Finite Group Databasebeta

← C13×#10001 #15696340

Subgroups — C13×#10001 #15696340

Order 3328.

568 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3101C211yesmaximal, characteristic
2C13×#3078C211yesmaximal, characteristic, complemented
3C13×#2536C211yesmaximal, characteristic
4C13×#1518C211yesmaximal, characteristic, complemented
5C13×#1486C211yesmaximal, characteristic
6C13×#1479C211yesmaximal, characteristic, complemented
7C13×#1286C211yesmaximal, characteristic, complemented
8C13×#533C2211yescharacteristic
9C2×C13×C22⋊Q8—21no—
10C2×C4×Q8×C13C2211yescharacteristic
11C2×C4×D4×C13C2211yescharacteristic
12C13×#483—21no—
13C13×#479—22no—
14C13×#477—21no—
15C13×#476—21no—
16C13×#475—21no—
17C13×#461—21no—
18C13×#450—21no—
19C4×C13×SD16—22no—
20C13×#431C2211yescharacteristic
21C13×#431C2211yescharacteristic
22C13×#428—21no—
23C13×#423C2211yescharacteristic
24C13×#419—21no—
25C13×#398—21no—
26C13×#394—21no—
27C13×#388—22no—
28C13×#382C2211yescharacteristic
29C13×#380—21no—
30C13×#328—22no—
31C13×Q8⋊C8—22no—
32C13×D4⋊C8—22no—
33C22×Q8×C13D411yescharacteristic
34C22×D4×C13D411yescharacteristic
35C23×C4×C13—21no—
36C2×C13×SD16—22no—
37C2×C13×M16—21no—
38C13×C4⋊Q8D411yescharacteristic
39C13×C4⋊Q8D411yescharacteristic
40C13×#125—21no—
41C13×C22⋊Q8—21no—
42C13×C22⋊Q8—21no—
43C13×C22⋊Q8—42no—
44C13×C22⋊Q8—42no—
45C4×Q8×C13—21no—
46C4×Q8×C13—21no—
47C4×Q8×C13—21no—
48C4×Q8×C13—21no—
49C4×Q8×C13—21no—
50C4×Q8×C13—21no—
51C4×D4×C13—21no—
52C4×D4×C13—21no—
53C4×D4×C13—21no—
54C4×D4×C13—21no—
55C13×#117—21no—
56C2×C13×C4⋊C4—22no—
57C2×C13×C4⋊C4—21no—
58C2×C13×C4⋊C4—21no—
59C2×C13×C4⋊C4D411yescharacteristic
60C2×C13×C4⋊C4D411yescharacteristic
61C2×C13×C22⋊C4—22no—
62C2×C13×C22⋊C4—22no—
63C2×C13×C22⋊C4—21no—
64C2×C42×C13—21no—
65C2×C42×C13C2311yescharacteristic
66C13×#107—22no—
67C13×#106—22no—
68C13×#106—22no—
69C13×C4⋊C8—21no—
70C13×C4⋊C8—21no—
71C13×C4⋊C8—21no—
72C13×C4⋊C8D412yes—
73C13×#103—22no—
74C13×#103—22no—
75C13×#103—22no—
76C13×#102—22no—
77C13×C22⋊C8—21no—
78C13×C22⋊C8—21no—
79C4×C8×C13—21no—
80C4×C8×C13D412yes—
81C13×#95—22no—
82C13×#95—21no—
83C13×#95D412yes—
84#10001C1311yesmaximal, characteristic, direct product factor, Sylow
85C24×C13—21no—
86C2×Q8×C13—21no—
87C2×Q8×C13—21no—
88C2×Q8×C13—21no—
89C2×Q8×C13—21no—
90C2×Q8×C13—21no—
91C2×Q8×C13—21no—
92C2×Q8×C13—21no—
93C2×Q8×C13SD1612yescomplemented
94C2×D4×C13—21no—
95C2×D4×C13—21no—
96C2×D4×C13—42no—
97C22×C4×C13—21no—
98C22×C4×C13—22no—
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13—41no—
102C22×C4×C13—41no—
103C22×C4×C13—41no—
104C22×C4×C13—41no—
105C22×C4×C13—41no—
106C22×C4×C13—41no—
107C22×C4×C13C2×D411yescharacteristic
108C22×C4×C13C2×D411yescharacteristic
109C22×C4×C13C2×D411yescharacteristic
110C13×SD16—44no—
111C13×M16—41no—
112C13×M16—41no—
113C2×C8×C13—22no—
114C2×C8×C13—22no—
115C2×C8×C13—41no—
116C13×C4⋊C4—21no—
117C13×C4⋊C4—21no—
118C13×C4⋊C4—21no—
119C13×C4⋊C4—21no—
120C13×C4⋊C4—21no—
121C13×C4⋊C4—21no—
122C13×C4⋊C4—21no—
123C13×C4⋊C4—21no—
124C13×C4⋊C4—44no—
125C13×C4⋊C4—41no—
126C13×C4⋊C4—41no—
127C13×C4⋊C4—41no—
128C13×C4⋊C4—41no—
129C13×C4⋊C4—41no—
130C13×C4⋊C4—41no—
131C13×C22⋊C4—44no—
132C13×C22⋊C4—44no—
133C13×C22⋊C4—41no—
134C13×C22⋊C4—41no—
135C13×C22⋊C4—41no—
136C42×C13—41no—
