Finite Group Databasebeta

← C3×#10605499 #14326672

Subgroups — C3×#10605499 #14326672

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×C4⋊C4C211yesmaximal, characteristic
2C3×C4×C5×C4⋊C4C211yesmaximal, characteristic, complemented
3C3×#65276C211yesmaximal, characteristic
4C3×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
5C3×#65262C211yesmaximal, characteristic, complemented
6C3×C4×#685C211yesmaximal, characteristic
7C3×C4×#685C212yesmaximal
8C3×#65222C212yesmaximal, complemented
9C3×#65217C211yesmaximal, characteristic, complemented
10C3×#64956C212yesmaximal
11C3×#64941C212yesmaximal, complemented
12#10605499C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C4×D5C2211yescharacteristic
14C22×C3×C4×D5C2212yes—
15C2×C3×C5×C4⋊C4C2211yescharacteristic
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17C2×C3×C42×C5C2211yescharacteristic
18C2×C3×C42×C5C2212yes—
19C2×C3×#685C2211yescharacteristic
20C2×C3×#685C2212yes—
21C2×C3×#685C2211yescharacteristic
22C2×C3×C4⋊Dic5C2211yescharacteristic
23C2×C3×C4⋊Dic5C2211yescharacteristic
24C2×C3×#683C2212yes—
25C2×C3×#683C2212yes—
26C2×C3×#683C2212yes—
27C2×C3×C4×Dic5C2211yescharacteristic
28C2×C3×C4×Dic5C2212yes—
29C3×D5×C4⋊C4C418yescomplemented
30C3×C5×#95C2212yes—
31C3×#3963C2211yescharacteristic
32C3×#3963C2212yes—
33C3×#3963C2212yes—
34C3×#3963C2212yes—
35C3×#3963C2212yes—
36C3×#3963C2211yescharacteristic
37C3×#2345—51nomaximal, Hall
38C2×D5×C4⋊C4C2×C311yescharacteristic
39C4×C5×C4⋊C4C2×C311yescharacteristic, complemented
40#65276C2×C311yescharacteristic
41C4⋊C4×Dic5C2×C311yescharacteristic, complemented
42#65262C2×C311yescharacteristic, complemented
43C4×#685C2×C311yescharacteristic
44C4×#685C2×C312yes—
45#65222C2×C312yescomplemented
46#65217C2×C311yescharacteristic, complemented
47#64956C2×C312yes—
48#64941C2×C312yescomplemented
49C23×C3×D5C2311yescharacteristic
50C22×C3×C4×C5C2312yes—
51C22×C3×C4×C5C2311yescharacteristic
52C22×C3×C4×C5C2312yes—
53C22×C3×C4×C5C2311yescharacteristic
54C22×C3×C4×C5C2311yescharacteristic
55C22×C3×Dic5C2311yescharacteristic
56C22×C3×Dic5C2312yes—
57C22×C3×Dic5C2311yescharacteristic
58C22×C3×Dic5C2312yes—
59C22×C3×Dic5C2311yescharacteristic
60C2×C3×C4×D5—22no—
61C2×C3×C4×D5—22no—
62C2×C3×C4×D5—42no—
63C2×C3×C4×D5—42no—
64C2×C3×C4×D5C2×C414yes—
65C2×C3×C4×D5C2×C418yes—
66C3×C5×C4⋊C4—22no—
67C3×C5×C4⋊C4C2×C414yes—
68C3×C42×C5—22no—
69C3×C42×C5—42no—
70C3×#685—22no—
71C3×#685—24no—
72C3×#685Q814yes—
73C3×C4⋊Dic5—22no—
74C3×C4⋊Dic5C2×C414yes—
75C3×#683—42no—
76C3×#683—42no—
77C3×#683C2×C418yes—
78C3×C4×Dic5—22no—
79C3×C4×Dic5—42no—
80C22×C3×C4⋊C4—51no—
81C3×#389—51no—
82C3×#389—51no—
83C3×#387—52no—
84C3×#387—52no—
85C3×#380—51no—
86C3×#380—52no—
87C3×C4×C4⋊C4—51no—
88C3×C4×C4⋊C4D511yescharacteristic, complemented
89C3×C4×C22⋊C4—51no—
90C3×C4×C22⋊C4—52no—
