Finite Group Databasebeta

← #14313433

Subgroups — #14313433

Order 1920.

516 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5832C211yesmaximal, characteristic
2#11751341C211yesmaximal, characteristic, complemented
3C3×#65529C211yesmaximal, characteristic, complemented
4#11746010C212yesmaximal, complemented
5#11746007C212yesmaximal, complemented
6#10602612—31nomaximal, Hall
7C2×C3×C5×#41C2211yescharacteristic
8C2×C5×#235C411yescharacteristic, complemented
9#91815—21no—
10C5×#947C411yescharacteristic, complemented
11C5×#944C411yescharacteristic, complemented
12C5×#940C2211yescharacteristic
13C5×#939—21no—
14C5×#939—21no—
15C5×#936C2211yescharacteristic
16C4×C5×#67—21no—
17C4×C5×#67—21no—
18C2×C4×C5×Dic3C411yescharacteristic, complemented
19C3×#4072—21no—
20#91118—21no—
21#91118C2212yes—
22C3×#3966—21no—
23C3×#3966C2212yes—
24#70060—51nomaximal, Hall
25C5×#532—31no—
26#65529—31no—
27#65529D311yescharacteristic, complemented
28#64765—32no—
29#64761—32no—
30C3×C5×#41—41no—
31C3×C5×#41—41no—
32C2×C3×C5×Q8C2×C411yescharacteristic
33C2×C3×C5×D4D411yescharacteristic
34C2×C3×C5×D4D411yescharacteristic
35C2×C3×C5×D4C2311yescharacteristic
36C22×C3×C4×C5C2×C411yescharacteristic
37C22×C3×C4×C5D411yescharacteristic
38C22×C3×C4×C5D411yescharacteristic
39C2×C5×#67—21no—
40C2×C5×#67—21no—
41C2×C5×#67—21no—
42C22×C5×Dic3—21no—
43C5×#235—41no—
44C5×#235—41no—
45C2×C5×D12C2×C411yescharacteristic
46C2×C4×C5×D3—21no—
47C2×C5×Dic6C2×C411yescharacteristic
48#6719—22no—
49C4⋊Dic15—41no—
50C4×Dic15—41no—
51C5×#217—21no—
52C5×#217—21no—
53C5×(C2×D3)⋊C4—21no—
54C5×(C2×D3)⋊C4—21no—
55C5×Dic3⋊C4—21no—
56C5×Dic3⋊C4—21no—
57C4×C5×Dic3—21no—
58C4×C5×Dic3C2×C411yescharacteristic
59C4×C5×Dic3C2×C411yescharacteristic
60C3×C22⋊Dic5—22no—
61C3×C4⋊Dic5—41no—
62C3×C4×Dic5—41no—
63#5832D511yescharacteristic
64C3×#410—51no—
65#5240—51no—
66#4474—52no—
67#4473—52no—
68C2×C5×#41—31no—
69C2×C5×#41C2×D311yescharacteristic
70C5×C4⋊Q8—31no—
71C5×#127—31no—
72C5×#124—31no—
73C5×#124—31no—
74C5×#121—61no—
75C5×#121—61no—
76C4×C5×D4—61no—
77C4×C5×D4—61no—
78C2×C42×C5—31no—
79#4072—21no—
80#4072—61no—
81#3966—21no—
82#3966—32no—
83#3966—61no—
84#3966C2×D312yes—
85#2126—151noSylow
86C23×C3×C5C22⋊C411yescharacteristic
87C23×C3×C5C2×D411yescharacteristic
88C23×C3×C5C2×D411yescharacteristic
89C22×C5×D3—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×C5C22⋊C411yescharacteristic
103C2×C3×C4×C5C22×C411yescharacteristic
104C2×Dic15—42no—
105C5×#67—42no—
106C5×#67—42no—
107C5×#67—42no—
108C2×C5×Dic3—21no—
109C2×C5×Dic3—21no—
110C2×C5×Dic3—21no—
111C2×C5×Dic3—42no—
112C5×D12—41no—
113C4×C5×D3—41no—
114C4×C5×D3—41no—
115C5×Dic6—41no—
116C2×C3×Dic5—42no—
117C2×C3×#41C2×D511yescharacteristic
118C2×#235Dic511yescharacteristic, complemented
119C3×#117—101no—
120#947Dic511yescharacteristic, complemented
121#944Dic511yescharacteristic, complemented
122#940C2×D511yescharacteristic
123#939—21no—
124#939—21no—
125#936C2×D511yescharacteristic
126C4×#67—21no—
127C4×#67—21no—
128#926—101no—
129C2×C4×Dic3Dic511yescharacteristic, complemented
130C3×#99—52no—
131C3×#99—101no—
132#834—52no—
133#834—101no—
134C5×#41—41no—
135C5×#41—41no—
136C5×#41—121no—
137C5×#41—121no—
138C2×C5×Q8—31no—
139C2×C5×Q8C4×D311yescharacteristic
140C2×C5×D4—31no—
141C2×C5×D4—61no—
142C2×C5×D4—61no—
143C2×C5×D4—61no—
144C2×C5×D4D1211yescharacteristic
145C2×C5×D4#6711yescharacteristic
