Finite Group Databasebeta

← C13×#9944 #15696283

Subgroups — C13×#9944 #15696283

Order 3328.

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

normal subgroups only

This group has 654 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×#3095C211yesmaximal, characteristic, complemented
2C13×#2561C211yesmaximal, characteristic
3C13×#2482C211yesmaximal, characteristic
4C13×#1826C211yesmaximal, characteristic, complemented
5C13×#1511C211yesmaximal, characteristic, complemented
6C13×#1462C211yesmaximal, characteristic
7C13×#1284C211yesmaximal, characteristic, complemented
8C2×C13×C22⋊Q8C2211yescharacteristic
9C2×C13×#117C2211yescharacteristic
10C22×C13×C22⋊C4C2211yescharacteristic
11C13×#485—22no—
12C13×#484—21no—
13C13×#483—21no—
14C13×#428—21no—
15C13×#419—21no—
16C13×#407C2211yescharacteristic
17C13×#407C2211yescharacteristic
18C13×#399—21no—
19C13×#397—21no—
20C13×#397—21no—
21C13×#393—21no—
22C13×#388—22no—
23C13×#388—22no—
24C13×#385—21no—
25C13×#381—21no—
26C13×#381C2211yescharacteristic
27C13×#379—21no—
28C13×#379—21no—
29C4×C13×C22⋊C4C2211yescharacteristic
30C13×#339—22no—
31C13×#328—22no—
32C13×#323—22no—
33C25×C13D411yescharacteristic
34C22×Q8×C13D411yescharacteristic
35C23×C4×C13D411yescharacteristic
36C23×C4×C13C2311yescharacteristic
37C2×C13×M16—21no—
38C2×C13×M16—21no—
39C13×C22⋊Q8—21no—
40C13×C22⋊Q8—21no—
41C13×C22⋊Q8—21no—
42C13×C22⋊Q8—21no—
43C13×#117—21no—
44C13×#117—21no—
45C13×#117—21no—
46C13×#117—21no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4—22no—
49C2×C13×C4⋊C4D411yescharacteristic
50C2×C13×C4⋊C4D411yescharacteristic
51C2×C13×C4⋊C4D411yescharacteristic
52C2×C13×C22⋊C4—22no—
53C2×C13×C22⋊C4—22no—
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—21no—
61C2×C13×C22⋊C4—21no—
62C2×C13×C22⋊C4—21no—
63C2×C13×C22⋊C4—21no—
64C2×C13×C22⋊C4—22no—
65C2×C13×C22⋊C4—22no—
66C2×C42×C13—21no—
67C2×C42×C13D412yes—
68C13×#107—22no—
69C13×#106—22no—
70C13×#103—22no—
71C13×#103—22no—
72C13×C22⋊C8—21no—
73C13×C22⋊C8—21no—
74C13×C22⋊C8—21no—
75C13×C22⋊C8D412yes—
76C13×#95—22no—
77C13×#95—22no—
78C13×#95—22no—
79C13×#95—21no—
80C13×#95—21no—
81C13×#95D412yes—
82#9944C1311yesmaximal, characteristic, direct product factor, Sylow
83C24×C13—21no—
84C24×C13—21no—
85C24×C13—21no—
86C24×C13—42no—
87C24×C13—42no—
88C24×C13—42no—
89C24×C13C2×D411yescharacteristic
90C2×Q8×C13—21no—
91C2×Q8×C13—21no—
92C2×Q8×C13—42no—
93C22×C4×C13—21no—
94C22×C4×C13—22no—
95C22×C4×C13—22no—
96C22×C4×C13—21no—
97C22×C4×C13—21no—
98C22×C4×C13—21no—
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13—21no—
102C22×C4×C13—42no—
103C22×C4×C13—42no—
104C22×C4×C13C2×D411yescharacteristic
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13C2×D411yescharacteristic
107C22×C4×C13C2×D411yescharacteristic
108C22×C4×C13C2×D411yescharacteristic
109C22×C4×C13#4111yescharacteristic
110C13×M16—42no—
111C13×M16—42no—
112C2×C8×C13—22no—
113C2×C8×C13—41no—
114C13×C4⋊C4—21no—
115C13×C4⋊C4—21no—
116C13×C4⋊C4—21no—
117C13×C4⋊C4—21no—
118C13×C4⋊C4—21no—
119C13×C4⋊C4—21no—
120C13×C4⋊C4—41no—