137C42×C13—41no—
138C42×C13—41no—
139C42×C13C2×D411yescharacteristic
140C42×C13C2×D411yescharacteristic
141C42×C13C2×D411yescharacteristic
142C42×C13#4111yescharacteristic
143#3101C2×C1311yescharacteristic
144#3078C2×C1311yescharacteristic, complemented
145#2536C2×C1311yescharacteristic
146#1518C2×C1311yescharacteristic, complemented
147#1486C2×C1311yescharacteristic
148#1479C2×C1311yescharacteristic, complemented
149#1286C2×C1311yescharacteristic, complemented
150C23×C13—22no—
151C23×C13—41no—
152C23×C13—41no—
153C23×C13—41no—
154C23×C13—41no—
155C23×C13—41no—
156C23×C13—41no—
157C23×C13#12011yescharacteristic
158Q8×C13—22no—
159Q8×C13—22no—
160Q8×C13—42no—
161Q8×C13—41no—
162Q8×C13—41no—
163Q8×C13—81no—
164D4×C13—22no—
165D4×C13—22no—
166D4×C13—41no—
167D4×C13—41no—
168C2×C4×C13—22no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13—42no—
174C2×C4×C13—42no—
175C2×C4×C13—42no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13—41no—
179C2×C4×C13—41no—
180C2×C4×C13—42no—
181C2×C4×C13—41no—
182C2×C4×C13—41no—
183C2×C4×C13—81no—
184C2×C4×C13—81no—
185C2×C4×C13—81no—
186C2×C4×C13—81no—
187C2×C4×C13#12011yescharacteristic
188C2×C4×C13#12011yescharacteristic
189C2×C4×C13#12111yescharacteristic
190C2×C4×C13#12111yescharacteristic
191C2×C4×C13#12111yescharacteristic
192C2×C4×C13#12711yescharacteristic
193C2×C4×C13C2×SD1611yescharacteristic
194C2×C4×C13#13511yescharacteristic
195C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
196C2×C4×C13#13711yescharacteristic
197C8×C13—42no—
198C8×C13—42no—
199C8×C13—81no—
200#533C22×C1311yescharacteristic
201C2×C22⋊Q8—21no—
202C2×C4×Q8C22×C1311yescharacteristic
203C2×C4×D4C22×C1311yescharacteristic
204#483—21no—
205#479—22no—
206#477—21no—
207#476—21no—
208#475—21no—
209#461—21no—
210#450—21no—
211C4×SD16—22no—
212#431C22×C1311yescharacteristic
213#431C22×C1311yescharacteristic
214#428—21no—
215#423C22×C1311yescharacteristic
216#419—21no—
217#398—21no—
218#394—21no—
219#388—22no—
220#382C22×C1311yescharacteristic
221#380—21no—
222#328—22no—
223Q8⋊C8—22no—
224D4⋊C8—22no—
225C22×C13—21no—
226C22×C13—21no—
227C22×C13—42no—
228C22×C13—42no—
229C22×C13—42no—
230C22×C13—81no—
231C22×C13—81no—
232C22×C13—81no—
233C22×C13—81no—
234C22×C13#39211yescharacteristic
235C22×C13#45011yescharacteristic
236C22×C13#45211yescharacteristic
237C4×C13—21no—
238C4×C13—21no—
239C4×C13—21no—
240C4×C13—21no—
241C4×C13—42no—
242C4×C13—82no—
243C4×C13—81no—
244C4×C13—81no—
245C4×C13—81no—
246C4×C13—81no—
247C4×C13#44811yescharacteristic
248C4×C13#44911yescharacteristic
249C4×C13#46511yescharacteristic
250C4×C13#46811yescharacteristic
251C22×Q8D4×C1311yescharacteristic
252C22×D4D4×C1311yescharacteristic
253C23×C4—21no—
254C2×SD16—22no—
255C2×M16—21no—
256C4⋊Q8D4×C1311yescharacteristic
257C4⋊Q8D4×C1311yescharacteristic
258#125—21no—
259C22⋊Q8—21no—
260C22⋊Q8—21no—
261C22⋊Q8—42no—
262C22⋊Q8—42no—
263C4×Q8—21no—
264C4×Q8—21no—
265C4×Q8—21no—
266C4×Q8—21no—
267C4×Q8—21no—
268C4×Q8—21no—
269C4×D4—21no—
270C4×D4—21no—
271C4×D4—21no—
272C4×D4—21no—
273#117—21no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4D4×C1311yescharacteristic
278C2×C4⋊C4D4×C1311yescharacteristic
279C2×C22⋊C4—22no—
280C2×C22⋊C4—22no—
281C2×C22⋊C4—21no—
282C2×C42—21no—
