Finite Group Databasebeta

← C3×#10600994 #14300722

Subgroups — C3×#10600994 #14300722

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4084C211yesmaximal, characteristic
2C2×C3×#4038C211yesmaximal, characteristic, complemented
3C2×C3×C5×#102C211yesmaximal, characteristic, complemented
4C2×C3×#3964C211yesmaximal, characteristic, complemented
5C2×C3×#3952C211yesmaximal, characteristic, complemented
6C3×#64771C211yesmaximal, characteristic, complemented
7C3×#64749C211yesmaximal, characteristic, complemented
8#10600994C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×C3×C22⋊D5—21no—
11C22×C3×C4×D5C2211yescharacteristic
12C22×C3×C5×C8C2211yescharacteristic
13C2×C3×C5×C4⋊C4C2211yescharacteristic
14C2×C3×C22⋊Dic5—21no—
15C3×#4084—22no—
16C3×#4084C414yescomplemented
17C2×C3×#685—21no—
18C2×C3×C4⋊Dic5C2211yescharacteristic
19C2×C3×C4⋊Dic5C2211yescharacteristic
20C2×C3×C4×Dic5—21no—
21C22×C3×#168C2211yescharacteristic
22C3×#4038—22no—
23C3×#4038—22no—
24C3×C5×#102—22no—
25C3×#3964—22no—
26C3×#3952—22no—
27C3×#1875—51nomaximal, Hall
28C2×#4084C2×C311yescharacteristic
29C2×#4038C2×C311yescharacteristic, complemented
30C2×C5×#102C2×C311yescharacteristic, complemented
31C2×#3964C2×C311yescharacteristic, complemented
32C2×#3952C2×C311yescharacteristic, complemented
33#64771C2×C311yescharacteristic, complemented
34#64749C2×C311yescharacteristic, complemented
35C24×C3×C5—21no—
36C23×C3×D5D411yescharacteristic
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4—21no—
42C2×C3×C5×D4C2×C412yes—
43C22×C3×C4×C5—21no—
44C22×C3×C4×C5C2311yescharacteristic
45C2×C3×C22⋊D5—24no—
46C2×C3×C22⋊D5—42no—
47C2×C3×C22⋊D5—42no—
48C22×C3×Dic5—21no—
49C22×C3×Dic5—21no—
50C22×C3×Dic5D411yescharacteristic
51C2×C3×C4×D5—21no—
52C2×C3×C4×D5—21no—
53C2×C3×C4×D5—21no—
54C2×C3×C4×D5—21no—
55C2×C3×C4×D5C2×C412yes—
56C2×C3×C4×D5D412yes—
57C2×C3×C5×C8—21no—
58C2×C3×C5×C8—21no—
59C2×C3×C5×C8—21no—
60C3×C5×C4⋊C4—21no—
61C3×C5×C4⋊C4D412yescomplemented
62C3×C22⋊Dic5—24no—
63C3×#685—24no—
64C3×C4⋊Dic5—21no—
65C3×C4⋊Dic5—21no—
66C3×C4⋊Dic5C2×C412yes—
67C3×C4⋊Dic5D412yescomplemented
68C3×C4×Dic5—24no—
69C2×C3×#168—21no—
70C2×C3×#168—21no—
71C2×C3×#168—21no—
72C2×C3×#121—51no—
73C2×C3×#117—51no—
74C2×C3×#102—51no—
75C2×C3×#102D511yescharacteristic, complemented
76C2×C3×C22⋊C8—51no—
77C3×#340—51no—
78C3×#340—51no—
79C22×C5×D4C22×C311yescharacteristic
80C22×C22⋊D5—21no—
81C22×C4×D5C22×C311yescharacteristic
82C22×C5×C8C22×C311yescharacteristic
83C2×C5×C4⋊C4C22×C311yescharacteristic
84C2×C22⋊Dic5—21no—
85#4084—22no—
86#4084C3×C414yescomplemented
87C2×#685—21no—
88C2×C4⋊Dic5C22×C311yescharacteristic
89C2×C4⋊Dic5C22×C311yescharacteristic
90C2×C4×Dic5—21no—
91C22×#168C22×C311yescharacteristic
92#4038—22no—
93#4038—22no—
94C5×#102—22no—
95#3964—22no—
96#3952—22no—
97#1875—51noSylow
98C23×C3×C5—22no—
99C23×C3×C5—41no—
100C23×C3×C5—41no—
101C23×C3×C5—41no—
102C23×C3×C5—41no—
103C23×C3×C5—41no—
