Subgroups — C₁₃×#2657 #13111715

Order 1664.

844 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#127	C₂	1	3	yes	maximal, complemented
2	C₂×C₁₃×#124	C₂	1	3	yes	maximal, complemented
3	C₁₃×#392	C₂	1	8	yes	maximal, complemented
4	C₁₃×#376	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×Q₈×C₁₃	C₂²	1	1	yes	characteristic
6	C₂²×D₄×C₁₃	C₂²	1	3	yes	—
7	C₂²×D₄×C₁₃	C₂²	1	12	yes	—
8	C₁₃×#127	—	2	12	no	—
9	C₁₃×#124	—	2	12	no	—
10	C₂×C₁₃×C₂²⋊C₄	C₂²	1	12	yes	—
11	C₂×C₄²×C₁₃	C₂²	1	3	yes	—
12	C₁₃×#95	C₂²	1	4	yes	—
13	C₂⁴×C₁₃	C₂³	1	6	yes	—
14	C₂×Q₈×C₁₃	—	2	6	no	—
15	C₂×D₄×C₁₃	—	2	6	no	—
16	C₂×D₄×C₁₃	—	2	24	no	—
17	C₂×D₄×C₁₃	—	2	12	no	—
18	C₂×D₄×C₁₃	—	4	24	no	—
19	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
20	C₂²×C₄×C₁₃	C₂³	1	6	yes	—
21	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
22	C₁₃×C₂²⋊C₄	—	2	24	no	—
23	C₄²×C₁₃	D₄	1	12	yes	complemented
24	#2657	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂³×C₁₃	—	2	6	no	—
26	C₂³×C₁₃	—	2	12	no	—
27	C₂³×C₁₃	—	2	24	no	—
28	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
29	Q₈×C₁₃	—	4	4	no	—
30	D₄×C₁₃	—	4	48	no	—
31	D₄×C₁₃	—	4	12	no	—
32	C₂×C₄×C₁₃	—	2	12	no	—
33	C₂×C₄×C₁₃	—	2	6	no	—
34	C₂×C₄×C₁₃	C₂×D₄	1	12	yes	—
35	C₂×C₄×C₁₃	C₂×D₄	1	6	yes	—
36	C₂×#127	C₂×C₁₃	1	3	yes	complemented
37	C₂×#124	C₂×C₁₃	1	3	yes	complemented
38	#392	C₂×C₁₃	1	8	yes	complemented
39	#376	C₂×C₁₃	1	1	yes	characteristic, complemented
40	C₂²×C₁₃	—	4	6	no	—
41	C₂²×C₁₃	—	4	24	no	—
42	C₂²×C₁₃	—	4	12	no	—
43	C₂²×C₁₃	C₂²×D₄	1	3	yes	—
44	C₂²×C₁₃	H(5,𝔽₂)	1	4	yes	—
45	C₄×C₁₃	—	2	12	no	—
46	C₄×C₁₃	—	4	2	no	—
47	C₄×C₁₃	#127	1	4	yes	—
48	C₂²×Q₈	C₂²×C₁₃	1	1	yes	characteristic
49	C₂²×D₄	C₂²×C₁₃	1	3	yes	—
50	C₂²×D₄	C₂²×C₁₃	1	12	yes	—
51	#127	—	2	12	no	—
52	#124	—	2	12	no	—
53	C₂×C₂²⋊C₄	C₂²×C₁₃	1	12	yes	—
54	C₂×C₄²	C₂²×C₁₃	1	3	yes	—
55	#95	C₂²×C₁₃	1	4	yes	—
56	C₂×C₁₃	—	8	6	no	—
57	C₂×C₁₃	C₂×#127	1	1	yes	characteristic
58	C₂×C₁₃	#535	1	6	yes	—
59	C₂⁴	C₂³×C₁₃	1	6	yes	—
60	C₂×Q₈	—	2	6	no	—
61	C₂×D₄	—	2	6	no	—
62	C₂×D₄	—	2	24	no	—
63	C₂×D₄	—	2	12	no	—
64	C₂×D₄	—	4	24	no	—
65	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
66	C₂²×C₄	C₂³×C₁₃	1	6	yes	—
67	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
68	C₂²⋊C₄	—	2	24	no	—
69	C₄²	D₄×C₁₃	1	12	yes	complemented
70	C₁₃	#2657	1	1	yes	characteristic, direct product factor, Sylow
71	C₂³	—	2	6	no	—
72	C₂³	—	2	12	no	—
73	C₂³	—	2	24	no	—
74	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
75	Q₈	—	4	4	no	—
76	D₄	—	4	48	no	—
77	D₄	—	4	12	no	—
78	C₂×C₄	—	2	12	no	—
79	C₂×C₄	—	2	6	no	—
80	C₂×C₄	C₂×D₄×C₁₃	1	12	yes	—
81	C₂×C₄	C₂×D₄×C₁₃	1	6	yes	—
82	C₂²	—	4	6	no	—
83	C₂²	—	4	24	no	—
84	C₂²	—	4	12	no	—
85	C₂²	C₂²×D₄×C₁₃	1	3	yes	—
86	C₂²	C₁₃×H(5,𝔽₂)	1	4	yes	—
87	C₄	—	2	12	no	—
88	C₄	—	4	2	no	—
89	C₄	C₁₃×#127	1	4	yes	—
90	C₂	—	8	6	no	—
91	C₂	C₂×C₁₃×#127	1	1	yes	characteristic
92	C₂	C₁₃×#535	1	6	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#127	C₂	semidirect
2. C₂×C₁₃×#124	C₂	semidirect
3. C₁₃×#392	C₂	semidirect
4. C₁₃×#376	C₂	semidirect
23. C₄²×C₁₃	D₄	semidirect
24. #2657	C₁₃	direct (N × H)
36. C₂×#127	C₂×C₁₃	semidirect
37. C₂×#124	C₂×C₁₃	semidirect
38. #392	C₂×C₁₃	semidirect
39. #376	C₂×C₁₃	semidirect
69. C₄²	D₄×C₁₃	semidirect
70. C₁₃	#2657	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×C₁₃×#127	2
C₂×C₁₃×#124	2
C₁₃×#392	2
C₁₃×#376	2
#2657	13

Subgroups — C13×#2657 #13111715

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2657 #13111715