Finite Group Databasebeta

← #14325827

Subgroups — #14325827

Order 1920.

1080 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91764C211yesmaximal, characteristic
2C5×#4937C211yesmaximal, characteristic, complemented
3C3×C4×C4⋊Dic5C211yesmaximal, characteristic, complemented
4#11748904C212yesmaximal
5#11748898C212yesmaximal, complemented
6#11748875C212yesmaximal, complemented
7#11748829C212yesmaximal, complemented
8#11748694C212yesmaximal, complemented
9#11748678C212yesmaximal, complemented
10#10605993—31nomaximal, Hall
11C22×D60C2211yescharacteristic
12C22×Dic30C2211yescharacteristic
13C22×#1200C2212yes—
14C2×C3×C42×C5C2211yescharacteristic
15C2×#6714C2212yes—
16C2×#6714C2212yes—
17#91764C418yescomplemented
18C2×C3×C4⋊Dic5C2212yes—
19C2×C3×C4×Dic5C2211yescharacteristic
20C2×C3×C4×Dic5C2211yescharacteristic
21C2×#6669C2212yes—
22C2×#6667C2212yes—
23C2×#6667C2212yes—
24C2×#6667C2212yes—
25C2×Dic3×Dic5C2212yes—
26C5×C3⋊#95C2212yes—
27C5×C3⋊#95C2211yescharacteristic
28C5×C3⋊#95C2212yes—
29C5×C3⋊#95C2211yescharacteristic
30C3×#3963C2212yes—
31#90994C2212yes—
32#90994C2212yes—
33#73632—51nomaximal, Hall
34C2×#4021—31no—
35C5×#383—31no—
36C4×C4⋊Dic5D311yescharacteristic, complemented
37#64959—32no—
38#64958—32no—
39#64957—32no—
40#64955—32no—
41#64954—32no—
42#64935—32no—
43C23×D15C2312yes—
44C22×C3×C4×C5C2311yescharacteristic
45C22×C3×C4×C5C2311yescharacteristic
46C22×C3×C4×C5C2311yescharacteristic
47C22×Dic15C2312yes—
48C2×D60—42no—
49C2×D60C2×C414yes—
50C2×Dic30—42no—
51C2×Dic30C2×C414yescomplemented
52C22×C5×Dic3C2312yes—
53C22×C5×Dic3C2312yes—
54C22×C3×Dic5C2312yes—
55C22×C3×Dic5C2312yes—
56C2×#1200—24no—
57C2×#1200—42no—
58C2×#1200—42no—
59C3×C42×C5C2×C414yescomplemented
60#6714C2×C418yescomplemented
61#6714C2×C418yescomplemented
62C3×C4⋊Dic5—24no—
63C3×C4×Dic5—41no—
64C3×C4×Dic5—41no—
65#6669—42no—
66#6667—24no—
67#6667—42no—
68#6667—42no—
69Dic3×Dic5—42no—
70C2×#875—51no—
71C3×C4×C4⋊C4—51no—
72#4990—52no—
73#4989—52no—
74#4940—52no—
75C4×(C2×D3)⋊C4—52no—
76#4937D511yescharacteristic, complemented
77#4665—52no—
78#4646—52no—
79C22×D20—31no—
80C22×C4×D5—32no—
81C22×Dic10—31no—
82C2×C42×C5C2×D311yescharacteristic
83C2×#685—32no—
84C2×#685—32no—
85C2×#685—32no—
86C2×#685—32no—
87C2×#685—32no—
88C2×C4⋊Dic5C2×D312yes—
89C2×#683—32no—
90C2×C4×Dic5—32no—
91C2×C4×Dic5C2×D311yescharacteristic
92C2×C4×Dic5C2×D311yescharacteristic
93#4021—38no—
94C5×#95—32no—
95C5×#95—32no—
96C5×#95—31no—
97C5×#95—31no—
98#3963—32no—
99#3963—32no—
100#3963C2×D312yes—
101#2337—151noSylow
102C23×C3×C5C2411yescharacteristic
103C22×D15—22no—
104C22×D15—22no—
105C22×D15—22no—
106C22×D15—22no—
107C22×D15—22no—
108C22×D15—22no—
109C22×D15C22×C414yes—
110C2×C3×C4×C5—22no—
