Finite Group Databasebeta

← C3×#10605364 #14326780

Subgroups — C3×#10605364 #14326780

Order 1920.

1008 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4038C211yesmaximal, characteristic
2C3×C4×C5×C4⋊C4C211yesmaximal, characteristic, complemented
3C3×#65276C211yesmaximal, characteristic
4C3×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
5C3×#65262C211yesmaximal, characteristic, complemented
6C3×#65229C212yesmaximal
7C3×C4×#685C211yesmaximal, characteristic
8C3×#65221C212yesmaximal, complemented
9C3×#65217C211yesmaximal, characteristic, complemented
10C3×#64958C212yesmaximal
11C3×#64939C212yesmaximal, complemented
12#10605364C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C4×D5C2211yescharacteristic
14C2×C3×C5×C4⋊C4C2211yescharacteristic
15C2×C3×C5×C4⋊C4C2211yescharacteristic
16C2×C3×C42×C5C2211yescharacteristic
17C2×C3×C42×C5C2212yes—
18C2×C3×#685C2211yescharacteristic
19C2×C3×#685C2211yescharacteristic
20C2×C3×#685C2212yes—
21C2×C3×#685C2212yes—
22C2×C3×C4⋊Dic5C2211yescharacteristic
23C2×C3×C4⋊Dic5C2211yescharacteristic
24C2×C3×#683C2212yes—
25C2×C3×#683C2212yes—
26C2×C3×C4×Dic5C2212yes—
27C2×C3×C4×Dic5C2211yescharacteristic
28C2×C3×C4×Dic5C2212yes—
29C3×#4038C418yescomplemented
30C3×C5×#95C2212yes—
31C3×#3963C2211yescharacteristic
32C3×#3963C2212yes—
33C3×#3963C2212yes—
34C3×#3963C2212yes—
35C3×#3963C2212yes—
36C3×#3963C2211yescharacteristic
37C3×#2346—51nomaximal, Hall
38C2×#4038C2×C311yescharacteristic
39C4×C5×C4⋊C4C2×C311yescharacteristic, complemented
40#65276C2×C311yescharacteristic
41C4⋊C4×Dic5C2×C311yescharacteristic, complemented
42#65262C2×C311yescharacteristic, complemented
43#65229C2×C312yes—
44C4×#685C2×C311yescharacteristic
45#65221C2×C312yescomplemented
46#65217C2×C311yescharacteristic, complemented
47#64958C2×C312yes—
48#64939C2×C312yescomplemented
49C23×C3×D5C2311yescharacteristic
50C22×C3×C4×C5C2312yes—
51C22×C3×C4×C5C2311yescharacteristic
52C22×C3×C4×C5C2312yes—
53C22×C3×C4×C5C2311yescharacteristic
54C22×C3×C4×C5C2311yescharacteristic
55C22×C3×Dic5C2311yescharacteristic
56C22×C3×Dic5C2312yes—
57C22×C3×Dic5C2311yescharacteristic
58C22×C3×Dic5C2312yes—
59C22×C3×Dic5C2311yescharacteristic
60C2×C3×C4×D5—22no—
61C2×C3×C4×D5—22no—
62C2×C3×C4×D5C2×C414yes—
63C3×C5×C4⋊C4—22no—
64C3×C5×C4⋊C4C2×C414yes—
65C3×C42×C5—24no—
66C3×C42×C5—22no—
67C3×#685—22no—
68C3×#685—22no—
69C3×#685—42no—
70C3×#685C2×C418yes—
71C3×C4⋊Dic5—22no—
72C3×C4⋊Dic5C2×C414yes—
73C3×#683—42no—
74C3×#683—42no—
75C3×C4×Dic5—22no—
76C3×C4×Dic5—24no—
77C3×C4×Dic5C2×C418yes—
78C2×C3×#117—51no—
79C3×#389—51no—
80C3×#389—51no—
81C3×#388—52no—
82C3×#388—52no—
83C3×#382—52no—
84C3×#380—51no—
85C3×C4×C4⋊C4—51no—
86C3×C4×C4⋊C4D511yescharacteristic, complemented
87C3×C4×C22⋊C4—51no—
88C3×#376—52no—
