Finite Group Databasebeta

← C3×#10613969 #14326579

Subgroups — C3×#10613969 #14326579

Order 1920.

1208 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#117C211yesmaximal, characteristic
2C22×C3×#683C211yesmaximal, characteristic
3C2×C3×#4023C211yesmaximal, characteristic
4C3×#65500C211yesmaximal, characteristic
5C3×#65267C212yesmaximal, complemented
6C3×#65261C212yesmaximal, complemented
7C3×#65232C211yesmaximal, characteristic
8C3×#65231C211yesmaximal, characteristic
9C3×C22⋊C4×Dic5C211yesmaximal, characteristic
10C3×#65222C212yesmaximal, complemented
11C3×C4×#683C212yesmaximal, complemented
12#10613969C311yesmaximal, characteristic, direct product factor, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C23×C3×Dic5C2211yescharacteristic
15C23×C3×Dic5C2211yescharacteristic
16C3×C5×#117—24no—
17C2×C3×C5×C4⋊C4C2212yes—
18C2×C3×C5×C22⋊C4C2211yescharacteristic
19C2×C3×C5×C22⋊C4C2211yescharacteristic
20C2×C3×C42×C5C2212yes—
21C2×C3×C22⋊Dic5C2211yescharacteristic
22C2×C3×C22⋊Dic5C2211yescharacteristic
23C2×C3×#683C418yescomplemented
24C2×C3×#683C2212yes—
25C2×C3×#683C2212yes—
26C2×C3×#683C2211yescharacteristic
27C2×C3×#683C2211yescharacteristic
28C2×C3×#683C2211yescharacteristic
29C2×C3×#683C2211yescharacteristic
30C2×C3×C4×Dic5C2212yes—
31C2×C3×C4×Dic5C2212yes—
32C3×#4023—24no—
33C3×#3963C2212yes—
34C3×#3963C2212yes—
35C3×#3963C2212yes—
36C3×#3963C2212yes—
37C3×#3963C2212yes—
38C3×#3963C2212yes—
39C3×#2344—51nomaximal, Hall
40C2×C5×#117C2×C311yescharacteristic
41C22×#683C2×C311yescharacteristic
42C2×#4023C2×C311yescharacteristic
43#65500C2×C311yescharacteristic
44#65267C2×C312yescomplemented
45#65261C2×C312yescomplemented
46#65232C2×C311yescharacteristic
47#65231C2×C311yescharacteristic
48C22⋊C4×Dic5C2×C311yescharacteristic
49#65222C2×C312yescomplemented
50C4×#683C2×C312yescomplemented
51C24×C3×C5C2311yescharacteristic
52C22×C3×C4×C5—22no—
53C22×C3×C4×C5—22no—
54C22×C3×C4×C5C2×C414yes—
55C22×C3×C4×C5C2312yes—
56C22×C3×C4×C5C2311yescharacteristic
57C22×C3×C4×C5C2311yescharacteristic
58C22×C3×C4×C5C2312yes—
59C22×C3×Dic5—22no—
60C22×C3×Dic5—22no—
61C22×C3×Dic5—24no—
62C22×C3×Dic5C2×C414yes—
63C22×C3×Dic5C2×C414yes—
64C22×C3×Dic5C2312yes—
65C22×C3×Dic5C2312yes—
66C22×C3×Dic5C2311yescharacteristic
67C22×C3×Dic5C2311yescharacteristic
68C22×C3×Dic5C2311yescharacteristic
69C22×C3×Dic5C2311yescharacteristic
70C3×C5×C4⋊C4—24no—
71C3×C5×C22⋊C4—22no—
72C3×C5×C22⋊C4D414yes—
73C3×C42×C5—24no—
74C3×C22⋊Dic5—22no—
75C3×C22⋊Dic5—22no—
76C3×#683—24no—
77C3×#683—24no—
78C3×#683C2×C414yes—
79C3×#683C2×C414yes—
80C3×#683C2×C414yes—
81C3×#683C2×C414yes—
82C3×C4×Dic5—24no—
83C3×C4×Dic5—24no—
84C2×C3×#117—51no—