104C23×C3×C5—41no—
105C23×C3×C5C2×D411yescharacteristic
106C22×C3×D5—21no—
107C22×C3×D5—21no—
108C22×C3×D5—21no—
109C22×C3×D5—21no—
110C22×C3×D5—21no—
111C22×C3×D5—21no—
112C22×C3×D5C22⋊C412yes—
113C3×C5×D4—22no—
114C3×C5×D4—22no—
115C3×C5×D4—41no—
116C3×C5×D4—41no—
117C2×C3×C4×C5—22no—
118C2×C3×C4×C5—41no—
119C2×C3×C4×C5—41no—
120C2×C3×C4×C5C22×C411yescharacteristic
121C2×C3×C4×C5C2×D411yescharacteristic
122C2×C3×C4×C5C2×D411yescharacteristic
123C2×C3×C4×C5C2×D411yescharacteristic
124C2×C3×C4×C5#4111yescharacteristic
125C2×C3×C4×C5#4111yescharacteristic
126C3×C22⋊D5—48no—
127C2×C3×Dic5—21no—
128C2×C3×Dic5—21no—
129C2×C3×Dic5—22no—
130C2×C3×Dic5—22no—
131C2×C3×Dic5—41no—
132C2×C3×Dic5—41no—
133C2×C3×Dic5—41no—
134C2×C3×Dic5—41no—
135C2×C3×Dic5C22⋊C412yes—
136C3×C4×D5—22no—
137C3×C4×D5—22no—
138C3×C4×D5—22no—
139C3×C4×D5—22no—
140C3×C5×C8—41no—
141C3×#168—41no—
142C22×C3×D4—101no—
143C22×C3×D4C2×D511yescharacteristic
144C23×C3×C4—51no—
145C22×C3×C8—51no—
146C22×C3×C8C2×D511yescharacteristic
147C3×#121—54no—
148C3×#121—102no—
149C3×#117—102no—
150C3×#117—102no—
151C2×C3×C4⋊C4—51no—
152C2×C3×C4⋊C4—51no—
153C2×C3×C4⋊C4C2×D511yescharacteristic
154C2×C3×C22⋊C4—101no—
155C2×C3×C22⋊C4—101no—
156C2×C3×C42—101no—
157C3×#102—22no—
158C3×#102—102no—
159C3×C22⋊C8—102no—
160C24×C5—21no—
161C23×D5C3×D411yescharacteristic
162C2×C5×D4—21no—
163C2×C5×D4—21no—
164C2×C5×D4—21no—
165C2×C5×D4—21no—
166C2×C5×D4—21no—
167C2×C5×D4C2×C3×C412yes—
168C22×C4×C5—21no—
169C22×C4×C5C23×C311yescharacteristic
170C2×C22⋊D5—24no—
171C2×C22⋊D5—42no—
172C2×C22⋊D5—42no—
173C22×Dic5—21no—
174C22×Dic5—21no—
175C22×Dic5C3×D411yescharacteristic
176C2×C4×D5—21no—
177C2×C4×D5—21no—
178C2×C4×D5—21no—
179C2×C4×D5—21no—
180C2×C4×D5C2×C3×C412yes—
181C2×C4×D5C3×D412yes—
182C2×C5×C8—21no—
183C2×C5×C8—21no—
184C2×C5×C8—21no—
185C5×C4⋊C4—21no—
186C5×C4⋊C4C3×D412yescomplemented
187C22⋊Dic5—24no—
188#685—24no—
189C4⋊Dic5—21no—
190C4⋊Dic5—21no—
191C4⋊Dic5C2×C3×C412yes—
192C4⋊Dic5C3×D412yescomplemented
193C4×Dic5—24no—
194C2×#168—21no—
195C2×#168—21no—
196C2×#168—21no—
197C2×#121—51no—
198C2×#117—51no—
199C2×#102—51no—
200C2×#102C3×D511yescharacteristic, complemented
201C2×C22⋊C8—51no—
202#340—51no—
203#340—51no—
204C22×C3×C5—42no—
205C22×C3×C5—42no—
206C22×C3×C5—42no—
207C22×C3×C5—81no—
208C22×C3×C5—81no—
209C22×C3×C5—81no—
210C22×C3×C5—81no—
211C22×C3×C5C2×C22⋊C411yescharacteristic
212C22×C3×C5#12011yescharacteristic
213C22×C3×C5#12311yescharacteristic
214C22×C3×C5#13511yescharacteristic
215C22×C3×C5#13511yescharacteristic
216C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
217C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
218C2×C3×D5—22no—
219C2×C3×D5—22no—
220C2×C3×D5—22no—
221C2×C3×D5—41no—
222C2×C3×D5—41no—
223C2×C3×D5—41no—
224C2×C3×D5—41no—
225C3×C4×C5—42no—
226C3×C4×C5C4×D411yescharacteristic
227C3×C4×C5C4×D411yescharacteristic
228C3×C4×C5#12111yescharacteristic
229C3×C4×C5#12111yescharacteristic
