Finite Group Databasebeta

← C3×#10597729⋊C3 #72242002

Subgroups — C3×#10597729⋊C3 #72242002

Order 5616.

664 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C3⋊AGL(1,𝔽13)C212yesmaximal, complemented
2C22×C32×D13⋊C3C211yesmaximal, characteristic
3C3×#10597729C311yesmaximal, characteristic, complemented
4#10597729⋊C3C311yesmaximal, characteristic, direct product factor
5#10597729⋊C3C311yesmaximal, characteristic, direct product factor
6#10597729⋊C3C311yesmaximal, characteristic, direct product factor
7C3×(C22⋊#261)⋊C3—31nomaximal
8C22×C32×C13⋊C3C411yescharacteristic, complemented
9C2×C32×D13⋊C3—22no—
10C2×C32×D13⋊C3C411yescharacteristic, complemented
11C2×C32×D13⋊C3C2211yescharacteristic
12C3×C3⋊AGL(1,𝔽13)—22no—
13C22×C32×D13C2×C311yescharacteristic
14C2×C3×C3⋊#261C2×C312yescomplemented
15C22×C3×D13⋊C3—21no—
16C22×C3×D13⋊C3—21no—
17C22×C3×D13⋊C3—21no—
18C22×C3×D13⋊C3—21no—
19C22×C3×D13⋊C3D311yescharacteristic
20C22×C3×D13⋊C3C2×C311yescharacteristic
21C22×C3×D13⋊C3C2×C311yescharacteristic
22C22×C3×D13⋊C3C2×C311yescharacteristic
23C2×C3⋊AGL(1,𝔽13)C2×C312yescomplemented
24C2×C3⋊AGL(1,𝔽13)C2×C312yescomplemented
25C2×C3⋊AGL(1,𝔽13)C2×C312yescomplemented
26C2×C3×AGL(1,𝔽13)—32no—
27C2×C32×C13⋊C3—21no—
28C2×C32×C13⋊C3C2×C411yescharacteristic
29C32×D13⋊C3—21no—
30C32×D13⋊C3D412yes—
31#10597729C3211yescharacteristic, complemented
32C3×C22⋊#261—31no—
33(C22⋊#261)⋊C3—31no—
34(C22⋊#261)⋊C3—31no—
35(C22⋊#261)⋊C3—31no—
36C22×C32×C13C3×C411yescharacteristic, complemented
37C2×C32×D13—22no—
38C2×C32×D13C3×C411yescharacteristic, complemented
39C2×C32×D13C22×C311yescharacteristic
40C22×C3×C13⋊C3—21no—
41C22×C3×C13⋊C3—21no—
42C22×C3×C13⋊C3—21no—
43C22×C3×C13⋊C3—21no—
44C22×C3×C13⋊C3Dic311yescharacteristic, complemented
45C22×C3×C13⋊C3C3×C411yescharacteristic, complemented
46C22×C3×C13⋊C3C3×C411yescharacteristic, complemented
47C22×C3×C13⋊C3C3×C411yescharacteristic, complemented
48C3×C3⋊#261—22no—
49C2×C3×D13⋊C3—22no—
50C2×C3×D13⋊C3—22no—
51C2×C3×D13⋊C3—22no—
52C2×C3×D13⋊C3—22no—
53C2×C3×D13⋊C3—22no—
54C2×C3×D13⋊C3—22no—
55C2×C3×D13⋊C3—22no—
56C2×C3×D13⋊C3—22no—
57C2×C3×D13⋊C3—22no—
58C2×C3×D13⋊C3—22no—
59C2×C3×D13⋊C3—22no—
60C2×C3×D13⋊C3—22no—
61C2×C3×D13⋊C3—21no—
62C2×C3×D13⋊C3—21no—
63C2×C3×D13⋊C3—21no—
64C2×C3×D13⋊C3—21no—
65C2×C3×D13⋊C3—21no—
66C2×C3×D13⋊C3—21no—
67C2×C3×D13⋊C3—21no—
68C2×C3×D13⋊C3—21no—
69C2×C3×D13⋊C3Dic311yescharacteristic, complemented
