Finite Group Databasebeta

← C13×#24623 #15710962

Subgroups — C13×#24623 #15710962

Order 3328.

718 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3094C211yesmaximal, characteristic
2C2×C13×#481C211yesmaximal, characteristic
3C13×#2924C211yesmaximal, characteristic, complemented
4C2×C13×#428C211yesmaximal, characteristic, complemented
5C13×#2090C212yesmaximal, complemented
6C13×#2063C212yesmaximal, complemented
7C13×#1951C212yesmaximal, complemented
8C13×#1931C212yesmaximal, complemented
9C13×#1900C211yesmaximal, characteristic
10C13×#1855C211yesmaximal, characteristic, complemented
11C13×#1821C211yesmaximal, characteristic, complemented
12C22×C13×M16C2211yescharacteristic
13C2×C13×#121C2211yescharacteristic
14C2×C13×#117C2211yescharacteristic
15C22×C13×C4⋊C4C2211yescharacteristic
16C13×#482—21no—
17C13×#482—21no—
18C13×#481—21no—
19C13×#481—21no—
20C13×#481—21no—
21C13×#481—22no—
22C13×#480—21no—
23C13×#433—22no—
24C13×#432—21no—
25C13×#431—21no—
26C2×C13×#108C2212yes—
27C13×#428—21no—
28C13×#428—21no—
29C13×#428C2212yes—
30C13×#428C2211yescharacteristic
31C13×#428C2211yescharacteristic
32C13×#428C2212yes—
33C2×C13×#107—21no—
34C2×C13×#106—21no—
35C2×C13×#106C2212yes—
36C13×#424C2212yes—
37C13×#418C2211yescharacteristic
38C13×#418C2211yescharacteristic
39C2×C13×#102C2212yes—
40C2×C13×#100C2212yes—
41C13×#407C2211yescharacteristic
42C13×#407C2211yescharacteristic
43C2×C13×C22⋊C8C2211yescharacteristic
44C13×#405C2212yes—
45C13×#343C2212yes—
46C13×#343C2212yes—
47C13×#343C2212yes—
48C13×#341C2212yes—
49C22×D4×C13—21no—
50C22×D4×C13C2311yescharacteristic
51C23×C4×C13—21no—
52C23×C4×C13C2311yescharacteristic
53C2×C13×M16—21no—
54C2×C13×M16—24no—
55C2×C13×M16C2312yes—
56C2×C13×M16C2311yescharacteristic
57C2×C13×M16C2311yescharacteristic
58C2×C13×M16C2312yes—
59C22×C8×C13—21no—
60C22×C8×C13C2312yes—
61C13×#121—21no—
62C13×#121—21no—
63C13×#121—21no—
64C13×#121—21no—
65C13×#117—21no—
66C13×#117—21no—
67C13×#117D411yescharacteristic
68C13×#117D411yescharacteristic
69C13×#117C2311yescharacteristic
70C13×#117C2311yescharacteristic
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4D411yescharacteristic
77C2×C13×C4⋊C4D411yescharacteristic
78C2×C13×C4⋊C4C2312yes—
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C22⋊C4—21no—
81C2×C13×C22⋊C4—21no—
82C2×C42×C13—21no—
83C13×#108—24no—
84C13×#107—22no—
85C13×#107—22no—
86C13×#107—21no—
87C13×#107—21no—
88C13×#106—22no—
89C13×#106—22no—
90C13×#106—22no—
91C13×#106—22no—
92C13×#106—21no—
93C13×#106—21no—
94C13×C4⋊C8—22no—
95C13×C4⋊C8—22no—
96C13×#102—22no—
97C13×#102—22no—
98C13×#102—21no—
99C13×#102—21no—
100C13×#102—21no—
101C13×#102—21no—
102C13×#100—24no—
103C13×C22⋊C8—21no—
104C13×C22⋊C8—21no—
105C13×C22⋊C8—21no—
106C13×C22⋊C8—21no—
107C13×C22⋊C8D411yescharacteristic
108C13×C22⋊C8D411yescharacteristic
109C13×C22⋊C8D412yes—
110C13×#97—22no—
111C4×C8×C13—22no—
