Finite Group Databasebeta

← C13×#9958 #15696297

Subgroups — C13×#9958 #15696297

Order 3328.

594 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3187C211yesmaximal, characteristic
2C2×C13×#484C211yesmaximal, characteristic, complemented
3C13×#2504C211yesmaximal, characteristic
4C13×#1996C211yesmaximal, characteristic, complemented
5C13×#1824C211yesmaximal, characteristic, complemented
6C13×#1519C211yesmaximal, characteristic
7C13×#1282C211yesmaximal, characteristic, complemented
8C2×C13×C22⋊Q8C2211yescharacteristic
9C2×C13×#121C2211yescharacteristic
10C22×C13×C4⋊C4C2211yescharacteristic
11C13×#484—22no—
12C13×#484—22no—
13C13×#483—21no—
14C13×#481—21no—
15C13×#465—22no—
16C13×#450—21no—
17C13×#448—21no—
18C2×C13×#107—21no—
19C2×C13×#103—21no—
20C2×C13×C22⋊C8C2211yescharacteristic
21C2×C13×C22⋊C8C2211yescharacteristic
22C13×#397—22no—
23C13×#390—21no—
24C13×#386—22no—
25C13×#382—21no—
26C13×#380C2211yescharacteristic
27C4×C13×C22⋊C4C2211yescharacteristic
28C13×#342—22no—
29C13×#340—22no—
30C13×#327—22no—
31C22×Q8×C13D411yescharacteristic
32C22×D4×C13—21no—
33C22×D4×C13D411yescharacteristic
34C23×C4×C13—21no—
35C23×C4×C13C2311yescharacteristic
36C2×C13×SD16—22no—
37C22×C8×C13—21no—
38C22×C8×C13D412yes—
39C13×C22⋊Q8—21no—
40C13×C22⋊Q8—21no—
41C13×C22⋊Q8—21no—
42C13×C22⋊Q8—21no—
43C13×#121—21no—
44C13×#121—21no—
45C13×#121—21no—
46C13×#121—21no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4D411yescharacteristic
55C2×C13×C4⋊C4D412yes—
56C2×C13×C4⋊C4D411yescharacteristic
57C2×C13×C22⋊C4—21no—
58C2×C13×C22⋊C4—21no—
59C2×C13×C22⋊C4—21no—
60C2×C13×C22⋊C4—24no—
61C2×C13×C22⋊C4D412yes—
62C2×C42×C13—21no—
63C13×#107—24no—
64C13×#106—22no—
65C13×#103—24no—
66C13×#103—22no—
67C13×#102—22no—
68C13×C22⋊C8—21no—
69C13×C22⋊C8—21no—
70C13×C22⋊C8—21no—
71C13×C22⋊C8D412yes—
72C13×#95—24no—
73C13×#95—21no—
74C13×#95—21no—
75#9958C1311yesmaximal, characteristic, direct product factor, Sylow
76C24×C13—21no—
77C24×C13C2×D411yescharacteristic
78C2×Q8×C13—21no—
79C2×Q8×C13—21no—
80C2×Q8×C13—42no—
81C2×D4×C13—21no—
82C2×D4×C13—21no—
83C2×D4×C13—42no—
84C2×D4×C13—41no—
85C2×D4×C13—41no—
86C2×D4×C13—42no—
87C2×D4×C13—42no—
88C22×C4×C13—21no—
89C22×C4×C13—22no—
90C22×C4×C13—22no—
91C22×C4×C13—21no—
92C22×C4×C13—21no—
93C22×C4×C13—42no—
94C22×C4×C13—41no—
95C22×C4×C13—41no—
96C22×C4×C13—41no—
97C22×C4×C13—82no—
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13C2×D411yescharacteristic
103C22×C4×C13#4111yescharacteristic
104C13×SD16—82no—
105C2×C8×C13—22no—
106C2×C8×C13—22no—
107C2×C8×C13—42no—
108C2×C8×C13—42no—
109C13×C4⋊C4—21no—
110C13×C4⋊C4—21no—
111C13×C4⋊C4—22no—
112C13×C4⋊C4—21no—
113C13×C4⋊C4—22no—
114C13×C4⋊C4—21no—
115C13×C4⋊C4—42no—
116C13×C4⋊C4—41no—
117C13×C4⋊C4—41no—
118C13×C4⋊C4—41no—
119C13×C4⋊C4—41no—
120C13×C22⋊C4—22no—
121C13×C22⋊C4—22no—
122C13×C22⋊C4—41no—
123C13×C22⋊C4—41no—
124C13×C22⋊C4—41no—
125C13×C22⋊C4—41no—
126C13×C22⋊C4—42no—
