Finite Group Databasebeta

← C13×#13232 #15699571

Subgroups — C13×#13232 #15699571

Order 3328.

448 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3057C211yesmaximal, characteristic
2C13×#2135C211yesmaximal, characteristic, complemented
3C13×#2134C211yesmaximal, characteristic
4C13×#2123C211yesmaximal, characteristic, complemented
5C13×#2122C211yesmaximal, characteristic
6C13×#1813C211yesmaximal, characteristic, complemented
7C13×#1757C211yesmaximal, characteristic, complemented
8C22×C13×SD16C411yescharacteristic, complemented
9C2×C13×#131C2211yescharacteristic
10C13×#536C2211yescharacteristic
11C13×#535C2211yescharacteristic
12C13×#468—21no—
13C13×#468—21no—
14C13×#465—21no—
15C13×#465—21no—
16C2×C13×#108—21no—
17C13×#427C411yescharacteristic, complemented
18C13×#419C411yescharacteristic, complemented
19C13×#418C411yescharacteristic, complemented
20C13×#413C2211yescharacteristic
21C13×#413C2211yescharacteristic
22C13×#413C2211yescharacteristic
23C13×#410C2211yescharacteristic
24C13×#405—21no—
25C13×#356—22no—
26C13×#355—22no—
27C13×#352—22no—
28C13×AΣL(1,𝔽16)—22no—
29C13×#344—21no—
30C13×#338—21no—
31C2×C13×#41C2311yescharacteristic
32C22×Q8×C13C2×C411yescharacteristic
33C22×D4×C13C2×C411yescharacteristic
34C2×C13×SD16—21no—
35C2×C13×SD16—21no—
36C2×C13×SD16—41no—
37C2×C13×SD16—41no—
38C13×#131—41no—
39C13×#131—41no—
40C2×C13×M16—21no—
41C2×C13×M16—21no—
42C2×C13×M16—21no—
43C2×C13×M16C2×C411yescharacteristic
44C2×C13×M16D411yescharacteristic
45C2×C13×M16D411yescharacteristic
46C22×C8×C13C2×C411yescharacteristic
47C22×C8×C13D411yescharacteristic
48C22×C8×C13D411yescharacteristic
49C13×C4⋊Q8—21no—
50C13×#127—21no—
51C13×#124—21no—
52C13×#124—21no—
53C13×#123—21no—
54C13×#123—21no—
55C13×C22⋊Q8—21no—
56C13×C22⋊Q8—21no—
57C13×#121—21no—
58C13×#121—21no—
59C13×#120—21no—
60C13×#120—21no—
61C13×#117—21no—
62C13×#117C2×C411yescharacteristic
63C13×#117C2×C411yescharacteristic
64C13×#108—41no—
65C13×#108—41no—
66C13×#107—21no—
67C13×#106—21no—
68C13×#103—21no—
69C13×#103—21no—
70C13×#102—21no—
71C13×#102—21no—
72C13×#101—21no—
73C13×#101—21no—
74C13×#101D412yes—
75C13×#100—21no—
76C13×#100—21no—
77C13×#100—21no—
78C13×#99—21no—
79C13×#99D412yes—
80C13×#97—41no—
81C4×C8×C13—41no—
82#13232C1311yesmaximal, characteristic, direct product factor, Sylow
83C24×C13—21no—
84C13×#41—41no—
85C13×#41—41no—
86C2×Q8×C13—21no—
87C2×Q8×C13—21no—
88C2×Q8×C13—41no—
89C2×Q8×C13—41no—
90C2×Q8×C13C2×D411yescharacteristic
91C2×D4×C13—21no—
92C2×D4×C13—21no—
93C2×D4×C13—41no—
94C2×D4×C13—41no—
95C2×D4×C13—41no—
96C2×D4×C13—41no—
97C2×D4×C13C2×D411yescharacteristic
98C2×D4×C13#4111yescharacteristic
99C2×D4×C13#4111yescharacteristic
100C22×C4×C13—21no—
101C22×C4×C13C22×C411yescharacteristic
102C22×C4×C13C2×D411yescharacteristic
103C22×C4×C13C2×D411yescharacteristic
104C13×SD16—42no—
105C13×SD16—41no—
106C13×SD16—41no—
107C13×M16—22no—
108C13×M16—41no—
109C13×M16—41no—
110C13×M16—41no—
111C13×M16—41no—
112C13×M16—41no—
113C13×M16—41no—
114C13×M16—41no—
115C13×M16—41no—
116C2×C8×C13—21no—
117C2×C8×C13—21no—
118C2×C8×C13—21no—
119C2×C8×C13—21no—
120C2×C8×C13—21no—
121C2×C8×C13—21no—
122C2×C8×C13—41no—
123C2×C8×C13—41no—
124C2×C8×C13—41no—
125C2×C8×C13C22⋊C411yescharacteristic
126C2×C8×C13C22⋊C411yescharacteristic
127C2×C8×C13C22⋊C411yescharacteristic