91C22×C4×D5C22×C311yescharacteristic
92C22×C4×D5C22×C312yes—
93C2×C5×C4⋊C4C22×C311yescharacteristic
94C2×C5×C4⋊C4C22×C311yescharacteristic
95C2×C42×C5C22×C311yescharacteristic
96C2×C42×C5C22×C312yes—
97C2×#685C22×C311yescharacteristic
98C2×#685C22×C312yes—
99C2×#685C22×C311yescharacteristic
100C2×C4⋊Dic5C22×C311yescharacteristic
101C2×C4⋊Dic5C22×C311yescharacteristic
102C2×#683C22×C312yes—
103C2×#683C22×C312yes—
104C2×#683C22×C312yes—
105C2×C4×Dic5C22×C311yescharacteristic
106C2×C4×Dic5C22×C312yes—
107D5×C4⋊C4C3×C418yescomplemented
108C5×#95C22×C312yes—
109#3963C22×C311yescharacteristic
110#3963C22×C312yes—
111#3963C22×C312yes—
112#3963C22×C312yes—
113#3963C22×C312yes—
114#3963C22×C311yescharacteristic
115#2345—51noSylow
116C23×C3×C5C2411yescharacteristic
117C22×C3×D5—21no—
118C22×C3×D5—21no—
119C22×C3×D5—21no—
120C22×C3×D5—21no—
121C22×C3×D5C22×C412yes—
122C22×C3×D5C2×Q812yes—
123C22×C3×D5#4112yes—
124C2×C3×C4×C5—21no—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5—21no—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5—21no—
130C2×C3×C4×C5—21no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5C22×C414yes—
135C2×C3×C4×C5C22×C412yes—
136C2×C3×C4×C5C2×Q812yes—
137C2×C3×C4×C5#4112yes—
138C2×C3×C4×C5#4112yes—
139C2×C3×Dic5—21no—
140C2×C3×Dic5—21no—
141C2×C3×Dic5—21no—
142C2×C3×Dic5—21no—
143C2×C3×Dic5—22no—
144C2×C3×Dic5—22no—
145C2×C3×Dic5—21no—
146C2×C3×Dic5—22no—
147C2×C3×Dic5—21no—
148C2×C3×Dic5—22no—
149C2×C3×Dic5—22no—
150C2×C3×Dic5—21no—
151C2×C3×Dic5C22×C412yes—
152C2×C3×Dic5C22×C414yes—
153C2×C3×Dic5C2×Q812yes—
154C3×C4×D5—28no—
155C3×C4×D5—48no—
156C23×C3×C4—51no—
157C23×C3×C4—52no—
158C2×C3×C4⋊C4—52no—
159C2×C3×C4⋊C4—51no—
160C2×C3×C4⋊C4—58no—
161C2×C3×C4⋊C4—51no—
162C2×C3×C4⋊C4—52no—
163C2×C3×C4⋊C4—52no—
164C2×C3×C4⋊C4C2×D511yescharacteristic
165C2×C3×C4⋊C4C2×D511yescharacteristic
166C2×C3×C22⋊C4—51no—
167C2×C3×C22⋊C4—52no—
168C2×C3×C22⋊C4—51no—
169C2×C3×C42—51no—
170C2×C3×C42—52no—
171C2×C3×C42C2×D511yescharacteristic
172C2×C3×C42C2×D512yes—
173C3×#95—51no—
174C3×#95—51no—
175C3×#95—52no—
176C3×#95—52no—
177C3×#95—52no—
178C3×#95—52no—
179C3×#95C2×D512yes—
180C23×D5C23×C311yescharacteristic
181C22×C4×C5C23×C312yes—
182C22×C4×C5C23×C311yescharacteristic
183C22×C4×C5C23×C312yes—
184C22×C4×C5C23×C311yescharacteristic
185C22×C4×C5C23×C311yescharacteristic
186C22×Dic5C23×C311yescharacteristic
187C22×Dic5C23×C312yes—
188C22×Dic5C23×C311yescharacteristic
189C22×Dic5C23×C312yes—
190C22×Dic5C23×C311yescharacteristic
191C2×C4×D5—22no—
192C2×C4×D5—22no—
193C2×C4×D5—42no—
194C2×C4×D5—42no—
195C2×C4×D5C2×C3×C414yes—
196C2×C4×D5C2×C3×C418yes—
197C5×C4⋊C4—22no—
198C5×C4⋊C4C2×C3×C414yes—
199C42×C5—22no—
200C42×C5—42no—
201#685—22no—
202#685—24no—
203#685C3×Q814yes—
204C4⋊Dic5—22no—
205C4⋊Dic5C2×C3×C414yes—
206#683—42no—
207#683—42no—
