Finite Group Databasebeta

← C3×#10605486 #14321079

Subgroups — C3×#10605486 #14321079

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4018C211yesmaximal, characteristic
2C2×C3×#4018C211yesmaximal, characteristic
3C2×C3×C42×D5C211yesmaximal, characteristic
4C3×C4×C5×C4⋊C4C211yesmaximal, characteristic, complemented
5C3×#65278C212yesmaximal
6C3×#65261C212yesmaximal, complemented
7C3×C4×C4⋊Dic5C211yesmaximal, characteristic, complemented
8C3×C4×#683C211yesmaximal, characteristic, complemented
9C3×C4×#683C211yesmaximal, characteristic, complemented
10C3×#64957C212yesmaximal
11C3×#64936C212yesmaximal, complemented
12#10605486C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C4×D5C2212yes—
14C22×C3×C4×D5C2211yescharacteristic
15C2×C3×C5×C4⋊C4C2212yes—
16C2×C3×C42×C5C2211yescharacteristic
17C2×C3×C42×C5C2211yescharacteristic
18C2×C3×C42×C5C2211yescharacteristic
19C2×C3×#685C2212yes—
20C2×C3×#685C2211yescharacteristic
21C2×C3×#685C2211yescharacteristic
22C2×C3×C4⋊Dic5C2212yes—
23C2×C3×#683C2212yes—
24C2×C3×#683C2212yes—
25C2×C3×#683C2212yes—
26C2×C3×#683C2211yescharacteristic
27C2×C3×#683C2211yescharacteristic
28C2×C3×C4×Dic5C2212yes—
29C2×C3×C4×Dic5C2211yescharacteristic
30C2×C3×C4×Dic5C2211yescharacteristic
31C2×C3×C4×Dic5C2211yescharacteristic
32C3×#4018—24no—
33C3×#4018C418yescomplemented
34C3×C42×D5—24no—
35C3×C5×#95C2212yes—
36C3×#3963C2212yes—
37C3×#3963C2212yes—
38C3×#3963C2212yes—
39C3×#2296—51nomaximal, Hall
40C2×#4018C2×C311yescharacteristic
41C2×#4018C2×C311yescharacteristic
42C2×C42×D5C2×C311yescharacteristic
43C4×C5×C4⋊C4C2×C311yescharacteristic, complemented
44#65278C2×C312yes—
45#65261C2×C312yescomplemented
46C4×C4⋊Dic5C2×C311yescharacteristic, complemented
47C4×#683C2×C311yescharacteristic, complemented
48C4×#683C2×C311yescharacteristic, complemented
49#64957C2×C312yes—
50#64936C2×C312yescomplemented
51C23×C3×D5C2311yescharacteristic
52C22×C3×C4×C5C2312yes—
53C22×C3×C4×C5C2311yescharacteristic
54C22×C3×C4×C5C2311yescharacteristic
55C22×C3×C4×C5C2312yes—
56C22×C3×C4×C5C2311yescharacteristic
57C22×C3×Dic5C2312yes—
58C22×C3×Dic5C2311yescharacteristic
59C22×C3×Dic5C2311yescharacteristic
60C22×C3×Dic5C2312yes—
61C22×C3×Dic5C2311yescharacteristic
62C2×C3×C4×D5—24no—
63C2×C3×C4×D5—24no—
64C2×C3×C4×D5—24no—
65C2×C3×C4×D5C2×C414yes—
66C2×C3×C4×D5D414yes—
67C2×C3×C4×D5Q814yes—
68C3×C5×C4⋊C4—24no—
69C3×C42×C5—22no—
70C3×C42×C5—22no—
71C3×C42×C5C2×C414yescomplemented
72C3×#685—24no—
73C3×#685C2×C414yes—
74C3×#685C2×C414yes—
75C3×C4⋊Dic5—24no—
76C3×#683—24no—
77C3×#683—24no—
78C3×#683—24no—
79C3×#683C2×C414yescomplemented
80C3×#683C2×C414yescomplemented
81C3×C4×Dic5—22no—
82C3×C4×Dic5—22no—
83C3×C4×Dic5—24no—
