Finite Group Databasebeta

← #14307978

Subgroups — #14307978

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×#91389C211yesmaximal, characteristic, complemented
2#11754271C211yesmaximal, characteristic
3C2×#91309C211yesmaximal, characteristic
4C2×#91108C211yesmaximal, characteristic, complemented
5C2×C5×#825C211yesmaximal, characteristic
6C3×#65409C211yesmaximal, characteristic, complemented
7#11745974C211yesmaximal, characteristic, complemented
8#10601182—31nomaximal, Hall
9C22×Dic30C2211yescharacteristic
10C2×C5×#235C2211yescharacteristic
11C22×C3×Dic10C2211yescharacteristic
12C2×C3×C5×M16C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C2×C4×C5×Dic3C2211yescharacteristic
15C3×#4072C2211yescharacteristic
16C2×Dic3⋊Dic5—22no—
17#91543—22no—
18#91389—22no—
19#91389—22no—
20#91376—21no—
21#91373—21no—
22#91365—22no—
23C2×#6661—21no—
24#91309—22no—
25#91309—22no—
26C2×#6656—21no—
27#91108—22no—
28C5×#825—22no—
29C3×#3948—22no—
30#70346—51nomaximal, Hall
31#66159—31no—
32C2×#4097—31no—
33C2×#4015—31no—
34C2×C5×#104—31no—
35C2×#3956—31no—
36#65409D311yescharacteristic, complemented
37#64743—31no—
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15D412yes—
40C2×Dic30—21no—
41C2×Dic30—21no—
42C2×Dic30—21no—
43C2×Dic30—21no—
44C2×Dic30—21no—
45C2×Dic30—21no—
46C2×C5×#67—21no—
47C22×C5×Dic3—21no—
48C5×#235—21no—
49C5×#235—21no—
50C5×#235—21no—
51C5×#235—21no—
52C2×C5×D12D411yescharacteristic
53C2×C4×C5×D3—21no—
54C2×C5×Dic6D411yescharacteristic
55C22×C3×Dic5—21no—
56C2×C3×Dic10—21no—
57C2×C3×Dic10—21no—
58C2×C3×Dic10—21no—
59C2×C3×Dic10—21no—
60C2×C3×Dic10—21no—
61C2×C3×Dic10D412yes—
62C3×C5×M16—21no—
63C3×C5×M16—21no—
64C2×C3×C5×C8—21no—
65#6710—21no—
66#6710D412yes—
67C2×C3⋊#168—21no—
68C4×C5×Dic3—21no—
69C4×C5×Dic3D412yes—
70C3×C22⋊Dic5—21no—
71C3×C4⋊Dic5D412yes—
72C3×C4×Dic5—21no—
73Dic3⋊Dic5—28no—
74#6668—24no—
75(C2×D3)⋊Dic5—24no—
76#6661—24no—
77#6656—24no—
78C2×#944—51no—
79C2×#942—51no—
80#5526—51no—
81C3×#419—51no—
82C2×#825D511yescharacteristic
83C2×#824—51no—
84#4532—51no—
85C2×C5×#41—31no—
86C22×Dic10—31no—
87C22×Dic10C2×D311yescharacteristic
88C2×C5×M16C2×D311yescharacteristic
89C2×C42×C5—31no—
90#4097—62no—
91#4097—62no—
92#4090—61no—
93C2×#689—61no—
94#4082—61no—
95#4081—62no—
96C2×#687—61no—
97#4072C2×D311yescharacteristic
98C2×C4⋊Dic5—62no—
99#4070—62no—
100C2×#681—31no—
101#4015—62no—
102#4015—62no—
103C5×#104—62no—
104#3956—62no—
105#3948—22no—
106#2005—151noSylow
107C23×C3×C5C2×D411yescharacteristic
108C22×C5×D3—21no—
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114C2×C3×C4×C5#4111yescharacteristic
115C2×Dic15—22no—
116C2×Dic15—22no—
117C2×Dic15—22no—
118Dic30—41no—
119Dic30—41no—
