Finite Group Databasebeta

← #14435440

Subgroups — #14435440

Order 1920.

772 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756359C211yesmaximal, characteristic
2C2×#91331C211yesmaximal, characteristic, complemented
3C5×#5034C211yesmaximal, characteristic
4C3×#65329C211yesmaximal, characteristic
5#11749018C212yesmaximal, complemented
6#11749007C212yesmaximal, complemented
7#11748556C211yesmaximal, characteristic, complemented
8#11748464C211yesmaximal, characteristic, complemented
9#11748338C211yesmaximal, characteristic, complemented
10#11747302C212yesmaximal, complemented
11#11747274C212yesmaximal, complemented
12#10613042—31nomaximal, Hall
13C22×C3×Dic10C2211yescharacteristic
14C3×C5×#121C2211yescharacteristic
15#91825C2211yescharacteristic
16#91824—21no—
17D4×Dic15—21no—
18D4×Dic15C2211yescharacteristic
19#91813C2211yescharacteristic
20C2×C4×Dic15C2211yescharacteristic
21#91779C2211yescharacteristic
22#91776C2211yescharacteristic
23#91768—21no—
24#91766—21no—
25C2×C5×C4⋊Dic3C2211yescharacteristic
26C2×C3×#687C2212yes—
27C2×#6668—21no—
28C2×Dic3×Dic5—21no—
29#91331—21no—
30#91331—21no—
31#91331C2212yes—
32#91331C2212yes—
33C2×#6662C2212yes—
34C5×#832C2212yes—
35C5×#830C2211yescharacteristic
36C5×#808C2212yes—
37C3×C22⋊#168C2211yescharacteristic
38C3×#3942C2212yes—
39#90988C2212yes—
40#90983C2212yes—
41#90975C2212yes—
42#90971C2212yes—
43#90954C2212yes—
44#80031—51nomaximal, Hall
45#65934—31no—
46C2×#4033—31no—
47C5×#481—31no—
48#65329D311yescharacteristic
49#65259—31no—
50#65146—32no—
51#65142—32no—
52#65056—32no—
53#65046—32no—
54#65028—31no—
55#65008—31no—
56C2×C3×C5×D4—21no—
57C2×C3×C5×D4C2311yescharacteristic
58C22×C3×C4×C5C2311yescharacteristic
59C22×Dic15—21no—
60C22×Dic15D411yescharacteristic
61C22×Dic15D411yescharacteristic
62C2×Dic30C2311yescharacteristic
63C22×C5×Dic3—21no—
64C22×C3×Dic5—21no—
65C2×C3×Dic10—21no—
66C2×C3×Dic10—24no—
67C2×C3×Dic10C2312yes—
68C3×C5×C4⋊C4C2311yescharacteristic
69C3×C5×C22⋊C4—21no—
70#6719—21no—
71#6719—21no—
72#6719—21no—
73#6719—21no—
74C4⋊Dic15—21no—
75C4⋊Dic15C2311yescharacteristic
76#6712—21no—
77#6712—21no—
78#6712—21no—
79C4×Dic15—21no—
80C4×Dic15D411yescharacteristic
81C4×Dic15D411yescharacteristic
82C4×Dic15C2311yescharacteristic
83C4×Dic15C2311yescharacteristic
84C5×C4⋊Dic3—21no—
85C5×C4⋊Dic3C2312yes—
86C2×C5×C3⋊C8C2312yes—
87C3×#687—24no—
88C2×C3×#168C2312yes—
89#6668—22no—
90#6668—22no—
91Dic3×Dic5—22no—
92Dic3×Dic5—22no—
93#6662—24no—
94C2×Q8×Dic3—51no—
95#5600—51no—
96C3×#448—51no—
97#5228—51no—
98#5166—52no—
99#5164—52no—
100#5034D511yescharacteristic
101#4796—52no—
102#4789—52no—
103#4722—51no—
104#4719—51no—
105C22×Dic10C2×D311yescharacteristic
106C5×#121C2×D311yescharacteristic
107C2×C5×C4⋊C4—31no—
108#4082—31no—
109#4081—61no—
110D4×Dic5—31no—
111D4×Dic5—61no—
112C2×#687C2×D312yes—
113#4070—31no—
