Finite Group Databasebeta

← C4×C13×#555 #15720504

Subgroups — C4×C13×#555 #15720504

Order 3328.

2564 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#555C211yesmaximal, characteristic
2C13×#2372C214yesmaximal, complemented
3C13×#2369C211yesmaximal, characteristic, complemented
4C13×#2363C214yesmaximal, complemented
5C13×#2354C212yesmaximal, complemented
6C13×#2346C214yesmaximal, complemented
7C4×C13×C4⋊Q8C211yesmaximal, characteristic, complemented
8C4×C13×#124C214yesmaximal, complemented
9C4×C13×#121C214yesmaximal, complemented
10C42×D4×C13C212yesmaximal, complemented
11C4×C13×#117C214yesmaximal, complemented
12C13×#555C4116yesdirect product factor
13C2×C13×C4⋊Q8C2211yescharacteristic
14C2×C13×#124C2214yes—
15C2×C13×#121C2214yes—
16C2×C4×Q8×C13C2212yes—
17C2×C4×D4×C13C2212yes—
18C2×C4×D4×C13C2212yes—
19C2×C4×D4×C13C2214yes—
20C2×C4×D4×C13C2212yes—
21C2×C13×#117C2214yes—
22C2×C13×#117C2214yes—
23C22×C42×C13C2214yes—
24C13×#391C2214yes—
25C13×#391C2212yes—
26C13×#390C2214yes—
27C13×#390C2214yes—
28C13×#389C2214yes—
29C13×#389C2214yes—
30C13×#388C2218yes—
31C13×#388C2218yes—
32C13×#388C2218yes—
33C13×#386C2218yes—
34C13×#384C2211yescharacteristic
35C13×#382C2214yes—
36C13×#380C2214yes—
37C4×C13×C4⋊C4C2212yes—
38C4×C13×C4⋊C4C2214yes—
39C4×C13×C4⋊C4C2214yes—
40C4×C13×C4⋊C4C2214yes—
41C4×C13×C4⋊C4C2212yes—
42C4×C13×C4⋊C4C2212yes—
43C4×C13×C22⋊C4C2218yes—
44C4×C13×C22⋊C4C2218yes—
45C4×C13×C22⋊C4C2214yes—
46C4×C13×C22⋊C4C2214yes—
47C4×C13×C22⋊C4C2214yes—
48C13×#376C2218yes—
49C43×C13C2214yes—
50C43×C13C2211yescharacteristic
51C22×Q8×C13C2312yes—
52C22×D4×C13C2312yes—
53C22×D4×C13C2314yes—
54C23×C4×C13C2314yes—
55C23×C4×C13C2314yes—
56C23×C4×C13C2314yes—
57C13×C4⋊Q8C2×C418yescomplemented
58C13×#124C2×C4132yescomplemented
59C13×#121C2×C4132yescomplemented
60C4×Q8×C13—44no—
61C4×D4×C13—28no—
62C4×D4×C13—28no—
63C4×D4×C13—48no—
64C4×D4×C13C2×C4116yescomplemented
65C13×#117—216no—
66C13×#117C2×C4132yescomplemented
67C2×C13×C4⋊C4C2312yes—
68C2×C13×C4⋊C4C2314yes—
69C2×C13×C4⋊C4C2314yes—
70C2×C13×C4⋊C4C2314yes—
71C2×C13×C4⋊C4C2312yes—
72C2×C13×C4⋊C4C2312yes—
73C2×C13×C4⋊C4C2314yes—
74C2×C13×C4⋊C4C2312yes—
75C2×C13×C22⋊C4C2314yes—
76C2×C13×C22⋊C4C2318yes—
77C2×C13×C22⋊C4C2314yes—
78C2×C13×C22⋊C4C2318yes—
79C2×C13×C22⋊C4C2318yes—
80C2×C13×C22⋊C4C2314yes—
81C2×C42×C13—216no—
82C2×C42×C13C2312yes—
83C2×C42×C13C2314yes—
84C2×C42×C13C2314yes—
