Finite Group Databasebeta

← C3×#10605498 #14326564

Subgroups — C3×#10605498 #14326564

Order 1920.

1208 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
1C2×C3×D5×C4⋊C4C211yesmaximal, characteristic
2C2×C3×#4018C212yesmaximal
3C3×C4×C5×C4⋊C4C211yesmaximal, characteristic, complemented
4C3×#65276C211yesmaximal, characteristic
5C3×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
6C3×#65262C211yesmaximal, characteristic, complemented
7C3×C4×#685C211yesmaximal, characteristic
8C3×#65222C212yesmaximal, complemented
9C3×#65217C211yesmaximal, characteristic, complemented
10C3×#64953C212yesmaximal
11C3×#64941C212yesmaximal, complemented
12#10605498C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C4×D5C2212yes—
14C22×C3×C4×D5C2211yescharacteristic
15C2×C3×C5×C4⋊C4C2211yescharacteristic
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17C2×C3×C42×C5C2211yescharacteristic
18C2×C3×C42×C5C2212yes—
19C2×C3×#685C2211yescharacteristic
20C2×C3×#685C2212yes—
21C2×C3×#685C2211yescharacteristic
22C2×C3×C4⋊Dic5C2211yescharacteristic
23C2×C3×C4⋊Dic5C2211yescharacteristic
24C2×C3×#683C2212yes—
25C2×C3×#683C2212yes—
26C2×C3×#683C2212yes—
27C2×C3×C4×Dic5C2212yes—
28C2×C3×C4×Dic5C2211yescharacteristic
29C3×D5×C4⋊C4C418yescomplemented
30C3×#4018—28no—
31C3×C5×#95C2212yes—
32C3×#3963C2211yescharacteristic
33C3×#3963C2212yes—
34C3×#3963C2212yes—
35C3×#3963C2212yes—
36C3×#3963C2212yes—
37C3×#3963C2211yescharacteristic
38C3×#2344—51nomaximal, Hall
39C2×D5×C4⋊C4C2×C311yescharacteristic
40C2×#4018C2×C312yes—
41C4×C5×C4⋊C4C2×C311yescharacteristic, complemented
42#65276C2×C311yescharacteristic
43C4⋊C4×Dic5C2×C311yescharacteristic, complemented
44#65262C2×C311yescharacteristic, complemented
45C4×#685C2×C311yescharacteristic
46#65222C2×C312yescomplemented
47#65217C2×C311yescharacteristic, complemented
48#64953C2×C312yes—
49#64941C2×C312yescomplemented
50C23×C3×D5C2311yescharacteristic
51C22×C3×C4×C5C2311yescharacteristic
52C22×C3×C4×C5C2312yes—
53C22×C3×C4×C5C2312yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×C3×C4×C5C2311yescharacteristic
56C22×C3×Dic5C2311yescharacteristic
57C22×C3×Dic5C2312yes—
58C22×C3×Dic5C2311yescharacteristic
59C22×C3×Dic5C2312yes—
60C22×C3×Dic5C2311yescharacteristic
61C2×C3×C4×D5—24no—
62C2×C3×C4×D5—24no—
63C2×C3×C4×D5—22no—
64C2×C3×C4×D5—22no—
65C2×C3×C4×D5C2×C418yes—
66C2×C3×C4×D5C2×C414yes—
67C3×C5×C4⋊C4—22no—
68C3×C5×C4⋊C4C2×C414yes—
69C3×C42×C5—24no—
70C3×C42×C5—22no—
71C3×#685—24no—
72C3×#685—22no—
73C3×#685D414yes—
74C3×C4⋊Dic5—22no—
75C3×C4⋊Dic5C2×C414yes—
76C3×#683—24no—
77C3×#683—24no—
78C3×#683C2×C418yes—
79C3×C4×Dic5—22no—
80C3×C4×Dic5—24no—
81C2×C3×#117—52no—
82C22×C3×C4⋊C4—51no—
83C3×#389—51no—
84C3×#389—51no—
85C3×#387—52no—
86C3×#387—52no—
87C3×#381—52no—
88C3×#380—51no—
89C3×C4×C4⋊C4—51no—
90C3×C4×C4⋊C4D511yescharacteristic, complemented
91C3×C4×C22⋊C4—51no—
