Finite Group Databasebeta

← C13×#8473 #15694812

Subgroups — C13×#8473 #15694812

Order 3328.

732 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3503C211yesmaximal, characteristic
2C13×#1997C211yesmaximal, characteristic, complemented
3C13×#1966C211yesmaximal, characteristic, complemented
4C13×#1561C211yesmaximal, characteristic, complemented
5C13×#1526C211yesmaximal, characteristic, complemented
6C13×#1489C211yesmaximal, characteristic
7C13×#1489C211yesmaximal, characteristic
8Q82×C13—21no—
9C13×#557—21no—
10C13×#554—21no—
11C13×#554—22no—
12D4×Q8×C13—22no—
13D4×Q8×C13—21no—
14C13×#544—22no—
15C13×#544C412yes—
16C13×#533—21no—
17C13×#533C2211yescharacteristic
18C2×C13×C4⋊Q8—21no—
19C2×C13×C4⋊Q8C2211yescharacteristic
20C13×#520C412yes—
21C4×C13×#41C2211yescharacteristic
22C13×#423C2211yescharacteristic
23C13×#423C2211yescharacteristic
24C2×C13×#101—22no—
25C4×C13×M16C2211yescharacteristic
26C4×C13×M16C2211yescharacteristic
27C13×#343—22no—
28C13×#332—21no—
29C13×#332—21no—
30C13×#330—22no—
31C13×Q8⋊C8—21no—
32C13×Q8⋊C8—21no—
33C13×D4⋊C8—21no—
34C13×D4⋊C8—21no—
35C2×C13×#41C2×C411yescharacteristic
36C22×Q8×C13—22no—
37C22×Q8×C13D412yes—
38C2×C13×M16—21no—
39C2×C13×M16—21no—
40C2×C13×M16—21no—
41C2×C13×M16—21no—
42C13×C4⋊Q8—22no—
43C13×C4⋊Q8—22no—
44C13×C4⋊Q8—24no—
45C13×C4⋊Q8—22no—
46C13×C4⋊Q8—22no—
47C13×C4⋊Q8—21no—
48C13×C4⋊Q8—21no—
49C13×C4⋊Q8—21no—
50C13×C4⋊Q8—21no—
51C13×C4⋊Q8D411yescharacteristic
52C13×C4⋊Q8D411yescharacteristic
53C13×#125—24no—
54C13×#125—22no—
55C13×#125—22no—
56C13×#125D412yes—
57C13×C22⋊Q8—22no—
58C13×C22⋊Q8—22no—
59C13×C22⋊Q8—24no—
60C13×C22⋊Q8—24no—
61C13×C22⋊Q8—24no—
62C13×C22⋊Q8—21no—
63C13×C22⋊Q8—21no—
64C4×Q8×C13—22no—
65C4×Q8×C13—22no—
66C4×Q8×C13—22no—
67C4×Q8×C13—21no—
68C4×Q8×C13—21no—
69C4×Q8×C13D411yescharacteristic
70C4×Q8×C13D411yescharacteristic
71C4×D4×C13—22no—
72C4×D4×C13—24no—
73C4×D4×C13—21no—
74C4×D4×C13—21no—
75C4×D4×C13D411yescharacteristic
76C4×D4×C13D411yescharacteristic
77C13×#117—22no—
78C13×#117—21no—
79C13×#117C2×C411yescharacteristic
80C13×#117C2×C412yes—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4C2×C412yes—
84C2×C13×C4⋊C4D412yes—
85C2×C42×C13—21no—
86C2×C42×C13C2311yescharacteristic
87C13×C4⋊C8—21no—
88C13×C4⋊C8—21no—
89C13×C4⋊C8—21no—
90C13×C4⋊C8—21no—
91C13×#101—44no—
92C13×#97—21no—
93C13×#97—21no—
94C4×C8×C13—21no—
95C4×C8×C13—21no—
96#8473C1311yesmaximal, characteristic, direct product factor, Sylow
97C13×#41—22no—
98C13×#41—22no—
99C2×Q8×C13—24no—
100C2×Q8×C13—21no—
101C2×Q8×C13—22no—
102C2×Q8×C13—21no—
103C2×Q8×C13—22no—
104C2×Q8×C13—42no—
105C2×Q8×C13—42no—
106C2×Q8×C13—82no—
107C2×Q8×C13—82no—
108C2×Q8×C13C22⋊C411yescharacteristic
