Finite Group Databasebeta

← #14471599

Subgroups — #14471599

Order 1920.

700 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#554C211yesmaximal, characteristic, complemented
2#11756343C211yesmaximal, characteristic, complemented
3#11751194C211yesmaximal, characteristic, complemented
4#11751185C211yesmaximal, characteristic, complemented
5#11751169C212yesmaximal, complemented
6#11751164C212yesmaximal, complemented
7Q8×C3⋊#168C211yesmaximal, characteristic, complemented
8#11751120C211yesmaximal, characteristic, complemented
9C4×#6716C212yesmaximal, complemented
10#11751117C212yesmaximal
11C4×#6715C211yesmaximal, characteristic
12#10615368—31nomaximal, Hall
13C3×C5×C4⋊Q8C2211yescharacteristic
14C3×C5×#125C2212yes—
15C3×C5×C22⋊Q8—21no—
16C3×C5×C22⋊Q8—22no—
17C3×C4×C5×Q8C2211yescharacteristic
18C3×C4×C5×D4C2211yescharacteristic
19C3×C4×C5×D4C2212yes—
20C2×C3×C5×C4⋊C4—21no—
21#91835—21no—
22C2×#6716C2212yes—
23C2×#6715C2211yescharacteristic
24#91787—22no—
25#91781—21no—
26#91764C2212yes—
27C4×D60C2211yescharacteristic
28#91758C2211yescharacteristic
29C4×Dic30C2212yes—
30#91116C2211yescharacteristic
31#91094C2212yes—
32#91094C2212yes—
33#91094C2212yes—
34#91093C2211yescharacteristic
35#91093C2212yes—
36#91092C2212yes—
37#91091C2211yescharacteristic
38C4⋊(C3⋊#168)C2211yescharacteristic
39C4⋊(C3⋊#168)C2212yes—
40C4×C3⋊#168C2212yes—
41C4×C3⋊#168C2211yescharacteristic
42#83637—51nomaximal, Hall
43C5×#554D311yescharacteristic, complemented
44#65918—31no—
45#65382—31no—
46#65373—31no—
47#65357—32no—
48#65352—32no—
49Q8×#168—31no—
50#65308—31no—
51C4×#687—32no—
52#65305—32no—
53C4×#686—31no—
54C2×C3×C5×Q8—21no—
55C2×C3×C5×Q8D411yescharacteristic
56C2×C3×C5×D4C2311yescharacteristic
57C22×C3×C4×C5—21no—
58C22×C3×C4×C5—22no—
59C2×D60C2311yescharacteristic
60C2×C4×D15—21no—
61C2×Dic30C2312yes—
62C3×C5×C4⋊C4—22no—
63C3×C5×C4⋊C4—21no—
64C3×C5×C4⋊C4—22no—
65C3×C5×C4⋊C4D411yescharacteristic
66C3×C5×C4⋊C4D412yes—
67C3×C5×C4⋊C4C2311yescharacteristic
68C3×C5×C4⋊C4C2312yes—
69C3×C5×C22⋊C4—21no—
70C3×C5×C22⋊C4—22no—
71C3×C42×C5C2312yes—
72C3×C42×C5C2311yescharacteristic
73#6716—24no—
74#6715—22no—
75#6714—21no—
76#6714—22no—
77#6714—22no—
78C4⋊Dic15—21no—
79C4⋊Dic15—21no—
80C4⋊Dic15C2311yescharacteristic
81#6712—22no—
82C4×Dic15—22no—
83C2×C3⋊#168C2311yescharacteristic
84C2×C3⋊#168C2312yes—
85C2×C3⋊#168C2311yescharacteristic
86C3×#554D511yescharacteristic, complemented
87#5584—51no—
88#5093—51no—
89#5084—51no—
90#5068—52no—
91#5063—52no—
92Q8×C3⋊C8—51no—
93#5019—51no—
94C4×#214—52no—
95#5016—52no—
96C4×#213—51no—
97C5×C4⋊Q8C2×D311yescharacteristic
98C5×#125C2×D312yes—
99C5×C22⋊Q8—21no—
100C5×C22⋊Q8—22no—
101C4×C5×Q8C2×D311yescharacteristic
102C4×C5×D4C2×D311yescharacteristic
103C4×C5×D4C2×D312yes—
104C2×C5×C4⋊C4—21no—
105#4092—61no—
