Finite Group Databasebeta

← C13×#12190 #15698529

Subgroups — C13×#12190 #15698529

Order 3328.

678 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 678 conjugacy classes of subgroups — too many to draw. Only its 70 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×#2670C211yesmaximal, characteristic, complemented
2C13×#2021C211yesmaximal, characteristic, complemented
3C13×#1601C211yesmaximal, characteristic, complemented
4C13×#1595C211yesmaximal, characteristic, complemented
5C13×#1351C211yesmaximal, characteristic, complemented
6C13×#1343C211yesmaximal, characteristic, complemented
7C13×#1316C211yesmaximal, characteristic, complemented
8C13×#534C2211yescharacteristic
9C2×C13×#124—21no—
10C2×C13×#120—21no—
11C2×C13×#120—21no—
12C13×#448—21no—
13C13×#447—21no—
14C2×C13×#99—21no—
15C13×#394—21no—
16C13×#393C2211yescharacteristic
17C13×#392—21no—
18C13×#392C2211yescharacteristic
19C13×#390—21no—
20C13×#388—21no—
21C13×#379C2211yescharacteristic
22C13×#342C2211yescharacteristic
23C13×#327—21no—
24C13×#327—21no—
25C13×#323C2211yescharacteristic
26C13×#323C2211yescharacteristic
27C25×C13D411yescharacteristic
28C22×Q8×C13D411yescharacteristic, complemented
29C22×D4×C13—21no—
30C22×D4×C13—21no—
31C22×D4×C13—21no—
32C22×D4×C13—21no—
33C22×D4×C13—41no—
34C22×D4×C13D411yescharacteristic, complemented
35C2×C13×SD16—41no—
36C2×C13×D8—41no—
37C13×#124—44no—
38C13×#123—41no—
39C13×#121—21no—
40C13×#121—21no—
41C13×#120—44no—
42C13×#120—42no—
43C13×#120—41no—
44C13×#120—42no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4—21no—
48C2×C13×C22⋊C4—21no—
49C2×C13×C22⋊C4—21no—
50C2×C13×C22⋊C4—21no—
51C2×C13×C22⋊C4—21no—
52C2×C13×C22⋊C4—21no—
53C2×C13×C22⋊C4—21no—
54C2×C13×C22⋊C4—21no—
55C2×C13×C22⋊C4—41no—
56C2×C13×C22⋊C4D411yescharacteristic
57C2×C13×C22⋊C4C2311yescharacteristic
58C2×C42×C13—21no—
59C13×#103—41no—
60C13×#102—41no—
61C13×#99—42no—
62C13×C22⋊C8—21no—
63C13×C22⋊C8—21no—
64C13×#95—21no—
65C13×#95D411yescharacteristic, complemented
66C13×#95D411yescharacteristic, complemented
67#12190C1311yesmaximal, characteristic, direct product factor, Sylow
68C24×C13—21no—
69C24×C13—21no—
70C24×C13—21no—
71C24×C13—21no—
72C24×C13—21no—
73C24×C13—41no—
74C24×C13—41no—
75C24×C13—42no—
76C24×C13—81no—
77C24×C13C2×D411yescharacteristic
78C2×Q8×C13—42no—
79C2×Q8×C13—41no—
80C2×D4×C13—21no—
81C2×D4×C13—21no—
82C2×D4×C13—41no—
83C2×D4×C13—42no—
84C2×D4×C13—42no—
85C2×D4×C13—41no—
86C2×D4×C13—41no—
87C2×D4×C13—42no—
88C2×D4×C13—41no—
89C2×D4×C13—42no—
90C2×D4×C13—44no—
91C2×D4×C13—41no—
92C2×D4×C13—41no—
93C2×D4×C13—41no—
94C2×D4×C13—41no—
95C2×D4×C13—41no—
96C2×D4×C13—81no—
97C2×D4×C13—81no—
98C2×D4×C13—81no—
99C2×D4×C13—81no—
100C2×D4×C13—81no—
101C2×D4×C13—82no—
102C2×D4×C13—82no—
103C22×C4×C13—21no—
104C22×C4×C13—21no—
105C22×C4×C13—21no—
106C22×C4×C13—21no—
107C22×C4×C13—21no—
108C22×C4×C13—41no—
109C22×C4×C13C2×D411yescharacteristic
110C22×C4×C13C2×D411yescharacteristic
111C13×SD16—82no—
112C13×D8—82no—
113C2×C8×C13—41no—
114C2×C8×C13—41no—
115C13×C4⋊C4—21no—
116C13×C4⋊C4—21no—
117C13×C4⋊C4—81no—
118C13×C22⋊C4—24no—
119C13×C22⋊C4—22no—
120C13×C22⋊C4—41no—
121C13×C22⋊C4—42no—
122C13×C22⋊C4—42no—
123C13×C22⋊C4—42no—
124C13×C22⋊C4—42no—
125C13×C22⋊C4—41no—
126C13×C22⋊C4—41no—
127C13×C22⋊C4—42no—
128C13×C22⋊C4—44no—
129C13×C22⋊C4—41no—
130C13×C22⋊C4—41no—
131C13×C22⋊C4—81no—
132C13×C22⋊C4—81no—
133C42×C13—42no—
134#2670C2×C1311yescharacteristic, complemented
135#2021C2×C1311yescharacteristic, complemented
136#1601C2×C1311yescharacteristic, complemented
137#1595C2×C1311yescharacteristic, complemented
