Finite Group Databasebeta

← C13×#9935 #15696274

Subgroups — C13×#9935 #15696274

Order 3328.

750 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 750 conjugacy classes of subgroups — too many to draw. Only its 102 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×#3195C211yesmaximal, characteristic, complemented
2C13×#3007C211yesmaximal, characteristic
3C13×#2616C211yesmaximal, characteristic
4C13×#1996C211yesmaximal, characteristic, complemented
5C13×#1789C211yesmaximal, characteristic
6C13×#1508C211yesmaximal, characteristic, complemented
7C13×#1305C211yesmaximal, characteristic, complemented
8C22×C13×#41C2211yescharacteristic
9C2×C13×#137—21no—
10C2×C13×C22⋊Q8—21no—
11C2×C13×C22⋊Q8C2211yescharacteristic
12C2×C13×C22⋊Q8C2211yescharacteristic
13C13×#483—21no—
14C13×#483—21no—
15C13×#470—22no—
16C13×#452—22no—
17C13×#451—21no—
18C13×#451—21no—
19C13×#451—21no—
20C13×#450—21no—
21C2×C13×#104—22no—
22C13×#417—21no—
23C13×#407C2211yescharacteristic
24C13×#407C2211yescharacteristic
25C13×#395—21no—
26C13×#394—21no—
27C13×#394—22no—
28C13×#380—21no—
29C13×#380C2211yescharacteristic
30C4×C13×C22⋊C4C2211yescharacteristic
31C13×#342—22no—
32C13×#328—22no—
33C2×C13×#41—21no—
34C2×C13×#41—21no—
35C2×C13×#41—21no—
36C2×C13×#41—21no—
37C2×C13×#41—44no—
38C22×Q8×C13D411yescharacteristic
39C22×Q8×C13D411yescharacteristic
40C22×Q8×C13D411yescharacteristic
41C22×D4×C13—21no—
42C22×D4×C13D411yescharacteristic
43C23×C4×C13—21no—
44C23×C4×C13C2311yescharacteristic
45C13×#137—44no—
46C2×C13×Q16—22no—
47C2×C13×Q16—22no—
48C2×C13×SD16—22no—
49C2×C13×M16—21no—
50C2×C13×M16D412yes—
51C13×C22⋊Q8—21no—
52C13×C22⋊Q8—21no—
53C13×C22⋊Q8—21no—
54C13×C22⋊Q8—21no—
55C13×C22⋊Q8—21no—
56C13×C22⋊Q8—21no—
57C13×C22⋊Q8—21no—
58C13×C22⋊Q8—21no—
59C13×C22⋊Q8—44no—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—21no—
62C2×C13×C4⋊C4—21no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4D411yescharacteristic
65C2×C13×C4⋊C4D411yescharacteristic
66C2×C13×C22⋊C4—21no—
67C2×C13×C22⋊C4—22no—
68C2×C13×C22⋊C4—21no—
69C2×C13×C22⋊C4—21no—
70C2×C13×C22⋊C4—22no—
71C2×C13×C22⋊C4D412yes—
72C2×C42×C13—21no—
73C13×#106—22no—
74C13×#104—44no—
75C13×#103—22no—
76C13×#103—22no—
77C13×#103—22no—
78C13×#102—22no—
79C13×C22⋊C8—21no—
80C13×C22⋊C8—21no—
81C13×C22⋊C8—21no—
82C13×C22⋊C8D412yes—
83C13×#95—22no—
84C13×#95—21no—
85C13×#95—21no—
86#9935C1311yesmaximal, characteristic, direct product factor, Sylow
87C24×C13—21no—
88C24×C13C2×D411yescharacteristic
89C13×#41—24no—
90C13×#41—24no—
91C13×#41—42no—
92C13×#41—42no—
93C13×#41—42no—
94C13×#41—42no—
95C13×#41—42no—
96C13×#41—42no—
97C2×Q8×C13—21no—
98C2×Q8×C13—21no—
99C2×Q8×C13—21no—
100C2×Q8×C13—21no—
101C2×Q8×C13—21no—
102C2×Q8×C13—21no—
103C2×Q8×C13—42no—
104C2×Q8×C13—42no—
105C2×Q8×C13—42no—
106C2×D4×C13—21no—
107C2×D4×C13—21no—
108C2×D4×C13—42no—
109C2×D4×C13—42no—
110C2×D4×C13—42no—
111C2×D4×C13—41no—
112C2×D4×C13—41no—
113C22×C4×C13—24no—
114C22×C4×C13—21no—
115C22×C4×C13—21no—
116C22×C4×C13—22no—
117C22×C4×C13—21no—
118C22×C4×C13—21no—
119C22×C4×C13—21no—
120C22×C4×C13—42no—
121C22×C4×C13—42no—
122C22×C4×C13—41no—
123C22×C4×C13—41no—
124C22×C4×C13—41no—
125C22×C4×C13C2×D411yescharacteristic
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13#4111yescharacteristic
131C13×Q16—44no—
132C13×Q16—82no—
133C13×SD16—44no—
134C13×M16—42no—
135C13×M16—42no—
136C2×C8×C13—22no—
137C2×C8×C13—22no—
138C13×C4⋊C4—21no—
139C13×C4⋊C4—21no—
140C13×C4⋊C4—21no—
141C13×C4⋊C4—21no—
