Finite Group Databasebeta

← C13×#32699 #15719038

Subgroups — C13×#32699 #15719038

Order 3328.

538 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2102C211yesmaximal, characteristic, complemented
2C13×#2081C211yesmaximal, characteristic, complemented
3C13×#2081C211yesmaximal, characteristic, complemented
4C13×#2070C211yesmaximal, characteristic, complemented
5C13×#2048C211yesmaximal, characteristic
6C13×#2003C211yesmaximal, characteristic
7C13×#1967C211yesmaximal, characteristic, complemented
8C13×#1932C211yesmaximal, characteristic, complemented
9C13×#1915C211yesmaximal, characteristic, complemented
10C13×#1912C211yesmaximal, characteristic, complemented
11C13×#1903C211yesmaximal, characteristic
12C13×#1888C211yesmaximal, characteristic, complemented
13C13×#1861C211yesmaximal, characteristic, complemented
14C13×#1841C211yesmaximal, characteristic, complemented
15C13×#1830C211yesmaximal, characteristic, complemented
16C2×C13×AGL(1,ℤ/8)C2211yescharacteristic
17C13×#568C2211yescharacteristic
18C13×#536C2211yescharacteristic
19C2×C13×#124C2211yescharacteristic
20C13×#519C2211yescharacteristic
21C13×#430C2211yescharacteristic
22C13×#430C2211yescharacteristic
23C13×#430C2211yescharacteristic
24C13×#423C2211yescharacteristic
25C13×#421C2211yescharacteristic
26C13×#421C2211yescharacteristic
27C2×C13×#104C2211yescharacteristic
28C13×#418C2211yescharacteristic
29C13×#418C2211yescharacteristic
30C13×#418C2211yescharacteristic
31C13×#413C2211yescharacteristic
32C2×C13×#101C2211yescharacteristic
33C2×C13×#101C2211yescharacteristic
34C2×C13×#101C2211yescharacteristic
35C2×C13×#101C2211yescharacteristic
36C2×C13×#100C2211yescharacteristic
37C2×C13×#100C2211yescharacteristic
38C4×C13×M16C2211yescharacteristic
39C13×#344C2211yescharacteristic
40C13×#344C2211yescharacteristic
41C13×#344C2211yescharacteristic
42C13×#344C2211yescharacteristic
43C13×#344C2211yescharacteristic
44C13×#344C2211yescharacteristic
45C13×#339C2211yescharacteristic
46C13×#339C2211yescharacteristic
47C13×#339C2211yescharacteristic
48C13×#338C2211yescharacteristic
49C13×H(3,ℤ/4)C2211yescharacteristic
50C13×H(3,ℤ/4)C2211yescharacteristic
51C2×C13×#41C2311yescharacteristic
52C22×Q8×C13C2311yescharacteristic
53C22×D4×C13C2311yescharacteristic
54C13×AGL(1,ℤ/8)—41no—
55C13×AGL(1,ℤ/8)—41no—
56C2×C13×SD16—21no—
57C2×C13×D8—21no—
58C13×#131—41no—
59C13×#131—41no—
60C2×C13×M16—41no—
61C2×C13×M16C2311yescharacteristic
62C2×C13×M16C2311yescharacteristic
63C2×C13×M16C2311yescharacteristic
64C2×C13×M16C2311yescharacteristic
65C2×C13×M16C2311yescharacteristic
66C2×C13×M16C2311yescharacteristic
67C2×C13×M16C2311yescharacteristic
68C2×C13×M16C2311yescharacteristic
69C13×C4⋊Q8—21no—
70C13×#124—21no—
71C13×#124—21no—
72C13×#124—21no—
73C13×#124—41no—
74C13×#123—22no—
75C13×C22⋊Q8—41no—
76C4×Q8×C13—41no—
77C4×Q8×C13—41no—
78C13×#117—22no—
79C13×#117C2311yescharacteristic
80C13×#117C2311yescharacteristic
81C13×#117C2311yescharacteristic
82C2×C13×C22⋊C4—22no—
83C2×C42×C13C2311yescharacteristic
84C13×#108—41no—
85C13×#108—41no—
86C13×#108—41no—
87C13×C4⋊C8—41no—
88C13×#104—21no—
89C13×#104—21no—
90C13×#104—41no—
91C13×#104—41no—
92C13×#102—41no—
93C13×#102—41no—
94C13×#102—41no—
