Finite Group Databasebeta

← C13×#11843 #15698182

Subgroups — C13×#11843 #15698182

Order 3328.

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

normal subgroups only

This group has 620 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×#2539C211yesmaximal, characteristic
2C13×#1819C211yesmaximal, characteristic, complemented
3C2×C13×#323C211yesmaximal, characteristic, complemented
4C13×#1352C212yesmaximal, complemented
5C13×#1343C212yesmaximal, complemented
6C2×C13×#123—21no—
7C2×C13×#121C411yescharacteristic, complemented
8C2×C13×#120—21no—
9C22×C13×C22⋊C4C2211yescharacteristic
10C2×C13×C22⋊C8—21no—
11C13×#399C411yescharacteristic, complemented
12C13×#399C2211yescharacteristic
13C13×#392C411yescharacteristic, complemented
14C13×#392C2211yescharacteristic
15C13×#390—21no—
16C13×#390—21no—
17C13×#379—21no—
18C4×C13×C22⋊C4C411yescharacteristic, complemented
19C13×#342—21no—
20C13×#342C2212yes—
21C13×#323—21no—
22C13×#323C2212yes—
23C25×C13D411yescharacteristic
24C22×D4×C13—21no—
25C22×D4×C13—21no—
26C22×D4×C13—21no—
27C22×D4×C13C2×C411yescharacteristic
28C23×C4×C13C2×C411yescharacteristic
29C23×C4×C13D411yescharacteristic
30C22×C8×C13—41no—
31C13×#123—44no—
32C13×#121—41no—
33C13×#121—41no—
34C13×#120—44no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—22no—
45C2×C13×C22⋊C4—41no—
46C2×C13×C22⋊C4—41no—
47C2×C13×C22⋊C4—41no—
48C2×C13×C22⋊C4—41no—
49C2×C13×C22⋊C4C2×C411yescharacteristic
50C2×C13×C22⋊C4D411yescharacteristic
51C2×C13×C22⋊C4D411yescharacteristic
52C2×C13×C22⋊C4C2311yescharacteristic
53C2×C42×C13—21no—
54C13×C22⋊C8—22no—
55C13×C22⋊C8—41no—
56C13×#95C2×C411yescharacteristic
57C13×#95C2×C411yescharacteristic
58#11843C1311yesmaximal, characteristic, direct product factor, Sylow
59C24×C13—21no—
60C24×C13—21no—
61C24×C13—22no—
62C24×C13—21no—
63C24×C13—41no—
64C24×C13—42no—
65C24×C13—81no—
66C24×C13C22⋊C411yescharacteristic
67C24×C13C22⋊C411yescharacteristic
68C24×C13C2×D411yescharacteristic
69C2×D4×C13—41no—
70C2×D4×C13—42no—
71C2×D4×C13—42no—
72C2×D4×C13—42no—
73C2×D4×C13—42no—
74C2×D4×C13—42no—
75C2×D4×C13—41no—
76C2×D4×C13—41no—
77C2×D4×C13—42no—
78C2×D4×C13—81no—
79C2×D4×C13—81no—
80C2×D4×C13—81no—
81C22×C4×C13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—21no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—42no—
89C22×C4×C13—42no—
90C22×C4×C13—81no—
91C22×C4×C13C22⋊C411yescharacteristic
92C22×C4×C13C22⋊C411yescharacteristic
93C22×C4×C13C22×C411yescharacteristic
94C22×C4×C13C2×D411yescharacteristic
95C2×C8×C13—42no—
96C2×C8×C13—82no—
97C13×C4⋊C4—41no—
98C13×C4⋊C4—42no—
99C13×C4⋊C4—42no—
100C13×C22⋊C4—24no—
101C13×C22⋊C4—41no—
102C13×C22⋊C4—41no—
103C13×C22⋊C4—41no—
104C13×C22⋊C4—41no—
105C13×C22⋊C4—42no—
106C13×C22⋊C4—42no—
107C13×C22⋊C4—42no—
108C13×C22⋊C4—42no—
109C13×C22⋊C4—42no—
110C13×C22⋊C4—42no—
111C13×C22⋊C4—42no—
112C13×C22⋊C4—82no—
113C13×C22⋊C4—82no—
114C42×C13—81no—
115#2539C2×C1311yescharacteristic
116#1819C2×C1311yescharacteristic, complemented
117C2×#323C2×C1311yescharacteristic, complemented
118#1352C2×C1312yescomplemented
119#1343C2×C1312yescomplemented
120C23×C13—22no—
121C23×C13—21no—
122C23×C13—21no—
123C23×C13—21no—
