Finite Group Databasebeta

← C13×#32977 #15719316

Subgroups — C13×#32977 #15719316

Order 3328.

1382 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C13×H(5,𝔽2)C211yesmaximal, characteristic
2C13×#2579C213yesmaximal, complemented
3C13×#1867C213yesmaximal, complemented
4C13×#1867C213yesmaximal, complemented
5C13×#1799C213yesmaximal, complemented
6C13×#1790C211yesmaximal, characteristic
7C13×#1790C211yesmaximal, characteristic
8C2×C13×H(5,𝔽2)C2211yescharacteristic
9C13×#520—23no—
10C13×#518—23no—
11C13×#518C2213yes—
12C4×C13×#41—23no—
13C2×C4×D4×C13—23no—
14C2×C4×D4×C13C2213yes—
15C22×C13×C4⋊C4C2211yescharacteristic, complemented
16C2×C13×#99C2213yes—
17C2×C13×#99C2213yes—
18C13×#398—23no—
19C13×#396—23no—
20C13×#387—23no—
21C13×#386C2213yes—
22C13×#386C2213yes—
23C13×#385—23no—
24C13×#385C2213yescomplemented
25C13×#385C2213yescomplemented
26C13×#380C2213yescomplemented
27C13×#342C2216yescomplemented
28C13×H(5,𝔽2)—26no—
29C13×H(5,𝔽2)Q814yes—
30C2×C13×#41—23no—
31C22×D4×C13—23no—
32C22×D4×C13C2313yes—
33C23×C4×C13—21no—
34C23×C4×C13D413yes—
35C23×C4×C13C2311yescharacteristic
36C23×C4×C13C2311yescharacteristic
37C23×C4×C13C2311yescharacteristic
38C4×Q8×C13—21no—
39C4×Q8×C13—23no—
40C4×D4×C13—23no—
41C4×D4×C13—26no—
42C4×D4×C13—23no—
43C4×D4×C13—26no—
44C4×D4×C13—26no—
45C4×D4×C13—26no—
46C4×D4×C13—26no—
47C13×#117—26no—
48C13×#117—23no—
49C2×C13×C4⋊C4—23no—
50C2×C13×C4⋊C4—23no—
51C2×C13×C4⋊C4—23no—
52C2×C13×C4⋊C4—23no—
53C2×C13×C4⋊C4—23no—
54C2×C13×C4⋊C4—23no—
55C2×C13×C4⋊C4D413yes—
56C2×C13×C22⋊C4—23no—
57C2×C13×C22⋊C4—23no—
58C2×C13×C22⋊C4—23no—
59C2×C13×C22⋊C4—23no—
60C2×C13×C22⋊C4D413yes—
61C2×C13×C22⋊C4C2313yes—
62C2×C13×C22⋊C4C2313yes—
63C2×C13×C22⋊C4C2313yes—
64C2×C42×C13—23no—
65C2×C42×C13D413yes—
66C13×#99—26no—
67C13×#99—26no—
68C13×#95—23no—
69C13×#95—23no—
70C13×#95—23no—
71C13×#95—23no—
72C13×#95—23no—
73#32977C1311yesmaximal, characteristic, direct product factor, Sylow
74C24×C13—21no—
75C24×C13C2×D413yes—
76C24×C13C2411yescharacteristic
77C13×#41—212no—
78C13×#41—212no—
79C2×Q8×C13—21no—
80C2×D4×C13—23no—
81C2×D4×C13—212no—
82C2×D4×C13—212no—
83C2×D4×C13—26no—
84C2×D4×C13—26no—
85C2×D4×C13C2×Q816yes—
86C2×D4×C13#4116yes—
87C22×C4×C13—23no—
88C22×C4×C13—23no—
89C22×C4×C13—23no—
90C22×C4×C13—23no—
91C22×C4×C13—23no—
92C22×C4×C13—23no—
93C22×C4×C13—23no—
94C22×C4×C13—23no—
95C22×C4×C13—23no—
96C22×C4×C13—42no—
97C22×C4×C13—81no—
98C22×C4×C13—81no—
99C22×C4×C13—83no—
100C22×C4×C13—82no—
101C22×C4×C13C2×D413yes—
102C22×C4×C13C2×D413yes—
103C22×C4×C13C2×D413yes—
104C22×C4×C13C2×D413yes—
105C22×C4×C13C2×D413yes—
106C13×C4⋊C4—23no—
107C13×C4⋊C4—23no—
108C13×C4⋊C4—26no—
109C13×C4⋊C4—46no—
110C13×C4⋊C4—41no—
111C13×C4⋊C4—43no—
112C13×C4⋊C4—83no—
113C13×C4⋊C4—83no—
114C13×C22⋊C4—26no—
115C13×C22⋊C4—26no—
116C13×C22⋊C4—26no—
117C13×C22⋊C4—26no—
118C13×C22⋊C4—26no—
119C13×C22⋊C4—46no—
120C13×C22⋊C4—83no—
121C42×C13—26no—
122C42×C13—23no—
123C42×C13—23no—
