Finite Group Databasebeta

← #14288311

Subgroups — #14288311

Order 1920.

456 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 82 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#11754478C211yesmaximal, characteristic
2#11750822C211yesmaximal, characteristic, complemented
3#11748788C211yesmaximal, characteristic
4#11748445C211yesmaximal, characteristic, complemented
5C5×#4468C211yesmaximal, characteristic
6C3×#64687C211yesmaximal, characteristic, complemented
7#11745964C211yesmaximal, characteristic, complemented
8#10598909—31nomaximal, Hall
9C2×C4⋊Dic15C2211yescharacteristic
10#91813C2211yescharacteristic
11C2×C5×(C2×D3)⋊C4C2211yescharacteristic
12C3×#4070C2211yescharacteristic
13#91575—21no—
14D3×C22⋊Dic5—21no—
15C2×(C2×D3)⋊Dic5—21no—
16#91436—21no—
17#91432—21no—
18#91417—21no—
19#91410—21no—
20C3×C5×C22⋊C8C2211yescharacteristic
21#91101—21no—
22#91100—21no—
23C5×#830C2211yescharacteristic
24C3×#3963C2211yescharacteristic
25#90994—21no—
26#90987—21no—
27#90971—21no—
28#68320—51nomaximal, Hall
29#65817—31no—
30#65242—31no—
31#65010—31no—
32#65010—31no—
33C5×#323—31no—
34#64687—31no—
35#64687D311yescharacteristic, complemented
36C23×C5×D3D411yescharacteristic
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15—21no—
39C2×Dic30D411yescharacteristic
40C22×C5×Dic3D411yescharacteristic
41C22×C3×Dic5—21no—
42C2×C3×Dic10D411yescharacteristic
43C2×#1204—21no—
44C2×D3×Dic5—21no—
45C2×D3×Dic5—21no—
46C2×C3×C5×C8—21no—
47#6719—21no—
48C4⋊Dic15—21no—
49C4⋊Dic15—21no—
50C4⋊Dic15D411yescharacteristic
51#6712—21no—
52C5×(C2×D3)⋊C4—21no—
53C5×(C2×D3)⋊C4—21no—
54C2×C5×C3⋊C8—21no—
55C3×C22⋊Dic5—21no—
56C3×C4⋊Dic5D411yescharacteristic
57C3×#683—21no—
58Dic3⋊Dic5—21no—
59#6669—21no—
60#6668—21no—
61(C2×D3)⋊Dic5—21no—
62(C2×D3)⋊Dic5—21no—
63(C2×D3)⋊Dic5—42no—
64#5634—51no—
65#5043—51no—
66#4721—51no—
67#4674—51no—
68C3×#328—51no—
69#4468D511yescharacteristic
70#4452—51no—
71C2×C5×C22⋊C4—31no—
72C2×C22⋊Dic5—61no—
73C2×C22⋊Dic5—61no—
74C2×C4⋊Dic5—31no—
75#4070—31no—
76#4070—61no—
77#4070C2×D311yescharacteristic
78#4024—61no—
79#4024—61no—
80#4024—61no—
81#4024—61no—
82C5×C22⋊C8—31no—
83C5×C22⋊C8C2×D311yescharacteristic
84#3963—61no—
85#3963C2×D311yescharacteristic
86#3949—61no—
87#3949—61no—
88#3948—61no—
89#3948—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—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×Dic15—21no—
101C2×Dic15—21no—
102C2×Dic15—41no—
103C2×Dic15—41no—
104C2×Dic15—41no—
105Dic30—41no—
106C2×C5×Dic3—21no—
107C2×C5×Dic3—41no—
108C2×C3×Dic5—21no—
109C2×C3×Dic5—21no—
110C2×C3×Dic5—41no—
111C2×C3×Dic5—41no—
112C2×C3×Dic5—41no—
113C3×Dic10—41no—
114#1204—81no—
115D3×Dic5—81no—
116D3×Dic5—81no—
117C3×C5×C8—41no—
118C5×C3⋊C8—41no—
119C3×C22⋊Q8—51no—
120#946—101no—
121C2×(C2×D3)⋊C4—101no—
122C2×(C2×D3)⋊C4C2×D511yescharacteristic
123C2×C4⋊Dic3—51no—
124#924—51no—
125#897—101no—
126#896—101no—
127#896—101no—
