Finite Group Databasebeta

← C13×#13423 #15699762

Subgroups — C13×#13423 #15699762

Order 3328.

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

normal subgroups only

This group has 558 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×#2709C211yesmaximal, characteristic
2C2×C13×#353C211yesmaximal, characteristic
3C2×C13×#352C211yesmaximal, characteristic, complemented
4C13×#1890C211yesmaximal, characteristic, complemented
5C13×#1887C211yesmaximal, characteristic
6C13×#1867C211yesmaximal, characteristic, complemented
7C13×#1390C211yesmaximal, characteristic, complemented
8C2×C13×#127C2211yescharacteristic
9C2×C13×#123C2211yescharacteristic
10C13×#518C2211yescharacteristic
11C13×#418—21no—
12C2×C13×#100C2211yescharacteristic
13C2×C13×#99C2211yescharacteristic
14C2×C13×#99C2211yescharacteristic
15C13×#394—21no—
16C13×#394—21no—
17C13×#394—21no—
18C13×#387—21no—
19C13×#386—21no—
20C13×#386—21no—
21C13×#386C2211yescharacteristic
22C13×#385—21no—
23C13×#381—21no—
24C13×#353—22no—
25C13×#352—22no—
26C13×#342—21no—
27C13×#342—21no—
28C13×#339—21no—
29C22×D4×C13—21no—
30C22×D4×C13—21no—
31C22×D4×C13D411yescharacteristic
32C22×D4×C13C2311yescharacteristic
33C23×C4×C13D411yescharacteristic
34C23×C4×C13D411yescharacteristic
35C2×C13×M16—21no—
36C13×#127—21no—
37C13×#127—21no—
38C13×#127—21no—
39C13×#127—21no—
40C13×#123—21no—
41C13×#123—21no—
42C13×#123—21no—
43C13×#123—21no—
44C4×D4×C13—41no—
45C4×D4×C13—41no—
46C13×#117—21no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—41no—
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⋊C4D411yescharacteristic
61C2×C13×C22⋊C4D411yescharacteristic
62C2×C42×C13D411yescharacteristic
63C13×#102—41no—
64C13×#102—41no—
65C13×#100—21no—
66C13×#100—21no—
67C13×#99—21no—
68C13×#99—21no—
69C13×#99—21no—
70C13×#99D412yes—
71C13×#95—21no—
72C13×#95—21no—
73C13×#95—21no—
74C13×#95—21no—
75C13×#95—41no—
76C13×#95—41no—
77C13×#95—41no—
78#13423C1311yesmaximal, characteristic, direct product factor, Sylow
79C24×C13—21no—
80C24×C13C2×D411yescharacteristic
81C24×C13C2×D411yescharacteristic
82C2×D4×C13—21no—
83C2×D4×C13—21no—
84C2×D4×C13—41no—
85C2×D4×C13—41no—
86C2×D4×C13—41no—
87C2×D4×C13—41no—
88C2×D4×C13—42no—
89C2×D4×C13—42no—
90C2×D4×C13—41no—
91C2×D4×C13—41no—
92C2×D4×C13—41no—
93C2×D4×C13—41no—
94C2×D4×C13—81no—
95C2×D4×C13—81no—
96C2×D4×C13C2×D411yescharacteristic
97C2×D4×C13#4111yescharacteristic
98C2×D4×C13#4111yescharacteristic
99C2×D4×C13#4111yescharacteristic
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—21no—
110C22×C4×C13—21no—
111C22×C4×C13—41no—
112C22×C4×C13—41no—
113C22×C4×C13—41no—
114C22×C4×C13—41no—
115C22×C4×C13—41no—
116C22×C4×C13—81no—
117C22×C4×C13C2×D411yescharacteristic
118C13×M16—41no—
119C13×M16—41no—
120C2×C8×C13—41no—
121C13×C4⋊C4—21no—
122C13×C4⋊C4—21no—
123C13×C4⋊C4—42no—
124C13×C4⋊C4—41no—
125C13×C4⋊C4—41no—
126C13×C4⋊C4—82no—
127C13×C22⋊C4—22no—
128C13×C22⋊C4—21no—
129C13×C22⋊C4—21no—
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—
144C42×C13—21no—
145C42×C13—21no—
146C42×C13—41no—
147#2709C2×C1311yescharacteristic
148C2×#353C2×C1311yescharacteristic
149C2×#352C2×C1311yescharacteristic, complemented
