Finite Group Databasebeta

← C3×#10605854 #14327502

Subgroups — C3×#10605854 #14327502

Order 1920.

1176 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×C4×C22⋊D5C211yesmaximal, characteristic
2C3×C5×#381C211yesmaximal, characteristic, complemented
3C3×C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
4C3×#65245C212yesmaximal
5C3×#65234C212yesmaximal, complemented
6C3×#64956C211yesmaximal, characteristic, complemented
7C3×#64955C212yesmaximal, complemented
8C3×D5×#95C211yesmaximal, characteristic, complemented
9C3×#64941C212yesmaximal, complemented
10C3×#64940C211yesmaximal, characteristic, complemented
11C3×#64937C211yesmaximal, characteristic, complemented
12#10605854C311yesmaximal, characteristic, direct product factor, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×C3×C22⋊D5C2211yescharacteristic
15C22×C3×C4×D5C2212yes—
16C22×C3×C4×D5C2211yescharacteristic
17C2×C3×C5×C22⋊C4C2212yes—
18C2×C3×C22⋊Dic5C2212yes—
19C2×C3×C22⋊Dic5C2211yescharacteristic
20C3×C4×C22⋊D5C418yescomplemented
21C2×C3×#685C2212yes—
22C2×C3×#685C2211yescharacteristic
23C2×C3×#683C2212yes—
24C2×C3×#683C2211yescharacteristic
25C2×C3×C4×Dic5C2212yes—
26C2×C3×C4×Dic5C2212yes—
27C2×C3×C4×Dic5C2211yescharacteristic
28C3×C5×#95C2211yescharacteristic
29C3×C5×#95C2211yescharacteristic
30C3×C5×#95C2212yes—
31C3×#3963C2212yes—
32C3×#3963C2211yescharacteristic
33C3×#3963C2212yes—
34C3×#3963C2212yes—
35C3×#3963C2211yescharacteristic
36C3×#3963C2212yes—
37C3×#2353—51nomaximal, Hall
38C2×C4×C22⋊D5C2×C311yescharacteristic
39C5×#381C2×C311yescharacteristic, complemented
40C4×C22⋊Dic5C2×C311yescharacteristic, complemented
41#65245C2×C312yes—
42#65234C2×C312yescomplemented
43#64956C2×C311yescharacteristic, complemented
44#64955C2×C312yescomplemented
45D5×#95C2×C311yescharacteristic, complemented
46#64941C2×C312yescomplemented
47#64940C2×C311yescharacteristic, complemented
48#64937C2×C311yescharacteristic, complemented
49C24×C3×C5C2311yescharacteristic
50C23×C3×D5C2311yescharacteristic
51C22×C3×C4×C5—42no—
52C22×C3×C4×C5C2×C414yescomplemented
53C22×C3×C4×C5C2312yes—
54C22×C3×C4×C5C2312yes—
55C22×C3×C4×C5C2311yescharacteristic
56C22×C3×C4×C5C2311yescharacteristic
57C2×C3×C22⋊D5—22no—
58C2×C3×C22⋊D5—22no—
59C2×C3×C22⋊D5C2×C414yes—
60C22×C3×Dic5C2312yes—
61C22×C3×Dic5C2311yescharacteristic
62C22×C3×Dic5C2311yescharacteristic
63C22×C3×Dic5C2311yescharacteristic
64C22×C3×Dic5C2312yes—
65C2×C3×C4×D5—24no—
66C2×C3×C4×D5—24no—
67C2×C3×C4×D5—42no—
68C2×C3×C4×D5—42no—
69C2×C3×C4×D5C2×C414yes—
70C3×C5×C22⋊C4—42no—
71C3×C22⋊Dic5—24no—
72C3×C22⋊Dic5C2×C414yescomplemented
73C3×#685—24no—
74C3×#685C2×C414yes—
75C3×#683—42no—
76C3×#683C2×C414yescomplemented
77C3×C4×Dic5—24no—
78C3×C4×Dic5—42no—
79C3×C4×Dic5C2×C414yescomplemented
