Finite Group Databasebeta

← #14307970

Subgroups — #14307970

Order 1920.

724 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
1C2×C5×#869C211yesmaximal, characteristic, complemented
2#11754251C211yesmaximal, characteristic
3C2×#91307C211yesmaximal, characteristic
4C2×C3×#3937C211yesmaximal, characteristic
5#11748409C211yesmaximal, characteristic, complemented
6C2×#90962C211yesmaximal, characteristic, complemented
7#11746344C211yesmaximal, characteristic, complemented
8#10602588—31nomaximal, Hall
9C22×C5×Dic6C2211yescharacteristic
10C22×C5×Dic6C2211yescharacteristic
11C2×C3×#709C2211yescharacteristic
12C2×C3×C42×C5C2211yescharacteristic
13#91815C2211yescharacteristic
14C2×#6710C2211yescharacteristic
15C2×C5×C4⋊Dic3—22no—
16C5×#869—22no—
17C5×#869—22no—
18C2×C3×#681C2211yescharacteristic
19#91536—22no—
20#91385—21no—
21#91368—21no—
22#91359—22no—
23C2×#6661—21no—
24#91307—22no—
25#91307—22no—
26C2×#6655—21no—
27C3×#3937—22no—
28#90973—22no—
29#90962—22no—
30#70389—51nomaximal, Hall
31C2×C5×C4⋊Q8—31no—
32#66150—31no—
33C2×#4088—31no—
34C2×#3968—31no—
35#65514—31no—
36C2×#3937D311yescharacteristic
37#64743—31no—
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5C2311yescharacteristic
40C22×C5×Dic3—21no—
41C22×C5×Dic3D412yes—
42C2×C5×Dic6—21no—
43C2×C5×Dic6—21no—
44C2×C5×Dic6—21no—
45C2×C5×Dic6—21no—
46C2×C5×Dic6—21no—
47C2×C5×Dic6—21no—
48C2×C5×Dic6—21no—
49C2×C5×Dic6—21no—
50C2×C5×Dic6—21no—
51C2×C5×Dic6—21no—
52C2×C5×Dic6—21no—
53C2×C5×Dic6D412yes—
54C2×C3×C22⋊D5—21no—
55C3×#709—21no—
56C3×#709—21no—
57C3×#709—21no—
58C3×#709—21no—
59C2×C3×D20D411yescharacteristic
60C2×C3×C4×D5—21no—
61C2×C3×Dic10D411yescharacteristic
62C3×C42×C5—21no—
63C3×C42×C5D412yes—
64#6719—21no—
65C4⋊Dic15D412yes—
66C4×Dic15—21no—
67#6710—21no—
68#6710D412yes—
69C2×C3⋊#168—21no—
70C5×C4⋊Dic3—28no—
71C3×#681—21no—
72C3×#681—21no—
73C2×C3×#168—21no—
74#6669—24no—
75#6665—24no—
76#6661—24no—
77#6655—24no—
78#5825—51no—
79C2×#951—51no—
80C2×#869D511yescharacteristic, complemented
81C2×C3×#104—51no—
82C2×#824—51no—
83#5120—51no—
84#4523—51no—
85C22×C5×Q8—31no—
86C22×C5×Q8—31no—
87C2×#709C2×D311yescharacteristic
88C5×C4⋊Q8—62no—
89C5×C4⋊Q8—62no—
90C2×C5×C4⋊C4—62no—
91C2×C42×C5C2×D311yescharacteristic
92#4093—61no—
93#4092—62no—
94#4090—61no—
95C2×#689—61no—
96#4088—62no—
97#4088—62no—
98C2×#688—61no—
99#4075—62no—
100#4072—31no—
101C2×#681—31no—
102C2×#681C2×D311yescharacteristic
103#3968—62no—
104#3967—62no—
105#3937—22no—
106#2005—151noSylow
107C23×C3×C5C2×D411yescharacteristic
108C22×C3×D5—21no—
109C2×C3×C4×C5—24no—
110C2×C3×C4×C5—22no—
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5C2×D411yescharacteristic
116C2×C3×C4×C5#4111yescharacteristic
