Finite Group Databasebeta

← #14297568

Subgroups — #14297568

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Dic5×D12C211yesmaximal, characteristic
2C2×C5×#823C211yesmaximal, characteristic
3C3×#65407C211yesmaximal, characteristic, complemented
4#11748431C211yesmaximal, characteristic, complemented
5C2×#90959C211yesmaximal, characteristic
6#11746375C211yesmaximal, characteristic, complemented
7#11745987C211yesmaximal, characteristic, complemented
8#10600856—31nomaximal, Hall
9C22×C5×D12C2211yescharacteristic
10C22×D3×Dic5C412yes—
11C2×C3×C5×M16C2211yescharacteristic
12C2×C4⋊Dic15C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C2×C3×C4×Dic5C2211yescharacteristic
16C2×C3×#681C2211yescharacteristic
17C2×(C2×D3)⋊Dic5C412yes—
18Dic5×D12—21no—
19Dic5×D12—21no—
20Dic5×D12—21no—
21Dic5×D12—21no—
22C5×#823—22no—
23C3×#3946—21no—
24C3×#3946—21no—
25#90982—21no—
26#90982—21no—
27#90959—22no—
28#70527—51nomaximal, Hall
29C2×D4×Dic5—31no—
30C2×C5×#100—31no—
31C2×#3965—31no—
32#65407—31no—
33#65407D311yescharacteristic, complemented
34#64774—31no—
35#64774—31no—
36C23×C5×D3C2×C412yes—
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15C2×C412yes—
39C2×C5×D12—21no—
40C2×C5×D12—21no—
41C2×C5×D12—21no—
42C2×C5×D12—21no—
43C2×C5×D12D412yes—
44C2×C5×D12Q812yes—
45C22×C3×Dic5C2×C411yescharacteristic
46C22×C3×Dic5C2×C411yescharacteristic
47C2×D3×Dic5—22no—
48C2×D3×Dic5—22no—
49C2×D3×Dic5—44no—
50C3×C5×M16—21no—
51C3×C5×M16—21no—
52C2×C3×C5×C8—21no—
53C4⋊Dic15—21no—
54C4⋊Dic15—21no—
55#6710—21no—
56#6710—21no—
57C2×C3⋊#168—21no—
58C5×#208—21no—
59C5×#208—21no—
60C2×C5×C3⋊C8—21no—
61C3×C4×Dic5D411yescharacteristic
62C3×C4×Dic5D411yescharacteristic
63C3×C4×Dic5D411yescharacteristic
64C3×C4×Dic5D411yescharacteristic
65C3×#681—21no—
66C3×#681—21no—
67C2×C3×#168—21no—
68(C2×D3)⋊Dic5—22no—
69(C2×D3)⋊Dic5—22no—
70C2×C4×D12—51no—
71C3×#423—51no—
72C2×#823—51no—
73C2×#823D511yescharacteristic
74#4924—51no—
75#4554—51no—
76#4554—51no—
77C22×C5×D4—31no—
78C23×Dic5—32no—
79C2×C5×M16—31no—
80C2×C5×M16C2×D311yescharacteristic
81C2×C22⋊Dic5—32no—
82D4×Dic5—61no—
83D4×Dic5—61no—
84D4×Dic5—61no—
85D4×Dic5—61no—
86C2×C4⋊Dic5—31no—
87C2×C4×Dic5C2×D311yescharacteristic
88C2×#681—31no—
89C2×#681C2×D311yescharacteristic
90C5×#100—62no—
91#3965—62no—
92#3946—21no—
93#3946—21no—
94#3946—61no—
95#3946—61no—
96#1800—151noSylow
97C23×C3×C5C22×C411yescharacteristic
98C22×C5×D3—22no—
99C22×C5×D3—22no—
100C22×C5×D3—42no—
101C22×C5×D3—42no—
102C22×C5×D3C4⋊C414yes—
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C3×C4×C5C2×Q811yescharacteristic
107C2×C3×C4×C5#4111yescharacteristic
108C2×C3×C4×C5#4111yescharacteristic
109C2×Dic15—22no—
110C2×Dic15—42no—
111C5×D12—22no—
112C5×D12—22no—
