Finite Group Databasebeta

← #14288571

Subgroups — #14288571

Order 1920.

472 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 85 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#11756393C211yesmaximal, characteristic
2#11751145C211yesmaximal, characteristic, complemented
3#11750823C211yesmaximal, characteristic, complemented
4#11750778C211yesmaximal, characteristic
5C3×C5×#328C211yesmaximal, characteristic, complemented
6#11746289C211yesmaximal, characteristic
7#11746273C211yesmaximal, characteristic, complemented
8#10599115—31nomaximal, Hall
9C3×C5×C22⋊Q8C2211yescharacteristic
10#91835—21no—
11C2×#6714—21no—
12C2×#6714C2211yescharacteristic
13C2×C4⋊Dic15—21no—
14C2×C4⋊Dic15C2211yescharacteristic
15#91813C2211yescharacteristic
16#91786—21no—
17#91785—21no—
18#91785—21no—
19C22⋊C4×D15—21no—
20#91767—21no—
21C3×C5×C22⋊C8C2211yescharacteristic
22C3×C5×#95C2211yescharacteristic
23#91119—21no—
24#91114C2211yescharacteristic
25#91102—21no—
26#91100—21no—
27#91091—21no—
28#68322—51nomaximal, Hall
29#65968—31no—
30#65333—31no—
31#65011—31no—
32#64966—31no—
33C5×#328D311yescharacteristic, complemented
34#64688—31no—
35#64672—31no—
36C23×D15D411yescharacteristic
37C2×C3×C5×Q8D411yescharacteristic
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5C2311yescharacteristic
40C22×Dic15—21no—
41C22×Dic15D411yescharacteristic
42C2×C4×D15—21no—
43C2×C4×D15—21no—
44C2×Dic30—21no—
45C2×Dic30D411yescharacteristic
46C2×C3×C5×C8—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4D411yescharacteristic
49C3×C5×C22⋊C4—21no—
50#6719—21no—
51#6714—21no—
52#6714—21no—
53#6714—21no—
54#6714—21no—
55#6714—42no—
56C4⋊Dic15—21no—
57C4⋊Dic15—21no—
58C4⋊Dic15—21no—
59C4⋊Dic15—42no—
60C4⋊Dic15D411yescharacteristic
61#6712—21no—
62#6712—21no—
63#6712—21no—
64C2×C3⋊#168—21no—
65#5634—51no—
66#5044—51no—
67#4722—51no—
68#4677—51no—
69C3×#328D511yescharacteristic, complemented
70#4468—51no—
71#4452—51no—
72C5×C22⋊Q8C2×D311yescharacteristic
73#4092—61no—
74C2×#685—31no—
75C2×#685—61no—
76C2×C4⋊Dic5—31no—
77C2×C4⋊Dic5—61no—
78#4070—31no—
79#4043—61no—
80#4042—61no—
81#4042—61no—
82D5×C22⋊C4—61no—
83#4024—61no—
84C5×C22⋊C8C2×D311yescharacteristic
85C5×#95C2×D311yescharacteristic
86#3967—61no—
87C22⋊#168—31no—
88#3950—61no—
89#3948—61no—
90#3939—61no—
91#1614—151noSylow
92C23×C3×C5C2×D411yescharacteristic
93C22×D15—21no—
94C22×D15—21no—
95C22×D15—41no—
96C22×D15—41no—
97C22×D15Q1612yes—
98C3×C5×Q8—41no—
99C2×C3×C4×C5—22no—
100C2×C3×C4×C5—21no—
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×Dic15—21no—
108C2×Dic15—21no—
109C2×Dic15—21no—
110C2×Dic15—41no—
111C2×Dic15—41no—
112C2×Dic15—41no—
113C2×Dic15—41no—
114C4×D15—81no—
115C4×D15—81no—
116Dic30—41no—
117Dic30—81no—
118C3×C5×C8—41no—
119C3⋊#168—41no—
120C3×C22⋊Q8C2×D511yescharacteristic
121#946—101no—
122C2×(C2×D3)⋊C4—51no—
123C2×(C2×D3)⋊C4—101no—
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×#95C2×D511yescharacteristic
134#835—101no—
135#830—51no—
136#818—101no—
137#816—101no—
138#807—101no—
139C23×D5—31no—
