Finite Group Databasebeta

← #14326712

Subgroups — #14326712

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×Dic3⋊C4C211yesmaximal, characteristic
2#11751313C211yesmaximal, characteristic
3C3×C4×C22⋊Dic5C211yesmaximal, characteristic
4#11749513C211yesmaximal, characteristic
5#11749513C211yesmaximal, characteristic
6Dic3×C22⋊Dic5C211yesmaximal, characteristic
7Dic3×C22⋊Dic5C211yesmaximal, characteristic
8#11748693C212yesmaximal, complemented
9#11748684C212yesmaximal, complemented
10Dic5×Dic3⋊C4C212yesmaximal, complemented
11#11748573C212yesmaximal, complemented
12#10613891—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C23×C5×Dic3C2211yescharacteristic
15C23×C5×Dic3C2211yescharacteristic
16C2×#6719C2211yescharacteristic
17C2×#6719C2211yescharacteristic
18C2×C4⋊Dic15C2212yes—
19C2×C5×Dic3⋊C4C418yescomplemented
20C2×C5×Dic3⋊C4C2211yescharacteristic
21C2×C5×Dic3⋊C4C2211yescharacteristic
22C2×C5×Dic3⋊C4C2211yescharacteristic
23C2×C5×Dic3⋊C4C2211yescharacteristic
24C2×C3×C22⋊Dic5C2211yescharacteristic
25C2×C3×C22⋊Dic5C2211yescharacteristic
26C2×C3×C4×Dic5C2212yes—
27C2×Dic3⋊Dic5C2212yes—
28C2×Dic3⋊Dic5C2212yes—
29C2×Dic3×Dic5C2212yes—
30C2×Dic3×Dic5C2212yes—
31#91115C2212yes—
32C3×#3963C2212yes—
33#90994C2212yes—
34#90994C2212yes—
35#90994C2212yes—
36#90994C2212yes—
37#73458—51nomaximal, Hall
38C22×C5×C4⋊C4—31no—
39#65501—31no—
40#65501—31no—
41#65501—31no—
42C4×C22⋊Dic5—31no—
43C4×C22⋊Dic5—31no—
44C4×C22⋊Dic5D311yescharacteristic
45#65274—32no—
46#65270—32no—
47#65270—32no—
48C4⋊C4×Dic5—32no—
49C24×C3×C5C2311yescharacteristic
50C22×C3×C4×C5—42no—
51C22×C3×C4×C5C2×C414yes—
52C22×C3×C4×C5C2311yescharacteristic
53C22×C3×C4×C5C2311yescharacteristic
54C22×Dic15C2312yes—
55C22×Dic15C2312yes—
56C22×C5×Dic3—24no—
57C22×C5×Dic3—42no—
58C22×C5×Dic3C2×C414yes—
59C22×C5×Dic3C2×C414yes—
60C22×C5×Dic3C2311yescharacteristic
61C22×C5×Dic3C2311yescharacteristic
62C22×C5×Dic3C2311yescharacteristic
63C22×C5×Dic3C2311yescharacteristic
64C22×C3×Dic5C2312yes—
65C22×C3×Dic5C2312yes—
66#6719—22no—
67#6719—22no—
68C4⋊Dic15—42no—
69C5×Dic3⋊C4C2×C414yes—
70C5×Dic3⋊C4C2×C414yes—
71C5×Dic3⋊C4C2×C414yes—
72C5×Dic3⋊C4C2×C414yes—
73C3×C22⋊Dic5—22no—
74C3×C22⋊Dic5Q814yes—
75C3×C4×Dic5—42no—
76Dic3⋊Dic5—24no—
77Dic3⋊Dic5—42no—
78Dic3×Dic5—24no—
79Dic3×Dic5—42no—
80C22×Dic3⋊C4D511yescharacteristic
81C3×C4×C22⋊C4—51no—
82#5212—51no—
