Finite Group Databasebeta

← #14298385

Subgroups — #14298385

Order 1920.

632 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×D5×C4⋊Dic3C211yesmaximal, characteristic
2C3×#65415C211yesmaximal, characteristic
3#11748341C211yesmaximal, characteristic
4#11746375C211yesmaximal, characteristic, complemented
5C5×#4554C211yesmaximal, characteristic, complemented
6#11745987C211yesmaximal, characteristic, complemented
7#11745986C211yesmaximal, characteristic, complemented
8#10599783—31nomaximal, Hall
9C22×C3×C4×D5C2211yescharacteristic
10C22×D5×Dic3C412yes—
11C2×C3×C5×M16C2211yescharacteristic
12C2×C4⋊Dic15C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C2×C5×C4⋊Dic3C2211yescharacteristic
15C2×C5×#208C2211yescharacteristic
16C2×C3×#681C2211yescharacteristic
17C2×#6668C412yes—
18D5×C4⋊Dic3—21no—
19D5×C4⋊Dic3—21no—
20D5×C4⋊Dic3—21no—
21D5×C4⋊Dic3—21no—
22C3×#3952—21no—
23C3×#3952—21no—
24#90955—21no—
25#90955—21no—
26#69973—51nomaximal, Hall
27C2×D5×C4⋊C4—31no—
28#65415—31no—
29#65415D311yescharacteristic
30C5×#343—31no—
31#64774—31no—
32#64774—31no—
33#64750—31no—
34C23×C3×D5C2×C411yescharacteristic
35C22×C3×C4×C5C2311yescharacteristic
36C22×Dic15C2×C412yes—
37C22×C5×Dic3C2×C412yes—
38C22×C3×Dic5C2×C411yescharacteristic
39C2×C3×C4×D5—21no—
40C2×C3×C4×D5—21no—
41C2×C3×C4×D5—21no—
42C2×C3×C4×D5—21no—
43C2×C3×C4×D5D411yescharacteristic
44C2×C3×C4×D5D411yescharacteristic
45C2×C3×C4×D5D411yescharacteristic
46C2×C3×C4×D5D411yescharacteristic
47C2×D5×Dic3—22no—
48C2×D5×Dic3—22no—
49C2×D5×Dic3—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×C4⋊Dic3—21no—
59C5×C4⋊Dic3—21no—
60C5×#208—21no—
61C5×#208—21no—
62C2×C5×C3⋊C8—21no—
63C3×#681—21no—
64C3×#681—21no—
65C2×C3×#168—21no—
66#6668—22no—
67#6668—22no—
68C22×C4⋊Dic3—51no—
69C3×#407—51no—
70#5207—51no—
71#4554—51no—
72#4554—51no—
73#4554—51no—
74#4554D511yescharacteristic, complemented
75C22×C4×D5—32no—
76C22×C4×D5C2×D311yescharacteristic
77C2×C5×M16—31no—
78C2×C5×M16C2×D311yescharacteristic
79C2×C5×C4⋊C4—31no—
80C2×C4⋊Dic5—31no—
81C2×#683—32no—
82C2×#681—31no—
83C2×#681C2×D311yescharacteristic
84D5×C4⋊C4—61no—
85D5×C4⋊C4—61no—
86D5×C4⋊C4—61no—
87D5×C4⋊C4—61no—
88#3952—21no—
89#3952—21no—
90#3952—61no—
91#3952—61no—
92#1821—151noSylow
93C23×C3×C5C22×C411yescharacteristic
94C22×C3×D5—21no—
95C22×C3×D5—21no—
96C22×C3×D5—22no—
97C22×C3×D5—22no—
98C22×C3×D5C22⋊C411yescharacteristic
99C22×C3×D5C22⋊C411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×C3×C4×C5#4111yescharacteristic
104C2×C3×C4×C5#4111yescharacteristic
105C2×C3×C4×C5#4111yescharacteristic
106C2×Dic15—22no—
107C2×Dic15—42no—
108C2×C5×Dic3—22no—
109C2×C5×Dic3—42no—
110C2×C3×Dic5—21no—
111C2×C3×Dic5—21no—
112C2×C3×Dic5C22⋊C411yescharacteristic
113C2×C3×Dic5C22⋊C411yescharacteristic
114C3×C4×D5—21no—
115C3×C4×D5—21no—