111C2×C3×C4×C5—21no—
112C2×C3×C4×C5—22no—
113C2×C3×C4×C5—21no—
114C2×C3×C4×C5C22×C412yes—
115C2×C3×C4×C5C22×C412yes—
116C2×C3×C4×C5C22×C412yes—
117C2×Dic15—22no—
118C2×Dic15—22no—
119C2×Dic15C22×C414yes—
120D60—44no—
121Dic30—44no—
122C2×C5×Dic3—22no—
123C2×C5×Dic3—22no—
124C2×C5×Dic3—22no—
125C2×C5×Dic3—22no—
126C2×C5×Dic3—22no—
127C2×C5×Dic3—22no—
128C2×C3×Dic5—22no—
129C2×C3×Dic5—22no—
130C2×C3×Dic5—22no—
131C2×C3×Dic5—22no—
132C2×C3×Dic5—22no—
133C2×C3×Dic5#4114yes—
134#1200—48no—
135C22×D12—51no—
136C22×C4×D3—52no—
137C22×Dic6—51no—
138C2×C3×C4⋊C4—52no—
139C2×C3×C42—51no—
140C2×C3×C42—51no—
141C2×C3×C42C2×D511yescharacteristic
142C2×(C2×D3)⋊C4—52no—
143C2×(C2×D3)⋊C4—52no—
144C2×(C2×D3)⋊C4—52no—
145C2×(C2×D3)⋊C4—52no—
146C2×(C2×D3)⋊C4—52no—
147C2×Dic3⋊C4—52no—
148C2×C4×Dic3—52no—
149#875—58no—
150C3×#95—52no—
151C3⋊#95—52no—
152C3⋊#95—52no—
153C3⋊#95C2×D512yes—
154C3⋊#95C2×D512yes—
155C3⋊#95C2×D511yescharacteristic
156C3⋊#95C2×D511yescharacteristic
157C23×D5—32no—
158C22×C4×C5—32no—
159C22×C4×C5—32no—
160C22×C4×C5C22×D311yescharacteristic
161C22×C4×C5C22×D311yescharacteristic
162C22×C4×C5C22×D311yescharacteristic
163C22×Dic5—32no—
164C22×Dic5C22×D312yes—
165C22×Dic5C22×D312yes—
166C2×D20—34no—
167C2×D20—122no—
168C2×C4×D5—64no—
169C2×C4×D5—122no—
170C2×C4×D5—122no—
171C2×Dic10—34no—
172C2×Dic10—122no—
173C42×C5C4×D314yescomplemented
174#685—38no—
175#685—38no—
176#685—64no—
177#685—122no—
178#685—122no—
179C4⋊Dic5—24no—
180#683—122no—
181C4×Dic5—41no—
182C4×Dic5—41no—
183C4×Dic5—122no—
184C2×#124—151no—
185#391—152no—
186#388—152no—
187#388—152no—
188#386—152no—
189#385—152no—
190#383—31no—
191C4×C4⋊C4—51no—
192C4×C22⋊C4—152no—
193C22×C3×C5C23×C411yescharacteristic
194C22×C3×C5C2×#4112yes—
195C22×C3×C5H(5,𝔽2)11yescharacteristic
196C22×C3×C5H(5,𝔽2)12yes—
197C22×C3×C52−1+411yescharacteristic
198C2×D15—24no—
199C2×D15—24no—
200C2×D15—24no—
201C2×D15—42no—
202C2×D15—42no—
203C2×D15—42no—
204C2×D15—42no—
205C3×C4×C5—22no—
206C3×C4×C5—22no—
207C3×C4×C5—22no—
208Dic15—24no—
209C3×Dic5—24no—
210C3×Dic5—42no—
211C5×Dic3—42no—
212C5×Dic3—42no—
213C23×D3—52no—
214C22×C3×C4—52no—
215C22×C3×C4—52no—
216C22×C3×C4C22×D511yescharacteristic
217C22×C3×C4C22×D511yescharacteristic
218C22×C3×C4C22×D511yescharacteristic
219C22×Dic3—52no—
220C22×Dic3C22×D512yes—
221C22×Dic3C22×D512yes—
222C2×D12—54no—
223C2×D12—202no—
224C2×C4×D3—104no—
225C2×C4×D3—202no—
226C2×C4×D3—202no—
227C2×Dic6—54no—
228C2×Dic6—202no—
229C3×C4⋊C4—104no—
230C3×C42—201no—
231C3×C42—201no—
232C3×C42C4×D514yescomplemented
233(C2×D3)⋊C4—58no—
234(C2×D3)⋊C4—58no—
235(C2×D3)⋊C4—104no—
236(C2×D3)⋊C4—202no—
237(C2×D3)⋊C4—202no—
238Dic3⋊C4—202no—
239C4×Dic3—202no—
240C23×C5C23×D311yescharacteristic
