Finite Group Databasebeta

← C3×#10605145 #14320553

Subgroups — C3×#10605145 #14320553

Order 1920.

1392 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×C4×D20C211yesmaximal, characteristic
2C2×C3×#4018C211yesmaximal, characteristic, complemented
3C2×C3×C42×D5C211yesmaximal, characteristic, complemented
4C3×C5×#376C211yesmaximal, characteristic, complemented
5C3×C4×#685C211yesmaximal, characteristic, complemented
6C3×C4×#685C211yesmaximal, characteristic, complemented
7C3×C4×C4⋊Dic5C211yesmaximal, characteristic, complemented
8C3×#64959C212yesmaximal, complemented
9C3×#64957C212yesmaximal, complemented
10C3×#64954C212yesmaximal
11C3×#64942C212yesmaximal, complemented
12#10605145C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×D20C2211yescharacteristic
14C22×C3×C4×D5C2212yes—
15C22×C3×C4×D5C2211yescharacteristic
16C22×C3×C4×D5C2211yescharacteristic
17C2×C3×C42×C5C2211yescharacteristic
18C2×C3×C42×C5C2211yescharacteristic
19C2×C3×C42×C5C2211yescharacteristic
20C2×C3×#685C2212yes—
21C2×C3×#685C2212yes—
22C2×C3×#685C2212yes—
23C2×C3×#685C2211yescharacteristic
24C2×C3×#685C2211yescharacteristic
25C2×C3×C4⋊Dic5C2212yes—
26C2×C3×C4⋊Dic5C2211yescharacteristic
27C2×C3×#683C2212yes—
28C2×C3×C4×Dic5C2212yes—
29C2×C3×C4×Dic5C2211yescharacteristic
30C2×C3×C4×Dic5C2211yescharacteristic
31C3×C4×D20C418yescomplemented
32C3×#4018—24no—
33C3×C42×D5—24no—
34C3×C5×#95C2212yes—
35C3×C5×#95C2212yes—
36C3×#3963C2212yes—
37C3×#3963C2212yes—
38C3×#3963C2212yes—
39C3×#2290—51nomaximal, Hall
40C2×C4×D20C2×C311yescharacteristic
41C2×#4018C2×C311yescharacteristic, complemented
42C2×C42×D5C2×C311yescharacteristic, complemented
43C5×#376C2×C311yescharacteristic, complemented
44C4×#685C2×C311yescharacteristic, complemented
45C4×#685C2×C311yescharacteristic, complemented
46C4×C4⋊Dic5C2×C311yescharacteristic, complemented
47#64959C2×C312yescomplemented
48#64957C2×C312yescomplemented
49#64954C2×C312yes—
50#64942C2×C312yescomplemented
51C23×C3×D5C2311yescharacteristic
52C23×C3×D5C2311yescharacteristic
53C22×C3×C4×C5C2312yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×C3×C4×C5C2311yescharacteristic
56C22×C3×C4×C5C2312yes—
57C22×C3×C4×C5C2311yescharacteristic
58C22×C3×Dic5C2312yes—
59C22×C3×Dic5C2311yescharacteristic
60C22×C3×Dic5C2311yescharacteristic
61C22×C3×Dic5C2312yes—
62C2×C3×D20—24no—
63C2×C3×D20C2×C414yes—
64C2×C3×C4×D5—24no—
65C2×C3×C4×D5—24no—
66C2×C3×C4×D5—22no—
67C2×C3×C4×D5—22no—
68C2×C3×C4×D5—22no—
69C2×C3×C4×D5—22no—