85C2×C42×C13C2318yes—
86C2×C42×C13C2311yescharacteristic
87C2×C42×C13C2314yes—
88C2×C42×C13C2314yes—
89C2×C42×C13C2311yescharacteristic
90C2×C42×C13C2314yes—
91C2×C42×C13C2311yescharacteristic
92C2×C42×C13C2314yes—
93C2×C42×C13C2312yes—
94C13×#95C2314yes—
95C13×#95C2314yes—
96C13×#95C2314yes—
97C13×#95C2318yes—
98C13×#95C2318yes—
99C13×#95C2318yes—
100C4×#555C1311yesmaximal, characteristic, direct product factor, Sylow
101C24×C13C2414yes—
102C2×Q8×C13—42no—
103C2×Q8×C13—42no—
104C2×Q8×C13C22×C418yes—
105C2×D4×C13—24no—
106C2×D4×C13—24no—
107C2×D4×C13—44no—
108C2×D4×C13—44no—
109C2×D4×C13C22×C418yes—
110C2×D4×C13C22×C4116yes—
111C22×C4×C13—28no—
112C22×C4×C13—28no—
113C22×C4×C13—28no—
114C22×C4×C13—28no—
115C22×C4×C13—28no—
116C22×C4×C13—28no—
117C22×C4×C13—28no—
118C22×C4×C13—44no—
119C22×C4×C13C22×C4116yes—
120C22×C4×C13C2414yes—
121C22×C4×C13C2411yescharacteristic
122C22×C4×C13C2414yes—
123C22×C4×C13C2414yes—
124C22×C4×C13C2411yescharacteristic
125C22×C4×C13C2414yes—
126C22×C4×C13C2412yes—
127C22×C4×C13C2414yes—
128C22×C4×C13C2412yes—
129C22×C4×C13C2411yescharacteristic
130C13×C4⋊C4—28no—
131C13×C4⋊C4—24no—
132C13×C4⋊C4—44no—
133C13×C4⋊C4—44no—
134C13×C4⋊C4—42no—
135C13×C4⋊C4C22×C418yes—
136C13×C4⋊C4C22×C4116yes—
137C13×C4⋊C4#4118yes—
138C13×C22⋊C4—216no—
139C13×C22⋊C4—28no—
140C13×C22⋊C4—28no—
141C13×C22⋊C4—48no—
142C13×C22⋊C4C22×C4132yes—
143C13×C22⋊C4C22×C4116yes—
144C42×C13—28no—
145C42×C13—28no—
146C42×C13—28no—
147C42×C13—216no—
148C42×C13—24no—
149C42×C13—28no—
150C42×C13—22no—
151C42×C13—44no—
152C42×C13—41no—
153C42×C13C22×C4116yes—
154C42×C13C22×C414yes—
155C42×C13#4118yes—
156C2×#555C2×C1311yescharacteristic
157#2372C2×C1314yescomplemented
158#2369C2×C1311yescharacteristic, complemented
159#2363C2×C1314yescomplemented
160#2354C2×C1312yescomplemented
161#2346C2×C1314yescomplemented
162C4×C4⋊Q8C2×C1311yescharacteristic, complemented
163C4×#124C2×C1314yescomplemented
164C4×#121C2×C1314yescomplemented
165C42×D4C2×C1312yescomplemented
166C4×#117C2×C1314yescomplemented
167C23×C13—24no—
168C23×C13—24no—
169C23×C13—24no—
170C23×C13—24no—
171C23×C13—24no—
172C23×C13—24no—
173C23×C13C23×C418yes—
174C23×C13C2511yescharacteristic
175Q8×C13—48no—
176D4×C13—216no—
177D4×C13—416no—
178C2×C4×C13—24no—
179C2×C4×C13—24no—
180C2×C4×C13—24no—
181C2×C4×C13—22no—
182C2×C4×C13—24no—
183C2×C4×C13—21no—
184C2×C4×C13—24no—
