Finite Group Databasebeta

← C3×#10599675 #14301757

Subgroups — C3×#10599675 #14301757

Order 1920.

760 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
1C22×C3×C8×D5C211yesmaximal, characteristic
2C2×C3×#4043C211yesmaximal, characteristic
3C2×C3×#3948C211yesmaximal, characteristic, complemented
4C3×#65276C211yesmaximal, characteristic
5C2×C3×#3942C211yesmaximal, characteristic, complemented
6C3×C5×#340C211yesmaximal, characteristic, complemented
7C3×#64749C211yesmaximal, characteristic, complemented
8#10599675C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C4×D5C2211yescharacteristic
10C22×C3×Dic10C2211yescharacteristic
11C22×C3×C5×C8C2211yescharacteristic
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13C2×C3×C5×C4⋊C4C2211yescharacteristic
14C2×C3×#685—21no—
15C2×C3×#685—21no—
16C2×C3×C4⋊Dic5—21no—
17C2×C3×C4⋊Dic5C2211yescharacteristic
18C22×C3×#168C2211yescharacteristic
19C2×C3×C8×D5—22no—
20C2×C3×C8×D5—22no—
21C2×C3×C8×D5—22no—
22C3×#4043—22no—
23C3×#4043C414yescomplemented
24C3×#3963—21no—
25C3×#3948—22no—
26C3×#3942—22no—
27C3×#1892—51nomaximal, Hall
28C22×C8×D5C2×C311yescharacteristic
29C2×#4043C2×C311yescharacteristic
30C2×#3948C2×C311yescharacteristic, complemented
31#65276C2×C311yescharacteristic
32C2×#3942C2×C311yescharacteristic, complemented
33C5×#340C2×C311yescharacteristic, complemented
34#64749C2×C311yescharacteristic, complemented
35C23×C3×D5D411yescharacteristic
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5C2311yescharacteristic
39C22×C3×Dic5—21no—
40C22×C3×Dic5—21no—
41C22×C3×Dic5D411yescharacteristic
42C2×C3×C4×D5—21no—
43C2×C3×C4×D5—21no—
44C2×C3×C4×D5—21no—
45C2×C3×C4×D5—21no—
46C2×C3×C4×D5C2×C412yes—
47C2×C3×C4×D5D412yes—
48C2×C3×Dic10—21no—
49C2×C3×Dic10—21no—
50C2×C3×Dic10—21no—
51C2×C3×Dic10—21no—
52C2×C3×Dic10—21no—
53C2×C3×Dic10C2×C412yes—
54C2×C3×C5×C8—21no—
55C2×C3×C5×C8—21no—
56C2×C3×C5×C8D412yes—
57C3×C5×C4⋊C4—21no—
58C3×C5×C4⋊C4—21no—
59C3×C5×C4⋊C4—21no—
60C3×C5×C4⋊C4C2×C412yes—
61C3×#685—24no—
62C3×#685—42no—
63C3×C4⋊Dic5—24no—
64C3×C4⋊Dic5—21no—
65C3×C4⋊Dic5—21no—
66C2×C3×#168—21no—
67C2×C3×#168—21no—
68C2×C3×#168D412yes—
69C3×C8×D5—28no—
70C23×C3×C8—51no—
71C2×C3×C22⋊Q8—51no—
72C2×C3×#103—51no—
73C2×C3×#103—51no—
74C3×#380—51no—
75C3×#340—51no—
76C3×#340D511yescharacteristic, complemented
77C22×C4×D5C22×C311yescharacteristic
78C22×Dic10C22×C311yescharacteristic
79C22×C5×C8C22×C311yescharacteristic
80C2×C5×C4⋊C4C22×C311yescharacteristic
81C2×C5×C4⋊C4C22×C311yescharacteristic
82C2×#685—21no—
83C2×#685—21no—
84C2×C4⋊Dic5—21no—
85C2×C4⋊Dic5C22×C311yescharacteristic
86C22×#168C22×C311yescharacteristic
87C2×C8×D5—22no—
88C2×C8×D5—22no—
89C2×C8×D5—22no—
90#4043—22no—