70C2×C3×C4×D5—24no—
71C2×C3×C4×D5C2×C414yes—
72C2×C3×C4×D5C2×C414yescomplemented
73C3×C42×C5—22no—
74C3×C42×C5C2×C414yescomplemented
75C3×C42×C5D414yescomplemented
76C3×#685—24no—
77C3×#685—24no—
78C3×#685—24no—
79C3×#685C2×C414yes—
80C3×#685C2×C414yescomplemented
81C3×C4⋊Dic5—24no—
82C3×C4⋊Dic5C2×C414yescomplemented
83C3×#683—24no—
84C3×C4×Dic5—24no—
85C3×C4×Dic5—22no—
86C3×C4×Dic5—22no—
87C2×C3×C4×D4—51no—
88C2×C3×#117—51no—
89C22×C3×C42—51no—
90C3×#388—52no—
91C3×#387—52no—
92C3×#386—52no—
93C3×#385—52no—
94C3×C4×C4⋊C4—51no—
95C3×C4×C22⋊C4—51no—
96C3×C4×C22⋊C4—51no—
97C3×#376D511yescharacteristic, complemented
98C22×D20C22×C311yescharacteristic
99C22×C4×D5C22×C312yes—
100C22×C4×D5C22×C311yescharacteristic
101C22×C4×D5C22×C311yescharacteristic
102C2×C42×C5C22×C311yescharacteristic
103C2×C42×C5C22×C311yescharacteristic
104C2×C42×C5C22×C311yescharacteristic
105C2×#685C22×C312yes—
106C2×#685C22×C312yes—
107C2×#685C22×C312yes—
108C2×#685C22×C311yescharacteristic
109C2×#685C22×C311yescharacteristic
110C2×C4⋊Dic5C22×C312yes—
111C2×C4⋊Dic5C22×C311yescharacteristic
112C2×#683C22×C312yes—
113C2×C4×Dic5C22×C312yes—
114C2×C4×Dic5C22×C311yescharacteristic
115C2×C4×Dic5C22×C311yescharacteristic
116C4×D20C3×C418yescomplemented
117#4018—24no—
118C42×D5—24no—
119C5×#95C22×C312yes—
120C5×#95C22×C312yes—
121#3963C22×C312yes—
122#3963C22×C312yes—
123#3963C22×C312yes—
124#2290—51noSylow
125C23×C3×C5C2411yescharacteristic
126C22×C3×D5—21no—
127C22×C3×D5—21no—
128C22×C3×D5—22no—
129C22×C3×D5—21no—
130C22×C3×D5—22no—
131C22×C3×D5—21no—
132C22×C3×D5—22no—
133C22×C3×D5C22×C412yes—
134C22×C3×D5C22×C412yes—
135C22×C3×D5#4114yes—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5—22no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5C22×C412yes—
144C2×C3×C4×C5C22×C412yes—
145C2×C3×C4×C5C22×C412yes—
146C2×C3×C4×C5C2×D414yes—
147C2×C3×C4×C5C2×D412yes—
148C2×C3×C4×C5#4112yes—
149C2×C3×Dic5—21no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—21no—
152C2×C3×Dic5—21no—
153C2×C3×Dic5—21no—
154C2×C3×Dic5—22no—
155C2×C3×Dic5—22no—
156C2×C3×Dic5—22no—
157C2×C3×Dic5—22no—
158C2×C3×Dic5C22×C412yes—
159C2×C3×Dic5C22×C412yes—
160C2×C3×Dic5#4114yes—
161C3×D20—28no—
162C3×C4×D5—216no—
163C3×C4×D5—28no—
164C3×C4×D5—28no—
165C22×C3×D4—51no—
166C23×C3×C4—51no—
167C23×C3×C4—51no—
168C23×C3×C4—52no—
169C3×C4×D4—58no—
170C3×#117—104no—
171C2×C3×C4⋊C4—51no—
172C2×C3×C4⋊C4—52no—
173C2×C3×C4⋊C4—52no—
174C2×C3×C22⋊C4—51no—
175C2×C3×C22⋊C4—51no—
176C2×C3×C22⋊C4—52no—
