Finite Group Databasebeta

← C13×#34594 #15720933

Subgroups — C13×#34594 #15720933

Order 3328.

2362 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#529C212yesmaximal, complemented
2C13×#2664C214yesmaximal, complemented
3C13×#2662C214yesmaximal, complemented
4C13×#2659C211yesmaximal, characteristic, complemented
5C13×#2656C211yesmaximal, characteristic
6C13×#2639C212yesmaximal, complemented
7C13×#2618C214yesmaximal, complemented
8C13×#2396C214yesmaximal, complemented
9C13×#2392C214yesmaximal, complemented
10C4×C13×#121C214yesmaximal, complemented
11C2×C4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
12C13×#529—216no—
13C2×C13×#126C2214yes—
14C2×C13×#125C2212yes—
15C2×C13×#124C2212yes—
16C2×C13×#123C2214yes—
17C2×C13×C22⋊Q8C2212yes—
18C2×C13×#121C2214yes—
19C2×C13×#121C2212yes—
20C2×C4×Q8×C13C2212yes—
21C2×C4×D4×C13C2214yes—
22C2×C4×D4×C13C2212yes—
23C2×C4×D4×C13C2214yes—
24C2×C13×#117C2214yes—
25C22×C13×C4⋊C4C2212yes—
26C22×C42×C13C2212yes—
27C22×C42×C13C2211yescharacteristic
28C13×#400C2214yes—
29C13×#399C2214yes—
30C13×#398C2218yes—
31C13×#398C2214yes—
32C13×#397C2214yes—
33C13×#396C2218yes—
34C13×#396C2218yes—
35C13×#395C2214yes—
36C13×#394C2218yes—
37C13×#394C2214yes—
38C13×#393C2214yes—
39C13×#392C2214yes—
40C13×#390C2214yes—
41C13×#389C2214yes—
42C13×#388C2218yes—
43C13×#386C2218yes—
44C13×#380C2214yes—
45C4×C13×C4⋊C4C2214yes—
46C4×C13×C4⋊C4C2214yes—
47C4×C13×C4⋊C4C2214yes—
48C4×C13×C22⋊C4C2218yes—
49C2×C13×#95C2211yescharacteristic
50C2×C13×#95C2211yescharacteristic
51C22×Q8×C13C2312yes—
52C22×D4×C13C2314yes—
53C22×D4×C13C2314yes—
54C22×D4×C13C2312yes—
55C23×C4×C13C2314yes—
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2312yes—
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2312yes—
61C13×#126—216no—
62C13×#125—28no—
63C13×#124—28no—
64C13×#123—216no—
65C13×C22⋊Q8—28no—
66C13×#121—28no—
67C13×#121—216no—
68C4×Q8×C13—28no—
69C4×D4×C13—216no—
70C4×D4×C13—28no—
71C4×D4×C13—48no—
72C13×#117—216no—
73C2×C13×C4⋊C4—28no—
74C2×C13×C4⋊C4C2318yes—
75C2×C13×C4⋊C4C2314yes—
76C2×C13×C4⋊C4C2314yes—
77C2×C13×C4⋊C4C2314yes—
78C2×C13×C4⋊C4C2314yes—
79C2×C13×C4⋊C4C2314yes—
80C2×C13×C4⋊C4C2312yes—
81C2×C13×C4⋊C4C2312yes—
82C2×C13×C4⋊C4C2314yes—
83C2×C13×C4⋊C4C2314yes—
84C2×C13×C22⋊C4C2318yes—
85C2×C13×C22⋊C4C2314yes—
86C2×C13×C22⋊C4C2314yes—
87C2×C13×C22⋊C4C2314yes—
88C2×C13×C22⋊C4C2314yes—
89C2×C13×C22⋊C4C2314yes—
90C2×C13×C22⋊C4C2318yes—
91C2×C13×C22⋊C4C2318yes—
92C2×C42×C13—44no—
93C2×C42×C13D418yescomplemented
94C2×C42×C13C2314yes—
95C2×C42×C13C2314yes—
96C2×C42×C13C2314yes—
97C2×C42×C13C2312yes—
98C2×C42×C13C2312yes—
99C13×#95C2318yes—
100C13×#95C2318yes—
101C13×#95C2314yes—
102C13×#95C2314yes—
103C13×#95C2318yes—
104#34594C1311yesmaximal, characteristic, direct product factor, Sylow
105C24×C13C2414yes—
106C24×C13C2411yescharacteristic
107C2×Q8×C13—24no—
108C2×Q8×C13—44no—