114C2×#683—61no—
115C2×C4×Dic5—31no—
116C2×C4×Dic5—61no—
117C2×Dic20—32no—
118#4036—31no—
119#4033—32no—
120#4033—32no—
121#4033—31no—
122#4033—61no—
123#4033—61no—
124#4025—61no—
125#4023—61no—
126C5×#106—32no—
127C5×#102—32no—
128C5×C22⋊C8—31no—
129C22⋊#168C2×D311yescharacteristic
130#3948—32no—
131#3947—32no—
132#3946—32no—
133#3942—32no—
134#3942C2×D312yes—
135#3939—32no—
136#3117—151noSylow
137C23×C3×C5—21no—
138C23×C3×C5C2×D411yescharacteristic
139C3×C5×D4—22no—
140C3×C5×D4—42no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2411yescharacteristic
145C2×Dic15—22no—
146C2×Dic15—21no—
147C2×Dic15—21no—
148C2×Dic15—41no—
149C2×Dic15—42no—
150C2×Dic15C2×D411yescharacteristic
151C2×Dic15C2×D411yescharacteristic
152C2×Dic15C2×D411yescharacteristic
153C2×Dic15C2×D411yescharacteristic
154Dic30—22no—
155C2×C5×Dic3—22no—
156C2×C5×Dic3—42no—
157C2×C3×Dic5—24no—
158C2×C3×Dic5—22no—
159C3×Dic10—24no—
160C3×Dic10—22no—
161C3×Dic10#4114yes—
162C3×#168—22no—
163C5×C3⋊C8—22no—
164C22×C3×Q8—51no—
165C2×C3×SD16—52no—
166C3×#121C2×D511yescharacteristic
167Q8×Dic3—52no—
168Q8×Dic3—52no—
169Q8×Dic3—101no—
170Q8×Dic3—101no—
171C2×#216—52no—
172#936—51no—
173#935—101no—
174D4×Dic3—51no—
175D4×Dic3—101no—
176C2×C4⋊Dic3—101no—
177C2×C4⋊Dic3C2×D511yescharacteristic
178#924—51no—
179C2×C4×Dic3—51no—
180C2×C4×Dic3—101no—
181#890—51no—
182#887—51no—
183#879—101no—
184#877—101no—
185C3×#103—52no—
186C3×C22⋊C8—51no—
187#835—52no—
188#832C2×D512yes—
189#830C2×D511yescharacteristic
190#818—52no—
191#816—52no—
192#815—52no—
193Dic3⋊C8—52no—
194#808C2×D512yes—
195C2×C5×D4—21no—
196C2×C5×D4C22×D311yescharacteristic
197C22×C4×C5—61no—
198C22×C4×C5C22×D311yescharacteristic
199C22×Dic5—21no—
200C22×Dic5—31no—
201C22×Dic5—31no—
202C22×Dic5—61no—
203C2×Dic10—21no—
204C2×Dic10—24no—
205C2×Dic10—31no—
206C2×Dic10C22×D312yes—
207C2×C5×C8—32no—
208C5×C4⋊C4—32no—
209C5×C4⋊C4—61no—
210C5×C4⋊C4C22×D311yescharacteristic
211C5×C22⋊C4—21no—
212C22⋊Dic5—61no—
213C22⋊Dic5—61no—
214C22⋊Dic5—61no—
215C22⋊Dic5—61no—
216#687—24no—
217C4⋊Dic5—31no—
218C4⋊Dic5—61no—
219#683—62no—
220#683—62no—
221#683—61no—
222#683—61no—
223#683—61no—
224C4×Dic5—31no—
225C4×Dic5—31no—
226C4×Dic5—31no—
227C4×Dic5—31no—
228C4×Dic5—62no—
229C4×Dic5—62no—
230C4×Dic5—61no—
231C2×#168C22×D312yes—
232Dic20—64no—
233#529—151no—
234C2×C4×Q8—151no—
235#484—151no—
236#481—31no—
237#479—152no—
238#464—152no—
239#451—151no—
240#448—51no—
241#441—152no—
242#440—152no—
243#432—151no—
244C22×C3×C5—21no—
245C22×C3×C5—21no—
246C22×C3×C5—41no—
247C22×C3×C5—41no—
248C22×C3×C5—41no—
249C22×C3×C5#13712yes—
250C22×C3×C5C22×D411yescharacteristic
251C3×C4×C5—21no—
252C3×C4×C5—41no—
253C3×C4×C5C2×#4112yes—
254Dic15—21no—
255Dic15—21no—
256Dic15—21no—
257Dic15—21no—
258Dic15—41no—
259Dic15—41no—
260C3×Dic5—24no—
261C5×Dic3—42no—
262C2×C3×Q8—52no—
263C2×C3×Q8—104no—