85C2×C3×#117D511yescharacteristic
86C22×C3×C4⋊C4—51no—
87C3×#389—52no—
88C3×#387—52no—
89C3×#387—52no—
90C3×#381—51no—
91C3×#381—51no—
92C3×#380—51no—
93C3×C4×C4⋊C4—52no—
94C3×C4×C22⋊C4—51no—
95C23×C4×C5C22×C311yescharacteristic
96C23×Dic5C22×C311yescharacteristic
97C23×Dic5C22×C311yescharacteristic
98C5×#117—24no—
99C2×C5×C4⋊C4C22×C312yes—
100C2×C5×C22⋊C4C22×C311yescharacteristic
101C2×C5×C22⋊C4C22×C311yescharacteristic
102C2×C42×C5C22×C312yes—
103C2×C22⋊Dic5C22×C311yescharacteristic
104C2×C22⋊Dic5C22×C311yescharacteristic
105C2×#683C3×C418yescomplemented
106C2×#683C22×C312yes—
107C2×#683C22×C312yes—
108C2×#683C22×C311yescharacteristic
109C2×#683C22×C311yescharacteristic
110C2×#683C22×C311yescharacteristic
111C2×#683C22×C311yescharacteristic
112C2×C4×Dic5C22×C312yes—
113C2×C4×Dic5C22×C312yes—
114#4023—24no—
115#3963C22×C312yes—
116#3963C22×C312yes—
117#3963C22×C312yes—
118#3963C22×C312yes—
119#3963C22×C312yes—
120#3963C22×C312yes—
121#2344—51noSylow
122C23×C3×C5—22no—
123C23×C3×C5—22no—
124C23×C3×C5C22×C412yes—
125C23×C3×C5C2×D412yes—
126C23×C3×C5#4112yes—
127C23×C3×C5C2411yescharacteristic
128C2×C3×C4×C5—28no—
129C2×C3×C4×C5—21no—
130C2×C3×C4×C5—21no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5—21no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5C22×C412yes—
139C2×C3×C4×C5C22×C412yes—
140C2×C3×C4×C5C2×D414yes—
141C2×C3×Dic5—28no—
142C2×C3×Dic5—21no—
143C2×C3×Dic5—21no—
144C2×C3×Dic5—22no—
145C2×C3×Dic5—21no—
146C2×C3×Dic5—21no—
147C2×C3×Dic5—28no—
148C2×C3×Dic5—22no—
149C2×C3×Dic5—22no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—22no—
152C2×C3×Dic5—22no—
153C2×C3×Dic5—22no—
154C2×C3×Dic5C22×C412yes—
155C2×C3×Dic5C22×C412yes—
156C2×C3×Dic5C22×C412yes—
157C2×C3×Dic5C22×C412yes—
158C2×C3×Dic5#4114yes—
159C23×C3×C4—51no—
160C23×C3×C4—51no—
161C23×C3×C4C2×D511yescharacteristic
162C3×#117—24no—
163C3×#117—104no—
164C2×C3×C4⋊C4—58no—
165C2×C3×C4⋊C4—51no—
166C2×C3×C4⋊C4—51no—
167C2×C3×C4⋊C4—51no—
168C2×C3×C4⋊C4—51no—
169C2×C3×C4⋊C4—52no—
170C2×C3×C4⋊C4—52no—
171C2×C3×C4⋊C4C2×D512yes—
172C2×C3×C22⋊C4—51no—
173C2×C3×C22⋊C4—51no—
174C2×C3×C22⋊C4C2×D511yescharacteristic
175C2×C3×C22⋊C4C2×D511yescharacteristic
176C2×C3×C42—52no—
177C2×C3×C42—52no—
178C2×C3×C42C2×D512yes—
179C3×#95—52no—
180C3×#95—52no—
181C3×#95—52no—
182C3×#95—52no—
183C3×#95—52no—
184C3×#95—52no—
185C24×C5C23×C311yescharacteristic
186C22×C4×C5—22no—
187C22×C4×C5—22no—
188C22×C4×C5C2×C3×C414yes—
189C22×C4×C5C23×C312yes—
190C22×C4×C5C23×C311yescharacteristic
191C22×C4×C5C23×C311yescharacteristic
192C22×C4×C5C23×C312yes—
193C22×Dic5—22no—
194C22×Dic5—22no—
195C22×Dic5—24no—
196C22×Dic5C2×C3×C414yes—