124C23×C13—21no—
125C23×C13—21no—
126C23×C13—21no—
127C23×C13—21no—
128C23×C13—41no—
129C23×C13—42no—
130C23×C13—42no—
131C23×C13—41no—
132C23×C13—41no—
133C23×C13—41no—
134C23×C13—41no—
135C23×C13—42no—
136C23×C13—41no—
137C23×C13—41no—
138C23×C13—41no—
139C23×C13—41no—
140C23×C13—42no—
141C23×C13—41no—
142C23×C13—41no—
143C23×C13—41no—
144C23×C13—81no—
145C23×C13—81no—
146C23×C13—84no—
147C23×C13—84no—
148C23×C13#9911yescharacteristic
149C23×C13#9911yescharacteristic
150C23×C13C2×C22⋊C411yescharacteristic
151C23×C13#13512yes—
152D4×C13—84no—
153D4×C13—84no—
154D4×C13—82no—
155D4×C13—82no—
156D4×C13—82no—
157C2×C4×C13—22no—
158C2×C4×C13—22no—
159C2×C4×C13—21no—
160C2×C4×C13—21no—
161C2×C4×C13—21no—
162C2×C4×C13—21no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—42no—
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—81no—
176C2×C4×C13—81no—
177C2×C4×C13—81no—
178C2×C4×C13—82no—
179C2×C4×C13—82no—
180C2×C4×C13—82no—
181C8×C13—82no—
182C2×#123—21no—
183C2×#121C4×C1311yescharacteristic, complemented
184C2×#120—21no—
185C22×C22⋊C4C22×C1311yescharacteristic
186C2×C22⋊C8—21no—
187#399C4×C1311yescharacteristic, complemented
188#399C22×C1311yescharacteristic
189#392C4×C1311yescharacteristic, complemented
190#392C22×C1311yescharacteristic
191#390—21no—
192#390—21no—
193#379—21no—
194C4×C22⋊C4C4×C1311yescharacteristic, complemented
195#342—21no—
196#342C22×C1312yes—
197#323—21no—
198#323C22×C1312yes—
199C22×C13—21no—
200C22×C13—21no—
201C22×C13—21no—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13—21no—
205C22×C13—22no—
206C22×C13—21no—
207C22×C13—42no—
208C22×C13—42no—
209C22×C13—42no—
210C22×C13—42no—
211C22×C13—41no—
212C22×C13—41no—
213C22×C13—41no—
214C22×C13—41no—
215C22×C13—41no—
216C22×C13—81no—
217C22×C13—84no—
218C22×C13—81no—
219C22×C13—81no—
220C22×C13—81no—
221C22×C13—81no—
222C22×C13—81no—
223C22×C13—84no—
224C22×C13—81no—
225C22×C13—81no—
226C22×C13—81no—
227C22×C13#35312yes—
228C22×C13C2×#9911yescharacteristic
229C22×C13#41611yescharacteristic
230C22×C13#42111yescharacteristic
231C4×C13—42no—
232C4×C13—42no—
233C4×C13—41no—
234C4×C13—41no—
235C4×C13—41no—
236C4×C13—41no—
237C4×C13—81no—
238C4×C13—162no—
239C25D4×C1311yescharacteristic
240C22×D4—21no—
241C22×D4—21no—
242C22×D4—21no—
243C22×D4C2×C4×C1311yescharacteristic
244C23×C4C2×C4×C1311yescharacteristic
245C23×C4D4×C1311yescharacteristic
246C22×C8—41no—
247#123—44no—
248#121—41no—
249#121—41no—
250#120—44no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4C2×C4×C1311yescharacteristic
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—22no—
261C2×C22⋊C4—41no—
262C2×C22⋊C4—41no—
263C2×C22⋊C4—41no—
264C2×C22⋊C4—41no—
265C2×C22⋊C4C2×C4×C1311yescharacteristic
266C2×C22⋊C4D4×C1311yescharacteristic
267C2×C22⋊C4D4×C1311yescharacteristic
268C2×C22⋊C4C23×C1311yescharacteristic
269C2×C42—21no—
270C22⋊C8—22no—
271C22⋊C8—41no—
272#95C2×C4×C1311yescharacteristic
273#95C2×C4×C1311yescharacteristic
274C2×C13—21no—
275C2×C13—21no—
276C2×C13—22no—
277C2×C13—42no—
278C2×C13—41no—
279C2×C13—81no—
280C2×C13—161no—
281C2×C13#151611yescharacteristic
282C2×C13#212111yescharacteristic
283C2×C13C2×#35311yescharacteristic
