Finite Group Databasebeta

← C3×#10604941 #14296838

Subgroups — C3×#10604941 #14296838

Order 1920.

1760 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D4×D5C211yesmaximal, characteristic
2C3×#65800C212yesmaximal, complemented
3C2×C3×#4011C212yesmaximal, complemented
4C2×C3×#3999C212yesmaximal, complemented
5#10604941C311yesmaximal, characteristic, direct product factor, Hall
6C24×C3×D5C411yescharacteristic, complemented
7C24×C3×D5C2211yescharacteristic
8C22×C3×C5×D4C411yescharacteristic, complemented
9C22×C3×C22⋊D5C411yescharacteristic, complemented
10C22×C3×C22⋊D5C2211yescharacteristic
11C2×C3×D4×D5—24no—
12C2×C3×D4×D5—24no—
13C2×C3×D4×D5—24no—
14C22×C3×D20C2211yescharacteristic
15C22×C3×C4×D5C411yescharacteristic, complemented
16C2×C3×C22⋊AGL(1,𝔽5)—24no—
17C2×C3×C22⋊AGL(1,𝔽5)C2214yescomplemented
18C3×#4011—24no—
19C3×#3999—24no—
20C3×#1781—51nomaximal, Hall
21C22×D4×D5C2×C311yescharacteristic
22#65800C2×C312yescomplemented
23C2×#4011C2×C312yescomplemented
24C2×#3999C2×C312yescomplemented
25C24×C3×C5C2×C411yescharacteristic
26C24×C3×C5C2×C411yescharacteristic
27C23×C3×D5—22no—
28C23×C3×D5—22no—
29C23×C3×D5—22no—
30C23×C3×D5—22no—
31C23×C3×D5—22no—
32C23×C3×D5—44no—
33C23×C3×D5—44no—
34C23×C3×D5C2×C411yescharacteristic
35C23×C3×D5C2×C411yescharacteristic
36C23×C3×D5D414yes—
37C23×C3×D5C2311yescharacteristic
38C22×C3×AGL(1,𝔽5)—24no—
39C2×C3×C5×D4—22no—
40C2×C3×C5×D4—22no—
41C2×C3×C5×D4—22no—
42C22×C3×C4×C5C2×C411yescharacteristic
43C2×C3×C22⋊D5—22no—
44C2×C3×C22⋊D5—22no—
45C2×C3×C22⋊D5—22no—
46C2×C3×C22⋊D5—22no—
47C2×C3×C22⋊D5—22no—
48C2×C3×C22⋊D5D414yes—
49C22×C3×Dic5C2×C411yescharacteristic
50C3×D4×D5—232no—
51C2×C3×D20—22no—
52C2×C3×D20—22no—
53C2×C3×D20D414yes—
54C2×C3×C4×D5—22no—
55C2×C3×C4×D5—22no—
56C2×C3×C4×D5—22no—
57C3×C22⋊AGL(1,𝔽5)—24no—
58C3×C22⋊AGL(1,𝔽5)—24no—
59C3×C22⋊AGL(1,𝔽5)—48no—
60C23×C3×D4—51no—
61C2×C3×#99—52no—
62C2×C3×#99—52no—
63C3×#379—52no—
64C24×D5C3×C411yescharacteristic, complemented
65C24×D5C22×C311yescharacteristic
66C22×C5×D4C3×C411yescharacteristic, complemented
67C22×C22⋊D5C3×C411yescharacteristic, complemented
68C22×C22⋊D5C22×C311yescharacteristic
69C2×D4×D5—24no—
70C2×D4×D5—24no—
71C2×D4×D5—24no—
72C22×D20C22×C311yescharacteristic
73C22×C4×D5C3×C411yescharacteristic, complemented
74C2×C22⋊AGL(1,𝔽5)—24no—
75C2×C22⋊AGL(1,𝔽5)C22×C314yescomplemented
76#4011—24no—
77#3999—24no—
78#1781—51noSylow
79C23×C3×C5—21no—
80C23×C3×C5—21no—
81C23×C3×C5—21no—
82C23×C3×C5—21no—
83C23×C3×C5—42no—
84C23×C3×C5—42no—
85C23×C3×C5C22⋊C412yes—
86C23×C3×C5C22⋊C412yescomplemented
87C23×C3×C5C22×C411yescharacteristic
88C22×C3×D5—21no—
89C22×C3×D5—21no—
90C22×C3×D5—24no—
91C22×C3×D5—28no—
