Finite Group Databasebeta

← #14283419

Subgroups — #14283419

Order 1920.

572 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756550C211yesmaximal, characteristic
2C3×C5×#407C211yesmaximal, characteristic, complemented
3#11751313C211yesmaximal, characteristic, complemented
4#11746291C212yesmaximal, complemented
5#11746288C212yesmaximal, complemented
6#10600772—31nomaximal, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C2×#6817C411yescharacteristic, complemented
9C2×C3×C5×M16—21no—
10#91842—21no—
11C2×#6719—21no—
12#91819C411yescharacteristic, complemented
13#91819C2211yescharacteristic
14#91818—21no—
15C4×#1220—21no—
16C4×#1220—21no—
17#91815C411yescharacteristic, complemented
18C2×C4⋊Dic15—21no—
19#91813C411yescharacteristic, complemented
20#91813C2211yescharacteristic
21C3×C5×C22⋊C8—21no—
22C3×C5×C22⋊C8C2212yes—
23#91115C2212yes—
24#69979—51nomaximal, Hall
25#66125—31no—
26C5×#407D311yescharacteristic, complemented
27#65501—31no—
28#64690—32no—
29#64687—32no—
30C24×C3×C5D411yescharacteristic
31C22×C3×C4×C5—42no—
32C22×C3×C4×C5C2×C411yescharacteristic
33C22×C3×C4×C5C2×C411yescharacteristic
34C22×C3×C4×C5D411yescharacteristic
35C22×C3×C4×C5D411yescharacteristic
36C22×C3×C4×C5D411yescharacteristic
37C22×C3×C4×C5C2311yescharacteristic
38C2×#1220—21no—
39C2×#1220—21no—
40C2×#1220—21no—
41C22×Dic15—22no—
42#6817—42no—
43C2×D60C2×C411yescharacteristic
44C2×C4×D15—21no—
45C2×Dic30C2×C411yescharacteristic
46C3×C5×M16—42no—
47C2×C3×C5×C8—22no—
48#6719—21no—
49#6719—21no—
50#6719—21no—
51#6719—42no—
52#6714—21no—
53#6714—21no—
54C4⋊Dic15—42no—
55C4⋊Dic15C2×C411yescharacteristic
56C4⋊Dic15C2×C411yescharacteristic
57#6712—21no—
58#6712—21no—
59C4×Dic15—21no—
60#5791—51no—
61C3×#407D511yescharacteristic, complemented
62#5212—51no—
63#4470—52no—
64#4467—52no—
65C23×C4×C5C2×D311yescharacteristic
66C2×#709—31no—
67C2×C5×M16—21no—
68#4099—61no—
69C2×C22⋊Dic5—61no—
70#4076—31no—
71#4076—31no—
72#4075—61no—
73C4×C22⋊D5—61no—
74C4×C22⋊D5—61no—
75#4072—31no—
76C2×C4⋊Dic5—61no—
77#4070—31no—
78#4070—31no—
79C5×C22⋊C8—21no—
80C5×C22⋊C8C2×D312yes—
81#3963—32no—
82#1513—151noSylow
83C23×C3×C5—21no—
84C23×C3×C5—21no—
85C23×C3×C5—41no—
86C23×C3×C5—41no—
87C23×C3×C5C22⋊C411yescharacteristic
88C23×C3×C5C22⋊C411yescharacteristic
89C23×C3×C5C2×D411yescharacteristic
90C22×D15—21no—
91C2×C3×C4×C5—22no—
92C2×C3×C4×C5—22no—
93C2×C3×C4×C5—22no—
94C2×C3×C4×C5—41no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5C22⋊C411yescharacteristic
98C2×C3×C4×C5C22⋊C411yescharacteristic
99C2×C3×C4×C5C22×C411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101#1220—42no—
102#1220—42no—
103#1220—41no—