91#4043C3×C414yescomplemented
92#3963—21no—
93#3948—22no—
94#3942—22no—
95#1892—51noSylow
96C23×C3×C5C2×D411yescharacteristic
97C22×C3×D5—21no—
98C22×C3×D5—21no—
99C22×C3×D5—21no—
100C22×C3×D5—21no—
101C22×C3×D5C22⋊C412yes—
102C22×C3×D5SD1612yes—
103C22×C3×D5Q1612yes—
104C2×C3×C4×C5—22no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5—41no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5C22×C411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114C2×C3×C4×C5#4111yescharacteristic
115C2×C3×C4×C5#4111yescharacteristic
116C2×C3×Dic5—21no—
117C2×C3×Dic5—21no—
118C2×C3×Dic5—22no—
119C2×C3×Dic5—41no—
120C2×C3×Dic5—41no—
121C2×C3×Dic5—41no—
122C2×C3×Dic5—41no—
123C2×C3×Dic5—41no—
124C2×C3×Dic5C22⋊C412yes—
125C3×C4×D5—22no—
126C3×C4×D5—22no—
127C3×C4×D5—22no—
128C3×C4×D5—22no—
129C3×Dic10—22no—
130C3×Dic10—22no—
131C3×Dic10—41no—
132C3×Dic10—41no—
133C3×C5×C8—22no—
134C3×#168—22no—
135C22×C3×Q8—51no—
136C23×C3×C4—51no—
137C22×C3×C8—51no—
138C22×C3×C8—102no—
139C22×C3×C8—102no—
140C22×C3×C8—102no—
141C22×C3×C8C2×D511yescharacteristic
142C3×C22⋊Q8—54no—
143C3×C22⋊Q8—102no—
144C2×C3×C4⋊C4—51no—
145C2×C3×C4⋊C4—101no—
146C2×C3×C4⋊C4C2×D511yescharacteristic
147C2×C3×C4⋊C4C2×D511yescharacteristic
148C2×C3×C22⋊C4—101no—
149C2×C3×C22⋊C4—101no—
150C3×#103—102no—
151C3×#103—102no—
152C3×#95—101no—
153C23×D5C3×D411yescharacteristic
154C22×C4×C5—21no—
155C22×C4×C5—21no—
156C22×C4×C5C23×C311yescharacteristic
157C22×Dic5—21no—
158C22×Dic5—21no—
159C22×Dic5C3×D411yescharacteristic
160C2×C4×D5—21no—
161C2×C4×D5—21no—
162C2×C4×D5—21no—
163C2×C4×D5—21no—
164C2×C4×D5C2×C3×C412yes—
165C2×C4×D5C3×D412yes—
166C2×Dic10—21no—
167C2×Dic10—21no—
168C2×Dic10—21no—
169C2×Dic10—21no—
170C2×Dic10—21no—
171C2×Dic10C2×C3×C412yes—
172C2×C5×C8—21no—
173C2×C5×C8—21no—
174C2×C5×C8C3×D412yes—
175C5×C4⋊C4—21no—
176C5×C4⋊C4—21no—
177C5×C4⋊C4—21no—
178C5×C4⋊C4C2×C3×C412yes—
179#685—24no—
180#685—42no—
181C4⋊Dic5—24no—
182C4⋊Dic5—21no—
183C4⋊Dic5—21no—
184C2×#168—21no—
185C2×#168—21no—
186C2×#168C3×D412yes—
187C8×D5—28no—
188C23×C8—51no—
189C2×C22⋊Q8—51no—
190C2×#103—51no—
191C2×#103—51no—
192#380—51no—
193#340—51no—
194#340C3×D511yescharacteristic, complemented
195C22×C3×C5C2×C22⋊C411yescharacteristic
196C22×C3×C5#12111yescharacteristic
197C22×C3×C5#12111yescharacteristic
198C22×C3×C5C2×SD1611yescharacteristic
199C22×C3×C5C2×Q1611yescharacteristic
200C22×C3×C5#13511yescharacteristic
201C22×C3×C5#13511yescharacteristic
202C2×C3×D5—22no—
203C2×C3×D5—22no—
204C2×C3×D5—22no—
205C2×C3×D5—22no—
206C2×C3×D5—22no—
207C2×C3×D5—22no—
208C2×C3×D5#10314yescomplemented
209C3×C4×C5—42no—
210C3×C4×C5—81no—
211C3×C4×C5C4×D411yescharacteristic
212C3×C4×C5C4×D411yescharacteristic
