Subgroups — C₁₃×#32850 #15719189

Order 3328.

604 conjugacy classes of subgroups.

The subgroup lattice has 208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2859	C₂	1	2	yes	maximal
2	C₁₃×#2100	C₂	1	4	yes	maximal
3	C₁₃×#2087	C₂	1	4	yes	maximal
4	C₁₃×#2083	C₂	1	4	yes	maximal
5	C₁₃×#1831	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×#125	—	2	2	no	—
7	C₂×C₁₃×#107	C₂²	1	4	yes	—
8	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
9	C₁₃×#389	—	2	2	no	—
10	C₁₃×#389	—	2	2	no	—
11	C₁₃×#389	C₂²	1	4	yes	—
12	C₁₃×#389	C₂²	1	4	yes	—
13	C₁₃×#384	C₂²	1	2	yes	—
14	C₁₃×#384	C₂²	1	2	yes	—
15	C₁₃×#382	—	2	2	no	—
16	C₄³×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#340	C₂²	1	8	yes	—
18	C₁₃×#340	C₂²	1	4	yes	—
19	C₁₃×#336	C₂²	1	4	yes	—
20	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
21	C₁₃×#125	—	4	8	no	—
22	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
23	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
24	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
25	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
26	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
27	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
28	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
29	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
30	C₂×C₄²×C₁₃	D₄	1	2	yes	—
31	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
34	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
35	C₁₃×#107	—	4	4	no	—
36	C₁₃×C₄⋊C₈	—	4	2	no	—
37	C₁₃×#95	—	2	4	no	—
38	C₁₃×#95	—	2	4	no	—
39	#32850	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂²×C₄×C₁₃	—	2	4	no	—
41	C₂²×C₄×C₁₃	—	2	4	no	—
42	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
45	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
46	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
47	C₂×C₈×C₁₃	—	2	4	no	—
48	C₂×C₈×C₁₃	—	2	8	no	—
49	C₁₃×C₄⋊C₄	—	2	4	no	—
50	C₁₃×C₄⋊C₄	—	2	8	no	—
51	C₁₃×C₄⋊C₄	—	2	4	no	—
52	C₁₃×C₄⋊C₄	—	4	4	no	—
53	C₁₃×C₄⋊C₄	—	4	4	no	—
54	C₁₃×C₄⋊C₄	—	4	4	no	—
55	C₁₃×C₄⋊C₄	—	4	8	no	—
56	C₁₃×C₄⋊C₄	—	4	4	no	—
57	C₁₃×C₄⋊C₄	—	4	8	no	—
58	C₄²×C₁₃	—	2	4	no	—
59	C₄²×C₁₃	—	2	1	no	—
60	C₄²×C₁₃	—	2	4	no	—
61	C₄²×C₁₃	—	2	1	no	—
62	C₄²×C₁₃	—	4	1	no	—
63	C₄²×C₁₃	Q₁₆	1	4	yes	—
64	#2859	C₂×C₁₃	1	2	yes	—
65	#2100	C₂×C₁₃	1	4	yes	—
66	#2087	C₂×C₁₃	1	4	yes	—
67	#2083	C₂×C₁₃	1	4	yes	—
68	#1831	C₂×C₁₃	1	1	yes	characteristic
69	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
70	C₂×C₄×C₁₃	—	2	2	no	—
71	C₂×C₄×C₁₃	—	2	2	no	—
72	C₂×C₄×C₁₃	—	2	1	no	—
73	C₂×C₄×C₁₃	—	2	2	no	—
74	C₂×C₄×C₁₃	—	2	2	no	—
75	C₂×C₄×C₁₃	—	2	1	no	—
76	C₂×C₄×C₁₃	—	2	1	no	—
77	C₂×C₄×C₁₃	—	2	2	no	—
78	C₂×C₄×C₁₃	—	4	4	no	—
79	C₂×C₄×C₁₃	—	4	4	no	—
80	C₂×C₄×C₁₃	—	4	4	no	—
81	C₂×C₄×C₁₃	—	4	4	no	—
82	C₂×C₄×C₁₃	—	4	4	no	—
83	C₂×C₄×C₁₃	—	4	4	no	—
84	C₂×C₄×C₁₃	C₂×Q₁₆	1	4	yes	—
85	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
86	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
87	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
88	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
89	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
90	C₈×C₁₃	—	4	4	no	—
91	C₂×#125	—	2	2	no	—
92	C₂×#107	C₂²×C₁₃	1	4	yes	—
93	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
94	#389	—	2	2	no	—
95	#389	—	2	2	no	—
96	#389	C₂²×C₁₃	1	4	yes	—
97	#389	C₂²×C₁₃	1	4	yes	—
98	#384	C₂²×C₁₃	1	2	yes	—
99	#384	C₂²×C₁₃	1	2	yes	—
100	#382	—	2	2	no	—
101	C₄³	C₂²×C₁₃	1	1	yes	characteristic
102	#340	C₂²×C₁₃	1	8	yes	—
103	#340	C₂²×C₁₃	1	4	yes	—
104	#336	C₂²×C₁₃	1	4	yes	—
105	C₂²×C₁₃	#536	1	2	yes	—
