Finite Group Databasebeta

← #14301715

Subgroups — #14301715

Order 1920.

684 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
1#11756985C211yesmaximal, characteristic, complemented
2C3×#65990C211yesmaximal, characteristic
3#11752436C211yesmaximal, characteristic, complemented
4#11752414C212yesmaximal, complemented
5#11746738C212yesmaximal, complemented
6#10604535—31nomaximal, Hall
7C2×C3×#711C2211yescharacteristic
8C22×C3×C4×D5C2211yescharacteristic
9C2×#6762—21no—
10C2×#6762C2212yes—
11C2×#6762C2212yes—
12#91990—24no—
13D5⋊#208—21no—
14C3×C5×#123C411yescharacteristic
15C3×#4083C411yescharacteristic
16C3×#4075C411yescharacteristic
17C3×#4042—21no—
18C3×#4039—21no—
19C3×#4030—21no—
20C3×#4028C411yescharacteristic
21C3×#4027—21no—
22C3×#4023C2211yescharacteristic
23#91242—21no—
24#91234—21no—
25#91232—24no—
26#71714—51nomaximal, Hall
27#66256—31no—
28#65990D311yescharacteristic
29#65777—31no—
30#65755—32no—
31#64867—32no—
32C23×C3×D5C2×C411yescharacteristic
33C2×C3×C5×D4C2×C411yescharacteristic
34C22×C3×C4×C5C2×C411yescharacteristic
35C2×C3×C22⋊D5—21no—
36C2×C3×C22⋊D5C2×C411yescharacteristic
37C2×C3×C22⋊D5D411yescharacteristic
38C22×C3×Dic5D411yescharacteristic
39C22×C3×Dic5C2311yescharacteristic
40C3×#711—22no—
41C3×#711—22no—
42C2×C3×D20—21no—
43C2×C3×C4×D5—22no—
44C2×C3×C4×D5—21no—
45C2×C3×C4×D5—21no—
46C2×C3×C4×D5—22no—
47C2×C3×C4×D5D411yescharacteristic
48C2×C3×Dic10D411yescharacteristic
49#6762—22no—
50#6762—22no—
51#6762—22no—
52#6762—22no—
53#6762—22no—
54C2×C3⋊#170—22no—
55C2×C3⋊#170—22no—
56C2×C3⋊#170D414yescomplemented
57#6758—22no—
58D5⋊(C3⋊C8)—22no—
59C3×C5×C4⋊C4—21no—
60C3×C5×C22⋊C4—21no—
61C3×C5×C22⋊C4C2×C411yescharacteristic
62C3×C22⋊Dic5C2×C411yescharacteristic
63C3×#685—21no—
64C3×#685—21no—
65C3×#685—21no—
66C3×#683—21no—
67C3×#683—21no—
68C3×C4×Dic5—21no—
69C3×#525—51no—
70#5819—51no—
71#5237—51no—
72#5207—52no—
73#4533—52no—
74C2×#711C2×D311yescharacteristic
75C22×C4×D5C2×D311yescharacteristic
76C2×#704—32no—
77C2×#704—32no—
78C2×#704—61no—
79#4131—64no—
80D5⋊M16—61no—
81C5×#123Dic311yescharacteristic
82#4083Dic311yescharacteristic
83#4075Dic311yescharacteristic
84#4042—21no—
85#4039—21no—
86#4030—21no—
87#4028Dic311yescharacteristic
88#4027—21no—
89#4023C2×D311yescharacteristic
90#4013—61no—
91#4005—61no—
92#4003—64no—
93#1891—151noSylow
94C23×C3×C5C22⋊C411yescharacteristic
95C23×C3×C5C22×C411yescharacteristic
96C22×C3×D5—21no—
97C22×C3×D5—22no—
98C22×C3×D5—42no—
99C22×C3×D5C22⋊C411yescharacteristic
100C3×C5×D4—22no—
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—22no—
104C2×C3×C4×C5C22⋊C411yescharacteristic
105C3×C22⋊D5—22no—
106C3×C22⋊D5—22no—
107C3×C22⋊D5—42no—
