Finite Group Databasebeta

← #14297536

Subgroups — #14297536

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91770C211yesmaximal, characteristic
2#11749516C212yesmaximal, complemented
3C2×#90997C212yesmaximal
4C5×#4526C211yesmaximal, characteristic, complemented
5C3×#64746C211yesmaximal, characteristic, complemented
6#10599752—31nomaximal, Hall
7C22×#1220C2211yescharacteristic
8C23×Dic15C2211yescharacteristic
9C22×C4×D15C411yescharacteristic, complemented
10C2×C3×C5×C22⋊C4C2211yescharacteristic
11C2×#6714C411yescharacteristic, complemented
12C2×#6712C411yescharacteristic, complemented
13C2×C4×Dic15C411yescharacteristic, complemented
14#91770—22no—
15#91770—22no—
16C2×C5×#217C2212yes—
17C2×C3×C22⋊Dic5C2212yes—
18C2×#6669—22no—
19#90997—24no—
20#90994—22no—
21#68959—51nomaximal, Hall
22C2×#4027—31no—
23C2×#3938—32no—
24#65231—32no—
25C5×#342—31no—
26#64746D311yescharacteristic, complemented
27C24×C3×C5C2311yescharacteristic
28C23×D15C2×C411yescharacteristic
29C22×C3×C4×C5C2×C411yescharacteristic
30C22×C3×C4×C5C2×C411yescharacteristic
31C2×#1220—22no—
32C2×#1220—22no—
33C2×#1220D412yes—
34C2×#1220Q812yes—
35C22×Dic15—42no—
36C22×Dic15C2×C411yescharacteristic
37C22×Dic15C2×C411yescharacteristic
38C22×Dic15C2×C411yescharacteristic
39C22×Dic15D412yes—
40C22×Dic15D412yes—
41C2×C4×D15—21no—
42C2×C4×D15—21no—
43C2×C4×D15—42no—
44C22×C5×Dic3—22no—
45C22×C3×Dic5—22no—
46C3×C5×C22⋊C4—22no—
47#6714—22no—
48#6712—22no—
49C4×Dic15—21no—
50C4×Dic15—21no—
51C5×#217—22no—
52C5×#217—22no—
53C3×C22⋊Dic5—22no—
54C3×C22⋊Dic5—22no—
55#6669—44no—
56C2×#67⋊C4—51no—
57C2×#806—52no—
58#4942—52no—
59C3×#342—51no—
60#4526D511yescharacteristic, complemented
61C22×C22⋊D5—31no—
62C23×Dic5—31no—
63C22×C4×D5—31no—
64C2×C5×C22⋊C4—32no—
65C2×C5×C22⋊C4C2×D311yescharacteristic
66C2×C22⋊Dic5C2×D312yes—
67C2×#685—31no—
68C2×#683—31no—
69C2×#683—62no—
70C2×C4×Dic5—31no—
71#4027—62no—
72#4027—62no—
73#3963—62no—
74#3938—64no—
75#1799—151noSylow
76C23×C3×C5—41no—
77C23×C3×C5—41no—
78C23×C3×C5C22×C411yescharacteristic
79C23×C3×C5C2×D412yes—
80C23×C3×C5C2×D411yescharacteristic
81C23×C3×C5C2×Q811yescharacteristic
82C23×C3×C5#4112yes—
83C22×D15—21no—
84C22×D15—21no—
85C22×D15—41no—
86C22×D15—41no—
87C22×D15C4⋊C412yescomplemented
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5—41no—
92#1220—24no—
93#1220—24no—
94C2×Dic15—21no—
95C2×Dic15—21no—
96C2×Dic15—24no—
97C2×Dic15—22no—
98C2×Dic15—41no—
99C2×Dic15—42no—
100C2×Dic15C22⋊C411yescharacteristic
101C2×Dic15C22⋊C412yes—
102C2×Dic15C22⋊C411yescharacteristic
103C2×Dic15C4⋊C412yescomplemented
104C4×D15—42no—
105C4×D15—42no—
106C2×C5×Dic3—42no—