116C3×C4×D5—21no—
117C3×C4×D5—21no—
118C3×C4×D5—21no—
119C3×C4×D5—21no—
120C3×C4×D5—21no—
121C3×C4×D5—21no—
122D5×Dic3—44no—
123D5×Dic3—44no—
124C3×C5×C8—41no—
125C3⋊#168—41no—
126C3×#168—41no—
127C5×C3⋊C8—41no—
128C23×C3×C4—51no—
129C23×Dic3—52no—
130C2×C3×M16—51no—
131C2×C3×M16C2×D511yescharacteristic
132C2×C4⋊Dic3—51no—
133C2×C4⋊Dic3—52no—
134C2×C4⋊Dic3—101no—
135C2×C4⋊Dic3—101no—
136C2×C4⋊Dic3—101no—
137C2×C4⋊Dic3—101no—
138C2×C4⋊Dic3C2×D511yescharacteristic
139C2×#208—51no—
140C2×#208C2×D511yescharacteristic
141C3×C22⋊C8—101no—
142C3×C22⋊C8—101no—
143#830—101no—
144#830—101no—
145C23×D5C4×D311yescharacteristic
146C22×C4×C5—32no—
147C22×C4×C5C22×D311yescharacteristic
148C22×Dic5—32no—
149C22×Dic5C4×D311yescharacteristic
150C2×C4×D5—21no—
151C2×C4×D5—21no—
152C2×C4×D5—21no—
153C2×C4×D5—21no—
154C2×C4×D5—62no—
155C2×C4×D5—62no—
156C2×C4×D5—124no—
157C2×C4×D5D1211yescharacteristic
158C2×C4×D5D1211yescharacteristic
159C2×C4×D5#6711yescharacteristic
160C2×C4×D5#6711yescharacteristic
161C5×M16—21no—
162C5×M16—21no—
163C5×M16—61no—
164C5×M16—61no—
165C2×C5×C8—21no—
166C2×C5×C8—61no—
167C5×C4⋊C4—61no—
168C5×C4⋊C4—61no—
169C4⋊Dic5—61no—
170C4⋊Dic5—61no—
171#683—62no—
172#683—62no—
173#681—21no—
174#681—21no—
175#681—61no—
176#681—61no—
177C2×#168—21no—
178C2×#168—61no—
179C22×C4⋊C4—151no—
180#407—51no—
181#407—151no—
182#343—31no—
183#343—151no—
184#343—151no—
185#343—151no—
186C22×C3×C5—21no—
187C22×C3×C5—21no—
188C22×C3×C5C2×C22⋊C411yescharacteristic
189C22×C3×C5#11711yescharacteristic
190C22×C3×C5#11711yescharacteristic
191C2×C3×D5—24no—
192C2×C3×D5—24no—
193C2×C3×D5—21no—
194C2×C3×D5—21no—
195C2×C3×D5—21no—
196C2×C3×D5—21no—
197C2×C3×D5#10012yes—
198C2×C3×D5#10112yes—
199C3×C4×C5#12311yescharacteristic
200C3×C4×C5#12311yescharacteristic
201C3×C4×C5#12311yescharacteristic
202C3×C4×C5#12311yescharacteristic
203Dic15—42no—
204C3×Dic5—21no—
205C3×Dic5—21no—
206C5×Dic3—42no—
207C24×C3—51no—
208C22×C3×C4—51no—
209C22×C3×C4—51no—
210C22×C3×C4—51no—
211C22×C3×C4—51no—
212C22×C3×C4—51no—
213C22×C3×C4—101no—
214C22×C3×C4—101no—
215C22×C3×C4—101no—
216C22×C3×C4—101no—
217C22×C3×C4C22×D511yescharacteristic
218C22×Dic3—52no—
219C22×Dic3—102no—
220C22×Dic3—102no—
221C22×Dic3—204no—
222C22×Dic3C4×D512yes—
223C3×M16—21no—
224C3×M16—21no—
225C3×M16—101no—
226C3×M16—101no—
227C2×C3×C8—21no—
228C2×C3×C8—101no—
229C4⋊Dic3—21no—
230C4⋊Dic3—21no—
231C4⋊Dic3—102no—
232C4⋊Dic3—102no—
233C4⋊Dic3—101no—
234C4⋊Dic3—101no—
235#208—21no—
236#208—21no—
237#208—101no—
238#208—101no—
239C2×C3⋊C8—21no—
240C2×C3⋊C8—101no—
241C23×C5C2×C4×D311yescharacteristic
242C22×D5—21no—
243C22×D5—21no—
244C22×D5—22no—
245C22×D5—22no—
246C22×D5(C2×D3)⋊C411yescharacteristic
247C22×D5(C2×D3)⋊C411yescharacteristic
248C2×C4×C5—62no—
249C2×C4×C5—122no—
250C2×C4×C5C2×D1211yescharacteristic