120Dic30—41no—
121Dic30—41no—
122C5×#67—41no—
123C5×#67—41no—
124C2×C5×Dic3—24no—
125C2×C5×Dic3—22no—
126C2×C5×Dic3—21no—
127C5×D12—21no—
128C5×D12—21no—
129C4×C5×D3—41no—
130C4×C5×D3—41no—
131C5×Dic6—21no—
132C5×Dic6—21no—
133C2×C3×Dic5—22no—
134C2×C3×Dic5—22no—
135C2×C3×Dic5—41no—
136C2×C3×Dic5—41no—
137C3×Dic10—22no—
138C3×Dic10—22no—
139C3×Dic10—41no—
140C3×Dic10—41no—
141C3×C5×C8—41no—
142C3⋊#168—22no—
143C22×C3×Q8—51no—
144C2×#235C2×D511yescharacteristic
145C22×Dic6—51no—
146C2×C3×M16C2×D511yescharacteristic
147C3×#117—51no—
148#944—102no—
149#944—102no—
150C2×#216—101no—
151#942—102no—
152#942—102no—
153C2×#215—101no—
154C2×Dic3⋊C4—102no—
155C2×C4×Dic3C2×D511yescharacteristic
156C2×#208—51no—
157#897—102no—
158#886—102no—
159#875—101no—
160#869—101no—
161C3×#103—102no—
162#825—22no—
163#824—102no—
164C5×#41—61no—
165C5×#41—61no—
166C5×#41—61no—
167C5×#41—61no—
168C2×C5×Q8—31no—
169C2×C5×D4—31no—
170C2×C5×D4—61no—
171C22×C4×C5—61no—
172C22×C4×C5—61no—
173C22×C4×C5C22×D311yescharacteristic
174C22×Dic5—21no—
175C22×Dic5—32no—
176C2×Dic10—21no—
177C2×Dic10—21no—
178C2×Dic10—21no—
179C2×Dic10—21no—
180C2×Dic10—21no—
181C2×Dic10—61no—
182C2×Dic10—61no—
183C2×Dic10—61no—
184C2×Dic10—61no—
185C2×Dic10—61no—
186C2×Dic10—61no—
187C2×Dic10D1212yes—
188C5×M16—21no—
189C5×M16—21no—
190C2×C5×C8—21no—
191C42×C5—32no—
192C42×C5—61no—
193C22⋊Dic5—21no—
194C22⋊Dic5—64no—
195#689—64no—
196#687—64no—
197C4⋊Dic5—68no—
198C4⋊Dic5#6712yes—
199#683—64no—
200C4×Dic5—21no—
201#681—32no—
202#681—61no—
203C2×#168—61no—
204C2×#137—151no—
205#536—151no—
206C2×C4⋊Q8—151no—
207C2×#104—31no—
208#419—51no—
209C2×#101—151no—
210#339—151no—
211C22×C3×C5—22no—
212C22×C3×C5#12011yescharacteristic
213C22×C3×C5#12011yescharacteristic
214C22×C3×C5#12111yescharacteristic
215C2×C5×D3—41no—
216C2×C5×D3—42no—
217C3×C4×C5#12011yescharacteristic
218C3×C4×C5#12111yescharacteristic
219C3×C4×C5#12111yescharacteristic
220C3×C4×C5#12711yescharacteristic
221Dic15—42no—
222C3×Dic5—42no—
223C3×Dic5—42no—
224C5×Dic3—24no—
225C5×Dic3—41no—
226C2×C3×Q8—52no—
227C2×C3×Q8—101no—
228C2×C3×Q8—101no—
229C2×C3×Q8—101no—
230C2×C3×Q8—101no—
231C2×C3×Q8—101no—
232C22×C3×C4—101no—
233C22×C3×C4C22×D511yescharacteristic
234C2×#67—21no—
235C22×Dic3—21no—
236C22×Dic3—52no—
237#235—21no—
238#235—21no—
239#235—21no—
240#235—21no—
241C2×D12D2011yescharacteristic
242C2×C4×D3—21no—
243C2×Dic6—101no—
244C2×Dic6—101no—
245C2×Dic6—101no—
246C2×Dic6—101no—
247C2×Dic6—101no—
248C2×Dic6—101no—
249C2×Dic6D2011yescharacteristic
250C3×M16—21no—
251C3×M16—21no—
252C2×C3×C8—21no—
253C3×C4⋊C4—52no—
254C3×C22⋊C4—101no—
255C3×C42—101no—
256#216—104no—
257#215—104no—
258(C2×D3)⋊C4—104no—