107C2×C5×Dic3—42no—
108C2×C5×Dic3—42no—
109C2×C3×Dic5—42no—
110C2×C3×Dic5—42no—
111C2×C3×Dic5—42no—
112C22×#67—51no—
113C23×Dic3—51no—
114C22×C4×D3—51no—
115C2×C3×C22⋊C4—52no—
116C2×C3×C22⋊C4C2×D511yescharacteristic
117C2×#217C2×D512yes—
118C2×(C2×D3)⋊C4—51no—
119C2×Dic3⋊C4—51no—
120C2×Dic3⋊C4—102no—
121C2×C4×Dic3—51no—
122#67⋊C4—102no—
123#67⋊C4—102no—
124C3⋊#95—102no—
125#806—104no—
126C24×C5C22×D311yescharacteristic
127C23×D5—31no—
128C22×C4×C5—62no—
129C22×C4×C5C4×D311yescharacteristic
130C22×C4×C5C4×D311yescharacteristic
131C2×C22⋊D5—32no—
132C2×C22⋊D5—32no—
133C2×C22⋊D5—62no—
134C2×C22⋊D5—62no—
135C22×Dic5—22no—
136C22×Dic5—31no—
137C22×Dic5—31no—
138C22×Dic5—32no—
139C22×Dic5—31no—
140C22×Dic5—32no—
141C22×Dic5—122no—
142C2×C4×D5—61no—
143C2×C4×D5—61no—
144C2×C4×D5—122no—
145C5×C22⋊C4—22no—
146C5×C22⋊C4—62no—
147C5×C22⋊C4—62no—
148C22⋊Dic5—22no—
149C22⋊Dic5—22no—
150#685—62no—
151#683—62no—
152#683—124no—
153C4×Dic5—61no—
154C4×Dic5—61no—
155C2×C4×D4—151no—
156C2×#99—152no—
157#380—152no—
158#342—31no—
159#342—51no—
160C22×C3×C5—22no—
161C22×C3×C5—21no—
162C22×C3×C5—22no—
163C22×C3×C5—21no—
164C22×C3×C5—41no—
165C22×C3×C5—41no—
166C22×C3×C5—42no—
167C22×C3×C5C2×C22⋊C411yescharacteristic
168C22×C3×C5C2×C4⋊C411yescharacteristic
169C22×C3×C5#11711yescharacteristic
170C22×C3×C5#12112yes—
171C22×C3×C5C22⋊Q812yes—
172C2×D15—22no—
173C2×D15—42no—
174C2×D15—41no—
175C2×D15—41no—
176C2×D15—42no—
177C3×C4×C5—41no—
178C3×C4×C5—41no—
179Dic15—22no—
180Dic15—21no—
181Dic15—22no—
182Dic15#9912yescomplemented
183C3×Dic5—82no—
184C5×Dic3—82no—
185C24×C3C22×D511yescharacteristic
186C23×D3—51no—
187C22×C3×C4—102no—
188C22×C3×C4C4×D511yescharacteristic
189C22×C3×C4C4×D511yescharacteristic
190C2×#67—52no—
191C2×#67—52no—
192C2×#67—102no—
193C2×#67—102no—
194C22×Dic3—22no—
195C22×Dic3—51no—
196C22×Dic3—51no—
197C22×Dic3—52no—
198C22×Dic3—51no—
199C22×Dic3—52no—
200C22×Dic3—202no—
201C2×C4×D3—101no—
202C2×C4×D3—101no—
203C2×C4×D3—202no—
204C3×C22⋊C4—22no—
205C3×C22⋊C4—102no—
206C3×C22⋊C4—102no—
207#217—22no—
208#217—22no—
209(C2×D3)⋊C4—102no—
210Dic3⋊C4—102no—
211Dic3⋊C4—204no—
212C4×Dic3—101no—
213C4×Dic3—101no—
214C23×C5—41no—
215C23×C5—41no—
216C23×C5C2×C4×D311yescharacteristic
217C23×C5#23512yes—
218C23×C5D3×D411yescharacteristic
219C23×C5D3×D412yes—
220C23×C5D3×Q811yescharacteristic
221C22×D5—32no—
222C22×D5—61no—
223C22×D5—61no—
224C22×D5—121no—
225C22×D5—121no—
226C2×C4×C5—21no—
227C2×C4×C5—21no—
228C2×C4×C5—41no—
229C2×C4×C5—41no—
230C2×C4×C5—122no—
231C2×C4×C5—122no—
232C2×C4×C5—122no—
233C22⋊D5—64no—
234C22⋊D5—64no—
235C2×Dic5—31no—
236C2×Dic5—31no—
237C2×Dic5—32no—