92C22×C4×D5C22×C312yes—
93C22×C4×D5C22×C311yescharacteristic
94C2×C5×C4⋊C4C22×C311yescharacteristic
95C2×C5×C4⋊C4C22×C311yescharacteristic
96C2×C42×C5C22×C312yes—
97C2×C42×C5C22×C311yescharacteristic
98C2×#685C22×C312yes—
99C2×#685C22×C311yescharacteristic
100C2×#685C22×C311yescharacteristic
101C2×C4⋊Dic5C22×C311yescharacteristic
102C2×C4⋊Dic5C22×C311yescharacteristic
103C2×#683C22×C312yes—
104C2×#683C22×C312yes—
105C2×#683C22×C312yes—
106C2×C4×Dic5C22×C312yes—
107C2×C4×Dic5C22×C311yescharacteristic
108D5×C4⋊C4C3×C418yescomplemented
109#4018—28no—
110C5×#95C22×C312yes—
111#3963C22×C311yescharacteristic
112#3963C22×C312yes—
113#3963C22×C312yes—
114#3963C22×C312yes—
115#3963C22×C312yes—
116#3963C22×C311yescharacteristic
117#2344—51noSylow
118C23×C3×C5C2411yescharacteristic
119C22×C3×D5—21no—
120C22×C3×D5—21no—
121C22×C3×D5—21no—
122C22×C3×D5—21no—
123C22×C3×D5C22×C412yes—
124C22×C3×D5C2×D412yes—
125C22×C3×D5#4112yes—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5—21no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5—21no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—21no—
136C2×C3×C4×C5C22×C414yes—
137C2×C3×C4×C5C22×C412yes—
138C2×C3×C4×C5C2×D412yes—
139C2×C3×C4×C5#4112yes—
140C2×C3×C4×C5#4112yes—
141C2×C3×Dic5—22no—
142C2×C3×Dic5—21no—
143C2×C3×Dic5—21no—
144C2×C3×Dic5—21no—
145C2×C3×Dic5—22no—
146C2×C3×Dic5—21no—
147C2×C3×Dic5—22no—
148C2×C3×Dic5—21no—
149C2×C3×Dic5—22no—
150C2×C3×Dic5—21no—
151C2×C3×Dic5—22no—
152C2×C3×Dic5—21no—
153C2×C3×Dic5C22×C412yes—
154C2×C3×Dic5C22×C414yes—
155C2×C3×Dic5C2×D412yes—
156C3×C4×D5—216no—
157C3×C4×D5—28no—
158C23×C3×C4—51no—
159C23×C3×C4—52no—
160C3×#117—108no—
161C2×C3×C4⋊C4—52no—
162C2×C3×C4⋊C4—51no—
163C2×C3×C4⋊C4—58no—
164C2×C3×C4⋊C4—51no—
165C2×C3×C4⋊C4—52no—
166C2×C3×C4⋊C4—52no—
167C2×C3×C4⋊C4C2×D511yescharacteristic
168C2×C3×C4⋊C4C2×D511yescharacteristic
169C2×C3×C22⋊C4—51no—
170C2×C3×C22⋊C4—51no—
171C2×C3×C22⋊C4—52no—
172C2×C3×C42—51no—
173C2×C3×C42—52no—
174C2×C3×C42C2×D511yescharacteristic
175C2×C3×C42C2×D512yes—
176C3×#95—51no—
177C3×#95—51no—
178C3×#95—52no—
179C3×#95—52no—
180C3×#95—52no—
181C3×#95—52no—
182C3×#95C2×D512yes—
183C23×D5C23×C311yescharacteristic
184C22×C4×C5C23×C312yes—
185C22×C4×C5C23×C311yescharacteristic
186C22×C4×C5C23×C312yes—
187C22×C4×C5C23×C311yescharacteristic
188C22×C4×C5C23×C311yescharacteristic
189C22×Dic5C23×C311yescharacteristic
190C22×Dic5C23×C312yes—
191C22×Dic5C23×C311yescharacteristic
192C22×Dic5C23×C312yes—
193C22×Dic5C23×C311yescharacteristic
194C2×C4×D5—24no—
195C2×C4×D5—24no—
196C2×C4×D5—22no—
197C2×C4×D5—22no—
198C2×C4×D5C2×C3×C418yes—
199C2×C4×D5C2×C3×C414yes—
200C5×C4⋊C4—22no—
201C5×C4⋊C4C2×C3×C414yes—
202C42×C5—24no—
203C42×C5—22no—
204#685—24no—
205#685—22no—
206#685C3×D414yes—
207C4⋊Dic5—22no—
208C4⋊Dic5C2×C3×C414yes—
209#683—24no—
210#683—24no—
211#683C2×C3×C418yes—
212C4×Dic5—22no—