142C13×C4⋊C4—42no—
143C13×C4⋊C4—44no—
144C13×C4⋊C4—41no—
145C13×C4⋊C4—41no—
146C13×C4⋊C4—41no—
147C13×C4⋊C4—41no—
148C13×C22⋊C4—22no—
149C13×C22⋊C4—41no—
150C13×C22⋊C4—44no—
151C13×C22⋊C4—41no—
152C13×C22⋊C4—41no—
153C13×C22⋊C4—41no—
154C13×C22⋊C4—41no—
155C13×C22⋊C4—42no—
156C13×C22⋊C4—82no—
157C42×C13—42no—
158#3195C2×C1311yescharacteristic, complemented
159#3007C2×C1311yescharacteristic
160#2616C2×C1311yescharacteristic
161#1996C2×C1311yescharacteristic, complemented
162#1789C2×C1311yescharacteristic
163#1508C2×C1311yescharacteristic, complemented
164#1305C2×C1311yescharacteristic, complemented
165C23×C13—21no—
166C23×C13—21no—
167C23×C13—22no—
168C23×C13—41no—
169C23×C13—41no—
170C23×C13—41no—
171C23×C13—41no—
172C23×C13—41no—
173C23×C13—41no—
174C23×C13—41no—
175C23×C13—41no—
176C23×C13#12011yescharacteristic
177C23×C13#12111yescharacteristic
178C23×C13#12711yescharacteristic
179Q8×C13—22no—
180Q8×C13—22no—
181Q8×C13—41no—
182Q8×C13—41no—
183Q8×C13—42no—
184Q8×C13—42no—
185Q8×C13—42no—
186Q8×C13—81no—
187D4×C13—22no—
188D4×C13—22no—
189D4×C13—41no—
190D4×C13—41no—
191D4×C13—44no—
192D4×C13—44no—
193C2×C4×C13—22no—
194C2×C4×C13—22no—
195C2×C4×C13—22no—
196C2×C4×C13—22no—
197C2×C4×C13—41no—
198C2×C4×C13—41no—
199C2×C4×C13—41no—
200C2×C4×C13—44no—
201C2×C4×C13—41no—
202C2×C4×C13—41no—
203C2×C4×C13—44no—
204C2×C4×C13—42no—
205C2×C4×C13—42no—
206C2×C4×C13—42no—
207C2×C4×C13—42no—
208C2×C4×C13—41no—
209C2×C4×C13—41no—
210C2×C4×C13—41no—
211C2×C4×C13—41no—
212C2×C4×C13—42no—
213C2×C4×C13—41no—
214C2×C4×C13—41no—
215C2×C4×C13—81no—
216C2×C4×C13—81no—
217C2×C4×C13—81no—
218C2×C4×C13—81no—
219C2×C4×C13#12011yescharacteristic
220C2×C4×C13#12011yescharacteristic
221C2×C4×C13#12111yescharacteristic
222C2×C4×C13#12111yescharacteristic
223C8×C13—42no—
224C8×C13—42no—
225C22×#41C22×C1311yescharacteristic
226C2×#137—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8C22×C1311yescharacteristic
229C2×C22⋊Q8C22×C1311yescharacteristic
230#483—21no—
231#483—21no—
232#470—22no—
233#452—22no—
234#451—21no—
235#451—21no—
236#451—21no—
237#450—21no—
238C2×#104—22no—
239#417—21no—
240#407C22×C1311yescharacteristic
241#407C22×C1311yescharacteristic
242#395—21no—
243#394—21no—
244#394—22no—
245#380—21no—
246#380C22×C1311yescharacteristic
247C4×C22⋊C4C22×C1311yescharacteristic
248#342—22no—
249#328—22no—
250C22×C13—21no—
251C22×C13—21no—
252C22×C13—21no—
253C22×C13—21no—
254C22×C13—21no—
255C22×C13—21no—
256C22×C13—21no—
257C22×C13—21no—
258C22×C13—42no—
259C22×C13—42no—
260C22×C13—42no—
261C22×C13—81no—
262C22×C13—81no—
263C22×C13—81no—
264C22×C13—81no—
265C22×C13—81no—
266C22×C13—81no—
267C22×C13#39211yescharacteristic
268C22×C13#45511yescharacteristic
269C22×C13#45611yescharacteristic
270C4×C13—21no—
271C4×C13—21no—
272C4×C13—21no—
273C4×C13—42no—
274C4×C13—82no—
275C4×C13—82no—
276C4×C13—81no—
277C4×C13—81no—
278C4×C13—81no—
279C4×C13—81no—
280C4×C13B(4,𝔽2)12yes—
281C2×#41—21no—
282C2×#41—21no—
283C2×#41—21no—
284C2×#41—21no—
285C2×#41—44no—
286C22×Q8D4×C1311yescharacteristic
287C22×Q8D4×C1311yescharacteristic
288C22×Q8D4×C1311yescharacteristic
289C22×D4—21no—
290C22×D4D4×C1311yescharacteristic
291C23×C4—21no—
292C23×C4C23×C1311yescharacteristic
293#137—44no—
294C2×Q16—22no—
295C2×Q16—22no—
296C2×SD16—22no—
297C2×M16—21no—
298C2×M16D4×C1312yes—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—21no—
305C22⋊Q8—21no—
306C22⋊Q8—21no—
