Finite Group Databasebeta

← #14417252

Subgroups — #14417252

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#11756263C211yesmaximal, characteristic
2#11754188C211yesmaximal, characteristic, complemented
3C2×#91315C211yesmaximal, characteristic
4C5×#4964C211yesmaximal, characteristic, complemented
5C2×C3×#3942C211yesmaximal, characteristic, complemented
6#11748393C211yesmaximal, characteristic
7#11748324C211yesmaximal, characteristic, complemented
8#11747274C212yesmaximal, complemented
9#11747273C212yesmaximal, complemented
10#11747272C212yesmaximal, complemented
11#11747271C212yesmaximal, complemented
12#10610933—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×C3×Dic10C2211yescharacteristic
15C2×C3×C5×C4⋊C4C2211yescharacteristic
16C4×#1220—22no—
17#91815C2211yescharacteristic
18#91782C2212yes—
19#91781—21no—
20C4⋊C4×D15—21no—
21#91776C2212yes—
22C5×#926C2211yescharacteristic
23C2×C5×#208C2211yescharacteristic
24C22×C3×#168C2211yescharacteristic
25#91528—22no—
26#91331C2212yes—
27#91331C2212yes—
28Dic3×Dic10—21no—
29Dic3×Dic10—21no—
30C2×#6662C2212yes—
31#91315C418yescomplemented
32C2×#6658C2212yes—
33C5×#808C2212yes—
34C5×#807C2212yes—
35C3×#3942C2212yes—
36C3×#3942C2212yes—
37#90975C2211yescharacteristic
38#90975C2211yescharacteristic
39#90969C2211yescharacteristic
40#90969C2211yescharacteristic
41#90954C2212yes—
42#90951C2212yes—
43#78774—51nomaximal, Hall
44C2×#4055—31no—
45#65850—31no—
46#65838—31no—
47C5×#428—31no—
48#65411—31no—
49#65291—31no—
50C2×#3942D311yescharacteristic, complemented
51#65178—32no—
52#65162—32no—
53#65142—32no—
54#65141—32no—
55C22×C3×C4×C5—21no—
56C22×C3×C4×C5C2311yescharacteristic
57C2×#1220—21no—
58#6817—22no—
59#6817C2×C414yes—
60C2×D60C2311yescharacteristic
61C2×C4×D15—21no—
62C2×C4×D15—22no—
63C2×Dic30C2311yescharacteristic
64C22×C3×Dic5—21no—
65C2×C3×Dic10—21no—
66C2×C3×Dic10—22no—
67C2×C3×Dic10C2×C414yescomplemented
68C2×C3×Dic10C2312yes—
69C3×C5×C4⋊C4—21no—
70C3×C5×C4⋊C4C2312yes—
71#6719D412yes—
72#6714—22no—
73C4⋊Dic15D411yescharacteristic
74C4⋊Dic15D411yescharacteristic
75#6712—22no—
76C4×Dic15—22no—
77C4×Dic15C2312yes—
78C5×#217—21no—
79C5×C4⋊Dic3C2311yescharacteristic
80C5×C4⋊Dic3C2311yescharacteristic
81C4×C5×Dic3—21no—
82C5×#208C2×C414yescomplemented
83C2×C5×C3⋊C8C2312yes—
84C2×C3×#168—22no—
85C2×C3×#168C2311yescharacteristic
86C2×C3×#168C2311yescharacteristic
87#6668—22no—
88#6668—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#5101—51no—
99#4964D511yescharacteristic, complemented
100#4817—52no—
101#4790—52no—
102#4789—52no—
103#4788—52no—
104C2×#709—31no—
105C22×Dic10C2×D311yescharacteristic
106C2×C5×M16—31no—
