Finite Group Databasebeta

← C13×#13355 #15699694

Subgroups — C13×#13355 #15699694

Order 3328.

704 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 94 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×#3200C211yesmaximal, characteristic, complemented
2C13×#3027C211yesmaximal, characteristic
3C13×#3022C211yesmaximal, characteristic, complemented
4C13×#2134C211yesmaximal, characteristic, complemented
5C13×#2123C211yesmaximal, characteristic, complemented
6C13×#1791C211yesmaximal, characteristic, complemented
7C13×#1395C211yesmaximal, characteristic, complemented
8C13×#585C2211yescharacteristic
9C2×C13×#137—21no—
10C13×#536C2211yescharacteristic
11C13×#535—21no—
12C13×#535C2211yescharacteristic
13C13×#485—21no—
14C13×#482—21no—
15C13×#468—21no—
16C13×#465—21no—
17C13×B(4,𝔽2)—22no—
18C13×B(4,𝔽2)—22no—
19C13×#456—22no—
20C13×#455—22no—
21C13×#450—21no—
22C13×#448—21no—
23C13×#421—21no—
24C13×#413—21no—
25C13×#413C2211yescharacteristic
26C13×#413C2211yescharacteristic
27C13×#410—21no—
28C13×#410C2211yescharacteristic
29C13×#408—21no—
30C13×#408C2211yescharacteristic
31C13×#355—22no—
32C13×#352—22no—
33C13×2−1+4—21no—
34C13×2−1+4—41no—
35C13×H(5,𝔽2)—21no—
36C13×H(5,𝔽2)—21no—
37C13×H(5,𝔽2)—41no—
38C13×H(5,𝔽2)D412yes—
39C2×C13×#41—21no—
40C2×C13×#41—21no—
41C2×C13×#41—21no—
42C2×C13×#41—42no—
43C2×C13×#41C2311yescharacteristic
44C22×Q8×C13D411yescharacteristic, complemented
45C22×D4×C13D411yescharacteristic
46C13×#137—24no—
47C13×#137—42no—
48C2×C13×Q16—41no—
49C2×C13×SD16—21no—
50C2×C13×SD16—21no—
51C2×C13×SD16—41no—
52C2×C13×M16—21no—
53C2×C13×M16—21no—
54C2×C13×M16D411yescharacteristic, complemented
55C22×C8×C13D411yescharacteristic, complemented
56C13×C4⋊Q8—21no—
57C13×#127—21no—
58C13×#127—41no—
59C13×#124—21no—
60C13×#124—21no—
61C13×#124—41no—
62C13×#123—21no—
63C13×#123—21no—
64C13×C22⋊Q8—21no—
65C13×C22⋊Q8—21no—
66C13×#121—21no—
67C13×#121—21no—
68C13×#121—42no—
69C13×#120—24no—
70C13×#120—21no—
71C13×#120—21no—
72C13×#117—21no—
73C13×#117D411yescharacteristic
74C13×#117D411yescharacteristic, complemented
75C13×#107—21no—
76C13×#106—21no—
77C13×#104—24no—
78C13×#103—21no—
79C13×#103—21no—
80C13×#102—21no—
81C13×#102—21no—
82C13×#101—21no—
83C13×#101—41no—
84C13×#101D412yescomplemented
85C13×#100—21no—
86C13×#100—21no—
87C13×#100—41no—
88C13×#99—24no—
89C13×#99—21no—
90C13×#99D412yes—
91C13×C22⋊C8—21no—
92C13×C22⋊C8—21no—
93C13×C22⋊C8—42no—
94#13355C1311yesmaximal, characteristic, direct product factor, Sylow
95C24×C13—21no—
96C13×#41—22no—
97C13×#41—22no—
98C13×#41—41no—
99C13×#41—41no—
100C13×#41—42no—
101C13×#41—41no—
102C13×#41—41no—
103C13×#41—41no—
104C13×#41—41no—
105C13×#41—41no—
106C13×#41—42no—
107C13×#41—42no—
108C13×#41—42no—
109C13×#41—41no—
110C13×#41—41no—
111C13×#41—41no—
112C2×Q8×C13—21no—
