Finite Group Databasebeta

← #14287876

Subgroups — #14287876

Order 1920.

532 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C5×#5623C211yesmaximal, characteristic, complemented
2#11751147C211yesmaximal, characteristic
3#11748790C211yesmaximal, characteristic
4#11748554C211yesmaximal, characteristic
5C3×#64758C211yesmaximal, characteristic, complemented
6#11745962C211yesmaximal, characteristic, complemented
7#11745952C211yesmaximal, characteristic, complemented
8#10602695—31nomaximal, Hall
9C22×D60C2211yescharacteristic
10C3×C5×C22⋊Q8C2211yescharacteristic
11C2×#6717—21no—
12C5×#944—21no—
13C5×#924C2211yescharacteristic
14C2×C5×Dic3⋊C4C2211yescharacteristic
15C5×#889—21no—
16C5×#889—21no—
17C5×#888—21no—
18C5×#878—21no—
19C5×#877—21no—
20C2×#6667—21no—
21C2×#6667—21no—
22C2×#6660—21no—
23#91114C2211yescharacteristic
24#91093—21no—
25C3×#3963C2211yescharacteristic
26C3×C22⋊#168C2211yescharacteristic
27#90969—21no—
28#68325—51nomaximal, Hall
29C5×#544—31no—
30#65335—31no—
31#65335—31no—
32#65280—31no—
33#64758—31no—
34#64758D311yescharacteristic, complemented
35#64748—31no—
36C23×D15—21no—
37C2×C3×C5×Q8D411yescharacteristic
38C22×C3×C4×C5C2311yescharacteristic
39C2×D60—21no—
40C2×D60—21no—
41C2×D60—42no—
42C22×C5×Dic3D411yescharacteristic
43C22×C5×Dic3D411yescharacteristic
44C2×C5×Dic6—21no—
45C2×C5×Dic6D411yescharacteristic
46C22×C3×Dic5—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4D411yescharacteristic
49C3×C5×C22⋊C4—21no—
50#6717—42no—
51C2×C3⋊#168—21no—
52C5×#217—21no—
53C5×C4⋊Dic3—21no—
54C5×C4⋊Dic3D411yescharacteristic
55C5×Dic3⋊C4—21no—
56C5×Dic3⋊C4—21no—
57C5×Dic3⋊C4—21no—
58C5×Dic3⋊C4—21no—
59C5×Dic3⋊C4—21no—
60C5×Dic3⋊C4—21no—
61C5×Dic3⋊C4—21no—
62C4×C5×Dic3—21no—
63C4×C5×Dic3—21no—
64C2×C3×#168—21no—
65#6667—42no—
66#6667—42no—
67#6660—42no—
68#5623D511yescharacteristic, complemented
69#5046—51no—
70#4731—51no—
71#4672—51no—
72C3×#328—51no—
73#4469—51no—
74#4452—51no—
75C22×D20—31no—
76C5×C4⋊Q8—61no—
77C5×C4⋊Q8—61no—
78C5×#125—61no—
79C5×#125—61no—
80C5×C22⋊Q8—31no—
81C5×C22⋊Q8—61no—
82C5×C22⋊Q8C2×D311yescharacteristic
83C5×#117—61no—
84C2×C5×C4⋊C4—31no—
85C2×#688—61no—
86C2×#688—61no—
87C2×#685—61no—
88C2×#685—61no—
89#3963C2×D311yescharacteristic
90C22⋊#168—31no—
91C22⋊#168C2×D311yescharacteristic
92#3941—61no—
93#3941—61no—
94#1599—151noSylow
95C23×C3×C5C2×D411yescharacteristic
96C22×D15—22no—
97C22×D15—41no—
98C22×D15—41no—
99C22×D15—41no—
100C22×D15—41no—
101C22×D15—41no—
102C22×D15—41no—
103C3×C5×Q8—41no—
104C2×C3×C4×C5—21no—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109D60—22no—
110D60—22no—
111D60—41no—
112D60—41no—
113C2×C5×Dic3—21no—
114C2×C5×Dic3—21no—
115C2×C5×Dic3—21no—
116C2×C5×Dic3—21no—
117C2×C5×Dic3—21no—
118C2×C5×Dic3—41no—
119C2×C5×Dic3SD1612yescomplemented
120C5×Dic6—41no—
121C5×Dic6—81no—
122C2×C3×Dic5—41no—
123C2×C3×Dic5—41no—
124C2×C3×Dic5—41no—
125C3⋊#168—41no—
126C3×#168—41no—
127C22×D12—51no—
128C3×C22⋊Q8C2×D511yescharacteristic
129#944—21no—
130C2×#215—101no—
131C2×(C2×D3)⋊C4—101no—
132C2×(C2×D3)⋊C4—101no—
133#924C2×D511yescharacteristic
134C2×Dic3⋊C4C2×D511yescharacteristic
135C2×#204—101no—
136#889—21no—
137#889—21no—
138#888—21no—
139#878—21no—
140#877—21no—
141C3×C22⋊C8—51no—
142C3×#95—51no—
143#830—51no—
144#821—101no—
145#809—101no—
146C23×D5—61no—
147C2×C5×Q8—31no—
148C2×C5×Q8—61no—
149C2×C5×Q8D1211yescharacteristic
