Finite Group Databasebeta

← C3×#10605593 #14319915

Subgroups — C3×#10605593 #14319915

Order 1920.

2176 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C4×D5C211yesmaximal, characteristic
2C2×C3×#4038C212yesmaximal, complemented
3C3×C5×#380C211yesmaximal, characteristic, complemented
4C3×#65501C211yesmaximal, characteristic, complemented
5C3×#65276C212yesmaximal, complemented
6C3×#65244C212yesmaximal
7C3×C22⋊C4×Dic5C212yesmaximal, complemented
8C3×#64955C212yesmaximal, complemented
9C3×#64953C212yesmaximal, complemented
10#10605593C311yesmaximal, characteristic, direct product factor, Hall
11C24×C3×D5C2211yescharacteristic
12C23×C3×C4×C5C2211yescharacteristic
13C23×C3×Dic5C2211yescharacteristic
14C22×C3×C4×D5—28no—
15C22×C3×C4×D5C418yescomplemented
16C22×C3×C4×D5C2211yescharacteristic
17C22×C3×C4×D5C2211yescharacteristic
18C22×C3×C4×D5C2211yescharacteristic
19C22×C3×C4×D5C2211yescharacteristic
20C2×C3×C5×C4⋊C4C2212yescomplemented
21C2×C3×C5×C22⋊C4C2212yes—
22C2×C3×C22⋊Dic5C2212yes—
23C2×C3×#685C2214yes—
24C2×C3×#685C2214yes—
25C2×C3×C4⋊Dic5C2212yescomplemented
26C2×C3×C4×Dic5C2214yescomplemented
27C3×#4038—28no—
28C3×C5×#95C2212yescomplemented
29C3×#3963C2212yescomplemented
30C3×#3963C2214yescomplemented
31C3×#2280—51nomaximal, Hall
32C23×C4×D5C2×C311yescharacteristic
33C2×#4038C2×C312yescomplemented
34C5×#380C2×C311yescharacteristic, complemented
35#65501C2×C311yescharacteristic, complemented
36#65276C2×C312yescomplemented
37#65244C2×C312yes—
38C22⋊C4×Dic5C2×C312yescomplemented
39#64955C2×C312yescomplemented
40#64953C2×C312yescomplemented
41C24×C3×C5C2311yescharacteristic
42C23×C3×D5—22no—
43C23×C3×D5—22no—
44C23×C3×D5—24no—
45C23×C3×D5—24no—
46C23×C3×D5C2×C414yes—
47C23×C3×D5C2311yescharacteristic
48C23×C3×D5C2311yescharacteristic
49C22×C3×C4×C5—24no—
50C22×C3×C4×C5C2×C414yes—
51C22×C3×C4×C5C2314yes—
52C22×C3×C4×C5C2311yescharacteristic
53C22×C3×C4×C5C2311yescharacteristic
54C22×C3×Dic5—24no—
55C22×C3×Dic5C2×C414yes—
56C22×C3×Dic5C2314yes—
57C22×C3×Dic5C2311yescharacteristic
58C22×C3×Dic5C2311yescharacteristic
59C2×C3×C4×D5—24no—
60C2×C3×C4×D5—24no—
61C2×C3×C4×D5—24no—
62C2×C3×C4×D5—232no—
63C2×C3×C4×D5C2×C414yes—
64C2×C3×C4×D5C2×C414yes—
65C2×C3×C4×D5C2×C414yes—
66C2×C3×C4×D5C2×C414yes—
67C2×C3×C4×D5D418yes—
68C3×C5×C4⋊C4—24no—
69C3×C5×C22⋊C4—24no—
70C3×C22⋊Dic5—24no—
71C3×#685—28no—
72C3×#685—28no—
73C3×C4⋊Dic5—24no—
74C3×C4×Dic5—28no—
75C24×C3×C4—51no—
