Finite Group Databasebeta

← C13×#13420 #15699759

Subgroups — C13×#13420 #15699759

Order 3328.

600 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 90 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
1C13×#2697C211yesmaximal, characteristic
2C2×C13×#352C211yesmaximal, characteristic, complemented
3C2×C13×AΣL(1,𝔽16)C211yesmaximal, characteristic
4C13×#1890C211yesmaximal, characteristic, complemented
5C13×#1889C211yesmaximal, characteristic
6C13×#1856C211yesmaximal, characteristic, complemented
7C13×#1393C211yesmaximal, characteristic, complemented
8C2×C13×#123C2211yescharacteristic
9C2×C13×#120C2211yescharacteristic
10C13×#518C2211yescharacteristic
11C13×#428—21no—
12C2×C13×#100C2211yescharacteristic
13C2×C13×#99C2211yescharacteristic
14C2×C13×#99C2211yescharacteristic
15C13×#397—21no—
16C13×#396—21no—
17C13×#394—21no—
18C13×#390C2211yescharacteristic
19C13×#388—21no—
20C13×#386—21no—
21C13×#381—21no—
22C13×#379—21no—
23C13×#379—21no—
24C13×#352—22no—
25C13×AΣL(1,𝔽16)—22no—
26C13×#342—21no—
27C13×#342—21no—
28C13×#339—21no—
29C25×C13D411yescharacteristic
30C22×D4×C13—21no—
31C22×D4×C13C2311yescharacteristic
32C23×C4×C13D411yescharacteristic
33C2×C13×M16—21no—
34C13×#123—21no—
35C13×#123—21no—
36C13×#123—21no—
37C13×#123—21no—
38C13×#120—21no—
39C13×#120—21no—
40C13×#120—21no—
41C13×#120—21no—
42C4×D4×C13—41no—
43C4×D4×C13—41no—
44C13×#117—21no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4D411yescharacteristic
48C2×C13×C22⋊C4—21no—
49C2×C13×C22⋊C4—21no—
50C2×C13×C22⋊C4—21no—
51C2×C13×C22⋊C4—21no—
52C2×C13×C22⋊C4—21no—
53C2×C13×C22⋊C4—21no—
54C2×C13×C22⋊C4—21no—
55C2×C13×C22⋊C4—21no—
56C2×C13×C22⋊C4—21no—
57C2×C13×C22⋊C4—21no—
58C2×C13×C22⋊C4—21no—
59C2×C13×C22⋊C4—21no—
60C2×C13×C22⋊C4—41no—
61C2×C13×C22⋊C4—41no—
62C2×C13×C22⋊C4D411yescharacteristic
63C2×C13×C22⋊C4D411yescharacteristic
64C2×C42×C13D411yescharacteristic
65C13×#107—41no—
66C13×#106—41no—
67C13×#100—21no—
68C13×#100D412yes—
69C13×#99—21no—
70C13×#99—21no—
71C13×#99—21no—
72C13×#99—21no—
73C13×#95—21no—
74C13×#95—21no—
75C13×#95—21no—
76C13×#95—41no—
77C13×#95—41no—
78#13420C1311yesmaximal, characteristic, direct product factor, Sylow
79C24×C13—21no—
80C24×C13—21no—
81C24×C13—21no—
82C24×C13—41no—
83C24×C13—41no—
84C24×C13—42no—
85C24×C13—81no—
86C24×C13C2×D411yescharacteristic
87C24×C13C2×D411yescharacteristic
88C2×D4×C13—41no—
89C2×D4×C13—41no—
90C2×D4×C13—42no—
91C2×D4×C13—41no—
92C2×D4×C13—41no—
93C2×D4×C13—81no—
94C2×D4×C13C2×D411yescharacteristic
95C2×D4×C13#4111yescharacteristic
96C2×D4×C13#4111yescharacteristic
97C2×D4×C13#4111yescharacteristic
98C22×C4×C13—21no—
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13—21no—
102C22×C4×C13—21no—
103C22×C4×C13—21no—
104C22×C4×C13—21no—
105C22×C4×C13—21no—
106C22×C4×C13—21no—
107C22×C4×C13—21no—
108C22×C4×C13—21no—
109C22×C4×C13—41no—
110C22×C4×C13—41no—
111C22×C4×C13—41no—
112C22×C4×C13—41no—
113C22×C4×C13C2×D411yescharacteristic
114C13×M16—22no—
115C13×M16—41no—
116C2×C8×C13—41no—
117C13×C4⋊C4—21no—
118C13×C4⋊C4—21no—
119C13×C4⋊C4—41no—
120C13×C4⋊C4—41no—
121C13×C4⋊C4—41no—
122C13×C4⋊C4—81no—
123C13×C22⋊C4—21no—
124C13×C22⋊C4—21no—
125C13×C22⋊C4—21no—
126C13×C22⋊C4—21no—
127C13×C22⋊C4—42no—
128C13×C22⋊C4—41no—
129C13×C22⋊C4—41no—
130C13×C22⋊C4—41no—
131C13×C22⋊C4—41no—
132C13×C22⋊C4—41no—
133C13×C22⋊C4—41no—
134C13×C22⋊C4—41no—
135C13×C22⋊C4—41no—
136C13×C22⋊C4—41no—
137C13×C22⋊C4—41no—
138C13×C22⋊C4—41no—
139C13×C22⋊C4—81no—
140C13×C22⋊C4—81no—
141C13×C22⋊C4—81no—
142C13×C22⋊C4—81no—
143C13×C22⋊C4—81no—
