Finite Group Databasebeta

← #14283413

Subgroups — #14283413

Order 1920.

572 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 97 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#11756386C211yesmaximal, characteristic
2#11750827C211yesmaximal, characteristic, complemented
3#11750768C211yesmaximal, characteristic, complemented
4C3×C5×#328C211yesmaximal, characteristic, complemented
5#11746359C211yesmaximal, characteristic, complemented
6#11746291C211yesmaximal, characteristic, complemented
7#11746272C211yesmaximal, characteristic, complemented
8#10599130—31nomaximal, Hall
9C2×#6821C411yescharacteristic, complemented
10C22×C4×D15C2211yescharacteristic
11C3×C5×C22⋊Q8C2211yescharacteristic
12#91835C411yescharacteristic, complemented
13#91819C2211yescharacteristic
14C2×#6714—21no—
15C2×#6712—21no—
16C2×#6705—21no—
17#91784C411yescharacteristic, complemented
18#91783—21no—
19#91782—21no—
20#91781C411yescharacteristic, complemented
21#91771—21no—
22#91770—21no—
23C3×C5×C22⋊C8C2211yescharacteristic
24C3×C5×#95C2211yescharacteristic
25#91115C2211yescharacteristic
26#91114C2211yescharacteristic
27#91104—21no—
28#68337—51nomaximal, Hall
29#65961—31no—
30#65015—31no—
31#64956—31no—
32C5×#328D311yescharacteristic, complemented
33#64758—31no—
34#64690—31no—
35#64671—31no—
36C23×D15D411yescharacteristic
37C2×C3×C5×Q8C2×C411yescharacteristic
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5C2311yescharacteristic
40C2×#1220—21no—
41C22×Dic15—21no—
42C22×Dic15D411yescharacteristic
43#6821—42no—
44C2×D60—21no—
45C2×D60—21no—
46C2×D60C2×C411yescharacteristic
47C2×C4×D15—21no—
48C2×C4×D15—42no—
49C2×C4×D15C2×C411yescharacteristic
50C2×C4×D15C2×C411yescharacteristic
51C2×C4×D15D411yescharacteristic
52C2×C4×D15D411yescharacteristic
53C2×C3×C5×C8—21no—
54C3×C5×C4⋊C4—21no—
55C3×C5×C4⋊C4C2×C411yescharacteristic
56C3×C5×C22⋊C4—21no—
57#6714—21no—
58#6714—21no—
59#6714—21no—
60#6714—21no—
61#6714—42no—
62C4⋊Dic15C2×C411yescharacteristic
63#6712—21no—
64#6712—42no—
65C4×Dic15—21no—
66C2×C3⋊#168—21no—
67#6705—42no—
68#5627—51no—
69#4726—51no—
70#4667—51no—
71C3×#328D511yescharacteristic, complemented
72#4538—51no—
73#4470—51no—
74#4451—51no—
75C2×#713—31no—
76C22×C4×D5—31no—
77C5×C22⋊Q8C2×D311yescharacteristic
78#4092—31no—
79#4076—31no—
80C2×#685—61no—
81C2×#683—61no—
82C2×#676—61no—
83#4041—31no—
84#4040—61no—
85#4039—61no—
86#4038—31no—
87#4028—61no—
88#4027—61no—
89C5×C22⋊C8C2×D311yescharacteristic
90C5×#95C2×D311yescharacteristic
91#3963—31no—
92C22⋊#168—31no—
93#3952—61no—
94#1513—151noSylow
95C23×C3×C5C2×D411yescharacteristic
96C22×D15—21no—
97C22×D15—21no—
98C22×D15—21no—
99C22×D15—41no—
100C22×D15—41no—
101C22×D15C22⋊C411yescharacteristic
102C22×D15C22⋊C411yescharacteristic
103C3×C5×Q8—41no—
