Finite Group Databasebeta

← #14417270

Subgroups — #14417270

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#11754492C211yesmaximal, characteristic
2#11754188C211yesmaximal, characteristic, complemented
3C2×#91309C211yesmaximal, characteristic
4#11751202C211yesmaximal, characteristic, complemented
5C5×#5113C211yesmaximal, characteristic
6C2×C3×#3948C211yesmaximal, characteristic, complemented
7#11748470C211yesmaximal, characteristic, complemented
8#11747829C212yesmaximal, complemented
9#11747828C212yesmaximal, complemented
10#11747738C212yesmaximal, complemented
11#11747737C212yesmaximal, complemented
12#10610552—31nomaximal, Hall
13C2×C5×#235C2211yescharacteristic
14C22×C3×Dic10C2211yescharacteristic
15C22×C3×C5×C8C2211yescharacteristic
16#91815C2211yescharacteristic
17C2×#6710C2211yescharacteristic
18C5×#926C2211yescharacteristic
19C2×C3×C4⋊Dic5C2211yescharacteristic
20Dic5×#67—22no—
21#91528—22no—
22#91435C2212yes—
23D3×C4⋊Dic5—21no—
24#91344C2212yes—
25#91338—21no—
26#91331C2212yes—
27#91331C2212yes—
28Dic3×Dic10—21no—
29Dic3×Dic10—21no—
30C2×#6661C2212yes—
31#91309C418yescomplemented
32C2×#6656C2212yes—
33#91099C2212yes—
34C8×Dic15C2212yes—
35C5×#821C2211yescharacteristic
36C5×#821C2211yescharacteristic
37C5×#816C2211yescharacteristic
38C5×#816C2211yescharacteristic
39C3×#3948C2212yes—
40C3×#3948C2212yes—
41#90989C2212yes—
42#90986C2212yes—
43#78774—51nomaximal, Hall
44#66161—31no—
45C2×#4097—31no—
46#65850—31no—
47C5×#416—31no—
48C2×#3948D311yescharacteristic, complemented
49#65390—31no—
50#65284—31no—
51#65079—32no—
52#65078—32no—
53#65047—32no—
54#65046—32no—
55C22×C3×C4×C5C2311yescharacteristic
56C2×C5×#67—21no—
57C5×#235—22no—
58C5×#235C2×C414yes—
59C2×C5×D12C2311yescharacteristic
60C2×C4×C5×D3—21no—
61C2×C5×Dic6C2311yescharacteristic
62C22×C3×Dic5—21no—
63C22×C3×Dic5—21no—
64C2×C3×Dic10—21no—
65C2×C3×Dic10—22no—
66C2×C3×Dic10C2×C414yescomplemented
67C2×C3×Dic10C2312yes—
68C2×D3×Dic5—22no—
69C2×C3×C5×C8—22no—
70C2×C3×C5×C8C2311yescharacteristic
71C2×C3×C5×C8C2311yescharacteristic
72#6719D412yes—
73C4⋊Dic15D411yescharacteristic
74C4⋊Dic15D411yescharacteristic
75C4×Dic15C2312yes—
76#6710C2×C414yescomplemented
77C2×C3⋊#168C2312yes—
78C5×#217—21no—
79C5×C4⋊Dic3C2311yescharacteristic
80C5×C4⋊Dic3C2311yescharacteristic
81C4×C5×Dic3—21no—
82C3×C4⋊Dic5—21no—
83C3×C4⋊Dic5C2312yes—
84Dic3⋊Dic5—22no—
85#6668—22no—
86#6668—22no—
87(C2×D3)⋊Dic5—22no—
88Dic3×Dic5—22no—
89Dic3×Dic5—22no—
90Dic3×Dic5—22no—
91#6661C2×C418yescomplemented
92#6656C2×C418yescomplemented
93#5812—51no—
94C2×#942—51no—
95#5504—51no—
96C2×C3×#103—51no—
