Finite Group Databasebeta

← #14330184

Subgroups — #14330184

Order 1920.

1120 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4021C211yesmaximal, characteristic
2#11751033C211yesmaximal, characteristic, complemented
3C5×#4932C211yesmaximal, characteristic, complemented
4#11748896C212yesmaximal
5#11748884C212yesmaximal, complemented
6Dic3×#685C212yesmaximal, complemented
7#11748791C212yesmaximal, complemented
8#11748770C212yesmaximal, complemented
9#11748672C212yesmaximal, complemented
10#10605126—31nomaximal, Hall
11C22×C3×D20C2211yescharacteristic
12C22×C3×Dic10C2211yescharacteristic
13C22×D5×Dic3C2212yes—
14C2×C3×C42×C5C2211yescharacteristic
15C2×C4×Dic15C2212yes—
16C2×C4×C5×Dic3C2212yes—
17C2×C3×#685C2212yes—
18C2×C3×#685C2212yes—
19C3×#4021C418yescomplemented
20C2×#6668C2212yes—
21C2×#6665C2212yes—
22C2×#6665C2212yes—
23C2×#6665C2212yes—
24C2×Dic3×Dic5C2212yes—
25#91115C2211yescharacteristic
26#91115C2212yes—
27#91115C2211yescharacteristic
28C5×C3⋊#95C2211yescharacteristic
29C5×C3⋊#95C2212yes—
30C5×C3⋊#95C2211yescharacteristic
31#90994C2212yes—
32#90994C2212yes—
33#82956—51nomaximal, Hall
34C2×#4021D311yescharacteristic
35C5×#376—31no—
36#65229—32no—
37C4×#685—32no—
38#65221—31no—
39#64958—32no—
40#64955—32no—
41#64954—32no—
42#64935—32no—
43C23×C3×D5C2312yes—
44C22×C3×C4×C5C2311yescharacteristic
45C22×C3×C4×C5C2311yescharacteristic
46C22×C3×C4×C5C2311yescharacteristic
47C22×Dic15C2312yes—
48C22×Dic15C2312yes—
49C22×C5×Dic3C2312yes—
50C22×C5×Dic3C2312yes—
51C22×C3×Dic5C2312yes—
52C2×C3×D20—41no—
53C2×C3×D20—41no—
54C2×C3×D20C2×C414yes—
55C2×C3×Dic10—41no—
56C2×C3×Dic10—41no—
57C2×C3×Dic10C2×C414yescomplemented
58C2×D5×Dic3—24no—
59C2×D5×Dic3—24no—
60C2×D5×Dic3—42no—
61C3×C42×C5C2×C414yescomplemented
62C4×Dic15—24no—
63C4×C5×Dic3—24no—
64C3×#685C2×C418yescomplemented
65C3×#685C2×C418yescomplemented
66#6668—42no—
67#6665—24no—
68#6665—24no—
69#6665—42no—
70Dic3×Dic5—42no—
71C2×C3×#124—51no—
72#5229—52no—
73#5220—52no—
74#4951—52no—
75#4951—52no—
76Dic3×C22⋊C4—52no—
77Dic3×C22⋊C4—52no—
78#4932—51no—
79#4932D511yescharacteristic, complemented
80C22×D20C2×D311yescharacteristic
81C22×C4×D5—32no—
82C22×Dic10C2×D311yescharacteristic
83C2×C42×C5—32no—
84C2×C42×C5C2×D311yescharacteristic
85C2×#685—32no—
86C2×#685—32no—
87C2×#685—32no—
88C2×#685C2×D312yes—
89C2×#685C2×D312yes—
90C2×#683—32no—
91C2×C4×Dic5—32no—
92C2×C4×Dic5—32no—
93#4021Dic318yescomplemented
94C5×#95—32no—
95C5×#95—31no—
96C5×#95—31no—
97#3963—32no—
98#3963—31no—
99#3963—31no—
100#3963—32no—
101#3963—32no—
102#2372—151noSylow
103C23×C3×C5C2411yescharacteristic
104C22×C3×D5—22no—
105C22×C3×D5—22no—
106C22×C3×D5—22no—
107C22×C3×D5—22no—
108C22×C3×D5—22no—
109C22×C3×D5—22no—
110C22×C3×D5C22×C414yes—
111C2×C3×C4×C5—22no—
