Finite Group Databasebeta

← C3×#10602830 #14301019

Subgroups — C3×#10602830 #14301019

Order 1920.

876 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C5×D8C211yesmaximal, characteristic
2C2×C3×D4×Dic5C211yesmaximal, characteristic, complemented
3C3×#65510C211yesmaximal, characteristic, complemented
4C2×C3×#3964C211yesmaximal, characteristic, complemented
5C2×C3×#3964C211yesmaximal, characteristic, complemented
6C3×#64771C211yesmaximal, characteristic, complemented
7C3×#64770C211yesmaximal, characteristic, complemented
8#10602830C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×C3×C5×D4C2211yescharacteristic
11C23×C3×Dic5—21no—
12C2×C3×C5×D8—22no—
13C2×C3×C5×D8—22no—
14C2×C3×C5×D8C414yescomplemented
15C22×C3×C5×C8C2211yescharacteristic
16C2×C3×C22⋊Dic5—21no—
17C2×C3×C22⋊Dic5—21no—
18C2×C3×C22⋊Dic5—21no—
19C3×D4×Dic5—22no—
20C3×D4×Dic5—22no—
21C2×C3×C4⋊Dic5C2211yescharacteristic
22C2×C3×C4⋊Dic5C2211yescharacteristic
23C2×C3×C4×Dic5C2211yescharacteristic
24C22×C3×#168C2211yescharacteristic
25C3×#3964—22no—
26C3×#3964—22no—
27C3×#1879—51nomaximal, Hall
28C22×C5×D8C2×C311yescharacteristic
29C2×D4×Dic5C2×C311yescharacteristic, complemented
30#65510C2×C311yescharacteristic, complemented
31C2×#3964C2×C311yescharacteristic, complemented
32C2×#3964C2×C311yescharacteristic, complemented
33#64771C2×C311yescharacteristic, complemented
34#64770C2×C311yescharacteristic, complemented
35C24×C3×C5—21no—
36C24×C3×C5—21no—
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4—21no—
42C2×C3×C5×D4—21no—
43C2×C3×C5×D4—21no—
44C2×C3×C5×D4—21no—
45C2×C3×C5×D4C2×C412yes—
46C2×C3×C5×D4C2×C412yescomplemented
47C2×C3×C5×D4D412yes—
48C2×C3×C5×D4D412yes—
49C22×C3×C4×C5C2311yescharacteristic
50C22×C3×Dic5—24no—
51C22×C3×Dic5—21no—
52C22×C3×Dic5—21no—
53C22×C3×Dic5—42no—
54C22×C3×Dic5—42no—
55C22×C3×Dic5D411yescharacteristic
56C22×C3×Dic5D411yescharacteristic
57C3×C5×D8—28no—
58C2×C3×C5×C8—21no—
59C2×C3×C5×C8—21no—
60C2×C3×C5×C8C2×C412yescomplemented
61C3×C22⋊Dic5—24no—
62C3×C22⋊Dic5—42no—
63C3×C22⋊Dic5—42no—
64C3×C4⋊Dic5—21no—
65C3×C4⋊Dic5—21no—
66C3×C4⋊Dic5—21no—
67C3×C4⋊Dic5D412yes—
68C3×C4×Dic5—21no—
69C3×C4×Dic5—21no—
70C2×C3×#168—21no—
71C2×C3×#168—21no—
72C2×C3×#168—21no—
73C22×C3×D8D511yescharacteristic
74C2×C3×C4×D4—51no—
75C2×C3×#102—51no—
76C2×C3×#102—51no—
77C3×#390—51no—
78C3×#340—51no—
79C3×#336—51no—
80C22×C5×D4C22×C311yescharacteristic
81C22×C5×D4C22×C311yescharacteristic
82C23×Dic5—21no—
83C2×C5×D8—22no—
84C2×C5×D8—22no—