80C2×C3×C4×D4—51no—
81C3×#388—52no—
82C3×#387—52no—
83C3×#386—52no—
84C3×#383—51no—
85C3×#381D511yescharacteristic, complemented
86C3×#380—51no—
87C3×C4×C22⋊C4—51no—
88C3×C4×C22⋊C4—52no—
89C3×#376—51no—
90C2×C3×#95—51no—
91C23×C4×C5C22×C311yescharacteristic
92C22×C22⋊D5C22×C311yescharacteristic
93C22×C4×D5C22×C312yes—
94C22×C4×D5C22×C311yescharacteristic
95C2×C5×C22⋊C4C22×C312yes—
96C2×C22⋊Dic5C22×C312yes—
97C2×C22⋊Dic5C22×C311yescharacteristic
98C4×C22⋊D5C3×C418yescomplemented
99C2×#685C22×C312yes—
100C2×#685C22×C311yescharacteristic
101C2×#683C22×C312yes—
102C2×#683C22×C311yescharacteristic
103C2×C4×Dic5C22×C312yes—
104C2×C4×Dic5C22×C312yes—
105C2×C4×Dic5C22×C311yescharacteristic
106C5×#95C22×C311yescharacteristic
107C5×#95C22×C311yescharacteristic
108C5×#95C22×C312yes—
109#3963C22×C312yes—
110#3963C22×C311yescharacteristic
111#3963C22×C312yes—
112#3963C22×C312yes—
113#3963C22×C311yescharacteristic
114#3963C22×C312yes—
115#2353—51noSylow
116C23×C3×C5—22no—
117C23×C3×C5—21no—
118C23×C3×C5—21no—
119C23×C3×C5—22no—
120C23×C3×C5C22×C412yes—
121C23×C3×C5C2411yescharacteristic
122C22×C3×D5—22no—
123C22×C3×D5—22no—
124C22×C3×D5C22×C412yes—
125C22×C3×D5#4112yes—
126C22×C3×D5#4112yes—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5—22no—
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—44no—
136C2×C3×C4×C5C22×C412yes—
137C2×C3×C4×C5C22×C412yes—
138C3×C22⋊D5—28no—
139C2×C3×Dic5—22no—
140C2×C3×Dic5—22no—
141C2×C3×Dic5—21no—
142C2×C3×Dic5—21no—
143C2×C3×Dic5—22no—
144C2×C3×Dic5—22no—
145C2×C3×Dic5—22no—
146C2×C3×Dic5—22no—
147C2×C3×Dic5—22no—
148C2×C3×Dic5C22×C412yes—
149C2×C3×Dic5C22×C412yes—
150C2×C3×Dic5C22×C412yes—
151C2×C3×Dic5#4114yes—
152C3×C4×D5—44no—
153C3×C4×D5—48no—
154C22×C3×D4—51no—
155C23×C3×C4—51no—
156C23×C3×C4—52no—
157C23×C3×C4C2×D511yescharacteristic
158C3×C4×D4—58no—
159C2×C3×C4⋊C4—51no—
160C2×C3×C4⋊C4—52no—
161C2×C3×C22⋊C4—51no—
162C2×C3×C22⋊C4—51no—
163C2×C3×C22⋊C4—52no—
164C2×C3×C22⋊C4—52no—
165C2×C3×C22⋊C4C2×D512yes—
166C2×C3×C42—51no—
167C2×C3×C42—52no—
168C2×C3×C42—52no—
169C3×#95—51no—
170C3×#95—52no—
171C3×#95—52no—
172C3×#95—51no—
173C3×#95—52no—
174C3×#95—52no—
175C3×#95C2×D511yescharacteristic
176C3×#95C2×D511yescharacteristic
177C3×#95C2×D512yes—
178C24×C5C23×C311yescharacteristic
179C23×D5C23×C311yescharacteristic
180C22×C4×C5—42no—
181C22×C4×C5C2×C3×C414yescomplemented
182C22×C4×C5C23×C312yes—
183C22×C4×C5C23×C312yes—
184C22×C4×C5C23×C311yescharacteristic
185C22×C4×C5C23×C311yescharacteristic
186C2×C22⋊D5—22no—
187C2×C22⋊D5—22no—
188C2×C22⋊D5C2×C3×C414yes—
189C22×Dic5C23×C312yes—
190C22×Dic5C23×C311yescharacteristic
191C22×Dic5C23×C311yescharacteristic
192C22×Dic5C23×C311yescharacteristic
193C22×Dic5C23×C312yes—
194C2×C4×D5—24no—
195C2×C4×D5—24no—
196C2×C4×D5—42no—