106	C₂²×C₁₃	#537	1	1	yes	characteristic
107	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
108	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
109	C₂²×C₁₃	#575	1	1	yes	characteristic
110	C₄×C₁₃	—	2	4	no	—
111	C₄×C₁₃	—	2	4	no	—
112	C₄×C₁₃	—	2	2	no	—
113	C₄×C₁₃	—	4	1	no	—
114	C₄×C₁₃	—	8	4	no	—
115	C₄×C₁₃	—	8	4	no	—
116	C₄×C₁₃	#563	1	2	yes	—
117	C₄×C₁₃	#564	1	2	yes	—
118	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
119	#125	—	4	8	no	—
120	C₂×C₄⋊C₄	—	2	2	no	—
121	C₂×C₄⋊C₄	—	2	2	no	—
122	C₂×C₄⋊C₄	—	2	4	no	—
123	C₂×C₄⋊C₄	—	2	4	no	—
124	C₂×C₄⋊C₄	—	2	2	no	—
125	C₂×C₄⋊C₄	—	2	2	no	—
126	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
127	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
128	C₂×C₄²	D₄×C₁₃	1	2	yes	—
129	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
130	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
131	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
132	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
133	#107	—	4	4	no	—
134	C₄⋊C₈	—	4	2	no	—
135	#95	—	2	4	no	—
136	#95	—	2	4	no	—
137	C₂×C₁₃	#2822	1	1	yes	characteristic
138	C₂×C₁₃	#3230	1	2	yes	—
139	C₂×C₁₃	#3234	1	2	yes	—
140	C₂×C₁₃	#3249	1	1	yes	characteristic
141	C₂×C₁₃	#3253	1	1	yes	characteristic
142	C₂²×C₄	—	2	4	no	—
143	C₂²×C₄	—	2	4	no	—
144	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
145	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
146	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
147	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
148	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
149	C₂×C₈	—	2	4	no	—
150	C₂×C₈	—	2	8	no	—
151	C₄⋊C₄	—	2	4	no	—
152	C₄⋊C₄	—	2	8	no	—
153	C₄⋊C₄	—	2	4	no	—
154	C₄⋊C₄	—	4	4	no	—
155	C₄⋊C₄	—	4	4	no	—
156	C₄⋊C₄	—	4	8	no	—
157	C₄⋊C₄	—	4	4	no	—
158	C₄⋊C₄	—	4	8	no	—
159	C₄⋊C₄	—	4	4	no	—
160	C₄²	—	2	4	no	—
161	C₄²	—	2	1	no	—
162	C₄²	—	2	4	no	—
163	C₄²	—	2	1	no	—
164	C₄²	—	4	1	no	—
165	C₄²	C₁₃×Q₁₆	1	4	yes	—
166	C₁₃	#32850	1	1	yes	characteristic, direct product factor, Sylow
167	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	2	1	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	2	1	no	—
174	C₂×C₄	—	2	1	no	—
175	C₂×C₄	—	2	2	no	—
176	C₂×C₄	—	4	4	no	—
177	C₂×C₄	—	4	4	no	—
178	C₂×C₄	—	4	4	no	—
179	C₂×C₄	—	4	4	no	—
180	C₂×C₄	—	4	4	no	—
181	C₂×C₄	—	4	4	no	—
182	C₂×C₄	C₂×C₁₃×Q₁₆	1	4	yes	—
183	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
184	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
185	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
186	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
187	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
188	C₈	—	4	4	no	—
189	C₂²	C₁₃×#536	1	2	yes	—
190	C₂²	C₁₃×#537	1	1	yes	characteristic
191	C₂²	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
192	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
193	C₂²	C₁₃×#575	1	1	yes	characteristic
194	C₄	—	2	4	no	—
195	C₄	—	2	4	no	—
196	C₄	—	2	2	no	—
197	C₄	—	4	1	no	—
198	C₄	—	8	4	no	—
199	C₄	—	8	4	no	—
200	C₄	C₁₃×#563	1	2	yes	—
201	C₄	C₁₃×#564	1	2	yes	—
202	C₂	C₁₃×#2822	1	1	yes	characteristic
203	C₂	C₁₃×#3230	1	2	yes	—
204	C₂	C₁₃×#3234	1	2	yes	—
205	C₂	C₁₃×#3249	1	1	yes	characteristic
206	C₂	C₁₃×#3253	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
39. #32850	C₁₃	direct (N × H)
166. C₁₃	#32850	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2859	2
C₁₃×#2100	2
C₁₃×#2087	2
C₁₃×#2083	2
C₁₃×#1831	2
#32850	13

Subgroups — C13×#32850 #15719189

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32850 #15719189