Finite Group Databasebeta

← #14282960

Subgroups — #14282960

Order 1920.

668 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756365C211yesmaximal, characteristic
2#11750827C211yesmaximal, characteristic, complemented
3D15×#95C211yesmaximal, characteristic, complemented
4C3×C5×#327C211yesmaximal, characteristic, complemented
5#11746358C211yesmaximal, characteristic, complemented
6#11746288C211yesmaximal, characteristic, complemented
7#11746273C211yesmaximal, characteristic, complemented
8#10599095—31nomaximal, Hall
9C2×#6819C411yescharacteristic, complemented
10C22×C4×D15—21no—
11C22×C4×D15C2211yescharacteristic
12C3×C5×#121C2211yescharacteristic
13#91827C411yescharacteristic, complemented
14#91826—21no—
15D4×Dic15—21no—
16#91813C2211yescharacteristic
17C2×#6705—21no—
18#91786C411yescharacteristic, complemented
19#91781C411yescharacteristic, complemented
20#91772—21no—
21#91770—21no—
22C3×C5×C22⋊C8C2211yescharacteristic
23C3×C5×#95C2211yescharacteristic
24#91115—21no—
25#91115C2211yescharacteristic
26#91114C2211yescharacteristic
27#91104—21no—
28#68302—51nomaximal, Hall
29#65940—31no—
30#65015—31no—
31D5×#95—31no—
32C5×#327D311yescharacteristic, complemented
33#64757—31no—
34#64687—31no—
35#64672—31no—
36C23×D15D411yescharacteristic
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4C2×C411yescharacteristic, complemented
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5C2311yescharacteristic
41C2×#1220—21no—
42C2×#1220—21no—
43C22×Dic15—21no—
44C22×Dic15—21no—
45C22×Dic15D411yescharacteristic
46#6819—42no—
47C2×C4×D15—24no—
48C2×C4×D15—42no—
49C2×C4×D15—42no—
50C2×C4×D15—42no—
51C2×C4×D15C2×C411yescharacteristic
52C2×C4×D15C2×C411yescharacteristic
53C2×C4×D15D411yescharacteristic
54C2×C4×D15D411yescharacteristic
55C2×Dic30C2×C411yescharacteristic, complemented
56C2×C3×C5×C8—21no—
57C3×C5×C4⋊C4C2×C411yescharacteristic, complemented
58C3×C5×C22⋊C4—21no—
59#6719—21no—
60#6719—21no—
61#6714—21no—
62#6714—21no—
63C4⋊Dic15—21no—
64C4⋊Dic15C2×C411yescharacteristic, complemented
65#6712—21no—
66C4×Dic15—21no—
67C2×C3⋊#168—21no—
68#6705—42no—
69#5606—51no—
70#4726—51no—
71D3×#95—51no—
72C3×#327D511yescharacteristic, complemented
73#4537—51no—
74#4467—51no—
75#4452—51no—
76C2×#711—31no—
77C22×C4×D5—31no—
78C22×C4×D5—61no—
79C5×#121C2×D311yescharacteristic
80#4084—31no—
81#4083—61no—
82D4×Dic5—61no—
83#4070—31no—
84C2×#676—61no—
85#4043—31no—
86#4038—31no—
87#4029—61no—
88#4027—61no—
89C5×C22⋊C8C2×D311yescharacteristic
90C5×#95C2×D311yescharacteristic
91#3963—31no—
92#3963—61no—
93C22⋊#168—31no—
94#3952—61no—
95#1504—151noSylow
96C23×C3×C5—21no—
97C23×C3×C5C2×D411yescharacteristic
98C22×D15—21no—
99C22×D15—21no—
100C22×D15—22no—
101C22×D15—22no—
102C22×D15C22⋊C411yescharacteristic
103C22×D15C22⋊C411yescharacteristic
104C3×C5×D4—41no—
105C3×C5×D4—41no—
106C3×C5×D4—41no—
107C2×C3×C4×C5—22no—
108C2×C3×C4×C5—21no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5—41no—