112C2×C3×C4×C5—22no—
113C2×C3×C4×C5—21no—
114C2×C3×C4×C5—21no—
115C2×C3×C4×C5C22×C412yes—
116C2×C3×C4×C5C22×C412yes—
117C2×C3×C4×C5C22×C412yes—
118C2×Dic15—22no—
119C2×Dic15—22no—
120C2×Dic15—22no—
121C2×Dic15—22no—
122C2×Dic15—22no—
123C2×Dic15#4114yes—
124C2×C5×Dic3—22no—
125C2×C5×Dic3—22no—
126C2×C5×Dic3—22no—
127C2×C5×Dic3—22no—
128C2×C5×Dic3—22no—
129C2×C5×Dic3#4114yes—
130C2×C3×Dic5—22no—
131C2×C3×Dic5—22no—
132C2×C3×Dic5C22×C414yes—
133C3×D20—44no—
134C3×Dic10—44no—
135D5×Dic3—48no—
136C22×C3×Q8—51no—
137C22×C3×D4—51no—
138C23×Dic3—52no—
139C3×#124—58no—
140C2×C3×C22⋊C4—52no—
141C2×C3×C22⋊C4—52no—
142C2×C3×C42C2×D511yescharacteristic
143C2×#217—52no—
144C2×#217—52no—
145C2×#217—52no—
146C2×C4⋊Dic3—52no—
147C2×C4×Dic3—52no—
148C2×C4×Dic3—52no—
149C2×C4×Dic3C2×D512yes—
150C3⋊#95—51no—
151C3⋊#95—51no—
152C3⋊#95—52no—
153C3⋊#95—52no—
154C3⋊#95—52no—
155C3⋊#95C2×D511yescharacteristic
156C3⋊#95C2×D511yescharacteristic
157C3⋊#95C2×D512yes—
158C23×D5C22×D312yes—
159C22×C4×C5—32no—
160C22×C4×C5—32no—
161C22×C4×C5C22×D311yescharacteristic
162C22×C4×C5C22×D311yescharacteristic
163C22×C4×C5C22×D311yescharacteristic
164C22×Dic5—32no—
165C22×Dic5—32no—
166C22×Dic5C22×D312yes—
167C2×D20—41no—
168C2×D20—41no—
169C2×D20C2×Dic314yes—
170C2×C4×D5—64no—
171C2×C4×D5—64no—
172C2×C4×D5—122no—
173C2×Dic10—41no—
174C2×Dic10—41no—
175C2×Dic10C2×Dic314yescomplemented
176C42×C5—64no—
177C42×C5C2×Dic314yescomplemented
178#685—64no—
179#685—64no—
180#685—122no—
181#685C2×Dic318yescomplemented
182#685C2×Dic318yescomplemented
183#683—122no—
184C4×Dic5—64no—
185C4×Dic5—122no—
186C2×#124—51no—
187#391—152no—
188#388—152no—
189#388—152no—
190#386—152no—
191C4×C22⋊C4—152no—
192C4×C22⋊C4—152no—
193#376—31no—
194#376—151no—
195C22×C3×C5C23×C411yescharacteristic
196C22×C3×C5C2×#4112yes—
197C22×C3×C5C2×#4112yes—
198C22×C3×C5H(5,𝔽2)11yescharacteristic
199C22×C3×C5H(5,𝔽2)11yescharacteristic
200C2×C3×D5—24no—
201C2×C3×D5—24no—
202C2×C3×D5—24no—
203C2×C3×D5—42no—
204C2×C3×D5—42no—
205C2×C3×D5—42no—
206C2×C3×D5—42no—
207C3×C4×C5—22no—
208C3×C4×C5—22no—
209C3×C4×C5—22no—
210Dic15—24no—
211Dic15—42no—
212C3×Dic5—24no—
213C5×Dic3—24no—
214C5×Dic3—42no—
215C24×C3—52no—
216C2×C3×Q8—54no—
217C2×C3×Q8—201no—
218C2×C3×Q8—201no—
219C2×C3×D4—54no—
220C2×C3×D4—201no—
221C2×C3×D4—201no—
222C22×C3×C4—52no—
223C22×C3×C4C22×D511yescharacteristic
224C22×C3×C4C22×D511yescharacteristic
225C22×C3×C4C22×D511yescharacteristic
226C22×Dic3—52no—
227C22×Dic3—52no—
228C22×Dic3—104no—
229C22×Dic3—104no—
230C22×Dic3—202no—
231C22×Dic3C22×D512yes—
232C22×Dic3C22×D512yes—
233C3×C22⋊C4—58no—
234C3×C22⋊C4—58no—
235C3×C42C4×D514yescomplemented
236#217—104no—
237#217—104no—
238#217—202no—
239C4⋊Dic3—202no—
240C4×Dic3—24no—
241C4×Dic3—104no—
