Finite Group Databasebeta

← C13×#10412 #15696751

Subgroups — C13×#10412 #15696751

Order 3328.

516 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2563C211yesmaximal, characteristic
2C13×#1956C211yesmaximal, characteristic, complemented
3C13×#1948C211yesmaximal, characteristic, complemented
4C13×#1802C211yesmaximal, characteristic
5C2×C13×#333C211yesmaximal, characteristic, complemented
6C2×C13×D4⋊C8C211yesmaximal, characteristic
7C13×#1279C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C4×D4×C13C2211yescharacteristic
10C2×C13×#106—21no—
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×C13×C4⋊C8C2211yescharacteristic
13C2×C13×#103—22no—
14C2×C13×#102—21no—
15C2×C4×C8×C13C2211yescharacteristic
16C13×#393—22no—
17C13×#390—21no—
18C13×#384C2211yescharacteristic
19C13×#382—21no—
20C13×#380—21no—
21C13×#380—21no—
22C4×C13×C4⋊C4C2211yescharacteristic
23C13×#340—21no—
24C13×#340—21no—
25C13×#333—22no—
26C13×D4⋊C8—22no—
27C22×Q8×C13D412yes—
28C22×D4×C13D411yescharacteristic
29C23×C4×C13—21no—
30C22×C8×C13—21no—
31C22×C8×C13—21no—
32C22×C8×C13—21no—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C4×D4×C13—21no—
38C4×D4×C13—21no—
39C4×D4×C13—21no—
40C4×D4×C13—21no—
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4D411yescharacteristic
47C2×C13×C4⋊C4D411yescharacteristic
48C2×C13×C4⋊C4D411yescharacteristic
49C2×C13×C22⋊C4—21no—
50C2×C13×C22⋊C4—22no—
51C2×C13×C22⋊C4—22no—
52C2×C42×C13—21no—
53C2×C42×C13C2311yescharacteristic
54C13×#106—42no—
55C13×C4⋊C8—21no—
56C13×C4⋊C8—21no—
57C13×C4⋊C8—21no—
58C13×C4⋊C8D412yes—
59C13×#103—44no—
60C13×#102—42no—
61C4×C8×C13—21no—
62C4×C8×C13—21no—
63C13×#95—22no—
64C13×#95—22no—
65C13×#95—21no—
66#10412C1311yesmaximal, characteristic, direct product factor, Sylow
67C24×C13—21no—
68C2×Q8×C13—22no—
69C2×Q8×C13—22no—
70C2×Q8×C13—42no—
71C2×Q8×C13—42no—
72C2×D4×C13—21no—
73C2×D4×C13—21no—
74C2×D4×C13—21no—
75C2×D4×C13—21no—
76C2×D4×C13—21no—
77C2×D4×C13SD1612yes—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—21no—
81C22×C4×C13—22no—
82C22×C4×C13—41no—
83C22×C4×C13—41no—
84C22×C4×C13—41no—
85C22×C4×C13—41no—
86C22×C4×C13—41no—
87C22×C4×C13—41no—
88C22×C4×C13—41no—
89C22×C4×C13C2×D411yescharacteristic
90C22×C4×C13C2×D411yescharacteristic
91C22×C4×C13C2×D411yescharacteristic
92C2×C8×C13—22no—
93C2×C8×C13—22no—
94C2×C8×C13—41no—
95C2×C8×C13—41no—
96C2×C8×C13—41no—
97C2×C8×C13—41no—
98C2×C8×C13—41no—
99C2×C8×C13—41no—
100C2×C8×C13—41no—
101C13×C4⋊C4—21no—
102C13×C4⋊C4—21no—
103C13×C4⋊C4—21no—
104C13×C4⋊C4—21no—
105C13×C4⋊C4—21no—
106C13×C4⋊C4—21no—
107C13×C4⋊C4—42no—
108C13×C4⋊C4—41no—
109C13×C4⋊C4—41no—
110C13×C4⋊C4—41no—
111C13×C4⋊C4—41no—
112C13×C4⋊C4—41no—
113C13×C4⋊C4—41no—
114C13×C4⋊C4—41no—
115C13×C4⋊C4—41no—
116C13×C22⋊C4—41no—
117C13×C22⋊C4—41no—
118C13×C22⋊C4—82no—
119C13×C22⋊C4—82no—
120C42×C13—41no—
121C42×C13—41no—
122C42×C13C2×D411yescharacteristic
123C42×C13#4111yescharacteristic
124C42×C13#4111yescharacteristic
125C42×C13#4111yescharacteristic
126#2563C2×C1311yescharacteristic
127#1956C2×C1311yescharacteristic, complemented
128#1948C2×C1311yescharacteristic, complemented
129#1802C2×C1311yescharacteristic