85C2×C5×D8C3×C414yescomplemented
86C22×C5×C8C22×C311yescharacteristic
87C2×C22⋊Dic5—21no—
88C2×C22⋊Dic5—21no—
89C2×C22⋊Dic5—21no—
90D4×Dic5—22no—
91D4×Dic5—22no—
92C2×C4⋊Dic5C22×C311yescharacteristic
93C2×C4⋊Dic5C22×C311yescharacteristic
94C2×C4×Dic5C22×C311yescharacteristic
95C22×#168C22×C311yescharacteristic
96#3964—22no—
97#3964—22no—
98#1879—51noSylow
99C23×C3×C5—22no—
100C23×C3×C5—22no—
101C23×C3×C5—22no—
102C23×C3×C5—22no—
103C23×C3×C5—41no—
104C23×C3×C5—41no—
105C23×C3×C5—41no—
106C23×C3×C5—41no—
107C23×C3×C5—41no—
108C23×C3×C5—41no—
109C23×C3×C5—41no—
110C23×C3×C5—41no—
111C23×C3×C5—41no—
112C23×C3×C5—41no—
113C23×C3×C5C2×D411yescharacteristic
114C3×C5×D4—22no—
115C3×C5×D4—22no—
116C3×C5×D4—22no—
117C3×C5×D4—22no—
118C3×C5×D4—22no—
119C3×C5×D4—41no—
120C3×C5×D4—41no—
121C3×C5×D4C22⋊C414yescomplemented
122C2×C3×C4×C5C22×C411yescharacteristic
123C2×C3×C4×C5C2×D411yescharacteristic
124C2×C3×C4×C5C2×D411yescharacteristic
125C2×C3×C4×C5C2×D411yescharacteristic
126C2×C3×C4×C5#4111yescharacteristic
127C2×C3×C4×C5#4111yescharacteristic
128C2×C3×Dic5—21no—
129C2×C3×Dic5—21no—
130C2×C3×Dic5—21no—
131C2×C3×Dic5—22no—
132C2×C3×Dic5—21no—
133C2×C3×Dic5—21no—
134C2×C3×Dic5—48no—
135C2×C3×Dic5—41no—
136C2×C3×Dic5—41no—
137C2×C3×Dic5—41no—
138C2×C3×Dic5—41no—
139C2×C3×Dic5—41no—
140C2×C3×Dic5D812yescomplemented
141C3×C5×C8—22no—
142C3×#168—41no—
143C22×C3×D4C2×D511yescharacteristic
144C22×C3×D4C2×D511yescharacteristic
145C23×C3×C4—101no—
146C2×C3×D8—22no—
147C2×C3×D8—22no—
148C2×C3×D8Dic514yescomplemented
149C22×C3×C8—51no—
150C22×C3×C8C2×D511yescharacteristic
151C3×C4×D4—102no—
152C3×C4×D4—102no—
153C2×C3×C4⋊C4—51no—
154C2×C3×C4⋊C4—51no—
155C2×C3×C22⋊C4—101no—
156C2×C3×C22⋊C4—101no—
157C2×C3×C22⋊C4—101no—
158C2×C3×C42—51no—
159C3×#102—102no—
160C3×#102—102no—
161C24×C5—21no—
162C24×C5—21no—
163C2×C5×D4—21no—
164C2×C5×D4—21no—
165C2×C5×D4—21no—
166C2×C5×D4—21no—
167C2×C5×D4—21no—
168C2×C5×D4—21no—
169C2×C5×D4—21no—
170C2×C5×D4—21no—
171C2×C5×D4C2×C3×C412yes—
172C2×C5×D4C2×C3×C412yescomplemented
173C2×C5×D4C3×D412yes—
174C2×C5×D4C3×D412yes—
175C22×C4×C5C23×C311yescharacteristic
176C22×Dic5—24no—
177C22×Dic5—21no—
178C22×Dic5—21no—
179C22×Dic5—42no—
180C22×Dic5—42no—
181C22×Dic5C3×D411yescharacteristic
182C22×Dic5C3×D411yescharacteristic
183C5×D8—28no—
184C2×C5×C8—21no—
185C2×C5×C8—21no—
186C2×C5×C8C2×C3×C412yescomplemented
187C22⋊Dic5—24no—
188C22⋊Dic5—42no—
189C22⋊Dic5—42no—
190C4⋊Dic5—21no—
191C4⋊Dic5—21no—
192C4⋊Dic5—21no—
