Finite Group Databasebeta

← C13×#13219 #15699558

Subgroups — C13×#13219 #15699558

Order 3328.

624 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2534C211yesmaximal, characteristic
2C2×C13×#352C212yesmaximal, complemented
3C2×C13×AΣL(1,𝔽16)C212yesmaximal
4C13×#1799C211yesmaximal, characteristic, complemented
5C4×C13×#100C211yesmaximal, characteristic, complemented
6C2×C13×#123C2211yescharacteristic
7C2×C13×#120C2211yescharacteristic
8C2×C4×D4×C13C2211yescharacteristic
9C22×C13×C22⋊C4C411yescharacteristic, complemented
10C2×C13×#100C2212yes—
11C2×C13×#99C2212yes—
12C4×C13×M16—21no—
13C13×#396—21no—
14C13×#394—21no—
15C13×#388—21no—
16C13×#386—21no—
17C13×#381C411yescharacteristic, complemented
18C13×#380—21no—
19C13×#380C411yescharacteristic, complemented
20C13×#379C411yescharacteristic, complemented
21C13×#352—24no—
22C13×AΣL(1,𝔽16)—24no—
23C13×#343—21no—
24C13×#342—21no—
25C25×C13C2×C411yescharacteristic
26C22×D4×C13—21no—
27C22×D4×C13C2311yescharacteristic
28C23×C4×C13C2×C411yescharacteristic
29C23×C4×C13C2×C411yescharacteristic
30C23×C4×C13D411yescharacteristic
31C2×C13×M16—22no—
32C13×#123—22no—
33C13×#123—22no—
34C13×#120—22no—
35C13×#120—22no—
36C4×D4×C13—41no—
37C4×D4×C13—41no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4—41no—
41C2×C13×C4⋊C4D411yescharacteristic
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—22no—
48C2×C13×C22⋊C4—21no—
49C2×C13×C22⋊C4—41no—
50C2×C13×C22⋊C4—41no—
51C2×C13×C22⋊C4C2×C411yescharacteristic
52C2×C13×C22⋊C4C2×C411yescharacteristic
53C2×C13×C22⋊C4C2×C411yescharacteristic
54C2×C13×C22⋊C4D411yescharacteristic
55C2×C42×C13D411yescharacteristic
56C13×#100—22no—
57C13×#100D414yes—
58C13×#99—22no—
59C13×#99—22no—
60C13×#97—41no—
61C4×C8×C13—41no—
62C13×#95—21no—
63C13×#95—21no—
64C13×#95—21no—
65C13×#95—41no—
66#13219C1311yesmaximal, characteristic, direct product factor, Sylow
67C24×C13—21no—
68C24×C13—22no—
69C24×C13—41no—
70C24×C13—42no—
71C24×C13—41no—
72C24×C13—81no—
73C24×C13C22×C411yescharacteristic
74C24×C13C2×D411yescharacteristic
75C2×D4×C13—41no—
76C2×D4×C13—41no—
77C2×D4×C13—42no—
78C2×D4×C13—41no—
79C2×D4×C13—41no—
80C2×D4×C13—81no—
81C2×D4×C13C2×D412yes—
82C2×D4×C13#4112yes—
83C22×C4×C13—21no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—22no—
91C22×C4×C13—41no—
92C22×C4×C13—41no—
93C22×C4×C13—42no—
94C22×C4×C13—81no—
95C22×C4×C13—81no—
96C22×C4×C13C22⋊C411yescharacteristic
97C22×C4×C13C22⋊C411yescharacteristic
98C22×C4×C13C22⋊C411yescharacteristic
99C22×C4×C13C22⋊C411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
101C13×M16—24no—
102C13×M16—42no—
103C2×C8×C13—42no—
104C13×C4⋊C4—41no—
105C13×C4⋊C4—42no—
106C13×C4⋊C4—81no—
107C13×C4⋊C4—82no—
108C13×C22⋊C4—22no—
109C13×C22⋊C4—22no—
110C13×C22⋊C4—41no—
111C13×C22⋊C4—41no—
112C13×C22⋊C4—42no—
113C13×C22⋊C4—42no—
114C13×C22⋊C4—41no—
115C13×C22⋊C4—41no—
116C13×C22⋊C4—41no—
117C13×C22⋊C4—41no—
118C13×C22⋊C4—42no—
119C13×C22⋊C4—42no—
120C13×C22⋊C4—42no—
121C13×C22⋊C4—81no—
122C42×C13—21no—
123C42×C13—21no—
124#2534C2×C1311yescharacteristic
125C2×#352C2×C1312yescomplemented
126C2×AΣL(1,𝔽16)C2×C1312yes—
127#1799C2×C1311yescharacteristic, complemented
128C4×#100C2×C1311yescharacteristic, complemented
129C23×C13—21no—
130C23×C13—21no—
