Finite Group Databasebeta

← #14300337

Subgroups — #14300337

Order 1920.

748 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756557C211yesmaximal, characteristic
2C2×C5×#834C211yesmaximal, characteristic
3C3×#65509C211yesmaximal, characteristic
4#11749509C212yesmaximal, complemented
5#11746020C212yesmaximal, complemented
6#10600814—31nomaximal, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C23×C3×Dic5C2211yescharacteristic
9C2×#6719—21no—
10C2×#6719C2212yes—
11D4×Dic15—22no—
12D4×Dic15—22no—
13#91815—21no—
14C2×C5×#217C2212yes—
15C2×C3×C22⋊Dic5—21no—
16C2×C3×C22⋊Dic5C2211yescharacteristic
17C2×Dic3⋊Dic5—22no—
18C5×#834C414yescomplemented
19C3×#3963—21no—
20#90994—22no—
21#69597—51nomaximal, Hall
22#66132—31no—
23C2×C5×#99—31no—
24#65509D311yescharacteristic
25#65239—32no—
26#64747—32no—
27C24×C3×C5D411yescharacteristic
28C24×C3×C5C2311yescharacteristic
29C2×C3×C5×D4—22no—
30C2×C3×C5×D4—22no—
31C2×C3×C5×D4C2×C412yes—
32C2×C3×C5×D4Q812yes—
33C22×C3×C4×C5D411yescharacteristic
34C22×Dic15—21no—
35C22×Dic15—21no—
36C22×Dic15D412yes—
37C22×Dic15D412yes—
38C22×C5×Dic3—22no—
39C22×C3×Dic5—21no—
40C22×C3×Dic5—22no—
41C22×C3×Dic5—21no—
42C22×C3×Dic5—42no—
43#6719—22no—
44#6719—22no—
45#6719—22no—
46C4⋊Dic15—21no—
47C4⋊Dic15—21no—
48C4×Dic15—22no—
49C5×#217—22no—
50C5×#217C2×C414yescomplemented
51C3×C22⋊Dic5—22no—
52C3×C22⋊Dic5—42no—
53Dic3⋊Dic5—44no—
54#5798—51no—
55C3×#386—51no—
56C2×#834D511yescharacteristic
57#5210—52no—
58#4527—52no—
59C22×C5×D4C2×D311yescharacteristic
60C23×Dic5C2×D311yescharacteristic
61C2×C5×C22⋊C4—32no—
62C2×C22⋊Dic5—21no—
63C2×C22⋊Dic5—32no—
64C2×C22⋊Dic5—61no—
65C2×C22⋊Dic5C2×D311yescharacteristic
66D4×Dic5—62no—
67D4×Dic5—62no—
68#4072—61no—
69C2×C4⋊Dic5—62no—
70C5×#99—34no—
71#3963—21no—
72#3963—62no—
73#1867—151noSylow
74C23×C3×C5—21no—
75C23×C3×C5—21no—
76C23×C3×C5—41no—
77C23×C3×C5—41no—
78C23×C3×C5—41no—
79C23×C3×C5—41no—
80C23×C3×C5C4⋊C412yescomplemented
81C23×C3×C5C22×C411yescharacteristic
82C23×C3×C5C2×D411yescharacteristic
83C23×C3×C5C2×D412yes—
84C23×C3×C5C2×Q811yescharacteristic
85C23×C3×C5#4112yes—
86C3×C5×D4—24no—
87C3×C5×D4—24no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5C4⋊C412yescomplemented
91C2×Dic15—22no—
92C2×Dic15—22no—
93C2×Dic15—42no—
94C2×Dic15—42no—
95C2×Dic15—81no—
96C2×Dic15—81no—
97C2×C5×Dic3—24no—
98C2×C5×Dic3—42no—
99C2×C5×Dic3—42no—
100C2×C3×Dic5—24no—
101C2×C3×Dic5—22no—
102C2×C3×Dic5—41no—
103C2×C3×Dic5—42no—
104C2×C3×Dic5—41no—
105C2×C3×Dic5—41no—
106C2×C3×Dic5—41no—
107C2×C3×Dic5—41no—
108C22×C3×D4C2×D511yescharacteristic
109C23×C3×C4—51no—
