Finite Group Databasebeta

← C13×#11545 #15697884

Subgroups — C13×#11545 #15697884

Order 3328.

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

normal subgroups only

This group has 700 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×#2405C211yesmaximal, characteristic
2C13×#1462C211yesmaximal, characteristic, complemented
3C2×C13×#323C211yesmaximal, characteristic, complemented
4C13×#1326C212yesmaximal, complemented
5C13×#1316C212yesmaximal, complemented
6C23×D4×C13C411yescharacteristic
7C2×C13×#123—21no—
8C22×C13×C22⋊C4C2211yescharacteristic
9C13×#407—21no—
10C2×C13×C22⋊C8—21no—
11C13×#394—21no—
12C13×#394—21no—
13C13×#386—21no—
14C13×#385C411yescharacteristic
15C13×#385C2211yescharacteristic
16C13×#379C411yescharacteristic
17C13×#379C411yescharacteristic
18C13×#379C2211yescharacteristic
19C13×#323—21no—
20C13×#323—21no—
21C13×#323C2212yes—
22C13×#323C2212yes—
23C25×C13C2×C411yescharacteristic
24C25×C13C2×C411yescharacteristic
25C22×D4×C13—21no—
26C22×D4×C13—21no—
27C22×D4×C13—44no—
28C22×D4×C13—41no—
29C22×D4×C13—41no—
30C23×C4×C13C2×C411yescharacteristic
31C23×C4×C13D411yescharacteristic
32C23×C4×C13D411yescharacteristic
33C2×C13×M16—41no—
34C22×C8×C13—41no—
35C13×#123—44no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4—21no—
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—41no—
45C2×C13×C22⋊C4—41no—
46C2×C13×C22⋊C4C2×C411yescharacteristic
47C2×C13×C22⋊C4C2×C411yescharacteristic
48C2×C13×C22⋊C4C2×C411yescharacteristic
49C2×C13×C22⋊C4D411yescharacteristic
50C2×C13×C22⋊C4D411yescharacteristic
51C2×C13×C22⋊C4C2311yescharacteristic
52C13×C22⋊C8—22no—
53C13×C22⋊C8—22no—
54C13×C22⋊C8—41no—
55C13×C22⋊C8—41no—
56C13×#95—21no—
57C13×#95—21no—
58#11545C1311yesmaximal, characteristic, direct product factor, Sylow
59C24×C13—21no—
60C24×C13—21no—
61C24×C13—21no—
62C24×C13—22no—
63C24×C13—22no—
64C24×C13—41no—
65C24×C13—42no—
66C24×C13—41no—
67C24×C13—42no—
68C24×C13—41no—
69C24×C13—81no—
70C24×C13—81no—
71C24×C13C22⋊C411yescharacteristic
72C24×C13C22⋊C411yescharacteristic
73C24×C13C22×C411yescharacteristic
74C2×D4×C13—24no—
75C2×D4×C13—42no—
76C2×D4×C13—42no—
77C2×D4×C13—42no—
78C2×D4×C13—42no—
79C2×D4×C13—44no—
80C2×D4×C13—44no—
81C2×D4×C13—44no—
82C2×D4×C13—41no—
83C2×D4×C13—41no—
84C2×D4×C13—44no—
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—42no—
93C22×C4×C13—41no—
94C22×C4×C13—42no—
95C22×C4×C13—81no—
96C22×C4×C13C22⋊C411yescharacteristic
97C22×C4×C13C22⋊C411yescharacteristic
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C13×M16—82no—
101C2×C8×C13—42no—
102C2×C8×C13—42no—
103C2×C8×C13—82no—
104C13×C4⋊C4—42no—
105C13×C4⋊C4—42no—
106C13×C22⋊C4—22no—
107C13×C22⋊C4—41no—
108C13×C22⋊C4—41no—
109C13×C22⋊C4—41no—
110C13×C22⋊C4—41no—
111C13×C22⋊C4—42no—
112C13×C22⋊C4—42no—
113C13×C22⋊C4—42no—
114C13×C22⋊C4—41no—
115C13×C22⋊C4—81no—
116C13×C22⋊C4—81no—
117C13×C22⋊C4—81no—
118#2405C2×C1311yescharacteristic
119#1462C2×C1311yescharacteristic, complemented
120C2×#323C2×C1311yescharacteristic, complemented
121#1326C2×C1312yescomplemented
122#1316C2×C1312yescomplemented
123C23×C13—22no—
124C23×C13—21no—
125C23×C13—21no—
126C23×C13—21no—
127C23×C13—21no—
128C23×C13—22no—
