Finite Group Databasebeta

← C13×#13334 #15699673

Subgroups — C13×#13334 #15699673

Order 3328.

568 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3414C211yesmaximal, characteristic, complemented
2C2×C13×#509C211yesmaximal, characteristic, complemented
3C13×#3155C211yesmaximal, characteristic, complemented
4C13×#2145C211yesmaximal, characteristic, complemented
5C13×#2140C211yesmaximal, characteristic, complemented
6C13×#1976C211yesmaximal, characteristic, complemented
7C13×#1378C211yesmaximal, characteristic, complemented
8C2×C13×AGL(1,ℤ/8)—21no—
9C2×C13×#135C2211yescharacteristic
10C2×C13×#135C2211yescharacteristic
11C22×C13×D8C2211yescharacteristic
12C13×#535—21no—
13C13×#510—21no—
14C13×#510—21no—
15C13×#509—22no—
16C13×#509—21no—
17C13×#509—21no—
18C13×#509—22no—
19C13×#508—22no—
20C2×C13×SD32—21no—
21C2×C13×D16—21no—
22C2×C13×M32C2211yescharacteristic
23C2×C13×M32C2211yescharacteristic
24C13×#496—22no—
25C13×#495—21no—
26C13×#493—21no—
27C13×#427C2211yescharacteristic
28C13×#421—21no—
29C13×#410—21no—
30C13×#405C2211yescharacteristic
31C13×#360—22no—
32C13×#357—22no—
33C2×C13×#41—21no—
34C2×C13×#41—21no—
35C22×D4×C13—21no—
36C13×AGL(1,ℤ/8)—42no—
37C13×AGL(1,ℤ/8)—42no—
38C13×#135—21no—
39C13×#135—21no—
40C13×#135—21no—
41C13×#135—21no—
42C13×#135—21no—
43C13×#135—21no—
44C13×#135—21no—
45C13×#135—21no—
46C2×C13×Q16D411yescharacteristic
47C2×C13×Q16D411yescharacteristic, complemented
48C2×C13×SD16—22no—
49C2×C13×SD16—21no—
50C2×C13×SD16—21no—
51C2×C13×D8—22no—
52C2×C13×D8—21no—
53C2×C13×D8—21no—
54C2×C13×D8—21no—
55C2×C13×D8—21no—
56C2×C13×D8—21no—
57C2×C13×D8D411yescharacteristic
58C2×C13×D8D412yes—
59C2×C13×D8D411yescharacteristic, complemented
60C2×C13×M16D411yescharacteristic
61C22×C8×C13C2311yescharacteristic
62C13×#127—22no—
63C13×#124—22no—
64C13×#121—42no—
65C13×#120—42no—
66C13×#117—21no—
67C13×#117D411yescharacteristic
68C13×Q32—22no—
69C13×SD32—24no—
70C13×SD32—22no—
71C13×SD32—22no—
72C13×D16—24no—
73C13×D16—22no—
74C13×M32—21no—
75C13×M32—21no—
76C13×M32—21no—
77C13×M32D412yescomplemented
78C2×C13×C16—21no—
79C2×C13×C16D412yescomplemented
80C13×#107—21no—
81C13×#106—21no—
82C13×#104—42no—
83C13×#99—42no—
84C13×#97—21no—
85C4×C8×C13—21no—
86#13334C1311yesmaximal, characteristic, direct product factor, Sylow
87C24×C13—41no—
88C13×#41—41no—
89C13×#41—41no—
90C13×#41—41no—
91C13×#41—41no—
92C13×#41—41no—
93C13×#41—41no—
94C13×#41—41no—
95C13×#41—41no—
96C2×Q8×C13—21no—
97C2×Q8×C13—21no—
98C2×D4×C13—22no—
99C2×D4×C13—21no—
100C2×D4×C13—21no—
101C2×D4×C13—44no—
102C2×D4×C13—41no—
103C2×D4×C13—41no—
104C2×D4×C13—41no—
105C2×D4×C13—41no—
106C2×D4×C13—41no—
107C2×D4×C13—41no—
108C2×D4×C13—41no—
109C22×C4×C13—41no—
110C22×C4×C13—41no—
111C22×C4×C13C2×D411yescharacteristic
112C13×Q16—21no—
113C13×Q16—21no—
114C13×Q16—21no—
115C13×Q16—21no—
116C13×SD16—44no—
117C13×SD16—41no—
118C13×SD16—41no—
119C13×SD16—41no—
120C13×SD16—41no—
121C13×D8—21no—
122C13×D8—22no—
123C13×D8—21no—
124C13×D8—21no—
125C13×D8—22no—
126C13×D8—21no—
127C13×D8—44no—
128C13×D8—41no—
129C13×D8—41no—
130C13×M16—21no—
131C13×M16D812yes—
132C2×C8×C13—21no—
133C2×C8×C13C2×D411yescharacteristic
134C2×C8×C13C2×D411yescharacteristic
135C2×C8×C13C2×D411yescharacteristic
136C2×C8×C13C2×D411yescharacteristic
137C2×C8×C13C2×D411yescharacteristic
138C2×C8×C13#4111yescharacteristic
139C13×C4⋊C4—21no—
