Finite Group Databasebeta

← #14288391

Subgroups — #14288391

Order 1920.

508 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 85 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#11756356C211yesmaximal, characteristic
2#11751134C211yesmaximal, characteristic, complemented
3#11750837C211yesmaximal, characteristic, complemented
4#11750762C211yesmaximal, characteristic, complemented
5C3×C5×#327C211yesmaximal, characteristic, complemented
6#11746290C211yesmaximal, characteristic, complemented
7#11746272C211yesmaximal, characteristic, complemented
8#10599090—31nomaximal, Hall
9C2×#6819—21no—
10C3×C5×#121C2211yescharacteristic
11#91828—21no—
12#91828—21no—
13#91819C2211yescharacteristic
14C2×C4⋊Dic15—21no—
15C2×C4⋊Dic15C2211yescharacteristic
16C2×#6712C2211yescharacteristic
17#91785—21no—
18#91773—21no—
19#91767—21no—
20C3×C5×C22⋊C8C2211yescharacteristic
21C3×C5×#95C2211yescharacteristic
22#91116—21no—
23#91115—21no—
24#91114C2211yescharacteristic
25#91105—21no—
26#91102—21no—
27#91091—21no—
28#68297—51nomaximal, Hall
29#65931—31no—
30#65322—31no—
31#65025—31no—
32#64950—31no—
33C5×#327D311yescharacteristic, complemented
34#64689—31no—
35#64671—31no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4D411yescharacteristic
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5C2311yescharacteristic
40C2×#1220—21no—
41C2×#1220—21no—
42C2×#1220—21no—
43C22×Dic15—21no—
44C22×Dic15—21no—
45C22×Dic15D411yescharacteristic
46C22×Dic15D411yescharacteristic
47#6819—42no—
48#6819—42no—
49C2×D60D411yescharacteristic
50C2×C4×D15—21no—
51C2×Dic30—21no—
52C2×C3×C5×C8—21no—
53C3×C5×C4⋊C4D411yescharacteristic
54C3×C5×C22⋊C4—21no—
55#6719—21no—
56#6714—21no—
57#6714—21no—
58C4⋊Dic15—21no—
59C4⋊Dic15—21no—
60C4⋊Dic15—42no—
61C4⋊Dic15D411yescharacteristic
62#6712—21no—
63#6712—21no—
64#6712—21no—
65C2×C3⋊#168—21no—
66#5597—51no—
67#5033—51no—
68#4736—51no—
69#4661—51no—
70C3×#327D511yescharacteristic, complemented
71#4469—51no—
72#4451—51no—
73C2×#711—61no—
74C5×#121C2×D311yescharacteristic
75#4085—61no—
76#4085—61no—
77#4076—31no—
78C2×C4⋊Dic5—31no—
79C2×C4⋊Dic5—61no—
80C2×#683—31no—
81#4042—61no—
82#4030—61no—
83#4024—61no—
84C5×C22⋊C8C2×D311yescharacteristic
85C5×#95C2×D311yescharacteristic
86#3964—61no—
87#3963—61no—
88C22⋊#168—31no—
89#3953—61no—
90#3950—61no—
91#3939—61no—
92#1610—151noSylow
93C23×C3×C5—21no—
94C23×C3×C5C2×D411yescharacteristic
95C22×D15—21no—
96C3×C5×D4—41no—
97C3×C5×D4—41no—
98C3×C5×D4—41no—
99C2×C3×C4×C5—22no—
100C2×C3×C4×C5—21no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106#1220—42no—
107#1220—41no—
108#1220—41no—
109#1220—81no—
110C2×Dic15—21no—
111C2×Dic15—21no—
112C2×Dic15—21no—
113C2×Dic15—21no—
114C2×Dic15—42no—
115C2×Dic15—41no—
116C2×Dic15—41no—
117C2×Dic15—41no—
118C2×Dic15—41no—
119C2×Dic15D812yes—
120D60—41no—
121C4×D15—42no—
122Dic30—42no—
123C3×C5×C8—41no—
124C3⋊#168—41no—
125C2×#237—101no—
126C3×#121C2×D511yescharacteristic
127#939—101no—
128#939—101no—
129#930—51no—
130C2×C4⋊Dic3—51no—
131C2×C4⋊Dic3—101no—
132C2×Dic3⋊C4—51no—
133#896—101no—
134#884—101no—
135#878—101no—
136C3×C22⋊C8C2×D511yescharacteristic
137C3×#95C2×D511yescharacteristic
138#832—101no—
139C3⋊#95—101no—
140#830—51no—
141#821—101no—
142#818—101no—
143#807—101no—
144C2×C5×D4—21no—
145C2×C5×D4D1211yescharacteristic
146C22×C4×C5—21no—
147C22×C4×C5C22×D311yescharacteristic
