Finite Group Databasebeta

← #14417268

Subgroups — #14417268

Order 1920.

940 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754496C211yesmaximal, characteristic
2#11754188C211yesmaximal, characteristic, complemented
3C2×#91315C211yesmaximal, characteristic
4#11751214C211yesmaximal, characteristic
5C5×#5101C211yesmaximal, characteristic, complemented
6C2×C3×#3948C211yesmaximal, characteristic, complemented
7#11748453C211yesmaximal, characteristic, complemented
8#11747832C212yesmaximal, complemented
9#11747831C212yesmaximal, complemented
10#11747830C212yesmaximal, complemented
11#11747743C212yesmaximal, complemented
12#10610302—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×C3×Dic10C2211yescharacteristic
15C22×C3×C5×C8C2211yescharacteristic
16#91815C2211yescharacteristic
17C5×#926C2211yescharacteristic
18C2×C5×#208C2211yescharacteristic
19C2×C3×C4⋊Dic5C2211yescharacteristic
20#91552—22no—
21#91528—22no—
22#91437—21no—
23#91428C2212yes—
24#91347—21no—
25#91340C2212yes—
26#91331—21no—
27#91331—21no—
28Dic3×Dic10C2212yes—
29Dic3×Dic10C2212yes—
30C2×#6662C2212yes—
31#91315C418yescomplemented
32C2×#6658C2212yes—
33#91105C2211yescharacteristic
34#91105C2211yescharacteristic
35#91100C2211yescharacteristic
36#91100C2211yescharacteristic
37C5×#815C2212yes—
38C5×C8×Dic3C2212yes—
39C3×#3948C2212yes—
40C3×#3948C2212yes—
41#90990C2212yes—
42#90987C2212yes—
43#78774—51nomaximal, Hall
44C2×#4055—31no—
45#65857—31no—
46#65850—31no—
47C5×#405—31no—
48#65410—31no—
49#65402—31no—
50C2×#3948D311yescharacteristic, complemented
51#65005—32no—
52#64999—32no—
53C4×Dic20—32no—
54C4×#677—32no—
55C22×C3×C4×C5C2311yescharacteristic
56C2×#1220—21no—
57#6817—22no—
58#6817C2×C414yes—
59C2×D60C2311yescharacteristic
60C2×C4×D15—21no—
61C2×Dic30C2311yescharacteristic
62C22×C3×Dic5—21no—
63C22×C3×Dic5—21no—
64C2×C3×Dic10—21no—
65C2×C3×Dic10—22no—
66C2×C3×Dic10C2×C414yescomplemented
67C2×C3×Dic10C2312yes—
68C2×#1200—22no—
69C2×C3×C5×C8—22no—
70C2×C3×C5×C8C2311yescharacteristic
71C2×C3×C5×C8C2311yescharacteristic
72#6719—21no—
73C4⋊Dic15C2311yescharacteristic
74C4⋊Dic15C2311yescharacteristic
75C4×Dic15—21no—
76C5×#217D412yes—
77C5×C4⋊Dic3D411yescharacteristic
78C5×C4⋊Dic3D411yescharacteristic
79C4×C5×Dic3C2312yes—
80C5×#208C2×C414yescomplemented
81C2×C5×C3⋊C8C2312yes—
82C3×C4⋊Dic5—21no—
83C3×C4⋊Dic5C2312yes—
84#6669—22no—
85#6668—22no—
86#6668—22no—
87#6667—22no—
88Dic3×Dic5—22no—
89Dic3×Dic5—22no—
90Dic3×Dic5—22no—
91#6662C2×C418yescomplemented
92#6658C2×C418yescomplemented
93#5812—51no—
94C2×#942—51no—
95#5504—51no—
96C2×C3×#103—51no—
97#5113—51no—
98#5101D511yescharacteristic, complemented
99#4964—51no—
100#4817—52no—
101#4790—52no—
102#4789—52no—
103#4788—52no—
104C2×#709—31no—
105C22×Dic10C2×D311yescharacteristic
106C2×C5×M16—31no—
107C22×C5×C8C2×D311yescharacteristic
108C5×#117—31no—
109#4072—31no—
110C2×C4⋊Dic5C2×D311yescharacteristic
111#4055—38no—
112C2×Dic20—32no—
113C2×#677—32no—
