Finite Group Databasebeta

← #14300537

Subgroups — #14300537

Order 1920.

752 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#525C211yesmaximal, characteristic
2C22×#6710C211yesmaximal, characteristic, complemented
3C2×#91121C212yesmaximal, complemented
4C4×#6719C211yesmaximal, characteristic, complemented
5#11746353C212yesmaximal, complemented
6#10602506—31nomaximal, Hall
7C2×C3×C5×#41C2211yescharacteristic
8C23×C3×C4×C5C2211yescharacteristic
9C3×C5×#123—21no—
10C3×C5×C22⋊Q8C411yescharacteristic, complemented
11C3×C5×C22⋊Q8C411yescharacteristic, complemented
12C3×C5×#121C411yescharacteristic, complemented
13C3×C5×#121C411yescharacteristic, complemented
14C3×C5×#120—21no—
15C3×C4×C5×D4—21no—
16C3×C4×C5×D4—21no—
17C3×C5×#117C2211yescharacteristic
18C2×#6719—21no—
19C2×C4×Dic15C2212yes—
20C2×#6710—21no—
21C2×#6710—24no—
22C2×#6710C2212yes—
23C22×C3⋊#168—21no—
24#91121—24no—
25#91115—21no—
26#71713—51nomaximal, Hall
27C5×#525D311yescharacteristic
28C22×#681—31no—
29C2×#3969—32no—
30C4×C22⋊Dic5—31no—
31#64752—32no—
32C24×C3×C5D411yescharacteristic
33C3×C5×#41—22no—
34C3×C5×#41—22no—
35C2×C3×C5×Q8C2×C411yescharacteristic
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4C2×C411yescharacteristic
40C22×C3×C4×C5—22no—
41C22×C3×C4×C5—22no—
42C22×C3×C4×C5—21no—
43C22×C3×C4×C5C2×C411yescharacteristic
44C22×C3×C4×C5C2×C411yescharacteristic
45C22×C3×C4×C5D411yescharacteristic
46C22×C3×C4×C5D411yescharacteristic
47C22×C3×C4×C5D411yescharacteristic
48C22×C3×C4×C5C2311yescharacteristic
49C22×Dic15—22no—
50C3×C5×C4⋊C4—21no—
51C3×C5×C4⋊C4—21no—
52C3×C5×C4⋊C4C2×C411yescharacteristic
53C3×C5×C4⋊C4C2×C411yescharacteristic
54C3×C5×C22⋊C4—21no—
55C3×C5×C22⋊C4—21no—
56C3×C5×C22⋊C4—21no—
57C3×C5×C22⋊C4—21no—
58C3×C5×C22⋊C4—21no—
59C3×C42×C5—21no—
60#6719—24no—
61C4×Dic15—22no—
62C4×Dic15—22no—
63#6710—24no—
64#6710—22no—
65#6710D414yescomplemented
66C2×C3⋊#168—24no—
67C2×C3⋊#168—22no—
68C3×#525D511yescharacteristic
69C22×#208—51no—
70C2×#837—52no—
71C4×#217—51no—
72#4532—52no—
73C2×C5×#41C2×D311yescharacteristic
74C23×C4×C5C2×D311yescharacteristic
75C5×#123—21no—
76C5×C22⋊Q8Dic311yescharacteristic, complemented
77C5×C22⋊Q8Dic311yescharacteristic, complemented
78C5×#121Dic311yescharacteristic, complemented
79C5×#121Dic311yescharacteristic, complemented
80C5×#120—21no—
81C4×C5×D4—21no—
82C4×C5×D4—21no—
83C5×#117C2×D311yescharacteristic
84C2×C22⋊Dic5—61no—
85C2×C4×Dic5—32no—
86C2×#681—32no—
87C2×#681—64no—
88C2×#681—61no—
89C22×#168—61no—
90#3969—64no—
91#3963—61no—
92#1871—151noSylow
93C23×C3×C5—22no—
94C23×C3×C5—22no—
95C23×C3×C5—21no—
96C23×C3×C5—41no—
97C23×C3×C5C22⋊C411yescharacteristic
98C23×C3×C5C22⋊C411yescharacteristic
99C23×C3×C5C2×D411yescharacteristic
100C3×C5×Q8—22no—
101C3×C5×D4—22no—
102C3×C5×D4—42no—
103C3×C5×D4—42no—
104C3×C5×D4—42no—
105C2×C3×C4×C5—22no—
106C2×C3×C4×C5—22no—
107C2×C3×C4×C5—22no—
108C2×C3×C4×C5—21no—
109C2×C3×C4×C5—21no—
110C2×C3×C4×C5—21no—
111C2×C3×C4×C5—21no—
112C2×C3×C4×C5—21no—
113C2×C3×C4×C5—21no—
114C2×C3×C4×C5—21no—
115C2×C3×C4×C5—41no—
116C2×C3×C4×C5—41no—
117C2×C3×C4×C5C22⋊C411yescharacteristic
