Finite Group Databasebeta

← C3×#10605786 #14323139

Subgroups — C3×#10605786 #14323139

Order 1920.

1080 conjugacy classes of subgroups.

The subgroup lattice has 540 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×#65501C211yesmaximal, characteristic, complemented
4C3×#65246C212yesmaximal
5C3×#65234C212yesmaximal, complemented
6C3×#64959C212yesmaximal, complemented
7C3×#64956C211yesmaximal, characteristic, complemented
8C3×#64953C211yesmaximal, characteristic, complemented
9C3×#64938C211yesmaximal, characteristic, complemented
10C3×#64937C211yesmaximal, characteristic, complemented
11C3×#64936C212yesmaximal, complemented
12#10605786C311yesmaximal, characteristic, direct product factor, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×C3×C22⋊D5C2211yescharacteristic
15C22×C3×C4×D5C2211yescharacteristic
16C2×C3×C5×C22⋊C4C2212yes—
17C2×C3×C22⋊Dic5C2212yes—
18C2×C3×C22⋊Dic5C2211yescharacteristic
19C3×C4×C22⋊D5C418yescomplemented
20C2×C3×#685C2212yes—
21C2×C3×#685C2212yes—
22C2×C3×#685C2211yescharacteristic
23C2×C3×C4⋊Dic5C2212yes—
24C2×C3×#683C2212yes—
25C2×C3×#683C2212yes—
26C2×C3×#683C2211yescharacteristic
27C2×C3×C4×Dic5C2212yes—
28C2×C3×C4×Dic5C2212yes—
29C2×C3×C4×Dic5C2211yescharacteristic
30C3×C5×#95C2212yes—
31C3×C5×#95C2211yescharacteristic
32C3×C5×#95C2211yescharacteristic
33C3×#3963C2212yes—
34C3×#3963C2211yescharacteristic
35C3×#3963C2212yes—
36C3×#3963C2211yescharacteristic
37C3×#2319—51nomaximal, Hall
38C2×C4×C22⋊D5C2×C311yescharacteristic
39C5×#381C2×C311yescharacteristic, complemented
40#65501C2×C311yescharacteristic, complemented
41#65246C2×C312yes—
42#65234C2×C312yescomplemented
43#64959C2×C312yescomplemented
44#64956C2×C311yescharacteristic, complemented
45#64953C2×C311yescharacteristic, complemented
46#64938C2×C311yescharacteristic, complemented
47#64937C2×C311yescharacteristic, complemented
48#64936C2×C312yescomplemented
49C24×C3×C5C2311yescharacteristic
50C23×C3×D5C2311yescharacteristic
51C22×C3×C4×C5—42no—
52C22×C3×C4×C5C2×C414yes—
53C22×C3×C4×C5C2312yes—
54C22×C3×C4×C5C2312yes—
55C22×C3×C4×C5C2311yescharacteristic
56C22×C3×C4×C5C2311yescharacteristic
57C2×C3×C22⋊D5—24no—
58C2×C3×C22⋊D5C2×C414yes—
59C22×C3×Dic5C2312yes—
60C22×C3×Dic5C2312yes—
61C22×C3×Dic5C2311yescharacteristic
62C22×C3×Dic5C2311yescharacteristic
63C22×C3×Dic5C2311yescharacteristic
64C2×C3×C4×D5—42no—
65C2×C3×C4×D5C2×C414yes—
66C3×C5×C22⋊C4—42no—
67C3×C22⋊Dic5—42no—
68C3×C22⋊Dic5C2×C414yes—
69C3×#685—42no—
70C3×#685—42no—
71C3×#685C2×C414yes—
72C3×C4⋊Dic5—42no—
73C3×#683—24no—
74C3×#683—42no—
