Finite Group Databasebeta

← #14282811

Subgroups — #14282811

Order 1920.

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

normal subgroups only

This group has 608 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
2D15×C22⋊C8C211yesmaximal, characteristic, complemented
3#11750767C211yesmaximal, characteristic, complemented
4C3×C5×#327C211yesmaximal, characteristic, complemented
5#11746358C211yesmaximal, characteristic, complemented
6#11746288C211yesmaximal, characteristic, complemented
7#11746273C211yesmaximal, characteristic, complemented
8#10599094—31nomaximal, Hall
9C2×#6819C411yescharacteristic, complemented
10C22×C4×D15C2211yescharacteristic
11C3×C5×#121C2211yescharacteristic
12#91827C411yescharacteristic, complemented
13#91826—21no—
14D4×Dic15—21no—
15C2×#6714—21no—
16#91813C2211yescharacteristic
17C2×C4×Dic15—21no—
18C2×C8×D15—21no—
19#91786C411yescharacteristic, complemented
20#91781C411yescharacteristic, complemented
21#91772—21no—
22#91770—21no—
23C3×C5×C22⋊C8C2211yescharacteristic
24C3×C5×#95C2211yescharacteristic
25#91115C2211yescharacteristic
26#91114C2211yescharacteristic
27#91104—21no—
28#68301—51nomaximal, Hall
29#65940—31no—
30D5×C22⋊C8—31no—
31#64955—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
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—42no—
48C2×C4×D15C2×C411yescharacteristic
49C2×C4×D15C2×C411yescharacteristic
50C2×C4×D15D411yescharacteristic
51C2×C4×D15D411yescharacteristic
52C2×Dic30C2×C411yescharacteristic
53C2×C3×C5×C8—21no—
54C3×C5×C4⋊C4C2×C411yescharacteristic
55C3×C5×C22⋊C4—21no—
56#6719—21no—
57#6719—21no—
58#6714—24no—
59#6714—21no—
60#6714—21no—
61C4⋊Dic15—21no—
62C4⋊Dic15C2×C411yescharacteristic
63#6712—21no—
64C4×Dic15—21no—
65C4×Dic15—42no—
66C2×C3⋊#168—21no—
67C8×D15—42no—
68#5606—51no—
69D3×C22⋊C8—51no—
70#4666—51no—
71C3×#327D511yescharacteristic, complemented
72#4537—51no—
73#4467—51no—
74#4452—51no—
75C2×#711—31no—
76C22×C4×D5—31no—
77C5×#121C2×D311yescharacteristic
78#4084—31no—
79#4083—61no—
80D4×Dic5—61no—
81C2×#685—61no—
82#4070—31no—
83C2×C4×Dic5—61no—
84C2×C8×D5—61no—
85#4043—31no—
86#4038—31no—
87#4029—61no—
88#4027—61no—
89C5×C22⋊C8C2×D311yescharacteristic
90C5×#95C2×D311yescharacteristic
91#3963—31no—
92C22⋊#168—31no—
93#3952—61no—
94#1501—151noSylow
95C23×C3×C5—21no—
96C23×C3×C5C2×D411yescharacteristic
97C22×D15—21no—
98C22×D15—21no—
99C22×D15—22no—
100C22×D15—41no—
101C22×D15C22⋊C411yescharacteristic
102C22×D15C22⋊C411yescharacteristic
103C3×C5×D4—41no—
104C3×C5×D4—41no—
105C3×C5×D4—41no—
106C2×C3×C4×C5—22no—
107C2×C3×C4×C5—21no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5C22×C411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113#1220—42no—
