Finite Group Databasebeta

← C13×#18392 #15704731

Subgroups — C13×#18392 #15704731

Order 3328.

934 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3507C211yesmaximal, characteristic
2C13×#3209C211yesmaximal, characteristic, complemented
3C13×#3206C211yesmaximal, characteristic
4C13×#2567C211yesmaximal, characteristic, complemented
5C13×#1603C218yesmaximal, complemented
6C13×#1503C211yesmaximal, characteristic, complemented
7C13×#1502C211yesmaximal, characteristic
8C13×#1461C211yesmaximal, characteristic, complemented
9C13×#559—21no—
10C13×#557—21no—
11C13×#556—21no—
12C13×#556—22no—
13C13×#554—21no—
14C13×#552—22no—
15C13×#539C2214yes—
16C13×#536—21no—
17C13×#533C2211yescharacteristic
18C13×#532C2211yescharacteristic
19C2×C13×C4⋊Q8C2211yescharacteristic
20C13×#529—22no—
21C13×#520—21no—
22C2×C4×Q8×C13C2211yescharacteristic
23C13×#494—21no—
24C13×#492—21no—
25C13×#487—21no—
26C13×#487—21no—
27C13×#462—22no—
28C13×#461—22no—
29C13×#451C2214yes—
30C13×#448C2214yes—
31C13×#431C2211yescharacteristic
32C13×#431C2211yescharacteristic
33C13×#395C2214yes—
34C13×#391—21no—
35C13×#389—22no—
36C13×#384—21no—
37C4×C13×C4⋊C4C2211yescharacteristic
38C13×#328C2214yes—
39C13×#327C2214yes—
40C13×#324C2214yes—
41C2×C13×#41—21no—
42C22×Q8×C13D411yescharacteristic
43C22×Q8×C13C2312yes—
44C2×C13×Q16—24no—
45C2×C13×SD16—24no—
46C13×C4⋊Q8—22no—
47C13×C4⋊Q8—21no—
48C13×C4⋊Q8—21no—
49C13×C4⋊Q8—21no—
50C13×C4⋊Q8—21no—
51C13×C4⋊Q8D411yescharacteristic
52C13×C4⋊Q8D411yescharacteristic
53C13×C4⋊Q8D411yescharacteristic
54C13×#127D411yescharacteristic
55C13×#126—24no—
56C13×#126—24no—
57C13×#125—22no—
58C13×#125—24no—
59C13×#125—21no—
60C13×#124—22no—
61C13×#124—22no—
62C13×#124—21no—
63C13×#123—24no—
64C13×#123—24no—
65C13×C22⋊Q8—22no—
66C13×C22⋊Q8—22no—
67C13×C22⋊Q8—24no—
68C13×C22⋊Q8—21no—
69C13×C22⋊Q8C2312yes—
70C13×#121—21no—
71C13×#121C2312yes—
72C4×Q8×C13—22no—
73C4×Q8×C13—22no—
74C4×Q8×C13—21no—
75C4×Q8×C13—21no—
76C4×Q8×C13—21no—
77C4×Q8×C13—21no—
78C4×Q8×C13—21no—
79C4×Q8×C13D412yes—
80C4×D4×C13—22no—
81C4×D4×C13—22no—
82C4×D4×C13—24no—
83C4×D4×C13—21no—
84C4×D4×C13D412yes—
85C13×#117—22no—
86C13×#117—24no—
87C13×#117—21no—
88C2×C13×C4⋊C4—22no—
89C2×C13×C4⋊C4—21no—
90C2×C13×C4⋊C4—21no—
91C2×C13×C4⋊C4—21no—
92C2×C13×C4⋊C4—24no—
93C2×C13×C4⋊C4D411yescharacteristic
94C2×C13×C4⋊C4C2312yes—
95C2×C42×C13—21no—
96C2×C42×C13D412yes—
97C2×C42×C13C2311yescharacteristic
98C13×C4⋊C8—21no—
99C13×C4⋊C8—21no—
100C13×#103—24no—
101C13×#103—24no—
102C13×C22⋊C8C2312yes—
103C13×C22⋊C8C2312yes—
104C4×C8×C13—21no—
105C4×C8×C13—21no—
106C13×#95—24no—
107C13×#95C2312yes—
108#18392C1311yesmaximal, characteristic, direct product factor, Sylow