238C2×Dic5—32no—
239C2×Dic5—42no—
240C2×Dic5—42no—
241C2×Dic5—42no—
242C2×Dic5—64no—
243C2×Dic5—62no—
244C2×Dic5—61no—
245C2×Dic5—61no—
246C2×Dic5—122no—
247C2×Dic5—121no—
248C4×D5—122no—
249C4×D5—122no—
250C22×D4—151no—
251C23×C4—151no—
252C23×C4—151no—
253C4×D4—302no—
254C4×D4—302no—
255C2×C4⋊C4—151no—
256C2×C4⋊C4—302no—
257C2×C22⋊C4—32no—
258C2×C22⋊C4—52no—
259C2×C22⋊C4—151no—
260C2×C22⋊C4D3×D511yescharacteristic
261C2×C42—151no—
262#99—304no—
263#95—302no—
264C2×C3×C5—22no—
265C2×C3×C5—21no—
266C2×C3×C5—21no—
267C2×C3×C5—22no—
268C2×C3×C5#38011yescharacteristic
269C2×C3×C5C2×#9911yescharacteristic
270C2×C3×C5#41011yescharacteristic
271D15—42no—
272C23×C3—41no—
273C23×C3—41no—
274C23×C3C2×C4×D511yescharacteristic
275C23×C3#70912yes—
276C23×C3D4×D511yescharacteristic
277C23×C3D4×D512yes—
278C23×C3Q8×D511yescharacteristic
279C22×D3—52no—
280C22×D3—101no—
281C22×D3—101no—
282C22×D3—201no—
283C22×D3—201no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—202no—
289C2×C3×C4—202no—
290C2×C3×C4—202no—
291#67—104no—
292#67—104no—
293C2×Dic3—42no—
294C2×Dic3—42no—
295C2×Dic3—42no—
296C2×Dic3—51no—
297C2×Dic3—51no—
298C2×Dic3—52no—
299C2×Dic3—52no—
300C2×Dic3—104no—
301C2×Dic3—102no—
302C2×Dic3—101no—
303C2×Dic3—101no—
304C2×Dic3—202no—
305C2×Dic3—201no—
306C4×D3—202no—
307C4×D3—202no—
308C22×C5—22no—
309C22×C5—21no—
310C22×C5—22no—
311C22×C5—21no—
312C22×C5—42no—
313C22×C5—41no—
314C22×C5—41no—
315C22×C5#87211yescharacteristic
316C22×C5D3×C22⋊C411yescharacteristic
317C22×C5#88412yes—
318C22×C5D3×C4⋊C411yescharacteristic
319C22×C5#89612yes—
320C2×D5—62no—
321C2×D5—122no—
322C2×D5—121no—
323C2×D5—121no—
324C2×D5—122no—
325C4×C5—41no—
326C4×C5—41no—
327C4×C5—242no—
328Dic5—32no—
329Dic5—62no—
330Dic5—61no—
331Dic5—62no—
332Dic5—82no—
333C24—151no—
334C24C2×D3×D511yescharacteristic
335C2×D4—152no—
336C2×D4—152no—
337C2×D4—302no—
338C2×D4—302no—
339C22×C4—62no—
340C22×C4—102no—
341C22×C4—151no—
342C22×C4—151no—
343C22×C4—152no—
344C22×C4—151no—
345C22×C4—152no—
346C22×C4—301no—
347C22×C4—301no—
348C22×C4—602no—
349C22×C4—602no—
350C22×C4#120011yescharacteristic
351C22×C4#120011yescharacteristic
352C4⋊C4—302no—
353C4⋊C4—604no—
354C22⋊C4—22no—
355C22⋊C4—62no—
356C22⋊C4—62no—
357C22⋊C4—102no—
358C22⋊C4—102no—
359C22⋊C4—302no—
360C42—301no—
361C42—301no—
362C3×C5#179911yescharacteristic, complemented, Hall
363C22×C3—22no—
364C22×C3—21no—
365C22×C3—22no—
366C22×C3—21no—
367C22×C3—42no—
368C22×C3—41no—
369C22×C3—41no—
370C22×C3#401811yescharacteristic
371C22×C3D5×C22⋊C411yescharacteristic
372C22×C3#403012yes—
373C22×C3D5×C4⋊C411yescharacteristic
374C22×C3#404212yes—
