Finite Group Databasebeta

← C13×#12186 #15698525

Subgroups — C13×#12186 #15698525

Order 3328.

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

normal subgroups only

This group has 682 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×#2668C211yesmaximal, characteristic, complemented
2C13×#2021C211yesmaximal, characteristic, complemented
3C13×#1613C211yesmaximal, characteristic, complemented
4C13×#1595C211yesmaximal, characteristic, complemented
5C13×#1352C211yesmaximal, characteristic, complemented
6C13×#1343C211yesmaximal, characteristic, complemented
7C13×#1316C211yesmaximal, characteristic, complemented
8C13×#534C2211yescharacteristic
9C2×C13×#121—21no—
10C2×C13×#120—21no—
11C2×C13×#120—21no—
12C13×#481—21no—
13C13×#447—21no—
14C2×C13×#99—21no—
15C13×#399C2211yescharacteristic
16C13×#397—21no—
17C13×#394—21no—
18C13×#392C2211yescharacteristic
19C13×#386—21no—
20C13×#386—21no—
21C13×#379C2211yescharacteristic
22C13×#342C2211yescharacteristic
23C13×#327—21no—
24C13×#327—21no—
25C13×#323C2211yescharacteristic
26C13×#323C2211yescharacteristic
27C25×C13D411yescharacteristic
28C22×D4×C13—21no—
29C22×D4×C13—21no—
30C22×D4×C13—21no—
31C22×D4×C13—21no—
32C22×D4×C13—41no—
33C22×D4×C13D411yescharacteristic, complemented
34C23×C4×C13—21no—
35C2×C13×D8—41no—
36C13×#123—41no—
37C13×#121—21no—
38C13×#121—21no—
39C13×#121—44no—
40C13×#120—42no—
41C13×#120—41no—
42C13×#120—44no—
43C13×#120—42no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4D411yescharacteristic, complemented
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—41no—
55C2×C13×C22⋊C4D411yescharacteristic
56C2×C13×C22⋊C4C2311yescharacteristic
57C13×#106—41no—
58C13×#102—41no—
59C13×#102—41no—
60C13×#99—42no—
61C13×C22⋊C8—21no—
62C13×C22⋊C8—21no—
63C13×#95—21no—
64C13×#95—21no—
65C13×#95D411yescharacteristic, complemented
66C13×#95D411yescharacteristic, complemented
67#12186C1311yesmaximal, 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×D4×C13—24no—
79C2×D4×C13—21no—
80C2×D4×C13—21no—
81C2×D4×C13—41no—
82C2×D4×C13—42no—
83C2×D4×C13—41no—
84C2×D4×C13—41no—
85C2×D4×C13—42no—
86C2×D4×C13—42no—
87C2×D4×C13—41no—
88C2×D4×C13—42no—
89C2×D4×C13—44no—
90C2×D4×C13—41no—
91C2×D4×C13—41no—
92C2×D4×C13—41no—
93C2×D4×C13—41no—
94C2×D4×C13—41no—
95C2×D4×C13—81no—
96C2×D4×C13—81no—
97C2×D4×C13—81no—
98C2×D4×C13—81no—
99C2×D4×C13—82no—
100C2×D4×C13—82no—
101C22×C4×C13—21no—
102C22×C4×C13—21no—
103C22×C4×C13—21no—
104C22×C4×C13—21no—
105C22×C4×C13—21no—
106C22×C4×C13—42no—
107C22×C4×C13—41no—
108C22×C4×C13—81no—
109C22×C4×C13—81no—
110C22×C4×C13C2×D411yescharacteristic
111C22×C4×C13C2×D411yescharacteristic
112C13×D8—82no—
113C2×C8×C13—41no—
114C2×C8×C13—41no—
115C13×C4⋊C4—21no—
116C13×C4⋊C4—21no—
117C13×C4⋊C4—41no—
118C13×C4⋊C4—42no—
119C13×C22⋊C4—22no—
120C13×C22⋊C4—41no—
121C13×C22⋊C4—42no—
122C13×C22⋊C4—42no—
123C13×C22⋊C4—41no—
124C13×C22⋊C4—41no—
125C13×C22⋊C4—42no—
126C13×C22⋊C4—42no—
127C13×C22⋊C4—42no—
128C13×C22⋊C4—44no—
129C13×C22⋊C4—41no—
130C13×C22⋊C4—41no—
131C13×C22⋊C4—81no—
132C13×C22⋊C4—81no—
133#2668C2×C1311yescharacteristic, complemented
134#2021C2×C1311yescharacteristic, complemented
135#1613C2×C1311yescharacteristic, complemented
136#1595C2×C1311yescharacteristic, complemented
137#1352C2×C1311yescharacteristic, complemented
138#1343C2×C1311yescharacteristic, complemented
