Finite Group Databasebeta

← #14287893

Subgroups — #14287893

Order 1920.

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

normal subgroups only

This group has 532 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#11754182C211yesmaximal, characteristic, complemented
2C5×#4672C211yesmaximal, characteristic
3#11748543C211yesmaximal, characteristic
4#11748537C211yesmaximal, characteristic
5#11746273C211yesmaximal, characteristic, complemented
6C3×#64672C211yesmaximal, characteristic, complemented
7#11745952C211yesmaximal, characteristic, complemented
8#10600497—31nomaximal, Hall
9C22×C5×D12C2211yescharacteristic
10#91813C2211yescharacteristic
11C2×C5×(C2×D3)⋊C4—21no—
12C2×C5×(C2×D3)⋊C4—21no—
13C2×C5×Dic3⋊C4C2211yescharacteristic
14C3×#4070C2211yescharacteristic
15#91575—21no—
16#91529—21no—
17#91346—21no—
18#91343—21no—
19#91328—21no—
20#91327—21no—
21C2×#6659—21no—
22C2×#6656—21no—
23C3×C5×#95C2211yescharacteristic
24#91114C2211yescharacteristic
25C3×C22⋊#168C2211yescharacteristic
26#90967—21no—
27#90966—21no—
28#68325—51nomaximal, Hall
29#65834—31no—
30C5×#394—31no—
31#65507—31no—
32#65507—31no—
33#64748—31no—
34#64672—31no—
35#64672D311yescharacteristic, complemented
36C23×C5×D3—21no—
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5C2311yescharacteristic
39C2×Dic30D411yescharacteristic
40C22×C5×Dic3D411yescharacteristic
41C22×C5×Dic3D411yescharacteristic
42C2×C5×D12—21no—
43C2×C5×D12—21no—
44C2×C5×D12—42no—
45C2×C3×Dic10D411yescharacteristic
46C2×#1204—21no—
47#6719—21no—
48C4⋊Dic15D411yescharacteristic
49#6712—21no—
50C2×C3⋊#168—21no—
51C5×(C2×D3)⋊C4—42no—
52C5×(C2×D3)⋊C4—42no—
53C5×Dic3⋊C4—21no—
54C5×Dic3⋊C4—21no—
55C3×C22⋊Dic5—21no—
56C3×C4⋊Dic5D411yescharacteristic
57C3×#683—21no—
58C2×C3×#168—21no—
59Dic3⋊Dic5—21no—
60Dic3⋊Dic5—21no—
61Dic3⋊Dic5—21no—
62#6669—21no—
63#6668—21no—
64Dic3×Dic5—21no—
65Dic3×Dic5—21no—
66#6659—42no—
67#6656—42no—
68#5623—51no—
69#5046—51no—
70#4731—51no—
71#4672D511yescharacteristic
72C3×#328—51no—
73#4469—51no—
74#4452—51no—
75C22×C5×D4—31no—
76C2×C5×C4⋊C4—31no—
77C2×C5×C22⋊C4—61no—
78C2×C5×C22⋊C4—61no—
79C2×#687—61no—
80C2×#687—61no—
81#4072—61no—
82#4070—31no—
83#4070—61no—
84#4070C2×D311yescharacteristic
85#4036—61no—
86#4036—61no—
87#4034—61no—
88#4034—61no—
89C5×#95C2×D311yescharacteristic
90#3964—61no—
91#3964—61no—
92C22⋊#168—31no—
93C22⋊#168C2×D311yescharacteristic
94#1599—151noSylow
95C23×C3×C5C2×D411yescharacteristic
96C22×C5×D3—22no—
97C22×C5×D3—41no—
98C22×C5×D3—41no—
99C22×C5×D3—41no—
100C22×C5×D3—41no—
101C22×C5×D3—41no—
