Finite Group Databasebeta

← C13×#19060 #15705399

Subgroups — C13×#19060 #15705399

Order 3328.

822 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3553C211yesmaximal, characteristic
2C13×#3238C212yesmaximal, complemented
3C2×C13×#491C211yesmaximal, characteristic, complemented
4C13×#1664C214yesmaximal, complemented
5C13×#1663C212yesmaximal, complemented
6C13×#1662C212yesmaximal, complemented
7C13×#1534C211yesmaximal, characteristic, complemented
8C13×#1532C212yesmaximal, complemented
9C13×#564C2211yescharacteristic
10C13×#563C2212yes—
11C13×#562C2211yescharacteristic
12C13×#554—22no—
13C13×#553—22no—
14C13×#552—22no—
15C13×#541—22no—
16C13×#539—22no—
17C13×#539—22no—
18C2×C13×C4⋊Q8C2211yescharacteristic
19C13×#529C2212yes—
20C2×C13×#125C2211yescharacteristic
21C13×#501C2214yes—
22C13×#491—22no—
23C13×#491C2212yes—
24C13×#491C2212yes—
25C13×#489C2214yes—
26C13×#483—22no—
27C13×#480—22no—
28C13×#477—22no—
29C13×#476—22no—
30C13×#432C2212yes—
31C2×C13×#103—22no—
32C2×C13×#97C2211yescharacteristic
33C13×#330C2214yes—
34C13×#330C2212yes—
35C13×#330C2212yes—
36C13×#329C2214yes—
37C22×Q8×C13—21no—
38C22×C8×C13—21no—
39C13×C4⋊Q8—22no—
40C13×C4⋊Q8—22no—
41C13×C4⋊Q8—21no—
42C13×C4⋊Q8C2312yes—
43C13×#126—22no—
44C13×#126—22no—
45C13×#126—22no—
46C13×#126—22no—
47C13×#126—22no—
48C13×#125—22no—
49C13×#125—22no—
50C13×#125—22no—
51C13×#125—22no—
52C13×#125—22no—
53C13×#125—22no—
54C13×#125D412yes—
55C13×#125C2311yescharacteristic
56C13×#125C2311yescharacteristic
57C13×#125C2312yes—
58C13×#124C2312yes—
59C13×#123—22no—
60C13×#123—22no—
61C13×#123—22no—
62C13×#123—22no—
63C13×#123—22no—
64C13×C22⋊Q8—22no—
65C13×C22⋊Q8—22no—
66C13×C22⋊Q8—22no—
67C13×C22⋊Q8—22no—
68C13×C22⋊Q8—22no—
69C13×C22⋊Q8—22no—
70C13×C22⋊Q8D412yes—
71C13×#121—22no—
72C13×#121—22no—
73C13×#121D412yes—
74C4×Q8×C13—22no—
75C4×Q8×C13D412yes—
76C4×D4×C13—22no—
77C4×D4×C13—22no—
78C4×D4×C13—22no—
79C4×D4×C13—22no—
80C4×D4×C13D412yes—
81C13×#117—22no—
82C13×#117—22no—
83C2×C13×C4⋊C4—22no—
84C2×C13×C4⋊C4—22no—
85C2×C13×C4⋊C4—22no—
86C2×C13×C4⋊C4D412yes—
87C2×C42×C13C2311yescharacteristic
88C13×#107—24no—
89C13×#106—24no—
90C13×C4⋊C8—22no—
91C13×#103—24no—
92C13×#103—24no—
93C13×#103—24no—
94C13×#102—24no—
95C13×C22⋊C8—22no—
96C13×#97—21no—
97C13×#97C2312yes—
98C13×#97C2314yes—
99#19060C1311yesmaximal, characteristic, direct product factor, Sylow
100C2×Q8×C13—22no—
101C2×Q8×C13—22no—
102C2×Q8×C13—44no—
103C2×Q8×C13—41no—
104C2×Q8×C13C2×D412yes—
105C2×D4×C13—22no—
106C2×D4×C13—22no—
107C2×D4×C13C2×D412yes—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—41no—
113C22×C4×C13C2×D411yescharacteristic
114C22×C4×C13C2×D412yes—
115C2×C8×C13—22no—
116C2×C8×C13—24no—
117C2×C8×C13—42no—
118C13×C4⋊C4—22no—
119C13×C4⋊C4—22no—
120C13×C4⋊C4—22no—
121C13×C4⋊C4—22no—
122C13×C4⋊C4—22no—
123C13×C4⋊C4—22no—
124C13×C4⋊C4—22no—