112C2×C3×C4×C5C22×C411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114#1220—42no—
115#1220—42no—
116C2×Dic15—22no—
117C2×Dic15—21no—
118C2×Dic15—21no—
119C2×Dic15—41no—
120C2×Dic15—42no—
121C2×Dic15—41no—
122C2×Dic15—41no—
123C2×Dic15C22⋊C411yescharacteristic
124C2×Dic15C22⋊C411yescharacteristic
125C4×D15—22no—
126C4×D15—22no—
127C4×D15—41no—
128C4×D15—41no—
129C4×D15—48no—
130Dic30—41no—
131C3×C5×C8—41no—
132C3⋊#168—41no—
133C2×#237—51no—
134C22×C4×D3—51no—
135C22×C4×D3—101no—
136C3×#121C2×D511yescharacteristic
137#938—51no—
138#937—101no—
139D4×Dic3—101no—
140#924—51no—
141C2×ΓL(1,𝔽25)—101no—
142#897—51no—
143#892—51no—
144#883—101no—
145#67⋊C4—101no—
146C3×C22⋊C8C2×D511yescharacteristic
147C3×#95C2×D511yescharacteristic
148C3⋊#95—51no—
149C3⋊#95—101no—
150#830—51no—
151(C2×D3)⋊C8—101no—
152C23×D5—31no—
153C2×C5×D4—21no—
154C2×C5×D4C4×D311yescharacteristic, complemented
155C22×C4×C5—21no—
156C22×C4×C5C22×D311yescharacteristic
157C2×C22⋊D5—61no—
158C2×C22⋊D5—61no—
159C22×Dic5—31no—
160C22×Dic5—61no—
161C22×Dic5—61no—
162#711—122no—
163C2×C4×D5—31no—
164C2×C4×D5—31no—
165C2×C4×D5—31no—
166C2×C4×D5—31no—
167C2×C4×D5—64no—
168C2×C4×D5—122no—
169C2×C4×D5—122no—
170C2×C4×D5—122no—
171C2×Dic10—31no—
172C2×C5×C8—21no—
173C5×C4⋊C4C4×D311yescharacteristic, complemented
174C5×C22⋊C4—21no—
175C22⋊Dic5—61no—
176C22⋊Dic5—61no—
177#685—61no—
178#685—61no—
179C4⋊Dic5—31no—
180C4⋊Dic5—61no—
181#683—61no—
182C4×Dic5—61no—
183C2×#168—61no—
184#676—122no—
185#525—151no—
186#407—151no—
187C2×#95—151no—
188#328—151no—
189#328—151no—
190#327—151no—
191#327D1511yescharacteristic, complemented
192C22×C3×C5—21no—
193C22×C3×C5—21no—
194C22×C3×C5—41no—
195C22×C3×C5—41no—
196C22×C3×C5—41no—
197C22×C3×C5C2×C22⋊C411yescharacteristic
198C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
199C22×C3×C5#13711yescharacteristic
200C2×D15—24no—
201C2×D15—24no—
202C2×D15—21no—
203C2×D15—21no—
204C2×D15—21no—
205C2×D15—21no—
206C2×D15#9912yes—
207C2×D15#10412yes—
208C3×C4×C5—21no—
209C3×C4×C5—21no—
210C3×C4×C5—42no—
211C3×C4×C5—41no—
212Dic15—21no—
213Dic15—21no—
214Dic15—42no—
215Dic15—41no—
216Dic15—41no—
217C23×D3—51no—
218C2×C3×D4—21no—
219C2×C3×D4C4×D511yescharacteristic, complemented
220C22×C3×C4—21no—
221C22×C3×C4C22×D511yescharacteristic
222C2×#67—101no—
223C2×#67—101no—
224C22×Dic3—51no—
225C22×Dic3—101no—
226C22×Dic3—101no—
227#237—202no—
228C2×C4×D3—51no—
229C2×C4×D3—51no—
230C2×C4×D3—51no—
231C2×C4×D3—51no—
232C2×C4×D3—104no—
233C2×C4×D3—202no—
234C2×C4×D3—202no—
235C2×C4×D3—202no—
236C2×Dic6—51no—
237C2×C3×C8—21no—
238C3×C4⋊C4C4×D511yescharacteristic, complemented
239C3×C22⋊C4—21no—
240#217—101no—
241#217—101no—
242(C2×D3)⋊C4—101no—
243(C2×D3)⋊C4—101no—
244C4⋊Dic3—51no—
245C4⋊Dic3—101no—
246Dic3⋊C4—101no—
247C4×Dic3—101no—
248C2×C3⋊C8—101no—
249ΓL(1,𝔽25)—202no—
250C23×C5—21no—
251C23×C5D3×D411yescharacteristic
252C22×D5—31no—
253C22×D5—31no—
254C22×D5—62no—
255C22×D5—62no—
256C22×D5—61no—
257C22×D5—61no—
258C5×D4—41no—
259C5×D4—41no—
260C5×D4—41no—
261C2×C4×C5—22no—
