Finite Group Databasebeta

← #14295362

Subgroups — #14295362

Order 1920.

824 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
2C2×#91090C212yesmaximal
3C22⋊C4×Dic15C212yesmaximal, complemented
4C3×C5×#342C211yesmaximal, characteristic, complemented
5#11746347C211yesmaximal, characteristic, complemented
6#10599745—31nomaximal, Hall
7C22×#1220C2211yescharacteristic
8C23×Dic15C2211yescharacteristic
9C22×C4×D15C411yescharacteristic, complemented
10C2×C3×C5×C22⋊C4C2211yescharacteristic
11C2×C3×C5×C22⋊C4C2212yes—
12C2×#6719C2212yes—
13C2×#6714C411yescharacteristic, complemented
14C2×#6712C411yescharacteristic, complemented
15C2×C4×Dic15—22no—
16C2×C4×Dic15C411yescharacteristic, complemented
17#91770—22no—
18#91770—22no—
19#91115—22no—
20#91090C418yescomplemented
21#68952—51nomaximal, Hall
22C2×#4027—31no—
23C2×#3938—32no—
24C22⋊C4×Dic5—32no—
25C5×#342D311yescharacteristic, complemented
26#64746—31no—
27C24×C3×C5C2311yescharacteristic
28C23×D15C2×C411yescharacteristic
29C22×C3×C4×C5—22no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C22×C3×C4×C5C2×C411yescharacteristic
32C2×#1220—22no—
33C2×#1220—21no—
34C2×#1220—21no—
35C2×#1220C2×C414yes—
36C22×Dic15—22no—
37C22×Dic15—42no—
38C22×Dic15C2×C411yescharacteristic
39C22×Dic15C2×C411yescharacteristic
40C22×Dic15C2×C411yescharacteristic
41C22×Dic15D412yes—
42C22×Dic15D412yes—
43C2×C4×D15—21no—
44C2×C4×D15—21no—
45C2×C4×D15—42no—
46C3×C5×C22⋊C4—22no—
47C3×C5×C22⋊C4—22no—
48C3×C5×C22⋊C4C2×C414yescomplemented
49#6719—22no—
50#6719C2×C414yescomplemented
51#6714—22no—
52#6712—22no—
53C4×Dic15—21no—
54C4×Dic15—21no—
55C4×Dic15—44no—
56C2×#67⋊C4—51no—
57C2×#806—52no—
58Dic3×C22⋊C4—52no—
59C3×#342D511yescharacteristic, complemented
60#4526—51no—
61C22×C22⋊D5—31no—
62C23×Dic5—31no—
63C22×C4×D5—31no—
64C2×C5×C22⋊C4C2×D311yescharacteristic
65C2×C5×C22⋊C4C2×D312yes—
66C2×C22⋊Dic5—32no—
67C2×#685—31no—
68C2×#683—31no—
69C2×C4×Dic5—31no—
70C2×C4×Dic5—62no—
71#4027—62no—
72#4027—62no—
73#3963—62no—
74#3938—38no—
75C4×#99—151noSylow
76C23×C3×C5—41no—
77C23×C3×C5—41no—
78C23×C3×C5C22×C411yescharacteristic
79C23×C3×C5C22×C412yes—
80C23×C3×C5C2×D412yes—
81C23×C3×C5#4111yescharacteristic
82C23×C3×C5#4111yescharacteristic
83C22×D15—21no—
84C22×D15—21no—
85C22×D15—41no—
86C22×D15—41no—
87C22×D15C4212yescomplemented
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—24no—
91C2×C3×C4×C5—42no—
92C2×C3×C4×C5—42no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5—41no—
95#1220—24no—
96#1220—24no—
97C2×Dic15—21no—
98C2×Dic15—21no—
99C2×Dic15—24no—
100C2×Dic15—22no—
101C2×Dic15—24no—
102C2×Dic15—41no—
103C2×Dic15—42no—
104C2×Dic15—42no—
105C2×Dic15—42no—
