Finite Group Databasebeta

← #14307967

Subgroups — #14307967

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
1C3×#65860C211yesmaximal, characteristic
2C2×#91389C211yesmaximal, characteristic, complemented
3C2×#91313C211yesmaximal, characteristic
4#11751105C211yesmaximal, characteristic, complemented
5C2×#90977C211yesmaximal, characteristic
6C2×#90961C211yesmaximal, characteristic, complemented
7C5×#4532C211yesmaximal, characteristic, complemented
8#10599561—31nomaximal, Hall
9C22×Dic30C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C22×C3×Dic10C2211yescharacteristic
12C3×C5×#117C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C2×C4×C5×Dic3C2211yescharacteristic
15C2×C5×#208C2211yescharacteristic
16C3×#4043—22no—
17C3×#4032—22no—
18C3×#4021—21no—
19C3×#4015—21no—
20C2×Dic3⋊Dic5—22no—
21#91389—22no—
22#91389—22no—
23C2×#6662—21no—
24#91313—22no—
25#91313—22no—
26C2×#6657—21no—
27#91094—22no—
28#90977—22no—
29#90961—22no—
30#71868—51nomaximal, Hall
31C2×#4055—31no—
32#65860D311yescharacteristic
33C2×#4015—31no—
34C2×#3956—31no—
35#65293—31no—
36C2×#3937—31no—
37C5×#339—31no—
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15—21no—
40C2×Dic30—21no—
41C2×Dic30—21no—
42C2×Dic30—21no—
43C2×Dic30—21no—
44C2×Dic30—21no—
45C2×Dic30D412yes—
46C22×C5×Dic3—21no—
47C2×C3×C22⋊D5—21no—
48C22×C3×Dic5D412yes—
49C3×#709—21no—
50C3×#709—21no—
51C3×#709—21no—
52C3×#709—21no—
53C2×C3×D20D411yescharacteristic
54C2×C3×C4×D5—21no—
55C2×C3×Dic10—21no—
56C2×C3×Dic10—21no—
57C2×C3×Dic10—21no—
58C2×C3×Dic10—21no—
59C2×C3×Dic10—21no—
60C2×C3×Dic10—21no—
61C2×C3×Dic10D411yescharacteristic
62C3×C5×C4⋊C4D412yes—
63C3×C5×C22⋊C4—21no—
64C3×C42×C5—21no—
65#6710—21no—
66#6710—21no—
67C2×C3⋊#168—21no—
68C4×C5×Dic3—21no—
69C4×C5×Dic3D412yes—
70C5×#208—21no—
71C5×#208D412yes—
72C2×C5×C3⋊C8—21no—
73C3×#685—24no—
74C3×C4⋊Dic5—24no—
75Dic3⋊Dic5—28no—
76#6662—24no—
77#6657—24no—
78C3×#536—51no—
79C2×#951—51no—
80C2×#944—51no—
81C2×#837—51no—
82C2×#836—51no—
83#5004—51no—
84#4532D511yescharacteristic, complemented
85C2×#709C2×D311yescharacteristic
86C22×Dic10—31no—
87C22×Dic10C2×D311yescharacteristic
88C2×C5×M16—31no—
89C5×#117C2×D311yescharacteristic
90C2×C42×C5—31no—
91C2×C4⋊Dic5—62no—
92C2×#681—31no—
93#4055—62no—
94#4055—62no—
95C2×Dic20—61no—
96C2×#677—61no—
97#4043—22no—
98#4032—22no—
99#4021—21no—
100#4015—21no—
101#4015—62no—
102#4015—62no—
103#3956—62no—
104#3942—62no—
105#3937—62no—
106#2005—151noSylow
107C23×C3×C5C2×D411yescharacteristic
108C22×C3×D5—21no—
109C2×C3×C4×C5—22no—
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5#4111yescharacteristic
116C2×Dic15—22no—
117C2×Dic15—41no—