125C13×C4⋊C4—22no—
126C13×C4⋊C4—22no—
127C13×C4⋊C4—22no—
128C13×C4⋊C4—22no—
129C13×C4⋊C4—22no—
130C13×C4⋊C4—22no—
131C13×C4⋊C4—22no—
132C13×C4⋊C4—22no—
133C13×C4⋊C4—24no—
134C13×C4⋊C4—42no—
135C13×C4⋊C4C2×D412yes—
136C13×C4⋊C4C2×D412yes—
137C13×C4⋊C4C2×D412yes—
138C13×C4⋊C4C2×D412yes—
139C13×C22⋊C4—22no—
140C13×C22⋊C4—22no—
141C13×C22⋊C4—22no—
142C13×C22⋊C4—22no—
143C13×C22⋊C4—22no—
144C13×C22⋊C4—22no—
145C13×C22⋊C4—22no—
146C13×C22⋊C4—22no—
147C13×C22⋊C4—22no—
148C42×C13—22no—
149C42×C13—22no—
150C42×C13—22no—
151C42×C13C2×D411yescharacteristic
152C42×C13C2×D412yes—
153C42×C13C2411yescharacteristic
154#3553C2×C1311yescharacteristic
155#3238C2×C1312yescomplemented
156C2×#491C2×C1311yescharacteristic, complemented
157#1664C2×C1314yescomplemented
158#1663C2×C1312yescomplemented
159#1662C2×C1312yescomplemented
160#1534C2×C1311yescharacteristic, complemented
161#1532C2×C1312yescomplemented
162C23×C13—22no—
163C23×C13#12011yescharacteristic
164Q8×C13—42no—
165Q8×C13—44no—
166Q8×C13—82no—
167Q8×C13—82no—
168D4×C13—42no—
169D4×C13—44no—
170D4×C13—82no—
171C2×C4×C13—22no—
172C2×C4×C13—22no—
173C2×C4×C13—22no—
174C2×C4×C13—22no—
175C2×C4×C13—22no—
176C2×C4×C13—22no—
177C2×C4×C13—42no—
178C2×C4×C13—42no—
179C2×C4×C13—82no—
180C2×C4×C13—82no—
181C2×C4×C13—82no—
182C2×C4×C13—82no—
183C2×C4×C13—82no—
184C2×C4×C13#12012yes—
185C2×C4×C13#12011yescharacteristic
186C2×C4×C13C22×D411yescharacteristic
187C2×C4×C13C22×D412yes—
188C8×C13—44no—
189C8×C13—42no—
190#564C22×C1311yescharacteristic
191#563C22×C1312yes—
192#562C22×C1311yescharacteristic
193#554—22no—
194#553—22no—
195#552—22no—
196#541—22no—
197#539—22no—
198#539—22no—
199C2×C4⋊Q8C22×C1311yescharacteristic
200#529C22×C1312yes—
201C2×#125C22×C1311yescharacteristic
202#501C22×C1314yes—
203#491—22no—
204#491C22×C1312yes—
205#491C22×C1312yes—
206#489C22×C1314yes—
207#483—22no—
208#480—22no—
209#477—22no—
210#476—22no—
211#432C22×C1312yes—
212C2×#103—22no—
213C2×#97C22×C1311yescharacteristic
214#330C22×C1312yes—
215#330C22×C1314yes—
216#330C22×C1312yes—
217#329C22×C1314yes—
218C22×C13—22no—
219C22×C13—42no—
220C22×C13—42no—
221C22×C13—42no—
222C22×C13#45412yes—
223C22×C13C2×#12011yescharacteristic
224C4×C13—21no—
225C4×C13—21no—
226C4×C13—22no—
227C4×C13—22no—
228C4×C13—42no—
229C4×C13—42no—
230C4×C13—42no—
231C4×C13—42no—
232C4×C13—42no—
233C4×C13—82no—
234C22×Q8—21no—
235C22×C8—21no—
236C4⋊Q8—22no—
237C4⋊Q8—22no—
238C4⋊Q8—21no—
239C4⋊Q8C23×C1312yes—
240#126—22no—
241#126—22no—
242#126—22no—
243#126—22no—
244#126—22no—
245#125—22no—
246#125—22no—
247#125—22no—
248#125—22no—
249#125—22no—
250#125—22no—
251#125D4×C1312yes—
252#125C23×C1311yescharacteristic
253#125C23×C1311yescharacteristic
254#125C23×C1312yes—
255#124C23×C1312yes—
256#123—22no—
257#123—22no—
258#123—22no—
259#123—22no—
260#123—22no—
261C22⋊Q8—22no—
262C22⋊Q8—22no—
263C22⋊Q8—22no—
