Finite Group Databasebeta

← C13×#9955 #15696294

Subgroups — C13×#9955 #15696294

Order 3328.

888 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3189C211yesmaximal, characteristic, complemented
2C2×C13×#450C211yesmaximal, characteristic
3C13×#2435C211yesmaximal, characteristic
4C13×#1996C211yesmaximal, characteristic, complemented
5C13×#1786C211yesmaximal, characteristic
6C13×#1520C211yesmaximal, characteristic, complemented
7C13×#1282C211yesmaximal, characteristic, complemented
8C23×D4×C13C2211yescharacteristic
9C22×C13×SD16—21no—
10C2×C13×#124—21no—
11C2×C13×C22⋊Q8C2211yescharacteristic
12C2×C13×C22⋊Q8C2211yescharacteristic
13C13×#484—21no—
14C13×#484—21no—
15C13×#467—22no—
16C13×#451—21no—
17C13×#451—21no—
18C13×#450—22no—
19C13×#450—22no—
20C2×C13×#102—21no—
21C2×C13×#102—22no—
22C2×C13×C22⋊C8C2211yescharacteristic
23C2×C13×C22⋊C8C2211yescharacteristic
24C13×#394—22no—
25C13×#390—21no—
26C13×#380C2211yescharacteristic
27C13×#379—22no—
28C4×C13×C22⋊C4C2211yescharacteristic
29C13×#342—22no—
30C13×#328—22no—
31C25×C13—21no—
32C22×Q8×C13D411yescharacteristic
33C22×Q8×C13D411yescharacteristic
34C22×D4×C13—21no—
35C22×D4×C13—21no—
36C22×D4×C13—21no—
37C22×D4×C13—21no—
38C22×D4×C13—21no—
39C22×D4×C13—44no—
40C22×D4×C13D412yes—
41C23×C4×C13C2311yescharacteristic
42C2×C13×Q16—22no—
43C2×C13×SD16—24no—
44C2×C13×SD16—44no—
45C22×C8×C13—21no—
46C22×C8×C13D412yes—
47C13×#124—44no—
48C13×C22⋊Q8—21no—
49C13×C22⋊Q8—21no—
50C13×C22⋊Q8—21no—
51C13×C22⋊Q8—21no—
52C13×C22⋊Q8—21no—
53C13×C22⋊Q8—21no—
54C13×C22⋊Q8—21no—
55C13×C22⋊Q8—21no—
56C2×C13×C4⋊C4—21no—
57C2×C13×C4⋊C4—21no—
58C2×C13×C4⋊C4—21no—
59C2×C13×C4⋊C4D411yescharacteristic
60C2×C13×C4⋊C4D411yescharacteristic
61C2×C13×C22⋊C4—24no—
62C2×C13×C22⋊C4—21no—
63C2×C13×C22⋊C4—21no—
64C2×C13×C22⋊C4—21no—
65C2×C13×C22⋊C4—24no—
66C2×C13×C22⋊C4D412yes—
67C2×C42×C13—21no—
68C13×#107—22no—
69C13×#103—22no—
70C13×#103—22no—
71C13×#102—24no—
72C13×#102—44no—
73C13×C22⋊C8—21no—
74C13×C22⋊C8—21no—
75C13×C22⋊C8—21no—
76C13×C22⋊C8D412yes—
77C13×#95—21no—
78C13×#95—21no—
79#9955C1311yesmaximal, characteristic, direct product factor, Sylow
80C24×C13—22no—
81C24×C13—44no—
82C24×C13—41no—
83C24×C13—41no—
84C24×C13—42no—
85C24×C13—42no—
86C24×C13—82no—
87C24×C13C2×D411yescharacteristic
88C2×Q8×C13—21no—
89C2×Q8×C13—21no—
90C2×Q8×C13—21no—
91C2×Q8×C13—21no—
92C2×Q8×C13—42no—
93C2×Q8×C13—42no—
94C2×D4×C13—24no—
95C2×D4×C13—24no—
96C2×D4×C13—24no—
97C2×D4×C13—22no—
98C2×D4×C13—22no—
99C2×D4×C13—42no—
100C2×D4×C13—42no—
101C2×D4×C13—42no—
102C2×D4×C13—44no—
103C2×D4×C13—44no—
104C2×D4×C13—44no—
105C2×D4×C13—41no—
106C2×D4×C13—41no—
107C22×C4×C13—22no—
108C22×C4×C13—21no—
109C22×C4×C13—21no—
110C22×C4×C13—21no—
111C22×C4×C13—21no—
112C22×C4×C13—42no—
113C22×C4×C13—41no—
114C22×C4×C13C2×D411yescharacteristic
115C22×C4×C13C2×D411yescharacteristic
116C22×C4×C13C2×D411yescharacteristic
117C22×C4×C13C2×D411yescharacteristic
118C22×C4×C13C2×D411yescharacteristic
119C22×C4×C13#4111yescharacteristic
120C13×Q16—82no—
121C13×SD16—48no—
122C2×C8×C13—22no—
123C2×C8×C13—22no—
124C2×C8×C13—42no—
125C2×C8×C13—42no—
126C13×C4⋊C4—21no—
127C13×C4⋊C4—21no—
128C13×C4⋊C4—21no—
129C13×C4⋊C4—21no—
130C13×C4⋊C4—42no—
131C13×C4⋊C4—41no—
132C13×C4⋊C4—41no—
133C13×C4⋊C4—41no—
134C13×C4⋊C4—41no—
135C13×C22⋊C4—22no—
136C13×C22⋊C4—22no—
137C13×C22⋊C4—48no—
138C13×C22⋊C4—41no—