84C3×C4×Dic5C2×C414yescomplemented
85C2×C3×#117—51no—
86C2×C3×#117—51no—
87C22×C3×C42—51no—
88C3×#389—52no—
89C3×#389—52no—
90C3×#385—52no—
91C3×#385—52no—
92C3×C4×C4⋊C4—51no—
93C3×C4×C4⋊C4—51no—
94C3×C4×C4⋊C4—51no—
95C3×C4×C4⋊C4D511yescharacteristic, complemented
96C22×C4×D5C22×C312yes—
97C22×C4×D5C22×C311yescharacteristic
98C2×C5×C4⋊C4C22×C312yes—
99C2×C42×C5C22×C311yescharacteristic
100C2×C42×C5C22×C311yescharacteristic
101C2×C42×C5C22×C311yescharacteristic
102C2×#685C22×C312yes—
103C2×#685C22×C311yescharacteristic
104C2×#685C22×C311yescharacteristic
105C2×C4⋊Dic5C22×C312yes—
106C2×#683C22×C312yes—
107C2×#683C22×C312yes—
108C2×#683C22×C312yes—
109C2×#683C22×C311yescharacteristic
110C2×#683C22×C311yescharacteristic
111C2×C4×Dic5C22×C312yes—
112C2×C4×Dic5C22×C311yescharacteristic
113C2×C4×Dic5C22×C311yescharacteristic
114C2×C4×Dic5C22×C311yescharacteristic
115#4018—24no—
116#4018C3×C418yescomplemented
117C42×D5—24no—
118C5×#95C22×C312yes—
119#3963C22×C312yes—
120#3963C22×C312yes—
121#3963C22×C312yes—
122#2296—51noSylow
123C23×C3×C5C2411yescharacteristic
124C22×C3×D5—22no—
125C22×C3×D5—22no—
126C22×C3×D5C22×C412yes—
127C22×C3×D5C2×D412yes—
128C22×C3×D5C2×Q812yes—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5C22×C412yes—
137C2×C3×C4×C5C22×C412yes—
138C2×C3×C4×C5C22×C412yes—
139C2×C3×C4×C5C2×D412yes—
140C2×C3×C4×C5C2×Q812yes—
141C2×C3×C4×C5#4114yes—
142C2×C3×Dic5—22no—
143C2×C3×Dic5—22no—
144C2×C3×Dic5—22no—
145C2×C3×Dic5—22no—
146C2×C3×Dic5—22no—
147C2×C3×Dic5—22no—
148C2×C3×Dic5—22no—
149C2×C3×Dic5C22×C412yes—
150C2×C3×Dic5C22×C412yes—
151C2×C3×Dic5C22×C412yes—
152C2×C3×Dic5C2×D412yes—
153C2×C3×Dic5C2×Q812yes—
154C2×C3×Dic5#4114yes—
155C3×C4×D5—216no—
156C3×C4×D5C4⋊C4116yescomplemented
157C23×C3×C4—51no—
158C23×C3×C4—52no—
159C3×#117—58no—
160C3×#117—104no—
161C2×C3×C4⋊C4—51no—
162C2×C3×C4⋊C4—51no—
163C2×C3×C4⋊C4—52no—
164C2×C3×C4⋊C4—52no—
165C2×C3×C4⋊C4—52no—
166C2×C3×C4⋊C4—52no—
167C2×C3×C4⋊C4C2×D512yes—
168C2×C3×C22⋊C4—51no—
169C2×C3×C22⋊C4—51no—
170C2×C3×C22⋊C4—52no—
171C2×C3×C42—51no—
172C2×C3×C42—52no—
173C2×C3×C42—51no—
174C2×C3×C42—51no—
175C2×C3×C42—104no—
176C2×C3×C42C2×D511yescharacteristic
177C2×C3×C42C2×D511yescharacteristic
178C2×C3×C42C2×D511yescharacteristic
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×C311yescharacteristic
187C22×C4×C5C23×C312yes—
188C22×C4×C5C23×C311yescharacteristic
189C22×Dic5C23×C312yes—
190C22×Dic5C23×C311yescharacteristic
191C22×Dic5C23×C311yescharacteristic
192C22×Dic5C23×C312yes—
193C22×Dic5C23×C311yescharacteristic
194C2×C4×D5—24no—
195C2×C4×D5—24no—
196C2×C4×D5—24no—
197C2×C4×D5C2×C3×C414yes—
198C2×C4×D5C3×D414yes—
199C2×C4×D5C3×Q814yes—
200C5×C4⋊C4—24no—
