Finite Group Databasebeta

← C13×#10403 #15696742

Subgroups — C13×#10403 #15696742

Order 3328.

716 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2656C211yesmaximal, characteristic
2C13×#1874C212yesmaximal, complemented
3C2×C13×#327C212yesmaximal, complemented
4C13×#1442C211yesmaximal, characteristic, complemented
5C13×#1280C211yesmaximal, characteristic, complemented
6C2×C13×#121—21no—
7C2×C13×#121—21no—
8C2×C13×#121C2212yes—
9C22×C13×C4⋊C4C2211yescharacteristic
10C2×C13×#102—22no—
11C2×C13×C22⋊C8C2212yes—
12C13×#399—22no—
13C13×#392—22no—
14C2×C13×#95—21no—
15C2×C13×#95—21no—
16C2×C13×#95C2211yescharacteristic
17C2×C13×#95C2211yescharacteristic
18C13×#340—22no—
19C13×#327—24no—
20C22×D4×C13—22no—
21C22×D4×C13—21no—
22C22×D4×C13—21no—
23C22×D4×C13D412yes—
24C23×C4×C13—21no—
25C23×C4×C13—21no—
26C23×C4×C13D411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C23×C4×C13C2311yescharacteristic
29C22×C8×C13—22no—
30C13×#121—22no—
31C13×#121—22no—
32C13×#121—22no—
33C13×#121—22no—
34C13×#121—42no—
35C13×#121—42no—
36C13×#121—42no—
37C13×#121—42no—
38C2×C13×C4⋊C4—22no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4—42no—
42C2×C13×C4⋊C4D412yes—
43C2×C13×C22⋊C4—22no—
44C2×C13×C22⋊C4—22no—
45C2×C13×C22⋊C4—22no—
46C13×#102—44no—
47C13×C22⋊C8—22no—
48C13×C22⋊C8—22no—
49C13×#95—22no—
50C13×#95—21no—
51C13×#95—42no—
52C13×#95—42no—
53C13×#95D412yescomplemented
54#10403C1311yesmaximal, characteristic, direct product factor, Sylow
55C24×C13—22no—
56C24×C13C2×D411yescharacteristic
57C2×D4×C13—22no—
58C2×D4×C13—22no—
59C2×D4×C13—42no—
60C2×D4×C13—42no—
61C2×D4×C13—42no—
62C2×D4×C13—42no—
63C2×D4×C13—42no—
64C2×D4×C13—42no—
65C2×D4×C13—42no—
66C2×D4×C13—42no—
67C2×D4×C13—42no—
68C2×D4×C13—42no—
69C2×D4×C13—81no—
70C2×D4×C13—81no—
71C2×D4×C13—81no—
72C2×D4×C13—81no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—22no—
78C22×C4×C13—22no—
79C22×C4×C13—22no—
80C22×C4×C13—41no—
81C22×C4×C13—41no—
82C22×C4×C13—41no—
83C22×C4×C13—41no—
84C22×C4×C13—41no—
85C22×C4×C13—41no—
86C22×C4×C13—41no—
87C22×C4×C13—41no—
88C22×C4×C13—41no—
89C22×C4×C13—41no—
90C22×C4×C13—41no—
91C22×C4×C13—41no—
92C22×C4×C13—41no—
93C22×C4×C13—41no—
94C22×C4×C13—41no—
95C22×C4×C13—41no—
96C22×C4×C13—41no—
97C22×C4×C13—41no—
98C22×C4×C13D812yes—
99C22×C4×C13SD1612yes—
100C22×C4×C13C2×D412yes—
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13#4112yes—
103C22×C4×C13#4111yescharacteristic
104C2×C8×C13—42no—
105C2×C8×C13—42no—
106C2×C8×C13—42no—
107C13×C4⋊C4—24no—
108C13×C4⋊C4—22no—
109C13×C4⋊C4—22no—
110C13×C4⋊C4—42no—
111C13×C4⋊C4—42no—
112C13×C4⋊C4—42no—
113C13×C22⋊C4—44no—
114C13×C22⋊C4—44no—
115C13×C22⋊C4—42no—
116C13×C22⋊C4—42no—
117#2656C2×C1311yescharacteristic
118#1874C2×C1312yescomplemented
119C2×#327C2×C1312yescomplemented
120#1442C2×C1311yescharacteristic, complemented
121#1280C2×C1311yescharacteristic, complemented
122C23×C13—21no—
123C23×C13—21no—
124C23×C13—21no—
125C23×C13—21no—
126C23×C13—42no—
127C23×C13—42no—
128C23×C13—42no—