118C2×C3×C4×C5C22⋊C411yescharacteristic
119C2×C3×C4×C5C22×C411yescharacteristic
120C2×C3×C4×C5C2×D412yes—
121C2×C3×C4×C5C2×D411yescharacteristic
122C2×C3×C4×C5#4112yes—
123C2×Dic15—24no—
124C2×Dic15—42no—
125C2×Dic15—42no—
126C3⋊#168—24no—
127C2×C3×#41C2×D511yescharacteristic
128C23×C3×C4C2×D511yescharacteristic
129C3×#123—21no—
130C3×C22⋊Q8Dic511yescharacteristic, complemented
131C3×C22⋊Q8Dic511yescharacteristic, complemented
132C3×#121Dic511yescharacteristic, complemented
133C3×#121Dic511yescharacteristic, complemented
134C3×#120—21no—
135C3×C4×D4—21no—
136C3×C4×D4—21no—
137C3×#117C2×D511yescharacteristic
138C2×#217—101no—
139C2×C4×Dic3—52no—
140C2×#208—52no—
141C2×#208—104no—
142C2×#208—101no—
143C22×C3⋊C8—101no—
144#837—104no—
145C3⋊#95—101no—
146C24×C5#6711yescharacteristic
147C5×#41—22no—
148C5×#41—22no—
149C2×C5×Q8C2×Dic311yescharacteristic
150C2×C5×D4—21no—
151C2×C5×D4—21no—
152C2×C5×D4—21no—
153C2×C5×D4C2×Dic311yescharacteristic
154C22×C4×C5—22no—
155C22×C4×C5—22no—
156C22×C4×C5—21no—
157C22×C4×C5C2×Dic311yescharacteristic
158C22×C4×C5C2×Dic311yescharacteristic
159C22×C4×C5#6711yescharacteristic
160C22×C4×C5#6711yescharacteristic
161C22×C4×C5#6711yescharacteristic
162C22×C4×C5C22×D311yescharacteristic
163C22×Dic5—62no—
164C5×C4⋊C4—21no—
165C5×C4⋊C4—21no—
166C5×C4⋊C4C2×Dic311yescharacteristic
167C5×C4⋊C4C2×Dic311yescharacteristic
168C5×C22⋊C4—21no—
169C5×C22⋊C4—21no—
170C5×C22⋊C4—21no—
171C5×C22⋊C4—21no—
172C5×C22⋊C4—21no—
173C42×C5—21no—
174C22⋊Dic5—64no—
175C4×Dic5—62no—
176C4×Dic5—62no—
177#681—34no—
178#681—64no—
179#681—62no—
180C2×#168—64no—
181C2×#168—62no—
182C22×M16—151no—
183#525D1511yescharacteristic
184C2×#104—152no—
185C4×C22⋊C4—151no—
186#339—152no—
187C22×C3×C5—21no—
188C22×C3×C5—21no—
189C22×C3×C5—21no—
190C22×C3×C5—21no—
191C22×C3×C5—21no—
192C22×C3×C5—21no—
193C22×C3×C5—21no—
194C22×C3×C5—44no—
195C22×C3×C5—41no—
196C22×C3×C5—41no—
197C22×C3×C5—41no—
198C22×C3×C5#10412yescomplemented
199C22×C3×C5C2×C22⋊C411yescharacteristic
200C22×C3×C5#12112yes—
201C3×C4×C5—21no—
202C3×C4×C5—21no—
203C3×C4×C5—41no—
204C3×C4×C5—41no—
205C3×C4×C5—41no—
206C3×C4×C5C4×D412yes—
207C3×C4×C5#12011yescharacteristic
208C3×C4×C5#12311yescharacteristic
209Dic15—44no—
210C24×C3C22⋊D511yescharacteristic
211C3×#41—22no—
212C3×#41—22no—
213C2×C3×Q8C2×Dic511yescharacteristic
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4C2×Dic511yescharacteristic
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—21no—
221C22×C3×C4C2×Dic511yescharacteristic
222C22×C3×C4C2×Dic511yescharacteristic
223C22×C3×C4C22⋊D511yescharacteristic
224C22×C3×C4C22⋊D511yescharacteristic
225C22×C3×C4C22⋊D511yescharacteristic
226C22×C3×C4C22×D511yescharacteristic
227C22×Dic3—102no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4C2×Dic511yescharacteristic
231C3×C4⋊C4C2×Dic511yescharacteristic
232C3×C22⋊C4—21no—
233C3×C22⋊C4—21no—
234C3×C22⋊C4—21no—
235C3×C22⋊C4—21no—
236C3×C22⋊C4—21no—
237C3×C42—21no—
238#217—104no—
239C4×Dic3—102no—
240C4×Dic3—102no—
241#208—54no—
242#208—104no—
243#208—102no—
244C2×C3⋊C8—104no—
245C2×C3⋊C8—102no—
246C23×C5—22no—