83#4942—51no—
84#4942—51no—
85Dic3×C22⋊C4—51no—
86Dic3×C22⋊C4—51no—
87#4933—52no—
88C4×Dic3⋊C4—52no—
89#4655—52no—
90#4647—52no—
91C23×C4×C5—31no—
92C23×C4×C5—31no—
93C23×C4×C5C2×D311yescharacteristic
94C2×C5×C4⋊C4—38no—
95C2×C5×C4⋊C4—31no—
96C2×C5×C4⋊C4—31no—
97C2×C5×C4⋊C4—31no—
98C2×C5×C4⋊C4—31no—
99C2×C22⋊Dic5—31no—
100C2×C22⋊Dic5—31no—
101C2×C22⋊Dic5C2×D311yescharacteristic
102C2×C22⋊Dic5C2×D311yescharacteristic
103C2×C4⋊Dic5—32no—
104C2×C4⋊Dic5—32no—
105C2×C4⋊Dic5—32no—
106C2×C4×Dic5—32no—
107C2×C4×Dic5—32no—
108C2×C4×Dic5C2×D312yes—
109#3963—32no—
110#3963—32no—
111#3963—32no—
112#3963—32no—
113#3963—32no—
114#3963C2×D312yes—
115#2345—151noSylow
116C23×C3×C5—22no—
117C23×C3×C5—22no—
118C23×C3×C5C22×C412yes—
119C23×C3×C5C2×Q812yes—
120C23×C3×C5#4112yes—
121C23×C3×C5C2411yescharacteristic
122C2×C3×C4×C5—22no—
123C2×C3×C4×C5—22no—
124C2×C3×C4×C5—44no—
125C2×C3×C4×C5C22×C412yes—
126C2×C3×C4×C5C22×C412yes—
127C2×Dic15—22no—
128C2×Dic15—22no—
129C2×Dic15—22no—
130C2×Dic15—22no—
131C2×Dic15—22no—
132C2×Dic15—22no—
133C2×C5×Dic3—22no—
134C2×C5×Dic3—22no—
135C2×C5×Dic3—22no—
136C2×C5×Dic3—28no—
137C2×C5×Dic3—44no—
138C2×C5×Dic3C22×C412yes—
139C2×C5×Dic3C22×C412yes—
140C2×C5×Dic3C22×C412yes—
141C2×C5×Dic3C22×C412yes—
142C2×C5×Dic3#4114yes—
143C2×C3×Dic5—22no—
144C2×C3×Dic5—22no—
145C2×C3×Dic5—22no—
146C2×C3×Dic5—22no—
147C2×C3×Dic5—22no—
148C2×C3×Dic5C2×Q814yes—
149C23×C3×C4C2×D511yescharacteristic
150C23×Dic3C2×D511yescharacteristic
151C23×Dic3C2×D511yescharacteristic
152C2×C3×C22⋊C4—51no—
153C2×C3×C22⋊C4—51no—
154C2×C3×C42—52no—
155C2×#217—51no—
156C2×#217—51no—
157C2×C4⋊Dic3—52no—
158C2×Dic3⋊C4—52no—
159C2×Dic3⋊C4—52no—
160C2×Dic3⋊C4Dic518yescomplemented
161C2×Dic3⋊C4C2×D511yescharacteristic
162C2×Dic3⋊C4C2×D511yescharacteristic
163C2×Dic3⋊C4C2×D511yescharacteristic
164C2×Dic3⋊C4C2×D511yescharacteristic
165C2×C4×Dic3—52no—
166C2×C4×Dic3—52no—
167C3×#95—52no—
168C3⋊#95—52no—
169C3⋊#95—52no—
170C3⋊#95—52no—
171C3⋊#95—52no—
172C3⋊#95—52no—
173C24×C5C22×D311yescharacteristic
174C22×C4×C5—31no—
175C22×C4×C5—34no—
176C22×C4×C5—31no—
177C22×C4×C5—31no—
178C22×C4×C5—31no—
179C22×C4×C5—34no—
180C22×C4×C5—42no—
181C22×C4×C5—64no—
182C22×C4×C5—122no—
183C22×C4×C5C4×D314yes—
184C22×C4×C5C22×D311yescharacteristic
185C22×C4×C5C22×D311yescharacteristic
186C22×Dic5—32no—
187C22×Dic5—32no—
188C22×Dic5C22×D312yes—