140C2×C5×Q8D1211yescharacteristic
141C22×C4×C5—21no—
142C22×C4×C5C22×D311yescharacteristic
143C22×Dic5—31no—
144C22×Dic5—61no—
145C2×C4×D5—61no—
146C2×C4×D5—61no—
147C2×Dic10—31no—
148C2×Dic10—61no—
149C2×C5×C8—21no—
150C5×C4⋊C4—21no—
151C5×C4⋊C4D1211yescharacteristic
152C5×C22⋊C4—21no—
153C22⋊Dic5—61no—
154#685—61no—
155#685—61no—
156#685—61no—
157#685—61no—
158#685—122no—
159C4⋊Dic5—31no—
160C4⋊Dic5—61no—
161C4⋊Dic5—61no—
162C4⋊Dic5—61no—
163C4⋊Dic5—122no—
164#683—61no—
165#683—61no—
166#683—61no—
167C2×#168—61no—
168#543—151no—
169#484—151no—
170#484—151no—
171#399—151no—
172#328—151no—
173#328D1511yescharacteristic, complemented
174#323—151no—
175C22×C3×C5—21no—
176C22×C3×C5—21no—
177C22×C3×C5#12011yescharacteristic
178C22×C3×C5C2×Q1611yescharacteristic
179C22×C3×C5#13711yescharacteristic
180C2×D15—22no—
181C2×D15—41no—
182C2×D15—41no—
183C2×D15—42no—
184C2×D15—81no—
185C3×C4×C5—21no—
186C3×C4×C5—21no—
187C3×C4×C5—42no—
188C3×C4×C5—41no—
189C3×C4×C5—41no—
190Dic15—41no—
191Dic15—41no—
192Dic15—41no—
193Dic15—81no—
194C23×D3—51no—
195C2×C3×Q8D2011yescharacteristic
196C22×C3×C4—21no—
197C22×C3×C4C22×D511yescharacteristic
198C22×Dic3—51no—
199C22×Dic3—101no—
200C2×C4×D3—101no—
201C2×C4×D3—101no—
202C2×Dic6—51no—
203C2×Dic6—101no—
204C2×C3×C8—21no—
205C3×C4⋊C4—21no—
206C3×C4⋊C4D2011yescharacteristic
207C3×C22⋊C4—21no—
208#217—101no—
209(C2×D3)⋊C4—101no—
210(C2×D3)⋊C4—101no—
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—101no—
223C23×C5D3×D411yescharacteristic
224C22×D5—32no—
225C22×D5—61no—
226C22×D5—61no—
227C22×D5—121no—
228C22×D5—121no—
229C5×Q8—41no—
230C2×C4×C5—22no—
231C2×C4×C5—21no—
232C2×C4×C5—21no—
233C2×C4×C5—41no—
234C2×C4×C5—41no—
235C2×C4×C5—41no—
236C2×C4×C5C2×D1211yescharacteristic
237C2×C4×C5D3×D411yescharacteristic
238C2×Dic5—61no—
239C2×Dic5—61no—
240C2×Dic5—61no—
241C2×Dic5—121no—
242C2×Dic5—121no—
243C2×Dic5—121no—
244C2×Dic5—121no—
245C4×D5—241no—
246C4×D5—241no—
247Dic10—121no—
248Dic10—241no—
249C5×C8—41no—
250#168—121no—
251C22⋊Q8—151no—
252C22⋊Q8—301no—
253C22⋊Q8—301no—
254C22⋊Q8—301no—
255C22⋊Q8—301no—
256C22⋊Q8—301no—
257C22⋊Q8C2×D1511yescharacteristic
258C2×C4⋊C4—151no—
259C2×C4⋊C4—301no—
260C2×C22⋊C4—151no—
261C2×C22⋊C4—301no—
262C2×C22⋊C4—301no—
263#107—301no—
264#107—301no—
265#103—301no—
266#103—301no—
267C22⋊C8—151no—
268C22⋊C8C2×D1511yescharacteristic
269#95C2×D1511yescharacteristic
270C2×C3×C5—21no—
271C2×C3×C5—21no—
272C2×C3×C5#45111yescharacteristic
273C2×C3×C5#45311yescharacteristic
274C2×C3×C5#45811yescharacteristic
275D15—42no—
276C23×C3D4×D511yescharacteristic
277C22×D3—52no—
278C22×D3—101no—
279C22×D3—101no—
280C22×D3—201no—
281C22×D3—201no—
282C3×Q8—41no—
283C2×C3×C4—22no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4C2×D2011yescharacteristic
290C2×C3×C4D4×D511yescharacteristic
291C2×Dic3—101no—
292C2×Dic3—101no—
293C2×Dic3—101no—
294C2×Dic3—201no—
295C2×Dic3—201no—
296C2×Dic3—201no—
297C2×Dic3—201no—
298C4×D3—401no—
299C4×D3—401no—
300Dic6—201no—
301Dic6—401no—
302C3×C8—41no—
303C3⋊C8—201no—
304C22×C5—21no—
305C22×C5—21no—
