Finite Group Databasebeta

← #14283416

Subgroups — #14283416

Order 1920.

572 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#525C211yesmaximal, characteristic
2#11751313C211yesmaximal, characteristic, complemented
3#11751308C211yesmaximal, characteristic, complemented
4#11746359C212yesmaximal, complemented
5#11746358C212yesmaximal, complemented
6#10602502—31nomaximal, Hall
7C2×C3×C5×#41C411yescharacteristic, complemented
8C23×C3×C4×C5C2211yescharacteristic
9C3×C5×#123—21no—
10C3×C5×C22⋊Q8C411yescharacteristic, complemented
11C3×C5×C22⋊Q8C2211yescharacteristic
12C3×C5×#121C411yescharacteristic, complemented
13C3×C5×#121C2211yescharacteristic
14C3×C5×#120—21no—
15C3×C4×C5×D4—21no—
16C3×C4×C5×D4—21no—
17C3×C5×#117C411yescharacteristic, complemented
18C2×#6719—21no—
19C2×C4⋊Dic15—21no—
20C2×#6710—21no—
21#91115C2212yes—
22#91114—21no—
23#91114C2212yes—
24#71709—51nomaximal, Hall
25C5×#525D311yescharacteristic
26#65501—31no—
27#65496—31no—
28#64758—32no—
29#64757—32no—
30C24×C3×C5D411yescharacteristic
31C3×C5×#41—42no—
32C2×C3×C5×Q8C2×C411yescharacteristic
33C2×C3×C5×D4—21no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4C2×C411yescharacteristic
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5—42no—
39C22×C3×C4×C5C2×C411yescharacteristic
40C22×C3×C4×C5C2×C411yescharacteristic
41C22×C3×C4×C5D411yescharacteristic
42C22×C3×C4×C5D411yescharacteristic
43C22×C3×C4×C5D411yescharacteristic
44C22×C3×C4×C5C2311yescharacteristic
45C22×Dic15—22no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4C2×C411yescharacteristic
49C3×C5×C4⋊C4C2×C411yescharacteristic
50C3×C5×C22⋊C4—21no—
51C3×C5×C22⋊C4—21no—
52C3×C5×C22⋊C4—21no—
53C3×C5×C22⋊C4—21no—
54C3×C5×C22⋊C4—21no—
55C3×C42×C5—21no—
56#6719—42no—
57C4⋊Dic15—42no—
58#6710—42no—
59C2×C3⋊#168—22no—
60C3×#525D511yescharacteristic
61#5212—51no—
62#5207—51no—
63#4538—52no—
64#4537—52no—
65C2×C5×#41Dic311yescharacteristic, complemented
66C23×C4×C5C2×D311yescharacteristic
67C5×#123—21no—
68C5×C22⋊Q8Dic311yescharacteristic, complemented
69C5×C22⋊Q8C2×D311yescharacteristic
70C5×#121Dic311yescharacteristic, complemented
71C5×#121C2×D311yescharacteristic
72C5×#120—21no—
73C4×C5×D4—21no—
74C4×C5×D4—21no—
75C5×#117Dic311yescharacteristic, complemented
76C2×C22⋊Dic5—61no—
77C2×C4⋊Dic5—61no—
78C2×#681—61no—
79#3963—32no—
80C22⋊#168—32no—
81C22⋊#168—61no—
82#1513—151noSylow
83C23×C3×C5—21no—
84C23×C3×C5—21no—
85C23×C3×C5—21no—
86C23×C3×C5—41no—
87C23×C3×C5—41no—
88C23×C3×C5C22⋊C411yescharacteristic
89C23×C3×C5C22⋊C411yescharacteristic
90C23×C3×C5C2×D411yescharacteristic
91C3×C5×Q8—41no—
92C3×C5×D4—41no—
93C3×C5×D4—42no—
94C3×C5×D4—42no—
95C3×C5×D4—41no—
96C3×C5×D4—41no—
97C2×C3×C4×C5—22no—
98C2×C3×C4×C5—22no—
99C2×C3×C4×C5—22no—
100C2×C3×C4×C5—21no—
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5—42no—
107C2×C3×C4×C5C22⋊C411yescharacteristic
108C2×C3×C4×C5C22⋊C411yescharacteristic
