Subgroups — C₁₃×#2517 #13111575

Order 1664.

412 conjugacy classes of subgroups.

The subgroup lattice has 214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#399	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#397	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#397	C₂	1	2	yes	maximal
4	C₁₃×#387	C₂	1	2	yes	maximal, complemented
5	C₁₃×#387	C₂	1	2	yes	maximal, complemented
6	C₁₃×#387	C₂	1	2	yes	maximal, complemented
7	C₁₃×#385	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#382	C₂	1	2	yes	maximal, complemented
9	C₄×C₁₃×C₂²⋊C₄	C₂	1	2	yes	maximal
10	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
12	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
17	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
18	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₄²×C₁₃	C₂²	1	2	yes	—
21	C₂×C₄²×C₁₃	C₂²	1	2	yes	—
22	C₁₃×#95	C₂²	1	2	yes	—
23	C₁₃×#95	C₂²	1	2	yes	—
24	C₁₃×#95	C₂²	1	1	yes	characteristic
25	C₁₃×#95	C₂²	1	2	yes	—
26	C₁₃×#95	C₂²	1	2	yes	—
27	C₁₃×#95	C₂²	1	2	yes	—
28	C₁₃×#95	C₂²	1	2	yes	—
29	C₁₃×#95	C₂²	1	2	yes	—
30	C₁₃×#95	C₂²	1	1	yes	characteristic
31	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
32	C₂²×C₄×C₁₃	—	2	4	no	—
33	C₂²×C₄×C₁₃	—	4	1	no	—
34	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
35	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
36	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
37	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
38	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
39	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
40	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
41	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
42	C₁₃×C₄⋊C₄	—	2	4	no	—
43	C₁₃×C₄⋊C₄	—	2	4	no	—
44	C₁₃×C₄⋊C₄	—	2	4	no	—
45	C₁₃×C₄⋊C₄	—	4	1	no	—
46	C₁₃×C₄⋊C₄	—	4	1	no	—
47	C₁₃×C₂²⋊C₄	—	2	4	no	—
48	C₁₃×C₂²⋊C₄	—	2	2	no	—
49	C₁₃×C₂²⋊C₄	—	2	4	no	—
50	C₁₃×C₂²⋊C₄	—	4	1	no	—
51	C₄²×C₁₃	—	2	4	no	—
52	C₄²×C₁₃	—	4	2	no	—
53	#2517	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
54	C₂³×C₁₃	—	2	2	no	—
55	C₂³×C₁₃	—	2	2	no	—
56	C₂³×C₁₃	—	2	1	no	—
57	C₂³×C₁₃	—	2	1	no	—
58	C₂³×C₁₃	#41	1	2	yes	—
59	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
60	C₂×C₄×C₁₃	—	2	2	no	—
61	C₂×C₄×C₁₃	—	2	2	no	—
62	C₂×C₄×C₁₃	—	2	2	no	—
63	C₂×C₄×C₁₃	—	2	2	no	—
64	C₂×C₄×C₁₃	—	2	2	no	—
65	C₂×C₄×C₁₃	—	2	2	no	—
66	C₂×C₄×C₁₃	—	2	2	no	—
67	C₂×C₄×C₁₃	—	2	2	no	—
68	C₂×C₄×C₁₃	—	2	2	no	—
69	C₂×C₄×C₁₃	—	2	2	no	—
70	C₂×C₄×C₁₃	—	2	2	no	—
71	C₂×C₄×C₁₃	—	2	2	no	—
72	C₂×C₄×C₁₃	—	2	2	no	—
73	C₂×C₄×C₁₃	—	2	2	no	—
74	C₂×C₄×C₁₃	—	2	2	no	—
75	C₂×C₄×C₁₃	—	2	2	no	—
76	C₂×C₄×C₁₃	—	2	2	no	—
77	C₂×C₄×C₁₃	—	2	1	no	—
78	C₂×C₄×C₁₃	—	2	1	no	—
79	C₂×C₄×C₁₃	—	2	2	no	—
80	C₂×C₄×C₁₃	—	4	4	no	—
81	C₂×C₄×C₁₃	#41	1	4	yes	—
82	C₂×C₄×C₁₃	#41	1	4	yes	—
83	#399	C₂×C₁₃	1	1	yes	characteristic
84	#397	C₂×C₁₃	1	1	yes	characteristic
85	#397	C₂×C₁₃	1	2	yes	—
86	#387	C₂×C₁₃	1	2	yes	complemented
87	#387	C₂×C₁₃	1	2	yes	complemented
88	#387	C₂×C₁₃	1	2	yes	complemented
89	#385	C₂×C₁₃	1	1	yes	characteristic
90	#382	C₂×C₁₃	1	2	yes	complemented
91	C₄×C₂²⋊C₄	C₂×C₁₃	1	2	yes	—
92	C₂²×C₁₃	—	2	4	no	—
93	C₂²×C₁₃	—	2	2	no	—
94	C₂²×C₁₃	—	4	1	no	—
95	C₂²×C₁₃	—	4	2	no	—
96	C₂²×C₁₃	—	4	1	no	—
97	C₂²×C₁₃	C₂×#41	1	1	yes	characteristic
98	C₂²×C₁₃	C₂×#41	1	2	yes	—
99	C₂²×C₁₃	C₂×#41	1	2	yes	—
100	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
101	C₂²×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
102	C₄×C₁₃	—	2	4	no	—
103	C₄×C₁₃	—	2	4	no	—
104	C₄×C₁₃	—	4	2	no	—
105	C₄×C₁₃	—	4	2	no	—
106	C₄×C₁₃	—	4	2	no	—
107	C₄×C₁₃	—	4	1	no	—
108	C₄×C₁₃	—	4	2	no	—
109	C₄×C₁₃	—	4	1	no	—
110	C₂³×C₄	C₂²×C₁₃	1	1	yes	characteristic
111	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
112	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
