Finite Group Databasebeta

← #14288299

Subgroups — #14288299

Order 1920.

456 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C5×#5634C211yesmaximal, characteristic
2#11751144C211yesmaximal, characteristic, complemented
3#11748788C211yesmaximal, characteristic
4#11748447C211yesmaximal, characteristic, complemented
5C3×#64758C211yesmaximal, characteristic, complemented
6#11745962C211yesmaximal, characteristic, complemented
7#11745949C211yesmaximal, characteristic
8#10602683—31nomaximal, Hall
9C3×C5×C22⋊Q8C2211yescharacteristic
10C2×C4⋊Dic15C2211yescharacteristic
11C5×#946—21no—
12C2×C5×(C2×D3)⋊C4C2211yescharacteristic
13C5×#924C2211yescharacteristic
14C5×#897—21no—
15C5×#896—21no—
16C5×#896—21no—
17C5×D3×C22⋊C4—21no—
18C5×#878—21no—
19C2×(C2×D3)⋊Dic5—21no—
20#91119—21no—
21#91114C2211yescharacteristic
22#91092—21no—
23C3×#3963C2211yescharacteristic
24C3×C22⋊#168C2211yescharacteristic
25#90994—21no—
26#90985—21no—
27#90973—21no—
28#68320—51nomaximal, Hall
29C5×#543—31no—
30#65332—31no—
31#65332—31no—
32#65242—31no—
33#64758—31no—
34#64758D311yescharacteristic, complemented
35#64745—31no—
36C23×C5×D3D411yescharacteristic
37C2×C3×C5×Q8D411yescharacteristic
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15—21no—
40C22×C5×Dic3D411yescharacteristic
41C2×C4×C5×D3—21no—
42C2×C4×C5×D3—21no—
43C2×C5×Dic6—21no—
44C2×C5×Dic6D411yescharacteristic
45C22×C3×Dic5—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4D411yescharacteristic
48C3×C5×C22⋊C4—21no—
49C4⋊Dic15—21no—
50C4⋊Dic15—21no—
51C2×C3⋊#168—21no—
52C5×#217—21no—
53C5×(C2×D3)⋊C4—21no—
54C5×(C2×D3)⋊C4—21no—
55C5×(C2×D3)⋊C4—21no—
56C5×(C2×D3)⋊C4—21no—
57C5×C4⋊Dic3—21no—
58C5×C4⋊Dic3D411yescharacteristic
59C5×Dic3⋊C4—21no—
60C5×Dic3⋊C4—21no—
61C5×Dic3⋊C4—21no—
62C2×C3×#168—21no—
63(C2×D3)⋊Dic5—42no—
64#5634D511yescharacteristic
65#5043—51no—
66#4721—51no—
67#4674—51no—
68C3×#328—51no—
69#4468—51no—
70#4452—51no—
71C5×C22⋊Q8—31no—
72C5×C22⋊Q8—61no—
73C5×C22⋊Q8—61no—
74C5×C22⋊Q8—61no—
75C5×C22⋊Q8—61no—
76C5×C22⋊Q8—61no—
77C5×C22⋊Q8C2×D311yescharacteristic
78C2×C5×C22⋊C4—31no—
79C2×C5×C22⋊C4—61no—
80C2×C22⋊Dic5—61no—
81C2×C4⋊Dic5—31no—
82#3967—61no—
83#3967—61no—
84#3963—61no—
85#3963C2×D311yescharacteristic
86C22⋊#168—31no—
87C22⋊#168C2×D311yescharacteristic
88#3940—61no—
89#3940—61no—
90#1608—151noSylow
91C23×C3×C5C2×D411yescharacteristic
92C22×C5×D3—21no—
93C22×C5×D3—21no—
94C22×C5×D3—41no—
95C22×C5×D3—41no—
96C22×C5×D3SD1612yes—
97C3×C5×Q8—41no—
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×Dic15—41no—
104C2×Dic15—41no—
105C2×Dic15—41no—
106C2×C5×Dic3—21no—
107C2×C5×Dic3—21no—
108C2×C5×Dic3—21no—
109C2×C5×Dic3—41no—
110C4×C5×D3—81no—
111C4×C5×D3—81no—
112C5×Dic6—41no—
113C5×Dic6—81no—
114C2×C3×Dic5—41no—
115C2×C3×Dic5—41no—
116C2×C3×Dic5—41no—
117C3⋊#168—41no—
118C3×#168—41no—
119C3×C22⋊Q8C2×D511yescharacteristic
120#946—21no—
121C2×(C2×D3)⋊C4—101no—
122C2×(C2×D3)⋊C4C2×D511yescharacteristic
123C2×C4⋊Dic3—51no—
124#924C2×D511yescharacteristic
125#897—21no—
126#896—21no—
127#896—21no—
128D3×C22⋊C4—21no—
129#878—21no—
130C3×C22⋊C8—51no—
131C3×#95—51no—
132#835—101no—
133C3⋊#95—101no—
134#830—51no—
135#817—101no—
136#816—101no—
137#808—101no—
138C24×C5—31no—
139C2×C5×Q8—31no—
140C2×C5×Q8—61no—
