Finite Group Databasebeta

← C3×#10602777 #14300533

Subgroups — C3×#10602777 #14300533

Order 1920.

752 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C5×M16C211yesmaximal, characteristic, complemented
2C3×#66125C211yesmaximal, characteristic
3C3×C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
4C2×C3×#3957C212yesmaximal, complemented
5C3×#64775C212yesmaximal, complemented
6#10602777C311yesmaximal, characteristic, direct product factor, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C2×C3×#709C2211yescharacteristic
9C2×C3×C5×M16—21no—
10C2×C3×C5×M16—24no—
11C2×C3×C5×M16C2212yes—
12C22×C3×C5×C8—21no—
13C3×#4099—21no—
14C2×C3×C22⋊Dic5—21no—
15C3×#4076C411yescharacteristic, complemented
16C3×#4076C411yescharacteristic, complemented
17C3×#4075—21no—
18C3×C4×C22⋊D5—21no—
19C3×C4×C22⋊D5—21no—
20C3×#4072C2211yescharacteristic
21C3×#4070C411yescharacteristic, complemented
22C3×#4070C411yescharacteristic, complemented
23C2×C3×C4×Dic5C2212yes—
24C3×#3963—21no—
25C3×#3957—24no—
26C3×#1871—51nomaximal, Hall
27C22×C5×M16C2×C311yescharacteristic, complemented
28#66125C2×C311yescharacteristic
29C4×C22⋊Dic5C2×C311yescharacteristic, complemented
30C2×#3957C2×C312yescomplemented
31#64775C2×C312yescomplemented
32C24×C3×C5D411yescharacteristic
33C22×C3×C4×C5—22no—
34C22×C3×C4×C5—22no—
35C22×C3×C4×C5C2×C411yescharacteristic
36C22×C3×C4×C5C2×C411yescharacteristic
37C22×C3×C4×C5D411yescharacteristic
38C22×C3×C4×C5D411yescharacteristic
39C22×C3×C4×C5D411yescharacteristic
40C22×C3×C4×C5C2311yescharacteristic
41C2×C3×C22⋊D5—21no—
42C2×C3×C22⋊D5—21no—
43C2×C3×C22⋊D5—21no—
44C22×C3×Dic5—22no—
45C3×#709—22no—
46C3×#709—22no—
47C2×C3×D20C2×C411yescharacteristic
48C2×C3×C4×D5—21no—
49C2×C3×Dic10C2×C411yescharacteristic
50C3×C5×M16—24no—
51C3×C5×M16—22no—
52C3×C5×M16D414yescomplemented
53C2×C3×C5×C8—24no—
54C2×C3×C5×C8—22no—
55C3×C22⋊Dic5—24no—
56C3×C22⋊Dic5—21no—
57C3×C22⋊Dic5—21no—
58C3×C22⋊Dic5—21no—
59C3×#685—21no—
60C3×#685—21no—
61C3×C4⋊Dic5C2×C411yescharacteristic
62C3×C4⋊Dic5C2×C411yescharacteristic
63C3×#683—21no—
64C3×#683—21no—
65C3×C4×Dic5—21no—
66C3×C4×Dic5—22no—
67C3×C4×Dic5—22no—
68C22×C3×M16D511yescharacteristic, complemented
69C3×#525—51no—
70C2×C3×#104—52no—
71C3×C4×C22⋊C4—51no—
72C3×#339—52no—
73C23×C4×C5C22×C311yescharacteristic
74C2×#709C22×C311yescharacteristic
75C2×C5×M16—21no—
76C2×C5×M16—24no—
77C2×C5×M16C22×C312yes—
78C22×C5×C8—21no—
79#4099—21no—
80C2×C22⋊Dic5—21no—
81#4076C3×C411yescharacteristic, complemented
82#4076C3×C411yescharacteristic, complemented
83#4075—21no—
