Subgroups — C₂²×#88124 #13128089

Order 1664.

1192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄²×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊Dic₁₃	C₂	1	2	yes	maximal
3	C₂²×#6101	C₂	1	4	yes	maximal
4	C₂×#88124	C₂	1	24	yes	maximal, direct product factor
5	C₂³×C₄×C₁₃	C₂²	1	2	yes	—
6	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic
7	C₂³×Dic₁₃	C₂²	1	4	yes	—
8	C₂×C₄²×C₁₃	C₂²	1	12	yes	—
9	C₂×C₄⋊Dic₁₃	C₂²	1	24	yes	—
10	C₂×#6101	C₂²	1	48	yes	—
11	#88124	C₂²	1	64	yes	direct product factor
12	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
13	C₂²×C₄×C₁₃	—	2	8	no	—
14	C₂²×C₄×C₁₃	Q₈	1	8	yes	—
15	C₂²×C₄×C₁₃	C₂³	1	12	yes	—
16	C₂²×C₄×C₁₃	C₂³	1	6	yes	—
17	C₂²×Dic₁₃	—	2	16	no	—
18	C₂²×Dic₁₃	C₂³	1	24	yes	—
19	C₄²×C₁₃	C₂³	1	16	yes	—
20	C₄⋊Dic₁₃	C₂³	1	32	yes	—
21	#6101	C₂³	1	64	yes	—
22	C₂²×#125	—	13	1	no	maximal, Sylow
23	C₂³×C₁₃	C₂×Q₈	1	4	yes	—
24	C₂³×C₁₃	#41	1	8	yes	—
25	C₂³×C₁₃	C₂⁴	1	3	yes	—
26	C₂×C₄×C₁₃	—	2	24	no	—
27	C₂×C₄×C₁₃	C₂×Q₈	1	24	yes	—
28	C₂×C₄×C₁₃	C₂⁴	1	8	yes	—
29	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
30	C₂×Dic₁₃	—	2	48	no	—
31	C₂×Dic₁₃	C₂⁴	1	16	yes	—
32	C₂×#125	—	13	24	no	—
33	C₂²×C₄⋊C₄	—	13	4	no	—
34	C₂²×C₄⋊C₄	—	13	2	no	—
35	C₂²×C₄²	D₁₃	1	1	yes	characteristic
36	C₂²×C₁₃	#125	1	16	yes	complemented
37	C₂²×C₁₃	C₂²×Q₈	1	6	yes	—
38	C₂²×C₁₃	C₂×#41	1	12	yes	—
39	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
40	C₄×C₁₃	—	2	8	no	—
41	C₄×C₁₃	C₂²×Q₈	1	8	yes	—
42	Dic₁₃	—	2	16	no	—
43	C₂³×C₄	—	13	4	no	—
44	C₂³×C₄	C₂×D₁₃	1	2	yes	—
45	C₂³×C₄	C₂×D₁₃	1	1	yes	characteristic
46	#125	—	13	64	no	—
47	C₂×C₄⋊C₄	—	13	48	no	—
48	C₂×C₄⋊C₄	—	13	24	no	—
49	C₂×C₄²	C₂×D₁₃	1	12	yes	—
50	C₂×C₁₃	C₂×#125	1	12	yes	complemented
51	C₂×C₁₃	C₂³×Q₈	1	1	yes	characteristic
52	C₂×C₁₃	C₂²×#41	1	2	yes	—
53	C₂⁴	C₂²×D₁₃	1	1	yes	characteristic
54	C₂²×C₄	—	2	8	no	—
55	C₂²×C₄	—	13	24	no	—
56	C₂²×C₄	—	26	16	no	—
57	C₂²×C₄	Dic₂₆	1	8	yes	—
58	C₂²×C₄	C₂²×D₁₃	1	12	yes	—
59	C₂²×C₄	C₂²×D₁₃	1	6	yes	—
60	C₄⋊C₄	—	13	64	no	—
61	C₄⋊C₄	—	13	32	no	—
62	C₄²	C₂²×D₁₃	1	16	yes	—
63	C₁₃	C₂²×#125	1	1	yes	characteristic, complemented, Sylow
64	C₂³	C₂×Dic₂₆	1	4	yes	—
65	C₂³	#6127	1	8	yes	—
66	C₂³	C₂³×D₁₃	1	3	yes	—
67	C₂×C₄	—	2	24	no	—
68	C₂×C₄	—	13	16	no	—
69	C₂×C₄	—	26	48	no	—
70	C₂×C₄	C₂×Dic₂₆	1	24	yes	—
71	C₂×C₄	C₂³×D₁₃	1	8	yes	—
72	C₂×C₄	C₂³×D₁₃	1	4	yes	—
73	C₂²	#88124	1	16	yes	direct product factor
74	C₂²	C₂²×Dic₂₆	1	6	yes	—
75	C₂²	C₂×#6127	1	12	yes	—
76	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
77	C₄	—	2	8	no	—
78	C₄	—	26	16	no	—
79	C₄	C₂²×Dic₂₆	1	8	yes	—
80	C₂	C₂×#88124	1	12	yes	direct product factor
81	C₂	C₂³×Dic₂₆	1	1	yes	characteristic
82	C₂	C₂²×#6127	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂²×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁵
Frattini	C₂²	C₂⁴×D₁₃
Fitting	C₂²×C₄²×C₁₃	C₂
socle, prime radical	C₂⁴×C₁₃	C₂³
hypercenter	C₂²×C₄²	D₁₃
hypocenter	C₁₃	C₂²×#125
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
4. C₂×#88124	C₂	direct (N × H)
11. #88124	C₂²	direct (N × H)
36. C₂²×C₁₃	#125	semidirect
50. C₂×C₁₃	C₂×#125	semidirect
63. C₁₃	C₂²×#125	semidirect
73. C₂²	#88124	direct (N × H)
80. C₂	C₂×#88124	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄²×C₁₃	2
C₂²×C₄⋊Dic₁₃	2
C₂²×#6101	2
C₂×#88124	2
C₂²×#125	13

Subgroups — C22×#88124 #13128089

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#88124 #13128089