193C4⋊Dic5C3×D412yes—
194C4×Dic5—21no—
195C4×Dic5—21no—
196C2×#168—21no—
197C2×#168—21no—
198C2×#168—21no—
199C22×D8C3×D511yescharacteristic
200C2×C4×D4—51no—
201C2×#102—51no—
202C2×#102—51no—
203#390—51no—
204#340—51no—
205#336—51no—
206C22×C3×C5—24no—
207C22×C3×C5—42no—
208C22×C3×C5—42no—
209C22×C3×C5—42no—
210C22×C3×C5—42no—
211C22×C3×C5—42no—
212C22×C3×C5—42no—
213C22×C3×C5—42no—
214C22×C3×C5—42no—
215C22×C3×C5—42no—
216C22×C3×C5—81no—
217C22×C3×C5—81no—
218C22×C3×C5—81no—
219C22×C3×C5—81no—
220C22×C3×C5C4×D411yescharacteristic
221C22×C3×C5#12011yescharacteristic
222C22×C3×C5#12111yescharacteristic
223C22×C3×C5C2×D811yescharacteristic
224C22×C3×C5#13511yescharacteristic
225C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
226C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
227C3×C4×C5C2×C22⋊C411yescharacteristic
228C3×C4×C5C4×D411yescharacteristic
229C3×C4×C5#12111yescharacteristic
230C3×C4×C5#12311yescharacteristic
231C3×Dic5—22no—
232C3×Dic5—42no—
233C3×Dic5—41no—
234C3×Dic5—81no—
235C24×C3—21no—
236C24×C3—21no—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4C2×Dic512yes—
246C2×C3×D4C2×Dic512yescomplemented
247C2×C3×D4C22⋊D512yes—
248C2×C3×D4C22⋊D512yes—
249C22×C3×C4—51no—
250C22×C3×C4—51no—
251C22×C3×C4—104no—
252C22×C3×C4—101no—
253C22×C3×C4—101no—
254C22×C3×C4—202no—
255C22×C3×C4—202no—
256C22×C3×C4C22×D511yescharacteristic
257C3×D8—28no—
258C2×C3×C8—21no—
259C2×C3×C8—21no—
260C2×C3×C8—101no—
261C2×C3×C8—101no—
262C2×C3×C8—101no—
263C2×C3×C8C2×Dic512yescomplemented
264C3×C4⋊C4—52no—
265C3×C4⋊C4—101no—
266C3×C4⋊C4—101no—
267C3×C4⋊C4—101no—
268C3×C22⋊C4—104no—
269C3×C22⋊C4—202no—
270C3×C22⋊C4—202no—
271C3×C42—101no—
272C3×C42—101no—
273C23×C5—22no—
274C23×C5—22no—
275C23×C5—22no—
276C23×C5—22no—
277C23×C5—41no—
278C23×C5—41no—
279C23×C5—41no—
280C23×C5—41no—
281C23×C5—41no—
282C23×C5—41no—
283C23×C5—41no—
284C23×C5—41no—
285C23×C5—41no—
286C23×C5—41no—
287C23×C5C2×C3×D411yescharacteristic
288C5×D4—22no—
289C5×D4—22no—
290C5×D4—22no—
291C5×D4—22no—
292C5×D4—22no—
293C5×D4—41no—
294C5×D4—41no—
295C5×D4C3×C22⋊C414yescomplemented
296C2×C4×C5C22×C3×C411yescharacteristic
297C2×C4×C5C2×C3×D411yescharacteristic
298C2×C4×C5C2×C3×D411yescharacteristic
299C2×C4×C5C2×C3×D411yescharacteristic
300C2×C4×C5C3×#4111yescharacteristic
301C2×C4×C5C3×#4111yescharacteristic
302C2×Dic5—21no—
303C2×Dic5—21no—
304C2×Dic5—21no—
305C2×Dic5—22no—
306C2×Dic5—21no—
307C2×Dic5—21no—
308C2×Dic5—48no—
309C2×Dic5—41no—
310C2×Dic5—41no—