114#1220—42no—
115C2×Dic15—22no—
116C2×Dic15—22no—
117C2×Dic15—21no—
118C2×Dic15—21no—
119C2×Dic15—41no—
120C2×Dic15—41no—
121C2×Dic15—42no—
122C2×Dic15C22⋊C411yescharacteristic
123C2×Dic15C22⋊C411yescharacteristic
124C4×D15—22no—
125C4×D15—22no—
126C4×D15—41no—
127C4×D15—41no—
128Dic30—41no—
129C3×C5×C8—41no—
130C3⋊#168—41no—
131C2×#237—51no—
132C22×C4×D3—51no—
133C3×#121C2×D511yescharacteristic
134#938—51no—
135#937—101no—
136D4×Dic3—101no—
137C2×(C2×D3)⋊C4—101no—
138#924—51no—
139C2×C4×Dic3—101no—
140C2×D3×C8—101no—
141#897—51no—
142#892—51no—
143#883—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×D4—21no—
152C2×C5×D4C4×D311yescharacteristic
153C22×C4×C5—21no—
154C22×C4×C5C22×D311yescharacteristic
155C2×C22⋊D5—61no—
156C2×C22⋊D5—61no—
157C22×Dic5—31no—
158C22×Dic5—61no—
159C22×Dic5—61no—
160#711—122no—
161C2×C4×D5—31no—
162C2×C4×D5—31no—
163C2×C4×D5—31no—
164C2×C4×D5—31no—
165C2×C4×D5—122no—
166C2×Dic10—31no—
167C2×C5×C8—21no—
168C5×C4⋊C4C4×D311yescharacteristic
169C5×C22⋊C4—21no—
170C22⋊Dic5—61no—
171C22⋊Dic5—61no—
172#685—61no—
173#685—61no—
174#685—64no—
175C4⋊Dic5—31no—
176C4⋊Dic5—61no—
177#683—61no—
178C4×Dic5—61no—
179C4×Dic5—122no—
180C2×#168—61no—
181C8×D5—122no—
182#525—151no—
183C2×C22⋊C8—151no—
184C4×C22⋊C4—151no—
185#328—151no—
186#328—151no—
187#327—151no—
188#327D1511yescharacteristic, complemented
189C22×C3×C5—21no—
190C22×C3×C5—21no—
191C22×C3×C5—41no—
192C22×C3×C5—41no—
193C22×C3×C5—41no—
194C22×C3×C5C2×C22⋊C411yescharacteristic
195C22×C3×C5#13511yescharacteristic
196C22×C3×C5#13511yescharacteristic
197C2×D15—21no—
198C2×D15—21no—
199C2×D15—21no—
200C2×D15—21no—
201C2×D15—21no—
202C2×D15—42no—
203C2×D15—42no—
204C2×D15#10412yes—
205C3×C4×C5—21no—
206C3×C4×C5—21no—
207C3×C4×C5—42no—
208C3×C4×C5—41no—
209Dic15—21no—
210Dic15—42no—
211Dic15—41no—
212Dic15—41no—
213Dic15#9912yes—
214C23×D3—51no—
215C2×C3×D4—21no—
216C2×C3×D4C4×D511yescharacteristic
217C22×C3×C4—21no—
218C22×C3×C4C22×D511yescharacteristic
219C2×#67—101no—
220C2×#67—101no—
221C22×Dic3—51no—
222C22×Dic3—101no—
223C22×Dic3—101no—
224#237—202no—
225C2×C4×D3—51no—
226C2×C4×D3—51no—
227C2×C4×D3—51no—
228C2×C4×D3—51no—
229C2×C4×D3—202no—
230C2×Dic6—51no—
231C2×C3×C8—21no—
232C3×C4⋊C4C4×D511yescharacteristic
233C3×C22⋊C4—21no—
234#217—101no—
235#217—101no—
236(C2×D3)⋊C4—101no—
237(C2×D3)⋊C4—101no—
238(C2×D3)⋊C4—104no—
239C4⋊Dic3—51no—
240C4⋊Dic3—101no—
241Dic3⋊C4—101no—
242C4×Dic3—101no—
243C4×Dic3—202no—
244C2×C3⋊C8—101no—
245D3×C8—202no—
246C23×C5—21no—
247C23×C5D3×D411yescharacteristic
248C22×D5—31no—
249C22×D5—31no—
250C22×D5—62no—
251C22×D5—61no—
252C22×D5—61no—
