Subgroups — C₂×#11718039 #13117127

Order 1664.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#88034	C₂	1	1	yes	maximal, characteristic, complemented
4	#11718039	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₈×D₁₃	C₄	1	1	yes	characteristic
6	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
7	C₂×#6090	C₄	1	1	yes	characteristic
8	C₁₆×D₁₃	C₄	1	2	yes	—
9	C₁₆×D₁₃	C₂²	1	2	yes	—
10	C₁₃×C₃₂	C₂²	1	2	yes	complemented
11	#88034	C₂²	1	2	yes	complemented
12	C₂×C₄×D₁₃	C₈	1	1	yes	characteristic
13	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
14	C₂×#1055	C₈	1	1	yes	characteristic
15	C₈×D₁₃	C₈	1	2	yes	—
16	C₈×D₁₃	C₂×C₄	1	2	yes	—
17	C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
18	C₁₃×C₁₆	C₂³	1	1	yes	characteristic
19	#6090	C₂×C₄	1	2	yes	—
20	C₂×M₆₄	—	13	1	no	maximal, Sylow
21	C₂²×D₁₃	C₁₆	1	1	yes	characteristic
22	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
23	C₂×Dic₁₃	C₁₆	1	1	yes	characteristic
24	C₄×D₁₃	C₁₆	1	2	yes	—
25	C₄×D₁₃	C₂×C₈	1	2	yes	—
26	C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
27	C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
28	#1055	C₂×C₈	1	2	yes	—
29	C₂²×C₁₆	—	13	1	no	—
30	M₆₄	—	13	4	no	—
31	C₂×C₃₂	—	13	1	no	—
32	C₂×C₃₂	D₁₃	1	1	yes	characteristic, complemented
33	C₂²×C₁₃	C₂×C₁₆	1	1	yes	characteristic
34	C₂×D₁₃	—	2	2	no	—
35	C₂×D₁₃	C₂×C₁₆	1	2	yes	—
36	C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
37	C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
38	Dic₁₃	C₂×C₁₆	1	2	yes	—
39	C₂²×C₈	—	13	1	no	—
40	C₂×C₁₆	—	13	1	no	—
41	C₂×C₁₆	—	13	2	no	—
42	C₂×C₁₆	—	13	2	no	—
43	C₂×C₁₆	C₂×D₁₃	1	1	yes	characteristic
44	C₃₂	—	13	2	no	—
45	C₃₂	C₂×D₁₃	1	2	yes	complemented
46	C₂×C₁₃	M₆₄	1	2	yes	complemented
47	C₂×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
48	D₁₃	—	2	2	no	—
49	C₂²×C₄	—	13	1	no	—
50	C₂×C₈	—	13	1	no	—
51	C₂×C₈	—	13	2	no	—
52	C₂×C₈	—	13	2	no	—
53	C₂×C₈	C₄×D₁₃	1	1	yes	characteristic
54	C₁₆	—	13	2	no	—
55	C₁₆	C₄×D₁₃	1	1	yes	characteristic
56	C₁₆	C₂²×D₁₃	1	1	yes	characteristic
57	C₁₃	C₂×M₆₄	1	1	yes	characteristic, complemented, Sylow
58	C₂³	—	13	1	no	—
59	C₂×C₄	—	13	1	no	—
60	C₂×C₄	—	13	2	no	—
61	C₂×C₄	—	13	2	no	—
62	C₂×C₄	C₈×D₁₃	1	1	yes	characteristic
63	C₈	—	13	2	no	—
64	C₈	C₈×D₁₃	1	1	yes	characteristic
65	C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
66	C₂²	—	13	2	no	—
67	C₂²	—	26	2	no	—
68	C₂²	C₁₆×D₁₃	1	1	yes	characteristic
69	C₄	—	13	2	no	—
70	C₄	C₁₆×D₁₃	1	1	yes	characteristic
71	C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
72	C₂	—	26	2	no	—
73	C₂	#11718039	1	2	yes	direct product factor
74	C₂	C₂×C₁₆×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	C₂×D₁₃
commutator	C₂×C₁₃	C₂²×C₁₆
Frattini	C₁₆	C₂²×D₁₃
Fitting	C₂×C₁₃×C₃₂	C₂
socle	C₂²×C₁₃	C₂×C₁₆
prime radical	C₂²×D₁₃	C₁₆
cosocle	C₁₃×C₁₆	C₂³
hypercenter	C₂×C₃₂	D₁₃
hypocenter	C₁₃	C₂×M₆₄
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×C₃₂	C₂	semidirect
3. C₂×#88034	C₂	semidirect
4. #11718039	C₂	direct (N × H)
10. C₁₃×C₃₂	C₂²	semidirect
11. #88034	C₂²	semidirect
32. C₂×C₃₂	D₁₃	semidirect
45. C₃₂	C₂×D₁₃	semidirect
46. C₂×C₁₃	M₆₄	semidirect
57. C₁₃	C₂×M₆₄	semidirect
73. C₂	#11718039	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×C₁₆×D₁₃	2
C₂×C₁₃×C₃₂	2
C₂×#88034	2
#11718039	2
C₂×M₆₄	13

Subgroups — C2×#11718039 #13117127

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11718039 #13117127