118C2×Dic15—41no—
119Dic30—22no—
120Dic30—22no—
121Dic30—41no—
122Dic30—41no—
123C2×C5×Dic3—24no—
124C2×C5×Dic3—22no—
125C3×C22⋊D5—41no—
126C3×C22⋊D5—41no—
127C2×C3×Dic5—22no—
128C2×C3×Dic5—21no—
129C2×C3×Dic5—22no—
130C2×C3×Dic5—22no—
131C3×D20—21no—
132C3×D20—21no—
133C3×C4×D5—41no—
134C3×C4×D5—41no—
135C3×Dic10—21no—
136C3×Dic10—21no—
137C3×Dic10—41no—
138C3×Dic10—41no—
139C3×Dic10—41no—
140C3×Dic10—41no—
141C3⋊#168—41no—
142C5×C3⋊C8—22no—
143C2×C3×#41—51no—
144C22×C3×Q8—51no—
145C22×Dic6—51no—
146C3×C4⋊Q8—101no—
147C3×#124—101no—
148C3×#123—102no—
149C3×C22⋊Q8—102no—
150C3×#117C2×D511yescharacteristic
151#951—102no—
152#951—102no—
153#944—102no—
154#944—102no—
155C2×#216—101no—
156C2×#214—101no—
157C2×Dic3⋊C4—102no—
158C2×C4×Dic3C2×D511yescharacteristic
159C2×#208—51no—
160C2×#208C2×D511yescharacteristic
161#837—102no—
162#836—102no—
163#810—102no—
164C22×C4×C5—61no—
165C22×C4×C5C22×D311yescharacteristic
166C2×C22⋊D5—21no—
167C22×Dic5—61no—
168C22×Dic5#6712yes—
169#709—21no—
170#709—21no—
171#709—21no—
172#709—21no—
173C2×D20#6711yescharacteristic
174C2×C4×D5—21no—
175C2×Dic10—21no—
176C2×Dic10—21no—
177C2×Dic10—21no—
178C2×Dic10—21no—
179C2×Dic10—21no—
180C2×Dic10—21no—
181C2×Dic10—32no—
182C2×Dic10—61no—
183C2×Dic10—61no—
184C2×Dic10—61no—
185C2×Dic10—61no—
186C2×Dic10—61no—
187C2×Dic10#6711yescharacteristic
188C5×M16—32no—
189C5×M16—61no—
190C2×C5×C8—61no—
191C5×C4⋊C4#6712yes—
192C5×C22⋊C4—21no—
193C42×C5—21no—
194C42×C5—32no—
195C42×C5—61no—
196#685—24no—
197C4⋊Dic5—24no—
198C4⋊Dic5—68no—
199#681—61no—
200#681—61no—
201C2×#168—61no—
202Dic20—64no—
203#677—64no—
204C2×#137—151no—
205#536—51no—
206C2×C4⋊Q8—151no—
207C2×#104—151no—
208#419—151no—
209C2×#101—151no—
210#339—31no—
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—42no—
218C3×C4×C5#12011yescharacteristic
219C3×C4×C5#12111yescharacteristic
220C3×C4×C5#12111yescharacteristic
221C3×C4×C5#12711yescharacteristic
222Dic15—42no—
223C3×Dic5—41no—
224C3×Dic5—42no—
225C5×Dic3—24no—
226C3×#41—101no—
227C3×#41—101no—
228C3×#41—101no—
229C3×#41—101no—
230C2×C3×Q8—51no—
231C2×C3×Q8—101no—
232C2×C3×Q8—101no—
233C2×C3×Q8—101no—
234C2×C3×Q8—101no—
235C2×C3×Q8—101no—
236C2×C3×Q8—101no—
237C2×C3×D4—51no—
238C2×C3×D4—101no—
239C22×C3×C4—52no—
240C22×C3×C4—101no—
241C22×C3×C4C22×D511yescharacteristic
242C22×Dic3—21no—
243C22×Dic3—101no—
244C2×Dic6—52no—
245C2×Dic6—101no—
246C2×Dic6—101no—
247C2×Dic6—101no—
248C2×Dic6—101no—
249C2×Dic6—101no—
250C3×C4⋊C4—104no—
251C3×C4⋊C4D2012yes—
252C3×C22⋊C4—21no—
253C3×C22⋊C4—104no—
254C3×C42—21no—
255#216—104no—
256#214—104no—
257Dic3⋊C4—108no—
258C4×Dic3—21no—
259C4×Dic3D2012yes—
260#208—21no—