247C23×C5—22no—
248C23×C5—21no—
249C23×C5—41no—
250C23×C5#21711yescharacteristic
251C23×C5#21711yescharacteristic
252C23×C5C2×#6711yescharacteristic
253C5×Q8—22no—
254C5×D4—22no—
255C5×D4—42no—
256C5×D4—42no—
257C5×D4—42no—
258C2×C4×C5—22no—
259C2×C4×C5—22no—
260C2×C4×C5—22no—
261C2×C4×C5—21no—
262C2×C4×C5—21no—
263C2×C4×C5—21no—
264C2×C4×C5—21no—
265C2×C4×C5—21no—
266C2×C4×C5—21no—
267C2×C4×C5—21no—
268C2×C4×C5—41no—
269C2×C4×C5—41no—
270C2×C4×C5#21711yescharacteristic
271C2×C4×C5#21711yescharacteristic
272C2×C4×C5D3×D412yes—
273C2×C4×C5#23712yes—
274C2×C4×C5C22×Dic311yescharacteristic
275C2×C4×C5C2×#6711yescharacteristic
276C2×Dic5—64no—
277C2×Dic5—122no—
278C2×Dic5—122no—
279#168—64no—
280C2×#41C2×D1511yescharacteristic
281C23×C4C2×D1511yescharacteristic
282C2×M16—152no—
283C2×M16—304no—
284C2×M16—301no—
285C22×C8—301no—
286#123—21no—
287C22⋊Q8Dic1511yescharacteristic, complemented
288C22⋊Q8Dic1511yescharacteristic, complemented
289#121Dic1511yescharacteristic, complemented
290#121Dic1511yescharacteristic, complemented
291#120—21no—
292C4×D4—21no—
293C4×D4—21no—
294#117C2×D1511yescharacteristic
295C2×C22⋊C4—301no—
296C2×C42—152no—
297#104—304no—
298#95—301no—
299C2×C3×C5—22no—
300C2×C3×C5—22no—
301C2×C3×C5—41no—
302C2×C3×C5—81no—
303C2×C3×C5#38611yescharacteristic
304C2×C3×C5C2×#10411yescharacteristic
305C2×C3×C5#42111yescharacteristic
306C23×C3—22no—
307C23×C3—22no—
308C23×C3—21no—
309C23×C3—41no—
310C23×C3C22⋊Dic511yescharacteristic
311C23×C3C22⋊Dic511yescharacteristic
312C23×C3C2×C22⋊D511yescharacteristic
313C3×Q8—22no—
314C3×D4—22no—
315C3×D4—42no—
316C3×D4—42no—
317C3×D4—42no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—41no—
329C2×C3×C4—41no—
330C2×C3×C4C22⋊Dic511yescharacteristic
331C2×C3×C4C22⋊Dic511yescharacteristic
332C2×C3×C4D4×D512yes—
333C2×C3×C4#71112yes—
334C2×C3×C4C22×Dic511yescharacteristic
335C2×C3×C4C2×C22⋊D511yescharacteristic
336C2×Dic3—104no—
337C2×Dic3—202no—
338C2×Dic3—202no—
339C3⋊C8—104no—
340C22×C5—21no—
341C22×C5—21no—
342C22×C5—21no—
343C22×C5—21no—
344C22×C5—21no—
345C22×C5—21no—
346C22×C5—21no—
347C22×C5—44no—
348C22×C5—41no—
349C22×C5—41no—
350C22×C5—41no—
351C22×C5#83712yescomplemented
352C22×C5#93912yes—
353C22×C5C2×#21711yescharacteristic
354C4×C5—21no—
355C4×C5—21no—
356C4×C5—41no—
357C4×C5—41no—
358C4×C5—41no—
359C4×C5D4×Dic312yes—
360C4×C5#93511yescharacteristic
361C4×C5#93711yescharacteristic
362Dic5—124no—
363C24#122011yescharacteristic
364#41—22no—
365#41—22no—
366C2×Q8C2×Dic1511yescharacteristic
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4C2×Dic1511yescharacteristic
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—302no—
375C22×C4C2×Dic1511yescharacteristic
376C22×C4C2×Dic1511yescharacteristic
377C22×C4#122011yescharacteristic
378C22×C4#122011yescharacteristic
379C22×C4#122011yescharacteristic
380C22×C4C22×D1511yescharacteristic
381M16—154no—
382M16—304no—
383M16—302no—
384C2×C8—304no—
385C2×C8—302no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4C2×Dic1511yescharacteristic
389C4⋊C4C2×Dic1511yescharacteristic
390C22⋊C4—21no—
391C22⋊C4—21no—