230C3×Dic5—22no—
231C3×Dic5—42no—
232C3×Dic5—42no—
233C24×C3—21no—
234C24×C3—51no—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—104no—
241C2×C3×D4—202no—
242C2×C3×D4—202no—
243C2×C3×D4C4×D512yes—
244C22×C3×C4—21no—
245C22×C3×C4—51no—
246C22×C3×C4—52no—
247C22×C3×C4—52no—
248C22×C3×C4—101no—
249C22×C3×C4—101no—
250C22×C3×C4—101no—
251C22×C3×C4—101no—
252C22×C3×C4—101no—
253C22×C3×C4—101no—
254C22×C3×C4C22×D511yescharacteristic
255C2×C3×C8—21no—
256C2×C3×C8—21no—
257C2×C3×C8—21no—
258C2×C3×C8—101no—
259C2×C3×C8—101no—
260C2×C3×C8—101no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—52no—
263C3×C4⋊C4—52no—
264C3×C4⋊C4—101no—
265C3×C4⋊C4—101no—
266C3×C4⋊C4C22⋊D512yescomplemented
267C3×C22⋊C4—104no—
268C3×C22⋊C4—104no—
269C3×C42—104no—
270C23×C5—22no—
271C23×C5—41no—
272C23×C5—41no—
273C23×C5—41no—
274C23×C5—41no—
275C23×C5—41no—
276C23×C5—41no—
277C23×C5C2×C3×D411yescharacteristic
278C22×D5—21no—
279C22×D5—21no—
280C22×D5—21no—
281C22×D5—21no—
282C22×D5—21no—
283C22×D5—21no—
284C22×D5C3×C22⋊C412yes—
285C5×D4—22no—
286C5×D4—22no—
287C5×D4—41no—
288C5×D4—41no—
289C2×C4×C5—22no—
290C2×C4×C5—41no—
291C2×C4×C5—41no—
292C2×C4×C5C22×C3×C411yescharacteristic
293C2×C4×C5C2×C3×D411yescharacteristic
294C2×C4×C5C2×C3×D411yescharacteristic
295C2×C4×C5C2×C3×D411yescharacteristic
296C2×C4×C5C3×#4111yescharacteristic
297C2×C4×C5C3×#4111yescharacteristic
298C22⋊D5—48no—
299C2×Dic5—21no—
300C2×Dic5—21no—
301C2×Dic5—22no—
302C2×Dic5—22no—
303C2×Dic5—41no—
304C2×Dic5—41no—
305C2×Dic5—41no—
306C2×Dic5—41no—
307C2×Dic5C3×C22⋊C412yes—
308C4×D5—22no—
309C4×D5—22no—
310C4×D5—22no—
311C4×D5—22no—
312C5×C8—41no—
313#168—41no—
314C22×D4—101no—
315C22×D4C2×C3×D511yescharacteristic
316C23×C4—51no—
317C22×C8—51no—
318C22×C8C2×C3×D511yescharacteristic
319#121—54no—
320#121—102no—
321#117—102no—
322#117—102no—
323C2×C4⋊C4—51no—
324C2×C4⋊C4—51no—
325C2×C4⋊C4C2×C3×D511yescharacteristic
326C2×C22⋊C4—101no—
327C2×C22⋊C4—101no—
328C2×C42—101no—
329#102—22no—
330#102—102no—
331C22⋊C8—102no—
332C2×C3×C5—82no—
333C2×C3×C5#38611yescharacteristic
334C2×C3×C5#41611yescharacteristic
335C2×C3×C5#41811yescharacteristic
336C2×C3×C5#44911yescharacteristic
337C2×C3×C5#44911yescharacteristic
338C2×C3×C5#48211yescharacteristic
339C2×C3×C5#48211yescharacteristic
340C3×D5—42no—
341C23×C3—22no—
342C23×C3—41no—
343C23×C3—41no—
344C23×C3—41no—
345C23×C3—41no—
346C23×C3—41no—
347C23×C3—41no—
348C23×C3—52no—
349C23×C3—101no—
350C23×C3—101no—
351C23×C3—101no—
352C23×C3—101no—
353C23×C3—101no—
354C23×C3—101no—
355C23×C3D4×D511yescharacteristic
356C3×D4—22no—
357C3×D4—22no—
358C3×D4—41no—
359C3×D4—41no—
360C3×D4—208no—
361C2×C3×C4—22no—
362C2×C3×C4—41no—
363C2×C3×C4—41no—
364C2×C3×C4—52no—
365C2×C3×C4—101no—
366C2×C3×C4—101no—
367C2×C3×C4—102no—
368C2×C3×C4—102no—
369C2×C3×C4—102no—
370C2×C3×C4—102no—
371C2×C3×C4—102no—
372C2×C3×C4—102no—
373C2×C3×C4—201no—
374C2×C3×C4—201no—