129C23×C13—42no—
130C23×C13—42no—
131C23×C13—42no—
132C23×C13—42no—
133C23×C13#12011yescharacteristic
134C23×C13#12111yescharacteristic
135C23×C13#12411yescharacteristic
136C23×C13C2×D811yescharacteristic
137C23×C13C2×SD1611yescharacteristic
138C23×C13AGL(1,ℤ/8)11yescharacteristic
139C23×C13AGL(1,ℤ/8)11yescharacteristic
140D4×C13—44no—
141D4×C13—82no—
142D4×C13—84no—
143D4×C13—84no—
144D4×C13—82no—
145D4×C13—82no—
146D4×C13—82no—
147D4×C13—82no—
148C2×C4×C13—22no—
149C2×C4×C13—22no—
150C2×C4×C13—22no—
151C2×C4×C13—22no—
152C2×C4×C13—41no—
153C2×C4×C13—42no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—42no—
160C2×C4×C13—42no—
161C2×C4×C13—42no—
162C2×C4×C13—42no—
163C2×C4×C13—42no—
164C2×C4×C13—42no—
165C2×C4×C13—42no—
166C2×C4×C13—42no—
167C2×C4×C13—42no—
168C2×C4×C13—42no—
169C2×C4×C13—42no—
170C2×C4×C13—81no—
171C2×C4×C13—81no—
172C2×C4×C13—81no—
173C2×C4×C13—81no—
174C2×C4×C13—81no—
175C2×C4×C13—81no—
176C2×C4×C13—81no—
177C2×C4×C13—81no—
178C2×C4×C13—81no—
179C2×C4×C13—81no—
180C2×C4×C13#12112yes—
181C2×C4×C13#12312yes—
182C8×C13—82no—
183C2×#121—21no—
184C2×#121—21no—
185C2×#121C22×C1312yes—
186C22×C4⋊C4C22×C1311yescharacteristic
187C2×#102—22no—
188C2×C22⋊C8C22×C1312yes—
189#399—22no—
190#392—22no—
191C2×#95—21no—
192C2×#95—21no—
193C2×#95C22×C1311yescharacteristic
194C2×#95C22×C1311yescharacteristic
195#340—22no—
196#327—24no—
197C22×C13—21no—
198C22×C13—21no—
199C22×C13—21no—
200C22×C13—21no—
201C22×C13—21no—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13—21no—
205C22×C13—21no—
206C22×C13—21no—
207C22×C13—21no—
208C22×C13—21no—
209C22×C13—82no—
210C22×C13—82no—
211C22×C13—82no—
212C22×C13—82no—
213C22×C13—82no—
214C22×C13—82no—
215C22×C13—82no—
216C22×C13#39411yescharacteristic
217C22×C13#44711yescharacteristic
218C22×C13#45011yescharacteristic
219C22×C13#45411yescharacteristic
220C22×C13#45511yescharacteristic
221C22×C13B(4,𝔽2)11yescharacteristic
222C22×C13#45811yescharacteristic
223C22×C13#45911yescharacteristic
224C22×C13#46011yescharacteristic
225C22×C13#48611yescharacteristic
226C22×C13#49011yescharacteristic
227C4×C13—22no—
228C4×C13—22no—
229C4×C13—42no—
230C4×C13—42no—
231C4×C13—82no—
232C4×C13—82no—
233C4×C13—82no—
234C22×D4—22no—
235C22×D4—21no—
236C22×D4—21no—
237C22×D4D4×C1312yes—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4D4×C1311yescharacteristic
241C23×C4D4×C1311yescharacteristic
242C23×C4C23×C1311yescharacteristic
243C22×C8—22no—
244#121—22no—
245#121—22no—
246#121—22no—
247#121—22no—
248#121—42no—
249#121—42no—
250#121—42no—
251#121—42no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—42no—
256C2×C4⋊C4D4×C1312yes—
257C2×C22⋊C4—22no—
258C2×C22⋊C4—22no—
259C2×C22⋊C4—22no—
260#102—44no—
261C22⋊C8—22no—
262C22⋊C8—22no—
263#95—22no—
264#95—21no—
265#95—42no—
266#95—42no—
267#95D4×C1312yescomplemented
268C2×C13—21no—
269C2×C13—21no—
270C2×C13—21no—
271C2×C13—21no—
272C2×C13—162no—
273C2×C13#159811yescharacteristic
274C2×C13#160111yescharacteristic
275C2×C13#160711yescharacteristic