264C2×C3×Q8—101no—
265C2×C3×D4—21no—
266C2×C3×D4C22×D511yescharacteristic
267C22×C3×C4—101no—
268C22×C3×C4C22×D511yescharacteristic
269C22×Dic3—21no—
270C22×Dic3—51no—
271C22×Dic3—51no—
272C22×Dic3—101no—
273C2×Dic6—51no—
274C3×SD16—104no—
275C2×C3×C8—52no—
276C3×C4⋊C4C22×D511yescharacteristic
277C3×C22⋊C4—21no—
278#217—101no—
279#217—101no—
280#217—101no—
281#217—101no—
282#216—104no—
283C4⋊Dic3—21no—
284C4⋊Dic3—51no—
285C4⋊Dic3—102no—
286C4⋊Dic3—102no—
287C4⋊Dic3—101no—
288C4⋊Dic3C22×D512yes—
289Dic3⋊C4—101no—
290Dic3⋊C4—101no—
291Dic3⋊C4—101no—
292C4×Dic3—51no—
293C4×Dic3—51no—
294C4×Dic3—51no—
295C4×Dic3—51no—
296C4×Dic3—102no—
297C4×Dic3—102no—
298C4×Dic3—101no—
299C2×C3⋊C8C22×D512yes—
300C23×C5—21no—
301C23×C5D3×D411yescharacteristic
302C5×D4—22no—
303C5×D4—42no—
304C2×C4×C5—22no—
305C2×C4×C5—21no—
306C2×C4×C5—62no—
307C2×C4×C5—122no—
308C2×C4×C5D3×D411yescharacteristic
309C2×C4×C5C23×D311yescharacteristic
310C2×Dic5—24no—
311C2×Dic5—22no—
312C2×Dic5—31no—
313C2×Dic5—31no—
314C2×Dic5—31no—
315C2×Dic5—31no—
316C2×Dic5—62no—
317C2×Dic5—61no—
318C2×Dic5—61no—
319C2×Dic5—121no—
320C2×Dic5—122no—
321Dic10—24no—
322Dic10—22no—
323Dic10—62no—
324Dic10#23714yes—
325C5×C8—62no—
326#168—22no—
327C22×Q8—51no—
328C2×Q16—152no—
329C2×SD16—52no—
330#126—301no—
331#125—151no—
332#124—151no—
333#123—301no—
334C22⋊Q8—151no—
335#121D3×D511yescharacteristic
336C4×Q8—152no—
337C4×Q8—152no—
338C4×Q8—151no—
339C4×Q8—301no—
340C4×Q8—301no—
341C4×D4—151no—
342C4×D4—301no—
343#117—301no—
344C2×C4⋊C4—31no—
345C2×C4⋊C4—301no—
346C2×C42—151no—
347C2×C42—301no—
348#107—152no—
349#106—32no—
350C4⋊C8—152no—
351#103—52no—
352#103—152no—
353#103—152no—
354#102—32no—
355C22⋊C8—31no—
356C22⋊C8—51no—
357#97—152no—
358C2×C3×C5—22no—
359C2×C3×C5—81no—
360C2×C3×C5#52511yescharacteristic
361C2×C3×C5C2×#13711yescharacteristic
362C2×C3×C5#57511yescharacteristic
363C23×C3—21no—
364C23×C3D4×D511yescharacteristic
365C3×Q8—54no—
366C3×Q8—104no—
367C3×Q8—102no—
368C3×D4—22no—
369C3×D4—42no—
370C2×C3×C4—22no—
371C2×C3×C4—21no—
372C2×C3×C4—104no—
373C2×C3×C4—102no—
374C2×C3×C4D4×D511yescharacteristic
375C2×C3×C4C23×D511yescharacteristic
376C2×Dic3—22no—
377C2×Dic3—42no—
378C2×Dic3—51no—
379C2×Dic3—51no—
380C2×Dic3—51no—
381C2×Dic3—51no—
382C2×Dic3—102no—
383C2×Dic3—101no—
384C2×Dic3—101no—
385C2×Dic3—201no—
386C2×Dic3—202no—
387Dic6—102no—
388C3×C8—102no—
389C3⋊C8—22no—
390C22×C5—21no—
391C22×C5—21no—
392C22×C5—41no—
393C22×C5—41no—
394C22×C5—41no—
395C22×C5#91512yes—
396C22×C5C2×D3×D411yescharacteristic
397C4×C5—21no—
398C4×C5—41no—
399C4×C5—122no—
400C4×C5C2×#23712yes—
401Dic5—24no—
402Dic5—61no—
403Dic5—61no—
404Dic5—61no—
405Dic5—61no—
406Dic5—121no—
407Dic5—121no—
408C2×Q8—52no—
409C2×Q8—104no—
410C2×Q8—101no—
411C2×Q8—151no—
412C2×D4—21no—
413C2×D4C2×D3×D511yescharacteristic
414C22×C4—61no—
415C22×C4—101no—
