Subgroups — #13114966

Order 1664.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#382	C₂	1	1	yes	maximal, characteristic
2	#11718597	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#1055	C₂	1	1	yes	maximal, characteristic
4	#11718121	C₂	1	4	yes	maximal
5	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
6	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₁₃	C₂²	1	2	yes	—
8	C₂²×#1055	C₂²	1	2	yes	—
9	C₁₃×#95	—	2	2	no	—
10	#88071	—	2	2	no	—
11	C₄×#1055	C₄	1	4	yes	complemented
12	C₂²×C₄×C₁₃	—	2	2	no	—
13	C₂²×C₄×C₁₃	D₄	1	2	yes	—
14	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
15	C₂²×Dic₁₃	—	2	2	no	—
16	C₁₃×C₄⋊C₄	—	2	4	no	—
17	C₄²×C₁₃	C₂×C₄	1	2	yes	—
18	C₄²×C₁₃	Q₈	1	2	yes	—
19	C₄⋊Dic₁₃	—	2	4	no	—
20	C₂×#1055	—	2	2	no	—
21	C₂×#1055	—	2	2	no	—
22	C₂×#1055	C₂×C₄	1	4	yes	—
23	#1835	—	13	1	no	maximal, Sylow
24	C₂³×C₁₃	C₂×D₄	1	1	yes	characteristic
25	C₂×C₄×C₁₃	—	2	4	no	—
26	C₂×C₄×C₁₃	—	4	2	no	—
27	C₂×C₄×C₁₃	—	4	4	no	—
28	C₂×C₄×C₁₃	C₄⋊C₄	1	4	yes	—
29	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
31	C₂×C₄×C₁₃	#41	1	2	yes	—
32	C₂×C₄×C₁₃	#41	1	2	yes	—
33	C₂×Dic₁₃	—	4	2	no	—
34	C₂×Dic₁₃	—	4	4	no	—
35	#1055	—	2	4	no	—
36	C₂×C₄×C₈	—	13	1	no	—
37	#382	—	13	1	no	—
38	#382	D₁₃	1	1	yes	characteristic
39	#340	—	13	4	no	—
40	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
41	C₂²×C₁₃	#124	1	1	yes	characteristic
42	C₂²×C₁₃	#124	1	1	yes	characteristic
43	C₂²×C₁₃	#135	1	4	yes	—
44	C₄×C₁₃	—	2	4	no	—
45	C₄×C₁₃	—	8	2	no	—
46	C₄×C₁₃	#117	1	2	yes	—
47	C₄×C₁₃	#125	1	2	yes	—
48	Dic₁₃	—	8	2	no	—
49	C₂²×C₈	—	13	2	no	—
50	C₂×C₄⋊C₄	—	13	2	no	—
51	C₂×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
52	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
53	C₄×C₈	—	13	4	no	—
54	#95	—	2	2	no	—
55	#95	—	26	2	no	—
56	C₂×C₁₃	#382	1	1	yes	characteristic
57	C₂×C₁₃	#427	1	2	yes	—
58	C₂×C₁₃	#488	1	2	yes	—
59	C₂×C₁₃	#488	1	2	yes	—
60	C₂²×C₄	—	2	2	no	—
61	C₂²×C₄	—	26	2	no	—
62	C₂²×C₄	C₂²⋊D₁₃	1	2	yes	—
63	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
64	C₂×C₈	—	13	4	no	—
65	C₂×C₈	—	26	2	no	—
66	C₂×C₈	—	26	2	no	—
67	C₄⋊C₄	—	2	4	no	—
68	C₄⋊C₄	—	26	4	no	—
69	C₄²	Dic₂₆	1	2	yes	—
70	C₄²	C₄×D₁₃	1	2	yes	—
71	C₁₃	#1835	1	1	yes	characteristic, complemented, Sylow
72	C₂³	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
73	C₂×C₄	—	2	4	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	—	4	4	no	—
76	C₂×C₄	—	52	2	no	—
77	C₂×C₄	—	52	4	no	—
78	C₂×C₄	#6101	1	4	yes	—
79	C₂×C₄	C₂×Dic₂₆	1	1	yes	characteristic
80	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
81	C₂×C₄	#6129	1	2	yes	—
82	C₂×C₄	#6131	1	2	yes	—
83	C₈	—	26	4	no	—
84	C₂²	C₂×#6101	1	1	yes	characteristic
85	C₂²	#88190	1	1	yes	characteristic
86	C₂²	#88201	1	1	yes	characteristic
87	C₂²	#88204	1	4	yes	—
88	C₄	—	2	4	no	—
89	C₄	—	8	2	no	—
90	C₄	—	104	2	no	—
91	C₄	#88144	1	2	yes	—
92	C₄	#88146	1	2	yes	—
93	C₂	#11718638	1	1	yes	characteristic
94	C₂	#11718659	1	2	yes	—
95	C₂	#11718717	1	2	yes	—
96	C₂	#11718729	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₃
Fitting	C₁₃×#382	C₂
socle, prime radical	C₂³×C₁₃	C₂×D₄
cosocle	C₂²×C₄×C₁₃	C₂³
hypercenter	#382	D₁₃
hypocenter	C₁₃	#1835
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #382

Complements

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

N	H ≅ G/N	type
11. C₄×#1055	C₄	semidirect
71. C₁₃	#1835	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#382	2
#11718597	2
C₂×C₄×#1055	2
#11718121	2
#1835	13