311C2×Dic5—41no—
312C2×Dic5—41no—
313C2×Dic5—41no—
314C2×Dic5C3×D812yescomplemented
315C5×C8—22no—
316#168—41no—
317C22×D4C2×C3×D511yescharacteristic
318C22×D4C2×C3×D511yescharacteristic
319C23×C4—101no—
320C2×D8—22no—
321C2×D8—22no—
322C2×D8C3×Dic514yescomplemented
323C22×C8—51no—
324C22×C8C2×C3×D511yescharacteristic
325C4×D4—102no—
326C4×D4—102no—
327C2×C4⋊C4—51no—
328C2×C4⋊C4—51no—
329C2×C22⋊C4—101no—
330C2×C22⋊C4—101no—
331C2×C22⋊C4—101no—
332C2×C42—51no—
333#102—102no—
334#102—102no—
335C2×C3×C5—44no—
336C2×C3×C5—82no—
337C2×C3×C5#38611yescharacteristic
338C2×C3×C5C4×D811yescharacteristic
339C2×C3×C5#44211yescharacteristic
340C2×C3×C5#44711yescharacteristic
341C2×C3×C5#44911yescharacteristic
342C2×C3×C5#45911yescharacteristic
343C2×C3×C5#46311yescharacteristic
344C23×C3—22no—
345C23×C3—22no—
346C23×C3—22no—
347C23×C3—22no—
348C23×C3—41no—
349C23×C3—41no—
350C23×C3—41no—
351C23×C3—41no—
352C23×C3—41no—
353C23×C3—41no—
354C23×C3—41no—
355C23×C3—41no—
356C23×C3—41no—
357C23×C3—41no—
358C23×C3D4×D511yescharacteristic
359C3×D4—22no—
360C3×D4—22no—
361C3×D4—22no—
362C3×D4—22no—
363C3×D4—22no—
364C3×D4—41no—
365C3×D4—41no—
366C3×D4C22⋊Dic514yescomplemented
367C2×C3×C4—52no—
368C2×C3×C4—101no—
369C2×C3×C4—101no—
370C2×C3×C4—101no—
371C2×C3×C4—101no—
372C2×C3×C4—101no—
373C2×C3×C4—102no—
374C2×C3×C4—208no—
375C2×C3×C4—201no—
376C2×C3×C4—201no—
377C2×C3×C4—201no—
378C2×C3×C4—201no—
379C2×C3×C4—201no—
380C2×C3×C4D4×D511yescharacteristic
381C2×C3×C4#71111yescharacteristic
382C2×C3×C4#71111yescharacteristic
383C2×C3×C4C22×Dic511yescharacteristic
384C2×C3×C4C2×C22⋊D511yescharacteristic
385C2×C3×C4C2×C22⋊D511yescharacteristic
386C3×C8—22no—
387C3×C8—201no—
388C22×C5—24no—
389C22×C5—42no—
390C22×C5—42no—
391C22×C5—42no—
392C22×C5—42no—
393C22×C5—42no—
394C22×C5—42no—
395C22×C5—42no—
396C22×C5—42no—
397C22×C5—42no—
398C22×C5—81no—
399C22×C5—81no—
400C22×C5—81no—
401C22×C5—81no—
402C22×C5C3×C4×D411yescharacteristic
403C22×C5C3×#12011yescharacteristic
404C22×C5C3×#12111yescharacteristic
405C22×C5C2×C3×D811yescharacteristic
406C22×C5C3×#13511yescharacteristic
407C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
408C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
409C4×C5C2×C3×C22⋊C411yescharacteristic
410C4×C5C3×C4×D411yescharacteristic
411C4×C5C3×#12111yescharacteristic
412C4×C5C3×#12311yescharacteristic
413Dic5—22no—
414Dic5—42no—
415Dic5—41no—
416Dic5—81no—
417C24—21no—
418C24—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4C2×C3×Dic512yes—
