Finite Group Databasebeta

← C3×#10599097 #14283257

Subgroups — C3×#10599097 #14283257

Order 1920.

652 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×#121C211yesmaximal, characteristic
2C3×#65015C211yesmaximal, characteristic, complemented
3C3×#64953C211yesmaximal, characteristic, complemented
4C3×C5×#327C211yesmaximal, characteristic, complemented
5C3×#64757C211yesmaximal, characteristic, complemented
6C3×#64690C211yesmaximal, characteristic, complemented
7C3×#64671C211yesmaximal, characteristic, complemented
8#10599097C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×D4×D5—21no—
10C2×C3×D4×D5C411yescharacteristic, complemented
11C22×C3×C4×D5C2211yescharacteristic
12C3×C5×#121C2211yescharacteristic
13C3×#4085—21no—
14C3×#4084C411yescharacteristic, complemented
15C3×#4076C2211yescharacteristic
16C2×C3×#685—21no—
17C2×C3×#676—21no—
18C3×#4041C411yescharacteristic, complemented
19C3×D5×C4⋊C4C411yescharacteristic, complemented
20C3×#4030—21no—
21C3×D5×C22⋊C4—21no—
22C3×C5×C22⋊C8C2211yescharacteristic, complemented
23C3×C5×#95C2211yescharacteristic, complemented
24C3×#3963—21no—
25C3×#3963C2211yescharacteristic, complemented
26C3×C22⋊#168C2211yescharacteristic, complemented
27C3×#3952—21no—
28C3×#1510—51nomaximal, Hall
29D5×#121C2×C311yescharacteristic
30#65015C2×C311yescharacteristic, complemented
31#64953C2×C311yescharacteristic, complemented
32C5×#327C2×C311yescharacteristic, complemented
33#64757C2×C311yescharacteristic, complemented
34#64690C2×C311yescharacteristic, complemented
35#64671C2×C311yescharacteristic, complemented
36C23×C3×D5—21no—
37C23×C3×D5D411yescharacteristic
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4C2×C411yescharacteristic
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5C2311yescharacteristic
42C2×C3×C22⋊D5—21no—
43C2×C3×C22⋊D5—21no—
44C2×C3×C22⋊D5—21no—
45C22×C3×Dic5—21no—
46C22×C3×Dic5D411yescharacteristic
47C3×D4×D5—42no—
48C3×D4×D5—42no—
49C3×D4×D5—42no—
50C2×C3×D20—21no—
51C2×C3×D20C2×C411yescharacteristic
52C2×C3×C4×D5—21no—
53C2×C3×C4×D5—42no—
54C2×C3×C4×D5C2×C411yescharacteristic
55C2×C3×C4×D5C2×C411yescharacteristic
56C2×C3×C4×D5D411yescharacteristic
57C2×C3×C4×D5D411yescharacteristic
58C2×C3×C5×C8—21no—
59C3×C5×C4⋊C4C2×C411yescharacteristic
60C3×C5×C22⋊C4—21no—
61C3×C22⋊Dic5—21no—
62C3×#685—21no—
63C3×#685—21no—
64C3×#685—42no—
65C3×C4⋊Dic5C2×C411yescharacteristic
66C3×#683—21no—
67C2×C3×#168—21no—
68C3×#676—42no—
69C2×C3×#121—51no—
70C3×#407—51no—
71C3×#381—51no—
72C3×#327—51no—
73C3×#327—51no—
74C3×#327—51no—
75C3×#327D511yescharacteristic, complemented
76C2×D4×D5—21no—
77C2×D4×D5C3×C411yescharacteristic, complemented
78C22×C4×D5C22×C311yescharacteristic
79C5×#121C22×C311yescharacteristic
80#4085—21no—
81#4084C3×C411yescharacteristic, complemented
82#4076C22×C311yescharacteristic
