Finite Group Databasebeta

← C3×#10601006 #14301075

Subgroups — C3×#10601006 #14301075

Order 1920.

748 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#687C211yesmaximal, characteristic
2C2×C3×#4033C211yesmaximal, characteristic, complemented
3C2×C3×C5×#102C211yesmaximal, characteristic
4C3×#65510C211yesmaximal, characteristic
5C2×C3×#3948C211yesmaximal, characteristic, complemented
6C3×#64770C211yesmaximal, characteristic, complemented
7C3×#64749C211yesmaximal, characteristic, complemented
8#10601006C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×C3×Dic10C2211yescharacteristic
11C22×C3×C5×C8C2211yescharacteristic
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13C2×C3×C22⋊Dic5—21no—
14C2×C3×C22⋊Dic5—21no—
15C2×C3×#687—22no—
16C2×C3×#687—22no—
17C2×C3×#687C414yescomplemented
18C2×C3×C4⋊Dic5C2211yescharacteristic
19C2×C3×#683—21no—
20C2×C3×C4×Dic5—21no—
21C2×C3×C4×Dic5C2211yescharacteristic
22C22×C3×#168C2211yescharacteristic
23C3×#4033—22no—
24C3×#4033—22no—
25C3×C5×#102—22no—
26C3×#3948—22no—
27C3×#1880—51nomaximal, Hall
28C22×#687C2×C311yescharacteristic
29C2×#4033C2×C311yescharacteristic, complemented
30C2×C5×#102C2×C311yescharacteristic
31#65510C2×C311yescharacteristic
32C2×#3948C2×C311yescharacteristic, complemented
33#64770C2×C311yescharacteristic, complemented
34#64749C2×C311yescharacteristic, complemented
35C24×C3×C5—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4C2×C412yes—
42C22×C3×C4×C5—21no—
43C22×C3×C4×C5C2311yescharacteristic
44C22×C3×Dic5—21no—
45C22×C3×Dic5—21no—
46C22×C3×Dic5D411yescharacteristic
47C22×C3×Dic5D411yescharacteristic
48C2×C3×Dic10—21no—
49C2×C3×Dic10—21no—
50C2×C3×Dic10—21no—
51C2×C3×Dic10C2×C412yes—
52C2×C3×Dic10D412yes—
53C2×C3×Dic10D412yes—
54C2×C3×C5×C8—21no—
55C2×C3×C5×C8—21no—
56C2×C3×C5×C8—21no—
57C3×C5×C4⋊C4—21no—
58C3×C5×C4⋊C4D412yes—
59C3×C22⋊Dic5—42no—
60C3×C22⋊Dic5—42no—
61C3×#687—28no—
62C3×C4⋊Dic5—21no—
63C3×C4⋊Dic5—21no—
64C3×#683—24no—
65C3×C4×Dic5—24no—
66C3×C4×Dic5—21no—
67C3×C4×Dic5—21no—
68C2×C3×#168—21no—
69C2×C3×#168—21no—
70C2×C3×#168C2×C412yes—
71C22×C3×SD16—51no—
72C2×C3×C4×Q8—51no—
73C2×C3×#103—51no—
74C2×C3×#102D511yescharacteristic
75C3×#390—51no—
76C3×#340—51no—
77C3×#336—51no—
78C22×C5×D4C22×C311yescharacteristic
79C22×Dic10C22×C311yescharacteristic
80C22×C5×C8C22×C311yescharacteristic
81C2×C5×C4⋊C4C22×C311yescharacteristic
82C2×C22⋊Dic5—21no—
83C2×C22⋊Dic5—21no—
84C2×#687—22no—
85C2×#687—22no—
86C2×#687C3×C414yescomplemented
87C2×C4⋊Dic5C22×C311yescharacteristic
88C2×#683—21no—
89C2×C4×Dic5—21no—
90C2×C4×Dic5C22×C311yescharacteristic
91C22×#168C22×C311yescharacteristic
92#4033—22no—
93#4033—22no—
94C5×#102—22no—
