Finite Group Databasebeta

← #14288331

Subgroups — #14288331

Order 1920.

432 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 83 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#11756361C211yesmaximal, characteristic
2#11751134C211yesmaximal, characteristic
3#11750822C211yesmaximal, characteristic, complemented
4#11750762C211yesmaximal, characteristic, complemented
5C3×C5×#327C211yesmaximal, characteristic
6#11746290C211yesmaximal, characteristic, complemented
7#11746273C211yesmaximal, characteristic, complemented
8#10599089—31nomaximal, Hall
9C3×C5×#121C2211yescharacteristic
10#91824—21no—
11#91824—21no—
12D4×Dic15—21no—
13C2×C4⋊Dic15—21no—
14C2×C4⋊Dic15C2211yescharacteristic
15#91813C2211yescharacteristic
16C2×#6712C2211yescharacteristic
17#91778—21no—
18#91768—21no—
19#91767—21no—
20C3×C5×C22⋊C8C2211yescharacteristic
21C3×C5×#95C2211yescharacteristic
22#91116—21no—
23#91115—21no—
24#91114C2211yescharacteristic
25#91101—21no—
26#91100—21no—
27#91091—21no—
28#68296—51nomaximal, Hall
29#65936—31no—
30#65322—31no—
31#65010—31no—
32#64950—31no—
33C5×#327D311yescharacteristic
34#64689—31no—
35#64672—31no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4D411yescharacteristic
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5C2311yescharacteristic
40C22×Dic15—21no—
41C22×Dic15—21no—
42C22×Dic15D411yescharacteristic
43C22×Dic15D411yescharacteristic
44C2×Dic30D411yescharacteristic
45C2×C3×C5×C8—21no—
46C3×C5×C4⋊C4D411yescharacteristic
47C3×C5×C22⋊C4—21no—
48#6719—21no—
49#6719—21no—
50#6719—21no—
51#6719—21no—
52C4⋊Dic15—21no—
53C4⋊Dic15—21no—
54C4⋊Dic15—21no—
55C4⋊Dic15—42no—
56C4⋊Dic15D411yescharacteristic
57#6712—21no—
58#6712—21no—
59#6712—21no—
60#6712—21no—
61#6712—21no—
62C4×Dic15—21no—
63C2×C3⋊#168—21no—
64#5602—51no—
65#5033—51no—
66#4721—51no—
67#4661—51no—
68C3×#327D511yescharacteristic
69#4469—51no—
70#4452—51no—
71C5×#121C2×D311yescharacteristic
72#4081—61no—
73#4081—61no—
74D4×Dic5—61no—
75C2×C4⋊Dic5—31no—
76C2×C4⋊Dic5—61no—
77#4070—31no—
78C2×#683—31no—
79#4035—61no—
80#4025—61no—
81#4024—61no—
82C5×C22⋊C8C2×D311yescharacteristic
83C5×#95C2×D311yescharacteristic
84#3964—61no—
85#3963—61no—
86C22⋊#168—31no—
87#3949—61no—
88#3948—61no—
89#3939—61no—
90#1609—151noSylow
91C23×C3×C5—21no—
92C23×C3×C5C2×D411yescharacteristic
93C3×C5×D4—41no—
94C3×C5×D4—41no—
95C3×C5×D4—41no—
96C2×C3×C4×C5—22no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×Dic15—21no—
104C2×Dic15—21no—
105C2×Dic15—21no—
106C2×Dic15—21no—
107C2×Dic15—21no—
108C2×Dic15—21no—
109C2×Dic15—41no—
110C2×Dic15—41no—
111C2×Dic15—41no—
112C2×Dic15—41no—
113C2×Dic15—81no—
114Dic30—41no—
115C3×C5×C8—41no—
116C3⋊#168—41no—
117C3×#121C2×D511yescharacteristic
118#935—101no—
119#935—101no—
120D4×Dic3—101no—
121C2×C4⋊Dic3—51no—
122C2×C4⋊Dic3—101no—
123#924—51no—
124C2×Dic3⋊C4—51no—
125#889—101no—
126#879—101no—
127#878—101no—
128C3×C22⋊C8C2×D511yescharacteristic
129C3×#95C2×D511yescharacteristic
130#832—101no—
131C3⋊#95—101no—
132#830—51no—
133#817—101no—
134#816—101no—
135#807—101no—
136C2×C5×D4—21no—
