Finite Group Databasebeta

← C13×#10233 #15696572

Subgroups — C13×#10233 #15696572

Order 3328.

644 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#474C211yesmaximal, characteristic
2C2×C13×#462C211yesmaximal, characteristic, complemented
3C13×#2538C211yesmaximal, characteristic
4C13×#1990C211yesmaximal, characteristic, complemented
5C2×C13×Q8⋊C8C211yesmaximal, characteristic, complemented
6C2×C13×D4⋊C8C211yesmaximal, characteristic
7C13×#1296C211yesmaximal, characteristic, complemented
8C22×C13×Q16—21no—
9C2×C13×C4⋊Q8C2211yescharacteristic
10C2×C13×C22⋊Q8—21no—
11C2×C4×Q8×C13C2211yescharacteristic
12C2×C4×D4×C13C2211yescharacteristic
13C13×#474—22no—
14C13×#474—22no—
15C13×#462—22no—
16C13×#462—22no—
17C2×C13×#107—21no—
18C2×C13×C4⋊C8C2211yescharacteristic
19C2×C13×C4⋊C8C2211yescharacteristic
20C2×C13×#103—21no—
21C2×C13×#102—21no—
22C2×C4×C8×C13C2211yescharacteristic
23C13×#396—22no—
24C13×#390—21no—
25C13×#389—21no—
26C13×#384C2211yescharacteristic
27C13×#380—21no—
28C13×#340—22no—
29C13×Q8⋊C8—22no—
30C13×D4⋊C8—22no—
31C22×Q8×C13—21no—
32C22×Q8×C13D411yescharacteristic
33C22×D4×C13D411yescharacteristic
34C23×C4×C13—21no—
35C2×C13×Q16—24no—
36C2×C13×Q16—42no—
37C2×C13×Q16—42no—
38C22×C8×C13—21no—
39C22×C8×C13—21no—
40C22×C8×C13—21no—
41C13×C4⋊Q8—21no—
42C13×C4⋊Q8—21no—
43C13×C4⋊Q8—21no—
44C13×C4⋊Q8D412yes—
45C13×C22⋊Q8—42no—
46C13×C22⋊Q8—42no—
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—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4—21no—
57C2×C13×C4⋊C4—22no—
58C2×C13×C4⋊C4—21no—
59C2×C13×C4⋊C4—21no—
60C2×C13×C4⋊C4—21no—
61C2×C13×C4⋊C4D411yescharacteristic
62C2×C13×C4⋊C4D411yescharacteristic
63C2×C13×C4⋊C4D412yes—
64C2×C13×C22⋊C4—22no—
65C2×C13×C22⋊C4—21no—
66C2×C13×C22⋊C4—22no—
67C2×C42×C13—21no—
68C2×C42×C13C2311yescharacteristic
69C13×#107—24no—
70C13×C4⋊C8—21no—
71C13×C4⋊C8—21no—
72C13×C4⋊C8D412yes—
73C13×C4⋊C8D412yes—
74C13×#103—24no—
75C13×#102—24no—
76C4×C8×C13—21no—
77C4×C8×C13—21no—
78C13×#95—22no—
79#10233C1311yesmaximal, characteristic, direct product factor, Sylow
80C24×C13—21no—
81C2×Q8×C13—21no—
82C2×Q8×C13—21no—
83C2×Q8×C13—22no—
84C2×Q8×C13—21no—
85C2×Q8×C13—21no—
86C2×Q8×C13—21no—
87C2×Q8×C13—41no—
88C2×Q8×C13—41no—
89C2×Q8×C13—41no—
90C2×Q8×C13—41no—
91C2×Q8×C13—41no—
92C2×Q8×C13D812yes—
93C2×D4×C13—21no—
94C2×D4×C13—21no—
95C2×D4×C13—21no—
96C2×D4×C13—21no—
97C2×D4×C13—21no—
98C2×D4×C13Q1612yescomplemented
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13—21no—
102C22×C4×C13—22no—
103C22×C4×C13—41no—
104C22×C4×C13—41no—
105C22×C4×C13—41no—
106C22×C4×C13—41no—
107C22×C4×C13—41no—
108C22×C4×C13—41no—
109C22×C4×C13—41no—
110C22×C4×C13C2×D411yescharacteristic
111C22×C4×C13C2×D411yescharacteristic