83C2×#685—21no—
84C2×#676—21no—
85#4041C3×C411yescharacteristic, complemented
86D5×C4⋊C4C3×C411yescharacteristic, complemented
87#4030—21no—
88D5×C22⋊C4—21no—
89C5×C22⋊C8C22×C311yescharacteristic, complemented
90C5×#95C22×C311yescharacteristic, complemented
91#3963—21no—
92#3963C22×C311yescharacteristic, complemented
93C22⋊#168C22×C311yescharacteristic, complemented
94#3952—21no—
95#1510—51noSylow
96C23×C3×C5—21no—
97C23×C3×C5C2×D411yescharacteristic
98C22×C3×D5—21no—
99C22×C3×D5—21no—
100C22×C3×D5—22no—
101C22×C3×D5—21no—
102C22×C3×D5—41no—
103C22×C3×D5—42no—
104C22×C3×D5—42no—
105C22×C3×D5—42no—
106C22×C3×D5C22⋊C411yescharacteristic
107C22×C3×D5C22⋊C411yescharacteristic
108C3×C5×D4—41no—
109C3×C5×D4—41no—
110C3×C5×D4—41no—
111C2×C3×C4×C5—21no—
112C2×C3×C4×C5—41no—
113C2×C3×C4×C5—41no—
114C2×C3×C4×C5—41no—
115C2×C3×C4×C5—41no—
116C2×C3×C4×C5C22×C411yescharacteristic
117C2×C3×C4×C5C2×D411yescharacteristic
118C3×C22⋊D5—42no—
119C3×C22⋊D5—42no—
120C3×C22⋊D5—41no—
121C3×C22⋊D5—41no—
122C2×C3×Dic5—21no—
123C2×C3×Dic5—41no—
124C2×C3×Dic5—41no—
125C2×C3×Dic5—41no—
126C2×C3×Dic5—41no—
127C2×C3×Dic5C22⋊C411yescharacteristic
128C2×C3×Dic5C22⋊C411yescharacteristic
129C3×D20—41no—
130C3×D20—42no—
131C3×C4×D5—22no—
132C3×C4×D5—22no—
133C3×C4×D5—41no—
134C3×C4×D5—41no—
135C3×C4×D5—42no—
136C3×C5×C8—41no—
137C3×#168—41no—
138C22×C3×D4—51no—
139C22×C3×D4—101no—
140C23×C3×C4—51no—
141C2×C3×M16—101no—
142C3×#121—51no—
143C3×#121—51no—
144C3×#121—51no—
145C3×#121—101no—
146C3×#121—101no—
147C3×#121C2×D511yescharacteristic
148C2×C3×C4⋊C4—51no—
149C2×C3×C22⋊C4—101no—
150C2×C3×C22⋊C4—101no—
151C3×C22⋊C8—51no—
152C3×C22⋊C8—101no—
153C3×C22⋊C8C2×D511yescharacteristic, complemented
154C3×#95—51no—
155C3×#95—101no—
156C3×#95C2×D511yescharacteristic, complemented
157C23×D5—21no—
158C23×D5C3×D411yescharacteristic
159C2×C5×D4—21no—
160C2×C5×D4C2×C3×C411yescharacteristic
161C22×C4×C5—21no—
162C22×C4×C5C23×C311yescharacteristic
163C2×C22⋊D5—21no—
164C2×C22⋊D5—21no—
165C2×C22⋊D5—21no—
166C22×Dic5—21no—
167C22×Dic5C3×D411yescharacteristic
168D4×D5—42no—
169D4×D5—42no—
170D4×D5—42no—
171C2×D20—21no—
172C2×D20C2×C3×C411yescharacteristic
173C2×C4×D5—21no—
174C2×C4×D5—42no—
175C2×C4×D5C2×C3×C411yescharacteristic
176C2×C4×D5C2×C3×C411yescharacteristic
177C2×C4×D5C3×D411yescharacteristic
178C2×C4×D5C3×D411yescharacteristic
179C2×C5×C8—21no—
180C5×C4⋊C4C2×C3×C411yescharacteristic
181C5×C22⋊C4—21no—
182C22⋊Dic5—21no—
183#685—21no—
184#685—21no—
185#685—42no—
186C4⋊Dic5C2×C3×C411yescharacteristic
187#683—21no—
188C2×#168—21no—
189#676—42no—
190C2×#121—51no—
191#407—51no—
192#381—51no—
193#327—51no—
194#327—51no—
195#327—51no—
196#327C3×D511yescharacteristic, complemented
197C22×C3×C5—21no—
198C22×C3×C5—21no—
199C22×C3×C5—41no—
200C22×C3×C5—41no—
201C22×C3×C5—41no—
202C22×C3×C5C2×C22⋊C411yescharacteristic
