Finite Group Databasebeta

← C13×#13338 #15699677

Subgroups — C13×#13338 #15699677

Order 3328.

566 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
1C2×C13×#510C211yesmaximal, characteristic, complemented
2C22×C13×SD32C211yesmaximal, characteristic, complemented
3C13×#3155C211yesmaximal, characteristic
4C2×C13×#361C211yesmaximal, characteristic, complemented
5C2×C13×#359C211yesmaximal, characteristic, complemented
6C13×#1979C211yesmaximal, characteristic, complemented
7C13×#1379C211yesmaximal, characteristic, complemented
8C2×C13×AGL(1,ℤ/8)—21no—
9C2×C13×#135C2211yescharacteristic
10C22×C13×Q16C2211yescharacteristic
11C22×C13×D8C2211yescharacteristic
12C13×#535—21no—
13C13×#510—22no—
14C13×#510—22no—
15C2×C13×Q32—21no—
16C2×C13×SD32—22no—
17C2×C13×SD32—22no—
18C2×C13×SD32—21no—
19C2×C13×SD32—22no—
20C2×C13×M32C2211yescharacteristic
21C22×C13×C16C2211yescharacteristic
22C13×#496—22no—
23C13×#495—21no—
24C13×#493—21no—
25C2×C13×#108C2211yescharacteristic
26C13×#419—21no—
27C2×C13×#101—21no—
28C13×#405C2211yescharacteristic
29C13×#361—22no—
30C13×#359—22no—
31C2×C13×#41—21no—
32C22×Q8×C13—21no—
33C22×D4×C13—21no—
34C13×AGL(1,ℤ/8)—42no—
35C13×AGL(1,ℤ/8)—42no—
36C13×#135—21no—
37C13×#135—21no—
38C13×#135—21no—
39C13×#135—21no—
40C2×C13×Q16—21no—
41C2×C13×Q16—21no—
42C2×C13×Q16—21no—
43C2×C13×Q16—21no—
44C2×C13×Q16—21no—
45C2×C13×Q16D411yescharacteristic
46C2×C13×Q16D412yescomplemented
47C2×C13×SD16—22no—
48C2×C13×SD16—21no—
49C2×C13×D8—22no—
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×#127—22no—
61C13×#124—22no—
62C13×#121—42no—
63C13×#120—42no—
64C13×#117D411yescharacteristic
65C13×Q32—24no—
66C13×SD32—28no—
67C13×SD32—24no—
68C13×M32—21no—
69C13×M32D412yescomplemented
70C2×C13×C16—21no—
71C2×C13×C16—21no—
72C2×C13×C16—21no—
73C2×C13×C16D412yescomplemented
74C13×#108—21no—
75C13×#108—21no—
76C13×#103—42no—
77C13×#101—42no—
78C13×#97—21no—
79C4×C8×C13—21no—
80#13338C1311yesmaximal, characteristic, direct product factor, Sylow
81C24×C13—41no—
82C13×#41—41no—
83C13×#41—41no—
84C13×#41—41no—
85C13×#41—41no—
86C2×Q8×C13—21no—
87C2×Q8×C13—22no—
88C2×Q8×C13—41no—
89C2×Q8×C13—41no—
90C2×Q8×C13—41no—
91C2×Q8×C13—41no—
92C2×Q8×C13—41no—
93C2×D4×C13—22no—
94C2×D4×C13—21no—
95C2×D4×C13—44no—
96C2×D4×C13—41no—
97C2×D4×C13—41no—
98C2×D4×C13—41no—
99C2×D4×C13—41no—
100C2×D4×C13—41no—
101C2×D4×C13—41no—
102C22×C4×C13—41no—
103C22×C4×C13—41no—
104C22×C4×C13C2×D411yescharacteristic
105C13×Q16—22no—
106C13×Q16—22no—
107C13×Q16—21no—
108C13×Q16—21no—
109C13×Q16—41no—
110C13×Q16—41no—
111C13×SD16—44no—
112C13×SD16—41no—
113C13×SD16—41no—
114C13×D8—22no—
115C13×D8—21no—
116C13×D8—22no—
117C13×D8—21no—
118C13×D8—44no—
119C13×D8—41no—
120C13×D8—41no—
121C13×M16—21no—
122C13×M16—41no—
123C13×M16—41no—
124C13×M16D812yes—
125C2×C8×C13—21no—
126C2×C8×C13—41no—
127C2×C8×C13C2×D411yescharacteristic
128C2×C8×C13C2×D411yescharacteristic
129C2×C8×C13C2×D411yescharacteristic
130C2×C8×C13C2×D411yescharacteristic
131C2×C8×C13C2×D411yescharacteristic
132C2×C8×C13#4111yescharacteristic
133C13×C4⋊C4D812yes—
134C13×C22⋊C4—21no—