112C22×C4×C13C2×D411yescharacteristic
113C13×Q16—48no—
114C2×C8×C13—22no—
115C2×C8×C13—22no—
116C2×C8×C13—22no—
117C2×C8×C13—41no—
118C2×C8×C13—41no—
119C2×C8×C13—41no—
120C2×C8×C13—41no—
121C2×C8×C13—41no—
122C2×C8×C13—41no—
123C13×C4⋊C4—22no—
124C13×C4⋊C4—21no—
125C13×C4⋊C4—21no—
126C13×C4⋊C4—22no—
127C13×C4⋊C4—21no—
128C13×C4⋊C4—21no—
129C13×C4⋊C4—42no—
130C13×C4⋊C4—44no—
131C13×C4⋊C4—41no—
132C13×C4⋊C4—41no—
133C13×C4⋊C4—41no—
134C13×C4⋊C4—41no—
135C13×C4⋊C4—41no—
136C13×C4⋊C4—41no—
137C13×C4⋊C4—41no—
138C13×C4⋊C4—41no—
139C13×C22⋊C4—44no—
140C13×C22⋊C4—41no—
141C13×C22⋊C4—41no—
142C13×C22⋊C4—82no—
143C42×C13—41no—
144C42×C13—41no—
145C42×C13C2×D411yescharacteristic
146C42×C13C2×D411yescharacteristic
147C42×C13C2×D411yescharacteristic
148C42×C13#4111yescharacteristic
149C2×#474C2×C1311yescharacteristic
150C2×#462C2×C1311yescharacteristic, complemented
151#2538C2×C1311yescharacteristic
152#1990C2×C1311yescharacteristic, complemented
153C2×Q8⋊C8C2×C1311yescharacteristic, complemented
154C2×D4⋊C8C2×C1311yescharacteristic
155#1296C2×C1311yescharacteristic, complemented
156C23×C13—22no—
157C23×C13—41no—
158C23×C13—41no—
159C23×C13—41no—
160C23×C13—41no—
161C23×C13—41no—
162C23×C13—41no—
163C23×C13#12011yescharacteristic
164Q8×C13—22no—
165Q8×C13—22no—
166Q8×C13—41no—
167Q8×C13—41no—
168Q8×C13—42no—
169Q8×C13—42no—
170Q8×C13—81no—
171Q8×C13—81no—
172D4×C13—22no—
173D4×C13—22no—
174D4×C13—41no—
175D4×C13—41no—
176C2×C4×C13—21no—
177C2×C4×C13—21no—
178C2×C4×C13—22no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13—41no—
182C2×C4×C13—41no—
183C2×C4×C13—42no—
184C2×C4×C13—42no—
185C2×C4×C13—41no—
186C2×C4×C13—41no—
187C2×C4×C13—42no—
188C2×C4×C13—41no—
189C2×C4×C13—42no—
190C2×C4×C13—41no—
191C2×C4×C13—81no—
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
201C2×C4×C13#12111yescharacteristic
202C2×C4×C13#12711yescharacteristic
203C2×C4×C13C2×D811yescharacteristic
204C2×C4×C13C2×Q1611yescharacteristic
205C2×C4×C13#13511yescharacteristic
206C2×C4×C13#13511yescharacteristic
207C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
208C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
209C2×C4×C13#13711yescharacteristic
210C2×C4×C13#13711yescharacteristic
211C8×C13—42no—
212C8×C13—42no—
213C8×C13—42no—
214C22×Q16—21no—
215C2×C4⋊Q8C22×C1311yescharacteristic
216C2×C22⋊Q8—21no—
217C2×C4×Q8C22×C1311yescharacteristic
218C2×C4×D4C22×C1311yescharacteristic
219#474—22no—
220#474—22no—
221#462—22no—
222#462—22no—
223C2×#107—21no—
224C2×C4⋊C8C22×C1311yescharacteristic
225C2×C4⋊C8C22×C1311yescharacteristic
226C2×#103—21no—
227C2×#102—21no—
228C2×C4×C8C22×C1311yescharacteristic
229#396—22no—
230#390—21no—
231#389—21no—
232#384C22×C1311yescharacteristic
233#380—21no—
234#340—22no—