110C2×C3×C22⋊C4—51no—
111C2×C3×C22⋊C4—101no—
112C2×#217—52no—
113C2×#217—101no—
114C2×#217C2×D512yes—
115D4×Dic3—102no—
116D4×Dic3—102no—
117#926—101no—
118C2×Dic3⋊C4—102no—
119C3×#95—101no—
120#834Dic514yescomplemented
121C3⋊#95—102no—
122C24×C5#6711yescharacteristic
123C24×C5C22×D311yescharacteristic
124C2×C5×D4—22no—
125C2×C5×D4—22no—
126C2×C5×D4Dic612yes—
127C2×C5×D4C4×D312yes—
128C22×C4×C5—62no—
129C22×C4×C5#6711yescharacteristic
130C22×Dic5—22no—
131C22×Dic5—21no—
132C22×Dic5—21no—
133C22×Dic5—32no—
134C22×Dic5—32no—
135C22×Dic5—42no—
136C22×Dic5—61no—
137C22×Dic5—61no—
138C5×C22⋊C4—34no—
139C5×C22⋊C4—62no—
140C22⋊Dic5—22no—
141C22⋊Dic5—42no—
142C22⋊Dic5—62no—
143C22⋊Dic5—62no—
144C22⋊Dic5—62no—
145C4⋊Dic5—61no—
146C4⋊Dic5—61no—
147C4⋊Dic5—124no—
148C4×Dic5—62no—
149#518—151no—
150C2×#99—31no—
151#386—51no—
152#385—152no—
153#342—152no—
154C22×C3×C5—21no—
155C22×C3×C5—22no—
156C22×C3×C5—21no—
157C22×C3×C5—22no—
158C22×C3×C5—22no—
159C22×C3×C5—41no—
160C22×C3×C5—41no—
161C22×C3×C5—42no—
162C22×C3×C5—42no—
163C22×C3×C5—41no—
164C22×C3×C5—41no—
165C22×C3×C5—81no—
166C22×C3×C5C2×C4⋊C411yescharacteristic
167C22×C3×C5C4×D412yes—
168C22×C3×C5#12011yescharacteristic
169C22×C3×C5C22⋊Q812yes—
170C22×C3×C5#12311yescharacteristic
171C3×C4×C5—22no—
172Dic15—42no—
173Dic15—42no—
174C3×Dic5—42no—
175C3×Dic5—81no—
176C5×Dic3—44no—
177C24×C3D2011yescharacteristic
178C24×C3C22×D511yescharacteristic
179C2×C3×D4—22no—
180C2×C3×D4—22no—
181C2×C3×D4Dic1012yes—
182C2×C3×D4C2×Dic512yes—
183C22×C3×C4—101no—
184C22×C3×C4—102no—
185C22×C3×C4—101no—
186C22×C3×C4—202no—
187C22×C3×C4D2011yescharacteristic
188C22×Dic3—22no—
189C22×Dic3—52no—
190C22×Dic3—52no—
191C22×Dic3—101no—
192C22×Dic3—101no—
193C3×C22⋊C4—102no—
194C3×C22⋊C4—202no—
195#217—22no—
196#217—102no—
197#217—102no—
198#217—102no—
199#217C2×Dic514yescomplemented
200C4⋊Dic3—101no—
201C4⋊Dic3—101no—
202Dic3⋊C4—204no—
203C4×Dic3—102no—
204C23×C5—21no—
205C23×C5—21no—
206C23×C5—41no—
207C23×C5—41no—
208C23×C5—41no—
209C23×C5—41no—
210C23×C5Dic3⋊C412yescomplemented
211C23×C5C2×Dic611yescharacteristic
212C23×C5C2×C4×D311yescharacteristic
213C23×C5D3×D412yes—
214C23×C5#23712yes—
215C23×C5C2×#6711yescharacteristic
216C5×D4—24no—
217C5×D4—24no—
218C2×C4×C5—21no—
219C2×C4×C5—21no—
220C2×C4×C5—64no—
221C2×C4×C5—122no—
222C2×C4×C5—122no—
223C2×C4×C5Dic3⋊C412yescomplemented
224C2×Dic5—24no—
225C2×Dic5—22no—
226C2×Dic5—41no—
227C2×Dic5—42no—
228C2×Dic5—41no—
229C2×Dic5—41no—
230C2×Dic5—41no—
231C2×Dic5—41no—
232C2×Dic5—62no—
233C2×Dic5—62no—
234C2×Dic5—122no—
235C2×Dic5—122no—
