Finite Group Databasebeta

← #14313625

Subgroups — #14313625

Order 1920.

500 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756591C211yesmaximal, characteristic
2C3×C5×#413C211yesmaximal, characteristic, complemented
3#11751338C211yesmaximal, characteristic, complemented
4#11746299C212yesmaximal, complemented
5#11746298C212yesmaximal, complemented
6#10600941—31nomaximal, Hall
7C2×C3×C5×#41C2211yescharacteristic
8C2×#6817C411yescharacteristic
9C2×C3×C5×M16—21no—
10#91836C2211yescharacteristic
11#91833C2211yescharacteristic
12#91829C411yescharacteristic
13#91828—21no—
14#91828—21no—
15#91825C411yescharacteristic
16C4×#1220—21no—
17C4×#1220—21no—
18C2×C4×Dic15C411yescharacteristic
19C2×#6710—21no—
20C3×C5×#101C2212yes—
21C3×C5×#100—21no—
22#91120C2212yes—
23#91117—21no—
24#70148—51nomaximal, Hall
25#66166—31no—
26C5×#413D311yescharacteristic, complemented
27#65526—31no—
28#64698—32no—
29#64697—32no—
30C3×C5×#41—41no—
31C3×C5×#41—41no—
32C2×C3×C5×Q8C2311yescharacteristic
33C2×C3×C5×D4C2×C411yescharacteristic
34C2×C3×C5×D4D411yescharacteristic
35C2×C3×C5×D4D411yescharacteristic
36C22×C3×C4×C5C2×C411yescharacteristic
37C22×C3×C4×C5D411yescharacteristic
38C22×C3×C4×C5D411yescharacteristic
39C2×#1220—21no—
40C2×#1220—21no—
41C2×#1220—21no—
42C22×Dic15—21no—
43#6817—41no—
44#6817—41no—
45C2×D60C2×C411yescharacteristic
46C2×C4×D15—21no—
47C2×Dic30C2×C411yescharacteristic
48C3×C5×M16—22no—
49C3×C5×M16—41no—
50C2×C3×C5×C8—41no—
51#6719—21no—
52#6719—21no—
53#6714—21no—
54#6714—21no—
55#6712—21no—
56#6712—21no—
57C4×Dic15—21no—
58C4×Dic15C2×C411yescharacteristic
59C4×Dic15C2×C411yescharacteristic
60#6710—22no—
61#6710—41no—
62C2×C3⋊#168—41no—
63#5832—51no—
64C3×#413D511yescharacteristic, complemented
65#5237—51no—
66#4478—52no—
67#4477—52no—
68C2×C5×#41C2×D311yescharacteristic
69C2×#709—31no—
70C2×C5×M16—21no—
71#4093—31no—
72#4090—31no—
73#4086—31no—
74#4085—61no—
75#4085—61no—
76#4082—31no—
77C4×C22⋊D5—61no—
78C4×C22⋊D5—61no—
79C2×C4×Dic5—31no—
80C2×#681—61no—
81C5×#101C2×D312yes—
82C5×#100—21no—
83#3968—32no—
84#3965—61no—
85#2132—151noSylow
86C23×C3×C5C22⋊C411yescharacteristic
87C23×C3×C5C22⋊C411yescharacteristic
88C23×C3×C5C22⋊C411yescharacteristic
89C22×D15—21no—
90C3×C5×Q8—41no—
91C3×C5×D4—41no—
92C3×C5×D4—41no—
93C3×C5×D4—41no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5C22⋊C411yescharacteristic
101C2×C3×C4×C5C22×C411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104#1220—42no—
105#1220—42no—
106#1220—42no—
107C2×Dic15—21no—
108C2×Dic15—21no—
109C2×Dic15—21no—
110C2×Dic15—42no—
111D60—41no—
112C4×D15—41no—
113C4×D15—41no—
114Dic30—41no—
115C3×C5×C8—42no—
116C3⋊#168—42no—
117C2×C3×#41C2×D511yescharacteristic
118C2×#235—51no—
119C2×C3×M16—21no—
120#947—51no—
121#944—51no—
122#940—51no—
123#939—101no—
124#939—101no—
125#936—51no—
126C4×#67—101no—
127C4×#67—101no—
128C2×C4×Dic3—51no—
129C2×#208—101no—
130C3×#101C2×D512yes—
131C3×#100—21no—
132#836—52no—
133#833—101no—
134C5×#41—41no—
135C5×#41—41no—
136C2×C5×Q8C22×D311yescharacteristic
137C2×C5×D4C4×D311yescharacteristic
138C2×C5×D4D1211yescharacteristic
139C2×C5×D4#6711yescharacteristic
140C22×C4×C5C4×D311yescharacteristic
141C22×C4×C5D1211yescharacteristic
142C22×C4×C5#6711yescharacteristic
143C2×C22⋊D5—61no—