124C4×H(5,𝔽2)C2×C1311yescharacteristic
125#2579C2×C1313yescomplemented
126#1867C2×C1313yescomplemented
127#1867C2×C1313yescomplemented
128#1799C2×C1313yescomplemented
129#1790C2×C1311yescharacteristic
130#1790C2×C1311yescharacteristic
131C23×C13—24no—
132C23×C13—23no—
133C23×C13—23no—
134C23×C13—41no—
135C23×C13—41no—
136C23×C13—43no—
137C23×C13—43no—
138C23×C13—81no—
139C23×C13—81no—
140C23×C13C22⋊Q816yes—
141C23×C13C22×D413yes—
142C23×C13C22×Q811yescharacteristic
143C23×C13C2×#4113yes—
144Q8×C13—24no—
145D4×C13—212no—
146D4×C13—212no—
147D4×C13—212no—
148C2×C4×C13—212no—
149C2×C4×C13—23no—
150C2×C4×C13—23no—
151C2×C4×C13—26no—
152C2×C4×C13—23no—
153C2×C4×C13—23no—
154C2×C4×C13—43no—
155C2×C4×C13—43no—
156C2×C4×C13—46no—
157C2×C4×C13—43no—
158C2×C4×C13—41no—
159C2×C4×C13—43no—
160C2×C4×C13—43no—
161C2×C4×C13—43no—
162C2×C4×C13—43no—
163C2×C4×C13—43no—
164C2×C4×C13—43no—
165C2×C4×C13—43no—
166C2×C4×C13—43no—
167C2×C4×C13—41no—
168C2×C4×C13—43no—
169C2×C4×C13—43no—
170C2×C4×C13—83no—
171C2×C4×C13—83no—
172C2×C4×C13—83no—
173C2×C4×C13#12011yescharacteristic
174C2×C4×C13#12013yes—
175C2×C4×C13C22⋊Q816yes—
176C2×H(5,𝔽2)C22×C1311yescharacteristic
177#520—23no—
178#518—23no—
179#518C22×C1313yes—
180C4×#41—23no—
181C2×C4×D4—23no—
182C2×C4×D4C22×C1313yes—
183C22×C4⋊C4C22×C1311yescharacteristic, complemented
184C2×#99C22×C1313yes—
185C2×#99C22×C1313yes—
186#398—23no—
187#396—23no—
188#387—23no—
189#386C22×C1313yes—
190#386C22×C1313yes—
191#385—23no—
192#385C22×C1313yescomplemented
193#385C22×C1313yescomplemented
194#380C22×C1313yescomplemented
195#342C22×C1316yescomplemented
196C22×C13—23no—
197C22×C13—23no—
198C22×C13—26no—
199C22×C13—41no—
200C22×C13—43no—
201C22×C13—46no—
202C22×C13—43no—
203C22×C13—43no—
204C22×C13—83no—
205C22×C13—84no—
206C22×C13C2×#12011yescharacteristic
207C22×C13C2×C22⋊Q813yes—
208C22×C13#52513yes—
209C4×C13—26no—
210C4×C13—21no—
211C4×C13—23no—
212C4×C13—42no—
213C4×C13—43no—
214C4×C13—43no—
215C4×C13—83no—
216C4×C13—83no—
217C4×C13—81no—
218H(5,𝔽2)—26no—
219H(5,𝔽2)Q8×C1314yes—
220C2×#41—23no—
221C22×D4—23no—
222C22×D4C23×C1313yes—
223C23×C4—21no—
224C23×C4D4×C1313yes—
225C23×C4C23×C1311yescharacteristic
226C23×C4C23×C1311yescharacteristic
227C23×C4C23×C1311yescharacteristic
228C4×Q8—21no—
229C4×Q8—23no—
230C4×D4—23no—
231C4×D4—26no—
232C4×D4—23no—
233C4×D4—26no—
234C4×D4—26no—
235C4×D4—26no—
236C4×D4—26no—
237#117—26no—
238#117—23no—
239C2×C4⋊C4—23no—
240C2×C4⋊C4—23no—
241C2×C4⋊C4—23no—
242C2×C4⋊C4—23no—
243C2×C4⋊C4—23no—
244C2×C4⋊C4—23no—
245C2×C4⋊C4D4×C1313yes—
246C2×C22⋊C4—23no—
247C2×C22⋊C4—23no—
248C2×C22⋊C4—23no—
249C2×C22⋊C4—23no—
250C2×C22⋊C4D4×C1313yes—
251C2×C22⋊C4C23×C1313yes—
252C2×C22⋊C4C23×C1313yes—
253C2×C22⋊C4C23×C1313yes—
254C2×C42—23no—
255C2×C42D4×C1313yes—
256#99—26no—
257#99—26no—
258#95—23no—
259#95—23no—
260#95—23no—
261#95—23no—
262#95—23no—
263C2×C13—23no—
264C2×C13—23no—
265C2×C13—46no—
266C2×C13#284811yescharacteristic
267C2×C13#302511yescharacteristic