104#1220—41no—
105C2×Dic15—21no—
106C2×Dic15—21no—
107C2×Dic15—21no—
108C2×Dic15—42no—
109C2×Dic15—42no—
110C2×Dic15—42no—
111D60—41no—
112C4×D15—42no—
113Dic30—41no—
114C3×C5×C8—42no—
115C23×C3×C4C2×D511yescharacteristic
116C2×#235—51no—
117C2×C3×M16—21no—
118#953—101no—
119C2×#217—101no—
120#930—51no—
121#930—51no—
122#929—101no—
123C4×#67—101no—
124C4×#67—101no—
125#926—51no—
126C2×C4⋊Dic3—101no—
127#924—51no—
128#924—51no—
129C3×C22⋊C8—21no—
130C3×C22⋊C8C2×D512yes—
131C3⋊#95—52no—
132C24×C5D1211yescharacteristic
133C22×C4×C5—42no—
134C22×C4×C5C4×D311yescharacteristic
135C22×C4×C5C4×D311yescharacteristic
136C22×C4×C5D1211yescharacteristic
137C22×C4×C5#6711yescharacteristic
138C22×C4×C5#6711yescharacteristic
139C22×C4×C5C22×D311yescharacteristic
140C2×C22⋊D5—61no—
141C2×C22⋊D5—61no—
142C2×C22⋊D5—61no—
143C22×Dic5—62no—
144#709—122no—
145C2×D20—31no—
146C2×C4×D5—61no—
147C2×Dic10—31no—
148C5×M16—42no—
149C2×C5×C8—22no—
150C22⋊Dic5—61no—
151C22⋊Dic5—61no—
152C22⋊Dic5—61no—
153C22⋊Dic5—122no—
154#685—61no—
155#685—61no—
156C4⋊Dic5—31no—
157C4⋊Dic5—31no—
158C4⋊Dic5—122no—
159#683—61no—
160#683—61no—
161C4×Dic5—61no—
162#525—151no—
163#407D1511yescharacteristic, complemented
164#380—151no—
165#328—152no—
166#327—152no—
167C22×C3×C5—21no—
168C22×C3×C5—21no—
169C22×C3×C5—21no—
170C22×C3×C5—21no—
171C22×C3×C5—21no—
172C22×C3×C5—21no—
173C22×C3×C5—21no—
174C22×C3×C5—21no—
175C22×C3×C5—42no—
176C22×C3×C5—42no—
177C22×C3×C5C2×C22⋊C411yescharacteristic
178C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
179C22×C3×C5#13711yescharacteristic
180C2×D15—41no—
181C2×D15—41no—
182C2×D15—41no—
183C3×C4×C5—21no—
184C3×C4×C5—21no—
185C3×C4×C5—21no—
186C3×C4×C5#9912yes—
187Dic15—41no—
188Dic15—41no—
189Dic15—41no—
190Dic15—82no—
191C24×C3D2011yescharacteristic
192C22×C3×C4—42no—
193C22×C3×C4C4×D511yescharacteristic
194C22×C3×C4C4×D511yescharacteristic
195C22×C3×C4D2011yescharacteristic
196C22×C3×C4C22⋊D511yescharacteristic
197C22×C3×C4C22⋊D511yescharacteristic
198C22×C3×C4C22×D511yescharacteristic
199C2×#67—101no—
200C2×#67—101no—
201C2×#67—101no—
202C22×Dic3—102no—
203#235—202no—
204C2×D12—51no—
205C2×C4×D3—101no—
206C2×Dic6—51no—
207C3×M16—42no—
208C2×C3×C8—22no—
209#217—101no—
210#217—101no—
211#217—101no—
212#217—202no—
213(C2×D3)⋊C4—101no—
214(C2×D3)⋊C4—101no—
215C4⋊Dic3—51no—
216C4⋊Dic3—51no—
217C4⋊Dic3—202no—
218Dic3⋊C4—101no—
219Dic3⋊C4—101no—
220C4×Dic3—101no—
221C23×C5—21no—
222C23×C5—21no—
223C23×C5—41no—
224C23×C5—41no—
225C23×C5(C2×D3)⋊C411yescharacteristic
226C23×C5(C2×D3)⋊C411yescharacteristic
227C23×C5C2×D1211yescharacteristic
228C22×D5—61no—
229C2×C4×C5—22no—
230C2×C4×C5—22no—