428C2×D4C2×C3×Dic512yescomplemented
429C2×D4C3×C22⋊D512yes—
430C2×D4C3×C22⋊D512yes—
431C22×C4—51no—
432C22×C4—51no—
433C22×C4—104no—
434C22×C4—101no—
435C22×C4—101no—
436C22×C4—202no—
437C22×C4—202no—
438C22×C4C22×C3×D511yescharacteristic
439D8—28no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—101no—
443C2×C8—101no—
444C2×C8—101no—
445C2×C8C2×C3×Dic512yescomplemented
446C4⋊C4—52no—
447C4⋊C4—101no—
448C4⋊C4—101no—
449C4⋊C4—101no—
450C22⋊C4—104no—
451C22⋊C4—202no—
452C22⋊C4—202no—
453C42—101no—
454C42—101no—
455C3×C5#187911yescharacteristic, complemented, Hall
456C22×C3—24no—
457C22×C3—42no—
458C22×C3—42no—
459C22×C3—42no—
460C22×C3—42no—
461C22×C3—42no—
462C22×C3—42no—
463C22×C3—42no—
464C22×C3—42no—
465C22×C3—42no—
466C22×C3—81no—
467C22×C3—81no—
468C22×C3—81no—
469C22×C3—81no—
470C22×C3D5×D811yescharacteristic
471C22×C3#405711yescharacteristic
472C22×C3#405711yescharacteristic
473C22×C3#405811yescharacteristic
474C22×C3D4×Dic511yescharacteristic
475C22×C3#408311yescharacteristic
476C22×C3#408511yescharacteristic
477C3×C4—102no—
478C3×C4—202no—
479C3×C4—201no—
480C3×C4—401no—
481C3×C4D4×Dic511yescharacteristic
482C3×C4#408111yescharacteristic
483C3×C4#408511yescharacteristic
484C3×C4C2×C22⋊Dic511yescharacteristic
485C2×C5—44no—
486C2×C5—82no—
487C2×C5C3×#38611yescharacteristic
488C2×C5C3×C4×D811yescharacteristic
489C2×C5C3×#44211yescharacteristic
490C2×C5C3×#44711yescharacteristic
491C2×C5C3×#44911yescharacteristic
492C2×C5C3×#45911yescharacteristic
493C2×C5C3×#46311yescharacteristic
494C23—22no—
495C23—22no—
496C23—22no—
497C23—22no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23C3×D4×D511yescharacteristic
509D4—22no—
510D4—22no—
511D4—22no—
512D4—22no—
513D4—22no—
514D4—41no—
515D4—41no—
516D4C3×C22⋊Dic514yescomplemented
517C2×C4—52no—
518C2×C4—101no—
519C2×C4—101no—
520C2×C4—101no—
521C2×C4—102no—
522C2×C4—101no—
523C2×C4—101no—
524C2×C4—208no—
525C2×C4—201no—
526C2×C4—201no—
527C2×C4—201no—
528C2×C4—201no—
529C2×C4—201no—
530C2×C4C3×D4×D511yescharacteristic
531C2×C4C3×#71111yescharacteristic
532C2×C4C3×#71111yescharacteristic
533C2×C4C22×C3×Dic511yescharacteristic
534C2×C4C2×C3×C22⋊D511yescharacteristic
535C2×C4C2×C3×C22⋊D511yescharacteristic
536C8—22no—
537C8—201no—
538C2×C3—44no—
539C2×C3—82no—
540C2×C3D8×Dic511yescharacteristic
541C2×C3#6543911yescharacteristic
542C2×C3#6544111yescharacteristic
543C2×C3#6544211yescharacteristic
544C2×C3#6544511yescharacteristic
