Finite Group Databasebeta

← C13×#62817 #15749156

Subgroups — C13×#62817 #15749156

Order 3328.

9494 conjugacy classes of subgroups.

The subgroup lattice has 258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3532C2124yesmaximal, complemented
2C13×#3490C2118yesmaximal, complemented
3C13×#3484C2118yesmaximal, complemented
4C22×C13×#120C213yesmaximal, complemented
5C26×C13C2211yescharacteristic, complemented
6C2×C13×H(5,𝔽2)C2216yescomplemented
7C23×D4×C13C2219yescomplemented
8C13×H(3,𝔽4)C2218yescomplemented
9C13×#560C22124yescomplemented
10C13×#551C22172yescomplemented
11C13×#546C221144yescomplemented
12D42×C13C22172yescomplemented
13C13×#543C2216yescomplemented
14C13×#538C22172yescomplemented
15C13×#535C22136yescomplemented
16C13×#534C22118yescomplemented
17C13×#534C22136yescomplemented
18C13×#525C22136yescomplemented
19C2×C13×#120C22136yescomplemented
20C2×C13×#120C22136yescomplemented
21C2×C13×#120C22112yescomplemented
22C13×#518C22118yescomplemented
23C22×C13×C22⋊C4C2219yescomplemented
24C25×C13—412no—
25C25×C13C2319yes—
26C25×C13C2316yes—
27C25×C13C2313yescomplemented
28C13×H(5,𝔽2)—424no—
29C2×C13×#41C23136yescomplemented
30C22×D4×C13—436no—
31C22×D4×C13C23118yes—
32C22×D4×C13C23118yescomplemented
33C22×D4×C13C23172yescomplemented
34C22×D4×C13C23136yescomplemented
35C23×C4×C13C2319yescomplemented
36C13×#127C23124yescomplemented
37C13×#126C23148yescomplemented
38C13×#124C23172yescomplemented
39C13×#123C23172yescomplemented
40C13×#123C23172yescomplemented
41C13×C22⋊Q8C23172yescomplemented
42C13×#121C231144yescomplemented
43C13×#121C23172yescomplemented
44C13×#120C23172yes—
45C13×#120C23124yescomplemented
46C13×#120C23172yescomplemented
47C13×#120C23124yescomplemented
48C13×#120C23172yescomplemented
49C13×#120C23124yescomplemented
50C4×D4×C13C231144yescomplemented
51C13×#117C23136yescomplemented
52C2×C13×C22⋊C4C23118yes—
53C2×C13×C22⋊C4C23118yescomplemented
54C2×C13×C22⋊C4C23172yescomplemented
55C2×C13×C22⋊C4C23136yescomplemented
56#62817C1311yesmaximal, characteristic, direct product factor, Sylow
57C24×C13—236no—
58C24×C13—436no—
59C24×C13—436no—
60C24×C13—418no—
61C24×C13—464no—
62C24×C13C2413yes—
63C24×C13C24118yes—
64C24×C13C2419yes—
65C24×C13C24118yes—
66C24×C13C2412yes—
67C24×C13C2413yes—
68C24×C13C2414yescomplemented
69C13×#41—472no—
70C2×Q8×C13C24112yescomplemented
71C2×D4×C13—272no—
72C2×D4×C13—436no—
73C2×D4×C13—4144no—
74C2×D4×C13—472no—
75C2×D4×C13C24172yes—
76C2×D4×C13C24172yes—
77C2×D4×C13C24136yescomplemented
78C22×C4×C13—418no—
79C22×C4×C13C24118yes—
80C22×C4×C13C24136yes—
81C22×C4×C13C24136yescomplemented
82C13×C4⋊C4C24172yescomplemented
83C13×C22⋊C4C24172yes—
84C13×C22⋊C4C24172yes—
85C13×C22⋊C4C24172yescomplemented
86C42×C13C24124yescomplemented
87#3532C2×C13124yescomplemented
88#3490C2×C13118yescomplemented
89#3484C2×C13118yescomplemented
90C22×#120C2×C1313yescomplemented
91C23×C13—218no—
92C23×C13—272no—
93C23×C13—218no—
94C23×C13—236no—
95C23×C13—46no—
96C23×C13—418no—
97C23×C13—418no—
98C23×C13—46no—
99C23×C13—436no—
100C23×C13—412no—
101C23×C13—4144no—
102C23×C13—496no—
103C23×C13—824no—
104C23×C13H(5,𝔽2)112yescomplemented
105C23×C13C2516yes—
106C23×C13C25112yes—
107C23×C13C2519yes—
108Q8×C13—412no—
109D4×C13—2144no—
110D4×C13—472no—
111D4×C13—436no—
112C2×C4×C13—236no—
113C2×C4×C13—436no—
114C2×C4×C13—436no—
115C2×C4×C13C25136yes—