113C5×D12—22no—
114C5×D12—22no—
115C2×C3×Dic5—22no—
116C2×C3×Dic5—41no—
117C2×C3×Dic5C22⋊C411yescharacteristic
118C2×C3×Dic5C22⋊C411yescharacteristic
119C2×C3×Dic5C22⋊C411yescharacteristic
120C2×C3×Dic5C22⋊C411yescharacteristic
121D3×Dic5—44no—
122D3×Dic5—44no—
123C3×C5×C8—41no—
124C3⋊#168—41no—
125C3×#168—41no—
126C5×C3⋊C8—41no—
127C22×D12C2×D511yescharacteristic
128C22×C4×D3—52no—
129C2×C3×M16—51no—
130C2×C3×M16C2×D511yescharacteristic
131C2×C3×C42—51no—
132C2×(C2×D3)⋊C4—52no—
133C2×C4⋊Dic3—51no—
134C2×#208—51no—
135C2×#208C2×D511yescharacteristic
136C4×D12—101no—
137C4×D12—101no—
138C4×D12—101no—
139C4×D12—101no—
140C3×C4⋊C8—101no—
141C3×C4⋊C8—101no—
142#823—22no—
143#823—102no—
144C4⋊(C3⋊C8)—101no—
145C4⋊(C3⋊C8)—101no—
146C24×C5—32no—
147C2×C5×D4—32no—
148C2×C5×D4—32no—
149C2×C5×D4—61no—
150C2×C5×D4—61no—
151C2×C5×D4—61no—
152C2×C5×D4—61no—
153C22×C4×C5C22×D311yescharacteristic
154C22×Dic5—32no—
155C22×Dic5—62no—
156C22×Dic5—62no—
157C22×Dic5—124no—
158C22×Dic5C4×D311yescharacteristic
159C22×Dic5C4×D311yescharacteristic
160C5×M16—21no—
161C5×M16—21no—
162C5×M16—61no—
163C5×M16—61no—
164C2×C5×C8—21no—
165C2×C5×C8—61no—
166C22⋊Dic5—62no—
167C22⋊Dic5—62no—
168C4⋊Dic5—61no—
169C4⋊Dic5—61no—
170C4×Dic5D1211yescharacteristic
171C4×Dic5D1211yescharacteristic
172C4×Dic5#6711yescharacteristic
173C4×Dic5#6711yescharacteristic
174#681—21no—
175#681—21no—
176#681—61no—
177#681—61no—
178C2×#168—21no—
179C2×#168—61no—
180C2×C4×D4—151no—
181#423—51no—
182#423—151no—
183C2×#100—31no—
184C2×#100—151no—
185#343—151no—
186#343—151no—
187C22×C3×C5—21no—
188C22×C3×C5—21no—
189C22×C3×C5C2×C22⋊C411yescharacteristic
190C22×C3×C5C2×C4⋊C411yescharacteristic
191C22×C3×C5#11711yescharacteristic
192C2×C5×D3—24no—
193C2×C5×D3—44no—
194C2×C5×D3—42no—
195C2×C5×D3—42no—
196C2×C5×D3—44no—
197C3×C4×C5#12111yescharacteristic
198C3×C4×C5#12111yescharacteristic
199C3×C4×C5C22⋊Q811yescharacteristic
200C3×C4×C5C22⋊Q811yescharacteristic
201Dic15—42no—
202C3×Dic5—21no—
203C3×Dic5—21no—
204C3×Dic5—21no—
205C3×Dic5#10012yescomplemented
206C23×D3C4×D512yes—
207C22×C3×C4—51no—
208C22×C3×C4—51no—
209C22×C3×C4C22×D511yescharacteristic
210C22×Dic3—52no—
211C2×D12—21no—
212C2×D12—21no—
213C2×D12—21no—
214C2×D12—21no—
215C2×D12Dic1012yes—
216C2×D12C22⋊D512yes—
217C2×C4×D3—102no—
218C2×C4×D3—102no—
219C2×C4×D3—204no—
220C3×M16—21no—
221C3×M16—21no—
222C3×M16—101no—
223C3×M16—101no—
224C2×C3×C8—21no—
225C2×C3×C8—101no—
226C3×C42—51no—
227C3×C42—51no—
228C3×C42—51no—
229C3×C42—51no—
230(C2×D3)⋊C4—102no—
231(C2×D3)⋊C4—102no—
232C4⋊Dic3—101no—
233C4⋊Dic3—101no—
234#208—21no—
235#208—21no—
236#208—101no—
237#208—101no—
238C2×C3⋊C8—21no—
239C2×C3⋊C8—101no—
240C23×C5—34no—
241C23×C5—62no—
242C23×C5—62no—
