Finite Group Databasebeta

← #14301117

Subgroups — #14301117

Order 1920.

748 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#214C211yesmaximal, characteristic
2C2×#91344C211yesmaximal, characteristic, complemented
3#11751322C211yesmaximal, characteristic
4C2×C3×#3964C211yesmaximal, characteristic
5C2×#90973C211yesmaximal, characteristic, complemented
6#11745980C211yesmaximal, characteristic, complemented
7#11745968C211yesmaximal, characteristic, complemented
8#10602841—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×C5×Dic6C2211yescharacteristic
11C2×#6719—21no—
12C2×#6719—21no—
13C2×C4⋊Dic15C2211yescharacteristic
14C2×C4×Dic15C2211yescharacteristic
15C2×C5×#214—22no—
16C2×C5×#214—22no—
17C2×C5×#214C414yescomplemented
18C22×C5×C3⋊C8C2211yescharacteristic
19C2×C3×C4⋊Dic5C2211yescharacteristic
20C22×C3×#168C2211yescharacteristic
21C2×Dic3⋊Dic5—21no—
22C2×Dic3×Dic5—21no—
23#91344—22no—
24#91344—22no—
25C3×#3964—22no—
26#90973—22no—
27#70213—51nomaximal, Hall
28C22×C5×SD16—31no—
29C2×Q8×Dic5—31no—
30C2×#3967—31no—
31#65510—31no—
32C2×#3964D311yescharacteristic
33#64771—31no—
34#64770—31no—
35C24×C3×C5—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4C2×C412yes—
42C22×C3×C4×C5C2311yescharacteristic
43C22×Dic15—21no—
44C22×Dic15D411yescharacteristic
45C22×Dic15D411yescharacteristic
46C22×C5×Dic3—21no—
47C2×C5×Dic6—21no—
48C2×C5×Dic6—21no—
49C2×C5×Dic6—21no—
50C2×C5×Dic6C2×C412yes—
51C2×C5×Dic6D412yes—
52C2×C5×Dic6D412yes—
53C22×C3×Dic5—21no—
54#6719—42no—
55#6719—42no—
56C4⋊Dic15—21no—
57C4⋊Dic15—21no—
58C4×Dic15—21no—
59C4×Dic15—21no—
60C5×#214—28no—
61C2×C5×C3⋊C8—21no—
62C2×C5×C3⋊C8—21no—
63C2×C5×C3⋊C8C2×C412yes—
64C3×C4⋊Dic5—21no—
65C3×C4⋊Dic5D412yes—
66C2×C3×#168—21no—
67C2×C3×#168—21no—
68C2×C3×#168—21no—
69Dic3⋊Dic5—24no—
70Dic3×Dic5—24no—
71C22×#214D511yescharacteristic
72C2×#887—51no—
73C2×C3×#102—51no—
74#5221—51no—
75C2×#816—51no—
76#4550—51no—
77#4529—51no—
78C22×C5×Q8—31no—
79C22×C5×D4C2×D311yescharacteristic
80C2×C5×SD16—34no—
81C2×C5×SD16—62no—
82C2×C5×SD16—62no—
83C22×C5×C8—31no—
84C2×C22⋊Dic5—61no—
85C2×C22⋊Dic5—61no—
86Q8×Dic5—62no—
87Q8×Dic5—62no—
88C2×C4⋊Dic5—31no—
89C2×C4⋊Dic5—61no—
90C2×C4⋊Dic5C2×D311yescharacteristic
91C2×C4×Dic5—31no—
92C2×C4×Dic5—61no—
93C22×#168C2×D311yescharacteristic
94#3967—62no—
95#3964—22no—
96#1880—151noSylow
97C23×C3×C5—22no—
98C23×C3×C5—41no—
99C23×C3×C5—41no—
100C23×C3×C5—41no—
101C23×C3×C5—41no—
102C23×C3×C5—41no—
103C23×C3×C5—41no—
104C23×C3×C5C2×D411yescharacteristic
105C3×C5×D4—22no—
106C3×C5×D4—22no—
107C3×C5×D4—41no—
108C3×C5×D4—41no—
109C2×C3×C4×C5C22×C411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5#4111yescharacteristic
114C2×C3×C4×C5#4111yescharacteristic
115C2×Dic15—21no—
116C2×Dic15—21no—
117C2×Dic15—21no—
118C2×Dic15—21no—
119C2×Dic15—21no—
120C2×Dic15—41no—
121C2×Dic15—41no—
122C2×Dic15—41no—
123C2×Dic15SD1612yescomplemented
124C2×C5×Dic3—22no—
125C2×C5×Dic3—22no—
126C2×C5×Dic3—22no—
127C5×Dic6—22no—
128C5×Dic6—22no—
129C5×Dic6—22no—
130C5×Dic6C22⋊C414yescomplemented
131C2×C3×Dic5—22no—
132C2×C3×Dic5—41no—
133C2×C3×Dic5—41no—
