Finite Group Databasebeta

← C3×#10605177 #14323538

Subgroups — C3×#10605177 #14323538

Order 1920.

1264 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C22⋊D5C211yesmaximal, characteristic
2C22×C3×#683C211yesmaximal, characteristic, complemented
3C2×C3×#4032C211yesmaximal, characteristic
4C3×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
5C3×#65247C211yesmaximal, characteristic
6C3×#65239C211yesmaximal, characteristic, complemented
7C3×#65232C211yesmaximal, characteristic, complemented
8C3×#65229C212yesmaximal, complemented
9C3×#65217C212yesmaximal, complemented
10C3×#64957C212yesmaximal, complemented
11C3×#64942C212yesmaximal, complemented
12#10605177C311yesmaximal, characteristic, direct product factor, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×C3×C22⋊D5C2211yescharacteristic
15C23×C3×Dic5C2211yescharacteristic
16C23×C3×Dic5C2211yescharacteristic
17C22×C3×C4×D5C2211yescharacteristic
18C2×C3×C5×C22⋊C4C2211yescharacteristic
19C2×C3×C5×C22⋊C4C2211yescharacteristic
20C2×C3×C42×C5C2212yes—
21C2×C3×C22⋊Dic5C2211yescharacteristic
22C3×C4×C22⋊D5—24no—
23C2×C3×#685C2211yescharacteristic
24C2×C3×#685C2212yes—
25C2×C3×#685C2212yes—
26C2×C3×C4⋊Dic5C2212yes—
27C2×C3×C4⋊Dic5C2212yes—
28C2×C3×#683—24no—
29C2×C3×#683C2212yes—
30C2×C3×#683C2212yes—
31C2×C3×#683C2211yescharacteristic
32C2×C3×C4×Dic5C2211yescharacteristic
33C3×#4032C418yescomplemented
34C3×C5×#95C2212yes—
35C3×#3963C2212yes—
36C3×#3963C2212yes—
37C3×#3963C2212yes—
38C3×#3963C2212yes—
39C3×#2322—51nomaximal, Hall
40C2×C4×C22⋊D5C2×C311yescharacteristic
41C22×#683C2×C311yescharacteristic, complemented
42C2×#4032C2×C311yescharacteristic
43C4×C5×C22⋊C4C2×C311yescharacteristic, complemented
44#65247C2×C311yescharacteristic
45#65239C2×C311yescharacteristic, complemented
46#65232C2×C311yescharacteristic, complemented
47#65229C2×C312yescomplemented
48#65217C2×C312yescomplemented
49#64957C2×C312yescomplemented
50#64942C2×C312yescomplemented
51C24×C3×C5C2311yescharacteristic
52C23×C3×D5C2311yescharacteristic
53C22×C3×C4×C5—42no—
54C22×C3×C4×C5D414yes—
55C22×C3×C4×C5C2312yes—
56C22×C3×C4×C5C2312yes—
57C22×C3×C4×C5C2311yescharacteristic
58C22×C3×C4×C5C2311yescharacteristic
59C2×C3×C22⋊D5—22no—
60C2×C3×C22⋊D5—22no—
61C2×C3×C22⋊D5C2×C414yes—
62C22×C3×Dic5—22no—
63C22×C3×Dic5—22no—
64C22×C3×Dic5—22no—
65C22×C3×Dic5—42no—
66C22×C3×Dic5C2×C414yescomplemented
67C22×C3×Dic5C2311yescharacteristic