139#1316C2×C1311yescharacteristic, complemented
140C23×C13—21no—
141C23×C13—21no—
142C23×C13—22no—
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—42no—
156C23×C13—42no—
157C23×C13—41no—
158C23×C13—41no—
159C23×C13—41no—
160C23×C13—41no—
161C23×C13—41no—
162C23×C13—41no—
163C23×C13—41no—
164C23×C13—81no—
165C23×C13—82no—
166C23×C13—81no—
167C23×C13—84no—
168C23×C13—82no—
169C23×C13—81no—
170C23×C13—81no—
171C23×C13—81no—
172C23×C13#12011yescharacteristic
173C23×C13#13511yescharacteristic
174C23×C13AGL(1,ℤ/8)11yescharacteristic
175D4×C13—42no—
176D4×C13—84no—
177D4×C13—81no—
178D4×C13—81no—
179D4×C13—81no—
180D4×C13—81no—
181D4×C13—81no—
182D4×C13—82no—
183D4×C13—82no—
184D4×C13—84no—
185D4×C13—88no—
186D4×C13—81no—
187D4×C13—81no—
188C2×C4×C13—22no—
189C2×C4×C13—21no—
190C2×C4×C13—21no—
191C2×C4×C13—41no—
192C2×C4×C13—41no—
193C2×C4×C13—41no—
194C2×C4×C13—41no—
195C2×C4×C13—42no—
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—41no—
203C2×C4×C13—41no—
204C2×C4×C13—41no—
205C2×C4×C13—41no—
206C2×C4×C13—41no—
207C2×C4×C13—41no—
208C2×C4×C13—84no—
209C2×C4×C13—81no—
210C2×C4×C13—81no—
211C8×C13—81no—
212C8×C13—81no—
213#534C22×C1311yescharacteristic
214C2×#121—21no—
215C2×#120—21no—
216C2×#120—21no—
217#481—21no—
218#447—21no—
219C2×#99—21no—
220#399C22×C1311yescharacteristic
221#397—21no—
222#394—21no—
223#392C22×C1311yescharacteristic
224#386—21no—
225#386—21no—
226#379C22×C1311yescharacteristic
227#342C22×C1311yescharacteristic
228#327—21no—
229#327—21no—
230#323C22×C1311yescharacteristic
231#323C22×C1311yescharacteristic
232C22×C13—21no—
233C22×C13—21no—
234C22×C13—21no—
235C22×C13—21no—
236C22×C13—41no—
237C22×C13—41no—
238C22×C13—42no—
239C22×C13—42no—
240C22×C13—42no—
241C22×C13—42no—
242C22×C13—41no—
243C22×C13—41no—
244C22×C13—44no—
245C22×C13—42no—
246C22×C13—42no—
247C22×C13—81no—
248C22×C13—81no—
249C22×C13—81no—
250C22×C13—81no—
251C22×C13—81no—
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—81no—
262C22×C13—81no—
263C22×C13—161no—
264C22×C13#44911yescharacteristic
265C22×C13#45311yescharacteristic
266C22×C13B(4,𝔽2)11yescharacteristic
267C4×C13—42no—
268C4×C13—41no—
269C4×C13—41no—
270C4×C13—81no—
271C4×C13—81no—
272C4×C13—82no—
273C4×C13—81no—
274C4×C13—81no—
275C25D4×C1311yescharacteristic
276C22×D4—21no—
277C22×D4—21no—
278C22×D4—21no—
279C22×D4—21no—
280C22×D4—41no—
281C22×D4D4×C1311yescharacteristic, complemented
282C23×C4—21no—
283C2×D8—41no—
284#123—41no—
285#121—21no—
286#121—21no—
287#121—44no—
288#120—42no—
289#120—41no—
290#120—44no—
291#120—42no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4D4×C1311yescharacteristic, complemented
294C2×C22⋊C4—21no—
295C2×C22⋊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—41no—
303C2×C22⋊C4D4×C1311yescharacteristic
304C2×C22⋊C4C23×C1311yescharacteristic
305#106—41no—
306#102—41no—
307#102—41no—
308#99—42no—
309C22⋊C8—21no—
310C22⋊C8—21no—
311#95—21no—
312#95—21no—
313#95D4×C1311yescharacteristic, complemented
314#95D4×C1311yescharacteristic, complemented
315C2×C13—21no—
316C2×C13—21no—
317C2×C13—41no—
318C2×C13—41no—
319C2×C13—82no—
320C2×C13—82no—
321C2×C13—161no—
322C2×C13#160011yescharacteristic
323C2×C13#219611yescharacteristic
324C2×C13#220011yescharacteristic
325C24—21no—
326C24—21no—
327C24—21no—
328C24—21no—
329C24—21no—
330C24—41no—
331C24—41no—
332C24—42no—
333C24—81no—
334C24C2×D4×C1311yescharacteristic