117C2×Dic15—22no—
118C2×C5×Dic3—22no—
119C2×C5×Dic3—22no—
120C2×C5×Dic3—22no—
121C2×C5×Dic3—22no—
122C2×C5×Dic3—41no—
123C2×C5×Dic3—41no—
124C5×Dic6—22no—
125C5×Dic6—22no—
126C5×Dic6—41no—
127C5×Dic6—41no—
128C5×Dic6—41no—
129C5×Dic6—41no—
130C5×Dic6—41no—
131C5×Dic6—41no—
132C3×C22⋊D5—41no—
133C3×C22⋊D5—41no—
134C2×C3×Dic5—21no—
135C3×D20—21no—
136C3×D20—21no—
137C3×C4×D5—41no—
138C3×C4×D5—41no—
139C3×Dic10—21no—
140C3×Dic10—21no—
141C3⋊#168—22no—
142C3×#168—41no—
143C2×C3×#41—51no—
144C22×Dic6C2×D511yescharacteristic
145C22×Dic6C2×D511yescharacteristic
146C2×C3×M16—51no—
147C2×C3×C42C2×D511yescharacteristic
148#951—102no—
149#951—102no—
150#944—101no—
151C2×#216—101no—
152#936—101no—
153#935—102no—
154C2×#214—101no—
155#926—51no—
156C2×C4⋊Dic3—22no—
157#924—102no—
158C2×#208—51no—
159#869—22no—
160#869—22no—
161C3×#104—102no—
162#824—102no—
163#816—102no—
164C2×C5×Q8—32no—
165C2×C5×Q8—61no—
166C2×C5×Q8—61no—
167C2×C5×Q8—61no—
168C2×C5×Q8—61no—
169C2×C5×Q8—61no—
170C2×C5×Q8—61no—
171C2×C5×Q8—61no—
172C2×C5×Q8—61no—
173C2×C5×Q8—61no—
174C2×C5×Q8—61no—
175C2×C5×Q8—61no—
176C22×C4×C5—21no—
177C22×C4×C5—32no—
178C22×C4×C5—61no—
179C22×C4×C5C22×D311yescharacteristic
180C2×C22⋊D5—21no—
181#709—21no—
182#709—21no—
183#709—21no—
184#709—21no—
185C2×D20D1211yescharacteristic
186C2×C4×D5—21no—
187C2×Dic10D1211yescharacteristic
188C5×C4⋊C4—68no—
189C42×C5—21no—
190C42×C5#6712yes—
191C22⋊Dic5—61no—
192#689—64no—
193#688—64no—
194#685—64no—
195C4⋊Dic5—32no—
196#683—64no—
197C4×Dic5—61no—
198#681—21no—
199#681—21no—
200#681—32no—
201#681—61no—
202C2×#168—21no—
203C2×#168—61no—
204C2×#137—151no—
205#536—151no—
206C2×C4⋊Q8—31no—
207C2×#104—51no—
208#419—151no—
209C2×#101—151no—
210#339—151no—
211C22×C3×C5—22no—
212C22×C3×C5#12011yescharacteristic
213C22×C3×C5#12011yescharacteristic
214C22×C3×C5#12111yescharacteristic
215C2×C3×D5—41no—
216C2×C3×D5—42no—
217C3×C4×C5—24no—
218C3×C4×C5#12011yescharacteristic
219C3×C4×C5#12111yescharacteristic
220C3×C4×C5#12111yescharacteristic
221C3×C4×C5#12711yescharacteristic
222Dic15—42no—
223C3×Dic5—41no—
224C5×Dic3—42no—
225C5×Dic3—42no—
226C3×#41—101no—
227C3×#41—101no—
228C3×#41—101no—
229C3×#41—101no—
230C2×C3×Q8—51no—
231C2×C3×D4—51no—
232C2×C3×D4—101no—
233C22×C3×C4—21no—
234C22×C3×C4—101no—
235C22×C3×C4C22×D511yescharacteristic
236C22×Dic3—21no—
237C22×Dic3C22⋊D512yes—
238C2×Dic6—21no—
239C2×Dic6—21no—
240C2×Dic6—21no—
241C2×Dic6—21no—
242C2×Dic6—21no—
243C2×Dic6—21no—
244C2×Dic6—21no—
245C2×Dic6—21no—
246C2×Dic6—21no—
247C2×Dic6—21no—
248C2×Dic6—21no—
249C2×Dic6C22⋊D512yes—
250C3×M16—101no—
251C3×M16—101no—
252C2×C3×C8—101no—
253C3×C42—21no—
254C3×C42C22⋊D512yes—
255#217—104no—
256#217—101no—
257#216—104no—