114#4038—61no—
115D5×C4⋊C4—61no—
116#4033—61no—
117#4033—61no—
118#4027—62no—
119#4023—62no—
120C4×D20—32no—
121C4×Dic10—32no—
122C4×Dic10—32no—
123C4×Dic10—32no—
124C5×#97—32no—
125C4×C5×C8—32no—
126#3953—31no—
127#3953—31no—
128#3950—32no—
129#3949—32no—
130#3948—31no—
131#3948—31no—
132#3948C2×D312yes—
133#3948C2×D312yes—
134#2947—151noSylow
135C23×C3×C5C2×D411yescharacteristic
136C22×D15—21no—
137C2×C3×C4×C5C22×C412yes—
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5#4112yes—
140C2×C3×C4×C5C2411yescharacteristic
141#1220—24no—
142C2×Dic15—21no—
143C2×Dic15—21no—
144C2×Dic15—21no—
145D60—21no—
146D60C22×C412yes—
147C4×D15—24no—
148Dic30—21no—
149Dic30C22×C412yes—
150C2×C5×Dic3C2×D412yes—
151C2×C5×Dic3C2×D412yes—
152C2×C3×Dic5—24no—
153C2×C3×Dic5—22no—
154C2×C3×Dic5—22no—
155C2×C3×Dic5—81no—
156C3×Dic10—24no—
157C3×Dic10—22no—
158C3×Dic10C22×C414yes—
159#1200—82no—
160C3×C5×C8—21no—
161C3×C5×C8—21no—
162C5×C3⋊C8C22×C414yes—
163C22×C3×Q8—51no—
164C2×#235—51no—
165C22×C3×C8C2×D511yescharacteristic
166C2×C3×C4⋊C4—51no—
167Q8×Dic3—52no—
168Q8×Dic3—52no—
169Q8×Dic3—101no—
170Q8×Dic3—101no—
171C2×#216—52no—
172#942—58no—
173C2×#215—52no—
174C4×#67—102no—
175#926—51no—
176#926—102no—
177#926C2×D511yescharacteristic
178C2×#208C2×D511yescharacteristic
179#893—52no—
180#892—101no—
181D3×C4⋊C4—101no—
182#887—52no—
183C3×#103—52no—
184C3×#103—52no—
185#821—51no—
186#821—51no—
187#816—51no—
188#816—51no—
189#815C2×D512yes—
190C8×Dic3C2×D512yes—
191#808—52no—
192#807—52no—
193C22×C4×C5C22×D311yescharacteristic
194C2×C22⋊D5—61no—
195C22×Dic5—21no—
196C22×Dic5—21no—
197#709—34no—
198#709—62no—
199C2×D20—31no—
200C2×C4×D5—61no—
201C2×C4×D5—62no—
202C2×Dic10—21no—
203C2×Dic10—22no—
204C2×Dic10—31no—
205C2×Dic10C4×D314yescomplemented
206C2×Dic10C22×D312yes—
207C5×M16—34no—
208C2×C5×C8—22no—
209C2×C5×C8—32no—
210C2×C5×C8C22×D311yescharacteristic
211C2×C5×C8C22×D311yescharacteristic
212C5×C4⋊C4—31no—
213C5×C4⋊C4—31no—
214C5×C22⋊C4—32no—
215C42×C5—32no—
216C22⋊Dic5—61no—
217#685—62no—
218C4⋊Dic5—21no—
219C4⋊Dic5—31no—
220C4⋊Dic5—31no—
221C4⋊Dic5C22×D312yes—
222#683—62no—
223#683—62no—
224#683—62no—
225C4×Dic5—62no—
226C4×Dic5—62no—
227C4×Dic5—62no—
228C4×Dic5—61no—
229Dic20—38no—
230#677—38no—
231C2×#137—151no—
232#520—151no—
233#519—151no—
234#441—152no—
235#440—152no—
236C4×Q16—152no—
237C4×SD16—152no—
238#428—151no—
239#416—151no—
240C2×#103—51no—
241#405—31no—
242C22×C3×C5—21no—
243C22×C3×C5—21no—
244C22×C3×C5C4×D412yes—
245C22×C3×C5C22×D411yescharacteristic
246C2×D15—22no—
247C2×D15—41no—
248C2×D15—41no—
249C3×C4×C5C4×D412yes—
250C3×C4×C5C23×C411yescharacteristic
251C3×C4×C5C2×#4111yescharacteristic
252Dic15—22no—
253Dic15—41no—
254Dic15—41no—
255C3×Dic5—24no—
256C3×Dic5—42no—
257C5×Dic3—22no—
258C5×Dic3—22no—
259C2×C3×Q8—54no—
260C2×C3×Q8—52no—
261C2×C3×Q8—101no—
262C2×C3×Q8—102no—
263C22×C3×C4—101no—
264C22×C3×C4—101no—
265C22×C3×C4C22×D511yescharacteristic
266C2×#67—101no—
267#235—54no—