185C2×C4×C13—22no—
186C2×C4×C13—24no—
187C2×C4×C13—21no—
188C2×C4×C13—232no—
189C2×C4×C13—24no—
190C2×C4×C13—22no—
191C2×C4×C13—28no—
192C2×C4×C13—24no—
193C2×C4×C13—24no—
194C2×C4×C13—21no—
195C2×C4×C13—24no—
196C2×C4×C13—416no—
197C2×C4×C13—416no—
198C2×C4×C13C23×C418yes—
199C2×C4×C13C23×C412yes—
200C2×C4×C13C23×C418yes—
201C2×C4×C13C23×C414yes—
202C2×C4×C13C2×#4114yes—
203C2×C4×C13C2×#4118yes—
204C2×C4×C13C2×#4114yes—
205C2×C4×C13C2×#4114yes—
206C2×C4×C13C2×#4114yes—
207C2×C4×C13H(5,𝔽2)12yes—
208#555C4×C13116yesdirect product factor
209C2×C4⋊Q8C22×C1311yescharacteristic
210C2×#124C22×C1314yes—
211C2×#121C22×C1314yes—
212C2×C4×Q8C22×C1312yes—
213C2×C4×D4C22×C1312yes—
214C2×C4×D4C22×C1312yes—
215C2×C4×D4C22×C1314yes—
216C2×C4×D4C22×C1312yes—
217C2×#117C22×C1314yes—
218C2×#117C22×C1314yes—
219C22×C42C22×C1314yes—
220#391C22×C1312yes—
221#391C22×C1314yes—
222#390C22×C1314yes—
223#390C22×C1314yes—
224#389C22×C1314yes—
225#389C22×C1314yes—
226#388C22×C1318yes—
227#388C22×C1318yes—
228#388C22×C1318yes—
229#386C22×C1318yes—
230#384C22×C1311yescharacteristic
231#382C22×C1314yes—
232#380C22×C1314yes—
233C4×C4⋊C4C22×C1314yes—
234C4×C4⋊C4C22×C1312yes—
235C4×C4⋊C4C22×C1314yes—
236C4×C4⋊C4C22×C1312yes—
237C4×C4⋊C4C22×C1314yes—
238C4×C4⋊C4C22×C1312yes—
239C4×C22⋊C4C22×C1314yes—
240C4×C22⋊C4C22×C1318yes—
241C4×C22⋊C4C22×C1314yes—
242C4×C22⋊C4C22×C1318yes—
243C4×C22⋊C4C22×C1314yes—
244#376C22×C1318yes—
245C43C22×C1311yescharacteristic
246C43C22×C1314yes—
247C22×C13—28no—
248C22×C13—28no—
249C22×C13—28no—
250C22×C13—44no—
251C22×C13—44no—
252C22×C13—44no—
253C22×C13—44no—
254C22×C13C24×C411yescharacteristic
255C22×C13C22×#4112yes—
256C22×C13C22×#4112yes—
257C22×C13C2×H(5,𝔽2)11yescharacteristic
258C22×C13#58511yescharacteristic
259C4×C13—28no—
260C4×C13—28no—
261C4×C13—22no—
262C4×C13—24no—
263C4×C13—28no—
264C4×C13—44no—
265C4×C13—41no—
266C4×C13—44no—
267C4×C13C4×#4118yes—
268C4×C13#55514yesdirect product factor
269C22×Q8C23×C1312yes—
270C22×D4C23×C1312yes—
271C22×D4C23×C1314yes—
272C23×C4C23×C1314yes—
273C23×C4C23×C1314yes—
274C23×C4C23×C1314yes—
275C4⋊Q8C2×C4×C1318yescomplemented
276#124C2×C4×C13132yescomplemented
277#121C2×C4×C13132yescomplemented
278C4×Q8—44no—
279C4×D4—28no—
280C4×D4—28no—
281C4×D4—48no—
282C4×D4C2×C4×C13116yescomplemented
283#117—216no—
284#117C2×C4×C13132yescomplemented
285C2×C4⋊C4C23×C1314yes—
286C2×C4⋊C4C23×C1312yes—
