Finite Group Databasebeta

← #14299441

Subgroups — #14299441

Order 1920.

632 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91815C211yesmaximal, characteristic
2C3×C5×#380C211yesmaximal, characteristic
3C2×#91114C211yesmaximal, characteristic
4C2×#91092C211yesmaximal, characteristic, complemented
5C2×#91091C211yesmaximal, characteristic, complemented
6#11746350C211yesmaximal, characteristic, complemented
7#11746350C211yesmaximal, characteristic, complemented
8#10600299—31nomaximal, Hall
9C23×C3×C4×C5C2211yescharacteristic
10C2×C3×C5×C4⋊C4C2211yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C2×C3×C5×C22⋊C4—21no—
13C2×#6719—21no—
14#91815—22no—
15#91815—22no—
16C2×C4⋊Dic15C2211yescharacteristic
17C2×C4⋊Dic15C2211yescharacteristic
18C2×C4×Dic15—21no—
19C22×C3⋊#168C2211yescharacteristic
20C22×C3⋊#168C2211yescharacteristic
21C3×C5×#95—21no—
22#91114C414yescomplemented
23#91092—22no—
24#91091—22no—
25#69506—51nomaximal, Hall
26C2×#4072—31no—
27C5×#380D311yescharacteristic
28C2×C22⋊#168—31no—
29C2×#3940—31no—
30C2×#3939—31no—
31#64749—31no—
32#64749—31no—
33C24×C3×C5D411yescharacteristic
34C22×C3×C4×C5—21no—
35C22×C3×C4×C5—21no—
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5C2×C412yes—
41C22×C3×C4×C5D411yescharacteristic
42C22×C3×C4×C5Q812yes—
43C22×C3×C4×C5C2311yescharacteristic
44C22×Dic15—21no—
45C22×Dic15—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C22⋊C4—42no—
51#6719—24no—
52C4⋊Dic15—21no—
53C4⋊Dic15—21no—
54C4⋊Dic15D412yes—
55C4⋊Dic15D412yes—
56C4×Dic15—24no—
57C2×C3⋊#168—21no—
58C2×C3⋊#168—21no—
59C2×C3⋊#168—21no—
60C2×C3⋊#168—21no—
61C2×C3⋊#168C2×C412yes—
62C2×C3⋊#168C2×C412yes—
63C2×#926—51no—
64C3×#380D511yescharacteristic
65C2×#830—51no—
66C2×#808—51no—
67C2×#807—51no—
68#4529—51no—
69#4529—51no—
70C23×C4×C5C2×D311yescharacteristic
71C2×C5×C4⋊C4C2×D311yescharacteristic
72C2×C5×C4⋊C4C2×D311yescharacteristic
73C2×C5×C22⋊C4—21no—
74C2×C22⋊Dic5—61no—
75#4072—62no—
76#4072—62no—
77C2×C4⋊Dic5—31no—
78C2×C4⋊Dic5—31no—
79C2×C4×Dic5—61no—
80C22×#168—31no—
81C22×#168—31no—
82C5×#95—21no—
83C22⋊#168—34no—
84#3940—62no—
85#3939—62no—
86#1854—151noSylow
87C23×C3×C5—21no—
88C23×C3×C5—21no—
89C23×C3×C5—21no—
90C23×C3×C5—21no—
91C23×C3×C5—21no—
92C23×C3×C5—21no—
93C23×C3×C5C4⋊C412yes—
94C23×C3×C5C2×D411yescharacteristic
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—22no—
98C2×C3×C4×C5—22no—
99C2×C3×C4×C5—22no—
100C2×C3×C4×C5—22no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5C4⋊C412yes—
108C2×C3×C4×C5C22×C411yescharacteristic
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×Q811yescharacteristic
112C2×C3×C4×C5#4111yescharacteristic
113C2×C3×C4×C5#4111yescharacteristic
114C2×Dic15—22no—
115C2×Dic15—22no—
116C2×Dic15—41no—
117C2×Dic15—41no—
118C2×Dic15—41no—
119C2×Dic15—41no—
120C3⋊#168—22no—