264C22⋊Q8—22no—
265C22⋊Q8—22no—
266C22⋊Q8—22no—
267C22⋊Q8D4×C1312yes—
268#121—22no—
269#121—22no—
270#121D4×C1312yes—
271C4×Q8—22no—
272C4×Q8D4×C1312yes—
273C4×D4—22no—
274C4×D4—22no—
275C4×D4—22no—
276C4×D4—22no—
277C4×D4D4×C1312yes—
278#117—22no—
279#117—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4D4×C1312yes—
284C2×C42C23×C1311yescharacteristic
285#107—24no—
286#106—24no—
287C4⋊C8—22no—
288#103—24no—
289#103—24no—
290#103—24no—
291#102—24no—
292C22⋊C8—22no—
293#97—21no—
294#97C23×C1312yes—
295#97C23×C1314yes—
296C2×C13—22no—
297C2×C13—82no—
298C2×C13C2×#45411yescharacteristic
299C2×C13#302212yes—
300C2×Q8—22no—
301C2×Q8—22no—
302C2×Q8—44no—
303C2×Q8—41no—
304C2×Q8C2×D4×C1312yes—
305C2×D4—22no—
306C2×D4—22no—
307C2×D4C2×D4×C1312yes—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—41no—
313C22×C4C2×D4×C1311yescharacteristic
314C22×C4C2×D4×C1312yes—
315C2×C8—22no—
316C2×C8—24no—
317C2×C8—42no—
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—24no—
334C4⋊C4—42no—
335C4⋊C4C2×D4×C1312yes—
336C4⋊C4C2×D4×C1312yes—
337C4⋊C4C2×D4×C1312yes—
338C4⋊C4C2×D4×C1312yes—
339C22⋊C4—22no—
340C22⋊C4—22no—
341C22⋊C4—22no—
342C22⋊C4—22no—
343C22⋊C4—22no—
344C22⋊C4—22no—
345C22⋊C4—22no—
346C22⋊C4—22no—
347C22⋊C4—22no—
348C42—22no—
349C42—22no—
350C42—22no—
351C42C2×D4×C1311yescharacteristic
352C42C2×D4×C1312yes—
353C42C24×C1311yescharacteristic
354C13#1906011yescharacteristic, direct product factor, Sylow
355C23—22no—
356C23C13×#12011yescharacteristic
357Q8—42no—
358Q8—44no—
359Q8—82no—
360Q8—82no—
361D4—42no—
362D4—44no—
363D4—82no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—82no—
373C2×C4—82no—
374C2×C4—82no—
375C2×C4—82no—
376C2×C4—82no—
377C2×C4C13×#12012yes—
378C2×C4C13×#12011yescharacteristic
379C2×C4C22×D4×C1311yescharacteristic
380C2×C4C22×D4×C1312yes—
381C8—44no—
382C8—42no—
383C22—22no—
384C22—42no—
385C22—42no—
386C22—42no—
387C22C13×#45412yes—
388C22C2×C13×#12011yescharacteristic
389C4—21no—
390C4—21no—
391C4—22no—
392C4—22no—
393C4—42no—
394C4—42no—
395C4—42no—
396C4—42no—
397C4—42no—
398C4—82no—
399C2—22no—
400C2—82no—
401C2C2×C13×#45411yescharacteristic
402C2C13×#302212yes—
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC42C24×C13
prime radicalC13×#3553C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#3238C2semidirect
3. C2×C13×#491C2semidirect
4. C13×#1664C2semidirect
5. C13×#1663C2semidirect
6. C13×#1662C2semidirect
7. C13×#1534C2semidirect
8. C13×#1532C2semidirect
99. #19060C13direct (N × H)
155. #3238C2×C13semidirect
156. C2×#491C2×C13semidirect
157. #1664C2×C13semidirect
158. #1663C2×C13semidirect
159. #1662C2×C13semidirect
160. #1534C2×C13semidirect
161. #1532C2×C13semidirect
354. C13#19060direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35532
C13×#32382
C2×C13×#4912
C13×#16642
C13×#16632
C13×#16622
C13×#15342
C13×#15322
#1906013