76C2×C3×#117—52no—
77C3×#381—52no—
78C3×#380—51no—
79C3×#380—52no—
80C3×#380D511yescharacteristic, complemented
81C3×#379—52no—
82C3×C4×C22⋊C4—52no—
83C3×C4×C22⋊C4—52no—
84C24×D5C22×C311yescharacteristic
85C23×C4×C5C22×C311yescharacteristic
86C23×Dic5C22×C311yescharacteristic
87C22×C4×D5—28no—
88C22×C4×D5C3×C418yescomplemented
89C22×C4×D5C22×C311yescharacteristic
90C22×C4×D5C22×C311yescharacteristic
91C22×C4×D5C22×C311yescharacteristic
92C22×C4×D5C22×C311yescharacteristic
93C2×C5×C4⋊C4C22×C312yescomplemented
94C2×C5×C22⋊C4C22×C312yes—
95C2×C22⋊Dic5C22×C312yes—
96C2×#685C22×C314yes—
97C2×#685C22×C314yes—
98C2×C4⋊Dic5C22×C312yescomplemented
99C2×C4×Dic5C22×C314yescomplemented
100#4038—28no—
101C5×#95C22×C312yescomplemented
102#3963C22×C312yescomplemented
103#3963C22×C314yescomplemented
104#2280—51noSylow
105C23×C3×C5—22no—
106C23×C3×C5—22no—
107C23×C3×C5C22×C412yes—
108C23×C3×C5#4112yes—
109C23×C3×C5#4112yes—
110C23×C3×C5C2411yescharacteristic
111C22×C3×D5—216no—
112C22×C3×D5—216no—
113C22×C3×D5—28no—
114C22×C3×D5—22no—
115C22×C3×D5—21no—
116C22×C3×D5—21no—
117C22×C3×D5—22no—
118C22×C3×D5—21no—
119C22×C3×D5—21no—
120C22×C3×D5—28no—
121C22×C3×D5—28no—
122C22×C3×D5C22×C412yes—
123C22×C3×D5C22×C412yes—
124C22×C3×D5C2×D414yes—
125C22×C3×D5#4114yes—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5—28no—
128C2×C3×C4×C5—24no—
129C2×C3×C4×C5—24no—
130C2×C3×C4×C5—24no—
131C2×C3×C4×C5C22×C412yes—
132C2×C3×C4×C5C22×C412yes—
133C2×C3×C4×C5C2×D414yes—
134C2×C3×Dic5—22no—
135C2×C3×Dic5—28no—
136C2×C3×Dic5—24no—
137C2×C3×Dic5—24no—
138C2×C3×Dic5—24no—
139C2×C3×Dic5C22×C412yes—
140C2×C3×Dic5C22×C412yes—
141C2×C3×Dic5C2×D414yes—
142C3×C4×D5—28no—
143C3×C4×D5—28no—
144C3×C4×D5—28no—
145C3×C4×D5C22⋊C4116yescomplemented
146C25×C3—51no—
147C23×C3×C4—51no—
148C23×C3×C4—51no—
149C23×C3×C4—58no—
150C23×C3×C4—51no—
151C23×C3×C4—51no—
152C23×C3×C4—51no—
153C23×C3×C4—108no—
154C23×C3×C4C2×D511yescharacteristic
155C3×#117—108no—
156C2×C3×C4⋊C4—52no—
157C2×C3×C4⋊C4C2×D512yescomplemented
158C2×C3×C22⋊C4—52no—
159C2×C3×C22⋊C4—54no—
160C2×C3×C22⋊C4—54no—
161C2×C3×C22⋊C4C2×D512yes—
162C2×C3×C42—54no—
163C3×#95—54no—
164C3×#95—52no—
165C3×#95C2×D512yescomplemented
166C24×C5C23×C311yescharacteristic
167C23×D5—22no—
168C23×D5—22no—
169C23×D5—24no—
170C23×D5—24no—
171C23×D5C2×C3×C414yes—
172C23×D5C23×C311yescharacteristic
173C23×D5C23×C311yescharacteristic
174C22×C4×C5—24no—
175C22×C4×C5C2×C3×C414yes—
