Finite Group Databasebeta

← #14313139

Subgroups — #14313139

Order 1920.

528 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#525C211yesmaximal, characteristic
2#11751341C211yesmaximal, characteristic, complemented
3#11751338C211yesmaximal, characteristic, complemented
4#11746360C212yesmaximal, complemented
5#11746357C212yesmaximal, complemented
6#10602509—31nomaximal, Hall
7C2×C3×C5×#41C2211yescharacteristic
8C23×C3×C4×C5C411yescharacteristic, complemented
9C3×C5×#123C411yescharacteristic, complemented
10C3×C5×#123C2211yescharacteristic
11C3×C5×C22⋊Q8—21no—
12C3×C5×#121—21no—
13C3×C5×#120C411yescharacteristic, complemented
14C3×C5×#120C2211yescharacteristic
15C3×C4×C5×D4—21no—
16C3×C4×C5×D4—21no—
17C3×C5×#117C411yescharacteristic, complemented
18#91815—21no—
19C2×#6710—21no—
20#91120—21no—
21#91118—21no—
22#91118C2212yes—
23#91117C2212yes—
24#71716—51nomaximal, Hall
25C5×#525D311yescharacteristic
26#65529—31no—
27#65526—31no—
28#64759—32no—
29#64756—32no—
30C24×C3×C5C2×C411yescharacteristic
31C3×C5×#41—41no—
32C3×C5×#41—41no—
33C2×C3×C5×Q8D411yescharacteristic
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4C2×C411yescharacteristic
37C2×C3×C5×D4D411yescharacteristic
38C2×C3×C5×D4C2311yescharacteristic
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5—41no—
42C22×C3×C4×C5—41no—
43C22×C3×C4×C5C2×C411yescharacteristic
44C22×C3×C4×C5C2×C411yescharacteristic
45C22×C3×C4×C5D411yescharacteristic
46C22×C3×C4×C5D411yescharacteristic
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C22⋊C4—21no—
51C3×C5×C22⋊C4—21no—
52C3×C5×C22⋊C4—21no—
53C3×C5×C22⋊C4—21no—
54C3×C5×C22⋊C4C2×C411yescharacteristic
55C3×C5×C22⋊C4C2×C411yescharacteristic
56C3×C42×C5—21no—
57#6719—22no—
58C4⋊Dic15—41no—
59C4×Dic15—41no—
60#6710—22no—
61#6710—41no—
62C2×C3⋊#168—41no—
63C3×#525D511yescharacteristic
64#5240—51no—
65#5237—51no—
66#4539—52no—
67#4536—52no—
68C2×C5×#41C2×D311yescharacteristic
69C23×C4×C5Dic311yescharacteristic, complemented
70C5×#123Dic311yescharacteristic, complemented
71C5×#123C2×D311yescharacteristic
72C5×C22⋊Q8—21no—
73C5×#121—21no—
74C5×#120Dic311yescharacteristic, complemented
75C5×#120C2×D311yescharacteristic
76C4×C5×D4—21no—
77C4×C5×D4—21no—
78C5×#117Dic311yescharacteristic, complemented
79#4072—61no—
80C2×#681—61no—
81#3968—61no—
82#3966—32no—
83#3966—61no—
84#3965—32no—
85#2120—151noSylow
86C23×C3×C5—21no—
87C23×C3×C5—41no—
88C23×C3×C5—42no—
89C23×C3×C5C22⋊C411yescharacteristic
90C23×C3×C5C22×C411yescharacteristic
91C23×C3×C5C2×D411yescharacteristic
92C3×C5×Q8—41no—
93C3×C5×D4—41no—
94C3×C5×D4—41no—
95C3×C5×D4—41no—
96C3×C5×D4—42no—
97C3×C5×D4—42no—
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5—21no—
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—21no—