144C13×C22⋊C4—82no—
145C13×C22⋊C4—82no—
146C42×C13—41no—
147C42×C13—41no—
148#2697C2×C1311yescharacteristic
149C2×#352C2×C1311yescharacteristic, complemented
150C2×AΣL(1,𝔽16)C2×C1311yescharacteristic
151#1890C2×C1311yescharacteristic, complemented
152#1889C2×C1311yescharacteristic
153#1856C2×C1311yescharacteristic, complemented
154#1393C2×C1311yescharacteristic, complemented
155C23×C13—21no—
156C23×C13—21no—
157C23×C13—21no—
158C23×C13—21no—
159C23×C13—22no—
160C23×C13—41no—
161C23×C13—41no—
162C23×C13—41no—
163C23×C13—41no—
164C23×C13—41no—
165C23×C13—41no—
166C23×C13—41no—
167C23×C13—42no—
168C23×C13—42no—
169C23×C13—42no—
170C23×C13—41no—
171C23×C13—41no—
172C23×C13—41no—
173C23×C13—81no—
174C23×C13—82no—
175C23×C13—81no—
176C23×C13—84no—
177C23×C13—82no—
178C23×C13—81no—
179C23×C13#12011yescharacteristic
180C23×C13#12111yescharacteristic
181C23×C13#12111yescharacteristic
182C23×C13#12311yescharacteristic
183C23×C13#12311yescharacteristic
184D4×C13—41no—
185D4×C13—41no—
186D4×C13—41no—
187D4×C13—41no—
188D4×C13—82no—
189D4×C13—82no—
190C2×C4×C13—21no—
191C2×C4×C13—21no—
192C2×C4×C13—41no—
193C2×C4×C13—41no—
194C2×C4×C13—41no—
195C2×C4×C13—41no—
196C2×C4×C13—41no—
197C2×C4×C13—41no—
198C2×C4×C13—41no—
199C2×C4×C13—42no—
200C2×C4×C13—41no—
201C2×C4×C13—41no—
202C2×C4×C13—41no—
203C2×C4×C13—41no—
204C2×C4×C13—41no—
205C2×C4×C13—41no—
206C2×C4×C13—41no—
207C2×C4×C13—41no—
208C2×C4×C13—41no—
209C2×C4×C13—41no—
210C2×C4×C13—81no—
211C2×C4×C13—81no—
212C2×C4×C13—81no—
213C2×C4×C13—81no—
214C2×C4×C13—81no—
215C2×C4×C13—81no—
216C2×C4×C13—81no—
217C2×C4×C13—81no—
218C2×C4×C13—81no—
219C2×C4×C13—81no—
220C2×C4×C13—81no—
221C2×C4×C13#12111yescharacteristic
222C2×C4×C13#12411yescharacteristic
223C8×C13—42no—
224C2×#123C22×C1311yescharacteristic
225C2×#120C22×C1311yescharacteristic
226#518C22×C1311yescharacteristic
227#428—21no—
228C2×#100C22×C1311yescharacteristic
229C2×#99C22×C1311yescharacteristic
230C2×#99C22×C1311yescharacteristic
231#397—21no—
232#396—21no—
233#394—21no—
234#390C22×C1311yescharacteristic
235#388—21no—
236#386—21no—
237#381—21no—
238#379—21no—
239#379—21no—
240#352—22no—
241AΣL(1,𝔽16)—22no—
242#342—21no—
243#342—21no—
244#339—21no—
245C22×C13—21no—
246C22×C13—21no—
247C22×C13—21no—
248C22×C13—21no—
249C22×C13—21no—
250C22×C13—21no—
251C22×C13—41no—
252C22×C13—41no—
253C22×C13—41no—
254C22×C13—41no—
255C22×C13—42no—
256C22×C13—42no—
257C22×C13—41no—
258C22×C13—41no—
259C22×C13—41no—
260C22×C13—41no—
261C22×C13—44no—
262C22×C13—42no—
263C22×C13—81no—
264C22×C13—81no—
265C22×C13—81no—
266C22×C13—81no—
267C22×C13—82no—
268C22×C13—82no—
269C22×C13—82no—
270C22×C13—81no—
271C22×C13—81no—
272C22×C13#39411yescharacteristic
273C22×C13B(4,𝔽2)11yescharacteristic
274C22×C13#45811yescharacteristic
275C4×C13—21no—
276C4×C13—21no—
277C4×C13—81no—
278C4×C13—81no—
279C4×C13—81no—
280C4×C13—81no—
281C4×C13—81no—
282C4×C13—81no—
283C4×C13—81no—
284C4×C13—161no—
285C4×C13—161no—
286C25D4×C1311yescharacteristic
287C22×D4—21no—
288C22×D4C23×C1311yescharacteristic
289C23×C4D4×C1311yescharacteristic
290C2×M16—21no—
291#123—21no—
292#123—21no—
293#123—21no—
294#123—21no—
295#120—21no—
296#120—21no—
297#120—21no—
298#120—21no—
299C4×D4—41no—
300C4×D4—41no—
301#117—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4D4×C1311yescharacteristic
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—41no—
318C2×C22⋊C4—41no—
319C2×C22⋊C4D4×C1311yescharacteristic
320C2×C22⋊C4D4×C1311yescharacteristic
321C2×C42D4×C1311yescharacteristic
322#107—41no—
323#106—41no—
324#100—21no—
