Finite Group Databasebeta

← C3×#10599563 #14297811

Subgroups — C3×#10599563 #14297811

Order 1920.

624 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65856C211yesmaximal, characteristic
2C2×C3×#3957C211yesmaximal, characteristic
3C3×#65407C211yesmaximal, characteristic, complemented
4C3×C4×#683C211yesmaximal, characteristic, complemented
5C2×C3×#3937C211yesmaximal, characteristic
6C3×C5×#339C211yesmaximal, characteristic, complemented
7C3×#64752C211yesmaximal, characteristic, complemented
8#10599563C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#709C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12C2×C3×C42×C5C2211yescharacteristic
13C2×C3×#683—21no—
14C2×C3×C4×Dic5C2211yescharacteristic
15C2×C3×C4×Dic5C2211yescharacteristic
16C2×C3×#681C2211yescharacteristic
17C3×#4039C411yescharacteristic, complemented
18C3×#4039C411yescharacteristic, complemented
19C3×#4033C411yescharacteristic, complemented
20C3×#4033C411yescharacteristic, complemented
21C3×#4027—21no—
22C3×#4027—21no—
23C3×#4018—21no—
24C3×C42×D5—21no—
25C3×#3963—21no—
26C3×#3957—22no—
27C3×#3946—21no—
28C3×#3946—21no—
29C3×#3937—22no—
30C3×#1806—51nomaximal, Hall
31#65856C2×C311yescharacteristic
32C2×#3957C2×C311yescharacteristic
33#65407C2×C311yescharacteristic, complemented
34C4×#683C2×C311yescharacteristic, complemented
35C2×#3937C2×C311yescharacteristic
36C5×#339C2×C311yescharacteristic, complemented
37#64752C2×C311yescharacteristic, complemented
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5C2311yescharacteristic
40C2×C3×C22⋊D5—21no—
41C22×C3×Dic5—21no—
42C22×C3×Dic5D411yescharacteristic
43C22×C3×Dic5D411yescharacteristic
44C3×#709—21no—
45C3×#709—21no—
46C3×#709D412yes—
47C3×#709Q812yes—
48C2×C3×D20C2×C411yescharacteristic
49C2×C3×C4×D5—21no—
50C2×C3×C4×D5—21no—
51C2×C3×C4×D5—21no—
52C2×C3×Dic10C2×C411yescharacteristic
53C3×C5×M16—21no—
54C3×C5×M16—21no—
55C2×C3×C5×C8—21no—
56C3×C5×C4⋊C4C2×C411yescharacteristic
57C3×C5×C4⋊C4C2×C411yescharacteristic
58C3×C5×C22⋊C4—21no—
59C3×C42×C5—21no—
60C3×C42×C5—21no—
61C3×C42×C5—21no—
62C3×#685—21no—
63C3×#685—21no—
64C3×#683—24no—
65C3×#683—21no—
66C3×#683—21no—
67C3×C4×Dic5—21no—
68C3×C4×Dic5—21no—
69C3×C4×Dic5—21no—
70C3×C4×Dic5—21no—
71C3×C4×Dic5C2×C411yescharacteristic
72C3×C4×Dic5C2×C411yescharacteristic
73C3×C4×Dic5D411yescharacteristic
74C3×C4×Dic5D411yescharacteristic
75C3×#681—21no—
76C3×#681—21no—
77C2×C3×#168—21no—
78C3×C4×#41—51no—
79C3×#423—51no—
80C2×C3×#104—51no—
81C2×C3×#104—51no—
82C3×C4×C4⋊C4—51no—
83C3×#339—51no—
84C3×#339D511yescharacteristic, complemented
85C2×#709C22×C311yescharacteristic
86C2×C5×M16C22×C311yescharacteristic
87C5×#117C22×C311yescharacteristic
88C2×C42×C5C22×C311yescharacteristic
89C2×#683—21no—