102C22×C5×D3—41no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×Dic15—21no—
110C2×Dic15—21no—
111Dic30—41no—
112C2×C5×Dic3—21no—
113C2×C5×Dic3—21no—
114C2×C5×Dic3—21no—
115C2×C5×Dic3—41no—
116C2×C5×Dic3SD1612yescomplemented
117C5×D12—22no—
118C5×D12—22no—
119C5×D12—41no—
120C5×D12—41no—
121C2×C3×Dic5—21no—
122C2×C3×Dic5—21no—
123C3×Dic10—41no—
124#1204—81no—
125C3⋊#168—41no—
126C3×#168—41no—
127C22×D12C2×D511yescharacteristic
128C3×C22⋊Q8—51no—
129#944—101no—
130C2×#215—101no—
131C2×(C2×D3)⋊C4—21no—
132C2×(C2×D3)⋊C4—21no—
133#924—51no—
134C2×Dic3⋊C4C2×D511yescharacteristic
135C2×#204—101no—
136#889—101no—
137#889—101no—
138#888—101no—
139#878—101no—
140#877—101no—
141C3×C22⋊C8—51no—
142C3×#95C2×D511yescharacteristic
143#830—51no—
144#821—101no—
145#809—101no—
146C24×C5—61no—
147C2×C5×D4—61no—
148C2×C5×D4—61no—
149C2×C5×D4—122no—
150C22×C4×C5—21no—
151C22×C4×C5—31no—
152C22×C4×C5—31no—
153C22×C4×C5C22×D311yescharacteristic
154C2×Dic10—31no—
155C2×Dic10—61no—
156C2×Dic10D1211yescharacteristic
157C5×C4⋊C4—61no—
158C5×C4⋊C4—61no—
159C5×C22⋊C4—122no—
160C5×C22⋊C4—122no—
161C22⋊Dic5—21no—
162C22⋊Dic5—61no—
163#687—122no—
164#687—122no—
165C4⋊Dic5—31no—
166C4⋊Dic5—61no—
167C4⋊Dic5—61no—
168C4⋊Dic5—61no—
169C4⋊Dic5D1211yescharacteristic
170#683—21no—
171#683—61no—
172#683—61no—
173#683—61no—
174C4×Dic5—61no—
175C4×Dic5—61no—
176C2×#168—21no—
177C2×#168—61no—
178#544—151no—
179#450—151no—
180#450—151no—
181#394—31no—
182#328—51no—
183#328—151no—
184#324—151no—
185C22×C3×C5—21no—
186C22×C3×C5—21no—
187C22×C3×C5#12011yescharacteristic
188C22×C3×C5C2×SD1611yescharacteristic
189C22×C3×C5#13711yescharacteristic
190C2×C5×D3—42no—
191C2×C5×D3—42no—
192C2×C5×D3—42no—
193C2×C5×D3—81no—
194C2×C5×D3—81no—
195C2×C5×D3—81no—
196C2×C5×D3—81no—
197C3×C4×C5—21no—
198C3×C4×C5—21no—
199C3×C4×C5—81no—
200Dic15—41no—
201Dic15—41no—
202C3×Dic5—41no—
203C3×Dic5—41no—
204C5×Dic3—22no—
205C5×Dic3—41no—
206C23×D3—21no—
207C2×C3×Q8—51no—
208C22×C3×C4—21no—
209C22×C3×C4C22×D511yescharacteristic
210C22×Dic3C22⋊D511yescharacteristic
211C22×Dic3C22⋊D511yescharacteristic
212C2×D12—21no—
213C2×D12—21no—
214C2×D12—42no—
215C2×Dic6—51no—
216C2×Dic6—101no—
217C2×C3×C8—101no—
218C3×C4⋊C4—51no—
219C3×C4⋊C4—101no—
220C3×C22⋊C4—101no—
221#217—101no—
222#215—202no—
223(C2×D3)⋊C4—42no—
224(C2×D3)⋊C4—42no—
225C4⋊Dic3—51no—
226C4⋊Dic3—101no—
227Dic3⋊C4—21no—
228Dic3⋊C4—21no—
229Dic3⋊C4—101no—
230Dic3⋊C4—101no—
231Dic3⋊C4—101no—
232Dic3⋊C4—101no—
233Dic3⋊C4—101no—
234C4×Dic3—101no—
235C4×Dic3—101no—
236C2×C3⋊C8—101no—