242C4×Dic3—202no—
243C23×C5C23×D311yescharacteristic
244C22×D5—22no—
245C22×D5—22no—
246C22×D5—22no—
247C22×D5—22no—
248C22×D5—22no—
249C22×D5—22no—
250C22×D5C22×Dic314yes—
251C2×C4×C5—21no—
252C2×C4×C5—21no—
253C2×C4×C5—22no—
254C2×C4×C5—22no—
255C2×C4×C5—34no—
256C2×C4×C5—62no—
257C2×C4×C5—62no—
258C2×C4×C5—62no—
259C2×C4×C5—62no—
260C2×C4×C5—62no—
261C2×C4×C5C22×Dic312yes—
262C2×C4×C5C22×Dic312yes—
263C2×C4×C5C22×Dic312yes—
264C2×Dic5—22no—
265C2×Dic5—22no—
266C2×Dic5—34no—
267C2×Dic5—62no—
268C2×Dic5—62no—
269C2×Dic5—62no—
270C2×Dic5—62no—
271C2×Dic5—62no—
272C2×Dic5C22×Dic314yes—
273D20—44no—
274C4×D5—128no—
275Dic10—44no—
276C22×Q8—51no—
277C22×D4—51no—
278C23×C4—152no—
279#124—58no—
280C2×C4⋊C4—152no—
281C2×C22⋊C4—52no—
282C2×C22⋊C4—52no—
283C2×C22⋊C4—152no—
284C2×C22⋊C4—152no—
285C2×C22⋊C4—152no—
286C2×C42—32no—
287C2×C42—152no—
288C2×C42—152no—
289C2×C42D3×D511yescharacteristic
290#95—31no—
291#95—32no—
292#95—31no—
293#95—152no—
294#95—152no—
295#95—151no—
296#95—152no—
297#95—151no—
298C2×C3×C5C4×#4111yescharacteristic
299C2×C3×C5C4×#4111yescharacteristic
300C2×C3×C5#51811yescharacteristic
301C2×C3×C5#55112yes—
302C2×C3×C5#55512yes—
303C3×D5—44no—
304C23×C3—54no—
305C23×C3—102no—
306C23×C3—102no—
307C23×C3—102no—
308C23×C3—102no—
309C23×C3—102no—
310C23×C3—102no—
311C23×C3C23×D511yescharacteristic
312C3×Q8—204no—
313C3×D4—204no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—54no—
319C2×C3×C4—102no—
320C2×C3×C4—102no—
321C2×C3×C4C2×C4×D512yes—
322C2×C3×C4C2×C4×D512yes—
323C2×C3×C4C2×C4×D512yes—
324C2×Dic3—22no—
325C2×Dic3—22no—
326C2×Dic3—22no—
327C2×Dic3—22no—
328C2×Dic3—22no—
329C2×Dic3—54no—
330C2×Dic3—102no—
331C2×Dic3—102no—
332C2×Dic3—102no—
333C2×Dic3—102no—
334C2×Dic3—102no—
335C2×Dic3—208no—
336C2×Dic3#70914yes—
337C22×C5#100411yescharacteristic
338C22×C5#100411yescharacteristic
339C22×C5D3×#4112yes—
340C22×C5D3×#4112yes—
341C22×C5C23×Dic311yescharacteristic
342C2×D5—24no—
343C2×D5—24no—
344C2×D5—24no—
345C2×D5—42no—
346C2×D5—42no—
347C2×D5—42no—
348C2×D5—42no—
349C4×C5—22no—
350C4×C5—22no—
351C4×C5—22no—
352C4×C5—64no—
353C4×C5—122no—
354Dic5—24no—
355Dic5—64no—
356Dic5—122no—
357C24—52no—
358C2×Q8—54no—
359C2×Q8—201no—
360C2×Q8—201no—
361C2×D4—54no—
362C2×D4—201no—
363C2×D4—201no—
364C22×C4—32no—
365C22×C4—32no—
366C22×C4—52no—
367C22×C4—152no—
368C22×C4—152no—
369C22×C4—304no—
370C22×C4—304no—
371C22×C4—602no—
372C22×C4C2×D3×D511yescharacteristic
373C22×C4C2×D3×D511yescharacteristic
374C22×C4C2×D3×D511yescharacteristic
375C4⋊C4—602no—
376C22⋊C4—58no—
377C22⋊C4—58no—
378C22⋊C4—304no—
379C22⋊C4—304no—
380C22⋊C4—602no—
381C42—64no—
382C42—304no—
383C42—602no—
384C42D5×Dic314yescomplemented
385C3×C5#237211yescharacteristic, complemented, Hall