128D3×C22⋊C4—101no—
129#878—101no—
130C3×C22⋊C8C2×D511yescharacteristic
131C3×#95—51no—
132#835—101no—
133C3⋊#95—101no—
134#830C2×D511yescharacteristic
135#817—101no—
136#816—101no—
137#808—101no—
138C24×C5—31no—
139C22×C4×C5—31no—
140C22×C4×C5C22×D311yescharacteristic
141C22×Dic5—21no—
142C22×Dic5—61no—
143C22×Dic5—61no—
144C22×Dic5—61no—
145C2×Dic10—31no—
146C2×Dic10—61no—
147C2×Dic10D1211yescharacteristic
148C2×C5×C8—21no—
149C2×C5×C8—61no—
150C5×C22⋊C4—61no—
151C5×C22⋊C4—61no—
152C22⋊Dic5—21no—
153C22⋊Dic5—61no—
154C22⋊Dic5—61no—
155C22⋊Dic5—61no—
156C22⋊Dic5—122no—
157C4⋊Dic5—31no—
158C4⋊Dic5—61no—
159C4⋊Dic5—61no—
160C4⋊Dic5—61no—
161C4⋊Dic5D1211yescharacteristic
162#683—21no—
163#683—61no—
164#683—61no—
165#683—61no—
166#543—151no—
167#483—151no—
168#483—151no—
169#397—151no—
170#328—51no—
171#328—151no—
172#323—31no—
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—
185Dic15—41no—
186Dic15—41no—
187Dic15—81no—
188C3×Dic5—41no—
189C3×Dic5—41no—
190C3×Dic5—81no—
191C5×Dic3—41no—
192C23×D3D2011yescharacteristic
193C2×C3×Q8—51no—
194C22×C3×C4—101no—
195C22×C3×C4C22×D511yescharacteristic
196C22×Dic3—101no—
197C22×Dic3D2011yescharacteristic
198C2×C4×D3—101no—
199C2×C4×D3—101no—
200C2×Dic6—51no—
201C2×Dic6—101no—
202C2×C3×C8—21no—
203C3×C4⋊C4—51no—
204C3×C4⋊C4—101no—
205C3×C22⋊C4—101no—
206#217—101no—
207(C2×D3)⋊C4—21no—
208(C2×D3)⋊C4—21no—
209(C2×D3)⋊C4—101no—
210(C2×D3)⋊C4—101no—
211(C2×D3)⋊C4—202no—
212C4⋊Dic3—51no—
213C4⋊Dic3—101no—
214C4⋊Dic3—101no—
215C4⋊Dic3—101no—
216Dic3⋊C4—101no—
217Dic3⋊C4—101no—
218Dic3⋊C4—101no—
219C2×C3⋊C8—21no—
220C23×C5—32no—
221C23×C5—61no—
222C23×C5—61no—
223C23×C5—121no—
224C23×C5—121no—
225C23×C5D3×D411yescharacteristic
226C2×C4×C5—41no—
227C2×C4×C5—61no—
228C2×C4×C5—121no—
229C2×C4×C5C2×D1211yescharacteristic
230C2×C4×C5D3×D411yescharacteristic
231C2×Dic5—21no—
232C2×Dic5—21no—
233C2×Dic5—41no—
234C2×Dic5—41no—
235C2×Dic5—41no—
236C2×Dic5—61no—
237C2×Dic5—61no—
238C2×Dic5—121no—
239C2×Dic5—121no—
240C2×Dic5—121no—
241C2×Dic5—241no—
242C2×Dic5—241no—
243Dic10—41no—
244Dic10—121no—
245Dic10—241no—
246C5×C8—41no—
247C5×C8—121no—
248C22⋊Q8—51no—
249C22⋊Q8—151no—
250C22⋊Q8—301no—
251C22⋊Q8—301no—
252C22⋊Q8—301no—
253C22⋊Q8—301no—
254C22⋊Q8—301no—
255C2×C4⋊C4—151no—
256C2×C22⋊C4—31no—
257C2×C22⋊C4—301no—
258C2×C22⋊C4—301no—
259#106—301no—
260#106—301no—
261#103—301no—
262#103—301no—
263C22⋊C8—31no—
264C22⋊C8D3×D511yescharacteristic
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×D2011yescharacteristic
274C22×D3—21no—
275C22×D3—21no—
276C22×D3—41no—
277C22×D3—41no—
278C22×D3#67712yes—
279C3×Q8—201no—
280C2×C3×C4—41no—
281C2×C3×C4—101no—
282C2×C3×C4—101no—
283C2×C3×C4—201no—
284C2×C3×C4—201no—
285C2×C3×C4—201no—
286C2×C3×C4D4×D511yescharacteristic
287C2×C3×C4D4×D511yescharacteristic
288C2×Dic3—21no—
289C2×Dic3—41no—
290C2×Dic3—101no—
291C2×Dic3—101no—
292C2×Dic3—201no—
293C2×Dic3—201no—
294C2×Dic3—201no—
