
94	C₂	C₁₃×#347	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃	C₄²
commutator	C₄	C₄×C₈×C₁₃
Frattini, cosocle	C₂²×C₈	C₂²×C₁₃
socle	C₂²×C₁₃	#97
prime radical	C₂³×C₁₃	M₁₆
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
8. C₂×C₁₃×C₁₆	C₄	semidirect
22. #1375	C₁₃	direct (N × H)
51. C₂×C₁₆	C₄×C₁₃	semidirect
69. C₁₃	#1375	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×M₃₂	2
C₂×C₁₃×#97	2
#1375	13

Subgroups — C13×#1375 #13110433

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#1375 #13110433