95C13×#101—21no—
96C13×#101—41no—
97C13×#101—41no—
98C13×#101—41no—
99C13×#101—41no—
100C13×#100—21no—
101C13×#100—41no—
102C13×#100—41no—
103C13×#97—21no—
104C4×C8×C13—21no—
105#32699C1311yesmaximal, characteristic, direct product factor, Sylow
106C24×C13—21no—
107C13×#41—21no—
108C13×#41—21no—
109C13×#41—21no—
110C13×#41—21no—
111C2×Q8×C13—21no—
112C2×Q8×C13—21no—
113C2×Q8×C13—21no—
114C2×Q8×C13—21no—
115C2×Q8×C13—21no—
116C2×Q8×C13—21no—
117C2×Q8×C13#4111yescharacteristic
118C2×D4×C13—21no—
119C2×D4×C13—21no—
120C2×D4×C13—21no—
121C2×D4×C13—21no—
122C2×D4×C13—21no—
123C2×D4×C13—21no—
124C2×D4×C13—21no—
125C2×D4×C13#4111yescharacteristic
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13#4112yes—
129C22×C4×C13C2411yescharacteristic
130C13×SD16—42no—
131C13×D8—42no—
132C13×M16—21no—
133C13×M16—21no—
134C13×M16—21no—
135C13×M16—21no—
136C13×M16—21no—
137C13×M16—21no—
138C13×M16—21no—
139C13×M16—21no—
140C13×M16—21no—
141C13×M16—21no—
142C13×M16—21no—
143C13×M16—21no—
144C13×M16—21no—
145C13×M16—21no—
146C13×M16—21no—
147C13×M16—21no—
148C13×M16—42no—
149C2×C8×C13—21no—
150C2×C8×C13—21no—
151C2×C8×C13—21no—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C2×C8×C13—21no—
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13—42no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—42no—
162C13×C4⋊C4—42no—
163C13×C22⋊C4—21no—
164C13×C22⋊C4—21no—
165C13×C22⋊C4—21no—
166C13×C22⋊C4—42no—
167C13×C22⋊C4—42no—
168C13×C22⋊C4—42no—
169C42×C13—21no—
170C42×C13—21no—
171C42×C13—21no—
172C42×C13—21no—
173C42×C13—42no—
174C42×C13#4111yescharacteristic
175C42×C13#4111yescharacteristic
176#2102C2×C1311yescharacteristic, complemented
177#2081C2×C1311yescharacteristic, complemented
178#2081C2×C1311yescharacteristic, complemented
179#2070C2×C1311yescharacteristic, complemented
180#2048C2×C1311yescharacteristic
181#2003C2×C1311yescharacteristic
182#1967C2×C1311yescharacteristic, complemented
183#1932C2×C1311yescharacteristic, complemented
184#1915C2×C1311yescharacteristic, complemented
185#1912C2×C1311yescharacteristic, complemented
186#1903C2×C1311yescharacteristic
187#1888C2×C1311yescharacteristic, complemented
188#1861C2×C1311yescharacteristic, complemented
189#1841C2×C1311yescharacteristic, complemented
190#1830C2×C1311yescharacteristic, complemented
191C23×C13—21no—
192C23×C13—41no—
193C23×C13—41no—
194C23×C13—41no—
195C23×C13—82no—
196C23×C13C2×#4111yescharacteristic
197Q8×C13—21no—
198Q8×C13—21no—
199Q8×C13—41no—
200Q8×C13—41no—
201Q8×C13—41no—
202Q8×C13—41no—
203D4×C13—21no—
204D4×C13—21no—
205D4×C13—41no—
206D4×C13—41no—
207D4×C13—41no—
208D4×C13—41no—
209D4×C13—41no—
210D4×C13—41no—
211C2×C4×C13—22no—
212C2×C4×C13—21no—
213C2×C4×C13—21no—
214C2×C4×C13—22no—
215C2×C4×C13—22no—
216C2×C4×C13—21no—
217C2×C4×C13—41no—
218C2×C4×C13—41no—
219C2×C4×C13—41no—
220C2×C4×C13—41no—
221C2×C4×C13—41no—
222C2×C4×C13—81no—
223C2×C4×C13C2×#4111yescharacteristic
224C2×C4×C13C2×#4111yescharacteristic
225C2×C4×C13H(5,𝔽2)11yescharacteristic
226C2×C4×C13H(5,𝔽2)11yescharacteristic
227C2×C4×C13H(5,𝔽2)11yescharacteristic
228C2×C4×C13H(5,𝔽2)11yescharacteristic
229C8×C13—41no—
230C8×C13—41no—
231C8×C13—41no—
232C8×C13—41no—
233C8×C13—41no—
234C8×C13—41no—