70C2×C3×D13⋊C3C3×C411yescharacteristic, complemented
71C2×C3×D13⋊C3C3×C411yescharacteristic, complemented
72C2×C3×D13⋊C3C3×C411yescharacteristic, complemented
73C2×C3×D13⋊C3C2×D311yescharacteristic
74C2×C3×D13⋊C3C22×C311yescharacteristic
75C2×C3×D13⋊C3C22×C311yescharacteristic
76C2×C3×D13⋊C3C22×C311yescharacteristic
77C3⋊AGL(1,𝔽13)—22no—
78C3⋊AGL(1,𝔽13)—22no—
79C3⋊AGL(1,𝔽13)—22no—
80C3×AGL(1,𝔽13)—62no—
81C32×#217—131nomaximal, Hall
82C32×C13⋊C3C22⋊C411yescharacteristic, complemented, Hall
83C22×C3×D13—21no—
84C22×C3×D13C3×D311yescharacteristic
85C22×C3×D13C2×C3211yescharacteristic
86C2×C3⋊#261C2×C3212yescomplemented
87C2×C3×#261—32no—
88C22×D13⋊C3—21no—
89C22×D13⋊C3—21no—
90C22×D13⋊C3—21no—
91C22×D13⋊C3C3×D311yescharacteristic
92C22×D13⋊C3C3×D311yescharacteristic
93C22×D13⋊C3C3×D311yescharacteristic
94C2×AGL(1,𝔽13)—32no—
95C2×AGL(1,𝔽13)—32no—
96C2×AGL(1,𝔽13)—32no—
97C2×C32×C13—21no—
98C2×C32×C13C2×C3×C411yescharacteristic
99C32×D13—21no—
100C32×D13C3×D412yes—
101C2×C3×C13⋊C3—21no—
102C2×C3×C13⋊C3—21no—
103C2×C3×C13⋊C3—21no—
104C2×C3×C13⋊C3—21no—
105C2×C3×C13⋊C3—21no—
106C2×C3×C13⋊C3—21no—
107C2×C3×C13⋊C3—21no—
108C2×C3×C13⋊C3—21no—
109C2×C3×C13⋊C3—21no—
110C2×C3×C13⋊C3—21no—
111C2×C3×C13⋊C3—21no—
112C2×C3×C13⋊C3—21no—
113C2×C3×C13⋊C3—21no—
114C2×C3×C13⋊C3—21no—
115C2×C3×C13⋊C3—21no—
116C2×C3×C13⋊C3—21no—
117C2×C3×C13⋊C3C2×Dic311yescharacteristic
118C2×C3×C13⋊C3C2×C3×C411yescharacteristic
119C2×C3×C13⋊C3C2×C3×C411yescharacteristic
120C2×C3×C13⋊C3C2×C3×C411yescharacteristic
121C3×D13⋊C3—21no—
122C3×D13⋊C3—21no—
123C3×D13⋊C3—21no—
124C3×D13⋊C3—21no—
125C3×D13⋊C3—21no—
126C3×D13⋊C3—21no—
127C3×D13⋊C3—21no—
128C3×D13⋊C3—21no—
129C3×D13⋊C3—21no—
130C3×D13⋊C3—21no—
131C3×D13⋊C3—21no—
132C3×D13⋊C3—21no—
133C3×D13⋊C3—22no—
134C3×D13⋊C3—22no—
135C3×D13⋊C3—22no—
136C3×D13⋊C3—22no—
137C3×D13⋊C3#6712yes—
138C3×D13⋊C3C3×D412yes—
139C3×D13⋊C3C3×D412yes—
140C3×D13⋊C3C3×D412yes—
141C23×C33—131no—
142C2×C32×Dic3—132no—
143C22⋊#261—31noHall
144C22×C3×C13—21no—
145C22×C3×C13C3×Dic311yescharacteristic, complemented
146C22×C3×C13C32×C411yescharacteristic, complemented
147C2×C3×D13—22no—
148C2×C3×D13—22no—
149C2×C3×D13—22no—
150C2×C3×D13—22no—
151C2×C3×D13—21no—
152C2×C3×D13—21no—
153C2×C3×D13C3×Dic311yescharacteristic, complemented
154C2×C3×D13C32×C411yescharacteristic, complemented
155C2×C3×D13C2×C3×D311yescharacteristic
156C2×C3×D13C22×C3211yescharacteristic
157C22×C13⋊C3—21no—
158C22×C13⋊C3—21no—
159C22×C13⋊C3—21no—