90C2×C4×Dic5C22×C311yescharacteristic
91C2×C4×Dic5C22×C311yescharacteristic
92C2×#681C22×C311yescharacteristic
93#4039C3×C411yescharacteristic, complemented
94#4039C3×C411yescharacteristic, complemented
95#4033C3×C411yescharacteristic, complemented
96#4033C3×C411yescharacteristic, complemented
97#4027—21no—
98#4027—21no—
99#4018—21no—
100C42×D5—21no—
101#3963—21no—
102#3957—22no—
103#3946—21no—
104#3946—21no—
105#3937—22no—
106#1806—51noSylow
107C23×C3×C5C2×D411yescharacteristic
108C22×C3×D5—21no—
109C2×C3×C4×C5—22no—
110C2×C3×C4×C5—21no—
111C2×C3×C4×C5—21no—
112C2×C3×C4×C5—41no—
113C2×C3×C4×C5—41no—
114C2×C3×C4×C5C22×C411yescharacteristic
115C2×C3×C4×C5C2×D411yescharacteristic
116C2×C3×C4×C5C2×D411yescharacteristic
117C2×C3×C4×C5C2×Q811yescharacteristic
118C2×C3×C4×C5#4111yescharacteristic
119C2×C3×C4×C5#4111yescharacteristic
120C3×C22⋊D5—22no—
121C3×C22⋊D5—22no—
122C2×C3×Dic5—21no—
123C2×C3×Dic5—22no—
124C2×C3×Dic5—22no—
125C2×C3×Dic5—41no—
126C2×C3×Dic5—41no—
127C2×C3×Dic5—41no—
128C2×C3×Dic5C22⋊C411yescharacteristic
129C2×C3×Dic5C22⋊C411yescharacteristic
130C2×C3×Dic5C22⋊C411yescharacteristic
131C2×C3×Dic5C22⋊C411yescharacteristic
132C3×D20—21no—
133C3×D20C4⋊C412yescomplemented
134C3×C4×D5—22no—
135C3×C4×D5—22no—
136C3×C4×D5—42no—
137C3×C4×D5—42no—
138C3×Dic10—21no—
139C3×Dic10C4⋊C412yescomplemented
140C3×C5×C8—41no—
141C3×#168—41no—
142C2×C3×#41—51no—
143C2×C3×M16—51no—
144C2×C3×M16C2×D511yescharacteristic
145C3×C4×Q8—51no—
146C3×C4×Q8—51no—
147C3×C4×D4—51no—
148C3×C4×D4—51no—
149C3×C4×D4—101no—
150C3×C4×D4—101no—
151C3×#117—101no—
152C3×#117C2×D511yescharacteristic
153C2×C3×C4⋊C4—101no—
154C2×C3×C42—51no—
155C2×C3×C42—51no—
156C2×C3×C42—101no—
157C2×C3×C42C2×D511yescharacteristic
158C3×C4⋊C8—101no—
159C3×C4⋊C8—101no—
160C3×#104—102no—
161C3×#104—102no—
162C3×#95—101no—
163C22×C4×C5—21no—
164C22×C4×C5C23×C311yescharacteristic
165C2×C22⋊D5—21no—
166C22×Dic5—21no—
167C22×Dic5C3×D411yescharacteristic
168C22×Dic5C3×D411yescharacteristic
169#709—21no—
170#709—21no—
171#709C3×D412yes—
172#709C3×Q812yes—
173C2×D20C2×C3×C411yescharacteristic
174C2×C4×D5—21no—
175C2×C4×D5—21no—
176C2×C4×D5—21no—
177C2×Dic10C2×C3×C411yescharacteristic
178C5×M16—21no—
179C5×M16—21no—
180C2×C5×C8—21no—
181C5×C4⋊C4C2×C3×C411yescharacteristic
182C5×C4⋊C4C2×C3×C411yescharacteristic
183C5×C22⋊C4—21no—
184C42×C5—21no—
185C42×C5—21no—
186C42×C5—21no—
187#685—21no—
188#685—21no—
189#683—24no—
190#683—21no—
191#683—21no—
192C4×Dic5—21no—
193C4×Dic5—21no—
194C4×Dic5—21no—
195C4×Dic5—21no—
196C4×Dic5C2×C3×C411yescharacteristic
197C4×Dic5C2×C3×C411yescharacteristic
198C4×Dic5C3×D411yescharacteristic
199C4×Dic5C3×D411yescharacteristic
200#681—21no—
201#681—21no—
202C2×#168—21no—