268C2×C13#302611yescharacteristic
269C24—21no—
270C24C2×D4×C1313yes—
271C24C24×C1311yescharacteristic
272#41—212no—
273#41—212no—
274C2×Q8—21no—
275C2×D4—23no—
276C2×D4—212no—
277C2×D4—212no—
278C2×D4—26no—
279C2×D4—26no—
280C2×D4C2×Q8×C1316yes—
281C2×D4C13×#4116yes—
282C22×C4—23no—
283C22×C4—23no—
284C22×C4—23no—
285C22×C4—23no—
286C22×C4—23no—
287C22×C4—23no—
288C22×C4—23no—
289C22×C4—23no—
290C22×C4—23no—
291C22×C4—42no—
292C22×C4—81no—
293C22×C4—81no—
294C22×C4—83no—
295C22×C4—82no—
296C22×C4C2×D4×C1313yes—
297C22×C4C2×D4×C1313yes—
298C22×C4C2×D4×C1313yes—
299C22×C4C2×D4×C1313yes—
300C22×C4C2×D4×C1313yes—
301C4⋊C4—23no—
302C4⋊C4—23no—
303C4⋊C4—26no—
304C4⋊C4—46no—
305C4⋊C4—41no—
306C4⋊C4—43no—
307C4⋊C4—83no—
308C4⋊C4—83no—
309C22⋊C4—26no—
310C22⋊C4—26no—
311C22⋊C4—26no—
312C22⋊C4—26no—
313C22⋊C4—26no—
314C22⋊C4—46no—
315C22⋊C4—83no—
316C42—26no—
317C42—23no—
318C42—23no—
319C13#3297711yescharacteristic, direct product factor, Sylow
320C23—24no—
321C23—23no—
322C23—23no—
323C23—41no—
324C23—41no—
325C23—43no—
326C23—43no—
327C23—81no—
328C23—81no—
329C23C13×C22⋊Q816yes—
330C23C22×D4×C1313yes—
331C23C22×Q8×C1311yescharacteristic
332C23C2×C13×#4113yes—
333Q8—24no—
334D4—212no—
335D4—212no—
336D4—212no—
337C2×C4—212no—
338C2×C4—23no—
339C2×C4—23no—
340C2×C4—26no—
341C2×C4—23no—
342C2×C4—23no—
343C2×C4—43no—
344C2×C4—43no—
345C2×C4—46no—
346C2×C4—43no—
347C2×C4—41no—
348C2×C4—43no—
349C2×C4—43no—
350C2×C4—43no—
351C2×C4—43no—
352C2×C4—43no—
353C2×C4—43no—
354C2×C4—43no—
355C2×C4—43no—
356C2×C4—41no—
357C2×C4—43no—
358C2×C4—43no—
359C2×C4—83no—
360C2×C4—83no—
361C2×C4—83no—
362C2×C4C13×#12011yescharacteristic
363C2×C4C13×#12013yes—
364C2×C4C13×C22⋊Q816yes—
365C22—23no—
366C22—23no—
367C22—26no—
368C22—41no—
369C22—43no—
370C22—46no—
371C22—43no—
372C22—43no—
373C22—83no—
374C22—84no—
375C22C2×C13×#12011yescharacteristic
376C22C2×C13×C22⋊Q813yes—
377C22C13×#52513yes—
378C4—21no—
379C4—23no—
380C4—26no—
381C4—42no—
382C4—43no—
383C4—43no—
384C4—83no—
385C4—83no—
386C4—81no—
387C2—23no—
388C2—23no—
389C2—46no—
390C2C13×#284811yescharacteristic
391C2C13×#302511yescharacteristic
392C2C13×#302611yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC24C24×C13
prime radicalC2×C13×H(5,𝔽2)C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2579C2semidirect
3. C13×#1867C2semidirect
4. C13×#1867C2semidirect
5. C13×#1799C2semidirect
15. C22×C13×C4⋊C4C22semidirect
24. C13×#385C22semidirect
25. C13×#385C22semidirect
26. C13×#380C22semidirect
27. C13×#342C22semidirect
73. #32977C13direct (N × H)
125. #2579C2×C13semidirect
126. #1867C2×C13semidirect
127. #1867C2×C13semidirect
128. #1799C2×C13semidirect
183. C22×C4⋊C4C22×C13semidirect
192. #385C22×C13semidirect
193. #385C22×C13semidirect
194. #380C22×C13semidirect
195. #342C22×C13semidirect
319. C13#32977direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C13×H(5,𝔽2)2
C13×#25792
C13×#18672
C13×#17992
C13×#17902
#3297713