Finite Group Databasebeta

← C13×#13337 #15699676

Subgroups — C13×#13337 #15699676

Order 3328.

554 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#509C211yesmaximal, characteristic
2C22×C13×SD32C211yesmaximal, characteristic, complemented
3C13×#3156C211yesmaximal, characteristic, complemented
4C2×C13×#362C211yesmaximal, characteristic, complemented
5C2×C13×#359C211yesmaximal, characteristic, complemented
6C13×#1978C211yesmaximal, characteristic, complemented
7C13×#1379C211yesmaximal, characteristic, complemented
8C2×C13×#137—21no—
9C2×C13×#135C2211yescharacteristic
10C22×C13×Q16C2211yescharacteristic
11C22×C13×D8C2211yescharacteristic
12C13×#536—21no—
13C13×#509—22no—
14C13×#509—22no—
15C2×C13×SD32—22no—
16C2×C13×SD32—21no—
17C2×C13×SD32—22no—
18C2×C13×SD32—22no—
19C2×C13×D16—21no—
20C2×C13×M32C2211yescharacteristic
21C22×C13×C16C2211yescharacteristic
22C13×#497—22no—
23C13×#495—21no—
24C13×#494—21no—
25C2×C13×#108C2211yescharacteristic
26C13×#418—21no—
27C2×C13×#100—21no—
28C13×#405C2211yescharacteristic
29C13×#362—22no—
30C13×#359—22no—
31C2×C13×#41—21no—
32C22×Q8×C13—21no—
33C22×D4×C13—21no—
34C13×#137—42no—
35C13×#137—42no—
36C13×#135—21no—
37C13×#135—21no—
38C13×#135—21no—
39C13×#135—21no—
40C2×C13×Q16—22no—
41C2×C13×Q16—21no—
42C2×C13×Q16—21no—
43C2×C13×Q16—21no—
44C2×C13×Q16—21no—
45C2×C13×Q16—21no—
46C2×C13×Q16D411yescharacteristic
47C2×C13×Q16D412yes—
48C2×C13×SD16—22no—
49C2×C13×SD16—21no—
50C2×C13×D8—21no—
51C2×C13×D8—21no—
52C2×C13×D8—21no—
53C2×C13×D8—21no—
54C2×C13×D8—21no—
55C2×C13×D8D411yescharacteristic
56C2×C13×D8D412yes—
57C2×C13×M16—21no—
58C2×C13×M16D411yescharacteristic
59C22×C8×C13C2311yescharacteristic
60C13×C4⋊Q8—22no—
61C13×#124—22no—
62C13×#123—42no—
63C13×C22⋊Q8—42no—
64C13×#117D411yescharacteristic
65C13×SD32—28no—
66C13×SD32—24no—
67C13×D16—24no—
68C13×M32—21no—
69C13×M32D412yes—
70C2×C13×C16—21no—
71C2×C13×C16—21no—
72C2×C13×C16—21no—
73C2×C13×C16D412yes—
74C13×#108—21no—
75C13×#108—21no—
76C13×#102—42no—
77C13×#100—42no—
78C13×#97—21no—
79C4×C8×C13—21no—
80#13337C1311yesmaximal, characteristic, direct product factor, Sylow
81C24×C13—41no—
82C13×#41—41no—
83C13×#41—41no—
84C13×#41—41no—
85C13×#41—41no—
86C2×Q8×C13—22no—
87C2×Q8×C13—21no—
88C2×Q8×C13—41no—
89C2×Q8×C13—41no—
90C2×Q8×C13—41no—
91C2×Q8×C13—41no—
92C2×Q8×C13—41no—
93C2×D4×C13—21no—
94C2×D4×C13—22no—
95C2×D4×C13—41no—
96C2×D4×C13—41no—
97C2×D4×C13—41no—
98C2×D4×C13—41no—
99C2×D4×C13—41no—
100C2×D4×C13—41no—
101C22×C4×C13—41no—
102C22×C4×C13—41no—
103C22×C4×C13C2×D411yescharacteristic
104C13×Q16—22no—
105C13×Q16—21no—
106C13×Q16—22no—
107C13×Q16—21no—
108C13×Q16—44no—
109C13×Q16—41no—
110C13×Q16—41no—
111C13×SD16—44no—
112C13×SD16—41no—
113C13×SD16—41no—
114C13×D8—21no—
115C13×D8—22no—
116C13×D8—22no—
117C13×D8—21no—
118C13×D8—41no—
119C13×D8—41no—
120C13×M16—21no—
121C13×M16—41no—
122C13×M16—41no—
123C13×M16D812yes—
124C2×C8×C13—21no—
125C2×C8×C13—41no—
126C2×C8×C13C2×D411yescharacteristic
127C2×C8×C13C2×D411yescharacteristic
128C2×C8×C13C2×D411yescharacteristic
129C2×C8×C13C2×D411yescharacteristic
