Finite Group Databasebeta

← #14305800

Subgroups — #14305800

Order 1920.

872 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91829C211yesmaximal, characteristic
2C2×C3×C5×#102C211yesmaximal, characteristic, complemented
3C2×#91116C211yesmaximal, characteristic, complemented
4C2×#91105C211yesmaximal, characteristic, complemented
5C2×C8×Dic15C211yesmaximal, characteristic, complemented
6#11751076C211yesmaximal, characteristic, complemented
7C2×#91093C211yesmaximal, characteristic, complemented
8#10600950—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×#1220—22no—
11C22×D60C2211yescharacteristic
12C22×C3×C5×C8C2211yescharacteristic
13C2×C3×C5×C4⋊C4C2211yescharacteristic
14#91829—22no—
15#91829C414yescomplemented
16C2×C4⋊Dic15C2211yescharacteristic
17C2×#6712—22no—
18C2×C4×Dic15C2211yescharacteristic
19C22×C3⋊#168C2211yescharacteristic
20C3×C5×#102—22no—
21#91116—22no—
22#91105—22no—
23C8×Dic15—22no—
24#91093—22no—
25#70157—51nomaximal, Hall
26C2×#4086—31no—
27C2×C5×#102D311yescharacteristic, complemented
28C2×#3964—31no—
29C2×#3953—31no—
30C2×C8×Dic5—31no—
31#65265—31no—
32C2×#3941—31no—
33C24×C3×C5—21no—
34C23×D15—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4C2×C412yes—
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5C2311yescharacteristic
43C2×#1220—28no—
44C2×#1220—44no—
45C2×#1220—44no—
46C22×Dic15—21no—
47C22×Dic15D412yes—
48C2×D60—21no—
49C2×D60—21no—
50C2×D60—21no—
51C2×D60—21no—
52C2×D60—21no—
53C2×D60C2×C412yes—
54C2×C3×C5×C8—21no—
55C2×C3×C5×C8—21no—
56C2×C3×C5×C8D412yescomplemented
57C3×C5×C4⋊C4—21no—
58C3×C5×C4⋊C4—21no—
59C4⋊Dic15—21no—
60C4⋊Dic15—21no—
61#6712—44no—
62C4×Dic15C2×C412yes—
63C4×Dic15D412yes—
64C2×C3⋊#168—21no—
65C2×C3⋊#168—21no—
66C2×C3⋊#168D412yescomplemented
67C2×#940—51no—
68C2×C3×#102D511yescharacteristic, complemented
69C2×#832—51no—
70C2×#821—51no—
71C2×C8×Dic3—51no—
72#4975—51no—
73C2×#809—51no—
74C22×C5×D4C2×D311yescharacteristic
75C22×C22⋊D5—62no—
76C22×D20—31no—
77C22×C5×C8C2×D311yescharacteristic
78C2×C5×C4⋊C4C2×D311yescharacteristic
79#4086—34no—
80#4086—62no—
81C2×C4⋊Dic5—31no—
82C2×#683—62no—
83C2×C4×Dic5—31no—
84C22×#168—31no—
85C5×#102—22no—
86#3964—62no—
87#3953—62no—
88C8×Dic5—62no—
89#3941—62no—
90#1957—151noSylow
91C23×C3×C5—22no—
92C23×C3×C5—41no—
93C23×C3×C5—41no—
94C23×C3×C5—42no—
95C23×C3×C5—42no—
96C23×C3×C5C2×D411yescharacteristic
97C22×D15—22no—
98C22×D15—41no—
99C22×D15—41no—
100C22×D15—42no—
101C22×D15—42no—
102C3×C5×D4—22no—
103C3×C5×D4—22no—
104C3×C5×D4—41no—
105C3×C5×D4—41no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5—42no—
108C2×C3×C4×C5C22×C411yescharacteristic
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5#4111yescharacteristic
113C2×C3×C4×C5#4111yescharacteristic
114#1220—416no—
115C2×Dic15—41no—
116C2×Dic15—42no—
117C2×Dic15C22⋊C414yes—
118C2×Dic15D814yes—
119C2×Dic15SD1614yes—