116C26C22×C1311yescharacteristic, complemented
117C2×H(5,𝔽2)C22×C1316yescomplemented
118C23×D4C22×C1319yescomplemented
119H(3,𝔽4)C22×C1318yescomplemented
120#560C22×C13124yescomplemented
121#551C22×C13172yescomplemented
122#546C22×C131144yescomplemented
123D42C22×C13172yescomplemented
124#543C22×C1316yescomplemented
125#538C22×C13172yescomplemented
126#535C22×C13136yescomplemented
127#534C22×C13118yescomplemented
128#534C22×C13136yescomplemented
129#525C22×C13136yescomplemented
130C2×#120C22×C13136yescomplemented
131C2×#120C22×C13136yescomplemented
132C2×#120C22×C13112yescomplemented
133#518C22×C13118yescomplemented
134C22×C22⋊C4C22×C1319yescomplemented
135C22×C13—224no—
136C22×C13—218no—
137C22×C13—236no—
138C22×C13—218no—
139C22×C13—412no—
140C22×C13—472no—
141C22×C13—436no—
142C22×C13—48no—
143C22×C13—836no—
144C22×C13—164no—
145C22×C13C2×H(5,𝔽2)118yes—
146C22×C13C2611yescharacteristic
147C4×C13—236no—
148C25—412no—
149C25C23×C1319yes—
150C25C23×C1316yes—
151C25C23×C1313yescomplemented
152H(5,𝔽2)—424no—
153C2×#41C23×C13136yescomplemented
154C22×D4—436no—
155C22×D4C23×C13118yes—
156C22×D4C23×C13118yescomplemented
157C22×D4C23×C13172yescomplemented
158C22×D4C23×C13136yescomplemented
159C23×C4C23×C1319yescomplemented
160#127C23×C13124yescomplemented
161#126C23×C13148yescomplemented
162#124C23×C13172yescomplemented
163#123C23×C13172yescomplemented
164#123C23×C13172yescomplemented
165C22⋊Q8C23×C13172yescomplemented
166#121C23×C131144yescomplemented
167#121C23×C13172yescomplemented
168#120C23×C13172yes—
169#120C23×C13124yescomplemented
170#120C23×C13172yescomplemented
171#120C23×C13124yescomplemented
172#120C23×C13172yescomplemented
173#120C23×C13124yescomplemented
174C4×D4C23×C131144yescomplemented
175#117C23×C13136yescomplemented
176C2×C22⋊C4C23×C13118yes—
177C2×C22⋊C4C23×C13118yescomplemented
178C2×C22⋊C4C23×C13172yescomplemented
179C2×C22⋊C4C23×C13136yescomplemented
180C2×C13—218no—
181C2×C13—46no—
182C2×C13—412no—
183C2×C13C22×H(5,𝔽2)13yes—
184C24—236no—
185C24—436no—
186C24—436no—
187C24—418no—
188C24—464no—
189C24C24×C1313yes—
190C24C24×C13118yes—
191C24C24×C1319yes—
192C24C24×C13118yes—
193C24C24×C1312yes—
194C24C24×C1313yes—
195C24C24×C1314yescomplemented
196#41—472no—
197C2×Q8C24×C13112yescomplemented
198C2×D4—272no—
199C2×D4—436no—
200C2×D4—4144no—
201C2×D4—472no—
202C2×D4C24×C13172yes—
203C2×D4C24×C13172yes—
204C2×D4C24×C13136yescomplemented
205C22×C4—418no—
206C22×C4C24×C13118yes—
207C22×C4C24×C13136yes—
208C22×C4C24×C13136yescomplemented
209C4⋊C4C24×C13172yescomplemented
210C22⋊C4C24×C13172yes—
211C22⋊C4C24×C13172yes—
212C22⋊C4C24×C13172yescomplemented
213C42C24×C13124yescomplemented
214C13#6281711yescharacteristic, direct product factor, Sylow
215C23—218no—
216C23—272no—
217C23—218no—
218C23—236no—
219C23—46no—
220C23—418no—
221C23—418no—
222C23—46no—
223C23—436no—
224C23—412no—
225C23—4144no—
226C23—496no—
227C23—824no—
228C23C13×H(5,𝔽2)112yescomplemented
229C23C25×C1316yes—
230C23C25×C13112yes—
231C23C25×C1319yes—
232Q8—412no—
233D4—2144no—
234D4—472no—
235D4—436no—
236C2×C4—236no—
237C2×C4—436no—
238C2×C4—436no—
239C2×C4C25×C13136yes—
240C22—224no—
241C22—218no—
242C22—236no—
243C22—218no—
244C22—412no—
245C22—472no—
246C22—436no—
247C22—48no—
248C22—836no—
249C22—164no—
250C22C2×C13×H(5,𝔽2)118yes—
251C22C26×C1311yescharacteristic
252C4—236no—
253C2—218no—
254C2—46no—