107C5×#117—31no—
108C2×C5×C4⋊C4C2×D311yescharacteristic
109C4×C22⋊D5—62no—
110#4072—31no—
111C22×#168C2×D311yescharacteristic
112#4055—38no—
113C2×Dic20—32no—
114C2×#677—32no—
115#4039—32no—
116#4038—61no—
117D5×C4⋊C4—61no—
118#4033—32no—
119#4033—32no—
120#4033—32no—
121#4023—62no—
122C4×Dic10—61no—
123C4×Dic10—61no—
124C5×#107—32no—
125C5×#106—32no—
126#3947—32no—
127C8×Dic5—32no—
128#3942—31no—
129#3942—31no—
130#3942C2×D312yes—
131#3942C2×D312yes—
132#3941—31no—
133#3941—31no—
134#2947—151noSylow
135C23×C3×C5C2×D411yescharacteristic
136C22×D15—21no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—81no—
139C2×C3×C4×C5C22×C412yes—
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5#4112yes—
142C2×C3×C4×C5C2411yescharacteristic
143#1220—24no—
144C2×Dic15—21no—
145C2×Dic15C2×D412yes—
146C2×Dic15C2×D412yes—
147D60—21no—
148D60C22×C412yes—
149C4×D15—24no—
150C4×D15—82no—
151Dic30—21no—
152Dic30C22×C412yes—
153C2×C5×Dic3—21no—
154C2×C5×Dic3—21no—
155C2×C3×Dic5—24no—
156C2×C3×Dic5—22no—
157C3×Dic10—24no—
158C3×Dic10—22no—
159C3×Dic10C22×C414yes—
160C3×#168—21no—
161C3×#168—21no—
162C5×C3⋊C8C22×C414yes—
163C22×C3×Q8—51no—
164C2×#235—51no—
165C22×C3×C8—51no—
166C2×C3×C4⋊C4C2×D511yescharacteristic
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#815—52no—
190C8×Dic3—52no—
191#808C2×D512yes—
192#807C2×D512yes—
193C22×C4×C5—21no—
194C22×C4×C5C22×D311yescharacteristic
195C2×C22⋊D5—61no—
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—32no—
209C5×C4⋊C4—21no—
210C5×C4⋊C4—31no—
211C5×C4⋊C4—31no—
212C5×C4⋊C4C22×D312yes—
213C5×C22⋊C4—61no—
214C42×C5—61no—
215C22⋊Dic5—32no—
216#685—62no—
217C4⋊Dic5—31no—
218C4⋊Dic5—31no—
219#683—62no—
220#683—62no—
221#683—62no—
222C4×Dic5—32no—
223C4×Dic5—62no—
224C4×Dic5—62no—
225C4×Dic5—62no—
226C2×#168—22no—
227C2×#168C22×D311yescharacteristic
228C2×#168C22×D311yescharacteristic
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—31no—
239#416—151no—
240C2×#103—51no—
241#405—151no—
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×C5—42no—
250C3×C4×C5C4×D412yes—
251C3×C4×C5C23×C411yescharacteristic
252C3×C4×C5C2×#4111yescharacteristic
253Dic15—22no—
254Dic15—22no—
255Dic15—22no—
256C3×Dic5—24no—
257C5×Dic3—41no—
258C5×Dic3—41no—
259C2×C3×Q8—54no—
260C2×C3×Q8—52no—
261C2×C3×Q8—101no—
262C2×C3×Q8—102no—
263C22×C3×C4—21no—
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—51no—
274C2×C3×C8—51no—
275C2×C3×C8—102no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4C22×D512yes—
278#217—21no—
279#217—52no—
280#216—58no—
281#215—58no—
282(C2×D3)⋊C4—102no—
283C4⋊Dic3—51no—
284C4⋊Dic3—51no—
285C4⋊Dic3—102no—
286C4⋊Dic3—102no—