120D60—22no—
121D60—22no—
122D60—41no—
123D60—41no—
124C3×C5×C8—22no—
125C3⋊#168—22no—
126C22×C3×D4C2×D511yescharacteristic
127C22×#67—102no—
128C22×D12—51no—
129C22×C3×C8C2×D511yescharacteristic
130C2×C3×C4⋊C4C2×D511yescharacteristic
131#940—54no—
132#940—102no—
133C2×C4⋊Dic3—51no—
134C2×Dic3⋊C4—102no—
135C2×C4×Dic3—51no—
136C22×C3⋊C8—51no—
137C3×#102—22no—
138#832—102no—
139#821—102no—
140C8×Dic3—102no—
141#809—102no—
142C24×C5—21no—
143C23×D5—61no—
144C2×C5×D4—21no—
145C2×C5×D4—21no—
146C2×C5×D4—21no—
147C2×C5×D4—21no—
148C2×C5×D4—21no—
149C2×C5×D4C4×D312yes—
150C22×C4×C5—21no—
151C22×C4×C5C22×D311yescharacteristic
152C2×C22⋊D5—68no—
153C2×C22⋊D5—124no—
154C2×C22⋊D5—124no—
155C22×Dic5—32no—
156C22×Dic5—61no—
157C2×D20—32no—
158C2×D20—61no—
159C2×D20—61no—
160C2×D20—61no—
161C2×D20—61no—
162C2×D20—61no—
163C2×C5×C8—21no—
164C2×C5×C8—21no—
165C2×C5×C8#6712yescomplemented
166C5×C4⋊C4—21no—
167C5×C4⋊C4—21no—
168C4⋊Dic5—61no—
169C4⋊Dic5—61no—
170#683—124no—
171C4×Dic5—32no—
172C4×Dic5—32no—
173C2×#168—32no—
174C2×#168—61no—
175C2×#168—61no—
176C2×#127—151no—
177C2×#102—151no—
178C2×#102—151no—
179C2×#102—151no—
180C2×#102D1511yescharacteristic, complemented
181C2×C4×C8—151no—
182#384—151no—
183C22×C3×C5—42no—
184C22×C3×C5—44no—
185C22×C3×C5—82no—
186C22×C3×C5—81no—
187C22×C3×C5—81no—
188C22×C3×C5C2×C22⋊C411yescharacteristic
189C22×C3×C5#12411yescharacteristic
190C22×C3×C5#12711yescharacteristic
191C22×C3×C5C2×D812yes—
192C22×C3×C5C2×SD1612yes—
193C2×D15—42no—
194C2×D15—44no—
195C2×D15—82no—
196C2×D15—81no—
197C2×D15—81no—
198C3×C4×C5—81no—
199C3×C4×C5C4×D411yescharacteristic
200C3×C4×C5C4×D411yescharacteristic
201C3×C4×C5#12111yescharacteristic
202C3×C4×C5#12111yescharacteristic
203Dic15—81no—
204Dic15#10218yescomplemented
205C24×C3—21no—
206C23×D3—101no—
207C2×C3×D4—21no—
208C2×C3×D4—21no—
209C2×C3×D4—21no—
210C2×C3×D4—21no—
211C2×C3×D4—21no—
212C2×C3×D4C4×D512yes—
213C22×C3×C4—21no—
214C22×C3×C4C22×D511yescharacteristic
215C2×#67—108no—
216C2×#67—204no—
217C2×#67—204no—
218C22×Dic3—52no—
219C22×Dic3—101no—
220C2×D12—52no—
221C2×D12—101no—
222C2×D12—101no—
223C2×D12—101no—
224C2×D12—101no—
225C2×D12—101no—
226C2×C3×C8—21no—
227C2×C3×C8—21no—
228C2×C3×C8C22⋊D512yescomplemented
229C3×C4⋊C4—21no—
230C3×C4⋊C4—21no—
231C4⋊Dic3—101no—
232C4⋊Dic3—101no—
233Dic3⋊C4—204no—
234C4×Dic3—52no—
235C4×Dic3—52no—
236C2×C3⋊C8—52no—
237C2×C3⋊C8—101no—
238C2×C3⋊C8—101no—
239C23×C5—22no—
240C23×C5—41no—
241C23×C5—42no—
242C23×C5—42no—
243C23×C5—41no—
244C23×C5D3×D411yescharacteristic
245C22×D5—62no—
246C22×D5—121no—
247C22×D5—122no—
248C22×D5—122no—
249C22×D5—121no—
250C5×D4—22no—
251C5×D4—22no—
252C5×D4—41no—
253C5×D4—41no—
254C2×C4×C5—42no—
255C2×C4×C5—41no—
256C2×C4×C5C2×C4×D311yescharacteristic
257C2×C4×C5#23511yescharacteristic
258C2×C4×C5D3×D411yescharacteristic
259C2×C4×C5D3×D411yescharacteristic