109C2×D4×C13—21no—
110C2×D4×C13C22⋊C411yescharacteristic
111C22×C4×C13—21no—
112C22×C4×C13—24no—
113C22×C4×C13—21no—
114C22×C4×C13—21no—
115C22×C4×C13C22⋊C414yes—
116C22×C4×C13C22×C411yescharacteristic
117C22×C4×C13C2×D411yescharacteristic
118C22×C4×C13C2×D411yescharacteristic
119C13×M16—22no—
120C13×M16—22no—
121C13×M16—41no—
122C13×M16—41no—
123C13×M16—42no—
124C13×M16—42no—
125C2×C8×C13—41no—
126C2×C8×C13—41no—
127C2×C8×C13—41no—
128C2×C8×C13—41no—
129C13×C4⋊C4—24no—
130C13×C4⋊C4—24no—
131C13×C4⋊C4—24no—
132C13×C4⋊C4—24no—
133C13×C4⋊C4—22no—
134C13×C4⋊C4—22no—
135C13×C4⋊C4—21no—
136C13×C4⋊C4—22no—
137C13×C4⋊C4—22no—
138C13×C4⋊C4—21no—
139C13×C4⋊C4—21no—
140C13×C4⋊C4—21no—
141C13×C4⋊C4—22no—
142C13×C4⋊C4—22no—
143C13×C4⋊C4C22⋊C412yes—
144C13×C4⋊C4C22⋊C412yes—
145C13×C4⋊C4C22⋊C411yescharacteristic
146C13×C4⋊C4C22⋊C411yescharacteristic
147C13×C22⋊C4—24no—
148C13×C22⋊C4—22no—
149C13×C22⋊C4—21no—
150C13×C22⋊C4—21no—
151C13×C22⋊C4—21no—
152C42×C13—24no—
153C42×C13—21no—
154C42×C13—22no—
155C42×C13—21no—
156C42×C13—21no—
157C42×C13C2×D411yescharacteristic
158C42×C13C2×D411yescharacteristic
159C42×C13C2×D411yescharacteristic
160C42×C13C2×D411yescharacteristic
161#3503C2×C1311yescharacteristic
162#1997C2×C1311yescharacteristic, complemented
163#1966C2×C1311yescharacteristic, complemented
164#1561C2×C1311yescharacteristic, complemented
165#1526C2×C1311yescharacteristic, complemented
166#1489C2×C1311yescharacteristic
167#1489C2×C1311yescharacteristic
168C23×C13—21no—
169C23×C13C2×C22⋊C411yescharacteristic
170Q8×C13—21no—
171Q8×C13—42no—
172Q8×C13—41no—
173Q8×C13—41no—
174Q8×C13—42no—
175Q8×C13—41no—
176Q8×C13—41no—
177Q8×C13—82no—
178Q8×C13—84no—
179Q8×C13#10112yescomplemented
180D4×C13—24no—
181D4×C13—21no—
182D4×C13#10112yescomplemented
183C2×C4×C13—24no—
184C2×C4×C13—21no—
185C2×C4×C13—21no—
186C2×C4×C13—21no—
187C2×C4×C13—21no—
188C2×C4×C13—21no—
189C2×C4×C13—21no—
190C2×C4×C13—21no—
191C2×C4×C13—22no—
192C2×C4×C13—21no—
193C2×C4×C13—21no—
194C2×C4×C13—24no—
195C2×C4×C13—22no—
196C2×C4×C13—41no—
197C2×C4×C13—41no—
198C2×C4×C13—41no—
199C2×C4×C13—41no—
200C2×C4×C13—44no—
201C2×C4×C13—84no—
202C2×C4×C13C2×C22⋊C411yescharacteristic
203C2×C4×C13C2×C22⋊C411yescharacteristic
204C2×C4×C13#12011yescharacteristic
205C2×C4×C13#12011yescharacteristic
206C2×C4×C13#12011yescharacteristic
207C2×C4×C13#12011yescharacteristic
208C8×C13—42no—
209C8×C13—42no—
210C8×C13—81no—
211C8×C13—81no—
212Q82—21no—
213#557—21no—
214#554—21no—
215#554—22no—
216D4×Q8—22no—
217D4×Q8—21no—
218#544—22no—
219#544C4×C1312yes—
220#533—21no—
221#533C22×C1311yescharacteristic
222C2×C4⋊Q8—21no—
223C2×C4⋊Q8C22×C1311yescharacteristic