75C3×#683C2×C414yes—
76C3×C4×Dic5—24no—
77C3×C4×Dic5—42no—
78C3×C4×Dic5C2×C414yes—
79C2×C3×C4×D4—51no—
80C3×#390—52no—
81C3×#389—52no—
82C3×#388—52no—
83C3×#388—52no—
84C3×#381—51no—
85C3×#381D511yescharacteristic, complemented
86C3×#380—51no—
87C3×#380—51no—
88C3×C4×C4⋊C4—51no—
89C3×#376—51no—
90C23×C4×C5C22×C311yescharacteristic
91C22×C22⋊D5C22×C311yescharacteristic
92C22×C4×D5C22×C311yescharacteristic
93C2×C5×C22⋊C4C22×C312yes—
94C2×C22⋊Dic5C22×C312yes—
95C2×C22⋊Dic5C22×C311yescharacteristic
96C4×C22⋊D5C3×C418yescomplemented
97C2×#685C22×C312yes—
98C2×#685C22×C312yes—
99C2×#685C22×C311yescharacteristic
100C2×C4⋊Dic5C22×C312yes—
101C2×#683C22×C312yes—
102C2×#683C22×C312yes—
103C2×#683C22×C311yescharacteristic
104C2×C4×Dic5C22×C312yes—
105C2×C4×Dic5C22×C312yes—
106C2×C4×Dic5C22×C311yescharacteristic
107C5×#95C22×C312yes—
108C5×#95C22×C311yescharacteristic
109C5×#95C22×C311yescharacteristic
110#3963C22×C312yes—
111#3963C22×C311yescharacteristic
112#3963C22×C312yes—
113#3963C22×C311yescharacteristic
114#2319—51noSylow
115C23×C3×C5—22no—
116C23×C3×C5—21no—
117C23×C3×C5—22no—
118C23×C3×C5—21no—
119C23×C3×C5C22×C412yes—
120C23×C3×C5C2411yescharacteristic
121C22×C3×D5—22no—
122C22×C3×D5—21no—
123C22×C3×D5—22no—
124C22×C3×D5—21no—
125C22×C3×D5C22×C412yes—
126C2×C3×C4×C5—22no—
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—44no—
135C2×C3×C4×C5C22×C412yes—
136C2×C3×C4×C5C22×C412yes—
137C3×C22⋊D5—28no—
138C2×C3×Dic5—21no—
139C2×C3×Dic5—22no—
140C2×C3×Dic5—21no—
141C2×C3×Dic5—22no—
142C2×C3×Dic5—22no—
143C2×C3×Dic5—22no—
144C2×C3×Dic5—22no—
145C2×C3×Dic5—22no—
146C2×C3×Dic5—22no—
147C2×C3×Dic5C22×C412yes—
148C2×C3×Dic5C22×C412yes—
149C2×C3×Dic5C22×C412yes—
150C2×C3×Dic5#4114yes—
151C3×C4×D5—44no—
152C22×C3×D4—51no—
153C23×C3×C4—51no—
154C23×C3×C4C2×D511yescharacteristic
155C3×C4×D4—58no—
156C2×C3×C4⋊C4—51no—
157C2×C3×C4⋊C4—52no—
158C2×C3×C4⋊C4—52no—
159C2×C3×C4⋊C4—52no—
160C2×C3×C22⋊C4—51no—
161C2×C3×C22⋊C4—51no—
162C2×C3×C22⋊C4—52no—
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—51no—
172C3×#95—52no—
173C3×#95C2×D511yescharacteristic
174C3×#95C2×D511yescharacteristic
175C3×#95C2×D512yes—
176C24×C5C23×C311yescharacteristic
177C23×D5C23×C311yescharacteristic
178C22×C4×C5—42no—
179C22×C4×C5C2×C3×C414yes—
180C22×C4×C5C23×C312yes—
181C22×C4×C5C23×C312yes—
182C22×C4×C5C23×C311yescharacteristic
183C22×C4×C5C23×C311yescharacteristic
184C2×C22⋊D5—24no—
185C2×C22⋊D5C2×C3×C414yes—
186C22×Dic5C23×C312yes—
187C22×Dic5C23×C312yes—
188C22×Dic5C23×C311yescharacteristic
189C22×Dic5C23×C311yescharacteristic
