Finite Group Databasebeta

← #14417272

Subgroups — #14417272

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
1C2×C5×#951C211yesmaximal, characteristic
2C3×#66161C211yesmaximal, characteristic
3#11754211C211yesmaximal, characteristic, complemented
4#11751334C211yesmaximal, characteristic
5#11749247C212yesmaximal, complemented
6Dic5×#216C212yesmaximal, complemented
7#11749001C212yesmaximal, complemented
8Dic5×#214C212yesmaximal, complemented
9#11748453C211yesmaximal, characteristic, complemented
10C2×#90972C211yesmaximal, characteristic, complemented
11#11748320C211yesmaximal, characteristic, complemented
12#10615696—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×C5×Dic6C2211yescharacteristic
15#91815C2211yescharacteristic
16C22×C3⋊#168C2211yescharacteristic
17C5×#951C418yescomplemented
18C2×C5×#216C2212yes—
19C2×C5×#214C2212yes—
20C2×C5×#208C2211yescharacteristic
21C3×Q8×Dic5C2212yes—
22C3×D4×Dic5—22no—
23C3×D4×Dic5C2212yes—
24C3×#4072—21no—
25C3×#4072C2211yescharacteristic
26C2×C3×C4⋊Dic5—21no—
27C2×C3×C4⋊Dic5C2211yescharacteristic
28#91529—22no—
29#91344—21no—
30#91344—21no—
31Dic5×Dic6C2212yes—
32Dic5×Dic6C2212yes—
33#91119C2211yescharacteristic
34#91119C2211yescharacteristic
35#91116C2211yescharacteristic
36#91116C2211yescharacteristic
37#90990C2212yes—
38#90987C2212yes—
39#90972C2212yes—
40#90972C2212yes—
41#90952C2212yes—
42Dic5×C3⋊C8C2212yes—
43#82571—51nomaximal, Hall
44C2×C5×#137—31no—
45#66161D311yescharacteristic
46#66146—31no—
47#65522—31no—
48C2×#3967—31no—
49#65473—32no—
50Q16×Dic5—32no—
51#65453—32no—
52SD16×Dic5—32no—
53#65411—31no—
54#65410—31no—
55C3×C5×#41—22no—
56C3×C5×#41C2×C414yes—
57C2×C3×C5×Q8C2311yescharacteristic
58C2×C3×C5×D4—21no—
59C2×C3×C5×D4C2311yescharacteristic
60C22×C3×C4×C5—21no—
61C22×C3×C4×C5C2311yescharacteristic
62C22×C5×Dic3—21no—
63C2×C5×Dic6—21no—
64C2×C5×Dic6—22no—
65C2×C5×Dic6C2×C414yescomplemented
66C2×C5×Dic6C2312yes—
67C22×C3×Dic5—21no—
68C22×C3×Dic5—22no—
69#6719—21no—
70C4⋊Dic15C2311yescharacteristic
71C4⋊Dic15C2311yescharacteristic
72C4×Dic15—21no—
73C2×C3⋊#168—22no—
74C2×C3⋊#168C2311yescharacteristic
75C2×C3⋊#168C2311yescharacteristic
76C5×#216C2×C418yescomplemented
77C5×#214C2×C418yescomplemented
78C5×#208C2×C414yescomplemented
79C2×C5×C3⋊C8C2312yes—
80C3×C22⋊Dic5—22no—
81C3×C22⋊Dic5D412yes—
82C3×C4⋊Dic5—21no—
83C3×C4⋊Dic5—22no—
84C3×C4⋊Dic5D411yescharacteristic
85C3×C4⋊Dic5D411yescharacteristic