276C2×C13#161611yescharacteristic
277C2×C13#204011yescharacteristic
278C2×C13#204111yescharacteristic
279C2×C13#204411yescharacteristic
280C24—22no—
281C24C2×D4×C1311yescharacteristic
282C2×D4—22no—
283C2×D4—22no—
284C2×D4—42no—
285C2×D4—42no—
286C2×D4—42no—
287C2×D4—42no—
288C2×D4—42no—
289C2×D4—42no—
290C2×D4—42no—
291C2×D4—42no—
292C2×D4—42no—
293C2×D4—42no—
294C2×D4—81no—
295C2×D4—81no—
296C2×D4—81no—
297C2×D4—81no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4C13×D812yes—
324C22×C4C13×SD1612yes—
325C22×C4C2×D4×C1312yes—
326C22×C4C2×D4×C1311yescharacteristic
327C22×C4C13×#4112yes—
328C22×C4C13×#4111yescharacteristic
329C2×C8—42no—
330C2×C8—42no—
331C2×C8—42no—
332C4⋊C4—24no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—42no—
336C4⋊C4—42no—
337C4⋊C4—42no—
338C22⋊C4—44no—
339C22⋊C4—44no—
340C22⋊C4—42no—
341C22⋊C4—42no—
342C13#1040311yescharacteristic, direct product factor, Sylow
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—42no—
348C23—42no—
349C23—42no—
350C23—42no—
351C23—42no—
352C23—42no—
353C23—42no—
354C23C13×#12011yescharacteristic
355C23C13×#12111yescharacteristic
356C23C13×#12411yescharacteristic
357C23C2×C13×D811yescharacteristic
358C23C2×C13×SD1611yescharacteristic
359C23C13×AGL(1,ℤ/8)11yescharacteristic
360C23C13×AGL(1,ℤ/8)11yescharacteristic
361D4—44no—
362D4—82no—
363D4—84no—
364D4—84no—
365D4—82no—
366D4—82no—
367D4—82no—
368D4—82no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4C13×#12112yes—
402C2×C4C13×#12312yes—
403C8—82no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—82no—
417C22—82no—
418C22—82no—
419C22—82no—
420C22—82no—
421C22—82no—
422C22—82no—
423C22C13×#39411yescharacteristic
424C22C13×#44711yescharacteristic
425C22C13×#45011yescharacteristic
426C22C13×#45411yescharacteristic
427C22C13×#45511yescharacteristic
428C22C13×B(4,𝔽2)11yescharacteristic
429C22C13×#45811yescharacteristic
430C22C13×#45911yescharacteristic
431C22C13×#46011yescharacteristic
432C22C13×#48611yescharacteristic
433C22C13×#49011yescharacteristic
434C4—22no—
435C4—22no—
436C4—42no—
437C4—42no—
438C4—82no—
439C4—82no—
440C4—82no—
441C2—21no—
442C2—21no—
443C2—21no—
444C2—21no—
445C2—162no—
446C2C13×#159811yescharacteristic
447C2C13×#160111yescharacteristic
448C2C13×#160711yescharacteristic
449C2C13×#161611yescharacteristic
450C2C13×#204011yescharacteristic
451C2C13×#204111yescharacteristic
452C2C13×#204411yescharacteristic
subgroupG/H
center, socleC23×C13#120
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC13×#2656C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#1874C2semidirect
3. C2×C13×#327C2semidirect
4. C13×#1442C2semidirect
5. C13×#1280C2semidirect
53. C13×#95D4semidirect
54. #10403C13direct (N × H)
118. #1874C2×C13semidirect
119. C2×#327C2×C13semidirect
120. #1442C2×C13semidirect
121. #1280C2×C13semidirect
267. #95D4×C13semidirect
342. C13#10403direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26562
C13×#18742
C2×C13×#3272
C13×#14422
C13×#12802
#1040313