545C2×C3#6544711yescharacteristic
546C2×C3#6550911yescharacteristic
547C5C3×#187911yescharacteristic, complemented, Sylow
548C22—24no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—42no—
558C22—81no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22C3×D5×D811yescharacteristic
563C22C3×#405711yescharacteristic
564C22C3×#405711yescharacteristic
565C22C3×#405811yescharacteristic
566C22C3×D4×Dic511yescharacteristic
567C22C3×#408311yescharacteristic
568C22C3×#408511yescharacteristic
569C4—102no—
570C4—202no—
571C4—201no—
572C4—401no—
573C4C3×D4×Dic511yescharacteristic
574C4C3×#408111yescharacteristic
575C4C3×#408511yescharacteristic
576C4C2×C3×C22⋊Dic511yescharacteristic
577C3#1060283011yescharacteristic, direct product factor, Sylow
578C2—44no—
579C2—82no—
580C2C3×D8×Dic511yescharacteristic
581C2C3×#6543911yescharacteristic
582C2C3×#6544111yescharacteristic
583C2C3×#6544211yescharacteristic
584C2C3×#6544511yescharacteristic
585C2C3×#6544711yescharacteristic
586C2C3×#6550911yescharacteristic
subgroupG/H
centerC23×C3D4×D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
Fitting, prime radicalC22×C3×C5×D8C2
socleC23×C3×C5C2×D4
cosocleC22×C4×C5C23×C3
hypercenterC22×C3×D8D5
hypocenterC5C3×#1879
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C22×C3×D8

Complements

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

NH ≅ G/Ntype
2. C2×C3×D4×Dic5C2semidirect
3. C3×#65510C2semidirect
4. C2×C3×#3964C2semidirect
5. C2×C3×#3964C2semidirect
6. C3×#64771C2semidirect
7. C3×#64770C2semidirect
8. #10602830C3direct (N × H)
14. C2×C3×C5×D8C4semidirect
29. C2×D4×Dic5C2×C3semidirect
30. #65510C2×C3semidirect
31. C2×#3964C2×C3semidirect
32. C2×#3964C2×C3semidirect
33. #64771C2×C3semidirect
34. #64770C2×C3semidirect
46. C2×C3×C5×D4C2×C4semidirect
60. C2×C3×C5×C8C2×C4semidirect
85. C2×C5×D8C3×C4semidirect
121. C3×C5×D4C22⋊C4semidirect
140. C2×C3×Dic5D8semidirect
148. C2×C3×D8Dic5semidirect
172. C2×C5×D4C2×C3×C4semidirect
186. C2×C5×C8C2×C3×C4semidirect
246. C2×C3×D4C2×Dic5semidirect
263. C2×C3×C8C2×Dic5semidirect
295. C5×D4C3×C22⋊C4semidirect
314. C2×Dic5C3×D8semidirect
322. C2×D8C3×Dic5semidirect
366. C3×D4C22⋊Dic5semidirect
428. C2×D4C2×C3×Dic5semidirect
445. C2×C8C2×C3×Dic5semidirect
455. C3×C5#1879semidirect
516. D4C3×C22⋊Dic5semidirect
547. C5C3×#1879semidirect
577. C3#10602830direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C5×D82
C2×C3×D4×Dic52
C3×#655102
C2×C3×#39642
C3×#647712
C3×#647702
#106028303
C3×#18795