Finite Group Databasebeta

← C13×#9251 #15695590

Subgroups — C13×#9251 #15695590

Order 3328.

528 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#474C211yesmaximal, characteristic
2D4×C13×M16C211yesmaximal, characteristic
3C13×#1966C211yesmaximal, characteristic, complemented
4C13×#1546C211yesmaximal, characteristic, complemented
5C13×#1486C211yesmaximal, characteristic
6C13×#1292C211yesmaximal, characteristic, complemented
7C13×#1283C211yesmaximal, characteristic, complemented
8C22×C13×M16—21no—
9C2×C13×C4⋊Q8C2211yescharacteristic
10C2×C4×D4×C13C2211yescharacteristic
11C13×#474—21no—
12C13×#474—21no—
13C13×#474—21no—
14C13×#474—21no—
15C13×#436—21no—
16C13×#435—22no—
17C8×D4×C13—21no—
18C13×#431C2211yescharacteristic
19C2×C13×#107C412yes—
20C13×#423C2211yescharacteristic
21C13×#423C2211yescharacteristic
22C2×C13×C4⋊C8C2211yescharacteristic
23C2×C13×#102C412yes—
24C2×C13×#101—21no—
25C2×C13×#101—21no—
26C13×#407—21no—
27C4×C13×M16C2211yescharacteristic
28C13×#332—22no—
29C13×D4⋊C8—21no—
30C13×D4⋊C8—21no—
31C22×Q8×C13—21no—
32C22×D4×C13C2×C411yescharacteristic
33C23×C4×C13—21no—
34C2×C13×M16—22no—
35C2×C13×M16—21no—
36C2×C13×M16—21no—
37C2×C13×M16—42no—
38C2×C13×M16—42no—
39C2×C13×M16D411yescharacteristic
40C2×C13×M16D411yescharacteristic
41C22×C8×C13—22no—
42C22×C8×C13C2×C412yes—
43C13×C4⋊Q8—21no—
44C13×C4⋊Q8—21no—
45C13×C4⋊Q8—21no—
46C13×C4⋊Q8—21no—
47C4×D4×C13—21no—
48C4×D4×C13—21no—
49C4×D4×C13D411yescharacteristic
50C4×D4×C13D411yescharacteristic
51C4×D4×C13D411yescharacteristic
52C4×D4×C13D411yescharacteristic
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4C2×C412yes—
55C2×C13×C4⋊C4C2×C411yescharacteristic
56C2×C13×C22⋊C4—21no—
57C2×C42×C13C2311yescharacteristic
58C13×#107—22no—
59C13×#107—22no—
60C13×C4⋊C8—21no—
61C13×C4⋊C8—21no—
62C13×C4⋊C8—21no—
63C13×C4⋊C8—21no—
64C13×C4⋊C8—21no—
65C13×C4⋊C8—21no—
66C13×C4⋊C8D412yes—
67C13×#102—22no—
68C13×#102—22no—
69C13×#101—42no—
70C13×#101—42no—
71C13×C22⋊C8—22no—
72C13×C22⋊C8—22no—
73C13×C22⋊C8—21no—
74C13×#97—21no—
75C4×C8×C13—21no—
76C4×C8×C13—21no—
77#9251C1311yesmaximal, characteristic, direct product factor, Sylow
78C24×C13—21no—
79C2×Q8×C13—41no—
80C2×Q8×C13—41no—
81C2×Q8×C13—41no—
82C2×Q8×C13—41no—
83C2×Q8×C13—41no—
84C2×Q8×C13—41no—
85C2×D4×C13—22no—
86C2×D4×C13—21no—
87C2×D4×C13—41no—
88C2×D4×C13C22⋊C411yescharacteristic
89C2×D4×C13C22⋊C411yescharacteristic
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13—21no—
93C22×C4×C13—21no—
94C22×C4×C13—21no—
95C22×C4×C13—22no—
96C22×C4×C13—41no—
97C22×C4×C13—41no—
98C22×C4×C13—41no—
99C22×C4×C13—41no—
100C22×C4×C13C22×C411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13#4111yescharacteristic
103C13×M16—21no—
104C13×M16—21no—
105C13×M16—21no—
106C13×M16—44no—
107C13×M16—41no—
108C13×M16—41no—
109C13×M16—41no—
110C13×M16—41no—
111C13×M16D812yes—
112C2×C8×C13—21no—
113C2×C8×C13—22no—
114C2×C8×C13—21no—
115C2×C8×C13—22no—
116C2×C8×C13—44no—
117C2×C8×C13—42no—
118C2×C8×C13—41no—
119C2×C8×C13—41no—
120C13×C4⋊C4—21no—
121C13×C4⋊C4—22no—
122C13×C4⋊C4—22no—
123C13×C4⋊C4—41no—
124C13×C4⋊C4—41no—
125C13×C4⋊C4C22⋊C411yescharacteristic
126C13×C4⋊C4C22⋊C411yescharacteristic
127C13×C22⋊C4—21no—
128C13×C22⋊C4—21no—
129C13×C22⋊C4—21no—
130C13×C22⋊C4—21no—