287C4⋊Dic3C22×D511yescharacteristic
288C4⋊Dic3C22×D511yescharacteristic
289Dic3⋊C4—102no—
290C4×Dic3—21no—
291C4×Dic3—52no—
292C4×Dic3—102no—
293C4×Dic3—102no—
294C4×Dic3—102no—
295#208C4×D514yescomplemented
296C2×C3⋊C8C22×D512yes—
297C23×C5D3×D411yescharacteristic
298C22×D5—61no—
299C2×C4×C5—22no—
300C2×C4×C5—61no—
301C2×C4×C5—61no—
302C2×C4×C5—81no—
303C2×C4×C5C2×C4×D312yes—
304C2×C4×C5D3×D411yescharacteristic
305C2×C4×C5#23712yes—
306C2×C4×C5C23×D311yescharacteristic
307C22⋊D5—64no—
308C2×Dic5—24no—
309C2×Dic5—22no—
310C2×Dic5—32no—
311C2×Dic5—32no—
312C2×Dic5—61no—
313D20—32no—
314D20—61no—
315C4×D5—64no—
316C4×D5—242no—
317Dic10—24no—
318Dic10—22no—
319Dic10—32no—
320Dic10—61no—
321Dic10C2×C4×D314yes—
322C5×C8—34no—
323#168—21no—
324#168—21no—
325C2×#41—151no—
326C22×Q8—51no—
327#137—158no—
328C2×Q16—152no—
329C2×SD16—152no—
330C2×M16—31no—
331C22×C8—51no—
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—301no—
344C2×C4⋊C4D3×D511yescharacteristic
345#107—32no—
346#106—32no—
347#103—52no—
348#103—52no—
349#103—151no—
350#103—151no—
351#102—151no—
352#102—151no—
353#97—152no—
354C4×C8—152no—
355C2×C3×C5—22no—
356C2×C3×C5C2×C4×D411yescharacteristic
357C2×C3×C5#57711yescharacteristic
358C2×C3×C5#57811yescharacteristic
359D15—42no—
360C23×C3D4×D511yescharacteristic
361C22×D3—101no—
362C3×Q8—54no—
363C3×Q8—102no—
364C3×Q8—104no—
365C2×C3×C4—22no—
366C2×C3×C4—81no—
367C2×C3×C4—102no—
368C2×C3×C4—104no—
369C2×C3×C4C2×C4×D512yes—
370C2×C3×C4D4×D511yescharacteristic
371C2×C3×C4#71312yes—
372C2×C3×C4C23×D511yescharacteristic
373#67—104no—
374C2×Dic3—21no—
375C2×Dic3—21no—
376C2×Dic3—52no—
377C2×Dic3—52no—
378C2×Dic3—101no—
379D12—52no—
380D12—101no—
381C4×D3—104no—
382C4×D3—402no—
383Dic6—52no—
384Dic6—101no—
385C3×C8—101no—
386C3×C8—101no—
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—42no—
396C4×C5—121no—
397C4×C5—121no—
398C4×C5#67⋊C412yes—
399C4×C5C22×C4×D311yescharacteristic
400C4×C5C2×#23711yescharacteristic
401Dic5—24no—
402Dic5—62no—
403Dic5—62no—
404Dic5—62no—
405#41—154no—
406#41—302no—
407C2×Q8—54no—
408C2×Q8—52no—
409C2×Q8—102no—
410C2×Q8—101no—
411C2×Q8—151no—
412C2×D4—151no—
413C2×D4—301no—
414C22×C4—21no—
415C22×C4—101no—
416C22×C4—302no—
417C22×C4—301no—
418C22×C4C2×D3×D511yescharacteristic
419Q16—158no—
420SD16—158no—
421M16—34no—
422C2×C8—32no—
423C2×C8—51no—
424C2×C8—51no—
425C2×C8—102no—
426C4⋊C4—21no—
427C4⋊C4—31no—
428C4⋊C4—31no—
429C4⋊C4—151no—
430C4⋊C4—151no—
431C4⋊C4—302no—
432C4⋊C4—302no—
433C4⋊C4—302no—
434C4⋊C4C2×D3×D512yes—
435C22⋊C4—61no—
436C22⋊C4—152no—
437C22⋊C4—302no—
438C42—61no—
439C42—152no—
440C42—302no—
441C42—302no—
442C42—302no—