203C4×#41—51no—
204#423—51no—
205C2×#104—51no—
206C2×#104—51no—
207C4×C4⋊C4—51no—
208#339—51no—
209#339C3×D511yescharacteristic, complemented
210C22×C3×C5—21no—
211C22×C3×C5—21no—
212C22×C3×C5C2×C22⋊C411yescharacteristic
213C22×C3×C5#12111yescharacteristic
214C22×C3×C5C22⋊Q811yescharacteristic
215C2×C3×D5—22no—
216C2×C3×D5—41no—
217C2×C3×D5—41no—
218C3×C4×C5—42no—
219C3×C4×C5—41no—
220C3×C4×C5—41no—
221C3×C4×C5C2×C4⋊C411yescharacteristic
222C3×C4×C5#11711yescharacteristic
223C3×C4×C5#12111yescharacteristic
224C3×C4×C5C22⋊Q811yescharacteristic
225C3×Dic5—22no—
226C3×Dic5—21no—
227C3×Dic5—21no—
228C3×Dic5—21no—
229C3×Dic5—42no—
230C3×Dic5#10412yescomplemented
231C3×#41—52no—
232C3×#41—52no—
233C3×#41—101no—
234C3×#41—101no—
235C2×C3×Q8—51no—
236C2×C3×D4—51no—
237C2×C3×D4—101no—
238C22×C3×C4—21no—
239C22×C3×C4—51no—
240C22×C3×C4—51no—
241C22×C3×C4—101no—
242C22×C3×C4—101no—
243C22×C3×C4—101no—
244C22×C3×C4—101no—
245C22×C3×C4C22×D511yescharacteristic
246C3×M16—21no—
247C3×M16—21no—
248C3×M16—101no—
249C3×M16—101no—
250C2×C3×C8—21no—
251C2×C3×C8—101no—
252C3×C4⋊C4—101no—
253C3×C4⋊C4—101no—
254C3×C4⋊C4—104no—
255C3×C4⋊C4C4×D511yescharacteristic
256C3×C4⋊C4C4×D511yescharacteristic
257C3×C22⋊C4—21no—
258C3×C22⋊C4—101no—
259C3×C22⋊C4—101no—
260C3×C42—21no—
261C3×C42—21no—
262C3×C42—21no—
263C3×C42—51no—
264C3×C42—51no—
265C3×C42—51no—
266C3×C42—51no—
267C3×C42—101no—
268C3×C42—101no—
269C3×C42—101no—
270C3×C42—101no—
271C23×C5C2×C3×D411yescharacteristic
272C22×D5—21no—
273C2×C4×C5—22no—
274C2×C4×C5—21no—
275C2×C4×C5—21no—
276C2×C4×C5—41no—
277C2×C4×C5—41no—
278C2×C4×C5C22×C3×C411yescharacteristic
279C2×C4×C5C2×C3×D411yescharacteristic
280C2×C4×C5C2×C3×D411yescharacteristic
281C2×C4×C5C2×C3×Q811yescharacteristic
282C2×C4×C5C3×#4111yescharacteristic
283C2×C4×C5C3×#4111yescharacteristic
284C22⋊D5—22no—
285C22⋊D5—22no—
286C2×Dic5—21no—
287C2×Dic5—22no—
288C2×Dic5—22no—
289C2×Dic5—41no—
290C2×Dic5—41no—
291C2×Dic5—41no—
292C2×Dic5C3×C22⋊C411yescharacteristic
293C2×Dic5C3×C22⋊C411yescharacteristic
294C2×Dic5C3×C22⋊C411yescharacteristic
295C2×Dic5C3×C22⋊C411yescharacteristic
296D20—21no—
297D20C3×C4⋊C412yescomplemented
298C4×D5—22no—
299C4×D5—22no—
300C4×D5—42no—
301C4×D5—42no—
302Dic10—21no—
303Dic10C3×C4⋊C412yescomplemented
304C5×C8—41no—
305#168—41no—
306C2×#41—51no—
307C2×M16—51no—
308C2×M16C2×C3×D511yescharacteristic
309C4×Q8—51no—
310C4×Q8—51no—
311C4×D4—51no—
312C4×D4—51no—
313C4×D4—101no—
314C4×D4—101no—
315#117—101no—
316#117C2×C3×D511yescharacteristic
317C2×C4⋊C4—101no—
318C2×C42—51no—
319C2×C42—51no—
320C2×C42—101no—
321C2×C42C2×C3×D511yescharacteristic
322C4⋊C8—101no—
323C4⋊C8—101no—
324#104—102no—
325#104—102no—
326#95—101no—
327C2×C3×C5—21no—
328C2×C3×C5—21no—