84C4×C22⋊D5—21no—
85C4×C22⋊D5—21no—
86#4072C22×C311yescharacteristic
87#4070C3×C411yescharacteristic, complemented
88#4070C3×C411yescharacteristic, complemented
89C2×C4×Dic5C22×C312yes—
90#3963—21no—
91#3957—24no—
92#1871—51noSylow
93C23×C3×C5—22no—
94C23×C3×C5—22no—
95C23×C3×C5—41no—
96C23×C3×C5C22⋊C411yescharacteristic
97C23×C3×C5C22⋊C411yescharacteristic
98C23×C3×C5C2×D411yescharacteristic
99C22×C3×D5—21no—
100C2×C3×C4×C5—22no—
101C2×C3×C4×C5—22no—
102C2×C3×C4×C5—22no—
103C2×C3×C4×C5—21no—
104C2×C3×C4×C5—21no—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5C22⋊C411yescharacteristic
108C2×C3×C4×C5C22⋊C411yescharacteristic
109C2×C3×C4×C5C22×C411yescharacteristic
110C2×C3×C4×C5C2×D412yes—
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5#4112yes—
113C3×C22⋊D5—42no—
114C3×C22⋊D5—42no—
115C3×C22⋊D5—42no—
116C2×C3×Dic5—24no—
117C2×C3×Dic5—21no—
118C2×C3×Dic5—21no—
119C2×C3×Dic5—21no—
120C2×C3×Dic5—42no—
121C2×C3×Dic5—42no—
122C3×D20—22no—
123C3×C4×D5—41no—
124C3×C4×D5—41no—
125C3×Dic10—22no—
126C3×C5×C8—24no—
127C2×C3×#41—51no—
128C23×C3×C4C2×D511yescharacteristic
129C2×C3×M16—21no—
130C2×C3×M16—24no—
131C2×C3×M16C2×D512yes—
132C22×C3×C8—21no—
133C3×#123—101no—
134C3×C22⋊Q8—51no—
135C3×C22⋊Q8—51no—
136C3×#121—51no—
137C3×#121—51no—
138C3×#120—101no—
139C3×C4×D4—101no—
140C3×C4×D4—101no—
141C3×#117—51no—
142C2×C3×C22⋊C4—101no—
143C2×C3×C42—52no—
144C3×#104—104no—
145C3×#95—101no—
146C24×C5C3×D411yescharacteristic
147C22×C4×C5—22no—
148C22×C4×C5—22no—
149C22×C4×C5C2×C3×C411yescharacteristic
150C22×C4×C5C2×C3×C411yescharacteristic
151C22×C4×C5C3×D411yescharacteristic
152C22×C4×C5C3×D411yescharacteristic
153C22×C4×C5C3×D411yescharacteristic
154C22×C4×C5C23×C311yescharacteristic
155C2×C22⋊D5—21no—
156C2×C22⋊D5—21no—
157C2×C22⋊D5—21no—
158C22×Dic5—22no—
159#709—22no—
160#709—22no—
161C2×D20C2×C3×C411yescharacteristic
162C2×C4×D5—21no—
163C2×Dic10C2×C3×C411yescharacteristic
164C5×M16—24no—
165C5×M16—22no—
166C5×M16C3×D414yescomplemented
167C2×C5×C8—24no—
168C2×C5×C8—22no—
169C22⋊Dic5—24no—
170C22⋊Dic5—21no—
171C22⋊Dic5—21no—
172C22⋊Dic5—21no—
173#685—21no—
174#685—21no—
175C4⋊Dic5C2×C3×C411yescharacteristic
176C4⋊Dic5C2×C3×C411yescharacteristic
177#683—21no—
178#683—21no—
179C4×Dic5—21no—
180C4×Dic5—22no—
181C4×Dic5—22no—
182C22×M16C3×D511yescharacteristic, complemented
183#525—51no—
184C2×#104—52no—
185C4×C22⋊C4—51no—
186#339—52no—
187C22×C3×C5—21no—
188C22×C3×C5—21no—
189C22×C3×C5—21no—
190C22×C3×C5—21no—
191C22×C3×C5—21no—
192C22×C3×C5—21no—
193C22×C3×C5—21no—
194C22×C3×C5—44no—