129C23×C13—21no—
130C23×C13—21no—
131C23×C13—21no—
132C23×C13—41no—
133C23×C13—42no—
134C23×C13—42no—
135C23×C13—41no—
136C23×C13—41no—
137C23×C13—41no—
138C23×C13—41no—
139C23×C13—41no—
140C23×C13—42no—
141C23×C13—41no—
142C23×C13—41no—
143C23×C13—42no—
144C23×C13—42no—
145C23×C13—41no—
146C23×C13—41no—
147C23×C13—41no—
148C23×C13—42no—
149C23×C13—81no—
150C23×C13—81no—
151C23×C13—82no—
152C23×C13—84no—
153C23×C13—84no—
154C23×C13—84no—
155C23×C13—84no—
156C23×C13—82no—
157C23×C13#9911yescharacteristic
158C23×C13#9911yescharacteristic
159C23×C13C2×C22⋊C411yescharacteristic
160C23×C13#13112yes—
161D4×C13—44no—
162D4×C13—48no—
163D4×C13—44no—
164C2×C4×C13—22no—
165C2×C4×C13—21no—
166C2×C4×C13—21no—
167C2×C4×C13—21no—
168C2×C4×C13—21no—
169C2×C4×C13—42no—
170C2×C4×C13—41no—
171C2×C4×C13—42no—
172C2×C4×C13—42no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13—41no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13—42no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13—41no—
182C2×C4×C13—41no—
183C2×C4×C13—41no—
184C2×C4×C13—41no—
185C2×C4×C13—81no—
186C2×C4×C13—81no—
187C8×C13—82no—
188C8×C13—82no—
189C23×D4C4×C1311yescharacteristic
190C2×#123—21no—
191C22×C22⋊C4C22×C1311yescharacteristic
192#407—21no—
193C2×C22⋊C8—21no—
194#394—21no—
195#394—21no—
196#386—21no—
197#385C4×C1311yescharacteristic
198#385C22×C1311yescharacteristic
199#379C4×C1311yescharacteristic
200#379C4×C1311yescharacteristic
201#379C22×C1311yescharacteristic
202#323—21no—
203#323—21no—
204#323C22×C1312yes—
205#323C22×C1312yes—
206C22×C13—21no—
207C22×C13—21no—
208C22×C13—21no—
209C22×C13—21no—
210C22×C13—21no—
211C22×C13—21no—
212C22×C13—22no—
213C22×C13—21no—
214C22×C13—42no—
215C22×C13—42no—
216C22×C13—42no—
217C22×C13—42no—
218C22×C13—42no—
219C22×C13—42no—
220C22×C13—41no—
221C22×C13—41no—
222C22×C13—42no—
223C22×C13—41no—
224C22×C13—41no—
225C22×C13—41no—
226C22×C13—84no—
227C22×C13—81no—
228C22×C13—81no—
229C22×C13—81no—
230C22×C13—81no—
231C22×C13—84no—
232C22×C13—84no—
233C22×C13—84no—
234C22×C13—81no—
235C22×C13—81no—
236C22×C13AΣL(1,𝔽16)12yes—
237C22×C13#40811yescharacteristic
238C22×C13C2×#9911yescharacteristic
239C22×C13#41311yescharacteristic
240C4×C13—41no—
241C4×C13—42no—
242C4×C13—41no—
243C4×C13—41no—
244C4×C13—41no—
245C4×C13—81no—
246C4×C13—81no—
247C25C2×C4×C1311yescharacteristic
248C25C2×C4×C1311yescharacteristic
249C22×D4—21no—
250C22×D4—21no—
251C22×D4—44no—
252C22×D4—41no—
253C22×D4—41no—
254C23×C4C2×C4×C1311yescharacteristic
255C23×C4D4×C1311yescharacteristic
256C23×C4D4×C1311yescharacteristic
257C2×M16—41no—
258C22×C8—41no—
259#123—44no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—41no—
269C2×C22⋊C4—41no—
270C2×C22⋊C4C2×C4×C1311yescharacteristic
271C2×C22⋊C4C2×C4×C1311yescharacteristic
272C2×C22⋊C4C2×C4×C1311yescharacteristic
273C2×C22⋊C4D4×C1311yescharacteristic
274C2×C22⋊C4D4×C1311yescharacteristic
275C2×C22⋊C4C23×C1311yescharacteristic
276C22⋊C8—22no—
277C22⋊C8—22no—
278C22⋊C8—41no—
279C22⋊C8—41no—
280#95—21no—
281#95—21no—
282C2×C13—21no—
283C2×C13—21no—
284C2×C13—22no—
285C2×C13—41no—
286C2×C13—42no—
287C2×C13—82no—
288C2×C13—81no—
289C2×C13#146811yescharacteristic
290C2×C13C2×AΣL(1,𝔽16)11yescharacteristic