295C4×D3—401no—
296C4×D3—401no—
297Dic6—201no—
298Dic6—401no—
299C3×C8—41no—
300C3⋊C8—41no—
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—121no—
314Dic5—41no—
315Dic5—41no—
316Dic5—81no—
317Dic5—121no—
318Dic5—121no—
319Dic5—241no—
320C24—31no—
321C2×Q8—51no—
322C2×Q8—151no—
323C2×Q8—301no—
324C22×C4—31no—
325C22×C4—101no—
326C22×C4—301no—
327C22×C4—301no—
328C22×C4—301no—
329C22×C4C2×D3×D511yescharacteristic
330C2×C8—21no—
331C2×C8—61no—
332C4⋊C4—51no—
333C4⋊C4—101no—
334C4⋊C4—151no—
335C4⋊C4—301no—
336C4⋊C4—301no—
337C4⋊C4—301no—
338C4⋊C4—301no—
339C4⋊C4—301no—
340C4⋊C4—301no—
341C22⋊C4—61no—
342C22⋊C4—61no—
343C22⋊C4—101no—
344C22⋊C4—301no—
345C22⋊C4—301no—
346C22⋊C4—301no—
347C22⋊C4—602no—
348C3×C5#160811yescharacteristic, complemented, Hall
349C22×C3—21no—
350C22×C3—21no—
351C22×C3#402811yescharacteristic
352C22×C3C2×#67711yescharacteristic
353C22×C3#405511yescharacteristic
354C2×D3—22no—
355C2×D3—41no—
356C2×D3—41no—
357C2×D3—42no—
358C2×D3—81no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—201no—
362C3×C4—201no—
363C3×C4—401no—
364Dic3—41no—
365Dic3—201no—
366Dic3—201no—
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×D2011yescharacteristic
380Q8—201no—
381Q8—601no—
382Q8—1201no—
383C2×C4—41no—
384C2×C4—61no—
385C2×C4—101no—
386C2×C4—101no—
387C2×C4—121no—
388C2×C4—201no—
389C2×C4—201no—
390C2×C4—201no—
391C2×C4—301no—
392C2×C4—301no—
393C2×C4—601no—
394C2×C4—601no—
395C2×C4—601no—
396C2×C4—1201no—
397C2×C4—1201no—
398C2×C4D5×D1211yescharacteristic
399C2×C4#679011yescharacteristic
400C8—41no—
401C8—121no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3#6502711yescharacteristic
405C2×C3#6503111yescharacteristic
406C2×C3#6503511yescharacteristic
407D3—42no—
408C5#6832011yescharacteristic, complemented, Sylow
409C22—21no—
410C22—21no—
411C22—62no—
412C22—122no—
413C22—121no—
414C22—121no—
415C22—241no—
416C22D3×#67711yescharacteristic
417C22#9126311yescharacteristic
418C22#9147611yescharacteristic
419C4—21no—
420C4—21no—
421C4—121no—
422C4—201no—
423C4—201no—
424C4—401no—
425C4—601no—
426C4—601no—
427C4—1201no—
428C3#1059890911yescharacteristic, complemented, Sylow
429C2—21no—
430C2—21no—
431C2—122no—
432C2#1174713611yescharacteristic
433C2#1174813211yescharacteristic
434C2#1174825111yescharacteristic
subgroupG/H
centerC22#91476
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5#120
prime radicalC23×C5×D3D4
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#1608
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #11750822C2semidirect
4. #11748445C2semidirect
6. C3×#64687C2semidirect
7. #11745964C2semidirect
35. #64687D3semidirect
348. C3×C5#1608semidirect
408. C5#68320semidirect
428. C3#10598909semidirect

Maximal subgroups

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

subgroupindex
#117544782
#117508222
#117487882
#117484452
C5×#44682
C3×#646872
#117459642
#105989093
#683205