329C2×C3×C5#38011yescharacteristic
330C2×C3×C5C2×#10411yescharacteristic
331C2×C3×C5#42111yescharacteristic
332C3×D5—42no—
333C23×C3—101no—
334C23×C3D4×D511yescharacteristic
335C3×Q8—52no—
336C3×Q8—101no—
337C3×D4—52no—
338C3×D4—102no—
339C3×D4—102no—
340C3×D4—101no—
341C2×C3×C4—22no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—41no—
345C2×C3×C4—41no—
346C2×C3×C4—51no—
347C2×C3×C4—51no—
348C2×C3×C4—51no—
349C2×C3×C4—51no—
350C2×C3×C4—102no—
351C2×C3×C4—101no—
352C2×C3×C4—102no—
353C2×C3×C4—102no—
354C2×C3×C4—102no—
355C2×C3×C4—202no—
356C2×C3×C4—202no—
357C2×C3×C4—201no—
358C2×C3×C4—201no—
359C2×C3×C4—201no—
360C2×C3×C4C2×C4×D511yescharacteristic
361C2×C3×C4#70911yescharacteristic
362C2×C3×C4#70911yescharacteristic
363C2×C3×C4D4×D511yescharacteristic
364C2×C3×C4D4×D511yescharacteristic
365C2×C3×C4Q8×D511yescharacteristic
366C3×C8—41no—
367C3×C8—201no—
368C22×C5—21no—
369C22×C5—21no—
370C22×C5C2×C3×C22⋊C411yescharacteristic
371C22×C5C3×#12111yescharacteristic
372C22×C5C3×C22⋊Q811yescharacteristic
373C2×D5—22no—
374C2×D5—41no—
375C2×D5—41no—
376C4×C5—42no—
377C4×C5—41no—
378C4×C5—41no—
379C4×C5C2×C3×C4⋊C411yescharacteristic
380C4×C5C3×#11711yescharacteristic
381C4×C5C3×#12111yescharacteristic
382C4×C5C3×C22⋊Q811yescharacteristic
383Dic5—22no—
384Dic5—21no—
385Dic5—21no—
386Dic5—21no—
387Dic5—42no—
388Dic5C3×#10412yescomplemented
389#41—52no—
390#41—52no—
391#41—101no—
392#41—101no—
393C2×Q8—51no—
394C2×D4—51no—
395C2×D4—101no—
396C22×C4—21no—
397C22×C4—51no—
398C22×C4—51no—
399C22×C4—101no—
400C22×C4—101no—
401C22×C4—101no—
402C22×C4—101no—
403C22×C4C22×C3×D511yescharacteristic
404M16—21no—
405M16—21no—
406M16—101no—
407M16—101no—
408C2×C8—21no—
409C2×C8—101no—
410C4⋊C4—101no—
411C4⋊C4—101no—
412C4⋊C4—104no—
413C4⋊C4C3×C4×D511yescharacteristic
414C4⋊C4C3×C4×D511yescharacteristic
415C22⋊C4—21no—
416C22⋊C4—101no—
417C22⋊C4—101no—
418C42—21no—
419C42—21no—
420C42—21no—
421C42—51no—
422C42—51no—
423C42—51no—
424C42—51no—
425C42—101no—
426C42—101no—
427C42—101no—
428C42—101no—
429C3×C5#180611yescharacteristic, complemented, Hall
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—102no—
433C22×C3—201no—
434C22×C3—201no—
435C22×C3D5×C22⋊C411yescharacteristic
436C22×C3#403011yescharacteristic
437C22×C3#404211yescharacteristic
438C3×C4—42no—
439C3×C4—41no—
440C3×C4—41no—
441C3×C4—52no—
442C3×C4—101no—
443C3×C4—101no—
444C3×C4—101no—
445C3×C4—102no—
446C3×C4—202no—
447C3×C4#401811yescharacteristic
448C3×C4#403011yescharacteristic
449C3×C4D5×C4⋊C411yescharacteristic
450C3×C4#404211yescharacteristic
451C2×C5—21no—
452C2×C5—21no—
453C2×C5C3×#38011yescharacteristic
454C2×C5C2×C3×#10411yescharacteristic
455C2×C5C3×#42111yescharacteristic
456D5—42no—
457C23—101no—