134C3×#168—41no—
135C5×C3⋊C8—22no—
136C22×C3×D4C2×D511yescharacteristic
137C22×Dic6C2×D511yescharacteristic
138C22×C3×C8—51no—
139C2×C3×C4⋊C4—51no—
140C2×#217—101no—
141C2×#217—101no—
142C2×#214—22no—
143C2×#214—22no—
144C2×#214Dic514yescomplemented
145C2×C4⋊Dic3—51no—
146C2×Dic3⋊C4—101no—
147C2×C4×Dic3—51no—
148C2×C4×Dic3—101no—
149C22×C3⋊C8C2×D511yescharacteristic
150#887—102no—
151#887—102no—
152C3×#102—102no—
153#816—102no—
154C24×C5—21no—
155C2×C5×Q8—32no—
156C2×C5×Q8—32no—
157C2×C5×Q8—32no—
158C2×C5×Q8—61no—
159C2×C5×Q8—61no—
160C2×C5×Q8—61no—
161C2×C5×D4—21no—
162C2×C5×D4—21no—
163C2×C5×D4—21no—
164C2×C5×D4—21no—
165C2×C5×D4—21no—
166C2×C5×D4C4×D312yes—
167C22×C4×C5—61no—
168C22×C4×C5C22×D311yescharacteristic
169C22×Dic5—21no—
170C22×Dic5—31no—
171C22×Dic5—31no—
172C22×Dic5—61no—
173C5×SD16—68no—
174C2×C5×C8—32no—
175C2×C5×C8—61no—
176C2×C5×C8—61no—
177C22⋊Dic5—122no—
178C22⋊Dic5—122no—
179C4⋊Dic5—21no—
180C4⋊Dic5—64no—
181C4⋊Dic5—61no—
182C4⋊Dic5—61no—
183C4⋊Dic5#6712yes—
184C4×Dic5—64no—
185C4×Dic5—61no—
186C4×Dic5—61no—
187C2×#168—21no—
188C2×#168—21no—
189C2×#168—21no—
190C22×SD16—31no—
191C2×C4×Q8—151no—
192C2×#103—151no—
193C2×#102—51no—
194#390—151no—
195#340—151no—
196#336—151no—
197C22×C3×C5—42no—
198C22×C3×C5—42no—
199C22×C3×C5—42no—
200C22×C3×C5—81no—
201C22×C3×C5—81no—
202C22×C3×C5—81no—
203C22×C3×C5—81no—
204C22×C3×C5C4×D411yescharacteristic
205C22×C3×C5#12011yescharacteristic
206C22×C3×C5#12111yescharacteristic
207C22×C3×C5C2×SD1611yescharacteristic
208C22×C3×C5#13511yescharacteristic
209C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
210C22×C3×C5#13711yescharacteristic
211C3×C4×C5C2×C22⋊C411yescharacteristic
212C3×C4×C5C4×D411yescharacteristic
213C3×C4×C5#12111yescharacteristic
214C3×C4×C5#12311yescharacteristic
215Dic15—22no—
216Dic15—41no—
217Dic15—81no—
218C3×Dic5—42no—
219C5×Dic3—24no—
220C24×C3—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4C2×Dic512yes—
227C22×C3×C4—101no—
228C22×C3×C4C22×D511yescharacteristic
229C22×Dic3—21no—
230C22×Dic3—51no—
231C22×Dic3—51no—
232C22×Dic3—101no—
233C2×Dic6—21no—
234C2×Dic6—21no—
235C2×Dic6—21no—
236C2×Dic6C2×Dic512yes—
237C2×Dic6C22⋊D512yes—
238C2×Dic6C22⋊D512yes—
239C2×C3×C8—101no—
240C2×C3×C8—101no—
241C2×C3×C8—101no—
242C3×C4⋊C4—52no—
243C3×C4⋊C4—101no—
244#217—202no—
245#217—202no—
246#214—28no—
247C4⋊Dic3—101no—
248C4⋊Dic3—101no—
249Dic3⋊C4—104no—
250C4×Dic3—104no—
251C4×Dic3—101no—
252C4×Dic3—101no—
253C2×C3⋊C8—21no—
254C2×C3⋊C8—21no—
255C2×C3⋊C8C2×Dic512yes—
256C23×C5—22no—
257C23×C5—41no—
258C23×C5—41no—
259C23×C5—41no—
260C23×C5—41no—
261C23×C5—41no—
262C23×C5—41no—
263C23×C5D3×D411yescharacteristic
264C5×Q8—34no—
265C5×Q8—62no—
266C5×Q8—62no—
267C5×Q8—62no—
268C5×D4—22no—
269C5×D4—22no—
270C5×D4—41no—
271C5×D4—41no—
272C2×C4×C5—62no—
273C2×C4×C5—62no—
274C2×C4×C5—62no—
275C2×C4×C5C2×C4×D311yescharacteristic
276C2×C4×C5#23511yescharacteristic
277C2×C4×C5D3×D411yescharacteristic
278C2×C4×C5D3×D411yescharacteristic
279C2×C4×C5#23711yescharacteristic
280C2×C4×C5C2×#6711yescharacteristic
281C2×Dic5—22no—
282C2×Dic5—32no—
283C2×Dic5—41no—