146C2×C5×D4C22×D311yescharacteristic
147C22×C4×C5—61no—
148C22×C4×C5—61no—
149C22×C4×C5C4×D311yescharacteristic
150C22×C4×C5D1211yescharacteristic
151C22×C4×C5#6711yescharacteristic
152C5×C4⋊C4—61no—
153C5×C4⋊C4—61no—
154C5×C22⋊C4—61no—
155C5×C22⋊C4—61no—
156C5×C22⋊C4—61no—
157C5×C22⋊C4—61no—
158C42×C5—31no—
159C42×C5—31no—
160C42×C5—61no—
161C22⋊Dic5—22no—
162C22⋊Dic5—62no—
163C4⋊Dic5—41no—
164C4⋊Dic5—121no—
165C4×Dic5—41no—
166C4×Dic5—121no—
167#532—31no—
168#410—51no—
169#410—151no—
170#354—152no—
171#353—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×C5×D3—41no—
180C2×C5×D3—41no—
181C2×C5×D3—41no—
182C3×C4×C5—21no—
183C3×C4×C5—21no—
184C3×C4×C5—21no—
185C3×C4×C5#9911yescharacteristic
186C3×C4×C5#9911yescharacteristic
187Dic15—82no—
188C3×Dic5—82no—
189C5×Dic3—22no—
190C5×Dic3—41no—
191C5×Dic3—41no—
192C3×#41—41no—
193C3×#41—41no—
194C2×C3×Q8C2×Dic511yescharacteristic
195C2×C3×D4C22⋊D511yescharacteristic
196C2×C3×D4C22⋊D511yescharacteristic
197C2×C3×D4C22×D511yescharacteristic
198C22×C3×C4C2×Dic511yescharacteristic
199C22×C3×C4C22⋊D511yescharacteristic
200C22×C3×C4C22⋊D511yescharacteristic
201C2×#67—21no—
202C2×#67—21no—
203C2×#67—21no—
204C22×Dic3—21no—
205#235—41no—
206#235—41no—
207C2×D12C2×Dic511yescharacteristic
208C2×C4×D3—21no—
209C2×Dic6C2×Dic511yescharacteristic
210C3×C4⋊C4—201no—
211C3×C22⋊C4—102no—
212C3×C42—201no—
213#217—21no—
214#217—21no—
215#217—102no—
216(C2×D3)⋊C4—21no—
217(C2×D3)⋊C4—21no—
218C4⋊Dic3—201no—
219Dic3⋊C4—21no—
220Dic3⋊C4—21no—
221C4×Dic3—21no—
222C4×Dic3—201no—
223C4×Dic3C2×Dic511yescharacteristic
224C4×Dic3C2×Dic511yescharacteristic
225C23×C5—61no—
226C23×C5(C2×D3)⋊C411yescharacteristic
227C23×C5C2×D1211yescharacteristic
228C23×C5C2×#6711yescharacteristic
229C5×Q8—41no—
230C5×Q8—121no—
231C5×D4—41no—
232C5×D4—41no—
233C5×D4—41no—
234C5×D4—121no—
235C5×D4—122no—
236C5×D4—122no—
237C5×D4—122no—
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—61no—
245C2×C4×C5—61no—
246C2×C4×C5—61no—
247C2×C4×C5—122no—
248C2×C4×C5—121no—
249C2×C4×C5—121no—
250C2×C4×C5(C2×D3)⋊C411yescharacteristic
251C2×C4×C5(C2×D3)⋊C411yescharacteristic
252C2×C4×C5(C2×D3)⋊C411yescharacteristic
253C2×C4×C5C2×C4×D311yescharacteristic
254C2×Dic5—42no—
255C2×Dic5—122no—
256C2×#41—31no—
257C2×#41D3×D511yescharacteristic
258C4⋊Q8—31no—
259#127—31no—
260#124—31no—
261#124—31no—
262#121—61no—
263#121—61no—
264C4×D4—61no—
265C4×D4—61no—
266#117—101no—
267#117—301no—
268C2×C42—31no—
269#99—52no—
270#99—101no—
271#99—152no—
272#99—301no—
273C2×C3×C5—21no—
274C2×C3×C5—41no—
275C2×C3×C5—41no—
276C2×C3×C5—41no—
277C2×C3×C5C2×#9911yescharacteristic
278C5×D3—81no—
279C23×C3C22⋊Dic511yescharacteristic
280C23×C3C2×C22⋊D511yescharacteristic
281C23×C3C2×C22⋊D511yescharacteristic
282C22×D3—21no—
283C3×Q8—41no—
284C3×D4—41no—
285C3×D4—41no—
286C3×D4—41no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—202no—
294C2×C3×C4C22⋊Dic511yescharacteristic
295C2×C3×C4C22⋊Dic511yescharacteristic
296C2×C3×C4C22⋊Dic511yescharacteristic
297C2×C3×C4C22×Dic511yescharacteristic
298#67—42no—
299#67—42no—
300#67—42no—
301C2×Dic3—21no—
302C2×Dic3—21no—
303C2×Dic3—21no—
304C2×Dic3—42no—
305C2×Dic3—202no—
306D12—41no—
307C4×D3—41no—
308C4×D3—41no—
309Dic6—41no—
310C22×C5—21no—
311C22×C5—21no—
312C22×C5—21no—
313C22×C5—41no—
314C22×C5—41no—
315C22×C5—41no—
316C22×C5—121no—
317C22×C5—121no—
318C22×C5—121no—
319C22×C5C2×(C2×D3)⋊C411yescharacteristic