130C2×C8×C13C2×D411yescharacteristic
131C2×C8×C13#4111yescharacteristic
132C13×C4⋊C4—44no—
133C13×C4⋊C4D812yes—
134C13×C22⋊C4—21no—
135C13×C22⋊C4—44no—
136C42×C13—21no—
137C13×C16—22no—
138C13×C16—22no—
139C2×#509C2×C1311yescharacteristic
140C22×SD32C2×C1311yescharacteristic, complemented
141#3156C2×C1311yescharacteristic, complemented
142C2×#362C2×C1311yescharacteristic, complemented
143C2×#359C2×C1311yescharacteristic, complemented
144#1978C2×C1311yescharacteristic, complemented
145#1379C2×C1311yescharacteristic, complemented
146C23×C13—41no—
147C23×C13—42no—
148C23×C13—81no—
149C23×C13—81no—
150C23×C13—162no—
151C23×C13AGL(1,ℤ/8)11yescharacteristic
152Q8×C13—41no—
153Q8×C13—42no—
154Q8×C13—42no—
155Q8×C13—41no—
156Q8×C13—81no—
157Q8×C13—81no—
158D4×C13—42no—
159D4×C13—41no—
160D4×C13—41no—
161D4×C13—42no—
162D4×C13—81no—
163D4×C13—81no—
164D4×C13—81no—
165D4×C13—81no—
166C2×C4×C13—22no—
167C2×C4×C13—42no—
168C2×C4×C13—41no—
169C2×C4×C13—81no—
170C2×C4×C13—81no—
171C2×C4×C13—81no—
172C2×C4×C13—81no—
173C2×C4×C13#12011yescharacteristic
174C2×C4×C13#12111yescharacteristic
175C2×C4×C13#12711yescharacteristic
176C2×C4×C13C2×D811yescharacteristic
177C2×C4×C13C2×D811yescharacteristic
178C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
179C8×C13—22no—
180C8×C13—81no—
181C8×C13#12011yescharacteristic
182C8×C13#12011yescharacteristic
183C8×C13#12111yescharacteristic
184C8×C13#12111yescharacteristic
185C2×#137—21no—
186C2×#135C22×C1311yescharacteristic
187C22×Q16C22×C1311yescharacteristic
188C22×D8C22×C1311yescharacteristic
189#536—21no—
190#509—22no—
191#509—22no—
192C2×SD32—22no—
193C2×SD32—21no—
194C2×SD32—22no—
195C2×SD32—22no—
196C2×D16—21no—
197C2×M32C22×C1311yescharacteristic
198C22×C16C22×C1311yescharacteristic
199#497—22no—
200#495—21no—
201#494—21no—
202C2×#108C22×C1311yescharacteristic
203#418—21no—
204C2×#100—21no—
205#405C22×C1311yescharacteristic
206#362—22no—
207#359—22no—
208C22×C13—22no—
209C22×C13—82no—
210C22×C13—81no—
211C22×C13—82no—
212C22×C13—162no—
213C22×C13—162no—
214C22×C13—162no—
215C22×C13#44711yescharacteristic
216C22×C13#45911yescharacteristic
217C22×C13#49611yescharacteristic
218C4×C13—42no—
219C4×C13—81no—
220C4×C13—82no—
221C4×C13#39211yescharacteristic
222C4×C13#44711yescharacteristic
223C4×C13#45911yescharacteristic
224C4×C13#49311yescharacteristic
225C2×#41—21no—
226C22×Q8—21no—
227C22×D4—21no—
228#137—42no—
229#137—42no—
230#135—21no—
231#135—21no—
232#135—21no—
233#135—21no—
234C2×Q16—22no—
235C2×Q16—21no—
236C2×Q16—21no—
237C2×Q16—21no—
238C2×Q16—21no—
239C2×Q16—21no—
240C2×Q16D4×C1312yes—
241C2×Q16D4×C1311yescharacteristic
242C2×SD16—22no—
243C2×SD16—21no—
244C2×D8—21no—
245C2×D8—21no—
246C2×D8—21no—
247C2×D8—21no—
248C2×D8—21no—
249C2×D8D4×C1312yes—
250C2×D8D4×C1311yescharacteristic
251C2×M16—21no—
252C2×M16D4×C1311yescharacteristic
253C22×C8C23×C1311yescharacteristic
254C4⋊Q8—22no—
255#124—22no—
256#123—42no—
257C22⋊Q8—42no—
258#117D4×C1311yescharacteristic
259SD32—28no—
260SD32—24no—
261D16—24no—
262M32—21no—
263M32D4×C1312yes—
264C2×C16—21no—
265C2×C16—21no—