92C22×C3×D5—21no—
93C22×C3×D5—21no—
94C22×C3×D5—28no—
95C22×C3×D5—28no—
96C22×C3×D5—44no—
97C22×C3×D5—42no—
98C22×C3×D5—48no—
99C22×C3×D5—48no—
100C22×C3×D5—48no—
101C22×C3×D5—48no—
102C22×C3×D5—44no—
103C22×C3×D5—44no—
104C22×C3×D5—42no—
105C22×C3×D5C22⋊C412yes—
106C22×C3×D5C22⋊C412yescomplemented
107C22×C3×D5C2×D412yes—
108C22×C3×D5C2×D412yes—
109C22×C3×D5C2×D412yes—
110C2×C3×AGL(1,𝔽5)—48no—
111C2×C3×AGL(1,𝔽5)—44no—
112C3×C5×D4—28no—
113C2×C3×C4×C5—21no—
114C2×C3×C4×C5—21no—
115C2×C3×C4×C5C22⋊C412yescomplemented
116C3×C22⋊D5—28no—
117C3×C22⋊D5—28no—
118C2×C3×Dic5—21no—
119C2×C3×Dic5—21no—
120C2×C3×Dic5C22⋊C412yescomplemented
121C3×D20—28no—
122C3×C4×D5—28no—
123C25×C3—51no—
124C25×C3—51no—
125C22×C3×D4—51no—
126C22×C3×D4—51no—
127C22×C3×D4—51no—
128C22×C3×D4—104no—
129C22×C3×D4—104no—
130C22×C3×D4—104no—
131C22×C3×D4AGL(1,𝔽5)11yescharacteristic, complemented
132C23×C3×C4—51no—
133C2×C3×C22⋊C4—54no—
134C2×C3×C22⋊C4—104no—
135C3×#99—104no—
136C3×#99—104no—
137C24×C5C2×C3×C411yescharacteristic
138C24×C5C2×C3×C411yescharacteristic
139C23×D5—22no—
140C23×D5—22no—
141C23×D5—22no—
142C23×D5—22no—
143C23×D5—22no—
144C23×D5—44no—
145C23×D5—44no—
146C23×D5C2×C3×C411yescharacteristic
147C23×D5C2×C3×C411yescharacteristic
148C23×D5C3×D414yes—
149C23×D5C23×C311yescharacteristic
150C22×AGL(1,𝔽5)—24no—
151C2×C5×D4—22no—
152C2×C5×D4—22no—
153C2×C5×D4—22no—
154C22×C4×C5C2×C3×C411yescharacteristic
155C2×C22⋊D5—22no—
156C2×C22⋊D5—22no—
157C2×C22⋊D5—22no—
158C2×C22⋊D5—22no—
159C2×C22⋊D5—22no—
160C2×C22⋊D5C3×D414yes—
161C22×Dic5C2×C3×C411yescharacteristic
162D4×D5—232no—
163C2×D20—22no—
164C2×D20—22no—
165C2×D20C3×D414yes—
166C2×C4×D5—22no—
167C2×C4×D5—22no—
168C2×C4×D5—22no—
169C22⋊AGL(1,𝔽5)—24no—
170C22⋊AGL(1,𝔽5)—24no—
171C22⋊AGL(1,𝔽5)—48no—
172C23×D4—51no—
173C2×#99—52no—
174C2×#99—52no—
175#379—52no—
176C22×C3×C5—22no—
177C22×C3×C5—22no—
178C22×C3×C5—22no—
179C22×C3×C5—24no—
180C22×C3×C5—42no—
181C22×C3×C5—42no—
182C22×C3×C5—42no—
183C22×C3×C5—42no—
184C22×C3×C5—42no—
185C22×C3×C5C2×C22⋊C411yescharacteristic
186C22×C3×C5C2×C22⋊C411yescharacteristic
187C22×C3×C5C2×C22⋊C411yescharacteristic
188C2×C3×D5—24no—
189C2×C3×D5—24no—
190C2×C3×D5—22no—
191C2×C3×D5—24no—
192C2×C3×D5—22no—
193C2×C3×D5—22no—
194C2×C3×D5—42no—
195C2×C3×D5—42no—
196C2×C3×D5—416no—
197C2×C3×D5—416no—
198C2×C3×D5—42no—
199C2×C3×D5—42no—
200C2×C3×D5—42no—
201C2×C3×D5#9914yescomplemented
202C2×C3×D5#12014yes—
203C3×AGL(1,𝔽5)—84no—
204C3×C4×C5—22no—
205C3×Dic5—22no—
206C24×C3—51no—
207C24×C3—51no—
208C24×C3—54no—
209C24×C3—51no—
210C24×C3—102no—
211C24×C3—102no—
212C24×C3—102no—
213C24×C3—102no—
214C24×C3—102no—
215C24×C3—204no—
216C24×C3—204no—
217C24×C3C2×AGL(1,𝔽5)11yescharacteristic