68C22×C3×Dic5C2311yescharacteristic
69C22×C3×Dic5C2312yes—
70C22×C3×Dic5C2312yes—
71C22×C3×Dic5C2311yescharacteristic
72C2×C3×C4×D5—22no—
73C2×C3×C4×D5—42no—
74C3×C5×C22⋊C4—22no—
75C3×C5×C22⋊C4C2×C414yescomplemented
76C3×C42×C5—42no—
77C3×C22⋊Dic5—22no—
78C3×#685—22no—
79C3×#685—42no—
80C3×#685C2×C418yescomplemented
81C3×C4⋊Dic5—42no—
82C3×C4⋊Dic5C2×C418yescomplemented
83C3×#683—24no—
84C3×#683—24no—
85C3×#683—22no—
86C3×C4×Dic5—22no—
87C2×C3×#123—51no—
88C2×C3×C4×D4—51no—
89C22×C3×C4⋊C4—51no—
90C3×#389—52no—
91C3×#388—52no—
92C3×#387—52no—
93C3×#386—51no—
94C3×#385—51no—
95C3×#385—52no—
96C3×#381—51no—
97C3×C4×C22⋊C4D511yescharacteristic, complemented
98C23×C4×C5C22×C311yescharacteristic
99C22×C22⋊D5C22×C311yescharacteristic
100C23×Dic5C22×C311yescharacteristic
101C23×Dic5C22×C311yescharacteristic
102C22×C4×D5C22×C311yescharacteristic
103C2×C5×C22⋊C4C22×C311yescharacteristic
104C2×C5×C22⋊C4C22×C311yescharacteristic
105C2×C42×C5C22×C312yes—
106C2×C22⋊Dic5C22×C311yescharacteristic
107C4×C22⋊D5—24no—
108C2×#685C22×C311yescharacteristic
109C2×#685C22×C312yes—
110C2×#685C22×C312yes—
111C2×C4⋊Dic5C22×C312yes—
112C2×C4⋊Dic5C22×C312yes—
113C2×#683—24no—
114C2×#683C22×C312yes—
115C2×#683C22×C312yes—
116C2×#683C22×C311yescharacteristic
117C2×C4×Dic5C22×C311yescharacteristic
118#4032C3×C418yescomplemented
119C5×#95C22×C312yes—
120#3963C22×C312yes—
121#3963C22×C312yes—
122#3963C22×C312yes—
123#3963C22×C312yes—
124#2322—51noSylow
125C23×C3×C5—22no—
126C23×C3×C5—22no—
127C23×C3×C5C22×C412yes—
128C23×C3×C5C2×D412yes—
129C23×C3×C5#4112yes—
130C23×C3×C5C2411yescharacteristic
131C22×C3×D5—21no—
132C22×C3×D5—21no—
133C22×C3×D5—22no—
134C22×C3×D5—22no—
135C22×C3×D5C22×C412yes—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5—22no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5—44no—
144C2×C3×C4×C5C22×C414yes—
145C2×C3×C4×C5C2×D412yes—
146C2×C3×C4×C5C2×D412yes—
147C3×C22⋊D5—28no—
148C2×C3×Dic5—28no—
149C2×C3×Dic5—21no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—22no—
152C2×C3×Dic5—21no—
153C2×C3×Dic5—21no—
154C2×C3×Dic5—22no—
155C2×C3×Dic5—21no—
156C2×C3×Dic5—22no—
157C2×C3×Dic5—22no—
158C2×C3×Dic5—22no—
159C2×C3×Dic5—22no—
160C2×C3×Dic5—44no—
161C2×C3×Dic5C22×C412yes—
162C2×C3×Dic5C22×C414yes—
163C3×C4×D5—44no—
164C22×C3×D4—51no—
165C23×C3×C4—51no—
166C23×C3×C4—51no—
167C23×C3×C4—51no—
168C23×C3×C4C2×D511yescharacteristic
169C3×#123—58no—
170C3×C4×D4—104no—