284C2×Dic5—41no—
285C2×Dic5—61no—
286C2×Dic5—61no—
287C2×Dic5—61no—
288C2×Dic5—61no—
289C2×Dic5—61no—
290C2×Dic5—121no—
291C2×Dic5—121no—
292C2×Dic5—121no—
293C5×C8—62no—
294#168—41no—
295C22×Q8—31no—
296C22×D4D3×D511yescharacteristic
297C2×SD16—34no—
298C2×SD16—62no—
299C2×SD16—62no—
300C22×C8—31no—
301C22×C8—51no—
302C4×Q8—302no—
303C4×Q8—302no—
304C2×C4⋊C4—51no—
305C2×C4⋊C4—151no—
306C2×C4⋊C4—301no—
307C2×C22⋊C4—301no—
308C2×C22⋊C4—301no—
309C2×C42—151no—
310C2×C42—301no—
311#103—302no—
312#102—102no—
313C2×C3×C5—82no—
314C2×C3×C5#38611yescharacteristic
315C2×C3×C5C4×SD1611yescharacteristic
316C2×C3×C5#44011yescharacteristic
317C2×C3×C5#44811yescharacteristic
318C2×C3×C5#44911yescharacteristic
319C2×C3×C5#46011yescharacteristic
320C2×C3×C5#46411yescharacteristic
321C23×C3—22no—
322C23×C3—41no—
323C23×C3—41no—
324C23×C3—41no—
325C23×C3—41no—
326C23×C3—41no—
327C23×C3—41no—
328C23×C3D4×D511yescharacteristic
329C3×D4—22no—
330C3×D4—22no—
331C3×D4—41no—
332C3×D4—41no—
333C2×C3×C4—102no—
334C2×C3×C4—201no—
335C2×C3×C4—201no—
336C2×C3×C4D4×D511yescharacteristic
337C2×C3×C4#71111yescharacteristic
338C2×C3×C4#71111yescharacteristic
339C2×C3×C4C22×Dic511yescharacteristic
340C2×C3×C4C2×C22⋊D511yescharacteristic
341C2×C3×C4C2×C22⋊D511yescharacteristic
342C2×Dic3—22no—
343C2×Dic3—22no—
344C2×Dic3—22no—
345C2×Dic3—52no—
346C2×Dic3—101no—
347C2×Dic3—101no—
348C2×Dic3—101no—
349C2×Dic3—101no—
350C2×Dic3—101no—
351C2×Dic3—201no—
352C2×Dic3—201no—
353C2×Dic3—201no—
354Dic6—22no—
355Dic6—22no—
356Dic6—22no—
357Dic6C22⋊Dic514yescomplemented
358C3×C8—201no—
359C3⋊C8—22no—
360C22×C5—42no—
361C22×C5—42no—
362C22×C5—42no—
363C22×C5—81no—
364C22×C5—81no—
365C22×C5—81no—
366C22×C5—81no—
367C22×C5#67⋊C411yescharacteristic
368C22×C5#88411yescharacteristic
369C22×C5#91111yescharacteristic
370C22×C5#91211yescharacteristic
371C22×C5D3×SD1611yescharacteristic
372C22×C5#91511yescharacteristic
373C22×C5#93711yescharacteristic
374C4×C5—64no—
375C4×C5D3×C22⋊C411yescharacteristic
376C4×C5#88311yescharacteristic
377C4×C5C4×#6711yescharacteristic
378C4×C5#93811yescharacteristic
379Dic5—42no—
380Dic5—62no—
381Dic5—121no—
382Dic5—241no—
383C24—21no—
384C2×Q8—32no—
385C2×Q8—32no—
386C2×Q8—32no—
387C2×Q8—61no—
388C2×Q8—61no—
389C2×Q8—61no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4D3×Dic512yes—
396C22×C4—61no—
397C22×C4—101no—
398C22×C4—151no—
399C22×C4—151no—
400C22×C4—301no—
401C22×C4C2×D3×D511yescharacteristic
402SD16—68no—
403C2×C8—32no—
404C2×C8—61no—
405C2×C8—61no—
406C2×C8—101no—
407C2×C8—101no—
408C2×C8—101no—
409C4⋊C4—52no—
410C4⋊C4—101no—
411C4⋊C4—304no—
412C4⋊C4—301no—
413C4⋊C4—301no—
414C22⋊C4—602no—
415C22⋊C4—602no—
416C42—304no—
417C42—301no—
418C42—301no—
419C3×C5#188011yescharacteristic, complemented, Hall
420C22×C3—42no—
421C22×C3—42no—
422C22×C3—42no—
423C22×C3—81no—
424C22×C3—81no—
425C22×C3—81no—
426C22×C3—81no—
427C22×C3D5×SD1611yescharacteristic
428C22×C3#406011yescharacteristic
429C22×C3#406111yescharacteristic
430C22×C3#406211yescharacteristic
431C22×C3D4×Dic511yescharacteristic
432C22×C3#408311yescharacteristic