112#24623C1311yesmaximal, characteristic, direct product factor, Sylow
113C24×C13—21no—
114C24×C13#4111yescharacteristic
115C2×D4×C13—21no—
116C2×D4×C13—21no—
117C2×D4×C13—22no—
118C2×D4×C13—22no—
119C2×D4×C13—41no—
120C2×D4×C13—41no—
121C2×D4×C13—82no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—22no—
128C22×C4×C13—41no—
129C22×C4×C13—41no—
130C22×C4×C13—82no—
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13#4111yescharacteristic
136C22×C4×C13C2411yescharacteristic
137C13×M16—24no—
138C13×M16—22no—
139C13×M16—22no—
140C13×M16—22no—
141C13×M16—22no—
142C13×M16—22no—
143C13×M16#4114yes—
144C2×C8×C13—24no—
145C2×C8×C13—22no—
146C2×C8×C13—22no—
147C2×C8×C13—22no—
148C2×C8×C13—22no—
149C2×C8×C13—21no—
150C2×C8×C13—21no—
151C2×C8×C13C2×D412yes—
152C2×C8×C13C2×D412yes—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—22no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—22no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—41no—
160C13×C4⋊C4—41no—
161C13×C4⋊C4C2×D411yescharacteristic
162C13×C4⋊C4C2×D411yescharacteristic
163C13×C4⋊C4C2×D411yescharacteristic
164C13×C4⋊C4C2×D411yescharacteristic
165C13×C22⋊C4—21no—
166C13×C22⋊C4—21no—
167C13×C22⋊C4—21no—
168C13×C22⋊C4—21no—
169C13×C22⋊C4—41no—
170C13×C22⋊C4—41no—
171C42×C13—21no—
172C42×C13—21no—
173C42×C13—21no—
174C42×C13—21no—
175#3094C2×C1311yescharacteristic
176C2×#481C2×C1311yescharacteristic
177#2924C2×C1311yescharacteristic, complemented
178C2×#428C2×C1311yescharacteristic, complemented
179#2090C2×C1312yescomplemented
180#2063C2×C1312yescomplemented
181#1951C2×C1312yescomplemented
182#1931C2×C1312yescomplemented
183#1900C2×C1311yescharacteristic
184#1855C2×C1311yescharacteristic, complemented
185#1821C2×C1311yescharacteristic, complemented
186C23×C13—22no—
187C23×C13—22no—
188C23×C13—41no—
189C23×C13—41no—
190C23×C13—42no—
191C23×C13—81no—
192C23×C13—81no—
193C23×C13#12111yescharacteristic
194C23×C13#12111yescharacteristic
195C23×C13C2×#4111yescharacteristic
196D4×C13—41no—
197D4×C13—41no—
198D4×C13—42no—
199D4×C13—82no—
200D4×C13—82no—
201C2×C4×C13—22no—
202C2×C4×C13—21no—
203C2×C4×C13—21no—
204C2×C4×C13—21no—
205C2×C4×C13—21no—
206C2×C4×C13—22no—
207C2×C4×C13—22no—
208C2×C4×C13—21no—
209C2×C4×C13—21no—
210C2×C4×C13—21no—
211C2×C4×C13—21no—
212C2×C4×C13—42no—
213C2×C4×C13—41no—
214C2×C4×C13—42no—
215C2×C4×C13—81no—
216C2×C4×C13—82no—
217C2×C4×C13—82no—
218C2×C4×C13—82no—
219C2×C4×C13—81no—
220C2×C4×C13#12111yescharacteristic
221C2×C4×C13#12111yescharacteristic
222C2×C4×C13C22×D411yescharacteristic
223C2×C4×C13C22×D411yescharacteristic
224C2×C4×C13C2×#4112yes—
225C2×C4×C132−1+412yes—
226C8×C13—24no—
227C8×C13—22no—
228C8×C13—22no—
229C8×C13—41no—
230C8×C13—41no—
231C8×C13—42no—
232C22×M16C22×C1311yescharacteristic
233C2×#121C22×C1311yescharacteristic
234C2×#117C22×C1311yescharacteristic
235C22×C4⋊C4C22×C1311yescharacteristic
236#482—21no—
237#482—21no—
