Finite Group Databasebeta

← C13×#9956 #15696295

Subgroups — C13×#9956 #15696295

Order 3328.

770 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3187C211yesmaximal, characteristic
2C2×C13×#451C211yesmaximal, characteristic, complemented
3C13×#2436C211yesmaximal, characteristic
4C13×#1996C211yesmaximal, characteristic, complemented
5C13×#1787C211yesmaximal, characteristic, complemented
6C13×#1519C211yesmaximal, characteristic
7C13×#1282C211yesmaximal, characteristic, complemented
8C23×Q8×C13C2211yescharacteristic
9C22×C13×Q16—21no—
10C2×C13×#124—21no—
11C2×C13×C22⋊Q8C2211yescharacteristic
12C2×C13×#121C2211yescharacteristic
13C13×#483—21no—
14C13×#481—21no—
15C13×#465—22no—
16C13×#451—22no—
17C13×#451—22no—
18C13×#450—21no—
19C13×#448—21no—
20C2×C13×#103—21no—
21C2×C13×#103—22no—
22C2×C13×C22⋊C8C2211yescharacteristic
23C2×C13×C22⋊C8C2211yescharacteristic
24C13×#393—22no—
25C13×#391—21no—
26C13×#386—22no—
27C13×#380C2211yescharacteristic
28C4×C13×C22⋊C4C2211yescharacteristic
29C13×#342—22no—
30C13×#327—22no—
31C22×Q8×C13—21no—
32C22×Q8×C13—21no—
33C22×Q8×C13—21no—
34C22×Q8×C13—21no—
35C22×Q8×C13—21no—
36C22×Q8×C13—44no—
37C22×Q8×C13D412yes—
38C22×Q8×C13D411yescharacteristic
39C22×D4×C13—21no—
40C22×D4×C13D411yescharacteristic
41C23×C4×C13—21no—
42C23×C4×C13C2311yescharacteristic
43C2×C13×Q16—24no—
44C2×C13×Q16—44no—
45C2×C13×SD16—22no—
46C22×C8×C13—21no—
47C22×C8×C13D412yes—
48C13×#124—44no—
49C13×C22⋊Q8—21no—
50C13×C22⋊Q8—21no—
51C13×C22⋊Q8—21no—
52C13×C22⋊Q8—21no—
53C13×#121—21no—
54C13×#121—21no—
55C13×#121—21no—
56C13×#121—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⋊C4D412yes—
66C2×C42×C13—21no—
67C13×#106—22no—
68C13×#103—24no—
69C13×#103—22no—
70C13×#103—44no—
71C13×#102—22no—
72C13×C22⋊C8—21no—
73C13×C22⋊C8—21no—
74C13×C22⋊C8—21no—
75C13×C22⋊C8D412yes—
76C13×#95—24no—
77C13×#95—21no—
78C13×#95—21no—
79#9956C1311yesmaximal, characteristic, direct product factor, Sylow
80C24×C13—21no—
81C24×C13C2×D411yescharacteristic
82C2×Q8×C13—24no—
83C2×Q8×C13—24no—
84C2×Q8×C13—24no—
85C2×Q8×C13—22no—
86C2×Q8×C13—21no—
87C2×Q8×C13—21no—
88C2×Q8×C13—22no—
89C2×Q8×C13—44no—
90C2×Q8×C13—42no—
91C2×Q8×C13—42no—
92C2×Q8×C13—42no—
93C2×Q8×C13—42no—
94C2×Q8×C13—44no—
95C2×Q8×C13—44no—
96C2×Q8×C13—41no—
97C2×Q8×C13—41no—
98C2×D4×C13—21no—
99C2×D4×C13—21no—
100C2×D4×C13—42no—
101C2×D4×C13—41no—
102C2×D4×C13—41no—
103C2×D4×C13—42no—
104C2×D4×C13—42no—
105C22×C4×C13—22no—
106C22×C4×C13—21no—
107C22×C4×C13—22no—
108C22×C4×C13—21no—
109C22×C4×C13—21no—
110C22×C4×C13—42no—
111C22×C4×C13—44no—
112C22×C4×C13—41no—
113C22×C4×C13—41no—
114C22×C4×C13—41no—
115C22×C4×C13C2×D411yescharacteristic
116C22×C4×C13C2×D411yescharacteristic
117C22×C4×C13C2×D411yescharacteristic
118C22×C4×C13C2×D411yescharacteristic
119C22×C4×C13C2×D411yescharacteristic
120C22×C4×C13#4111yescharacteristic
121C13×Q16—48no—
122C13×SD16—82no—
123C2×C8×C13—22no—
124C2×C8×C13—22no—
125C2×C8×C13—42no—
126C2×C8×C13—42no—
127C13×C4⋊C4—21no—
128C13×C4⋊C4—21no—
129C13×C4⋊C4—21no—
130C13×C4⋊C4—21no—
131C13×C4⋊C4—42no—
132C13×C4⋊C4—41no—
133C13×C4⋊C4—41no—
134C13×C22⋊C4—22no—
135C13×C22⋊C4—22no—
136C13×C22⋊C4—48no—
137C13×C22⋊C4—41no—
138C13×C22⋊C4—41no—
139C13×C22⋊C4—41no—
140C13×C22⋊C4—41no—
141C13×C22⋊C4—42no—
