Finite Group Databasebeta

← #14324403

Subgroups — #14324403

Order 1920.

1480 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91782C211yesmaximal, characteristic, complemented
2C2×#91458C211yesmaximal, characteristic
3C2×#91434C211yesmaximal, characteristic, complemented
4C5×#4977C211yesmaximal, characteristic, complemented
5C3×#65277C211yesmaximal, characteristic, complemented
6#11748917C214yesmaximal, complemented
7#11748872C214yesmaximal, complemented
8#11748768C211yesmaximal, characteristic, complemented
9#11748611C211yesmaximal, characteristic, complemented
10#10605884—31nomaximal, Hall
11C22×D60C2211yescharacteristic
12C22×C4×D15C2212yes—
13C22×C3×D20C2211yescharacteristic
14C22×#1202C2214yes—
15C22×D5×Dic3C2212yes—
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17C2×#6714C2212yes—
18C2×C4×Dic15C2211yescharacteristic
19#91782—24no—
20C2×C5×C4⋊Dic3C2211yescharacteristic
21C2×C4×C5×Dic3C2211yescharacteristic
22C2×C3×#685C2214yes—
23C2×C3×C4×Dic5C2211yescharacteristic
24C2×#6667C2214yes—
25C2×#6665C2212yes—
26#91458C418yescomplemented
27#91434—24no—
28C5×C3⋊#95C2214yes—
29#90994C2212yes—
30#90994C2212yes—
31#76298—51nomaximal, Hall
32C2×#4039—31no—
33C2×#4039—31no—
34C2×#4020—31no—
35C5×#382—31no—
36#65277—31no—
37#65277D311yescharacteristic, complemented
38#65221—31no—
39#64954—34no—
40#64954—34no—
41C23×D15C2312yes—
42C23×C3×D5C2312yes—
43C22×C3×C4×C5C2312yes—
44C22×C3×C4×C5C2311yescharacteristic
45C22×Dic15C2311yescharacteristic
46C22×Dic15C2311yescharacteristic
47C2×D60—22no—
48C2×D60—22no—
49C2×D60C2×C414yescomplemented
50C2×C4×D15—24no—
51C2×C4×D15—44no—
52C22×C5×Dic3C2312yes—
53C22×C5×Dic3C2312yes—
54C22×C3×Dic5C2312yes—
55C2×C3×D20—22no—
56C2×C3×D20—22no—
57C2×C3×D20C2×C414yescomplemented
58C2×#1202—44no—
59C2×#1202—44no—
60C2×#1202C2×C4116yescomplemented
61C2×D5×Dic3—24no—
62C2×D5×Dic3—44no—
63C3×C5×C4⋊C4—22no—
64#6714—24no—
65C4×Dic15D414yescomplemented
66C5×C4⋊Dic3—22no—
67C4×C5×Dic3C2×C414yescomplemented
68C3×#685—44no—
69C3×C4×Dic5—22no—
70#6667—44no—
71#6665—24no—
72C2×#940—51no—
73C2×D4×Dic3—51no—
74C2×#893—51no—
75C3×#390—51no—
76#4977D511yescharacteristic, complemented
77#4958—54no—
78#4956—54no—
79#4939—51no—
80#4932—51no—
81C22×D20—31no—
82C22×D20—34no—
83C22×D20C2×D311yescharacteristic
84C22×C4×D5—32no—
85C22×C4×D5—32no—
86C2×C5×C4⋊C4—31no—
87C2×C5×C4⋊C4C2×D311yescharacteristic
88C2×C42×C5—31no—
89C2×#685—32no—
90C2×#685—32no—
91C2×#685—34no—
92C2×#685C2×D314yes—
93C2×C4×Dic5—31no—
94C2×C4×Dic5C2×D311yescharacteristic
95#4039—64no—
96#4039—64no—
97#4020—38no—
98C5×#95—34no—
99#3963—32no—
100#3963—32no—
101#2328—151noSylow
102C23×C3×C5C2411yescharacteristic
103C22×D15—22no—
104C22×D15—22no—
105C22×D15—24no—
106C22×D15—24no—
107C22×D15C22×C414yes—
108C22×C3×D5—22no—
109C22×C3×D5—22no—