104C2×C3×C4×C5—21no—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5—41no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5C22×C411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112#1220—41no—
113#1220—41no—
114C2×Dic15—22no—
115C2×Dic15—21no—
116C2×Dic15—41no—
117C2×Dic15—41no—
118C2×Dic15—41no—
119C2×Dic15C22⋊C411yescharacteristic
120C2×Dic15C22⋊C411yescharacteristic
121D60—41no—
122D60—42no—
123D60—42no—
124C4×D15—22no—
125C4×D15—22no—
126C4×D15—41no—
127C4×D15—41no—
128C4×D15—42no—
129C3×C5×C8—41no—
130C3⋊#168—41no—
131C2×#239—51no—
132C22×C4×D3—51no—
133C3×C22⋊Q8C2×D511yescharacteristic
134#946—51no—
135#930—51no—
136C2×(C2×D3)⋊C4—101no—
137C2×Dic3⋊C4—101no—
138C2×ΓL(1,𝔽25)—101no—
139#895—51no—
140#894—101no—
141#893—101no—
142#892—51no—
143#882—101no—
144#67⋊C4—101no—
145C3×C22⋊C8C2×D511yescharacteristic
146C3×#95C2×D511yescharacteristic
147C3⋊#95—51no—
148#830—51no—
149(C2×D3)⋊C8—101no—
150C23×D5—31no—
151C2×C5×Q8C4×D311yescharacteristic
152C22×C4×C5—21no—
153C22×C4×C5C22×D311yescharacteristic
154C2×C22⋊D5—61no—
155C22×Dic5—31no—
156C22×Dic5—61no—
157#713—122no—
158C2×D20—31no—
159C2×D20—61no—
160C2×D20—61no—
161C2×C4×D5—31no—
162C2×C4×D5—31no—
163C2×C4×D5—31no—
164C2×C4×D5—31no—
165C2×C4×D5—61no—
166C2×C4×D5—122no—
167C2×C5×C8—21no—
168C5×C4⋊C4—21no—
169C5×C4⋊C4C4×D311yescharacteristic
170C5×C22⋊C4—21no—
171#685—61no—
172#685—61no—
173#685—61no—
174#685—61no—
175#685—122no—
176C4⋊Dic5—31no—
177#683—61no—
178#683—122no—
179C4×Dic5—61no—
180C2×#168—61no—
181#676—122no—
182#525—151no—
183#407—151no—
184#380—151no—
185#328—151no—
186#328D1511yescharacteristic, complemented
187#327—151no—
188#327—151no—
189C22×C3×C5—21no—
190C22×C3×C5—21no—
191C22×C3×C5C2×C22⋊C411yescharacteristic
192C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
193C22×C3×C5#13711yescharacteristic
194C2×D15—21no—
195C2×D15—21no—
196C2×D15—21no—
197C2×D15—21no—
198C2×D15—21no—
199C2×D15—21no—
200C2×D15—42no—
201C2×D15—42no—
202C2×D15—41no—
203C2×D15—41no—
204C2×D15—41no—
205C3×C4×C5—21no—
206C3×C4×C5—21no—
207C3×C4×C5—41no—
208C3×C4×C5—41no—
209C3×C4×C5—81no—
210Dic15—21no—
211Dic15—41no—
212Dic15—81no—
213Dic15#9912yes—
214C23×D3—51no—
215C2×C3×Q8C4×D511yescharacteristic
216C22×C3×C4—21no—
217C22×C3×C4C22×D511yescharacteristic
218C2×#67—101no—
219C22×Dic3—51no—
220C22×Dic3—101no—
221#239—202no—
222C2×D12—51no—
223C2×D12—101no—
224C2×D12—101no—
225C2×C4×D3—51no—
226C2×C4×D3—51no—
227C2×C4×D3—51no—
228C2×C4×D3—51no—
229C2×C4×D3—101no—
230C2×C4×D3—202no—
231C2×C3×C8—21no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4C4×D511yescharacteristic
234C3×C22⋊C4—21no—
235(C2×D3)⋊C4—101no—
236(C2×D3)⋊C4—101no—
237(C2×D3)⋊C4—101no—
238(C2×D3)⋊C4—101no—
239(C2×D3)⋊C4—202no—
240C4⋊Dic3—51no—
241Dic3⋊C4—101no—
242Dic3⋊C4—202no—
243C4×Dic3—101no—
244C2×C3⋊C8—101no—
245ΓL(1,𝔽25)—202no—
246C23×C5D3×D411yescharacteristic
247C22×D5—31no—