189C22×Dic5C22×D312yes—
190C5×C4⋊C4—34no—
191C5×C4⋊C4—34no—
192C5×C4⋊C4—34no—
193C5×C4⋊C4—34no—
194C22⋊Dic5—22no—
195C22⋊Dic5—62no—
196C22⋊Dic5—62no—
197C22⋊Dic5Dic614yes—
198C4⋊Dic5—64no—
199C4⋊Dic5—122no—
200C4⋊Dic5—122no—
201C4×Dic5—42no—
202C4×Dic5—64no—
203C4×Dic5—122no—
204C22×C4⋊C4—31no—
205#389—152no—
206#387—152no—
207#387—152no—
208#380—151no—
209#380—151no—
210#380—151no—
211C4×C4⋊C4—152no—
212C4×C22⋊C4—51no—
213C4×C22⋊C4—151no—
214C4×C22⋊C4—151no—
215C22×C3×C5—22no—
216C22×C3×C5—22no—
217C22×C3×C5—24no—
218C22×C3×C5—24no—
219C22×C3×C5C4×Q814yes—
220C22×C3×C5C23×C411yescharacteristic
221C22×C3×C5C22×Q811yescharacteristic
222C22×C3×C5C2×#4112yes—
223C22×C3×C5C2×#4111yescharacteristic
224C22×C3×C5H(5,𝔽2)12yes—
225C3×C4×C5—22no—
226C3×C4×C5—22no—
227Dic15—42no—
228Dic15—42no—
229C3×Dic5—24no—
230C3×Dic5—42no—
231C5×Dic3—22no—
232C5×Dic3—22no—
233C5×Dic3—22no—
234C5×Dic3#11714yes—
235C24×C3C22×D511yescharacteristic
236C22×C3×C4—42no—
237C22×C3×C4—52no—
238C22×C3×C4—52no—
239C22×C3×C4C2×Dic514yes—
240C22×C3×C4C22×D511yescharacteristic
241C22×C3×C4C22×D511yescharacteristic
242C22×Dic3—24no—
243C22×Dic3—42no—
244C22×Dic3—52no—
245C22×Dic3—52no—
246C22×Dic3C2×Dic514yes—
247C22×Dic3C2×Dic514yes—
248C22×Dic3C22×D511yescharacteristic
249C22×Dic3C22×D511yescharacteristic
250C22×Dic3C22×D511yescharacteristic
251C22×Dic3C22×D511yescharacteristic
252C3×C22⋊C4—54no—
253C3×C22⋊C4—102no—
254C3×C42—202no—
255#217—102no—
256#217—102no—
257C4⋊Dic3—202no—
258Dic3⋊C4—104no—
259Dic3⋊C4—202no—
260Dic3⋊C4C2×Dic514yes—
261Dic3⋊C4C2×Dic514yes—
262Dic3⋊C4C2×Dic514yes—
263Dic3⋊C4C2×Dic514yes—
264C4×Dic3—104no—
265C4×Dic3—202no—
266C23×C5—22no—
267C23×C5—22no—
268C23×C5C2×Dic612yes—
269C23×C5C2×C4×D312yes—
270C23×C5#23512yes—
271C23×C5C23×D311yescharacteristic
272C2×C4×C5—22no—
273C2×C4×C5—22no—
274C2×C4×C5—32no—
275C2×C4×C5—34no—
276C2×C4×C5—32no—
277C2×C4×C5—32no—
278C2×C4×C5—32no—
279C2×C4×C5—44no—
280C2×C4×C5—68no—
281C2×C4×C5—62no—
282C2×C4×C5—62no—
283C2×C4×C5—62no—
284C2×C4×C5—124no—
285C2×C4×C5C2×C4×D312yes—
286C2×C4×C5C2×C4×D312yes—
287C2×Dic5—22no—
288C2×Dic5—22no—
289C2×Dic5—22no—
290C2×Dic5—22no—
291C2×Dic5—22no—
292C2×Dic5—62no—
293C2×Dic5—62no—
294C2×Dic5—62no—
295C2×Dic5—62no—
296C2×Dic5—62no—
297C2×Dic5—62no—
298C2×Dic5C2×Dic614yes—
299C23×C4—31no—
300C23×C4—31no—
301C23×C4D3×D511yescharacteristic
302C2×C4⋊C4—38no—