197C22×Dic5C2×C3×C414yes—
198C22×Dic5C23×C312yes—
199C22×Dic5C23×C312yes—
200C22×Dic5C23×C311yescharacteristic
201C22×Dic5C23×C311yescharacteristic
202C22×Dic5C23×C311yescharacteristic
203C22×Dic5C23×C311yescharacteristic
204C5×C4⋊C4—24no—
205C5×C22⋊C4—22no—
206C5×C22⋊C4C3×D414yes—
207C42×C5—24no—
208C22⋊Dic5—22no—
209C22⋊Dic5—22no—
210#683—24no—
211#683—24no—
212#683C2×C3×C414yes—
213#683C2×C3×C414yes—
214#683C2×C3×C414yes—
215#683C2×C3×C414yes—
216C4×Dic5—24no—
217C4×Dic5—24no—
218C2×#117—51no—
219C2×#117C3×D511yescharacteristic
220C22×C4⋊C4—51no—
221#389—52no—
222#387—52no—
223#387—52no—
224#381—51no—
225#381—51no—
226#380—51no—
227C4×C4⋊C4—52no—
228C4×C22⋊C4—51no—
229C22×C3×C5—22no—
230C22×C3×C5—22no—
231C22×C3×C5—24no—
232C22×C3×C5—24no—
233C22×C3×C5C4×D414yes—
234C22×C3×C5C23×C411yescharacteristic
235C22×C3×C5C22×D411yescharacteristic
236C22×C3×C5C2×#4111yescharacteristic
237C22×C3×C5C2×#4112yes—
238C22×C3×C52−1+412yes—
239C3×C4×C5—22no—
240C3×C4×C5—22no—
241C3×C4×C5—24no—
242C3×C4×C5—42no—
243C3×Dic5—22no—
244C3×Dic5—22no—
245C3×Dic5—22no—
246C3×Dic5—42no—
247C3×Dic5—42no—
248C3×Dic5#11714yescomplemented
249C24×C3C22×D511yescharacteristic
250C22×C3×C4—22no—
251C22×C3×C4—22no—
252C22×C3×C4—51no—
253C22×C3×C4—54no—
254C22×C3×C4—54no—
255C22×C3×C4—51no—
256C22×C3×C4—51no—
257C22×C3×C4—51no—
258C22×C3×C4—52no—
259C22×C3×C4—52no—
260C22×C3×C4—104no—
261C22×C3×C4—102no—
262C22×C3×C4—102no—
263C22×C3×C4C4×D514yes—
264C22×C3×C4C22×D512yes—
265C22×C3×C4C22×D511yescharacteristic
266C22×C3×C4C22×D511yescharacteristic
267C22×C3×C4C22×D512yes—
268C3×C4⋊C4—24no—
269C3×C4⋊C4—54no—
270C3×C4⋊C4—54no—
271C3×C4⋊C4—54no—
272C3×C4⋊C4—54no—
273C3×C4⋊C4—104no—
274C3×C4⋊C4—104no—
275C3×C22⋊C4—22no—
276C3×C22⋊C4—102no—
277C3×C22⋊C4—102no—
278C3×C22⋊C4C22⋊D514yes—
279C3×C42—24no—
280C3×C42—104no—
281C3×C42—104no—
282C23×C5—22no—
283C23×C5—22no—
284C23×C5C22×C3×C412yes—
285C23×C5C2×C3×D412yes—
286C23×C5C3×#4112yes—
287C23×C5C24×C311yescharacteristic
288C2×C4×C5—28no—
289C2×C4×C5—21no—
290C2×C4×C5—21no—
291C2×C4×C5—22no—
292C2×C4×C5—21no—
293C2×C4×C5—21no—
294C2×C4×C5—22no—
295C2×C4×C5—22no—
296C2×C4×C5—22no—
297C2×C4×C5—22no—
298C2×C4×C5C22×C3×C412yes—
299C2×C4×C5C22×C3×C412yes—
300C2×C4×C5C2×C3×D414yes—
301C2×Dic5—28no—
302C2×Dic5—21no—
303C2×Dic5—21no—
304C2×Dic5—21no—
305C2×Dic5—21no—
306C2×Dic5—22no—
307C2×Dic5—28no—
308C2×Dic5—22no—
309C2×Dic5—22no—
310C2×Dic5—22no—
311C2×Dic5—22no—
312C2×Dic5—22no—
313C2×Dic5—22no—
314C2×Dic5C22×C3×C412yes—
315C2×Dic5C22×C3×C412yes—
316C2×Dic5C22×C3×C412yes—
317C2×Dic5C22×C3×C412yes—
318C2×Dic5C3×#4114yes—
319C23×C4—51no—
320C23×C4—51no—
321C23×C4C2×C3×D511yescharacteristic