135C13×C22⋊C4—44no—
136C42×C13—21no—
137C13×C16—22no—
138C13×C16—22no—
139C2×#510C2×C1311yescharacteristic, complemented
140C22×SD32C2×C1311yescharacteristic, complemented
141#3155C2×C1311yescharacteristic
142C2×#361C2×C1311yescharacteristic, complemented
143C2×#359C2×C1311yescharacteristic, complemented
144#1979C2×C1311yescharacteristic, complemented
145#1379C2×C1311yescharacteristic, complemented
146C23×C13—42no—
147C23×C13—41no—
148C23×C13—81no—
149C23×C13—81no—
150C23×C13—162no—
151C23×C13AGL(1,ℤ/8)11yescharacteristic
152Q8×C13—41no—
153Q8×C13—42no—
154Q8×C13—41no—
155Q8×C13—42no—
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—
166D4×C13—164no—
167C2×C4×C13—22no—
168C2×C4×C13—41no—
169C2×C4×C13—42no—
170C2×C4×C13—81no—
171C2×C4×C13—81no—
172C2×C4×C13—81no—
173C2×C4×C13—81no—
174C2×C4×C13#12011yescharacteristic
175C2×C4×C13#12111yescharacteristic
176C2×C4×C13#12711yescharacteristic
177C2×C4×C13C2×D811yescharacteristic
178C2×C4×C13C2×D811yescharacteristic
179C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
180C8×C13—22no—
181C8×C13—81no—
182C8×C13#12011yescharacteristic
183C8×C13#12011yescharacteristic
184C8×C13#12111yescharacteristic
185C8×C13#12111yescharacteristic
186C2×AGL(1,ℤ/8)—21no—
187C2×#135C22×C1311yescharacteristic
188C22×Q16C22×C1311yescharacteristic
189C22×D8C22×C1311yescharacteristic
190#535—21no—
191#510—22no—
192#510—22no—
193C2×Q32—21no—
194C2×SD32—22no—
195C2×SD32—22no—
196C2×SD32—21no—
197C2×SD32—22no—
198C2×M32C22×C1311yescharacteristic
199C22×C16C22×C1311yescharacteristic
200#496—22no—
201#495—21no—
202#493—21no—
203C2×#108C22×C1311yescharacteristic
204#419—21no—
205C2×#101—21no—
206#405C22×C1311yescharacteristic
207#361—22no—
208#359—22no—
209C22×C13—22no—
210C22×C13—82no—
211C22×C13—84no—
212C22×C13—81no—
213C22×C13—82no—
214C22×C13—162no—
215C22×C13—162no—
216C22×C13#44711yescharacteristic
217C22×C13#45911yescharacteristic
218C22×C13#49611yescharacteristic
219C4×C13—42no—
220C4×C13—81no—
221C4×C13—82no—
222C4×C13#39211yescharacteristic
223C4×C13#44711yescharacteristic
224C4×C13#45911yescharacteristic
225C4×C13#49311yescharacteristic
226C2×#41—21no—
227C22×Q8—21no—
228C22×D4—21no—
229AGL(1,ℤ/8)—42no—
230AGL(1,ℤ/8)—42no—
231#135—21no—
232#135—21no—
233#135—21no—
234#135—21no—
235C2×Q16—21no—
236C2×Q16—21no—
237C2×Q16—21no—
238C2×Q16—21no—
239C2×Q16—21no—
240C2×Q16D4×C1311yescharacteristic
241C2×Q16D4×C1312yescomplemented
242C2×SD16—22no—
243C2×SD16—21no—
244C2×D8—22no—
245C2×D8—21no—
246C2×D8—21no—
247C2×D8—21no—
248C2×D8—21no—
249C2×D8—21no—
250C2×D8D4×C1312yes—
251C2×D8D4×C1311yescharacteristic
252C2×M16—21no—
253C2×M16D4×C1311yescharacteristic
254C22×C8C23×C1311yescharacteristic
255#127—22no—
256#124—22no—
257#121—42no—
258#120—42no—
259#117D4×C1311yescharacteristic
260Q32—24no—
261SD32—28no—
262SD32—24no—
263M32—21no—
264M32D4×C1312yescomplemented
265C2×C16—21no—
266C2×C16—21no—
267C2×C16—21no—
268C2×C16D4×C1312yescomplemented
269#108—21no—
270#108—21no—
271#103—42no—
272#101—42no—
273#97—21no—
274C4×C8—21no—
275C2×C13—21no—
276C2×C13—21no—
277C2×C13—161no—
278C2×C13—162no—