97#5113D511yescharacteristic
98#5101—51no—
99#4964—51no—
100#4817—52no—
101#4790—52no—
102#4789—52no—
103#4788—52no—
104C2×C5×#41—31no—
105C22×Dic10C2×D311yescharacteristic
106C22×C5×C8C2×D311yescharacteristic
107C5×#117—31no—
108#4097—38no—
109Q8×Dic5—32no—
110C2×#689—32no—
111D4×Dic5—32no—
112D4×Dic5—62no—
113C2×#687—32no—
114#4072—31no—
115#4072—61no—
116C2×C4⋊Dic5—61no—
117C2×C4⋊Dic5C2×D311yescharacteristic
118C2×#681—31no—
119#4033—32no—
120#4033—32no—
121#4023—62no—
122C4×Dic10—61no—
123C4×Dic10—61no—
124C5×#103—31no—
125C5×#103—31no—
126C5×#102—31no—
127C5×#102—31no—
128#3948C2×D312yes—
129#3948C2×D312yes—
130#3947—32no—
131C8×Dic5—32no—
132#3940—32no—
133#3939—32no—
134#2947—151noSylow
135C23×C3×C5C2×D411yescharacteristic
136C22×C5×D3—21no—
137C2×C3×C4×C5C22×C412yes—
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5#4112yes—
140C2×C3×C4×C5C2411yescharacteristic
141C2×Dic15C2×D412yes—
142C2×Dic15C2×D412yes—
143C5×#67—24no—
144C2×C5×Dic3—21no—
145C2×C5×Dic3—21no—
146C2×C5×Dic3—21no—
147C5×D12—21no—
148C5×D12C22×C412yes—
149C4×C5×D3—24no—
150C5×Dic6—21no—
151C5×Dic6C22×C412yes—
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—
159D3×Dic5—82no—
160C3×C5×C8—21no—
161C3×C5×C8—21no—
162C3⋊#168C22×C414yes—
163C22×C3×Q8—51no—
164C2×#235C2×D511yescharacteristic
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×#208—51no—
179#893—52no—
180#892—101no—
181D3×C4⋊C4—101no—
182#887—52no—
183C3×#103—52no—
184C3×#103—52no—
185#821C2×D511yescharacteristic
186#821C2×D511yescharacteristic
187#816C2×D511yescharacteristic
188#816C2×D511yescharacteristic
189#815—52no—
190C8×Dic3—52no—
191#808—52no—
192#807—52no—
193C5×#41—34no—
194C5×#41—62no—
195C2×C5×Q8—31no—
196C2×C5×D4—31no—
197C2×C5×D4—61no—
198C22×C4×C5—61no—
199C22×C4×C5C22×D311yescharacteristic
200C22×Dic5—21no—
201C22×Dic5—21no—
202C22×Dic5—62no—
203C2×Dic10—21no—
204C2×Dic10—22no—
205C2×Dic10C4×D314yescomplemented
206C2×Dic10C22×D312yes—
207C2×C5×C8—22no—
208C2×C5×C8C22×D311yescharacteristic
209C2×C5×C8C22×D311yescharacteristic
210C5×C4⋊C4—31no—
211C5×C4⋊C4—31no—
212C5×C22⋊C4—61no—
213C42×C5—61no—
214C22⋊Dic5—32no—
215C22⋊Dic5—62no—
216#689—38no—
217#687—38no—
218C4⋊Dic5—21no—
219C4⋊Dic5—31no—
220C4⋊Dic5—31no—
221C4⋊Dic5—62no—
222C4⋊Dic5C22×D312yes—
223#683—62no—
224#683—62no—
225C4×Dic5—32no—
226C4×Dic5—62no—
227C4×Dic5—62no—
228C4×Dic5—62no—
229#681—34no—
230C2×#168—32no—
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—31no—
240C2×#103—51no—
241#405—151no—
242C22×C3×C5—21no—
243C22×C3×C5—21no—
244C22×C3×C5C4×D412yes—
245C22×C3×C5C22×D411yescharacteristic
246C2×C5×D3—22no—
247C2×C5×D3—41no—