190C22×Dic5C23×C311yescharacteristic
191C2×C4×D5—42no—
192C2×C4×D5C2×C3×C414yes—
193C5×C22⋊C4—42no—
194C22⋊Dic5—42no—
195C22⋊Dic5C2×C3×C414yes—
196#685—42no—
197#685—42no—
198#685C2×C3×C414yes—
199C4⋊Dic5—42no—
200#683—24no—
201#683—42no—
202#683C2×C3×C414yes—
203C4×Dic5—24no—
204C4×Dic5—42no—
205C4×Dic5C2×C3×C414yes—
206C2×C4×D4—51no—
207#390—52no—
208#389—52no—
209#388—52no—
210#388—52no—
211#381—51no—
212#381C3×D511yescharacteristic, complemented
213#380—51no—
214#380—51no—
215C4×C4⋊C4—51no—
216#376—51no—
217C22×C3×C5—22no—
218C22×C3×C5—22no—
219C22×C3×C5—22no—
220C22×C3×C5—42no—
221C22×C3×C5—42no—
222C22×C3×C5C23×C411yescharacteristic
223C22×C3×C5C2×#4112yes—
224C22×C3×C5H(5,𝔽2)12yes—
225C22×C3×C5H(5,𝔽2)11yescharacteristic
226C22×C3×C52−1+411yescharacteristic
227C2×C3×D5—22no—
228C2×C3×D5—22no—
229C2×C3×D5—22no—
230C2×C3×D5—42no—
231C2×C3×D5—42no—
232C3×C4×C5—22no—
233C3×C4×C5—22no—
234C3×C4×C5—42no—
235C3×C4×C5—42no—
236C3×Dic5—22no—
237C3×Dic5—22no—
238C3×Dic5—42no—
239C3×Dic5—42no—
240C3×Dic5#11714yes—
241C24×C3—51no—
242C24×C3C22×D511yescharacteristic
243C2×C3×D4—54no—
244C2×C3×D4—104no—
245C22×C3×C4—42no—
246C22×C3×C4—51no—
247C22×C3×C4—51no—
248C22×C3×C4—51no—
249C22×C3×C4—54no—
250C22×C3×C4—52no—
251C22×C3×C4—52no—
252C22×C3×C4—202no—
253C22×C3×C4C4×D514yes—
254C22×C3×C4C22×D512yes—
255C22×C3×C4C22×D512yes—
256C22×C3×C4C22×D511yescharacteristic
257C22×C3×C4C22×D511yescharacteristic
258C3×C4⋊C4—54no—
259C3×C4⋊C4—104no—
260C3×C4⋊C4—202no—
261C3×C4⋊C4—202no—
262C3×C22⋊C4—42no—
263C3×C22⋊C4—54no—
264C3×C22⋊C4—54no—
265C3×C22⋊C4—202no—
266C3×C22⋊C4—202no—
267C3×C22⋊C4—202no—
268C3×C42—54no—
269C3×C42—104no—
270C3×C42—202no—
271C23×C5—22no—
272C23×C5—21no—
273C23×C5—22no—
274C23×C5—21no—
275C23×C5C22×C3×C412yes—
276C23×C5C24×C311yescharacteristic
277C22×D5—22no—
278C22×D5—21no—
279C22×D5—22no—
280C22×D5—21no—
281C22×D5C22×C3×C412yes—
282C2×C4×C5—22no—
283C2×C4×C5—22no—
284C2×C4×C5—22no—
285C2×C4×C5—22no—
286C2×C4×C5—22no—
287C2×C4×C5—22no—
288C2×C4×C5—22no—
289C2×C4×C5—22no—
290C2×C4×C5—44no—
291C2×C4×C5C22×C3×C412yes—
292C2×C4×C5C22×C3×C412yes—
293C22⋊D5—28no—
294C2×Dic5—21no—
295C2×Dic5—22no—
296C2×Dic5—21no—
297C2×Dic5—22no—
298C2×Dic5—22no—
299C2×Dic5—22no—
300C2×Dic5—22no—
301C2×Dic5—22no—
302C2×Dic5—22no—
303C2×Dic5C22×C3×C412yes—
304C2×Dic5C22×C3×C412yes—
305C2×Dic5C22×C3×C412yes—
306C2×Dic5C3×#4114yes—
307C4×D5—44no—
308C22×D4—51no—
309C23×C4—51no—
310C23×C4C2×C3×D511yescharacteristic
311C4×D4—58no—
312C2×C4⋊C4—51no—
313C2×C4⋊C4—52no—
314C2×C4⋊C4—52no—
315C2×C4⋊C4—52no—
316C2×C22⋊C4—51no—