231C2×C4×C5—22no—
232C2×C4×C5—41no—
233C2×C4×C5—41no—
234C2×C4×C5—41no—
235C2×C4×C5(C2×D3)⋊C411yescharacteristic
236C2×C4×C5(C2×D3)⋊C411yescharacteristic
237C2×C4×C5C2×C4×D311yescharacteristic
238C2×C4×C5C2×#6711yescharacteristic
239C22⋊D5—122no—
240C22⋊D5—122no—
241C22⋊D5—121no—
242C22⋊D5—121no—
243C2×Dic5—61no—
244C2×Dic5—61no—
245C2×Dic5—61no—
246C2×Dic5—122no—
247C2×Dic5—122no—
248C2×Dic5—122no—
249D20—121no—
250C4×D5—122no—
251Dic10—121no—
252C5×C8—42no—
253C2×#41—151no—
254C23×C4C2×D1511yescharacteristic
255C2×M16—21no—
256#123—301no—
257C22⋊Q8—151no—
258C22⋊Q8—151no—
259#121—151no—
260#121—151no—
261#120—301no—
262C4×D4—301no—
263C4×D4—301no—
264#117—151no—
265C2×C4⋊C4—301no—
266C2×C22⋊C4—301no—
267C22⋊C8—21no—
268C22⋊C8C2×D1512yes—
269#95—152no—
270C2×C3×C5—21no—
271C2×C3×C5—21no—
272C2×C3×C5—41no—
273C2×C3×C5—41no—
274C2×C3×C5C2×#9911yescharacteristic
275C2×C3×C5#41711yescharacteristic
276C2×C3×C5#42111yescharacteristic
277D15—81no—
278C23×C3—21no—
279C23×C3—21no—
280C23×C3—41no—
281C23×C3—41no—
282C23×C3#68511yescharacteristic
283C23×C3#68511yescharacteristic
284C23×C3C2×D2011yescharacteristic
285C22×D3—101no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4#68511yescharacteristic
293C2×C3×C4#68511yescharacteristic
294C2×C3×C4C2×C4×D511yescharacteristic
295C2×C3×C4C2×C22⋊D511yescharacteristic
296#67—202no—
297#67—202no—
298#67—201no—
299#67—201no—
300C2×Dic3—101no—
301C2×Dic3—101no—
302C2×Dic3—101no—
303C2×Dic3—202no—
304C2×Dic3—202no—
305C2×Dic3—202no—
306D12—201no—
307C4×D3—202no—
308Dic6—201no—
309C3×C8—42no—
310C22×C5—21no—
311C22×C5—21no—
312C22×C5—21no—
313C22×C5—21no—
314C22×C5—21no—
315C22×C5—21no—
316C22×C5—21no—
317C22×C5—21no—
318C22×C5—42no—
319C22×C5—42no—
320C22×C5#90811yescharacteristic
321C22×C5#90911yescharacteristic
322C22×C5C2×(C2×D3)⋊C411yescharacteristic
323C2×D5—121no—
324C2×D5—121no—
325C2×D5—121no—
326C4×C5—21no—
327C4×C5—21no—
328C4×C5—21no—
329C4×C5#80612yes—
330Dic5—121no—
331Dic5—121no—
332Dic5—121no—
333Dic5—242no—
334C24D6011yescharacteristic
335#41—602no—
336C2×Q8—151no—
337C2×D4—151no—
338C2×D4—301no—
339C2×D4—301no—
340C2×D4—301no—
341C22×C4—42no—
342C22×C4—301no—
343C22×C4—302no—
344C22×C4C4×D1511yescharacteristic
345C22×C4C4×D1511yescharacteristic
346C22×C4D6011yescharacteristic
347C22×C4#122011yescharacteristic
348C22×C4#122011yescharacteristic
349C22×C4C22×D1511yescharacteristic
350M16—42no—
351C2×C8—22no—
352C4⋊C4—151no—
353C4⋊C4—151no—
354C4⋊C4—301no—
355C4⋊C4—301no—
356C4⋊C4—602no—
357C22⋊C4—301no—
358C22⋊C4—301no—
359C22⋊C4—301no—
360C22⋊C4—301no—
361C22⋊C4—301no—
362C22⋊C4—602no—
363C42—301no—
364C3×C5#151311yescharacteristic, complemented, Hall