109C2×D4×C13—28no—
110C2×D4×C13—216no—
111C2×D4×C13—24no—
112C2×D4×C13—28no—
113C2×D4×C13—44no—
114C2×D4×C13—44no—
115C2×D4×C13—44no—
116C22×C4×C13—24no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—24no—
120C22×C4×C13—28no—
121C22×C4×C13—28no—
122C22×C4×C13—28no—
123C22×C4×C13—42no—
124C22×C4×C13—42no—
125C22×C4×C13—42no—
126C22×C4×C13—42no—
127C22×C4×C13—42no—
128C22×C4×C13C2×D414yes—
129C22×C4×C13C2×D414yes—
130C22×C4×C13C2×D414yes—
131C22×C4×C13#4118yes—
132C22×C4×C13C2414yes—
133C22×C4×C13C2414yes—
134C22×C4×C13C2414yes—
135C22×C4×C13C2414yes—
136C22×C4×C13C2412yes—
137C22×C4×C13C2411yescharacteristic
138C22×C4×C13C2412yes—
139C22×C4×C13C2414yes—
140C22×C4×C13C2411yescharacteristic
141C13×C4⋊C4—28no—
142C13×C4⋊C4—28no—
143C13×C4⋊C4—24no—
144C13×C4⋊C4—28no—
145C13×C4⋊C4—24no—
146C13×C4⋊C4—28no—
147C13×C4⋊C4—216no—
148C13×C4⋊C4—28no—
149C13×C4⋊C4—44no—
150C13×C4⋊C4—44no—
151C13×C22⋊C4—28no—
152C13×C22⋊C4—28no—
153C13×C22⋊C4—28no—
154C13×C22⋊C4—28no—
155C13×C22⋊C4—28no—
156C13×C22⋊C4—216no—
157C13×C22⋊C4—48no—
158C13×C22⋊C4—48no—
159C42×C13—28no—
160C42×C13—28no—
161C42×C13—44no—
162C42×C13C2×D418yes—
163C42×C13C2×D418yes—
164C2×#529C2×C1312yescomplemented
165#2664C2×C1314yescomplemented
166#2662C2×C1314yescomplemented
167#2659C2×C1311yescharacteristic, complemented
168#2656C2×C1311yescharacteristic
169#2639C2×C1312yescomplemented
170#2618C2×C1314yescomplemented
171#2396C2×C1314yescomplemented
172#2392C2×C1314yescomplemented
173C4×#121C2×C1314yescomplemented
174C2×C4×C4⋊C4C2×C1311yescharacteristic, complemented
175C23×C13—21no—
176C23×C13—21no—
177C23×C13—22no—
178C23×C13—24no—
179C23×C13—28no—
180C23×C13—24no—
181C23×C13—24no—
182C23×C13—28no—
183C23×C13C22×D412yes—
184C23×C13C2×#4114yes—
185C23×C13C2511yescharacteristic
186Q8×C13—48no—
187D4×C13—48no—
188D4×C13—416no—
189D4×C13—416no—
190C2×C4×C13—28no—
191C2×C4×C13—24no—
192C2×C4×C13—24no—
193C2×C4×C13—21no—
194C2×C4×C13—21no—
195C2×C4×C13—24no—
196C2×C4×C13—24no—
197C2×C4×C13—28no—
198C2×C4×C13—24no—
199C2×C4×C13—24no—
200C2×C4×C13—24no—
201C2×C4×C13—28no—
202C2×C4×C13—24no—
203C2×C4×C13—24no—
204C2×C4×C13—24no—
205C2×C4×C13—24no—
206C2×C4×C13—24no—
207C2×C4×C13—28no—
208C2×C4×C13—44no—
209C2×C4×C13—48no—
210C2×C4×C13—48no—
211C2×C4×C13—416no—
212C2×C4×C13C22×D414yes—
213C2×C4×C13C22×D412yes—
214C2×C4×C13C22×D414yes—
215C2×C4×C13C22×D412yes—
216C2×C4×C13C2×#4118yes—
217C2×C4×C13H(5,𝔽2)12yes—
218C2×C4×C132−1+412yes—
219#529—216no—
220C2×#126C22×C1314yes—
221C2×#125C22×C1312yes—
222C2×#124C22×C1312yes—
223C2×#123C22×C1314yes—
224C2×C22⋊Q8C22×C1312yes—
225C2×#121C22×C1314yes—
226C2×#121C22×C1312yes—
227C2×C4×Q8C22×C1312yes—
228C2×C4×D4C22×C1312yes—
229C2×C4×D4C22×C1314yes—
230C2×C4×D4C22×C1314yes—
231C2×#117C22×C1314yes—
232C22×C4⋊C4C22×C1312yes—
233C22×C42C22×C1312yes—
234C22×C42C22×C1311yescharacteristic
235#400C22×C1314yes—