392C22⋊C4—21no—
393C22⋊C4—21no—
394C22⋊C4—21no—
395C22⋊C4—304no—
396C42—21no—
397C42—302no—
398C42—302no—
399C3×C5#187111yescharacteristic, complemented, Hall
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—44no—
408C22×C3—41no—
409C22×C3—41no—
410C22×C3—41no—
411C22×C3#396912yescomplemented
412C22×C3#408512yes—
413C22×C3C2×C22⋊Dic511yescharacteristic
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—41no—
417C3×C4—41no—
418C3×C4—41no—
419C3×C4D4×Dic512yes—
420C3×C4#408111yescharacteristic
421C3×C4#408311yescharacteristic
422Dic3—204no—
423C2×C5—22no—
424C2×C5—22no—
425C2×C5—41no—
426C2×C5—81no—
427C2×C5#522011yescharacteristic
428C2×C5C2×#83711yescharacteristic
429C2×C5#523611yescharacteristic
430C23—22no—
431C23—22no—
432C23—21no—
433C23—41no—
434C23#671911yescharacteristic
435C23#671911yescharacteristic
436C23C2×#122011yescharacteristic
437Q8—22no—
438D4—22no—
439D4—42no—
440D4—42no—
441D4—42no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—304no—
455C2×C4—602no—
456C2×C4—602no—
457C2×C4#671911yescharacteristic
458C2×C4#671911yescharacteristic
459C2×C4D4×D1512yes—
460C2×C4#681912yes—
461C2×C4C22×Dic1511yescharacteristic
462C2×C4C2×#122011yescharacteristic
463C8—304no—
464C2×C3—22no—
465C2×C3—22no—
466C2×C3—41no—
467C2×C3—81no—
468C2×C3#6550911yescharacteristic
469C2×C3C2×#396911yescharacteristic
470C2×C3#6552511yescharacteristic
471C5#7171311yescharacteristic, complemented, Sylow
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—44no—
480C22—41no—
481C22—41no—
482C22—41no—
483C22#9112112yescomplemented
484C22#9182812yes—
485C22C2×#671911yescharacteristic
486C4—21no—
487C4—21no—
488C4—41no—
489C4—41no—
490C4—41no—
491C4—604no—
492C4D4×Dic1512yes—
493C4#9182411yescharacteristic
494C4#9182611yescharacteristic
495C3#1060250611yescharacteristic, complemented, Sylow
496C2—22no—
497C2—22no—
498C2—41no—
499C2—81no—
500C2#1175132111yescharacteristic
501C2C2×#9112111yescharacteristic
502C2#1175133711yescharacteristic
subgroupG/H
centerC2×C4C2×#1220
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
Fitting, prime radicalC3×C5×#525C2
socleC22×C3×C5C2×C22⋊C4
cosocleC22×C3×C4×C5C23
hypercenter#525D15
hypocenterC3×C5#1871
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
2. C22×#6710C2semidirect
3. C2×#91121C2semidirect
4. C4×#6719C2semidirect
5. #11746353C2semidirect
10. C3×C5×C22⋊Q8C4semidirect
11. C3×C5×C22⋊Q8C4semidirect
12. C3×C5×#121C4semidirect
13. C3×C5×#121C4semidirect
65. #6710D4semidirect
76. C5×C22⋊Q8Dic3semidirect
77. C5×C22⋊Q8Dic3semidirect
78. C5×#121Dic3semidirect
79. C5×#121Dic3semidirect
130. C3×C22⋊Q8Dic5semidirect
131. C3×C22⋊Q8Dic5semidirect
132. C3×#121Dic5semidirect
133. C3×#121Dic5semidirect
198. C22×C3×C5#104semidirect
287. C22⋊Q8Dic15semidirect
288. C22⋊Q8Dic15semidirect
289. #121Dic15semidirect
290. #121Dic15semidirect
351. C22×C5#837semidirect
399. C3×C5#1871semidirect
411. C22×C3#3969semidirect
471. C5#71713semidirect
483. C22#91121semidirect
495. C3#10602506semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5252
C22×#67102
C2×#911212
C4×#67192
#117463532
#106025063
#717135