213C3×C4×C5#12011yescharacteristic
214C3×C4×C5#12311yescharacteristic
215C3×Dic5—22no—
216C3×Dic5—42no—
217C3×Dic5—81no—
218C24×C3—51no—
219C2×C3×Q8—52no—
220C2×C3×Q8—101no—
221C2×C3×Q8—101no—
222C2×C3×Q8—101no—
223C2×C3×Q8—101no—
224C2×C3×Q8—101no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—51no—
228C22×C3×C4—52no—
229C22×C3×C4—52no—
230C22×C3×C4—101no—
231C22×C3×C4—101no—
232C22×C3×C4—101no—
233C22×C3×C4—101no—
234C22×C3×C4—101no—
235C22×C3×C4—101no—
236C22×C3×C4C22×D511yescharacteristic
237C2×C3×C8—21no—
238C2×C3×C8—21no—
239C2×C3×C8—52no—
240C2×C3×C8—108no—
241C2×C3×C8—101no—
242C2×C3×C8—101no—
243C2×C3×C8D2012yes—
244C3×C4⋊C4—21no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—21no—
247C3×C4⋊C4—104no—
248C3×C4⋊C4—101no—
249C3×C4⋊C4—101no—
250C3×C4⋊C4C4×D512yes—
251C3×C22⋊C4—104no—
252C3×C22⋊C4—202no—
253C23×C5C2×C3×D411yescharacteristic
254C22×D5—21no—
255C22×D5—21no—
256C22×D5—21no—
257C22×D5—21no—
258C22×D5C3×C22⋊C412yes—
259C22×D5C3×SD1612yes—
260C22×D5C3×Q1612yes—
261C2×C4×C5—22no—
262C2×C4×C5—41no—
263C2×C4×C5—41no—
264C2×C4×C5—41no—
265C2×C4×C5—41no—
266C2×C4×C5—41no—
267C2×C4×C5C22×C3×C411yescharacteristic
268C2×C4×C5C2×C3×D411yescharacteristic
269C2×C4×C5C2×C3×D411yescharacteristic
270C2×C4×C5C2×C3×D411yescharacteristic
271C2×C4×C5C3×#4111yescharacteristic
272C2×C4×C5C3×#4111yescharacteristic
273C2×Dic5—21no—
274C2×Dic5—21no—
275C2×Dic5—22no—
276C2×Dic5—41no—
277C2×Dic5—41no—
278C2×Dic5—41no—
279C2×Dic5—41no—
280C2×Dic5—41no—
281C2×Dic5C3×C22⋊C412yes—
282C4×D5—22no—
283C4×D5—22no—
284C4×D5—22no—
285C4×D5—22no—
286Dic10—22no—
287Dic10—22no—
288Dic10—41no—
289Dic10—41no—
290C5×C8—22no—
291#168—22no—
292C22×Q8—51no—
293C23×C4—51no—
294C22×C8—51no—
295C22×C8—102no—
296C22×C8—102no—
297C22×C8—102no—
298C22×C8C2×C3×D511yescharacteristic
299C22⋊Q8—54no—
300C22⋊Q8—102no—
301C2×C4⋊C4—51no—
302C2×C4⋊C4—101no—
303C2×C4⋊C4C2×C3×D511yescharacteristic
304C2×C4⋊C4C2×C3×D511yescharacteristic
305C2×C22⋊C4—101no—
306C2×C22⋊C4—101no—
307#103—102no—
308#103—102no—
309#95—101no—
310C2×C3×C5#38611yescharacteristic
311C2×C3×C5C2×#10311yescharacteristic
312C2×C3×C5#41611yescharacteristic
313C2×C3×C5#46511yescharacteristic
314C2×C3×C5#46511yescharacteristic
315C2×C3×C5#46711yescharacteristic
316C2×C3×C5#46711yescharacteristic
317C3×D5—24no—
318C23×C3—52no—
319C23×C3—52no—
320C23×C3—52no—
321C23×C3—101no—
322C23×C3—101no—
323C23×C3—101no—
324C23×C3—101no—
325C23×C3D4×D511yescharacteristic
326C3×Q8—102no—
327C3×Q8—102no—
328C3×Q8—201no—
329C3×Q8—201no—
330C2×C3×C4—22no—
331C2×C3×C4—41no—
332C2×C3×C4—41no—
333C2×C3×C4—41no—
334C2×C3×C4—41no—
335C2×C3×C4—41no—
336C2×C3×C4—52no—
337C2×C3×C4—101no—
338C2×C3×C4—101no—
