Finite Group Databasebeta

← C13×#10016 #15696355

Subgroups — C13×#10016 #15696355

Order 3328.

560 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3104C211yesmaximal, characteristic, complemented
2C13×#3101C211yesmaximal, characteristic
3C13×#2398C211yesmaximal, characteristic
4C13×#1995C211yesmaximal, characteristic, complemented
5C13×#1487C211yesmaximal, characteristic, complemented
6C13×#1486C211yesmaximal, characteristic
7C13×#1274C211yesmaximal, characteristic, complemented
8C13×#533C2211yescharacteristic
9C2×C4×Q8×C13C2211yescharacteristic
10C2×C4×D4×C13C2211yescharacteristic
11C13×#484—21no—
12C13×#483—21no—
13C13×#477—21no—
14C13×#476—21no—
15C13×#462—21no—
16C13×#461—21no—
17C13×#451—21no—
18C13×#450—21no—
19C4×C13×Q16—22no—
20C4×C13×SD16—22no—
21C13×#431C2211yescharacteristic
22C13×#431C2211yescharacteristic
23C13×#423C2211yescharacteristic
24C13×#400—21no—
25C13×#397—21no—
26C13×#394—21no—
27C13×#393—21no—
28C4×C13×C22⋊C4—22no—
29C13×#376C2211yescharacteristic
30C13×#339—22no—
31C13×Q8⋊C8—22no—
32C13×D4⋊C8—22no—
33C22×Q8×C13D411yescharacteristic
34C22×D4×C13D411yescharacteristic
35C23×C4×C13—21no—
36C2×C13×Q16—22no—
37C2×C13×SD16—22no—
38C2×C13×M16—21no—
39C13×C4⋊Q8D411yescharacteristic
40C13×C4⋊Q8D411yescharacteristic
41C13×#125—21no—
42C13×C22⋊Q8—21no—
43C13×C22⋊Q8—21no—
44C4×Q8×C13—21no—
45C4×Q8×C13—21no—
46C4×Q8×C13—21no—
47C4×Q8×C13—21no—
48C4×Q8×C13—21no—
49C4×Q8×C13—21no—
50C4×D4×C13—21no—
51C4×D4×C13—21no—
52C4×D4×C13—21no—
53C4×D4×C13—21no—
54C13×#117—21no—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4D411yescharacteristic
57C2×C13×C4⋊C4D411yescharacteristic
58C2×C13×C22⋊C4—22no—
59C2×C13×C22⋊C4—22no—
60C2×C13×C22⋊C4—21no—
61C2×C42×C13—21no—
62C2×C42×C13D412yes—
63C2×C42×C13C2311yescharacteristic
64C13×#107—22no—
65C13×#106—22no—
66C13×C4⋊C8—21no—
67C13×C4⋊C8—21no—
68C13×C4⋊C8—21no—
69C13×C4⋊C8—21no—
70C13×#103—22no—
71C13×#103—22no—
72C13×#103—22no—
73C13×#102—22no—
74C13×C22⋊C8—21no—
75C13×C22⋊C8—21no—
76C4×C8×C13D412yes—
77C4×C8×C13D412yes—
78C13×#95—22no—
79C13×#95—22no—
80C13×#95—21no—
81C13×#95—21no—
82#10016C1311yesmaximal, characteristic, direct product factor, Sylow
83C24×C13—21no—
84C2×Q8×C13—21no—
85C2×Q8×C13—21no—
86C2×Q8×C13—21no—
87C2×Q8×C13—21no—
88C2×Q8×C13—42no—
89C2×D4×C13—21no—
90C2×D4×C13—21no—
91C2×D4×C13—42no—
92C22×C4×C13—21no—
93C22×C4×C13—22no—
94C22×C4×C13—21no—
95C22×C4×C13—21no—
96C22×C4×C13—41no—
97C22×C4×C13—41no—
98C22×C4×C13—42no—
99C22×C4×C13—42no—
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13C2×D411yescharacteristic
103C13×Q16—44no—
104C13×SD16—44no—
105C13×M16—42no—
106C2×C8×C13—22no—
107C2×C8×C13—22no—
108C2×C8×C13—41no—
109C13×C4⋊C4—21no—
110C13×C4⋊C4—21no—
111C13×C4⋊C4—21no—
112C13×C4⋊C4—21no—
113C13×C4⋊C4—21no—
114C13×C4⋊C4—21no—
115C13×C4⋊C4—21no—
116C13×C4⋊C4—21no—
117C13×C4⋊C4—41no—
118C13×C4⋊C4—41no—
119C13×C4⋊C4—41no—
120C13×C4⋊C4—41no—
121C13×C22⋊C4—44no—
122C13×C22⋊C4—44no—
123C13×C22⋊C4—41no—