106C2×Dic15C4212yescomplemented
107C2×Dic15C22⋊C411yescharacteristic
108C2×Dic15C22⋊C412yes—
109C2×Dic15C22⋊C411yescharacteristic
110C4×D15—42no—
111C4×D15—42no—
112C22×#67—51no—
113C23×Dic3—51no—
114C22×C4×D3—51no—
115C2×C3×C22⋊C4C2×D511yescharacteristic
116C2×C3×C22⋊C4C2×D512yes—
117C2×#217—52no—
118C2×(C2×D3)⋊C4—51no—
119C2×Dic3⋊C4—51no—
120C2×C4×Dic3—51no—
121C2×C4×Dic3—102no—
122#67⋊C4—102no—
123#67⋊C4—102no—
124C3⋊#95—102no—
125#806—58no—
126C24×C5C22×D311yescharacteristic
127C23×D5—31no—
128C22×C4×C5—22no—
129C22×C4×C5C4×D311yescharacteristic
130C22×C4×C5C4×D311yescharacteristic
131C2×C22⋊D5—34no—
132C2×C22⋊D5—62no—
133C2×C22⋊D5—61no—
134C2×C22⋊D5—61no—
135C22×Dic5—31no—
136C22×Dic5—31no—
137C22×Dic5—32no—
138C22×Dic5—31no—
139C22×Dic5—32no—
140C22×Dic5—62no—
141C22×Dic5—122no—
142C2×C4×D5—61no—
143C2×C4×D5—61no—
144C2×C4×D5—122no—
145C5×C22⋊C4—22no—
146C5×C22⋊C4—22no—
147C5×C22⋊C4C4×D314yescomplemented
148C22⋊Dic5—34no—
149C22⋊Dic5—62no—
150#685—62no—
151#683—62no—
152C4×Dic5—61no—
153C4×Dic5—61no—
154C4×Dic5—124no—
155C2×C4×D4—151no—
156C2×#99—152no—
157C4×C22⋊C4—152no—
158#342—151no—
159#342D1511yescharacteristic, complemented
160C22×C3×C5—22no—
161C22×C3×C5—21no—
162C22×C3×C5—22no—
163C22×C3×C5—21no—
164C22×C3×C5—42no—
165C22×C3×C5—41no—
166C22×C3×C5—41no—
167C22×C3×C5C2×C4211yescharacteristic
168C22×C3×C5C2×C22⋊C411yescharacteristic
169C22×C3×C5#11711yescharacteristic
170C22×C3×C5C4×D412yes—
171C22×C3×C5C4×D412yes—
172C2×D15—22no—
173C2×D15—42no—
174C2×D15—41no—
175C2×D15—41no—
176C2×D15—42no—
177C3×C4×C5—44no—
178C3×C4×C5—41no—
179C3×C4×C5—41no—
180Dic15—22no—
181Dic15—21no—
182Dic15—22no—
183Dic15—44no—
184Dic15#9912yescomplemented
185C24×C3C22×D511yescharacteristic
186C23×D3—51no—
187C22×C3×C4—22no—
188C22×C3×C4C4×D511yescharacteristic
189C22×C3×C4C4×D511yescharacteristic
190C2×#67—54no—
191C2×#67—102no—
192C2×#67—101no—
193C2×#67—101no—
194C22×Dic3—51no—
195C22×Dic3—51no—
196C22×Dic3—52no—
197C22×Dic3—51no—
198C22×Dic3—52no—
199C22×Dic3—102no—
200C22×Dic3—202no—
201C2×C4×D3—101no—
202C2×C4×D3—101no—
203C2×C4×D3—202no—
204C3×C22⋊C4—22no—
205C3×C22⋊C4—22no—
206C3×C22⋊C4C4×D514yescomplemented
207#217—54no—
208#217—102no—
209(C2×D3)⋊C4—102no—
210Dic3⋊C4—102no—
211C4×Dic3—101no—
212C4×Dic3—101no—
213C4×Dic3—204no—
214C23×C5—41no—
215C23×C5—41no—
216C23×C5C2×C4×D311yescharacteristic
217C23×C5C2×C4×D312yes—
218C23×C5D3×D412yes—
219C23×C5#23711yescharacteristic
220C23×C5#23911yescharacteristic
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—24no—
229C2×C4×C5—42no—
230C2×C4×C5—42no—
231C2×C4×C5—41no—
232C2×C4×C5—41no—
233C22⋊D5—64no—
234C22⋊D5—64no—
235C2×Dic5—31no—
236C2×Dic5—32no—