203C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
204C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
205C2×C3×D5—21no—
206C2×C3×D5—21no—
207C2×C3×D5—21no—
208C2×C3×D5—21no—
209C2×C3×D5—21no—
210C2×C3×D5—42no—
211C2×C3×D5—42no—
212C2×C3×D5—41no—
213C2×C3×D5—41no—
214C2×C3×D5—41no—
215C2×C3×D5—84no—
216C2×C3×D5#9912yes—
217C3×C4×C5—21no—
218C3×C4×C5—21no—
219C3×C4×C5—41no—
220C3×C4×C5—81no—
221C3×Dic5—21no—
222C3×Dic5—21no—
223C3×Dic5—41no—
224C3×Dic5—81no—
225C24×C3—51no—
226C24×C3—101no—
227C2×C3×D4—21no—
228C2×C3×D4—51no—
229C2×C3×D4—101no—
230C2×C3×D4—101no—
231C2×C3×D4—101no—
232C2×C3×D4—101no—
233C2×C3×D4—202no—
234C2×C3×D4—202no—
235C2×C3×D4—202no—
236C2×C3×D4C4×D511yescharacteristic
237C22×C3×C4—21no—
238C22×C3×C4—51no—
239C22×C3×C4—51no—
240C22×C3×C4—51no—
241C22×C3×C4—51no—
242C22×C3×C4—51no—
243C22×C3×C4—101no—
244C22×C3×C4—101no—
245C22×C3×C4—202no—
246C22×C3×C4C22×D511yescharacteristic
247C3×M16—202no—
248C2×C3×C8—21no—
249C2×C3×C8—101no—
250C3×C4⋊C4—51no—
251C3×C4⋊C4—101no—
252C3×C4⋊C4C4×D511yescharacteristic
253C3×C22⋊C4—21no—
254C3×C22⋊C4—101no—
255C3×C22⋊C4—101no—
256C3×C22⋊C4—101no—
257C3×C22⋊C4—202no—
258C23×C5—21no—
259C23×C5C2×C3×D411yescharacteristic
260C22×D5—21no—
261C22×D5—21no—
262C22×D5—22no—
263C22×D5—21no—
264C22×D5—41no—
265C22×D5—42no—
266C22×D5—42no—
267C22×D5—42no—
268C22×D5C3×C22⋊C411yescharacteristic
269C22×D5C3×C22⋊C411yescharacteristic
270C5×D4—41no—
271C5×D4—41no—
272C5×D4—41no—
273C2×C4×C5—21no—
274C2×C4×C5—41no—
275C2×C4×C5—41no—
276C2×C4×C5—41no—
277C2×C4×C5—41no—
278C2×C4×C5C22×C3×C411yescharacteristic
279C2×C4×C5C2×C3×D411yescharacteristic
280C22⋊D5—42no—
281C22⋊D5—42no—
282C22⋊D5—41no—
283C22⋊D5—41no—
284C2×Dic5—21no—
285C2×Dic5—41no—
286C2×Dic5—41no—
287C2×Dic5—41no—
288C2×Dic5—41no—
289C2×Dic5C3×C22⋊C411yescharacteristic
290C2×Dic5C3×C22⋊C411yescharacteristic
291D20—41no—
292D20—42no—
293C4×D5—22no—
294C4×D5—22no—
295C4×D5—41no—
296C4×D5—41no—
297C4×D5—42no—
298C5×C8—41no—
299#168—41no—
300C22×D4—51no—
301C22×D4—101no—
302C23×C4—51no—
303C2×M16—101no—
304#121—51no—
305#121—51no—
306#121—51no—
307#121—101no—
308#121—101no—
309#121C2×C3×D511yescharacteristic
310C2×C4⋊C4—51no—
311C2×C22⋊C4—101no—
312C2×C22⋊C4—101no—
313C22⋊C8—51no—
314C22⋊C8—101no—
315C22⋊C8C2×C3×D511yescharacteristic, complemented
316#95—51no—
317#95—101no—
318#95C2×C3×D511yescharacteristic, complemented
319C2×C3×C5—21no—
320C2×C3×C5—21no—
321C2×C3×C5—81no—
322C2×C3×C5C2×#9911yescharacteristic
323C2×C3×C5#41811yescharacteristic
324C2×C3×C5#42111yescharacteristic
325C3×D5—22no—
326C3×D5—41no—
327C3×D5—81no—
328C23×C3—21no—
329C23×C3—51no—
330C23×C3—51no—
331C23×C3—102no—
332C23×C3—101no—
333C23×C3—101no—
334C23×C3—101no—
335C23×C3—201no—
336C23×C3—202no—
337C23×C3—202no—
338C23×C3—202no—
339C23×C3D4×D511yescharacteristic