241C22×D5—34no—
242C22×D5—62no—
243C22×D5—62no—
244C22×D5—62no—
245C22×D5—62no—
246C22×D5—62no—
247C22×D5—62no—
248C2×C4×C5—22no—
249C2×C4×C5—21no—
250C2×C4×C5—21no—
251C2×C4×C5—22no—
252C2×C4×C5—62no—
253C2×C4×C5—62no—
254C2×C4×C5—62no—
255C2×C4×C5—62no—
256C2×C4×C5—62no—
257C2×C4×C5—62no—
258C2×C4×C5C2×C4×D312yes—
259C2×C4×C5C2×C4×D312yes—
260C2×C4×C5C2×C4×D312yes—
261C2×Dic5—22no—
262C2×Dic5—22no—
263C2×Dic5—22no—
264C2×Dic5—22no—
265C2×Dic5—22no—
266C2×Dic5—34no—
267C2×Dic5—62no—
268C2×Dic5—62no—
269C2×Dic5#23514yes—
270D20—124no—
271C4×D5—128no—
272Dic10—124no—
273C22×Q8—151no—
274C22×D4—151no—
275C23×C4—152no—
276#124—158no—
277C2×C4⋊C4—52no—
278C2×C4⋊C4—152no—
279C2×C22⋊C4—152no—
280C2×C22⋊C4—152no—
281C2×C22⋊C4—152no—
282C2×C22⋊C4—152no—
283C2×C22⋊C4—152no—
284C2×C42—51no—
285C2×C42—51no—
286C2×C42—152no—
287C2×C42D3×D511yescharacteristic
288#95—32no—
289#95—31no—
290#95—32no—
291#95—31no—
292#95—52no—
293#95—152no—
294#95—152no—
295C2×C3×C5C4×#4111yescharacteristic
296C2×C3×C5#51811yescharacteristic
297C2×C3×C5#52011yescharacteristic
298C2×C3×C5#53812yes—
299C2×C3×C5#54212yes—
300D15—44no—
301C23×C3C23×D511yescharacteristic
302C22×D3—54no—
303C22×D3—102no—
304C22×D3—102no—
305C22×D3—102no—
306C22×D3—102no—
307C22×D3—102no—
308C22×D3—102no—
309C2×C3×C4—22no—
310C2×C3×C4—21no—
311C2×C3×C4—22no—
312C2×C3×C4—21no—
313C2×C3×C4—54no—
314C2×C3×C4—102no—
315C2×C3×C4—102no—
316C2×C3×C4—102no—
317C2×C3×C4—102no—
318C2×C3×C4—102no—
319C2×C3×C4C2×C4×D512yes—
320C2×C3×C4C2×C4×D512yes—
321C2×C3×C4C2×C4×D512yes—
322C2×Dic3—22no—
323C2×Dic3—22no—
324C2×Dic3—22no—
325C2×Dic3—22no—
326C2×Dic3—22no—
327C2×Dic3—22no—
328C2×Dic3—54no—
329C2×Dic3—102no—
330C2×Dic3—102no—
331D12—204no—
332C4×D3—208no—
333Dic6—204no—
334C22×C5C22×C4×D311yescharacteristic
335C22×C5C2×#23512yes—
336C22×C5#100411yescharacteristic
337C22×C5#100711yescharacteristic
338C22×C5#100912yes—
339C2×D5—64no—
340C2×D5—64no—
341C2×D5—64no—
342C2×D5—122no—
343C2×D5—122no—
344C2×D5—122no—
345C2×D5—122no—
346C4×C5—22no—
347C4×C5—22no—
348C4×C5—22no—
349C4×C5—122no—
350C4×C5—122no—
351Dic5—24no—
352Dic5—42no—
353Dic5—64no—
354C24—152no—
355C2×Q8—154no—
356C2×Q8—602no—
357C2×D4—154no—
358C2×D4—602no—
359C22×C4—32no—
360C22×C4—32no—
361C22×C4—52no—
362C22×C4—52no—
363C22×C4—152no—
364C22×C4—304no—
365C22×C4—602no—
366C22×C4—602no—
367C22×C4C2×D3×D511yescharacteristic
368C22×C4C2×D3×D511yescharacteristic
369C22×C4C2×D3×D511yescharacteristic
370C4⋊C4—104no—
371C4⋊C4—602no—
372C22⋊C4—158no—
373C22⋊C4—158no—
374C22⋊C4—304no—
375C22⋊C4—602no—
376C22⋊C4—602no—
377C42—201no—
378C42—201no—
379C42—602no—
380C42#120014yescomplemented
381C3×C5#233711yescharacteristic, complemented, Hall