121C3⋊#168—22no—
122C23×C3×C4C2×D511yescharacteristic
123C2×C3×C4⋊C4C2×D511yescharacteristic
124C2×C3×C4⋊C4C2×D511yescharacteristic
125C2×C3×C22⋊C4—21no—
126C2×#217—101no—
127#926—102no—
128#926—102no—
129C2×C4⋊Dic3—51no—
130C2×C4⋊Dic3—51no—
131C2×C4×Dic3—101no—
132C22×C3⋊C8—51no—
133C22×C3⋊C8—51no—
134C3×#95—21no—
135#830—54no—
136#808—102no—
137#807—102no—
138C24×C5#6711yescharacteristic
139C22×C4×C5—21no—
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5Dic612yes—
146C22×C4×C5C4×D312yes—
147C22×C4×C5#6711yescharacteristic
148C22×C4×C5C22×D311yescharacteristic
149C22×Dic5—61no—
150C22×Dic5—61no—
151C5×C4⋊C4—21no—
152C5×C4⋊C4—21no—
153C5×C4⋊C4—21no—
154C5×C4⋊C4—21no—
155C5×C22⋊C4—42no—
156C22⋊Dic5—64no—
157C4⋊Dic5—32no—
158C4⋊Dic5—32no—
159C4⋊Dic5—61no—
160C4⋊Dic5—61no—
161C4×Dic5—64no—
162C2×#168—32no—
163C2×#168—32no—
164C2×#168—61no—
165C2×#168—61no—
166C2×#168—61no—
167C2×#168—61no—
168C2×#117—151no—
169C2×#107—151no—
170C2×#106—151no—
171C2×C22⋊C8—151no—
172#380D1511yescharacteristic
173#340—151no—
174#340—151no—
175C22×C3×C5—22no—
176C22×C3×C5—22no—
177C22×C3×C5—22no—
178C22×C3×C5—41no—
179C22×C3×C5—41no—
180C22×C3×C5—41no—
181C22×C3×C5—41no—
182C22×C3×C5C2×C4⋊C411yescharacteristic
183C22×C3×C5#12011yescharacteristic
184C22×C3×C5#12311yescharacteristic
185C22×C3×C5#13511yescharacteristic
186C22×C3×C5#13511yescharacteristic
187C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
188C22×C3×C5#13711yescharacteristic
189C3×C4×C5—22no—
190C3×C4×C5—81no—
191C3×C4×C5—81no—
192C3×C4×C5C4×D411yescharacteristic
193C3×C4×C5C4×D411yescharacteristic
194C3×C4×C5C22⋊Q811yescharacteristic
195C3×C4×C5C22⋊Q811yescharacteristic
196Dic15—42no—
197Dic15—42no—
198C24×C3C22⋊D511yescharacteristic
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4Dic1012yes—
206C22×C3×C4C4×D512yes—
207C22×C3×C4C22⋊D511yescharacteristic
208C22×C3×C4C22×D511yescharacteristic
209C22×Dic3—101no—
210C22×Dic3—101no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—21no—
214C3×C4⋊C4—21no—
215C3×C22⋊C4—42no—
216#217—104no—
217C4⋊Dic3—52no—
218C4⋊Dic3—52no—
219C4⋊Dic3—101no—
220C4⋊Dic3—101no—
221C4×Dic3—104no—
222C2×C3⋊C8—52no—
223C2×C3⋊C8—52no—
224C2×C3⋊C8—101no—
225C2×C3⋊C8—101no—
226C2×C3⋊C8—101no—
227C2×C3⋊C8—101no—
228C23×C5—21no—
229C23×C5—21no—
230C23×C5—21no—
231C23×C5—21no—
232C23×C5—21no—
233C23×C5—21no—
234C23×C5Dic3⋊C412yes—
235C23×C5C2×#6711yescharacteristic
236C2×C4×C5—21no—
237C2×C4×C5—21no—
238C2×C4×C5—22no—
239C2×C4×C5—22no—
240C2×C4×C5—22no—
241C2×C4×C5—22no—
242C2×C4×C5—41no—
243C2×C4×C5—41no—
244C2×C4×C5—41no—
245C2×C4×C5—41no—
246C2×C4×C5—41no—
247C2×C4×C5—41no—
248C2×C4×C5Dic3⋊C412yes—
249C2×C4×C5C2×Dic611yescharacteristic
250C2×C4×C5C2×C4×D311yescharacteristic
251C2×C4×C5D3×D411yescharacteristic
252C2×C4×C5D3×D411yescharacteristic