458C23C3×D4×D511yescharacteristic
459Q8—52no—
460Q8—101no—
461D4—52no—
462D4—102no—
463D4—102no—
464D4—101no—
465C2×C4—22no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—51no—
471C2×C4—51no—
472C2×C4—51no—
473C2×C4—51no—
474C2×C4—102no—
475C2×C4—101no—
476C2×C4—102no—
477C2×C4—102no—
478C2×C4—102no—
479C2×C4—202no—
480C2×C4—202no—
481C2×C4—201no—
482C2×C4—201no—
483C2×C4—201no—
484C2×C4C2×C3×C4×D511yescharacteristic
485C2×C4C3×#70911yescharacteristic
486C2×C4C3×#70911yescharacteristic
487C2×C4C3×D4×D511yescharacteristic
488C2×C4C3×D4×D511yescharacteristic
489C2×C4C3×Q8×D511yescharacteristic
490C8—41no—
491C8—201no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—202no—
495C2×C3#6495611yescharacteristic
496C2×C3D5×#10411yescharacteristic
497C2×C3#6511011yescharacteristic
498C5C3×#180611yescharacteristic, complemented, Sylow
499C22—21no—
500C22—21no—
501C22—102no—
502C22—201no—
503C22—201no—
504C22C3×D5×C22⋊C411yescharacteristic
505C22C3×#403011yescharacteristic
506C22C3×#404211yescharacteristic
507C4—42no—
508C4—41no—
509C4—41no—
510C4—52no—
511C4—101no—
512C4—101no—
513C4—101no—
514C4—102no—
515C4—202no—
516C4C3×#401811yescharacteristic
517C4C3×#403011yescharacteristic
518C4C3×D5×C4⋊C411yescharacteristic
519C4C3×#404211yescharacteristic
520C3#1059956311yescharacteristic, direct product factor, Sylow
521C2—21no—
522C2—21no—
523C2—202no—
524C2C3×#6495611yescharacteristic
525C2C3×D5×#10411yescharacteristic
526C2C3×#6511011yescharacteristic
subgroupG/H
centerC2×C3×C4D4×D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#339C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×#709C22
cosocleC22×C4×C5C23×C3
hypercenterC3×#339D5
hypocenterC5C3×#1806
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C3×#339

Complements

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

NH ≅ G/Ntype
3. C3×#65407C2semidirect
4. C3×C4×#683C2semidirect
6. C3×C5×#339C2semidirect
7. C3×#64752C2semidirect
8. #10599563C3direct (N × H)
17. C3×#4039C4semidirect
18. C3×#4039C4semidirect
19. C3×#4033C4semidirect
20. C3×#4033C4semidirect
33. #65407C2×C3semidirect
34. C4×#683C2×C3semidirect
36. C5×#339C2×C3semidirect
37. #64752C2×C3semidirect
84. C3×#339D5semidirect
93. #4039C3×C4semidirect
94. #4039C3×C4semidirect
95. #4033C3×C4semidirect
96. #4033C3×C4semidirect
133. C3×D20C4⋊C4semidirect
139. C3×Dic10C4⋊C4semidirect
209. #339C3×D5semidirect
230. C3×Dic5#104semidirect
297. D20C3×C4⋊C4semidirect
303. Dic10C3×C4⋊C4semidirect
388. Dic5C3×#104semidirect
429. C3×C5#1806semidirect
498. C5C3×#1806semidirect
520. C3#10599563direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658562
C2×C3×#39572
C3×#654072
C3×C4×#6832
C2×C3×#39372
C3×C5×#3392
C3×#647522
#105995633
C3×#18065