177C2×C3×C22⋊C4—52no—
178C2×C3×C22⋊C4—52no—
179C2×C3×C42—52no—
180C2×C3×C42—51no—
181C2×C3×C42—51no—
182C2×C3×C42—104no—
183C2×C3×C42C2×D511yescharacteristic
184C2×C3×C42C2×D511yescharacteristic
185C2×C3×C42C2×D511yescharacteristic
186C3×#95—52no—
187C3×#95—52no—
188C3×#95—52no—
189C3×#95C2×D512yes—
190C3×#95C2×D512yes—
191C23×D5C23×C311yescharacteristic
192C23×D5C23×C311yescharacteristic
193C22×C4×C5C23×C312yes—
194C22×C4×C5C23×C311yescharacteristic
195C22×C4×C5C23×C311yescharacteristic
196C22×C4×C5C23×C312yes—
197C22×C4×C5C23×C311yescharacteristic
198C22×Dic5C23×C312yes—
199C22×Dic5C23×C311yescharacteristic
200C22×Dic5C23×C311yescharacteristic
201C22×Dic5C23×C312yes—
202C2×D20—24no—
203C2×D20C2×C3×C414yes—
204C2×C4×D5—24no—
205C2×C4×D5—24no—
206C2×C4×D5—22no—
207C2×C4×D5—22no—
208C2×C4×D5—22no—
209C2×C4×D5—22no—
210C2×C4×D5—24no—
211C2×C4×D5C2×C3×C414yes—
212C2×C4×D5C2×C3×C414yescomplemented
213C42×C5—22no—
214C42×C5C2×C3×C414yescomplemented
215C42×C5C3×D414yescomplemented
216#685—24no—
217#685—24no—
218#685—24no—
219#685C2×C3×C414yes—
220#685C2×C3×C414yescomplemented
221C4⋊Dic5—24no—
222C4⋊Dic5C2×C3×C414yescomplemented
223#683—24no—
224C4×Dic5—24no—
225C4×Dic5—22no—
226C4×Dic5—22no—
227C2×C4×D4—51no—
228C2×#117—51no—
229C22×C42—51no—
230#388—52no—
231#387—52no—
232#386—52no—
233#385—52no—
234C4×C4⋊C4—51no—
235C4×C22⋊C4—51no—
236C4×C22⋊C4—51no—
237#376C3×D511yescharacteristic, complemented
238C22×C3×C5C23×C411yescharacteristic
239C22×C3×C5C22×D411yescharacteristic
240C22×C3×C5C2×#4111yescharacteristic
241C22×C3×C5C2×#4112yes—
242C22×C3×C5C2×#4112yes—
243C2×C3×D5—22no—
244C2×C3×D5—22no—
245C2×C3×D5—24no—
246C2×C3×D5—24no—
247C2×C3×D5—22no—
248C2×C3×D5—22no—
249C2×C3×D5—22no—
250C2×C3×D5—42no—
251C2×C3×D5—42no—
252C2×C3×D5#11714yescomplemented
253C3×C4×C5—22no—
254C3×C4×C5—22no—
255C3×C4×C5—24no—
256C3×C4×C5—42no—
257C3×C4×C5C4×D414yes—
258C3×Dic5—22no—
259C3×Dic5—22no—
260C3×Dic5—24no—
261C3×Dic5—42no—
262C24×C3—51no—
263C24×C3—51no—
264C2×C3×D4—54no—
265C2×C3×D4—104no—
266C22×C3×C4—51no—
267C22×C3×C4—52no—
268C22×C3×C4—51no—
269C22×C3×C4—54no—
270C22×C3×C4—54no—
271C22×C3×C4—52no—
272C22×C3×C4—104no—
273C22×C3×C4—104no—
274C22×C3×C4—104no—
275C22×C3×C4—102no—
276C22×C3×C4—102no—
277C22×C3×C4—102no—
278C22×C3×C4—102no—
279C22×C3×C4C22×D512yes—
280C22×C3×C4C22×D511yescharacteristic
281C22×C3×C4C22×D511yescharacteristic
282C22×C3×C4C22×D512yes—
283C22×C3×C4C22×D511yescharacteristic
284C3×C4⋊C4—54no—
285C3×C4⋊C4—104no—