160C22×C13⋊C3C3×Dic311yescharacteristic, complemented
161C22×C13⋊C3C3×Dic311yescharacteristic, complemented
162C22×C13⋊C3C3×Dic311yescharacteristic, complemented
163C3⋊#261—22no—
164C3×#261—62no—
165C2×D13⋊C3—22no—
166C2×D13⋊C3—22no—
167C2×D13⋊C3—22no—
168C2×D13⋊C3—22no—
169C2×D13⋊C3—22no—
170C2×D13⋊C3—22no—
171C2×D13⋊C3—22no—
172C2×D13⋊C3—22no—
173C2×D13⋊C3—22no—
174C2×D13⋊C3—21no—
175C2×D13⋊C3—21no—
176C2×D13⋊C3—21no—
177C2×D13⋊C3—21no—
178C2×D13⋊C3—21no—
179C2×D13⋊C3—21no—
180C2×D13⋊C3C3×Dic311yescharacteristic, complemented
181C2×D13⋊C3C3×Dic311yescharacteristic, complemented
182C2×D13⋊C3C3×Dic311yescharacteristic, complemented
183C2×D13⋊C3C2×C3×D311yescharacteristic
184C2×D13⋊C3C2×C3×D311yescharacteristic
185C2×D13⋊C3C2×C3×D311yescharacteristic
186AGL(1,𝔽13)—62no—
187AGL(1,𝔽13)—62no—
188AGL(1,𝔽13)—62no—
189C32×C22⋊C4—391no—
190C3×#217—131no—
191C3×#217—131no—
192C3×#217—131no—
193C3×#217—131no—
194C32×C13C3×C22⋊C411yescharacteristic, complemented
195C3×C13⋊C3—21no—
196C3×C13⋊C3—21no—
197C3×C13⋊C3—21no—
198C3×C13⋊C3—21no—
199C3×C13⋊C3#21711yescharacteristic, complemented
200C3×C13⋊C3C3×C22⋊C411yescharacteristic, complemented
201C3×C13⋊C3C3×C22⋊C411yescharacteristic, complemented
202C3×C13⋊C3C3×C22⋊C411yescharacteristic, complemented
203C22×C33—131no—
204C22×C33—131no—
205C22×C33—131no—
206C22×C33—262no—
207C32×Dic3—262no—
208C22×D13C32×D311yescharacteristic
209C2×#261—32no—
210C2×C3×C13—21no—
211C2×C3×C13—21no—
212C2×C3×C13—21no—
213C2×C3×C13—21no—
214C2×C3×C13—21no—
215C2×C3×C13C2×C3×Dic311yescharacteristic
216C2×C3×C13C2×C32×C411yescharacteristic
217C3×D13—21no—
218C3×D13—21no—
219C3×D13—21no—
220C3×D13—21no—
221C3×D13—22no—
222C3×D13C3×#6712yes—
223C3×D13C32×D412yes—
224C2×C13⋊C3—21no—
225C2×C13⋊C3—21no—
226C2×C13⋊C3—21no—
227C2×C13⋊C3—21no—
228C2×C13⋊C3—21no—
229C2×C13⋊C3—21no—
230C2×C13⋊C3—21no—
231C2×C13⋊C3—21no—
232C2×C13⋊C3—21no—
233C2×C13⋊C3—21no—
234C2×C13⋊C3—21no—
235C2×C13⋊C3—21no—
236C2×C13⋊C3C2×C3×Dic311yescharacteristic
237C2×C13⋊C3C2×C3×Dic311yescharacteristic
238C2×C13⋊C3C2×C3×Dic311yescharacteristic
239D13⋊C3—21no—
240D13⋊C3—21no—
241D13⋊C3—21no—
242D13⋊C3—21no—
243D13⋊C3—21no—
244D13⋊C3—21no—
245D13⋊C3—21no—
246D13⋊C3—21no—
247D13⋊C3—21no—
248D13⋊C3—22no—
249D13⋊C3—22no—
250D13⋊C3—22no—
251D13⋊C3C3×#6712yes—
252D13⋊C3C3×#6712yes—
253D13⋊C3C3×#6712yes—
254C23×C32—131no—
255C23×C32—131no—
256C23×C32—131no—
257C23×C32—131no—
258C23×C32—131no—
