Finite Group Databasebeta

← C13×#9940 #15696279

Subgroups — C13×#9940 #15696279

Order 3328.

768 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 768 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3094C211yesmaximal, characteristic, complemented
2C13×#2539C211yesmaximal, characteristic
3C13×#2482C211yesmaximal, characteristic, complemented
4C13×#1826C211yesmaximal, characteristic, complemented
5C13×#1510C211yesmaximal, characteristic, complemented
6C13×#1462C211yesmaximal, characteristic, complemented
7C13×#1284C211yesmaximal, characteristic, complemented
8C2×C13×#123—21no—
9C2×C13×#121C2211yescharacteristic
10C2×C13×#120—21no—
11C2×C13×#117C2211yescharacteristic
12C22×C13×C22⋊C4C2211yescharacteristic
13C13×#482—22no—
14C13×#481—21no—
15C13×#480—21no—
16C13×#428—21no—
17C13×#418—21no—
18C13×#407C2211yescharacteristic
19C13×#407C2211yescharacteristic
20C13×#399—21no—
21C13×#399—21no—
22C13×#397—21no—
23C13×#392—21no—
24C13×#390—22no—
25C13×#388—22no—
26C13×#385—21no—
27C13×#381C2211yescharacteristic
28C13×#379—21no—
29C4×C13×C22⋊C4C2211yescharacteristic
30C13×#339—22no—
31C13×#327—22no—
32C13×#323—22no—
33C25×C13D411yescharacteristic
34C22×D4×C13—21no—
35C22×D4×C13—22no—
36C22×D4×C13D411yescharacteristic
37C23×C4×C13D411yescharacteristic
38C23×C4×C13C2311yescharacteristic
39C2×C13×M16—21no—
40C2×C13×M16—21no—
41C13×#123—44no—
42C13×#121—21no—
43C13×#121—21no—
44C13×#121—21no—
45C13×#121—21no—
46C13×#120—44no—
47C13×#117—21no—
48C13×#117—21no—
49C13×#117—21no—
50C13×#117—21no—
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4—22no—
53C2×C13×C4⋊C4D411yescharacteristic
54C2×C13×C4⋊C4D411yescharacteristic, complemented
55C2×C13×C4⋊C4D411yescharacteristic, complemented
56C2×C13×C22⋊C4—21no—
57C2×C13×C22⋊C4—22no—
58C2×C13×C22⋊C4—22no—
59C2×C13×C22⋊C4—22no—
60C2×C13×C22⋊C4—21no—
61C2×C13×C22⋊C4—21no—
62C2×C13×C22⋊C4—21no—
63C2×C13×C22⋊C4—21no—
64C2×C13×C22⋊C4—21no—
65C2×C13×C22⋊C4—21no—
66C2×C13×C22⋊C4—21no—
67C2×C13×C22⋊C4—21no—
68C2×C13×C22⋊C4—21no—
69C2×C13×C22⋊C4—22no—
70C2×C42×C13—21no—
71C2×C42×C13D412yes—
72C13×#107—22no—
73C13×#106—22no—
74C13×#102—22no—
75C13×#102—22no—
76C13×C22⋊C8—21no—
77C13×C22⋊C8—21no—
78C13×C22⋊C8—21no—
79C13×C22⋊C8D412yescomplemented
80C13×#95—22no—
81C13×#95—21no—
82C13×#95—21no—
83C13×#95D412yescomplemented
84#9940C1311yesmaximal, characteristic, direct product factor, Sylow
85C24×C13—21no—
86C24×C13—21no—
87C24×C13—21no—
88C24×C13—21no—
89C24×C13—42no—
90C24×C13—42no—
91C24×C13—42no—
92C24×C13C2×D411yescharacteristic
93C2×D4×C13—21no—
94C2×D4×C13—21no—
95C2×D4×C13—42no—
96C2×D4×C13—44no—
97C2×D4×C13—42no—
98C2×D4×C13—42no—
99C2×D4×C13—44no—
100C2×D4×C13—41no—
101C2×D4×C13—41no—
102C2×D4×C13—82no—
103C22×C4×C13—22no—
104C22×C4×C13—22no—
105C22×C4×C13—21no—
106C22×C4×C13—21no—
107C22×C4×C13—21no—
108C22×C4×C13—21no—
109C22×C4×C13—21no—
110C22×C4×C13—21no—
111C22×C4×C13—42no—
112C22×C4×C13—42no—
113C22×C4×C13C2×D411yescharacteristic
114C22×C4×C13C2×D411yescharacteristic
115C22×C4×C13C2×D411yescharacteristic
116C22×C4×C13C2×D411yescharacteristic
117C22×C4×C13C2×D411yescharacteristic
118C22×C4×C13#4111yescharacteristic
119C13×M16—42no—
120C13×M16—42no—
121C2×C8×C13—22no—
122C2×C8×C13—41no—
123C13×C4⋊C4—21no—
124C13×C4⋊C4—21no—
125C13×C4⋊C4—21no—
126C13×C4⋊C4—21no—
127C13×C4⋊C4—21no—
128C13×C4⋊C4—21no—
129C13×C4⋊C4—44no—
130C13×C4⋊C4—82no—
131C13×C22⋊C4—24no—
132C13×C22⋊C4—44no—
133C13×C22⋊C4—44no—
134C13×C22⋊C4—42no—
135C13×C22⋊C4—44no—
136C13×C22⋊C4—41no—