286C3×C4⋊C4—104no—
287C3×C22⋊C4—54no—
288C3×C22⋊C4—54no—
289C3×C22⋊C4—104no—
290C3×C22⋊C4—104no—
291C3×C22⋊C4—104no—
292C3×C42—22no—
293C3×C42—104no—
294C3×C42—102no—
295C3×C42—102no—
296C3×C42C4×D514yescomplemented
297C3×C42D2014yescomplemented
298C23×C5C24×C311yescharacteristic
299C22×D5—21no—
300C22×D5—21no—
301C22×D5—22no—
302C22×D5—21no—
303C22×D5—22no—
304C22×D5—21no—
305C22×D5—22no—
306C22×D5C22×C3×C412yes—
307C22×D5C22×C3×C412yes—
308C22×D5C3×#4114yes—
309C2×C4×C5—22no—
310C2×C4×C5—22no—
311C2×C4×C5—22no—
312C2×C4×C5—22no—
313C2×C4×C5—22no—
314C2×C4×C5—22no—
315C2×C4×C5—22no—
316C2×C4×C5C22×C3×C412yes—
317C2×C4×C5C22×C3×C412yes—
318C2×C4×C5C22×C3×C412yes—
319C2×C4×C5C2×C3×D414yes—
320C2×C4×C5C2×C3×D412yes—
321C2×C4×C5C3×#4112yes—
322C2×Dic5—21no—
323C2×Dic5—22no—
324C2×Dic5—21no—
325C2×Dic5—21no—
326C2×Dic5—21no—
327C2×Dic5—22no—
328C2×Dic5—22no—
329C2×Dic5—22no—
330C2×Dic5—22no—
331C2×Dic5C22×C3×C412yes—
332C2×Dic5C22×C3×C412yes—
333C2×Dic5C3×#4114yes—
334D20—28no—
335C4×D5—216no—
336C4×D5—28no—
337C4×D5—28no—
338C22×D4—51no—
339C23×C4—51no—
340C23×C4—51no—
341C23×C4—52no—
342C4×D4—58no—
343#117—104no—
344C2×C4⋊C4—51no—
345C2×C4⋊C4—52no—
346C2×C4⋊C4—52no—
347C2×C22⋊C4—51no—
348C2×C22⋊C4—51no—
349C2×C22⋊C4—52no—
350C2×C22⋊C4—52no—
351C2×C22⋊C4—52no—
352C2×C42—51no—
353C2×C42—51no—
354C2×C42—52no—
355C2×C42—104no—
356C2×C42C2×C3×D511yescharacteristic
357C2×C42C2×C3×D511yescharacteristic
358C2×C42C2×C3×D511yescharacteristic
359#95—52no—
360#95—52no—
361#95—52no—
362#95C2×C3×D512yes—
363#95C2×C3×D512yes—
364C2×C3×C5C2×#11711yescharacteristic
365C2×C3×C5C2×C4×D411yescharacteristic
366C2×C3×C5C4×#4111yescharacteristic
367C2×C3×C5#52512yes—
368C2×C3×C5#52912yes—
369C3×D5—24no—
370C3×D5—42no—
371C23×C3—52no—
372C23×C3—54no—
373C23×C3—52no—
374C23×C3—101no—
375C23×C3—101no—
376C23×C3—102no—
377C23×C3—101no—
378C23×C3—101no—
379C23×C3—102no—
380C23×C3—102no—
381C23×C3C23×D511yescharacteristic
382C3×D4—108no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—52no—
391C2×C3×C4—52no—
392C2×C3×C4—54no—
393C2×C3×C4—1016no—
394C2×C3×C4—101no—
395C2×C3×C4—102no—
396C2×C3×C4—101no—
397C2×C3×C4—101no—
398C2×C3×C4—101no—
399C2×C3×C4—102no—
400C2×C3×C4—108no—
401C2×C3×C4—108no—
402C2×C3×C4—102no—
403C2×C3×C4—102no—
404C2×C3×C4—102no—
405C2×C3×C4C2×C4×D512yes—
406C2×C3×C4C2×C4×D512yes—
407C2×C3×C4C2×C4×D512yes—
408C2×C3×C4C2×D2014yes—
409C2×C3×C4C2×D2012yes—
410C2×C3×C4#70912yes—
411C22×C5C23×C3×C411yescharacteristic
412C22×C5C22×C3×D411yescharacteristic
