Finite Group Databasebeta

← #14288181

Subgroups — #14288181

Order 1920.

520 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 83 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#11756253C211yesmaximal, characteristic
2C3×C5×#393C211yesmaximal, characteristic, complemented
3#11751329C211yesmaximal, characteristic, complemented
4#11751328C211yesmaximal, characteristic, complemented
5#11746346C211yesmaximal, characteristic, complemented
6#11746273C211yesmaximal, characteristic, complemented
7#11746272C211yesmaximal, characteristic, complemented
8#10600493—31nomaximal, Hall
9C22×C3×C5×Q8C2211yescharacteristic
10C2×C3×C5×C22⋊C4—21no—
11C2×C3×C5×C22⋊C4C2211yescharacteristic
12#91842—21no—
13C2×#6718—21no—
14C2×#6717—21no—
15#91819C2211yescharacteristic
16C4×#1220—21no—
17#91813C2211yescharacteristic
18#91774—21no—
19#91773—21no—
20#91772—21no—
21#91768—21no—
22C3×C5×#95—21no—
23C3×C5×#95C2211yescharacteristic
24#91119—21no—
25#91119—21no—
26#91114C2211yescharacteristic
27#91114C2211yescharacteristic
28#69700—51nomaximal, Hall
29#65828—31no—
30C5×#393D311yescharacteristic, complemented
31#65517—31no—
32#65516—31no—
33#64745—31no—
34#64672—31no—
35#64671—31no—
36C24×C3×C5D411yescharacteristic
37C2×C3×C5×Q8—21no—
38C2×C3×C5×Q8—21no—
39C2×C3×C5×Q8—42no—
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5D411yescharacteristic
43C22×C3×C4×C5C2311yescharacteristic
44C2×#1220—21no—
45C2×#1220—21no—
46C2×#1220—21no—
47C2×D60D411yescharacteristic
48C2×C4×D15—21no—
49C2×Dic30D411yescharacteristic
50C3×C5×C22⋊C4—21no—
51C3×C5×C22⋊C4—21no—
52C3×C5×C22⋊C4—42no—
53#6719—21no—
54#6719—21no—
55#6719—21no—
56#6718—42no—
57#6717—42no—
58#6714—21no—
59#6714—21no—
60C4⋊Dic15D411yescharacteristic
61C4⋊Dic15D411yescharacteristic
62#6712—21no—
63#6712—21no—
64C4×Dic15—21no—
65C2×C3⋊#168—21no—
66C2×C3⋊#168—21no—
67#5494—51no—
68C3×#393D511yescharacteristic, complemented
69#5228—51no—
70#5227—51no—
71#4525—51no—
72#4452—51no—
73#4451—51no—
74C22×C5×Q8C2×D311yescharacteristic
75C2×C5×C22⋊C4—21no—
76C2×C5×C22⋊C4C2×D311yescharacteristic
77#4099—61no—
78C2×#689—61no—
79C2×#688—61no—
80#4076—31no—
81C4×C22⋊D5—61no—
82#4070—31no—
83#4031—61no—
84#4030—61no—
85#4029—61no—
86#4025—61no—
87C5×#95—21no—
88C5×#95C2×D311yescharacteristic
89#3967—61no—
90#3967—61no—
91C22⋊#168—31no—
92C22⋊#168—31no—
93#1606—151noSylow
94C23×C3×C5—21no—
95C23×C3×C5—21no—
96C23×C3×C5—21no—
97C23×C3×C5—41no—
98C23×C3×C5—41no—
99C23×C3×C5C2×D411yescharacteristic
100C22×D15—21no—
101C3×C5×Q8—22no—
102C3×C5×Q8—22no—
103C3×C5×Q8—41no—
104C3×C5×Q8—41no—
105C2×C3×C4×C5—22no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—41no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5—41no—
112C2×C3×C4×C5—41no—
113C2×C3×C4×C5—41no—
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5C2×D411yescharacteristic
116#1220—41no—
117#1220—41no—
118#1220—81no—
119#1220—81no—
120C2×Dic15—21no—
121C2×Dic15—21no—
122C2×Dic15—21no—
123D60—41no—
124C4×D15—81no—
125Dic30—41no—
126C3⋊#168—41no—
127C3⋊#168—41no—
128C22×C3×Q8C2×D511yescharacteristic
129C2×C3×C22⋊C4—21no—
130C2×C3×C22⋊C4C2×D511yescharacteristic
131#953—101no—
132C2×#216—101no—
133C2×#215—101no—
134#930—51no—
135C4×#67—101no—
136#924—51no—
137#885—101no—
138#884—101no—
139#883—101no—
140#879—101no—
141C3×#95—21no—
142C3×#95C2×D511yescharacteristic
143#835—101no—
144#835—101no—
145#830—51no—
146#830—51no—
147C24×C5#6711yescharacteristic
148C2×C5×Q8—21no—
149C2×C5×Q8—21no—
150C2×C5×Q8—42no—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5#6711yescharacteristic