109C13×#41—42no—
110C13×#41—42no—
111C2×Q8×C13—21no—
112C2×Q8×C13—21no—
113C2×Q8×C13—21no—
114C2×Q8×C13—21no—
115C2×Q8×C13—22no—
116C2×Q8×C13—22no—
117C2×Q8×C13—22no—
118C2×Q8×C13—22no—
119C2×Q8×C13—82no—
120C2×Q8×C13C2×D412yes—
121C2×D4×C13—22no—
122C2×D4×C13—21no—
123C2×D4×C13—21no—
124C2×D4×C13C2×D412yes—
125C22×C4×C13—22no—
126C22×C4×C13—24no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13C2×D412yes—
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D412yes—
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2411yescharacteristic
134C13×Q16—84no—
135C13×SD16—84no—
136C2×C8×C13—22no—
137C2×C8×C13—22no—
138C13×C4⋊C4—24no—
139C13×C4⋊C4—24no—
140C13×C4⋊C4—24no—
141C13×C4⋊C4—24no—
142C13×C4⋊C4—21no—
143C13×C4⋊C4—21no—
144C13×C4⋊C4—21no—
145C13×C4⋊C4—21no—
146C13×C4⋊C4—22no—
147C13×C4⋊C4—21no—
148C13×C4⋊C4—21no—
149C13×C4⋊C4—22no—
150C13×C4⋊C4—22no—
151C13×C4⋊C4—22no—
152C13×C4⋊C4—41no—
153C13×C4⋊C4—41no—
154C13×C4⋊C4—41no—
155C13×C4⋊C4—41no—
156C13×C4⋊C4—84no—
157C13×C4⋊C4C2×D412yes—
158C13×C4⋊C4C2×D412yes—
159C13×C22⋊C4—24no—
160C13×C22⋊C4—24no—
161C13×C22⋊C4—24no—
162C13×C22⋊C4—22no—
163C13×C22⋊C4—22no—
164C13×C22⋊C4—22no—
165C42×C13—24no—
166C42×C13—22no—
167C42×C13—22no—
168C42×C13—22no—
169C42×C13—42no—
170C42×C13C2×D411yescharacteristic
171C42×C13C2×D411yescharacteristic
172C42×C13C2×D411yescharacteristic
173C42×C13C2×D411yescharacteristic
174#3507C2×C1311yescharacteristic
175#3209C2×C1311yescharacteristic, complemented
176#3206C2×C1311yescharacteristic
177#2567C2×C1311yescharacteristic, complemented
178#1603C2×C1318yescomplemented
179#1503C2×C1311yescharacteristic, complemented
180#1502C2×C1311yescharacteristic
181#1461C2×C1311yescharacteristic, complemented
182C23×C13—22no—
183C23×C13C22×D411yescharacteristic
184Q8×C13—42no—
185Q8×C13—44no—
186Q8×C13—44no—
187Q8×C13—42no—
188Q8×C13—42no—
189Q8×C13—42no—
190Q8×C13—42no—
191D4×C13—42no—
192D4×C13—42no—
193D4×C13—42no—
194D4×C13—42no—
195D4×C13—42no—
196C2×C4×C13—22no—
197C2×C4×C13—24no—
198C2×C4×C13—22no—
199C2×C4×C13—22no—
200C2×C4×C13—22no—
201C2×C4×C13—22no—
202C2×C4×C13—22no—
203C2×C4×C13—22no—
204C2×C4×C13—22no—
205C2×C4×C13—41no—
206C2×C4×C13—42no—
207C2×C4×C13—42no—
208C2×C4×C13—44no—
209C2×C4×C13—42no—
210C2×C4×C13—44no—
211C2×C4×C13—42no—
212C2×C4×C13—84no—
213C2×C4×C13#12011yescharacteristic
214C2×C4×C13#12011yescharacteristic
215C2×C4×C13#12011yescharacteristic
216C2×C4×C13#12011yescharacteristic
217C2×C4×C13#13512yes—
218C2×C4×C13#13712yes—
219C2×C4×C13C22×D411yescharacteristic
220C2×C4×C13C22×D411yescharacteristic
221C8×C13—42no—
222C8×C13—42no—
223#559—21no—
224#557—21no—
225#556—21no—
