Subgroups — C₁₃×#33974 #15720313

Order 3328.

462 conjugacy classes of subgroups.

The subgroup lattice has 112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#504	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2258	C₂	1	8	yes	maximal, complemented
3	C₂×C₁₃×M₆₄	C₂	1	6	yes	maximal, complemented
4	C₂×C₁₃×#131	C₄	1	1	yes	characteristic
5	C₁₃×#504	C₄	1	4	yes	—
6	C₁₃×#504	C₂²	1	4	yes	—
7	C₂×C₁₃×M₃₂	C₄	1	3	yes	—
8	C₂²×C₁₃×C₁₆	C₂²	1	3	yes	—
9	C₁₃×M₆₄	C₂²	1	4	yes	—
10	C₁₃×M₆₄	C₂²	1	12	yes	complemented
11	C₂×C₁₃×C₃₂	C₂²	1	12	yes	complemented
12	C₂×C₁₃×#41	C₈	1	1	yes	characteristic
13	C₁₃×#131	C₈	1	4	yes	—
14	C₁₃×#131	C₂×C₄	1	4	yes	—
15	C₂×C₁₃×M₁₆	C₈	1	3	yes	—
16	C₂²×C₈×C₁₃	C₂×C₄	1	3	yes	—
17	C₁₃×M₃₂	C₂×C₄	1	12	yes	—
18	C₂×C₁₃×C₁₆	C₂×C₄	1	3	yes	—
19	C₂×C₁₃×C₁₆	C₂×C₄	1	6	yes	—
20	C₂×C₁₃×C₁₆	C₂³	1	6	yes	—
21	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
22	C₁₃×C₃₂	C₂³	1	8	yes	—
23	#33974	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₁₃×#41	C₁₆	1	4	yes	—
25	C₁₃×#41	C₂×C₈	1	4	yes	—
26	C₂×Q₈×C₁₃	C₁₆	1	1	yes	characteristic
27	C₂×D₄×C₁₃	C₁₆	1	3	yes	—
28	C₂²×C₄×C₁₃	C₂×C₈	1	3	yes	—
29	C₁₃×M₁₆	C₂×C₈	1	12	yes	—
30	C₂×C₈×C₁₃	C₂×C₈	1	3	yes	—
31	C₂×C₈×C₁₃	C₂×C₈	1	6	yes	—
32	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₈×C₁₃	C₂²×C₄	1	6	yes	—
34	C₁₃×C₁₆	C₂²×C₄	1	1	yes	characteristic
35	C₁₃×C₁₆	C₂²×C₄	1	6	yes	—
36	C₁₃×C₁₆	C₂⁴	1	1	yes	characteristic
37	C₂×#504	C₂×C₁₃	1	1	yes	characteristic
38	#2258	C₂×C₁₃	1	8	yes	complemented
39	C₂×M₆₄	C₂×C₁₃	1	6	yes	complemented
40	C₂³×C₁₃	C₂×C₁₆	1	3	yes	—
41	Q₈×C₁₃	C₂×C₁₆	1	4	yes	—
42	D₄×C₁₃	C₂×C₁₆	1	12	yes	—
43	C₂×C₄×C₁₃	C₂×C₁₆	1	3	yes	—
44	C₂×C₄×C₁₃	C₂×C₁₆	1	6	yes	—
45	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
46	C₂×C₄×C₁₃	C₂²×C₈	1	6	yes	—
47	C₈×C₁₃	C₂²×C₈	1	1	yes	characteristic
48	C₈×C₁₃	C₂²×C₈	1	6	yes	—
49	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
50	C₂×#131	C₄×C₁₃	1	1	yes	characteristic
51	#504	C₄×C₁₃	1	4	yes	—
52	#504	C₂²×C₁₃	1	4	yes	—
53	C₂×M₃₂	C₄×C₁₃	1	3	yes	—
54	C₂²×C₁₆	C₂²×C₁₃	1	3	yes	—
55	M₆₄	C₂²×C₁₃	1	4	yes	—
56	M₆₄	C₂²×C₁₃	1	12	yes	complemented
57	C₂×C₃₂	C₂²×C₁₃	1	12	yes	complemented
58	C₂²×C₁₃	—	4	3	no	—
59	C₂²×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
60	C₂²×C₁₃	C₂²×C₁₆	1	6	yes	—
61	C₄×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
62	C₄×C₁₃	C₂²×C₁₆	1	6	yes	—