127C13×C22⋊C4—84no—
128C42×C13—42no—
129#3187C2×C1311yescharacteristic
130C2×#484C2×C1311yescharacteristic, complemented
131#2504C2×C1311yescharacteristic
132#1996C2×C1311yescharacteristic, complemented
133#1824C2×C1311yescharacteristic, complemented
134#1519C2×C1311yescharacteristic
135#1282C2×C1311yescharacteristic, complemented
136C23×C13—41no—
137C23×C13—41no—
138C23×C13—42no—
139C23×C13—42no—
140C23×C13—41no—
141C23×C13—42no—
142C23×C13#12011yescharacteristic
143C23×C13#12111yescharacteristic
144C23×C13#12711yescharacteristic
145C23×C13#13512yes—
146C23×C13#13712yes—
147Q8×C13—42no—
148Q8×C13—42no—
149D4×C13—42no—
150D4×C13—81no—
151D4×C13—82no—
152D4×C13—81no—
153D4×C13—81no—
154C2×C4×C13—22no—
155C2×C4×C13—22no—
156C2×C4×C13—22no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—42no—
161C2×C4×C13—42no—
162C2×C4×C13—44no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—42no—
167C2×C4×C13—42no—
168C2×C4×C13—42no—
169C2×C4×C13—82no—
170C2×C4×C13—82no—
171C2×C4×C13—81no—
172C2×C4×C13—81no—
173C2×C4×C13—81no—
174C2×C4×C13—81no—
175C2×C4×C13—81no—
176C2×C4×C13#12011yescharacteristic
177C2×C4×C13#12011yescharacteristic
178C2×C4×C13#12111yescharacteristic
179C2×C4×C13#12111yescharacteristic
180C8×C13—42no—
181C8×C13—42no—
182C2×C22⋊Q8C22×C1311yescharacteristic
183C2×#121C22×C1311yescharacteristic
184C22×C4⋊C4C22×C1311yescharacteristic
185#484—22no—
186#484—22no—
187#483—21no—
188#481—21no—
189#465—22no—
190#450—21no—
191#448—21no—
192C2×#107—21no—
193C2×#103—21no—
194C2×C22⋊C8C22×C1311yescharacteristic
195C2×C22⋊C8C22×C1311yescharacteristic
196#397—22no—
197#390—21no—
198#386—22no—
199#382—21no—
200#380C22×C1311yescharacteristic
201C4×C22⋊C4C22×C1311yescharacteristic
202#342—22no—
203#340—22no—
204#327—22no—
205C22×C13—21no—
206C22×C13—21no—
207C22×C13—21no—
208C22×C13—21no—
209C22×C13—21no—
210C22×C13—21no—
211C22×C13—42no—
212C22×C13—42no—
213C22×C13—84no—
214C22×C13—81no—
215C22×C13—81no—
216C22×C13—81no—
217C22×C13#39211yescharacteristic
218C22×C13#45212yes—
219C22×C13#46412yes—
220C22×C13#49511yescharacteristic
221C22×C13#49711yescharacteristic
222C4×C13—21no—
223C4×C13—21no—
224C4×C13—21no—
225C4×C13—82no—
226C4×C13—82no—
227C4×C13—81no—
228C4×C13—81no—
229C4×C13—81no—
230C4×C13—161no—
231C4×C13#45812yes—
232C22×Q8D4×C1311yescharacteristic
233C22×D4—21no—
234C22×D4D4×C1311yescharacteristic
235C23×C4—21no—
236C23×C4C23×C1311yescharacteristic
237C2×SD16—22no—
238C22×C8—21no—
239C22×C8D4×C1312yes—
240C22⋊Q8—21no—
241C22⋊Q8—21no—
242C22⋊Q8—21no—
243C22⋊Q8—21no—
244#121—21no—
245#121—21no—
246#121—21no—
247#121—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4D4×C1312yes—
256C2×C4⋊C4D4×C1311yescharacteristic
257C2×C4⋊C4D4×C1311yescharacteristic
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—24no—
262C2×C22⋊C4D4×C1312yes—
263C2×C42—21no—
264#107—24no—
265#106—22no—
266#103—24no—
267#103—22no—
268#102—22no—
269C22⋊C8—21no—
270C22⋊C8—21no—