171C2×C3×C4⋊C4—52no—
172C2×C3×C4⋊C4—52no—
173C2×C3×C4⋊C4—52no—
174C2×C3×C4⋊C4—51no—
175C2×C3×C4⋊C4—52no—
176C2×C3×C4⋊C4—104no—
177C2×C3×C22⋊C4—52no—
178C2×C3×C22⋊C4—51no—
179C2×C3×C22⋊C4—51no—
180C2×C3×C22⋊C4—52no—
181C2×C3×C22⋊C4C2×D511yescharacteristic
182C2×C3×C22⋊C4C2×D511yescharacteristic
183C2×C3×C42—51no—
184C2×C3×C42C2×D512yes—
185C3×#95—52no—
186C3×#95—52no—
187C3×#95—52no—
188C3×#95—52no—
189C3×#95C2×D512yes—
190C24×C5C23×C311yescharacteristic
191C23×D5C23×C311yescharacteristic
192C22×C4×C5—42no—
193C22×C4×C5C3×D414yes—
194C22×C4×C5C23×C312yes—
195C22×C4×C5C23×C312yes—
196C22×C4×C5C23×C311yescharacteristic
197C22×C4×C5C23×C311yescharacteristic
198C2×C22⋊D5—22no—
199C2×C22⋊D5—22no—
200C2×C22⋊D5C2×C3×C414yes—
201C22×Dic5—22no—
202C22×Dic5—22no—
203C22×Dic5—22no—
204C22×Dic5—42no—
205C22×Dic5C2×C3×C414yescomplemented
206C22×Dic5C23×C311yescharacteristic
207C22×Dic5C23×C311yescharacteristic
208C22×Dic5C23×C312yes—
209C22×Dic5C23×C312yes—
210C22×Dic5C23×C311yescharacteristic
211C2×C4×D5—22no—
212C2×C4×D5—42no—
213C5×C22⋊C4—22no—
214C5×C22⋊C4C2×C3×C414yescomplemented
215C42×C5—42no—
216C22⋊Dic5—22no—
217#685—22no—
218#685—42no—
219#685C2×C3×C418yescomplemented
220C4⋊Dic5—42no—
221C4⋊Dic5C2×C3×C418yescomplemented
222#683—24no—
223#683—24no—
224#683—22no—
225C4×Dic5—22no—
226C2×#123—51no—
227C2×C4×D4—51no—
228C22×C4⋊C4—51no—
229#389—52no—
230#388—52no—
231#387—52no—
232#386—51no—
233#385—51no—
234#385—52no—
235#381—51no—
236C4×C22⋊C4C3×D511yescharacteristic, complemented
237C22×C3×C5—24no—
238C22×C3×C5—22no—
239C22×C3×C5—22no—
240C22×C3×C5—24no—
241C22×C3×C5C4×D414yes—
242C22×C3×C5C23×C411yescharacteristic
243C22×C3×C5C22×D411yescharacteristic
244C22×C3×C5C2×#4111yescharacteristic
245C22×C3×C5H(5,𝔽2)12yes—
246C22×C3×C52−1+412yes—
247C2×C3×D5—22no—
248C2×C3×D5—24no—
249C2×C3×D5—41no—
250C2×C3×D5—41no—
251C2×C3×D5—42no—
252C3×C4×C5—24no—
253C3×C4×C5—22no—
254C3×C4×C5—22no—
255C3×C4×C5—42no—
256C3×Dic5—24no—
257C3×Dic5—22no—
258C3×Dic5—41no—
259C3×Dic5—42no—
260C3×Dic5—41no—
261C24×C3—51no—
262C24×C3C22×D511yescharacteristic
263C2×C3×D4—54no—
264C2×C3×D4—102no—
265C2×C3×D4—102no—
266C22×C3×C4—42no—
267C22×C3×C4—54no—
268C22×C3×C4—51no—
269C22×C3×C4—52no—
270C22×C3×C4—51no—
271C22×C3×C4—51no—
272C22×C3×C4—52no—
273C22×C3×C4—102no—
274C22×C3×C4—102no—
275C22×C3×C4—102no—
276C22×C3×C4—102no—
277C22×C3×C4—202no—
278C22×C3×C4—202no—
279C22×C3×C4D2014yes—