144C2×C22⋊D5—61no—
145C2×C22⋊D5—61no—
146C22×Dic5—61no—
147#709—121no—
148#709—121no—
149C2×D20—31no—
150C2×C4×D5—61no—
151C2×Dic10—31no—
152C5×M16—22no—
153C5×M16—41no—
154C2×C5×C8—41no—
155C22⋊Dic5—61no—
156C22⋊Dic5—61no—
157#685—61no—
158#685—61no—
159#683—61no—
160#683—61no—
161C4×Dic5—31no—
162C4×Dic5—31no—
163C4×Dic5—61no—
164#681—62no—
165#681—121no—
166C2×#168—121no—
167#532—151no—
168#413—151no—
169#413D1511yescharacteristic, complemented
170#356—152no—
171#355—152no—
172C22×C3×C5—21no—
173C22×C3×C5—21no—
174C22×C3×C5—21no—
175C22×C3×C5—41no—
176C22×C3×C5—41no—
177C22×C3×C5—41no—
178C22×C3×C5C2×C22⋊C411yescharacteristic
179C2×D15—41no—
180C2×D15—41no—
181C2×D15—41no—
182C3×C4×C5—21no—
183C3×C4×C5—21no—
184C3×C4×C5—21no—
185C3×C4×C5#9911yescharacteristic
186C3×C4×C5#9911yescharacteristic
187Dic15—22no—
188Dic15—41no—
189Dic15—41no—
190C3×#41—41no—
191C3×#41—41no—
192C2×C3×Q8C22×D511yescharacteristic
193C2×C3×D4C4×D511yescharacteristic
194C2×C3×D4D2011yescharacteristic
195C2×C3×D4C22⋊D511yescharacteristic
196C22×C3×C4C4×D511yescharacteristic
197C22×C3×C4D2011yescharacteristic
198C22×C3×C4C22⋊D511yescharacteristic
199C2×#67—101no—
200C2×#67—101no—
201C2×#67—101no—
202C22×Dic3—101no—
203#235—201no—
204#235—201no—
205C2×D12—51no—
206C2×C4×D3—101no—
207C2×Dic6—51no—
208C3×M16—22no—
209C3×M16—41no—
210C2×C3×C8—41no—
211#217—101no—
212#217—101no—
213(C2×D3)⋊C4—101no—
214(C2×D3)⋊C4—101no—
215Dic3⋊C4—101no—
216Dic3⋊C4—101no—
217C4×Dic3—51no—
218C4×Dic3—51no—
219C4×Dic3—101no—
220#208—102no—
221#208—201no—
222C2×C3⋊C8—201no—
223C23×C5(C2×D3)⋊C411yescharacteristic
224C23×C5(C2×D3)⋊C411yescharacteristic
225C23×C5(C2×D3)⋊C411yescharacteristic
226C22×D5—61no—
227C5×Q8—41no—
228C5×D4—41no—
229C5×D4—41no—
230C5×D4—41no—
231C2×C4×C5—21no—
232C2×C4×C5—21no—
233C2×C4×C5—21no—
234C2×C4×C5—21no—
235C2×C4×C5—21no—
236C2×C4×C5—21no—
237C2×C4×C5(C2×D3)⋊C411yescharacteristic
238C2×C4×C5C2×C4×D311yescharacteristic
239C2×C4×C5C2×D1211yescharacteristic
240C2×C4×C5C2×#6711yescharacteristic
241C22⋊D5—122no—
242C22⋊D5—122no—
243C22⋊D5—122no—
244C2×Dic5—61no—
245C2×Dic5—61no—
246C2×Dic5—61no—
247C2×Dic5—122no—
248D20—121no—
249C4×D5—121no—
250C4×D5—121no—
251Dic10—121no—
252C5×C8—42no—
253#168—122no—
254C2×#41—151no—
255C2×#41C2×D1511yescharacteristic
256C2×M16—21no—
257C2×M16—301no—
258C4⋊Q8—151no—
259#127—151no—
260#124—151no—
261#124—151no—
262#121—301no—
263#121—301no—
264C4×D4—301no—
265C4×D4—301no—
266C2×C42—151no—
267#101—152no—
268#101C2×D1512yes—
269#100—21no—
270#100—301no—
271C2×C3×C5—21no—
272C2×C3×C5—41no—
273C2×C3×C5—41no—
274C2×C3×C5—41no—
275C2×C3×C5C2×#9911yescharacteristic
276D15—81no—
277C23×C3#68511yescharacteristic
278C23×C3#68511yescharacteristic
279C23×C3#68511yescharacteristic
280C22×D3—101no—
281C3×Q8—41no—
282C3×D4—41no—
283C3×D4—41no—
284C3×D4—41no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4#68511yescharacteristic
292C2×C3×C4C2×C4×D511yescharacteristic
293C2×C3×C4C2×D2011yescharacteristic
294C2×C3×C4C2×C22⋊D511yescharacteristic
295#67—202no—
296#67—202no—
297#67—202no—
298C2×Dic3—101no—
299C2×Dic3—101no—
300C2×Dic3—101no—
301C2×Dic3—202no—
302D12—201no—
303C4×D3—201no—
304C4×D3—201no—
305Dic6—201no—
306C3×C8—42no—
307C3⋊C8—202no—
308C22×C5—21no—
309C22×C5—21no—