140C13×C4⋊C4—41no—
141C13×C22⋊C4—44no—
142C13×C22⋊C4—41no—
143C13×C22⋊C4D812yes—
144C42×C13—21no—
145C42×C13—41no—
146C13×C16—22no—
147C13×C16—22no—
148#3414C2×C1311yescharacteristic, complemented
149C2×#509C2×C1311yescharacteristic, complemented
150#3155C2×C1311yescharacteristic, complemented
151#2145C2×C1311yescharacteristic, complemented
152#2140C2×C1311yescharacteristic, complemented
153#1976C2×C1311yescharacteristic, complemented
154#1378C2×C1311yescharacteristic, complemented
155C23×C13—42no—
156C23×C13—41no—
157C23×C13—41no—
158C23×C13—81no—
159C23×C13—81no—
160C23×C13—162no—
161C23×C13C2×D811yescharacteristic
162Q8×C13—41no—
163Q8×C13—41no—
164Q8×C13—41no—
165Q8×C13—41no—
166D4×C13—42no—
167D4×C13—41no—
168D4×C13—41no—
169D4×C13—41no—
170D4×C13—42no—
171D4×C13—41no—
172D4×C13—81no—
173D4×C13—81no—
174D4×C13—81no—
175D4×C13—81no—
176D4×C13—81no—
177D4×C13—81no—
178D4×C13—164no—
179C2×C4×C13—22no—
180C2×C4×C13—41no—
181C2×C4×C13—41no—
182C2×C4×C13—81no—
183C2×C4×C13—81no—
184C2×C4×C13—81no—
185C2×C4×C13—81no—
186C2×C4×C13—81no—
187C2×C4×C13#12011yescharacteristic
188C2×C4×C13#12111yescharacteristic
189C2×C4×C13#12711yescharacteristic
190C2×C4×C13C2×D811yescharacteristic
191C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
193C8×C13—22no—
194C8×C13#12011yescharacteristic
195C8×C13#12011yescharacteristic
196C8×C13#12111yescharacteristic
197C8×C13#12111yescharacteristic
198C2×AGL(1,ℤ/8)—21no—
199C2×#135C22×C1311yescharacteristic
200C2×#135C22×C1311yescharacteristic
201C22×D8C22×C1311yescharacteristic
202#535—21no—
203#510—21no—
204#510—21no—
205#509—22no—
206#509—21no—
207#509—21no—
208#509—22no—
209#508—22no—
210C2×SD32—21no—
211C2×D16—21no—
212C2×M32C22×C1311yescharacteristic
213C2×M32C22×C1311yescharacteristic
214#496—22no—
215#495—21no—
216#493—21no—
217#427C22×C1311yescharacteristic
218#421—21no—
219#410—21no—
220#405C22×C1311yescharacteristic
221#360—22no—
222#357—22no—
223C22×C13—41no—
224C22×C13—82no—
225C22×C13—84no—
226C22×C13—81no—
227C22×C13—81no—
228C22×C13—82no—
229C22×C13—161no—
230C22×C13—162no—
231C22×C13—162no—
232C22×C13#44711yescharacteristic
233C22×C13#45911yescharacteristic
234C22×C13#49311yescharacteristic
235C4×C13—42no—
236C4×C13—81no—
237C4×C13—81no—
238C4×C13—161no—
239C4×C13#39211yescharacteristic
240C4×C13#44711yescharacteristic
241C4×C13#45911yescharacteristic
242C4×C13#49611yescharacteristic
243C2×#41—21no—
244C2×#41—21no—
245C22×D4—21no—
246AGL(1,ℤ/8)—42no—
247AGL(1,ℤ/8)—42no—
248#135—21no—
249#135—21no—
250#135—21no—
251#135—21no—
252#135—21no—
253#135—21no—
254#135—21no—
255#135—21no—
256C2×Q16D4×C1311yescharacteristic
257C2×Q16D4×C1311yescharacteristic, complemented
258C2×SD16—22no—
259C2×SD16—21no—
260C2×SD16—21no—
261C2×D8—22no—
262C2×D8—21no—
263C2×D8—21no—
264C2×D8—21no—
265C2×D8—21no—
266C2×D8—21no—
267C2×D8D4×C1312yes—
268C2×D8D4×C1311yescharacteristic
269C2×D8D4×C1311yescharacteristic, complemented
270C2×M16D4×C1311yescharacteristic
271C22×C8C23×C1311yescharacteristic
272#127—22no—
273#124—22no—
274#121—42no—
275#120—42no—
276#117—21no—
277#117D4×C1311yescharacteristic
278Q32—22no—
279SD32—24no—
280SD32—22no—
281SD32—22no—
282D16—24no—
283D16—22no—
284M32—21no—
285M32—21no—
286M32—21no—
287M32D4×C1312yescomplemented
288C2×C16—21no—
289C2×C16D4×C1312yescomplemented
290#107—21no—
291#106—21no—
292#104—42no—
293#99—42no—
294#97—21no—