89C22×C4×D5C22×C311yescharacteristic
90C2×C5×C4⋊C4C22×C311yescharacteristic
91C2×C5×C4⋊C4C22×C311yescharacteristic
92C2×C42×C5C22×C311yescharacteristic
93C2×C42×C5C22×C312yes—
94C2×#685C22×C311yescharacteristic
95C2×#685C22×C311yescharacteristic
96C2×#685C22×C312yes—
97C2×#685C22×C312yes—
98C2×C4⋊Dic5C22×C311yescharacteristic
99C2×C4⋊Dic5C22×C311yescharacteristic
100C2×#683C22×C312yes—
101C2×#683C22×C312yes—
102C2×C4×Dic5C22×C312yes—
103C2×C4×Dic5C22×C311yescharacteristic
104C2×C4×Dic5C22×C312yes—
105#4038C3×C418yescomplemented
106C5×#95C22×C312yes—
107#3963C22×C311yescharacteristic
108#3963C22×C312yes—
109#3963C22×C312yes—
110#3963C22×C312yes—
111#3963C22×C312yes—
112#3963C22×C311yescharacteristic
113#2346—51noSylow
114C23×C3×C5C2411yescharacteristic
115C22×C3×D5—21no—
116C22×C3×D5—21no—
117C22×C3×D5—21no—
118C22×C3×D5—21no—
119C22×C3×D5—21no—
120C22×C3×D5—21no—
121C22×C3×D5C22×C412yes—
122C2×C3×C4×C5—22no—
123C2×C3×C4×C5—22no—
124C2×C3×C4×C5—21no—
125C2×C3×C4×C5—21no—
126C2×C3×C4×C5—21no—
127C2×C3×C4×C5—21no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5—21no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5C22×C414yes—
133C2×C3×C4×C5C22×C412yes—
134C2×C3×C4×C5#4112yes—
135C2×C3×C4×C5#4112yes—
136C2×C3×C4×C5#4112yes—
137C2×C3×Dic5—21no—
138C2×C3×Dic5—21no—
139C2×C3×Dic5—21no—
140C2×C3×Dic5—22no—
141C2×C3×Dic5—22no—
142C2×C3×Dic5—21no—
143C2×C3×Dic5—21no—
144C2×C3×Dic5—22no—
145C2×C3×Dic5—22no—
146C2×C3×Dic5—21no—
147C2×C3×Dic5—21no—
148C2×C3×Dic5—22no—
149C2×C3×Dic5C22×C412yes—
150C2×C3×Dic5C22×C414yes—
151C2×C3×Dic5#4112yes—
152C3×C4×D5—28no—
153C23×C3×C4—51no—
154C3×#117—58no—
155C2×C3×C4⋊C4—51no—
156C2×C3×C4⋊C4—51no—
157C2×C3×C4⋊C4—52no—
158C2×C3×C4⋊C4—52no—
159C2×C3×C4⋊C4C2×D511yescharacteristic
160C2×C3×C4⋊C4C2×D511yescharacteristic
161C2×C3×C22⋊C4—52no—
162C2×C3×C22⋊C4—51no—
163C2×C3×C22⋊C4—51no—
164C2×C3×C22⋊C4—52no—
165C2×C3×C42—52no—
166C2×C3×C42—52no—
167C2×C3×C42—51no—
168C2×C3×C42C2×D512yes—
169C2×C3×C42C2×D511yescharacteristic
170C3×#95—51no—
171C3×#95—52no—
172C3×#95—52no—
173C3×#95—52no—
174C3×#95—51no—
175C3×#95—52no—
176C3×#95C2×D512yes—
177C23×D5C23×C311yescharacteristic
178C22×C4×C5C23×C312yes—
179C22×C4×C5C23×C311yescharacteristic
180C22×C4×C5C23×C312yes—
181C22×C4×C5C23×C311yescharacteristic
182C22×C4×C5C23×C311yescharacteristic
183C22×Dic5C23×C311yescharacteristic
184C22×Dic5C23×C312yes—
185C22×Dic5C23×C311yescharacteristic
186C22×Dic5C23×C312yes—
187C22×Dic5C23×C311yescharacteristic
188C2×C4×D5—22no—
189C2×C4×D5—22no—
190C2×C4×D5C2×C3×C414yes—
191C5×C4⋊C4—22no—
192C5×C4⋊C4C2×C3×C414yes—
193C42×C5—22no—
194C42×C5—24no—
195#685—22no—
196#685—22no—
197#685—42no—
198#685C2×C3×C418yes—
199C4⋊Dic5—22no—
200C4⋊Dic5C2×C3×C414yes—
201#683—42no—
202#683—42no—