375C2×D3—102no—
376C2×D3—202no—
377C2×D3—201no—
378C2×D3—201no—
379C2×D3—202no—
380C3×C4—41no—
381C3×C4—41no—
382C3×C4—402no—
383Dic3—52no—
384Dic3—82no—
385Dic3—101no—
386Dic3—102no—
387Dic3—102no—
388C2×C5—22no—
389C2×C5—21no—
390C2×C5—21no—
391C2×C5—22no—
392C2×C5#466711yescharacteristic
393C2×C5#474011yescharacteristic
394C2×C5D3×#9911yescharacteristic
395D5—122no—
396C23—41no—
397C23—41no—
398C23—152no—
399C23—301no—
400C23—301no—
401C23—601no—
402C23—601no—
403C23D15⋊Q811yescharacteristic
404C23#677112yes—
405C23#677711yescharacteristic
406C23C2×#120011yescharacteristic
407C23#679012yes—
408D4—304no—
409D4—304no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—122no—
415C2×C4—122no—
416C2×C4—122no—
417C2×C4—151no—
418C2×C4—152no—
419C2×C4—151no—
420C2×C4—152no—
421C2×C4—202no—
422C2×C4—202no—
423C2×C4—202no—
424C2×C4—304no—
425C2×C4—302no—
426C2×C4—301no—
427C2×C4—301no—
428C2×C4—602no—
429C2×C4—602no—
430C2×C4—602no—
431C2×C4—601no—
432C2×C3—22no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—22no—
436C2×C3#6495611yescharacteristic
437C2×C3#6502911yescharacteristic
438C2×C3D5×#9911yescharacteristic
439D3—202no—
440C5#6895911yescharacteristic, complemented, Sylow
441C22—21no—
442C22—22no—
443C22—21no—
444C22—22no—
445C22—41no—
446C22—42no—
447C22—41no—
448C22—302no—
449C22—602no—
450C22—602no—
451C22—601no—
452C22—601no—
453C22#9137712yes—
454C22#9138611yescharacteristic
455C22#9143711yescharacteristic
456C22#9146112yes—
457C22#9156111yescharacteristic
458C4—41no—
459C4—41no—
460C4—152no—
461C4—242no—
462C4—301no—
463C4—302no—
464C4—302no—
465C4—402no—
466C3#1059975211yescharacteristic, complemented, Sylow
467C2—22no—
468C2—21no—
469C2—21no—
470C2—22no—
471C2—602no—
472C2#1174886311yescharacteristic
473C2#1174917111yescharacteristic
474C2#1174917411yescharacteristic
subgroupG/H
centerC22#91561
commutatorC23×C3×C5C22×C4
FrattiniC24C2×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×#1220C22
cosocleC24×C3×C5C23
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#1799
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #11749516C2semidirect
4. C5×#4526C2semidirect
5. C3×#64746C2semidirect
9. C22×C4×D15C4semidirect
11. C2×#6714C4semidirect
12. C2×#6712C4semidirect
13. C2×C4×Dic15C4semidirect
26. #64746D3semidirect
60. #4526D5semidirect
87. C22×D15C4⋊C4semidirect
103. C2×Dic15C4⋊C4semidirect
182. Dic15#99semidirect
362. C3×C5#1799semidirect
440. C5#68959semidirect
466. C3#10599752semidirect

Maximal subgroups

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

subgroupindex
C2×#917702
#117495162
C2×#909972
C5×#45262
C3×#647462
#105997523
#689595