95#3948—22no—
96#1880—51noSylow
97C23×C3×C5—22no—
98C23×C3×C5—41no—
99C23×C3×C5—41no—
100C23×C3×C5—41no—
101C23×C3×C5—41no—
102C23×C3×C5—41no—
103C23×C3×C5—41no—
104C23×C3×C5C2×D411yescharacteristic
105C3×C5×D4—22no—
106C3×C5×D4—22no—
107C3×C5×D4—41no—
108C3×C5×D4—41no—
109C2×C3×C4×C5—22no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5—41no—
112C2×C3×C4×C5C22×C411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5C2×D411yescharacteristic
116C2×C3×C4×C5#4111yescharacteristic
117C2×C3×C4×C5#4111yescharacteristic
118C2×C3×Dic5—22no—
119C2×C3×Dic5—21no—
120C2×C3×Dic5—22no—
121C2×C3×Dic5—22no—
122C2×C3×Dic5—21no—
123C2×C3×Dic5—21no—
124C2×C3×Dic5—21no—
125C2×C3×Dic5—21no—
126C2×C3×Dic5—41no—
127C2×C3×Dic5—41no—
128C2×C3×Dic5—41no—
129C2×C3×Dic5SD1612yescomplemented
130C3×Dic10—22no—
131C3×Dic10—22no—
132C3×Dic10—22no—
133C3×Dic10C22⋊C414yescomplemented
134C3×C5×C8—41no—
135C3×#168—22no—
136C22×C3×Q8—51no—
137C22×C3×D4C2×D511yescharacteristic
138C2×C3×SD16—54no—
139C2×C3×SD16—102no—
140C2×C3×SD16—102no—
141C22×C3×C8—51no—
142C22×C3×C8C2×D511yescharacteristic
143C3×C4×Q8—102no—
144C3×C4×Q8—102no—
145C2×C3×C4⋊C4—51no—
146C2×C3×C4⋊C4—101no—
147C2×C3×C4⋊C4C2×D511yescharacteristic
148C2×C3×C22⋊C4—101no—
149C2×C3×C22⋊C4—101no—
150C2×C3×C42—51no—
151C2×C3×C42—101no—
152C3×#103—102no—
153C3×#102—22no—
154C24×C5—21no—
155C2×C5×D4—21no—
156C2×C5×D4—21no—
157C2×C5×D4—21no—
158C2×C5×D4—21no—
159C2×C5×D4—21no—
160C2×C5×D4C2×C3×C412yes—
161C22×C4×C5—21no—
162C22×C4×C5C23×C311yescharacteristic
163C22×Dic5—21no—
164C22×Dic5—21no—
165C22×Dic5C3×D411yescharacteristic
166C22×Dic5C3×D411yescharacteristic
167C2×Dic10—21no—
168C2×Dic10—21no—
169C2×Dic10—21no—
170C2×Dic10C2×C3×C412yes—
171C2×Dic10C3×D412yes—
172C2×Dic10C3×D412yes—
173C2×C5×C8—21no—
174C2×C5×C8—21no—
175C2×C5×C8—21no—
176C5×C4⋊C4—21no—
177C5×C4⋊C4C3×D412yes—
178C22⋊Dic5—42no—
179C22⋊Dic5—42no—
180#687—28no—
181C4⋊Dic5—21no—
182C4⋊Dic5—21no—
183#683—24no—
184C4×Dic5—24no—
185C4×Dic5—21no—
186C4×Dic5—21no—
187C2×#168—21no—
188C2×#168—21no—
189C2×#168C2×C3×C412yes—
190C22×SD16—51no—
191C2×C4×Q8—51no—
192C2×#103—51no—
193C2×#102C3×D511yescharacteristic
194#390—51no—
195#340—51no—
196#336—51no—
197C22×C3×C5—42no—
198C22×C3×C5—42no—
199C22×C3×C5—42no—
200C22×C3×C5—81no—
201C22×C3×C5—81no—
202C22×C3×C5—81no—
203C22×C3×C5—81no—
204C22×C3×C5C4×D411yescharacteristic
205C22×C3×C5#12011yescharacteristic
206C22×C3×C5#12111yescharacteristic
207C22×C3×C5C2×SD1611yescharacteristic
208C22×C3×C5#13511yescharacteristic
209C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
210C22×C3×C5#13711yescharacteristic
211C3×C4×C5—42no—
212C3×C4×C5C2×C22⋊C411yescharacteristic