287C2×C4⋊C4C23×C1314yes—
288C2×C4⋊C4C23×C1314yes—
289C2×C4⋊C4C23×C1312yes—
290C2×C4⋊C4C23×C1312yes—
291C2×C4⋊C4C23×C1314yes—
292C2×C4⋊C4C23×C1312yes—
293C2×C22⋊C4C23×C1318yes—
294C2×C22⋊C4C23×C1314yes—
295C2×C22⋊C4C23×C1314yes—
296C2×C22⋊C4C23×C1318yes—
297C2×C22⋊C4C23×C1318yes—
298C2×C22⋊C4C23×C1314yes—
299C2×C42—216no—
300C2×C42C23×C1318yes—
301C2×C42C23×C1314yes—
302C2×C42C23×C1312yes—
303C2×C42C23×C1311yescharacteristic
304C2×C42C23×C1314yes—
305C2×C42C23×C1314yes—
306C2×C42C23×C1314yes—
307C2×C42C23×C1311yescharacteristic
308C2×C42C23×C1314yes—
309C2×C42C23×C1314yes—
310C2×C42C23×C1311yescharacteristic
311C2×C42C23×C1312yes—
312#95C23×C1314yes—
313#95C23×C1318yes—
314#95C23×C1318yes—
315#95C23×C1318yes—
316#95C23×C1314yes—
317#95C23×C1314yes—
318C2×C13—48no—
319C2×C13C2×C4×#4112yes—
320C2×C13C4×H(5,𝔽2)11yescharacteristic
321C2×C13C2×#55511yescharacteristic
322C2×C13#347512yes—
323C2×C13#348311yescharacteristic
324C24C24×C1314yes—
325C2×Q8—42no—
326C2×Q8—42no—
327C2×Q8C22×C4×C1318yes—
328C2×D4—24no—
329C2×D4—24no—
330C2×D4—44no—
331C2×D4—44no—
332C2×D4C22×C4×C1318yes—
333C2×D4C22×C4×C13116yes—
334C22×C4—28no—
335C22×C4—28no—
336C22×C4—28no—
337C22×C4—28no—
338C22×C4—28no—
339C22×C4—28no—
340C22×C4—28no—
341C22×C4—44no—
342C22×C4C22×C4×C13116yes—
343C22×C4C24×C1314yes—
344C22×C4C24×C1311yescharacteristic
345C22×C4C24×C1314yes—
346C22×C4C24×C1314yes—
347C22×C4C24×C1311yescharacteristic
348C22×C4C24×C1314yes—
349C22×C4C24×C1312yes—
350C22×C4C24×C1314yes—
351C22×C4C24×C1312yes—
352C22×C4C24×C1311yescharacteristic
353C4⋊C4—28no—
354C4⋊C4—24no—
355C4⋊C4—44no—
356C4⋊C4—44no—
357C4⋊C4—42no—
358C4⋊C4C22×C4×C1318yes—
359C4⋊C4C22×C4×C13116yes—
360C4⋊C4C13×#4118yes—
361C22⋊C4—216no—
362C22⋊C4—28no—
363C22⋊C4—28no—
364C22⋊C4—48no—
365C22⋊C4C22×C4×C13132yes—
366C22⋊C4C22×C4×C13116yes—
367C42—28no—
368C42—28no—
369C42—28no—
370C42—216no—
371C42—24no—
372C42—28no—
373C42—22no—
374C42—44no—
375C42—41no—
376C42C22×C4×C13116yes—
377C42C22×C4×C1314yes—
378C42C13×#4118yes—
379C13C4×#55511yescharacteristic, direct product factor, Sylow
380C23—24no—
381C23—24no—
382C23—24no—
383C23—24no—
384C23—24no—
385C23—24no—
386C23C23×C4×C1318yes—
387C23C25×C1311yescharacteristic
388Q8—48no—
389D4—216no—
390D4—416no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—22no—
395C2×C4—24no—
396C2×C4—21no—
397C2×C4—24no—
398C2×C4—22no—
399C2×C4—24no—