224#520C4×C1312yes—
225C4×#41C22×C1311yescharacteristic
226#423C22×C1311yescharacteristic
227#423C22×C1311yescharacteristic
228C2×#101—22no—
229C4×M16C22×C1311yescharacteristic
230C4×M16C22×C1311yescharacteristic
231#343—22no—
232#332—21no—
233#332—21no—
234#330—22no—
235Q8⋊C8—21no—
236Q8⋊C8—21no—
237D4⋊C8—21no—
238D4⋊C8—21no—
239C22×C13—21no—
240C22×C13—21no—
241C22×C13—21no—
242C22×C13—22no—
243C22×C13—41no—
244C22×C13—41no—
245C22×C13#37911yescharacteristic
246C4×C13—21no—
247C4×C13—21no—
248C4×C13—21no—
249C4×C13—22no—
250C4×C13—41no—
251C4×C13—44no—
252C4×C13—42no—
253C4×C13—41no—
254C4×C13—42no—
255C4×C13C2×#10111yescharacteristic
256C4×C13C2×#10111yescharacteristic
257C4×C13#45311yescharacteristic
258C4×C13#45411yescharacteristic
259C4×C13#45511yescharacteristic
260C4×C13#45611yescharacteristic
261C2×#41C2×C4×C1311yescharacteristic
262C22×Q8—22no—
263C22×Q8D4×C1312yes—
264C2×M16—21no—
265C2×M16—21no—
266C2×M16—21no—
267C2×M16—21no—
268C4⋊Q8—22no—
269C4⋊Q8—22no—
270C4⋊Q8—24no—
271C4⋊Q8—22no—
272C4⋊Q8—22no—
273C4⋊Q8—21no—
274C4⋊Q8—21no—
275C4⋊Q8—21no—
276C4⋊Q8—21no—
277C4⋊Q8D4×C1311yescharacteristic
278C4⋊Q8D4×C1311yescharacteristic
279#125—24no—
280#125—22no—
281#125—22no—
282#125D4×C1312yes—
283C22⋊Q8—22no—
284C22⋊Q8—22no—
285C22⋊Q8—24no—
286C22⋊Q8—24no—
287C22⋊Q8—24no—
288C22⋊Q8—21no—
289C22⋊Q8—21no—
290C4×Q8—22no—
291C4×Q8—22no—
292C4×Q8—22no—
293C4×Q8—21no—
294C4×Q8—21no—
295C4×Q8D4×C1311yescharacteristic
296C4×Q8D4×C1311yescharacteristic
297C4×D4—22no—
298C4×D4—24no—
299C4×D4—21no—
300C4×D4—21no—
301C4×D4D4×C1311yescharacteristic
302C4×D4D4×C1311yescharacteristic
303#117—22no—
304#117—21no—
305#117C2×C4×C1311yescharacteristic
306#117C2×C4×C1312yes—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4C2×C4×C1312yes—
310C2×C4⋊C4D4×C1312yes—
311C2×C42—21no—
312C2×C42C23×C1311yescharacteristic
313C4⋊C8—21no—
314C4⋊C8—21no—
315C4⋊C8—21no—
316C4⋊C8—21no—
317#101—44no—
318#97—21no—
319#97—21no—
320C4×C8—21no—
321C4×C8—21no—
322C2×C13—41no—
323C2×C13—42no—
324C2×C13#178411yescharacteristic
325C2×C13#179211yescharacteristic
326C2×C13#179311yescharacteristic
327#41—22no—
328#41—22no—
329C2×Q8—24no—
330C2×Q8—21no—
331C2×Q8—22no—
332C2×Q8—21no—
333C2×Q8—22no—
334C2×Q8—42no—
335C2×Q8—42no—
336C2×Q8—82no—
337C2×Q8—82no—
338C2×Q8C13×C22⋊C411yescharacteristic
339C2×D4—21no—
340C2×D4C13×C22⋊C411yescharacteristic
341C22×C4—21no—
342C22×C4—24no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4C13×C22⋊C414yes—
346C22×C4C22×C4×C1311yescharacteristic
347C22×C4C2×D4×C1311yescharacteristic
348C22×C4C2×D4×C1311yescharacteristic
349M16—22no—
350M16—22no—
351M16—41no—
352M16—41no—
353M16—42no—
354M16—42no—
355C2×C8—41no—