307C22⋊Q8—44no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4D4×C1311yescharacteristic
313C2×C4⋊C4D4×C1311yescharacteristic
314C2×C22⋊C4—21no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4D4×C1312yes—
320C2×C42—21no—
321#106—22no—
322#104—44no—
323#103—22no—
324#103—22no—
325#103—22no—
326#102—22no—
327C22⋊C8—21no—
328C22⋊C8—21no—
329C22⋊C8—21no—
330C22⋊C8D4×C1312yes—
331#95—22no—
332#95—21no—
333#95—21no—
334C2×C13—21no—
335C2×C13—21no—
336C2×C13—41no—
337C2×C13—41no—
338C2×C13—82no—
339C2×C13#200711yescharacteristic
340C2×C13#200911yescharacteristic
341C2×C13#202111yescharacteristic
342C24—21no—
343C24C2×D4×C1311yescharacteristic
344#41—24no—
345#41—24no—
346#41—42no—
347#41—42no—
348#41—42no—
349#41—42no—
350#41—42no—
351#41—42no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—42no—
359C2×Q8—42no—
360C2×Q8—42no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—42no—
364C2×D4—42no—
365C2×D4—42no—
366C2×D4—41no—
367C2×D4—41no—
368C22×C4—24no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4C2×D4×C1311yescharacteristic
381C22×C4C2×D4×C1311yescharacteristic
382C22×C4C2×D4×C1311yescharacteristic
383C22×C4C2×D4×C1311yescharacteristic
384C22×C4C2×D4×C1311yescharacteristic
385C22×C4C13×#4111yescharacteristic
386Q16—44no—
387Q16—82no—
388SD16—44no—
389M16—42no—
390M16—42no—
391C2×C8—22no—
392C2×C8—22no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—42no—
398C4⋊C4—44no—
399C4⋊C4—41no—
400C4⋊C4—41no—
401C4⋊C4—41no—
402C4⋊C4—41no—
403C22⋊C4—22no—
404C22⋊C4—44no—
405C22⋊C4—41no—
406C22⋊C4—41no—
407C22⋊C4—41no—
408C22⋊C4—41no—
409C22⋊C4—41no—
410C22⋊C4—42no—
411C22⋊C4—82no—
412C42—42no—
413C13#993511yescharacteristic, direct product factor, Sylow
414C23—21no—
415C23—21no—
416C23—22no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23C13×#12011yescharacteristic
426C23C13×#12111yescharacteristic
427C23C13×#12711yescharacteristic
428Q8—22no—
429Q8—22no—
430Q8—41no—
431Q8—41no—
432Q8—42no—
433Q8—42no—
434Q8—42no—
435Q8—81no—
436D4—22no—
437D4—22no—
438D4—41no—
439D4—41no—
440D4—44no—
441D4—44no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—44no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—44no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—81no—
465C2×C4—81no—
466C2×C4—81no—
467C2×C4—81no—
468C2×C4C13×#12011yescharacteristic
469C2×C4C13×#12011yescharacteristic
470C2×C4C13×#12111yescharacteristic
471C2×C4C13×#12111yescharacteristic
472C8—42no—
473C8—42no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—42no—
483C22—42no—
484C22—42no—
485C22—81no—
486C22—81no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22C13×#39211yescharacteristic
492C22C13×#45511yescharacteristic
493C22C13×#45611yescharacteristic
494C4—21no—
495C4—21no—
496C4—21no—
497C4—42no—
498C4—82no—
499C4—82no—
500C4—81no—
501C4—81no—
502C4—81no—
503C4—81no—
504C4C13×B(4,𝔽2)12yes—
505C2—21no—
506C2—21no—
507C2—41no—
508C2—41no—
509C2—82no—
510C2C13×#200711yescharacteristic
511C2C13×#200911yescharacteristic
512C2C13×#202111yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC22×C13×#41C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3195C2semidirect
4. C13×#1996C2semidirect
6. C13×#1508C2semidirect
7. C13×#1305C2semidirect
86. #9935C13direct (N × H)
158. #3195C2×C13semidirect
161. #1996C2×C13semidirect
163. #1508C2×C13semidirect
164. #1305C2×C13semidirect
413. C13#9935direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31952
C13×#30072
C13×#26162
C13×#19962
C13×#17892
C13×#15082
C13×#13052
#993513