322#117—24no—
323#117—104no—
324C2×C4⋊C4—58no—
325C2×C4⋊C4—51no—
326C2×C4⋊C4—51no—
327C2×C4⋊C4—51no—
328C2×C4⋊C4—51no—
329C2×C4⋊C4—52no—
330C2×C4⋊C4—52no—
331C2×C4⋊C4C2×C3×D512yes—
332C2×C22⋊C4—51no—
333C2×C22⋊C4—51no—
334C2×C22⋊C4C2×C3×D511yescharacteristic
335C2×C22⋊C4C2×C3×D511yescharacteristic
336C2×C42—52no—
337C2×C42—52no—
338C2×C42C2×C3×D512yes—
339#95—52no—
340#95—52no—
341#95—52no—
342#95—52no—
343#95—52no—
344#95—52no—
345C2×C3×C5—24no—
346C2×C3×C5C2×#11711yescharacteristic
347C2×C3×C5C2×C4×D411yescharacteristic
348C2×C3×C5#51911yescharacteristic
349C2×C3×C5#54712yes—
350C2×C3×C5#55212yes—
351C23×C3—22no—
352C23×C3—22no—
353C23×C3C2×C4×D512yes—
354C23×C3#70912yes—
355C23×C3C2×C22⋊D512yes—
356C23×C3C23×D511yescharacteristic
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—28no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—52no—
368C2×C3×C4—54no—
369C2×C3×C4—52no—
370C2×C3×C4—52no—
371C2×C3×C4—52no—
372C2×C3×C4—108no—
373C2×C3×C4—101no—
374C2×C3×C4—101no—
375C2×C3×C4—102no—
376C2×C3×C4—101no—
377C2×C3×C4—101no—
378C2×C3×C4—108no—
379C2×C3×C4—102no—
380C2×C3×C4—102no—
381C2×C3×C4—102no—
382C2×C3×C4—102no—
383C2×C3×C4—102no—
384C2×C3×C4—102no—
385C2×C3×C4C2×C4×D512yes—
386C2×C3×C4C2×C4×D512yes—
387C2×C3×C4C2×C22⋊D514yes—
388C22×C5—22no—
389C22×C5—22no—
390C22×C5—24no—
391C22×C5—24no—
392C22×C5C3×C4×D414yes—
393C22×C5C23×C3×C411yescharacteristic
394C22×C5C22×C3×D411yescharacteristic
395C22×C5C2×C3×#4111yescharacteristic
396C22×C5C2×C3×#4112yes—
397C22×C5C3×2−1+412yes—
398C4×C5—22no—
399C4×C5—22no—
400C4×C5—24no—
401C4×C5—42no—
402Dic5—22no—
403Dic5—22no—
404Dic5—22no—
405Dic5—42no—
406Dic5—42no—
407Dic5C3×#11714yescomplemented
408C24C22×C3×D511yescharacteristic
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—51no—
412C22×C4—54no—
413C22×C4—54no—
414C22×C4—51no—
415C22×C4—51no—
416C22×C4—51no—
417C22×C4—52no—
418C22×C4—52no—
419C22×C4—104no—
420C22×C4—102no—
421C22×C4—102no—
422C22×C4C3×C4×D514yes—
423C22×C4C22×C3×D512yes—
424C22×C4C22×C3×D511yescharacteristic
425C22×C4C22×C3×D511yescharacteristic
426C22×C4C22×C3×D512yes—
427C4⋊C4—24no—
428C4⋊C4—54no—
429C4⋊C4—54no—
430C4⋊C4—54no—
431C4⋊C4—54no—
432C4⋊C4—104no—
433C4⋊C4—104no—
434C22⋊C4—22no—
435C22⋊C4—102no—
436C22⋊C4—102no—
437C22⋊C4C3×C22⋊D514yes—
438C42—24no—
439C42—104no—
440C42—104no—
441C3×C5#234411yescharacteristic, complemented, Hall
442C22×C3—22no—
443C22×C3—22no—
444C22×C3—24no—
445C22×C3—24no—
446C22×C3C4×C22⋊D514yes—
447C22×C3C22×C4×D511yescharacteristic
448C22×C3C2×#70911yescharacteristic
449C22×C3D5×#4112yes—
450C22×C3#415012yes—
451C22×C3C22×C22⋊D511yescharacteristic
452C3×C4—22no—
453C3×C4—22no—