356C2×C8—41no—
357C2×C8—41no—
358C2×C8—41no—
359C4⋊C4—24no—
360C4⋊C4—24no—
361C4⋊C4—24no—
362C4⋊C4—24no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—21no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4C13×C22⋊C412yes—
374C4⋊C4C13×C22⋊C412yes—
375C4⋊C4C13×C22⋊C411yescharacteristic
376C4⋊C4C13×C22⋊C411yescharacteristic
377C22⋊C4—24no—
378C22⋊C4—22no—
379C22⋊C4—21no—
380C22⋊C4—21no—
381C22⋊C4—21no—
382C42—24no—
383C42—21no—
384C42—22no—
385C42—21no—
386C42—21no—
387C42C2×D4×C1311yescharacteristic
388C42C2×D4×C1311yescharacteristic
389C42C2×D4×C1311yescharacteristic
390C42C2×D4×C1311yescharacteristic
391C13#847311yescharacteristic, direct product factor, Sylow
392C23—21no—
393C23C2×C13×C22⋊C411yescharacteristic
394Q8—21no—
395Q8—42no—
396Q8—41no—
397Q8—41no—
398Q8—42no—
399Q8—41no—
400Q8—41no—
401Q8—82no—
402Q8—84no—
403Q8C13×#10112yescomplemented
404D4—24no—
405D4—21no—
406D4C13×#10112yescomplemented
407C2×C4—24no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—22no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—24no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—44no—
425C2×C4—84no—
426C2×C4C2×C13×C22⋊C411yescharacteristic
427C2×C4C2×C13×C22⋊C411yescharacteristic
428C2×C4C13×#12011yescharacteristic
429C2×C4C13×#12011yescharacteristic
430C2×C4C13×#12011yescharacteristic
431C2×C4C13×#12011yescharacteristic
432C8—42no—
433C8—42no—
434C8—81no—
435C8—81no—
436C22—21no—
437C22—22no—
438C22—21no—
439C22—21no—
440C22—41no—
441C22—41no—
442C22C13×#37911yescharacteristic
443C4—21no—
444C4—22no—
445C4—21no—
446C4—21no—
447C4—41no—
448C4—44no—
449C4—42no—
450C4—41no—
451C4—42no—
452C4C2×C13×#10111yescharacteristic
453C4C2×C13×#10111yescharacteristic
454C4C13×#45311yescharacteristic
455C4C13×#45411yescharacteristic
456C4C13×#45511yescharacteristic
457C4C13×#45611yescharacteristic
458C2—41no—
459C2—42no—
460C2C13×#178411yescharacteristic
461C2C13×#179211yescharacteristic
462C2C13×#179311yescharacteristic
subgroupG/H
center, socleC22×C13#379
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC2×C13×#41C2×C4
LCSG ▷ C22×C4 ▷ 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×#1997C2semidirect
3. C13×#1966C2semidirect
4. C13×#1561C2semidirect
5. C13×#1526C2semidirect
96. #8473C13direct (N × H)
162. #1997C2×C13semidirect
163. #1966C2×C13semidirect
164. #1561C2×C13semidirect
165. #1526C2×C13semidirect
179. Q8×C13#101semidirect
182. D4×C13#101semidirect
391. C13#8473direct (N × H)
403. Q8C13×#101semidirect
406. D4C13×#101semidirect

Maximal subgroups

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

subgroupindex
C13×#35032
C13×#19972
C13×#19662
C13×#15612
C13×#15262
C13×#14892
#847313