236#399C22×C1314yes—
237#398C22×C1318yes—
238#398C22×C1314yes—
239#397C22×C1314yes—
240#396C22×C1318yes—
241#396C22×C1318yes—
242#395C22×C1314yes—
243#394C22×C1318yes—
244#394C22×C1314yes—
245#393C22×C1314yes—
246#392C22×C1314yes—
247#390C22×C1314yes—
248#389C22×C1314yes—
249#388C22×C1318yes—
250#386C22×C1318yes—
251#380C22×C1314yes—
252C4×C4⋊C4C22×C1314yes—
253C4×C4⋊C4C22×C1314yes—
254C4×C4⋊C4C22×C1314yes—
255C4×C22⋊C4C22×C1318yes—
256C2×#95C22×C1311yescharacteristic
257C2×#95C22×C1311yescharacteristic
258C22×C13—22no—
259C22×C13—22no—
260C22×C13—24no—
261C22×C13—24no—
262C22×C13—44no—
263C22×C13—44no—
264C22×C13—44no—
265C22×C13—48no—
266C22×C13—48no—
267C22×C13#53214yes—
268C22×C13C23×D411yescharacteristic
269C22×C13C22×#4112yes—
270C22×C13C2×H(5,𝔽2)11yescharacteristic
271C22×C13C2×2−1+411yescharacteristic
272C22×C13#58512yes—
273C4×C13—24no—
274C4×C13—22no—
275C4×C13—24no—
276C4×C13—28no—
277C4×C13—44no—
278C4×C13—44no—
279C4×C13—44no—
280C4×C13—44no—
281C4×C13#53714yes—
282C22×Q8C23×C1312yes—
283C22×D4C23×C1314yes—
284C22×D4C23×C1312yes—
285C22×D4C23×C1314yes—
286C23×C4C23×C1314yes—
287C23×C4C23×C1311yescharacteristic
288C23×C4C23×C1311yescharacteristic
289C23×C4C23×C1312yes—
290C23×C4C23×C1311yescharacteristic
291C23×C4C23×C1312yes—
292#126—216no—
293#125—28no—
294#124—28no—
295#123—216no—
296C22⋊Q8—28no—
297#121—28no—
298#121—216no—
299C4×Q8—28no—
300C4×D4—216no—
301C4×D4—28no—
302C4×D4—48no—
303#117—216no—
304C2×C4⋊C4—28no—
305C2×C4⋊C4C23×C1318yes—
306C2×C4⋊C4C23×C1314yes—
307C2×C4⋊C4C23×C1314yes—
308C2×C4⋊C4C23×C1312yes—
309C2×C4⋊C4C23×C1314yes—
310C2×C4⋊C4C23×C1312yes—
311C2×C4⋊C4C23×C1314yes—
312C2×C4⋊C4C23×C1314yes—
313C2×C4⋊C4C23×C1314yes—
314C2×C4⋊C4C23×C1314yes—
315C2×C22⋊C4C23×C1314yes—
316C2×C22⋊C4C23×C1314yes—
317C2×C22⋊C4C23×C1314yes—
318C2×C22⋊C4C23×C1314yes—
319C2×C22⋊C4C23×C1314yes—
320C2×C22⋊C4C23×C1318yes—
321C2×C22⋊C4C23×C1318yes—
322C2×C22⋊C4C23×C1318yes—
323C2×C42—44no—
324C2×C42D4×C1318yescomplemented
325C2×C42C23×C1314yes—
326C2×C42C23×C1314yes—
327C2×C42C23×C1314yes—
328C2×C42C23×C1312yes—
329C2×C42C23×C1312yes—
330#95C23×C1314yes—
331#95C23×C1314yes—
332#95C23×C1318yes—
333#95C23×C1318yes—
334#95C23×C1318yes—
335C2×C13—24no—
336C2×C13—84no—
337C2×C13C2×#53211yescharacteristic
338C2×C13C2×#53711yescharacteristic
339C2×C13#344911yescharacteristic
340C2×C13#345912yes—
341C2×C13#346112yes—
342C24C24×C1314yes—
343C24C24×C1311yescharacteristic
344C2×Q8—24no—
345C2×Q8—44no—
346C2×D4—28no—
347C2×D4—216no—
348C2×D4—24no—
349C2×D4—28no—
350C2×D4—44no—
351C2×D4—44no—
352C2×D4—44no—
353C22×C4—24no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—24no—
357C22×C4—28no—
358C22×C4—28no—
359C22×C4—28no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4C2×D4×C1314yes—
366C22×C4C2×D4×C1314yes—
367C22×C4C2×D4×C1314yes—
368C22×C4C13×#4118yes—
369C22×C4C24×C1314yes—
370C22×C4C24×C1314yes—