121C13×C4⋊C4—41no—
122C13×C4⋊C4—82no—
123C13×C22⋊C4—42no—
124C13×C22⋊C4—42no—
125C13×C22⋊C4—44no—
126C13×C22⋊C4—44no—
127C13×C22⋊C4—41no—
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—82no—
136C13×C22⋊C4—82no—
137C42×C13—42no—
138C42×C13—41no—
139C42×C13—41no—
140#3095C2×C1311yescharacteristic, complemented
141#2561C2×C1311yescharacteristic
142#2482C2×C1311yescharacteristic
143#1826C2×C1311yescharacteristic, complemented
144#1511C2×C1311yescharacteristic, complemented
145#1462C2×C1311yescharacteristic
146#1284C2×C1311yescharacteristic, complemented
147C23×C13—22no—
148C23×C13—22no—
149C23×C13—22no—
150C23×C13—22no—
151C23×C13—22no—
152C23×C13—41no—
153C23×C13—42no—
154C23×C13—41no—
155C23×C13—41no—
156C23×C13—42no—
157C23×C13—41no—
158C23×C13—41no—
159C23×C13—42no—
160C23×C13—42no—
161C23×C13—81no—
162C23×C13—81no—
163C23×C13—88no—
164C23×C13#12011yescharacteristic
165C23×C13#12011yescharacteristic
166C23×C13#12111yescharacteristic
167Q8×C13—42no—
168Q8×C13—81no—
169C2×C4×C13—22no—
170C2×C4×C13—22no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13—42no—
176C2×C4×C13—42no—
177C2×C4×C13—42no—
178C2×C4×C13—42no—
179C2×C4×C13—42no—
180C2×C4×C13—42no—
181C2×C4×C13—42no—
182C2×C4×C13—41no—
183C2×C4×C13—41no—
184C2×C4×C13—41no—
185C2×C4×C13—41no—
186C2×C4×C13—41no—
187C2×C4×C13—42no—
188C2×C4×C13—42no—
189C2×C4×C13—42no—
190C2×C4×C13—42no—
191C2×C4×C13—42no—
192C2×C4×C13—81no—
193C2×C4×C13#12011yescharacteristic
194C2×C4×C13#12111yescharacteristic
195C2×C4×C13#12111yescharacteristic
196C2×C4×C13#12711yescharacteristic
197C8×C13—42no—
198C8×C13—81no—
199C2×C22⋊Q8C22×C1311yescharacteristic
200C2×#117C22×C1311yescharacteristic
201C22×C22⋊C4C22×C1311yescharacteristic
202#485—22no—
203#484—21no—
204#483—21no—
205#428—21no—
206#419—21no—
207#407C22×C1311yescharacteristic
208#407C22×C1311yescharacteristic
209#399—21no—
210#397—21no—
211#397—21no—
212#393—21no—
213#388—22no—
214#388—22no—
215#385—21no—
216#381—21no—
217#381C22×C1311yescharacteristic
218#379—21no—
219#379—21no—
220C4×C22⋊C4C22×C1311yescharacteristic
221#339—22no—
222#328—22no—
223#323—22no—
224C22×C13—21no—
225C22×C13—21no—
226C22×C13—21no—
227C22×C13—21no—
228C22×C13—21no—
229C22×C13—21no—
230C22×C13—21no—
231C22×C13—44no—
232C22×C13—44no—
233C22×C13—44no—
234C22×C13—42no—
235C22×C13—82no—
236C22×C13—82no—
237C22×C13—82no—
238C22×C13—82no—
239C22×C13—81no—
240C22×C13—81no—
241C22×C13#39211yescharacteristic
242C22×C13#45512yes—
243C22×C13#45812yes—
244C4×C13—21no—
245C4×C13—21no—
246C4×C13—21no—
247C4×C13—21no—
248C4×C13—82no—
249C4×C13—82no—
250C4×C13—81no—
251C4×C13—81no—
252C4×C13—81no—
253C4×C13—81no—
254C4×C13—81no—
255C25D4×C1311yescharacteristic
256C22×Q8D4×C1311yescharacteristic
257C23×C4D4×C1311yescharacteristic
258C23×C4C23×C1311yescharacteristic
259C2×M16—21no—
260C2×M16—21no—
261C22⋊Q8—21no—
262C22⋊Q8—21no—
263C22⋊Q8—21no—
264C22⋊Q8—21no—
265#117—21no—
266#117—21no—
267#117—21no—
268#117—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4D4×C1311yescharacteristic