325#100D4×C1312yes—
326#99—21no—
327#99—21no—
328#99—21no—
329#99—21no—
330#95—21no—
331#95—21no—
332#95—21no—
333#95—41no—
334#95—41no—
335C2×C13—21no—
336C2×C13—21no—
337C2×C13—41no—
338C2×C13—41no—
339C2×C13—41no—
340C2×C13—41no—
341C2×C13—82no—
342C2×C13#204411yescharacteristic
343C2×C13#219711yescharacteristic
344C2×C13#220011yescharacteristic
345C24—21no—
346C24—21no—
347C24—21no—
348C24—41no—
349C24—41no—
350C24—42no—
351C24—81no—
352C24C2×D4×C1311yescharacteristic
353C24C2×D4×C1311yescharacteristic
354C2×D4—41no—
355C2×D4—41no—
356C2×D4—42no—
357C2×D4—41no—
358C2×D4—41no—
359C2×D4—81no—
360C2×D4C2×D4×C1311yescharacteristic
361C2×D4C13×#4111yescharacteristic
362C2×D4C13×#4111yescharacteristic
363C2×D4C13×#4111yescharacteristic
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4C2×D4×C1311yescharacteristic
380M16—22no—
381M16—41no—
382C2×C8—41no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4—81no—
389C22⋊C4—21no—
390C22⋊C4—21no—
391C22⋊C4—21no—
392C22⋊C4—21no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—42no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C22⋊C4—41no—
403C22⋊C4—41no—
404C22⋊C4—41no—
405C22⋊C4—81no—
406C22⋊C4—81no—
407C22⋊C4—81no—
408C22⋊C4—81no—
409C22⋊C4—81no—
410C22⋊C4—82no—
411C22⋊C4—82no—
412C42—41no—
413C42—41no—
414C13#1342011yescharacteristic, direct product factor, Sylow
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—22no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23—42no—
428C23—42no—
429C23—42no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—81no—
434C23—82no—
435C23—81no—
436C23—82no—
437C23—84no—
438C23—81no—
439C23C13×#12011yescharacteristic
440C23C13×#12111yescharacteristic
441C23C13×#12111yescharacteristic
442C23C13×#12311yescharacteristic
443C23C13×#12311yescharacteristic
444D4—41no—
445D4—41no—
446D4—41no—
447D4—41no—
448D4—82no—
449D4—82no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—42no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—81no—
471C2×C4—81no—
472C2×C4—81no—
473C2×C4—81no—
474C2×C4—81no—
475C2×C4—81no—
476C2×C4—81no—
477C2×C4—81no—
478C2×C4—81no—
479C2×C4—81no—
480C2×C4—81no—
481C2×C4C13×#12111yescharacteristic
482C2×C4C13×#12411yescharacteristic
483C8—42no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—21no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—42no—
495C22—42no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—44no—
501C22—42no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22—82no—
507C22—82no—
508C22—82no—
509C22—81no—
510C22—81no—
511C22C13×#39411yescharacteristic
512C22C13×B(4,𝔽2)11yescharacteristic
513C22C13×#45811yescharacteristic
514C4—21no—
515C4—21no—
516C4—81no—
517C4—81no—
518C4—81no—
519C4—81no—
520C4—81no—
521C4—81no—
522C4—81no—
523C4—161no—
524C4—161no—
525C2—21no—
526C2—21no—
527C2—41no—
528C2—41no—
529C2—41no—
530C2—41no—
531C2—82no—
532C2C13×#204411yescharacteristic
533C2C13×#219711yescharacteristic
534C2C13×#220011yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C13
prime radicalC2×C13×#120C22
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C13 ◁ C22×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#352C2semidirect
4. C13×#1890C2semidirect
6. C13×#1856C2semidirect
7. C13×#1393C2semidirect
78. #13420C13direct (N × H)
149. C2×#352C2×C13semidirect
151. #1890C2×C13semidirect
153. #1856C2×C13semidirect
154. #1393C2×C13semidirect
414. C13#13420direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26972
C2×C13×#3522
C2×C13×AΣL(1,𝔽16)2
C13×#18902
C13×#18892
C13×#18562
C13×#13932
#1342013