303C2×C4⋊C4—31no—
304C2×C4⋊C4—31no—
305C2×C4⋊C4—31no—
306C2×C4⋊C4—31no—
307C2×C4⋊C4—152no—
308C2×C4⋊C4—152no—
309C2×C4⋊C4—152no—
310C2×C22⋊C4—51no—
311C2×C22⋊C4—51no—
312C2×C22⋊C4—151no—
313C2×C22⋊C4—151no—
314C2×C42—52no—
315C2×C42—152no—
316C2×C42—152no—
317#95—52no—
318#95—152no—
319#95—152no—
320#95—152no—
321#95—152no—
322#95—152no—
323C2×C3×C5—24no—
324C2×C3×C5C2×#11711yescharacteristic
325C2×C3×C5C2×C4×Q811yescharacteristic
326C2×C3×C5#51811yescharacteristic
327C2×C3×C5#55312yes—
328C2×C3×C5#55412yes—
329C23×C3—22no—
330C23×C3—22no—
331C23×C3Q8×D512yes—
332C23×C3#71312yes—
333C23×C3C22×Dic512yes—
334C23×C3C23×D511yescharacteristic
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—44no—
338C2×C3×C4—54no—
339C2×C3×C4—102no—
340C2×C3×C4—102no—
341C2×C3×C4—102no—
342C2×C3×C4—102no—
343C2×C3×C4—102no—
344C2×C3×C4C22×Dic512yes—
345C2×C3×C4C22×Dic512yes—
346C2×Dic3—22no—
347C2×Dic3—22no—
348C2×Dic3—22no—
349C2×Dic3—28no—
350C2×Dic3—44no—
351C2×Dic3—102no—
352C2×Dic3—102no—
353C2×Dic3—102no—
354C2×Dic3—102no—
355C2×Dic3—102no—
356C2×Dic3—102no—
357C2×Dic3#70914yes—
358C2×Dic3C22×Dic512yes—
359C2×Dic3C22×Dic512yes—
360C2×Dic3C22×Dic512yes—
361C2×Dic3C22×Dic512yes—
362C22×C5—22no—
363C22×C5—22no—
364C22×C5—24no—
365C22×C5—24no—
366C22×C5C4×Dic614yes—
367C22×C5C22×Dic611yescharacteristic
368C22×C5C22×C4×D311yescharacteristic
369C22×C5C2×#23511yescharacteristic
370C22×C5#100412yes—
371C22×C5D3×#4112yes—
372C4×C5—22no—
373C4×C5—22no—
374C4×C5—34no—
375C4×C5—62no—
376C4×C5—62no—
377C4×C5—62no—
378Dic5—24no—
379Dic5—42no—
380Dic5—122no—
381Dic5—122no—
382C24C2×D3×D511yescharacteristic
383C22×C4—31no—
384C22×C4—34no—
385C22×C4—31no—
386C22×C4—31no—
387C22×C4—31no—
388C22×C4—34no—
389C22×C4—42no—
390C22×C4—52no—
391C22×C4—52no—
392C22×C4—64no—
393C22×C4—122no—
394C22×C4—152no—
395C22×C4—152no—
396C22×C4D3×Dic514yes—
397C22×C4C2×D3×D511yescharacteristic
398C22×C4C2×D3×D511yescharacteristic
399C4⋊C4—34no—
400C4⋊C4—34no—
401C4⋊C4—34no—
402C4⋊C4—34no—
403C4⋊C4—304no—
404C4⋊C4—602no—
405C4⋊C4—602no—
406C22⋊C4—54no—
407C22⋊C4—102no—
408C22⋊C4—302no—
409C22⋊C4—302no—
410C42—202no—
411C42—304no—
412C42—602no—
413C3×C5#234511yescharacteristic, complemented, Hall
414C22×C3—24no—
415C22×C3—24no—
416C22×C3—22no—
417C22×C3—22no—
418C22×C3Q8×Dic514yes—
419C22×C3C2×#70912yes—
420C22×C3#414412yes—
421C22×C3C2×Q8×D511yescharacteristic