195C22×C3×C5#10412yescomplemented
196C22×C3×C5C2×C22⋊C411yescharacteristic
197C22×C3×C5#12112yes—
198C2×C3×D5—41no—
199C2×C3×D5—41no—
200C2×C3×D5—41no—
201C3×C4×C5—21no—
202C3×C4×C5—21no—
203C3×C4×C5C4×D412yes—
204C3×C4×C5#12011yescharacteristic
205C3×C4×C5#12311yescharacteristic
206C3×Dic5—44no—
207C3×Dic5—41no—
208C3×Dic5—41no—
209C3×Dic5—41no—
210C24×C3D2011yescharacteristic
211C3×#41—102no—
212C3×#41—102no—
213C2×C3×Q8—51no—
214C2×C3×D4—51no—
215C2×C3×D4—101no—
216C2×C3×D4—101no—
217C2×C3×D4—101no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—102no—
221C22×C3×C4—101no—
222C22×C3×C4C4×D511yescharacteristic
223C22×C3×C4C4×D511yescharacteristic
224C22×C3×C4D2011yescharacteristic
225C22×C3×C4C22⋊D511yescharacteristic
226C22×C3×C4C22⋊D511yescharacteristic
227C22×C3×C4C22×D511yescharacteristic
228C3×M16—24no—
229C3×M16—22no—
230C3×M16C22⋊D514yescomplemented
231C2×C3×C8—24no—
232C2×C3×C8—22no—
233C3×C4⋊C4—51no—
234C3×C4⋊C4—51no—
235C3×C4⋊C4—101no—
236C3×C4⋊C4—101no—
237C3×C22⋊C4—104no—
238C3×C22⋊C4—101no—
239C3×C22⋊C4—101no—
240C3×C22⋊C4—101no—
241C3×C22⋊C4—101no—
242C3×C22⋊C4—101no—
243C3×C42—101no—
244C3×C42—102no—
245C3×C42—102no—
246C23×C5—22no—
247C23×C5—22no—
248C23×C5—41no—
249C23×C5C3×C22⋊C411yescharacteristic
250C23×C5C3×C22⋊C411yescharacteristic
251C23×C5C2×C3×D411yescharacteristic
252C22×D5—21no—
253C2×C4×C5—22no—
254C2×C4×C5—22no—
255C2×C4×C5—22no—
256C2×C4×C5—21no—
257C2×C4×C5—21no—
258C2×C4×C5—21no—
259C2×C4×C5—21no—
260C2×C4×C5C3×C22⋊C411yescharacteristic
261C2×C4×C5C3×C22⋊C411yescharacteristic
262C2×C4×C5C22×C3×C411yescharacteristic
263C2×C4×C5C2×C3×D412yes—
264C2×C4×C5C2×C3×D411yescharacteristic
265C2×C4×C5C3×#4112yes—
266C22⋊D5—42no—
267C22⋊D5—42no—
268C22⋊D5—42no—
269C2×Dic5—24no—
270C2×Dic5—21no—
271C2×Dic5—21no—
272C2×Dic5—21no—
273C2×Dic5—42no—
274C2×Dic5—42no—
275D20—22no—
276C4×D5—41no—
277C4×D5—41no—
278Dic10—22no—
279C5×C8—24no—
280C2×#41—51no—
281C23×C4C2×C3×D511yescharacteristic
282C2×M16—21no—
283C2×M16—24no—
284C2×M16C2×C3×D512yes—
285C22×C8—21no—
286#123—101no—
287C22⋊Q8—51no—
288C22⋊Q8—51no—
289#121—51no—
290#121—51no—
291#120—101no—
292C4×D4—101no—
293C4×D4—101no—
294#117—51no—
295C2×C22⋊C4—101no—
296C2×C42—52no—
297#104—104no—
298#95—101no—
299C2×C3×C5—22no—
300C2×C3×C5—22no—
301C2×C3×C5—41no—
302C2×C3×C5#38611yescharacteristic
303C2×C3×C5C2×#10411yescharacteristic
304C2×C3×C5#42111yescharacteristic
305C3×D5—81no—
306C23×C3—22no—
307C23×C3—22no—
308C23×C3—41no—
309C23×C3—101no—
310C23×C3#68511yescharacteristic
311C23×C3#68511yescharacteristic