280C22×C3×C4C22×D512yes—
281C22×C3×C4C22×D512yes—
282C22×C3×C4C22×D511yescharacteristic
283C22×C3×C4C22×D511yescharacteristic
284C3×C4⋊C4—58no—
285C3×C4⋊C4—104no—
286C3×C4⋊C4—104no—
287C3×C4⋊C4—102no—
288C3×C4⋊C4—202no—
289C3×C22⋊C4—22no—
290C3×C22⋊C4—58no—
291C3×C22⋊C4—102no—
292C3×C22⋊C4—102no—
293C3×C22⋊C4—202no—
294C3×C22⋊C4C4×D514yescomplemented
295C3×C42—42no—
296C3×C42—102no—
297C23×C5—22no—
298C23×C5—22no—
299C23×C5C22×C3×C412yes—
300C23×C5C2×C3×D412yes—
301C23×C5C3×#4112yes—
302C23×C5C24×C311yescharacteristic
303C22×D5—21no—
304C22×D5—21no—
305C22×D5—22no—
306C22×D5—22no—
307C22×D5C22×C3×C412yes—
308C2×C4×C5—22no—
309C2×C4×C5—22no—
310C2×C4×C5—22no—
311C2×C4×C5—22no—
312C2×C4×C5—22no—
313C2×C4×C5—22no—
314C2×C4×C5—22no—
315C2×C4×C5—44no—
316C2×C4×C5C22×C3×C414yes—
317C2×C4×C5C2×C3×D412yes—
318C2×C4×C5C2×C3×D412yes—
319C22⋊D5—28no—
320C2×Dic5—28no—
321C2×Dic5—21no—
322C2×Dic5—22no—
323C2×Dic5—22no—
324C2×Dic5—21no—
325C2×Dic5—21no—
326C2×Dic5—22no—
327C2×Dic5—21no—
328C2×Dic5—22no—
329C2×Dic5—22no—
330C2×Dic5—22no—
331C2×Dic5—22no—
332C2×Dic5—44no—
333C2×Dic5C22×C3×C412yes—
334C2×Dic5C22×C3×C414yes—
335C4×D5—44no—
336C22×D4—51no—
337C23×C4—51no—
338C23×C4—51no—
339C23×C4—51no—
340C23×C4C2×C3×D511yescharacteristic
341#123—58no—
342C4×D4—104no—
343C2×C4⋊C4—52no—
344C2×C4⋊C4—52no—
345C2×C4⋊C4—52no—
346C2×C4⋊C4—51no—
347C2×C4⋊C4—52no—
348C2×C4⋊C4—104no—
349C2×C22⋊C4—52no—
350C2×C22⋊C4—51no—
351C2×C22⋊C4—51no—
352C2×C22⋊C4—52no—
353C2×C22⋊C4C2×C3×D511yescharacteristic
354C2×C22⋊C4C2×C3×D511yescharacteristic
355C2×C42—51no—
356C2×C42C2×C3×D512yes—
357#95—52no—
358#95—52no—
359#95—52no—
360#95—52no—
361#95C2×C3×D512yes—
362C2×C3×C5—24no—
363C2×C3×C5C2×C4×D411yescharacteristic
364C2×C3×C5#52012yes—
365C2×C3×C5#53411yescharacteristic
366C2×C3×C5#53611yescharacteristic
367C2×C3×C5#53912yes—
368C3×D5—42no—
369C23×C3—22no—
370C23×C3—22no—
371C23×C3—52no—
372C23×C3—101no—
373C23×C3—101no—
374C23×C3—102no—
375C23×C3—102no—
376C23×C3C2×C4×D512yes—
377C23×C3C2×D2012yes—
378C23×C3#70912yes—
379C23×C3C23×D511yescharacteristic
380C3×D4—108no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—44no—
389C2×C3×C4—54no—
390C2×C3×C4—52no—
391C2×C3×C4—101no—
392C2×C3×C4—102no—
393C2×C3×C4—102no—
394C2×C3×C4—101no—
395C2×C3×C4—108no—
396C2×C3×C4—101no—
397C2×C3×C4—101no—
398C2×C3×C4—102no—
399C2×C3×C4—102no—
400C2×C3×C4—102no—
401C2×C3×C4—102no—
402C2×C3×C4—102no—