137C2×C5×D4D1211yescharacteristic
138C22×C4×C5—21no—
139C22×C4×C5C22×D311yescharacteristic
140C22×Dic5—31no—
141C22×Dic5—31no—
142C22×Dic5—61no—
143C22×Dic5—61no—
144C2×Dic10—31no—
145C2×C5×C8—21no—
146C5×C4⋊C4D1211yescharacteristic
147C5×C22⋊C4—21no—
148C22⋊Dic5—61no—
149C22⋊Dic5—61no—
150C22⋊Dic5—61no—
151C22⋊Dic5—61no—
152C4⋊Dic5—31no—
153C4⋊Dic5—61no—
154C4⋊Dic5—61no—
155C4⋊Dic5—61no—
156C4⋊Dic5—122no—
157#683—61no—
158#683—61no—
159#683—61no—
160#683—61no—
161#683—61no—
162C4×Dic5—61no—
163C2×#168—61no—
164#539—151no—
165#483—151no—
166#480—151no—
167#398—151no—
168#328—151no—
169#327D1511yescharacteristic
170#324—151no—
171C22×C3×C5—21no—
172C22×C3×C5—21no—
173C22×C3×C5—41no—
174C22×C3×C5—41no—
175C22×C3×C5—41no—
176C22×C3×C5#12011yescharacteristic
177C22×C3×C5#13511yescharacteristic
178C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
179C3×C4×C5—21no—
180C3×C4×C5—21no—
181C3×C4×C5—42no—
182C3×C4×C5—41no—
183Dic15—41no—
184Dic15—41no—
185Dic15—41no—
186Dic15—41no—
187Dic15—81no—
188C2×C3×D4—21no—
189C2×C3×D4D2011yescharacteristic
190C22×C3×C4—21no—
191C22×C3×C4C22×D511yescharacteristic
192C22×Dic3—51no—
193C22×Dic3—51no—
194C22×Dic3—101no—
195C22×Dic3—101no—
196C2×Dic6—51no—
197C2×C3×C8—21no—
198C3×C4⋊C4D2011yescharacteristic
199C3×C22⋊C4—21no—
200#217—101no—
201#217—101no—
202#217—101no—
203#217—101no—
204C4⋊Dic3—51no—
205C4⋊Dic3—101no—
206C4⋊Dic3—101no—
207C4⋊Dic3—101no—
208C4⋊Dic3—202no—
209Dic3⋊C4—101no—
210Dic3⋊C4—101no—
211Dic3⋊C4—101no—
212Dic3⋊C4—101no—
213Dic3⋊C4—101no—
214C4×Dic3—101no—
215C2×C3⋊C8—101no—
216C23×C5—21no—
217C23×C5D3×D411yescharacteristic
218C5×D4—41no—
219C5×D4—41no—
220C5×D4—41no—
221C2×C4×C5—22no—
222C2×C4×C5—21no—
223C2×C4×C5—41no—
224C2×C4×C5—41no—
225C2×C4×C5—41no—
226C2×C4×C5C2×D1211yescharacteristic
227C2×C4×C5D3×D411yescharacteristic
228C2×Dic5—61no—
229C2×Dic5—61no—
230C2×Dic5—61no—
231C2×Dic5—61no—
232C2×Dic5—61no—
233C2×Dic5—61no—
234C2×Dic5—121no—
235C2×Dic5—121no—
236C2×Dic5—121no—
237C2×Dic5—121no—
238C2×Dic5—241no—
239Dic10—121no—
240C5×C8—41no—
241#168—121no—
242#126—301no—
243#125—301no—
244#123—301no—
245#123—301no—
246C22⋊Q8—151no—
247C22⋊Q8—301no—
248#121C2×D1511yescharacteristic
249C4×D4—301no—
250C2×C4⋊C4—151no—
251C2×C4⋊C4—151no—
252C2×C4⋊C4—301no—
253#107—301no—
254#106—301no—
255#103—301no—
256#102—301no—
257C22⋊C8—151no—
258C22⋊C8C2×D1511yescharacteristic
259#95—301no—
260#95C2×D1511yescharacteristic
261C2×C3×C5—21no—
262C2×C3×C5—21no—
263C2×C3×C5—81no—
264C2×C3×C5#44911yescharacteristic
265C2×C3×C5#45611yescharacteristic
266C2×C3×C5#45811yescharacteristic
267C23×C3—21no—
268C23×C3D4×D511yescharacteristic
269C3×D4—41no—
270C3×D4—41no—
271C3×D4—41no—
272C2×C3×C4—22no—
273C2×C3×C4—21no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4C2×D2011yescharacteristic
278C2×C3×C4D4×D511yescharacteristic
279C2×Dic3—101no—
280C2×Dic3—101no—
281C2×Dic3—101no—
282C2×Dic3—101no—
283C2×Dic3—101no—
284C2×Dic3—101no—
285C2×Dic3—201no—
286C2×Dic3—201no—
287C2×Dic3—201no—
288C2×Dic3—201no—
289C2×Dic3—401no—
290Dic6—201no—
291C3×C8—41no—
292C3⋊C8—201no—