106C2×#687—32no—
107C2×#686—31no—
108#4044—62no—
109#4038—61no—
110#4021—32no—
111C4×D20—31no—
112#4015—31no—
113C4×Dic10—32no—
114#3964—31no—
115#3942—32no—
116#3942—32no—
117#3942—32no—
118#3941—31no—
119#3941—32no—
120#3940—32no—
121#3939—31no—
122C4⋊#168—32no—
123C4⋊#168—31no—
124C4×#168—31no—
125C4×#168—32no—
126#3360—151noSylow
127C23×C3×C5—21no—
128C22×D15—21no—
129C3×C5×Q8—22no—
130C3×C5×Q8—81no—
131C3×C5×D4—21no—
132C3×C5×D4#4112yes—
133C2×C3×C4×C5—21no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—42no—
136C2×C3×C4×C5—82no—
137C2×C3×C4×C5C2×D412yes—
138C2×C3×C4×C5C2×D412yes—
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2411yescharacteristic
142C2×Dic15—21no—
143C2×Dic15—22no—
144D60—21no—
145D60—21no—
146C4×D15—42no—
147Dic30—22no—
148Dic30—22no—
149C3⋊#168—21no—
150C3⋊#168—22no—
151C3⋊#168—21no—
152C3×C4⋊Q8C2×D511yescharacteristic
153C3×#125C2×D512yes—
154C3×C22⋊Q8—21no—
155C3×C22⋊Q8—22no—
156C3×C4×Q8C2×D511yescharacteristic
157C3×C4×D4C2×D511yescharacteristic
158C3×C4×D4C2×D512yes—
159C2×C3×C4⋊C4—21no—
160#946—101no—
161C2×#214—52no—
162C2×#213—51no—
163#898—102no—
164#892—101no—
165#875—52no—
166C4×D12—51no—
167#869—51no—
168C4×Dic6—52no—
169#832—51no—
170#810—52no—
171#810—52no—
172#810—52no—
173#809—51no—
174#809—52no—
175#808—52no—
176#807—51no—
177C4⋊(C3⋊C8)—52no—
178C4⋊(C3⋊C8)—51no—
179C4×C3⋊C8—51no—
180C4×C3⋊C8—52no—
181C2×C5×Q8—21no—
182C2×C5×Q8#6711yescharacteristic
183C2×C5×D4C22×D311yescharacteristic
184C22×C4×C5—21no—
185C22×C4×C5—22no—
186C2×D20—31no—
187C2×C4×D5—61no—
188C2×Dic10—32no—
189C5×C4⋊C4—22no—
190C5×C4⋊C4—21no—
191C5×C4⋊C4—22no—
192C5×C4⋊C4#6711yescharacteristic
193C5×C4⋊C4#6712yes—
194C5×C4⋊C4C22×D311yescharacteristic
195C5×C4⋊C4C22×D312yes—
196C5×C22⋊C4—21no—
197C5×C22⋊C4—22no—
198C42×C5C22×D312yes—
199C42×C5C22×D311yescharacteristic
200#687—64no—
201#686—62no—
202#685—61no—
203#685—62no—
204#685—62no—
205C4⋊Dic5—31no—
206C4⋊Dic5—61no—
207C4⋊Dic5—61no—
208#683—62no—
209C4×Dic5—62no—
210C2×#168—31no—
211C2×#168—31no—
212C2×#168—32no—
213#556—151no—
214#554D1511yescharacteristic, complemented
215#488—152no—
216#487—151no—
217#479—152no—
218#476—151no—
219#463—152no—
220#461—151no—
221C8×Q8—151no—
222C4×SD16—152no—
223C4×D8—151no—
224C22×C3×C5—22no—
225C22×C3×C5—41no—
226C22×C3×C5—41no—
227C22×C3×C5C22×D411yescharacteristic
228C2×D15—41no—
229C2×D15—41no—
230C2×D15—41no—
231C3×C4×C5—22no—
232C3×C4×C5—22no—
233C3×C4×C5—21no—
234C3×C4×C5—41no—
235C3×C4×C5—42no—
236C3×C4×C5#13512yes—
237C3×C4×C5C2×#4111yescharacteristic
238C3×C4×C52−1+411yescharacteristic
239Dic15—42no—
240Dic15—41no—
241C2×C3×Q8—21no—
242C2×C3×Q8C22⋊D511yescharacteristic
243C2×C3×D4C22×D511yescharacteristic
244C22×C3×C4—21no—
245C22×C3×C4—22no—
246C2×D12—51no—
247C2×C4×D3—101no—
248C2×Dic6—52no—