142C42×C13—42no—
143#3187C2×C1311yescharacteristic
144C2×#451C2×C1311yescharacteristic, complemented
145#2436C2×C1311yescharacteristic
146#1996C2×C1311yescharacteristic, complemented
147#1787C2×C1311yescharacteristic, complemented
148#1519C2×C1311yescharacteristic
149#1282C2×C1311yescharacteristic, complemented
150C23×C13—41no—
151C23×C13—41no—
152C23×C13—42no—
153C23×C13—42no—
154C23×C13—41no—
155C23×C13—42no—
156C23×C13#12011yescharacteristic
157C23×C13#12111yescharacteristic
158C23×C13#12711yescharacteristic
159C23×C13#13512yes—
160C23×C13#13712yes—
161Q8×C13—24no—
162Q8×C13—24no—
163Q8×C13—42no—
164Q8×C13—44no—
165Q8×C13—42no—
166Q8×C13—42no—
167Q8×C13—44no—
168Q8×C13—42no—
169D4×C13—42no—
170D4×C13—81no—
171D4×C13—82no—
172D4×C13—81no—
173D4×C13—81no—
174C2×C4×C13—22no—
175C2×C4×C13—22no—
176C2×C4×C13—22no—
177C2×C4×C13—24no—
178C2×C4×C13—41no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13—42no—
182C2×C4×C13—44no—
183C2×C4×C13—44no—
184C2×C4×C13—42no—
185C2×C4×C13—42no—
186C2×C4×C13—42no—
187C2×C4×C13—41no—
188C2×C4×C13—41no—
189C2×C4×C13—41no—
190C2×C4×C13—42no—
191C2×C4×C13—42no—
192C2×C4×C13—81no—
193C2×C4×C13—81no—
194C2×C4×C13—81no—
195C2×C4×C13—81no—
196C2×C4×C13—81no—
197C2×C4×C13#12011yescharacteristic
198C2×C4×C13#12011yescharacteristic
199C2×C4×C13#12111yescharacteristic
200C2×C4×C13#12111yescharacteristic
201C8×C13—42no—
202C8×C13—42no—
203C23×Q8C22×C1311yescharacteristic
204C22×Q16—21no—
205C2×#124—21no—
206C2×C22⋊Q8C22×C1311yescharacteristic
207C2×#121C22×C1311yescharacteristic
208#483—21no—
209#481—21no—
210#465—22no—
211#451—22no—
212#451—22no—
213#450—21no—
214#448—21no—
215C2×#103—21no—
216C2×#103—22no—
217C2×C22⋊C8C22×C1311yescharacteristic
218C2×C22⋊C8C22×C1311yescharacteristic
219#393—22no—
220#391—21no—
221#386—22no—
222#380C22×C1311yescharacteristic
223C4×C22⋊C4C22×C1311yescharacteristic
224#342—22no—
225#327—22no—
226C22×C13—21no—
227C22×C13—21no—
228C22×C13—21no—
229C22×C13—21no—
230C22×C13—21no—
231C22×C13—21no—
232C22×C13—42no—
233C22×C13—42no—
234C22×C13—84no—
235C22×C13—81no—
236C22×C13—81no—
237C22×C13—81no—
238C22×C13#39211yescharacteristic
239C22×C13#45212yes—
240C22×C13#46412yes—
241C22×C13#49511yescharacteristic
242C22×C13#49711yescharacteristic
243C4×C13—21no—
244C4×C13—21no—
245C4×C13—21no—
246C4×C13—44no—
247C4×C13—82no—
248C4×C13—81no—
249C4×C13—81no—
250C4×C13—81no—
251C4×C13—161no—
252C4×C13B(4,𝔽2)12yes—
253C22×Q8—21no—
254C22×Q8—21no—
255C22×Q8—21no—
256C22×Q8—21no—
257C22×Q8—21no—
258C22×Q8—44no—
259C22×Q8D4×C1311yescharacteristic
260C22×Q8D4×C1312yes—
261C22×D4—21no—
262C22×D4D4×C1311yescharacteristic
263C23×C4—21no—
264C23×C4C23×C1311yescharacteristic
265C2×Q16—24no—
266C2×Q16—44no—
267C2×SD16—22no—
268C22×C8—21no—
269C22×C8D4×C1312yes—
270#124—44no—
271C22⋊Q8—21no—
272C22⋊Q8—21no—
273C22⋊Q8—21no—
274C22⋊Q8—21no—
275#121—21no—
276#121—21no—
277#121—21no—
278#121—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4D4×C1311yescharacteristic
282C2×C4⋊C4D4×C1311yescharacteristic
283C2×C22⋊C4—24no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4D4×C1312yes—
288C2×C42—21no—
289#106—22no—
290#103—24no—
291#103—22no—
292#103—44no—
293#102—22no—
294C22⋊C8—21no—
295C22⋊C8—21no—
296C22⋊C8—21no—
