Finite Group Databasebeta

← C13×#12852 #15699191

Subgroups — C13×#12852 #15699191

Order 3328.

992 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 992 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#386C211yesmaximal, characteristic
2C13×#1783C211yesmaximal, characteristic
3C13×#1781C211yesmaximal, characteristic
4C13×#1390C214yesmaximal, complemented
5C23×D4×C13C2211yescharacteristic
6C24×C4×C13C411yescharacteristic, complemented
7C22×C13×C22⋊C4—21no—
8C22×C13×C22⋊C4C411yescharacteristic, complemented
9C2×C13×#100—21no—
10C2×C13×#100C2212yes—
11C2×C13×#99—21no—
12C2×C13×#99C2212yes—
13C13×#407—21no—
14C13×#386—21no—
15C13×#386—21no—
16C13×#386C412yescomplemented
17C13×#386C2212yes—
18C13×#379—21no—
19C2×C13×#95—21no—
20C25×C13C2×C411yescharacteristic
21C25×C13D411yescharacteristic
22C22×D4×C13—24no—
23C22×D4×C13—41no—
24C22×D4×C13—41no—
25C22×D4×C13—42no—
26C22×D4×C13C2×C411yescharacteristic
27C22×D4×C13D411yescharacteristic
28C22×D4×C13D411yescharacteristic
29C22×D4×C13C2311yescharacteristic
30C23×C4×C13—21no—
31C23×C4×C13—21no—
32C23×C4×C13—21no—
33C23×C4×C13—44no—
34C23×C4×C13—41no—
35C23×C4×C13—41no—
36C23×C4×C13C2×C412yes—
37C23×C4×C13D411yescharacteristic
38C2×C13×M16—22no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—22no—
41C2×C13×C22⋊C4—22no—
42C2×C13×C22⋊C4—22no—
43C2×C13×C22⋊C4—44no—
44C2×C13×C22⋊C4—42no—
45C2×C13×C22⋊C4—41no—
46C2×C13×C22⋊C4—41no—
47C2×C13×C22⋊C4C2×C412yes—
48C13×#100—24no—
49C13×#100—42no—
50C13×#99—24no—
51C13×#99—42no—
52C13×C22⋊C8—41no—
53C13×C22⋊C8—41no—
54C13×#95—22no—
55C13×#95—22no—
56#12852C1311yesmaximal, characteristic, direct product factor, Sylow
57C24×C13—22no—
58C24×C13—21no—
59C24×C13—21no—
60C24×C13—22no—
61C24×C13—22no—
62C24×C13—21no—
63C24×C13—21no—
64C24×C13—41no—
65C24×C13—42no—
66C24×C13—42no—
67C24×C13—42no—
68C24×C13—42no—
69C24×C13C22⋊C411yescharacteristic
70C24×C13C22⋊C411yescharacteristic
71C24×C13C22⋊C411yescharacteristic
72C24×C13C22×C411yescharacteristic
73C24×C13C2×D411yescharacteristic
74C2×D4×C13—22no—
75C2×D4×C13—22no—
76C2×D4×C13—22no—
77C2×D4×C13—22no—
78C2×D4×C13—22no—
79C2×D4×C13—41no—
80C2×D4×C13—41no—
81C2×D4×C13—41no—
82C2×D4×C13—41no—
83C2×D4×C13—41no—
84C2×D4×C13—41no—
85C2×D4×C13—48no—
86C2×D4×C13—48no—
87C2×D4×C13#4114yes—
88C22×C4×C13—24no—
89C22×C4×C13—21no—
90C22×C4×C13—21no—
91C22×C4×C13—22no—
92C22×C4×C13—22no—
93C22×C4×C13—22no—
94C22×C4×C13—41no—
95C22×C4×C13—44no—
96C22×C4×C13—44no—
97C22×C4×C13—42no—
98C22×C4×C13—42no—
99C22×C4×C13—48no—
100C22×C4×C13—44no—
101C22×C4×C13—41no—
102C22×C4×C13—41no—
103C22×C4×C13—42no—
104C22×C4×C13—44no—
105C22×C4×C13—42no—
106C22×C4×C13—42no—
107C22×C4×C13—42no—
108C22×C4×C13—42no—
109C22×C4×C13C22⋊C411yescharacteristic
110C22×C4×C13C2×D411yescharacteristic
111C13×M16—42no—
112C13×M16—42no—
113C2×C8×C13—42no—
114C13×C22⋊C4—44no—
115C13×C22⋊C4—44no—
116C13×C22⋊C4—42no—
117C13×C22⋊C4—42no—
118C13×C22⋊C4—42no—
119C13×C22⋊C4—42no—
120C13×C22⋊C4—82no—
121C13×C22⋊C4—82no—
122C2×#386C2×C1311yescharacteristic
123#1783C2×C1311yescharacteristic
124#1781C2×C1311yescharacteristic
125#1390C2×C1314yescomplemented
126C23×C13—22no—
127C23×C13—22no—
128C23×C13—21no—
129C23×C13—21no—
130C23×C13—24no—
131C23×C13—24no—
132C23×C13—21no—
133C23×C13—21no—
134C23×C13—21no—
135C23×C13—21no—
136C23×C13—21no—
137C23×C13—21no—
138C23×C13—21no—