268#235—102no—
269C2×D12—51no—
270C2×C4×D3—101no—
271C2×C4×D3—102no—
272C2×Dic6—51no—
273C2×C3×C8—22no—
274C2×C3×C8C22×D511yescharacteristic
275C2×C3×C8C22×D511yescharacteristic
276C3×C4⋊C4—52no—
277C3×C4⋊C4—101no—
278#217—101no—
279#217D2012yes—
280#216—58no—
281#215—58no—
282(C2×D3)⋊C4—102no—
283C4⋊Dic3—51no—
284C4⋊Dic3—51no—
285C4⋊Dic3—102no—
286C4⋊Dic3—102no—
287C4⋊Dic3D2011yescharacteristic
288C4⋊Dic3D2011yescharacteristic
289Dic3⋊C4—102no—
290C4×Dic3—101no—
291C4×Dic3—102no—
292C4×Dic3—102no—
293C4×Dic3—102no—
294C4×Dic3C22×D512yes—
295#208C4×D514yescomplemented
296C2×C3⋊C8C22×D512yes—
297C23×C5D3×D411yescharacteristic
298C22×D5—61no—
299C2×C4×C5—32no—
300C2×C4×C5—32no—
301C2×C4×C5C2×C4×D312yes—
302C2×C4×C5D3×D411yescharacteristic
303C2×C4×C5#23712yes—
304C2×C4×C5C23×D311yescharacteristic
305C22⋊D5—64no—
306C2×Dic5—24no—
307C2×Dic5—22no—
308C2×Dic5—22no—
309C2×Dic5—61no—
310C2×Dic5—61no—
311C2×Dic5—61no—
312C2×Dic5—81no—
313D20—32no—
314D20—61no—
315C4×D5—64no—
316C4×D5—242no—
317Dic10—24no—
318Dic10—22no—
319Dic10—32no—
320Dic10—61no—
321Dic10C2×C4×D314yes—
322C5×C8—21no—
323C5×C8—21no—
324C5×C8—34no—
325C2×#41—151no—
326C22×Q8—51no—
327#137—158no—
328C2×Q16—152no—
329C2×SD16—152no—
330C2×M16—31no—
331C22×C8D3×D511yescharacteristic
332C4×Q8—152no—
333C4×Q8—152no—
334C4×Q8—152no—
335C4×Q8—301no—
336C4×Q8—301no—
337C4×D4—152no—
338C4×D4—302no—
339#117—31no—
340#117—151no—
341#117—302no—
342#117—301no—
343C2×C4⋊C4—51no—
344C2×C4⋊C4—301no—
345#107—152no—
346#106—152no—
347#103—52no—
348#103—52no—
349#103—151no—
350#103—151no—
351#102—151no—
352#102—151no—
353#97—32no—
354C4×C8—32no—
355C2×C3×C5—22no—
356C2×C3×C5C2×C4×D411yescharacteristic
357C2×C3×C5#57711yescharacteristic
358C2×C3×C5#57811yescharacteristic
359D15—42no—
360C23×C3C2×D2011yescharacteristic
361C22×D3—101no—
362C3×Q8—54no—
363C3×Q8—102no—
364C3×Q8—104no—
365C2×C3×C4—102no—
366C2×C3×C4—104no—
367C2×C3×C4—102no—
368C2×C3×C4—401no—
369C2×C3×C4C2×C4×D512yes—
370C2×C3×C4C2×D2011yescharacteristic
371C2×C3×C4#70912yes—
372C2×C3×C4C23×D511yescharacteristic
373#67—104no—
374C2×Dic3—101no—
375C2×Dic3—101no—
376C2×Dic3—101no—
377C2×Dic3C2×D2012yes—
378C2×Dic3C2×D2012yes—
379D12—52no—
380D12—101no—
381C4×D3—104no—
382C4×D3—402no—
383Dic6—52no—
384Dic6—101no—
385C3×C8—21no—
386C3×C8—21no—
387C3⋊C8C2×C4×D514yes—
388C22×C5—21no—
389C22×C5—21no—
390C22×C5#67⋊C412yes—
391C22×C5C2×D3×D411yescharacteristic
392C2×D5—62no—
393C2×D5—121no—
394C2×D5—121no—
395C4×C5—62no—
396C4×C5—62no—
397C4×C5#67⋊C412yes—
398C4×C5C22×C4×D311yescharacteristic
399C4×C5C2×#23711yescharacteristic
400Dic5—24no—
401Dic5—42no—
402Dic5—62no—
403Dic5—121no—
404Dic5—121no—
405#41—154no—
406#41—302no—
407C2×Q8—54no—
408C2×Q8—52no—
409C2×Q8—101no—
410C2×Q8—102no—
411C2×Q8—151no—
412C2×D4—151no—
413C2×D4—301no—
414C22×C4—101no—
415C22×C4—101no—
416C22×C4—302no—
417C22×C4—301no—
418C22×C4C2×D3×D511yescharacteristic
419Q16—158no—
420SD16—158no—
421M16—34no—