128C2×C8×C13C22⋊C411yescharacteristic
129C13×C4⋊C4—21no—
130C13×C4⋊C4—21no—
131C13×C4⋊C4—41no—
132C13×C4⋊C4—41no—
133C13×C4⋊C4—41no—
134C13×C22⋊C4—21no—
135C13×C22⋊C4—21no—
136C13×C22⋊C4—22no—
137C13×C22⋊C4—41no—
138C13×C22⋊C4—41no—
139C13×C22⋊C4—41no—
140C13×C22⋊C4—41no—
141C42×C13—21no—
142C42×C13—21no—
143C42×C13—41no—
144#3057C2×C1311yescharacteristic
145#2135C2×C1311yescharacteristic, complemented
146#2134C2×C1311yescharacteristic
147#2123C2×C1311yescharacteristic, complemented
148#2122C2×C1311yescharacteristic
149#1813C2×C1311yescharacteristic, complemented
150#1757C2×C1311yescharacteristic, complemented
151C23×C13—41no—
152C23×C13—81no—
153C23×C13—161no—
154C23×C13C4×D411yescharacteristic
155C23×C13#12111yescharacteristic
156C23×C13#12411yescharacteristic
157Q8×C13—41no—
158Q8×C13—41no—
159Q8×C13—41no—
160Q8×C13—81no—
161D4×C13—41no—
162D4×C13—41no—
163D4×C13—41no—
164D4×C13—41no—
165D4×C13—41no—
166D4×C13—81no—
167D4×C13—161no—
168D4×C13—161no—
169C2×C4×C13—21no—
170C2×C4×C13—21no—
171C2×C4×C13—21no—
172C2×C4×C13—21no—
173C2×C4×C13—21no—
174C2×C4×C13—21no—
175C2×C4×C13—42no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13—41no—
179C2×C4×C13—81no—
180C2×C4×C13C2×C22⋊C411yescharacteristic
181C2×C4×C13C4×D411yescharacteristic
182C2×C4×C13#12111yescharacteristic
183C2×C4×C13#12711yescharacteristic
184C8×C13—21no—
185C8×C13—21no—
186C8×C13—21no—
187C8×C13—42no—
188C8×C13—81no—
189C8×C13—81no—
190C8×C13#9911yescharacteristic
191C8×C13#9911yescharacteristic
192C22×SD16C4×C1311yescharacteristic, complemented
193C2×#131C22×C1311yescharacteristic
194#536C22×C1311yescharacteristic
195#535C22×C1311yescharacteristic
196#468—21no—
197#468—21no—
198#465—21no—
199#465—21no—
200C2×#108—21no—
201#427C4×C1311yescharacteristic, complemented
202#419C4×C1311yescharacteristic, complemented
203#418C4×C1311yescharacteristic, complemented
204#413C22×C1311yescharacteristic
205#413C22×C1311yescharacteristic
206#413C22×C1311yescharacteristic
207#410C22×C1311yescharacteristic
208#405—21no—
209#356—22no—
210#355—22no—
211#352—22no—
212AΣL(1,𝔽16)—22no—
213#344—21no—
214#338—21no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13—21no—
218C22×C13—41no—
219C22×C13—41no—
220C22×C13—41no—
221C22×C13—81no—
222C22×C13—81no—
223C22×C13—81no—
224C22×C13—162no—
225C22×C13#39011yescharacteristic
226C4×C13—21no—
227C4×C13—21no—
228C4×C13—21no—
229C4×C13—81no—
230C4×C13—81no—
231C4×C13—82no—
232C4×C13—81no—
233C4×C13C2×#9911yescharacteristic
234C4×C13#41011yescharacteristic
235C2×#41C23×C1311yescharacteristic
236C22×Q8C2×C4×C1311yescharacteristic
237C22×D4C2×C4×C1311yescharacteristic
238C2×SD16—21no—
239C2×SD16—21no—
240C2×SD16—41no—
241C2×SD16—41no—
242#131—41no—
243#131—41no—
244C2×M16—21no—
245C2×M16—21no—
246C2×M16—21no—
247C2×M16C2×C4×C1311yescharacteristic
248C2×M16D4×C1311yescharacteristic
249C2×M16D4×C1311yescharacteristic
250C22×C8C2×C4×C1311yescharacteristic
251C22×C8D4×C1311yescharacteristic
252C22×C8D4×C1311yescharacteristic
253C4⋊Q8—21no—
254#127—21no—
255#124—21no—
256#124—21no—
257#123—21no—
258#123—21no—
259C22⋊Q8—21no—
260C22⋊Q8—21no—
261#121—21no—
262#121—21no—
263#120—21no—
264#120—21no—
265#117—21no—
266#117C2×C4×C1311yescharacteristic
267#117C2×C4×C1311yescharacteristic
268#108—41no—
269#108—41no—
270#107—21no—