201C42×C5—22no—
202C42×C5—22no—
203C42×C5C2×C3×C414yescomplemented
204#685—24no—
205#685C2×C3×C414yes—
206#685C2×C3×C414yes—
207C4⋊Dic5—24no—
208#683—24no—
209#683—24no—
210#683—24no—
211#683C2×C3×C414yescomplemented
212#683C2×C3×C414yescomplemented
213C4×Dic5—22no—
214C4×Dic5—22no—
215C4×Dic5—24no—
216C4×Dic5C2×C3×C414yescomplemented
217C2×#117—51no—
218C2×#117—51no—
219C22×C42—51no—
220#389—52no—
221#389—52no—
222#385—52no—
223#385—52no—
224C4×C4⋊C4—51no—
225C4×C4⋊C4—51no—
226C4×C4⋊C4—51no—
227C4×C4⋊C4C3×D511yescharacteristic, complemented
228C22×C3×C5C23×C411yescharacteristic
229C22×C3×C5C22×D411yescharacteristic
230C22×C3×C5C22×Q811yescharacteristic
231C22×C3×C5C2×#4112yes—
232C22×C3×C5C2×#4112yes—
233C2×C3×D5—22no—
234C2×C3×D5—22no—
235C2×C3×D5—24no—
236C2×C3×D5—24no—
237C2×C3×D5C2×C4⋊C414yes—
238C3×C4×C5—22no—
239C3×C4×C5—22no—
240C3×C4×C5—24no—
241C3×C4×C5—42no—
242C3×C4×C5C2×C4⋊C414yes—
243C3×Dic5—22no—
244C3×Dic5—22no—
245C3×Dic5—24no—
246C3×Dic5—42no—
247C3×Dic5C2×C4⋊C414yes—
248C24×C3—51no—
249C22×C3×C4—51no—
250C22×C3×C4—54no—
251C22×C3×C4—54no—
252C22×C3×C4—54no—
253C22×C3×C4—52no—
254C22×C3×C4—51no—
255C22×C3×C4—51no—
256C22×C3×C4—52no—
257C22×C3×C4—104no—
258C22×C3×C4—104no—
259C22×C3×C4—104no—
260C22×C3×C4C22×D512yes—
261C22×C3×C4C22×D511yescharacteristic
262C22×C3×C4C22×D511yescharacteristic
263C22×C3×C4C22×D512yes—
264C22×C3×C4C22×D511yescharacteristic
265C3×C4⋊C4—24no—
266C3×C4⋊C4—54no—
267C3×C4⋊C4—54no—
268C3×C4⋊C4—104no—
269C3×C4⋊C4—104no—
270C3×C4⋊C4—104no—
271C3×C4⋊C4—104no—
272C3×C22⋊C4—54no—
273C3×C22⋊C4—54no—
274C3×C22⋊C4—104no—
275C3×C42—22no—
276C3×C42—22no—
277C3×C42—54no—
278C3×C42—104no—
279C3×C42—102no—
280C3×C42—102no—
281C3×C42C4×D514yescomplemented
282C23×C5C24×C311yescharacteristic
283C22×D5—22no—
284C22×D5—22no—
285C22×D5C22×C3×C412yes—
286C22×D5C2×C3×D412yes—
287C22×D5C2×C3×Q812yes—
288C2×C4×C5—22no—
289C2×C4×C5—22no—
290C2×C4×C5—22no—
291C2×C4×C5—22no—
292C2×C4×C5—22no—
293C2×C4×C5—22no—
294C2×C4×C5—22no—
295C2×C4×C5C22×C3×C412yes—
296C2×C4×C5C22×C3×C412yes—
297C2×C4×C5C22×C3×C412yes—
298C2×C4×C5C2×C3×D412yes—
299C2×C4×C5C2×C3×Q812yes—
300C2×C4×C5C3×#4114yes—
301C2×Dic5—22no—
302C2×Dic5—22no—
303C2×Dic5—22no—
304C2×Dic5—22no—
305C2×Dic5—22no—
306C2×Dic5—22no—
307C2×Dic5—22no—
308C2×Dic5C22×C3×C412yes—
309C2×Dic5C22×C3×C412yes—
310C2×Dic5C22×C3×C412yes—
311C2×Dic5C2×C3×D412yes—
312C2×Dic5C2×C3×Q812yes—
313C2×Dic5C3×#4114yes—
314C4×D5—216no—
315C4×D5C3×C4⋊C4116yescomplemented
316C23×C4—51no—
317C23×C4—52no—
318#117—58no—
319#117—104no—
320C2×C4⋊C4—51no—
321C2×C4⋊C4—51no—
322C2×C4⋊C4—52no—
323C2×C4⋊C4—52no—
324C2×C4⋊C4—52no—
325C2×C4⋊C4—52no—
326C2×C4⋊C4C2×C3×D512yes—
327C2×C22⋊C4—51no—