113C2×Q8×C13—21no—
114C2×Q8×C13—21no—
115C2×Q8×C13—21no—
116C2×Q8×C13—21no—
117C2×Q8×C13—41no—
118C2×Q8×C13—41no—
119C2×Q8×C13—42no—
120C2×Q8×C13C2×D411yescharacteristic
121C2×D4×C13—21no—
122C2×D4×C13—21no—
123C2×D4×C13—21no—
124C2×D4×C13—22no—
125C2×D4×C13—22no—
126C2×D4×C13—21no—
127C2×D4×C13—21no—
128C2×D4×C13—41no—
129C2×D4×C13—41no—
130C2×D4×C13—42no—
131C2×D4×C13—42no—
132C2×D4×C13—42no—
133C2×D4×C13—41no—
134C2×D4×C13—44no—
135C2×D4×C13—41no—
136C2×D4×C13—41no—
137C2×D4×C13C2×D411yescharacteristic
138C2×D4×C13C2×D411yescharacteristic
139C2×D4×C13#4111yescharacteristic
140C22×C4×C13—22no—
141C22×C4×C13—22no—
142C22×C4×C13—21no—
143C22×C4×C13—41no—
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C13×Q16—44no—
148C13×SD16—44no—
149C13×SD16—81no—
150C13×SD16—81no—
151C13×M16—22no—
152C13×M16—41no—
153C13×M16—41no—
154C13×M16—41no—
155C13×M16—41no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—41no—
159C2×C8×C13—41no—
160C2×C8×C13—41no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—41no—
164C13×C4⋊C4—41no—
165C13×C4⋊C4—41no—
166C13×C22⋊C4—21no—
167C13×C22⋊C4—22no—
168C13×C22⋊C4—21no—
169C13×C22⋊C4—44no—
170C13×C22⋊C4—41no—
171C13×C22⋊C4—41no—
172C13×C22⋊C4—41no—
173C13×C22⋊C4—41no—
174C42×C13—21no—
175C42×C13—21no—
176C42×C13—41no—
177#3200C2×C1311yescharacteristic, complemented
178#3027C2×C1311yescharacteristic
179#3022C2×C1311yescharacteristic, complemented
180#2134C2×C1311yescharacteristic, complemented
181#2123C2×C1311yescharacteristic, complemented
182#1791C2×C1311yescharacteristic, complemented
183#1395C2×C1311yescharacteristic, complemented
184C23×C13—22no—
185C23×C13—22no—
186C23×C13—41no—
187C23×C13—42no—
188C23×C13—41no—
189C23×C13—161no—
190C23×C13#12011yescharacteristic
191C23×C13#12111yescharacteristic
192C23×C13#12111yescharacteristic
193Q8×C13—22no—
194Q8×C13—41no—
195Q8×C13—41no—
196Q8×C13—41no—
197Q8×C13—42no—
198Q8×C13—41no—
199Q8×C13—41no—
200Q8×C13—41no—
201D4×C13—22no—
202D4×C13—41no—
203D4×C13—41no—
204D4×C13—41no—
205D4×C13—41no—
206D4×C13—41no—
207D4×C13—42no—
208D4×C13—42no—
209D4×C13—42no—
210D4×C13—42no—
211D4×C13—41no—
212D4×C13—41no—
213D4×C13—41no—
214D4×C13—81no—
215D4×C13—161no—
216D4×C13—161no—
217D4×C13—164no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—22no—
225C2×C4×C13—22no—
226C2×C4×C13—42no—
227C2×C4×C13—42no—
228C2×C4×C13—42no—
229C2×C4×C13—41no—
230C2×C4×C13—42no—
231C2×C4×C13—42no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—81no—
236C2×C4×C13#12011yescharacteristic
237C2×C4×C13#12011yescharacteristic
238C2×C4×C13#12111yescharacteristic
239C2×C4×C13#12711yescharacteristic
240C8×C13—42no—
241C8×C13—41no—
242C8×C13—41no—
243C8×C13—81no—
244#585C22×C1311yescharacteristic
245C2×#137—21no—
246#536C22×C1311yescharacteristic
247#535—21no—
248#535C22×C1311yescharacteristic