317C2×C22⋊C4—51no—
318C2×C22⋊C4—52no—
319C2×C22⋊C4—52no—
320C2×C22⋊C4—52no—
321C2×C22⋊C4C2×C3×D512yes—
322C2×C42—51no—
323C2×C42—52no—
324C2×C42—52no—
325#95—51no—
326#95—52no—
327#95—51no—
328#95—52no—
329#95C2×C3×D511yescharacteristic
330#95C2×C3×D511yescharacteristic
331#95C2×C3×D512yes—
332C2×C3×C5—42no—
333C2×C3×C5C2×#11711yescharacteristic
334C2×C3×C5#51811yescharacteristic
335C2×C3×C5#52011yescharacteristic
336C2×C3×C5#54012yes—
337C2×C3×C5#54212yes—
338C3×D5—42no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3—21no—
342C23×C3—21no—
343C23×C3—52no—
344C23×C3—102no—
345C23×C3—102no—
346C23×C3—101no—
347C23×C3—101no—
348C23×C3C2×C4×D512yes—
349C23×C3C23×D511yescharacteristic
350C3×D4—108no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—44no—
360C2×C3×C4—52no—
361C2×C3×C4—54no—
362C2×C3×C4—52no—
363C2×C3×C4—52no—
364C2×C3×C4—102no—
365C2×C3×C4—101no—
366C2×C3×C4—101no—
367C2×C3×C4—102no—
368C2×C3×C4—102no—
369C2×C3×C4—102no—
370C2×C3×C4—102no—
371C2×C3×C4—102no—
372C2×C3×C4—102no—
373C2×C3×C4—204no—
374C2×C3×C4C2×C4×D512yes—
375C2×C3×C4C2×C4×D512yes—
376C22×C5—22no—
377C22×C5—22no—
378C22×C5—22no—
379C22×C5—42no—
380C22×C5—42no—
381C22×C5C23×C3×C411yescharacteristic
382C22×C5C2×C3×#4112yes—
383C22×C5C3×H(5,𝔽2)12yes—
384C22×C5C3×H(5,𝔽2)11yescharacteristic
385C22×C5C3×2−1+411yescharacteristic
386C2×D5—22no—
387C2×D5—22no—
388C2×D5—22no—
389C2×D5—42no—
390C2×D5—42no—
391C4×C5—22no—
392C4×C5—22no—
393C4×C5—42no—
394C4×C5—42no—
395Dic5—22no—
396Dic5—22no—
397Dic5—42no—
398Dic5—42no—
399Dic5C3×#11714yes—
400C24—51no—
401C24C22×C3×D511yescharacteristic
402C2×D4—54no—
403C2×D4—104no—
404C22×C4—42no—
405C22×C4—51no—
406C22×C4—51no—
407C22×C4—51no—
408C22×C4—54no—
409C22×C4—52no—
410C22×C4—52no—
411C22×C4—202no—
412C22×C4C3×C4×D514yes—
413C22×C4C22×C3×D512yes—
414C22×C4C22×C3×D512yes—
415C22×C4C22×C3×D511yescharacteristic
416C22×C4C22×C3×D511yescharacteristic
417C4⋊C4—54no—
418C4⋊C4—104no—
419C4⋊C4—202no—
420C4⋊C4—202no—
421C22⋊C4—42no—
422C22⋊C4—54no—
423C22⋊C4—54no—
424C22⋊C4—202no—
425C22⋊C4—202no—
426C22⋊C4—202no—
427C42—54no—
428C42—104no—
429C42—202no—
430C3×C5#231911yescharacteristic, complemented, Hall
431C22×C3—22no—
432C22×C3—22no—
433C22×C3—22no—
434C22×C3—42no—
435C22×C3—42no—
436C22×C3—102no—
437C22×C3—102no—
438C22×C3—102no—
439C22×C3—202no—
440C22×C3—202no—
441C22×C3C22×C4×D511yescharacteristic
442C22×C3#414412yes—
443C22×C3D5×#4112yes—
444C22×C3#414911yescharacteristic
445C22×C3#415011yescharacteristic
446C3×C4—22no—
447C3×C4—22no—
448C3×C4—42no—
449C3×C4—42no—
450C3×C4—54no—
451C3×C4—102no—