271C22⋊C8—21no—
272C22⋊C8D4×C1312yes—
273#95—24no—
274#95—21no—
275#95—21no—
276C2×C13—22no—
277C2×C13—21no—
278C2×C13—22no—
279C2×C13—21no—
280C2×C13—161no—
281C2×C13#200811yescharacteristic
282C2×C13#201511yescharacteristic
283C2×C13#202211yescharacteristic
284C24—21no—
285C24C2×D4×C1311yescharacteristic
286C2×Q8—21no—
287C2×Q8—21no—
288C2×Q8—42no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—42no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—42no—
295C2×D4—42no—
296C22×C4—21no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—42no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—82no—
306C22×C4C2×D4×C1311yescharacteristic
307C22×C4C2×D4×C1311yescharacteristic
308C22×C4C2×D4×C1311yescharacteristic
309C22×C4C2×D4×C1311yescharacteristic
310C22×C4C2×D4×C1311yescharacteristic
311C22×C4C13×#4111yescharacteristic
312SD16—82no—
313C2×C8—22no—
314C2×C8—22no—
315C2×C8—42no—
316C2×C8—42no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—22no—
320C4⋊C4—21no—
321C4⋊C4—22no—
322C4⋊C4—21no—
323C4⋊C4—42no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C22⋊C4—22no—
329C22⋊C4—22no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—42no—
335C22⋊C4—84no—
336C42—42no—
337C13#995811yescharacteristic, direct product factor, Sylow
338C23—41no—
339C23—41no—
340C23—42no—
341C23—42no—
342C23—41no—
343C23—42no—
344C23C13×#12011yescharacteristic
345C23C13×#12111yescharacteristic
346C23C13×#12711yescharacteristic
347C23C13×#13512yes—
348C23C13×#13712yes—
349Q8—42no—
350Q8—42no—
351D4—42no—
352D4—81no—
353D4—82no—
354D4—81no—
355D4—81no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—44no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—82no—
372C2×C4—82no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4C13×#12011yescharacteristic
379C2×C4C13×#12011yescharacteristic
380C2×C4C13×#12111yescharacteristic
381C2×C4C13×#12111yescharacteristic
382C8—42no—
383C8—42no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—42no—
391C22—42no—
392C22—84no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22C13×#39211yescharacteristic
397C22C13×#45212yes—
398C22C13×#46412yes—
399C22C13×#49511yescharacteristic
400C22C13×#49711yescharacteristic
401C4—21no—
402C4—21no—
403C4—21no—
404C4—82no—
405C4—82no—
406C4—81no—
407C4—81no—
408C4—81no—
409C4—161no—
410C4C13×#45812yes—
411C2—22no—
412C2—21no—
413C2—22no—
414C2—21no—
415C2—161no—
416C2C13×#200811yescharacteristic
417C2C13×#201511yescharacteristic
418C2C13×#202211yescharacteristic
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×#484C2semidirect
4. C13×#1996C2semidirect
5. C13×#1824C2semidirect
7. C13×#1282C2semidirect
75. #9958C13direct (N × H)
130. C2×#484C2×C13semidirect
132. #1996C2×C13semidirect
133. #1824C2×C13semidirect
135. #1282C2×C13semidirect
337. C13#9958direct (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×#4842
C13×#25042
C13×#19962
C13×#18242
C13×#15192
C13×#12822
#995813