248C2×C5×D3—41no—
249C3×C4×C5C4×D412yes—
250C3×C4×C5C23×C411yescharacteristic
251C3×C4×C5C2×#4111yescharacteristic
252Dic15—22no—
253Dic15—22no—
254C3×Dic5—24no—
255C3×Dic5—42no—
256C5×Dic3—22no—
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—101no—
264C22×C3×C4—101no—
265C22×C3×C4C22×D511yescharacteristic
266C2×#67—21no—
267#235—22no—
268#235C4×D514yes—
269C2×D12C22×D511yescharacteristic
270C2×C4×D3—21no—
271C2×C4×D3—102no—
272C2×Dic6C22×D511yescharacteristic
273C2×C3×C8—22no—
274C2×C3×C8C22×D511yescharacteristic
275C2×C3×C8C22×D511yescharacteristic
276C3×C4⋊C4—52no—
277C3×C4⋊C4—101no—
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#208—54no—
296C2×C3⋊C8—52no—
297C23×C5—61no—
298C23×C5D3×D411yescharacteristic
299C5×Q8—32no—
300C5×Q8—61no—
301C5×D4—32no—
302C5×D4—64no—
303C5×D4—61no—
304C2×C4×C5—61no—
305C2×C4×C5—64no—
306C2×C4×C5—61no—
307C2×C4×C5—61no—
308C2×C4×C5C2×C4×D312yes—
309C2×C4×C5D3×D411yescharacteristic
310C2×C4×C5#23712yes—
311C2×C4×C5C23×D311yescharacteristic
312C2×Dic5—24no—
313C2×Dic5—22no—
314C2×Dic5—22no—
315C2×Dic5—32no—
316C2×Dic5—32no—
317C2×Dic5—81no—
318C2×Dic5—242no—
319Dic10—24no—
320Dic10—22no—
321Dic10C2×C4×D314yes—
322C5×C8—21no—
323C5×C8—21no—
324#168—34no—
325C2×#41—31no—
326C22×Q8—51no—
327#137—158no—
328C2×Q16—152no—
329C2×SD16—152no—
330C2×M16—151no—
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—31no—
348#103—31no—
349#103—52no—
350#103—52no—
351#102—31no—
352#102—31no—
353#97—152no—
354C4×C8—152no—
355C2×C3×C5—22no—
356C2×C3×C5C2×C4×D411yescharacteristic
357C2×C3×C5#57711yescharacteristic
358C2×C3×C5#57811yescharacteristic
359C5×D3—42no—
360C23×C3D4×D511yescharacteristic
361C22×D3—21no—
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×C4D4×D511yescharacteristic
371C2×C3×C4#71112yes—
372C2×C3×C4C23×D511yescharacteristic
373#67—24no—
374C2×Dic3—21no—
375C2×Dic3—21no—
376C2×Dic3—21no—
377C2×Dic3—52no—
378C2×Dic3—52no—
379D12—21no—
380D12C2×C4×D512yes—
381C4×D3—24no—
382C4×D3—402no—
383Dic6—21no—
384Dic6C2×C4×D512yes—
385C3×C8—21no—
386C3×C8—21no—
387C3⋊C8—54no—
388C22×C5—21no—
389C22×C5—21no—
390C22×C5—62no—
391C22×C5—121no—
392C22×C5—121no—
393C22×C5#67⋊C412yes—
394C22×C5C2×D3×D411yescharacteristic
395C4×C5—62no—
396C4×C5—121no—
397C4×C5—121no—
398C4×C5#67⋊C412yes—
399C4×C5C22×C4×D311yescharacteristic
400C4×C5C2×#23711yescharacteristic
401Dic5—24no—
402Dic5—42no—
403Dic5—62no—
404Dic5—62no—
405#41—34no—
406#41—62no—
407C2×Q8—31no—
408C2×Q8—54no—
409C2×Q8—52no—
410C2×Q8—101no—
411C2×Q8—102no—
412C2×D4—31no—
413C2×D4—61no—
414C22×C4—61no—
415C22×C4—101no—
416C22×C4—101no—
417C22×C4—302no—