110C22×C3×D5—24no—
111C22×C3×D5—24no—
112C22×C3×D5C22×C414yes—
113C2×C3×C4×C5—22no—
114C2×C3×C4×C5—24no—
115C2×C3×C4×C5C22×C412yes—
116C2×C3×C4×C5C2×D412yes—
117C2×C3×C4×C5#4112yes—
118C2×Dic15—22no—
119C2×Dic15—22no—
120C2×Dic15C2×D412yes—
121C2×Dic15C2×D412yes—
122D60—28no—
123C4×D15—48no—
124C2×C5×Dic3—22no—
125C2×C5×Dic3—22no—
126C2×C5×Dic3—22no—
127C2×C5×Dic3—24no—
128C2×C5×Dic3C22×C414yes—
129C2×C3×Dic5—22no—
130C2×C3×Dic5—22no—
131C2×C3×Dic5—22no—
132C3×D20—28no—
133#1202—416no—
134D5×Dic3—48no—
135C22×C3×D4—51no—
136C22×#67—54no—
137C23×Dic3—52no—
138C22×D12—51no—
139C22×C4×D3—52no—
140C2×C3×C4⋊C4C2×D511yescharacteristic
141C2×C3×C22⋊C4—54no—
142C2×C3×C42—51no—
143C2×#217—52no—
144#940—58no—
145D4×Dic3—104no—
146C2×(C2×D3)⋊C4—52no—
147C2×(C2×D3)⋊C4—54no—
148C2×C4⋊Dic3C2×D511yescharacteristic
149C2×C4×Dic3—51no—
150C2×C4×Dic3C2×D511yescharacteristic
151#893—104no—
152C3⋊#95—52no—
153C3⋊#95—52no—
154C3⋊#95C2×D514yes—
155C23×D5—32no—
156C23×D5C22×D312yes—
157C22×C4×C5—32no—
158C22×C4×C5—32no—
159C22×C4×C5C22×D312yes—
160C22×C4×C5C22×D311yescharacteristic
161C22×Dic5—31no—
162C22×Dic5—31no—
163C22×Dic5C22×D312yes—
164C2×D20—22no—
165C2×D20—22no—
166C2×D20—34no—
167C2×D20—316no—
168C2×D20—62no—
169C2×D20—62no—
170C2×D20—124no—
171C2×D20—124no—
172C2×D20C4×D314yescomplemented
173C2×C4×D5—64no—
174C2×C4×D5—64no—
175C2×C4×D5—124no—
176C2×C4×D5—124no—
177C5×C4⋊C4—22no—
178C5×C4⋊C4—62no—
179C42×C5—34no—
180#685—44no—
181#685—64no—
182#685—64no—
183#685—124no—
184C4×Dic5—22no—
185C4×Dic5—34no—
186C2×#127—151no—
187C2×C4×D4—151no—
188C2×C4×D4—151no—
189#390—51no—
190#390—151no—
191#386—154no—
192#386—154no—
193#382—31no—
194#376—151no—
195C22×C3×C5C23×C411yescharacteristic
196C22×C3×C5C22×D411yescharacteristic
197C22×C3×C5C2×#4111yescharacteristic
198C22×C3×C5H(5,𝔽2)12yes—
199C22×C3×C5H(5,𝔽2)12yes—
200C2×D15—24no—
201C2×D15—28no—
202C2×D15—42no—
203C2×D15—42no—
204C2×D15—44no—
205C2×C3×D5—24no—
206C2×C3×D5—28no—
207C2×C3×D5—42no—
208C2×C3×D5—42no—
209C2×C3×D5—44no—
210C3×C4×C5—42no—
211C3×C4×C5C4×D414yes—
212Dic15—22no—
213Dic15—22no—
214C3×Dic5—42no—
215C5×Dic3—24no—
216C5×Dic3—42no—
217C24×C3—52no—
218C23×D3—52no—
219C2×C3×D4—54no—
220C2×C3×D4—102no—
221C2×C3×D4—102no—
222C22×C3×C4—52no—
223C22×C3×C4C22×D512yes—
224C22×C3×C4C22×D511yescharacteristic
225C2×#67—516no—
226C2×#67—204no—
227C2×#67—204no—
228C22×Dic3—51no—
229C22×Dic3—51no—
230C22×Dic3—104no—
231C22×Dic3—204no—
232C22×Dic3C22×D512yes—
233C22×Dic3C22×D512yes—
234C2×D12—54no—
235C2×D12—102no—
236C2×D12—102no—
237C2×C4×D3—104no—
238C2×C4×D3—204no—
239C3×C4⋊C4—22no—
240C3×C22⋊C4—204no—
241C3×C42—102no—
242#217—104no—
243(C2×D3)⋊C4—104no—
244(C2×D3)⋊C4—204no—
245C4⋊Dic3—22no—
246C4×Dic3—54no—
247C4×Dic3C4×D514yescomplemented
248C23×C5C23×D311yescharacteristic