328C2×C22⋊C4—51no—
329C2×C22⋊C4—52no—
330C2×C42—51no—
331C2×C42—51no—
332C2×C42—51no—
333C2×C42—52no—
334C2×C42—104no—
335C2×C42C2×C3×D511yescharacteristic
336C2×C42C2×C3×D511yescharacteristic
337C2×C42C2×C3×D511yescharacteristic
338#95—52no—
339#95—52no—
340#95—52no—
341#95C2×C3×D512yes—
342C2×C3×C5C22×C4⋊C411yescharacteristic
343C2×C3×C5C4×#4111yescharacteristic
344C2×C3×C5C4×#4111yescharacteristic
345C2×C3×C5#52512yes—
346C2×C3×C5#53312yes—
347C3×D5—24no—
348C23×C3—52no—
349C23×C3—52no—
350C23×C3—52no—
351C23×C3—102no—
352C23×C3—102no—
353C23×C3C23×D511yescharacteristic
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—52no—
362C2×C3×C4—52no—
363C2×C3×C4—52no—
364C2×C3×C4—516no—
365C2×C3×C4—52no—
366C2×C3×C4—52no—
367C2×C3×C4—54no—
368C2×C3×C4—1016no—
369C2×C3×C4—102no—
370C2×C3×C4—102no—
371C2×C3×C4—102no—
372C2×C3×C4—102no—
373C2×C3×C4—102no—
374C2×C3×C4—102no—
375C2×C3×C4—102no—
376C2×C3×C4C2×C4×D512yes—
377C2×C3×C4C2×C4×D512yes—
378C2×C3×C4C2×C4×D512yes—
379C2×C3×C4#70914yes—
380C2×C3×C4D4×D512yes—
381C2×C3×C4Q8×D512yes—
382C22×C5C23×C3×C411yescharacteristic
383C22×C5C22×C3×D411yescharacteristic
384C22×C5C22×C3×Q811yescharacteristic
385C22×C5C2×C3×#4112yes—
386C22×C5C2×C3×#4112yes—
387C2×D5—22no—
388C2×D5—22no—
389C2×D5—24no—
390C2×D5—24no—
391C2×D5C2×C3×C4⋊C414yes—
392C4×C5—22no—
393C4×C5—22no—
394C4×C5—24no—
395C4×C5—42no—
396C4×C5C2×C3×C4⋊C414yes—
397Dic5—22no—
398Dic5—22no—
399Dic5—24no—
400Dic5—42no—
401Dic5C2×C3×C4⋊C414yes—
402C24—51no—
403C22×C4—51no—
404C22×C4—54no—
405C22×C4—54no—
406C22×C4—54no—
407C22×C4—52no—
408C22×C4—51no—
409C22×C4—51no—
410C22×C4—52no—
411C22×C4—104no—
412C22×C4—104no—
413C22×C4—104no—
414C22×C4C22×C3×D512yes—
415C22×C4C22×C3×D511yescharacteristic
416C22×C4C22×C3×D511yescharacteristic
417C22×C4C22×C3×D512yes—
418C22×C4C22×C3×D511yescharacteristic
419C4⋊C4—24no—
420C4⋊C4—54no—
421C4⋊C4—54no—
422C4⋊C4—104no—
423C4⋊C4—104no—
424C4⋊C4—104no—
425C4⋊C4—104no—
426C22⋊C4—54no—
427C22⋊C4—54no—
428C22⋊C4—104no—
429C42—22no—
430C42—22no—
431C42—54no—
432C42—104no—
433C42—102no—
434C42—102no—
435C42C3×C4×D514yescomplemented
436C3×C5#229611yescharacteristic, complemented, Hall
437C22×C3—54no—
438C22×C3—102no—
439C22×C3—102no—
440C22×C3—104no—
441C22×C3—104no—
442C22×C3C22×C4×D511yescharacteristic
443C22×C3C2×#70912yes—
444C22×C3C2×D4×D511yescharacteristic
445C22×C3C2×Q8×D511yescharacteristic
446C22×C3D5×#4112yes—
447C3×C4—22no—
448C3×C4—22no—
449C3×C4—24no—
450C3×C4—42no—
451C3×C4—54no—
452C3×C4—102no—
453C3×C4—102no—
454C3×C4—104no—
455C3×C4—202no—
456C3×C4D5×C4⋊C414yes—
457C2×C5C22×C3×C4⋊C411yescharacteristic
458C2×C5C3×C4×#4111yescharacteristic
459C2×C5C3×C4×#4111yescharacteristic