218C24×C3C2×AGL(1,𝔽5)11yescharacteristic
219C2×C3×D4—22no—
220C2×C3×D4—22no—
221C2×C3×D4—22no—
222C2×C3×D4—54no—
223C2×C3×D4—54no—
224C2×C3×D4—102no—
225C2×C3×D4—102no—
226C2×C3×D4—102no—
227C2×C3×D4—1032no—
228C2×C3×D4—102no—
229C2×C3×D4—102no—
230C2×C3×D4—102no—
231C2×C3×D4—102no—
232C22×C3×C4—51no—
233C22×C3×C4—102no—
234C22×C3×C4—102no—
235C22×C3×C4—102no—
236C22×C3×C4—104no—
237C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
238C3×C22⋊C4—104no—
239C3×C22⋊C4—104no—
240C3×C22⋊C4—208no—
241C23×C5—21no—
242C23×C5—21no—
243C23×C5—21no—
244C23×C5—21no—
245C23×C5—42no—
246C23×C5—42no—
247C23×C5C3×C22⋊C412yes—
248C23×C5C3×C22⋊C412yescomplemented
249C23×C5C22×C3×C411yescharacteristic
250C22×D5—21no—
251C22×D5—21no—
252C22×D5—24no—
253C22×D5—28no—
254C22×D5—21no—
255C22×D5—21no—
256C22×D5—28no—
257C22×D5—28no—
258C22×D5—44no—
259C22×D5—42no—
260C22×D5—48no—
261C22×D5—48no—
262C22×D5—48no—
263C22×D5—48no—
264C22×D5—44no—
265C22×D5—44no—
266C22×D5—42no—
267C22×D5C3×C22⋊C412yes—
268C22×D5C3×C22⋊C412yescomplemented
269C22×D5C2×C3×D412yes—
270C22×D5C2×C3×D412yes—
271C22×D5C2×C3×D412yes—
272C2×AGL(1,𝔽5)—48no—
273C2×AGL(1,𝔽5)—44no—
274C5×D4—28no—
275C2×C4×C5—21no—
276C2×C4×C5—21no—
277C2×C4×C5C3×C22⋊C412yescomplemented
278C22⋊D5—28no—
279C22⋊D5—28no—
280C2×Dic5—21no—
281C2×Dic5—21no—
282C2×Dic5C3×C22⋊C412yescomplemented
283D20—28no—
284C4×D5—28no—
285C25—51no—
286C25—51no—
287C22×D4—51no—
288C22×D4—51no—
289C22×D4—51no—
290C22×D4—104no—
291C22×D4—104no—
292C22×D4—104no—
293C22×D4C3×AGL(1,𝔽5)11yescharacteristic, complemented
294C23×C4—51no—
295C2×C22⋊C4—54no—
296C2×C22⋊C4—104no—
297#99—104no—
298#99—104no—
299C2×C3×C5—21no—
300C2×C3×C5—21no—
301C2×C3×C5—42no—
302C2×C3×C5—42no—
303C2×C3×C5#37911yescharacteristic
304C2×C3×C5C2×#9912yes—
305C3×D5—24no—
306C3×D5—24no—
307C3×D5—42no—
308C23×C3—21no—
309C23×C3—21no—
310C23×C3—21no—
311C23×C3—21no—
312C23×C3—42no—
313C23×C3—42no—
314C23×C3—52no—
315C23×C3—52no—
316C23×C3—52no—
317C23×C3—52no—
318C23×C3—52no—
319C23×C3—104no—
320C23×C3—108no—
321C23×C3—108no—
322C23×C3—108no—
323C23×C3—101no—
324C23×C3—101no—
325C23×C3—101no—
326C23×C3—101no—
327C23×C3—202no—
328C23×C3—204no—
329C23×C3—202no—
330C23×C3—204no—
331C23×C3—208no—
332C23×C3—208no—
333C23×C3—208no—
334C23×C3—208no—
335C23×C3—204no—
336C23×C3C22⋊AGL(1,𝔽5)12yes—
337C23×C3C22⋊AGL(1,𝔽5)12yescomplemented
338C23×C3C22×AGL(1,𝔽5)11yescharacteristic
339C3×D4—28no—
340C3×D4—108no—
341C3×D4—108no—
342C3×D4—108no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—52no—
346C2×C3×C4—108no—
347C2×C3×C4—101no—
348C2×C3×C4—101no—
349C2×C3×C4—204no—
350C2×C3×C4—208no—
351C2×C3×C4C22⋊AGL(1,𝔽5)12yescomplemented
