Finite Group Databasebeta

← #14300496

Subgroups — #14300496

Order 1920.

816 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6710C211yesmaximal, characteristic, complemented
2C2×C3×C4×C22⋊D5C211yesmaximal, characteristic
3C2×C5×#830C211yesmaximal, characteristic, complemented
4C2×#90955C212yesmaximal, complemented
5#11745966C212yesmaximal, complemented
6#10600746—31nomaximal, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C22×C3×C22⋊D5C411yescharacteristic
9C22×C3×C4×D5C2211yescharacteristic
10C2×#6710—22no—
11C2×#6710—24no—
12C22×C3⋊#168C2212yes—
13C22×C5×C3⋊C8C2212yes—
14C2×C3×C22⋊Dic5C411yescharacteristic
15C3×C4×C22⋊D5—22no—
16C3×C4×C22⋊D5—22no—
17C2×C3×#685C411yescharacteristic
18C2×C3×#683C411yescharacteristic
19C2×C3×C4×Dic5C2211yescharacteristic
20C5×#830—22no—
21#90955—24no—
22#71611—51nomaximal, Hall
23C2×C4×C22⋊D5D311yescharacteristic
24C22×#681—31no—
25C2×C5×C22⋊C8—31no—
26C2×#3952—32no—
27#64770—32no—
28C24×C3×C5C2×C411yescharacteristic
29C23×C3×D5C2×C411yescharacteristic
30C22×C3×C4×C5—22no—
31C22×C3×C4×C5—22no—
32C22×C3×C4×C5C2×C411yescharacteristic
33C22×C3×C4×C5D412yes—
34C22×C3×C4×C5D412yes—
35C22×C3×C4×C5C2311yescharacteristic
36C2×C3×C22⋊D5—22no—
37C2×C3×C22⋊D5—22no—
38C2×C3×C22⋊D5—22no—
39C22×C3×Dic5C2×C411yescharacteristic
40C22×C3×Dic5C2×C411yescharacteristic
41C22×C3×Dic5C2×C411yescharacteristic
42C2×C3×C4×D5—22no—
43C2×C3×C4×D5—21no—
44C2×C3×C4×D5—21no—
45C2×C3×C4×D5—22no—
46#6710—28no—
47C2×C3⋊#168—22no—
48C2×C3⋊#168—22no—
49C2×C3⋊#168D414yescomplemented
50C2×C5×C3⋊C8—22no—
51C2×C5×C3⋊C8—22no—
52C2×C5×C3⋊C8—22no—
53C3×C22⋊Dic5—22no—
54C3×#685—22no—
55C3×#683—22no—
56C3×C4×Dic5—21no—
57C3×C4×Dic5—21no—
58C2×C3×C4×D4—51no—
59C22×#208—51no—
60C2×#830—52no—
61C2×#830D511yescharacteristic, complemented
62#4524—52no—
63C23×C4×C5C2×D311yescharacteristic
64C22×C22⋊D5Dic311yescharacteristic
65C22×C4×D5C2×D311yescharacteristic
66C22×C5×C8—32no—
67C2×C22⋊Dic5Dic311yescharacteristic
68C4×C22⋊D5—22no—
69C4×C22⋊D5—22no—
70C2×#685Dic311yescharacteristic
71C2×#683Dic311yescharacteristic
72C2×C4×Dic5C2×D311yescharacteristic
73C2×#681—64no—
74C2×#681—62no—
75C22×#168—32no—
76C5×C22⋊C8—62no—
77#3952—64no—
78#1870—151noSylow
79C23×C3×C5—22no—
80C23×C3×C5—21no—
81C23×C3×C5—21no—
82C23×C3×C5—22no—
83C23×C3×C5C22⋊C412yes—
84C23×C3×C5C22×C411yescharacteristic
85C22×C3×D5—21no—
86C22×C3×D5—22no—
87C22×C3×D5—21no—
88C22×C3×D5—22no—
89C22×C3×D5M1612yescomplemented
90C2×C3×C4×C5—22no—
91C2×C3×C4×C5—22no—
92C2×C3×C4×C5—24no—
93C2×C3×C4×C5—22no—
94C2×C3×C4×C5C22⋊C412yes—
95C2×C3×C4×C5C2×D412yes—
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5#4112yes—
99C3×C22⋊D5—28no—
100C2×C3×Dic5—21no—
101C2×C3×Dic5—21no—