197C2×C4×D5—42no—
198C2×C4×D5C2×C3×C414yes—
199C5×C22⋊C4—42no—
200C22⋊Dic5—24no—
201C22⋊Dic5C2×C3×C414yescomplemented
202#685—24no—
203#685C2×C3×C414yes—
204#683—42no—
205#683C2×C3×C414yescomplemented
206C4×Dic5—24no—
207C4×Dic5—42no—
208C4×Dic5C2×C3×C414yescomplemented
209C2×C4×D4—51no—
210#388—52no—
211#387—52no—
212#386—52no—
213#383—51no—
214#381C3×D511yescharacteristic, complemented
215#380—51no—
216C4×C22⋊C4—51no—
217C4×C22⋊C4—52no—
218#376—51no—
219C2×#95—51no—
220C22×C3×C5—22no—
221C22×C3×C5—22no—
222C22×C3×C5—22no—
223C22×C3×C5—42no—
224C22×C3×C5—42no—
225C22×C3×C5C23×C411yescharacteristic
226C22×C3×C5C2×#4111yescharacteristic
227C22×C3×C5C2×#4111yescharacteristic
228C22×C3×C5C2×#4112yes—
229C22×C3×C5H(5,𝔽2)12yes—
230C2×C3×D5—22no—
231C2×C3×D5—22no—
232C2×C3×D5—24no—
233C2×C3×D5—24no—
234C2×C3×D5#11714yes—
235C3×C4×C5—22no—
236C3×C4×C5—22no—
237C3×C4×C5—42no—
238C3×C4×C5—42no—
239C3×Dic5—22no—
240C3×Dic5—22no—
241C3×Dic5—22no—
242C3×Dic5—24no—
243C3×Dic5—42no—
244C24×C3—51no—
245C24×C3C22×D511yescharacteristic
246C2×C3×D4—54no—
247C2×C3×D4—102no—
248C2×C3×D4—102no—
249C22×C3×C4—42no—
250C22×C3×C4—51no—
251C22×C3×C4—52no—
252C22×C3×C4—51no—
253C22×C3×C4—51no—
254C22×C3×C4—54no—
255C22×C3×C4—52no—
256C22×C3×C4—104no—
257C22×C3×C4—104no—
258C22×C3×C4—202no—
259C22×C3×C4—202no—
260C22×C3×C4C4×D514yescomplemented
261C22×C3×C4C22×D512yes—
262C22×C3×C4C22×D512yes—
263C22×C3×C4C22×D511yescharacteristic
264C22×C3×C4C22×D511yescharacteristic
265C3×C4⋊C4—54no—
266C3×C4⋊C4—202no—
267C3×C22⋊C4—42no—
268C3×C22⋊C4—54no—
269C3×C22⋊C4—54no—
270C3×C22⋊C4—104no—
271C3×C22⋊C4—104no—
272C3×C42—54no—
273C3×C42—104no—
274C3×C42—202no—
275C23×C5—22no—
276C23×C5—21no—
277C23×C5—21no—
278C23×C5—22no—
279C23×C5C22×C3×C412yes—
280C23×C5C24×C311yescharacteristic
281C22×D5—22no—
282C22×D5—22no—
283C22×D5C22×C3×C412yes—
284C22×D5C3×#4112yes—
285C22×D5C3×#4112yes—
286C2×C4×C5—22no—
287C2×C4×C5—22no—
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—44no—
295C2×C4×C5C22×C3×C412yes—
296C2×C4×C5C22×C3×C412yes—
297C22⋊D5—28no—
298C2×Dic5—22no—
299C2×Dic5—22no—
300C2×Dic5—21no—
301C2×Dic5—21no—
302C2×Dic5—22no—
303C2×Dic5—22no—
304C2×Dic5—22no—
305C2×Dic5—22no—
306C2×Dic5—22no—
307C2×Dic5C22×C3×C412yes—
308C2×Dic5C22×C3×C412yes—
309C2×Dic5C22×C3×C412yes—
310C2×Dic5C3×#4114yes—
311C4×D5—44no—
312C4×D5—48no—
313C22×D4—51no—
314C23×C4—51no—
315C23×C4—52no—
316C23×C4C2×C3×D511yescharacteristic
317C4×D4—58no—
318C2×C4⋊C4—51no—
319C2×C4⋊C4—52no—
320C2×C22⋊C4—51no—
321C2×C22⋊C4—51no—
322C2×C22⋊C4—52no—
323C2×C22⋊C4—52no—
324C2×C22⋊C4C2×C3×D512yes—
325C2×C42—51no—
326C2×C42—52no—
327C2×C42—52no—
328#95—51no—
329#95—52no—
330#95—52no—
331#95—51no—
332#95—52no—
333#95—52no—
334#95C2×C3×D511yescharacteristic