176C22×C4×C5C23×C314yes—
177C22×C4×C5C23×C311yescharacteristic
178C22×C4×C5C23×C311yescharacteristic
179C22×Dic5—24no—
180C22×Dic5C2×C3×C414yes—
181C22×Dic5C23×C314yes—
182C22×Dic5C23×C311yescharacteristic
183C22×Dic5C23×C311yescharacteristic
184C2×C4×D5—24no—
185C2×C4×D5—24no—
186C2×C4×D5—24no—
187C2×C4×D5—232no—
188C2×C4×D5C2×C3×C414yes—
189C2×C4×D5C2×C3×C414yes—
190C2×C4×D5C2×C3×C414yes—
191C2×C4×D5C2×C3×C414yes—
192C2×C4×D5C3×D418yes—
193C5×C4⋊C4—24no—
194C5×C22⋊C4—24no—
195C22⋊Dic5—24no—
196#685—28no—
197#685—28no—
198C4⋊Dic5—24no—
199C4×Dic5—28no—
200C24×C4—51no—
201C2×#117—52no—
202#381—52no—
203#380—51no—
204#380—52no—
205#380C3×D511yescharacteristic, complemented
206#379—52no—
207C4×C22⋊C4—52no—
208C4×C22⋊C4—52no—
209C22×C3×C5—22no—
210C22×C3×C5—22no—
211C22×C3×C5—24no—
212C22×C3×C5—24no—
213C22×C3×C5#11714yescomplemented
214C22×C3×C5C23×C411yescharacteristic
215C22×C3×C5C22×D412yes—
216C22×C3×C5C2×#4111yescharacteristic
217C22×C3×C5C2×#4111yescharacteristic
218C22×C3×C5C2×#4112yes—
219C2×C3×D5—232no—
220C2×C3×D5—22no—
221C2×C3×D5—22no—
222C2×C3×D5—22no—
223C2×C3×D5—22no—
224C2×C3×D5—24no—
225C2×C3×D5—24no—
226C2×C3×D5—24no—
227C2×C3×D5—24no—
228C2×C3×D5C2×C22⋊C414yes—
229C2×C3×D5#11714yescomplemented
230C3×C4×C5—22no—
231C3×C4×C5—44no—
232C3×C4×C5C2×C22⋊C414yes—
233C3×Dic5—22no—
234C3×Dic5—44no—
235C3×Dic5C2×C22⋊C414yes—
236C24×C3—51no—
237C24×C3—51no—
238C24×C3—54no—
239C24×C3—104no—
240C24×C3—104no—
241C24×C3—102no—
242C24×C3—102no—
243C24×C3C22×D511yescharacteristic
244C22×C3×C4—24no—
245C22×C3×C4—51no—
246C22×C3×C4—54no—
247C22×C3×C4—58no—
248C22×C3×C4—54no—
249C22×C3×C4—51no—
250C22×C3×C4—54no—
251C22×C3×C4—54no—
252C22×C3×C4—54no—
253C22×C3×C4—54no—
254C22×C3×C4—104no—
255C22×C3×C4—1032no—
256C22×C3×C4—104no—
257C22×C3×C4—104no—
258C22×C3×C4—104no—
259C22×C3×C4C4×D514yes—
260C22×C3×C4C22×D514yes—
261C22×C3×C4C22×D511yescharacteristic
262C22×C3×C4C22×D511yescharacteristic
263C3×C4⋊C4—24no—
264C3×C4⋊C4—104no—
265C3×C22⋊C4—24no—
266C3×C22⋊C4—108no—
267C3×C22⋊C4—108no—
268C3×C22⋊C4—104no—
269C3×C42—108no—
270C23×C5—22no—
271C23×C5—22no—
272C23×C5C22×C3×C412yes—
273C23×C5C3×#4112yes—
274C23×C5C3×#4112yes—
275C23×C5C24×C311yescharacteristic
276C22×D5—216no—
277C22×D5—216no—
278C22×D5—28no—
279C22×D5—22no—
280C22×D5—21no—
281C22×D5—21no—
282C22×D5—21no—
283C22×D5—21no—
284C22×D5—22no—
285C22×D5—28no—
286C22×D5—28no—
287C22×D5C22×C3×C412yes—