266C2×C16—21no—
267C2×C16D4×C1312yes—
268#108—21no—
269#108—21no—
270#102—42no—
271#100—42no—
272#97—21no—
273C4×C8—21no—
274C2×C13—21no—
275C2×C13—21no—
276C2×C13—161no—
277C2×C13—162no—
278C2×C13#201111yescharacteristic
279C2×C13#219312yes—
280C24—41no—
281#41—41no—
282#41—41no—
283#41—41no—
284#41—41no—
285C2×Q8—22no—
286C2×Q8—21no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×D4—21no—
293C2×D4—22no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4C2×D4×C1311yescharacteristic
303Q16—22no—
304Q16—21no—
305Q16—22no—
306Q16—21no—
307Q16—44no—
308Q16—41no—
309Q16—41no—
310SD16—44no—
311SD16—41no—
312SD16—41no—
313D8—21no—
314D8—22no—
315D8—22no—
316D8—21no—
317D8—41no—
318D8—41no—
319M16—21no—
320M16—41no—
321M16—41no—
322M16C13×D812yes—
323C2×C8—21no—
324C2×C8—41no—
325C2×C8C2×D4×C1311yescharacteristic
326C2×C8C2×D4×C1311yescharacteristic
327C2×C8C2×D4×C1311yescharacteristic
328C2×C8C2×D4×C1311yescharacteristic
329C2×C8C2×D4×C1311yescharacteristic
330C2×C8C13×#4111yescharacteristic
331C4⋊C4—44no—
332C4⋊C4C13×D812yes—
333C22⋊C4—21no—
334C22⋊C4—44no—
335C42—21no—
336C16—22no—
337C16—22no—
338C13#1333711yescharacteristic, direct product factor, Sylow
339C23—41no—
340C23—42no—
341C23—81no—
342C23—81no—
343C23—162no—
344C23C13×AGL(1,ℤ/8)11yescharacteristic
345Q8—41no—
346Q8—42no—
347Q8—42no—
348Q8—41no—
349Q8—81no—
350Q8—81no—
351D4—42no—
352D4—41no—
353D4—41no—
354D4—42no—
355D4—81no—
356D4—81no—
357D4—81no—
358D4—81no—
359C2×C4—22no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—81no—
366C2×C4C13×#12011yescharacteristic
367C2×C4C13×#12111yescharacteristic
368C2×C4C13×#12711yescharacteristic
369C2×C4C2×C13×D811yescharacteristic
370C2×C4C2×C13×D811yescharacteristic
371C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
372C8—22no—
373C8—81no—
374C8C13×#12011yescharacteristic
375C8C13×#12011yescharacteristic
376C8C13×#12111yescharacteristic
377C8C13×#12111yescharacteristic
378C22—22no—
379C22—81no—
380C22—82no—
381C22—82no—
382C22—162no—
383C22—162no—
384C22—162no—
385C22C13×#44711yescharacteristic
386C22C13×#45911yescharacteristic
387C22C13×#49611yescharacteristic
388C4—42no—
389C4—81no—
390C4—82no—
391C4C13×#39211yescharacteristic
392C4C13×#44711yescharacteristic
393C4C13×#45911yescharacteristic
394C4C13×#49311yescharacteristic
395C2—21no—
396C2—21no—
397C2—161no—
398C2—162no—
399C2C13×#201111yescharacteristic
400C2C13×#219312yes—
subgroupG/H
center, socleC22×C13#447
commutator, Frattini, cosocleC22×C8C23×C13
prime radicalC2×C13×#509C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C13×SD32C2semidirect
3. C13×#3156C2semidirect
4. C2×C13×#362C2semidirect
5. C2×C13×#359C2semidirect
6. C13×#1978C2semidirect
7. C13×#1379C2semidirect
80. #13337C13direct (N × H)
140. C22×SD32C2×C13semidirect
141. #3156C2×C13semidirect
142. C2×#362C2×C13semidirect
143. C2×#359C2×C13semidirect
144. #1978C2×C13semidirect
145. #1379C2×C13semidirect
338. C13#13337direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5092
C22×C13×SD322
C13×#31562
C2×C13×#3622
C2×C13×#3592
C13×#19782
C13×#13792
#1333713