109C2×C3×C4×C5C22×C411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×Dic15—42no—
112C2×Dic15—42no—
113C2×Dic15—42no—
114C3⋊#168—42no—
115C2×C3×#41Dic511yescharacteristic, complemented
116C23×C3×C4C2×D511yescharacteristic
117C3×#123—21no—
118C3×C22⋊Q8Dic511yescharacteristic, complemented
119C3×C22⋊Q8C2×D511yescharacteristic
120C3×#121Dic511yescharacteristic, complemented
121C3×#121C2×D511yescharacteristic
122C3×#120—21no—
123C3×C4×D4—21no—
124C3×C4×D4—21no—
125C3×#117Dic511yescharacteristic, complemented
126C2×#217—101no—
127C2×C4⋊Dic3—101no—
128C2×#208—101no—
129C3⋊#95—52no—
130#830—52no—
131#830—101no—
132C24×C5#6711yescharacteristic
133C5×#41—42no—
134C2×C5×Q8C2×Dic311yescharacteristic
135C2×C5×D4—21no—
136C2×C5×D4—21no—
137C2×C5×D4—21no—
138C2×C5×D4C2×Dic311yescharacteristic
139C22×C4×C5—21no—
140C22×C4×C5—42no—
141C22×C4×C5C2×Dic311yescharacteristic
142C22×C4×C5C2×Dic311yescharacteristic
143C22×C4×C5#6711yescharacteristic
144C22×C4×C5#6711yescharacteristic
145C22×C4×C5#6711yescharacteristic
146C22×C4×C5C22×D311yescharacteristic
147C22×Dic5—62no—
148C5×C4⋊C4—21no—
149C5×C4⋊C4—21no—
150C5×C4⋊C4C2×Dic311yescharacteristic
151C5×C4⋊C4C2×Dic311yescharacteristic
152C5×C22⋊C4—21no—
153C5×C22⋊C4—21no—
154C5×C22⋊C4—21no—
155C5×C22⋊C4—21no—
156C5×C22⋊C4—21no—
157C42×C5—21no—
158C22⋊Dic5—122no—
159C4⋊Dic5—122no—
160#681—122no—
161C2×#168—62no—
162#525D1511yescharacteristic
163#407—151no—
164#380—151no—
165#328—152no—
166#327—152no—
167C22×C3×C5—21no—
168C22×C3×C5—21no—
169C22×C3×C5—21no—
170C22×C3×C5—21no—
171C22×C3×C5—21no—
172C22×C3×C5—21no—
173C22×C3×C5—21no—
174C22×C3×C5—21no—
175C22×C3×C5—42no—
176C22×C3×C5—42no—
177C22×C3×C5—41no—
178C22×C3×C5—41no—
179C22×C3×C5—41no—
180C22×C3×C5C2×C22⋊C411yescharacteristic
181C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
182C22×C3×C5#13711yescharacteristic
183C3×C4×C5—21no—
184C3×C4×C5—21no—
185C3×C4×C5—21no—
186C3×C4×C5—41no—
187C3×C4×C5—41no—
188C3×C4×C5—41no—
189C3×C4×C5#9912yes—
190Dic15—82no—
191C24×C3C22⋊D511yescharacteristic
192C3×#41—42no—
193C2×C3×Q8C2×Dic511yescharacteristic
194C2×C3×D4—21no—
195C2×C3×D4—21no—
196C2×C3×D4—21no—
197C2×C3×D4C2×Dic511yescharacteristic
198C22×C3×C4—21no—
199C22×C3×C4—42no—
200C22×C3×C4C2×Dic511yescharacteristic
201C22×C3×C4C2×Dic511yescharacteristic
202C22×C3×C4C22⋊D511yescharacteristic
203C22×C3×C4C22⋊D511yescharacteristic
204C22×C3×C4C22⋊D511yescharacteristic
205C22×C3×C4C22×D511yescharacteristic
206C22×Dic3—102no—
207C3×C4⋊C4—21no—
208C3×C4⋊C4—21no—
209C3×C4⋊C4C2×Dic511yescharacteristic
210C3×C4⋊C4C2×Dic511yescharacteristic
211C3×C22⋊C4—21no—
212C3×C22⋊C4—21no—
213C3×C22⋊C4—21no—
214C3×C22⋊C4—21no—
215C3×C22⋊C4—21no—
216C3×C42—21no—
217#217—202no—
218C4⋊Dic3—202no—
219#208—202no—
220C2×C3⋊C8—102no—
221C23×C5—21no—
222C23×C5—21no—
223C23×C5—21no—
224C23×C5—41no—
225C23×C5—41no—
226C23×C5#21711yescharacteristic