288C22×D5C22×C3×C412yes—
289C22×D5C2×C3×D414yes—
290C22×D5C3×#4114yes—
291C2×C4×C5—22no—
292C2×C4×C5—28no—
293C2×C4×C5—24no—
294C2×C4×C5—24no—
295C2×C4×C5—24no—
296C2×C4×C5C22×C3×C412yes—
297C2×C4×C5C22×C3×C412yes—
298C2×C4×C5C2×C3×D414yes—
299C2×Dic5—22no—
300C2×Dic5—28no—
301C2×Dic5—24no—
302C2×Dic5—24no—
303C2×Dic5—24no—
304C2×Dic5C22×C3×C412yes—
305C2×Dic5C22×C3×C412yes—
306C2×Dic5C2×C3×D414yes—
307C4×D5—28no—
308C4×D5—28no—
309C4×D5—28no—
310C4×D5C3×C22⋊C4116yescomplemented
311C25—51no—
312C23×C4—51no—
313C23×C4—51no—
314C23×C4—58no—
315C23×C4—51no—
316C23×C4—51no—
317C23×C4—51no—
318C23×C4—108no—
319C23×C4C2×C3×D511yescharacteristic
320#117—108no—
321C2×C4⋊C4—52no—
322C2×C4⋊C4C2×C3×D512yescomplemented
323C2×C22⋊C4—52no—
324C2×C22⋊C4—54no—
325C2×C22⋊C4—54no—
326C2×C22⋊C4C2×C3×D512yes—
327C2×C42—54no—
328#95—54no—
329#95—52no—
330#95C2×C3×D512yescomplemented
331C2×C3×C5—24no—
332C2×C3×C5C22×C22⋊C411yescharacteristic
333C2×C3×C5C2×#11711yescharacteristic
334C2×C3×C5C2×#11711yescharacteristic
335C2×C3×C5#52512yes—
336C2×C3×C5#52512yes—
337C3×D5—24no—
338C3×D5—24no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3—52no—
342C23×C3—52no—
343C23×C3—54no—
344C23×C3—54no—
345C23×C3—108no—
346C23×C3—108no—
347C23×C3—1016no—
348C23×C3—1016no—
349C23×C3—102no—
350C23×C3—101no—
351C23×C3—101no—
352C23×C3—101no—
353C23×C3—101no—
354C23×C3—102no—
355C23×C3—108no—
356C23×C3C2×C4×D512yes—
357C23×C3#71112yes—
358C23×C3#71312yes—
359C23×C3C23×D511yescharacteristic
360C2×C3×C4—22no—
361C2×C3×C4—28no—
362C2×C3×C4—24no—
363C2×C3×C4—24no—
364C2×C3×C4—24no—
365C2×C3×C4—52no—
366C2×C3×C4—54no—
367C2×C3×C4—516no—
368C2×C3×C4—52no—
369C2×C3×C4—108no—
370C2×C3×C4—108no—
371C2×C3×C4—108no—
372C2×C3×C4—102no—
373C2×C3×C4—108no—
374C2×C3×C4—104no—
375C2×C3×C4—104no—
376C2×C3×C4—104no—
377C2×C3×C4C2×C4×D512yes—
378C2×C3×C4C2×C4×D512yes—
379C2×C3×C4D4×D514yes—
380C22×C5—22no—
381C22×C5—22no—
382C22×C5—24no—
383C22×C5—24no—
384C22×C5C3×#11714yescomplemented
385C22×C5C23×C3×C411yescharacteristic
386C22×C5C22×C3×D412yes—
387C22×C5C2×C3×#4111yescharacteristic
388C22×C5C2×C3×#4111yescharacteristic
389C22×C5C2×C3×#4112yes—
390C2×D5—232no—
391C2×D5—22no—
392C2×D5—22no—
393C2×D5—22no—
394C2×D5—22no—
395C2×D5—24no—
396C2×D5—24no—
397C2×D5—24no—
398C2×D5—24no—
399C2×D5C2×C3×C22⋊C414yes—
400C2×D5C3×#11714yescomplemented
401C4×C5—22no—
402C4×C5—44no—
403C4×C5C2×C3×C22⋊C414yes—
404Dic5—22no—
405Dic5—44no—