375C2×C3×C4—201no—
376C2×C3×C4—201no—
377C2×C3×C4C2×C4×D511yescharacteristic
378C2×C3×C4#70911yescharacteristic
379C2×C3×C4D4×D511yescharacteristic
380C2×C3×C4D4×D511yescharacteristic
381C2×C3×C4#71111yescharacteristic
382C2×C3×C4C2×C22⋊D511yescharacteristic
383C3×C8—41no—
384C3×C8—201no—
385C22×C5—42no—
386C22×C5—42no—
387C22×C5—42no—
388C22×C5—81no—
389C22×C5—81no—
390C22×C5—81no—
391C22×C5—81no—
392C22×C5C2×C3×C22⋊C411yescharacteristic
393C22×C5C3×#12011yescharacteristic
394C22×C5C3×#12311yescharacteristic
395C22×C5C3×#13511yescharacteristic
396C22×C5C3×#13511yescharacteristic
397C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
398C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
399C2×D5—22no—
400C2×D5—22no—
401C2×D5—22no—
402C2×D5—41no—
403C2×D5—41no—
404C2×D5—41no—
405C2×D5—41no—
406C4×C5—42no—
407C4×C5C3×C4×D411yescharacteristic
408C4×C5C3×C4×D411yescharacteristic
409C4×C5C3×#12111yescharacteristic
410C4×C5C3×#12111yescharacteristic
411Dic5—22no—
412Dic5—42no—
413Dic5—42no—
414C24—21no—
415C24—51no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—104no—
422C2×D4—202no—
423C2×D4—202no—
424C2×D4C3×C4×D512yes—
425C22×C4—21no—
426C22×C4—51no—
427C22×C4—52no—
428C22×C4—52no—
429C22×C4—101no—
430C22×C4—101no—
431C22×C4—101no—
432C22×C4—101no—
433C22×C4—101no—
434C22×C4—101no—
435C22×C4C22×C3×D511yescharacteristic
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—101no—
440C2×C8—101no—
441C2×C8—101no—
442C4⋊C4—21no—
443C4⋊C4—52no—
444C4⋊C4—52no—
445C4⋊C4—101no—
446C4⋊C4—101no—
447C4⋊C4C3×C22⋊D512yescomplemented
448C22⋊C4—104no—
449C22⋊C4—104no—
450C42—104no—
451C3×C5#187511yescharacteristic, complemented, Hall
452C22×C3—42no—
453C22×C3—42no—
454C22×C3—42no—
455C22×C3—81no—
456C22×C3—81no—
457C22×C3—81no—
458C22×C3—81no—
459C22×C3—102no—
460C22×C3—102no—
461C22×C3—102no—
462C22×C3—201no—
463C22×C3—201no—
464C22×C3—201no—
465C22×C3—201no—
466C22×C3D5×C22⋊C411yescharacteristic
467C22×C3#402911yescharacteristic
468C22×C3#405711yescharacteristic
469C22×C3#405811yescharacteristic
470C22×C3#406011yescharacteristic
471C22×C3#406211yescharacteristic
472C22×C3#408311yescharacteristic
473C3×C4—42no—
474C3×C4—102no—
475C3×C4—202no—
476C3×C4—202no—
477C3×C4#402711yescharacteristic
478C3×C4#403011yescharacteristic
479C3×C4C4×C22⋊D511yescharacteristic
480C3×C4#408411yescharacteristic
481C2×C5—82no—
482C2×C5C3×#38611yescharacteristic
483C2×C5C3×#41611yescharacteristic
484C2×C5C3×#41811yescharacteristic
485C2×C5C3×#44911yescharacteristic
486C2×C5C3×#44911yescharacteristic
487C2×C5C3×#48211yescharacteristic
488C2×C5C3×#48211yescharacteristic
489D5—42no—
490C23—22no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—52no—
498C23—101no—
499C23—101no—
500C23—101no—
501C23—101no—
502C23—101no—
503C23—101no—
504C23C3×D4×D511yescharacteristic
505D4—22no—
506D4—22no—
507D4—41no—
508D4—41no—
509D4—208no—
510C2×C4—22no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—52no—