237C2×Dic5—31no—
238C2×Dic5—32no—
239C2×Dic5—64no—
240C2×Dic5—62no—
241C2×Dic5—61no—
242C2×Dic5—61no—
243C2×Dic5—64no—
244C2×Dic5—122no—
245C2×Dic5—121no—
246C2×Dic5—122no—
247C2×Dic5—122no—
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×C22⋊C4—152no—
257C2×C22⋊C4—151no—
258C2×C22⋊C4C2×D1511yescharacteristic
259C2×C22⋊C4C2×D1512yes—
260C2×C42—151no—
261C2×C42—302no—
262#99—158no—
263#95—302no—
264C2×C3×C5—22no—
265C2×C3×C5—22no—
266C2×C3×C5—21no—
267C2×C3×C5—21no—
268C2×C3×C5C4×C22⋊C411yescharacteristic
269C2×C3×C5C2×#9911yescharacteristic
270C2×C3×C5#41011yescharacteristic
271D15—42no—
272C23×C3—41no—
273C23×C3—41no—
274C23×C3C2×C4×D511yescharacteristic
275C23×C3C2×C4×D512yes—
276C23×C3D4×D512yes—
277C23×C3#71111yescharacteristic
278C23×C3#71311yescharacteristic
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—24no—
287C2×C3×C4—42no—
288C2×C3×C4—42no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291#67—104no—
292#67—104no—
293C2×Dic3—51no—
294C2×Dic3—52no—
295C2×Dic3—51no—
296C2×Dic3—52no—
297C2×Dic3—104no—
298C2×Dic3—102no—
299C2×Dic3—101no—
300C2×Dic3—101no—
301C2×Dic3—104no—
302C2×Dic3—202no—
303C2×Dic3—201no—
304C2×Dic3—202no—
305C2×Dic3—202no—
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×C5C42×D311yescharacteristic
316C22×C5D3×C22⋊C411yescharacteristic
317C22×C5#67⋊C412yes—
318C22×C5#89211yescharacteristic
319C22×C5#89312yes—
320C2×D5—62no—
321C2×D5—122no—
322C2×D5—121no—
323C2×D5—121no—
324C2×D5—122no—
325C4×C5—44no—
326C4×C5—41no—
327C4×C5—41no—
328Dic5—32no—
329Dic5—62no—
330Dic5—61no—
331Dic5—62no—
332Dic5—124no—
333C24—151no—
334C24C22×D1511yescharacteristic
335C2×D4—154no—
336C2×D4—302no—
337C2×D4—301no—
338C2×D4—301no—
339C22×C4—22no—
340C22×C4—151no—
341C22×C4—151no—
342C22×C4—152no—
343C22×C4—151no—
344C22×C4—152no—
345C22×C4—301no—
346C22×C4—301no—
347C22×C4—302no—
348C22×C4—602no—
349C22×C4—602no—
350C22×C4C4×D1511yescharacteristic
351C22×C4C4×D1511yescharacteristic
352C4⋊C4—302no—
353C22⋊C4—22no—
354C22⋊C4—22no—
355C22⋊C4—154no—
356C22⋊C4—302no—
357C22⋊C4—302no—
358C22⋊C4C4×D1514yescomplemented
359C42—301no—
360C42—301no—
361C42—604no—
362C3×C5C4×#9911yescharacteristic, complemented, Hall
363C22×C3—22no—
364C22×C3—21no—
365C22×C3—22no—
366C22×C3—21no—
367C22×C3—42no—
368C22×C3—41no—
369C22×C3—41no—
370C22×C3C42×D511yescharacteristic
371C22×C3D5×C22⋊C411yescharacteristic
372C22×C3#402712yes—
373C22×C3#403811yescharacteristic
374C22×C3#403912yes—
375C2×D3—102no—
376C2×D3—202no—
377C2×D3—201no—
378C2×D3—201no—
379C2×D3—202no—
380C3×C4—44no—
381C3×C4—41no—
382C3×C4—41no—
383Dic3—52no—
384Dic3—101no—
385Dic3—102no—
386Dic3—102no—
387Dic3—204no—
388C2×C5—22no—