235Q8⋊C8—22no—
236D4⋊C8—22no—
237C22×C13—42no—
238C22×C13—42no—
239C22×C13—42no—
240C22×C13—81no—
241C22×C13—81no—
242C22×C13—81no—
243C22×C13—81no—
244C22×C13#39211yescharacteristic
245C22×C13#44711yescharacteristic
246C22×C13#44911yescharacteristic
247C22×C13#45111yescharacteristic
248C22×C13#45211yescharacteristic
249C22×C13#45511yescharacteristic
250C22×C13#45611yescharacteristic
251C4×C13—21no—
252C4×C13—21no—
253C4×C13—42no—
254C4×C13—82no—
255C4×C13—81no—
256C4×C13—82no—
257C4×C13—81no—
258C4×C13#44711yescharacteristic
259C4×C13#44911yescharacteristic
260C4×C13#45111yescharacteristic
261C4×C13#45211yescharacteristic
262C4×C13#46611yescharacteristic
263C4×C13#46711yescharacteristic
264C4×C13#46911yescharacteristic
265C4×C13#47011yescharacteristic
266C22×Q8—21no—
267C22×Q8D4×C1311yescharacteristic
268C22×D4D4×C1311yescharacteristic
269C23×C4—21no—
270C2×Q16—24no—
271C2×Q16—42no—
272C2×Q16—42no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C4⋊Q8—21no—
277C4⋊Q8—21no—
278C4⋊Q8—21no—
279C4⋊Q8D4×C1312yes—
280C22⋊Q8—42no—
281C22⋊Q8—42no—
282C4×Q8—21no—
283C4×Q8—21no—
284C4×Q8—21no—
285C4×Q8—21no—
286C4×D4—21no—
287C4×D4—21no—
288C4×D4—21no—
289C4×D4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4D4×C1311yescharacteristic
297C2×C4⋊C4D4×C1311yescharacteristic
298C2×C4⋊C4D4×C1312yes—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—22no—
302C2×C42—21no—
303C2×C42C23×C1311yescharacteristic
304#107—24no—
305C4⋊C8—21no—
306C4⋊C8—21no—
307C4⋊C8D4×C1312yes—
308C4⋊C8D4×C1312yes—
309#103—24no—
310#102—24no—
311C4×C8—21no—
312C4×C8—21no—
313#95—22no—
314C2×C13—82no—
315C2×C13#164111yescharacteristic
316C2×C13#164411yescharacteristic
317C2×C13#164911yescharacteristic
318C2×C13#165211yescharacteristic
319C2×C13#199911yescharacteristic
320C2×C13#200111yescharacteristic
321C2×C13#200711yescharacteristic
322C24—21no—
323C2×Q8—21no—
324C2×Q8—21no—
325C2×Q8—22no—
326C2×Q8—21no—
327C2×Q8—21no—
328C2×Q8—21no—
329C2×Q8—41no—
330C2×Q8—41no—
331C2×Q8—41no—
332C2×Q8—41no—
333C2×Q8—41no—
334C2×Q8C13×D812yes—
335C2×D4—21no—
336C2×D4—21no—
337C2×D4—21no—
338C2×D4—21no—
339C2×D4—21no—
340C2×D4C13×Q1612yescomplemented
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—22no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4C2×D4×C1311yescharacteristic
353C22×C4C2×D4×C1311yescharacteristic
354C22×C4C2×D4×C1311yescharacteristic
355Q16—48no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—41no—
360C2×C8—41no—
361C2×C8—41no—
362C2×C8—41no—
363C2×C8—41no—
364C2×C8—41no—
365C4⋊C4—22no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—42no—
372C4⋊C4—44no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C22⋊C4—44no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—82no—