249C22×D5—22no—
250C22×D5—22no—
251C22×D5—24no—
252C22×D5—24no—
253C22×D5—34no—
254C22×D5—62no—
255C22×D5—62no—
256C22×D5—64no—
257C22×D5—64no—
258C22×D5C2×C4×D314yes—
259C2×C4×C5—22no—
260C2×C4×C5—24no—
261C2×C4×C5—34no—
262C2×C4×C5—62no—
263C2×C4×C5—62no—
264C2×C4×C5—62no—
265C2×C4×C5—64no—
266C2×C4×C5C2×C4×D312yes—
267C2×C4×C5D3×D412yes—
268C2×C4×C5#23712yes—
269C2×Dic5—22no—
270C2×Dic5—22no—
271C2×Dic5—22no—
272C2×Dic5—32no—
273C2×Dic5—32no—
274C2×Dic5—62no—
275C2×Dic5—62no—
276D20—28no—
277D20—68no—
278D20—1216no—
279C4×D5—128no—
280C4×D5—128no—
281C22×D4—51no—
282C22×D4—154no—
283C22×D4—151no—
284C23×C4—152no—
285C23×C4—152no—
286#127—158no—
287C4×D4—304no—
288C4×D4—304no—
289C2×C4⋊C4—31no—
290C2×C4⋊C4D3×D511yescharacteristic
291C2×C22⋊C4—54no—
292C2×C22⋊C4—152no—
293C2×C22⋊C4—152no—
294C2×C22⋊C4—154no—
295C2×C42—31no—
296C2×C42—51no—
297C2×C42—151no—
298#95—34no—
299#95—152no—
300#95—152no—
301C2×C3×C5C2×C4×D411yescharacteristic
302C2×C3×C5#51812yes—
303C2×C3×C5#53511yescharacteristic
304C2×C3×C5#53511yescharacteristic
305C2×C3×C5#54012yes—
306D15—44no—
307C3×D5—44no—
308C23×C3—54no—
309C23×C3—102no—
310C23×C3—102no—
311C23×C3—104no—
312C23×C3—104no—
313C23×C3C23×D511yescharacteristic
314C22×D3—54no—
315C22×D3—102no—
316C22×D3—102no—
317C22×D3—104no—
318C22×D3—104no—
319C3×D4—108no—
320C2×C3×C4—22no—
321C2×C3×C4—24no—
322C2×C3×C4—102no—
323C2×C3×C4—102no—
324C2×C3×C4—102no—
325C2×C3×C4C2×C4×D512yes—
326C2×C3×C4D4×D512yes—
327C2×C3×C4#71312yes—
328#67—2016no—
329C2×Dic3—22no—
330C2×Dic3—22no—
331C2×Dic3—22no—
332C2×Dic3—24no—
333C2×Dic3—52no—
334C2×Dic3—52no—
335C2×Dic3—102no—
336C2×Dic3—102no—
337C2×Dic3—208no—
338C2×Dic3C2×C4×D514yes—
339D12—108no—
340C4×D3—208no—
341C22×C5C22×C4×D311yescharacteristic
342C22×C5C2×D3×D411yescharacteristic
343C22×C5C2×#23711yescharacteristic
344C22×C5#100412yes—
345C22×C5#100912yes—
346C2×D5—24no—
347C2×D5—28no—
348C2×D5—42no—
349C2×D5—42no—
350C2×D5—44no—
351C2×D5—64no—
352C2×D5—68no—
353C2×D5—122no—
354C2×D5—122no—
355C2×D5—124no—
356C4×C5—42no—
357C4×C5—64no—
358C4×C5—122no—
359C4×C5#67⋊C414yes—
360Dic5—42no—
361Dic5—62no—
362Dic5—62no—
363C24—52no—
364C24—152no—
365C2×D4—54no—
366C2×D4—102no—
367C2×D4—102no—
368C2×D4—1516no—
369C2×D4—154no—
370C2×D4—302no—
371C2×D4—302no—
372C2×D4—604no—
373C2×D4—604no—
374C22×C4—32no—
375C22×C4—32no—
376C22×C4—52no—
377C22×C4—151no—
378C22×C4—151no—
379C22×C4—304no—
380C22×C4—304no—
381C22×C4—604no—
382C22×C4—604no—
383C22×C4C2×D3×D512yes—
384C22×C4C2×D3×D511yescharacteristic
385C4⋊C4—22no—
386C4⋊C4—62no—
387C22⋊C4—204no—
388C22⋊C4—304no—
389C22⋊C4—304no—
390C22⋊C4—604no—
391C42—34no—
392C42—102no—
393C42—154no—
394C3×C5#232811yescharacteristic, complemented, Hall
395C22×C3—104no—
396C22×C3—108no—
397C22×C3—202no—
398C22×C3—202no—