249C3×C4⋊C4—22no—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—22no—
252C3×C4⋊C4C22⋊D511yescharacteristic
253C3×C4⋊C4C22⋊D512yes—
254C3×C4⋊C4C22×D511yescharacteristic
255C3×C4⋊C4C22×D512yes—
256C3×C22⋊C4—21no—
257C3×C22⋊C4—22no—
258C3×C42C22×D512yes—
259C3×C42C22×D511yescharacteristic
260#214—104no—
261#213—102no—
262(C2×D3)⋊C4—101no—
263(C2×D3)⋊C4—102no—
264(C2×D3)⋊C4—102no—
265C4⋊Dic3—51no—
266C4⋊Dic3—101no—
267C4⋊Dic3—101no—
268Dic3⋊C4—102no—
269C4×Dic3—102no—
270C2×C3⋊C8—51no—
271C2×C3⋊C8—51no—
272C2×C3⋊C8—52no—
273C23×C5—21no—
274C22×D5—61no—
275C5×Q8—22no—
276C5×Q8—81no—
277C5×D4—21no—
278C5×D4#23912yes—
279C2×C4×C5—21no—
280C2×C4×C5—22no—
281C2×C4×C5—42no—
282C2×C4×C5—82no—
283C2×C4×C5C2×#6712yes—
284C2×C4×C5C2×#6712yes—
285C2×C4×C5C2×#6711yescharacteristic
286C2×C4×C5C2×#6711yescharacteristic
287C2×C4×C5C23×D311yescharacteristic
288C2×Dic5—61no—
289C2×Dic5—62no—
290D20—61no—
291D20—61no—
292C4×D5—122no—
293Dic10—62no—
294Dic10—62no—
295#168—61no—
296#168—62no—
297#168—61no—
298C2×SD16—152no—
299C2×D8—151no—
300C4⋊Q8—151no—
301C4⋊Q8C2×D1511yescharacteristic
302#126—302no—
303#125C2×D1512yes—
304#124—152no—
305C22⋊Q8—21no—
306C22⋊Q8—22no—
307C22⋊Q8—301no—
308C4×Q8—152no—
309C4×Q8C2×D1511yescharacteristic
310C4×D4—151no—
311C4×D4C2×D1511yescharacteristic
312C4×D4C2×D1512yes—
313#117—301no—
314C2×C4⋊C4—21no—
315#107—151no—
316#106—152no—
317C4⋊C8—151no—
318C4⋊C8—152no—
319#103—152no—
320#103—152no—
321#103—152no—
322#102—151no—
323#102—151no—
324#102—152no—
325C4×C8—151no—
326C4×C8—152no—
327C2×C3×C5—42no—
328C2×C3×C5#54811yescharacteristic
329C2×C3×C5C2×#13511yescharacteristic
330C2×C3×C5#57711yescharacteristic
331D15—81no—
332C23×C3—21no—
333C22×D3—101no—
334C3×Q8—22no—
335C3×Q8—81no—
336C3×D4—21no—
337C3×D4#71312yes—
338C2×C3×C4—21no—
339C2×C3×C4—22no—
340C2×C3×C4—42no—
341C2×C3×C4—82no—
342C2×C3×C4C2×C22⋊D512yes—
343C2×C3×C4C2×C22⋊D512yes—
344C2×C3×C4C2×C22⋊D511yescharacteristic
345C2×C3×C4C2×C22⋊D511yescharacteristic
346C2×C3×C4C23×D511yescharacteristic
347C2×Dic3—101no—
348C2×Dic3—102no—
349D12—101no—
350D12—101no—
351C4×D3—202no—
352Dic6—102no—
353Dic6—102no—
354C3⋊C8—101no—
355C3⋊C8—102no—
356C3⋊C8—101no—
357C22×C5—22no—
358C22×C5—41no—
359C22×C5—41no—
360C22×C5C22×#6711yescharacteristic
361C2×D5—121no—
362C2×D5—121no—
363C2×D5—121no—
364C4×C5—22no—
365C4×C5—22no—
366C4×C5—21no—
367C4×C5—41no—
368C4×C5—42no—
369C4×C5#95012yes—
370C4×C5C2×#23911yescharacteristic
371C4×C5#100711yescharacteristic
372Dic5—122no—
373Dic5—121no—
374C2×Q8—21no—
375C2×Q8—152no—
376C2×Q8#122011yescharacteristic
377C2×D4—151no—
378C2×D4C22×D1511yescharacteristic
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—301no—
382SD16—304no—
383D8—302no—
384C2×C8—151no—
385C2×C8—152no—
386C2×C8—151no—
387C4⋊C4—22no—
388C4⋊C4—21no—
389C4⋊C4—22no—
