Subgroups — C₁₃×#33496 #15719835

Order 3328.

526 conjugacy classes of subgroups.

The subgroup lattice has 128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₁₃×C₁₆	C₂	1	8	yes	maximal, complemented
3	C₁₃×#2162	C₂	1	6	yes	maximal
4	C₂×C₄×Q₈×C₁₃	C₄	1	1	yes	characteristic
5	C₈×Q₈×C₁₃	C₄	1	4	yes	—
6	C₈×Q₈×C₁₃	C₂²	1	4	yes	—
7	C₂×C₁₃×C₄⋊C₈	C₄	1	3	yes	—
8	C₂×C₄×C₈×C₁₃	C₂²	1	3	yes	—
9	C₁₃×C₄⋊C₁₆	C₂²	1	12	yes	—
10	C₁₃×C₂²⋊C₁₆	C₂²	1	4	yes	—
11	C₄×C₁₃×C₁₆	C₂²	1	12	yes	—
12	C₂²×Q₈×C₁₃	C₈	1	1	yes	characteristic
13	C₂²×C₈×C₁₃	C₂×C₄	1	3	yes	—
14	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
15	C₄×Q₈×C₁₃	C₈	1	4	yes	—
16	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	—
17	C₂×C₁₃×C₄⋊C₄	C₈	1	3	yes	—
18	C₂×C₄²×C₁₃	C₂×C₄	1	3	yes	—
19	C₂×C₁₃×C₁₆	C₂³	1	8	yes	—
20	C₁₃×C₄⋊C₈	C₂×C₄	1	12	yes	—
21	C₄×C₈×C₁₃	C₂×C₄	1	6	yes	—
22	C₄×C₈×C₁₃	C₂³	1	6	yes	—
23	#33496	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₂×Q₈×C₁₃	C₁₆	1	8	yes	complemented
25	C₂×Q₈×C₁₃	C₂×C₈	1	4	yes	—
26	C₂²×C₄×C₁₃	C₂×C₈	1	3	yes	—
27	C₂²×C₄×C₁₃	C₂×C₈	1	3	yes	—
28	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₈×C₁₃	—	2	2	no	—
30	C₂×C₈×C₁₃	—	4	3	no	—
31	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₈×C₁₃	C₂²×C₄	1	6	yes	—
33	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
34	C₁₃×C₄⋊C₄	C₂×C₈	1	12	yes	—
35	C₄²×C₁₃	C₂×C₈	1	6	yes	—
36	C₄²×C₁₃	C₂²×C₄	1	6	yes	—
37	C₁₃×C₁₆	—	2	8	no	—
38	C₂×C₈×Q₈	C₂×C₁₃	1	1	yes	characteristic
39	Q₈×C₁₆	C₂×C₁₃	1	8	yes	complemented
40	#2162	C₂×C₁₃	1	6	yes	—
41	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
42	Q₈×C₁₃	C₂×C₁₆	1	16	yes	—
43	C₂×C₄×C₁₃	—	2	1	no	—
44	C₂×C₄×C₁₃	—	2	1	no	—
45	C₂×C₄×C₁₃	—	4	3	no	—
46	C₂×C₄×C₁₃	C₂×C₁₆	1	12	yes	—
47	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
48	C₂×C₄×C₁₃	C₂²×C₈	1	6	yes	—
49	C₂×C₄×C₁₃	C₂²×C₈	1	6	yes	—
50	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
51	C₈×C₁₃	—	2	1	no	—
52	C₈×C₁₃	—	2	6	no	—
53	C₈×C₁₃	2₋¹⁺⁴	1	2	yes	—
54	C₂×C₄×Q₈	C₄×C₁₃	1	1	yes	characteristic
55	C₈×Q₈	C₄×C₁₃	1	4	yes	—
56	C₈×Q₈	C₂²×C₁₃	1	4	yes	—
57	C₂×C₄⋊C₈	C₄×C₁₃	1	3	yes	—
58	C₂×C₄×C₈	C₂²×C₁₃	1	3	yes	—
59	C₄⋊C₁₆	C₂²×C₁₃	1	12	yes	—
60	C₂²⋊C₁₆	C₂²×C₁₃	1	4	yes	—
61	C₄×C₁₆	C₂²×C₁₃	1	12	yes	—
62	C₂²×C₁₃	—	2	1	no	—
63	C₂²×C₁₃	—	2	1	no	—
64	C₂²×C₁₃	C₂²×C₁₆	1	2	yes	—
65	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
66	C₄×C₁₃	—	2	6	no	—
67	C₄×C₁₃	—	2	1	no	—
68	C₄×C₁₃	C₂²×C₁₆	1	12	yes	—
69	C₄×C₁₃	#519	1	1	yes	characteristic
70	C₄×C₁₃	#568	1	1	yes	characteristic