284C24—21no—
285C24—21no—
286C24—22no—
287C24—21no—
288C24—41no—
289C24—42no—
290C24—81no—
291C24C13×C22⋊C411yescharacteristic
292C24C13×C22⋊C411yescharacteristic
293C24C2×D4×C1311yescharacteristic
294C2×D4—41no—
295C2×D4—42no—
296C2×D4—42no—
297C2×D4—42no—
298C2×D4—42no—
299C2×D4—42no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—42no—
303C2×D4—81no—
304C2×D4—81no—
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—42no—
314C22×C4—42no—
315C22×C4—81no—
316C22×C4C13×C22⋊C411yescharacteristic
317C22×C4C13×C22⋊C411yescharacteristic
318C22×C4C22×C4×C1311yescharacteristic
319C22×C4C2×D4×C1311yescharacteristic
320C2×C8—42no—
321C2×C8—82no—
322C4⋊C4—41no—
323C4⋊C4—42no—
324C4⋊C4—42no—
325C22⋊C4—24no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—42no—
331C22⋊C4—42no—
332C22⋊C4—42no—
333C22⋊C4—42no—
334C22⋊C4—42no—
335C22⋊C4—42no—
336C22⋊C4—42no—
337C22⋊C4—82no—
338C22⋊C4—82no—
339C42—81no—
340C13#1184311yescharacteristic, direct product factor, Sylow
341C23—21no—
342C23—21no—
343C23—21no—
344C23—22no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—41no—
350C23—42no—
351C23—42no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—42no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—42no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23—81no—
366C23—81no—
367C23—84no—
368C23—84no—
369C23C13×#9911yescharacteristic
370C23C13×#9911yescharacteristic
371C23C2×C13×C22⋊C411yescharacteristic
372C23C13×#13512yes—
373D4—84no—
374D4—84no—
375D4—82no—
376D4—82no—
377D4—82no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—82no—
400C2×C4—82no—
401C2×C4—82no—
402C8—82no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—22no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—42no—
412C22—42no—
413C22—42no—
414C22—42no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—81no—
421C22—84no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22—81no—
427C22—84no—
428C22—81no—
429C22—81no—
430C22—81no—
431C22C13×#35312yes—
432C22C2×C13×#9911yescharacteristic
433C22C13×#41611yescharacteristic
434C22C13×#42111yescharacteristic
435C4—42no—
436C4—42no—
437C4—41no—
438C4—41no—
439C4—41no—
440C4—41no—
441C4—81no—
442C4—162no—
443C2—21no—
444C2—21no—
445C2—22no—
446C2—42no—
447C2—41no—
448C2—81no—
449C2—161no—
450C2C13×#151611yescharacteristic
451C2C13×#212111yescharacteristic
452C2C2×C13×#35311yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC13×#2539C2
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C24×C13 ◁ C22×C13×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#1819C2semidirect
3. C2×C13×#323C2semidirect
4. C13×#1352C2semidirect
5. C13×#1343C2semidirect
7. C2×C13×#121C4semidirect
11. C13×#399C4semidirect
13. C13×#392C4semidirect
18. C4×C13×C22⋊C4C4semidirect
58. #11843C13direct (N × H)
116. #1819C2×C13semidirect
117. C2×#323C2×C13semidirect
118. #1352C2×C13semidirect
119. #1343C2×C13semidirect
183. C2×#121C4×C13semidirect
187. #399C4×C13semidirect
189. #392C4×C13semidirect
194. C4×C22⋊C4C4×C13semidirect
340. C13#11843direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25392
C13×#18192
C2×C13×#3232
C13×#13522
C13×#13432
#1184313