203C4×Dic5—22no—
204C4×Dic5—24no—
205C4×Dic5C2×C3×C418yes—
206C2×#117—51no—
207#389—51no—
208#389—51no—
209#388—52no—
210#388—52no—
211#382—52no—
212#380—51no—
213C4×C4⋊C4—51no—
214C4×C4⋊C4C3×D511yescharacteristic, complemented
215C4×C22⋊C4—51no—
216#376—52no—
217C22×C3×C5C23×C411yescharacteristic
218C22×C3×C5C2×#4111yescharacteristic
219C22×C3×C5C2×#4111yescharacteristic
220C22×C3×C5C2×#4111yescharacteristic
221C22×C3×C5C2×#4111yescharacteristic
222C22×C3×C5H(5,𝔽2)11yescharacteristic
223C22×C3×C52−1+411yescharacteristic
224C2×C3×D5—22no—
225C2×C3×D5—22no—
226C2×C3×D5—22no—
227C2×C3×D5—41no—
228C2×C3×D5—41no—
229C2×C3×D5—41no—
230C2×C3×D5—41no—
231C3×C4×C5—24no—
232C3×C4×C5—22no—
233C3×C4×C5—41no—
234C3×C4×C5—42no—
235C3×C4×C5#11714yes—
236C3×Dic5—22no—
237C3×Dic5—24no—
238C3×Dic5—22no—
239C3×Dic5—42no—
240C3×Dic5—41no—
241C24×C3—51no—
242C22×C3×C4—51no—
243C22×C3×C4—51no—
244C22×C3×C4—52no—
245C22×C3×C4—54no—
246C22×C3×C4—51no—
247C22×C3×C4—52no—
248C22×C3×C4—102no—
249C22×C3×C4—102no—
250C22×C3×C4C22×D512yes—
251C22×C3×C4C22×D511yescharacteristic
252C22×C3×C4C22×D512yes—
253C22×C3×C4C22×D511yescharacteristic
254C22×C3×C4C22×D511yescharacteristic
255C3×C4⋊C4—22no—
256C3×C4⋊C4—54no—
257C3×C4⋊C4—102no—
258C3×C4⋊C4—202no—
259C3×C4⋊C4—202no—
260C3×C4⋊C4C4×D514yes—
261C3×C22⋊C4—58no—
262C3×C22⋊C4—102no—
263C3×C22⋊C4—102no—
264C3×C22⋊C4—202no—
265C3×C42—22no—
266C3×C42—24no—
267C3×C42—58no—
268C3×C42—104no—
269C3×C42—102no—
270C23×C5C24×C311yescharacteristic
271C22×D5—21no—
272C22×D5—21no—
273C22×D5—21no—
274C22×D5—21no—
275C22×D5—21no—
276C22×D5—21no—
277C22×D5C22×C3×C412yes—
278C2×C4×C5—22no—
279C2×C4×C5—21no—
280C2×C4×C5—22no—
281C2×C4×C5—21no—
282C2×C4×C5—21no—
283C2×C4×C5—21no—
284C2×C4×C5—22no—
285C2×C4×C5—22no—
286C2×C4×C5—21no—
287C2×C4×C5—22no—
288C2×C4×C5C22×C3×C414yes—
289C2×C4×C5C22×C3×C412yes—
290C2×C4×C5C3×#4112yes—
291C2×C4×C5C3×#4112yes—
292C2×C4×C5C3×#4112yes—
293C2×Dic5—21no—
294C2×Dic5—21no—
295C2×Dic5—21no—
296C2×Dic5—22no—
297C2×Dic5—22no—
298C2×Dic5—21no—
299C2×Dic5—21no—
300C2×Dic5—22no—
301C2×Dic5—22no—
302C2×Dic5—21no—
303C2×Dic5—21no—
304C2×Dic5—22no—
305C2×Dic5C22×C3×C412yes—
306C2×Dic5C22×C3×C414yes—
307C2×Dic5C3×#4112yes—
308C4×D5—28no—
309C23×C4—51no—
310#117—58no—
311C2×C4⋊C4—51no—
312C2×C4⋊C4—51no—
313C2×C4⋊C4—52no—
314C2×C4⋊C4—52no—
315C2×C4⋊C4C2×C3×D511yescharacteristic
316C2×C4⋊C4C2×C3×D511yescharacteristic
317C2×C22⋊C4—52no—
318C2×C22⋊C4—51no—
319C2×C22⋊C4—51no—
320C2×C22⋊C4—52no—
321C2×C42—52no—
322C2×C42—52no—
323C2×C42—51no—
324C2×C42C2×C3×D512yes—
325C2×C42C2×C3×D511yescharacteristic
326#95—51no—
327#95—52no—
328#95—52no—
329#95—52no—
330#95—51no—
331#95—52no—
332#95C2×C3×D512yes—
333C2×C3×C5C2×#11711yescharacteristic
334C2×C3×C5C4×#4111yescharacteristic