251C2×C4×C5#23711yescharacteristic
252C2×C4×C5#23711yescharacteristic
253C2×C4×C5#23711yescharacteristic
254C2×C4×C5#23711yescharacteristic
255C2×C4×C5C2×#6711yescharacteristic
256C2×Dic5—21no—
257C2×Dic5—21no—
258C2×Dic5—62no—
259C2×Dic5—122no—
260C2×Dic5(C2×D3)⋊C411yescharacteristic
261C2×Dic5(C2×D3)⋊C411yescharacteristic
262C4×D5—21no—
263C4×D5—21no—
264C4×D5—21no—
265C4×D5—21no—
266C4×D5—21no—
267C4×D5—21no—
268C4×D5—21no—
269C4×D5—21no—
270C4×D5—124no—
271C4×D5—124no—
272C5×C8—41no—
273C5×C8—121no—
274#168—41no—
275#168—121no—
276C23×C4—51no—
277C23×C4—152no—
278C2×M16—31no—
279C2×M16—51no—
280C2×M16—151no—
281C2×M16D3×D511yescharacteristic
282C2×C4⋊C4—31no—
283C2×C4⋊C4—152no—
284C2×C4⋊C4—151no—
285C2×C4⋊C4—301no—
286C2×C4⋊C4—301no—
287C2×C4⋊C4—301no—
288C2×C4⋊C4—301no—
289C22⋊C8—101no—
290C22⋊C8—101no—
291C22⋊C8—301no—
292C22⋊C8—301no—
293C2×C3×C5—21no—
294C2×C3×C5—21no—
295C2×C3×C5#38111yescharacteristic
296C2×C3×C5C2×#10011yescharacteristic
297C2×C3×C5C2×#10111yescharacteristic
298C3×D5—22no—
299C3×D5—22no—
300C23×C3—51no—
301C23×C3—51no—
302C23×C3—102no—
303C23×C3—102no—
304C23×C3—101no—
305C23×C3—101no—
306C23×C3C2×C4×D511yescharacteristic
307C2×C3×C4—51no—
308C2×C3×C4—51no—
309C2×C3×C4—101no—
310C2×C3×C4—101no—
311C2×C3×C4—101no—
312C2×C3×C4—101no—
313C2×C3×C4—101no—
314C2×C3×C4—101no—
315C2×C3×C4—101no—
316C2×C3×C4—101no—
317C2×C3×C4—101no—
318C2×C3×C4—101no—
319C2×C3×C4#70911yescharacteristic
320C2×C3×C4#70911yescharacteristic
321C2×C3×C4D4×D511yescharacteristic
322C2×C3×C4D4×D511yescharacteristic
323C2×C3×C4#71111yescharacteristic
324C2×C3×C4#71311yescharacteristic
325C2×Dic3—22no—
326C2×Dic3—42no—
327C2×Dic3—102no—
328C2×Dic3—204no—
329C2×Dic3—204no—
330C2×Dic3—202no—
331C3×C8—41no—
332C3×C8—201no—
333C3⋊C8—41no—
334C3⋊C8—201no—
335C22×C5—21no—
336C22×C5—21no—
337C22×C5#87711yescharacteristic
338C22×C5#87711yescharacteristic
339C22×C5C2×(C2×D3)⋊C411yescharacteristic
340C2×D5—24no—
341C2×D5—24no—
342C2×D5—21no—
343C2×D5—21no—
344C2×D5—21no—
345C2×D5—21no—
346C2×D5#82312yes—
347C2×D5#82412yes—
348C4×C5—122no—
349C4×C5#88611yescharacteristic
350C4×C5#88611yescharacteristic
351C4×C5#93511yescharacteristic
352C4×C5#93511yescharacteristic
353Dic5—21no—
354Dic5—21no—
355Dic5—122no—
356C24—51no—
357C22×C4—32no—
358C22×C4—51no—
359C22×C4—51no—
360C22×C4—51no—
361C22×C4—51no—
362C22×C4—51no—
363C22×C4—101no—
364C22×C4—101no—
365C22×C4—101no—
366C22×C4—101no—
367C22×C4—152no—
368C22×C4—302no—
369C22×C4—302no—
370C22×C4—604no—
371C22×C4C2×D3×D511yescharacteristic
372M16—21no—
373M16—21no—
374M16—61no—
375M16—61no—
376M16—101no—
377M16—101no—
378M16—301no—
379M16—301no—
380C2×C8—21no—
381C2×C8—61no—
382C2×C8—101no—
383C2×C8—301no—
384C4⋊C4—61no—
385C4⋊C4—61no—
386C4⋊C4—302no—
387C4⋊C4—302no—
388C4⋊C4—301no—
389C4⋊C4—301no—