139C23×C13—21no—
140C23×C13—21no—
141C23×C13—42no—
142C23×C13—42no—
143C23×C13—42no—
144C23×C13—48no—
145C23×C13—48no—
146C23×C13—42no—
147C23×C13—41no—
148C23×C13—41no—
149C23×C13—41no—
150C23×C13—41no—
151C23×C13—41no—
152C23×C13—41no—
153C23×C13—41no—
154C23×C13—41no—
155C23×C13—48no—
156C23×C13—42no—
157C23×C13—42no—
158C23×C13—42no—
159C23×C13—42no—
160C23×C13—81no—
161C23×C13—81no—
162C23×C13—84no—
163C23×C13#9911yescharacteristic
164C23×C13#9911yescharacteristic
165C23×C13#9912yes—
166C23×C13C2×C22⋊C411yescharacteristic
167C23×C13#11712yes—
168C23×C13#12312yes—
169D4×C13—44no—
170D4×C13—44no—
171D4×C13—44no—
172D4×C13—44no—
173C2×C4×C13—21no—
174C2×C4×C13—21no—
175C2×C4×C13—24no—
176C2×C4×C13—21no—
177C2×C4×C13—21no—
178C2×C4×C13—21no—
179C2×C4×C13—42no—
180C2×C4×C13—42no—
181C2×C4×C13—42no—
182C2×C4×C13—44no—
183C2×C4×C13—48no—
184C2×C4×C13—44no—
185C2×C4×C13—44no—
186C2×C4×C13—42no—
187C2×C4×C13—44no—
188C2×C4×C13—42no—
189C2×C4×C13—42no—
190C2×C4×C13—42no—
191C2×C4×C13—84no—
192C2×C4×C13—82no—
193C2×C4×C13—82no—
194C2×C4×C13—82no—
195C2×C4×C13#12312yes—
196C8×C13—82no—
197C23×D4C22×C1311yescharacteristic
198C24×C4C4×C1311yescharacteristic, complemented
199C22×C22⋊C4—21no—
200C22×C22⋊C4C4×C1311yescharacteristic, complemented
201C2×#100—21no—
202C2×#100C22×C1312yes—
203C2×#99—21no—
204C2×#99C22×C1312yes—
205#407—21no—
206#386—21no—
207#386—21no—
208#386C4×C1312yescomplemented
209#386C22×C1312yes—
210#379—21no—
211C2×#95—21no—
212C22×C13—24no—
213C22×C13—24no—
214C22×C13—21no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13—21no—
218C22×C13—21no—
219C22×C13—21no—
220C22×C13—22no—
221C22×C13—22no—
222C22×C13—22no—
223C22×C13—42no—
224C22×C13—42no—
225C22×C13—42no—
226C22×C13—42no—
227C22×C13—42no—
228C22×C13—48no—
229C22×C13—48no—
230C22×C13—42no—
231C22×C13—41no—
232C22×C13—41no—
233C22×C13—41no—
234C22×C13—41no—
235C22×C13—41no—
236C22×C13—41no—
237C22×C13—41no—
238C22×C13—41no—
239C22×C13—41no—
240C22×C13—81no—
241C22×C13—84no—
242C22×C13—84no—
243C22×C13—81no—
244C22×C13AΣL(1,𝔽16)12yes—
245C22×C13#35212yes—
246C22×C13#38111yescharacteristic
247C22×C13C2×#9911yescharacteristic
248C22×C13C2×#9911yescharacteristic
249C4×C13—22no—
250C4×C13—41no—
251C4×C13—44no—
252C4×C13—82no—
253C4×C13—162no—
254C25C2×C4×C1311yescharacteristic
255C25D4×C1311yescharacteristic
256C22×D4—24no—
257C22×D4—41no—
258C22×D4—41no—
259C22×D4—42no—
260C22×D4C2×C4×C1311yescharacteristic
261C22×D4D4×C1311yescharacteristic
262C22×D4D4×C1311yescharacteristic
263C22×D4C23×C1311yescharacteristic
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—44no—
268C23×C4—41no—
269C23×C4—41no—
270C23×C4C2×C4×C1312yes—
271C23×C4D4×C1311yescharacteristic
272C2×M16—22no—
273C2×C22⋊C4—22no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—22no—
276C2×C22⋊C4—22no—
277C2×C22⋊C4—44no—
278C2×C22⋊C4—42no—
279C2×C22⋊C4—41no—
280C2×C22⋊C4—41no—
281C2×C22⋊C4C2×C4×C1312yes—
282#100—24no—
283#100—42no—
284#99—24no—
285#99—42no—
286C22⋊C8—41no—
287C22⋊C8—41no—
288#95—22no—
289#95—22no—
290C2×C13—21no—
291C2×C13—21no—
292C2×C13—22no—
293C2×C13—22no—
294C2×C13—42no—
295C2×C13—42no—
296C2×C13—42no—
297C2×C13—81no—
298C2×C13#181911yescharacteristic
299C2×C13C2×AΣL(1,𝔽16)11yescharacteristic
300C2×C13C2×#35211yescharacteristic
301C24—22no—
302C24—21no—
303C24—21no—
304C24—22no—
305C24—22no—