259C23×C32—261no—
260C23×C32—261no—
261C23×C32—261no—
262C23×C32—261no—
263C2×C32×C4—392no—
264C2×C3×Dic3—132no—
265C2×C3×Dic3—132no—
266C2×C3×Dic3—132no—
267C2×C3×Dic3—132no—
268C2×C33—132no—
269C2×C33—131no—
270C2×C33—261no—
271C2×C33—261no—
272C22×C13C32×Dic311yescharacteristic, complemented
273C2×D13—22no—
274C2×D13C32×Dic311yescharacteristic, complemented
275C2×D13C2×C32×D311yescharacteristic
276#261—62no—
277C3×C22⋊C4—391no—
278C3×C22⋊C4—391no—
279C3×C22⋊C4—391no—
280C3×C22⋊C4—391no—
281#217—131no—
282C3×C13—21no—
283C3×C13C3×#21711yescharacteristic, complemented
284C3×C13C32×C22⋊C411yescharacteristic, complemented
285C13⋊C3—21no—
286C13⋊C3—21no—
287C13⋊C3—21no—
288C13⋊C3C3×#21711yescharacteristic, complemented
289C13⋊C3C3×#21711yescharacteristic, complemented
290C13⋊C3C3×#21711yescharacteristic, complemented
291C22×C32—131no—
292C22×C32—131no—
293C22×C32—131no—
294C22×C32—131no—
295C22×C32—131no—
296C22×C32—131no—
297C22×C32—131no—
298C22×C32—131no—
299C22×C32—131no—
300C22×C32—131no—
301C22×C32—261no—
302C22×C32—261no—
303C22×C32—261no—
304C22×C32—261no—
305C22×C32—261no—
306C22×C32—261no—
307C22×C32—261no—
308C22×C32—261no—
309C22×C32—262no—
310C22×C32—262no—
311C22×C32—262no—
312C22×C32—262no—
313C22×C32—262no—
314C22×C32—262no—
315C22×C32—262no—
316C22×C32—262no—
317C22×C32—262no—
318C22×C32—262no—
319C22×C32—262no—
320C22×C32—262no—
321C22×C32—262no—
322C22×C32—521no—
323C22×C32—521no—
324C22×C32—521no—
325C22×C32—521no—
326C22×C32—521no—
327C22×C32—521no—
328C22×C32—521no—
329C22×C32—521no—
330C22×C32AGL(1,𝔽13)11yescharacteristic, complemented
331C32×C4—782no—
332C3×Dic3—262no—
333C3×Dic3—262no—
334C3×Dic3—262no—
335C3×Dic3—262no—
336C33—131noSylow
337C2×C13—21no—
338C2×C13C2×C32×Dic311yescharacteristic
339D13—21no—
340D13C32×#6712yes—
341C23×C3—131no—
342C23×C3—131no—
343C23×C3—131no—
344C23×C3—131no—
345C23×C3—131no—
346C23×C3—261no—
347C23×C3—261no—
348C23×C3—261no—
349C23×C3—261no—
350C2×C3×C4—392no—
351C2×C3×C4—392no—
352C2×C3×C4—392no—
353C2×C3×C4—392no—
354C2×Dic3—132no—
355C2×C32—21no—
356C2×C32—132no—
357C2×C32—132no—
358C2×C32—132no—
359C2×C32—132no—
360C2×C32—132no—
361C2×C32—262no—
362C2×C32—262no—
363C2×C32—262no—
364C2×C32—262no—
365C2×C32—261no—
366C2×C32—261no—
367C2×C32—261no—
368C2×C32—261no—
369C2×C32—261no—
370C2×C32—261no—
371C2×C32—261no—
372C2×C32—261no—
373C2×C32—261no—
374C2×C32—261no—
375C2×C32—261no—
376C2×C32—261no—
377C2×C32—261no—