150C22×C4×C5—31no—
151C22×C4×C5—31no—
152C22×C4×C5C22×D311yescharacteristic
153C22×Dic5—21no—
154C2×D20—61no—
155C2×D20—61no—
156C2×D20—122no—
157C5×C4⋊C4—21no—
158C5×C4⋊C4—31no—
159C5×C4⋊C4—61no—
160C5×C4⋊C4—61no—
161C5×C4⋊C4—61no—
162C5×C4⋊C4—61no—
163C5×C4⋊C4—61no—
164C5×C4⋊C4—61no—
165C5×C4⋊C4—61no—
166C5×C4⋊C4—61no—
167C5×C4⋊C4D1211yescharacteristic
168C5×C22⋊C4—21no—
169C5×C22⋊C4—61no—
170C42×C5—61no—
171C42×C5—61no—
172#688—122no—
173#688—122no—
174#685—122no—
175#685—122no—
176C2×#168—21no—
177C2×#168—61no—
178#544—31no—
179#450—151no—
180#450—151no—
181#394—151no—
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×D15—42no—
191C2×D15—42no—
192C2×D15—42no—
193C2×D15—81no—
194C2×D15—81no—
195C2×D15—81no—
196C2×D15—81no—
197C3×C4×C5—21no—
198C3×C4×C5—21no—
199C3×C4×C5—41no—
200C3×C4×C5—41no—
201C3×Dic5—81no—
202C5×Dic3—22no—
203C5×Dic3—41no—
204C5×Dic3—41no—
205C5×Dic3—41no—
206C23×D3—101no—
207C2×C3×Q8C22⋊D511yescharacteristic
208C22×C3×C4—101no—
209C22×C3×C4C22×D511yescharacteristic
210C22×Dic3C22⋊D511yescharacteristic
211C22×Dic3C22⋊D511yescharacteristic
212C2×D12—101no—
213C2×D12—101no—
214C2×D12—202no—
215C2×Dic6—21no—
216C2×Dic6C22⋊D511yescharacteristic
217C2×C3×C8—101no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4C22⋊D511yescharacteristic
220C3×C22⋊C4—21no—
221#217—21no—
222#215—202no—
223(C2×D3)⋊C4—202no—
224(C2×D3)⋊C4—202no—
225C4⋊Dic3—21no—
226C4⋊Dic3C22⋊D511yescharacteristic
227Dic3⋊C4—21no—
228Dic3⋊C4—21no—
229Dic3⋊C4—21no—
230Dic3⋊C4—21no—
231Dic3⋊C4—21no—
232Dic3⋊C4—21no—
233Dic3⋊C4—21no—
234C4×Dic3—21no—
235C4×Dic3—21no—
236C2×C3⋊C8—101no—
237#204—202no—
238C23×C5D3×D411yescharacteristic
239C22×D5—62no—
240C22×D5—121no—
241C22×D5—121no—
242C22×D5—121no—
243C22×D5—121no—
244C22×D5—121no—
245C22×D5—121no—
246C5×Q8—41no—
247C5×Q8—121no—
248C5×Q8—241no—
249C2×C4×C5—21no—
250C2×C4×C5—21no—
251C2×C4×C5—32no—
252C2×C4×C5—41no—
253C2×C4×C5—61no—
254C2×C4×C5—61no—
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—41no—
262C2×Dic5—41no—
263C2×Dic5—41no—
264D20—62no—
265D20—62no—
266D20—121no—
267D20—121no—
268#168—41no—
269#168—121no—
270C22×D4—151no—
271C2×SD16—301no—
272C2×SD16—301no—
273C4⋊Q8—61no—
274C4⋊Q8—61no—
275#125—61no—
276#125—61no—
277C22⋊Q8—31no—
278C22⋊Q8—61no—
279C22⋊Q8D3×D511yescharacteristic
280#117—61no—
281C2×C4⋊C4—31no—
282C2×C22⋊C4—301no—
283C2×C22⋊C4—301no—
284#102—301no—
285#102—301no—
286C22⋊C8—51no—
287C22⋊C8—151no—
288#95—51no—
289C2×C3×C5—21no—
290C2×C3×C5—21no—
291C2×C3×C5#44811yescharacteristic
292C2×C3×C5#45411yescharacteristic
293C2×C3×C5B(4,𝔽2)11yescharacteristic
294D15—82no—
295C23×C3C2×C22⋊D511yescharacteristic
296C22×D3—102no—
297C22×D3—201no—
298C22×D3—201no—
299C22×D3—201no—
300C22×D3—201no—
301C22×D3—201no—
302C22×D3—201no—
303C3×Q8—41no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—41no—
307C2×C3×C4—201no—
308C2×C3×C4—201no—
309C2×C3×C4—201no—
310C2×C3×C4C2×C22⋊D511yescharacteristic
311C2×C3×C4C2×C22⋊D511yescharacteristic
312C2×Dic3—21no—
313C2×Dic3—21no—
314C2×Dic3—21no—
315C2×Dic3—21no—
316C2×Dic3—21no—
317C2×Dic3—41no—
318C2×Dic3#68812yescomplemented
319D12—102no—
320D12—102no—
321D12—201no—
322D12—201no—
323Dic6—41no—
324Dic6—81no—
325C3×C8—201no—
326C3⋊C8—201no—
327C22×C5—21no—
328C22×C5—21no—
329C22×C5#88211yescharacteristic
330C22×C5D3×SD1611yescharacteristic
331C22×C5#91811yescharacteristic