213C4×Dic5—24no—
214C2×#117—52no—
215C22×C4⋊C4—51no—
216#389—51no—
217#389—51no—
218#387—52no—
219#387—52no—
220#381—52no—
221#380—51no—
222C4×C4⋊C4—51no—
223C4×C4⋊C4C3×D511yescharacteristic, complemented
224C4×C22⋊C4—51no—
225C22×C3×C5C23×C411yescharacteristic
226C22×C3×C5C22×D411yescharacteristic
227C22×C3×C5C2×#4111yescharacteristic
228C22×C3×C5C2×#4111yescharacteristic
229C22×C3×C5C2×#4111yescharacteristic
230C22×C3×C52−1+411yescharacteristic
231C22×C3×C52−1+411yescharacteristic
232C2×C3×D5—22no—
233C2×C3×D5—22no—
234C2×C3×D5—22no—
235C2×C3×D5—22no—
236C2×C3×D5—22no—
237C2×C3×D5—22no—
238C2×C3×D5C4×D414yes—
239C3×C4×C5—24no—
240C3×C4×C5—22no—
241C3×C4×C5—42no—
242C3×C4×C5—41no—
243C3×C4×C5#11714yescomplemented
244C3×Dic5—22no—
245C3×Dic5—24no—
246C3×Dic5—22no—
247C3×Dic5—42no—
248C3×Dic5—41no—
249C24×C3—51no—
250C22×C3×C4—51no—
251C22×C3×C4—52no—
252C22×C3×C4—51no—
253C22×C3×C4—58no—
254C22×C3×C4—54no—
255C22×C3×C4—51no—
256C22×C3×C4—52no—
257C22×C3×C4—104no—
258C22×C3×C4—104no—
259C22×C3×C4—102no—
260C22×C3×C4—102no—
261C22×C3×C4C22×D511yescharacteristic
262C22×C3×C4C22×D512yes—
263C22×C3×C4C22×D512yes—
264C22×C3×C4C22×D511yescharacteristic
265C22×C3×C4C22×D511yescharacteristic
266C3×C4⋊C4—22no—
267C3×C4⋊C4—58no—
268C3×C4⋊C4—54no—
269C3×C4⋊C4—104no—
270C3×C4⋊C4—102no—
271C3×C4⋊C4—104no—
272C3×C4⋊C4C4×D514yes—
273C3×C22⋊C4—54no—
274C3×C22⋊C4—102no—
275C3×C22⋊C4—104no—
276C3×C42—22no—
277C3×C42—24no—
278C3×C42—104no—
279C3×C42—102no—
280C23×C5C24×C311yescharacteristic
281C22×D5—21no—
282C22×D5—21no—
283C22×D5—21no—
284C22×D5—21no—
285C22×D5C22×C3×C412yes—
286C22×D5C2×C3×D412yes—
287C22×D5C3×#4112yes—
288C2×C4×C5—22no—
289C2×C4×C5—21no—
290C2×C4×C5—22no—
291C2×C4×C5—21no—
292C2×C4×C5—22no—
293C2×C4×C5—21no—
294C2×C4×C5—21no—
295C2×C4×C5—22no—
296C2×C4×C5—22no—
297C2×C4×C5—21no—
298C2×C4×C5C22×C3×C414yes—
299C2×C4×C5C22×C3×C412yes—
300C2×C4×C5C2×C3×D412yes—
301C2×C4×C5C3×#4112yes—
302C2×C4×C5C3×#4112yes—
303C2×Dic5—22no—
304C2×Dic5—21no—
305C2×Dic5—21no—
306C2×Dic5—21no—
307C2×Dic5—22no—
308C2×Dic5—21no—
309C2×Dic5—22no—
310C2×Dic5—21no—
311C2×Dic5—22no—
312C2×Dic5—21no—
313C2×Dic5—22no—
314C2×Dic5—21no—
315C2×Dic5C22×C3×C412yes—
316C2×Dic5C22×C3×C414yes—
317C2×Dic5C2×C3×D412yes—
318C4×D5—216no—
319C4×D5—28no—
320C23×C4—52no—
321C23×C4—51no—
322#117—108no—
323C2×C4⋊C4—52no—
324C2×C4⋊C4—51no—
325C2×C4⋊C4—58no—
326C2×C4⋊C4—52no—
327C2×C4⋊C4—52no—
328C2×C4⋊C4—51no—
329C2×C4⋊C4C2×C3×D511yescharacteristic
330C2×C4⋊C4C2×C3×D511yescharacteristic
331C2×C22⋊C4—51no—
332C2×C22⋊C4—52no—
333C2×C22⋊C4—51no—
334C2×C42—52no—
335C2×C42—51no—
336C2×C42C2×C3×D512yes—
337C2×C42C2×C3×D511yescharacteristic
338#95—51no—
339#95—51no—
340#95—52no—
341#95—52no—
342#95—52no—
343#95—52no—
344#95C2×C3×D512yes—
345C2×C3×C5C2×#11711yescharacteristic
346C2×C3×C5C2×C4×D411yescharacteristic
347C2×C3×C5#51911yescharacteristic