261#208—101no—
262#208—101no—
263#208D2012yes—
264C2×C3⋊C8—21no—
265C2×C3⋊C8—101no—
266C23×C5C2×#6711yescharacteristic
267C22×D5—21no—
268C2×C4×C5—22no—
269C2×C4×C5—64no—
270C2×C4×C5—62no—
271C2×C4×C5D3×D411yescharacteristic
272C2×C4×C5D3×D411yescharacteristic
273C2×C4×C5D3×D411yescharacteristic
274C2×C4×C5#23711yescharacteristic
275C2×C4×C5C2×#6711yescharacteristic
276C2×C4×C5C2×#6711yescharacteristic
277C22⋊D5—41no—
278C22⋊D5—41no—
279C2×Dic5—22no—
280C2×Dic5—22no—
281C2×Dic5—21no—
282C2×Dic5—22no—
283C2×Dic5—62no—
284C2×Dic5—121no—
285C2×Dic5—121no—
286D20—21no—
287D20—21no—
288C4×D5—41no—
289C4×D5—41no—
290Dic10—21no—
291Dic10—21no—
292Dic10—41no—
293Dic10—41no—
294Dic10—41no—
295Dic10—41no—
296Dic10—62no—
297Dic10—62no—
298Dic10—121no—
299Dic10—121no—
300C5×C8—62no—
301#168—121no—
302C2×#41—51no—
303C22×Q8—51no—
304C22×Q8—151no—
305#137—302no—
306#137—302no—
307C2×Q16—301no—
308C2×SD16—301no—
309C2×M16—31no—
310C2×M16—151no—
311C4⋊Q8—101no—
312C4⋊Q8—302no—
313C4⋊Q8—302no—
314#124—101no—
315#123—102no—
316C22⋊Q8—102no—
317#117D3×D511yescharacteristic
318C2×C4⋊C4—302no—
319C2×C42—31no—
320#104—302no—
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×C3D4×D511yescharacteristic
330C3×Q8—101no—
331C3×Q8—101no—
332C3×Q8—201no—
333C3×Q8—201no—
334C3×Q8—201no—
335C3×Q8—201no—
336C3×D4—101no—
337C3×D4—101no—
338C3×D4—201no—
339C3×D4—201no—
340C2×C3×C4—22no—
341C2×C3×C4—102no—
342C2×C3×C4—102no—
343C2×C3×C4—101no—
344C2×C3×C4—102no—
345C2×C3×C4—201no—
346C2×C3×C4—201no—
347C2×C3×C4C2×D2011yescharacteristic
348C2×C3×C4C2×D2011yescharacteristic
349C2×C3×C4C2×D2011yescharacteristic
350C2×C3×C4D4×D511yescharacteristic
351C2×C3×C4D4×D511yescharacteristic
352C2×C3×C4#71311yescharacteristic
353C2×Dic3—24no—
354C2×Dic3—22no—
355C2×Dic3—102no—
356C2×Dic3—201no—
357C2×Dic3—201no—
358Dic6—102no—
359Dic6—102no—
360Dic6—201no—
361Dic6—201no—
362C3⋊C8—22no—
363C3⋊C8—201no—
364C22×C5—22no—
365C22×C5#93711yescharacteristic
366C22×C5#93911yescharacteristic
367C22×C5#95311yescharacteristic
368C2×D5—41no—
369C2×D5—42no—
370C4×C5—42no—
371C4×C5—64no—
372C4×C5#93711yescharacteristic
373C4×C5#93811yescharacteristic
374C4×C5#93911yescharacteristic
375C4×C5#94011yescharacteristic
376Dic5—41no—
377Dic5—42no—
378Dic5—122no—
379#41—101no—
380#41—101no—
381#41—101no—
382#41—101no—
383C2×Q8—51no—
384C2×Q8—101no—
385C2×Q8—101no—
386C2×Q8—101no—
387C2×Q8—101no—
388C2×Q8—101no—
389C2×Q8—101no—
390C2×Q8—152no—
391C2×Q8—301no—
392C2×Q8—301no—
393C2×Q8—301no—
394C2×Q8—301no—
395C2×Q8—301no—
396C2×D4—51no—
397C2×D4—101no—
398C22×C4—52no—
399C22×C4—61no—
400C22×C4—101no—
401C22×C4—301no—
402C22×C4C2×D3×D511yescharacteristic
