Subgroups — #13129779

Order 1664.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718637	C₂	1	1	yes	maximal, characteristic
2	#11718285	C₂	1	2	yes	maximal
3	C₂×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
4	C₂×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
5	C₂×#6101	—	2	2	no	—
6	C₂×C₄×Dic₁₃	C₄	1	1	yes	characteristic
7	C₂²⋊#1057	—	2	2	no	—
8	C₂²×C₄×C₁₃	—	2	1	no	—
9	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
10	C₂²×Dic₁₃	—	2	1	no	—
11	C₂²×Dic₁₃	D₄	1	2	yes	—
12	C₂×#1057	—	4	2	no	—
13	C₁₃×C₄⋊C₄	—	4	1	no	—
14	C₄⋊Dic₁₃	—	4	1	no	—
15	#6101	—	4	4	no	—
16	C₄×Dic₁₃	—	2	1	no	—
17	C₄×Dic₁₃	C₈	1	2	yes	complemented
18	#1325	—	13	1	no	maximal, Sylow
19	C₂³×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
20	C₂×C₄×C₁₃	—	2	1	no	—
21	C₂×C₄×C₁₃	—	2	1	no	—
22	C₂×C₄×C₁₃	—	4	2	no	—
23	C₂×C₄×C₁₃	—	4	1	no	—
24	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
25	C₂×C₄×C₁₃	M₁₆	1	1	yes	characteristic
26	C₂×Dic₁₃	—	2	2	no	—
27	C₂×Dic₁₃	—	2	2	no	—
28	C₂×Dic₁₃	—	2	2	no	—
29	C₂×Dic₁₃	—	2	2	no	—
30	C₂×Dic₁₃	—	4	2	no	—
31	#1057	—	8	2	no	—
32	#384	—	13	1	no	—
33	#324	—	13	2	no	—
34	C₂²×C₁₃	—	2	1	no	—
35	C₂²×C₁₃	—	2	1	no	—
36	C₂²×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
37	C₂²×C₁₃	#99	1	1	yes	characteristic
38	C₂²×C₁₃	#101	1	1	yes	characteristic
39	C₄×C₁₃	—	2	1	no	—
40	C₄×C₁₃	—	2	1	no	—
41	C₄×C₁₃	—	8	1	no	—
42	Dic₁₃	—	2	4	no	—
43	Dic₁₃	—	4	2	no	—
44	C₂×C₄⋊C₄	—	13	1	no	—
45	C₂×C₄⋊C₄	—	26	2	no	—
46	C₂×C₄⋊C₄	#261	1	1	yes	characteristic
47	C₂×C₄²	—	13	1	no	—
48	C₂²⋊C₈	—	26	2	no	—
49	C₂×C₁₃	—	2	1	no	—
50	C₂×C₁₃	—	2	1	no	—
51	C₂×C₁₃	#324	1	1	yes	characteristic
52	C₂×C₁₃	#353	1	1	yes	characteristic
53	C₂×C₁₃	#356	1	1	yes	characteristic
54	C₂²×C₄	—	2	1	no	—
55	C₂²×C₄	—	13	2	no	—
56	C₂²×C₄	—	26	1	no	—
57	C₂²×C₄	C₂×#261	1	1	yes	characteristic
58	C₂×C₈	—	52	2	no	—
59	C₄⋊C₄	—	4	1	no	—
60	C₄⋊C₄	—	52	1	no	—
61	C₄⋊C₄	—	52	4	no	—
62	C₄²	—	13	2	no	—
63	C₄²	—	26	1	no	—
64	C₁₃	#1325	1	1	yes	characteristic, complemented, Sylow
65	C₂³	C₂²⋊#261	1	1	yes	characteristic
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	—	4	2	no	—
69	C₂×C₄	—	4	1	no	—
70	C₂×C₄	—	26	2	no	—
71	C₂×C₄	—	26	2	no	—
72	C₂×C₄	—	26	2	no	—
73	C₂×C₄	—	26	2	no	—
74	C₂×C₄	—	52	2	no	—
75	C₂×C₄	D₁₃⋊C₈	1	1	yes	characteristic
76	C₂×C₄	#6118	1	1	yes	characteristic
77	C₈	—	104	2	no	—
78	C₂²	—	2	1	no	—
79	C₂²	—	2	1	no	—
80	C₂²	#88111	1	1	yes	characteristic
81	C₂²	#88113	1	1	yes	characteristic
82	C₂²	#88119	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	2	1	no	—
85	C₄	—	8	1	no	—
86	C₄	—	26	4	no	—
87	C₄	—	52	2	no	—
88	C₂	—	2	1	no	—
89	C₂	—	2	1	no	—
90	C₂	#11718286	1	1	yes	characteristic
91	C₂	#11718294	1	1	yes	characteristic
92	C₂	#11718301	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#88119
commutator	C₂×C₄×C₁₃	C₂×C₈
Frattini	C₂²×C₄	C₂×#261
Fitting	C₂×C₁₃×C₄⋊C₄	C₄
socle	C₂²×C₁₃	#99
prime radical	C₂³×C₁₃	C₂²⋊C₄
cosocle	C₂×C₄⋊Dic₁₃	C₂²
hypercenter	C₂×C₄⋊C₄	#261
hypocenter	C₁₃	#1325
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
17. C₄×Dic₁₃	C₈	semidirect
64. C₁₃	#1325	semidirect

Maximal subgroups

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

subgroup	index
#11718637	2
#11718285	2
#1325	13