104C2×C3×C4×C5—21no—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—42no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5C22⋊C411yescharacteristic
112C2×C3×C4×C5C22⋊C411yescharacteristic
113C2×C3×C4×C5C22⋊C411yescharacteristic
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×Dic15—42no—
116C3⋊#168—42no—
117C2×C3×#41C2×D511yescharacteristic
118C23×C3×C4Dic511yescharacteristic, complemented
119C3×#123Dic511yescharacteristic, complemented
120C3×#123C2×D511yescharacteristic
121C3×C22⋊Q8—21no—
122C3×#121—21no—
123C3×#120Dic511yescharacteristic, complemented
124C3×#120C2×D511yescharacteristic
125C3×C4×D4—21no—
126C3×C4×D4—21no—
127C3×#117Dic511yescharacteristic, complemented
128#926—101no—
129C2×#208—101no—
130#836—101no—
131#834—52no—
132#834—101no—
133#833—52no—
134C24×C5C2×Dic311yescharacteristic
135C5×#41—41no—
136C5×#41—41no—
137C2×C5×Q8#6711yescharacteristic
138C2×C5×D4—21no—
139C2×C5×D4—21no—
140C2×C5×D4C2×Dic311yescharacteristic
141C2×C5×D4#6711yescharacteristic
142C2×C5×D4C22×D311yescharacteristic
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5—41no—
146C22×C4×C5—41no—
147C22×C4×C5C2×Dic311yescharacteristic
148C22×C4×C5C2×Dic311yescharacteristic
149C22×C4×C5#6711yescharacteristic
150C22×C4×C5#6711yescharacteristic
151C5×C4⋊C4—21no—
152C5×C4⋊C4—21no—
153C5×C4⋊C4—21no—
154C5×C22⋊C4—21no—
155C5×C22⋊C4—21no—
156C5×C22⋊C4—21no—
157C5×C22⋊C4—21no—
158C5×C22⋊C4C2×Dic311yescharacteristic
159C5×C22⋊C4C2×Dic311yescharacteristic
160C42×C5—21no—
161C22⋊Dic5—62no—
162C4⋊Dic5—121no—
163C4×Dic5—121no—
164#681—62no—
165#681—121no—
166C2×#168—121no—
167#525D1511yescharacteristic
168#413—151no—
169#410—151no—
170#352—152no—
171AΣL(1,𝔽16)—152no—
172C22×C3×C5—22no—
173C22×C3×C5—21no—
174C22×C3×C5—21no—
175C22×C3×C5—21no—
176C22×C3×C5—41no—
177C22×C3×C5—41no—
178C22×C3×C5—41no—
179C22×C3×C5—41no—
180C22×C3×C5—42no—
181C22×C3×C5—42no—
182C22×C3×C5—41no—
183C22×C3×C5C2×C22⋊C411yescharacteristic
184C3×C4×C5—21no—
185C3×C4×C5—21no—
186C3×C4×C5—21no—
187C3×C4×C5—41no—
188C3×C4×C5—41no—
189C3×C4×C5—41no—
190C3×C4×C5#9911yescharacteristic
191C3×C4×C5#9911yescharacteristic
192Dic15—82no—
193C24×C3C2×Dic511yescharacteristic
194C3×#41—41no—
195C3×#41—41no—
196C2×C3×Q8C22⋊D511yescharacteristic
197C2×C3×D4—21no—
198C2×C3×D4—21no—
199C2×C3×D4C2×Dic511yescharacteristic
200C2×C3×D4C22⋊D511yescharacteristic
201C2×C3×D4C22×D511yescharacteristic
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—41no—
205C22×C3×C4—41no—
206C22×C3×C4C2×Dic511yescharacteristic
207C22×C3×C4C2×Dic511yescharacteristic
208C22×C3×C4C22⋊D511yescharacteristic
209C22×C3×C4C22⋊D511yescharacteristic
210C3×C4⋊C4—21no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—21no—
213C3×C22⋊C4—21no—
214C3×C22⋊C4—21no—
215C3×C22⋊C4—21no—
216C3×C22⋊C4—21no—
217C3×C22⋊C4C2×Dic511yescharacteristic
218C3×C22⋊C4C2×Dic511yescharacteristic
219C3×C42—21no—
220#217—102no—