141C2×C5×Q8D1211yescharacteristic
142C22×C4×C5—31no—
143C22×C4×C5—61no—
144C22×C4×C5—61no—
145C22×C4×C5C22×D311yescharacteristic
146C22×Dic5—21no—
147C22×Dic5—61no—
148C5×C4⋊C4—21no—
149C5×C4⋊C4—31no—
150C5×C4⋊C4—61no—
151C5×C4⋊C4—61no—
152C5×C4⋊C4—61no—
153C5×C4⋊C4—61no—
154C5×C4⋊C4D1211yescharacteristic
155C5×C22⋊C4—21no—
156C5×C22⋊C4—61no—
157C5×C22⋊C4—61no—
158C5×C22⋊C4—61no—
159C5×C22⋊C4—61no—
160C5×C22⋊C4—61no—
161C22⋊Dic5—122no—
162C4⋊Dic5—61no—
163C4⋊Dic5—61no—
164C2×#168—21no—
165C2×#168—61no—
166#543—31no—
167#483—151no—
168#483—151no—
169#397—151no—
170#328—51no—
171#328—151no—
172#323—151no—
173C22×C3×C5—21no—
174C22×C3×C5—21no—
175C22×C3×C5#12011yescharacteristic
176C22×C3×C5C2×SD1611yescharacteristic
177C22×C3×C5#13711yescharacteristic
178C2×C5×D3—22no—
179C2×C5×D3—41no—
180C2×C5×D3—41no—
181C2×C5×D3—42no—
182C2×C5×D3—81no—
183C3×C4×C5—21no—
184C3×C4×C5—21no—
185C3×C4×C5—41no—
186C3×C4×C5—41no—
187Dic15—81no—
188C3×Dic5—81no—
189C5×Dic3—41no—
190C5×Dic3—41no—
191C5×Dic3—41no—
192C23×D3C22⋊D511yescharacteristic
193C2×C3×Q8C22⋊D511yescharacteristic
194C22×C3×C4—101no—
195C22×C3×C4C22×D511yescharacteristic
196C22×Dic3—101no—
197C22×Dic3C22⋊D511yescharacteristic
198C2×C4×D3—21no—
199C2×C4×D3—21no—
200C2×Dic6—21no—
201C2×Dic6C22⋊D511yescharacteristic
202C2×C3×C8—101no—
203C3×C4⋊C4—21no—
204C3×C4⋊C4C22⋊D511yescharacteristic
205C3×C22⋊C4—21no—
206#217—21no—
207(C2×D3)⋊C4—21no—
208(C2×D3)⋊C4—21no—
209(C2×D3)⋊C4—21no—
210(C2×D3)⋊C4—21no—
211(C2×D3)⋊C4—202no—
212C4⋊Dic3—21no—
213C4⋊Dic3—101no—
214C4⋊Dic3—101no—
215C4⋊Dic3C22⋊D511yescharacteristic
216Dic3⋊C4—21no—
217Dic3⋊C4—21no—
218Dic3⋊C4—21no—
219C2×C3⋊C8—101no—
220C23×C5—32no—
221C23×C5—61no—
222C23×C5—61no—
223C23×C5—121no—
224C23×C5—121no—
225C23×C5D3×D411yescharacteristic
226C5×Q8—41no—
227C5×Q8—121no—
228C5×Q8—241no—
229C2×C4×C5—21no—
230C2×C4×C5—21no—
231C2×C4×C5—41no—
232C2×C4×C5—61no—
233C2×C4×C5—61no—
234C2×C4×C5—61no—
235C2×C4×C5—121no—
236C2×C4×C5—241no—
237C2×C4×C5—241no—
238C2×C4×C5C2×D1211yescharacteristic
239C2×C4×C5D3×D411yescharacteristic
240C2×Dic5—41no—
241C2×Dic5—41no—
242C2×Dic5—41no—
243C2×Dic5—121no—
244C2×Dic5—121no—
245C2×Dic5—121no—
246#168—41no—
247#168—121no—
248C22⋊Q8—31no—
249C22⋊Q8—61no—
250C22⋊Q8—61no—
251C22⋊Q8—61no—
252C22⋊Q8—61no—
253C22⋊Q8—61no—
254C22⋊Q8D3×D511yescharacteristic
255C2×C4⋊C4—151no—
256C2×C22⋊C4—31no—
257C2×C22⋊C4—61no—
258C2×C22⋊C4—301no—
259#106—301no—
260#106—301no—
261#103—301no—
262#103—301no—
263C22⋊C8—51no—
264C22⋊C8—151no—
265#95—51no—
266#95—301no—
267C2×C3×C5—21no—
268C2×C3×C5—21no—
269C2×C3×C5#44811yescharacteristic
270C2×C3×C5#45511yescharacteristic
271C2×C3×C5#45811yescharacteristic
272C5×D3—42no—
273C23×C3C2×C22⋊D511yescharacteristic
274C22×D3—21no—
275C22×D3—21no—
276C22×D3—41no—
277C22×D3—41no—
278C22×D3#68812yes—
279C3×Q8—41no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—41no—
283C2×C3×C4—201no—
284C2×C3×C4—201no—
285C2×C3×C4—201no—
286C2×C3×C4C2×C22⋊D511yescharacteristic
287C2×C3×C4C2×C22⋊D511yescharacteristic
288C2×Dic3—21no—
289C2×Dic3—21no—
290C2×Dic3—21no—
291C2×Dic3—41no—
292C2×Dic3—201no—
293C2×Dic3—201no—
294C2×Dic3—201no—
295C4×D3—81no—
296C4×D3—81no—
297Dic6—41no—
298Dic6—81no—
299C3×C8—201no—
300C3⋊C8—201no—