86C3×C4⋊Dic5C2312yes—
87C3×C4×Dic5—22no—
88C3×C4×Dic5C2312yes—
89Dic3⋊Dic5—22no—
90Dic3⋊Dic5—22no—
91Dic3×Dic5—22no—
92Dic3×Dic5—22no—
93C3×#520—51no—
94C2×#951D511yescharacteristic
95#5516—51no—
96#5233—51no—
97#5030—52no—
98C4×#216—52no—
99#5018—52no—
100C4×#214—52no—
101#4997—51no—
102C2×#810—51no—
103#4964—51no—
104C2×C5×#41C2×D311yescharacteristic
105C22×C5×Q8—31no—
106C5×#137—38no—
107C2×C5×Q16—32no—
108C2×C5×SD16—32no—
109C2×C5×M16—31no—
110Q8×Dic5—32no—
111Q8×Dic5—32no—
112Q8×Dic5—61no—
113Q8×Dic5—61no—
114Q8×Dic5C2×D312yes—
115D4×Dic5—22no—
116D4×Dic5C2×D312yes—
117#4072—21no—
118#4072—31no—
119#4072—62no—
120#4072C2×D311yescharacteristic
121C2×C4⋊Dic5—21no—
122C2×C4⋊Dic5C2×D311yescharacteristic
123C22×#168—31no—
124#3967—31no—
125#3967—31no—
126#3967—32no—
127#3967—32no—
128#3964—31no—
129#3964—31no—
130#3950—32no—
131#3949—32no—
132#3947—32no—
133C8×Dic5—32no—
134#2947—151noSylow
135C23×C3×C5—21no—
136C23×C3×C5C2×D411yescharacteristic
137C3×C5×Q8—21no—
138C3×C5×Q8C22×C412yes—
139C3×C5×D4—24no—
140C3×C5×D4—21no—
141C3×C5×D4C22×C412yes—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—24no—
144C2×C3×C4×C5C22×C412yes—
145C2×C3×C4×C5C2×D411yescharacteristic
146C2×C3×C4×C5#4112yes—
147C2×C3×C4×C5C2411yescharacteristic
148C2×Dic15—21no—
149C2×Dic15—21no—
150C2×C5×Dic3—24no—
151C2×C5×Dic3—22no—
152C5×Dic6—24no—
153C5×Dic6—22no—
154C5×Dic6C22×C414yes—
155C2×C3×Dic5—22no—
156C2×C3×Dic5—82no—
157C2×C3×Dic5—81no—
158C2×C3×Dic5C2×D412yes—
159C2×C3×Dic5C2×D412yes—
160C3⋊#168—21no—
161C3⋊#168—21no—
162C5×C3⋊C8C22×C414yes—
163C2×C3×#41C2×D511yescharacteristic
164C22×Dic6C2×D511yescharacteristic
165C3×C4×Q8—52no—
166C3×C4×D4—52no—
167C3×C4×D4—102no—
168C3×#117—51no—
169C3×#117—101no—
170C2×C3×C4⋊C4—51no—
171C2×C3×C4⋊C4—101no—
172#951Dic518yescomplemented
173C2×#216C2×D512yes—
174C2×#214C2×D512yes—
175#926—51no—
176C2×#208C2×D511yescharacteristic
177C22×C3⋊C8—51no—
178#887—101no—
179#887—101no—
180#877—102no—
181C4×Dic6—52no—
182C4×Dic6—52no—
183#835—51no—
184#835—51no—
185#832—51no—
186#832—51no—
187#810—52no—
188#810—52no—
189#808—52no—
190#807—52no—
191#803—52no—
192C4×C3⋊C8—52no—
193C5×#41—22no—
194C5×#41C4×D314yes—
195C2×C5×Q8—34no—
196C2×C5×Q8—32no—
197C2×C5×Q8—62no—
198C2×C5×Q8—61no—
199C2×C5×Q8C22×D311yescharacteristic
200C2×C5×D4—21no—
201C2×C5×D4C22×D311yescharacteristic
202C22×C4×C5—21no—
203C22×C4×C5—61no—
204C22×C4×C5C22×D311yescharacteristic
205C22×Dic5—21no—