124C13×C22⋊C4—41no—
125C13×C22⋊C4—41no—
126C42×C13—22no—
127C42×C13—22no—
128C42×C13—41no—
129C42×C13—41no—
130C42×C13—41no—
131C42×C13C2×D411yescharacteristic
132C42×C13C2×D411yescharacteristic
133C42×C13C2×D411yescharacteristic
134C42×C13#4111yescharacteristic
135#3104C2×C1311yescharacteristic, complemented
136#3101C2×C1311yescharacteristic
137#2398C2×C1311yescharacteristic
138#1995C2×C1311yescharacteristic, complemented
139#1487C2×C1311yescharacteristic, complemented
140#1486C2×C1311yescharacteristic
141#1274C2×C1311yescharacteristic, complemented
142C23×C13—22no—
143C23×C13—42no—
144C23×C13—41no—
145C23×C13—41no—
146C23×C13—42no—
147C23×C13#12011yescharacteristic
148Q8×C13—22no—
149Q8×C13—22no—
150Q8×C13—41no—
151Q8×C13—41no—
152Q8×C13—42no—
153Q8×C13—42no—
154D4×C13—22no—
155D4×C13—22no—
156D4×C13—41no—
157D4×C13—41no—
158C2×C4×C13—22no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—42no—
164C2×C4×C13—42no—
165C2×C4×C13—42no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—42no—
171C2×C4×C13—42no—
172C2×C4×C13—82no—
173C2×C4×C13—81no—
174C2×C4×C13—81no—
175C2×C4×C13#12011yescharacteristic
176C2×C4×C13#12011yescharacteristic
177C2×C4×C13#12111yescharacteristic
178C2×C4×C13#12111yescharacteristic
179C2×C4×C13#12111yescharacteristic
180C2×C4×C13#12711yescharacteristic
181C2×C4×C13#13512yes—
182C2×C4×C13#13712yes—
183C8×C13—42no—
184C8×C13—42no—
185C8×C13—81no—
186#533C22×C1311yescharacteristic
187C2×C4×Q8C22×C1311yescharacteristic
188C2×C4×D4C22×C1311yescharacteristic
189#484—21no—
190#483—21no—
191#477—21no—
192#476—21no—
193#462—21no—
194#461—21no—
195#451—21no—
196#450—21no—
197C4×Q16—22no—
198C4×SD16—22no—
199#431C22×C1311yescharacteristic
200#431C22×C1311yescharacteristic
201#423C22×C1311yescharacteristic
202#400—21no—
203#397—21no—
204#394—21no—
205#393—21no—
206C4×C22⋊C4—22no—
207#376C22×C1311yescharacteristic
208#339—22no—
209Q8⋊C8—22no—
210D4⋊C8—22no—
211C22×C13—21no—
212C22×C13—21no—
213C22×C13—44no—
214C22×C13—42no—
215C22×C13—82no—
216C22×C13—81no—
217C22×C13—81no—
218C22×C13#39211yescharacteristic
219C22×C13#45212yes—
220C4×C13—21no—
221C4×C13—21no—
222C4×C13—21no—
223C4×C13—21no—
224C4×C13—42no—
225C4×C13—82no—
226C4×C13—81no—
227C4×C13—81no—
228C4×C13—81no—
229C4×C13—81no—
230C4×C13#46412yes—
231C4×C13#49511yescharacteristic
232C4×C13#49711yescharacteristic
233C22×Q8D4×C1311yescharacteristic
234C22×D4D4×C1311yescharacteristic
235C23×C4—21no—
236C2×Q16—22no—
237C2×SD16—22no—
238C2×M16—21no—
239C4⋊Q8D4×C1311yescharacteristic
240C4⋊Q8D4×C1311yescharacteristic
241#125—21no—
242C22⋊Q8—21no—
243C22⋊Q8—21no—
244C4×Q8—21no—
245C4×Q8—21no—
246C4×Q8—21no—
247C4×Q8—21no—
248C4×Q8—21no—
249C4×Q8—21no—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4—21no—
253C4×D4—21no—
254#117—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4D4×C1311yescharacteristic
257C2×C4⋊C4D4×C1311yescharacteristic
258C2×C22⋊C4—22no—
259C2×C22⋊C4—22no—
260C2×C22⋊C4—21no—