243C23×C5—122no—
244C23×C5—122no—
245C23×C5C2×C4×D311yescharacteristic
246C5×D4—62no—
247C5×D4—62no—
248C5×D4—62no—
249C5×D4—62no—
250C2×C4×C5C2×D1211yescharacteristic
251C2×C4×C5D3×D411yescharacteristic
252C2×C4×C5#23711yescharacteristic
253C2×C4×C5D3×Q811yescharacteristic
254C2×C4×C5#23911yescharacteristic
255C2×C4×C5C2×#6711yescharacteristic
256C2×Dic5—22no—
257C2×Dic5—41no—
258C2×Dic5—62no—
259C2×Dic5—124no—
260C2×Dic5—124no—
261C2×Dic5—122no—
262C2×Dic5(C2×D3)⋊C411yescharacteristic
263C2×Dic5(C2×D3)⋊C411yescharacteristic
264C2×Dic5(C2×D3)⋊C411yescharacteristic
265C2×Dic5(C2×D3)⋊C411yescharacteristic
266C5×C8—41no—
267C5×C8—121no—
268#168—41no—
269#168—121no—
270C22×D4—31no—
271C23×C4—152no—
272C2×M16—31no—
273C2×M16—51no—
274C2×M16—151no—
275C2×M16D3×D511yescharacteristic
276C4×D4—301no—
277C4×D4—301no—
278C4×D4—301no—
279C4×D4—301no—
280C2×C4⋊C4—151no—
281C2×C22⋊C4—152no—
282C2×C42—51no—
283C4⋊C8—101no—
284C4⋊C8—101no—
285C4⋊C8—301no—
286C4⋊C8—301no—
287#100—62no—
288#100—302no—
289C2×C3×C5—21no—
290C2×C3×C5—21no—
291C2×C3×C5#38011yescharacteristic
292C2×C3×C5C2×#10011yescharacteristic
293C2×C3×C5#41311yescharacteristic
294C5×D3—44no—
295C23×C3C2×C4×D511yescharacteristic
296C22×D3—22no—
297C22×D3—22no—
298C22×D3—42no—
299C22×D3—42no—
300C22×D3#68314yes—
301C2×C3×C4—51no—
302C2×C3×C4—51no—
303C2×C3×C4—51no—
304C2×C3×C4—51no—
305C2×C3×C4—102no—
306C2×C3×C4—201no—
307C2×C3×C4C2×Dic1011yescharacteristic
308C2×C3×C4D4×D511yescharacteristic
309C2×C3×C4D4×D511yescharacteristic
310C2×C3×C4#71111yescharacteristic
311C2×C3×C4#71111yescharacteristic
312C2×C3×C4C2×C22⋊D511yescharacteristic
313C2×Dic3—102no—
314C2×Dic3—202no—
315D12—22no—
316D12—22no—
317D12—22no—
318D12—22no—
319C4×D3—204no—
320C4×D3—204no—
321C3×C8—41no—
322C3×C8—201no—
323C3⋊C8—41no—
324C3⋊C8—201no—
325C22×C5—21no—
326C22×C5—21no—
327C22×C5—64no—
328C22×C5—124no—
329C22×C5—124no—
330C22×C5—122no—
331C22×C5—122no—
332C22×C5D3×C4⋊C411yescharacteristic
333C22×C5#89211yescharacteristic
334C22×C5C2×(C2×D3)⋊C411yescharacteristic
335C4×C5#89511yescharacteristic
336C4×C5#89711yescharacteristic
337C4×C5#93811yescharacteristic
338C4×C5#94611yescharacteristic
339Dic5—21no—
340Dic5—21no—
341Dic5—21no—
342Dic5—122no—
343Dic5#82312yescomplemented
344C24—32no—
345C2×D4—32no—
346C2×D4—32no—
347C2×D4—61no—
348C2×D4—61no—
349C2×D4—61no—
350C2×D4—61no—
351C22×C4—51no—
352C22×C4—51no—
353C22×C4—152no—
354C22×C4—302no—
355C22×C4—302no—
356C22×C4—604no—
357C22×C4C2×D3×D511yescharacteristic
358M16—21no—
359M16—21no—
360M16—61no—
361M16—61no—
362M16—101no—
363M16—101no—
364M16—301no—
365M16—301no—
366C2×C8—21no—
367C2×C8—61no—
368C2×C8—101no—
369C2×C8—301no—
370C4⋊C4—301no—
371C4⋊C4—301no—
372C22⋊C4—302no—