227C23×C5#21711yescharacteristic
228C23×C5C2×#6711yescharacteristic
229C5×Q8—41no—
230C5×D4—41no—
231C5×D4—42no—
232C5×D4—42no—
233C5×D4—41no—
234C5×D4—41no—
235C2×C4×C5—22no—
236C2×C4×C5—22no—
237C2×C4×C5—22no—
238C2×C4×C5—21no—
239C2×C4×C5—21no—
240C2×C4×C5—21no—
241C2×C4×C5—41no—
242C2×C4×C5—41no—
243C2×C4×C5—41no—
244C2×C4×C5—42no—
245C2×C4×C5#21711yescharacteristic
246C2×C4×C5#21711yescharacteristic
247C2×C4×C5C22×Dic311yescharacteristic
248C2×C4×C5C2×#6711yescharacteristic
249C2×Dic5—122no—
250C2×Dic5—122no—
251C2×Dic5—122no—
252#168—122no—
253C2×#41Dic1511yescharacteristic, complemented
254C23×C4C2×D1511yescharacteristic
255C2×M16—301no—
256#123—21no—
257C22⋊Q8Dic1511yescharacteristic, complemented
258C22⋊Q8C2×D1511yescharacteristic
259#121Dic1511yescharacteristic, complemented
260#121C2×D1511yescharacteristic
261#120—21no—
262C4×D4—21no—
263C4×D4—21no—
264#117Dic1511yescharacteristic, complemented
265C2×C4⋊C4—301no—
266C2×C22⋊C4—301no—
267C22⋊C8—152no—
268C22⋊C8—301no—
269#95—152no—
270C2×C3×C5—21no—
271C2×C3×C5—21no—
272C2×C3×C5—41no—
273C2×C3×C5—41no—
274C2×C3×C5—81no—
275C2×C3×C5C2×#9911yescharacteristic
276C2×C3×C5#41711yescharacteristic
277C2×C3×C5#42111yescharacteristic
278C23×C3—21no—
279C23×C3—21no—
280C23×C3—21no—
281C23×C3—41no—
282C23×C3—41no—
283C23×C3C22⋊Dic511yescharacteristic
284C23×C3C22⋊Dic511yescharacteristic
285C23×C3C2×C22⋊D511yescharacteristic
286C3×Q8—41no—
287C3×D4—41no—
288C3×D4—42no—
289C3×D4—42no—
290C3×D4—41no—
291C3×D4—41no—
292C2×C3×C4—22no—
293C2×C3×C4—22no—
294C2×C3×C4—22no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—41no—
299C2×C3×C4—41no—
300C2×C3×C4—41no—
301C2×C3×C4—42no—
302C2×C3×C4C22⋊Dic511yescharacteristic
303C2×C3×C4C22⋊Dic511yescharacteristic
304C2×C3×C4C22×Dic511yescharacteristic
305C2×C3×C4C2×C22⋊D511yescharacteristic
306C2×Dic3—202no—
307C2×Dic3—202no—
308C2×Dic3—202no—
309C3⋊C8—202no—
310C22×C5—21no—
311C22×C5—21no—
312C22×C5—21no—
313C22×C5—21no—
314C22×C5—21no—
315C22×C5—21no—
316C22×C5—21no—
317C22×C5—21no—
318C22×C5—42no—
319C22×C5—42no—
320C22×C5—41no—
321C22×C5—41no—
322C22×C5—41no—
323C22×C5#94911yescharacteristic
324C22×C5#95111yescharacteristic
325C22×C5C2×#21711yescharacteristic
326C4×C5—21no—
327C4×C5—21no—
328C4×C5—21no—
329C4×C5—41no—
330C4×C5—41no—
331C4×C5—41no—
332C4×C5#83412yes—
333Dic5—242no—
334C24#122011yescharacteristic
335#41—42no—
336C2×Q8C2×Dic1511yescharacteristic
337C2×D4—21no—
338C2×D4—21no—
339C2×D4—21no—
340C2×D4C2×Dic1511yescharacteristic
341C22×C4—21no—
342C22×C4—42no—
343C22×C4—302no—
344C22×C4C2×Dic1511yescharacteristic
345C22×C4C2×Dic1511yescharacteristic
346C22×C4#122011yescharacteristic
347C22×C4#122011yescharacteristic
348C22×C4#122011yescharacteristic
349C22×C4C22×D1511yescharacteristic
350M16—602no—
351C2×C8—302no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—602no—
355C4⋊C4C2×Dic1511yescharacteristic