378C2×C32—521no—
379C2×C32—521no—
380C2×C32—521no—
381C2×C32—521no—
382C2×C32—521no—
383C2×C32—521no—
384C2×C32—521no—
385C2×C32—521no—
386C2×C32—521no—
387C2×C32—521no—
388C2×C32—521no—
389C2×C32—521no—
390C2×C32—521no—
391C2×C32—521no—
392C2×C32—521no—
393C2×C32—521no—
394C2×C32—521no—
395C2×C32—521no—
396C2×C32—521no—
397C2×C32—521no—
398C2×C32C2×AGL(1,𝔽13)11yescharacteristic
399C22⋊C4—391noSylow
400C13C32×#21711yescharacteristic, complemented, Sylow
401C22×C3—21no—
402C22×C3—131no—
403C22×C3—131no—
404C22×C3—131no—
405C22×C3—131no—
406C22×C3—131no—
407C22×C3—131no—
408C22×C3—131no—
409C22×C3—131no—
410C22×C3—131no—
411C22×C3—131no—
412C22×C3—131no—
413C22×C3—261no—
414C22×C3—261no—
415C22×C3—261no—
416C22×C3—261no—
417C22×C3—261no—
418C22×C3—261no—
419C22×C3—261no—
420C22×C3—261no—
421C22×C3—262no—
422C22×C3—262no—
423C22×C3—262no—
424C22×C3—262no—
425C22×C3—262no—
426C22×C3—262no—
427C22×C3—262no—
428C22×C3—262no—
429C22×C3—262no—
430C22×C3—262no—
431C22×C3—262no—
432C22×C3—262no—
433C22×C3—262no—
434C22×C3—521no—
435C22×C3—521no—
436C22×C3—521no—
437C22×C3—521no—
438C22×C3—521no—
439C22×C3C3×AGL(1,𝔽13)11yescharacteristic, complemented
440C22×C3C3⋊AGL(1,𝔽13)11yescharacteristic, complemented
441C3×C4—782no—
442C3×C4—782no—
443C3×C4—782no—
444C3×C4—782no—
445Dic3—262no—
446C32—521no—
447C32—521no—
448C32—521no—
449C32—521no—
450C32—521no—
451C32—521no—
452C32—521no—
453C32—521no—
454C32(C22⋊#261)⋊C311yescharacteristic, complemented
455C23—131no—
456C2×C4—392no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—132no—
463C2×C3—132no—
464C2×C3—132no—
465C2×C3—132no—
466C2×C3—132no—
467C2×C3—131no—
468C2×C3—261no—
469C2×C3—262no—
470C2×C3—262no—
471C2×C3—262no—
472C2×C3—262no—
473C2×C3—261no—
474C2×C3—261no—
475C2×C3—261no—
476C2×C3—261no—
477C2×C3—261no—
478C2×C3—261no—
479C2×C3—261no—
480C2×C3—261no—
481C2×C3—261no—
482C2×C3—261no—
483C2×C3—261no—
484C2×C3—261no—
485C2×C3—261no—
486C2×C3—521no—
487C2×C3—521no—
488C2×C3—521no—
489C2×C3—521no—
490C2×C3—521no—
491C2×C3—521no—
492C2×C3—521no—
493C2×C3—521no—
494C2×C3—521no—
495C2×C3—521no—
496C2×C3—521no—
497C2×C3—521no—
498C2×C3—521no—
499C2×C3C2×C3×AGL(1,𝔽13)11yescharacteristic
500C2×C3C2×C3⋊AGL(1,𝔽13)11yescharacteristic
501C22—131no—
502C22—131no—
503C22—262no—
504C22C3×C3⋊AGL(1,𝔽13)11yescharacteristic, complemented
505C4—782no—
506C3—21no—
507C3—131no—
508C3—521no—
509C3—521no—
510C3—521no—
511C3—521no—