206C22×Dic5—22no—
207C5×Q16—38no—
208C5×SD16—38no—
209C5×M16—34no—
210C2×C5×C8—32no—
211C22⋊Dic5—22no—
212C22⋊Dic5—61no—
213C22⋊Dic5#6712yes—
214C4⋊Dic5—21no—
215C4⋊Dic5—22no—
216C4⋊Dic5—31no—
217C4⋊Dic5—31no—
218C4⋊Dic5—62no—
219C4⋊Dic5—62no—
220C4⋊Dic5#6711yescharacteristic
221C4⋊Dic5#6711yescharacteristic
222C4⋊Dic5C22×D312yes—
223C4×Dic5—22no—
224C4×Dic5—61no—
225C4×Dic5—62no—
226C4×Dic5—62no—
227C4×Dic5C22×D312yes—
228C2×#168—31no—
229C2×#168—31no—
230C2×#168—62no—
231C2×#137—31no—
232#520—51no—
233#519—151no—
234#441—152no—
235#440—152no—
236C4×Q16—152no—
237C4×SD16—152no—
238#428—151no—
239#416—151no—
240C2×#103—151no—
241#405—151no—
242C22×C3×C5—21no—
243C22×C3×C5—21no—
244C22×C3×C5—22no—
245C22×C3×C5—41no—
246C22×C3×C5—41no—
247C22×C3×C5C4×D412yes—
248C22×C3×C5C22×D411yescharacteristic
249C3×C4×C5—22no—
250C3×C4×C5C4×D412yes—
251C3×C4×C5C23×C411yescharacteristic
252C3×C4×C5C2×#4111yescharacteristic
253Dic15—41no—
254Dic15—41no—
255C3×Dic5—22no—
256C3×Dic5—22no—
257C3×Dic5—42no—
258C5×Dic3—24no—
259C3×#41—22no—
260C3×#41C2×Dic514yes—
261C2×C3×Q8C22×D511yescharacteristic
262C2×C3×D4—21no—
263C2×C3×D4C22×D511yescharacteristic
264C22×C3×C4—21no—
265C22×C3×C4—102no—
266C22×C3×C4—101no—
267C22×C3×C4C22×D511yescharacteristic
268C22×Dic3—21no—
269C2×Dic6—21no—
270C2×Dic6—22no—
271C2×Dic6C2×Dic514yescomplemented
272C2×Dic6C22×D512yes—
273C3×C4⋊C4—51no—
274C3×C4⋊C4—51no—
275C3×C4⋊C4—52no—
276C3×C4⋊C4—102no—
277C3×C4⋊C4—101no—
278C3×C22⋊C4—52no—
279C3×C22⋊C4—102no—
280C3×C42—52no—
281C3×C42—102no—
282#217—101no—
283#216C2×Dic518yescomplemented
284#214C2×Dic518yescomplemented
285C4⋊Dic3—51no—
286C4⋊Dic3—51no—
287Dic3⋊C4—102no—
288Dic3⋊C4—102no—
289C4×Dic3—102no—
290C4×Dic3—102no—
291C4×Dic3—101no—
292#208C2×Dic514yescomplemented
293C2×C3⋊C8—51no—
294C2×C3⋊C8—51no—
295C2×C3⋊C8—102no—
296C2×C3⋊C8C22×D512yes—
297C23×C5—21no—
298C23×C5C2×#6711yescharacteristic
299C5×Q8—21no—
300C5×Q8—34no—
301C5×Q8—64no—
302C5×Q8—62no—
303C5×Q8C2×C4×D312yes—
304C5×D4—24no—
305C5×D4—21no—
306C5×D4C2×C4×D312yes—
307C2×C4×C5—21no—
308C2×C4×C5—24no—
309C2×C4×C5—64no—
310C2×C4×C5—62no—
311C2×C4×C5C2×C4×D312yes—
312C2×C4×C5#23512yes—
313C2×C4×C5C2×#6711yescharacteristic
314C2×C4×C5C23×D311yescharacteristic
315C2×Dic5—22no—
316C2×Dic5—61no—
317C2×Dic5—61no—
318C2×Dic5—82no—
319C2×Dic5—81no—
320C2×Dic5C2×#6712yes—
321C2×Dic5C2×#6712yes—
322C5×C8—34no—
323#168—61no—
324#168—61no—