416C22×C4—151no—
417C22×C4—151no—
418C22×C4—301no—
419C22×C4C2×D3×D511yescharacteristic
420Q16—304no—
421SD16—104no—
422C2×C8—32no—
423C2×C8—52no—
424C4⋊C4—32no—
425C4⋊C4—61no—
426C4⋊C4—151no—
427C4⋊C4—301no—
428C4⋊C4—301no—
429C4⋊C4—301no—
430C4⋊C4—302no—
431C4⋊C4—302no—
432C4⋊C4—301no—
433C4⋊C4C2×D3×D511yescharacteristic
434C22⋊C4—21no—
435C22⋊C4—301no—
436C22⋊C4—301no—
437C22⋊C4—301no—
438C22⋊C4—301no—
439C42—151no—
440C42—151no—
441C42—151no—
442C42—151no—
443C42—301no—
444C42—302no—
445C42—302no—
446C3×C5#311711yescharacteristic, complemented, Hall
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—41no—
450C22×C3—41no—
451C22×C3—41no—
452C22×C3#406112yes—
453C22×C3C2×D4×D511yescharacteristic
454C3×C4—21no—
455C3×C4—41no—
456C3×C4—104no—
457C3×C4D5×#4112yes—
458Dic3—42no—
459Dic3—101no—
460Dic3—101no—
461Dic3—101no—
462Dic3—101no—
463Dic3—201no—
464Dic3—201no—
465C2×C5—22no—
466C2×C5—81no—
467C2×C5#558611yescharacteristic
468C2×C5C2×#91511yescharacteristic
469C2×C5#577711yescharacteristic
470C23—21no—
471C23#679011yescharacteristic
472Q8—54no—
473Q8—104no—
474Q8—102no—
475Q8—302no—
476D4—22no—
477D4—42no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—62no—
481C2×C4—104no—
482C2×C4—102no—
483C2×C4—122no—
484C2×C4—151no—
485C2×C4—151no—
486C2×C4—151no—
487C2×C4—151no—
488C2×C4—302no—
489C2×C4—301no—
490C2×C4—301no—
491C2×C4—601no—
492C2×C4—602no—
493C2×C4#679011yescharacteristic
494C2×C4C22×D3×D511yescharacteristic
495C8—62no—
496C8—102no—
497C2×C3—22no—
498C2×C3—81no—
499C2×C3#6599011yescharacteristic
500C2×C3C2×#406111yescharacteristic
501C2×C3#6610711yescharacteristic
502C5#8003111yescharacteristic, complemented, Sylow
503C22—21no—
504C22—21no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22#9148812yes—
509C22C2×#679011yescharacteristic
510C4—21no—
511C4—41no—
512C4—104no—
513C4—122no—
514C4—301no—
515C4—301no—
516C4—301no—
517C4—301no—
518C4—601no—
519C4—601no—
520C4D5×#23712yes—
521C3#1061304211yescharacteristic, complemented, Sylow
522C2—22no—
523C2—81no—
524C2C2×#9148811yescharacteristic
525C2#1175481511yescharacteristic
526C2#1175535211yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
Fitting, prime radicalC3×C5×#121C22
socleC22×C3×C5C22×D4
hypercenter#121D3×D5
hypocenterC3×C5#3117
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. C2×#91331C2semidirect
5. #11749018C2semidirect
6. #11749007C2semidirect
7. #11748556C2semidirect
8. #11748464C2semidirect
9. #11748338C2semidirect
10. #11747302C2semidirect
11. #11747274C2semidirect
446. C3×C5#3117semidirect
502. C5#80031semidirect
521. C3#10613042semidirect

Maximal subgroups

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

subgroupindex
#117563592
C2×#913312
C5×#50342
C3×#653292
#117490182
#117490072
#117485562
#117484642
#117483382
#117473022
#117472742
#106130423
#800315