208#683C2×C3×C418yes—
209C4×Dic5—22no—
210C4×Dic5—42no—
211C22×C4⋊C4—51no—
212#389—51no—
213#389—51no—
214#387—52no—
215#387—52no—
216#380—51no—
217#380—52no—
218C4×C4⋊C4—51no—
219C4×C4⋊C4C3×D511yescharacteristic, complemented
220C4×C22⋊C4—51no—
221C4×C22⋊C4—52no—
222C22×C3×C5C23×C411yescharacteristic
223C22×C3×C5C22×Q811yescharacteristic
224C22×C3×C5C2×#4111yescharacteristic
225C22×C3×C5C2×#4111yescharacteristic
226C22×C3×C5C2×#4111yescharacteristic
227C22×C3×C5H(5,𝔽2)11yescharacteristic
228C22×C3×C5H(5,𝔽2)11yescharacteristic
229C2×C3×D5—22no—
230C2×C3×D5—22no—
231C2×C3×D5—22no—
232C2×C3×D5—22no—
233C2×C3×D5—22no—
234C2×C3×D5—22no—
235C2×C3×D5C4×Q814yes—
236C3×C4×C5—24no—
237C3×C4×C5—22no—
238C3×C4×C5—41no—
239C3×C4×C5—42no—
240C3×C4×C5#11714yes—
241C3×Dic5—22no—
242C3×Dic5—24no—
243C3×Dic5—22no—
244C3×Dic5—42no—
245C3×Dic5—41no—
246C24×C3—51no—
247C22×C3×C4—51no—
248C22×C3×C4—51no—
249C22×C3×C4—52no—
250C22×C3×C4—54no—
251C22×C3×C4—58no—
252C22×C3×C4—51no—
253C22×C3×C4—52no—
254C22×C3×C4—102no—
255C22×C3×C4—102no—
256C22×C3×C4—202no—
257C22×C3×C4—202no—
258C22×C3×C4C22×D512yes—
259C22×C3×C4C22×D511yescharacteristic
260C22×C3×C4C22×D512yes—
261C22×C3×C4C22×D511yescharacteristic
262C22×C3×C4C22×D511yescharacteristic
263C3×C4⋊C4—22no—
264C3×C4⋊C4—58no—
265C3×C4⋊C4—54no—
266C3×C4⋊C4—102no—
267C3×C4⋊C4—202no—
268C3×C4⋊C4—202no—
269C3×C4⋊C4C4×D514yes—
270C3×C22⋊C4—54no—
271C3×C22⋊C4—102no—
272C3×C22⋊C4—104no—
273C3×C42—22no—
274C3×C42—42no—
275C3×C42—102no—
276C3×C42—202no—
277C23×C5C24×C311yescharacteristic
278C22×D5—21no—
279C22×D5—21no—
280C22×D5—21no—
281C22×D5—21no—
282C22×D5C22×C3×C412yes—
283C22×D5C2×C3×Q812yes—
284C22×D5C3×#4112yes—
285C2×C4×C5—21no—
286C2×C4×C5—22no—
287C2×C4×C5—21no—
288C2×C4×C5—22no—
289C2×C4×C5—22no—
290C2×C4×C5—21no—
291C2×C4×C5—21no—
292C2×C4×C5—22no—
293C2×C4×C5—21no—
294C2×C4×C5—22no—
295C2×C4×C5C22×C3×C414yes—
296C2×C4×C5C22×C3×C412yes—
297C2×C4×C5C2×C3×Q812yes—
298C2×C4×C5C3×#4112yes—
299C2×C4×C5C3×#4112yes—
300C2×Dic5—21no—
301C2×Dic5—21no—
302C2×Dic5—21no—
303C2×Dic5—21no—
304C2×Dic5—22no—
305C2×Dic5—22no—
306C2×Dic5—21no—
307C2×Dic5—22no—
308C2×Dic5—21no—
309C2×Dic5—22no—
310C2×Dic5—22no—
311C2×Dic5—21no—
312C2×Dic5C22×C3×C412yes—
313C2×Dic5C22×C3×C414yes—
314C2×Dic5C2×C3×Q812yes—
315C4×D5—28no—
316C4×D5—48no—
317C23×C4—51no—
318C23×C4—52no—
319C2×C4⋊C4—52no—
320C2×C4⋊C4—51no—
321C2×C4⋊C4—58no—
322C2×C4⋊C4—51no—
323C2×C4⋊C4—52no—
324C2×C4⋊C4—52no—
325C2×C4⋊C4C2×C3×D511yescharacteristic
326C2×C4⋊C4C2×C3×D511yescharacteristic
327C2×C22⋊C4—51no—
328C2×C22⋊C4—52no—
329C2×C22⋊C4—51no—
330C2×C42—51no—
331C2×C42—52no—
332C2×C42C2×C3×D511yescharacteristic
333C2×C42C2×C3×D512yes—
334#95—51no—
335#95—51no—
336#95—52no—
337#95—52no—
338#95—52no—
339#95—52no—
340#95C2×C3×D512yes—
341C2×C3×C5C2×#11711yescharacteristic