71	C₂²×Q₈	C₈×C₁₃	1	1	yes	characteristic
72	C₂²×C₈	C₂×C₄×C₁₃	1	3	yes	—
73	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
74	C₄×Q₈	C₈×C₁₃	1	4	yes	—
75	C₄×Q₈	C₂×C₄×C₁₃	1	4	yes	—
76	C₂×C₄⋊C₄	C₈×C₁₃	1	3	yes	—
77	C₂×C₄²	C₂×C₄×C₁₃	1	3	yes	—
78	C₂×C₁₆	C₂³×C₁₃	1	8	yes	—
79	C₄⋊C₈	C₂×C₄×C₁₃	1	12	yes	—
80	C₄×C₈	C₂×C₄×C₁₃	1	6	yes	—
81	C₄×C₈	C₂³×C₁₃	1	6	yes	—
82	C₂×C₁₃	—	2	2	no	—
83	C₂×C₁₃	#2982	1	1	yes	characteristic
84	C₂×C₁₃	C₂³×C₁₆	1	1	yes	characteristic
85	C₂×C₁₃	#3407	1	1	yes	characteristic
86	C₂×Q₈	C₁₃×C₁₆	1	8	yes	complemented
87	C₂×Q₈	C₂×C₈×C₁₃	1	4	yes	—
88	C₂²×C₄	C₂×C₈×C₁₃	1	3	yes	—
89	C₂²×C₄	C₂×C₈×C₁₃	1	3	yes	—
90	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
91	C₂×C₈	—	2	2	no	—
92	C₂×C₈	—	4	3	no	—
93	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
94	C₂×C₈	C₂²×C₄×C₁₃	1	6	yes	—
95	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
96	C₄⋊C₄	C₂×C₈×C₁₃	1	12	yes	—
97	C₄²	C₂×C₈×C₁₃	1	6	yes	—
98	C₄²	C₂²×C₄×C₁₃	1	6	yes	—
99	C₁₆	—	2	8	no	—
100	C₁₃	#33496	1	1	yes	characteristic, direct product factor, Sylow
101	C₂³	C₂²×C₈×C₁₃	1	1	yes	characteristic
102	Q₈	C₂×C₁₃×C₁₆	1	16	yes	—
103	C₂×C₄	—	2	1	no	—
104	C₂×C₄	—	2	1	no	—
105	C₂×C₄	—	4	3	no	—
106	C₂×C₄	C₂×C₁₃×C₁₆	1	12	yes	—
107	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
108	C₂×C₄	C₂²×C₈×C₁₃	1	6	yes	—
109	C₂×C₄	C₂²×C₈×C₁₃	1	6	yes	—
110	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
111	C₈	—	2	1	no	—
112	C₈	—	2	6	no	—
113	C₈	C₁₃×2₋¹⁺⁴	1	2	yes	—
114	C₂²	—	2	1	no	—
115	C₂²	—	2	1	no	—
116	C₂²	C₂²×C₁₃×C₁₆	1	2	yes	—
117	C₂²	C₂³×C₈×C₁₃	1	1	yes	characteristic
118	C₄	—	2	6	no	—
119	C₄	—	2	1	no	—
120	C₄	C₂²×C₁₃×C₁₆	1	12	yes	—
121	C₄	C₁₃×#519	1	1	yes	characteristic
122	C₄	C₁₃×#568	1	1	yes	characteristic
123	C₂	—	2	2	no	—
124	C₂	C₁₃×#2982	1	1	yes	characteristic
125	C₂	C₂³×C₁₃×C₁₆	1	1	yes	characteristic
126	C₂	C₁₃×#3407	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₃	C₂⁴
commutator	C₂	C₂³×C₁₃×C₁₆
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂³×C₈
prime radical	C₂³×C₁₃	C₂²×C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. Q₈×C₁₃×C₁₆	C₂	semidirect
23. #33496	C₁₃	direct (N × H)
24. C₂×Q₈×C₁₃	C₁₆	semidirect
39. Q₈×C₁₆	C₂×C₁₃	semidirect
86. C₂×Q₈	C₁₃×C₁₆	semidirect
100. C₁₃	#33496	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×C₈×Q₈×C₁₃	2
Q₈×C₁₃×C₁₆	2
C₁₃×#2162	2
#33496	13

Subgroups — C13×#33496 #15719835

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33496 #15719835