291C2×C13#212111yescharacteristic
292C24—21no—
293C24—21no—
294C24—21no—
295C24—22no—
296C24—22no—
297C24—41no—
298C24—41no—
299C24—42no—
300C24—42no—
301C24—41no—
302C24—81no—
303C24—81no—
304C24C13×C22⋊C411yescharacteristic
305C24C13×C22⋊C411yescharacteristic
306C24C22×C4×C1311yescharacteristic
307C2×D4—24no—
308C2×D4—42no—
309C2×D4—42no—
310C2×D4—42no—
311C2×D4—42no—
312C2×D4—44no—
313C2×D4—44no—
314C2×D4—44no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—44no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—42no—
326C22×C4—41no—
327C22×C4—42no—
328C22×C4—81no—
329C22×C4C13×C22⋊C411yescharacteristic
330C22×C4C13×C22⋊C411yescharacteristic
331C22×C4C2×D4×C1311yescharacteristic
332C22×C4C2×D4×C1311yescharacteristic
333M16—82no—
334C2×C8—42no—
335C2×C8—42no—
336C2×C8—82no—
337C4⋊C4—42no—
338C4⋊C4—42no—
339C22⋊C4—22no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—42no—
345C22⋊C4—42no—
346C22⋊C4—42no—
347C22⋊C4—41no—
348C22⋊C4—81no—
349C22⋊C4—81no—
350C22⋊C4—81no—
351C13#1154511yescharacteristic, direct product factor, Sylow
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—22no—
357C23—22no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—41no—
362C23—42no—
363C23—42no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—42no—
370C23—41no—
371C23—41no—
372C23—42no—
373C23—42no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—42no—
378C23—81no—
379C23—81no—
380C23—82no—
381C23—84no—
382C23—84no—
383C23—84no—
384C23—84no—
385C23—82no—
386C23C13×#9911yescharacteristic
387C23C13×#9911yescharacteristic
388C23C2×C13×C22⋊C411yescharacteristic
389C23C13×#13112yes—
390D4—44no—
391D4—48no—
392D4—44no—
393C2×C4—22no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—42no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—81no—
415C2×C4—81no—
416C8—82no—
417C8—82no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—22no—
425C22—21no—
426C22—42no—
427C22—42no—
428C22—42no—
429C22—42no—
430C22—42no—
431C22—42no—
432C22—41no—
433C22—41no—
434C22—42no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—84no—
439C22—81no—
440C22—81no—
441C22—81no—
442C22—81no—
443C22—84no—
444C22—84no—
445C22—84no—
446C22—81no—
447C22—81no—
448C22C13×AΣL(1,𝔽16)12yes—
449C22C13×#40811yescharacteristic
450C22C2×C13×#9911yescharacteristic
451C22C13×#41311yescharacteristic
452C4—41no—
453C4—42no—
454C4—41no—
455C4—41no—
456C4—41no—
457C4—81no—
458C4—81no—
459C2—21no—
460C2—21no—
461C2—22no—
462C2—41no—
463C2—42no—
464C2—82no—
465C2—81no—
466C2C13×#146811yescharacteristic
467C2C2×C13×AΣL(1,𝔽16)11yescharacteristic
468C2C13×#212111yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC24C22×C4×C13
Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC23×D4×C13C4
LCSG ▷ C24 ▷ C22 ▷ 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×#1462C2semidirect
3. C2×C13×#323C2semidirect
4. C13×#1326C2semidirect
5. C13×#1316C2semidirect
58. #11545C13direct (N × H)
119. #1462C2×C13semidirect
120. C2×#323C2×C13semidirect
121. #1326C2×C13semidirect
122. #1316C2×C13semidirect
351. C13#11545direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#24052
C13×#14622
C2×C13×#3232
C13×#13262
C13×#13162
#1154513