443C3×C5#294711yescharacteristic, complemented, Hall
444C22×C3—21no—
445C22×C3—21no—
446C22×C3#403912yes—
447C22×C3C2×D4×D511yescharacteristic
448C2×D3—102no—
449C2×D3—201no—
450C2×D3—201no—
451C3×C4—42no—
452C3×C4—104no—
453C3×C4#403912yes—
454C3×C4C22×C4×D511yescharacteristic
455C3×C4C2×#71311yescharacteristic
456Dic3—41no—
457Dic3—41no—
458Dic3—102no—
459Dic3—102no—
460Dic3—102no—
461C2×C5—22no—
462C2×C5C2×#67⋊C411yescharacteristic
463C2×C5#576211yescharacteristic
464C2×C5#576611yescharacteristic
465D5—122no—
466C23—301no—
467C23#679011yescharacteristic
468Q8—54no—
469Q8—104no—
470Q8—102no—
471Q8—152no—
472Q8—301no—
473D4—152no—
474D4—304no—
475D4—301no—
476C2×C4—22no—
477C2×C4—61no—
478C2×C4—61no—
479C2×C4—81no—
480C2×C4—104no—
481C2×C4—102no—
482C2×C4—152no—
483C2×C4—152no—
484C2×C4—301no—
485C2×C4—304no—
486C2×C4—1202no—
487C2×C4#676612yes—
488C2×C4C4×D3×D512yes—
489C2×C4#679011yescharacteristic
490C2×C4C22×D3×D511yescharacteristic
491C8—34no—
492C8—101no—
493C8—101no—
494C2×C3—22no—
495C2×C3C2×#403911yescharacteristic
496C2×C3#6610911yescharacteristic
497C2×C3#6611311yescharacteristic
498D3—202no—
499C5#7877411yescharacteristic, complemented, Sylow
500C22—21no—
501C22—21no—
502C22—302no—
503C22—601no—
504C22—601no—
505C22#9139612yes—
506C22C2×#679011yescharacteristic
507C4—42no—
508C4—104no—
509C4—121no—
510C4—121no—
511C4—302no—
512C4—302no—
513C4—302no—
514C4#9139612yes—
515C4C2×#676611yescharacteristic
516C4C2×C4×D3×D511yescharacteristic
517C3#1061093311yescharacteristic, complemented, Sylow
518C2—22no—
519C2—602no—
520C2C2×#9139611yescharacteristic
521C2#1175472811yescharacteristic
522C2#1175512211yescharacteristic
subgroupG/H
centerC22C2×#6790
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C22×D4
prime radicalC2×#6817C22
cosocleC2×C3×C4×C5C24
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2947
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11754188C2semidirect
4. C5×#4964C2semidirect
5. C2×C3×#3942C2semidirect
7. #11748324C2semidirect
8. #11747274C2semidirect
9. #11747273C2semidirect
10. #11747272C2semidirect
11. #11747271C2semidirect
31. #91315C4semidirect
50. C2×#3942D3semidirect
67. C2×C3×Dic10C2×C4semidirect
82. C5×#208C2×C4semidirect
91. #6662C2×C4semidirect
92. #6658C2×C4semidirect
99. #4964D5semidirect
205. C2×Dic10C4×D3semidirect
295. #208C4×D5semidirect
443. C3×C5#2947semidirect
499. C5#78774semidirect
517. C3#10610933semidirect

Maximal subgroups

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

subgroupindex
#117562632
#117541882
C2×#913152
C5×#49642
C2×C3×#39422
#117483932
#117483242
#117472742
#117472732
#117472722
#117472712
#106109333
#787745