Finite Group Databasebeta

← #14288593

Subgroups — #14288593

Order 1920.

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

normal subgroups only

This group has 472 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#11750823C211yesmaximal, characteristic, complemented
3#11748762C211yesmaximal, characteristic
4#11748403C211yesmaximal, characteristic, complemented
5C5×#4468C211yesmaximal, characteristic
6C3×#64687C211yesmaximal, characteristic, complemented
7#11745964C211yesmaximal, characteristic, complemented
8#10598910—31nomaximal, Hall
9C2×C4⋊Dic15C2211yescharacteristic
10#91813C2211yescharacteristic
11C2×C5×(C2×D3)⋊C4C2211yescharacteristic
12C3×#4070C2211yescharacteristic
13#91575—21no—
14D3×C22⋊Dic5—21no—
15C2×#6668—21no—
16C2×(C2×D3)⋊Dic5—21no—
17#91436—21no—
18#91432—21no—
19#91417—21no—
20#91410—21no—
21C3×C5×C22⋊C8C2211yescharacteristic
22#91102—21no—
23#91100—21no—
24C5×#830C2211yescharacteristic
25C3×#3963C2211yescharacteristic
26#90990—21no—
27#90971—21no—
28#68322—51nomaximal, Hall
29#65817—31no—
30#65238—31no—
31#65011—31no—
32#65011—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#6668—42no—
62(C2×D3)⋊Dic5—21no—
63(C2×D3)⋊Dic5—21no—
64(C2×D3)⋊Dic5—42no—
65#5634—51no—
66#5044—51no—
67#4722—51no—
68#4677—51no—
69C3×#328—51no—
70#4468D511yescharacteristic
71#4452—51no—
72C2×C5×C22⋊C4—31no—
73C2×C22⋊Dic5—61no—
74C2×C22⋊Dic5—61no—
75C2×C4⋊Dic5—31no—
76#4070—31no—
77#4070—61no—
78#4070C2×D311yescharacteristic
79C2×#683—61no—
80#4024—61no—
81#4024—61no—
82#4024—61no—
83#4024—61no—
84C5×C22⋊C8—31no—
85C5×C22⋊C8C2×D311yescharacteristic
86#3963C2×D311yescharacteristic
87#3950—61no—
88#3950—61no—
89#3948—61no—
90#3948—61no—
91#1614—151noSylow
92C23×C3×C5C2×D411yescharacteristic
93C22×C5×D3—21no—
94C22×C5×D3—21no—
95C22×C5×D3—41no—
96C22×C5×D3—41no—
97C22×C5×D3Q1612yes—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×Dic15—21no—
102C2×Dic15—21no—
103C2×Dic15—41no—
104C2×Dic15—41no—
105C2×Dic15—41no—
106Dic30—41no—
107C2×C5×Dic3—21no—
108C2×C5×Dic3—41no—
109C2×C3×Dic5—22no—
110C2×C3×Dic5—21no—
111C2×C3×Dic5—21no—
112C2×C3×Dic5—41no—
113C2×C3×Dic5—41no—
114C3×Dic10—41no—
115#1204—81no—
116D3×Dic5—81no—
117D3×Dic5—81no—
118C3×C5×C8—41no—
119C5×C3⋊C8—41no—
120C3×C22⋊Q8—51no—
121#946—101no—
122C2×(C2×D3)⋊C4—101no—
123C2×(C2×D3)⋊C4C2×D511yescharacteristic
124C2×C4⋊Dic3—51no—
125C2×C4⋊Dic3—101no—
126#924—51no—
127#897—101no—
128#896—101no—
129#896—101no—
130D3×C22⋊C4—101no—
131#878—101no—
132C3×C22⋊C8C2×D511yescharacteristic
133C3×#95—51no—
134#835—101no—
135#830C2×D511yescharacteristic
136#818—101no—
137#816—101no—
138#807—101no—
139C24×C5—31no—
140C22×C4×C5—31no—
141C22×C4×C5C22×D311yescharacteristic
142C22×Dic5—21no—
143C22×Dic5—61no—
144C22×Dic5—61no—
145C22×Dic5—61no—
146C2×Dic10—31no—
147C2×Dic10—61no—
148C2×Dic10D1211yescharacteristic
149C2×C5×C8—21no—
150C2×C5×C8—61no—
151C5×C22⋊C4—61no—
152C5×C22⋊C4—61no—
153C22⋊Dic5—21no—
154C22⋊Dic5—61no—
155C22⋊Dic5—61no—
156C22⋊Dic5—61no—