248C22×D5—31no—
249C22×D5—61no—
250C22×D5—61no—
251C22×D5—61no—
252C22×D5—121no—
253C22×D5—121no—
254C5×Q8—41no—
255C2×C4×C5—21no—
256C2×C4×C5—21no—
257C2×C4×C5—41no—
258C2×C4×C5—41no—
259C2×C4×C5—41no—
260C2×C4×C5—41no—
261C2×C4×C5C2×C4×D311yescharacteristic
262C2×C4×C5D3×D411yescharacteristic
263C22⋊D5—121no—
264C22⋊D5—121no—
265C2×Dic5—31no—
266C2×Dic5—31no—
267C2×Dic5—62no—
268C2×Dic5—61no—
269C2×Dic5—121no—
270C2×Dic5—121no—
271C2×Dic5—121no—
272D20—121no—
273D20—122no—
274D20—122no—
275C4×D5—62no—
276C4×D5—62no—
277C4×D5—122no—
278C4×D5—121no—
279C4×D5—121no—
280C5×C8—41no—
281#168—121no—
282C2×#41—151no—
283C23×C4—151no—
284C2×M16—301no—
285#123—301no—
286C22⋊Q8—151no—
287C22⋊Q8C2×D1511yescharacteristic
288#121—151no—
289#121—151no—
290#120—301no—
291C4×D4—301no—
292C4×D4—301no—
293#117—151no—
294C2×C4⋊C4—301no—
295C2×C22⋊C4—301no—
296C22⋊C8—151no—
297C22⋊C8—301no—
298C22⋊C8C2×D1511yescharacteristic
299#95—151no—
300#95C2×D1511yescharacteristic
301C2×C3×C5—21no—
302C2×C3×C5—21no—
303C2×C3×C5C2×#9911yescharacteristic
304C2×C3×C5#41711yescharacteristic
305C2×C3×C5#42111yescharacteristic
306D15—41no—
307D15—41no—
308D15—81no—
309C23×C3D4×D511yescharacteristic
310C22×D3—51no—
311C22×D3—51no—
312C22×D3—101no—
313C22×D3—101no—
314C22×D3—101no—
315C22×D3—201no—
316C22×D3—201no—
317C3×Q8—41no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—41no—
324C2×C3×C4C2×C4×D511yescharacteristic
325C2×C3×C4D4×D511yescharacteristic
326#67—201no—
327#67—201no—
328C2×Dic3—51no—
329C2×Dic3—51no—
330C2×Dic3—102no—
331C2×Dic3—101no—
332C2×Dic3—201no—
333C2×Dic3—201no—
334C2×Dic3—201no—
335D12—201no—
336D12—202no—
337D12—202no—
338C4×D3—102no—
339C4×D3—102no—
340C4×D3—202no—
341C4×D3—201no—
342C4×D3—201no—
343C3×C8—41no—
344C3⋊C8—201no—
345C22×C5—21no—
346C22×C5—21no—
347C22×C5D3×C22⋊C411yescharacteristic
348C22×C5#91411yescharacteristic
349C22×C5#91811yescharacteristic
350C2×D5—61no—
351C2×D5—61no—
352C2×D5—61no—
353C2×D5—61no—
354C2×D5—61no—
355C2×D5—61no—
356C2×D5—122no—
357C2×D5—122no—
358C2×D5—121no—
359C2×D5—121no—
360C2×D5—121no—
361C4×C5—21no—
362C4×C5—21no—
363C4×C5—41no—
364C4×C5—41no—
365C4×C5—81no—
366Dic5—32no—
367Dic5—61no—
368Dic5—121no—
369Dic5—241no—
370C24—151no—
371#41—602no—
372C2×Q8C4×D1511yescharacteristic
373C2×D4—151no—
374C2×D4—301no—
375C2×D4—301no—
376C2×D4—301no—
377C22×C4—21no—
378C22×C4—151no—
379C22×C4—151no—
380C22×C4—151no—
381C22×C4—151no—
382C22×C4—151no—
383C22×C4—301no—
384C22×C4—301no—
385C22×C4—602no—
386C22×C4C22×D1511yescharacteristic
387M16—602no—
388C2×C8—21no—
389C2×C8—301no—
390C4⋊C4—21no—
391C4⋊C4—151no—
392C4⋊C4—301no—
393C4⋊C4—602no—
394C4⋊C4C4×D1511yescharacteristic
395C22⋊C4—21no—
396C22⋊C4—301no—
397C22⋊C4—301no—
398C22⋊C4—301no—
399C22⋊C4—301no—
400C22⋊C4—602no—
401C42—301no—
402C3×C5#151311yescharacteristic, complemented, Hall