452C3×C4—102no—
453C3×C4—202no—
454C3×C4—202no—
455C2×C5—42no—
456C2×C5C2×C3×#11711yescharacteristic
457C2×C5C3×#51811yescharacteristic
458C2×C5C3×#52011yescharacteristic
459C2×C5C3×#54012yes—
460C2×C5C3×#54212yes—
461D5—42no—
462C23—22no—
463C23—22no—
464C23—21no—
465C23—21no—
466C23—52no—
467C23—102no—
468C23—102no—
469C23—101no—
470C23—101no—
471C23C2×C3×C4×D512yes—
472C23C23×C3×D511yescharacteristic
473D4—108no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—44no—
483C2×C4—52no—
484C2×C4—54no—
485C2×C4—52no—
486C2×C4—52no—
487C2×C4—102no—
488C2×C4—101no—
489C2×C4—101no—
490C2×C4—102no—
491C2×C4—102no—
492C2×C4—102no—
493C2×C4—102no—
494C2×C4—102no—
495C2×C4—102no—
496C2×C4—204no—
497C2×C4C2×C3×C4×D512yes—
498C2×C4C2×C3×C4×D512yes—
499C2×C3—42no—
500C2×C3—202no—
501C2×C3#6582011yescharacteristic
502C2×C3D5×#11711yescharacteristic
503C2×C3#6585711yescharacteristic
504C2×C3#6599612yes—
505C2×C3#6599712yes—
506C5C3×#231911yescharacteristic, complemented, Sylow
507C22—22no—
508C22—22no—
509C22—22no—
510C22—42no—
511C22—42no—
512C22—102no—
513C22—102no—
514C22—102no—
515C22—202no—
516C22—202no—
517C22C22×C3×C4×D511yescharacteristic
518C22C3×#414412yes—
519C22C3×D5×#4112yes—
520C22C3×#414911yescharacteristic
521C22C3×#415011yescharacteristic
522C4—22no—
523C4—22no—
524C4—42no—
525C4—42no—
526C4—54no—
527C4—102no—
528C4—102no—
529C4—202no—
530C4—202no—
531C3#1060578611yescharacteristic, direct product factor, Sylow
532C2—42no—
533C2—202no—
534C2C3×#6582011yescharacteristic
535C2C3×D5×#11711yescharacteristic
536C2C3×#6585711yescharacteristic
537C2C3×#6599612yes—
538C2C3×#6599712yes—
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×#2319
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×#65501C2semidirect
5. C3×#65234C2semidirect
6. C3×#64959C2semidirect
7. C3×#64956C2semidirect
8. C3×#64953C2semidirect
9. C3×#64938C2semidirect
10. C3×#64937C2semidirect
11. C3×#64936C2semidirect
12. #10605786C3direct (N × H)
19. C3×C4×C22⋊D5C4semidirect
39. C5×#381C2×C3semidirect
40. #65501C2×C3semidirect
42. #65234C2×C3semidirect
43. #64959C2×C3semidirect
44. #64956C2×C3semidirect
45. #64953C2×C3semidirect
46. #64938C2×C3semidirect
47. #64937C2×C3semidirect
48. #64936C2×C3semidirect
85. C3×#381D5semidirect
96. C4×C22⋊D5C3×C4semidirect
212. #381C3×D5semidirect
430. C3×C5#2319semidirect
506. C5C3×#2319semidirect
531. C3#10605786direct (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×#655012
C3×#652462
C3×#652342
C3×#649592
C3×#649562
C3×#649532
C3×#649382
C3×#649372
C3×#649362
#106057863
C3×#23195