279C2×C13#201111yescharacteristic
280C2×C13#219412yes—
281C24—41no—
282#41—41no—
283#41—41no—
284#41—41no—
285#41—41no—
286C2×Q8—21no—
287C2×Q8—22no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×D4—22no—
294C2×D4—21no—
295C2×D4—44no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4C2×D4×C1311yescharacteristic
305Q16—22no—
306Q16—22no—
307Q16—21no—
308Q16—21no—
309Q16—41no—
310Q16—41no—
311SD16—44no—
312SD16—41no—
313SD16—41no—
314D8—22no—
315D8—21no—
316D8—22no—
317D8—21no—
318D8—44no—
319D8—41no—
320D8—41no—
321M16—21no—
322M16—41no—
323M16—41no—
324M16C13×D812yes—
325C2×C8—21no—
326C2×C8—41no—
327C2×C8C2×D4×C1311yescharacteristic
328C2×C8C2×D4×C1311yescharacteristic
329C2×C8C2×D4×C1311yescharacteristic
330C2×C8C2×D4×C1311yescharacteristic
331C2×C8C2×D4×C1311yescharacteristic
332C2×C8C13×#4111yescharacteristic
333C4⋊C4C13×D812yes—
334C22⋊C4—21no—
335C22⋊C4—44no—
336C42—21no—
337C16—22no—
338C16—22no—
339C13#1333811yescharacteristic, direct product factor, Sylow
340C23—42no—
341C23—41no—
342C23—81no—
343C23—81no—
344C23—162no—
345C23C13×AGL(1,ℤ/8)11yescharacteristic
346Q8—41no—
347Q8—42no—
348Q8—41no—
349Q8—42no—
350Q8—81no—
351Q8—81no—
352D4—42no—
353D4—41no—
354D4—41no—
355D4—42no—
356D4—81no—
357D4—81no—
358D4—81no—
359D4—81no—
360D4—164no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—81no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4C13×#12011yescharacteristic
369C2×C4C13×#12111yescharacteristic
370C2×C4C13×#12711yescharacteristic
371C2×C4C2×C13×D811yescharacteristic
372C2×C4C2×C13×D811yescharacteristic
373C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
374C8—22no—
375C8—81no—
376C8C13×#12011yescharacteristic
377C8C13×#12011yescharacteristic
378C8C13×#12111yescharacteristic
379C8C13×#12111yescharacteristic
380C22—22no—
381C22—81no—
382C22—82no—
383C22—82no—
384C22—84no—
385C22—162no—
386C22—162no—
387C22C13×#44711yescharacteristic
388C22C13×#45911yescharacteristic
389C22C13×#49611yescharacteristic
390C4—42no—
391C4—81no—
392C4—82no—
393C4C13×#39211yescharacteristic
394C4C13×#44711yescharacteristic
395C4C13×#45911yescharacteristic
396C4C13×#49311yescharacteristic
397C2—21no—
398C2—21no—
399C2—162no—
400C2—161no—
401C2C13×#201111yescharacteristic
402C2C13×#219412yes—
subgroupG/H
center, socleC22×C13#447
commutator, Frattini, cosocleC22×C8C23×C13
prime radicalC13×#3155C2
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
1. C2×C13×#510C2semidirect
2. C22×C13×SD32C2semidirect
4. C2×C13×#361C2semidirect
5. C2×C13×#359C2semidirect
6. C13×#1979C2semidirect
7. C13×#1379C2semidirect
46. C2×C13×Q16D4semidirect
69. C13×M32D4semidirect
73. C2×C13×C16D4semidirect
80. #13338C13direct (N × H)
139. C2×#510C2×C13semidirect
140. C22×SD32C2×C13semidirect
142. C2×#361C2×C13semidirect
143. C2×#359C2×C13semidirect
144. #1979C2×C13semidirect
145. #1379C2×C13semidirect
241. C2×Q16D4×C13semidirect
264. M32D4×C13semidirect
268. C2×C16D4×C13semidirect
339. C13#13338direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5102
C22×C13×SD322
C13×#31552
C2×C13×#3612
C2×C13×#3592
C13×#19792
C13×#13792
#1333813