235C8×C13—41no—
236C8×C13—41no—
237C2×AGL(1,ℤ/8)C22×C1311yescharacteristic
238#568C22×C1311yescharacteristic
239#536C22×C1311yescharacteristic
240C2×#124C22×C1311yescharacteristic
241#519C22×C1311yescharacteristic
242#430C22×C1311yescharacteristic
243#430C22×C1311yescharacteristic
244#430C22×C1311yescharacteristic
245#423C22×C1311yescharacteristic
246#421C22×C1311yescharacteristic
247#421C22×C1311yescharacteristic
248C2×#104C22×C1311yescharacteristic
249#418C22×C1311yescharacteristic
250#418C22×C1311yescharacteristic
251#418C22×C1311yescharacteristic
252#413C22×C1311yescharacteristic
253C2×#101C22×C1311yescharacteristic
254C2×#101C22×C1311yescharacteristic
255C2×#101C22×C1311yescharacteristic
256C2×#101C22×C1311yescharacteristic
257C2×#100C22×C1311yescharacteristic
258C2×#100C22×C1311yescharacteristic
259C4×M16C22×C1311yescharacteristic
260#344C22×C1311yescharacteristic
261#344C22×C1311yescharacteristic
262#344C22×C1311yescharacteristic
263#344C22×C1311yescharacteristic
264#344C22×C1311yescharacteristic
265#344C22×C1311yescharacteristic
266#339C22×C1311yescharacteristic
267#339C22×C1311yescharacteristic
268#339C22×C1311yescharacteristic
269#338C22×C1311yescharacteristic
270H(3,ℤ/4)C22×C1311yescharacteristic
271H(3,ℤ/4)C22×C1311yescharacteristic
272C22×C13—41no—
273C22×C13—41no—
274C22×C13—81no—
275C22×C13—82no—
276C22×C13—81no—
277C22×C13—161no—
278C22×C13—161no—
279C22×C13#53811yescharacteristic
280C22×C13#55111yescharacteristic
281C22×C13#55111yescharacteristic
282C4×C13—41no—
283C4×C13—41no—
284C4×C13—42no—
285C4×C13—41no—
286C4×C13—81no—
287C4×C13—81no—
288C4×C13—81no—
289C4×C13#53811yescharacteristic
290C4×C13#54011yescharacteristic
291C4×C13#55311yescharacteristic
292C4×C13#56011yescharacteristic
293C2×#41C23×C1311yescharacteristic
294C22×Q8C23×C1311yescharacteristic
295C22×D4C23×C1311yescharacteristic
296AGL(1,ℤ/8)—41no—
297AGL(1,ℤ/8)—41no—
298C2×SD16—21no—
299C2×D8—21no—
300#131—41no—
301#131—41no—
302C2×M16—41no—
303C2×M16C23×C1311yescharacteristic
304C2×M16C23×C1311yescharacteristic
305C2×M16C23×C1311yescharacteristic
306C2×M16C23×C1311yescharacteristic
307C2×M16C23×C1311yescharacteristic
308C2×M16C23×C1311yescharacteristic
309C2×M16C23×C1311yescharacteristic
310C2×M16C23×C1311yescharacteristic
311C4⋊Q8—21no—
312#124—21no—
313#124—21no—
314#124—21no—
315#124—41no—
316#123—22no—
317C22⋊Q8—41no—
318C4×Q8—41no—
319C4×Q8—41no—
320#117—22no—
321#117C23×C1311yescharacteristic
322#117C23×C1311yescharacteristic
323#117C23×C1311yescharacteristic
324C2×C22⋊C4—22no—
325C2×C42C23×C1311yescharacteristic
326#108—41no—
327#108—41no—
328#108—41no—
329C4⋊C8—41no—
330#104—21no—
331#104—21no—
332#104—41no—
333#104—41no—
334#102—41no—
335#102—41no—
336#102—41no—
337#101—21no—
338#101—41no—
339#101—41no—
340#101—41no—
341#101—41no—
342#100—21no—
343#100—41no—
344#100—41no—
345#97—21no—
346C4×C8—21no—
347C2×C13—21no—
348C2×C13—21no—
349C2×C13—21no—
350C2×C13—81no—
351C2×C13—161no—
352C2×C13#274911yescharacteristic
353C24—21no—
354#41—21no—
355#41—21no—
356#41—21no—
357#41—21no—
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8—21no—
361C2×Q8—21no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8C13×#4111yescharacteristic