102C2×C3×Dic5—21no—
103C2×C3×Dic5—21no—
104C2×C3×Dic5—22no—
105C2×C3×Dic5—22no—
106C2×C3×Dic5M1612yescomplemented
107C3×C4×D5—41no—
108C3×C4×D5—42no—
109C3×C4×D5—41no—
110C3⋊#168—24no—
111C5×C3⋊C8—42no—
112C22×C3×D4—51no—
113C23×C3×C4—51no—
114C23×C3×C4C2×D511yescharacteristic
115C3×C4×D4—102no—
116C3×C4×D4—102no—
117C2×C3×C4⋊C4—51no—
118C2×C3×C22⋊C4—51no—
119C2×C3×C22⋊C4—51no—
120C2×C3×C42—51no—
121C2×#208—104no—
122C2×#208—102no—
123C22×C3⋊C8—52no—
124C22×C3⋊C8C2×D512yes—
125#830—22no—
126#830—104no—
127C24×C5C2×Dic311yescharacteristic
128C23×D5C2×Dic311yescharacteristic
129C22×C4×C5—22no—
130C22×C4×C5—22no—
131C22×C4×C5C2×Dic311yescharacteristic
132C22×C4×C5#6712yes—
133C22×C4×C5#6712yes—
134C22×C4×C5C22×D311yescharacteristic
135C2×C22⋊D5—22no—
136C2×C22⋊D5—22no—
137C2×C22⋊D5—22no—
138C22×Dic5C2×Dic311yescharacteristic
139C22×Dic5C2×Dic311yescharacteristic
140C22×Dic5C2×Dic311yescharacteristic
141C2×C4×D5—22no—
142C2×C4×D5—22no—
143C2×C4×D5—21no—
144C2×C4×D5—21no—
145C2×C5×C8—62no—
146C2×C5×C8—62no—
147C2×C5×C8—62no—
148C22⋊Dic5—22no—
149#685—22no—
150#683—22no—
151C4×Dic5—21no—
152C4×Dic5—21no—
153#681—68no—
154C2×#168—34no—
155C2×#168—62no—
156C2×#168—62no—
157C22×M16—151no—
158C2×C4×D4—51no—
159C2×C22⋊C8—31no—
160C2×C22⋊C8—152no—
161#336—152no—
162C22×C3×C5—22no—
163C22×C3×C5—22no—
164C22×C3×C5—22no—
165C22×C3×C5—42no—
166C22×C3×C5—42no—
167C22×C3×C5C2×C22⋊C411yescharacteristic
168C22×C3×C5C4×D412yes—
169C22×C3×C5C2×M1611yescharacteristic
170C22×C3×C5C2×M1611yescharacteristic
171C22×C3×C5#13112yes—
172C2×C3×D5—22no—
173C2×C3×D5—24no—
174C2×C3×D5—41no—
175C2×C3×D5—41no—
176C2×C3×D5—42no—
177C3×C4×C5—22no—
178C3×C4×C5#12011yescharacteristic
179C3×C4×C5#12112yes—
180C3×C4×C5#12311yescharacteristic
181C3×Dic5—22no—
182C3×Dic5—41no—
183C3×Dic5—41no—
184C24×C3—51no—
185C24×C3C4×D511yescharacteristic
186C2×C3×D4—102no—
187C2×C3×D4—102no—
188C2×C3×D4—102no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—51no—
192C22×C3×C4—51no—
193C22×C3×C4—51no—
194C22×C3×C4—101no—
195C22×C3×C4—102no—
196C22×C3×C4—102no—
197C22×C3×C4—101no—
198C22×C3×C4C4×D511yescharacteristic
199C22×C3×C4D2012yes—
200C22×C3×C4C22⋊D512yes—
201C22×C3×C4C22×D511yescharacteristic
202C3×C4⋊C4—102no—
203C3×C22⋊C4—102no—
204C3×C22⋊C4—102no—
205C3×C42—101no—
206C3×C42—101no—
207#208—108no—
208C2×C3⋊C8—22no—
209C2×C3⋊C8—22no—
210C2×C3⋊C8—22no—
211C2×C3⋊C8—54no—
212C2×C3⋊C8—102no—
213C2×C3⋊C8—102no—
214C23×C5—21no—
215C23×C5—21no—
216C23×C5—22no—
217C23×C5—22no—
218C23×C5#21712yes—
219C23×C5C22×Dic311yescharacteristic
220C22×D5—21no—
221C22×D5—22no—
222C22×D5—22no—
223C22×D5—21no—
224C22×D5#20812yescomplemented
225C2×C4×C5—22no—
226C2×C4×C5—22no—
227C2×C4×C5—22no—