63	C₄×C₁₃	C₂³×C₈	1	1	yes	characteristic
64	C₂×#41	C₈×C₁₃	1	1	yes	characteristic
65	#131	C₈×C₁₃	1	4	yes	—
66	#131	C₂×C₄×C₁₃	1	4	yes	—
67	C₂×M₁₆	C₈×C₁₃	1	3	yes	—
68	C₂²×C₈	C₂×C₄×C₁₃	1	3	yes	—
69	M₃₂	C₂×C₄×C₁₃	1	12	yes	—
70	C₂×C₁₆	C₂×C₄×C₁₃	1	3	yes	—
71	C₂×C₁₆	C₂×C₄×C₁₃	1	6	yes	—
72	C₂×C₁₆	C₂³×C₁₃	1	6	yes	—
73	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
74	C₃₂	C₂³×C₁₃	1	8	yes	—
75	C₂×C₁₃	—	2	1	no	—
76	C₂×C₁₃	—	2	6	no	—
77	C₂×C₁₃	C₂³×C₁₆	1	1	yes	characteristic
78	#41	C₁₃×C₁₆	1	4	yes	—
79	#41	C₂×C₈×C₁₃	1	4	yes	—
80	C₂×Q₈	C₁₃×C₁₆	1	1	yes	characteristic
81	C₂×D₄	C₁₃×C₁₆	1	3	yes	—
82	C₂²×C₄	C₂×C₈×C₁₃	1	3	yes	—
83	M₁₆	C₂×C₈×C₁₃	1	12	yes	—
84	C₂×C₈	C₂×C₈×C₁₃	1	3	yes	—
85	C₂×C₈	C₂×C₈×C₁₃	1	6	yes	—
86	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
87	C₂×C₈	C₂²×C₄×C₁₃	1	6	yes	—
88	C₁₆	C₂²×C₄×C₁₃	1	1	yes	characteristic
89	C₁₆	C₂²×C₄×C₁₃	1	6	yes	—
90	C₁₆	C₂⁴×C₁₃	1	1	yes	characteristic
91	C₁₃	#33974	1	1	yes	characteristic, direct product factor, Sylow
92	C₂³	C₂×C₁₃×C₁₆	1	3	yes	—
93	Q₈	C₂×C₁₃×C₁₆	1	4	yes	—
94	D₄	C₂×C₁₃×C₁₆	1	12	yes	—
95	C₂×C₄	C₂×C₁₃×C₁₆	1	3	yes	—
96	C₂×C₄	C₂×C₁₃×C₁₆	1	6	yes	—
97	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
98	C₂×C₄	C₂²×C₈×C₁₃	1	6	yes	—
99	C₈	C₂²×C₈×C₁₃	1	1	yes	characteristic
100	C₈	C₂²×C₈×C₁₃	1	6	yes	—
101	C₈	C₂³×C₄×C₁₃	1	1	yes	characteristic
102	C₂²	—	4	3	no	—
103	C₂²	C₂²×C₁₃×C₁₆	1	1	yes	characteristic
104	C₂²	C₂²×C₁₃×C₁₆	1	6	yes	—
105	C₄	C₂²×C₁₃×C₁₆	1	1	yes	characteristic
106	C₄	C₂²×C₁₃×C₁₆	1	6	yes	—
107	C₄	C₂³×C₈×C₁₃	1	1	yes	characteristic
108	C₂	—	2	1	no	—
109	C₂	—	2	6	no	—
110	C₂	C₂³×C₁₃×C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₁₃×C₁₆	C₂⁴
commutator	C₂	C₂³×C₁₃×C₁₆
Frattini, cosocle	C₁₆	C₂⁴×C₁₃
socle	C₂×C₁₃	C₂³×C₁₆
prime radical	C₂×C₁₃×#41	C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₁₃×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2258	C₂	semidirect
3. C₂×C₁₃×M₆₄	C₂	semidirect
10. C₁₃×M₆₄	C₂²	semidirect
11. C₂×C₁₃×C₃₂	C₂²	semidirect
23. #33974	C₁₃	direct (N × H)
38. #2258	C₂×C₁₃	semidirect
39. C₂×M₆₄	C₂×C₁₃	semidirect
56. M₆₄	C₂²×C₁₃	semidirect
57. C₂×C₃₂	C₂²×C₁₃	semidirect
91. C₁₃	#33974	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×#504	2
C₁₃×#2258	2
C₂×C₁₃×M₆₄	2
#33974	13

Subgroups — C13×#33974 #15720313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33974 #15720313