406Dic5C2×C3×C22⋊C414yes—
407C24—51no—
408C24—51no—
409C24—54no—
410C24—104no—
411C24—104no—
412C24—102no—
413C24—102no—
414C24C22×C3×D511yescharacteristic
415C22×C4—24no—
416C22×C4—51no—
417C22×C4—54no—
418C22×C4—58no—
419C22×C4—54no—
420C22×C4—51no—
421C22×C4—54no—
422C22×C4—54no—
423C22×C4—54no—
424C22×C4—54no—
425C22×C4—104no—
426C22×C4—1032no—
427C22×C4—104no—
428C22×C4—104no—
429C22×C4—104no—
430C22×C4C3×C4×D514yes—
431C22×C4C22×C3×D514yes—
432C22×C4C22×C3×D511yescharacteristic
433C22×C4C22×C3×D511yescharacteristic
434C4⋊C4—24no—
435C4⋊C4—104no—
436C22⋊C4—24no—
437C22⋊C4—108no—
438C22⋊C4—108no—
439C22⋊C4—104no—
440C42—108no—
441C3×C5#228011yescharacteristic, complemented, Hall
442C22×C3—22no—
443C22×C3—22no—
444C22×C3—24no—
445C22×C3—24no—
446C22×C3—54no—
447C22×C3—54no—
448C22×C3—1032no—
449C22×C3—102no—
450C22×C3—102no—
451C22×C3—102no—
452C22×C3—102no—
453C22×C3—104no—
454C22×C3—104no—
455C22×C3—104no—
456C22×C3—104no—
457C22×C3#403814yescomplemented
458C22×C3C22×C4×D511yescharacteristic
459C22×C3C2×D4×D512yes—
460C22×C3C2×#71111yescharacteristic
461C22×C3C2×#71311yescharacteristic
462C22×C3D5×#4112yes—
463C3×C4—22no—
464C3×C4—44no—
465C3×C4—54no—
466C3×C4—102no—
467C3×C4—204no—
468C3×C4D5×C22⋊C414yes—
469C2×C5—24no—
470C2×C5C22×C3×C22⋊C411yescharacteristic
471C2×C5C2×C3×#11711yescharacteristic
472C2×C5C2×C3×#11711yescharacteristic
473C2×C5C3×#52512yes—
474C2×C5C3×#52512yes—
475D5—24no—
476D5—24no—
477C23—22no—
478C23—22no—
479C23—52no—
480C23—52no—
481C23—54no—
482C23—54no—
483C23—108no—
484C23—108no—
485C23—1016no—
486C23—1016no—
487C23—102no—
488C23—101no—
489C23—101no—
490C23—101no—
491C23—101no—
492C23—102no—
493C23—108no—
494C23C2×C3×C4×D512yes—
495C23C3×#71112yes—
496C23C3×#71312yes—
497C23C23×C3×D511yescharacteristic
498C2×C4—22no—
499C2×C4—28no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—52no—
504C2×C4—54no—
505C2×C4—516no—
506C2×C4—52no—
507C2×C4—108no—
508C2×C4—108no—
509C2×C4—108no—
510C2×C4—102no—
511C2×C4—108no—
512C2×C4—104no—
513C2×C4—104no—
514C2×C4—104no—
515C2×C4C2×C3×C4×D512yes—
516C2×C4C2×C3×C4×D512yes—
517C2×C4C3×D4×D514yes—
518C2×C3—24no—
519C2×C3—104no—
520C2×C3—104no—
521C2×C3C2×D5×C22⋊C411yescharacteristic
522C2×C3C2×#403811yescharacteristic
523C2×C3D5×#11711yescharacteristic
524C2×C3#6594012yes—
525C2×C3#6596112yes—
526C5C3×#228011yescharacteristic, complemented, Sylow
527C22—22no—
528C22—24no—
529C22—24no—
530C22—22no—