108C2×C3×Dic5—21no—
109C2×C3×Dic5—21no—
110C2×C3×Dic5—21no—
111C2×C3×Dic5C22⋊C411yescharacteristic
112C2×C3×Dic5C2×D412yes—
113C2×C3×Dic5C2×D411yescharacteristic
114C2×C3×Dic5C2×D411yescharacteristic
115C2×C3×Dic5#4112yes—
116C3×D20—42no—
117C3×C4×D5—21no—
118C3×C4×D5—21no—
119C3×C4×D5—41no—
120C3×C4×D5—42no—
121C3×C4×D5—41no—
122C3×Dic10—22no—
123C3⋊#170—24no—
124C3⋊#170—42no—
125C2×C3×#41—51no—
126C23×C3×C4—51no—
127C3×#123—51no—
128C3×#123AGL(1,𝔽5)11yescharacteristic
129C3×C22⋊Q8—101no—
130C3×#121—101no—
131C3×#120—51no—
132C3×#120—51no—
133C3×C4×D4—101no—
134C3×C4×D4—101no—
135C3×#117—51no—
136#948—104no—
137C2×#208—52no—
138C2×#208—52no—
139C2×#208—101no—
140C2×#208—101no—
141#836—101no—
142#833—101no—
143#830—104no—
144C23×D5C2×Dic311yescharacteristic
145C2×C5×D4C2×Dic311yescharacteristic
146C22×C4×C5C2×Dic311yescharacteristic
147C2×C22⋊D5—21no—
148C2×C22⋊D5C2×Dic311yescharacteristic
149C2×C22⋊D5#6711yescharacteristic
150C22×Dic5#6711yescharacteristic
151C22×Dic5C22×D311yescharacteristic
152#711—22no—
153#711—22no—
154C2×D20—21no—
155C2×C4×D5—22no—
156C2×C4×D5—22no—
157C2×C4×D5—21no—
158C2×C4×D5—21no—
159C2×C4×D5#6711yescharacteristic
160C2×Dic10#6711yescharacteristic
161#704—62no—
162#704—62no—
163#704—62no—
164#704—62no—
165#704—62no—
166C2×#170—34no—
167C2×#170—62no—
168C2×#170—62no—
169#700—62no—
170D5⋊C8—62no—
171C5×C4⋊C4—21no—
172C5×C22⋊C4—21no—
173C5×C22⋊C4C2×Dic311yescharacteristic
174C22⋊Dic5C2×Dic311yescharacteristic
175#685—21no—
176#685—21no—
177#685—21no—
178#683—21no—
179#683—21no—
180C4×Dic5—21no—
181#568—151no—
182#525—51no—
183#413—151no—
184#407—152no—
185#344—152no—
186C22×C3×C5—21no—
187C22×C3×C5—41no—
188C22×C3×C5—41no—
189C22×C3×C5C2×C22⋊C411yescharacteristic
190C22×C3×C5C4×D412yes—
191C2×C3×D5—22no—
192C2×C3×D5—24no—
193C2×C3×D5—21no—
194C2×C3×D5—41no—
195C2×C3×D5—42no—
196C2×C3×D5—41no—
197C2×C3×D5—41no—
198C3×C4×C5—21no—
199C3×C4×C5—41no—
200C3×C4×C5—41no—
201C3×Dic5—21no—
202C3×Dic5—41no—
203C3×Dic5#12011yescharacteristic
204C3×Dic5#12112yes—
205C3×Dic5#12311yescharacteristic
206C24×C3—51no—
207C3×#41—102no—
208C3×#41—102no—
209C2×C3×Q8—51no—
210C2×C3×D4—51no—
211C2×C3×D4—51no—
212C2×C3×D4—101no—
213C2×C3×D4—101no—
214C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
215C22×C3×C4—51no—
216C22×C3×C4—51no—
217C22×C3×C4—51no—
218C22×C3×C4—102no—
219C22×C3×C4—101no—
220C22×C3×C4—101no—
221C22×C3×C4—102no—
222C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
223C3×C4⋊C4—21no—
224C3×C4⋊C4—101no—
225C3×C4⋊C4—101no—
226C3×C22⋊C4—21no—
227C3×C22⋊C4—51no—
228C3×C22⋊C4—101no—
229C3×C22⋊C4—101no—
230C3×C22⋊C4—101no—
231C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
232C3×C42—101no—