226#556—22no—
227#554—21no—
228#552—22no—
229#539C22×C1314yes—
230#536—21no—
231#533C22×C1311yescharacteristic
232#532C22×C1311yescharacteristic
233C2×C4⋊Q8C22×C1311yescharacteristic
234#529—22no—
235#520—21no—
236C2×C4×Q8C22×C1311yescharacteristic
237#494—21no—
238#492—21no—
239#487—21no—
240#487—21no—
241#462—22no—
242#461—22no—
243#451C22×C1314yes—
244#448C22×C1314yes—
245#431C22×C1311yescharacteristic
246#431C22×C1311yescharacteristic
247#395C22×C1314yes—
248#391—21no—
249#389—22no—
250#384—21no—
251C4×C4⋊C4C22×C1311yescharacteristic
252#328C22×C1314yes—
253#327C22×C1314yes—
254#324C22×C1314yes—
255C22×C13—21no—
256C22×C13—21no—
257C22×C13—42no—
258C22×C13—42no—
259C22×C13—42no—
260C22×C13C2×#12011yescharacteristic
261C22×C13C2×#13511yescharacteristic
262C22×C13C2×#13711yescharacteristic
263C4×C13—21no—
264C4×C13—21no—
265C4×C13—21no—
266C4×C13—44no—
267C4×C13—42no—
268C4×C13—42no—
269C4×C13—42no—
270C4×C13—42no—
271C4×C13—42no—
272C4×C13—82no—
273C4×C13#45212yes—
274C4×C13#45212yes—
275C4×C13#45612yes—
276C2×#41—21no—
277C22×Q8D4×C1311yescharacteristic
278C22×Q8C23×C1312yes—
279C2×Q16—24no—
280C2×SD16—24no—
281C4⋊Q8—22no—
282C4⋊Q8—21no—
283C4⋊Q8—21no—
284C4⋊Q8—21no—
285C4⋊Q8—21no—
286C4⋊Q8D4×C1311yescharacteristic
287C4⋊Q8D4×C1311yescharacteristic
288C4⋊Q8D4×C1311yescharacteristic
289#127D4×C1311yescharacteristic
290#126—24no—
291#126—24no—
292#125—22no—
293#125—24no—
294#125—21no—
295#124—22no—
296#124—22no—
297#124—21no—
298#123—24no—
299#123—24no—
300C22⋊Q8—22no—
301C22⋊Q8—22no—
302C22⋊Q8—24no—
303C22⋊Q8—21no—
304C22⋊Q8C23×C1312yes—
305#121—21no—
306#121C23×C1312yes—
307C4×Q8—22no—
308C4×Q8—22no—
309C4×Q8—21no—
310C4×Q8—21no—
311C4×Q8—21no—
312C4×Q8—21no—
313C4×Q8—21no—
314C4×Q8D4×C1312yes—
315C4×D4—22no—
316C4×D4—22no—
317C4×D4—24no—
318C4×D4—21no—
319C4×D4D4×C1312yes—
320#117—22no—
321#117—24no—
322#117—21no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4D4×C1311yescharacteristic
329C2×C4⋊C4C23×C1312yes—
330C2×C42—21no—
331C2×C42D4×C1312yes—
332C2×C42C23×C1311yescharacteristic
333C4⋊C8—21no—
334C4⋊C8—21no—
335#103—24no—
336#103—24no—
337C22⋊C8C23×C1312yes—
338C22⋊C8C23×C1312yes—
339C4×C8—21no—
340C4×C8—21no—
341#95—24no—
342#95C23×C1312yes—
343C2×C13—21no—
344C2×C13—21no—
345C2×C13—82no—
346C2×C13C2×#45211yescharacteristic
347C2×C13C2×#45611yescharacteristic
348C2×C13#302711yescharacteristic
349#41—42no—
350#41—42no—
351C2×Q8—21no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—22no—
356C2×Q8—22no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8—82no—
360C2×Q8C2×D4×C1312yes—
361C2×D4—22no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4C2×D4×C1312yes—