332C2×D5—122no—
333C2×D5—122no—
334C2×D5—122no—
335C2×D5—241no—
336C2×D5—241no—
337C2×D5—241no—
338C2×D5—241no—
339C4×C5—21no—
340C4×C5—21no—
341C4×C5—41no—
342C4×C5—41no—
343C4×C5—62no—
344C4×C5—121no—
345C4×C5—121no—
346C4×C5—121no—
347Dic5—81no—
348C24—301no—
349C2×Q8—31no—
350C2×Q8—61no—
351C2×Q8#120311yescharacteristic
352C2×D4—301no—
353C2×D4—301no—
354C2×D4—602no—
355C22×C4—31no—
356C22×C4—31no—
357C22×C4—101no—
358C22×C4C2×D3×D511yescharacteristic
359SD16—602no—
360SD16—602no—
361C2×C8—101no—
362C2×C8—301no—
363C4⋊C4—21no—
364C4⋊C4—31no—
365C4⋊C4—61no—
366C4⋊C4—61no—
367C4⋊C4—61no—
368C4⋊C4—61no—
369C4⋊C4—61no—
370C4⋊C4—61no—
371C4⋊C4—61no—
372C4⋊C4—61no—
373C4⋊C4#120311yescharacteristic
374C22⋊C4—21no—
375C22⋊C4—61no—
376C22⋊C4—602no—
377C22⋊C4—602no—
378C42—61no—
379C42—61no—
380C3×C5#159911yescharacteristic, complemented, Hall
381C22×C3—21no—
382C22×C3—21no—
383C22×C3C2×#68811yescharacteristic
384C22×C3#408811yescharacteristic
385C22×C3#409911yescharacteristic
386C2×D3—202no—
387C2×D3—202no—
388C2×D3—202no—
389C2×D3—401no—
390C2×D3—401no—
391C2×D3—401no—
392C2×D3—401no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—41no—
396C3×C4—41no—
397C3×C4—401no—
398Dic3—22no—
399Dic3—41no—
400Dic3—41no—
401Dic3—41no—
402C2×C5—21no—
403C2×C5—21no—
404C2×C5#474111yescharacteristic
405C2×C5#480611yescharacteristic
406C2×C5#482711yescharacteristic
407D5—242no—
408C23—302no—
409C23—601no—
410C23—601no—
411C23—601no—
412C23—601no—
413C23—601no—
414C23—601no—
415C23D3×C22⋊D511yescharacteristic
416Q8—41no—
417Q8—121no—
418Q8—241no—
419D4—302no—
420D4—302no—
421D4—601no—
422D4—601no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—32no—
426C2×C4—41no—
427C2×C4—61no—
428C2×C4—61no—
429C2×C4—61no—
430C2×C4—61no—
431C2×C4—61no—
432C2×C4—121no—
433C2×C4—201no—
434C2×C4—201no—
435C2×C4—201no—
436C2×C4C2×#120311yescharacteristic
437C2×C4D3×C22⋊D511yescharacteristic
438C8—201no—
439C8—601no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3#6551611yescharacteristic
443C2×C3#6553311yescharacteristic
444C2×C3#6553411yescharacteristic
445D3—402no—
446C5#6832511yescharacteristic, complemented, Sylow
447C22—21no—
448C22—21no—
449C22—602no—
450C22—602no—
451C22—602no—
452C22—1201no—
453C22—1201no—
454C22—1201no—
455C22—1201no—
456C22D3×#68811yescharacteristic
457C22#9152011yescharacteristic
458C22#9157011yescharacteristic
459C4—21no—
460C4—21no—
461C4—41no—
462C4—41no—
463C4—62no—
464C4—121no—
465C4—121no—
466C4—121no—
467C4—401no—
468C3#1060269511yescharacteristic, complemented, Sylow
469C2—21no—
470C2—21no—
471C2—1202no—
472C2#1174917811yescharacteristic
473C2#1174927911yescharacteristic
474C2#1174945911yescharacteristic
subgroupG/H
centerC22#91570
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5#120
prime radicalC22×D60C22
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5#1599
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C5×#5623C2semidirect
5. C3×#64758C2semidirect
6. #11745962C2semidirect
7. #11745952C2semidirect
34. #64758D3semidirect
68. #5623D5semidirect
119. C2×C5×Dic3SD16semidirect
318. C2×Dic3#688semidirect
380. C3×C5#1599semidirect
446. C5#68325semidirect
468. C3#10602695semidirect

Maximal subgroups

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

subgroupindex
C5×#56232
#117511472
#117487902
#117485542
C3×#647582
#117459622
#117459522
#106026953
#683255