531C22—54no—
532C22—54no—
533C22—1032no—
534C22—102no—
535C22—104no—
536C22—104no—
537C22—104no—
538C22—104no—
539C22—102no—
540C22—102no—
541C22—102no—
542C22C3×#403814yescomplemented
543C22C22×C3×C4×D511yescharacteristic
544C22C2×C3×D4×D512yes—
545C22C2×C3×#71111yescharacteristic
546C22C2×C3×#71311yescharacteristic
547C22C3×D5×#4112yes—
548C4—22no—
549C4—44no—
550C4—54no—
551C4—102no—
552C4—204no—
553C4C3×D5×C22⋊C414yes—
554C3#1060559311yescharacteristic, direct product factor, Sylow
555C2—24no—
556C2—104no—
557C2—104no—
558C2C2×C3×D5×C22⋊C411yescharacteristic
559C2C2×C3×#403811yescharacteristic
560C2C3×D5×#11711yescharacteristic
561C2C3×#6594012yes—
562C2C3×#6596112yes—
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#380C2
socleC23×C3×C5C24
prime radicalC24×C3×D5C22
cosocleC23×C5C24×C3
hypercenterC3×#380D5
hypocenterC5C3×#2280
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#380

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4038C2semidirect
3. C3×C5×#380C2semidirect
4. C3×#65501C2semidirect
5. C3×#65276C2semidirect
7. C3×C22⋊C4×Dic5C2semidirect
8. C3×#64955C2semidirect
9. C3×#64953C2semidirect
10. #10605593C3direct (N × H)
15. C22×C3×C4×D5C4semidirect
20. C2×C3×C5×C4⋊C4C22semidirect
25. C2×C3×C4⋊Dic5C22semidirect
26. C2×C3×C4×Dic5C22semidirect
28. C3×C5×#95C22semidirect
29. C3×#3963C22semidirect
30. C3×#3963C22semidirect
33. C2×#4038C2×C3semidirect
34. C5×#380C2×C3semidirect
35. #65501C2×C3semidirect
36. #65276C2×C3semidirect
38. C22⋊C4×Dic5C2×C3semidirect
39. #64955C2×C3semidirect
40. #64953C2×C3semidirect
80. C3×#380D5semidirect
88. C22×C4×D5C3×C4semidirect
93. C2×C5×C4⋊C4C22×C3semidirect
98. C2×C4⋊Dic5C22×C3semidirect
99. C2×C4×Dic5C22×C3semidirect
101. C5×#95C22×C3semidirect
102. #3963C22×C3semidirect
103. #3963C22×C3semidirect
145. C3×C4×D5C22⋊C4semidirect
157. C2×C3×C4⋊C4C2×D5semidirect
165. C3×#95C2×D5semidirect
205. #380C3×D5semidirect
213. C22×C3×C5#117semidirect
229. C2×C3×D5#117semidirect
310. C4×D5C3×C22⋊C4semidirect
322. C2×C4⋊C4C2×C3×D5semidirect
330. #95C2×C3×D5semidirect
384. C22×C5C3×#117semidirect
400. C2×D5C3×#117semidirect
441. C3×C5#2280semidirect
457. C22×C3#4038semidirect
526. C5C3×#2280semidirect
542. C22C3×#4038semidirect
554. C3#10605593direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C4×D52
C2×C3×#40382
C3×C5×#3802
C3×#655012
C3×#652762
C3×#652442
C3×C22⋊C4×Dic52
C3×#649552
C3×#649532
#106055933
C3×#22805