213C3×C4×C5C4×D411yescharacteristic
214C3×C4×C5#12111yescharacteristic
215C3×C4×C5#12311yescharacteristic
216C3×Dic5—24no—
217C3×Dic5—22no—
218C3×Dic5—41no—
219C3×Dic5—81no—
220C24×C3—21no—
221C2×C3×Q8—52no—
222C2×C3×Q8—52no—
223C2×C3×Q8—52no—
224C2×C3×Q8—101no—
225C2×C3×Q8—101no—
226C2×C3×Q8—101no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4C4×D512yes—
233C22×C3×C4—21no—
234C22×C3×C4—51no—
235C22×C3×C4—51no—
236C22×C3×C4—101no—
237C22×C3×C4—101no—
238C22×C3×C4C22×D511yescharacteristic
239C3×SD16—108no—
240C2×C3×C8—21no—
241C2×C3×C8—21no—
242C2×C3×C8—21no—
243C2×C3×C8—52no—
244C2×C3×C8—101no—
245C2×C3×C8—101no—
246C3×C4⋊C4—21no—
247C3×C4⋊C4—104no—
248C3×C4⋊C4—101no—
249C3×C4⋊C4—101no—
250C3×C4⋊C4C22⋊D512yes—
251C3×C22⋊C4—202no—
252C3×C22⋊C4—202no—
253C3×C42—104no—
254C3×C42—101no—
255C3×C42—101no—
256C23×C5—22no—
257C23×C5—41no—
258C23×C5—41no—
259C23×C5—41no—
260C23×C5—41no—
261C23×C5—41no—
262C23×C5—41no—
263C23×C5C2×C3×D411yescharacteristic
264C5×D4—22no—
265C5×D4—22no—
266C5×D4—41no—
267C5×D4—41no—
268C2×C4×C5—22no—
269C2×C4×C5—41no—
270C2×C4×C5—41no—
271C2×C4×C5C22×C3×C411yescharacteristic
272C2×C4×C5C2×C3×D411yescharacteristic
273C2×C4×C5C2×C3×D411yescharacteristic
274C2×C4×C5C2×C3×D411yescharacteristic
275C2×C4×C5C3×#4111yescharacteristic
276C2×C4×C5C3×#4111yescharacteristic
277C2×Dic5—22no—
278C2×Dic5—21no—
279C2×Dic5—22no—
280C2×Dic5—22no—
281C2×Dic5—21no—
282C2×Dic5—21no—
283C2×Dic5—21no—
284C2×Dic5—21no—
285C2×Dic5—41no—
286C2×Dic5—41no—
287C2×Dic5—41no—
288C2×Dic5C3×SD1612yescomplemented
289Dic10—22no—
290Dic10—22no—
291Dic10—22no—
292Dic10C3×C22⋊C414yescomplemented
293C5×C8—41no—
294#168—22no—
295C22×Q8—51no—
296C22×D4C2×C3×D511yescharacteristic
297C2×SD16—54no—
298C2×SD16—102no—
299C2×SD16—102no—
300C22×C8—51no—
301C22×C8C2×C3×D511yescharacteristic
302C4×Q8—102no—
303C4×Q8—102no—
304C2×C4⋊C4—51no—
305C2×C4⋊C4—101no—
306C2×C4⋊C4C2×C3×D511yescharacteristic
307C2×C22⋊C4—101no—
308C2×C22⋊C4—101no—
309C2×C42—51no—
310C2×C42—101no—
311#103—102no—
312#102—22no—
313C2×C3×C5—82no—
314C2×C3×C5#38611yescharacteristic
315C2×C3×C5C4×SD1611yescharacteristic
316C2×C3×C5#44011yescharacteristic
317C2×C3×C5#44811yescharacteristic
318C2×C3×C5#44911yescharacteristic
319C2×C3×C5#46011yescharacteristic
320C2×C3×C5#46411yescharacteristic
321C23×C3—22no—
322C23×C3—41no—
323C23×C3—41no—
324C23×C3—41no—
325C23×C3—41no—
326C23×C3—41no—
327C23×C3—41no—
328C23×C3D4×D511yescharacteristic
329C3×Q8—54no—
330C3×Q8—102no—
331C3×Q8—102no—
332C3×Q8—102no—
333C3×D4—22no—
334C3×D4—22no—
335C3×D4—41no—
336C3×D4—41no—
337C2×C3×C4—22no—
338C2×C3×C4—41no—
339C2×C3×C4—41no—
340C2×C3×C4—52no—
341C2×C3×C4—102no—
342C2×C3×C4—102no—
