Finite Group Databasebeta

← C13×#10397 #15696736

Subgroups — C13×#10397 #15696736

Order 3328.

632 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2618C211yesmaximal, characteristic
2C13×#1874C211yesmaximal, characteristic
3C13×#1852C211yesmaximal, characteristic, complemented
4C2×C13×#327C211yesmaximal, characteristic
5C2×C13×#324C211yesmaximal, characteristic, complemented
6C13×#1441C211yesmaximal, characteristic, complemented
7C13×#1294C211yesmaximal, characteristic, complemented
8C2×C13×#123—21no—
9C2×C13×#121C2211yescharacteristic
10C22×C13×C4⋊C4C2211yescharacteristic
11C22×C13×C4⋊C4C2211yescharacteristic
12C2×C13×#107—21no—
13C2×C13×#102—21no—
14C2×C13×C22⋊C8C2211yescharacteristic
15C2×C13×C22⋊C8C2211yescharacteristic
16C13×#398—21no—
17C13×#396—21no—
18C13×#396—21no—
19C13×#394—21no—
20C13×#386—21no—
21C13×#380C2211yescharacteristic
22C2×C13×#95—21no—
23C2×C13×#95—21no—
24C2×C13×#95C2211yescharacteristic
25C13×#340—21no—
26C13×#340—21no—
27C13×#327—22no—
28C13×#324—22no—
29C22×D4×C13—21no—
30C22×D4×C13D411yescharacteristic
31C23×C4×C13—21no—
32C23×C4×C13—21no—
33C23×C4×C13D411yescharacteristic
34C23×C4×C13D411yescharacteristic
35C23×C4×C13C2311yescharacteristic
36C22×C8×C13—21no—
37C22×C8×C13—21no—
38C13×#123—42no—
39C13×#123—42no—
40C13×#121—21no—
41C13×#121—21no—
42C13×#121—21no—
43C13×#121—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4—42no—
55C2×C13×C4⋊C4D411yescharacteristic
56C2×C13×C4⋊C4D411yescharacteristic
57C2×C13×C4⋊C4D411yescharacteristic
58C2×C13×C22⋊C4—21no—
59C2×C13×C22⋊C4—21no—
60C2×C13×C22⋊C4—21no—
61C2×C13×C22⋊C4—21no—
62C2×C13×C22⋊C4—21no—
63C2×C13×C22⋊C4—21no—
64C13×#107—42no—
65C13×#102—42no—
66C13×C22⋊C8—21no—
67C13×C22⋊C8—21no—
68C13×C22⋊C8—21no—
69C13×C22⋊C8D412yes—
70C13×#95—21no—
71C13×#95—21no—
72C13×#95—21no—
73C13×#95—21no—
74C13×#95—21no—
75C13×#95—42no—
76C13×#95—42no—
77#10397C1311yesmaximal, characteristic, direct product factor, Sylow
78C24×C13—21no—
79C24×C13C2×D411yescharacteristic
80C2×D4×C13—21no—
81C2×D4×C13—21no—
82C2×D4×C13—41no—
83C2×D4×C13—41no—
84C2×D4×C13—41no—
85C2×D4×C13—41no—
86C2×D4×C13—41no—
87C2×D4×C13—41no—
88C2×D4×C13—41no—
89C2×D4×C13—41no—
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13—21no—
93C22×C4×C13—21no—
94C22×C4×C13—21no—
95C22×C4×C13—21no—
96C22×C4×C13—22no—
97C22×C4×C13—22no—
98C22×C4×C13—21no—
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13—21no—
102C22×C4×C13—21no—
103C22×C4×C13—21no—
104C22×C4×C13—41no—
105C22×C4×C13—41no—
106C22×C4×C13—41no—
107C22×C4×C13—41no—
108C22×C4×C13—41no—
109C22×C4×C13—41no—
110C22×C4×C13—41no—
111C22×C4×C13—41no—
112C22×C4×C13—41no—
113C22×C4×C13—41no—
114C22×C4×C13—41no—
115C22×C4×C13—41no—
116C22×C4×C13—41no—
117C22×C4×C13—41no—
118C22×C4×C13—41no—