306C24—21no—
307C24—21no—
308C24—41no—
309C24—42no—
310C24—42no—
311C24—42no—
312C24—42no—
313C24C13×C22⋊C411yescharacteristic
314C24C13×C22⋊C411yescharacteristic
315C24C13×C22⋊C411yescharacteristic
316C24C22×C4×C1311yescharacteristic
317C24C2×D4×C1311yescharacteristic
318C2×D4—22no—
319C2×D4—22no—
320C2×D4—22no—
321C2×D4—22no—
322C2×D4—22no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4—41no—
328C2×D4—41no—
329C2×D4—48no—
330C2×D4—48no—
331C2×D4C13×#4114yes—
332C22×C4—24no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—41no—
339C22×C4—44no—
340C22×C4—44no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—48no—
344C22×C4—44no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—42no—
348C22×C4—44no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4C13×C22⋊C411yescharacteristic
354C22×C4C2×D4×C1311yescharacteristic
355M16—42no—
356M16—42no—
357C2×C8—42no—
358C22⋊C4—44no—
359C22⋊C4—44no—
360C22⋊C4—42no—
361C22⋊C4—42no—
362C22⋊C4—42no—
363C22⋊C4—42no—
364C22⋊C4—82no—
365C22⋊C4—82no—
366C13#1285211yescharacteristic, direct product factor, Sylow
367C23—21no—
368C23—21no—
369C23—22no—
370C23—22no—
371C23—24no—
372C23—24no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—42no—
383C23—42no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23—41no—
388C23—42no—
389C23—48no—
390C23—48no—
391C23—42no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—48no—
397C23—42no—
398C23—42no—
399C23—42no—
400C23—42no—
401C23—81no—
402C23—81no—
403C23—84no—
404C23C13×#9911yescharacteristic
405C23C13×#9911yescharacteristic
406C23C13×#9912yes—
407C23C2×C13×C22⋊C411yescharacteristic
408C23C13×#11712yes—
409C23C13×#12312yes—
410D4—44no—
411D4—44no—
412D4—44no—
413D4—44no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—24no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—44no—
424C2×C4—48no—
425C2×C4—44no—
426C2×C4—42no—
427C2×C4—44no—
428C2×C4—44no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—84no—
433C2×C4—82no—
434C2×C4—82no—
435C2×C4—82no—
436C2×C4C13×#12312yes—
437C8—82no—
438C22—24no—
439C22—24no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—42no—
450C22—42no—
451C22—42no—
452C22—42no—
453C22—42no—
454C22—48no—
455C22—48no—
456C22—42no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—81no—
467C22—84no—
468C22—84no—
469C22—81no—
470C22C13×AΣL(1,𝔽16)12yes—
471C22C13×#35212yes—
472C22C13×#38111yescharacteristic
473C22C2×C13×#9911yescharacteristic
474C22C2×C13×#9911yescharacteristic
475C4—22no—
476C4—41no—
477C4—44no—
478C4—82no—
479C4—162no—
480C2—21no—
481C2—21no—
482C2—22no—
483C2—22no—
484C2—42no—
485C2—42no—
486C2—42no—
487C2—81no—
488C2C13×#181911yescharacteristic
489C2C2×C13×AΣL(1,𝔽16)11yescharacteristic
490C2C2×C13×#35211yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC24C22×C4×C13
Frattini, cosocleC22×D4C23×C13
prime radicalC23×D4×C13C22
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C24×C13 ◁ C23×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
4. C13×#1390C2semidirect
6. C24×C4×C13C4semidirect
8. C22×C13×C22⋊C4C4semidirect
16. C13×#386C4semidirect
56. #12852C13direct (N × H)
125. #1390C2×C13semidirect
198. C24×C4C4×C13semidirect
200. C22×C22⋊C4C4×C13semidirect
208. #386C4×C13semidirect
366. C13#12852direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3862
C13×#17832
C13×#17812
C13×#13902
#1285213