237#204—202no—
238C23×C5—62no—
239C23×C5—121no—
240C23×C5—121no—
241C23×C5—121no—
242C23×C5—121no—
243C23×C5—121no—
244C23×C5—121no—
245C23×C5D3×D411yescharacteristic
246C5×D4—62no—
247C5×D4—62no—
248C5×D4—121no—
249C5×D4—121no—
250C2×C4×C5—32no—
251C2×C4×C5—41no—
252C2×C4×C5—41no—
253C2×C4×C5—41no—
254C2×C4×C5—41no—
255C2×C4×C5—61no—
256C2×C4×C5—61no—
257C2×C4×C5—61no—
258C2×C4×C5—121no—
259C2×C4×C5C2×D1211yescharacteristic
260C2×C4×C5D3×D411yescharacteristic
261C2×Dic5—21no—
262C2×Dic5—21no—
263C2×Dic5—61no—
264C2×Dic5—61no—
265Dic10—41no—
266Dic10—121no—
267Dic10—241no—
268#168—41no—
269#168—121no—
270C22×D4—31no—
271C2×SD16—301no—
272C2×SD16—301no—
273C4⋊Q8—301no—
274C4⋊Q8—301no—
275#125—301no—
276#125—301no—
277C22⋊Q8—51no—
278C22⋊Q8—151no—
279C22⋊Q8—301no—
280#117—301no—
281C2×C4⋊C4—31no—
282C2×C22⋊C4—61no—
283C2×C22⋊C4—61no—
284#102—301no—
285#102—301no—
286C22⋊C8—51no—
287C22⋊C8—151no—
288#95D3×D511yescharacteristic
289C2×C3×C5—21no—
290C2×C3×C5—21no—
291C2×C3×C5#44811yescharacteristic
292C2×C3×C5#45411yescharacteristic
293C2×C3×C5B(4,𝔽2)11yescharacteristic
294C5×D3—82no—
295C23×C3C2×C22⋊D511yescharacteristic
296C22×D3—22no—
297C22×D3—41no—
298C22×D3—41no—
299C22×D3—41no—
300C22×D3—41no—
301C22×D3—41no—
302C22×D3—41no—
303C3×Q8—201no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—101no—
309C2×C3×C4—101no—
310C2×C3×C4D4×D511yescharacteristic
311C2×C3×C4D4×D511yescharacteristic
312C2×Dic3—21no—
313C2×Dic3—21no—
314C2×Dic3—21no—
315C2×Dic3—41no—
316C2×Dic3—101no—
317C2×Dic3—101no—
318C2×Dic3#68712yescomplemented
319D12—22no—
320D12—22no—
321D12—41no—
322D12—41no—
323Dic6—201no—
324Dic6—401no—
325C3×C8—201no—
326C3⋊C8—201no—
327C22×C5—21no—
328C22×C5—21no—
329C22×C5—122no—
330C22×C5—122no—
331C22×C5—122no—
332C22×C5—241no—
333C22×C5—241no—
334C22×C5—241no—
335C22×C5—241no—
336C22×C5#88211yescharacteristic
337C22×C5D3×SD1611yescharacteristic
338C22×C5#91811yescharacteristic
339C4×C5—21no—
340C4×C5—21no—
341C4×C5—62no—
342C4×C5—81no—
343C4×C5—121no—
344Dic5—41no—
345Dic5—41no—
346Dic5—121no—
347Dic5—121no—
348C24—61no—
349C2×Q8—51no—
350C2×Q8—151no—
351C2×Q8—301no—
352C2×D4—61no—
353C2×D4—61no—
354C2×D4—122no—
355C22×C4—21no—
356C22×C4—31no—
357C22×C4—31no—
358C22×C4C2×D3×D511yescharacteristic
359SD16—602no—
360SD16—602no—
361C2×C8—101no—
362C2×C8—301no—
363C4⋊C4—51no—
364C4⋊C4—61no—
365C4⋊C4—61no—
366C4⋊C4—101no—
367C4⋊C4—151no—
368C4⋊C4—301no—
369C4⋊C4—301no—
370C4⋊C4—301no—
371C4⋊C4—301no—
372C4⋊C4—301no—
373C4⋊C4—301no—
374C22⋊C4—101no—
375C22⋊C4—122no—
376C22⋊C4—122no—