154C22×C4×C5C22×D311yescharacteristic
155C2×C22⋊D5—61no—
156C2×C22⋊D5—61no—
157C2×C22⋊D5—61no—
158C2×D20—31no—
159C2×C4×D5—61no—
160C2×Dic10—31no—
161C5×C22⋊C4—21no—
162C5×C22⋊C4—21no—
163C5×C22⋊C4—42no—
164C22⋊Dic5—61no—
165C22⋊Dic5—61no—
166C22⋊Dic5—61no—
167#689—122no—
168#688—122no—
169#685—61no—
170#685—61no—
171C4⋊Dic5—31no—
172C4⋊Dic5—31no—
173#683—61no—
174#683—61no—
175C4×Dic5—61no—
176C2×#168—61no—
177C2×#168—61no—
178#538—151no—
179#451—151no—
180#448—151no—
181#393D1511yescharacteristic, complemented
182#328—151no—
183#327—151no—
184#323—151no—
185C22×C3×C5—21no—
186C22×C3×C5—21no—
187C22×C3×C5—42no—
188C22×C3×C5—41no—
189C22×C3×C5—41no—
190C22×C3×C5—41no—
191C22×C3×C5—81no—
192C22×C3×C5#12011yescharacteristic
193C22×C3×C5#13511yescharacteristic
194C22×C3×C5#13711yescharacteristic
195C2×D15—41no—
196C2×D15—41no—
197C2×D15—41no—
198C3×C4×C5—21no—
199C3×C4×C5—21no—
200C3×C4×C5—41no—
201C3×C4×C5—42no—
202C3×C4×C5—81no—
203Dic15—41no—
204Dic15—41no—
205Dic15—41no—
206C24×C3C22⋊D511yescharacteristic
207C2×C3×Q8—21no—
208C2×C3×Q8—21no—
209C2×C3×Q8—42no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4C22⋊D511yescharacteristic
213C22×C3×C4C22×D511yescharacteristic
214C2×#67—101no—
215C2×#67—101no—
216C2×#67—101no—
217C2×D12—51no—
218C2×C4×D3—101no—
219C2×Dic6—51no—
220C3×C22⋊C4—21no—
221C3×C22⋊C4—21no—
222C3×C22⋊C4—42no—
223#217—101no—
224#217—101no—
225#217—101no—
226#216—202no—
227#215—202no—
228(C2×D3)⋊C4—101no—
229(C2×D3)⋊C4—101no—
230C4⋊Dic3—51no—
231C4⋊Dic3—51no—
232Dic3⋊C4—101no—
233Dic3⋊C4—101no—
234C4×Dic3—101no—
235C2×C3⋊C8—101no—
236C2×C3⋊C8—101no—
237C23×C5—21no—
238C23×C5—21no—
239C23×C5—21no—
240C23×C5—41no—
241C23×C5—41no—
242C23×C5C2×#6711yescharacteristic
243C22×D5—61no—
244C5×Q8—22no—
245C5×Q8—22no—
246C5×Q8—41no—
247C5×Q8—41no—
248C2×C4×C5—22no—
249C2×C4×C5—21no—
250C2×C4×C5—41no—
251C2×C4×C5—41no—
252C2×C4×C5—41no—
253C2×C4×C5—41no—
254C2×C4×C5—41no—
255C2×C4×C5—41no—
256C2×C4×C5—41no—
257C2×C4×C5D3×D411yescharacteristic
258C2×C4×C5D3×D411yescharacteristic
259C22⋊D5—121no—
260C22⋊D5—121no—
261C22⋊D5—241no—
262C22⋊D5—241no—
263C2×Dic5—61no—
264C2×Dic5—61no—
265C2×Dic5—61no—
266D20—121no—
267C4×D5—241no—
268Dic10—121no—
269#168—121no—
270#168—121no—
271C22×Q8C2×D1511yescharacteristic
272C2×Q16—301no—
273C2×SD16—301no—
274#126—301no—
275#124—301no—
276#123—301no—
277C22⋊Q8—151no—
278#121—151no—
279#121—301no—
280#120—301no—
281C4×D4—301no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4C2×D1511yescharacteristic
284#103—301no—
285#103—301no—
286C22⋊C8—151no—
287C22⋊C8—151no—
288#95—21no—
289#95C2×D1511yescharacteristic
290C2×C3×C5—21no—
291C2×C3×C5—21no—
292C2×C3×C5—81no—
293C2×C3×C5#45211yescharacteristic
294C2×C3×C5#45511yescharacteristic
295C2×C3×C5B(4,𝔽2)11yescharacteristic
296D15—81no—
297C23×C3—21no—
298C23×C3—21no—
299C23×C3—21no—
300C23×C3—41no—
301C23×C3—41no—
302C23×C3C2×C22⋊D511yescharacteristic
303C22×D3—101no—
304C3×Q8—22no—
305C3×Q8—22no—
306C3×Q8—41no—
307C3×Q8—41no—
308C2×C3×C4—22no—
309C2×C3×C4—21no—
310C2×C3×C4—41no—
311C2×C3×C4—41no—
312C2×C3×C4—41no—
313C2×C3×C4—41no—
314C2×C3×C4—41no—
315C2×C3×C4—41no—
316C2×C3×C4—41no—
317C2×C3×C4D4×D511yescharacteristic
318C2×C3×C4D4×D511yescharacteristic
319#67—201no—
320#67—201no—
321#67—401no—
322#67—401no—
323C2×Dic3—101no—
324C2×Dic3—101no—
325C2×Dic3—101no—
326D12—201no—
327C4×D3—401no—
328Dic6—201no—
329C3⋊C8—201no—
330C3⋊C8—201no—
331C22×C5—21no—
332C22×C5—21no—
333C22×C5—42no—
334C22×C5—41no—
335C22×C5—41no—