233#208—102no—
234#208—102no—
235#208—102no—
236#208—102no—
237#208—102no—
238#208—102no—
239C2×C3⋊C8—54no—
240C2×C3⋊C8—102no—
241C2×C3⋊C8—102no—
242C2×C3⋊C8—102no—
243C23×C5#21711yescharacteristic
244C23×C5C22×Dic311yescharacteristic
245C22×D5—22no—
246C22×D5—21no—
247C22×D5—42no—
248C22×D5#21711yescharacteristic
249C5×D4—22no—
250C2×C4×C5—22no—
251C2×C4×C5—21no—
252C2×C4×C5—21no—
253C2×C4×C5#21711yescharacteristic
254C22⋊D5—22no—
255C22⋊D5—22no—
256C22⋊D5—42no—
257C2×Dic5—21no—
258C2×Dic5—21no—
259C2×Dic5—21no—
260C2×Dic5#21711yescharacteristic
261C2×Dic5D3×D412yes—
262C2×Dic5#23712yes—
263C2×Dic5C2×#6711yescharacteristic
264C2×Dic5C2×#6711yescharacteristic
265D20—42no—
266C4×D5—21no—
267C4×D5—21no—
268C4×D5—41no—
269C4×D5—41no—
270C4×D5—42no—
271Dic10—22no—
272#170—64no—
273#170—122no—
274C2×#41—51no—
275C23×C4—51no—
276#131—304no—
277C2×M16—152no—
278C2×M16—152no—
279C2×M16—301no—
280C2×M16—301no—
281#123—51no—
282#123ΓL(1,𝔽16)11yescharacteristic
283C22⋊Q8—101no—
284#121—101no—
285#120—51no—
286#120—51no—
287C4×D4—101no—
288C4×D4—101no—
289#117—51no—
290#101—301no—
291#100—301no—
292C22⋊C8—304no—
293C2×C3×C5—21no—
294C2×C3×C5—22no—
295C2×C3×C5—41no—
296C2×C3×C5#38611yescharacteristic
297C3×D5—42no—
298C3×D5—41no—
299C23×C3—51no—
300C23×C3—102no—
301C23×C3—101no—
302C23×C3—202no—
303C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
304C23×C3C22×AGL(1,𝔽5)11yescharacteristic
305C3×Q8—102no—
306C3×D4—22no—
307C3×D4—102no—
308C3×D4—102no—
309C3×D4—202no—
310C3×D4—202no—
311C2×C3×C4—22no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—52no—
315C2×C3×C4—52no—
316C2×C3×C4—51no—
317C2×C3×C4—51no—
318C2×C3×C4—51no—
319C2×C3×C4—101no—
320C2×C3×C4—101no—
321C2×C3×C4—101no—
322C2×C3×C4—101no—
323C2×C3×C4—101no—
324C2×C3×C4—201no—
325C2×C3×C4—202no—
326C2×C3×C4—201no—
327C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
328C3⋊C8—104no—
329C3⋊C8—202no—
330C22×C5—21no—
331C22×C5—41no—
332C22×C5—41no—
333C22×C5D4×Dic312yes—
334C22×C5C2×#21711yescharacteristic
335C2×D5—22no—
336C2×D5—24no—
337C2×D5—21no—
338C2×D5—41no—
339C2×D5—42no—
340C2×D5—41no—
341C2×D5—41no—
342C4×C5—21no—
343C4×C5—41no—
344C4×C5—41no—
345Dic5—21no—
346Dic5—41no—
347Dic5#93511yescharacteristic
348Dic5#93711yescharacteristic
349Dic5#93912yes—
350C24—51no—
351#41—102no—
352#41—102no—
353C2×Q8—51no—
354C2×D4—51no—
355C2×D4—51no—
356C2×D4—101no—
357C2×D4—101no—
358C2×D4C2×ΓL(1,𝔽16)11yescharacteristic
359C22×C4—51no—
360C22×C4—51no—
361C22×C4—51no—
362C22×C4—102no—
363C22×C4—101no—
364C22×C4—101no—
365C22×C4—102no—
366C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
367M16—302no—
368M16—302no—
369M16—302no—
370M16—302no—