390C3×C5#182111yescharacteristic, complemented, Hall
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—52no—
394C22×C3—52no—
395C22×C3—104no—
396C22×C3—104no—
397C22×C3—101no—
398C22×C3—101no—
399C22×C3—101no—
400C22×C3—101no—
401C22×C3#401811yescharacteristic
402C22×C3D5×C22⋊C411yescharacteristic
403C22×C3#403811yescharacteristic
404C3×C4—101no—
405C3×C4—101no—
406C3×C4#402911yescharacteristic
407C3×C4#402911yescharacteristic
408C3×C4#404011yescharacteristic
409C3×C4#404011yescharacteristic
410Dic3—42no—
411Dic3—202no—
412C2×C5—21no—
413C2×C5—21no—
414C2×C5#494311yescharacteristic
415C2×C5C2×#82311yescharacteristic
416C2×C5C2×#82411yescharacteristic
417D5—22no—
418D5—22no—
419C23—51no—
420C23—51no—
421C23—102no—
422C23—102no—
423C23—101no—
424C23—101no—
425C23C4×D3×D511yescharacteristic
426C2×C4—51no—
427C2×C4—51no—
428C2×C4—62no—
429C2×C4—101no—
430C2×C4—101no—
431C2×C4—101no—
432C2×C4—101no—
433C2×C4—101no—
434C2×C4—101no—
435C2×C4—101no—
436C2×C4—101no—
437C2×C4—101no—
438C2×C4—101no—
439C2×C4—122no—
440C2×C4—302no—
441C2×C4—604no—
442C2×C4—604no—
443C2×C4—602no—
444C2×C4#676511yescharacteristic
445C2×C4#676611yescharacteristic
446C2×C4D5×D1211yescharacteristic
447C2×C4#677911yescharacteristic
448C2×C4#678011yescharacteristic
449C2×C4D5×#6711yescharacteristic
450C8—41no—
451C8—121no—
452C8—201no—
453C8—601no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—102no—
457C2×C3—102no—
458C2×C3#6495311yescharacteristic
459C2×C3D5×#10011yescharacteristic
460C2×C3D5×#10111yescharacteristic
461C5#6997311yescharacteristic, complemented, Sylow
462C22—21no—
463C22—21no—
464C22—52no—
465C22—52no—
466C22—104no—
467C22—104no—
468C22—101no—
469C22—101no—
470C22—101no—
471C22—101no—
472C22#9139311yescharacteristic
473C22#9139411yescharacteristic
474C22D5×(C2×D3)⋊C411yescharacteristic
475C4—101no—
476C4—101no—
477C4—122no—
478C4—602no—
479C4#9140711yescharacteristic
480C4#9141311yescharacteristic
481C4#9141411yescharacteristic
482C4#9154811yescharacteristic
483C3#1059978311yescharacteristic, complemented, Sylow
484C2—21no—
485C2—21no—
486C2—102no—
487C2—102no—
488C2D5×#82311yescharacteristic
489C2D5×#82411yescharacteristic
490C2#1174887111yescharacteristic
subgroupG/H
centerC22D5×(C2×D3)⋊C4
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×D5C2×C4
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1821
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
4. #11746375C2semidirect
5. C5×#4554C2semidirect
6. #11745987C2semidirect
7. #11745986C2semidirect
74. #4554D5semidirect
390. C3×C5#1821semidirect
461. C5#69973semidirect
483. C3#10599783semidirect

Maximal subgroups

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

subgroupindex
C2×D5×C4⋊Dic32
C3×#654152
#117483412
#117463752
C5×#45542
#117459872
#117459862
#105997833
#699735