131C23×C13—21no—
132C23×C13—21no—
133C23×C13—22no—
134C23×C13—41no—
135C23×C13—41no—
136C23×C13—41no—
137C23×C13—41no—
138C23×C13—41no—
139C23×C13—41no—
140C23×C13—41no—
141C23×C13—42no—
142C23×C13—41no—
143C23×C13—41no—
144C23×C13—41no—
145C23×C13—42no—
146C23×C13—82no—
147C23×C13—84no—
148C23×C13—84no—
149C23×C13—82no—
150C23×C13C2×C22⋊C411yescharacteristic
151C23×C13C4×D412yes—
152C23×C13#12411yescharacteristic
153C23×C13#12711yescharacteristic
154D4×C13—42no—
155D4×C13—42no—
156D4×C13—82no—
157D4×C13—82no—
158C2×C4×C13—21no—
159C2×C4×C13—21no—
160C2×C4×C13—21no—
161C2×C4×C13—21no—
162C2×C4×C13—21no—
163C2×C4×C13—41no—
164C2×C4×C13—42no—
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—81no—
178C2×C4×C13—81no—
179C2×C4×C13—81no—
180C2×C4×C13—82no—
181C2×C4×C13—82no—
182C2×C4×C13—82no—
183C2×C4×C13—82no—
184C2×C4×C13#9911yescharacteristic
185C2×C4×C13#9911yescharacteristic
186C2×C4×C13#12112yes—
187C8×C13—44no—
188C2×#123C22×C1311yescharacteristic
189C2×#120C22×C1311yescharacteristic
190C2×C4×D4C22×C1311yescharacteristic
191C22×C22⋊C4C4×C1311yescharacteristic, complemented
192C2×#100C22×C1312yes—
193C2×#99C22×C1312yes—
194C4×M16—21no—
195#396—21no—
196#394—21no—
197#388—21no—
198#386—21no—
199#381C4×C1311yescharacteristic, complemented
200#380—21no—
201#380C4×C1311yescharacteristic, complemented
202#379C4×C1311yescharacteristic, complemented
203#352—24no—
204AΣL(1,𝔽16)—24no—
205#343—21no—
206#342—21no—
207C22×C13—21no—
208C22×C13—21no—
209C22×C13—21no—
210C22×C13—22no—
211C22×C13—21no—
212C22×C13—41no—
213C22×C13—41no—
214C22×C13—42no—
215C22×C13—42no—
216C22×C13—42no—
217C22×C13—42no—
218C22×C13—41no—
219C22×C13—41no—
220C22×C13—41no—
221C22×C13—41no—
222C22×C13—42no—
223C22×C13—81no—
224C22×C13—81no—
225C22×C13—81no—
226C22×C13—84no—
227C22×C13—84no—
228C22×C13—81no—
229C22×C13—81no—
230C22×C13#39011yescharacteristic
231C22×C13C2×#9911yescharacteristic
232C22×C13#41011yescharacteristic
233C4×C13—21no—
234C4×C13—21no—
235C4×C13—22no—
236C4×C13—41no—
237C4×C13—41no—
238C4×C13—41no—
239C4×C13—81no—
240C4×C13—81no—
241C4×C13—81no—
242C4×C13—162no—
243C25C2×C4×C1311yescharacteristic
244C22×D4—21no—
245C22×D4C23×C1311yescharacteristic
246C23×C4C2×C4×C1311yescharacteristic
247C23×C4C2×C4×C1311yescharacteristic
248C23×C4D4×C1311yescharacteristic
249C2×M16—22no—
250#123—22no—
251#123—22no—
252#120—22no—
253#120—22no—
254C4×D4—41no—
255C4×D4—41no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—41no—
259C2×C4⋊C4D4×C1311yescharacteristic
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—22no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—41no—
268C2×C22⋊C4—41no—
269C2×C22⋊C4C2×C4×C1311yescharacteristic
270C2×C22⋊C4C2×C4×C1311yescharacteristic
271C2×C22⋊C4C2×C4×C1311yescharacteristic
272C2×C22⋊C4D4×C1311yescharacteristic
273C2×C42D4×C1311yescharacteristic
274#100—22no—
275#100D4×C1314yes—
276#99—22no—
277#99—22no—
278#97—41no—
279C4×C8—41no—
280#95—21no—
281#95—21no—
282#95—21no—
283#95—41no—
284C2×C13—21no—
285C2×C13—21no—
286C2×C13—41no—
287C2×C13—42no—
288C2×C13—41no—
289C2×C13—82no—
290C2×C13#196411yescharacteristic
291C2×C13#212011yescharacteristic
292C2×C13#212111yescharacteristic
293C24—21no—
294C24—22no—
295C24—41no—
296C24—42no—
297C24—41no—