343C2×C3×C4—101no—
344C2×C3×C4—101no—
345C2×C3×C4—102no—
346C2×C3×C4—101no—
347C2×C3×C4—101no—
348C2×C3×C4—101no—
349C2×C3×C4—201no—
350C2×C3×C4—201no—
351C2×C3×C4—201no—
352C2×C3×C4C2×C4×D511yescharacteristic
353C2×C3×C4#70911yescharacteristic
354C2×C3×C4D4×D511yescharacteristic
355C2×C3×C4D4×D511yescharacteristic
356C2×C3×C4#71111yescharacteristic
357C2×C3×C4C2×C22⋊D511yescharacteristic
358C3×C8—41no—
359C3×C8—102no—
360C22×C5—42no—
361C22×C5—42no—
362C22×C5—42no—
363C22×C5—81no—
364C22×C5—81no—
365C22×C5—81no—
366C22×C5—81no—
367C22×C5C3×C4×D411yescharacteristic
368C22×C5C3×#12011yescharacteristic
369C22×C5C3×#12111yescharacteristic
370C22×C5C2×C3×SD1611yescharacteristic
371C22×C5C3×#13511yescharacteristic
372C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
373C22×C5C3×#13711yescharacteristic
374C4×C5—42no—
375C4×C5C2×C3×C22⋊C411yescharacteristic
376C4×C5C3×C4×D411yescharacteristic
377C4×C5C3×#12111yescharacteristic
378C4×C5C3×#12311yescharacteristic
379Dic5—24no—
380Dic5—22no—
381Dic5—41no—
382Dic5—81no—
383C24—21no—
384C2×Q8—52no—
385C2×Q8—52no—
386C2×Q8—52no—
387C2×Q8—101no—
388C2×Q8—101no—
389C2×Q8—101no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4C3×C4×D512yes—
396C22×C4—21no—
397C22×C4—51no—
398C22×C4—51no—
399C22×C4—101no—
400C22×C4—101no—
401C22×C4C22×C3×D511yescharacteristic
402SD16—108no—
403C2×C8—21no—
404C2×C8—21no—
405C2×C8—21no—
406C2×C8—52no—
407C2×C8—101no—
408C2×C8—101no—
409C4⋊C4—21no—
410C4⋊C4—104no—
411C4⋊C4—101no—
412C4⋊C4—101no—
413C4⋊C4C3×C22⋊D512yes—
414C22⋊C4—202no—
415C22⋊C4—202no—
416C42—104no—
417C42—101no—
418C42—101no—
419C3×C5#188011yescharacteristic, complemented, Hall
420C22×C3—42no—
421C22×C3—42no—
422C22×C3—42no—
423C22×C3—81no—
424C22×C3—81no—
425C22×C3—81no—
426C22×C3—81no—
427C22×C3#402711yescharacteristic
428C22×C3#403011yescharacteristic
429C22×C3#405711yescharacteristic
430C22×C3#405811yescharacteristic
431C22×C3D5×SD1611yescharacteristic
432C22×C3#406111yescharacteristic
433C22×C3#408311yescharacteristic
434C3×C4—42no—
435C3×C4—102no—
436C3×C4—104no—
437C3×C4—201no—
438C3×C4—401no—
439C3×C4D5×C22⋊C411yescharacteristic
440C3×C4#402911yescharacteristic
441C3×C4C4×C22⋊D511yescharacteristic
442C3×C4#408411yescharacteristic
443C2×C5—82no—
444C2×C5C3×#38611yescharacteristic
445C2×C5C3×C4×SD1611yescharacteristic
446C2×C5C3×#44011yescharacteristic
447C2×C5C3×#44811yescharacteristic
448C2×C5C3×#44911yescharacteristic
449C2×C5C3×#46011yescharacteristic
450C2×C5C3×#46411yescharacteristic
451C23—22no—
452C23—41no—
453C23—41no—
454C23—41no—
455C23—41no—
456C23—41no—
457C23—41no—
458C23C3×D4×D511yescharacteristic
459Q8—54no—
460Q8—102no—
461Q8—102no—
462Q8—102no—