271#106—21no—
272#103—21no—
273#103—21no—
274#102—21no—
275#102—21no—
276#101—21no—
277#101—21no—
278#101D4×C1312yes—
279#100—21no—
280#100—21no—
281#100—21no—
282#99—21no—
283#99D4×C1312yes—
284#97—41no—
285C4×C8—41no—
286C2×C13—21no—
287C2×C13—41no—
288C2×C13—41no—
289C2×C13—41no—
290C2×C13—161no—
291C2×C13#196411yescharacteristic
292C24—21no—
293#41—41no—
294#41—41no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8C2×D4×C1311yescharacteristic
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4C2×D4×C1311yescharacteristic
307C2×D4C13×#4111yescharacteristic
308C2×D4C13×#4111yescharacteristic
309C22×C4—21no—
310C22×C4C22×C4×C1311yescharacteristic
311C22×C4C2×D4×C1311yescharacteristic
312C22×C4C2×D4×C1311yescharacteristic
313SD16—42no—
314SD16—41no—
315SD16—41no—
316M16—22no—
317M16—41no—
318M16—41no—
319M16—41no—
320M16—41no—
321M16—41no—
322M16—41no—
323M16—41no—
324M16—41no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—21no—
329C2×C8—21no—
330C2×C8—21no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8C13×C22⋊C411yescharacteristic
335C2×C8C13×C22⋊C411yescharacteristic
336C2×C8C13×C22⋊C411yescharacteristic
337C2×C8C13×C22⋊C411yescharacteristic
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C22⋊C4—21no—
344C22⋊C4—21no—
345C22⋊C4—22no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C42—21no—
351C42—21no—
352C42—41no—
353C13#1323211yescharacteristic, direct product factor, Sylow
354C23—41no—
355C23—81no—
356C23—161no—
357C23C4×D4×C1311yescharacteristic
358C23C13×#12111yescharacteristic
359C23C13×#12411yescharacteristic
360Q8—41no—
361Q8—41no—
362Q8—41no—
363Q8—81no—
364D4—41no—
365D4—41no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—81no—
370D4—161no—
371D4—161no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—81no—
383C2×C4C2×C13×C22⋊C411yescharacteristic
384C2×C4C4×D4×C1311yescharacteristic
385C2×C4C13×#12111yescharacteristic
386C2×C4C13×#12711yescharacteristic
387C8—21no—
388C8—21no—
389C8—21no—
390C8—42no—
391C8—81no—
392C8—81no—
393C8C13×#9911yescharacteristic
394C8C13×#9911yescharacteristic
395C22—21no—
396C22—21no—
397C22—21no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—162no—
405C22C13×#39011yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—81no—
410C4—81no—
411C4—82no—
412C4—81no—
413C4C2×C13×#9911yescharacteristic
414C4C13×#41011yescharacteristic
415C2—21no—
416C2—41no—
417C2—41no—
418C2—41no—
419C2—161no—
420C2C13×#196411yescharacteristic
subgroupG/H
center, socleC2×C13#1964
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×#41C23×C13
prime radicalC13×#535C22
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C13×#131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2135C2semidirect
4. C13×#2123C2semidirect
6. C13×#1813C2semidirect
7. C13×#1757C2semidirect
8. C22×C13×SD16C4semidirect
17. C13×#427C4semidirect
18. C13×#419C4semidirect
19. C13×#418C4semidirect
82. #13232C13direct (N × H)
145. #2135C2×C13semidirect
147. #2123C2×C13semidirect
149. #1813C2×C13semidirect
150. #1757C2×C13semidirect
192. C22×SD16C4×C13semidirect
201. #427C4×C13semidirect
202. #419C4×C13semidirect
203. #418C4×C13semidirect
353. C13#13232direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#30572
C13×#21352
C13×#21342
C13×#21232
C13×#21222
C13×#18132
C13×#17572
#1323213