514C2×C4—101no—
515C2×C4—101no—
516C2×C4—102no—
517C2×C4—102no—
518C2×C4—102no—
519C2×C4—102no—
520C2×C4—102no—
521C2×C4—102no—
522C2×C4—201no—
523C2×C4—201no—
524C2×C4—201no—
525C2×C4—201no—
526C2×C4C2×C3×C4×D511yescharacteristic
527C2×C4C3×#70911yescharacteristic
528C2×C4C3×D4×D511yescharacteristic
529C2×C4C3×D4×D511yescharacteristic
530C2×C4C3×#71111yescharacteristic
531C2×C4C2×C3×C22⋊D511yescharacteristic
532C8—41no—
533C8—201no—
534C2×C3—82no—
535C2×C3—202no—
536C2×C3#6505911yescharacteristic
537C2×C3#6506111yescharacteristic
538C2×C3#6506811yescharacteristic
539C2×C3#6507311yescharacteristic
540C2×C3#6524511yescharacteristic
541C2×C3#6544711yescharacteristic
542C2×C3#6546111yescharacteristic
543C5C3×#187511yescharacteristic, complemented, Sylow
544C22—42no—
545C22—42no—
546C22—42no—
547C22—81no—
548C22—81no—
549C22—81no—
550C22—81no—
551C22—102no—
552C22—102no—
553C22—102no—
554C22—201no—
555C22—201no—
556C22—201no—
557C22—201no—
558C22C3×D5×C22⋊C411yescharacteristic
559C22C3×#402911yescharacteristic
560C22C3×#405711yescharacteristic
561C22C3×#405811yescharacteristic
562C22C3×#406011yescharacteristic
563C22C3×#406211yescharacteristic
564C22C3×#408311yescharacteristic
565C4—42no—
566C4—102no—
567C4—202no—
568C4—202no—
569C4C3×#402711yescharacteristic
570C4C3×#403011yescharacteristic
571C4C3×C4×C22⋊D511yescharacteristic
572C4C3×#408411yescharacteristic
573C3#1060099411yescharacteristic, direct product factor, Sylow
574C2—82no—
575C2—202no—
576C2C3×#6505911yescharacteristic
577C2C3×#6506111yescharacteristic
578C2C3×#6506811yescharacteristic
579C2C3×#6507311yescharacteristic
580C2C3×#6524511yescharacteristic
581C2C3×#6544711yescharacteristic
582C2C3×#6546111yescharacteristic
subgroupG/H
centerC23×C3D4×D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC2×C3×C5×#102C2
socleC23×C3×C5C2×D4
prime radicalC2×C3×#4084C2
cosocleC22×C4×C5C23×C3
hypercenterC2×C3×#102D5
hypocenterC5C3×#1875
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#102

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4038C2semidirect
3. C2×C3×C5×#102C2semidirect
4. C2×C3×#3964C2semidirect
5. C2×C3×#3952C2semidirect
6. C3×#64771C2semidirect
7. C3×#64749C2semidirect
8. #10600994C3direct (N × H)
16. C3×#4084C4semidirect
29. C2×#4038C2×C3semidirect
30. C2×C5×#102C2×C3semidirect
31. C2×#3964C2×C3semidirect
32. C2×#3952C2×C3semidirect
33. #64771C2×C3semidirect
34. #64749C2×C3semidirect
61. C3×C5×C4⋊C4D4semidirect
67. C3×C4⋊Dic5D4semidirect
75. C2×C3×#102D5semidirect
86. #4084C3×C4semidirect
186. C5×C4⋊C4C3×D4semidirect
192. C4⋊Dic5C3×D4semidirect
200. C2×#102C3×D5semidirect
266. C3×C4⋊C4C22⋊D5semidirect
447. C4⋊C4C3×C22⋊D5semidirect
451. C3×C5#1875semidirect
543. C5C3×#1875semidirect
573. C3#10600994direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40842
C2×C3×#40382
C2×C3×C5×#1022
C2×C3×#39642
C2×C3×#39522
C3×#647712
C3×#647492
#106009943
C3×#18755