403C22×C3—21no—
404C22×C3—21no—
405C22×C3D5×C22⋊C411yescharacteristic
406C22×C3#406011yescharacteristic
407C22×C3#406411yescharacteristic
408C2×D3—101no—
409C2×D3—101no—
410C2×D3—101no—
411C2×D3—101no—
412C2×D3—101no—
413C2×D3—101no—
414C2×D3—202no—
415C2×D3—202no—
416C2×D3—201no—
417C2×D3—201no—
418C2×D3—201no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—41no—
422C3×C4—41no—
423C3×C4—81no—
424Dic3—52no—
425Dic3—101no—
426Dic3—201no—
427Dic3—401no—
428C2×C5—21no—
429C2×C5—21no—
430C2×C5D3×#9911yescharacteristic
431C2×C5#480311yescharacteristic
432C2×C5#482111yescharacteristic
433D5—121no—
434D5—121no—
435D5—241no—
436C23—151no—
437C23—151no—
438C23—301no—
439C23—301no—
440C23—301no—
441C23—601no—
442C23—601no—
443C23D4×D1511yescharacteristic
444Q8—41no—
445D4—601no—
446D4—602no—
447D4—602no—
448D4—601no—
449D4—601no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—151no—
457C2×C4—151no—
458C2×C4—302no—
459C2×C4—302no—
460C2×C4—302no—
461C2×C4—301no—
462C2×C4—601no—
463C2×C4—601no—
464C2×C4—602no—
465C2×C4—601no—
466C2×C4—601no—
467C2×C4—601no—
468C2×C4C2×C4×D1511yescharacteristic
469C2×C4D4×D1511yescharacteristic
470C8—41no—
471C8—601no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3D5×#9911yescharacteristic
475C2×C3#6509211yescharacteristic
476C2×C3#6511011yescharacteristic
477D3—201no—
478D3—201no—
479D3—401no—
480C5#6833711yescharacteristic, complemented, Sylow
481C22—21no—
482C22—21no—
483C22—301no—
484C22—301no—
485C22—301no—
486C22—301no—
487C22—301no—
488C22—301no—
489C22—602no—
490C22—602no—
491C22—601no—
492C22—601no—
493C22—601no—
494C22C22⋊C4×D1511yescharacteristic
495C22#9180311yescharacteristic
496C22#9180711yescharacteristic
497C4—21no—
498C4—21no—
499C4—41no—
500C4—41no—
501C4—81no—
502C4—152no—
503C4—301no—
504C4—601no—
505C4—1201no—
506C3#1059913011yescharacteristic, complemented, Sylow
507C2—21no—
508C2—21no—
509C2—601no—
510C2—601no—
511C2—1201no—
512C2D15×#9911yescharacteristic
513C2#1175090411yescharacteristic
514C2#1175092211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#328C2
socleC22×C3×C5C2×C22⋊C4
prime radical#11756386C2
cosocleC22×C3×C4×C5C23
hypercenter#328D15
hypocenterC3×C5#1513
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #11750827C2semidirect
3. #11750768C2semidirect
4. C3×C5×#328C2semidirect
5. #11746359C2semidirect
6. #11746291C2semidirect
7. #11746272C2semidirect
9. C2×#6821C4semidirect
12. #91835C4semidirect
17. #91784C4semidirect
20. #91781C4semidirect
32. C5×#328D3semidirect
71. C3×#328D5semidirect
186. #328D15semidirect
402. C3×C5#1513semidirect
480. C5#68337semidirect
506. C3#10599130semidirect

Maximal subgroups

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

subgroupindex
#117563862
#117508272
#117507682
C3×C5×#3282
#117463592
#117462912
#117462722
#105991303
#683375