119C22×C4×C13—41no—
120C22×C4×C13D812yes—
121C22×C4×C13C2×D411yescharacteristic
122C22×C4×C13C2×D411yescharacteristic
123C22×C4×C13C2×D411yescharacteristic
124C22×C4×C13#4111yescharacteristic
125C22×C4×C13#4111yescharacteristic
126C22×C4×C13#4111yescharacteristic
127C2×C8×C13—22no—
128C2×C8×C13—41no—
129C2×C8×C13—41no—
130C2×C8×C13—41no—
131C2×C8×C13—41no—
132C2×C8×C13—41no—
133C13×C4⋊C4—22no—
134C13×C4⋊C4—22no—
135C13×C4⋊C4—21no—
136C13×C4⋊C4—21no—
137C13×C4⋊C4—41no—
138C13×C4⋊C4—41no—
139C13×C4⋊C4—41no—
140C13×C4⋊C4—41no—
141C13×C4⋊C4—42no—
142C13×C4⋊C4—42no—
143C13×C4⋊C4—41no—
144C13×C4⋊C4—41no—
145C13×C4⋊C4—41no—
146C13×C4⋊C4—41no—
147C13×C22⋊C4—42no—
148C13×C22⋊C4—42no—
149C13×C22⋊C4—41no—
150C13×C22⋊C4—41no—
151C13×C22⋊C4—41no—
152C13×C22⋊C4—41no—
153C13×C22⋊C4—81no—
154C13×C22⋊C4—81no—
155#2618C2×C1311yescharacteristic
156#1874C2×C1311yescharacteristic
157#1852C2×C1311yescharacteristic, complemented
158C2×#327C2×C1311yescharacteristic
159C2×#324C2×C1311yescharacteristic, complemented
160#1441C2×C1311yescharacteristic, complemented
161#1294C2×C1311yescharacteristic, complemented
162C23×C13—21no—
163C23×C13—21no—
164C23×C13—21no—
165C23×C13—21no—
166C23×C13—41no—
167C23×C13—41no—
168C23×C13—41no—
169C23×C13—41no—
170C23×C13—41no—
171C23×C13—41no—
172C23×C13—41no—
173C23×C13#12011yescharacteristic
174C23×C13#12111yescharacteristic
175C23×C13#12311yescharacteristic
176C23×C13C2×D811yescharacteristic
177C23×C13#13511yescharacteristic
178C23×C13AGL(1,ℤ/8)11yescharacteristic
179C23×C13#13711yescharacteristic
180D4×C13—42no—
181D4×C13—81no—
182D4×C13—81no—
183D4×C13—81no—
184D4×C13—81no—
185D4×C13—81no—
186C2×C4×C13—21no—
187C2×C4×C13—21no—
188C2×C4×C13—21no—
189C2×C4×C13—21no—
190C2×C4×C13—22no—
191C2×C4×C13—22no—
192C2×C4×C13—22no—
193C2×C4×C13—41no—
194C2×C4×C13—41no—
195C2×C4×C13—41no—
196C2×C4×C13—41no—
197C2×C4×C13—41no—
198C2×C4×C13—41no—
199C2×C4×C13—41no—
200C2×C4×C13—41no—
201C2×C4×C13—42no—
202C2×C4×C13—42no—
203C2×C4×C13—42no—
204C2×C4×C13—42no—
205C2×C4×C13—42no—
206C2×C4×C13—42no—
207C2×C4×C13—41no—
208C2×C4×C13—41no—
209C2×C4×C13—41no—
210C2×C4×C13—41no—
211C2×C4×C13—41no—
212C2×C4×C13—41no—
213C2×C4×C13—41no—
214C2×C4×C13—41no—
215C2×C4×C13—41no—
216C2×C4×C13—41no—
217C2×C4×C13—42no—
218C2×C4×C13—41no—
219C2×C4×C13—41no—
220C2×C4×C13—81no—
221C2×C4×C13—81no—
222C2×C4×C13—81no—
223C2×C4×C13—81no—
224C2×C4×C13—81no—
225C2×C4×C13—81no—
226C2×C4×C13—81no—
227C2×C4×C13—81no—
228C2×C4×C13—81no—
229C2×C4×C13#12111yescharacteristic
230C2×C4×C13#12111yescharacteristic
231C2×C4×C13#12311yescharacteristic
232C2×C4×C13#12411yescharacteristic
233C8×C13—42no—
234C8×C13—81no—
235C2×#123—21no—
236C2×#121C22×C1311yescharacteristic
237C22×C4⋊C4C22×C1311yescharacteristic
238C22×C4⋊C4C22×C1311yescharacteristic