352C22×C5—22no—
353C22×C5—22no—
354C22×C5—22no—
355C22×C5—24no—
356C22×C5—42no—
357C22×C5—42no—
358C22×C5—42no—
359C22×C5—42no—
360C22×C5—42no—
361C22×C5C2×C3×C22⋊C411yescharacteristic
362C22×C5C2×C3×C22⋊C411yescharacteristic
363C22×C5C2×C3×C22⋊C411yescharacteristic
364C2×D5—24no—
365C2×D5—24no—
366C2×D5—22no—
367C2×D5—24no—
368C2×D5—22no—
369C2×D5—22no—
370C2×D5—42no—
371C2×D5—42no—
372C2×D5—416no—
373C2×D5—416no—
374C2×D5—42no—
375C2×D5—42no—
376C2×D5—42no—
377C2×D5C3×#9914yescomplemented
378C2×D5C3×#12014yes—
379AGL(1,𝔽5)—84no—
380C4×C5—22no—
381Dic5—22no—
382C24—51no—
383C24—51no—
384C24—54no—
385C24—51no—
386C24—102no—
387C24—102no—
388C24—102no—
389C24—102no—
390C24—102no—
391C24—204no—
392C24—204no—
393C24C2×C3×AGL(1,𝔽5)11yescharacteristic
394C24C2×C3×AGL(1,𝔽5)11yescharacteristic
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—54no—
399C2×D4—54no—
400C2×D4—102no—
401C2×D4—102no—
402C2×D4—102no—
403C2×D4—1032no—
404C2×D4—102no—
405C2×D4—102no—
406C2×D4—102no—
407C2×D4—102no—
408C22×C4—51no—
409C22×C4—102no—
410C22×C4—102no—
411C22×C4—102no—
412C22×C4—104no—
413C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
414C22⋊C4—104no—
415C22⋊C4—104no—
416C22⋊C4—208no—
417C3×C5#178111yescharacteristic, complemented, Hall
418C22×C3—22no—
419C22×C3—22no—
420C22×C3—22no—
421C22×C3—24no—
422C22×C3—42no—
423C22×C3—42no—
424C22×C3—42no—
425C22×C3—42no—
426C22×C3—42no—
427C22×C3—54no—
428C22×C3—54no—
429C22×C3—104no—
430C22×C3—104no—
431C22×C3—102no—
432C22×C3—104no—
433C22×C3—102no—
434C22×C3—102no—
435C22×C3—202no—
436C22×C3—202no—
437C22×C3—202no—
438C22×C3—202no—
439C22×C3—2016no—
440C22×C3—2016no—
441C22×C3—202no—
442C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
443C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
444C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
445C3×C4—22no—
446C3×C4—102no—
447C3×C4—404no—
448C2×C5—21no—
449C2×C5—21no—
450C2×C5—42no—
451C2×C5—42no—
452C2×C5C3×#37911yescharacteristic
453C2×C5C2×C3×#9912yes—
454D5—24no—
455D5—24no—
456D5—42no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—42no—
462C23—42no—
463C23—52no—
464C23—52no—
465C23—52no—
466C23—52no—
467C23—52no—
468C23—104no—
469C23—108no—
470C23—108no—
471C23—108no—
472C23—101no—
473C23—101no—
474C23—101no—
475C23—101no—
476C23—202no—
477C23—204no—
478C23—202no—
479C23—204no—
480C23—208no—
481C23—208no—
482C23—208no—
483C23—208no—
484C23—204no—
485C23C3×C22⋊AGL(1,𝔽5)12yes—
486C23C3×C22⋊AGL(1,𝔽5)12yescomplemented
487C23C22×C3×AGL(1,𝔽5)11yescharacteristic
488D4—28no—
489D4—108no—
490D4—108no—
491D4—108no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—52no—
495C2×C4—108no—
496C2×C4—101no—
497C2×C4—101no—