365C22×C4—22no—
366C22×C4—24no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4C2×D4×C1312yes—
370C22×C4C2×D4×C1311yescharacteristic
371C22×C4C2×D4×C1312yes—
372C22×C4C2×D4×C1311yescharacteristic
373C22×C4C24×C1311yescharacteristic
374Q16—84no—
375SD16—84no—
376C2×C8—22no—
377C2×C8—22no—
378C4⋊C4—24no—
379C4⋊C4—24no—
380C4⋊C4—24no—
381C4⋊C4—24no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—22no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—41no—
393C4⋊C4—41no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4—84no—
397C4⋊C4C2×D4×C1312yes—
398C4⋊C4C2×D4×C1312yes—
399C22⋊C4—24no—
400C22⋊C4—24no—
401C22⋊C4—24no—
402C22⋊C4—22no—
403C22⋊C4—22no—
404C22⋊C4—22no—
405C42—24no—
406C42—22no—
407C42—22no—
408C42—22no—
409C42—42no—
410C42C2×D4×C1311yescharacteristic
411C42C2×D4×C1311yescharacteristic
412C42C2×D4×C1311yescharacteristic
413C42C2×D4×C1311yescharacteristic
414C13#1839211yescharacteristic, direct product factor, Sylow
415C23—22no—
416C23C22×D4×C1311yescharacteristic
417Q8—42no—
418Q8—44no—
419Q8—44no—
420Q8—42no—
421Q8—42no—
422Q8—42no—
423Q8—42no—
424D4—42no—
425D4—42no—
426D4—42no—
427D4—42no—
428D4—42no—
429C2×C4—22no—
430C2×C4—24no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—44no—
442C2×C4—42no—
443C2×C4—44no—
444C2×C4—42no—
445C2×C4—84no—
446C2×C4C13×#12011yescharacteristic
447C2×C4C13×#12011yescharacteristic
448C2×C4C13×#12011yescharacteristic
449C2×C4C13×#12011yescharacteristic
450C2×C4C13×#13512yes—
451C2×C4C13×#13712yes—
452C2×C4C22×D4×C1311yescharacteristic
453C2×C4C22×D4×C1311yescharacteristic
454C8—42no—
455C8—42no—
456C22—21no—
457C22—21no—
458C22—42no—
459C22—42no—
460C22—42no—
461C22C2×C13×#12011yescharacteristic
462C22C2×C13×#13511yescharacteristic
463C22C2×C13×#13711yescharacteristic
464C4—21no—
465C4—21no—
466C4—21no—
467C4—44no—
468C4—42no—
469C4—42no—
470C4—42no—
471C4—42no—
472C4—42no—
473C4—82no—
474C4C13×#45212yes—
475C4C13×#45212yes—
476C4C13×#45612yes—
477C2—21no—
478C2—21no—
479C2—82no—
480C2C2×C13×#45211yescharacteristic
481C2C2×C13×#45611yescharacteristic
482C2C13×#302711yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#532C22
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
2. C13×#3209C2semidirect
4. C13×#2567C2semidirect
5. C13×#1603C2semidirect
6. C13×#1503C2semidirect
8. C13×#1461C2semidirect
108. #18392C13direct (N × H)
175. #3209C2×C13semidirect
177. #2567C2×C13semidirect
178. #1603C2×C13semidirect
179. #1503C2×C13semidirect
181. #1461C2×C13semidirect
414. C13#18392direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35072
C13×#32092
C13×#32062
C13×#25672
C13×#16032
C13×#15032
C13×#15022
C13×#14612
#1839213