335C2×C3×C5#52011yescharacteristic
336C2×C3×C5#55211yescharacteristic
337C2×C3×C5#55211yescharacteristic
338C2×C3×C5#55511yescharacteristic
339C2×C3×C5#55511yescharacteristic
340C3×D5—42no—
341C23×C3—52no—
342C23×C3—101no—
343C23×C3—101no—
344C23×C3—101no—
345C23×C3—101no—
346C23×C3—101no—
347C23×C3—101no—
348C23×C3C23×D511yescharacteristic
349C2×C3×C4—21no—
350C2×C3×C4—22no—
351C2×C3×C4—21no—
352C2×C3×C4—22no—
353C2×C3×C4—21no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—21no—
357C2×C3×C4—22no—
358C2×C3×C4—21no—
359C2×C3×C4—52no—
360C2×C3×C4—54no—
361C2×C3×C4—52no—
362C2×C3×C4—101no—
363C2×C3×C4—101no—
364C2×C3×C4—101no—
365C2×C3×C4—102no—
366C2×C3×C4—101no—
367C2×C3×C4—102no—
368C2×C3×C4—108no—
369C2×C3×C4—101no—
370C2×C3×C4—102no—
371C2×C3×C4—101no—
372C2×C3×C4—102no—
373C2×C3×C4—102no—
374C2×C3×C4—101no—
375C2×C3×C4C2×C4×D514yes—
376C2×C3×C4C2×C4×D512yes—
377C2×C3×C4#70912yes—
378C2×C3×C4#70912yes—
379C2×C3×C4#71112yes—
380C22×C5C23×C3×C411yescharacteristic
381C22×C5C2×C3×#4111yescharacteristic
382C22×C5C2×C3×#4111yescharacteristic
383C22×C5C2×C3×#4111yescharacteristic
384C22×C5C2×C3×#4111yescharacteristic
385C22×C5C3×H(5,𝔽2)11yescharacteristic
386C22×C5C3×2−1+411yescharacteristic
387C2×D5—22no—
388C2×D5—22no—
389C2×D5—22no—
390C2×D5—41no—
391C2×D5—41no—
392C2×D5—41no—
393C2×D5—41no—
394C4×C5—24no—
395C4×C5—22no—
396C4×C5—41no—
397C4×C5—42no—
398C4×C5C3×#11714yes—
399Dic5—22no—
400Dic5—24no—
401Dic5—22no—
402Dic5—42no—
403Dic5—41no—
404C24—51no—
405C22×C4—51no—
406C22×C4—51no—
407C22×C4—52no—
408C22×C4—54no—
409C22×C4—51no—
410C22×C4—52no—
411C22×C4—102no—
412C22×C4—102no—
413C22×C4C22×C3×D512yes—
414C22×C4C22×C3×D511yescharacteristic
415C22×C4C22×C3×D512yes—
416C22×C4C22×C3×D511yescharacteristic
417C22×C4C22×C3×D511yescharacteristic
418C4⋊C4—22no—
419C4⋊C4—54no—
420C4⋊C4—102no—
421C4⋊C4—202no—
422C4⋊C4—202no—
423C4⋊C4C3×C4×D514yes—
424C22⋊C4—58no—
425C22⋊C4—102no—
426C22⋊C4—102no—
427C22⋊C4—202no—
428C42—22no—
429C42—24no—
430C42—58no—
431C42—104no—
432C42—102no—
433C3×C5#234611yescharacteristic, complemented, Hall
434C22×C3—102no—
435C22×C3—102no—
436C22×C3—102no—
437C22×C3—201no—
438C22×C3—201no—
439C22×C3—201no—
440C22×C3—201no—
441C22×C3C22×C4×D511yescharacteristic
442C22×C3C2×#70911yescharacteristic
443C22×C3C2×#70911yescharacteristic
444C22×C3C2×#71111yescharacteristic
445C22×C3#414711yescharacteristic
446C22×C3D5×#4111yescharacteristic
447C22×C3#414911yescharacteristic
448C3×C4—22no—
449C3×C4—24no—
450C3×C4—41no—
451C3×C4—42no—
452C3×C4—102no—
453C3×C4—104no—
454C3×C4—102no—
455C3×C4—202no—
456C3×C4—201no—
457C3×C4#401814yes—
458C2×C5C2×C3×#11711yescharacteristic
459C2×C5C3×C4×#4111yescharacteristic
460C2×C5C3×#52011yescharacteristic
461C2×C5C3×#55211yescharacteristic