249#485—21no—
250#482—21no—
251#468—21no—
252#465—21no—
253B(4,𝔽2)—22no—
254B(4,𝔽2)—22no—
255#456—22no—
256#455—22no—
257#450—21no—
258#448—21no—
259#421—21no—
260#413—21no—
261#413C22×C1311yescharacteristic
262#413C22×C1311yescharacteristic
263#410—21no—
264#410C22×C1311yescharacteristic
265#408—21no—
266#408C22×C1311yescharacteristic
267#355—22no—
268#352—22no—
269C22×C13—21no—
270C22×C13—21no—
271C22×C13—21no—
272C22×C13—41no—
273C22×C13—41no—
274C22×C13—41no—
275C22×C13—42no—
276C22×C13—81no—
277C22×C13—81no—
278C22×C13—82no—
279C22×C13—82no—
280C22×C13—84no—
281C22×C13—81no—
282C22×C13—161no—
283C22×C13#39211yescharacteristic
284C4×C13—21no—
285C4×C13—21no—
286C4×C13—21no—
287C4×C13—42no—
288C4×C13—81no—
289C4×C13—81no—
290C4×C13—82no—
291C4×C13—81no—
292C4×C13B(4,𝔽2)11yescharacteristic
293C4×C13B(4,𝔽2)11yescharacteristic
2942−1+4—21no—
2952−1+4—41no—
296H(5,𝔽2)—21no—
297H(5,𝔽2)—21no—
298H(5,𝔽2)—41no—
299H(5,𝔽2)D4×C1312yes—
300C2×#41—21no—
301C2×#41—21no—
302C2×#41—21no—
303C2×#41—42no—
304C2×#41C23×C1311yescharacteristic
305C22×Q8D4×C1311yescharacteristic, complemented
306C22×D4D4×C1311yescharacteristic
307#137—24no—
308#137—42no—
309C2×Q16—41no—
310C2×SD16—21no—
311C2×SD16—21no—
312C2×SD16—41no—
313C2×M16—21no—
314C2×M16—21no—
315C2×M16D4×C1311yescharacteristic, complemented
316C22×C8D4×C1311yescharacteristic, complemented
317C4⋊Q8—21no—
318#127—21no—
319#127—41no—
320#124—21no—
321#124—21no—
322#124—41no—
323#123—21no—
324#123—21no—
325C22⋊Q8—21no—
326C22⋊Q8—21no—
327#121—21no—
328#121—21no—
329#121—42no—
330#120—24no—
331#120—21no—
332#120—21no—
333#117—21no—
334#117D4×C1311yescharacteristic
335#117D4×C1311yescharacteristic, complemented
336#107—21no—
337#106—21no—
338#104—24no—
339#103—21no—
340#103—21no—
341#102—21no—
342#102—21no—
343#101—21no—
344#101—41no—
345#101D4×C1312yescomplemented
346#100—21no—
347#100—21no—
348#100—41no—
349#99—24no—
350#99—21no—
351#99D4×C1312yes—
352C22⋊C8—21no—
353C22⋊C8—21no—
354C22⋊C8—42no—
355C2×C13—21no—
356C2×C13—41no—
357C2×C13—41no—
358C2×C13—41no—
359C2×C13—82no—
360C2×C13—161no—
361C2×C13#202111yescharacteristic
362C24—21no—
363#41—22no—
364#41—22no—
365#41—41no—
366#41—41no—
367#41—42no—
368#41—41no—
369#41—41no—
370#41—41no—
371#41—41no—
372#41—41no—
373#41—42no—
374#41—42no—
375#41—42no—
376#41—41no—
377#41—41no—
378#41—41no—
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—41no—
385C2×Q8—41no—
386C2×Q8—42no—
387C2×Q8C2×D4×C1311yescharacteristic
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4—42no—
400C2×D4—41no—
401C2×D4—44no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4C2×D4×C1311yescharacteristic
405C2×D4C2×D4×C1311yescharacteristic
406C2×D4C13×#4111yescharacteristic
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—41no—