258#214—104no—
259C4⋊Dic3—28no—
260C4⋊Dic3—52no—
261Dic3⋊C4—104no—
262C4×Dic3—101no—
263#208—52no—
264#208—101no—
265C2×C3⋊C8—101no—
266C23×C5D3×D411yescharacteristic
267C22×D5—21no—
268C5×Q8—62no—
269C5×Q8—62no—
270C5×Q8—121no—
271C5×Q8—121no—
272C5×Q8—121no—
273C5×Q8—121no—
274C5×Q8—121no—
275C5×Q8—121no—
276C2×C4×C5—24no—
277C2×C4×C5—22no—
278C2×C4×C5—62no—
279C2×C4×C5—62no—
280C2×C4×C5—62no—
281C2×C4×C5—62no—
282C2×C4×C5—121no—
283C2×C4×C5—121no—
284C2×C4×C5C2×D1211yescharacteristic
285C2×C4×C5#23511yescharacteristic
286C2×C4×C5D3×D411yescharacteristic
287C2×C4×C5D3×D411yescharacteristic
288C2×C4×C5D3×D411yescharacteristic
289C2×C4×C5C2×#6711yescharacteristic
290C22⋊D5—41no—
291C22⋊D5—41no—
292C2×Dic5—21no—
293C2×Dic5—62no—
294D20—21no—
295D20—21no—
296C4×D5—41no—
297C4×D5—41no—
298Dic10—21no—
299Dic10—21no—
300#168—41no—
301#168—62no—
302C2×#41—51no—
303C22×Q8—31no—
304C22×Q8—31no—
305#137—302no—
306#137—302no—
307C2×Q16—301no—
308C2×SD16—301no—
309C2×M16—51no—
310C2×M16—151no—
311C4⋊Q8—62no—
312C4⋊Q8—62no—
313C4⋊Q8—301no—
314#124—301no—
315#123—302no—
316C22⋊Q8—302no—
317#117—151no—
318C2×C4⋊C4—62no—
319C2×C42D3×D511yescharacteristic
320#104—102no—
321#103—302no—
322#101—302no—
323C2×C3×C5—21no—
324C2×C3×C5—21no—
325C2×C3×C5#39211yescharacteristic
326C2×C3×C5#45612yes—
327C3×D5—81no—
328C23×C3—101no—
329C23×C3C2×C22⋊D511yescharacteristic
330C3×Q8—101no—
331C3×Q8—101no—
332C3×D4—101no—
333C3×D4—101no—
334C3×D4—201no—
335C3×D4—201no—
336C2×C3×C4—24no—
337C2×C3×C4—22no—
338C2×C3×C4—101no—
339C2×C3×C4—201no—
340C2×C3×C4—201no—
341C2×C3×C4D4×D511yescharacteristic
342C2×C3×C4D4×D511yescharacteristic
343C2×C3×C4D4×D511yescharacteristic
344C2×C3×C4#71111yescharacteristic
345C2×C3×C4C2×C22⋊D511yescharacteristic
346C2×C3×C4C2×C22⋊D511yescharacteristic
347C2×Dic3—22no—
348C2×Dic3—22no—
349C2×Dic3—22no—
350C2×Dic3—22no—
351C2×Dic3—41no—
352C2×Dic3—41no—
353C2×Dic3—102no—
354Dic6—22no—
355Dic6—22no—
356Dic6—41no—
357Dic6—41no—
358Dic6—41no—
359Dic6—41no—
360Dic6—41no—
361Dic6—41no—
362C3×C8—201no—
363C3⋊C8—102no—
364C22×C5—22no—
365C22×C5#88211yescharacteristic
366C22×C5#88411yescharacteristic
367C22×C5#93711yescharacteristic
368C2×D5—41no—
369C2×D5—42no—
370C4×C5—24no—
371C4×C5—122no—
372C4×C5—122no—
373C4×C5#88211yescharacteristic
374C4×C5#88411yescharacteristic
375C4×C5#93011yescharacteristic
376C4×C5#94011yescharacteristic
377Dic5—41no—
378Dic5—122no—
379#41—101no—
380#41—101no—
381#41—101no—
382#41—101no—
383C2×Q8—32no—
384C2×Q8—51no—
385C2×Q8—61no—
386C2×Q8—61no—
387C2×Q8—61no—
388C2×Q8—61no—
389C2×Q8—61no—
390C2×Q8—61no—
391C2×Q8—61no—
392C2×Q8—61no—
393C2×Q8—61no—
394C2×Q8—61no—
395C2×Q8—61no—
396C2×D4—51no—
397C2×D4—101no—