348C2×C3×C5#54711yescharacteristic
349C2×C3×C5#54711yescharacteristic
350C2×C3×C5#55211yescharacteristic
351C2×C3×C5#55211yescharacteristic
352C3×D5—24no—
353C23×C3—52no—
354C23×C3—52no—
355C23×C3—52no—
356C23×C3—101no—
357C23×C3—101no—
358C23×C3—101no—
359C23×C3—101no—
360C23×C3C23×D511yescharacteristic
361C2×C3×C4—21no—
362C2×C3×C4—22no—
363C2×C3×C4—21no—
364C2×C3×C4—22no—
365C2×C3×C4—21no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—22no—
371C2×C3×C4—52no—
372C2×C3×C4—54no—
373C2×C3×C4—52no—
374C2×C3×C4—1016no—
375C2×C3×C4—101no—
376C2×C3×C4—101no—
377C2×C3×C4—101no—
378C2×C3×C4—102no—
379C2×C3×C4—102no—
380C2×C3×C4—101no—
381C2×C3×C4—108no—
382C2×C3×C4—101no—
383C2×C3×C4—102no—
384C2×C3×C4—102no—
385C2×C3×C4—102no—
386C2×C3×C4—101no—
387C2×C3×C4—101no—
388C2×C3×C4C2×C4×D514yes—
389C2×C3×C4C2×C4×D512yes—
390C2×C3×C4#70912yes—
391C2×C3×C4#70912yes—
392C2×C3×C4D4×D512yes—
393C22×C5C23×C3×C411yescharacteristic
394C22×C5C22×C3×D411yescharacteristic
395C22×C5C2×C3×#4111yescharacteristic
396C22×C5C2×C3×#4111yescharacteristic
397C22×C5C2×C3×#4111yescharacteristic
398C22×C5C3×2−1+411yescharacteristic
399C22×C5C3×2−1+411yescharacteristic
400C2×D5—22no—
401C2×D5—22no—
402C2×D5—22no—
403C2×D5—22no—
404C2×D5—22no—
405C2×D5—22no—
406C2×D5C3×C4×D414yes—
407C4×C5—24no—
408C4×C5—22no—
409C4×C5—42no—
410C4×C5—41no—
411C4×C5C3×#11714yescomplemented
412Dic5—22no—
413Dic5—24no—
414Dic5—22no—
415Dic5—42no—
416Dic5—41no—
417C24—51no—
418C22×C4—51no—
419C22×C4—52no—
420C22×C4—51no—
421C22×C4—58no—
422C22×C4—54no—
423C22×C4—51no—
424C22×C4—52no—
425C22×C4—104no—
426C22×C4—104no—
427C22×C4—102no—
428C22×C4—102no—
429C22×C4C22×C3×D511yescharacteristic
430C22×C4C22×C3×D512yes—
431C22×C4C22×C3×D512yes—
432C22×C4C22×C3×D511yescharacteristic
433C22×C4C22×C3×D511yescharacteristic
434C4⋊C4—22no—
435C4⋊C4—58no—
436C4⋊C4—54no—
437C4⋊C4—104no—
438C4⋊C4—102no—
439C4⋊C4—104no—
440C4⋊C4C3×C4×D514yes—
441C22⋊C4—54no—
442C22⋊C4—104no—
443C22⋊C4—102no—
444C42—22no—
445C42—24no—
446C42—104no—
447C42—102no—
448C3×C5#234411yescharacteristic, complemented, Hall
449C22×C3—54no—
450C22×C3—102no—
451C22×C3—102no—
452C22×C3—102no—
453C22×C3—102no—
454C22×C3—102no—
455C22×C3—102no—
456C22×C3C22×C4×D511yescharacteristic
457C22×C3C2×#70911yescharacteristic
458C22×C3C2×#70911yescharacteristic
459C22×C3C2×D4×D511yescharacteristic
460C22×C3#414711yescharacteristic
461C22×C3D5×#4111yescharacteristic
462C22×C3#415011yescharacteristic
463C3×C4—22no—
464C3×C4—24no—
465C3×C4—41no—
466C3×C4—42no—
467C3×C4—102no—
468C3×C4—104no—
469C3×C4—102no—
470C3×C4—202no—
471C3×C4—201no—
472C3×C4#401814yescomplemented
473C2×C5C2×C3×#11711yescharacteristic
474C2×C5C2×C3×C4×D411yescharacteristic
475C2×C5C3×#51911yescharacteristic
476C2×C5C3×#54711yescharacteristic
477C2×C5C3×#54711yescharacteristic
478C2×C5C3×#55211yescharacteristic
479C2×C5C3×#55211yescharacteristic