463D4—22no—
464D4—22no—
465D4—41no—
466D4—41no—
467C2×C4—22no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—52no—
471C2×C4—101no—
472C2×C4—102no—
473C2×C4—102no—
474C2×C4—102no—
475C2×C4—101no—
476C2×C4—101no—
477C2×C4—101no—
478C2×C4—101no—
479C2×C4—201no—
480C2×C4—201no—
481C2×C4—201no—
482C2×C4C2×C3×C4×D511yescharacteristic
483C2×C4C3×#70911yescharacteristic
484C2×C4C3×D4×D511yescharacteristic
485C2×C4C3×D4×D511yescharacteristic
486C2×C4C3×#71111yescharacteristic
487C2×C4C2×C3×C22⋊D511yescharacteristic
488C8—41no—
489C8—102no—
490C2×C3—82no—
491C2×C3#6504611yescharacteristic
492C2×C3#6504711yescharacteristic
493C2×C3#6505111yescharacteristic
494C2×C3#6505611yescharacteristic
495C2×C3#6524511yescharacteristic
496C2×C3#6544711yescharacteristic
497C2×C3#6545911yescharacteristic
498C5C3×#188011yescharacteristic, complemented, Sylow
499C22—42no—
500C22—42no—
501C22—42no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22C3×#402711yescharacteristic
507C22C3×#403011yescharacteristic
508C22C3×#405711yescharacteristic
509C22C3×#405811yescharacteristic
510C22C3×D5×SD1611yescharacteristic
511C22C3×#406111yescharacteristic
512C22C3×#408311yescharacteristic
513C4—42no—
514C4—102no—
515C4—104no—
516C4—201no—
517C4—401no—
518C4C3×D5×C22⋊C411yescharacteristic
519C4C3×#402911yescharacteristic
520C4C3×C4×C22⋊D511yescharacteristic
521C4C3×#408411yescharacteristic
522C3#1060100611yescharacteristic, direct product factor, Sylow
523C2—82no—
524C2C3×#6504611yescharacteristic
525C2C3×#6504711yescharacteristic
526C2C3×#6505111yescharacteristic
527C2C3×#6505611yescharacteristic
528C2C3×#6524511yescharacteristic
529C2C3×#6544711yescharacteristic
530C2C3×#6545911yescharacteristic
subgroupG/H
centerC23×C3D4×D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC2×C3×C5×#102C2
socleC23×C3×C5C2×D4
prime radicalC22×C3×C5×D4C22
cosocleC22×C4×C5C23×C3
hypercenterC2×C3×#102D5
hypocenterC5C3×#1880
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#102

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4033C2semidirect
5. C2×C3×#3948C2semidirect
6. C3×#64770C2semidirect
7. C3×#64749C2semidirect
8. #10601006C3direct (N × H)
17. C2×C3×#687C4semidirect
29. C2×#4033C2×C3semidirect
32. C2×#3948C2×C3semidirect
33. #64770C2×C3semidirect
34. #64749C2×C3semidirect
86. C2×#687C3×C4semidirect
129. C2×C3×Dic5SD16semidirect
133. C3×Dic10C22⋊C4semidirect
288. C2×Dic5C3×SD16semidirect
292. Dic10C3×C22⋊C4semidirect
419. C3×C5#1880semidirect
498. C5C3×#1880semidirect
522. C3#10601006direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#6872
C2×C3×#40332
C2×C3×C5×#1022
C3×#655102
C2×C3×#39482
C3×#647702
C3×#647492
#106010063
C3×#18805