Finite Group Databasebeta

← C13×#12187 #15698526

Subgroups — C13×#12187 #15698526

Order 3328.

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

normal subgroups only

This group has 508 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×#2760C211yesmaximal, characteristic, complemented
2C13×#2022C211yesmaximal, characteristic, complemented
3C13×#1601C211yesmaximal, characteristic, complemented
4C13×#1595C211yesmaximal, characteristic
5C13×#1351C211yesmaximal, characteristic, complemented
6C13×#1343C211yesmaximal, characteristic, complemented
7C13×#1317C211yesmaximal, characteristic, complemented
8C13×#534C2211yescharacteristic
9C2×C13×#123—21no—
10C13×#448—21no—
11C13×#447—21no—
12C2×C13×#99—21no—
13C13×#401—21no—
14C13×#393—21no—
15C13×#393C2211yescharacteristic
16C13×#392C2211yescharacteristic
17C13×#386—21no—
18C13×#386—21no—
19C13×#386—21no—
20C13×#381—21no—
21C13×#381C2211yescharacteristic
22C13×#342C2211yescharacteristic
23C13×#327—21no—
24C13×#327—21no—
25C13×#323C2211yescharacteristic
26C13×#323C2211yescharacteristic
27C22×Q8×C13D411yescharacteristic
28C22×D4×C13—21no—
29C22×D4×C13—21no—
30C22×D4×C13D411yescharacteristic
31C23×C4×C13—21no—
32C23×C4×C13D411yescharacteristic
33C2×C13×SD16—41no—
34C2×C13×D8—41no—
35C13×#123—42no—
36C13×#123—41no—
37C13×#123—42no—
38C13×#121—21no—
39C13×#121—21no—
40C13×#120—41no—
41C2×C13×C4⋊C4—41no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4—21no—
48C2×C13×C22⋊C4—41no—
49C2×C13×C22⋊C4D411yescharacteristic
50C2×C13×C22⋊C4C2311yescharacteristic
51C13×#103—41no—
52C13×#102—41no—
53C13×#99—42no—
54C13×C22⋊C8—21no—
55C13×C22⋊C8—21no—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95—21no—
59C13×#95—21no—
60C13×#95—21no—
61C13×#95—21no—
62C13×#95—21no—
63C13×#95D411yescharacteristic
64C13×#95D411yescharacteristic
65#12187C1311yesmaximal, characteristic, direct product factor, Sylow
66C24×C13—21no—
67C24×C13—21no—
68C24×C13C2×D411yescharacteristic
69C2×Q8×C13—41no—
70C2×Q8×C13—81no—
71C2×D4×C13—21no—
72C2×D4×C13—21no—
73C2×D4×C13—41no—
74C2×D4×C13—42no—
75C2×D4×C13—41no—
76C2×D4×C13—41no—
77C2×D4×C13—41no—
78C2×D4×C13—42no—
79C2×D4×C13—41no—
80C2×D4×C13—41no—
81C2×D4×C13—41no—
82C2×D4×C13—41no—
83C2×D4×C13—41no—
84C2×D4×C13—81no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13—21no—
93C22×C4×C13—41no—
94C22×C4×C13—41no—
95C22×C4×C13—41no—
96C22×C4×C13—42no—
97C22×C4×C13—81no—
98C22×C4×C13—81no—
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
101C13×SD16—82no—
102C13×D8—82no—
103C2×C8×C13—41no—
104C2×C8×C13—41no—
105C13×C4⋊C4—21no—
106C13×C4⋊C4—21no—
107C13×C4⋊C4—44no—
108C13×C22⋊C4—22no—
109C13×C22⋊C4—41no—
110C13×C22⋊C4—41no—
111C13×C22⋊C4—41no—
112C13×C22⋊C4—44no—
113C13×C22⋊C4—41no—
114C13×C22⋊C4—41no—
115C13×C22⋊C4—81no—
116C13×C22⋊C4—81no—
117C13×C22⋊C4—81no—
118C13×C22⋊C4—81no—
119C13×C22⋊C4—81no—
120#2760C2×C1311yescharacteristic, complemented
121#2022C2×C1311yescharacteristic, complemented
122#1601C2×C1311yescharacteristic, complemented
123#1595C2×C1311yescharacteristic
124#1351C2×C1311yescharacteristic, complemented
125#1343C2×C1311yescharacteristic, complemented
126#1317C2×C1311yescharacteristic, complemented
127C23×C13—21no—
128C23×C13—21no—
129C23×C13—22no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13—41no—
133C23×C13—41no—
134C23×C13—41no—
135C23×C13—41no—
136C23×C13—41no—
137C23×C13—41no—
138C23×C13—41no—
139C23×C13—41no—
140C23×C13—41no—
141C23×C13—81no—
142C23×C13—81no—
143C23×C13#12011yescharacteristic
144C23×C13#13511yescharacteristic
145C23×C13AGL(1,ℤ/8)11yescharacteristic
146Q8×C13—42no—
147Q8×C13—81no—
148D4×C13—42no—
149D4×C13—81no—
150D4×C13—81no—
151D4×C13—81no—
152D4×C13—81no—
153D4×C13—81no—
154D4×C13—82no—
155D4×C13—82no—
156D4×C13—81no—
157D4×C13—81no—
158C2×C4×C13—21no—
159C2×C4×C13—21no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—42no—
163C2×C4×C13—42no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13—41no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13—41no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13—41no—
182C2×C4×C13—81no—
183C2×C4×C13—81no—
184C2×C4×C13—84no—
185C2×C4×C13—81no—
186C8×C13—81no—
187C8×C13—81no—
188#534C22×C1311yescharacteristic
189C2×#123—21no—
190#448—21no—
191#447—21no—
192C2×#99—21no—
193#401—21no—
194#393—21no—
195#393C22×C1311yescharacteristic