403Q16—304no—
404SD16—304no—
405M16—32no—
406M16—61no—
407M16—301no—
408M16—301no—
409C2×C8—61no—
410C2×C8—301no—
411C4⋊C4—104no—
412C4⋊C4—308no—
413C4⋊C4#120212yes—
414C22⋊C4—21no—
415C22⋊C4—104no—
416C42—21no—
417C42—32no—
418C42—61no—
419C3×C5#200511yescharacteristic, complemented, Hall
420C22×C3—22no—
421C22×C3—202no—
422C22×C3—201no—
423C22×C3#402811yescharacteristic
424C22×C3#402811yescharacteristic
425C22×C3#404111yescharacteristic
426C3×C4—42no—
427C3×C4—202no—
428C3×C4—201no—
429C3×C4#402011yescharacteristic
430C3×C4#402811yescharacteristic
431C3×C4#404111yescharacteristic
432C3×C4#404111yescharacteristic
433Dic3—24no—
434Dic3—202no—
435C2×C5—21no—
436C2×C5—21no—
437C2×C5#522311yescharacteristic
438C2×C5#524612yes—
439D5—81no—
440C23—101no—
441C23D5×#6711yescharacteristic
442Q8—101no—
443Q8—101no—
444Q8—201no—
445Q8—201no—
446Q8—201no—
447Q8—201no—
448Q8—302no—
449Q8—302no—
450Q8—601no—
451Q8—601no—
452D4—101no—
453D4—101no—
454D4—201no—
455D4—201no—
456C2×C4—22no—
457C2×C4—64no—
458C2×C4—62no—
459C2×C4—102no—
460C2×C4—102no—
461C2×C4—102no—
462C2×C4—101no—
463C2×C4—201no—
464C2×C4—201no—
465C2×C4—302no—
466C2×C4—601no—
467C2×C4—601no—
468C2×C4#676611yescharacteristic
469C2×C4D3×D2011yescharacteristic
470C2×C4D3×D2011yescharacteristic
471C2×C4#677711yescharacteristic
472C2×C4C2×#120211yescharacteristic
473C2×C4D5×#6711yescharacteristic
474C8—62no—
475C8—601no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—401no—
479C2×C3#6496011yescharacteristic
480C2×C3#6511512yes—
481C5#7186811yescharacteristic, complemented, Sylow
482C22—22no—
483C22—201no—
484C22—202no—
485C22#9140911yescharacteristic
486C22#9147411yescharacteristic
487C22#9156411yescharacteristic
488C4—42no—
489C4—64no—
490C4—202no—
491C4—201no—
492C4—602no—
493C4#9140911yescharacteristic
494C4#9145811yescharacteristic
495C4#9146511yescharacteristic
496C4#9147411yescharacteristic
497C3#1059956111yescharacteristic, complemented, Sylow
498C2—21no—
499C2—21no—
500C2—401no—
501C2#1174892311yescharacteristic
502C2#1174946412yes—
subgroupG/H
centerC22#91564
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5#120
prime radicalC2×C3×#709C22
hypercenter#117D3×D5
hypocenterC3×C5#2005
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C2×#91389C2semidirect
4. #11751105C2semidirect
6. C2×#90961C2semidirect
7. C5×#4532C2semidirect
84. #4532D5semidirect
419. C3×C5#2005semidirect
481. C5#71868semidirect
497. C3#10599561semidirect

Maximal subgroups

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

subgroupindex
C3×#658602
C2×#913892
C2×#913132
#117511052
C2×#909772
C2×#909612
C5×#45322
#105995613
#718685