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—42no—
374C22×C3—42no—
375C22×C3#405411yescharacteristic
376C22×C3#405511yescharacteristic
377C22×C3C2×#68511yescharacteristic
378C2×D3—201no—
379C2×D3—201no—
380C2×D3—201no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4#393812yes—
385Dic3—201no—
386Dic3—201no—
387Dic3—201no—
388Dic3—402no—
389C2×C5—21no—
390C2×C5—21no—
391C2×C5—41no—
392C2×C5—41no—
393C2×C5C2×#80611yescharacteristic
394C2×C5#513311yescharacteristic
395C2×C5#513911yescharacteristic
396D5—241no—
397C23—21no—
398C23—21no—
399C23—41no—
400C23—41no—
401C23—301no—
402C23#671411yescharacteristic
403C23#671411yescharacteristic
404C23C2×D6011yescharacteristic
405Q8—601no—
406D4—601no—
407D4—602no—
408D4—602no—
409D4—601no—
410D4—601no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—301no—
418C2×C4—301no—
419C2×C4—301no—
420C2×C4—602no—
421C2×C4—602no—
422C2×C4—602no—
423C2×C4—602no—
424C2×C4#671411yescharacteristic
425C2×C4#671411yescharacteristic
426C2×C4C2×C4×D1511yescharacteristic
427C2×C4C2×#122011yescharacteristic
428C8—42no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—41no—
432C2×C3—41no—
433C2×C3C2×#393811yescharacteristic
434C2×C3#6542211yescharacteristic
435C2×C3#6542811yescharacteristic
436D3—401no—
437C5#6997911yescharacteristic, complemented, Sylow
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—42no—
447C22—42no—
448C22—601no—
449C22—601no—
450C22—601no—
451C22#9179711yescharacteristic
452C22#9179811yescharacteristic
453C22C2×#671411yescharacteristic
454C4—21no—
455C4—21no—
456C4—21no—
457C4—601no—
458C4—601no—
459C4—601no—
460C4—1202no—
461C4#9109012yes—
462C3#1060077211yescharacteristic, complemented, Sylow
463C2—21no—
464C2—21no—
465C2—41no—
466C2—41no—
467C2—1201no—
468C2C2×#9109011yescharacteristic
469C2#1175123411yescharacteristic
470C2#1175124011yescharacteristic
subgroupG/H
centerC22C2×#6714
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#407C2
socleC22×C3×C5C2×C22⋊C4
prime radical#11756550C2
cosocleC22×C3×C4×C5C23
hypercenter#407D15
hypocenterC3×C5#1513
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C3×C5×#407C2semidirect
3. #11751313C2semidirect
4. #11746291C2semidirect
5. #11746288C2semidirect
8. C2×#6817C4semidirect
12. #91819C4semidirect
17. #91815C4semidirect
19. #91813C4semidirect
26. C5×#407D3semidirect
61. C3×#407D5semidirect
163. #407D15semidirect
364. C3×C5#1513semidirect
437. C5#69979semidirect
462. C3#10600772semidirect

Maximal subgroups

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

subgroupindex
#117565502
C3×C5×#4072
#117513132
#117462912
#117462882
#106007723
#699795