221C4⋊Dic3—201no—
222C4×Dic3—201no—
223#208—102no—
224#208—201no—
225C2×C3⋊C8—201no—
226C23×C5—21no—
227C23×C5—41no—
228C23×C5—42no—
229C23×C5#21711yescharacteristic
230C23×C5C22×Dic311yescharacteristic
231C23×C5C2×#6711yescharacteristic
232C5×Q8—41no—
233C5×D4—41no—
234C5×D4—41no—
235C5×D4—41no—
236C5×D4—42no—
237C5×D4—42no—
238C2×C4×C5—21no—
239C2×C4×C5—21no—
240C2×C4×C5—21no—
241C2×C4×C5—21no—
242C2×C4×C5—21no—
243C2×C4×C5—21no—
244C2×C4×C5—21no—
245C2×C4×C5—21no—
246C2×C4×C5—21no—
247C2×C4×C5—42no—
248C2×C4×C5—41no—
249C2×C4×C5—41no—
250C2×C4×C5—41no—
251C2×C4×C5#21711yescharacteristic
252C2×C4×C5#21711yescharacteristic
253C2×C4×C5#21711yescharacteristic
254C2×C4×C5C2×#6711yescharacteristic
255C2×Dic5—122no—
256#168—122no—
257C2×#41C2×D1511yescharacteristic
258C23×C4Dic1511yescharacteristic, complemented
259C2×M16—301no—
260#123Dic1511yescharacteristic, complemented
261#123C2×D1511yescharacteristic
262C22⋊Q8—21no—
263#121—21no—
264#120Dic1511yescharacteristic, complemented
265#120C2×D1511yescharacteristic
266C4×D4—21no—
267C4×D4—21no—
268#117—301no—
269#117Dic1511yescharacteristic, complemented
270#101—301no—
271#100—152no—
272#99—152no—
273#99—301no—
274C2×C3×C5—21no—
275C2×C3×C5—41no—
276C2×C3×C5—41no—
277C2×C3×C5—42no—
278C2×C3×C5—41no—
279C2×C3×C5C2×#9911yescharacteristic
280C23×C3—21no—
281C23×C3—41no—
282C23×C3—42no—
283C23×C3C22⋊Dic511yescharacteristic
284C23×C3C22×Dic511yescharacteristic
285C23×C3C2×C22⋊D511yescharacteristic
286C3×Q8—41no—
287C3×D4—41no—
288C3×D4—41no—
289C3×D4—41no—
290C3×D4—42no—
291C3×D4—42no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—42no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4C22⋊Dic511yescharacteristic
306C2×C3×C4C22⋊Dic511yescharacteristic
307C2×C3×C4C22⋊Dic511yescharacteristic
308C2×C3×C4C2×C22⋊D511yescharacteristic
309C2×Dic3—202no—
310C3⋊C8—202no—
311C22×C5—22no—
312C22×C5—21no—
313C22×C5—21no—
314C22×C5—21no—
315C22×C5—41no—
316C22×C5—41no—
317C22×C5—41no—
318C22×C5—41no—
319C22×C5—42no—
320C22×C5—42no—
321C22×C5—41no—
322C22×C5C2×#21711yescharacteristic
323C4×C5—21no—
324C4×C5—21no—
325C4×C5—21no—
326C4×C5—41no—
327C4×C5—41no—
328C4×C5—41no—
329C4×C5#83411yescharacteristic
330C4×C5#83411yescharacteristic
331Dic5—242no—
332C24C2×Dic1511yescharacteristic
333#41—41no—
334#41—41no—
335C2×Q8#122011yescharacteristic
336C2×D4—21no—
337C2×D4—21no—
338C2×D4C2×Dic1511yescharacteristic
339C2×D4#122011yescharacteristic
340C2×D4C22×D1511yescharacteristic
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4C2×Dic1511yescharacteristic
346C22×C4C2×Dic1511yescharacteristic
347C22×C4#122011yescharacteristic
348C22×C4#122011yescharacteristic
349M16—302no—
350M16—601no—
351C2×C8—601no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—21no—
355C4⋊C4—601no—
356C22⋊C4—21no—
357C22⋊C4—21no—
358C22⋊C4—21no—