138#1351C2×C1311yescharacteristic, complemented
139#1343C2×C1311yescharacteristic, complemented
140#1316C2×C1311yescharacteristic, complemented
141C23×C13—21no—
142C23×C13—21no—
143C23×C13—22no—
144C23×C13—41no—
145C23×C13—41no—
146C23×C13—41no—
147C23×C13—42no—
148C23×C13—41no—
149C23×C13—41no—
150C23×C13—41no—
151C23×C13—41no—
152C23×C13—41no—
153C23×C13—41no—
154C23×C13—41no—
155C23×C13—41no—
156C23×C13—42no—
157C23×C13—42no—
158C23×C13—41no—
159C23×C13—41no—
160C23×C13—41no—
161C23×C13—41no—
162C23×C13—41no—
163C23×C13—41no—
164C23×C13—41no—
165C23×C13—81no—
166C23×C13—82no—
167C23×C13—81no—
168C23×C13—84no—
169C23×C13—82no—
170C23×C13—81no—
171C23×C13—81no—
172C23×C13—81no—
173C23×C13#12011yescharacteristic
174C23×C13#13511yescharacteristic
175C23×C13AGL(1,ℤ/8)11yescharacteristic
176Q8×C13—42no—
177Q8×C13—81no—
178D4×C13—42no—
179D4×C13—82no—
180D4×C13—82no—
181D4×C13—84no—
182D4×C13—81no—
183D4×C13—81no—
184D4×C13—81no—
185D4×C13—81no—
186D4×C13—81no—
187D4×C13—84no—
188D4×C13—88no—
189D4×C13—81no—
190D4×C13—81no—
191C2×C4×C13—22no—
192C2×C4×C13—22no—
193C2×C4×C13—21no—
194C2×C4×C13—21no—
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—41no—
202C2×C4×C13—42no—
203C2×C4×C13—41no—
204C2×C4×C13—41no—
205C2×C4×C13—41no—
206C2×C4×C13—41no—
207C2×C4×C13—41no—
208C2×C4×C13—41no—
209C2×C4×C13—41no—
210C2×C4×C13—41no—
211C2×C4×C13—81no—
212C2×C4×C13—81no—
213C8×C13—81no—
214C8×C13—81no—
215#534C22×C1311yescharacteristic
216C2×#124—21no—
217C2×#120—21no—
218C2×#120—21no—
219#448—21no—
220#447—21no—
221C2×#99—21no—
222#394—21no—
223#393C22×C1311yescharacteristic
224#392—21no—
225#392C22×C1311yescharacteristic
226#390—21no—
227#388—21no—
228#379C22×C1311yescharacteristic
229#342C22×C1311yescharacteristic
230#327—21no—
231#327—21no—
232#323C22×C1311yescharacteristic
233#323C22×C1311yescharacteristic
234C22×C13—21no—
235C22×C13—21no—
236C22×C13—21no—
237C22×C13—21no—
238C22×C13—41no—
239C22×C13—41no—
240C22×C13—42no—
241C22×C13—42no—
242C22×C13—41no—
243C22×C13—41no—
244C22×C13—44no—
245C22×C13—42no—
246C22×C13—81no—
247C22×C13—81no—
248C22×C13—81no—
249C22×C13—81no—
250C22×C13—81no—
251C22×C13—81no—
252C22×C13—81no—
253C22×C13—82no—
254C22×C13—82no—
255C22×C13—82no—
256C22×C13—82no—
257C22×C13—81no—
258C22×C13—81no—
259C22×C13—81no—
260C22×C13—81no—
261C22×C13—81no—
262C22×C13—81no—
263C22×C13—81no—
264C22×C13—81no—
265C22×C13—161no—
266C22×C13#44911yescharacteristic
267C22×C13#45311yescharacteristic
268C22×C13B(4,𝔽2)11yescharacteristic
269C4×C13—42no—
270C4×C13—41no—
271C4×C13—42no—
272C4×C13—41no—
273C4×C13—81no—
274C4×C13—81no—
275C4×C13—82no—
276C4×C13—81no—
277C25D4×C1311yescharacteristic
278C22×Q8D4×C1311yescharacteristic, complemented
279C22×D4—21no—
280C22×D4—21no—
281C22×D4—21no—
282C22×D4—21no—
283C22×D4—41no—
284C22×D4D4×C1311yescharacteristic, complemented
285C2×SD16—41no—
286C2×D8—41no—
287#124—44no—
288#123—41no—
289#121—21no—
290#121—21no—
291#120—44no—
292#120—42no—
293#120—41no—
294#120—42no—
295C2×C4⋊C4—21no—
296C2×C22⋊C4—21no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—41no—
306C2×C22⋊C4D4×C1311yescharacteristic
307C2×C22⋊C4C23×C1311yescharacteristic
308C2×C42—21no—
309#103—41no—
310#102—41no—
311#99—42no—
312C22⋊C8—21no—
313C22⋊C8—21no—
314#95—21no—
315#95D4×C1311yescharacteristic, complemented
316#95D4×C1311yescharacteristic, complemented
317C2×C13—21no—
318C2×C13—21no—
319C2×C13—41no—
320C2×C13—41no—
321C2×C13—82no—
322C2×C13—161no—
323C2×C13—161no—
324C2×C13#160011yescharacteristic
325C2×C13#219611yescharacteristic
326C2×C13#219911yescharacteristic
327C24—21no—
328C24—21no—
329C24—21no—