377C22⋊C4—301no—
378C42—301no—
379C42—301no—
380C3×C5#159911yescharacteristic, complemented, Hall
381C22×C3—21no—
382C22×C3—21no—
383C22×C3C2×#68711yescharacteristic
384C22×C3#408311yescharacteristic
385C22×C3#409711yescharacteristic
386C2×D3—42no—
387C2×D3—42no—
388C2×D3—42no—
389C2×D3—81no—
390C2×D3—81no—
391C2×D3—81no—
392C2×D3—81no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—81no—
396C3×C4—201no—
397C3×C4—201no—
398Dic3—22no—
399Dic3—41no—
400Dic3—201no—
401Dic3—201no—
402C2×C5—21no—
403C2×C5—21no—
404C2×C5—242no—
405C2×C5#474111yescharacteristic
406C2×C5#480611yescharacteristic
407C2×C5#482711yescharacteristic
408C23—62no—
409C23—121no—
410C23—121no—
411C23—121no—
412C23—121no—
413C23—121no—
414C23—121no—
415C23D3×C22⋊D511yescharacteristic
416Q8—201no—
417Q8—601no—
418Q8—1201no—
419D4—62no—
420D4—62no—
421D4—121no—
422D4—121no—
423C2×C4—32no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—61no—
429C2×C4—61no—
430C2×C4—61no—
431C2×C4—101no—
432C2×C4—101no—
433C2×C4—121no—
434C2×C4—301no—
435C2×C4—301no—
436C2×C4D5×D1211yescharacteristic
437C2×C4#677711yescharacteristic
438C8—201no—
439C8—601no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3#6532111yescharacteristic
443C2×C3#6532911yescharacteristic
444C2×C3#6535111yescharacteristic
445D3—82no—
446C5#6832511yescharacteristic, complemented, Sylow
447C22—21no—
448C22—21no—
449C22—122no—
450C22—122no—
451C22—122no—
452C22—241no—
453C22—241no—
454C22—241no—
455C22—241no—
456C22#9147511yescharacteristic
457C22D3×#68711yescharacteristic
458C22#9151011yescharacteristic
459C4—21no—
460C4—21no—
461C4—62no—
462C4—81no—
463C4—121no—
464C4—201no—
465C4—201no—
466C4—601no—
467C4—601no—
468C3#1060049711yescharacteristic, complemented, Sylow
469C2—21no—
470C2—21no—
471C2—242no—
472C2#1174712311yescharacteristic
473C2#1174713411yescharacteristic
474C2#1174749411yescharacteristic
subgroupG/H
centerC22#91475
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#95C22
socleC22×C3×C5#120
prime radicalC22×C5×D12C22
hypercenter#95D3×D5
hypocenterC3×C5#1599
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
1. #11754182C2semidirect
5. #11746273C2semidirect
6. C3×#64672C2semidirect
7. #11745952C2semidirect
35. #64672D3semidirect
116. C2×C5×Dic3SD16semidirect
318. C2×Dic3#687semidirect
380. C3×C5#1599semidirect
446. C5#68325semidirect
468. C3#10600497semidirect

Maximal subgroups

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

subgroupindex
#117541822
C5×#46722
#117485432
#117485372
#117462732
C3×#646722
#117459522
#106004973
#683255