403C2×C3×C4—204no—
404C2×C3×C4—204no—
405C2×C3×C4C2×C4×D514yes—
406C2×C3×C4C2×D2012yes—
407C2×C3×C4C2×D2012yes—
408C22×C5—24no—
409C22×C5—22no—
410C22×C5—22no—
411C22×C5—24no—
412C22×C5C3×C4×D414yes—
413C22×C5C23×C3×C411yescharacteristic
414C22×C5C22×C3×D411yescharacteristic
415C22×C5C2×C3×#4111yescharacteristic
416C22×C5C3×H(5,𝔽2)12yes—
417C22×C5C3×2−1+412yes—
418C2×D5—22no—
419C2×D5—24no—
420C2×D5—41no—
421C2×D5—41no—
422C2×D5—42no—
423C4×C5—24no—
424C4×C5—22no—
425C4×C5—22no—
426C4×C5—42no—
427Dic5—24no—
428Dic5—22no—
429Dic5—41no—
430Dic5—42no—
431Dic5—41no—
432C24—51no—
433C24C22×C3×D511yescharacteristic
434C2×D4—54no—
435C2×D4—102no—
436C2×D4—102no—
437C22×C4—42no—
438C22×C4—54no—
439C22×C4—51no—
440C22×C4—52no—
441C22×C4—51no—
442C22×C4—51no—
443C22×C4—52no—
444C22×C4—102no—
445C22×C4—102no—
446C22×C4—102no—
447C22×C4—102no—
448C22×C4—202no—
449C22×C4—202no—
450C22×C4C3×D2014yes—
451C22×C4C22×C3×D512yes—
452C22×C4C22×C3×D512yes—
453C22×C4C22×C3×D511yescharacteristic
454C22×C4C22×C3×D511yescharacteristic
455C4⋊C4—58no—
456C4⋊C4—104no—
457C4⋊C4—104no—
458C4⋊C4—102no—
459C4⋊C4—202no—
460C22⋊C4—22no—
461C22⋊C4—58no—
462C22⋊C4—102no—
463C22⋊C4—102no—
464C22⋊C4—202no—
465C22⋊C4C3×C4×D514yescomplemented
466C42—42no—
467C42—102no—
468C3×C5#232211yescharacteristic, complemented, Hall
469C22×C3—22no—
470C22×C3—22no—
471C22×C3—24no—
472C22×C3—24no—
473C22×C3—102no—
474C22×C3—104no—
475C22×C3—201no—
476C22×C3—201no—
477C22×C3—202no—
478C22×C3C4×D2014yes—
479C22×C3C22×C4×D511yescharacteristic
480C22×C3C22×D2011yescharacteristic
481C22×C3C2×#70911yescharacteristic
482C22×C3#414412yes—
483C22×C3#415012yes—
484C3×C4—22no—
485C3×C4—22no—
486C3×C4—24no—
487C3×C4—42no—
488C3×C4—104no—
489C3×C4—102no—
490C3×C4—201no—
491C3×C4—202no—
492C3×C4—201no—
493C2×C5—24no—
494C2×C5C2×C3×C4×D411yescharacteristic
495C2×C5C3×#52012yes—
496C2×C5C3×#53411yescharacteristic
497C2×C5C3×#53611yescharacteristic
498C2×C5C3×#53912yes—
499D5—42no—
500C23—22no—
501C23—22no—
502C23—52no—
503C23—101no—
504C23—101no—
505C23—102no—
506C23—102no—
507C23C2×C3×C4×D512yes—
508C23C2×C3×D2012yes—
509C23C3×#70912yes—
510C23C23×C3×D511yescharacteristic
511D4—108no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—44no—
520C2×C4—54no—
521C2×C4—52no—
522C2×C4—101no—
523C2×C4—102no—
524C2×C4—102no—
525C2×C4—101no—
526C2×C4—108no—
527C2×C4—101no—
528C2×C4—101no—
529C2×C4—102no—
530C2×C4—102no—