342C2×C3×C5C2×C4×Q811yescharacteristic
343C2×C3×C5#51811yescharacteristic
344C2×C3×C5#55311yescharacteristic
345C2×C3×C5#55311yescharacteristic
346C2×C3×C5#55411yescharacteristic
347C2×C3×C5#55411yescharacteristic
348C3×D5—24no—
349C23×C3—52no—
350C23×C3—52no—
351C23×C3—52no—
352C23×C3—101no—
353C23×C3—101no—
354C23×C3—101no—
355C23×C3—101no—
356C23×C3C23×D511yescharacteristic
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—21no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—21no—
365C2×C3×C4—22no—
366C2×C3×C4—21no—
367C2×C3×C4—52no—
368C2×C3×C4—54no—
369C2×C3×C4—52no—
370C2×C3×C4—101no—
371C2×C3×C4—101no—
372C2×C3×C4—101no—
373C2×C3×C4—102no—
374C2×C3×C4—101no—
375C2×C3×C4—102no—
376C2×C3×C4—108no—
377C2×C3×C4—101no—
378C2×C3×C4—102no—
379C2×C3×C4—101no—
380C2×C3×C4—102no—
381C2×C3×C4—101no—
382C2×C3×C4—102no—
383C2×C3×C4—208no—
384C2×C3×C4C2×C4×D514yes—
385C2×C3×C4C2×C4×D512yes—
386C2×C3×C4#70912yes—
387C2×C3×C4#70912yes—
388C2×C3×C4Q8×D512yes—
389C22×C5C23×C3×C411yescharacteristic
390C22×C5C22×C3×Q811yescharacteristic
391C22×C5C2×C3×#4111yescharacteristic
392C22×C5C2×C3×#4111yescharacteristic
393C22×C5C2×C3×#4111yescharacteristic
394C22×C5C3×H(5,𝔽2)11yescharacteristic
395C22×C5C3×H(5,𝔽2)11yescharacteristic
396C2×D5—22no—
397C2×D5—22no—
398C2×D5—22no—
399C2×D5—22no—
400C2×D5—22no—
401C2×D5—22no—
402C2×D5C3×C4×Q814yes—
403C4×C5—24no—
404C4×C5—22no—
405C4×C5—41no—
406C4×C5—42no—
407C4×C5C3×#11714yes—
408Dic5—22no—
409Dic5—24no—
410Dic5—22no—
411Dic5—42no—
412Dic5—41no—
413C24—51no—
414C22×C4—51no—
415C22×C4—51no—
416C22×C4—52no—
417C22×C4—54no—
418C22×C4—58no—
419C22×C4—51no—
420C22×C4—52no—
421C22×C4—102no—
422C22×C4—102no—
423C22×C4—202no—
424C22×C4—202no—
425C22×C4C22×C3×D512yes—
426C22×C4C22×C3×D511yescharacteristic
427C22×C4C22×C3×D512yes—
428C22×C4C22×C3×D511yescharacteristic
429C22×C4C22×C3×D511yescharacteristic
430C4⋊C4—22no—
431C4⋊C4—58no—
432C4⋊C4—54no—
433C4⋊C4—102no—
434C4⋊C4—202no—
435C4⋊C4—202no—
436C4⋊C4C3×C4×D514yes—
437C22⋊C4—54no—
438C22⋊C4—102no—
439C22⋊C4—104no—
440C42—22no—
441C42—42no—
442C42—102no—
443C42—202no—
444C3×C5#234511yescharacteristic, complemented, Hall
445C22×C3—54no—
446C22×C3—102no—
447C22×C3—102no—
448C22×C3—102no—
449C22×C3—102no—
450C22×C3—102no—
451C22×C3—102no—
452C22×C3C22×C4×D511yescharacteristic
453C22×C3C2×#70911yescharacteristic
454C22×C3C2×#70911yescharacteristic
455C22×C3#414411yescharacteristic
456C22×C3C2×Q8×D511yescharacteristic
457C22×C3D5×#4111yescharacteristic
458C22×C3#414911yescharacteristic
459C3×C4—22no—
460C3×C4—24no—
461C3×C4—41no—
462C3×C4—42no—
463C3×C4—102no—
464C3×C4—104no—
465C3×C4—102no—
466C3×C4—202no—
467C3×C4—201no—
468C3×C4#401814yes—
469C2×C5C2×C3×#11711yescharacteristic
470C2×C5C2×C3×C4×Q811yescharacteristic
471C2×C5C3×#51811yescharacteristic