239C2×#107—21no—
240C2×#102—21no—
241C2×C22⋊C8C22×C1311yescharacteristic
242C2×C22⋊C8C22×C1311yescharacteristic
243#398—21no—
244#396—21no—
245#396—21no—
246#394—21no—
247#386—21no—
248#380C22×C1311yescharacteristic
249C2×#95—21no—
250C2×#95—21no—
251C2×#95C22×C1311yescharacteristic
252#340—21no—
253#340—21no—
254#327—22no—
255#324—22no—
256C22×C13—21no—
257C22×C13—21no—
258C22×C13—21no—
259C22×C13—21no—
260C22×C13—21no—
261C22×C13—21no—
262C22×C13—21no—
263C22×C13—21no—
264C22×C13—21no—
265C22×C13—21no—
266C22×C13—21no—
267C22×C13—21no—
268C22×C13—81no—
269C22×C13—81no—
270C22×C13—81no—
271C22×C13—81no—
272C22×C13—81no—
273C22×C13—81no—
274C22×C13—81no—
275C22×C13#39411yescharacteristic
276C22×C13#44711yescharacteristic
277C22×C13#45211yescharacteristic
278C22×C13#45411yescharacteristic
279C22×C13#45611yescharacteristic
280C22×C13B(4,𝔽2)11yescharacteristic
281C22×C13#45811yescharacteristic
282C22×C13#46611yescharacteristic
283C22×C13#46811yescharacteristic
284C22×C13#48011yescharacteristic
285C22×C13#48211yescharacteristic
286C4×C13—21no—
287C4×C13—21no—
288C4×C13—21no—
289C4×C13—21no—
290C4×C13—42no—
291C4×C13—82no—
292C4×C13—81no—
293C4×C13—82no—
294C4×C13—81no—
295C4×C13—81no—
296C4×C13—81no—
297C22×D4—21no—
298C22×D4D4×C1311yescharacteristic
299C23×C4—21no—
300C23×C4—21no—
301C23×C4D4×C1311yescharacteristic
302C23×C4D4×C1311yescharacteristic
303C23×C4C23×C1311yescharacteristic
304C22×C8—21no—
305C22×C8—21no—
306#123—42no—
307#123—42no—
308#121—21no—
309#121—21no—
310#121—21no—
311#121—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4D4×C1311yescharacteristic
324C2×C4⋊C4D4×C1311yescharacteristic
325C2×C4⋊C4D4×C1311yescharacteristic
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332#107—42no—
333#102—42no—
334C22⋊C8—21no—
335C22⋊C8—21no—
336C22⋊C8—21no—
337C22⋊C8D4×C1312yes—
338#95—21no—
339#95—21no—
340#95—21no—
341#95—21no—
342#95—21no—
343#95—42no—
344#95—42no—
345C2×C13—21no—
346C2×C13—21no—
347C2×C13—21no—
348C2×C13—21no—
349C2×C13—161no—
350C2×C13#159811yescharacteristic
351C2×C13#160311yescharacteristic
352C2×C13#161011yescharacteristic
353C2×C13#161511yescharacteristic
354C2×C13#203311yescharacteristic
355C2×C13#203811yescharacteristic
356C2×C13#204411yescharacteristic
357C24—21no—
358C24C2×D4×C1311yescharacteristic
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—41no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—41no—
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—41no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4C13×D812yes—
400C22×C4C2×D4×C1311yescharacteristic
401C22×C4C2×D4×C1311yescharacteristic
402C22×C4C2×D4×C1311yescharacteristic
403C22×C4C13×#4111yescharacteristic
404C22×C4C13×#4111yescharacteristic
405C22×C4C13×#4111yescharacteristic