335#95C2×C3×D511yescharacteristic
336#95C2×C3×D512yes—
337C2×C3×C5—42no—
338C2×C3×C5C2×#11711yescharacteristic
339C2×C3×C5C4×#4111yescharacteristic
340C2×C3×C5#51811yescharacteristic
341C2×C3×C5#55112yes—
342C2×C3×C5#55312yes—
343C3×D5—24no—
344C23×C3—22no—
345C23×C3—22no—
346C23×C3—21no—
347C23×C3—21no—
348C23×C3—52no—
349C23×C3—52no—
350C23×C3—52no—
351C23×C3—102no—
352C23×C3—102no—
353C23×C3C2×C4×D512yes—
354C23×C3C23×D511yescharacteristic
355C3×D4—108no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—44no—
365C2×C3×C4—52no—
366C2×C3×C4—52no—
367C2×C3×C4—52no—
368C2×C3×C4—54no—
369C2×C3×C4—102no—
370C2×C3×C4—102no—
371C2×C3×C4—102no—
372C2×C3×C4—102no—
373C2×C3×C4—101no—
374C2×C3×C4—101no—
375C2×C3×C4—102no—
376C2×C3×C4—102no—
377C2×C3×C4—102no—
378C2×C3×C4—204no—
379C2×C3×C4—208no—
380C2×C3×C4C2×C4×D512yes—
381C2×C3×C4C2×C4×D512yes—
382C22×C5—22no—
383C22×C5—22no—
384C22×C5—22no—
385C22×C5—42no—
386C22×C5—42no—
387C22×C5C23×C3×C411yescharacteristic
388C22×C5C2×C3×#4111yescharacteristic
389C22×C5C2×C3×#4111yescharacteristic
390C22×C5C2×C3×#4112yes—
391C22×C5C3×H(5,𝔽2)12yes—
392C2×D5—22no—
393C2×D5—22no—
394C2×D5—24no—
395C2×D5—24no—
396C2×D5C3×#11714yes—
397C4×C5—22no—
398C4×C5—22no—
399C4×C5—42no—
400C4×C5—42no—
401Dic5—22no—
402Dic5—22no—
403Dic5—22no—
404Dic5—24no—
405Dic5—42no—
406C24—51no—
407C24C22×C3×D511yescharacteristic
408C2×D4—54no—
409C2×D4—102no—
410C2×D4—102no—
411C22×C4—42no—
412C22×C4—51no—
413C22×C4—52no—
414C22×C4—51no—
415C22×C4—51no—
416C22×C4—54no—
417C22×C4—52no—
418C22×C4—104no—
419C22×C4—104no—
420C22×C4—202no—
421C22×C4—202no—
422C22×C4C3×C4×D514yescomplemented
423C22×C4C22×C3×D512yes—
424C22×C4C22×C3×D512yes—
425C22×C4C22×C3×D511yescharacteristic
426C22×C4C22×C3×D511yescharacteristic
427C4⋊C4—54no—
428C4⋊C4—202no—
429C22⋊C4—42no—
430C22⋊C4—54no—
431C22⋊C4—54no—
432C22⋊C4—104no—
433C22⋊C4—104no—
434C42—54no—
435C42—104no—
436C42—202no—
437C3×C5#235311yescharacteristic, complemented, Hall
438C22×C3—22no—
439C22×C3—22no—
440C22×C3—22no—
441C22×C3—42no—
442C22×C3—42no—
443C22×C3—54no—
444C22×C3—102no—
445C22×C3—102no—
446C22×C3—104no—
447C22×C3—104no—
448C22×C3C22×C4×D511yescharacteristic
449C22×C3#414412yes—
450C22×C3D5×#4111yescharacteristic
451C22×C3D5×#4111yescharacteristic
452C22×C3D5×#4112yes—
453C3×C4—22no—
454C3×C4—22no—
455C3×C4—42no—
456C3×C4—42no—
457C3×C4—102no—
458C3×C4—102no—
459C3×C4—102no—
460C3×C4—104no—
461C3×C4—202no—
462C2×C5—42no—
463C2×C5C2×C3×#11711yescharacteristic
464C2×C5C3×C4×#4111yescharacteristic
465C2×C5C3×#51811yescharacteristic
466C2×C5C3×#55112yes—
467C2×C5C3×#55312yes—
468D5—24no—
469C23—22no—
470C23—22no—
471C23—21no—
472C23—21no—
473C23—52no—
474C23—52no—
475C23—52no—
476C23—102no—
477C23—102no—
478C23C2×C3×C4×D512yes—