480D5—24no—
481C23—52no—
482C23—52no—
483C23—52no—
484C23—101no—
485C23—101no—
486C23—101no—
487C23—101no—
488C23C23×C3×D511yescharacteristic
489C2×C4—21no—
490C2×C4—22no—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—21no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—54no—
500C2×C4—52no—
501C2×C4—52no—
502C2×C4—1016no—
503C2×C4—101no—
504C2×C4—101no—
505C2×C4—101no—
506C2×C4—102no—
507C2×C4—102no—
508C2×C4—101no—
509C2×C4—108no—
510C2×C4—101no—
511C2×C4—102no—
512C2×C4—102no—
513C2×C4—101no—
514C2×C4—102no—
515C2×C4—101no—
516C2×C4C2×C3×C4×D514yes—
517C2×C4C2×C3×C4×D512yes—
518C2×C4C3×#70912yes—
519C2×C4C3×#70912yes—
520C2×C4C3×D4×D512yes—
521C2×C3—104no—
522C2×C3C2×#401811yescharacteristic
523C2×C3#6584111yescharacteristic
524C2×C3#6586311yescharacteristic
525C2×C3C4×D4×D511yescharacteristic
526C2×C3#6588511yescharacteristic
527C2×C3#6590611yescharacteristic
528C2×C3#6591511yescharacteristic
529C5C3×#234411yescharacteristic, complemented, Sylow
530C22—54no—
531C22—102no—
532C22—102no—
533C22—102no—
534C22—102no—
535C22—102no—
536C22—102no—
537C22C22×C3×C4×D511yescharacteristic
538C22C2×C3×#70911yescharacteristic
539C22C2×C3×#70911yescharacteristic
540C22C2×C3×D4×D511yescharacteristic
541C22C3×#414711yescharacteristic
542C22C3×D5×#4111yescharacteristic
543C22C3×#415011yescharacteristic
544C4—24no—
545C4—22no—
546C4—41no—
547C4—42no—
548C4—104no—
549C4—102no—
550C4—102no—
551C4—201no—
552C4—202no—
553C4C3×#401814yescomplemented
554C3#1060549811yescharacteristic, direct product factor, Sylow
555C2—104no—
556C2C2×C3×#401811yescharacteristic
557C2C3×#6584111yescharacteristic
558C2C3×#6586311yescharacteristic
559C2C3×C4×D4×D511yescharacteristic
560C2C3×#6588511yescharacteristic
561C2C3×#6590611yescharacteristic
562C2C3×#6591511yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C4×C5×C4⋊C4C2
socleC23×C3×C5C24
prime radicalC23×C3×D5C23
cosocleC23×C5C24×C3
hypercenterC3×C4×C4⋊C4D5
hypocenterC5C3×#2344
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C3×C4×C5×C4⋊C4C2semidirect
5. C3×C4⋊C4×Dic5C2semidirect
6. C3×#65262C2semidirect
8. C3×#65222C2semidirect
9. C3×#65217C2semidirect
11. C3×#64941C2semidirect
12. #10605498C3direct (N × H)
29. C3×D5×C4⋊C4C4semidirect
41. C4×C5×C4⋊C4C2×C3semidirect
43. C4⋊C4×Dic5C2×C3semidirect
44. #65262C2×C3semidirect
46. #65222C2×C3semidirect
47. #65217C2×C3semidirect
49. #64941C2×C3semidirect
90. C3×C4×C4⋊C4D5semidirect
108. D5×C4⋊C4C3×C4semidirect
223. C4×C4⋊C4C3×D5semidirect
243. C3×C4×C5#117semidirect
411. C4×C5C3×#117semidirect
448. C3×C5#2344semidirect
472. C3×C4#4018semidirect
529. C5C3×#2344semidirect
553. C4C3×#4018semidirect
554. C3#10605498direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D5×C4⋊C42
C2×C3×#40182
C3×C4×C5×C4⋊C42
C3×#652762
C3×C4⋊C4×Dic52
C3×#652622
C3×C4×#6852
C3×#652222
C3×#652172
C3×#649532
C3×#649412
#106054983
C3×#23445