253C2×C4×C5#23711yescharacteristic
254C2×C4×C5#23711yescharacteristic
255C2×Dic5—62no—
256C2×Dic5—62no—
257C2×Dic5—121no—
258C2×Dic5—121no—
259C2×Dic5—121no—
260C2×Dic5—121no—
261#168—62no—
262#168—62no—
263C23×C4C2×D1511yescharacteristic
264C22×C8—151no—
265C22×C8—151no—
266#117—302no—
267#117—302no—
268C2×C4⋊C4—151no—
269C2×C4⋊C4—151no—
270C2×C4⋊C4C2×D1511yescharacteristic
271C2×C4⋊C4C2×D1511yescharacteristic
272C2×C22⋊C4—21no—
273C2×C22⋊C4—301no—
274C2×C42—301no—
275#107—302no—
276#106—302no—
277C22⋊C8—154no—
278#95—21no—
279C2×C3×C5—42no—
280C2×C3×C5#38511yescharacteristic
281C2×C3×C5#42711yescharacteristic
282C2×C3×C5#42811yescharacteristic
283C2×C3×C5#44911yescharacteristic
284C2×C3×C5#45211yescharacteristic
285C2×C3×C5#48211yescharacteristic
286C2×C3×C5#48511yescharacteristic
287C23×C3—21no—
288C23×C3—21no—
289C23×C3—21no—
290C23×C3—21no—
291C23×C3—21no—
292C23×C3—21no—
293C23×C3#68312yes—
294C23×C3C2×C22⋊D511yescharacteristic
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—22no—
301C2×C3×C4—41no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4#68312yes—
308C2×C3×C4C2×Dic1011yescharacteristic
309C2×C3×C4C2×C4×D511yescharacteristic
310C2×C3×C4D4×D511yescharacteristic
311C2×C3×C4D4×D511yescharacteristic
312C2×C3×C4#71111yescharacteristic
313C2×C3×C4#71111yescharacteristic
314C2×Dic3—102no—
315C2×Dic3—102no—
316C2×Dic3—201no—
317C2×Dic3—201no—
318C2×Dic3—201no—
319C2×Dic3—201no—
320C3⋊C8—102no—
321C3⋊C8—102no—
322C22×C5—22no—
323C22×C5—22no—
324C22×C5—22no—
325C22×C5—41no—
326C22×C5—41no—
327C22×C5—41no—
328C22×C5—41no—
329C22×C5C2×Dic3⋊C411yescharacteristic
330C22×C5#93211yescharacteristic
331C22×C5#93511yescharacteristic
332C22×C5#93711yescharacteristic
333C22×C5#94211yescharacteristic
334C22×C5#95011yescharacteristic
335C22×C5#95011yescharacteristic
336C4×C5—22no—
337C4×C5—81no—
338C4×C5—81no—
339C4×C5#87811yescharacteristic
340C4×C5#87811yescharacteristic
341C4×C5#67⋊C411yescharacteristic
342C4×C5#67⋊C411yescharacteristic
343Dic5—122no—
344Dic5—122no—
345C24#122011yescharacteristic
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—301no—
353C22×C4—301no—
354C22×C4Dic3012yes—
355C22×C4C4×D1512yes—
356C22×C4#122011yescharacteristic
357C22×C4C22×D1511yescharacteristic
358C2×C8—152no—
359C2×C8—152no—
360C2×C8—301no—
361C2×C8—301no—
362C2×C8—301no—
363C2×C8—301no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—152no—
369C4⋊C4—152no—
370C4⋊C4—301no—
371C4⋊C4—301no—
372C22⋊C4—42no—
373C22⋊C4—304no—
374C42—304no—
375C3×C5#185411yescharacteristic, complemented, Hall
376C22×C3—22no—
377C22×C3—22no—
378C22×C3—22no—
379C22×C3—41no—
380C22×C3—41no—
381C22×C3—41no—
382C22×C3—41no—
383C22×C3C2×#68311yescharacteristic
384C22×C3#407811yescharacteristic
385C22×C3#408111yescharacteristic
386C22×C3#408311yescharacteristic