454C3×C4—24no—
455C3×C4—42no—
456C3×C4—54no—
457C3×C4—102no—
458C3×C4—102no—
459C3×C4—102no—
460C3×C4—202no—
461C3×C4—202no—
462C2×C5—24no—
463C2×C5C2×C3×#11711yescharacteristic
464C2×C5C2×C3×C4×D411yescharacteristic
465C2×C5C3×#51911yescharacteristic
466C2×C5C3×#54712yes—
467C2×C5C3×#55212yes—
468C23—22no—
469C23—22no—
470C23C2×C3×C4×D512yes—
471C23C3×#70912yes—
472C23C2×C3×C22⋊D512yes—
473C23C23×C3×D511yescharacteristic
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—28no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—52no—
485C2×C4—54no—
486C2×C4—52no—
487C2×C4—52no—
488C2×C4—52no—
489C2×C4—108no—
490C2×C4—101no—
491C2×C4—101no—
492C2×C4—102no—
493C2×C4—101no—
494C2×C4—101no—
495C2×C4—108no—
496C2×C4—102no—
497C2×C4—102no—
498C2×C4—102no—
499C2×C4—102no—
500C2×C4—102no—
501C2×C4—102no—
502C2×C4C2×C3×C4×D512yes—
503C2×C4C2×C3×C4×D512yes—
504C2×C4C2×C3×C22⋊D514yes—
505C2×C3—24no—
506C2×C3#6585011yescharacteristic
507C2×C3D5×#11711yescharacteristic
508C2×C3#6586512yes—
509C2×C3C2×C4×C22⋊D511yescharacteristic
510C2×C3#6615812yes—
511C5C3×#234411yescharacteristic, complemented, Sylow
512C22—22no—
513C22—22no—
514C22—24no—
515C22—24no—
516C22C3×C4×C22⋊D514yes—
517C22C22×C3×C4×D511yescharacteristic
518C22C2×C3×#70911yescharacteristic
519C22C3×D5×#4112yes—
520C22C3×#415012yes—
521C22C22×C3×C22⋊D511yescharacteristic
522C4—22no—
523C4—22no—
524C4—24no—
525C4—42no—
526C4—54no—
527C4—102no—
528C4—102no—
529C4—102no—
530C4—202no—
531C4—202no—
532C3#1061396911yescharacteristic, direct product factor, Sylow
533C2—24no—
534C2C3×#6585011yescharacteristic
535C2C3×D5×#11711yescharacteristic
536C2C3×#6586512yes—
537C2C2×C3×C4×C22⋊D511yescharacteristic
538C2C3×#6615812yes—
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC2×C3×C5×#117C2
socleC23×C3×C5C24
prime radicalC24×C3×C5C23
cosocleC23×C5C24×C3
hypercenterC2×C3×#117D5
hypocenterC5C3×#2344
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×#117

Complements

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

NH ≅ G/Ntype
5. C3×#65267C2semidirect
6. C3×#65261C2semidirect
10. C3×#65222C2semidirect
11. C3×C4×#683C2semidirect
12. #10613969C3direct (N × H)
23. C2×C3×#683C4semidirect
44. #65267C2×C3semidirect
45. #65261C2×C3semidirect
49. #65222C2×C3semidirect
50. C4×#683C2×C3semidirect
105. C2×#683C3×C4semidirect
248. C3×Dic5#117semidirect
407. Dic5C3×#117semidirect
441. C3×C5#2344semidirect
511. C5C3×#2344semidirect
532. C3#10613969direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1172
C22×C3×#6832
C2×C3×#40232
C3×#655002
C3×#652672
C3×#652612
C3×#652322
C3×#652312
C3×C22⋊C4×Dic52
C3×#652222
C3×C4×#6832
#106139693
C3×#23445