236C2×Dic5—241no—
237C2×Dic5—241no—
238C22×D4D3×D511yescharacteristic
239C23×C4—51no—
240C4×D4—302no—
241C4×D4—302no—
242#117—301no—
243C2×C4⋊C4—302no—
244C2×C22⋊C4—32no—
245C2×C22⋊C4—51no—
246C2×C22⋊C4—101no—
247C2×C22⋊C4—152no—
248C2×C22⋊C4—301no—
249#99—34no—
250#95—101no—
251#95—302no—
252C2×C3×C5—22no—
253C2×C3×C5—21no—
254C2×C3×C5—21no—
255C2×C3×C5—22no—
256C2×C3×C5—42no—
257C2×C3×C5#38511yescharacteristic
258C2×C3×C5B(4,𝔽2)11yescharacteristic
259C2×C3×C5#45811yescharacteristic
260C23×C3—21no—
261C23×C3—21no—
262C23×C3—41no—
263C23×C3—41no—
264C23×C3—41no—
265C23×C3—41no—
266C23×C3C4⋊Dic512yescomplemented
267C23×C3C2×Dic1011yescharacteristic
268C23×C3C2×D2011yescharacteristic
269C23×C3D4×D512yes—
270C23×C3#71112yes—
271C23×C3C22×Dic511yescharacteristic
272C3×D4—24no—
273C3×D4—24no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—104no—
277C2×C3×C4—102no—
278C2×C3×C4—202no—
279C2×C3×C4—201no—
280C2×C3×C4—201no—
281C2×C3×C4—201no—
282C2×C3×C4—201no—
283C2×C3×C4—201no—
284C2×C3×C4C4⋊Dic512yescomplemented
285C2×Dic3—24no—
286C2×Dic3—42no—
287C2×Dic3—42no—
288C2×Dic3—102no—
289C2×Dic3—102no—
290C2×Dic3—202no—
291C2×Dic3—202no—
292C2×Dic3—401no—
293C2×Dic3—401no—
294C22×C5—21no—
295C22×C5—22no—
296C22×C5—21no—
297C22×C5—22no—
298C22×C5—22no—
299C22×C5—41no—
300C22×C5—41no—
301C22×C5—42no—
302C22×C5—42no—
303C22×C5—41no—
304C22×C5—41no—
305C22×C5—81no—
306C22×C5#87812yes—
307C22×C5#67⋊C412yes—
308C22×C5C2×Dic3⋊C411yescharacteristic
309C22×C5#93511yescharacteristic
310C22×C5#93711yescharacteristic
311C4×C5—22no—
312C4×C5—124no—
313Dic5—42no—
314Dic5—81no—
315Dic5—122no—
316Dic5—122no—
317C24#120211yescharacteristic
318C24C2×D3×D511yescharacteristic
319C2×D4—22no—
320C2×D4—22no—
321C2×D4D3×Dic512yes—
322C2×D4#120412yes—
323C22×C4—62no—
324C22×C4—101no—
325C22×C4—102no—
326C22×C4—101no—
327C22×C4—152no—
328C22×C4—152no—
329C22×C4—202no—
330C22×C4—301no—
331C22×C4—301no—
332C22×C4#120211yescharacteristic
333C4⋊C4—301no—
334C4⋊C4—301no—
335C4⋊C4—604no—
336C22⋊C4—34no—
337C22⋊C4—62no—
338C22⋊C4—102no—
339C22⋊C4—202no—
340C22⋊C4—302no—
341C22⋊C4—302no—
342C22⋊C4—302no—
343C42—302no—
344C3×C5#186711yescharacteristic, complemented, Hall
345C22×C3—22no—
346C22×C3—21no—
347C22×C3—22no—
348C22×C3—21no—
349C22×C3—22no—
350C22×C3—41no—
351C22×C3—42no—
352C22×C3—41no—
353C22×C3—42no—
354C22×C3—41no—
355C22×C3—41no—
356C22×C3—81no—
357C22×C3#402412yes—
358C22×C3#402811yescharacteristic
359C22×C3#403211yescharacteristic
360C22×C3C2×C4⋊Dic511yescharacteristic
361C22×C3D4×Dic512yes—
362C3×C4—22no—
363C3×C4—202no—
364C3×C4—401no—