261C2×C42—21no—
262C2×C42D4×C1312yes—
263C2×C42C23×C1311yescharacteristic
264#107—22no—
265#106—22no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270#103—22no—
271#103—22no—
272#103—22no—
273#102—22no—
274C22⋊C8—21no—
275C22⋊C8—21no—
276C4×C8D4×C1312yes—
277C4×C8D4×C1312yes—
278#95—22no—
279#95—22no—
280#95—21no—
281#95—21no—
282C2×C13—22no—
283C2×C13—82no—
284C2×C13#201011yescharacteristic
285C2×C13#201011yescharacteristic
286C2×C13#201511yescharacteristic
287C24—21no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8—42no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—42no—
296C22×C4—21no—
297C22×C4—22no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4C2×D4×C1311yescharacteristic
305C22×C4C2×D4×C1311yescharacteristic
306C22×C4C2×D4×C1311yescharacteristic
307Q16—44no—
308SD16—44no—
309M16—42no—
310C2×C8—22no—
311C2×C8—22no—
312C2×C8—41no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C22⋊C4—44no—
326C22⋊C4—44no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C42—22no—
331C42—22no—
332C42—41no—
333C42—41no—
334C42—41no—
335C42C2×D4×C1311yescharacteristic
336C42C2×D4×C1311yescharacteristic
337C42C2×D4×C1311yescharacteristic
338C42C13×#4111yescharacteristic
339C13#1001611yescharacteristic, direct product factor, Sylow
340C23—22no—
341C23—42no—
342C23—41no—
343C23—41no—
344C23—42no—
345C23C13×#12011yescharacteristic
346Q8—22no—
347Q8—22no—
348Q8—41no—
349Q8—41no—
350Q8—42no—
351Q8—42no—
352D4—22no—
353D4—22no—
354D4—41no—
355D4—41no—
356C2×C4—22no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—82no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4C13×#12011yescharacteristic
374C2×C4C13×#12011yescharacteristic
375C2×C4C13×#12111yescharacteristic
376C2×C4C13×#12111yescharacteristic
377C2×C4C13×#12111yescharacteristic
378C2×C4C13×#12711yescharacteristic
379C2×C4C13×#13512yes—
380C2×C4C13×#13712yes—
381C8—42no—
382C8—42no—
383C8—81no—
384C22—21no—
385C22—21no—
386C22—44no—
387C22—42no—
388C22—82no—
389C22—81no—
390C22—81no—
391C22C13×#39211yescharacteristic
392C22C13×#45212yes—
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—42no—
398C4—82no—
399C4—81no—
400C4—81no—
401C4—81no—
402C4—81no—
403C4C13×#46412yes—
404C4C13×#49511yescharacteristic
405C4C13×#49711yescharacteristic
406C2—22no—
407C2—82no—
408C2C13×#201011yescharacteristic
409C2C13×#201011yescharacteristic
410C2C13×#201511yescharacteristic
subgroupG/H
centerC2×C4×C13#127
commutator, Frattini, cosocleC2×C42C23×C13
socleC22×C13#392
prime radicalC22×D4×C13D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3104C2semidirect
4. C13×#1995C2semidirect
5. C13×#1487C2semidirect
7. C13×#1274C2semidirect
82. #10016C13direct (N × H)
135. #3104C2×C13semidirect
138. #1995C2×C13semidirect
139. #1487C2×C13semidirect
141. #1274C2×C13semidirect
339. C13#10016direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31042
C13×#31012
C13×#23982
C13×#19952
C13×#14872
C13×#14862
C13×#12742
#1001613