336C22×C5—41no—
337C22×C5—81no—
338C22×C5#93711yescharacteristic
339C22×C5#94211yescharacteristic
340C22×C5#95011yescharacteristic
341C2×D5—121no—
342C2×D5—121no—
343C2×D5—121no—
344C4×C5—21no—
345C4×C5—21no—
346C4×C5—42no—
347C4×C5—41no—
348C4×C5—81no—
349Dic5—121no—
350Dic5—121no—
351Dic5—121no—
352C24#122011yescharacteristic
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—42no—
356C2×Q8—151no—
357C2×D4—151no—
358C2×D4—301no—
359C2×D4—301no—
360C2×D4—301no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—301no—
364C22×C4#122011yescharacteristic
365C22×C4C22×D1511yescharacteristic
366Q16—602no—
367SD16—602no—
368C2×C8—301no—
369C2×C8—301no—
370C4⋊C4—151no—
371C4⋊C4—151no—
372C4⋊C4—301no—
373C4⋊C4—301no—
374C22⋊C4—21no—
375C22⋊C4—21no—
376C22⋊C4—42no—
377C22⋊C4—301no—
378C22⋊C4—301no—
379C22⋊C4—301no—
380C22⋊C4—301no—
381C22⋊C4—301no—
382C42—301no—
383C3×C5#160611yescharacteristic, complemented, Hall
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—42no—
387C22×C3—41no—
388C22×C3—41no—
389C22×C3—41no—
390C22×C3—81no—
391C22×C3#408311yescharacteristic
392C22×C3#408811yescharacteristic
393C22×C3#409611yescharacteristic
394C2×D3—201no—
395C2×D3—201no—
396C2×D3—201no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—42no—
400C3×C4—41no—
401C3×C4—81no—
402Dic3—201no—
403Dic3—201no—
404Dic3—201no—
405C2×C5—21no—
406C2×C5—21no—
407C2×C5—81no—
408C2×C5#503211yescharacteristic
409C2×C5#504711yescharacteristic
410C2×C5#506111yescharacteristic
411D5—241no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—41no—
416C23—41no—
417C23—301no—
418C23C2×#122011yescharacteristic
419Q8—22no—
420Q8—22no—
421Q8—41no—
422Q8—41no—
423Q8—601no—
424D4—601no—
425D4—601no—
426D4—601no—
427D4—1201no—
428D4—1201no—
429C2×C4—22no—
430C2×C4—21no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—301no—
439C2×C4—301no—
440C2×C4—301no—
441C2×C4—1201no—
442C2×C4D4×D1511yescharacteristic
443C2×C4D4×D1511yescharacteristic
444C8—601no—
445C8—601no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—81no—
449C2×C3#6532111yescharacteristic
450C2×C3#6533611yescharacteristic
451C2×C3#6535011yescharacteristic
452D3—401no—
453C5#6970011yescharacteristic, complemented, Sylow
454C22—21no—
455C22—21no—
456C22—42no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—81no—
461C22—601no—
462C22—601no—
463C22—601no—
464C22#9182611yescharacteristic
465C22#9183111yescharacteristic
466C22#9183911yescharacteristic
467C4—21no—
468C4—21no—
469C4—42no—
470C4—41no—
471C4—81no—
472C4—601no—
473C4—601no—
474C4—601no—
475C3#1060049311yescharacteristic, complemented, Sylow
476C2—21no—
477C2—21no—
478C2—81no—
479C2—1201no—
480C2#1175113311yescharacteristic
481C2#1175114811yescharacteristic
482C2#1175116211yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#393C2
socleC22×C3×C5#120
prime radical#11756253C2
hypercenter#393D15
hypocenterC3×C5#1606
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #393

Complements

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

NH ≅ G/Ntype
2. C3×C5×#393C2semidirect
3. #11751329C2semidirect
4. #11751328C2semidirect
5. #11746346C2semidirect
6. #11746273C2semidirect
7. #11746272C2semidirect
30. C5×#393D3semidirect
68. C3×#393D5semidirect
181. #393D15semidirect
383. C3×C5#1606semidirect
453. C5#69700semidirect
475. C3#10600493semidirect

Maximal subgroups

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

subgroupindex
#117562532
C3×C5×#3932
#117513292
#117513282
#117463462
#117462732
#117462722
#106004933
#697005