259C4⋊Dic3—104no—
260Dic3⋊C4—108no—
261C4×Dic3—21no—
262C4×Dic3C22⋊D512yes—
263#208—52no—
264#208—101no—
265C2×C3⋊C8—101no—
266C23×C5—61no—
267C23×C5D3×D411yescharacteristic
268C5×Q8—61no—
269C5×Q8—61no—
270C5×D4—61no—
271C5×D4—61no—
272C5×D4—121no—
273C5×D4—121no—
274C2×C4×C5—64no—
275C2×C4×C5—62no—
276C2×C4×C5—61no—
277C2×C4×C5—121no—
278C2×C4×C5—121no—
279C2×C4×C5C2×D1211yescharacteristic
280C2×C4×C5#23511yescharacteristic
281C2×C4×C5D3×D411yescharacteristic
282C2×C4×C5D3×D411yescharacteristic
283C2×C4×C5D3×D411yescharacteristic
284C2×C4×C5C2×#6711yescharacteristic
285C2×Dic5—22no—
286C2×Dic5—22no—
287C2×Dic5—41no—
288C2×Dic5—41no—
289C2×Dic5—62no—
290C2×Dic5—62no—
291C2×Dic5—62no—
292Dic10—22no—
293Dic10—22no—
294Dic10—41no—
295Dic10—41no—
296Dic10—121no—
297Dic10—121no—
298Dic10—121no—
299Dic10—121no—
300C5×C8—41no—
301#168—62no—
302C2×#41—31no—
303C22×Q8—51no—
304C22×Q8—151no—
305#137—302no—
306#137—302no—
307C2×Q16—301no—
308C2×SD16—301no—
309C2×M16—151no—
310C2×M16D3×D511yescharacteristic
311C4⋊Q8—302no—
312C4⋊Q8—302no—
313C4⋊Q8—301no—
314#124—301no—
315#123—302no—
316C22⋊Q8—302no—
317#117—51no—
318C2×C4⋊C4—302no—
319C2×C42—31no—
320#104—62no—
321#103—102no—
322#101—302no—
323C2×C3×C5—21no—
324C2×C3×C5—21no—
325C2×C3×C5#39211yescharacteristic
326C2×C3×C5#45612yes—
327C5×D3—81no—
328C23×C3D4×D511yescharacteristic
329C22×D3—21no—
330C3×Q8—102no—
331C3×Q8—102no—
332C3×Q8—201no—
333C3×Q8—201no—
334C2×C3×C4—102no—
335C2×C3×C4—102no—
336C2×C3×C4—201no—
337C2×C3×C4—201no—
338C2×C3×C4C2×D2011yescharacteristic
339C2×C3×C4#70911yescharacteristic
340C2×C3×C4D4×D511yescharacteristic
341C2×C3×C4D4×D511yescharacteristic
342C2×C3×C4D4×D511yescharacteristic
343C2×C3×C4C2×C22⋊D511yescharacteristic
344#67—41no—
345#67—41no—
346C2×Dic3—24no—
347C2×Dic3—22no—
348C2×Dic3—21no—
349C2×Dic3—102no—
350C2×Dic3—102no—
351C2×Dic3—102no—
352D12—21no—
353D12—21no—
354C4×D3—41no—
355C4×D3—41no—
356Dic6—21no—
357Dic6—21no—
358Dic6—201no—
359Dic6—201no—
360Dic6—201no—
361Dic6—201no—
362C3×C8—41no—
363C3⋊C8—102no—
364C22×C5—22no—
365C22×C5—122no—
366C22×C5—121no—
367C22×C5#88211yescharacteristic
368C22×C5#88411yescharacteristic
369C22×C5#93711yescharacteristic
370C4×C5—64no—
371C4×C5—121no—
372C4×C5#88211yescharacteristic
373C4×C5#88411yescharacteristic
374C4×C5#93011yescharacteristic
375C4×C5#94011yescharacteristic
376Dic5—42no—
377Dic5—42no—
378Dic5—122no—
379#41—61no—
380#41—61no—
381#41—61no—
382#41—61no—
383C2×Q8—31no—
384C2×Q8—52no—
385C2×Q8—101no—
386C2×Q8—101no—
387C2×Q8—101no—
388C2×Q8—101no—
389C2×Q8—101no—
390C2×Q8—301no—
391C2×Q8—301no—
392C2×Q8—301no—
393C2×Q8—301no—
394C2×Q8—301no—
395C2×Q8—301no—
396C2×D4—31no—
397C2×D4—61no—