422C22×C3C2×#71311yescharacteristic
423C22×C3C23×Dic511yescharacteristic
424C3×C4—22no—
425C3×C4—22no—
426C3×C4—104no—
427C3×C4—202no—
428Dic3—22no—
429Dic3—22no—
430Dic3—22no—
431Dic3—202no—
432Dic3—202no—
433Dic3#407214yes—
434C2×C5—24no—
435C2×C5C2×C4×Dic611yescharacteristic
436C2×C5#548611yescharacteristic
437C2×C5D3×#11711yescharacteristic
438C2×C5#553912yes—
439C2×C5#554012yes—
440C23—22no—
441C23—22no—
442C23D5×Dic612yes—
443C23#677312yes—
444C23C2×D3×Dic512yes—
445C23C22×D3×D511yescharacteristic
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—34no—
449C2×C4—32no—
450C2×C4—32no—
451C2×C4—32no—
452C2×C4—32no—
453C2×C4—44no—
454C2×C4—54no—
455C2×C4—68no—
456C2×C4—62no—
457C2×C4—62no—
458C2×C4—62no—
459C2×C4—102no—
460C2×C4—102no—
461C2×C4—102no—
462C2×C4—102no—
463C2×C4—102no—
464C2×C4—124no—
465C2×C4—302no—
466C2×C4—302no—
467C2×C4—302no—
468C2×C4—302no—
469C2×C4—302no—
470C2×C4—302no—
471C2×C4C2×D3×Dic512yes—
472C2×C4C2×D3×Dic512yes—
473C2×C3—24no—
474C2×C3#6584512yes—
475C2×C3#6584812yes—
476C2×C3C2×#407211yescharacteristic
477C2×C3#6613211yescharacteristic
478C2×C3C2×Q8×Dic511yescharacteristic
479C5#7345811yescharacteristic, complemented, Sylow
480C22—24no—
481C22—22no—
482C22—24no—
483C22—22no—
484C22Dic5×Dic614yes—
485C22C2×D5×Dic611yescharacteristic
486C22C2×#677311yescharacteristic
487C22D3×#70912yes—
488C22C22×D3×Dic511yescharacteristic
489C22#9204912yes—
490C4—22no—
491C4—22no—
492C4—34no—
493C4—62no—
494C4—62no—
495C4—62no—
496C4—104no—
497C4—202no—
498C4—602no—
499C4—602no—
500C3#1061389111yescharacteristic, complemented, Sylow
501C2—24no—
502C2C2×Dic5×Dic611yescharacteristic
503C2#1175441912yes—
504C2D3×#407211yescharacteristic
505C2#1175458212yes—
506C2#1175541011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC24×C3×C5C23
hypercenterC23×C4D3×D5
hypocenterC3×C5#2345
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
8. #11748693C2semidirect
9. #11748684C2semidirect
10. Dic5×Dic3⋊C4C2semidirect
11. #11748573C2semidirect
19. C2×C5×Dic3⋊C4C4semidirect
160. C2×Dic3⋊C4Dic5semidirect
413. C3×C5#2345semidirect
479. C5#73458semidirect
500. C3#10613891semidirect

Maximal subgroups

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

subgroupindex
C22×C5×Dic3⋊C42
#117513132
C3×C4×C22⋊Dic52
#117495132
Dic3×C22⋊Dic52
#117486932
#117486842
Dic5×Dic3⋊C42
#117485732
#106138913
#734585