512C3—521no—
513C3C3×(C22⋊#261)⋊C311yescharacteristic, complemented
514C3#10597729⋊C311yescharacteristic, direct product factor
515C2—21no—
516C2—132no—
517C2—261no—
518C2C2×C3×C3⋊AGL(1,𝔽13)11yescharacteristic
subgroupG/H
centerC2×C3C2×C3⋊AGL(1,𝔽13)
commutatorC2×C3×C13C2×C32×C4
FrattiniC2C2×C3×C3⋊AGL(1,𝔽13)
FittingC22×C32×C13C3×C4
socleC2×C32×C13C2×C3×C4
prime radicalC22×C32×D13⋊C3C2
cosocleC2×C3×D13C22×C32
hypercenterC22×C3C3⋊AGL(1,𝔽13)
hypocenterC3×C13C32×C22⋊C4
LCSG ▷ C2×C3×C13 ▷ C3×C13
UCSC1 ◁ C2×C3 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
1. C2×C3×C3⋊AGL(1,𝔽13)C2semidirect
3. C3×#10597729C3semidirect
4. #10597729⋊C3C3direct (N × H)
5. #10597729⋊C3C3direct (N × H)
6. #10597729⋊C3C3direct (N × H)
8. C22×C32×C13⋊C3C4semidirect
10. C2×C32×D13⋊C3C4semidirect
14. C2×C3×C3⋊#261C2×C3semidirect
23. C2×C3⋊AGL(1,𝔽13)C2×C3semidirect
24. C2×C3⋊AGL(1,𝔽13)C2×C3semidirect
25. C2×C3⋊AGL(1,𝔽13)C2×C3semidirect
31. #10597729C32semidirect
36. C22×C32×C13C3×C4semidirect
38. C2×C32×D13C3×C4semidirect
44. C22×C3×C13⋊C3Dic3semidirect
45. C22×C3×C13⋊C3C3×C4semidirect
46. C22×C3×C13⋊C3C3×C4semidirect
47. C22×C3×C13⋊C3C3×C4semidirect
69. C2×C3×D13⋊C3Dic3semidirect
70. C2×C3×D13⋊C3C3×C4semidirect
71. C2×C3×D13⋊C3C3×C4semidirect
72. C2×C3×D13⋊C3C3×C4semidirect
82. C32×C13⋊C3C22⋊C4semidirect
86. C2×C3⋊#261C2×C32semidirect
145. C22×C3×C13C3×Dic3semidirect
146. C22×C3×C13C32×C4semidirect
153. C2×C3×D13C3×Dic3semidirect
154. C2×C3×D13C32×C4semidirect
160. C22×C13⋊C3C3×Dic3semidirect
161. C22×C13⋊C3C3×Dic3semidirect
162. C22×C13⋊C3C3×Dic3semidirect
180. C2×D13⋊C3C3×Dic3semidirect
181. C2×D13⋊C3C3×Dic3semidirect
182. C2×D13⋊C3C3×Dic3semidirect
194. C32×C13C3×C22⋊C4semidirect
199. C3×C13⋊C3#217semidirect
200. C3×C13⋊C3C3×C22⋊C4semidirect
201. C3×C13⋊C3C3×C22⋊C4semidirect
202. C3×C13⋊C3C3×C22⋊C4semidirect
272. C22×C13C32×Dic3semidirect
274. C2×D13C32×Dic3semidirect
283. C3×C13C3×#217semidirect
284. C3×C13C32×C22⋊C4semidirect
288. C13⋊C3C3×#217semidirect
289. C13⋊C3C3×#217semidirect
290. C13⋊C3C3×#217semidirect
330. C22×C32AGL(1,𝔽13)semidirect
400. C13C32×#217semidirect
439. C22×C3C3×AGL(1,𝔽13)semidirect
440. C22×C3C3⋊AGL(1,𝔽13)semidirect
454. C32(C22⋊#261)⋊C3semidirect
504. C22C3×C3⋊AGL(1,𝔽13)semidirect
513. C3C3×(C22⋊#261)⋊C3semidirect
514. C3#10597729⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C3⋊AGL(1,𝔽13)2
C22×C32×D13⋊C32
C3×#105977293
#10597729⋊C33
C3×(C22⋊#261)⋊C33
C32×#21713