283C2×C42C23×C1311yescharacteristic
284#107—22no—
285#106—22no—
286#106—22no—
287C4⋊C8—21no—
288C4⋊C8—21no—
289C4⋊C8—21no—
290C4⋊C8D4×C1312yes—
291#103—22no—
292#103—22no—
293#103—22no—
294#102—22no—
295C22⋊C8—21no—
296C22⋊C8—21no—
297C4×C8—21no—
298C4×C8D4×C1312yes—
299#95—22no—
300#95—21no—
301#95D4×C1312yes—
302C2×C13—21no—
303C2×C13—21no—
304C2×C13—82no—
305C2×C13#200011yescharacteristic
306C2×C13#200911yescharacteristic
307C2×C13#201011yescharacteristic
308C24—21no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8—21no—
315C2×Q8—21no—
316C2×Q8C13×SD1612yescomplemented
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—42no—
320C22×C4—21no—
321C22×C4—22no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4C2×D4×C1311yescharacteristic
331C22×C4C2×D4×C1311yescharacteristic
332C22×C4C2×D4×C1311yescharacteristic
333SD16—44no—
334M16—41no—
335M16—41no—
336C2×C8—22no—
337C2×C8—22no—
338C2×C8—41no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—44no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C22⋊C4—44no—
355C22⋊C4—44no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—41no—
359C42—41no—
360C42—41no—
361C42—41no—
362C42C2×D4×C1311yescharacteristic
363C42C2×D4×C1311yescharacteristic
364C42C2×D4×C1311yescharacteristic
365C42C13×#4111yescharacteristic
366C13#1000111yescharacteristic, direct product factor, Sylow
367C23—22no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23C13×#12011yescharacteristic
375Q8—22no—
376Q8—22no—
377Q8—42no—
378Q8—41no—
379Q8—41no—
380Q8—81no—
381D4—22no—
382D4—22no—
383D4—41no—
384D4—41no—
385C2×C4—22no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4C13×#12011yescharacteristic
405C2×C4C13×#12011yescharacteristic
406C2×C4C13×#12111yescharacteristic
407C2×C4C13×#12111yescharacteristic
408C2×C4C13×#12111yescharacteristic
409C2×C4C13×#12711yescharacteristic
410C2×C4C2×C13×SD1611yescharacteristic
411C2×C4C13×#13511yescharacteristic
412C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
413C2×C4C13×#13711yescharacteristic
414C8—42no—
415C8—42no—
416C8—81no—
417C22—21no—
418C22—21no—
419C22—42no—
420C22—42no—
421C22—42no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22C13×#39211yescharacteristic
427C22C13×#45011yescharacteristic
428C22C13×#45211yescharacteristic
429C4—21no—
430C4—21no—
431C4—21no—
432C4—21no—
433C4—42no—
434C4—82no—
435C4—81no—
436C4—81no—
437C4—81no—
438C4—81no—
439C4C13×#44811yescharacteristic
440C4C13×#44911yescharacteristic
441C4C13×#46511yescharacteristic
442C4C13×#46811yescharacteristic
443C2—21no—
444C2—21no—
445C2—82no—
446C2C13×#200011yescharacteristic
447C2C13×#200911yescharacteristic
448C2C13×#201011yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC2×C42C23×C13
prime radicalC22×D4×C13D4
LCSG ▷ C2×C42 ▷ 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×#3078C2semidirect
4. C13×#1518C2semidirect
6. C13×#1479C2semidirect
7. C13×#1286C2semidirect
84. #10001C13direct (N × H)
93. C2×Q8×C13SD16semidirect
144. #3078C2×C13semidirect
146. #1518C2×C13semidirect
148. #1479C2×C13semidirect
149. #1286C2×C13semidirect
316. C2×Q8C13×SD16semidirect
366. C13#10001direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31012
C13×#30782
C13×#25362
C13×#15182
C13×#14862
C13×#14792
C13×#12862
#1000113