238#481—21no—
239#481—21no—
240#481—21no—
241#481—22no—
242#480—21no—
243#433—22no—
244#432—21no—
245#431—21no—
246C2×#108C22×C1312yes—
247#428—21no—
248#428—21no—
249#428C22×C1312yes—
250#428C22×C1311yescharacteristic
251#428C22×C1311yescharacteristic
252#428C22×C1312yes—
253C2×#107—21no—
254C2×#106—21no—
255C2×#106C22×C1312yes—
256#424C22×C1312yes—
257#418C22×C1311yescharacteristic
258#418C22×C1311yescharacteristic
259C2×#102C22×C1312yes—
260C2×#100C22×C1312yes—
261#407C22×C1311yescharacteristic
262#407C22×C1311yescharacteristic
263C2×C22⋊C8C22×C1311yescharacteristic
264#405C22×C1312yes—
265#343C22×C1312yes—
266#343C22×C1312yes—
267#343C22×C1312yes—
268#341C22×C1312yes—
269C22×C13—21no—
270C22×C13—21no—
271C22×C13—21no—
272C22×C13—21no—
273C22×C13—21no—
274C22×C13—21no—
275C22×C13—21no—
276C22×C13—44no—
277C22×C13—81no—
278C22×C13—81no—
279C22×C13—81no—
280C22×C13—162no—
281C22×C13#47112yes—
282C22×C13C2×#12111yescharacteristic
283C22×C13#55212yes—
284C4×C13—21no—
285C4×C13—21no—
286C4×C13—41no—
287C4×C13—41no—
288C4×C13—41no—
289C4×C13—41no—
290C4×C13—81no—
291C4×C13—82no—
292C4×C13#52511yescharacteristic
293C4×C13#53611yescharacteristic
294C4×C13#54712yes—
295C22×D4—21no—
296C22×D4C23×C1311yescharacteristic
297C23×C4—21no—
298C23×C4C23×C1311yescharacteristic
299C2×M16—21no—
300C2×M16—24no—
301C2×M16C23×C1311yescharacteristic
302C2×M16C23×C1312yes—
303C2×M16C23×C1311yescharacteristic
304C2×M16C23×C1312yes—
305C22×C8—21no—
306C22×C8C23×C1312yes—
307#121—21no—
308#121—21no—
309#121—21no—
310#121—21no—
311#117—21no—
312#117—21no—
313#117D4×C1311yescharacteristic
314#117D4×C1311yescharacteristic
315#117C23×C1311yescharacteristic
316#117C23×C1311yescharacteristic
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4D4×C1311yescharacteristic
323C2×C4⋊C4D4×C1311yescharacteristic
324C2×C4⋊C4C23×C1312yes—
325C2×C4⋊C4C23×C1311yescharacteristic
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C42—21no—
329#108—24no—
330#107—22no—
331#107—22no—
332#107—21no—
333#107—21no—
334#106—22no—
335#106—22no—
336#106—22no—
337#106—22no—
338#106—21no—
339#106—21no—
340C4⋊C8—22no—
341C4⋊C8—22no—
342#102—22no—
343#102—22no—
344#102—21no—
345#102—21no—
346#102—21no—
347#102—21no—
348#100—24no—
349C22⋊C8—21no—
350C22⋊C8—21no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8D4×C1311yescharacteristic
354C22⋊C8D4×C1311yescharacteristic
355C22⋊C8D4×C1312yes—
356#97—22no—
357C4×C8—22no—
358C2×C13—22no—
359C2×C13—22no—
360C2×C13—41no—
361C2×C13—161no—
362C2×C13#241311yescharacteristic
363C2×C13C2×#47111yescharacteristic
364C2×C13#306811yescharacteristic
365C24—21no—
366C24C13×#4111yescharacteristic
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—82no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—22no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—82no—
383C22×C4C2×D4×C1311yescharacteristic
384C22×C4C2×D4×C1311yescharacteristic