293C22×C5—21no—
294C22×C5—21no—
295C22×C5—41no—
296C22×C5—41no—
297C22×C5—41no—
298C22×C5#88211yescharacteristic
299C22×C5#91111yescharacteristic
300C22×C5#91611yescharacteristic
301C4×C5—21no—
302C4×C5—21no—
303C4×C5—42no—
304C4×C5—41no—
305Dic5—121no—
306Dic5—121no—
307Dic5—121no—
308Dic5—121no—
309Dic5—241no—
310C2×Q8—151no—
311C2×D4—21no—
312C2×D4D6011yescharacteristic
313C22×C4—21no—
314C22×C4—151no—
315C22×C4—151no—
316C22×C4—301no—
317C22×C4—301no—
318C22×C4C22×D1511yescharacteristic
319C2×C8—21no—
320C2×C8—301no—
321C4⋊C4—151no—
322C4⋊C4—301no—
323C4⋊C4—301no—
324C4⋊C4—301no—
325C4⋊C4—301no—
326C4⋊C4—301no—
327C4⋊C4—301no—
328C4⋊C4—301no—
329C4⋊C4—301no—
330C4⋊C4—602no—
331C4⋊C4D6011yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—301no—
334C22⋊C4—301no—
335C22⋊C4—301no—
336C22⋊C4—301no—
337C42—301no—
338C3×C5#160911yescharacteristic, complemented, Hall
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—41no—
342C22×C3—41no—
343C22×C3—41no—
344C22×C3#402811yescharacteristic
345C22×C3#405711yescharacteristic
346C22×C3#406211yescharacteristic
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—42no—
350C3×C4—41no—
351Dic3—201no—
352Dic3—201no—
353Dic3—201no—
354Dic3—201no—
355Dic3—401no—
356C2×C5—21no—
357C2×C5—21no—
358C2×C5—81no—
359C2×C5#474211yescharacteristic
360C2×C5#478111yescharacteristic
361C2×C5#482611yescharacteristic
362C23—21no—
363C23D4×D1511yescharacteristic
364Q8—601no—
365D4—41no—
366D4—41no—
367D4—41no—
368C2×C4—22no—
369C2×C4—21no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—301no—
374C2×C4—301no—
375C2×C4—301no—
376C2×C4—301no—
377C2×C4—301no—
378C2×C4—301no—
379C2×C4—601no—
380C2×C4—601no—
381C2×C4—601no—
382C2×C4—601no—
383C2×C4—1201no—
384C2×C4C2×D6011yescharacteristic
385C2×C4D4×D1511yescharacteristic
386C8—41no—
387C8—601no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—81no—
391C2×C3#6503111yescharacteristic
392C2×C3#6507011yescharacteristic
393C2×C3#6511511yescharacteristic
394C5#6829611yescharacteristic, complemented, Sylow
395C22—21no—
396C22—21no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22#9177111yescharacteristic
401C22#9180011yescharacteristic
402C22#9180511yescharacteristic
403C4—21no—
404C4—21no—
405C4—42no—
406C4—41no—
407C4—601no—
408C4—601no—
409C4—601no—
410C4—601no—
411C4—1201no—
412C3#1059908911yescharacteristic, complemented, Sylow
413C2—21no—
414C2—21no—
415C2—81no—
416C2#1175084311yescharacteristic
417C2#1175088211yescharacteristic
418C2#1175092711yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#327C2
socleC22×C3×C5#120
prime radicalC3×C5×#121C22
hypercenter#327D15
hypocenterC3×C5#1609
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
3. #11750822C2semidirect
4. #11750762C2semidirect
6. #11746290C2semidirect
7. #11746273C2semidirect
338. C3×C5#1609semidirect
394. C5#68296semidirect
412. C3#10599089semidirect

Maximal subgroups

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

subgroupindex
#117563612
#117511342
#117508222
#117507622
C3×C5×#3272
#117462902
#117462732
#105990893
#682965