137C13×C22⋊C4—41no—
138C13×C22⋊C4—41no—
139C13×C22⋊C4—41no—
140C13×C22⋊C4—41no—
141C13×C22⋊C4—41no—
142C13×C22⋊C4—41no—
143C13×C22⋊C4—41no—
144C13×C22⋊C4—82no—
145C42×C13—42no—
146C42×C13—41no—
147C42×C13—41no—
148#3094C2×C1311yescharacteristic, complemented
149#2539C2×C1311yescharacteristic
150#2482C2×C1311yescharacteristic, complemented
151#1826C2×C1311yescharacteristic, complemented
152#1510C2×C1311yescharacteristic, complemented
153#1462C2×C1311yescharacteristic, complemented
154#1284C2×C1311yescharacteristic, complemented
155C23×C13—22no—
156C23×C13—22no—
157C23×C13—22no—
158C23×C13—22no—
159C23×C13—22no—
160C23×C13—41no—
161C23×C13—42no—
162C23×C13—41no—
163C23×C13—41no—
164C23×C13—42no—
165C23×C13—41no—
166C23×C13—41no—
167C23×C13—41no—
168C23×C13—42no—
169C23×C13—41no—
170C23×C13—42no—
171C23×C13—42no—
172C23×C13—41no—
173C23×C13—42no—
174C23×C13—81no—
175C23×C13—81no—
176C23×C13—88no—
177C23×C13#12011yescharacteristic
178C23×C13#12011yescharacteristic
179C23×C13#12111yescharacteristic
180D4×C13—42no—
181D4×C13—81no—
182D4×C13—88no—
183D4×C13—82no—
184D4×C13—82no—
185C2×C4×C13—22no—
186C2×C4×C13—22no—
187C2×C4×C13—24no—
188C2×C4×C13—41no—
189C2×C4×C13—41no—
190C2×C4×C13—41no—
191C2×C4×C13—41no—
192C2×C4×C13—42no—
193C2×C4×C13—42no—
194C2×C4×C13—41no—
195C2×C4×C13—42no—
196C2×C4×C13—42no—
197C2×C4×C13—42no—
198C2×C4×C13—42no—
199C2×C4×C13—41no—
200C2×C4×C13—41no—
201C2×C4×C13—41no—
202C2×C4×C13—41no—
203C2×C4×C13—41no—
204C2×C4×C13—42no—
205C2×C4×C13—42no—
206C2×C4×C13—42no—
207C2×C4×C13—81no—
208C2×C4×C13#12011yescharacteristic
209C2×C4×C13#12111yescharacteristic
210C2×C4×C13#12111yescharacteristic
211C2×C4×C13#12711yescharacteristic
212C8×C13—42no—
213C8×C13—81no—
214C2×#123—21no—
215C2×#121C22×C1311yescharacteristic
216C2×#120—21no—
217C2×#117C22×C1311yescharacteristic
218C22×C22⋊C4C22×C1311yescharacteristic
219#482—22no—
220#481—21no—
221#480—21no—
222#428—21no—
223#418—21no—
224#407C22×C1311yescharacteristic
225#407C22×C1311yescharacteristic
226#399—21no—
227#399—21no—
228#397—21no—
229#392—21no—
230#390—22no—
231#388—22no—
232#385—21no—
233#381C22×C1311yescharacteristic
234#379—21no—
235C4×C22⋊C4C22×C1311yescharacteristic
236#339—22no—
237#327—22no—
238#323—22no—
239C22×C13—21no—
240C22×C13—21no—
241C22×C13—21no—
242C22×C13—21no—
243C22×C13—21no—
244C22×C13—21no—
245C22×C13—21no—
246C22×C13—44no—
247C22×C13—44no—
248C22×C13—44no—
249C22×C13—42no—
250C22×C13—82no—
251C22×C13—82no—
252C22×C13—82no—
253C22×C13—82no—
254C22×C13—82no—
255C22×C13—82no—
256C22×C13—81no—
257C22×C13—81no—
258C22×C13—81no—
259C22×C13—81no—
260C22×C13—81no—
261C22×C13#39211yescharacteristic
262C22×C13#45312yes—
263C22×C13#45812yes—
264C4×C13—21no—
265C4×C13—21no—
266C4×C13—21no—
267C4×C13—21no—
268C4×C13—44no—
269C4×C13—82no—
270C4×C13—81no—
271C4×C13—81no—
272C4×C13—81no—
273C4×C13—81no—
274C25D4×C1311yescharacteristic
275C22×D4—21no—
276C22×D4—22no—
277C22×D4D4×C1311yescharacteristic
278C23×C4D4×C1311yescharacteristic
279C23×C4C23×C1311yescharacteristic
280C2×M16—21no—
281C2×M16—21no—
282#123—44no—
283#121—21no—
284#121—21no—
285#121—21no—
286#121—21no—
287#120—44no—
288#117—21no—
289#117—21no—
290#117—21no—
291#117—21no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4D4×C1311yescharacteristic
295C2×C4⋊C4D4×C1311yescharacteristic, complemented
296C2×C4⋊C4D4×C1311yescharacteristic, complemented
297C2×C22⋊C4—21no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—22no—
311C2×C42—21no—
312C2×C42D4×C1312yes—
313#107—22no—