297C22⋊C8D4×C1312yes—
298#95—24no—
299#95—21no—
300#95—21no—
301C2×C13—22no—
302C2×C13—21no—
303C2×C13—22no—
304C2×C13—21no—
305C2×C13—161no—
306C2×C13#200911yescharacteristic
307C2×C13#201511yescharacteristic
308C2×C13#202111yescharacteristic
309C24—21no—
310C24C2×D4×C1311yescharacteristic
311C2×Q8—24no—
312C2×Q8—24no—
313C2×Q8—24no—
314C2×Q8—22no—
315C2×Q8—21no—
316C2×Q8—21no—
317C2×Q8—22no—
318C2×Q8—44no—
319C2×Q8—42no—
320C2×Q8—42no—
321C2×Q8—42no—
322C2×Q8—42no—
323C2×Q8—44no—
324C2×Q8—44no—
325C2×Q8—41no—
326C2×Q8—41no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—42no—
330C2×D4—41no—
331C2×D4—41no—
332C2×D4—42no—
333C2×D4—42no—
334C22×C4—22no—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—42no—
340C22×C4—44no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4C2×D4×C1311yescharacteristic
345C22×C4C2×D4×C1311yescharacteristic
346C22×C4C2×D4×C1311yescharacteristic
347C22×C4C2×D4×C1311yescharacteristic
348C22×C4C2×D4×C1311yescharacteristic
349C22×C4C13×#4111yescharacteristic
350Q16—48no—
351SD16—82no—
352C2×C8—22no—
353C2×C8—22no—
354C2×C8—42no—
355C2×C8—42no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—42no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—48no—
366C22⋊C4—41no—
367C22⋊C4—41no—
368C22⋊C4—41no—
369C22⋊C4—41no—
370C22⋊C4—42no—
371C42—42no—
372C13#995611yescharacteristic, direct product factor, Sylow
373C23—41no—
374C23—41no—
375C23—42no—
376C23—42no—
377C23—41no—
378C23—42no—
379C23C13×#12011yescharacteristic
380C23C13×#12111yescharacteristic
381C23C13×#12711yescharacteristic
382C23C13×#13512yes—
383C23C13×#13712yes—
384Q8—24no—
385Q8—24no—
386Q8—42no—
387Q8—44no—
388Q8—42no—
389Q8—42no—
390Q8—44no—
391Q8—42no—
392D4—42no—
393D4—81no—
394D4—82no—
395D4—81no—
396D4—81no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—24no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—44no—
406C2×C4—44no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—81no—
416C2×C4—81no—
417C2×C4—81no—
418C2×C4—81no—
419C2×C4—81no—
420C2×C4C13×#12011yescharacteristic
421C2×C4C13×#12011yescharacteristic
422C2×C4C13×#12111yescharacteristic
423C2×C4C13×#12111yescharacteristic
424C8—42no—
425C8—42no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—42no—
433C22—42no—
434C22—84no—
435C22—81no—
436C22—81no—
437C22—81no—
438C22C13×#39211yescharacteristic
439C22C13×#45212yes—
440C22C13×#46412yes—
441C22C13×#49511yescharacteristic
442C22C13×#49711yescharacteristic
443C4—21no—
444C4—21no—
445C4—21no—
446C4—44no—
447C4—82no—
448C4—81no—
449C4—81no—
450C4—81no—
451C4—161no—
452C4C13×B(4,𝔽2)12yes—
453C2—22no—
454C2—21no—
455C2—22no—
456C2—21no—
457C2—161no—
458C2C13×#200911yescharacteristic
459C2C13×#201511yescharacteristic
460C2C13×#202111yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC2×C13×#121C22
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
2. C2×C13×#451C2semidirect
4. C13×#1996C2semidirect
5. C13×#1787C2semidirect
7. C13×#1282C2semidirect
79. #9956C13direct (N × H)
144. C2×#451C2×C13semidirect
146. #1996C2×C13semidirect
147. #1787C2×C13semidirect
149. #1282C2×C13semidirect
372. C13#9956direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31872
C2×C13×#4512
C13×#24362
C13×#19962
C13×#17872
C13×#15192
C13×#12822
#995613