131C42×C13C2×D411yescharacteristic
132C42×C13C2×D411yescharacteristic
133C42×C13C2×D411yescharacteristic
134C42×C13#4111yescharacteristic
135C2×#474C2×C1311yescharacteristic
136D4×M16C2×C1311yescharacteristic
137#1966C2×C1311yescharacteristic, complemented
138#1546C2×C1311yescharacteristic, complemented
139#1486C2×C1311yescharacteristic
140#1292C2×C1311yescharacteristic, complemented
141#1283C2×C1311yescharacteristic, complemented
142C23×C13—21no—
143C23×C13—21no—
144C23×C13—42no—
145C23×C13—41no—
146C23×C13—41no—
147C23×C13—81no—
148C23×C13C4×D411yescharacteristic
149Q8×C13—81no—
150Q8×C13—81no—
151Q8×C13—81no—
152Q8×C13—81no—
153D4×C13—21no—
154D4×C13—21no—
155D4×C13—21no—
156D4×C13—42no—
157D4×C13#10112yescomplemented
158C2×C4×C13—21no—
159C2×C4×C13—21no—
160C2×C4×C13—21no—
161C2×C4×C13—21no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
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—42no—
174C2×C4×C13—42no—
175C2×C4×C13—42no—
176C2×C4×C13C2×C22⋊C411yescharacteristic
177C2×C4×C13C4×D411yescharacteristic
178C2×C4×C13#12011yescharacteristic
179C2×C4×C13#12111yescharacteristic
180C2×C4×C13#12111yescharacteristic
181C2×C4×C13#12311yescharacteristic
182C2×C4×C13C2×D811yescharacteristic
183C2×C4×C13#13511yescharacteristic
184C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
186C8×C13—22no—
187C8×C13—42no—
188C8×C13—42no—
189C8×C13—41no—
190C8×C13—81no—
191C8×C13—81no—
192C22×M16—21no—
193C2×C4⋊Q8C22×C1311yescharacteristic
194C2×C4×D4C22×C1311yescharacteristic
195#474—21no—
196#474—21no—
197#474—21no—
198#474—21no—
199#436—21no—
200#435—22no—
201C8×D4—21no—
202#431C22×C1311yescharacteristic
203C2×#107C4×C1312yes—
204#423C22×C1311yescharacteristic
205#423C22×C1311yescharacteristic
206C2×C4⋊C8C22×C1311yescharacteristic
207C2×#102C4×C1312yes—
208C2×#101—21no—
209C2×#101—21no—
210#407—21no—
211C4×M16C22×C1311yescharacteristic
212#332—22no—
213D4⋊C8—21no—
214D4⋊C8—21no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13—22no—
218C22×C13—41no—
219C22×C13—41no—
220C22×C13—41no—
221C22×C13—41no—
222C22×C13—41no—
223C22×C13—82no—
224C22×C13—82no—
225C22×C13#38611yescharacteristic
226C22×C13C4×D811yescharacteristic
227C22×C13#44211yescharacteristic
228C4×C13—21no—
229C4×C13—21no—
230C4×C13—21no—
231C4×C13—41no—
232C4×C13—41no—
233C4×C13—82no—
234C4×C13C2×#10111yescharacteristic
235C4×C13#41311yescharacteristic
236C4×C13#44711yescharacteristic
237C4×C13#44911yescharacteristic
238C4×C13#45911yescharacteristic
239C4×C13#46311yescharacteristic
240C22×Q8—21no—
241C22×D4C2×C4×C1311yescharacteristic
242C23×C4—21no—
243C2×M16—22no—
244C2×M16—21no—
245C2×M16—21no—
246C2×M16—42no—
247C2×M16—42no—
248C2×M16D4×C1311yescharacteristic
249C2×M16D4×C1311yescharacteristic
250C22×C8—22no—
251C22×C8C2×C4×C1312yes—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4D4×C1311yescharacteristic
259C4×D4D4×C1311yescharacteristic
260C4×D4D4×C1311yescharacteristic
261C4×D4D4×C1311yescharacteristic
262C2×C4⋊C4—21no—
263C2×C4⋊C4C2×C4×C1312yes—
264C2×C4⋊C4C2×C4×C1311yescharacteristic
265C2×C22⋊C4—21no—
266C2×C42C23×C1311yescharacteristic
267#107—22no—
268#107—22no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8D4×C1312yes—
276#102—22no—
277#102—22no—
278#101—42no—
279#101—42no—
280C22⋊C8—22no—
281C22⋊C8—22no—