139C13×C22⋊C4—41no—
140C13×C22⋊C4—41no—
141C13×C22⋊C4—41no—
142C13×C22⋊C4—42no—
143C13×C22⋊C4—84no—
144C42×C13—42no—
145#3189C2×C1311yescharacteristic, complemented
146C2×#450C2×C1311yescharacteristic
147#2435C2×C1311yescharacteristic
148#1996C2×C1311yescharacteristic, complemented
149#1786C2×C1311yescharacteristic
150#1520C2×C1311yescharacteristic, complemented
151#1282C2×C1311yescharacteristic, complemented
152C23×C13—24no—
153C23×C13—41no—
154C23×C13—41no—
155C23×C13—44no—
156C23×C13—44no—
157C23×C13—44no—
158C23×C13—42no—
159C23×C13—42no—
160C23×C13—44no—
161C23×C13—82no—
162C23×C13—82no—
163C23×C13—88no—
164C23×C13—88no—
165C23×C13—82no—
166C23×C13—81no—
167C23×C13—81no—
168C23×C13#12011yescharacteristic
169C23×C13#12111yescharacteristic
170C23×C13#12711yescharacteristic
171C23×C13#13512yes—
172C23×C13#13712yes—
173Q8×C13—42no—
174Q8×C13—42no—
175Q8×C13—42no—
176Q8×C13—81no—
177D4×C13—24no—
178D4×C13—24no—
179D4×C13—42no—
180D4×C13—42no—
181D4×C13—44no—
182D4×C13—44no—
183C2×C4×C13—22no—
184C2×C4×C13—22no—
185C2×C4×C13—22no—
186C2×C4×C13—41no—
187C2×C4×C13—41no—
188C2×C4×C13—41no—
189C2×C4×C13—42no—
190C2×C4×C13—42no—
191C2×C4×C13—42no—
192C2×C4×C13—42no—
193C2×C4×C13—41no—
194C2×C4×C13—41no—
195C2×C4×C13—41no—
196C2×C4×C13—41no—
197C2×C4×C13—42no—
198C2×C4×C13—81no—
199C2×C4×C13—81no—
200C2×C4×C13—81no—
201C2×C4×C13—81no—
202C2×C4×C13—81no—
203C2×C4×C13#12011yescharacteristic
204C2×C4×C13#12011yescharacteristic
205C2×C4×C13#12111yescharacteristic
206C2×C4×C13#12111yescharacteristic
207C8×C13—42no—
208C8×C13—42no—
209C23×D4C22×C1311yescharacteristic
210C22×SD16—21no—
211C2×#124—21no—
212C2×C22⋊Q8C22×C1311yescharacteristic
213C2×C22⋊Q8C22×C1311yescharacteristic
214#484—21no—
215#484—21no—
216#467—22no—
217#451—21no—
218#451—21no—
219#450—22no—
220#450—22no—
221C2×#102—21no—
222C2×#102—22no—
223C2×C22⋊C8C22×C1311yescharacteristic
224C2×C22⋊C8C22×C1311yescharacteristic
225#394—22no—
226#390—21no—
227#380C22×C1311yescharacteristic
228#379—22no—
229C4×C22⋊C4C22×C1311yescharacteristic
230#342—22no—
231#328—22no—
232C22×C13—21no—
233C22×C13—21no—
234C22×C13—21no—
235C22×C13—21no—
236C22×C13—21no—
237C22×C13—21no—
238C22×C13—42no—
239C22×C13—42no—
240C22×C13—48no—
241C22×C13—44no—
242C22×C13—84no—
243C22×C13—84no—
244C22×C13—88no—
245C22×C13—84no—
246C22×C13—82no—
247C22×C13—82no—
248C22×C13#39211yescharacteristic
249C22×C13#45212yes—
250C22×C13#46412yes—
251C22×C13#49511yescharacteristic
252C22×C13#49711yescharacteristic
253C4×C13—21no—
254C4×C13—21no—
255C4×C13—21no—
256C4×C13—82no—
257C4×C13—81no—
258C4×C13—81no—
259C4×C13—81no—
260C4×C13—81no—
261C4×C13—161no—
262C4×C13B(4,𝔽2)12yes—
263C25—21no—
264C22×Q8D4×C1311yescharacteristic
265C22×Q8D4×C1311yescharacteristic
266C22×D4—21no—
267C22×D4—21no—
268C22×D4—21no—
269C22×D4—21no—
270C22×D4—21no—
271C22×D4—44no—
272C22×D4D4×C1312yes—
273C23×C4C23×C1311yescharacteristic
274C2×Q16—22no—
275C2×SD16—24no—
276C2×SD16—44no—
277C22×C8—21no—
278C22×C8D4×C1312yes—
279#124—44no—
280C22⋊Q8—21no—
281C22⋊Q8—21no—
282C22⋊Q8—21no—
283C22⋊Q8—21no—
284C22⋊Q8—21no—
285C22⋊Q8—21no—
286C22⋊Q8—21no—
287C22⋊Q8—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4D4×C1311yescharacteristic
292C2×C4⋊C4D4×C1311yescharacteristic
293C2×C22⋊C4—24no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—21no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4D4×C1312yes—