472C2×C5C3×#55311yescharacteristic
473C2×C5C3×#55311yescharacteristic
474C2×C5C3×#55411yescharacteristic
475C2×C5C3×#55411yescharacteristic
476D5—24no—
477C23—52no—
478C23—52no—
479C23—52no—
480C23—101no—
481C23—101no—
482C23—101no—
483C23—101no—
484C23C23×C3×D511yescharacteristic
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—21no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—21no—
493C2×C4—22no—
494C2×C4—21no—
495C2×C4—54no—
496C2×C4—52no—
497C2×C4—52no—
498C2×C4—101no—
499C2×C4—101no—
500C2×C4—101no—
501C2×C4—102no—
502C2×C4—101no—
503C2×C4—102no—
504C2×C4—108no—
505C2×C4—101no—
506C2×C4—102no—
507C2×C4—101no—
508C2×C4—102no—
509C2×C4—101no—
510C2×C4—102no—
511C2×C4—208no—
512C2×C4C2×C3×C4×D514yes—
513C2×C4C2×C3×C4×D512yes—
514C2×C4C3×#70912yes—
515C2×C4C3×#70912yes—
516C2×C4C3×Q8×D512yes—
517C2×C3—104no—
518C2×C3C2×#401811yescharacteristic
519C2×C3#6584511yescharacteristic
520C2×C3#6586411yescharacteristic
521C2×C3#6587911yescharacteristic
522C2×C3#6589211yescharacteristic
523C2×C3C4×Q8×D511yescharacteristic
524C2×C3#6591311yescharacteristic
525C5C3×#234511yescharacteristic, complemented, Sylow
526C22—54no—
527C22—102no—
528C22—102no—
529C22—102no—
530C22—102no—
531C22—102no—
532C22—102no—
533C22C22×C3×C4×D511yescharacteristic
534C22C2×C3×#70911yescharacteristic
535C22C2×C3×#70911yescharacteristic
536C22C3×#414411yescharacteristic
537C22C2×C3×Q8×D511yescharacteristic
538C22C3×D5×#4111yescharacteristic
539C22C3×#414911yescharacteristic
540C4—22no—
541C4—24no—
542C4—41no—
543C4—42no—
544C4—104no—
545C4—102no—
546C4—102no—
547C4—202no—
548C4—201no—
549C4C3×#401814yes—
550C3#1060549911yescharacteristic, direct product factor, Sylow
551C2—104no—
552C2C2×C3×#401811yescharacteristic
553C2C3×#6584511yescharacteristic
554C2C3×#6586411yescharacteristic
555C2C3×#6587911yescharacteristic
556C2C3×#6589211yescharacteristic
557C2C3×C4×Q8×D511yescharacteristic
558C2C3×#6591311yescharacteristic
subgroupG/H
centerC23×C3C23×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×#2345
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×C4×C5×C4⋊C4C2semidirect
4. C3×C4⋊C4×Dic5C2semidirect
5. C3×#65262C2semidirect
8. C3×#65222C2semidirect
9. C3×#65217C2semidirect
11. C3×#64941C2semidirect
12. #10605499C3direct (N × H)
29. C3×D5×C4⋊C4C4semidirect
39. C4×C5×C4⋊C4C2×C3semidirect
41. C4⋊C4×Dic5C2×C3semidirect
42. #65262C2×C3semidirect
45. #65222C2×C3semidirect
46. #65217C2×C3semidirect
48. #64941C2×C3semidirect
88. C3×C4×C4⋊C4D5semidirect
107. D5×C4⋊C4C3×C4semidirect
219. C4×C4⋊C4C3×D5semidirect
444. C3×C5#2345semidirect
525. C5C3×#2345semidirect
550. C3#10605499direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D5×C4⋊C42
C3×C4×C5×C4⋊C42
C3×#652762
C3×C4⋊C4×Dic52
C3×#652622
C3×C4×#6852
C3×#652222
C3×#652172
C3×#649562
C3×#649412
#106054993
C3×#23455