390C4⋊C4—151no—
391C4⋊C4—301no—
392C4⋊C4—302no—
393C4⋊C4—301no—
394C4⋊C4#122011yescharacteristic
395C4⋊C4#122012yes—
396C4⋊C4C22×D1512yes—
397C4⋊C4C22×D1511yescharacteristic
398C22⋊C4—21no—
399C22⋊C4—22no—
400C22⋊C4—302no—
401C22⋊C4—301no—
402C22⋊C4—302no—
403C42—302no—
404C42C22×D1511yescharacteristic
405C42C22×D1512yes—
406C3×C5#336011yescharacteristic, complemented, Hall
407C22×C3—22no—
408C22×C3—41no—
409C22×C3—41no—
410C22×C3C22×C22⋊D511yescharacteristic
411C2×D3—201no—
412C2×D3—201no—
413C2×D3—201no—
414C3×C4—22no—
415C3×C4—22no—
416C3×C4—21no—
417C3×C4—41no—
418C3×C4—42no—
419C3×C4#409612yes—
420C3×C4C2×#71311yescharacteristic
421C3×C4#414711yescharacteristic
422Dic3—202no—
423Dic3—201no—
424C2×C5—42no—
425C2×C5#581711yescharacteristic
426C2×C5C2×#95011yescharacteristic
427C2×C5#583611yescharacteristic
428D5—241no—
429C23—21no—
430C23—301no—
431Q8—22no—
432Q8—81no—
433Q8—302no—
434Q8—302no—
435D4—21no—
436D4—301no—
437D4—301no—
438D4#682112yes—
439C2×C4—21no—
440C2×C4—22no—
441C2×C4—42no—
442C2×C4—82no—
443C2×C4—301no—
444C2×C4—302no—
445C2×C4—602no—
446C2×C4C2×#122012yes—
447C2×C4C2×#122012yes—
448C2×C4C2×#122011yescharacteristic
449C2×C4C2×#122011yescharacteristic
450C2×C4C23×D1511yescharacteristic
451C8—301no—
452C8—302no—
453C8—301no—
454C2×C3—42no—
455C2×C3#6615111yescharacteristic
456C2×C3C2×#409611yescharacteristic
457C2×C3#6617011yescharacteristic
458D3—401no—
459C5#8363711yescharacteristic, complemented, Sylow
460C22—22no—
461C22—41no—
462C22—41no—
463C22—601no—
464C22—601no—
465C22—601no—
466C22C22×#122011yescharacteristic
467C4—22no—
468C4—22no—
469C4—21no—
470C4—41no—
471C4—42no—
472C4—602no—
473C4—601no—
474C4#9183912yes—
475C4C2×#682111yescharacteristic
476C4#9209811yescharacteristic
477C3#1061536811yescharacteristic, complemented, Sylow
478C2—42no—
479C2—1201no—
480C2#1175657611yescharacteristic
481C2C2×#9183911yescharacteristic
482C2#1175659511yescharacteristic
subgroupG/H
centerC22C22×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#554C2
socleC22×C3×C5C22×D4
prime radicalC2×#6715C22
hypercenter#554D15
hypocenterC3×C5#3360
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #554

Complements

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

NH ≅ G/Ntype
1. C3×C5×#554C2semidirect
2. #11756343C2semidirect
3. #11751194C2semidirect
4. #11751185C2semidirect
5. #11751169C2semidirect
6. #11751164C2semidirect
7. Q8×C3⋊#168C2semidirect
8. #11751120C2semidirect
9. C4×#6716C2semidirect
43. C5×#554D3semidirect
86. C3×#554D5semidirect
214. #554D15semidirect
406. C3×C5#3360semidirect
459. C5#83637semidirect
477. C3#10615368semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5542
#117563432
#117511942
#117511852
#117511692
#117511642
Q8×C3⋊#1682
#117511202
C4×#67162
#117511172
C4×#67152
#106153683
#836375