373C22⋊C4—302no—
374C42—51no—
375C42—51no—
376C42—51no—
377C42—51no—
378C3×C5#180011yescharacteristic, complemented, Hall
379C22×C3—21no—
380C22×C3—21no—
381C22×C3#402311yescharacteristic
382C22×C3D5×C22⋊C411yescharacteristic
383C22×C3C2×#68311yescharacteristic
384C2×D3—24no—
385C2×D3—44no—
386C2×D3—42no—
387C2×D3—42no—
388C2×D3—44no—
389C3×C4—52no—
390C3×C4—101no—
391C3×C4—101no—
392C3×C4—101no—
393C3×C4#402411yescharacteristic
394C3×C4#402411yescharacteristic
395C3×C4#408511yescharacteristic
396C3×C4#408511yescharacteristic
397Dic3—202no—
398C2×C5—21no—
399C2×C5—21no—
400C2×C5—124no—
401C2×C5#498711yescharacteristic
402C2×C5C2×#82311yescharacteristic
403C2×C5#513211yescharacteristic
404C23—34no—
405C23—62no—
406C23—62no—
407C23—122no—
408C23—122no—
409C23C4×D3×D511yescharacteristic
410D4—62no—
411D4—62no—
412D4—62no—
413D4—62no—
414C2×C4—51no—
415C2×C4—51no—
416C2×C4—51no—
417C2×C4—51no—
418C2×C4—102no—
419C2×C4—201no—
420C2×C4—302no—
421C2×C4—604no—
422C2×C4—604no—
423C2×C4—602no—
424C2×C4D3×Dic1011yescharacteristic
425C2×C4#676811yescharacteristic
426C2×C4D5×D1211yescharacteristic
427C2×C4#678011yescharacteristic
428C2×C4D5×#6711yescharacteristic
429C2×C4D3×C22⋊D511yescharacteristic
430C8—41no—
431C8—121no—
432C8—201no—
433C8—601no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3D5×#10011yescharacteristic
437C2×C3#6503411yescharacteristic
438C2×C3#6523111yescharacteristic
439D3—44no—
440C5#7052711yescharacteristic, complemented, Sylow
441C22—21no—
442C22—21no—
443C22—64no—
444C22—124no—
445C22—124no—
446C22—122no—
447C22—122no—
448C22D3×#68311yescharacteristic
449C22#9140011yescharacteristic
450C22D5×(C2×D3)⋊C411yescharacteristic
451C4—52no—
452C4—101no—
453C4—101no—
454C4—101no—
455C4—602no—
456C4#9141011yescharacteristic
457C4#9141611yescharacteristic
458C4#9141711yescharacteristic
459C4#9156511yescharacteristic
460C3#1060085611yescharacteristic, complemented, Sylow
461C2—21no—
462C2—21no—
463C2—124no—
464C2D5×#82311yescharacteristic
465C2#1174823011yescharacteristic
466C2#1174887411yescharacteristic
subgroupG/H
centerC22D5×(C2×D3)⋊C4
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C5×D12C22
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1800
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. C3×#65407C2semidirect
4. #11748431C2semidirect
6. #11746375C2semidirect
7. #11745987C2semidirect
33. #65407D3semidirect
205. C3×Dic5#100semidirect
343. Dic5#823semidirect
378. C3×C5#1800semidirect
440. C5#70527semidirect
460. C3#10600856semidirect

Maximal subgroups

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

subgroupindex
C2×Dic5×D122
C2×C5×#8232
C3×#654072
#117484312
C2×#909592
#117463752
#117459872
#106008563
#705275