339C2×C3×C4—102no—
340C2×C3×C4—102no—
341C2×C3×C4—102no—
342C2×C3×C4—102no—
343C2×C3×C4—102no—
344C2×C3×C4—201no—
345C2×C3×C4—201no—
346C2×C3×C4—201no—
347C2×C3×C4—201no—
348C2×C3×C4—201no—
349C2×C3×C4C2×C4×D511yescharacteristic
350C2×C3×C4C2×D2011yescharacteristic
351C2×C3×C4#70911yescharacteristic
352C2×C3×C4D4×D511yescharacteristic
353C2×C3×C4D4×D511yescharacteristic
354C2×C3×C4#71311yescharacteristic
355C3×C8—22no—
356C3×C8—102no—
357C22×C5C2×C3×C22⋊C411yescharacteristic
358C22×C5C3×#12111yescharacteristic
359C22×C5C3×#12111yescharacteristic
360C22×C5C2×C3×SD1611yescharacteristic
361C22×C5C2×C3×Q1611yescharacteristic
362C22×C5C3×#13511yescharacteristic
363C22×C5C3×#13511yescharacteristic
364C2×D5—22no—
365C2×D5—22no—
366C2×D5—22no—
367C2×D5—22no—
368C2×D5—22no—
369C2×D5—22no—
370C2×D5C3×#10314yescomplemented
371C4×C5—42no—
372C4×C5—81no—
373C4×C5C3×C4×D411yescharacteristic
374C4×C5C3×C4×D411yescharacteristic
375C4×C5C3×#12011yescharacteristic
376C4×C5C3×#12311yescharacteristic
377Dic5—22no—
378Dic5—42no—
379Dic5—81no—
380C24—51no—
381C2×Q8—52no—
382C2×Q8—101no—
383C2×Q8—101no—
384C2×Q8—101no—
385C2×Q8—101no—
386C2×Q8—101no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—51no—
390C22×C4—52no—
391C22×C4—52no—
392C22×C4—101no—
393C22×C4—101no—
394C22×C4—101no—
395C22×C4—101no—
396C22×C4—101no—
397C22×C4—101no—
398C22×C4C22×C3×D511yescharacteristic
399C2×C8—21no—
400C2×C8—21no—
401C2×C8—52no—
402C2×C8—108no—
403C2×C8—101no—
404C2×C8—101no—
405C2×C8C3×D2012yes—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—104no—
410C4⋊C4—101no—
411C4⋊C4—101no—
412C4⋊C4C3×C4×D512yes—
413C22⋊C4—104no—
414C22⋊C4—202no—
415C3×C5#189211yescharacteristic, complemented, Hall
416C22×C3—54no—
417C22×C3—102no—
418C22×C3—102no—
419C22×C3—102no—
420C22×C3—102no—
421C22×C3—102no—
422C22×C3—102no—
423C22×C3D5×C22⋊C411yescharacteristic
424C22×C3#403011yescharacteristic
425C22×C3#404111yescharacteristic
426C22×C3#405811yescharacteristic
427C22×C3D5×SD1611yescharacteristic
428C22×C3#406211yescharacteristic
429C22×C3D5×Q1611yescharacteristic
430C3×C4—42no—
431C3×C4—81no—
432C3×C4—102no—
433C3×C4—202no—
434C3×C4—401no—
435C3×C4C4×D2011yescharacteristic
436C3×C4#402811yescharacteristic
437C3×C4#403911yescharacteristic
438C3×C4#404011yescharacteristic
439C2×C5C3×#38611yescharacteristic
440C2×C5C2×C3×#10311yescharacteristic
441C2×C5C3×#41611yescharacteristic
442C2×C5C3×#46511yescharacteristic
443C2×C5C3×#46511yescharacteristic
444C2×C5C3×#46711yescharacteristic
445C2×C5C3×#46711yescharacteristic
446D5—24no—
447C23—52no—
448C23—52no—
449C23—52no—
450C23—101no—
451C23—101no—
452C23—101no—
453C23—101no—
454C23C3×D4×D511yescharacteristic
455Q8—102no—