371M16—302no—
372M16—302no—
373C2×C8—154no—
374C2×C8—302no—
375C2×C8—302no—
376C2×C8—302no—
377C4⋊C4—21no—
378C4⋊C4—101no—
379C4⋊C4—101no—
380C22⋊C4—21no—
381C22⋊C4—51no—
382C22⋊C4—101no—
383C22⋊C4—101no—
384C22⋊C4—101no—
385C22⋊C4C2×ΓL(1,𝔽16)11yescharacteristic
386C42—101no—
387C3×C5#189111yescharacteristic, complemented, Hall
388C22×C3—21no—
389C22×C3—41no—
390C22×C3—41no—
391C22×C3—102no—
392C22×C3—104no—
393C22×C3—101no—
394C22×C3—201no—
395C22×C3—201no—
396C22×C3—202no—
397C22×C3—201no—
398C22×C3D4×AGL(1,𝔽5)12yes—
399C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
400C3×C4—21no—
401C3×C4—41no—
402C3×C4—41no—
403C3×C4—51no—
404C3×C4—52no—
405C3×C4—51no—
406C3×C4—101no—
407C3×C4—201no—
408C2×C5—21no—
409C2×C5—22no—
410C2×C5—41no—
411C2×C5#522011yescharacteristic
412D5—42no—
413D5—41no—
414C23—51no—
415C23—102no—
416C23—101no—
417C23—202no—
418C23#676311yescharacteristic
419C23C22×ΓL(1,𝔽16)11yescharacteristic
420Q8—102no—
421D4—22no—
422D4—102no—
423D4—102no—
424D4—202no—
425D4—202no—
426C2×C4—22no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—52no—
430C2×C4—52no—
431C2×C4—51no—
432C2×C4—51no—
433C2×C4—51no—
434C2×C4—101no—
435C2×C4—101no—
436C2×C4—101no—
437C2×C4—101no—
438C2×C4—101no—
439C2×C4—201no—
440C2×C4—202no—
441C2×C4—201no—
442C2×C4#676311yescharacteristic
443C8—304no—
444C8—602no—
445C2×C3—21no—
446C2×C3—22no—
447C2×C3—41no—
448C2×C3—202no—
449C2×C3—201no—
450C2×C3#6577911yescharacteristic
451C5#7171411yescharacteristic, complemented, Sylow
452C22—21no—
453C22—41no—
454C22—41no—
455C22—102no—
456C22—104no—
457C22—101no—
458C22—201no—
459C22—201no—
460C22—202no—
461C22—201no—
462C22D4×ΓL(1,𝔽16)12yes—
463C22C2×#676311yescharacteristic
464C4—21no—
465C4—41no—
466C4—41no—
467C4—51no—
468C4—52no—
469C4—51no—
470C4—101no—
471C4—201no—
472C3#1060453511yescharacteristic, complemented, Sylow
473C2—21no—
474C2—22no—
475C2—41no—
476C2—202no—
477C2—201no—
478C2#1175243811yescharacteristic
subgroupG/H
centerC2#11752438
commutatorC23×C3×C5C22×C4
FrattiniC23C22×ΓL(1,𝔽16)
FittingC3×C5×#123C4
socleC2×C3×C5#386
prime radicalC3×#65990C2
cosocleC22×C3×Dic5C23
hypercenter#123ΓL(1,𝔽16)
hypocenterC3×C5#1891
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C23 ◁ #123

Complements

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

NH ≅ G/Ntype
1. #11756985C2semidirect
3. #11752436C2semidirect
4. #11752414C2semidirect
5. #11746738C2semidirect
56. C2×C3⋊#170D4semidirect
387. C3×C5#1891semidirect
451. C5#71714semidirect
472. C3#10604535semidirect

Maximal subgroups

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

subgroupindex
#117569852
C3×#659902
#117524362
#117524142
#117467382
#106045353
#717145