413C22×C5C2×C3×#4111yescharacteristic
414C22×C5C2×C3×#4112yes—
415C22×C5C2×C3×#4112yes—
416C2×D5—22no—
417C2×D5—22no—
418C2×D5—24no—
419C2×D5—24no—
420C2×D5—22no—
421C2×D5—22no—
422C2×D5—22no—
423C2×D5—42no—
424C2×D5—42no—
425C2×D5C3×#11714yescomplemented
426C4×C5—22no—
427C4×C5—22no—
428C4×C5—24no—
429C4×C5—42no—
430C4×C5C3×C4×D414yes—
431Dic5—22no—
432Dic5—22no—
433Dic5—24no—
434Dic5—42no—
435C24—51no—
436C24—51no—
437C2×D4—54no—
438C2×D4—104no—
439C22×C4—51no—
440C22×C4—52no—
441C22×C4—51no—
442C22×C4—54no—
443C22×C4—54no—
444C22×C4—52no—
445C22×C4—104no—
446C22×C4—104no—
447C22×C4—104no—
448C22×C4—102no—
449C22×C4—102no—
450C22×C4—102no—
451C22×C4—102no—
452C22×C4C22×C3×D512yes—
453C22×C4C22×C3×D511yescharacteristic
454C22×C4C22×C3×D511yescharacteristic
455C22×C4C22×C3×D512yes—
456C22×C4C22×C3×D511yescharacteristic
457C4⋊C4—54no—
458C4⋊C4—104no—
459C4⋊C4—104no—
460C22⋊C4—54no—
461C22⋊C4—54no—
462C22⋊C4—104no—
463C22⋊C4—104no—
464C22⋊C4—104no—
465C42—22no—
466C42—104no—
467C42—102no—
468C42—102no—
469C42C3×C4×D514yescomplemented
470C42C3×D2014yescomplemented
471C3×C5#229011yescharacteristic, complemented, Hall
472C22×C3—54no—
473C22×C3—102no—
474C22×C3—102no—
475C22×C3—104no—
476C22×C3—104no—
477C22×C3—102no—
478C22×C3—102no—
479C22×C3—102no—
480C22×C3—202no—
481C22×C3—202no—
482C22×C3C22×C4×D511yescharacteristic
483C22×C3C22×D2011yescharacteristic
484C22×C3C2×#70911yescharacteristic
485C22×C3D5×#4112yes—
486C22×C3D5×#4112yes—
487C3×C4—22no—
488C3×C4—22no—
489C3×C4—24no—
490C3×C4—42no—
491C3×C4—102no—
492C3×C4—102no—
493C3×C4—104no—
494C3×C4—202no—
495C3×C4C4×D2014yes—
496C2×C5C2×C3×#11711yescharacteristic
497C2×C5C2×C3×C4×D411yescharacteristic
498C2×C5C3×C4×#4111yescharacteristic
499C2×C5C3×#52512yes—
500C2×C5C3×#52912yes—
501D5—24no—
502D5—42no—
503C23—52no—
504C23—54no—
505C23—52no—
506C23—101no—
507C23—101no—
508C23—102no—
509C23—101no—
510C23—101no—
511C23—102no—
512C23—102no—
513C23C23×C3×D511yescharacteristic
514D4—108no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—52no—
523C2×C4—52no—
524C2×C4—54no—
525C2×C4—1016no—
526C2×C4—102no—
527C2×C4—101no—
528C2×C4—101no—
529C2×C4—101no—
530C2×C4—101no—
531C2×C4—102no—
532C2×C4—108no—
533C2×C4—108no—
534C2×C4—102no—
535C2×C4—102no—
536C2×C4—102no—
537C2×C4C2×C3×C4×D512yes—
538C2×C4C2×C3×C4×D512yes—
539C2×C4C2×C3×C4×D512yes—
540C2×C4C2×C3×D2014yes—
541C2×C4C2×C3×D2012yes—
542C2×C4C3×#70912yes—
543C2×C3—104no—
544C2×C3—202no—
545C2×C3C2×C4×D2011yescharacteristic