399C22×C3—204no—
400C22×C3C22×C4×D511yescharacteristic
401C22×C3C2×D4×D511yescharacteristic
402C22×C3C2×#71311yescharacteristic
403C22×C3#414912yes—
404C22×C3#414912yes—
405C2×D3—104no—
406C2×D3—108no—
407C2×D3—202no—
408C2×D3—202no—
409C2×D3—204no—
410C3×C4—42no—
411C3×C4—202no—
412C3×C4#403914yes—
413Dic3—24no—
414Dic3—42no—
415Dic3—102no—
416Dic3—102no—
417C2×C5C2×#67⋊C411yescharacteristic
418C2×C5#554512yes—
419C2×C5#561912yes—
420C2×C5#567411yescharacteristic
421C2×C5#571511yescharacteristic
422D5—44no—
423D5—124no—
424C23—54no—
425C23—102no—
426C23—104no—
427C23—104no—
428C23—102no—
429C23—154no—
430C23—302no—
431C23—304no—
432C23—304no—
433C23—302no—
434C23C22×D3×D511yescharacteristic
435D4—108no—
436D4—308no—
437D4—6016no—
438C2×C4—24no—
439C2×C4—22no—
440C2×C4—34no—
441C2×C4—62no—
442C2×C4—62no—
443C2×C4—64no—
444C2×C4—62no—
445C2×C4—102no—
446C2×C4—102no—
447C2×C4—102no—
448C2×C4—152no—
449C2×C4—152no—
450C2×C4—302no—
451C2×C4—302no—
452C2×C4—608no—
453C2×C4—608no—
454C2×C4#676612yes—
455C2×C4C4×D3×D512yes—
456C2×C4#679012yes—
457C2×C3—204no—
458C2×C3C2×#403911yescharacteristic
459C2×C3#6585512yes—
460C2×C3#6600811yescharacteristic
461C2×C3#6600811yescharacteristic
462C2×C3#6603212yes—
463D3—204no—
464C5#7629811yescharacteristic, complemented, Sylow
465C22—104no—
466C22—108no—
467C22—202no—
468C22—202no—
469C22—204no—
470C22—304no—
471C22—308no—
472C22—602no—
473C22—602no—
474C22—604no—
475C22C2×#676611yescharacteristic
476C22C2×C4×D3×D511yescharacteristic
477C22#9202612yes—
478C22#9203512yes—
479C22C2×#679011yescharacteristic
480C4—42no—
481C4—64no—
482C4—122no—
483C4—202no—
484C4—302no—
485C4—302no—
486C4#9139614yes—
487C3#1060588411yescharacteristic, complemented, Sylow
488C2—204no—
489C2—604no—
490C2#1175364912yes—
491C2#1175383912yes—
492C2C2×#9139611yescharacteristic
493C2#1175482311yescharacteristic
494C2#1175528611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91458C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2328
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#91782C2semidirect
3. C2×#91434C2semidirect
4. C5×#4977C2semidirect
5. C3×#65277C2semidirect
6. #11748917C2semidirect
7. #11748872C2semidirect
8. #11748768C2semidirect
9. #11748611C2semidirect
26. #91458C4semidirect
37. #65277D3semidirect
49. C2×D60C2×C4semidirect
57. C2×C3×D20C2×C4semidirect
60. C2×#1202C2×C4semidirect
65. C4×Dic15D4semidirect
67. C4×C5×Dic3C2×C4semidirect
76. #4977D5semidirect
172. C2×D20C4×D3semidirect
247. C4×Dic3C4×D5semidirect
394. C3×C5#2328semidirect
464. C5#76298semidirect
487. C3#10605884semidirect

Maximal subgroups

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

subgroupindex
C2×#917822
C2×#914582
C2×#914342
C5×#49772
C3×#652772
#117489172
#117488722
#117487682
#117486112
#106058843
#762985