312C23×C3C2×D2011yescharacteristic
313C3×Q8—102no—
314C3×D4—102no—
315C3×D4—202no—
316C3×D4—202no—
317C3×D4—202no—
318C2×C3×C4—22no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—104no—
326C2×C3×C4—101no—
327C2×C3×C4—101no—
328C2×C3×C4—101no—
329C2×C3×C4—202no—
330C2×C3×C4—202no—
331C2×C3×C4—201no—
332C2×C3×C4—201no—
333C2×C3×C4#68511yescharacteristic
334C2×C3×C4#68511yescharacteristic
335C2×C3×C4C2×C4×D511yescharacteristic
336C2×C3×C4#70912yes—
337C2×C3×C4C2×C22⋊D512yes—
338C2×C3×C4C2×C22⋊D511yescharacteristic
339C3×C8—24no—
340C22×C5—21no—
341C22×C5—21no—
342C22×C5—21no—
343C22×C5—21no—
344C22×C5—21no—
345C22×C5—21no—
346C22×C5—21no—
347C22×C5—44no—
348C22×C5C3×#10412yescomplemented
349C22×C5C2×C3×C22⋊C411yescharacteristic
350C22×C5C3×#12112yes—
351C2×D5—41no—
352C2×D5—41no—
353C2×D5—41no—
354C4×C5—21no—
355C4×C5—21no—
356C4×C5C3×C4×D412yes—
357C4×C5C3×#12011yescharacteristic
358C4×C5C3×#12311yescharacteristic
359Dic5—44no—
360Dic5—41no—
361Dic5—41no—
362Dic5—41no—
363C24C3×D2011yescharacteristic
364#41—102no—
365#41—102no—
366C2×Q8—51no—
367C2×D4—51no—
368C2×D4—101no—
369C2×D4—101no—
370C2×D4—101no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—102no—
374C22×C4—101no—
375C22×C4C3×C4×D511yescharacteristic
376C22×C4C3×C4×D511yescharacteristic
377C22×C4C3×D2011yescharacteristic
378C22×C4C3×C22⋊D511yescharacteristic
379C22×C4C3×C22⋊D511yescharacteristic
380C22×C4C22×C3×D511yescharacteristic
381M16—24no—
382M16—22no—
383M16C3×C22⋊D514yescomplemented
384C2×C8—24no—
385C2×C8—22no—
386C4⋊C4—51no—
387C4⋊C4—51no—
388C4⋊C4—101no—
389C4⋊C4—101no—
390C22⋊C4—104no—
391C22⋊C4—101no—
392C22⋊C4—101no—
393C22⋊C4—101no—
394C22⋊C4—101no—
395C22⋊C4—101no—
396C42—101no—
397C42—102no—
398C42—102no—
399C3×C5#187111yescharacteristic, complemented, Hall
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—44no—
408C22×C3—201no—
409C22×C3—201no—
410C22×C3—201no—
411C22×C3#395712yescomplemented
412C22×C3C2×#68511yescharacteristic
413C22×C3#407612yes—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—204no—
417C3×C4—201no—
418C3×C4—201no—
419C3×C4—201no—
420C3×C4C4×C22⋊D512yes—
421C3×C4#407511yescharacteristic
422C3×C4#409911yescharacteristic
423C2×C5—22no—
424C2×C5—22no—
425C2×C5—41no—
426C2×C5C3×#38611yescharacteristic
427C2×C5C2×C3×#10411yescharacteristic
428C2×C5C3×#42111yescharacteristic
429D5—81no—
430C23—22no—
431C23—22no—
432C23—41no—
433C23—101no—
434C23C3×#68511yescharacteristic
435C23C3×#68511yescharacteristic
436C23C2×C3×D2011yescharacteristic
437Q8—102no—
438D4—102no—
439D4—202no—
440D4—202no—