330C24—21no—
331C24—21no—
332C24—41no—
333C24—41no—
334C24—42no—
335C24—81no—
336C24C2×D4×C1311yescharacteristic
337C2×Q8—42no—
338C2×Q8—41no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—41no—
342C2×D4—42no—
343C2×D4—42no—
344C2×D4—41no—
345C2×D4—41no—
346C2×D4—42no—
347C2×D4—41no—
348C2×D4—42no—
349C2×D4—44no—
350C2×D4—41no—
351C2×D4—41no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4—41no—
355C2×D4—81no—
356C2×D4—81no—
357C2×D4—81no—
358C2×D4—81no—
359C2×D4—81no—
360C2×D4—82no—
361C2×D4—82no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—41no—
368C22×C4C2×D4×C1311yescharacteristic
369C22×C4C2×D4×C1311yescharacteristic
370SD16—82no—
371D8—82no—
372C2×C8—41no—
373C2×C8—41no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—81no—
377C22⋊C4—24no—
378C22⋊C4—22no—
379C22⋊C4—41no—
380C22⋊C4—42no—
381C22⋊C4—42no—
382C22⋊C4—42no—
383C22⋊C4—42no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—42no—
387C22⋊C4—44no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—81no—
391C22⋊C4—81no—
392C42—42no—
393C13#1219011yescharacteristic, direct product factor, Sylow
394C23—21no—
395C23—21no—
396C23—22no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—42no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23—41no—
408C23—41no—
409C23—42no—
410C23—42no—
411C23—41no—
412C23—41no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23—41no—
418C23—81no—
419C23—82no—
420C23—81no—
421C23—82no—
422C23—84no—
423C23—81no—
424C23—81no—
425C23—81no—
426C23C13×#12011yescharacteristic
427C23C13×#13511yescharacteristic
428C23C13×AGL(1,ℤ/8)11yescharacteristic
429Q8—42no—
430Q8—81no—
431D4—42no—
432D4—82no—
433D4—82no—
434D4—84no—
435D4—81no—
436D4—81no—
437D4—81no—
438D4—81no—
439D4—81no—
440D4—84no—
441D4—88no—
442D4—81no—
443D4—81no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—81no—
465C2×C4—81no—
466C8—81no—
467C8—81no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—41no—
473C22—41no—
474C22—42no—
475C22—42no—
476C22—41no—
477C22—41no—
478C22—44no—
479C22—42no—
480C22—81no—
481C22—81no—
482C22—81no—
483C22—81no—
484C22—81no—
485C22—81no—
486C22—81no—
487C22—82no—
488C22—82no—
489C22—82no—
490C22—82no—
491C22—81no—
492C22—81no—
493C22—81no—
494C22—81no—
495C22—81no—
496C22—81no—
497C22—81no—
498C22—81no—
499C22—161no—
500C22C13×#44911yescharacteristic
501C22C13×#45311yescharacteristic
502C22C13×B(4,𝔽2)11yescharacteristic
503C4—42no—
504C4—41no—
505C4—42no—
506C4—41no—
507C4—81no—
508C4—81no—
509C4—82no—
510C4—81no—
511C2—21no—
512C2—21no—
513C2—41no—
514C2—41no—
515C2—82no—
516C2—161no—
517C2—161no—
518C2C13×#160011yescharacteristic
519C2C13×#219611yescharacteristic
520C2C13×#219911yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C13
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C13 ◁ C2×C13×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2670C2semidirect
2. C13×#2021C2semidirect
3. C13×#1601C2semidirect
4. C13×#1595C2semidirect
5. C13×#1351C2semidirect
6. C13×#1343C2semidirect
7. C13×#1316C2semidirect
28. C22×Q8×C13D4semidirect
34. C22×D4×C13D4semidirect
65. C13×#95D4semidirect
66. C13×#95D4semidirect
67. #12190C13direct (N × H)
134. #2670C2×C13semidirect
135. #2021C2×C13semidirect
136. #1601C2×C13semidirect
137. #1595C2×C13semidirect
138. #1351C2×C13semidirect
139. #1343C2×C13semidirect
140. #1316C2×C13semidirect
278. C22×Q8D4×C13semidirect
284. C22×D4D4×C13semidirect
315. #95D4×C13semidirect
316. #95D4×C13semidirect
393. C13#12190direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26702
C13×#20212
C13×#16012
C13×#15952
C13×#13512
C13×#13432
C13×#13162
#1219013