Subgroups — #13114973

Order 1664.

188 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#423	C₂	1	1	yes	maximal, characteristic
2	#11718585	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#1055	C₂	1	1	yes	maximal, characteristic
4	#11718150	C₂	1	4	yes	maximal
5	C₂×C₁₃×M₁₆	C₂²	1	2	yes	—
6	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×#6099	C₂²	1	2	yes	—
8	C₂²×#1055	C₂²	1	2	yes	—
9	C₁₃×C₄⋊C₈	—	2	2	no	—
10	C₄⋊#1055	—	2	2	no	—
11	C₄×#1055	C₄	1	2	yes	—
12	C₄×#1055	C₄	1	2	yes	—
13	C₂²×C₄×C₁₃	Q₈	1	2	yes	—
14	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
15	C₁₃×M₁₆	—	2	4	no	—
16	C₂×C₈×C₁₃	—	2	2	no	—
17	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₄²×C₁₃	D₄	1	2	yes	—
20	#6099	—	2	4	no	—
21	C₂×#1055	—	2	2	no	—
22	C₂×#1055	—	2	2	no	—
23	C₂×#1055	—	2	2	no	—
24	C₂×#1055	C₂×C₄	1	4	yes	—
25	#1837	—	13	1	no	maximal, Sylow
26	C₂³×C₁₃	C₂×Q₈	1	1	yes	characteristic
27	C₂×C₄×C₁₃	—	2	4	no	—
28	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
30	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₁₃	#41	1	2	yes	—
33	C₂×C₄×C₁₃	#41	1	2	yes	—
34	C₈×C₁₃	—	4	2	no	—
35	#1055	—	2	4	no	—
36	#1055	—	4	2	no	—
37	#423	—	13	1	no	—
38	#423	D₁₃	1	1	yes	characteristic
39	C₂×C₄×C₈	—	13	1	no	—
40	#341	—	13	4	no	—
41	C₂²×C₁₃	—	2	2	no	—
42	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
43	C₂²×C₁₃	#125	1	2	yes	—
44	C₄×C₁₃	—	2	2	no	—
45	C₄×C₁₃	#108	1	4	yes	—
46	C₄×C₁₃	#117	1	2	yes	—
47	C₄×C₁₃	#124	1	1	yes	characteristic
48	C₄×C₁₃	#124	1	1	yes	characteristic
49	C₂×M₁₆	—	13	2	no	—
50	C₂×M₁₆	C₂×D₁₃	1	2	yes	—
51	C₂²×C₈	—	13	2	no	—
52	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
53	C₄⋊C₈	—	2	2	no	—
54	C₄⋊C₈	—	26	2	no	—
55	C₄×C₈	—	13	2	no	—
56	C₄×C₈	—	13	2	no	—
57	C₂×C₁₃	—	2	2	no	—
58	C₂×C₁₃	#382	1	1	yes	characteristic
59	C₂×C₁₃	C₂×#108	1	2	yes	—
60	C₂²×C₄	Dic₂₆	1	2	yes	—
61	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
62	M₁₆	—	2	4	no	—
63	M₁₆	—	26	4	no	—
64	C₂×C₈	—	2	2	no	—
65	C₂×C₈	—	13	4	no	—
66	C₂×C₈	—	26	2	no	—
67	C₂×C₈	—	26	2	no	—
68	C₂×C₈	—	26	2	no	—
69	C₄²	C₄×D₁₃	1	1	yes	characteristic
70	C₄²	C₄×D₁₃	1	1	yes	characteristic
71	C₄²	C₂²⋊D₁₃	1	2	yes	—
72	C₁₃	#1837	1	1	yes	characteristic, complemented, Sylow
73	C₂³	C₂×Dic₂₆	1	1	yes	characteristic
74	C₂×C₄	—	2	4	no	—
75	C₂×C₄	#6101	1	2	yes	—
76	C₂×C₄	#6101	1	2	yes	—
77	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
78	C₂×C₄	#6129	1	2	yes	—
79	C₂×C₄	#6131	1	2	yes	—
80	C₂×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
81	C₈	—	4	2	no	—
82	C₈	—	26	4	no	—
83	C₈	—	52	2	no	—
84	C₂²	—	2	2	no	—
85	C₂²	#88144	1	2	yes	—
86	C₂²	C₂×#6101	1	1	yes	characteristic
87	C₄	—	2	2	no	—
88	C₄	#88062	1	4	yes	—
89	C₄	#88146	1	2	yes	—
90	C₄	#88190	1	1	yes	characteristic
91	C₄	#88201	1	1	yes	characteristic
92	C₂	—	2	2	no	—
93	C₂	#11718638	1	1	yes	characteristic
94	C₂	C₂×#88062	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₃
Fitting	C₁₃×#423	C₂
socle	C₂²×C₁₃	C₂×C₄⋊C₄
prime radical	C₂³×C₁₃	C₂×Q₈
cosocle	C₂²×C₄×C₁₃	C₂³
hypercenter	#423	D₁₃
hypocenter	C₁₃	#1837
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #423

Complements

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

N	H ≅ G/N	type
72. C₁₃	#1837	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#423	2
#11718585	2
C₂×C₄×#1055	2
#11718150	2
#1837	13