157C22⋊Dic5—122no—
158C4⋊Dic5—31no—
159C4⋊Dic5—61no—
160C4⋊Dic5—61no—
161C4⋊Dic5—61no—
162C4⋊Dic5D1211yescharacteristic
163#683—21no—
164#683—61no—
165#683—61no—
166#683—61no—
167#683—122no—
168#543—151no—
169#484—151no—
170#484—151no—
171#399—151no—
172#328—51no—
173#328—151no—
174#323—31no—
175C22×C3×C5—21no—
176C22×C3×C5—21no—
177C22×C3×C5#12011yescharacteristic
178C22×C3×C5C2×Q1611yescharacteristic
179C22×C3×C5#13711yescharacteristic
180C2×C5×D3—22no—
181C2×C5×D3—41no—
182C2×C5×D3—41no—
183C2×C5×D3—42no—
184C2×C5×D3—81no—
185C3×C4×C5—21no—
186C3×C4×C5—21no—
187Dic15—41no—
188Dic15—41no—
189Dic15—81no—
190C3×Dic5—42no—
191C3×Dic5—41no—
192C3×Dic5—41no—
193C5×Dic3—41no—
194C23×D3D2011yescharacteristic
195C2×C3×Q8—51no—
196C22×C3×C4—101no—
197C22×C3×C4C22×D511yescharacteristic
198C22×Dic3—101no—
199C22×Dic3D2011yescharacteristic
200C2×C4×D3—101no—
201C2×C4×D3—101no—
202C2×Dic6—51no—
203C2×Dic6—101no—
204C2×C3×C8—21no—
205C3×C4⋊C4—51no—
206C3×C4⋊C4—101no—
207C3×C22⋊C4—101no—
208#217—101no—
209(C2×D3)⋊C4—21no—
210(C2×D3)⋊C4—21no—
211(C2×D3)⋊C4—101no—
212(C2×D3)⋊C4—101no—
213(C2×D3)⋊C4—202no—
214C4⋊Dic3—51no—
215C4⋊Dic3—101no—
216C4⋊Dic3—101no—
217C4⋊Dic3—101no—
218C4⋊Dic3—202no—
219Dic3⋊C4—101no—
220Dic3⋊C4—101no—
221Dic3⋊C4—101no—
222C2×C3⋊C8—21no—
223C23×C5—32no—
224C23×C5—61no—
225C23×C5—61no—
226C23×C5—121no—
227C23×C5—121no—
228C23×C5D3×D411yescharacteristic
229C2×C4×C5—41no—
230C2×C4×C5—61no—
231C2×C4×C5—121no—
232C2×C4×C5C2×D1211yescharacteristic
233C2×C4×C5D3×D411yescharacteristic
234C2×Dic5—22no—
235C2×Dic5—21no—
236C2×Dic5—21no—
237C2×Dic5—41no—
238C2×Dic5—41no—
239C2×Dic5—61no—
240C2×Dic5—61no—
241C2×Dic5—121no—
242C2×Dic5—121no—
243C2×Dic5—121no—
244C2×Dic5—241no—
245C2×Dic5—241no—
246Dic10—41no—
247Dic10—121no—
248Dic10—241no—
249C5×C8—41no—
250C5×C8—121no—
251C22⋊Q8—51no—
252C22⋊Q8—151no—
253C22⋊Q8—301no—
254C22⋊Q8—301no—
255C22⋊Q8—301no—
256C22⋊Q8—301no—
257C22⋊Q8—301no—
258C2×C4⋊C4—151no—
259C2×C4⋊C4—301no—
260C2×C22⋊C4—31no—
261C2×C22⋊C4—301no—
262C2×C22⋊C4—301no—
263#107—301no—
264#107—301no—
265#103—301no—
266#103—301no—
267C22⋊C8—31no—
268C22⋊C8D3×D511yescharacteristic
269#95—51no—
270C2×C3×C5—21no—
271C2×C3×C5—21no—
272C2×C3×C5#45111yescharacteristic
273C2×C3×C5#45311yescharacteristic
274C2×C3×C5#45811yescharacteristic
275C5×D3—42no—
276C23×C3C2×D2011yescharacteristic
277C22×D3—21no—
278C22×D3—21no—
279C22×D3—41no—
280C22×D3—41no—
281C22×D3Dic2012yes—
282C3×Q8—201no—
283C2×C3×C4—41no—
284C2×C3×C4—102no—
285C2×C3×C4—101no—
286C2×C3×C4—101no—
287C2×C3×C4—201no—
288C2×C3×C4—201no—
289C2×C3×C4D4×D511yescharacteristic
290C2×C3×C4D4×D511yescharacteristic
291C2×Dic3—21no—
292C2×Dic3—41no—
293C2×Dic3—101no—
294C2×Dic3—101no—
295C2×Dic3—201no—
296C2×Dic3—201no—
297C2×Dic3—201no—
298C4×D3—401no—
299C4×D3—401no—
300Dic6—201no—
301Dic6—401no—
302C3×C8—41no—
303C3⋊C8—41no—
304C22×C5—21no—
305C22×C5—21no—
306C22×C5—62no—
307C22×C5—122no—
308C22×C5—121no—
309C22×C5—121no—
310C22×C5—241no—