531C2×C4—102no—
532C2×C4—102no—
533C2×C4—102no—
534C2×C4—204no—
535C2×C4—204no—
536C2×C4C2×C3×C4×D514yes—
537C2×C4C2×C3×D2012yes—
538C2×C4C2×C3×D2012yes—
539C2×C3—24no—
540C2×C3—202no—
541C2×C3C2×C4×D2011yescharacteristic
542C2×C3#6582711yescharacteristic
543C2×C3#6586011yescharacteristic
544C2×C3#6588012yes—
545C2×C3#6589812yes—
546C5C3×#232211yescharacteristic, complemented, Sylow
547C22—22no—
548C22—24no—
549C22—24no—
550C22—22no—
551C22—104no—
552C22—102no—
553C22—201no—
554C22—202no—
555C22—201no—
556C22C3×C4×D2014yes—
557C22C22×C3×C4×D511yescharacteristic
558C22C22×C3×D2011yescharacteristic
559C22C2×C3×#70911yescharacteristic
560C22C3×#414412yes—
561C22C3×#415012yes—
562C4—24no—
563C4—22no—
564C4—22no—
565C4—42no—
566C4—104no—
567C4—102no—
568C4—201no—
569C4—201no—
570C4—202no—
571C3#1060517711yescharacteristic, direct product factor, Sylow
572C2—24no—
573C2—202no—
574C2C2×C3×C4×D2011yescharacteristic
575C2C3×#6582711yescharacteristic
576C2C3×#6586011yescharacteristic
577C2C3×#6588012yes—
578C2C3×#6589812yes—
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C4×C5×C22⋊C4C2
socleC23×C3×C5C24
prime radicalC22×C3×C22⋊D5C22
cosocleC23×C5C24×C3
hypercenterC3×C4×C22⋊C4D5
hypocenterC5C3×#2322
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×#683C2semidirect
4. C3×C4×C5×C22⋊C4C2semidirect
6. C3×#65239C2semidirect
7. C3×#65232C2semidirect
8. C3×#65229C2semidirect
9. C3×#65217C2semidirect
10. C3×#64957C2semidirect
11. C3×#64942C2semidirect
12. #10605177C3direct (N × H)
33. C3×#4032C4semidirect
41. C22×#683C2×C3semidirect
43. C4×C5×C22⋊C4C2×C3semidirect
45. #65239C2×C3semidirect
46. #65232C2×C3semidirect
47. #65229C2×C3semidirect
48. #65217C2×C3semidirect
49. #64957C2×C3semidirect
50. #64942C2×C3semidirect
66. C22×C3×Dic5C2×C4semidirect
75. C3×C5×C22⋊C4C2×C4semidirect
80. C3×#685C2×C4semidirect
82. C3×C4⋊Dic5C2×C4semidirect
97. C3×C4×C22⋊C4D5semidirect
118. #4032C3×C4semidirect
205. C22×Dic5C2×C3×C4semidirect
214. C5×C22⋊C4C2×C3×C4semidirect
219. #685C2×C3×C4semidirect
221. C4⋊Dic5C2×C3×C4semidirect
236. C4×C22⋊C4C3×D5semidirect
294. C3×C22⋊C4C4×D5semidirect
465. C22⋊C4C3×C4×D5semidirect
468. C3×C5#2322semidirect
546. C5C3×#2322semidirect
571. C3#10605177direct (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
C22×C3×#6832
C2×C3×#40322
C3×C4×C5×C22⋊C42
C3×#652472
C3×#652392
C3×#652322
C3×#652292
C3×#652172
C3×#649572
C3×#649422
#106051773
C3×#23225