150#1890C2×C1311yescharacteristic, complemented
151#1887C2×C1311yescharacteristic
152#1867C2×C1311yescharacteristic, complemented
153#1390C2×C1311yescharacteristic, complemented
154C23×C13—21no—
155C23×C13—21no—
156C23×C13—21no—
157C23×C13—21no—
158C23×C13—41no—
159C23×C13—41no—
160C23×C13—41no—
161C23×C13—41no—
162C23×C13—41no—
163C23×C13—41no—
164C23×C13—41no—
165C23×C13—41no—
166C23×C13—41no—
167C23×C13—41no—
168C23×C13—41no—
169C23×C13#12011yescharacteristic
170C23×C13#12111yescharacteristic
171C23×C13#12111yescharacteristic
172C23×C13#12311yescharacteristic
173C23×C13#12411yescharacteristic
174D4×C13—41no—
175D4×C13—41no—
176D4×C13—41no—
177D4×C13—41no—
178D4×C13—42no—
179D4×C13—81no—
180D4×C13—82no—
181D4×C13—82no—
182D4×C13—82no—
183D4×C13—82no—
184C2×C4×C13—21no—
185C2×C4×C13—21no—
186C2×C4×C13—22no—
187C2×C4×C13—41no—
188C2×C4×C13—41no—
189C2×C4×C13—42no—
190C2×C4×C13—41no—
191C2×C4×C13—41no—
192C2×C4×C13—41no—
193C2×C4×C13—41no—
194C2×C4×C13—41no—
195C2×C4×C13—41no—
196C2×C4×C13—42no—
197C2×C4×C13—42no—
198C2×C4×C13—41no—
199C2×C4×C13—41no—
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—81no—
207C2×C4×C13—81no—
208C2×C4×C13—81no—
209C2×C4×C13—81no—
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#12111yescharacteristic
218C2×C4×C13#12311yescharacteristic
219C8×C13—81no—
220C2×#127C22×C1311yescharacteristic
221C2×#123C22×C1311yescharacteristic
222#518C22×C1311yescharacteristic
223#418—21no—
224C2×#100C22×C1311yescharacteristic
225C2×#99C22×C1311yescharacteristic
226C2×#99C22×C1311yescharacteristic
227#394—21no—
228#394—21no—
229#394—21no—
230#387—21no—
231#386—21no—
232#386—21no—
233#386C22×C1311yescharacteristic
234#385—21no—
235#381—21no—
236#353—22no—
237#352—22no—
238#342—21no—
239#342—21no—
240#339—21no—
241C22×C13—21no—
242C22×C13—21no—
243C22×C13—21no—
244C22×C13—21no—
245C22×C13—21no—
246C22×C13—21no—
247C22×C13—41no—
248C22×C13—41no—
249C22×C13—41no—
250C22×C13—41no—
251C22×C13—41no—
252C22×C13—41no—
253C22×C13—41no—
254C22×C13—41no—
255C22×C13—81no—
256C22×C13—81no—
257C22×C13—81no—
258C22×C13—81no—
259C22×C13—81no—
260C22×C13—81no—
261C22×C13—81no—
262C22×C13—81no—
263C22×C13—81no—
264C22×C13#39411yescharacteristic
265C22×C13B(4,𝔽2)11yescharacteristic
266C22×C13#45811yescharacteristic
267C4×C13—21no—
268C4×C13—21no—
269C4×C13—42no—
270C4×C13—81no—
271C4×C13—81no—
272C4×C13—82no—
273C4×C13—81no—
274C4×C13—81no—
275C4×C13—81no—
276C4×C13—81no—
277C4×C13—161no—
278C22×D4—21no—
279C22×D4—21no—
280C22×D4D4×C1311yescharacteristic
281C22×D4C23×C1311yescharacteristic
282C23×C4D4×C1311yescharacteristic
283C23×C4D4×C1311yescharacteristic
284C2×M16—21no—
285#127—21no—
286#127—21no—
287#127—21no—
288#127—21no—
289#123—21no—
290#123—21no—
291#123—21no—
292#123—21no—
293C4×D4—41no—
294C4×D4—41no—
295#117—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—41no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4D4×C1311yescharacteristic
310C2×C22⋊C4D4×C1311yescharacteristic
311C2×C42D4×C1311yescharacteristic
312#102—41no—
313#102—41no—
314#100—21no—
315#100—21no—
316#99—21no—
317#99—21no—
318#99—21no—
319#99D4×C1312yes—
320#95—21no—
321#95—21no—
322#95—21no—
323#95—21no—
324#95—41no—
325#95—41no—