295C4×C8—21no—
296C2×C13—21no—
297C2×C13—21no—
298C2×C13—21no—
299C2×C13—161no—
300C2×C13—162no—
301C2×C13—161no—
302C2×C13#201111yescharacteristic
303C24—41no—
304#41—41no—
305#41—41no—
306#41—41no—
307#41—41no—
308#41—41no—
309#41—41no—
310#41—41no—
311#41—41no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×D4—22no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—44no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4C2×D4×C1311yescharacteristic
328Q16—21no—
329Q16—21no—
330Q16—21no—
331Q16—21no—
332SD16—44no—
333SD16—41no—
334SD16—41no—
335SD16—41no—
336SD16—41no—
337D8—21no—
338D8—22no—
339D8—21no—
340D8—21no—
341D8—22no—
342D8—21no—
343D8—44no—
344D8—41no—
345D8—41no—
346M16—21no—
347M16C13×D812yes—
348C2×C8—21no—
349C2×C8C2×D4×C1311yescharacteristic
350C2×C8C2×D4×C1311yescharacteristic
351C2×C8C2×D4×C1311yescharacteristic
352C2×C8C2×D4×C1311yescharacteristic
353C2×C8C2×D4×C1311yescharacteristic
354C2×C8C13×#4111yescharacteristic
355C4⋊C4—21no—
356C4⋊C4—41no—
357C22⋊C4—44no—
358C22⋊C4—41no—
359C22⋊C4C13×D812yes—
360C42—21no—
361C42—41no—
362C16—22no—
363C16—22no—
364C13#1333411yescharacteristic, direct product factor, Sylow
365C23—42no—
366C23—41no—
367C23—41no—
368C23—81no—
369C23—81no—
370C23—162no—
371C23C2×C13×D811yescharacteristic
372Q8—41no—
373Q8—41no—
374Q8—41no—
375Q8—41no—
376D4—42no—
377D4—41no—
378D4—41no—
379D4—41no—
380D4—42no—
381D4—41no—
382D4—81no—
383D4—81no—
384D4—81no—
385D4—81no—
386D4—81no—
387D4—81no—
388D4—164no—
389C2×C4—22no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4C13×#12011yescharacteristic
398C2×C4C13×#12111yescharacteristic
399C2×C4C13×#12711yescharacteristic
400C2×C4C2×C13×D811yescharacteristic
401C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
402C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
403C8—22no—
404C8C13×#12011yescharacteristic
405C8C13×#12011yescharacteristic
406C8C13×#12111yescharacteristic
407C8C13×#12111yescharacteristic
408C22—41no—
409C22—82no—
410C22—84no—
411C22—81no—
412C22—81no—
413C22—82no—
414C22—161no—
415C22—162no—
416C22—162no—
417C22C13×#44711yescharacteristic
418C22C13×#45911yescharacteristic
419C22C13×#49311yescharacteristic
420C4—42no—
421C4—81no—
422C4—81no—
423C4—161no—
424C4C13×#39211yescharacteristic
425C4C13×#44711yescharacteristic
426C4C13×#45911yescharacteristic
427C4C13×#49611yescharacteristic
428C2—21no—
429C2—21no—
430C2—21no—
431C2—162no—
432C2—161no—
433C2—161no—
434C2C13×#201111yescharacteristic
subgroupG/H
center, socleC2×C13#2011
commutator, Frattini, cosocleC22×C8C23×C13
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3414C2semidirect
2. C2×C13×#509C2semidirect
3. C13×#3155C2semidirect
4. C13×#2145C2semidirect
5. C13×#2140C2semidirect
6. C13×#1976C2semidirect
7. C13×#1378C2semidirect
47. C2×C13×Q16D4semidirect
59. C2×C13×D8D4semidirect
77. C13×M32D4semidirect
79. C2×C13×C16D4semidirect
86. #13334C13direct (N × H)
148. #3414C2×C13semidirect
149. C2×#509C2×C13semidirect
150. #3155C2×C13semidirect
151. #2145C2×C13semidirect
152. #2140C2×C13semidirect
153. #1976C2×C13semidirect
154. #1378C2×C13semidirect
257. C2×Q16D4×C13semidirect
269. C2×D8D4×C13semidirect
287. M32D4×C13semidirect
289. C2×C16D4×C13semidirect
364. C13#13334direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34142
C2×C13×#5092
C13×#31552
C13×#21452
C13×#21402
C13×#19762
C13×#13782
#1333413