371C22×C4C24×C1314yes—
372C22×C4C24×C1314yes—
373C22×C4C24×C1312yes—
374C22×C4C24×C1311yescharacteristic
375C22×C4C24×C1312yes—
376C22×C4C24×C1314yes—
377C22×C4C24×C1311yescharacteristic
378C4⋊C4—28no—
379C4⋊C4—28no—
380C4⋊C4—24no—
381C4⋊C4—28no—
382C4⋊C4—24no—
383C4⋊C4—28no—
384C4⋊C4—216no—
385C4⋊C4—28no—
386C4⋊C4—44no—
387C4⋊C4—44no—
388C22⋊C4—28no—
389C22⋊C4—28no—
390C22⋊C4—28no—
391C22⋊C4—28no—
392C22⋊C4—28no—
393C22⋊C4—216no—
394C22⋊C4—48no—
395C22⋊C4—48no—
396C42—28no—
397C42—28no—
398C42—44no—
399C42C2×D4×C1318yes—
400C42C2×D4×C1318yes—
401C13#3459411yescharacteristic, direct product factor, Sylow
402C23—21no—
403C23—21no—
404C23—22no—
405C23—24no—
406C23—28no—
407C23—24no—
408C23—24no—
409C23—28no—
410C23C22×D4×C1312yes—
411C23C2×C13×#4114yes—
412C23C25×C1311yescharacteristic
413Q8—48no—
414D4—48no—
415D4—416no—
416D4—416no—
417C2×C4—28no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—28no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—28no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—28no—
435C2×C4—44no—
436C2×C4—48no—
437C2×C4—48no—
438C2×C4—416no—
439C2×C4C22×D4×C1314yes—
440C2×C4C22×D4×C1312yes—
441C2×C4C22×D4×C1314yes—
442C2×C4C22×D4×C1312yes—
443C2×C4C2×C13×#4118yes—
444C2×C4C13×H(5,𝔽2)12yes—
445C2×C4C13×2−1+412yes—
446C22—22no—
447C22—22no—
448C22—24no—
449C22—24no—
450C22—44no—
451C22—44no—
452C22—44no—
453C22—48no—
454C22—48no—
455C22C13×#53214yes—
456C22C23×D4×C1311yescharacteristic
457C22C22×C13×#4112yes—
458C22C2×C13×H(5,𝔽2)11yescharacteristic
459C22C2×C13×2−1+411yescharacteristic
460C22C13×#58512yes—
461C4—24no—
462C4—22no—
463C4—24no—
464C4—28no—
465C4—44no—
466C4—44no—
467C4—44no—
468C4—44no—
469C4C13×#53714yes—
470C2—24no—
471C2—84no—
472C2C2×C13×#53211yescharacteristic
473C2C2×C13×#53711yescharacteristic
474C2C13×#344911yescharacteristic
475C2C13×#345912yes—
476C2C13×#346112yes—
subgroupG/H
centerC22×C4×C13C24
commutator, Frattini, cosocleC23C25×C13
socleC23×C13C25
prime radicalC13×#2656C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C13×#529C2semidirect
2. C13×#2664C2semidirect
3. C13×#2662C2semidirect
4. C13×#2659C2semidirect
6. C13×#2639C2semidirect
7. C13×#2618C2semidirect
8. C13×#2396C2semidirect
9. C13×#2392C2semidirect
10. C4×C13×#121C2semidirect
11. C2×C4×C13×C4⋊C4C2semidirect
93. C2×C42×C13D4semidirect
104. #34594C13direct (N × H)
164. C2×#529C2×C13semidirect
165. #2664C2×C13semidirect
166. #2662C2×C13semidirect
167. #2659C2×C13semidirect
169. #2639C2×C13semidirect
170. #2618C2×C13semidirect
171. #2396C2×C13semidirect
172. #2392C2×C13semidirect
173. C4×#121C2×C13semidirect
174. C2×C4×C4⋊C4C2×C13semidirect
324. C2×C42D4×C13semidirect
401. C13#34594direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5292
C13×#26642
C13×#26622
C13×#26592
C13×#26562
C13×#26392
C13×#26182
C13×#23962
C13×#23922
C4×C13×#1212
C2×C4×C13×C4⋊C42
#3459413