406C2×C8—22no—
407C2×C8—41no—
408C2×C8—41no—
409C2×C8—41no—
410C2×C8—41no—
411C2×C8—41no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—41no—
417C4⋊C4—41no—
418C4⋊C4—41no—
419C4⋊C4—41no—
420C4⋊C4—42no—
421C4⋊C4—42no—
422C4⋊C4—41no—
423C4⋊C4—41no—
424C4⋊C4—41no—
425C4⋊C4—41no—
426C22⋊C4—42no—
427C22⋊C4—42no—
428C22⋊C4—41no—
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—41no—
432C22⋊C4—81no—
433C22⋊C4—81no—
434C13#1039711yescharacteristic, direct product factor, Sylow
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23—41no—
444C23—41no—
445C23—41no—
446C23C13×#12011yescharacteristic
447C23C13×#12111yescharacteristic
448C23C13×#12311yescharacteristic
449C23C2×C13×D811yescharacteristic
450C23C13×#13511yescharacteristic
451C23C13×AGL(1,ℤ/8)11yescharacteristic
452C23C13×#13711yescharacteristic
453D4—42no—
454D4—81no—
455D4—81no—
456D4—81no—
457D4—81no—
458D4—81no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—81no—
494C2×C4—81no—
495C2×C4—81no—
496C2×C4—81no—
497C2×C4—81no—
498C2×C4—81no—
499C2×C4—81no—
500C2×C4—81no—
501C2×C4—81no—
502C2×C4C13×#12111yescharacteristic
503C2×C4C13×#12111yescharacteristic
504C2×C4C13×#12311yescharacteristic
505C2×C4C13×#12411yescharacteristic
506C8—42no—
507C8—81no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—81no—
521C22—81no—
522C22—81no—
523C22—81no—
524C22—81no—
525C22—81no—
526C22—81no—
527C22C13×#39411yescharacteristic
528C22C13×#44711yescharacteristic
529C22C13×#45211yescharacteristic
530C22C13×#45411yescharacteristic
531C22C13×#45611yescharacteristic
532C22C13×B(4,𝔽2)11yescharacteristic
533C22C13×#45811yescharacteristic
534C22C13×#46611yescharacteristic
535C22C13×#46811yescharacteristic
536C22C13×#48011yescharacteristic
537C22C13×#48211yescharacteristic
538C4—21no—
539C4—21no—
540C4—21no—
541C4—21no—
542C4—42no—
543C4—82no—
544C4—81no—
545C4—81no—
546C4—81no—
547C4—82no—
548C4—81no—
549C2—21no—
550C2—21no—
551C2—21no—
552C2—21no—
553C2—161no—
554C2C13×#159811yescharacteristic
555C2C13×#160311yescharacteristic
556C2C13×#161011yescharacteristic
557C2C13×#161511yescharacteristic
558C2C13×#203311yescharacteristic
559C2C13×#203811yescharacteristic
560C2C13×#204411yescharacteristic
subgroupG/H
center, socleC23×C13#120
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC2×C13×#121C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#1852C2semidirect
5. C2×C13×#324C2semidirect
6. C13×#1441C2semidirect
7. C13×#1294C2semidirect
77. #10397C13direct (N × H)
157. #1852C2×C13semidirect
159. C2×#324C2×C13semidirect
160. #1441C2×C13semidirect
161. #1294C2×C13semidirect
434. C13#10397direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26182
C13×#18742
C13×#18522
C2×C13×#3272
C2×C13×#3242
C13×#14412
C13×#12942
#1039713