335C2×D4—24no—
336C2×D4—21no—
337C2×D4—21no—
338C2×D4—41no—
339C2×D4—42no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—42no—
343C2×D4—42no—
344C2×D4—41no—
345C2×D4—42no—
346C2×D4—44no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4—41no—
352C2×D4—81no—
353C2×D4—81no—
354C2×D4—81no—
355C2×D4—81no—
356C2×D4—82no—
357C2×D4—82no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—42no—
364C22×C4—41no—
365C22×C4—81no—
366C22×C4—81no—
367C22×C4C2×D4×C1311yescharacteristic
368C22×C4C2×D4×C1311yescharacteristic
369D8—82no—
370C2×C8—41no—
371C2×C8—41no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—41no—
375C4⋊C4—42no—
376C22⋊C4—22no—
377C22⋊C4—41no—
378C22⋊C4—42no—
379C22⋊C4—42no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—42no—
383C22⋊C4—42no—
384C22⋊C4—42no—
385C22⋊C4—44no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—81no—
389C22⋊C4—81no—
390C13#1218611yescharacteristic, direct product factor, Sylow
391C23—21no—
392C23—21no—
393C23—22no—
394C23—22no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—42no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—42no—
407C23—42no—
408C23—41no—
409C23—41no—
410C23—41no—
411C23—41no—
412C23—41no—
413C23—41no—
414C23—41no—
415C23—81no—
416C23—82no—
417C23—81no—
418C23—82no—
419C23—84no—
420C23—81no—
421C23—81no—
422C23—81no—
423C23C13×#12011yescharacteristic
424C23C13×#13511yescharacteristic
425C23C13×AGL(1,ℤ/8)11yescharacteristic
426D4—42no—
427D4—84no—
428D4—81no—
429D4—81no—
430D4—81no—
431D4—81no—
432D4—81no—
433D4—82no—
434D4—82no—
435D4—84no—
436D4—88no—
437D4—81no—
438D4—81no—
439C2×C4—22no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—84no—
460C2×C4—81no—
461C2×C4—81no—
462C8—81no—
463C8—81no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—41no—
469C22—41no—
470C22—42no—
471C22—42no—
472C22—42no—
473C22—42no—
474C22—41no—
475C22—41no—
476C22—44no—
477C22—42no—
478C22—42no—
479C22—81no—
480C22—81no—
481C22—81no—
482C22—81no—
483C22—81no—
484C22—82no—
485C22—82no—
486C22—82no—
487C22—82no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22—81no—
492C22—81no—
493C22—81no—
494C22—81no—
495C22—161no—
496C22C13×#44911yescharacteristic
497C22C13×#45311yescharacteristic
498C22C13×B(4,𝔽2)11yescharacteristic
499C4—42no—
500C4—41no—
501C4—41no—
502C4—81no—
503C4—81no—
504C4—82no—
505C4—81no—
506C4—81no—
507C2—21no—
508C2—21no—
509C2—41no—
510C2—41no—
511C2—82no—
512C2—82no—
513C2—161no—
514C2C13×#160011yescharacteristic
515C2C13×#219611yescharacteristic
516C2C13×#220011yescharacteristic
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×#2668C2semidirect
2. C13×#2021C2semidirect
3. C13×#1613C2semidirect
4. C13×#1595C2semidirect
5. C13×#1352C2semidirect
6. C13×#1343C2semidirect
7. C13×#1316C2semidirect
33. C22×D4×C13D4semidirect
45. C2×C13×C4⋊C4D4semidirect
65. C13×#95D4semidirect
66. C13×#95D4semidirect
67. #12186C13direct (N × H)
133. #2668C2×C13semidirect
134. #2021C2×C13semidirect
135. #1613C2×C13semidirect
136. #1595C2×C13semidirect
137. #1352C2×C13semidirect
138. #1343C2×C13semidirect
139. #1316C2×C13semidirect
281. C22×D4D4×C13semidirect
293. C2×C4⋊C4D4×C13semidirect
313. #95D4×C13semidirect
314. #95D4×C13semidirect
390. C13#12186direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26682
C13×#20212
C13×#16132
C13×#15952
C13×#13522
C13×#13432
C13×#13162
#1218613