400C2×C4—21no—
401C2×C4—232no—
402C2×C4—24no—
403C2×C4—22no—
404C2×C4—28no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—21no—
408C2×C4—24no—
409C2×C4—416no—
410C2×C4—416no—
411C2×C4C23×C4×C1318yes—
412C2×C4C23×C4×C1312yes—
413C2×C4C23×C4×C1318yes—
414C2×C4C23×C4×C1314yes—
415C2×C4C2×C13×#4114yes—
416C2×C4C2×C13×#4118yes—
417C2×C4C2×C13×#4114yes—
418C2×C4C2×C13×#4114yes—
419C2×C4C2×C13×#4114yes—
420C2×C4C13×H(5,𝔽2)12yes—
421C22—28no—
422C22—28no—
423C22—28no—
424C22—44no—
425C22—44no—
426C22—44no—
427C22—44no—
428C22C24×C4×C1311yescharacteristic
429C22C22×C13×#4112yes—
430C22C22×C13×#4112yes—
431C22C2×C13×H(5,𝔽2)11yescharacteristic
432C22C13×#58511yescharacteristic
433C4—28no—
434C4—28no—
435C4—22no—
436C4—24no—
437C4—28no—
438C4—44no—
439C4—41no—
440C4—44no—
441C4C4×C13×#4118yes—
442C4C13×#55514yesdirect product factor
443C2—48no—
444C2C2×C4×C13×#4112yes—
445C2C4×C13×H(5,𝔽2)11yescharacteristic
446C2C2×C13×#55511yescharacteristic
447C2C13×#347512yes—
448C2C13×#348311yescharacteristic
subgroupG/H
centerC22×C4×C13C24
commutatorC22C24×C4×C13
Frattini, cosocleC23C25×C13
socleC23×C13C25
prime radicalC2×C13×#555C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2372C2semidirect
3. C13×#2369C2semidirect
4. C13×#2363C2semidirect
5. C13×#2354C2semidirect
6. C13×#2346C2semidirect
7. C4×C13×C4⋊Q8C2semidirect
8. C4×C13×#124C2semidirect
9. C4×C13×#121C2semidirect
10. C42×D4×C13C2semidirect
11. C4×C13×#117C2semidirect
12. C13×#555C4direct (N × H)
57. C13×C4⋊Q8C2×C4semidirect
58. C13×#124C2×C4semidirect
59. C13×#121C2×C4semidirect
64. C4×D4×C13C2×C4semidirect
66. C13×#117C2×C4semidirect
100. C4×#555C13direct (N × H)
157. #2372C2×C13semidirect
158. #2369C2×C13semidirect
159. #2363C2×C13semidirect
160. #2354C2×C13semidirect
161. #2346C2×C13semidirect
162. C4×C4⋊Q8C2×C13semidirect
163. C4×#124C2×C13semidirect
164. C4×#121C2×C13semidirect
165. C42×D4C2×C13semidirect
166. C4×#117C2×C13semidirect
208. #555C4×C13direct (N × H)
268. C4×C13#555direct (N × H)
275. C4⋊Q8C2×C4×C13semidirect
276. #124C2×C4×C13semidirect
277. #121C2×C4×C13semidirect
282. C4×D4C2×C4×C13semidirect
284. #117C2×C4×C13semidirect
379. C13C4×#555direct (N × H)
442. C4C13×#555direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5552
C13×#23722
C13×#23692
C13×#23632
C13×#23542
C13×#23462
C4×C13×C4⋊Q82
C4×C13×#1242
C4×C13×#1212
C42×D4×C132
C4×C13×#1172
C4×#55513