113	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
114	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
115	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
116	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
117	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
118	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
119	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
120	C₂×C₄²	C₂²×C₁₃	1	2	yes	—
121	C₂×C₄²	C₂²×C₁₃	1	2	yes	—
122	#95	C₂²×C₁₃	1	2	yes	—
123	#95	C₂²×C₁₃	1	2	yes	—
124	#95	C₂²×C₁₃	1	1	yes	characteristic
125	#95	C₂²×C₁₃	1	2	yes	—
126	#95	C₂²×C₁₃	1	2	yes	—
127	#95	C₂²×C₁₃	1	2	yes	—
128	#95	C₂²×C₁₃	1	2	yes	—
129	#95	C₂²×C₁₃	1	2	yes	—
130	#95	C₂²×C₁₃	1	1	yes	characteristic
131	C₂×C₁₃	—	4	2	no	—
132	C₂×C₁₃	#529	1	2	yes	—
133	C₂×C₁₃	#539	1	1	yes	characteristic
134	C₂×C₁₃	#551	1	1	yes	characteristic
135	C₂×C₁₃	#552	1	2	yes	—
136	C₂×C₁₃	#559	1	1	yes	characteristic
137	C₂⁴	C₂³×C₁₃	1	1	yes	characteristic
138	C₂²×C₄	—	2	4	no	—
139	C₂²×C₄	—	4	1	no	—
140	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
141	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
142	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
143	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
144	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
145	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
146	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
147	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
148	C₄⋊C₄	—	2	4	no	—
149	C₄⋊C₄	—	2	4	no	—
150	C₄⋊C₄	—	2	4	no	—
151	C₄⋊C₄	—	4	1	no	—
152	C₄⋊C₄	—	4	1	no	—
153	C₂²⋊C₄	—	2	4	no	—
154	C₂²⋊C₄	—	2	2	no	—
155	C₂²⋊C₄	—	2	4	no	—
156	C₂²⋊C₄	—	4	1	no	—
157	C₄²	—	2	4	no	—
158	C₄²	—	4	2	no	—
159	C₁₃	#2517	1	1	yes	characteristic, direct product factor, Sylow
160	C₂³	—	2	2	no	—
161	C₂³	—	2	2	no	—
162	C₂³	—	2	1	no	—
163	C₂³	—	2	1	no	—
164	C₂³	C₁₃×#41	1	2	yes	—
165	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
166	C₂×C₄	—	2	2	no	—
167	C₂×C₄	—	2	2	no	—
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	2	2	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	2	2	no	—
174	C₂×C₄	—	2	2	no	—
175	C₂×C₄	—	2	2	no	—
176	C₂×C₄	—	2	2	no	—
177	C₂×C₄	—	2	2	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	2	2	no	—
180	C₂×C₄	—	2	2	no	—
181	C₂×C₄	—	2	2	no	—
182	C₂×C₄	—	2	2	no	—
183	C₂×C₄	—	2	1	no	—
184	C₂×C₄	—	2	1	no	—
185	C₂×C₄	—	2	2	no	—
186	C₂×C₄	—	4	4	no	—
187	C₂×C₄	C₁₃×#41	1	4	yes	—
188	C₂×C₄	C₁₃×#41	1	4	yes	—
189	C₂²	—	2	4	no	—
190	C₂²	—	2	2	no	—
191	C₂²	—	4	1	no	—
192	C₂²	—	4	2	no	—
193	C₂²	—	4	1	no	—
194	C₂²	C₂×C₁₃×#41	1	1	yes	characteristic
195	C₂²	C₂×C₁₃×#41	1	2	yes	—
196	C₂²	C₂×C₁₃×#41	1	2	yes	—
197	C₂²	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
198	C₂²	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
199	C₄	—	2	4	no	—
200	C₄	—	2	4	no	—
201	C₄	—	4	2	no	—
202	C₄	—	4	2	no	—
203	C₄	—	4	2	no	—
204	C₄	—	4	1	no	—
205	C₄	—	4	2	no	—
206	C₄	—	4	1	no	—
207	C₂	—	4	2	no	—
208	C₂	C₁₃×#529	1	2	yes	—
209	C₂	C₁₃×#539	1	1	yes	characteristic
210	C₂	C₁₃×#551	1	1	yes	characteristic
211	C₂	C₁₃×#552	1	2	yes	—
212	C₂	C₁₃×#559	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂³
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
4. C₁₃×#387	C₂	semidirect
5. C₁₃×#387	C₂	semidirect
6. C₁₃×#387	C₂	semidirect
8. C₁₃×#382	C₂	semidirect
53. #2517	C₁₃	direct (N × H)
86. #387	C₂×C₁₃	semidirect
87. #387	C₂×C₁₃	semidirect
88. #387	C₂×C₁₃	semidirect
90. #382	C₂×C₁₃	semidirect
159. C₁₃	#2517	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×#399	2
C₁₃×#397	2
C₁₃×#387	2
C₁₃×#385	2
C₁₃×#382	2
C₄×C₁₃×C₂²⋊C₄	2
#2517	13

Subgroups — C13×#2517 #13111575

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2517 #13111575