340C3×D4—41no—
341C3×D4—41no—
342C3×D4—41no—
343C3×D4—201no—
344C3×D4—202no—
345C3×D4—202no—
346C3×D4—202no—
347C3×D4—201no—
348C3×D4—201no—
349C2×C3×C4—21no—
350C2×C3×C4—41no—
351C2×C3×C4—41no—
352C2×C3×C4—41no—
353C2×C3×C4—41no—
354C2×C3×C4—51no—
355C2×C3×C4—51no—
356C2×C3×C4—102no—
357C2×C3×C4—102no—
358C2×C3×C4—101no—
359C2×C3×C4—201no—
360C2×C3×C4—201no—
361C2×C3×C4—202no—
362C2×C3×C4—201no—
363C2×C3×C4—201no—
364C2×C3×C4—201no—
365C2×C3×C4—201no—
366C2×C3×C4C2×C4×D511yescharacteristic
367C2×C3×C4D4×D511yescharacteristic
368C3×C8—41no—
369C3×C8—201no—
370C22×C5—21no—
371C22×C5—21no—
372C22×C5—41no—
373C22×C5—41no—
374C22×C5—41no—
375C22×C5C2×C3×C22⋊C411yescharacteristic
376C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
377C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
378C2×D5—21no—
379C2×D5—21no—
380C2×D5—21no—
381C2×D5—21no—
382C2×D5—21no—
383C2×D5—42no—
384C2×D5—42no—
385C2×D5—41no—
386C2×D5—41no—
387C2×D5—41no—
388C2×D5—84no—
389C2×D5C3×#9912yes—
390C4×C5—21no—
391C4×C5—21no—
392C4×C5—41no—
393C4×C5—81no—
394Dic5—21no—
395Dic5—21no—
396Dic5—41no—
397Dic5—81no—
398C24—51no—
399C24—101no—
400C2×D4—21no—
401C2×D4—51no—
402C2×D4—101no—
403C2×D4—101no—
404C2×D4—101no—
405C2×D4—101no—
406C2×D4—202no—
407C2×D4—202no—
408C2×D4—202no—
409C2×D4C3×C4×D511yescharacteristic
410C22×C4—21no—
411C22×C4—51no—
412C22×C4—51no—
413C22×C4—51no—
414C22×C4—51no—
415C22×C4—51no—
416C22×C4—101no—
417C22×C4—101no—
418C22×C4—202no—
419C22×C4C22×C3×D511yescharacteristic
420M16—202no—
421C2×C8—21no—
422C2×C8—101no—
423C4⋊C4—51no—
424C4⋊C4—101no—
425C4⋊C4C3×C4×D511yescharacteristic
426C22⋊C4—21no—
427C22⋊C4—101no—
428C22⋊C4—101no—
429C22⋊C4—101no—
430C22⋊C4—202no—
431C3×C5#151011yescharacteristic, complemented, Hall
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—41no—
435C22×C3—41no—
436C22×C3—41no—
437C22×C3—52no—
438C22×C3—101no—
439C22×C3—101no—
440C22×C3—101no—
441C22×C3—101no—
442C22×C3—101no—
443C22×C3—202no—
444C22×C3—202no—
445C22×C3—201no—
446C22×C3—201no—
447C22×C3—201no—
448C22×C3—404no—
449C22×C3D5×C22⋊C411yescharacteristic
450C22×C3#405711yescharacteristic
451C22×C3#406011yescharacteristic
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—41no—
455C3×C4—81no—
456C3×C4—101no—
457C3×C4—101no—
458C3×C4—201no—
459C3×C4—401no—
460C2×C5—21no—
461C2×C5—21no—
462C2×C5—81no—
463C2×C5C2×C3×#9911yescharacteristic
464C2×C5C3×#41811yescharacteristic
465C2×C5C3×#42111yescharacteristic
466D5—22no—
467D5—41no—
468D5—81no—
469C23—21no—
470C23—51no—
471C23—51no—
472C23—102no—
473C23—101no—
474C23—101no—
475C23—101no—
476C23—201no—
477C23—202no—
478C23—202no—
479C23—202no—
480C23C3×D4×D511yescharacteristic
481D4—41no—
482D4—41no—
483D4—41no—
484D4—201no—
485D4—202no—
486D4—202no—
487D4—202no—
488D4—201no—
489D4—201no—