441D4—202no—
442C2×C4—22no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—104no—
450C2×C4—101no—
451C2×C4—101no—
452C2×C4—101no—
453C2×C4—202no—
454C2×C4—202no—
455C2×C4—201no—
456C2×C4—201no—
457C2×C4C3×#68511yescharacteristic
458C2×C4C3×#68511yescharacteristic
459C2×C4C2×C3×C4×D511yescharacteristic
460C2×C4C3×#70912yes—
461C2×C4C2×C3×C22⋊D512yes—
462C2×C4C2×C3×C22⋊D511yescharacteristic
463C8—24no—
464C2×C3—22no—
465C2×C3—22no—
466C2×C3—41no—
467C2×C3—401no—
468C2×C3C2×#395711yescharacteristic
469C2×C3#6542811yescharacteristic
470C2×C3#6550211yescharacteristic
471C5C3×#187111yescharacteristic, complemented, Sylow
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—44no—
480C22—201no—
481C22—201no—
482C22—201no—
483C22C3×#395712yescomplemented
484C22C2×C3×#68511yescharacteristic
485C22C3×#407612yes—
486C4—21no—
487C4—21no—
488C4—204no—
489C4—201no—
490C4—201no—
491C4—201no—
492C4C3×C4×C22⋊D512yes—
493C4C3×#407511yescharacteristic
494C4C3×#409911yescharacteristic
495C3#1060277711yescharacteristic, direct product factor, Sylow
496C2—22no—
497C2—22no—
498C2—41no—
499C2—401no—
500C2C2×C3×#395711yescharacteristic
501C2C3×#6542811yescharacteristic
502C2C3×#6550211yescharacteristic
subgroupG/H
centerC2×C3×C4C2×C22⋊D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC22×C3×C5×M16C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#66125C2
cosocleC22×C4×C5C23×C3
hypercenterC22×C3×M16D5
hypocenterC5C3×#1871
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C23×C3×C4 ◁ C22×C3×M16

Complements

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

NH ≅ G/Ntype
1. C22×C3×C5×M16C2semidirect
3. C3×C4×C22⋊Dic5C2semidirect
4. C2×C3×#3957C2semidirect
5. C3×#64775C2semidirect
6. #10602777C3direct (N × H)
15. C3×#4076C4semidirect
16. C3×#4076C4semidirect
21. C3×#4070C4semidirect
22. C3×#4070C4semidirect
27. C22×C5×M16C2×C3semidirect
29. C4×C22⋊Dic5C2×C3semidirect
30. C2×#3957C2×C3semidirect
31. #64775C2×C3semidirect
52. C3×C5×M16D4semidirect
68. C22×C3×M16D5semidirect
81. #4076C3×C4semidirect
82. #4076C3×C4semidirect
87. #4070C3×C4semidirect
88. #4070C3×C4semidirect
166. C5×M16C3×D4semidirect
182. C22×M16C3×D5semidirect
195. C22×C3×C5#104semidirect
230. C3×M16C22⋊D5semidirect
348. C22×C5C3×#104semidirect
383. M16C3×C22⋊D5semidirect
399. C3×C5#1871semidirect
411. C22×C3#3957semidirect
471. C5C3×#1871semidirect
483. C22C3×#3957semidirect
495. C3#10602777direct (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×M162
C3×#661252
C3×C4×C22⋊Dic52
C2×C3×#39572
C3×#647752
#106027773
C3×#18715