260C2×C4×C5#23711yescharacteristic
261C2×C4×C5C2×#6711yescharacteristic
262C22⋊D5—1216no—
263C2×Dic5—34no—
264C2×Dic5—34no—
265C2×Dic5—34no—
266C2×Dic5—122no—
267C2×Dic5—121no—
268D20—62no—
269D20—62no—
270D20—121no—
271D20—121no—
272C5×C8—22no—
273#168—62no—
274C22×D4—151no—
275C22×D4—302no—
276C22×D4C2×D1511yescharacteristic
277C22×C8—151no—
278C22×C8C2×D1511yescharacteristic
279#127—154no—
280#127—302no—
281C2×C4⋊C4—151no—
282C2×C4⋊C4—302no—
283C2×C4⋊C4C2×D1511yescharacteristic
284C2×C42—151no—
285#102—22no—
286#102—302no—
287#102—302no—
288#102—302no—
289C4×C8—302no—
290C2×C3×C5—82no—
291C2×C3×C5#39011yescharacteristic
292C2×C3×C5C2×#10212yes—
293C2×C3×C5#48612yes—
294C2×C3×C5#49211yescharacteristic
295C2×C3×C5#49311yescharacteristic
296D15—82no—
297C23×C3—22no—
298C23×C3—41no—
299C23×C3—42no—
300C23×C3—42no—
301C23×C3—41no—
302C23×C3D4×D511yescharacteristic
303C22×D3—102no—
304C22×D3—201no—
305C22×D3—202no—
306C22×D3—202no—
307C22×D3—201no—
308C3×D4—22no—
309C3×D4—22no—
310C3×D4—41no—
311C3×D4—41no—
312C2×C3×C4—42no—
313C2×C3×C4—41no—
314C2×C3×C4C2×C4×D511yescharacteristic
315C2×C3×C4#70911yescharacteristic
316C2×C3×C4D4×D511yescharacteristic
317C2×C3×C4D4×D511yescharacteristic
318C2×C3×C4#71111yescharacteristic
319C2×C3×C4C2×C22⋊D511yescharacteristic
320#67—2016no—
321C2×Dic3—54no—
322C2×Dic3—54no—
323C2×Dic3—54no—
324C2×Dic3—202no—
325C2×Dic3—201no—
326D12—102no—
327D12—102no—
328D12—201no—
329D12—201no—
330C3×C8—22no—
331C3⋊C8—102no—
332C22×C5—42no—
333C22×C5—44no—
334C22×C5—81no—
335C22×C5—81no—
336C22×C5—82no—
337C22×C5D3×C22⋊C411yescharacteristic
338C22×C5#88511yescharacteristic
339C22×C5D3×D812yes—
340C22×C5D3×SD1612yes—
341C22×C5#94011yescharacteristic
342C2×D5—122no—
343C2×D5—124no—
344C2×D5—241no—
345C2×D5—241no—
346C2×D5—242no—
347C4×C5—81no—
348C4×C5#67⋊C411yescharacteristic
349C4×C5#88411yescharacteristic
350C4×C5C4×#6711yescharacteristic
351C4×C5#93911yescharacteristic
352Dic5—38no—
353Dic5—241no—
354C24—21no—
355C24—301no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—152no—
362C2×D4—308no—
363C2×D4—301no—
364C2×D4—301no—
365C2×D4—301no—
366C2×D4—301no—
367C2×D4—301no—
368C2×D4—604no—
369C2×D4—604no—
370C2×D4C4×D1512yes—
371C22×C4—21no—
372C22×C4—152no—
373C22×C4—301no—
374C22×C4C22×D1511yescharacteristic
375C2×C8—21no—
376C2×C8—21no—
377C2×C8—152no—
378C2×C8—301no—
379C2×C8—301no—
380C2×C8#122012yescomplemented
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—301no—
384C4⋊C4—301no—
385C4⋊C4—604no—
386C42—152no—
387C42—152no—
388C3×C5#195711yescharacteristic, complemented, Hall
389C22×C3—44no—
390C22×C3—42no—
391C22×C3—82no—
392C22×C3—81no—
393C22×C3—81no—
394C22×C3D5×C22⋊C411yescharacteristic
395C22×C3#403111yescharacteristic
396C22×C3D5×D812yes—
397C22×C3D5×SD1612yes—
398C22×C3#408611yescharacteristic
399C2×D3—204no—
400C2×D3—202no—
401C2×D3—402no—