479C23C23×C3×D511yescharacteristic
480D4—108no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—44no—
490C2×C4—52no—
491C2×C4—52no—
492C2×C4—52no—
493C2×C4—54no—
494C2×C4—102no—
495C2×C4—102no—
496C2×C4—102no—
497C2×C4—102no—
498C2×C4—101no—
499C2×C4—101no—
500C2×C4—102no—
501C2×C4—102no—
502C2×C4—102no—
503C2×C4—204no—
504C2×C4—208no—
505C2×C4C2×C3×C4×D512yes—
506C2×C4C2×C3×C4×D512yes—
507C2×C3—42no—
508C2×C3—104no—
509C2×C3#6582011yescharacteristic
510C2×C3D5×#11711yescharacteristic
511C2×C3#6585611yescharacteristic
512C2×C3#6599312yes—
513C2×C3#6599512yes—
514C5C3×#235311yescharacteristic, complemented, Sylow
515C22—22no—
516C22—22no—
517C22—22no—
518C22—42no—
519C22—42no—
520C22—54no—
521C22—102no—
522C22—104no—
523C22—104no—
524C22—102no—
525C22C22×C3×C4×D511yescharacteristic
526C22C3×#414412yes—
527C22C3×D5×#4111yescharacteristic
528C22C3×D5×#4111yescharacteristic
529C22C3×D5×#4112yes—
530C4—22no—
531C4—22no—
532C4—42no—
533C4—42no—
534C4—102no—
535C4—102no—
536C4—104no—
537C4—102no—
538C4—202no—
539C3#1060585411yescharacteristic, direct product factor, Sylow
540C2—42no—
541C2—104no—
542C2C3×#6582011yescharacteristic
543C2C3×D5×#11711yescharacteristic
544C2C3×#6585611yescharacteristic
545C2C3×#6599312yes—
546C2C3×#6599512yes—
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#381C2
socleC23×C3×C5C24
prime radicalC22×C3×C22⋊D5C22
cosocleC23×C5C24×C3
hypercenterC3×#381D5
hypocenterC5C3×#2353
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#381

Complements

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

NH ≅ G/Ntype
2. C3×C5×#381C2semidirect
3. C3×C4×C22⋊Dic5C2semidirect
5. C3×#65234C2semidirect
6. C3×#64956C2semidirect
7. C3×#64955C2semidirect
8. C3×D5×#95C2semidirect
9. C3×#64941C2semidirect
10. C3×#64940C2semidirect
11. C3×#64937C2semidirect
12. #10605854C3direct (N × H)
20. C3×C4×C22⋊D5C4semidirect
39. C5×#381C2×C3semidirect
40. C4×C22⋊Dic5C2×C3semidirect
42. #65234C2×C3semidirect
43. #64956C2×C3semidirect
44. #64955C2×C3semidirect
45. D5×#95C2×C3semidirect
46. #64941C2×C3semidirect
47. #64940C2×C3semidirect
48. #64937C2×C3semidirect
52. C22×C3×C4×C5C2×C4semidirect
72. C3×C22⋊Dic5C2×C4semidirect
76. C3×#683C2×C4semidirect
79. C3×C4×Dic5C2×C4semidirect
85. C3×#381D5semidirect
98. C4×C22⋊D5C3×C4semidirect
181. C22×C4×C5C2×C3×C4semidirect
201. C22⋊Dic5C2×C3×C4semidirect
205. #683C2×C3×C4semidirect
208. C4×Dic5C2×C3×C4semidirect
214. #381C3×D5semidirect
260. C22×C3×C4C4×D5semidirect
422. C22×C4C3×C4×D5semidirect
437. C3×C5#2353semidirect
514. C5C3×#2353semidirect
539. C3#10605854direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×C22⋊D52
C3×C5×#3812
C3×C4×C22⋊Dic52
C3×#652452
C3×#652342
C3×#649562
C3×#649552
C3×D5×#952
C3×#649412
C3×#649402
C3×#649372
#106058543
C3×#23535