148C2×C22⋊D5—61no—
149C2×C22⋊D5—61no—
150C2×C22⋊D5—61no—
151C22×Dic5—31no—
152C22×Dic5—31no—
153C22×Dic5—61no—
154C22×Dic5—61no—
155#711—122no—
156#711—122no—
157C2×D20—31no—
158C2×C4×D5—61no—
159C2×Dic10—61no—
160C2×C5×C8—21no—
161C5×C4⋊C4D1211yescharacteristic
162C5×C22⋊C4—21no—
163C22⋊Dic5—61no—
164#685—61no—
165#685—61no—
166C4⋊Dic5—31no—
167C4⋊Dic5—61no—
168C4⋊Dic5—61no—
169C4⋊Dic5—122no—
170#683—61no—
171#683—61no—
172#683—61no—
173C2×#168—61no—
174#537—151no—
175#480—151no—
176#480—151no—
177#398—151no—
178#327—151no—
179#327D1511yescharacteristic, complemented
180#324—151no—
181C22×C3×C5—21no—
182C22×C3×C5—21no—
183C22×C3×C5—41no—
184C22×C3×C5—41no—
185C22×C3×C5—41no—
186C22×C3×C5#12011yescharacteristic
187C22×C3×C5C2×D811yescharacteristic
188C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
189C2×D15—41no—
190C2×D15—41no—
191C2×D15—41no—
192C3×C4×C5—21no—
193C3×C4×C5—21no—
194C3×C4×C5—42no—
195C3×C4×C5—41no—
196Dic15—22no—
197Dic15—41no—
198Dic15—41no—
199Dic15—81no—
200C2×C3×D4—21no—
201C2×C3×D4D2011yescharacteristic
202C22×C3×C4—21no—
203C22×C3×C4C22×D511yescharacteristic
204C2×#67—101no—
205C2×#67—101no—
206C2×#67—101no—
207C22×Dic3—51no—
208C22×Dic3—51no—
209C22×Dic3—101no—
210C22×Dic3—101no—
211#237—202no—
212#237—202no—
213C2×D12—51no—
214C2×C4×D3—101no—
215C2×Dic6—101no—
216C2×C3×C8—21no—
217C3×C4⋊C4D2011yescharacteristic
218C3×C22⋊C4—21no—
219#217—101no—
220(C2×D3)⋊C4—101no—
221(C2×D3)⋊C4—101no—
222C4⋊Dic3—51no—
223C4⋊Dic3—101no—
224C4⋊Dic3—101no—
225C4⋊Dic3—202no—
226Dic3⋊C4—101no—
227Dic3⋊C4—101no—
228Dic3⋊C4—101no—
229C2×C3⋊C8—101no—
230C23×C5—21no—
231C23×C5D3×D411yescharacteristic
232C22×D5—61no—
233C5×D4—41no—
234C5×D4—41no—
235C5×D4—41no—
236C2×C4×C5—22no—
237C2×C4×C5—21no—
238C2×C4×C5—41no—
239C2×C4×C5—41no—
240C2×C4×C5—41no—
241C2×C4×C5C2×D1211yescharacteristic
242C2×C4×C5D3×D411yescharacteristic
243C22⋊D5—122no—
244C22⋊D5—121no—
245C22⋊D5—121no—
246C22⋊D5—241no—
247C2×Dic5—32no—
248C2×Dic5—61no—
249C2×Dic5—61no—
250C2×Dic5—61no—
251C2×Dic5—61no—
252C2×Dic5—122no—
253C2×Dic5—121no—
254C2×Dic5—121no—
255C2×Dic5—121no—
256C2×Dic5—121no—
257D20—121no—
258C4×D5—122no—
259Dic10—122no—
260C5×C8—41no—
261#168—121no—
262C2×#41—301no—
263C22⋊Q8—301no—
264C22⋊Q8—301no—
265#121—151no—
266#121—301no—
267#121—301no—
268#121—301no—
269#121C2×D1511yescharacteristic
270C2×C4⋊C4—151no—
271C2×C4⋊C4—151no—
272C2×C4⋊C4—301no—
273#107—301no—
274#107—301no—
275#102—301no—
276#102—301no—
277C22⋊C8—151no—
278C22⋊C8C2×D1511yescharacteristic
279#95—301no—
280#95C2×D1511yescharacteristic
281C2×C3×C5—21no—
282C2×C3×C5—21no—
283C2×C3×C5—81no—
284C2×C3×C5#44711yescharacteristic
285C2×C3×C5#45611yescharacteristic
286C2×C3×C5#45811yescharacteristic
287D15—81no—
288C23×C3—21no—
289C23×C3D4×D511yescharacteristic
290C22×D3—101no—
291C3×D4—41no—
292C3×D4—41no—
293C3×D4—41no—
294C2×C3×C4—22no—
295C2×C3×C4—21no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4C2×D2011yescharacteristic
300C2×C3×C4D4×D511yescharacteristic
301#67—202no—
302#67—201no—
303#67—201no—
304#67—401no—
305C2×Dic3—52no—
306C2×Dic3—101no—
307C2×Dic3—101no—
308C2×Dic3—101no—
309C2×Dic3—101no—
310C2×Dic3—202no—
311C2×Dic3—201no—
312C2×Dic3—201no—
313C2×Dic3—201no—
314C2×Dic3—201no—
315D12—201no—
316C4×D3—202no—
317Dic6—202no—
318C3×C8—41no—
319C3⋊C8—201no—
320C22×C5—21no—
321C22×C5—21no—
322C22×C5—41no—
323C22×C5—41no—