253C22×D5—121no—
254C5×D4—41no—
255C5×D4—41no—
256C5×D4—41no—
257C2×C4×C5—22no—
258C2×C4×C5—21no—
259C2×C4×C5—41no—
260C2×C4×C5—41no—
261C2×C4×C5—41no—
262C2×C4×C5C2×C4×D311yescharacteristic
263C2×C4×C5D3×D411yescharacteristic
264C22⋊D5—122no—
265C22⋊D5—122no—
266C2×Dic5—31no—
267C2×Dic5—31no—
268C2×Dic5—62no—
269C2×Dic5—62no—
270C2×Dic5—61no—
271C2×Dic5—61no—
272C2×Dic5—122no—
273C2×Dic5—121no—
274C2×Dic5—121no—
275C4×D5—62no—
276C4×D5—62no—
277C4×D5—121no—
278C4×D5—121no—
279Dic10—121no—
280C5×C8—41no—
281#168—121no—
282C2×#41—151no—
283C23×C4—151no—
284C22×C8—301no—
285#123—301no—
286C22⋊Q8—151no—
287C22⋊Q8—151no—
288#121—151no—
289#121C2×D1511yescharacteristic
290#120—301no—
291C4×D4—301no—
292C4×D4—301no—
293#117—151no—
294C2×C22⋊C4—301no—
295C2×C42—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×C5—81no—
304C2×C3×C5C2×#9911yescharacteristic
305C2×C3×C5#41611yescharacteristic
306C2×C3×C5C2×#10411yescharacteristic
307D15—22no—
308D15—41no—
309C23×C3—21no—
310C23×C3D4×D511yescharacteristic
311C22×D3—51no—
312C22×D3—51no—
313C22×D3—102no—
314C22×D3—101no—
315C22×D3—101no—
316C22×D3—201no—
317C3×D4—41no—
318C3×D4—41no—
319C3×D4—41no—
320C2×C3×C4—22no—
321C2×C3×C4—21no—
322C2×C3×C4—41no—
323C2×C3×C4—41no—
324C2×C3×C4—41no—
325C2×C3×C4C2×C4×D511yescharacteristic
326C2×C3×C4D4×D511yescharacteristic
327#67—202no—
328#67—202no—
329C2×Dic3—51no—
330C2×Dic3—51no—
331C2×Dic3—102no—
332C2×Dic3—102no—
333C2×Dic3—101no—
334C2×Dic3—101no—
335C2×Dic3—202no—
336C2×Dic3—201no—
337C2×Dic3—201no—
338C4×D3—102no—
339C4×D3—102no—
340C4×D3—201no—
341C4×D3—201no—
342Dic6—201no—
343C3×C8—41no—
344C3⋊C8—201no—
345C22×C5—21no—
346C22×C5—21no—
347C22×C5—41no—
348C22×C5—41no—
349C22×C5—41no—
350C22×C5D3×C22⋊C411yescharacteristic
351C22×C5#91211yescharacteristic
352C22×C5#91611yescharacteristic
353C2×D5—32no—
354C2×D5—61no—
355C2×D5—61no—
356C2×D5—61no—
357C2×D5—61no—
358C2×D5—61no—
359C2×D5—122no—
360C2×D5—122no—
361C4×C5—21no—
362C4×C5—21no—
363C4×C5—42no—
364C4×C5—41no—
365Dic5—32no—
366Dic5—61no—
367Dic5—122no—
368Dic5—121no—
369Dic5—121no—
370C24—151no—
371#41—602no—
372C2×Q8—151no—
373C2×D4—21no—
374C2×D4—301no—
375C2×D4—301no—
376C2×D4C4×D1511yescharacteristic
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
387C2×C8—21no—
388C2×C8—301no—
389C2×C8—602no—
390C4⋊C4—151no—
391C4⋊C4—301no—
392C4⋊C4—301no—
393C4⋊C4C4×D1511yescharacteristic
394C22⋊C4—21no—
395C22⋊C4—301no—
396C22⋊C4—301no—
397C22⋊C4—304no—
398C22⋊C4—301no—
399C22⋊C4—301no—
400C42—301no—
401C42—602no—
402C3×C5#150111yescharacteristic, complemented, Hall
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—41no—
406C22×C3—41no—
407C22×C3—41no—