262C2×C4×C5—21no—
263C2×C4×C5—41no—
264C2×C4×C5—41no—
265C2×C4×C5—41no—
266C2×C4×C5C2×C4×D311yescharacteristic
267C2×C4×C5D3×D411yescharacteristic
268C22⋊D5—122no—
269C22⋊D5—122no—
270C2×Dic5—31no—
271C2×Dic5—31no—
272C2×Dic5—62no—
273C2×Dic5—61no—
274C2×Dic5—61no—
275C2×Dic5—121no—
276C2×Dic5—122no—
277C2×Dic5—121no—
278C2×Dic5—121no—
279C4×D5—62no—
280C4×D5—62no—
281C4×D5—121no—
282C4×D5—121no—
283C4×D5—128no—
284Dic10—121no—
285C5×C8—41no—
286#168—121no—
287C2×#41—151no—
288C23×C4—151no—
289C23×C4—301no—
290C2×M16—301no—
291#123—301no—
292C22⋊Q8—151no—
293C22⋊Q8—151no—
294#121—151no—
295#121C2×D1511yescharacteristic
296#120—301no—
297C4×D4—301no—
298C4×D4—301no—
299#117—151no—
300C22⋊C8—151no—
301C22⋊C8—301no—
302C22⋊C8C2×D1511yescharacteristic
303#95—151no—
304#95—301no—
305#95C2×D1511yescharacteristic
306C2×C3×C5—21no—
307C2×C3×C5—21no—
308C2×C3×C5—81no—
309C2×C3×C5C2×#9911yescharacteristic
310C2×C3×C5#41711yescharacteristic
311C2×C3×C5C2×#10411yescharacteristic
312D15—22no—
313D15—22no—
314C23×C3—21no—
315C23×C3D4×D511yescharacteristic
316C22×D3—51no—
317C22×D3—51no—
318C22×D3—102no—
319C22×D3—102no—
320C22×D3—101no—
321C22×D3—101no—
322C3×D4—41no—
323C3×D4—41no—
324C3×D4—41no—
325C2×C3×C4—22no—
326C2×C3×C4—21no—
327C2×C3×C4—41no—
328C2×C3×C4—41no—
329C2×C3×C4—41no—
330C2×C3×C4C2×C4×D511yescharacteristic
331C2×C3×C4D4×D511yescharacteristic
332#67—202no—
333#67—202no—
334C2×Dic3—51no—
335C2×Dic3—51no—
336C2×Dic3—102no—
337C2×Dic3—101no—
338C2×Dic3—101no—
339C2×Dic3—201no—
340C2×Dic3—202no—
341C2×Dic3—201no—
342C2×Dic3—201no—
343C4×D3—102no—
344C4×D3—102no—
345C4×D3—201no—
346C4×D3—201no—
347C4×D3—208no—
348Dic6—201no—
349C3×C8—41no—
350C3⋊C8—201no—
351C22×C5—21no—
352C22×C5—21no—
353C22×C5—41no—
354C22×C5—41no—
355C22×C5—41no—
356C22×C5D3×C22⋊C411yescharacteristic
357C22×C5#91111yescharacteristic
358C22×C5#91511yescharacteristic
359C2×D5—32no—
360C2×D5—32no—
361C2×D5—64no—
362C2×D5—64no—
363C2×D5—61no—
364C2×D5—61no—
365C2×D5—61no—
366C2×D5—61no—
367C4×C5—21no—
368C4×C5—21no—
369C4×C5—42no—
370C4×C5—41no—
371Dic5—61no—
372Dic5—61no—
373Dic5—122no—
374Dic5—121no—
375Dic5—121no—
376C24—151no—
377#41—602no—
378C2×Q8—151no—
379C2×D4—21no—
380C2×D4—301no—
381C2×D4—301no—
382C2×D4C4×D1511yescharacteristic, complemented
383C22×C4—21no—
384C22×C4—151no—
385C22×C4—151no—
386C22×C4—151no—
387C22×C4—151no—
388C22×C4—151no—
389C22×C4—304no—
390C22×C4—301no—
391C22×C4—301no—
392C22×C4—602no—
393C22×C4—602no—
394C22×C4—602no—
395C22×C4C22×D1511yescharacteristic
396M16—602no—
397C2×C8—21no—
398C2×C8—301no—
399C4⋊C4—151no—
400C4⋊C4—301no—
401C4⋊C4—301no—
402C4⋊C4C4×D1511yescharacteristic, complemented
403C22⋊C4—21no—
404C22⋊C4—301no—
405C22⋊C4—301no—
406C22⋊C4—301no—
407C22⋊C4—301no—
408C42—301no—
409C3×C5#150411yescharacteristic, complemented, Hall
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—41no—
413C22×C3—41no—
414C22×C3—41no—
415C22×C3D5×C22⋊C411yescharacteristic
416C22×C3#405711yescharacteristic
417C22×C3#406111yescharacteristic