301C22×C5—21no—
302C22×C5—21no—
303C22×C5—62no—
304C22×C5—122no—
305C22×C5—121no—
306C22×C5—121no—
307C22×C5—241no—
308C22×C5#88211yescharacteristic
309C22×C5D3×SD1611yescharacteristic
310C22×C5#91811yescharacteristic
311C4×C5—21no—
312C4×C5—21no—
313C4×C5—41no—
314C4×C5—41no—
315C4×C5—121no—
316C4×C5—121no—
317C4×C5—121no—
318Dic5—81no—
319Dic5—241no—
320C24—31no—
321C2×Q8—31no—
322C2×Q8—61no—
323C2×Q8#120311yescharacteristic
324C22×C4—31no—
325C22×C4—61no—
326C22×C4—61no—
327C22×C4—101no—
328C22×C4—301no—
329C22×C4C2×D3×D511yescharacteristic
330C2×C8—101no—
331C2×C8—301no—
332C4⋊C4—21no—
333C4⋊C4—31no—
334C4⋊C4—61no—
335C4⋊C4—61no—
336C4⋊C4—61no—
337C4⋊C4—61no—
338C4⋊C4—301no—
339C4⋊C4—301no—
340C4⋊C4#120311yescharacteristic
341C22⋊C4—21no—
342C22⋊C4—61no—
343C22⋊C4—61no—
344C22⋊C4—61no—
345C22⋊C4—61no—
346C22⋊C4—61no—
347C22⋊C4—602no—
348C3×C5#160811yescharacteristic, complemented, Hall
349C22×C3—21no—
350C22×C3—21no—
351C22×C3C2×#68811yescharacteristic
352C22×C3#408811yescharacteristic
353C22×C3#409911yescharacteristic
354C2×D3—22no—
355C2×D3—41no—
356C2×D3—41no—
357C2×D3—42no—
358C2×D3—81no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—41no—
362C3×C4—41no—
363C3×C4—401no—
364Dic3—41no—
365Dic3—41no—
366Dic3—41no—
367Dic3—401no—
368C2×C5—21no—
369C2×C5—21no—
370C2×C5—122no—
371C2×C5#474211yescharacteristic
372C2×C5#480611yescharacteristic
373C2×C5#482511yescharacteristic
374C23—32no—
375C23—61no—
376C23—61no—
377C23—121no—
378C23—121no—
379C23D3×C22⋊D511yescharacteristic
380Q8—41no—
381Q8—121no—
382Q8—241no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—41no—
386C2×C4—61no—
387C2×C4—61no—
388C2×C4—61no—
389C2×C4—121no—
390C2×C4—201no—
391C2×C4—201no—
392C2×C4—201no—
393C2×C4—241no—
394C2×C4—241no—
395C2×C4—601no—
396C2×C4—601no—
397C2×C4—601no—
398C2×C4C2×#120311yescharacteristic
399C2×C4D3×C22⋊D511yescharacteristic
400C8—201no—
401C8—601no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3#6551611yescharacteristic
405C2×C3#6553111yescharacteristic
406C2×C3#6553211yescharacteristic
407D3—42no—
408C5#6832011yescharacteristic, complemented, Sylow
409C22—21no—
410C22—21no—
411C22—62no—
412C22—122no—
413C22—121no—
414C22—121no—
415C22—241no—
416C22D3×#68811yescharacteristic
417C22#9152011yescharacteristic
418C22#9157011yescharacteristic
419C4—21no—
420C4—21no—
421C4—41no—
422C4—41no—
423C4—121no—
424C4—121no—
425C4—121no—
426C4—401no—
427C4—1201no—
428C3#1060268311yescharacteristic, complemented, Sylow
429C2—21no—
430C2—21no—
431C2—122no—
432C2#1174918411yescharacteristic
433C2#1174927911yescharacteristic
434C2#1174946611yescharacteristic
subgroupG/H
centerC22#91570
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5#120
prime radicalC23×C5×D3D4
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5#1608
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #11751144C2semidirect
4. #11748447C2semidirect
5. C3×#64758C2semidirect
6. #11745962C2semidirect
34. #64758D3semidirect
348. C3×C5#1608semidirect
408. C5#68320semidirect
428. C3#10602683semidirect

Maximal subgroups

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

subgroupindex
C5×#56342
#117511442
#117487882
#117484472
C3×#647582
#117459622
#117459492
#106026833
#683205