356C4⋊C4C2×Dic1511yescharacteristic
357C22⋊C4—21no—
358C22⋊C4—21no—
359C22⋊C4—21no—
360C22⋊C4—21no—
361C22⋊C4—21no—
362C22⋊C4—602no—
363C42—21no—
364C3×C5#151311yescharacteristic, complemented, Hall
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—42no—
374C22×C3—42no—
375C22×C3—41no—
376C22×C3—41no—
377C22×C3—41no—
378C22×C3#409511yescharacteristic
379C22×C3#409711yescharacteristic
380C22×C3C2×C22⋊Dic511yescharacteristic
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—41no—
385C3×C4—41no—
386C3×C4—41no—
387C3×C4#396612yes—
388Dic3—402no—
389C2×C5—21no—
390C2×C5—21no—
391C2×C5—41no—
392C2×C5—41no—
393C2×C5—81no—
394C2×C5C2×#83411yescharacteristic
395C2×C5#523211yescharacteristic
396C2×C5#523611yescharacteristic
397C23—21no—
398C23—21no—
399C23—21no—
400C23—41no—
401C23—41no—
402C23#671911yescharacteristic
403C23#671911yescharacteristic
404C23C2×#122011yescharacteristic
405Q8—41no—
406D4—41no—
407D4—42no—
408D4—42no—
409D4—41no—
410D4—41no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—42no—
421C2×C4—602no—
422C2×C4—602no—
423C2×C4—602no—
424C2×C4#671911yescharacteristic
425C2×C4#671911yescharacteristic
426C2×C4C22×Dic1511yescharacteristic
427C2×C4C2×#122011yescharacteristic
428C8—602no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—41no—
432C2×C3—41no—
433C2×C3—81no—
434C2×C3C2×#396611yescharacteristic
435C2×C3#6552111yescharacteristic
436C2×C3#6552511yescharacteristic
437C5#7170911yescharacteristic, complemented, Sylow
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—42no—
447C22—42no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22#9183811yescharacteristic
452C22#9184011yescharacteristic
453C22C2×#671911yescharacteristic
454C4—21no—
455C4—21no—
456C4—21no—
457C4—41no—
458C4—41no—
459C4—41no—
460C4—1202no—
461C4#9111812yes—
462C3#1060250211yescharacteristic, complemented, Sylow
463C2—21no—
464C2—21no—
465C2—41no—
466C2—41no—
467C2—81no—
468C2C2×#9111811yescharacteristic
469C2#1175133311yescharacteristic
470C2#1175133711yescharacteristic
subgroupG/H
centerC22C2×#6719
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#1513
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
2. #11751313C2semidirect
3. #11751308C2semidirect
4. #11746359C2semidirect
5. #11746358C2semidirect
7. C2×C3×C5×#41C4semidirect
10. C3×C5×C22⋊Q8C4semidirect
12. C3×C5×#121C4semidirect
17. C3×C5×#117C4semidirect
65. C2×C5×#41Dic3semidirect
68. C5×C22⋊Q8Dic3semidirect
70. C5×#121Dic3semidirect
75. C5×#117Dic3semidirect
115. C2×C3×#41Dic5semidirect
118. C3×C22⋊Q8Dic5semidirect
120. C3×#121Dic5semidirect
125. C3×#117Dic5semidirect
253. C2×#41Dic15semidirect
257. C22⋊Q8Dic15semidirect
259. #121Dic15semidirect
264. #117Dic15semidirect
364. C3×C5#1513semidirect
437. C5#71709semidirect
462. C3#10602502semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5252
#117513132
#117513082
#117463592
#117463582
#106025023
#717095