418C2×D3—52no—
419C2×D3—52no—
420C2×D3—104no—
421C2×D3—104no—
422C2×D3—101no—
423C2×D3—101no—
424C2×D3—101no—
425C2×D3—101no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—42no—
429C3×C4—41no—
430Dic3—101no—
431Dic3—101no—
432Dic3—202no—
433Dic3—201no—
434Dic3—201no—
435C2×C5—21no—
436C2×C5—21no—
437C2×C5—81no—
438C2×C5D3×#9911yescharacteristic
439C2×C5#477111yescharacteristic
440C2×C5D3×#10411yescharacteristic
441D5—62no—
442D5—62no—
443C23—21no—
444C23—151no—
445C23—151no—
446C23—302no—
447C23—302no—
448C23—301no—
449C23—301no—
450C23D4×D1511yescharacteristic
451Q8—601no—
452D4—41no—
453D4—41no—
454D4—41no—
455D4—602no—
456D4—602no—
457C2×C4—22no—
458C2×C4—21no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—151no—
463C2×C4—151no—
464C2×C4—302no—
465C2×C4—302no—
466C2×C4—302no—
467C2×C4—301no—
468C2×C4—301no—
469C2×C4—601no—
470C2×C4—601no—
471C2×C4—608no—
472C2×C4—601no—
473C2×C4—602no—
474C2×C4—601no—
475C2×C4—601no—
476C2×C4C2×C4×D1511yescharacteristic
477C2×C4D4×D1511yescharacteristic
478C8—41no—
479C8—601no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—81no—
483C2×C3D5×#9911yescharacteristic
484C2×C3#6506011yescharacteristic
485C2×C3D5×#10411yescharacteristic
486D3—102no—
487D3—102no—
488C5#6830211yescharacteristic, complemented, Sylow
489C22—21no—
490C22—21no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—152no—
495C22—152no—
496C22—304no—
497C22—304no—
498C22—301no—
499C22—301no—
500C22—301no—
501C22—301no—
502C22C22⋊C4×D1511yescharacteristic
503C22#9180011yescharacteristic
504C22#9180411yescharacteristic
505C4—21no—
506C4—21no—
507C4—42no—
508C4—41no—
509C4—301no—
510C4—301no—
511C4—602no—
512C4—601no—
513C4—601no—
514C3#1059909511yescharacteristic, complemented, Sylow
515C2—21no—
516C2—21no—
517C2—81no—
518C2—302no—
519C2—302no—
520C2D15×#9911yescharacteristic
521C2#1175087211yescharacteristic
522C2D15×#10411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#327C2
socleC22×C3×C5C2×C22⋊C4
prime radical#11756365C2
cosocleC22×C3×C4×C5C23
hypercenter#327D15
hypocenterC3×C5#1504
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #11750827C2semidirect
3. D15×#95C2semidirect
4. C3×C5×#327C2semidirect
5. #11746358C2semidirect
6. #11746288C2semidirect
7. #11746273C2semidirect
9. C2×#6819C4semidirect
13. #91827C4semidirect
18. #91786C4semidirect
19. #91781C4semidirect
32. C5×#327D3semidirect
38. C2×C3×C5×D4C2×C4semidirect
55. C2×Dic30C2×C4semidirect
57. C3×C5×C4⋊C4C2×C4semidirect
64. C4⋊Dic15C2×C4semidirect
72. C3×#327D5semidirect
154. C2×C5×D4C4×D3semidirect
173. C5×C4⋊C4C4×D3semidirect
191. #327D15semidirect
219. C2×C3×D4C4×D5semidirect
238. C3×C4⋊C4C4×D5semidirect
382. C2×D4C4×D15semidirect
402. C4⋊C4C4×D15semidirect
409. C3×C5#1504semidirect
488. C5#68302semidirect
514. C3#10599095semidirect

Maximal subgroups

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

subgroupindex
#117563652
#117508272
D15×#952
C3×C5×#3272
#117463582
#117462882
#117462732
#105990953
#683025