418C22×C4C2×D3×D511yescharacteristic
419Q16—158no—
420SD16—158no—
421M16—154no—
422C2×C8—22no—
423C2×C8—152no—
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—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#402712yes—
447C22×C3C2×D4×D511yescharacteristic
448C2×D3—22no—
449C2×D3—41no—
450C2×D3—41no—
451C3×C4—104no—
452C3×C4—202no—
453C3×C4#402712yes—
454C3×C4C22×C4×D511yescharacteristic
455C3×C4C2×#71111yescharacteristic
456Dic3—22no—
457Dic3—41no—
458Dic3—41no—
459Dic3—102no—
460Dic3—102no—
461C2×C5—22no—
462C2×C5—122no—
463C2×C5C2×#67⋊C411yescharacteristic
464C2×C5#576211yescharacteristic
465C2×C5#576611yescharacteristic
466C23—61no—
467C23#677711yescharacteristic
468Q8—32no—
469Q8—54no—
470Q8—61no—
471Q8—104no—
472Q8—102no—
473D4—32no—
474D4—64no—
475D4—61no—
476C2×C4—61no—
477C2×C4—64no—
478C2×C4—61no—
479C2×C4—61no—
480C2×C4—104no—
481C2×C4—102no—
482C2×C4—102no—
483C2×C4—152no—
484C2×C4—152no—
485C2×C4—401no—
486C2×C4—1202no—
487C2×C4C4×D3×D512yes—
488C2×C4#677711yescharacteristic
489C2×C4#678012yes—
490C2×C4C22×D3×D511yescharacteristic
491C8—21no—
492C8—21no—
493C8—154no—
494C2×C3—22no—
495C2×C3C2×#402711yescharacteristic
496C2×C3#6610411yescharacteristic
497C2×C3#6610511yescharacteristic
498D3—42no—
499C5#7877411yescharacteristic, complemented, Sylow
500C22—21no—
501C22—21no—
502C22—62no—
503C22—121no—
504C22—121no—
505C22#9144212yes—
506C22C2×#677711yescharacteristic
507C4—62no—
508C4—104no—
509C4—121no—
510C4—121no—
511C4—202no—
512C4—302no—
513C4—302no—
514C4#9144212yes—
515C4C2×C4×D3×D511yescharacteristic
516C4C2×#678011yescharacteristic
517C3#1061055211yescharacteristic, complemented, Sylow
518C2—22no—
519C2—122no—
520C2#1175398011yescharacteristic
521C2#1175401111yescharacteristic
522C2C2×#9144211yescharacteristic
subgroupG/H
centerC22C2×#6777
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#235C22
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
4. #11751202C2semidirect
6. C2×C3×#3948C2semidirect
7. #11748470C2semidirect
8. #11747829C2semidirect
9. #11747828C2semidirect
10. #11747738C2semidirect
11. #11747737C2semidirect
31. #91309C4semidirect
48. C2×#3948D3semidirect
66. C2×C3×Dic10C2×C4semidirect
76. #6710C2×C4semidirect
91. #6661C2×C4semidirect
92. #6656C2×C4semidirect
205. C2×Dic10C4×D3semidirect
443. C3×C5#2947semidirect
499. C5#78774semidirect
517. C3#10610552semidirect

Maximal subgroups

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

subgroupindex
#117544922
#117541882
C2×#913092
#117512022
C5×#51132
C2×C3×#39482
#117484702
#117478292
#117478282
#117477382
#117477372
#106105523
#787745