255C2—412no—
256C2C22×C13×H(5,𝔽2)13yes—
subgroupG/H
center, socleC22×C13C26
commutator, Frattini, cosocleC22C26×C13
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3532C2semidirect
2. C13×#3490C2semidirect
3. C13×#3484C2semidirect
4. C22×C13×#120C2semidirect
5. C26×C13C22semidirect
6. C2×C13×H(5,𝔽2)C22semidirect
7. C23×D4×C13C22semidirect
8. C13×H(3,𝔽4)C22semidirect
9. C13×#560C22semidirect
10. C13×#551C22semidirect
11. C13×#546C22semidirect
12. D42×C13C22semidirect
13. C13×#543C22semidirect
14. C13×#538C22semidirect
15. C13×#535C22semidirect
16. C13×#534C22semidirect
17. C13×#534C22semidirect
18. C13×#525C22semidirect
19. C2×C13×#120C22semidirect
20. C2×C13×#120C22semidirect
21. C2×C13×#120C22semidirect
22. C13×#518C22semidirect
23. C22×C13×C22⋊C4C22semidirect
27. C25×C13C23semidirect
29. C2×C13×#41C23semidirect
32. C22×D4×C13C23semidirect
33. C22×D4×C13C23semidirect
34. C22×D4×C13C23semidirect
35. C23×C4×C13C23semidirect
36. C13×#127C23semidirect
37. C13×#126C23semidirect
38. C13×#124C23semidirect
39. C13×#123C23semidirect
40. C13×#123C23semidirect
41. C13×C22⋊Q8C23semidirect
42. C13×#121C23semidirect
43. C13×#121C23semidirect
45. C13×#120C23semidirect
46. C13×#120C23semidirect
47. C13×#120C23semidirect
48. C13×#120C23semidirect
49. C13×#120C23semidirect
50. C4×D4×C13C23semidirect
51. C13×#117C23semidirect
53. C2×C13×C22⋊C4C23semidirect
54. C2×C13×C22⋊C4C23semidirect
55. C2×C13×C22⋊C4C23semidirect
56. #62817C13direct (N × H)
68. C24×C13C24semidirect
70. C2×Q8×C13C24semidirect
77. C2×D4×C13C24semidirect
81. C22×C4×C13C24semidirect
82. C13×C4⋊C4C24semidirect
85. C13×C22⋊C4C24semidirect
86. C42×C13C24semidirect
87. #3532C2×C13semidirect
88. #3490C2×C13semidirect
89. #3484C2×C13semidirect
90. C22×#120C2×C13semidirect
104. C23×C13H(5,𝔽2)semidirect
116. C26C22×C13semidirect
117. C2×H(5,𝔽2)C22×C13semidirect
118. C23×D4C22×C13semidirect
119. H(3,𝔽4)C22×C13semidirect
120. #560C22×C13semidirect
121. #551C22×C13semidirect
122. #546C22×C13semidirect
123. D42C22×C13semidirect
124. #543C22×C13semidirect
125. #538C22×C13semidirect
126. #535C22×C13semidirect
127. #534C22×C13semidirect
128. #534C22×C13semidirect
129. #525C22×C13semidirect
130. C2×#120C22×C13semidirect
131. C2×#120C22×C13semidirect
132. C2×#120C22×C13semidirect
133. #518C22×C13semidirect
134. C22×C22⋊C4C22×C13semidirect
151. C25C23×C13semidirect
153. C2×#41C23×C13semidirect
156. C22×D4C23×C13semidirect
157. C22×D4C23×C13semidirect
158. C22×D4C23×C13semidirect
159. C23×C4C23×C13semidirect
160. #127C23×C13semidirect
161. #126C23×C13semidirect
162. #124C23×C13semidirect
163. #123C23×C13semidirect
164. #123C23×C13semidirect
165. C22⋊Q8C23×C13semidirect
166. #121C23×C13semidirect
167. #121C23×C13semidirect
169. #120C23×C13semidirect
170. #120C23×C13semidirect
171. #120C23×C13semidirect
172. #120C23×C13semidirect
173. #120C23×C13semidirect
174. C4×D4C23×C13semidirect
175. #117C23×C13semidirect
177. C2×C22⋊C4C23×C13semidirect
178. C2×C22⋊C4C23×C13semidirect
179. C2×C22⋊C4C23×C13semidirect
195. C24C24×C13semidirect
197. C2×Q8C24×C13semidirect
204. C2×D4C24×C13semidirect
208. C22×C4C24×C13semidirect
209. C4⋊C4C24×C13semidirect
212. C22⋊C4C24×C13semidirect
213. C42C24×C13semidirect
214. C13#62817direct (N × H)
228. C23C13×H(5,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
C13×#35322
C13×#34902
C13×#34842
C22×C13×#1202
#6281713