325C2×#41D3×D511yescharacteristic
326C22×Q8—31no—
327#137—38no—
328C2×Q16—32no—
329C2×SD16—32no—
330C2×M16—31no—
331C22×C8—151no—
332C4×Q8—52no—
333C4×Q8—152no—
334C4×Q8—152no—
335C4×Q8—301no—
336C4×Q8—301no—
337C4×D4—52no—
338C4×D4—102no—
339#117—51no—
340#117—101no—
341#117—151no—
342#117—302no—
343C2×C4⋊C4—51no—
344C2×C4⋊C4—101no—
345#107—152no—
346#106—152no—
347#103—152no—
348#103—152no—
349#103—151no—
350#103—151no—
351#102—151no—
352#102—151no—
353#97—152no—
354C4×C8—152no—
355C2×C3×C5—22no—
356C2×C3×C5—42no—
357C2×C3×C5C2×C4×D411yescharacteristic
358C2×C3×C5#57711yescharacteristic
359C2×C3×C5#57811yescharacteristic
360C23×C3—21no—
361C23×C3D4×D511yescharacteristic
362C3×Q8—21no—
363C3×Q8C22×Dic512yes—
364C3×D4—24no—
365C3×D4—21no—
366C3×D4C22×Dic512yes—
367C2×C3×C4—21no—
368C2×C3×C4—24no—
369C2×C3×C4—52no—
370C2×C3×C4—52no—
371C2×C3×C4—102no—
372C2×C3×C4—402no—
373C2×C3×C4—401no—
374C2×C3×C4D4×D511yescharacteristic
375C2×C3×C4#71112yes—
376C2×C3×C4C22×Dic512yes—
377C2×C3×C4C23×D511yescharacteristic
378C2×Dic3—22no—
379C2×Dic3—24no—
380C2×Dic3—101no—
381C2×Dic3—101no—
382Dic6—22no—
383Dic6—24no—
384Dic6C22×Dic514yes—
385C3⋊C8—101no—
386C3⋊C8—101no—
387C3⋊C8C22×Dic514yes—
388C22×C5—21no—
389C22×C5—21no—
390C22×C5—22no—
391C22×C5—41no—
392C22×C5—41no—
393C22×C5C4×#6712yes—
394C22×C5C22×#6711yescharacteristic
395C4×C5—22no—
396C4×C5—64no—
397C4×C5C4×#6712yes—
398C4×C5C22×C4×D311yescharacteristic
399C4×C5C2×#23511yescharacteristic
400Dic5—22no—
401Dic5—22no—
402Dic5—42no—
403Dic5—121no—
404Dic5—121no—
405#41—22no—
406#41D3×Dic514yes—
407C2×Q8—34no—
408C2×Q8—32no—
409C2×Q8—62no—
410C2×Q8—61no—
411C2×Q8C2×D3×D511yescharacteristic
412C2×D4—21no—
413C2×D4C2×D3×D511yescharacteristic
414C22×C4—21no—
415C22×C4—61no—
416C22×C4—102no—
417C22×C4—101no—
418C22×C4C2×D3×D511yescharacteristic
419Q16—38no—
420SD16—38no—
421M16—34no—
422C2×C8—32no—
423C2×C8—151no—
424C2×C8—151no—
425C2×C8—302no—
426C4⋊C4—51no—
427C4⋊C4—51no—
428C4⋊C4—52no—
429C4⋊C4—102no—
430C4⋊C4—101no—
431C4⋊C4—151no—
432C4⋊C4—151no—
433C4⋊C4—302no—
434C4⋊C4—302no—
435C22⋊C4—52no—
436C22⋊C4—102no—
437C22⋊C4—301no—
438C42—52no—
439C42—102no—
440C42—302no—
441C42—302no—
442C42—301no—
443C3×C5#294711yescharacteristic, complemented, Hall
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—22no—
447C22×C3—41no—
448C22×C3—41no—
449C22×C3D4×Dic512yes—
450C22×C3C2×D4×D511yescharacteristic
451C3×C4—22no—
452C3×C4—102no—
453C3×C4—102no—
