Subgroups — #13117093

Order 1664.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#88068	C₂	1	4	yes	maximal, complemented
3	#11718356	C₂	1	1	yes	maximal, characteristic
4	C₄×#6090	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×Q₁₆	—	2	1	no	—
6	C₂×C₁₃×Q₁₆	C₂²	1	2	yes	—
7	C₁₃×C₄⋊Q₈	—	2	1	no	—
8	C₂×D₁₀₄	—	2	1	no	—
9	C₂×D₁₀₄	C₂²	1	2	yes	—
10	#88128	—	2	1	no	—
11	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	#88068	—	2	8	no	—
13	C₂×#6090	C₂²	1	2	yes	—
14	C₂×Q₈×C₁₃	—	2	2	no	—
15	C₂×D₅₂	—	2	2	no	—
16	C₂×D₅₂	—	4	2	no	—
17	C₁₃×Q₁₆	—	2	4	no	—
18	C₁₃×Q₁₆	—	4	2	no	—
19	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
20	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
21	C₁₃×C₄⋊C₄	—	4	2	no	—
22	C₄²×C₁₃	D₄	1	1	yes	characteristic
23	D₁₀₄	—	2	4	no	—
24	D₁₀₄	—	4	2	no	—
25	#6090	D₄	1	4	yes	complemented
26	#2248	—	13	1	no	maximal, Sylow
27	C₂²×D₁₃	—	4	2	no	—
28	Q₈×C₁₃	—	4	2	no	—
29	Q₈×C₁₃	—	4	2	no	—
30	C₂×C₄×C₁₃	—	4	2	no	—
31	C₂×C₄×C₁₃	D₈	1	2	yes	—
32	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
33	D₅₂	—	4	2	no	—
34	D₅₂	—	4	2	no	—
35	D₅₂	—	8	4	no	—
36	C₈×C₁₃	D₈	1	2	yes	—
37	C₈×C₁₃	C₂×D₄	1	2	yes	—
38	C₂×SD₃₂	—	13	4	no	—
39	#494	D₁₃	1	1	yes	characteristic, complemented
40	#493	—	13	1	no	—
41	C₄×C₁₆	—	13	1	no	—
42	C₂²×C₁₃	C₂×D₈	1	1	yes	characteristic
43	C₂×D₁₃	—	8	2	no	—
44	C₂×D₁₃	—	8	4	no	—
45	C₄×C₁₃	—	8	2	no	—
46	C₄×C₁₃	SD₃₂	1	4	yes	complemented
47	C₄×C₁₃	#127	1	1	yes	characteristic
48	C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
49	C₂×Q₁₆	—	2	1	no	—
50	C₂×Q₁₆	C₂×D₁₃	1	2	yes	—
51	C₂×D₈	—	13	2	no	—
52	C₂×D₈	—	26	1	no	—
53	C₄⋊Q₈	—	2	1	no	—
54	#127	—	26	1	no	—
55	SD₃₂	—	26	8	no	—
56	C₂×C₁₆	—	13	2	no	—
57	C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
58	C₂×C₁₃	#493	1	1	yes	characteristic
59	C₂×C₁₃	C₂×SD₃₂	1	2	yes	—
60	D₁₃	—	16	2	no	—
61	C₂×Q₈	—	2	2	no	—
62	C₂×D₄	—	26	2	no	—
63	C₂×D₄	—	52	2	no	—
64	Q₁₆	—	2	4	no	—
65	Q₁₆	—	4	2	no	—
66	D₈	—	26	4	no	—
67	D₈	—	52	2	no	—
68	C₂×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
69	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
70	C₄⋊C₄	—	4	2	no	—
71	C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
72	C₁₆	—	13	4	no	—
73	C₁₃	#2248	1	1	yes	characteristic, complemented, Sylow
74	C₂³	—	52	2	no	—
75	Q₈	—	4	2	no	—
76	Q₈	—	4	2	no	—
77	D₄	—	52	2	no	—
78	D₄	—	52	2	no	—
79	D₄	—	104	4	no	—
80	C₂×C₄	—	4	2	no	—
81	C₂×C₄	#6104	1	2	yes	—
82	C₂×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
83	C₈	#6104	1	2	yes	—
84	C₈	D₄×D₁₃	1	2	yes	—
85	C₂²	—	104	2	no	—
86	C₂²	—	104	4	no	—
87	C₂²	C₂×#6104	1	1	yes	characteristic
88	C₄	—	8	2	no	—
89	C₄	#88068	1	4	yes	complemented
90	C₄	C₂×#6104	1	1	yes	characteristic
91	C₄	#88194	1	1	yes	characteristic
92	C₂	—	208	2	no	—
93	C₂	#11718734	1	1	yes	characteristic
94	C₂	C₂×#88068	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#6104
commutator, cosocle	C₂×C₈×C₁₃	C₂³
Frattini	C₂×C₈	C₂²×D₁₃
Fitting	C₁₃×#494	C₂
socle	C₂²×C₁₃	C₂×D₈
prime radical	#11718356	C₂
hypercenter	#494	D₁₃
hypocenter	C₁₃	#2248
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #494

Complements

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

N	H ≅ G/N	type
1. C₁₃×#494	C₂	semidirect
2. C₂×#88068	C₂	semidirect
4. C₄×#6090	C₂	semidirect
25. #6090	D₄	semidirect
39. #494	D₁₃	semidirect
46. C₄×C₁₃	SD₃₂	semidirect
73. C₁₃	#2248	semidirect
89. C₄	#88068	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#494	2
C₂×#88068	2
#11718356	2
C₄×#6090	2
#2248	13