433C22×C3#408511yescharacteristic
434C3×C4—202no—
435C3×C4D4×Dic511yescharacteristic
436C3×C4#408111yescharacteristic
437C3×C4#408511yescharacteristic
438C3×C4C2×C22⋊Dic511yescharacteristic
439Dic3—24no—
440Dic3—102no—
441Dic3—201no—
442Dic3—401no—
443C2×C5—82no—
444C2×C5#475711yescharacteristic
445C2×C5#475811yescharacteristic
446C2×C5#476211yescharacteristic
447C2×C5#476711yescharacteristic
448C2×C5#495611yescharacteristic
449C2×C5#515811yescharacteristic
450C2×C5#517011yescharacteristic
451C23—22no—
452C23—41no—
453C23—41no—
454C23—41no—
455C23—41no—
456C23—41no—
457C23—41no—
458C23#679011yescharacteristic
459Q8—34no—
460Q8—62no—
461Q8—62no—
462Q8—62no—
463D4—22no—
464D4—22no—
465D4—41no—
466D4—41no—
467C2×C4—62no—
468C2×C4—62no—
469C2×C4—62no—
470C2×C4—102no—
471C2×C4—152no—
472C2×C4—201no—
473C2×C4—201no—
474C2×C4—301no—
475C2×C4—301no—
476C2×C4—301no—
477C2×C4—301no—
478C2×C4—301no—
479C2×C4—601no—
480C2×C4—601no—
481C2×C4—601no—
482C2×C4#678011yescharacteristic
483C2×C4C2×D3×Dic511yescharacteristic
484C2×C4#678211yescharacteristic
485C2×C4D5×#6711yescharacteristic
486C2×C4D3×C22⋊D511yescharacteristic
487C2×C4D3×C22⋊D511yescharacteristic
488C8—62no—
489C8—201no—
490C2×C3—82no—
491C2×C3SD16×Dic511yescharacteristic
492C2×C3#6545211yescharacteristic
493C2×C3#6545311yescharacteristic
494C2×C3#6545511yescharacteristic
495C2×C3#6545911yescharacteristic
496C2×C3#6546111yescharacteristic
497C2×C3#6550911yescharacteristic
498C5#7021311yescharacteristic, complemented, Sylow
499C22—42no—
500C22—42no—
501C22—42no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22#9148711yescharacteristic
507C22#9148811yescharacteristic
508C22#9149711yescharacteristic
509C22#9149811yescharacteristic
510C22#9155811yescharacteristic
511C22#67⋊Dic511yescharacteristic
512C22#9157711yescharacteristic
513C4—64no—
514C4—202no—
515C4—302no—
516C4—601no—
517C4—1201no—
518C4Dic5×#6711yescharacteristic
519C4D3×C22⋊Dic511yescharacteristic
520C4#9155511yescharacteristic
521C4#9156511yescharacteristic
522C3#1060284111yescharacteristic, complemented, Sylow
523C2—82no—
524C2#1174901511yescharacteristic
525C2#1174901611yescharacteristic
526C2#1174901911yescharacteristic
527C2#1174902011yescharacteristic
528C2#1174915611yescharacteristic
529C2#1174915811yescharacteristic
530C2#1174951911yescharacteristic
subgroupG/H
centerC23#6790
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
Fitting, prime radicalC22×C3×C5×D4C22
socleC23×C3×C5C2×D4
cosocleC22×C3×C4×C5C23
hypercenterC22×D4D3×D5
hypocenterC3×C5#1880
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#91344C2semidirect
5. C2×#90973C2semidirect
6. #11745980C2semidirect
7. #11745968C2semidirect
17. C2×C5×#214C4semidirect
123. C2×Dic15SD16semidirect
130. C5×Dic6C22⋊C4semidirect
144. C2×#214Dic5semidirect
357. Dic6C22⋊Dic5semidirect
419. C3×C5#1880semidirect
498. C5#70213semidirect
522. C3#10602841semidirect

Maximal subgroups

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

subgroupindex
C22×C5×#2142
C2×#913442
#117513222
C2×C3×#39642
C2×#909732
#117459802
#117459682
#106028413
#702135