389C2×C5—22no—
390C2×C5—21no—
391C2×C5—21no—
392C2×C5#466611yescharacteristic
393C2×C5#474011yescharacteristic
394C2×C5D3×#9911yescharacteristic
395D5—122no—
396C23—41no—
397C23—41no—
398C23—152no—
399C23—301no—
400C23—301no—
401C23—601no—
402C23—601no—
403C23C2×C4×D1511yescharacteristic
404C23C2×C4×D1512yes—
405C23D4×D1512yes—
406C23#681911yescharacteristic
407C23#682111yescharacteristic
408D4—304no—
409D4—304no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—24no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—151no—
418C2×C4—152no—
419C2×C4—151no—
420C2×C4—152no—
421C2×C4—304no—
422C2×C4—302no—
423C2×C4—301no—
424C2×C4—301no—
425C2×C4—304no—
426C2×C4—602no—
427C2×C4—602no—
428C2×C4—602no—
429C2×C4—601no—
430C2×C4—602no—
431C2×C4—602no—
432C2×C3—22no—
433C2×C3—22no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3#6495511yescharacteristic
437C2×C3#6502911yescharacteristic
438C2×C3D5×#9911yescharacteristic
439D3—202no—
440C5#6895211yescharacteristic, complemented, Sylow
441C22—22no—
442C22—21no—
443C22—22no—
444C22—21no—
445C22—42no—
446C22—41no—
447C22—41no—
448C22—302no—
449C22—602no—
450C22—602no—
451C22—601no—
452C22—601no—
453C22C42×D1511yescharacteristic
454C22C22⋊C4×D1511yescharacteristic
455C22#9177012yes—
456C22#9178111yescharacteristic
457C22#9178212yes—
458C4—44no—
459C4—41no—
460C4—41no—
461C4—152no—
462C4—302no—
463C4—301no—
464C4—302no—
465C4—604no—
466C3#1059974511yescharacteristic, complemented, Sylow
467C2—22no—
468C2—22no—
469C2—21no—
470C2—21no—
471C2—602no—
472C2#1175076711yescharacteristic
473C2#1175084111yescharacteristic
474C2D15×#9911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D15
commutatorC22×C3×C5C2×C42
FrattiniC24C22×D15
FittingC3×C5×#342C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×#1220C22
cosocleC24×C3×C5C23
hypercenter#342D15
hypocenterC3×C5C4×#99
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
3. C22⋊C4×Dic15C2semidirect
4. C3×C5×#342C2semidirect
5. #11746347C2semidirect
9. C22×C4×D15C4semidirect
13. C2×#6714C4semidirect
14. C2×#6712C4semidirect
16. C2×C4×Dic15C4semidirect
20. #91090C4semidirect
25. C5×#342D3semidirect
48. C3×C5×C22⋊C4C2×C4semidirect
50. #6719C2×C4semidirect
59. C3×#342D5semidirect
87. C22×D15C42semidirect
106. C2×Dic15C42semidirect
147. C5×C22⋊C4C4×D3semidirect
159. #342D15semidirect
184. Dic15#99semidirect
206. C3×C22⋊C4C4×D5semidirect
358. C22⋊C4C4×D15semidirect
362. C3×C5C4×#99semidirect
440. C5#68952semidirect
466. C3#10599745semidirect

Maximal subgroups

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

subgroupindex
C2×#917702
C2×#910902
C22⋊C4×Dic152
C3×C5×#3422
#117463472
#105997453
#689525