398C22×C4—21no—
399C22×C4—32no—
400C22×C4—61no—
401C22×C4—101no—
402C22×C4C2×D3×D511yescharacteristic
403Q16—304no—
404SD16—304no—
405M16—101no—
406M16—101no—
407M16—152no—
408M16—301no—
409C2×C8—101no—
410C2×C8—301no—
411C4⋊C4—68no—
412C4⋊C4—152no—
413C4⋊C4—304no—
414C22⋊C4—304no—
415C22⋊C4—301no—
416C42—21no—
417C42—301no—
418C42#120112yes—
419C3×C5#200511yescharacteristic, complemented, Hall
420C22×C3—22no—
421C22×C3—202no—
422C22×C3—201no—
423C22×C3#408311yescharacteristic
424C22×C3#408511yescharacteristic
425C22×C3#409911yescharacteristic
426C3×C4—24no—
427C3×C4—201no—
428C3×C4#408311yescharacteristic
429C3×C4#408411yescharacteristic
430C3×C4#408511yescharacteristic
431C3×C4#408611yescharacteristic
432Dic3—42no—
433Dic3—42no—
434Dic3—202no—
435C2×C5—21no—
436C2×C5—21no—
437C2×C5#482612yes—
438C2×C5#496011yescharacteristic
439D5—81no—
440C23—101no—
441C23D3×C22⋊D511yescharacteristic
442Q8—62no—
443Q8—62no—
444Q8—101no—
445Q8—101no—
446Q8—121no—
447Q8—121no—
448Q8—121no—
449Q8—121no—
450Q8—121no—
451Q8—121no—
452D4—101no—
453D4—101no—
454D4—201no—
455D4—201no—
456C2×C4—24no—
457C2×C4—22no—
458C2×C4—62no—
459C2×C4—62no—
460C2×C4—62no—
461C2×C4—62no—
462C2×C4—101no—
463C2×C4—121no—
464C2×C4—121no—
465C2×C4—201no—
466C2×C4—201no—
467C2×C4—302no—
468C2×C4#677211yescharacteristic
469C2×C4D5×D1211yescharacteristic
470C2×C4#677711yescharacteristic
471C2×C4#677711yescharacteristic
472C2×C4C2×#120111yescharacteristic
473C2×C4D3×C22⋊D511yescharacteristic
474C8—201no—
475C8—302no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—401no—
479C2×C3#6538412yes—
480C2×C3#6551211yescharacteristic
481C5#7038911yescharacteristic, complemented, Sylow
482C22—22no—
483C22—202no—
484C22—201no—
485C22#9145311yescharacteristic
486C22#9147511yescharacteristic
487C22#9156811yescharacteristic
488C4—24no—
489C4—122no—
490C4—122no—
491C4—201no—
492C4—602no—
493C4#9144911yescharacteristic
494C4#9145311yescharacteristic
495C4#9146311yescharacteristic
496C4#9147511yescharacteristic
497C3#1060258811yescharacteristic, complemented, Sylow
498C2—21no—
499C2—21no—
500C2—401no—
501C2#1174712212yes—
502C2#1174892711yescharacteristic
subgroupG/H
centerC22#91475
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5#120
prime radicalC2×C3×#709C22
hypercenterC2×C42D3×D5
hypocenterC3×C5#2005
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C5×#869C2semidirect
5. #11748409C2semidirect
6. C2×#90962C2semidirect
7. #11746344C2semidirect
80. C2×#869D5semidirect
419. C3×C5#2005semidirect
481. C5#70389semidirect
497. C3#10602588semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8692
#117542512
C2×#913072
C2×C3×#39372
#117484092
C2×#909622
#117463442
#106025883
#703895