408C22×C3D5×C22⋊C411yescharacteristic
409C22×C3#405811yescharacteristic
410C22×C3#406211yescharacteristic
411C2×D3—52no—
412C2×D3—101no—
413C2×D3—101no—
414C2×D3—101no—
415C2×D3—101no—
416C2×D3—101no—
417C2×D3—202no—
418C2×D3—202no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—42no—
422C3×C4—41no—
423Dic3—52no—
424Dic3—101no—
425Dic3—202no—
426Dic3—201no—
427Dic3—201no—
428C2×C5—21no—
429C2×C5—21no—
430C2×C5—81no—
431C2×C5D3×#9911yescharacteristic
432C2×C5#477211yescharacteristic
433C2×C5D3×#10411yescharacteristic
434D5—62no—
435D5—121no—
436C23—21no—
437C23—151no—
438C23—151no—
439C23—302no—
440C23—301no—
441C23—301no—
442C23—601no—
443C23D4×D1511yescharacteristic
444Q8—601no—
445D4—41no—
446D4—41no—
447D4—41no—
448D4—602no—
449D4—602no—
450C2×C4—22no—
451C2×C4—21no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—151no—
456C2×C4—151no—
457C2×C4—302no—
458C2×C4—302no—
459C2×C4—302no—
460C2×C4—302no—
461C2×C4—301no—
462C2×C4—301no—
463C2×C4—601no—
464C2×C4—601no—
465C2×C4—602no—
466C2×C4—601no—
467C2×C4—601no—
468C2×C4C2×C4×D1511yescharacteristic
469C2×C4D4×D1511yescharacteristic
470C8—41no—
471C8—601no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—81no—
475C2×C3D5×#9911yescharacteristic
476C2×C3#6506111yescharacteristic
477C2×C3D5×#10411yescharacteristic
478D3—102no—
479D3—201no—
480C5#6830111yescharacteristic, complemented, Sylow
481C22—21no—
482C22—21no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—152no—
487C22—301no—
488C22—301no—
489C22—301no—
490C22—301no—
491C22—301no—
492C22—602no—
493C22—602no—
494C22C22⋊C4×D1511yescharacteristic
495C22#9180111yescharacteristic
496C22#9180511yescharacteristic
497C4—21no—
498C4—21no—
499C4—42no—
500C4—41no—
501C4—152no—
502C4—301no—
503C4—602no—
504C4—601no—
505C4—601no—
506C3#1059909411yescharacteristic, complemented, Sylow
507C2—21no—
508C2—21no—
509C2—81no—
510C2—302no—
511C2—601no—
512C2D15×#9911yescharacteristic
513C2#1175087311yescharacteristic
514C2D15×#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#1501
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. D15×C22⋊C8C2semidirect
3. #11750767C2semidirect
4. C3×C5×#327C2semidirect
5. #11746358C2semidirect
6. #11746288C2semidirect
7. #11746273C2semidirect
9. C2×#6819C4semidirect
12. #91827C4semidirect
19. #91786C4semidirect
20. #91781C4semidirect
32. C5×#327D3semidirect
71. C3×#327D5semidirect
188. #327D15semidirect
402. C3×C5#1501semidirect
480. C5#68301semidirect
506. C3#10599094semidirect

Maximal subgroups

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

subgroupindex
#117563652
D15×C22⋊C82
#117507672
C3×C5×#3272
#117463582
#117462882
#117462732
#105990943
#683015