196#392C22×C1311yescharacteristic
197#386—21no—
198#386—21no—
199#386—21no—
200#381—21no—
201#381C22×C1311yescharacteristic
202#342C22×C1311yescharacteristic
203#327—21no—
204#327—21no—
205#323C22×C1311yescharacteristic
206#323C22×C1311yescharacteristic
207C22×C13—21no—
208C22×C13—21no—
209C22×C13—21no—
210C22×C13—21no—
211C22×C13—41no—
212C22×C13—41no—
213C22×C13—42no—
214C22×C13—42no—
215C22×C13—41no—
216C22×C13—41no—
217C22×C13—42no—
218C22×C13—81no—
219C22×C13—81no—
220C22×C13—81no—
221C22×C13—82no—
222C22×C13—81no—
223C22×C13—81no—
224C22×C13—81no—
225C22×C13—81no—
226C22×C13—81no—
227C22×C13—161no—
228C22×C13#44911yescharacteristic
229C22×C13#45311yescharacteristic
230C22×C13B(4,𝔽2)11yescharacteristic
231C4×C13—41no—
232C4×C13—41no—
233C4×C13—81no—
234C4×C13—81no—
235C4×C13—81no—
236C4×C13—82no—
237C4×C13—81no—
238C4×C13—81no—
239C4×C13—81no—
240C22×Q8D4×C1311yescharacteristic
241C22×D4—21no—
242C22×D4—21no—
243C22×D4D4×C1311yescharacteristic
244C23×C4—21no—
245C23×C4D4×C1311yescharacteristic
246C2×SD16—41no—
247C2×D8—41no—
248#123—42no—
249#123—41no—
250#123—42no—
251#121—21no—
252#121—21no—
253#120—41no—
254C2×C4⋊C4—41no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—41no—
262C2×C22⋊C4D4×C1311yescharacteristic
263C2×C22⋊C4C23×C1311yescharacteristic
264#103—41no—
265#102—41no—
266#99—42no—
267C22⋊C8—21no—
268C22⋊C8—21no—
269#95—21no—
270#95—21no—
271#95—21no—
272#95—21no—
273#95—21no—
274#95—21no—
275#95—21no—
276#95D4×C1311yescharacteristic
277#95D4×C1311yescharacteristic
278C2×C13—21no—
279C2×C13—21no—
280C2×C13—41no—
281C2×C13—41no—
282C2×C13—82no—
283C2×C13—161no—
284C2×C13#160011yescharacteristic
285C2×C13#219711yescharacteristic
286C2×C13#220011yescharacteristic
287C24—21no—
288C24—21no—
289C24C2×D4×C1311yescharacteristic
290C2×Q8—41no—
291C2×Q8—81no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—41no—
295C2×D4—42no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—42no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—81no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—42no—
318C22×C4—81no—
319C22×C4—81no—
320C22×C4C2×D4×C1311yescharacteristic
321C22×C4C2×D4×C1311yescharacteristic
322SD16—82no—
323D8—82no—
324C2×C8—41no—
325C2×C8—41no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—44no—
329C22⋊C4—22no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—44no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—81no—
337C22⋊C4—81no—
338C22⋊C4—81no—
339C22⋊C4—81no—
340C22⋊C4—81no—
341C13#1218711yescharacteristic, direct product factor, Sylow
342C23—21no—
343C23—21no—
344C23—22no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—81no—
357C23—81no—
358C23C13×#12011yescharacteristic
359C23C13×#13511yescharacteristic
360C23C13×AGL(1,ℤ/8)11yescharacteristic
361Q8—42no—
362Q8—81no—
363D4—42no—
364D4—81no—
365D4—81no—
366D4—81no—
367D4—81no—
368D4—81no—
369D4—82no—
370D4—82no—
371D4—81no—
372D4—81no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—84no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—81no—
401C8—81no—
402C8—81no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—41no—
408C22—41no—
409C22—42no—
410C22—42no—
411C22—41no—
412C22—41no—
413C22—42no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—82no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22—161no—
424C22C13×#44911yescharacteristic
425C22C13×#45311yescharacteristic
426C22C13×B(4,𝔽2)11yescharacteristic
427C4—41no—
428C4—41no—
429C4—81no—
430C4—81no—
431C4—81no—
432C4—82no—
433C4—81no—
434C4—81no—
435C4—81no—
436C2—21no—
437C2—21no—
438C2—41no—
439C2—41no—
440C2—82no—
441C2—161no—
442C2C13×#160011yescharacteristic
443C2C13×#219711yescharacteristic
444C2C13×#220011yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC13×#1595C2
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×#2760C2semidirect
2. C13×#2022C2semidirect
3. C13×#1601C2semidirect
5. C13×#1351C2semidirect
6. C13×#1343C2semidirect
7. C13×#1317C2semidirect
65. #12187C13direct (N × H)
120. #2760C2×C13semidirect
121. #2022C2×C13semidirect
122. #1601C2×C13semidirect
124. #1351C2×C13semidirect
125. #1343C2×C13semidirect
126. #1317C2×C13semidirect
341. C13#12187direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#27602
C13×#20222
C13×#16012
C13×#15952
C13×#13512
C13×#13432
C13×#13172
#1218713