490C2×C4—21no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—51no—
496C2×C4—51no—
497C2×C4—102no—
498C2×C4—102no—
499C2×C4—101no—
500C2×C4—201no—
501C2×C4—201no—
502C2×C4—202no—
503C2×C4—201no—
504C2×C4—201no—
505C2×C4—201no—
506C2×C4—201no—
507C2×C4C2×C3×C4×D511yescharacteristic
508C2×C4C3×D4×D511yescharacteristic
509C8—41no—
510C8—201no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—81no—
514C2×C3—102no—
515C2×C3—201no—
516C2×C3—401no—
517C2×C3D5×#9911yescharacteristic
518C2×C3#6505911yescharacteristic
519C2×C3#6511011yescharacteristic
520C5C3×#151011yescharacteristic, complemented, Sylow
521C22—21no—
522C22—21no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22—52no—
527C22—101no—
528C22—101no—
529C22—101no—
530C22—101no—
531C22—101no—
532C22—202no—
533C22—202no—
534C22—201no—
535C22—201no—
536C22—201no—
537C22—404no—
538C22C3×D5×C22⋊C411yescharacteristic
539C22C3×#405711yescharacteristic
540C22C3×#406011yescharacteristic
541C4—21no—
542C4—21no—
543C4—41no—
544C4—81no—
545C4—101no—
546C4—101no—
547C4—201no—
548C4—401no—
549C3#1059909711yescharacteristic, direct product factor, Sylow
550C2—21no—
551C2—21no—
552C2—81no—
553C2—102no—
554C2—201no—
555C2—401no—
556C2C3×D5×#9911yescharacteristic
557C2C3×#6505911yescharacteristic
558C2C3×#6511011yescharacteristic
subgroupG/H
centerC22×C3D5×C22⋊C4
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#327C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×D5×#121C2
cosocleC22×C4×C5C23×C3
hypercenterC3×#327D5
hypocenterC5C3×#1510
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#327

Complements

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

NH ≅ G/Ntype
2. C3×#65015C2semidirect
3. C3×#64953C2semidirect
4. C3×C5×#327C2semidirect
5. C3×#64757C2semidirect
6. C3×#64690C2semidirect
7. C3×#64671C2semidirect
8. #10599097C3direct (N × H)
10. C2×C3×D4×D5C4semidirect
14. C3×#4084C4semidirect
18. C3×#4041C4semidirect
19. C3×D5×C4⋊C4C4semidirect
22. C3×C5×C22⋊C8C22semidirect
23. C3×C5×#95C22semidirect
25. C3×#3963C22semidirect
26. C3×C22⋊#168C22semidirect
30. #65015C2×C3semidirect
31. #64953C2×C3semidirect
32. C5×#327C2×C3semidirect
33. #64757C2×C3semidirect
34. #64690C2×C3semidirect
35. #64671C2×C3semidirect
75. C3×#327D5semidirect
77. C2×D4×D5C3×C4semidirect
81. #4084C3×C4semidirect
85. #4041C3×C4semidirect
86. D5×C4⋊C4C3×C4semidirect
89. C5×C22⋊C8C22×C3semidirect
90. C5×#95C22×C3semidirect
92. #3963C22×C3semidirect
93. C22⋊#168C22×C3semidirect
153. C3×C22⋊C8C2×D5semidirect
156. C3×#95C2×D5semidirect
196. #327C3×D5semidirect
315. C22⋊C8C2×C3×D5semidirect
318. #95C2×C3×D5semidirect
431. C3×C5#1510semidirect
520. C5C3×#1510semidirect
549. C3#10599097direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D5×#1212
C3×#650152
C3×#649532
C3×C5×#3272
C3×#647572
C3×#646902
C3×#646712
#105990973
C3×#15105