228C2×C4×C5—24no—
229C2×C4×C5#21712yes—
230C2×C4×C5D3×D412yes—
231C2×C4×C5#23712yes—
232C2×C4×C5C2×#6711yescharacteristic
233C2×C4×C5C2×#6711yescharacteristic
234C22⋊D5—28no—
235C2×Dic5—21no—
236C2×Dic5—21no—
237C2×Dic5—22no—
238C2×Dic5—22no—
239C2×Dic5—21no—
240C2×Dic5—21no—
241C2×Dic5#20812yescomplemented
242C4×D5—41no—
243C4×D5—41no—
244C4×D5—42no—
245C5×C8—122no—
246#168—64no—
247C22×D4—51no—
248C23×C4—51no—
249C23×C4D3×D511yescharacteristic
250C2×M16—304no—
251C2×M16—302no—
252C22×C8—32no—
253C22×C8—152no—
254C4×D4—102no—
255C4×D4—102no—
256C2×C4⋊C4—51no—
257C2×C22⋊C4—51no—
258C2×C22⋊C4—51no—
259C2×C42—51no—
260C22⋊C8—62no—
261C22⋊C8—304no—
262C2×C3×C5—42no—
263C2×C3×C5#38611yescharacteristic
264C2×C3×C5#40711yescharacteristic
265C2×C3×C5#40811yescharacteristic
266C2×C3×C5#43512yes—
267C2×C3×C5#43612yes—
268C3×D5—42no—
269C23×C3—22no—
270C23×C3—22no—
271C23×C3—21no—
272C23×C3—21no—
273C23×C3—52no—
274C23×C3—102no—
275C23×C3—102no—
276C23×C3—101no—
277C23×C3—101no—
278C23×C3#68512yes—
279C23×C3C2×C4×D511yescharacteristic
280C3×D4—108no—
281C2×C3×C4—22no—
282C2×C3×C4—22no—
283C2×C3×C4—22no—
284C2×C3×C4—24no—
285C2×C3×C4—52no—
286C2×C3×C4—101no—
287C2×C3×C4—101no—
288C2×C3×C4—102no—
289C2×C3×C4—102no—
290C2×C3×C4—101no—
291C2×C3×C4—101no—
292C2×C3×C4—201no—
293C2×C3×C4—201no—
294C2×C3×C4—202no—
295C2×C3×C4#68512yes—
296C2×C3×C4C2×D2011yescharacteristic
297C2×C3×C4D4×D512yes—
298C2×C3×C4#71112yes—
299C2×C3×C4C2×C22⋊D511yescharacteristic
300C3⋊C8—42no—
301C3⋊C8—104no—
302C22×C5—22no—
303C22×C5—22no—
304C22×C5—22no—
305C22×C5—42no—
306C22×C5—42no—
307C22×C5C2×#20811yescharacteristic
308C22×C5C2×#20811yescharacteristic
309C22×C5D4×Dic312yes—
310C22×C5#94812yes—
311C22×C5C2×#21711yescharacteristic
312C2×D5—22no—
313C2×D5—24no—
314C2×D5—41no—
315C2×D5—41no—
316C2×D5—42no—
317C4×C5—22no—
318C4×C5#93511yescharacteristic
319C4×C5#93711yescharacteristic
320C4×C5#93912yes—
321Dic5—22no—
322Dic5—41no—
323Dic5—41no—
324C24—51no—
325C24D5×Dic311yescharacteristic
326C2×D4—102no—
327C2×D4—102no—
328C2×D4—102no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—51no—
332C22×C4—51no—
333C22×C4—51no—
334C22×C4—102no—
335C22×C4—101no—
336C22×C4—101no—
337C22×C4—102no—
338C22×C4D5×Dic311yescharacteristic
339C22×C4#120112yes—
340C22×C4#120212yes—
341C22×C4C2×D3×D511yescharacteristic
342M16—308no—
343C2×C8—62no—
344C2×C8—62no—
345C2×C8—62no—
346C2×C8—154no—
347C2×C8—302no—
348C2×C8—302no—
349C4⋊C4—102no—
350C22⋊C4—102no—
351C22⋊C4—102no—
352C42—101no—
353C42—101no—
354C3×C5#187011yescharacteristic, complemented, Hall
355C22×C3—22no—
356C22×C3—22no—
357C22×C3—22no—
358C22×C3—42no—
359C22×C3—42no—
360C22×C3—102no—
361C22×C3—104no—
362C22×C3—201no—
363C22×C3—201no—