385C42—41no—
386C42—41no—
387C42C2×D4×C1311yescharacteristic
388C42C2×D4×C1311yescharacteristic
389C42C2×D4×C1311yescharacteristic
390C42C13×#4111yescharacteristic
391C13#1023311yescharacteristic, direct product factor, Sylow
392C23—22no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23C13×#12011yescharacteristic
400Q8—22no—
401Q8—22no—
402Q8—41no—
403Q8—41no—
404Q8—42no—
405Q8—42no—
406Q8—81no—
407Q8—81no—
408D4—22no—
409D4—22no—
410D4—41no—
411D4—41no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—22no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—81no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4—81no—
431C2×C4—81no—
432C2×C4—81no—
433C2×C4C13×#12011yescharacteristic
434C2×C4C13×#12011yescharacteristic
435C2×C4C13×#12111yescharacteristic
436C2×C4C13×#12111yescharacteristic
437C2×C4C13×#12111yescharacteristic
438C2×C4C13×#12711yescharacteristic
439C2×C4C2×C13×D811yescharacteristic
440C2×C4C2×C13×Q1611yescharacteristic
441C2×C4C13×#13511yescharacteristic
442C2×C4C13×#13511yescharacteristic
443C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
444C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
445C2×C4C13×#13711yescharacteristic
446C2×C4C13×#13711yescharacteristic
447C8—42no—
448C8—42no—
449C8—42no—
450C22—42no—
451C22—42no—
452C22—42no—
453C22—81no—
454C22—81no—
455C22—81no—
456C22—81no—
457C22C13×#39211yescharacteristic
458C22C13×#44711yescharacteristic
459C22C13×#44911yescharacteristic
460C22C13×#45111yescharacteristic
461C22C13×#45211yescharacteristic
462C22C13×#45511yescharacteristic
463C22C13×#45611yescharacteristic
464C4—21no—
465C4—21no—
466C4—42no—
467C4—81no—
468C4—82no—
469C4—81no—
470C4—82no—
471C4C13×#44711yescharacteristic
472C4C13×#44911yescharacteristic
473C4C13×#45111yescharacteristic
474C4C13×#45211yescharacteristic
475C4C13×#46611yescharacteristic
476C4C13×#46711yescharacteristic
477C4C13×#46911yescharacteristic
478C4C13×#47011yescharacteristic
479C2—82no—
480C2C13×#164111yescharacteristic
481C2C13×#164411yescharacteristic
482C2C13×#164911yescharacteristic
483C2C13×#165211yescharacteristic
484C2C13×#199911yescharacteristic
485C2C13×#200111yescharacteristic
486C2C13×#200711yescharacteristic
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. C2×C13×#462C2semidirect
4. C13×#1990C2semidirect
5. C2×C13×Q8⋊C8C2semidirect
7. C13×#1296C2semidirect
79. #10233C13direct (N × H)
98. C2×D4×C13Q16semidirect
150. C2×#462C2×C13semidirect
152. #1990C2×C13semidirect
153. C2×Q8⋊C8C2×C13semidirect
155. #1296C2×C13semidirect
340. C2×D4C13×Q16semidirect
391. C13#10233direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#4742
C2×C13×#4622
C13×#25382
C13×#19902
C2×C13×Q8⋊C82
C2×C13×D4⋊C82
C13×#12962
#1023313