326#95—41no—
327C2×C13—21no—
328C2×C13—21no—
329C2×C13—41no—
330C2×C13—41no—
331C2×C13—41no—
332C2×C13—41no—
333C2×C13—161no—
334C2×C13#204411yescharacteristic
335C2×C13#219811yescharacteristic
336C2×C13#220011yescharacteristic
337C24—21no—
338C24C2×D4×C1311yescharacteristic
339C24C2×D4×C1311yescharacteristic
340C2×D4—21no—
341C2×D4—21no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—41no—
346C2×D4—42no—
347C2×D4—42no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4—41no—
352C2×D4—81no—
353C2×D4—81no—
354C2×D4C2×D4×C1311yescharacteristic
355C2×D4C13×#4111yescharacteristic
356C2×D4C13×#4111yescharacteristic
357C2×D4C13×#4111yescharacteristic
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—81no—
375C22×C4C2×D4×C1311yescharacteristic
376M16—41no—
377M16—41no—
378C2×C8—41no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—42no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—82no—
385C22⋊C4—22no—
386C22⋊C4—21no—
387C22⋊C4—21no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—81no—
398C22⋊C4—81no—
399C22⋊C4—81no—
400C22⋊C4—81no—
401C22⋊C4—81no—
402C42—21no—
403C42—21no—
404C42—41no—
405C13#1342311yescharacteristic, direct product factor, Sylow
406C23—21no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—41no—
411C23—41no—
412C23—41no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23C13×#12011yescharacteristic
422C23C13×#12111yescharacteristic
423C23C13×#12111yescharacteristic
424C23C13×#12311yescharacteristic
425C23C13×#12411yescharacteristic
426D4—41no—
427D4—41no—
428D4—41no—
429D4—41no—
430D4—42no—
431D4—81no—
432D4—82no—
433D4—82no—
434D4—82no—
435D4—82no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—22no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—81no—
459C2×C4—81no—
460C2×C4—81no—
461C2×C4—81no—
462C2×C4—81no—
463C2×C4—81no—
464C2×C4—81no—
465C2×C4—81no—
466C2×C4—81no—
467C2×C4—81no—
468C2×C4—81no—
469C2×C4C13×#12111yescharacteristic
470C2×C4C13×#12311yescharacteristic
471C8—81no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22—41no—
482C22—41no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—81no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22—81no—
492C22—81no—
493C22—81no—
494C22—81no—
495C22C13×#39411yescharacteristic
496C22C13×B(4,𝔽2)11yescharacteristic
497C22C13×#45811yescharacteristic
498C4—21no—
499C4—21no—
500C4—42no—
501C4—81no—
502C4—81no—
503C4—82no—
504C4—81no—
505C4—81no—
506C4—81no—
507C4—81no—
508C4—161no—
509C2—21no—
510C2—21no—
511C2—41no—
512C2—41no—
513C2—41no—
514C2—41no—
515C2—161no—
516C2C13×#204411yescharacteristic
517C2C13×#219811yescharacteristic
518C2C13×#220011yescharacteristic
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C13
prime radicalC2×C13×#127C22
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
3. C2×C13×#352C2semidirect
4. C13×#1890C2semidirect
6. C13×#1867C2semidirect
7. C13×#1390C2semidirect
78. #13423C13direct (N × H)
149. C2×#352C2×C13semidirect
150. #1890C2×C13semidirect
152. #1867C2×C13semidirect
153. #1390C2×C13semidirect
405. C13#13423direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#27092
C2×C13×#3532
C2×C13×#3522
C13×#18902
C13×#18872
C13×#18672
C13×#13902
#1342313