324C22×C5—41no—
325C22×C5#88211yescharacteristic
326C22×C5D3×D811yescharacteristic
327C22×C5#91411yescharacteristic
328C2×D5—121no—
329C2×D5—121no—
330C2×D5—121no—
331C4×C5—21no—
332C4×C5—21no—
333C4×C5—42no—
334C4×C5—41no—
335Dic5—62no—
336Dic5—121no—
337Dic5—121no—
338Dic5—241no—
339#41—602no—
340#41—602no—
341C2×Q8—301no—
342C2×D4—21no—
343C2×D4—151no—
344C2×D4—301no—
345C2×D4—301no—
346C2×D4—301no—
347C2×D4D6011yescharacteristic
348C22×C4—21no—
349C22×C4—151no—
350C22×C4—151no—
351C22×C4—301no—
352C22×C4—301no—
353C22×C4—301no—
354C22×C4C22×D1511yescharacteristic
355C2×C8—21no—
356C2×C8—301no—
357C4⋊C4—151no—
358C4⋊C4—301no—
359C4⋊C4—301no—
360C4⋊C4—301no—
361C4⋊C4—301no—
362C4⋊C4—301no—
363C4⋊C4—602no—
364C4⋊C4D6011yescharacteristic
365C22⋊C4—21no—
366C22⋊C4—301no—
367C22⋊C4—301no—
368C22⋊C4—301no—
369C3×C5#161011yescharacteristic, complemented, Hall
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—41no—
373C22×C3—41no—
374C22×C3—41no—
375C22×C3#402811yescharacteristic
376C22×C3D5×D811yescharacteristic
377C22×C3#406011yescharacteristic
378C2×D3—201no—
379C2×D3—201no—
380C2×D3—201no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—42no—
384C3×C4—41no—
385Dic3—102no—
386Dic3—201no—
387Dic3—201no—
388Dic3—401no—
389C2×C5—21no—
390C2×C5—21no—
391C2×C5—81no—
392C2×C5#474211yescharacteristic
393C2×C5#477311yescharacteristic
394C2×C5#482611yescharacteristic
395D5—241no—
396C23—21no—
397C23—301no—
398C23D4×D1511yescharacteristic
399Q8—602no—
400D4—41no—
401D4—41no—
402D4—41no—
403D4—601no—
404D4—602no—
405D4—601no—
406D4—601no—
407D4—1201no—
408C2×C4—22no—
409C2×C4—21no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—152no—
414C2×C4—301no—
415C2×C4—301no—
416C2×C4—301no—
417C2×C4—301no—
418C2×C4—602no—
419C2×C4—602no—
420C2×C4—601no—
421C2×C4—601no—
422C2×C4—601no—
423C2×C4—601no—
424C2×C4C2×D6011yescharacteristic
425C2×C4D4×D1511yescharacteristic
426C8—41no—
427C8—601no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—81no—
431C2×C3#6503111yescharacteristic
432C2×C3#6506211yescharacteristic
433C2×C3#6511511yescharacteristic
434D3—401no—
435C5#6829711yescharacteristic, complemented, Sylow
436C22—21no—
437C22—21no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—601no—
442C22—601no—
443C22—601no—
444C22#9177111yescharacteristic
445C22D8×D1511yescharacteristic
446C22#9180311yescharacteristic
447C4—21no—
448C4—21no—
449C4—42no—
450C4—41no—
451C4—302no—
452C4—601no—
453C4—601no—
454C4—1201no—
455C3#1059909011yescharacteristic, complemented, Sylow
456C2—21no—
457C2—21no—
458C2—81no—
459C2—1201no—
460C2#1175084311yescharacteristic
461C2#1175087411yescharacteristic
462C2#1175092711yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#327C2
socleC22×C3×C5#120
prime radical#11756356C2
hypercenter#327D15
hypocenterC3×C5#1610
LCSG ▷ C22×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. #11751134C2semidirect
3. #11750837C2semidirect
4. #11750762C2semidirect
5. C3×C5×#327C2semidirect
6. #11746290C2semidirect
7. #11746272C2semidirect
33. C5×#327D3semidirect
70. C3×#327D5semidirect
179. #327D15semidirect
369. C3×C5#1610semidirect
435. C5#68297semidirect
455. C3#10599090semidirect

Maximal subgroups

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

subgroupindex
#117563562
#117511342
#117508372
#117507622
C3×C5×#3272
#117462902
#117462722
#105990903
#682975