422C2×C8—22no—
423C2×C8—32no—
424C2×C8C2×D3×D511yescharacteristic
425C2×C8C2×D3×D511yescharacteristic
426C4⋊C4—31no—
427C4⋊C4—31no—
428C4⋊C4—52no—
429C4⋊C4—101no—
430C4⋊C4—151no—
431C4⋊C4—151no—
432C4⋊C4—302no—
433C4⋊C4—302no—
434C4⋊C4—302no—
435C22⋊C4—32no—
436C22⋊C4—302no—
437C22⋊C4—301no—
438C42—32no—
439C42—302no—
440C42—302no—
441C42—302no—
442C42—301no—
443C3×C5#294711yescharacteristic, complemented, Hall
444C22×C3—21no—
445C22×C3—21no—
446C22×C3C4×D2012yes—
447C22×C3C22×D2011yescharacteristic
448C2×D3—102no—
449C2×D3—201no—
450C2×D3—201no—
451C3×C4—104no—
452C3×C4—202no—
453C3×C4C4×D2012yes—
454C3×C4C22×C4×D511yescharacteristic
455C3×C4C2×#70911yescharacteristic
456Dic3—22no—
457Dic3—22no—
458Dic3—102no—
459Dic3—201no—
460Dic3—201no—
461C2×C5—22no—
462C2×C5C2×#67⋊C411yescharacteristic
463C2×C5#576211yescharacteristic
464C2×C5#576611yescharacteristic
465D5—122no—
466C23—301no—
467C23D3×D2011yescharacteristic
468Q8—54no—
469Q8—104no—
470Q8—102no—
471Q8—152no—
472Q8—301no—
473D4—152no—
474D4—304no—
475D4—301no—
476C2×C4—32no—
477C2×C4—32no—
478C2×C4—104no—
479C2×C4—102no—
480C2×C4—102no—
481C2×C4—301no—
482C2×C4—304no—
483C2×C4—301no—
484C2×C4—301no—
485C2×C4—401no—
486C2×C4—1202no—
487C2×C4C4×D3×D512yes—
488C2×C4D3×D2011yescharacteristic
489C2×C4#677912yes—
490C2×C4C22×D3×D511yescharacteristic
491C8—21no—
492C8—21no—
493C8—34no—
494C2×C3—22no—
495C2×C3C2×C4×D2011yescharacteristic
496C2×C3#6608511yescharacteristic
497C2×C3#6608711yescharacteristic
498D3—202no—
499C5#7877411yescharacteristic, complemented, Sylow
500C22—21no—
501C22—21no—
502C22—302no—
503C22—601no—
504C22—601no—
505C22#9139512yes—
506C22C2×D3×D2011yescharacteristic
507C4—62no—
508C4—62no—
509C4—104no—
510C4—202no—
511C4—302no—
512C4—601no—
513C4—601no—
514C4#9139512yes—
515C4C2×C4×D3×D511yescharacteristic
516C4C2×#677911yescharacteristic
517C3#1061030211yescharacteristic, complemented, Sylow
518C2—22no—
519C2—602no—
520C2#1175397011yescharacteristic
521C2#1175399111yescharacteristic
522C2C2×#9139511yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×#6817C22
cosocleC2×C3×C4×C5C24
hypercenterC22×C8D3×D5
hypocenterC3×C5#2947
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #11754188C2semidirect
5. C5×#5101C2semidirect
6. C2×C3×#3948C2semidirect
7. #11748453C2semidirect
8. #11747832C2semidirect
9. #11747831C2semidirect
10. #11747830C2semidirect
11. #11747743C2semidirect
31. #91315C4semidirect
50. C2×#3948D3semidirect
66. C2×C3×Dic10C2×C4semidirect
80. C5×#208C2×C4semidirect
91. #6662C2×C4semidirect
92. #6658C2×C4semidirect
98. #5101D5semidirect
205. C2×Dic10C4×D3semidirect
295. #208C4×D5semidirect
443. C3×C5#2947semidirect
499. C5#78774semidirect
517. C3#10610302semidirect

Maximal subgroups

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

subgroupindex
#117544962
#117541882
C2×#913152
#117512142
C5×#51012
C2×C3×#39482
#117484532
#117478322
#117478312
#117478302
#117477432
#106103023
#787745