460C2×C5C3×#52512yes—
461C2×C5C3×#53312yes—
462D5—24no—
463C23—52no—
464C23—52no—
465C23—52no—
466C23—102no—
467C23—102no—
468C23C23×C3×D511yescharacteristic
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—52no—
477C2×C4—52no—
478C2×C4—52no—
479C2×C4—516no—
480C2×C4—52no—
481C2×C4—52no—
482C2×C4—54no—
483C2×C4—1016no—
484C2×C4—102no—
485C2×C4—102no—
486C2×C4—102no—
487C2×C4—102no—
488C2×C4—102no—
489C2×C4—102no—
490C2×C4—102no—
491C2×C4C2×C3×C4×D512yes—
492C2×C4C2×C3×C4×D512yes—
493C2×C4C2×C3×C4×D512yes—
494C2×C4C3×#70914yes—
495C2×C4C3×D4×D512yes—
496C2×C4C3×Q8×D512yes—
497C2×C3—104no—
498C2×C3C4×#70911yescharacteristic
499C2×C3C2×D5×C4⋊C411yescharacteristic
500C2×C3#6585611yescharacteristic
501C2×C3#6588112yes—
502C2×C3#6591212yes—
503C5C3×#229611yescharacteristic, complemented, Sylow
504C22—54no—
505C22—102no—
506C22—104no—
507C22—104no—
508C22—102no—
509C22C22×C3×C4×D511yescharacteristic
510C22C2×C3×#70912yes—
511C22C2×C3×D4×D511yescharacteristic
512C22C2×C3×Q8×D511yescharacteristic
513C22C3×D5×#4112yes—
514C4—22no—
515C4—24no—
516C4—22no—
517C4—42no—
518C4—54no—
519C4—102no—
520C4—104no—
521C4—102no—
522C4—202no—
523C4C3×D5×C4⋊C414yes—
524C3#1060548611yescharacteristic, direct product factor, Sylow
525C2—104no—
526C2C3×C4×#70911yescharacteristic
527C2C2×C3×D5×C4⋊C411yescharacteristic
528C2C3×#6585611yescharacteristic
529C2C3×#6588112yes—
530C2C3×#6591212yes—
subgroupG/H
centerC22×C3×C4C22×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×#2296
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3×C4 ◁ C3×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C3×C4×C5×C4⋊C4C2semidirect
6. C3×#65261C2semidirect
7. C3×C4×C4⋊Dic5C2semidirect
8. C3×C4×#683C2semidirect
9. C3×C4×#683C2semidirect
11. C3×#64936C2semidirect
12. #10605486C3direct (N × H)
33. C3×#4018C4semidirect
43. C4×C5×C4⋊C4C2×C3semidirect
45. #65261C2×C3semidirect
46. C4×C4⋊Dic5C2×C3semidirect
47. C4×#683C2×C3semidirect
48. C4×#683C2×C3semidirect
50. #64936C2×C3semidirect
71. C3×C42×C5C2×C4semidirect
79. C3×#683C2×C4semidirect
80. C3×#683C2×C4semidirect
84. C3×C4×Dic5C2×C4semidirect
95. C3×C4×C4⋊C4D5semidirect
116. #4018C3×C4semidirect
156. C3×C4×D5C4⋊C4semidirect
203. C42×C5C2×C3×C4semidirect
211. #683C2×C3×C4semidirect
212. #683C2×C3×C4semidirect
216. C4×Dic5C2×C3×C4semidirect
227. C4×C4⋊C4C3×D5semidirect
281. C3×C42C4×D5semidirect
315. C4×D5C3×C4⋊C4semidirect
435. C42C3×C4×D5semidirect
436. C3×C5#2296semidirect
503. C5C3×#2296semidirect
524. C3#10605486direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40182
C2×C3×C42×D52
C3×C4×C5×C4⋊C42
C3×#652782
C3×#652612
C3×C4×C4⋊Dic52
C3×C4×#6832
C3×#649572
C3×#649362
#106054863
C3×#22965