299C2×C42—21no—
300#107—22no—
301#103—22no—
302#103—22no—
303#102—24no—
304#102—44no—
305C22⋊C8—21no—
306C22⋊C8—21no—
307C22⋊C8—21no—
308C22⋊C8D4×C1312yes—
309#95—21no—
310#95—21no—
311C2×C13—22no—
312C2×C13—21no—
313C2×C13—22no—
314C2×C13—21no—
315C2×C13—84no—
316C2×C13#200811yescharacteristic
317C2×C13#201511yescharacteristic
318C2×C13#202111yescharacteristic
319C24—22no—
320C24—44no—
321C24—41no—
322C24—41no—
323C24—42no—
324C24—42no—
325C24—82no—
326C24C2×D4×C1311yescharacteristic
327C2×Q8—21no—
328C2×Q8—21no—
329C2×Q8—21no—
330C2×Q8—21no—
331C2×Q8—42no—
332C2×Q8—42no—
333C2×D4—24no—
334C2×D4—24no—
335C2×D4—24no—
336C2×D4—22no—
337C2×D4—22no—
338C2×D4—42no—
339C2×D4—42no—
340C2×D4—42no—
341C2×D4—44no—
342C2×D4—44no—
343C2×D4—44no—
344C2×D4—41no—
345C2×D4—41no—
346C22×C4—22no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—42no—
352C22×C4—41no—
353C22×C4C2×D4×C1311yescharacteristic
354C22×C4C2×D4×C1311yescharacteristic
355C22×C4C2×D4×C1311yescharacteristic
356C22×C4C2×D4×C1311yescharacteristic
357C22×C4C2×D4×C1311yescharacteristic
358C22×C4C13×#4111yescharacteristic
359Q16—82no—
360SD16—48no—
361C2×C8—22no—
362C2×C8—22no—
363C2×C8—42no—
364C2×C8—42no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—42no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C22⋊C4—22no—
375C22⋊C4—22no—
376C22⋊C4—48no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—42no—
382C22⋊C4—84no—
383C42—42no—
384C13#995511yescharacteristic, direct product factor, Sylow
385C23—24no—
386C23—41no—
387C23—41no—
388C23—44no—
389C23—44no—
390C23—44no—
391C23—42no—
392C23—42no—
393C23—44no—
394C23—82no—
395C23—82no—
396C23—88no—
397C23—88no—
398C23—82no—
399C23—81no—
400C23—81no—
401C23C13×#12011yescharacteristic
402C23C13×#12111yescharacteristic
403C23C13×#12711yescharacteristic
404C23C13×#13512yes—
405C23C13×#13712yes—
406Q8—42no—
407Q8—42no—
408Q8—42no—
409Q8—81no—
410D4—24no—
411D4—24no—
412D4—42no—
413D4—42no—
414D4—44no—
415D4—44no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—81no—
432C2×C4—81no—
433C2×C4—81no—
434C2×C4—81no—
435C2×C4—81no—
436C2×C4C13×#12011yescharacteristic
437C2×C4C13×#12011yescharacteristic
438C2×C4C13×#12111yescharacteristic
439C2×C4C13×#12111yescharacteristic
440C8—42no—
441C8—42no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—42no—
449C22—42no—
450C22—48no—
451C22—44no—
452C22—84no—
453C22—84no—
454C22—88no—
455C22—84no—
456C22—82no—
457C22—82no—
458C22C13×#39211yescharacteristic
459C22C13×#45212yes—
460C22C13×#46412yes—
461C22C13×#49511yescharacteristic
462C22C13×#49711yescharacteristic
463C4—21no—
464C4—21no—
465C4—21no—
466C4—82no—
467C4—81no—
468C4—81no—
469C4—81no—
470C4—81no—
471C4—161no—
472C4C13×B(4,𝔽2)12yes—
473C2—22no—
474C2—21no—
475C2—22no—
476C2—21no—
477C2—84no—
478C2C13×#200811yescharacteristic
479C2C13×#201511yescharacteristic
480C2C13×#202111yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC23×D4×C13C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3189C2semidirect
4. C13×#1996C2semidirect
6. C13×#1520C2semidirect
7. C13×#1282C2semidirect
79. #9955C13direct (N × H)
145. #3189C2×C13semidirect
148. #1996C2×C13semidirect
150. #1520C2×C13semidirect
151. #1282C2×C13semidirect
384. C13#9955direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31892
C2×C13×#4502
C13×#24352
C13×#19962
C13×#17862
C13×#15202
C13×#12822
#995513