130C2×#333C2×C1311yescharacteristic, complemented
131C2×D4⋊C8C2×C1311yescharacteristic
132#1279C2×C1311yescharacteristic, complemented
133C23×C13—22no—
134C23×C13—41no—
135C23×C13—41no—
136C23×C13—41no—
137C23×C13—41no—
138C23×C13—41no—
139C23×C13—41no—
140C23×C13#12011yescharacteristic
141Q8×C13—44no—
142Q8×C13—82no—
143D4×C13—22no—
144D4×C13—22no—
145D4×C13—41no—
146D4×C13—41no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—41no—
150C2×C4×C13—42no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—42no—
159C2×C4×C13—41no—
160C2×C4×C13—42no—
161C2×C4×C13—81no—
162C2×C4×C13—81no—
163C2×C4×C13—81no—
164C2×C4×C13—81no—
165C2×C4×C13—81no—
166C2×C4×C13—81no—
167C2×C4×C13—81no—
168C2×C4×C13#12111yescharacteristic
169C2×C4×C13#12111yescharacteristic
170C2×C4×C13#12111yescharacteristic
171C2×C4×C13#12311yescharacteristic
172C2×C4×C13#12311yescharacteristic
173C2×C4×C13#12411yescharacteristic
174C2×C4×C13C2×SD1611yescharacteristic
175C2×C4×C13#13511yescharacteristic
176C2×C4×C13#13511yescharacteristic
177C2×C4×C13#13511yescharacteristic
178C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
179C2×C4×C13#13711yescharacteristic
180C2×C4×C13#13711yescharacteristic
181C2×C4×C13#13711yescharacteristic
182C8×C13—42no—
183C8×C13—42no—
184C8×C13—81no—
185C2×C4⋊Q8C22×C1311yescharacteristic
186C2×C4×D4C22×C1311yescharacteristic
187C2×#106—21no—
188C2×C4⋊C8C22×C1311yescharacteristic
189C2×C4⋊C8C22×C1311yescharacteristic
190C2×#103—22no—
191C2×#102—21no—
192C2×C4×C8C22×C1311yescharacteristic
193#393—22no—
194#390—21no—
195#384C22×C1311yescharacteristic
196#382—21no—
197#380—21no—
198#380—21no—
199C4×C4⋊C4C22×C1311yescharacteristic
200#340—21no—
201#340—21no—
202#333—22no—
203D4⋊C8—22no—
204C22×C13—42no—
205C22×C13—42no—
206C22×C13—42no—
207C22×C13—81no—
208C22×C13—81no—
209C22×C13—81no—
210C22×C13—81no—
211C22×C13#39411yescharacteristic
212C22×C13#44811yescharacteristic
213C22×C13#44911yescharacteristic
214C22×C13#45211yescharacteristic
215C22×C13#45211yescharacteristic
216C22×C13#45311yescharacteristic
217C22×C13#45511yescharacteristic
218C4×C13—21no—
219C4×C13—21no—
220C4×C13—81no—
221C4×C13—81no—
222C4×C13—82no—
223C4×C13—81no—
224C4×C13—161no—
225C4×C13#46311yescharacteristic
226C4×C13#46411yescharacteristic
227C4×C13#46511yescharacteristic
228C4×C13#47011yescharacteristic
229C4×C13#48311yescharacteristic
230C4×C13#48511yescharacteristic
231C4×C13#48811yescharacteristic
232C4×C13#48911yescharacteristic
233C22×Q8D4×C1312yes—
234C22×D4D4×C1311yescharacteristic
235C23×C4—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8—21no—
242C4⋊Q8—21no—
243C4×D4—21no—
244C4×D4—21no—
245C4×D4—21no—
246C4×D4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4D4×C1311yescharacteristic
253C2×C4⋊C4D4×C1311yescharacteristic
254C2×C4⋊C4D4×C1311yescharacteristic
255C2×C22⋊C4—21no—
256C2×C22⋊C4—22no—
257C2×C22⋊C4—22no—
258C2×C42—21no—
259C2×C42C23×C1311yescharacteristic
260#106—42no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8D4×C1312yes—
265#103—44no—
266#102—42no—
267C4×C8—21no—
268C4×C8—21no—
269#95—22no—
270#95—22no—
271#95—21no—
272C2×C13—82no—
273C2×C13#162211yescharacteristic
274C2×C13#163411yescharacteristic