546C2×C3D5×#11711yescharacteristic
547C2×C3#6585611yescharacteristic
548C2×C3#6585812yes—
549C2×C3#6586212yes—
550C5C3×#229011yescharacteristic, complemented, Sylow
551C22—54no—
552C22—102no—
553C22—104no—
554C22—104no—
555C22—102no—
556C22—102no—
557C22—102no—
558C22—102no—
559C22—202no—
560C22—202no—
561C22C22×C3×C4×D511yescharacteristic
562C22C22×C3×D2011yescharacteristic
563C22C2×C3×#70911yescharacteristic
564C22C3×D5×#4112yes—
565C22C3×D5×#4112yes—
566C4—22no—
567C4—22no—
568C4—24no—
569C4—42no—
570C4—104no—
571C4—102no—
572C4—102no—
573C4—202no—
574C4C3×C4×D2014yes—
575C3#1060514511yescharacteristic, direct product factor, Sylow
576C2—104no—
577C2—202no—
578C2C2×C3×C4×D2011yescharacteristic
579C2C3×D5×#11711yescharacteristic
580C2C3×#6585611yescharacteristic
581C2C3×#6585812yes—
582C2C3×#6586212yes—
subgroupG/H
centerC22×C3×C4C22×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#376C2
socleC23×C3×C5C24
prime radicalC22×C3×D20C22
cosocleC23×C5C24×C3
hypercenterC3×#376D5
hypocenterC5C3×#2290
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3×C4 ◁ C3×#376

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4018C2semidirect
3. C2×C3×C42×D5C2semidirect
4. C3×C5×#376C2semidirect
5. C3×C4×#685C2semidirect
6. C3×C4×#685C2semidirect
7. C3×C4×C4⋊Dic5C2semidirect
8. C3×#64959C2semidirect
9. C3×#64957C2semidirect
11. C3×#64942C2semidirect
12. #10605145C3direct (N × H)
31. C3×C4×D20C4semidirect
41. C2×#4018C2×C3semidirect
42. C2×C42×D5C2×C3semidirect
43. C5×#376C2×C3semidirect
44. C4×#685C2×C3semidirect
45. C4×#685C2×C3semidirect
46. C4×C4⋊Dic5C2×C3semidirect
47. #64959C2×C3semidirect
48. #64957C2×C3semidirect
50. #64942C2×C3semidirect
72. C2×C3×C4×D5C2×C4semidirect
74. C3×C42×C5C2×C4semidirect
75. C3×C42×C5D4semidirect
80. C3×#685C2×C4semidirect
82. C3×C4⋊Dic5C2×C4semidirect
97. C3×#376D5semidirect
116. C4×D20C3×C4semidirect
212. C2×C4×D5C2×C3×C4semidirect
214. C42×C5C2×C3×C4semidirect
215. C42×C5C3×D4semidirect
220. #685C2×C3×C4semidirect
222. C4⋊Dic5C2×C3×C4semidirect
237. #376C3×D5semidirect
252. C2×C3×D5#117semidirect
296. C3×C42C4×D5semidirect
297. C3×C42D20semidirect
425. C2×D5C3×#117semidirect
469. C42C3×C4×D5semidirect
470. C42C3×D20semidirect
471. C3×C5#2290semidirect
550. C5C3×#2290semidirect
575. C3#10605145direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×D202
C2×C3×#40182
C2×C3×C42×D52
C3×C5×#3762
C3×C4×#6852
C3×C4×C4⋊Dic52
C3×#649592
C3×#649572
C3×#649542
C3×#649422
#106051453
C3×#22905