454C3×C4—202no—
455C3×C4D4×Dic512yes—
456C3×C4C2×#71111yescharacteristic
457C3×C4C23×Dic511yescharacteristic
458Dic3—24no—
459Dic3—201no—
460Dic3—201no—
461C2×C5—22no—
462C2×C5—42no—
463C2×C5C2×C4×#6711yescharacteristic
464C2×C5#583611yescharacteristic
465C2×C5#583811yescharacteristic
466C23—21no—
467C23D5×#6711yescharacteristic
468Q8—21no—
469Q8—34no—
470Q8—62no—
471Q8—64no—
472Q8C2×D3×Dic512yes—
473D4—24no—
474D4—21no—
475D4C2×D3×Dic512yes—
476C2×C4—21no—
477C2×C4—24no—
478C2×C4—52no—
479C2×C4—52no—
480C2×C4—62no—
481C2×C4—64no—
482C2×C4—102no—
483C2×C4—301no—
484C2×C4—301no—
485C2×C4—402no—
486C2×C4—401no—
487C2×C4C2×D3×Dic512yes—
488C2×C4#678212yes—
489C2×C4D5×#6711yescharacteristic
490C2×C4C22×D3×D511yescharacteristic
491C8—34no—
492C8—301no—
493C8—301no—
494C2×C3—22no—
495C2×C3—42no—
496C2×C3#6611211yescharacteristic
497C2×C3#6611311yescharacteristic
498C2×C3C2×D4×Dic511yescharacteristic
499C5#8257111yescharacteristic, complemented, Sylow
500C22—21no—
501C22—21no—
502C22—22no—
503C22—41no—
504C22—41no—
505C22Dic5×#6712yes—
506C22C2×D5×#6711yescharacteristic
507C4—22no—
508C4—64no—
509C4—102no—
510C4—102no—
511C4—202no—
512C4—601no—
513C4—601no—
514C4Dic5×#6712yes—
515C4C22×D3×Dic511yescharacteristic
516C4C2×#678211yescharacteristic
517C3#1061569611yescharacteristic, complemented, Sylow
518C2—22no—
519C2—42no—
520C2#1175533511yescharacteristic
521C2#1175533611yescharacteristic
522C2C2×Dic5×#6711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
Fitting, prime radicalC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
cosocleC2×C3×C4×C5C24
hypercenterC2×#41D3×D5
hypocenterC3×C5#2947
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
3. #11754211C2semidirect
5. #11749247C2semidirect
6. Dic5×#216C2semidirect
7. #11749001C2semidirect
8. Dic5×#214C2semidirect
9. #11748453C2semidirect
10. C2×#90972C2semidirect
11. #11748320C2semidirect
17. C5×#951C4semidirect
65. C2×C5×Dic6C2×C4semidirect
76. C5×#216C2×C4semidirect
77. C5×#214C2×C4semidirect
78. C5×#208C2×C4semidirect
172. #951Dic5semidirect
271. C2×Dic6C2×Dic5semidirect
283. #216C2×Dic5semidirect
284. #214C2×Dic5semidirect
292. #208C2×Dic5semidirect
443. C3×C5#2947semidirect
499. C5#82571semidirect
517. C3#10615696semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9512
C3×#661612
#117542112
#117513342
#117492472
Dic5×#2162
#117490012
Dic5×#2142
#117484532
C2×#909722
#117483202
#106156963
#825715