402C2×D3—401no—
403C2×D3—401no—
404C3×C4—81no—
405C3×C4#402711yescharacteristic
406C3×C4#403011yescharacteristic
407C3×C4C4×C22⋊D511yescharacteristic
408C3×C4#408511yescharacteristic
409Dic3—58no—
410Dic3—401no—
411C2×C5—82no—
412C2×C5#476012yes—
413C2×C5D3×#10212yes—
414C2×C5#495711yescharacteristic
415C2×C5#515111yescharacteristic
416C2×C5#517511yescharacteristic
417D5—242no—
418C23—22no—
419C23—41no—
420C23—42no—
421C23—42no—
422C23—41no—
423C23—302no—
424C23—601no—
425C23—602no—
426C23—602no—
427C23—601no—
428C23D4×D1511yescharacteristic
429D4—22no—
430D4—22no—
431D4—41no—
432D4—41no—
433D4—302no—
434D4—302no—
435D4—6016no—
436D4—601no—
437D4—601no—
438C2×C4—42no—
439C2×C4—41no—
440C2×C4—154no—
441C2×C4—154no—
442C2×C4—154no—
443C2×C4—602no—
444C2×C4—601no—
445C2×C4C2×C4×D1511yescharacteristic
446C2×C4#681711yescharacteristic
447C2×C4D4×D1511yescharacteristic
448C2×C4D4×D1511yescharacteristic
449C2×C4#681911yescharacteristic
450C2×C4C2×#122011yescharacteristic
451C8—22no—
452C8—302no—
453C2×C3—82no—
454C2×C3#6504912yes—
455C2×C3D5×#10212yes—
456C2×C3#6524611yescharacteristic
457C2×C3#6544011yescharacteristic
458C2×C3#6546411yescharacteristic
459D3—402no—
460C5#7015711yescharacteristic, complemented, Sylow
461C22—42no—
462C22—44no—
463C22—81no—
464C22—81no—
465C22—82no—
466C22—602no—
467C22—604no—
468C22—1201no—
469C22—1201no—
470C22—1202no—
471C22C22⋊C4×D1511yescharacteristic
472C22#9177411yescharacteristic
473C22D8×D1512yes—
474C22SD16×D1512yes—
475C22#9182911yescharacteristic
476C4—81no—
477C4—158no—
478C4—1201no—
479C4#9177011yescharacteristic
480C4#9177311yescharacteristic
481C4C4×#122011yescharacteristic
482C4#9182811yescharacteristic
483C3#1060095011yescharacteristic, complemented, Sylow
484C2—82no—
485C2—1202no—
486C2#1175086112yes—
487C2D15×#10212yes—
488C2#1175105811yescharacteristic
489C2#1175125211yescharacteristic
490C2#1175127611yescharacteristic
subgroupG/H
centerC23D4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC2×C3×C5×#102C2
socleC23×C3×C5C2×D4
prime radicalC2×#91829C2
cosocleC22×C3×C4×C5C23
hypercenterC2×#102D15
hypocenterC3×C5#1957
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#102C2semidirect
3. C2×#91116C2semidirect
4. C2×#91105C2semidirect
5. C2×C8×Dic15C2semidirect
6. #11751076C2semidirect
7. C2×#91093C2semidirect
15. #91829C4semidirect
27. C2×C5×#102D3semidirect
56. C2×C3×C5×C8D4semidirect
66. C2×C3⋊#168D4semidirect
68. C2×C3×#102D5semidirect
165. C2×C5×C8#67semidirect
180. C2×#102D15semidirect
204. Dic15#102semidirect
228. C2×C3×C8C22⋊D5semidirect
380. C2×C8#1220semidirect
388. C3×C5#1957semidirect
460. C5#70157semidirect
483. C3#10600950semidirect

Maximal subgroups

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

subgroupindex
C2×#918292
C2×C3×C5×#1022
C2×#911162
C2×#911052
C2×C8×Dic152
#117510762
C2×#910932
#106009503
#701575