411C22×C4C2×D4×C1311yescharacteristic
412C22×C4C2×D4×C1311yescharacteristic
413C22×C4C2×D4×C1311yescharacteristic
414Q16—44no—
415SD16—44no—
416SD16—81no—
417SD16—81no—
418M16—22no—
419M16—41no—
420M16—41no—
421M16—41no—
422M16—41no—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—41no—
426C2×C8—41no—
427C2×C8—41no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—41no—
431C4⋊C4—41no—
432C4⋊C4—41no—
433C22⋊C4—21no—
434C22⋊C4—22no—
435C22⋊C4—21no—
436C22⋊C4—44no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C42—21no—
442C42—21no—
443C42—41no—
444C13#1335511yescharacteristic, direct product factor, Sylow
445C23—22no—
446C23—22no—
447C23—41no—
448C23—42no—
449C23—41no—
450C23—161no—
451C23C13×#12011yescharacteristic
452C23C13×#12111yescharacteristic
453C23C13×#12111yescharacteristic
454Q8—22no—
455Q8—41no—
456Q8—41no—
457Q8—41no—
458Q8—42no—
459Q8—41no—
460Q8—41no—
461Q8—41no—
462D4—22no—
463D4—41no—
464D4—41no—
465D4—41no—
466D4—41no—
467D4—41no—
468D4—42no—
469D4—42no—
470D4—42no—
471D4—42no—
472D4—41no—
473D4—41no—
474D4—41no—
475D4—81no—
476D4—161no—
477D4—161no—
478D4—164no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—81no—
497C2×C4C13×#12011yescharacteristic
498C2×C4C13×#12011yescharacteristic
499C2×C4C13×#12111yescharacteristic
500C2×C4C13×#12711yescharacteristic
501C8—42no—
502C8—41no—
503C8—41no—
504C8—81no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—42no—
512C22—81no—
513C22—81no—
514C22—82no—
515C22—82no—
516C22—84no—
517C22—81no—
518C22—161no—
519C22C13×#39211yescharacteristic
520C4—21no—
521C4—21no—
522C4—21no—
523C4—42no—
524C4—81no—
525C4—81no—
526C4—82no—
527C4—81no—
528C4C13×B(4,𝔽2)11yescharacteristic
529C4C13×B(4,𝔽2)11yescharacteristic
530C2—21no—
531C2—41no—
532C2—41no—
533C2—41no—
534C2—82no—
535C2—161no—
536C2C13×#202111yescharacteristic
subgroupG/H
center, socleC2×C13#2021
commutator, Frattini, cosocleC2×#41C23×C13
prime radicalC13×#3027C2
LCSG ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C13×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3200C2semidirect
3. C13×#3022C2semidirect
4. C13×#2134C2semidirect
5. C13×#2123C2semidirect
6. C13×#1791C2semidirect
7. C13×#1395C2semidirect
44. C22×Q8×C13D4semidirect
54. C2×C13×M16D4semidirect
55. C22×C8×C13D4semidirect
74. C13×#117D4semidirect
84. C13×#101D4semidirect
94. #13355C13direct (N × H)
177. #3200C2×C13semidirect
179. #3022C2×C13semidirect
180. #2134C2×C13semidirect
181. #2123C2×C13semidirect
182. #1791C2×C13semidirect
183. #1395C2×C13semidirect
305. C22×Q8D4×C13semidirect
315. C2×M16D4×C13semidirect
316. C22×C8D4×C13semidirect
335. #117D4×C13semidirect
345. #101D4×C13semidirect
444. C13#13355direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#32002
C13×#30272
C13×#30222
C13×#21342
C13×#21232
C13×#17912
C13×#13952
#1335513