364C22×C3—202no—
365C22×C3#402712yes—
366C22×C3#404712yes—
367C22×C3D5×M1611yescharacteristic
368C22×C3D5×M1611yescharacteristic
369C22×C3C2×#68511yescharacteristic
370C3×C4—22no—
371C3×C4—102no—
372C3×C4—201no—
373C3×C4—201no—
374C3×C4#402811yescharacteristic
375C3×C4#403211yescharacteristic
376C3×C4#408512yes—
377C2×C5—42no—
378C2×C5#501112yes—
379C2×C5#501212yes—
380C2×C5#520711yescharacteristic
381C2×C5#522011yescharacteristic
382C2×C5#523411yescharacteristic
383D5—42no—
384C23—21no—
385C23—21no—
386C23—22no—
387C23—22no—
388C23—52no—
389C23—101no—
390C23—101no—
391C23—102no—
392C23—102no—
393C23#666512yes—
394C23C2×D5×Dic311yescharacteristic
395D4—108no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—24no—
399C2×C4—22no—
400C2×C4—52no—
401C2×C4—101no—
402C2×C4—101no—
403C2×C4—101no—
404C2×C4—101no—
405C2×C4—102no—
406C2×C4—102no—
407C2×C4—201no—
408C2×C4—202no—
409C2×C4—201no—
410C2×C4#666512yes—
411C2×C4#678012yes—
412C2×C4C2×#120111yescharacteristic
413C2×C4C2×#120211yescharacteristic
414C2×C4#679012yes—
415C8—122no—
416C8—304no—
417C2×C3—42no—
418C2×C3—202no—
419C2×C3#6501712yes—
420C2×C3#6501812yes—
421C2×C3#6524711yescharacteristic
422C2×C3#6539911yescharacteristic
423C2×C3#6541511yescharacteristic
424C5#7161111yescharacteristic, complemented, Sylow
425C22—22no—
426C22—22no—
427C22—22no—
428C22—42no—
429C22—42no—
430C22—104no—
431C22—102no—
432C22—201no—
433C22—202no—
434C22—201no—
435C22D5×#20811yescharacteristic
436C22D5×#20811yescharacteristic
437C22#9128312yes—
438C22C2×#666511yescharacteristic
439C22#9155912yes—
440C4—22no—
441C4—102no—
442C4—201no—
443C4—201no—
444C4#9153711yescharacteristic
445C4#9157112yes—
446C4#9157211yescharacteristic
447C3#1060074611yescharacteristic, complemented, Sylow
448C2—42no—
449C2—202no—
450C2#1174833912yes—
451C2#1174834111yescharacteristic
452C2#1174834211yescharacteristic
453C2#1174849412yes—
454C2#1174950011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D3×D5
commutator, socleC23×C3×C5C22×C4
FittingC23×C3×C4×C5C22
prime radicalC22×C3×C22⋊D5C4
cosocleC22×C3×C4×C5C23
hypercenterC23×C4D3×D5
hypocenterC3×C5#1870
LCSG ▷ C23×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#6710C2semidirect
3. C2×C5×#830C2semidirect
4. C2×#90955C2semidirect
5. #11745966C2semidirect
49. C2×C3⋊#168D4semidirect
61. C2×#830D5semidirect
89. C22×C3×D5M16semidirect
106. C2×C3×Dic5M16semidirect
224. C22×D5#208semidirect
241. C2×Dic5#208semidirect
354. C3×C5#1870semidirect
424. C5#71611semidirect
447. C3#10600746semidirect

Maximal subgroups

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

subgroupindex
C22×#67102
C2×C3×C4×C22⋊D52
C2×C5×#8302
C2×#909552
#117459662
#106007463
#716115