365Dic3—44no—
366Dic3—202no—
367Dic3—202no—
368C2×C5—21no—
369C2×C5—22no—
370C2×C5—21no—
371C2×C5—22no—
372C2×C5—42no—
373C2×C5#494611yescharacteristic
374C2×C5#503211yescharacteristic
375C2×C5#505311yescharacteristic
376C23—21no—
377C23—21no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23Dic3⋊Dic512yescomplemented
383C23#678012yes—
384C23C2×D3×Dic511yescharacteristic
385C23C2×#120211yescharacteristic
386C23C2×#120411yescharacteristic
387C23#679012yes—
388D4—24no—
389D4—24no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—64no—
393C2×C4—102no—
394C2×C4—104no—
395C2×C4—122no—
396C2×C4—122no—
397C2×C4—202no—
398C2×C4—201no—
399C2×C4—201no—
400C2×C4—201no—
401C2×C4—201no—
402C2×C4—201no—
403C2×C4—302no—
404C2×C4—302no—
405C2×C4—602no—
406C2×C4—602no—
407C2×C4—1201no—
408C2×C4—1201no—
409C2×C4Dic3⋊Dic512yescomplemented
410C2×C3—22no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—22no—
414C2×C3—42no—
415C2×C3#6503011yescharacteristic
416C2×C3#6503111yescharacteristic
417C2×C3#6523911yescharacteristic
418C5#6959711yescharacteristic, complemented, Sylow
419C22—22no—
420C22—21no—
421C22—22no—
422C22—21no—
423C22—22no—
424C22—42no—
425C22—41no—
426C22—41no—
427C22—42no—
428C22—41no—
429C22—41no—
430C22—81no—
431C22#9153711yescharacteristic
432C22C2×Dic3⋊Dic511yescharacteristic
433C22#67⋊Dic512yes—
434C22#9157211yescharacteristic
435C22#9157612yes—
436C4—22no—
437C4—124no—
438C4—202no—
439C4—401no—
440C4—602no—
441C4—602no—
442C3#1060081411yescharacteristic, complemented, Sylow
443C2—22no—
444C2—21no—
445C2—21no—
446C2—22no—
447C2—42no—
448C2#1174917911yescharacteristic
449C2#1174918511yescharacteristic
450C2#1174951711yescharacteristic
subgroupG/H
centerC22#91572
commutatorC23×C3×C5C22×C4
FrattiniC24C2×D3×D5
Fitting, prime radicalC22×C3×C5×D4C22
socleC22×C3×C5#120
cosocleC24×C3×C5C23
hypercenterC22×D4D3×D5
hypocenterC3×C5#1867
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #11749509C2semidirect
5. #11746020C2semidirect
18. C5×#834C4semidirect
50. C5×#217C2×C4semidirect
80. C23×C3×C5C4⋊C4semidirect
90. C2×C3×C4×C5C4⋊C4semidirect
120. #834Dic5semidirect
199. #217C2×Dic5semidirect
210. C23×C5Dic3⋊C4semidirect
223. C2×C4×C5Dic3⋊C4semidirect
266. C23×C3C4⋊Dic5semidirect
284. C2×C3×C4C4⋊Dic5semidirect
344. C3×C5#1867semidirect
382. C23Dic3⋊Dic5semidirect
409. C2×C4Dic3⋊Dic5semidirect
418. C5#69597semidirect
442. C3#10600814semidirect

Maximal subgroups

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

subgroupindex
#117565572
C2×C5×#8342
C3×#655092
#117495092
#117460202
#106008143
#695975