382C22×C3C22×C4×D511yescharacteristic
383C22×C3D5×#4112yes—
384C22×C3#414911yescharacteristic
385C22×C3#414912yes—
386C22×C3#415011yescharacteristic
387C2×D3—104no—
388C2×D3—104no—
389C2×D3—104no—
390C2×D3—202no—
391C2×D3—202no—
392C2×D3—202no—
393C2×D3—202no—
394C3×C4—22no—
395C3×C4—22no—
396C3×C4—22no—
397C3×C4—104no—
398C3×C4—202no—
399Dic3—42no—
400Dic3—42no—
401Dic3—104no—
402C2×C5C4×#23511yescharacteristic
403C2×C5#550411yescharacteristic
404C2×C5#552111yescharacteristic
405C2×C5#556012yes—
406C2×C5#558212yes—
407D5—124no—
408C23—154no—
409C23—302no—
410C23—302no—
411C23—302no—
412C23—302no—
413C23—302no—
414C23—302no—
415C23C22×D3×D511yescharacteristic
416Q8—604no—
417D4—604no—
418C2×C4—21no—
419C2×C4—22no—
420C2×C4—21no—
421C2×C4—22no—
422C2×C4—54no—
423C2×C4—62no—
424C2×C4—62no—
425C2×C4—62no—
426C2×C4—62no—
427C2×C4—62no—
428C2×C4—62no—
429C2×C4—102no—
430C2×C4—102no—
431C2×C4—102no—
432C2×C4—102no—
433C2×C4—102no—
434C2×C4—154no—
435C2×C4—302no—
436C2×C4—302no—
437C2×C4—608no—
438C2×C4C2×#120012yes—
439C2×C4C2×#120012yes—
440C2×C4C2×#120012yes—
441C2×C3#6585511yescharacteristic
442C2×C3#6585611yescharacteristic
443C2×C3#6585711yescharacteristic
444C2×C3#6603812yes—
445C2×C3#6604412yes—
446D3—204no—
447C5#7363211yescharacteristic, complemented, Sylow
448C22—304no—
449C22—304no—
450C22—304no—
451C22—602no—
452C22—602no—
453C22—602no—
454C22—602no—
455C22#9200411yescharacteristic
456C22D5×#23512yes—
457C22#9201711yescharacteristic
458C22#9201912yes—
459C22C22×#120011yescharacteristic
460C4—22no—
461C4—22no—
462C4—22no—
463C4—104no—
464C4—122no—
465C4—122no—
466C4—202no—
467C4—304no—
468C3#1060599311yescharacteristic, complemented, Sylow
469C2—604no—
470C2#1175258912yes—
471C2#1175275612yes—
472C2#1175441411yescharacteristic
473C2#1175449611yescharacteristic
474C2#1175451511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×D60C22
hypercenterC2×C42D3×D5
hypocenterC3×C5#2337
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C5×#4937C2semidirect
3. C3×C4×C4⋊Dic5C2semidirect
5. #11748898C2semidirect
6. #11748875C2semidirect
7. #11748829C2semidirect
8. #11748694C2semidirect
9. #11748678C2semidirect
17. #91764C4semidirect
36. C4×C4⋊Dic5D3semidirect
51. C2×Dic30C2×C4semidirect
59. C3×C42×C5C2×C4semidirect
60. #6714C2×C4semidirect
61. #6714C2×C4semidirect
76. #4937D5semidirect
173. C42×C5C4×D3semidirect
232. C3×C42C4×D5semidirect
380. C42#1200semidirect
381. C3×C5#2337semidirect
447. C5#73632semidirect
468. C3#10605993semidirect

Maximal subgroups

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

subgroupindex
C2×#917642
C5×#49372
C3×C4×C4⋊Dic52
#117489042
#117488982
#117488752
#117488292
#117486942
#117486782
#106059933
#736325