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4C13×#4111yescharacteristic
373C22×C4—21no—
374C22×C4—21no—
375C22×C4C13×#4112yes—
376C22×C4C24×C1311yescharacteristic
377SD16—42no—
378D8—42no—
379M16—21no—
380M16—21no—
381M16—21no—
382M16—21no—
383M16—21no—
384M16—21no—
385M16—21no—
386M16—21no—
387M16—21no—
388M16—21no—
389M16—21no—
390M16—21no—
391M16—21no—
392M16—21no—
393M16—21no—
394M16—21no—
395M16—42no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8—21no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8—42no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—42no—
409C4⋊C4—42no—
410C22⋊C4—21no—
411C22⋊C4—21no—
412C22⋊C4—21no—
413C22⋊C4—42no—
414C22⋊C4—42no—
415C22⋊C4—42no—
416C42—21no—
417C42—21no—
418C42—21no—
419C42—21no—
420C42—42no—
421C42C13×#4111yescharacteristic
422C42C13×#4111yescharacteristic
423C13#3269911yescharacteristic, direct product factor, Sylow
424C23—21no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—82no—
429C23C2×C13×#4111yescharacteristic
430Q8—21no—
431Q8—21no—
432Q8—41no—
433Q8—41no—
434Q8—41no—
435Q8—41no—
436D4—21no—
437D4—21no—
438D4—41no—
439D4—41no—
440D4—41no—
441D4—41no—
442D4—41no—
443D4—41no—
444C2×C4—22no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—21no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—81no—
456C2×C4C2×C13×#4111yescharacteristic
457C2×C4C2×C13×#4111yescharacteristic
458C2×C4C13×H(5,𝔽2)11yescharacteristic
459C2×C4C13×H(5,𝔽2)11yescharacteristic
460C2×C4C13×H(5,𝔽2)11yescharacteristic
461C2×C4C13×H(5,𝔽2)11yescharacteristic
462C8—41no—
463C8—41no—
464C8—41no—
465C8—41no—
466C8—41no—
467C8—41no—
468C8—41no—
469C8—41no—
470C22—41no—
471C22—41no—
472C22—81no—
473C22—82no—
474C22—81no—
475C22—161no—
476C22—161no—
477C22C13×#53811yescharacteristic
478C22C13×#55111yescharacteristic
479C22C13×#55111yescharacteristic
480C4—41no—
481C4—41no—
482C4—42no—
483C4—41no—
484C4—81no—
485C4—81no—
486C4—81no—
487C4C13×#53811yescharacteristic
488C4C13×#54011yescharacteristic
489C4C13×#55311yescharacteristic
490C4C13×#56011yescharacteristic
491C2—21no—
492C2—21no—
493C2—21no—
494C2—81no—
495C2—161no—
496C2C13×#274911yescharacteristic
subgroupG/H
center, socleC2×C13#2749
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC2×C13×AGL(1,ℤ/8)C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2102C2semidirect
2. C13×#2081C2semidirect
3. C13×#2081C2semidirect
4. C13×#2070C2semidirect
7. C13×#1967C2semidirect
8. C13×#1932C2semidirect
9. C13×#1915C2semidirect
10. C13×#1912C2semidirect
12. C13×#1888C2semidirect
13. C13×#1861C2semidirect
14. C13×#1841C2semidirect
15. C13×#1830C2semidirect
105. #32699C13direct (N × H)
176. #2102C2×C13semidirect
177. #2081C2×C13semidirect
178. #2081C2×C13semidirect
179. #2070C2×C13semidirect
182. #1967C2×C13semidirect
183. #1932C2×C13semidirect
184. #1915C2×C13semidirect
185. #1912C2×C13semidirect
187. #1888C2×C13semidirect
188. #1861C2×C13semidirect
189. #1841C2×C13semidirect
190. #1830C2×C13semidirect
423. C13#32699direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#21022
C13×#20812
C13×#20702
C13×#20482
C13×#20032
C13×#19672
C13×#19322
C13×#19152
C13×#19122
C13×#19032
C13×#18882
C13×#18612
C13×#18412
C13×#18302
#3269913