386C22×C3—104no—
387C22×C3—104no—
388C22×C3—104no—
389C22×C3—202no—
390C22×C3—202no—
391C22×C3—202no—
392C22×C3—202no—
393C22×C3C22×C4×D511yescharacteristic
394C22×C3C2×#70912yes—
395C22×C3D5×#4112yes—
396C22×C3#414911yescharacteristic
397C22×C3#414911yescharacteristic
398C3×C4—22no—
399C3×C4—22no—
400C3×C4—22no—
401C3×C4—104no—
402Dic3—24no—
403Dic3—42no—
404Dic3—104no—
405Dic3—202no—
406C2×C5#567012yes—
407C2×C5#567912yes—
408C2×C5#579811yescharacteristic
409C2×C5Dic3×#4111yescharacteristic
410C2×C5Dic3×#4111yescharacteristic
411D5—44no—
412C23—54no—
413C23—102no—
414C23—102no—
415C23—102no—
416C23—102no—
417C23—102no—
418C23—102no—
419C23C22×D3×D511yescharacteristic
420Q8—204no—
421D4—204no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—34no—
427C2×C4—54no—
428C2×C4—62no—
429C2×C4—62no—
430C2×C4—62no—
431C2×C4—62no—
432C2×C4—62no—
433C2×C4—102no—
434C2×C4—102no—
435C2×C4—154no—
436C2×C4—302no—
437C2×C4—302no—
438C2×C4—302no—
439C2×C4—302no—
440C2×C4—302no—
441C2×C4—608no—
442C2×C4C2×D5×Dic312yes—
443C2×C4C2×D5×Dic312yes—
444C2×C4C2×D5×Dic312yes—
445C2×C3—204no—
446C2×C3C4×#70911yescharacteristic
447C2×C3#6585511yescharacteristic
448C2×C3#6585611yescharacteristic
449C2×C3#6586112yes—
450C2×C3#6586612yes—
451C5#8295611yescharacteristic, complemented, Sylow
452C22—104no—
453C22—104no—
454C22—104no—
455C22—202no—
456C22—202no—
457C22—202no—
458C22—202no—
459C22D3×#70912yes—
460C22#9201612yes—
461C22#9201711yescharacteristic
462C22#9201711yescharacteristic
463C22C22×D5×Dic311yescharacteristic
464C4—22no—
465C4—22no—
466C4—22no—
467C4—64no—
468C4—104no—
469C4—122no—
470C4—304no—
471C4—602no—
472C3#1060512611yescharacteristic, complemented, Sylow
473C2—204no—
474C2#1175260012yes—
475C2#1175276612yes—
476C2Dic3×#70911yescharacteristic
477C2#1175444411yescharacteristic
478C2#1175448811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×D20C22
hypercenterC2×C42D3×D5
hypocenterC3×C5#2372
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. #11751033C2semidirect
3. C5×#4932C2semidirect
5. #11748884C2semidirect
6. Dic3×#685C2semidirect
7. #11748791C2semidirect
8. #11748770C2semidirect
9. #11748672C2semidirect
19. C3×#4021C4semidirect
57. C2×C3×Dic10C2×C4semidirect
61. C3×C42×C5C2×C4semidirect
64. C3×#685C2×C4semidirect
65. C3×#685C2×C4semidirect
79. #4932D5semidirect
93. #4021Dic3semidirect
175. C2×Dic10C2×Dic3semidirect
177. C42×C5C2×Dic3semidirect
181. #685C2×Dic3semidirect
182. #685C2×Dic3semidirect
235. C3×C42C4×D5semidirect
384. C42D5×Dic3semidirect
385. C3×C5#2372semidirect
451. C5#82956semidirect
472. C3#10605126semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40212
#117510332
C5×#49322
#117488962
#117488842
Dic3×#6852
#117487912
#117487702
#117486722
#106051263
#829565