272C2×C4⋊C4D4×C1311yescharacteristic
273C2×C4⋊C4D4×C1311yescharacteristic
274C2×C22⋊C4—22no—
275C2×C22⋊C4—22no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—22no—
287C2×C22⋊C4—22no—
288C2×C42—21no—
289C2×C42D4×C1312yes—
290#107—22no—
291#106—22no—
292#103—22no—
293#103—22no—
294C22⋊C8—21no—
295C22⋊C8—21no—
296C22⋊C8—21no—
297C22⋊C8D4×C1312yes—
298#95—22no—
299#95—22no—
300#95—22no—
301#95—21no—
302#95—21no—
303#95D4×C1312yes—
304C2×C13—22no—
305C2×C13—22no—
306C2×C13—41no—
307C2×C13—82no—
308C2×C13#200411yescharacteristic
309C2×C13#201011yescharacteristic
310C2×C13#202211yescharacteristic
311C24—21no—
312C24—21no—
313C24—21no—
314C24—42no—
315C24—42no—
316C24—42no—
317C24C2×D4×C1311yescharacteristic
318C2×Q8—21no—
319C2×Q8—21no—
320C2×Q8—42no—
321C22×C4—21no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—42no—
331C22×C4—42no—
332C22×C4C2×D4×C1311yescharacteristic
333C22×C4C2×D4×C1311yescharacteristic
334C22×C4C2×D4×C1311yescharacteristic
335C22×C4C2×D4×C1311yescharacteristic
336C22×C4C2×D4×C1311yescharacteristic
337C22×C4C13×#4111yescharacteristic
338M16—42no—
339M16—42no—
340C2×C8—22no—
341C2×C8—41no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—82no—
351C22⋊C4—42no—
352C22⋊C4—42no—
353C22⋊C4—44no—
354C22⋊C4—44no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C22⋊C4—82no—
364C22⋊C4—82no—
365C42—42no—
366C42—41no—
367C42—41no—
368C13#994411yescharacteristic, direct product factor, Sylow
369C23—22no—
370C23—22no—
371C23—22no—
372C23—22no—
373C23—22no—
374C23—41no—
375C23—42no—
376C23—41no—
377C23—41no—
378C23—42no—
379C23—41no—
380C23—41no—
381C23—42no—
382C23—42no—
383C23—81no—
384C23—81no—
385C23—88no—
386C23C13×#12011yescharacteristic
387C23C13×#12011yescharacteristic
388C23C13×#12111yescharacteristic
389Q8—42no—
390Q8—81no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—81no—
415C2×C4C13×#12011yescharacteristic
416C2×C4C13×#12111yescharacteristic
417C2×C4C13×#12111yescharacteristic
418C2×C4C13×#12711yescharacteristic
419C8—42no—
420C8—81no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—44no—
429C22—44no—
430C22—44no—
431C22—42no—
432C22—82no—
433C22—82no—
434C22—82no—
435C22—82no—
436C22—81no—
437C22—81no—
438C22C13×#39211yescharacteristic
439C22C13×#45512yes—
440C22C13×#45812yes—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—21no—
445C4—82no—
446C4—82no—
447C4—81no—
448C4—81no—
449C4—81no—
450C4—81no—
451C4—81no—
452C2—22no—
453C2—22no—
454C2—41no—
455C2—82no—
456C2C13×#200411yescharacteristic
457C2C13×#201011yescharacteristic
458C2C13×#202211yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC25×C13D4
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×#3095C2semidirect
4. C13×#1826C2semidirect
5. C13×#1511C2semidirect
7. C13×#1284C2semidirect
82. #9944C13direct (N × H)
140. #3095C2×C13semidirect
143. #1826C2×C13semidirect
144. #1511C2×C13semidirect
146. #1284C2×C13semidirect
368. C13#9944direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#30952
C13×#25612
C13×#24822
C13×#18262
C13×#15112
C13×#14622
C13×#12842
#994413