311C22×C5#88211yescharacteristic
312C22×C5#91511yescharacteristic
313C22×C5D3×Q1611yescharacteristic
314C4×C5—21no—
315C4×C5—21no—
316C4×C5—121no—
317Dic5—42no—
318Dic5—41no—
319Dic5—41no—
320Dic5—121no—
321Dic5—121no—
322Dic5—241no—
323C24—31no—
324C2×Q8—51no—
325C2×Q8—151no—
326C2×Q8—301no—
327C22×C4—31no—
328C22×C4—101no—
329C22×C4—301no—
330C22×C4—301no—
331C22×C4—301no—
332C22×C4C2×D3×D511yescharacteristic
333C2×C8—21no—
334C2×C8—61no—
335C4⋊C4—51no—
336C4⋊C4—101no—
337C4⋊C4—151no—
338C4⋊C4—301no—
339C4⋊C4—301no—
340C4⋊C4—301no—
341C4⋊C4—301no—
342C4⋊C4—301no—
343C4⋊C4—301no—
344C4⋊C4—602no—
345C22⋊C4—61no—
346C22⋊C4—61no—
347C22⋊C4—101no—
348C22⋊C4—301no—
349C22⋊C4—301no—
350C22⋊C4—301no—
351C22⋊C4—602no—
352C3×C5#161411yescharacteristic, complemented, Hall
353C22×C3—21no—
354C22×C3—21no—
355C22×C3#402811yescharacteristic
356C22×C3C2×Dic2011yescharacteristic
357C22×C3#405511yescharacteristic
358C2×D3—22no—
359C2×D3—41no—
360C2×D3—41no—
361C2×D3—42no—
362C2×D3—81no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—202no—
366C3×C4—201no—
367C3×C4—201no—
368Dic3—41no—
369Dic3—201no—
370Dic3—201no—
371Dic3—401no—
372C2×C5—21no—
373C2×C5—21no—
374C2×C5—122no—
375C2×C5#474211yescharacteristic
376C2×C5#480911yescharacteristic
377C2×C5#482211yescharacteristic
378C23—32no—
379C23—61no—
380C23—61no—
381C23—121no—
382C23—121no—
383C23D3×D2011yescharacteristic
384Q8—201no—
385Q8—601no—
386Q8—1201no—
387C2×C4—41no—
388C2×C4—61no—
389C2×C4—102no—
390C2×C4—101no—
391C2×C4—101no—
392C2×C4—121no—
393C2×C4—201no—
394C2×C4—201no—
395C2×C4—301no—
396C2×C4—301no—
397C2×C4—601no—
398C2×C4—601no—
399C2×C4—601no—
400C2×C4—1201no—
401C2×C4—1201no—
402C2×C4D5×D1211yescharacteristic
403C2×C4#679011yescharacteristic
404C8—41no—
405C8—121no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3#6502811yescharacteristic
409C2×C3#6503111yescharacteristic
410C2×C3#6503611yescharacteristic
411D3—42no—
412C5#6832211yescharacteristic, complemented, Sylow
413C22—21no—
414C22—21no—
415C22—62no—
416C22—122no—
417C22—121no—
418C22—121no—
419C22—241no—
420C22D3×Dic2011yescharacteristic
421C22#9127411yescharacteristic
422C22#9147611yescharacteristic
423C4—21no—
424C4—21no—
425C4—121no—
426C4—202no—
427C4—201no—
428C4—201no—
429C4—601no—
430C4—601no—
431C4—1201no—
432C3#1059891011yescharacteristic, complemented, Sylow
433C2—21no—
434C2—21no—
435C2—122no—
436C2#1174713611yescharacteristic
437C2#1174813311yescharacteristic
438C2#1174824911yescharacteristic
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#1614
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. #11750823C2semidirect
4. #11748403C2semidirect
6. C3×#64687C2semidirect
7. #11745964C2semidirect
35. #64687D3semidirect
352. C3×C5#1614semidirect
412. C5#68322semidirect
432. C3#10598910semidirect

Maximal subgroups

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

subgroupindex
#117544782
#117508232
#117487622
#117484032
C5×#44682
C3×#646872
#117459642
#105989103
#683225