387C22×C3#408811yescharacteristic
388C22×C3#409611yescharacteristic
389C22×C3#409611yescharacteristic
390C3×C4—22no—
391C3×C4—81no—
392C3×C4—81no—
393C3×C4#402411yescharacteristic
394C3×C4#402411yescharacteristic
395C3×C4#402711yescharacteristic
396C3×C4#402711yescharacteristic
397Dic3—202no—
398Dic3—202no—
399C2×C5—42no—
400C2×C5#494611yescharacteristic
401C2×C5#496411yescharacteristic
402C2×C5#499811yescharacteristic
403C2×C5#503511yescharacteristic
404C2×C5#503711yescharacteristic
405C2×C5#504511yescharacteristic
406C2×C5#504711yescharacteristic
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23#671212yes—
414C23C2×#122011yescharacteristic
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—302no—
428C2×C4—302no—
429C2×C4—601no—
430C2×C4—601no—
431C2×C4—601no—
432C2×C4—601no—
433C2×C4#671212yes—
434C2×C4C2×Dic3011yescharacteristic
435C2×C4C2×C4×D1511yescharacteristic
436C2×C4D4×D1511yescharacteristic
437C2×C4D4×D1511yescharacteristic
438C2×C4#681911yescharacteristic
439C2×C4#681911yescharacteristic
440C8—302no—
441C8—302no—
442C2×C3—42no—
443C2×C3#6523511yescharacteristic
444C2×C3#6525311yescharacteristic
445C2×C3#6528711yescharacteristic
446C2×C3#6532411yescharacteristic
447C2×C3#6532611yescharacteristic
448C2×C3#6533411yescharacteristic
449C2×C3#6533611yescharacteristic
450C5#6950611yescharacteristic, complemented, Sylow
451C22—22no—
452C22—22no—
453C22—22no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22C2×#671211yescharacteristic
459C22#9182111yescharacteristic
460C22#9182411yescharacteristic
461C22#9182611yescharacteristic
462C22#9183111yescharacteristic
463C22#9183911yescharacteristic
464C22#9183911yescharacteristic
465C4—22no—
466C4—81no—
467C4—81no—
468C4—602no—
469C4—602no—
470C4#9176711yescharacteristic
471C4#9176711yescharacteristic
472C4#9177011yescharacteristic
473C4#9177011yescharacteristic
474C3#1060029911yescharacteristic, complemented, Sylow
475C2—42no—
476C2#1175104711yescharacteristic
477C2#1175106511yescharacteristic
478C2#1175109911yescharacteristic
479C2#1175113611yescharacteristic
480C2#1175113811yescharacteristic
481C2#1175114611yescharacteristic
482C2#1175114811yescharacteristic
subgroupG/H
centerC23C2×#1220
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#380C2
socleC23×C3×C5C2×D4
prime radicalC24×C3×C5D4
cosocleC22×C3×C4×C5C23
hypercenter#380D15
hypocenterC3×C5#1854
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
4. C2×#91092C2semidirect
5. C2×#91091C2semidirect
6. #11746350C2semidirect
7. #11746350C2semidirect
22. #91114C4semidirect
375. C3×C5#1854semidirect
450. C5#69506semidirect
474. C3#10600299semidirect

Maximal subgroups

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

subgroupindex
C2×#918152
C3×C5×#3802
C2×#911142
C2×#910922
C2×#910912
#117463502
#106002993
#695065