359C22⋊C4—21no—
360C22⋊C4—302no—
361C22⋊C4C2×Dic1511yescharacteristic
362C22⋊C4C2×Dic1511yescharacteristic
363C42—21no—
364C42—601no—
365C3×C5#212011yescharacteristic, complemented, Hall
366C22×C3—22no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—41no—
371C22×C3—41no—
372C22×C3—41no—
373C22×C3—41no—
374C22×C3—42no—
375C22×C3—42no—
376C22×C3—41no—
377C22×C3C2×C22⋊Dic511yescharacteristic
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—41no—
382C3×C4—41no—
383C3×C4—41no—
384C3×C4#396611yescharacteristic
385C3×C4#396611yescharacteristic
386Dic3—402no—
387C2×C5—21no—
388C2×C5—41no—
389C2×C5—42no—
390C2×C5—41no—
391C2×C5—41no—
392C2×C5C2×#83411yescharacteristic
393C23—21no—
394C23—41no—
395C23—42no—
396C23#671911yescharacteristic
397C23C22×Dic1511yescharacteristic
398C23C2×#122011yescharacteristic
399Q8—41no—
400D4—41no—
401D4—41no—
402D4—41no—
403D4—42no—
404D4—42no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—42no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—602no—
419C2×C4#671911yescharacteristic
420C2×C4#671911yescharacteristic
421C2×C4#671911yescharacteristic
422C2×C4C2×#122011yescharacteristic
423C8—602no—
424C2×C3—21no—
425C2×C3—41no—
426C2×C3—42no—
427C2×C3—41no—
428C2×C3—41no—
429C2×C3C2×#396611yescharacteristic
430C5#7171611yescharacteristic, complemented, Sylow
431C22—22no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—42no—
440C22—42no—
441C22—41no—
442C22C2×#671911yescharacteristic
443C4—21no—
444C4—21no—
445C4—21no—
446C4—41no—
447C4—41no—
448C4—41no—
449C4—1202no—
450C4#9111811yescharacteristic
451C4#9111811yescharacteristic
452C3#1060250911yescharacteristic, complemented, Sylow
453C2—21no—
454C2—41no—
455C2—42no—
456C2—41no—
457C2—41no—
458C2C2×#9111811yescharacteristic
subgroupG/H
centerC4#91118
commutatorC23×C3×C5C22×C4
FrattiniC2×D4C22×D15
Fitting, prime radicalC3×C5×#525C2
socleC2×C3×C5C2×#99
cosocleC2×C3×C5×D4C23
hypercenter#525D15
hypocenterC3×C5#2120
LCSG ▷ C23×C3×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #525

Complements

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

NH ≅ G/Ntype
2. #11751341C2semidirect
3. #11751338C2semidirect
4. #11746360C2semidirect
5. #11746357C2semidirect
8. C23×C3×C4×C5C4semidirect
9. C3×C5×#123C4semidirect
13. C3×C5×#120C4semidirect
17. C3×C5×#117C4semidirect
69. C23×C4×C5Dic3semidirect
70. C5×#123Dic3semidirect
74. C5×#120Dic3semidirect
78. C5×#117Dic3semidirect
118. C23×C3×C4Dic5semidirect
119. C3×#123Dic5semidirect
123. C3×#120Dic5semidirect
127. C3×#117Dic5semidirect
258. C23×C4Dic15semidirect
260. #123Dic15semidirect
264. #120Dic15semidirect
269. #117Dic15semidirect
365. C3×C5#2120semidirect
430. C5#71716semidirect
452. C3#10602509semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5252
#117513412
#117513382
#117463602
#117463572
#106025093
#717165