456Q8—102no—
457Q8—201no—
458Q8—201no—
459C2×C4—22no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—52no—
466C2×C4—101no—
467C2×C4—101no—
468C2×C4—102no—
469C2×C4—102no—
470C2×C4—102no—
471C2×C4—102no—
472C2×C4—102no—
473C2×C4—201no—
474C2×C4—201no—
475C2×C4—201no—
476C2×C4—201no—
477C2×C4—201no—
478C2×C4C2×C3×C4×D511yescharacteristic
479C2×C4C2×C3×D2011yescharacteristic
480C2×C4C3×#70911yescharacteristic
481C2×C4C3×D4×D511yescharacteristic
482C2×C4C3×D4×D511yescharacteristic
483C2×C4C3×#71311yescharacteristic
484C8—22no—
485C8—102no—
486C2×C3—104no—
487C2×C3#6495411yescharacteristic
488C2×C3#6506111yescharacteristic
489C2×C3#6506711yescharacteristic
490C2×C3D5×#10311yescharacteristic
491C2×C3#6510211yescharacteristic
492C2×C3#6515311yescharacteristic
493C2×C3#6517611yescharacteristic
494C5C3×#189211yescharacteristic, complemented, Sylow
495C22—54no—
496C22—102no—
497C22—102no—
498C22—102no—
499C22—102no—
500C22—102no—
501C22—102no—
502C22C3×D5×C22⋊C411yescharacteristic
503C22C3×#403011yescharacteristic
504C22C3×#404111yescharacteristic
505C22C3×#405811yescharacteristic
506C22C3×D5×SD1611yescharacteristic
507C22C3×#406211yescharacteristic
508C22C3×D5×Q1611yescharacteristic
509C4—42no—
510C4—81no—
511C4—102no—
512C4—202no—
513C4—401no—
514C4C3×C4×D2011yescharacteristic
515C4C3×#402811yescharacteristic
516C4C3×#403911yescharacteristic
517C4C3×#404011yescharacteristic
518C3#1059967511yescharacteristic, direct product factor, Sylow
519C2—104no—
520C2C3×#6495411yescharacteristic
521C2C3×#6506111yescharacteristic
522C2C3×#6506711yescharacteristic
523C2C3×D5×#10311yescharacteristic
524C2C3×#6510211yescharacteristic
525C2C3×#6515311yescharacteristic
526C2C3×#6517611yescharacteristic
subgroupG/H
centerC23×C3D4×D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#340C2
socleC23×C3×C5C2×D4
prime radicalC23×C3×D5D4
cosocleC22×C4×C5C23×C3
hypercenterC3×#340D5
hypocenterC5C3×#1892
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C3×#340

Complements

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

NH ≅ G/Ntype
3. C2×C3×#3948C2semidirect
5. C2×C3×#3942C2semidirect
6. C3×C5×#340C2semidirect
7. C3×#64749C2semidirect
8. #10599675C3direct (N × H)
23. C3×#4043C4semidirect
30. C2×#3948C2×C3semidirect
32. C2×#3942C2×C3semidirect
33. C5×#340C2×C3semidirect
34. #64749C2×C3semidirect
76. C3×#340D5semidirect
91. #4043C3×C4semidirect
194. #340C3×D5semidirect
208. C2×C3×D5#103semidirect
370. C2×D5C3×#103semidirect
415. C3×C5#1892semidirect
494. C5C3×#1892semidirect
518. C3#10599675direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C8×D52
C2×C3×#40432
C2×C3×#39482
C3×#652762
C2×C3×#39422
C3×C5×#3402
C3×#647492
#105996753
C3×#18925