298C24—81no—
299C24C22×C4×C1311yescharacteristic
300C24C2×D4×C1311yescharacteristic
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—42no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—81no—
307C2×D4C2×D4×C1312yes—
308C2×D4C13×#4112yes—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—22no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—42no—
320C22×C4—81no—
321C22×C4—81no—
322C22×C4C13×C22⋊C411yescharacteristic
323C22×C4C13×C22⋊C411yescharacteristic
324C22×C4C13×C22⋊C411yescharacteristic
325C22×C4C13×C22⋊C411yescharacteristic
326C22×C4C2×D4×C1311yescharacteristic
327M16—24no—
328M16—42no—
329C2×C8—42no—
330C4⋊C4—41no—
331C4⋊C4—42no—
332C4⋊C4—81no—
333C4⋊C4—82no—
334C22⋊C4—22no—
335C22⋊C4—22no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—42no—
339C22⋊C4—42no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—42no—
345C22⋊C4—42no—
346C22⋊C4—42no—
347C22⋊C4—81no—
348C42—21no—
349C42—21no—
350C13#1321911yescharacteristic, direct product factor, Sylow
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—22no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23—42no—
364C23—42no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—82no—
369C23—84no—
370C23—84no—
371C23—82no—
372C23C2×C13×C22⋊C411yescharacteristic
373C23C4×D4×C1312yes—
374C23C13×#12411yescharacteristic
375C23C13×#12711yescharacteristic
376D4—42no—
377D4—42no—
378D4—82no—
379D4—82no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—41no—
386C2×C4—42no—
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—41no—
398C2×C4—41no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—82no—
403C2×C4—82no—
404C2×C4—82no—
405C2×C4—82no—
406C2×C4C13×#9911yescharacteristic
407C2×C4C13×#9911yescharacteristic
408C2×C4C13×#12112yes—
409C8—44no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—22no—
414C22—21no—
415C22—41no—
416C22—41no—
417C22—42no—
418C22—42no—
419C22—42no—
420C22—42no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—42no—
426C22—81no—
427C22—81no—
428C22—81no—
429C22—84no—
430C22—84no—
431C22—81no—
432C22—81no—
433C22C13×#39011yescharacteristic
434C22C2×C13×#9911yescharacteristic
435C22C13×#41011yescharacteristic
436C4—21no—
437C4—21no—
438C4—22no—
439C4—41no—
440C4—41no—
441C4—41no—
442C4—81no—
443C4—81no—
444C4—81no—
445C4—162no—
446C2—21no—
447C2—21no—
448C2—41no—
449C2—42no—
450C2—41no—
451C2—82no—
452C2C13×#196411yescharacteristic
453C2C13×#212011yescharacteristic
454C2C13×#212111yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC24C22×C4×C13
Frattini, cosocleC22×D4C23×C13
prime radicalC2×C13×#120C22
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C4×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#352C2semidirect
4. C13×#1799C2semidirect
5. C4×C13×#100C2semidirect
9. C22×C13×C22⋊C4C4semidirect
17. C13×#381C4semidirect
19. C13×#380C4semidirect
20. C13×#379C4semidirect
66. #13219C13direct (N × H)
125. C2×#352C2×C13semidirect
127. #1799C2×C13semidirect
128. C4×#100C2×C13semidirect
191. C22×C22⋊C4C4×C13semidirect
199. #381C4×C13semidirect
201. #380C4×C13semidirect
202. #379C4×C13semidirect
350. C13#13219direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25342
C2×C13×#3522
C2×C13×AΣL(1,𝔽16)2
C13×#17992
C4×C13×#1002
#1321913