498C2×C4—204no—
499C2×C4—208no—
500C2×C4C3×C22⋊AGL(1,𝔽5)12yescomplemented
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—42no—
504C2×C3—42no—
505C2×C3—104no—
506C2×C3—104no—
507C2×C3—202no—
508C2×C3D5⋊#9912yes—
509C2×C3#6580011yescharacteristic
510C5C3×#178111yescharacteristic, complemented, Sylow
511C22—22no—
512C22—24no—
513C22—22no—
514C22—22no—
515C22—42no—
516C22—42no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—54no—
521C22—54no—
522C22—104no—
523C22—104no—
524C22—104no—
525C22—102no—
526C22—102no—
527C22—102no—
528C22—202no—
529C22—202no—
530C22—202no—
531C22—202no—
532C22—2016no—
533C22—2016no—
534C22—202no—
535C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
536C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
537C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
538C4—22no—
539C4—102no—
540C4—404no—
541C3#1060494111yescharacteristic, direct product factor, Sylow
542C2—21no—
543C2—21no—
544C2—42no—
545C2—42no—
546C2—104no—
547C2—104no—
548C2—202no—
549C2C3×D5⋊#9912yes—
550C2C3×#6580011yescharacteristic
subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC23×C5C22×C3×C4
FrattiniC23C22×C3×AGL(1,𝔽5)
FittingC22×C3×C5×D4C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D4×D5C2
cosocleC23×D5C23×C3
hypercenterC22×C3×D4AGL(1,𝔽5)
hypocenterC5C3×#1781
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C24×C3 ◁ C22×C3×D4

Complements

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

NH ≅ G/Ntype
2. C3×#65800C2semidirect
3. C2×C3×#4011C2semidirect
4. C2×C3×#3999C2semidirect
5. #10604941C3direct (N × H)
6. C24×C3×D5C4semidirect
8. C22×C3×C5×D4C4semidirect
9. C22×C3×C22⋊D5C4semidirect
15. C22×C3×C4×D5C4semidirect
17. C2×C3×C22⋊AGL(1,𝔽5)C22semidirect
22. #65800C2×C3semidirect
23. C2×#4011C2×C3semidirect
24. C2×#3999C2×C3semidirect
64. C24×D5C3×C4semidirect
66. C22×C5×D4C3×C4semidirect
67. C22×C22⋊D5C3×C4semidirect
73. C22×C4×D5C3×C4semidirect
75. C2×C22⋊AGL(1,𝔽5)C22×C3semidirect
86. C23×C3×C5C22⋊C4semidirect
106. C22×C3×D5C22⋊C4semidirect
115. C2×C3×C4×C5C22⋊C4semidirect
120. C2×C3×Dic5C22⋊C4semidirect
131. C22×C3×D4AGL(1,𝔽5)semidirect
201. C2×C3×D5#99semidirect
248. C23×C5C3×C22⋊C4semidirect
268. C22×D5C3×C22⋊C4semidirect
277. C2×C4×C5C3×C22⋊C4semidirect
282. C2×Dic5C3×C22⋊C4semidirect
293. C22×D4C3×AGL(1,𝔽5)semidirect
337. C23×C3C22⋊AGL(1,𝔽5)semidirect
351. C2×C3×C4C22⋊AGL(1,𝔽5)semidirect
377. C2×D5C3×#99semidirect
417. C3×C5#1781semidirect
486. C23C3×C22⋊AGL(1,𝔽5)semidirect
500. C2×C4C3×C22⋊AGL(1,𝔽5)semidirect
510. C5C3×#1781semidirect
541. C3#10604941direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D4×D52
C3×#658002
C2×C3×#40112
C2×C3×#39992
#106049413
C3×#17815