275C2×C13#164311yescharacteristic
276C2×C13#164611yescharacteristic
277C2×C13#203511yescharacteristic
278C2×C13#203711yescharacteristic
279C2×C13#204211yescharacteristic
280C24—21no—
281C2×Q8—22no—
282C2×Q8—22no—
283C2×Q8—42no—
284C2×Q8—42no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4C13×SD1612yes—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—22no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4C2×D4×C1311yescharacteristic
303C22×C4C2×D4×C1311yescharacteristic
304C22×C4C2×D4×C1311yescharacteristic
305C2×C8—22no—
306C2×C8—22no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—42no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—82no—
332C22⋊C4—82no—
333C42—41no—
334C42—41no—
335C42C2×D4×C1311yescharacteristic
336C42C13×#4111yescharacteristic
337C42C13×#4111yescharacteristic
338C42C13×#4111yescharacteristic
339C13#1041211yescharacteristic, direct product factor, Sylow
340C23—22no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23C13×#12011yescharacteristic
348Q8—44no—
349Q8—82no—
350D4—22no—
351D4—22no—
352D4—41no—
353D4—41no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4C13×#12111yescharacteristic
376C2×C4C13×#12111yescharacteristic
377C2×C4C13×#12111yescharacteristic
378C2×C4C13×#12311yescharacteristic
379C2×C4C13×#12311yescharacteristic
380C2×C4C13×#12411yescharacteristic
381C2×C4C2×C13×SD1611yescharacteristic
382C2×C4C13×#13511yescharacteristic
383C2×C4C13×#13511yescharacteristic
384C2×C4C13×#13511yescharacteristic
385C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
386C2×C4C13×#13711yescharacteristic
387C2×C4C13×#13711yescharacteristic
388C2×C4C13×#13711yescharacteristic
389C8—42no—
390C8—42no—
391C8—81no—
392C22—42no—
393C22—42no—
394C22—42no—
395C22—81no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22C13×#39411yescharacteristic
400C22C13×#44811yescharacteristic
401C22C13×#44911yescharacteristic
402C22C13×#45211yescharacteristic
403C22C13×#45211yescharacteristic
404C22C13×#45311yescharacteristic
405C22C13×#45511yescharacteristic
406C4—21no—
407C4—21no—
408C4—82no—
409C4—81no—
410C4—81no—
411C4—81no—
412C4—161no—
413C4C13×#46311yescharacteristic
414C4C13×#46411yescharacteristic
415C4C13×#46511yescharacteristic
416C4C13×#47011yescharacteristic
417C4C13×#48311yescharacteristic
418C4C13×#48511yescharacteristic
419C4C13×#48811yescharacteristic
420C4C13×#48911yescharacteristic
421C2—82no—
422C2C13×#162211yescharacteristic
423C2C13×#163411yescharacteristic
424C2C13×#164311yescharacteristic
425C2C13×#164611yescharacteristic
426C2C13×#203511yescharacteristic
427C2C13×#203711yescharacteristic
428C2C13×#204211yescharacteristic
subgroupG/H
center, socleC23×C13#120
commutator, Frattini, cosocleC2×C42C23×C13
prime radicalC22×D4×C13D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#1956C2semidirect
3. C13×#1948C2semidirect
5. C2×C13×#333C2semidirect
7. C13×#1279C2semidirect
66. #10412C13direct (N × H)
127. #1956C2×C13semidirect
128. #1948C2×C13semidirect
130. C2×#333C2×C13semidirect
132. #1279C2×C13semidirect
339. C13#10412direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25632
C13×#19562
C13×#19482
C13×#18022
C2×C13×#3332
C2×C13×D4⋊C82
C13×#12792
#1041213