310C22×C5—21no—
311C22×C5—41no—
312C22×C5—41no—
313C22×C5—41no—
314C22×C5C2×(C2×D3)⋊C411yescharacteristic
315C2×D5—121no—
316C2×D5—121no—
317C2×D5—121no—
318C4×C5—21no—
319C4×C5—21no—
320C4×C5—21no—
321C4×C5#80611yescharacteristic
322C4×C5#80611yescharacteristic
323Dic5—62no—
324Dic5—121no—
325Dic5—121no—
326#41—41no—
327#41—41no—
328#41—601no—
329#41—601no—
330C2×Q8—151no—
331C2×Q8C22×D1511yescharacteristic
332C2×D4—151no—
333C2×D4—301no—
334C2×D4—301no—
335C2×D4—301no—
336C2×D4C4×D1511yescharacteristic
337C2×D4D6011yescharacteristic
338C2×D4#122011yescharacteristic
339C22×C4—301no—
340C22×C4—301no—
341C22×C4C4×D1511yescharacteristic
342C22×C4D6011yescharacteristic
343C22×C4#122011yescharacteristic
344M16—22no—
345M16—41no—
346M16—302no—
347M16—601no—
348C2×C8—41no—
349C2×C8—601no—
350C4⋊C4—301no—
351C4⋊C4—301no—
352C22⋊C4—301no—
353C22⋊C4—301no—
354C22⋊C4—301no—
355C22⋊C4—301no—
356C42—151no—
357C42—151no—
358C42—301no—
359C3×C5#213211yescharacteristic, complemented, Hall
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—41no—
364C22×C3—41no—
365C22×C3—41no—
366C22×C3C2×#68511yescharacteristic
367C2×D3—201no—
368C2×D3—201no—
369C2×D3—201no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4#393811yescharacteristic
374C3×C4#393811yescharacteristic
375Dic3—102no—
376Dic3—201no—
377Dic3—201no—
378C2×C5—21no—
379C2×C5—41no—
380C2×C5—41no—
381C2×C5—41no—
382C2×C5C2×#80611yescharacteristic
383D5—241no—
384C23—301no—
385C23#671411yescharacteristic
386C23#671411yescharacteristic
387C23#671411yescharacteristic
388Q8—41no—
389Q8—601no—
390D4—41no—
391D4—41no—
392D4—41no—
393D4—601no—
394D4—602no—
395D4—602no—
396D4—602no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—301no—
404C2×C4—301no—
405C2×C4—301no—
406C2×C4—602no—
407C2×C4—601no—
408C2×C4—601no—
409C2×C4#671411yescharacteristic
410C2×C4C2×C4×D1511yescharacteristic
411C2×C4C2×D6011yescharacteristic
412C2×C4C2×#122011yescharacteristic
413C8—42no—
414C8—602no—
415C2×C3—21no—
416C2×C3—41no—
417C2×C3—41no—
418C2×C3—41no—
419C2×C3C2×#393811yescharacteristic
420D3—401no—
421C5#7014811yescharacteristic, complemented, Sylow
422C22—21no—
423C22—21no—
424C22—21no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—601no—
429C22—601no—
430C22—601no—
431C22C2×#671411yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—302no—
436C4—601no—
437C4—601no—
438C4#9109011yescharacteristic
439C4#9109011yescharacteristic
440C3#1060094111yescharacteristic, complemented, Sylow
441C2—21no—
442C2—41no—
443C2—41no—
444C2—41no—
445C2—1201no—
446C2C2×#9109011yescharacteristic
subgroupG/H
centerC4#91090
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×Q8C22×D15
FittingC3×C5×#413C2
socleC2×C3×C5C2×#99
prime radical#11756591C2
cosocleC2×C3×C5×Q8C23
hypercenter#413D15
hypocenterC3×C5#2132
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. C3×C5×#413C2semidirect
3. #11751338C2semidirect
4. #11746299C2semidirect
5. #11746298C2semidirect
26. C5×#413D3semidirect
64. C3×#413D5semidirect
169. #413D15semidirect
359. C3×C5#2132semidirect
421. C5#70148semidirect
440. C3#10600941semidirect

Maximal subgroups

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

subgroupindex
#117565912
C3×C5×#4132
#117513382
#117462992
#117462982
#106009413
#701485