282C22⋊C8—21no—
283#97—21no—
284C4×C8—21no—
285C4×C8—21no—
286C2×C13—21no—
287C2×C13—21no—
288C2×C13—42no—
289C2×C13—81no—
290C2×C13#187911yescharacteristic
291C2×C13#190111yescharacteristic
292C2×C13#190211yescharacteristic
293C24—21no—
294C2×Q8—41no—
295C2×Q8—41no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×D4—22no—
301C2×D4—21no—
302C2×D4—41no—
303C2×D4C13×C22⋊C411yescharacteristic
304C2×D4C13×C22⋊C411yescharacteristic
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—22no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4C22×C4×C1311yescharacteristic
316C22×C4C2×D4×C1311yescharacteristic
317C22×C4C13×#4111yescharacteristic
318M16—21no—
319M16—21no—
320M16—21no—
321M16—44no—
322M16—41no—
323M16—41no—
324M16—41no—
325M16—41no—
326M16C13×D812yes—
327C2×C8—21no—
328C2×C8—22no—
329C2×C8—21no—
330C2×C8—22no—
331C2×C8—44no—
332C2×C8—42no—
333C2×C8—41no—
334C2×C8—41no—
335C4⋊C4—21no—
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4C13×C22⋊C411yescharacteristic
341C4⋊C4C13×C22⋊C411yescharacteristic
342C22⋊C4—21no—
343C22⋊C4—21no—
344C22⋊C4—21no—
345C22⋊C4—21no—
346C42C2×D4×C1311yescharacteristic
347C42C2×D4×C1311yescharacteristic
348C42C2×D4×C1311yescharacteristic
349C42C13×#4111yescharacteristic
350C13#925111yescharacteristic, direct product factor, Sylow
351C23—21no—
352C23—21no—
353C23—42no—
354C23—41no—
355C23—41no—
356C23—81no—
357C23C4×D4×C1311yescharacteristic
358Q8—81no—
359Q8—81no—
360Q8—81no—
361Q8—81no—
362D4—21no—
363D4—21no—
364D4—21no—
365D4—42no—
366D4C13×#10112yescomplemented
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4C2×C13×C22⋊C411yescharacteristic
386C2×C4C4×D4×C1311yescharacteristic
387C2×C4C13×#12011yescharacteristic
388C2×C4C13×#12111yescharacteristic
389C2×C4C13×#12111yescharacteristic
390C2×C4C13×#12311yescharacteristic
391C2×C4C2×C13×D811yescharacteristic
392C2×C4C13×#13511yescharacteristic
393C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
394C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
395C8—22no—
396C8—42no—
397C8—42no—
398C8—41no—
399C8—81no—
400C8—81no—
401C22—21no—
402C22—21no—
403C22—22no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—82no—
410C22—82no—
411C22C13×#38611yescharacteristic
412C22C4×C13×D811yescharacteristic
413C22C13×#44211yescharacteristic
414C4—21no—
415C4—21no—
416C4—21no—
417C4—41no—
418C4—41no—
419C4—82no—
420C4C2×C13×#10111yescharacteristic
421C4C13×#41311yescharacteristic
422C4C13×#44711yescharacteristic
423C4C13×#44911yescharacteristic
424C4C13×#45911yescharacteristic
425C4C13×#46311yescharacteristic
426C2—21no—
427C2—21no—
428C2—42no—
429C2—81no—
430C2C13×#187911yescharacteristic
431C2C13×#190111yescharacteristic
432C2C13×#190211yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC22×D4×C13C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#1966C2semidirect
4. C13×#1546C2semidirect
6. C13×#1292C2semidirect
7. C13×#1283C2semidirect
77. #9251C13direct (N × H)
137. #1966C2×C13semidirect
138. #1546C2×C13semidirect
140. #1292C2×C13semidirect
141. #1283C2×C13semidirect
157. D4×C13#101semidirect
350. C13#9251direct (N × H)
366. D4C13×#101semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#4742
D4×C13×M162
C13×#19662
C13×#15462
C13×#14862
C13×#12922
C13×#12832
#925113