314#106—22no—
315#102—22no—
316#102—22no—
317C22⋊C8—21no—
318C22⋊C8—21no—
319C22⋊C8—21no—
320C22⋊C8D4×C1312yescomplemented
321#95—22no—
322#95—21no—
323#95—21no—
324#95D4×C1312yescomplemented
325C2×C13—22no—
326C2×C13—22no—
327C2×C13—41no—
328C2×C13—82no—
329C2×C13—161no—
330C2×C13#200211yescharacteristic
331C2×C13#201011yescharacteristic
332C2×C13#202211yescharacteristic
333C24—21no—
334C24—21no—
335C24—21no—
336C24—21no—
337C24—42no—
338C24—42no—
339C24—42no—
340C24C2×D4×C1311yescharacteristic
341C2×D4—21no—
342C2×D4—21no—
343C2×D4—42no—
344C2×D4—44no—
345C2×D4—42no—
346C2×D4—42no—
347C2×D4—44no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—82no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—42no—
360C22×C4—42no—
361C22×C4C2×D4×C1311yescharacteristic
362C22×C4C2×D4×C1311yescharacteristic
363C22×C4C2×D4×C1311yescharacteristic
364C22×C4C2×D4×C1311yescharacteristic
365C22×C4C2×D4×C1311yescharacteristic
366C22×C4C13×#4111yescharacteristic
367M16—42no—
368M16—42no—
369C2×C8—22no—
370C2×C8—41no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—44no—
378C4⋊C4—82no—
379C22⋊C4—24no—
380C22⋊C4—44no—
381C22⋊C4—44no—
382C22⋊C4—42no—
383C22⋊C4—44no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—82no—
393C42—42no—
394C42—41no—
395C42—41no—
396C13#994011yescharacteristic, direct product factor, Sylow
397C23—22no—
398C23—22no—
399C23—22no—
400C23—22no—
401C23—22no—
402C23—41no—
403C23—42no—
404C23—41no—
405C23—41no—
406C23—42no—
407C23—41no—
408C23—41no—
409C23—41no—
410C23—42no—
411C23—41no—
412C23—42no—
413C23—42no—
414C23—41no—
415C23—42no—
416C23—81no—
417C23—81no—
418C23—88no—
419C23C13×#12011yescharacteristic
420C23C13×#12011yescharacteristic
421C23C13×#12111yescharacteristic
422D4—42no—
423D4—81no—
424D4—88no—
425D4—82no—
426D4—82no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—24no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—81no—
450C2×C4C13×#12011yescharacteristic
451C2×C4C13×#12111yescharacteristic
452C2×C4C13×#12111yescharacteristic
453C2×C4C13×#12711yescharacteristic
454C8—42no—
455C8—81no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—44no—
464C22—44no—
465C22—44no—
466C22—42no—
467C22—82no—
468C22—82no—
469C22—82no—
470C22—82no—
471C22—82no—
472C22—82no—
473C22—81no—
474C22—81no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22C13×#39211yescharacteristic
479C22C13×#45312yes—
480C22C13×#45812yes—
481C4—21no—
482C4—21no—
483C4—21no—
484C4—21no—
485C4—44no—
486C4—82no—
487C4—81no—
488C4—81no—
489C4—81no—
490C4—81no—
491C2—22no—
492C2—22no—
493C2—41no—
494C2—82no—
495C2—161no—
496C2C13×#200211yescharacteristic
497C2C13×#201011yescharacteristic
498C2C13×#202211yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC13×#2539C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3094C2semidirect
3. C13×#2482C2semidirect
4. C13×#1826C2semidirect
5. C13×#1510C2semidirect
6. C13×#1462C2semidirect
7. C13×#1284C2semidirect
54. C2×C13×C4⋊C4D4semidirect
55. C2×C13×C4⋊C4D4semidirect
79. C13×C22⋊C8D4semidirect
83. C13×#95D4semidirect
84. #9940C13direct (N × H)
148. #3094C2×C13semidirect
150. #2482C2×C13semidirect
151. #1826C2×C13semidirect
152. #1510C2×C13semidirect
153. #1462C2×C13semidirect
154. #1284C2×C13semidirect
295. C2×C4⋊C4D4×C13semidirect
296. C2×C4⋊C4D4×C13semidirect
320. C22⋊C8D4×C13semidirect
324. #95D4×C13semidirect
396. C13#9940direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#30942
C13×#25392
C13×#24822
C13×#18262
C13×#15102
C13×#14622
C13×#12842
#994013