385C22×C4C2×D4×C1311yescharacteristic
386C22×C4C2×D4×C1311yescharacteristic
387C22×C4C13×#4111yescharacteristic
388C22×C4C24×C1311yescharacteristic
389M16—24no—
390M16—22no—
391M16—22no—
392M16—22no—
393M16—22no—
394M16—22no—
395M16C13×#4114yes—
396C2×C8—24no—
397C2×C8—22no—
398C2×C8—22no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8C2×D4×C1312yes—
404C2×C8C2×D4×C1312yes—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—22no—
408C4⋊C4—21no—
409C4⋊C4—22no—
410C4⋊C4—21no—
411C4⋊C4—41no—
412C4⋊C4—41no—
413C4⋊C4C2×D4×C1311yescharacteristic
414C4⋊C4C2×D4×C1311yescharacteristic
415C4⋊C4C2×D4×C1311yescharacteristic
416C4⋊C4C2×D4×C1311yescharacteristic
417C22⋊C4—21no—
418C22⋊C4—21no—
419C22⋊C4—21no—
420C22⋊C4—21no—
421C22⋊C4—41no—
422C22⋊C4—41no—
423C42—21no—
424C42—21no—
425C42—21no—
426C42—21no—
427C13#2462311yescharacteristic, direct product factor, Sylow
428C23—22no—
429C23—22no—
430C23—41no—
431C23—41no—
432C23—42no—
433C23—81no—
434C23—81no—
435C23C13×#12111yescharacteristic
436C23C13×#12111yescharacteristic
437C23C2×C13×#4111yescharacteristic
438D4—41no—
439D4—41no—
440D4—42no—
441D4—82no—
442D4—82no—
443C2×C4—22no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—42no—
457C2×C4—81no—
458C2×C4—82no—
459C2×C4—82no—
460C2×C4—82no—
461C2×C4—81no—
462C2×C4C13×#12111yescharacteristic
463C2×C4C13×#12111yescharacteristic
464C2×C4C22×D4×C1311yescharacteristic
465C2×C4C22×D4×C1311yescharacteristic
466C2×C4C2×C13×#4112yes—
467C2×C4C13×2−1+412yes—
468C8—24no—
469C8—22no—
470C8—22no—
471C8—41no—
472C8—41no—
473C8—42no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—44no—
482C22—81no—
483C22—81no—
484C22—81no—
485C22—162no—
486C22C13×#47112yes—
487C22C2×C13×#12111yescharacteristic
488C22C13×#55212yes—
489C4—21no—
490C4—21no—
491C4—41no—
492C4—41no—
493C4—41no—
494C4—41no—
495C4—81no—
496C4—82no—
497C4C13×#52511yescharacteristic
498C4C13×#53611yescharacteristic
499C4C13×#54712yes—
500C2—22no—
501C2—22no—
502C2—41no—
503C2—161no—
504C2C13×#241311yescharacteristic
505C2C2×C13×#47111yescharacteristic
506C2C13×#306811yescharacteristic
subgroupG/H
center, socleC22×C13C2×#121
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC2×C13×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#2924C2semidirect
4. C2×C13×#428C2semidirect
5. C13×#2090C2semidirect
6. C13×#2063C2semidirect
7. C13×#1951C2semidirect
8. C13×#1931C2semidirect
10. C13×#1855C2semidirect
11. C13×#1821C2semidirect
112. #24623C13direct (N × H)
177. #2924C2×C13semidirect
178. C2×#428C2×C13semidirect
179. #2090C2×C13semidirect
180. #2063C2×C13semidirect
181. #1951C2×C13semidirect
182. #1931C2×C13semidirect
184. #1855C2×C13semidirect
185. #1821C2×C13semidirect
427. C13#24623direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#30942
C2×C13×#4812
C13×#29242
C2×C13×#4282
C13×#20902
C13×#20632
C13×#19512
C13×#19312
C13×#19002
C13×#18552
C13×#18212
#2462313