306C22×C5#88211yescharacteristic
307C22×C5#91511yescharacteristic
308C22×C5D3×Q1611yescharacteristic
309C2×D5—62no—
310C2×D5—121no—
311C2×D5—121no—
312C2×D5—122no—
313C2×D5—241no—
314C4×C5—21no—
315C4×C5—21no—
316C4×C5—42no—
317C4×C5—41no—
318C4×C5—41no—
319Dic5—121no—
320Dic5—121no—
321Dic5—121no—
322Dic5—241no—
323C24—151no—
324C2×Q8—151no—
325C2×Q8—301no—
326C2×Q8D6011yescharacteristic
327C22×C4—21no—
328C22×C4—151no—
329C22×C4—301no—
330C22×C4—301no—
331C22×C4—301no—
332C22×C4C22×D1511yescharacteristic
333C2×C8—21no—
334C2×C8—301no—
335C4⋊C4—21no—
336C4⋊C4—151no—
337C4⋊C4—301no—
338C4⋊C4—301no—
339C4⋊C4—301no—
340C4⋊C4—301no—
341C4⋊C4—301no—
342C4⋊C4—301no—
343C4⋊C4—602no—
344C4⋊C4D6011yescharacteristic
345C22⋊C4—21no—
346C22⋊C4—301no—
347C22⋊C4—301no—
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×C3#406111yescharacteristic
357C22×C3D5×Q1611yescharacteristic
358C2×D3—102no—
359C2×D3—201no—
360C2×D3—201no—
361C2×D3—202no—
362C2×D3—401no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—42no—
366C3×C4—41no—
367C3×C4—41no—
368Dic3—201no—
369Dic3—201no—
370Dic3—201no—
371Dic3—401no—
372C2×C5—21no—
373C2×C5—21no—
374C2×C5#474211yescharacteristic
375C2×C5#480911yescharacteristic
376C2×C5#482211yescharacteristic
377D5—122no—
378C23—152no—
379C23—301no—
380C23—301no—
381C23—601no—
382C23—601no—
383C23D4×D1511yescharacteristic
384Q8—41no—
385Q8—601no—
386Q8—1201no—
387C2×C4—22no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—301no—
394C2×C4—301no—
395C2×C4—301no—
396C2×C4—601no—
397C2×C4—601no—
398C2×C4—601no—
399C2×C4—601no—
400C2×C4—1201no—
401C2×C4—1201no—
402C2×C4C2×D6011yescharacteristic
403C2×C4D4×D1511yescharacteristic
404C8—41no—
405C8—601no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3#6503111yescharacteristic
409C2×C3#6509711yescharacteristic
410C2×C3#6511111yescharacteristic
411D3—202no—
412C5#6832211yescharacteristic, complemented, Sylow
413C22—21no—
414C22—21no—
415C22—302no—
416C22—602no—
417C22—601no—
418C22—601no—
419C22—1201no—
420C22#9177111yescharacteristic
421C22#9180411yescharacteristic
422C22Q16×D1511yescharacteristic
423C4—21no—
424C4—21no—
425C4—42no—
426C4—41no—
427C4—41no—
428C4—601no—
429C4—601no—
430C4—601no—
431C4—1201no—
432C3#1059911511yescharacteristic, complemented, Sylow
433C2—21no—
434C2—21no—
435C2—602no—
436C2#1175084311yescharacteristic
437C2#1175091011yescharacteristic
438C2#1175092311yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#328C2
socleC22×C3×C5#120
prime radicalC23×D15D4
hypercenter#328D15
hypocenterC3×C5#1614
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #11751145C2semidirect
3. #11750823C2semidirect
5. C3×C5×#328C2semidirect
7. #11746273C2semidirect
33. C5×#328D3semidirect
69. C3×#328D5semidirect
173. #328D15semidirect
352. C3×C5#1614semidirect
412. C5#68322semidirect
432. C3#10599115semidirect

Maximal subgroups

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

subgroupindex
#117563932
#117511452
#117508232
#117507782
C3×C5×#3282
#117462892
#117462732
#105991153
#683225