462C2×C5C3×#55211yescharacteristic
463C2×C5C3×#55511yescharacteristic
464C2×C5C3×#55511yescharacteristic
465D5—42no—
466C23—52no—
467C23—101no—
468C23—101no—
469C23—101no—
470C23—101no—
471C23—101no—
472C23—101no—
473C23C23×C3×D511yescharacteristic
474C2×C4—21no—
475C2×C4—22no—
476C2×C4—21no—
477C2×C4—22no—
478C2×C4—21no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—21no—
482C2×C4—22no—
483C2×C4—21no—
484C2×C4—52no—
485C2×C4—54no—
486C2×C4—52no—
487C2×C4—101no—
488C2×C4—101no—
489C2×C4—101no—
490C2×C4—102no—
491C2×C4—101no—
492C2×C4—102no—
493C2×C4—108no—
494C2×C4—101no—
495C2×C4—102no—
496C2×C4—101no—
497C2×C4—102no—
498C2×C4—102no—
499C2×C4—101no—
500C2×C4C2×C3×C4×D514yes—
501C2×C4C2×C3×C4×D512yes—
502C2×C4C3×#70912yes—
503C2×C4C3×#70912yes—
504C2×C4C3×#71112yes—
505C2×C3—202no—
506C2×C3C2×#401811yescharacteristic
507C2×C3#6584711yescharacteristic
508C2×C3#6586611yescharacteristic
509C2×C3C4×#71111yescharacteristic
510C2×C3#6589711yescharacteristic
511C2×C3#6590811yescharacteristic
512C2×C3#6591511yescharacteristic
513C5C3×#234611yescharacteristic, complemented, Sylow
514C22—102no—
515C22—102no—
516C22—102no—
517C22—201no—
518C22—201no—
519C22—201no—
520C22—201no—
521C22C22×C3×C4×D511yescharacteristic
522C22C2×C3×#70911yescharacteristic
523C22C2×C3×#70911yescharacteristic
524C22C2×C3×#71111yescharacteristic
525C22C3×#414711yescharacteristic
526C22C3×D5×#4111yescharacteristic
527C22C3×#414911yescharacteristic
528C4—22no—
529C4—24no—
530C4—41no—
531C4—42no—
532C4—104no—
533C4—102no—
534C4—102no—
535C4—202no—
536C4—201no—
537C4C3×#401814yes—
538C3#1060536411yescharacteristic, direct product factor, Sylow
539C2—202no—
540C2C2×C3×#401811yescharacteristic
541C2C3×#6584711yescharacteristic
542C2C3×#6586611yescharacteristic
543C2C3×C4×#71111yescharacteristic
544C2C3×#6589711yescharacteristic
545C2C3×#6590811yescharacteristic
546C2C3×#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×#2346
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
2. C3×C4×C5×C4⋊C4C2semidirect
4. C3×C4⋊C4×Dic5C2semidirect
5. C3×#65262C2semidirect
8. C3×#65221C2semidirect
9. C3×#65217C2semidirect
11. C3×#64939C2semidirect
12. #10605364C3direct (N × H)
29. C3×#4038C4semidirect
39. C4×C5×C4⋊C4C2×C3semidirect
41. C4⋊C4×Dic5C2×C3semidirect
42. #65262C2×C3semidirect
45. #65221C2×C3semidirect
46. #65217C2×C3semidirect
48. #64939C2×C3semidirect
86. C3×C4×C4⋊C4D5semidirect
105. #4038C3×C4semidirect
214. C4×C4⋊C4C3×D5semidirect
433. C3×C5#2346semidirect
513. C5C3×#2346semidirect
538. C3#10605364direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40382
C3×C4×C5×C4⋊C42
C3×#652762
C3×C4⋊C4×Dic52
C3×#652622
C3×#652292
C3×C4×#6852
C3×#652212
C3×#652172
C3×#649582
C3×#649392
#106053643
C3×#23465