398C22×C4—61no—
399C22×C4—61no—
400C22×C4—101no—
401C22×C4—152no—
402C22×C4C2×D3×D511yescharacteristic
403Q16—304no—
404SD16—304no—
405M16—21no—
406M16—21no—
407M16—152no—
408M16—301no—
409C2×C8—21no—
410C2×C8—301no—
411C4⋊C4—52no—
412C4⋊C4—308no—
413C4⋊C4—304no—
414C22⋊C4—101no—
415C22⋊C4—304no—
416C42—32no—
417C42—61no—
418C42—101no—
419C3×C5#200511yescharacteristic, complemented, Hall
420C22×C3—22no—
421C22×C3#402811yescharacteristic
422C22×C3#403011yescharacteristic
423C22×C3#408311yescharacteristic
424C2×D3—42no—
425C2×D3—41no—
426C3×C4—202no—
427C3×C4—202no—
428C3×C4#402811yescharacteristic
429C3×C4#403011yescharacteristic
430C3×C4#407611yescharacteristic
431C3×C4#408611yescharacteristic
432Dic3—24no—
433Dic3—41no—
434Dic3—202no—
435C2×C5—21no—
436C2×C5—21no—
437C2×C5—241no—
438C2×C5#496011yescharacteristic
439C2×C5#520512yes—
440C23—61no—
441C23#677711yescharacteristic
442Q8—61no—
443Q8—61no—
444Q8—102no—
445Q8—102no—
446Q8—201no—
447Q8—201no—
448Q8—601no—
449Q8—601no—
450Q8—601no—
451Q8—601no—
452D4—61no—
453D4—61no—
454D4—121no—
455D4—121no—
456C2×C4—64no—
457C2×C4—62no—
458C2×C4—61no—
459C2×C4—102no—
460C2×C4—102no—
461C2×C4—121no—
462C2×C4—121no—
463C2×C4—201no—
464C2×C4—201no—
465C2×C4—302no—
466C2×C4—302no—
467C2×C4—302no—
468C2×C4#677111yescharacteristic
469C2×C4D5×D1211yescharacteristic
470C2×C4D3×D2011yescharacteristic
471C2×C4D5×#6711yescharacteristic
472C2×C4D3×C22⋊D511yescharacteristic
473C2×C4#679011yescharacteristic
474C8—41no—
475C8—302no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3#6511512yes—
479C2×C3#6524911yescharacteristic
480D3—81no—
481C5#7034611yescharacteristic, complemented, Sylow
482C22—22no—
483C22—121no—
484C22—122no—
485C22#9146111yescharacteristic
486C22#9147411yescharacteristic
487C22#9147511yescharacteristic
488C4—64no—
489C4—121no—
490C4—202no—
491C4—202no—
492C4—602no—
493C4#9144811yescharacteristic
494C4#9145411yescharacteristic
495C4#9147611yescharacteristic
496C4#9156711yescharacteristic
497C3#1060118211yescharacteristic, complemented, Sylow
498C2—21no—
499C2—21no—
500C2—241no—
501C2#1174825212yes—
502C2#1174892511yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5#120
prime radicalC2×C5×#235C22
hypercenterC2×M16D3×D5
hypocenterC3×C5#2005
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×#91389C2semidirect
4. C2×#91108C2semidirect
6. C3×#65409C2semidirect
7. #11745974C2semidirect
36. #65409D3semidirect
419. C3×C5#2005semidirect
481. C5#70346semidirect
497. C3#10601182semidirect

Maximal subgroups

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

subgroupindex
C2×#913892
#117542712
C2×#913092
C2×#911082
C2×C5×#8252
C3×#654092
#117459742
#106011823
#703465