320C4×C5—21no—
321C4×C5—21no—
322C4×C5—21no—
323C4×C5—62no—
324C4×C5—121no—
325C4×C5—121no—
326C4×C5#80611yescharacteristic
327C4×C5#80611yescharacteristic
328Dic5—82no—
329Dic5—242no—
330#41—41no—
331#41—41no—
332#41—121no—
333#41—121no—
334C2×Q8—31no—
335C2×Q8D3×Dic511yescharacteristic
336C2×D4—31no—
337C2×D4—61no—
338C2×D4—61no—
339C2×D4—61no—
340C2×D4#120111yescharacteristic
341C2×D4#120311yescharacteristic
342C2×D4C2×D3×D511yescharacteristic
343C22×C4—61no—
344C22×C4—61no—
345C22×C4D3×Dic511yescharacteristic
346C22×C4#120111yescharacteristic
347C22×C4#120311yescharacteristic
348C4⋊C4—61no—
349C4⋊C4—61no—
350C4⋊C4—201no—
351C4⋊C4—601no—
352C22⋊C4—61no—
353C22⋊C4—61no—
354C22⋊C4—61no—
355C22⋊C4—61no—
356C22⋊C4—102no—
357C22⋊C4—302no—
358C42—31no—
359C42—31no—
360C42—61no—
361C42—201no—
362C42—601no—
363C3×C5#212611yescharacteristic, complemented, Hall
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—41no—
368C22×C3—41no—
369C22×C3—41no—
370C22×C3C2×C22⋊Dic511yescharacteristic
371C2×D3—41no—
372C2×D3—41no—
373C2×D3—41no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—402no—
378C3×C4#396611yescharacteristic
379C3×C4#396611yescharacteristic
380Dic3—22no—
381Dic3—41no—
382Dic3—41no—
383Dic3—402no—
384C2×C5—21no—
385C2×C5—41no—
386C2×C5—41no—
387C2×C5—41no—
388C2×C5—241no—
389C2×C5C2×#80611yescharacteristic
390C23—61no—
391C23(C2×D3)⋊Dic511yescharacteristic
392C23C2×#120111yescharacteristic
393C23C2×#120311yescharacteristic
394Q8—41no—
395Q8—121no—
396D4—41no—
397D4—41no—
398D4—41no—
399D4—121no—
400D4—122no—
401D4—122no—
402D4—122no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—61no—
410C2×C4—61no—
411C2×C4—61no—
412C2×C4—122no—
413C2×C4—121no—
414C2×C4—121no—
415C2×C4—202no—
416C2×C4—602no—
417C2×C4(C2×D3)⋊Dic511yescharacteristic
418C2×C4(C2×D3)⋊Dic511yescharacteristic
419C2×C4(C2×D3)⋊Dic511yescharacteristic
420C2×C4C2×D3×Dic511yescharacteristic
421C2×C3—21no—
422C2×C3—41no—
423C2×C3—41no—
424C2×C3—41no—
425C2×C3C2×#396611yescharacteristic
426D3—81no—
427C5#7006011yescharacteristic, complemented, Sylow
428C22—21no—
429C22—21no—
430C22—21no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—121no—
435C22—121no—
436C22—121no—
437C22C2×(C2×D3)⋊Dic511yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—62no—
442C4—121no—
443C4—121no—
444C4—402no—
445C4—1202no—
446C4#9099611yescharacteristic
447C4#9099611yescharacteristic
448C3#1060261211yescharacteristic, complemented, Sylow
449C2—21no—
450C2—41no—
451C2—41no—
452C2—41no—
453C2—241no—
454C2C2×#9099611yescharacteristic
subgroupG/H
centerC4#90996
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×D4C2×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5C2×#99
prime radicalC5×#5832C2
cosocleC2×C3×C5×D4C23
hypercenterC2×#41D3×D5
hypocenterC3×C5#2126
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #11751341C2semidirect
3. C3×#65529C2semidirect
4. #11746010C2semidirect
5. #11746007C2semidirect
8. C2×C5×#235C4semidirect
10. C5×#947C4semidirect
11. C5×#944C4semidirect
18. C2×C4×C5×Dic3C4semidirect
27. #65529D3semidirect
118. C2×#235Dic5semidirect
120. #947Dic5semidirect
121. #944Dic5semidirect
129. C2×C4×Dic3Dic5semidirect
363. C3×C5#2126semidirect
427. C5#70060semidirect
448. C3#10602612semidirect

Maximal subgroups

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

subgroupindex
C5×#58322
#117513412
C3×#655292
#117460102
#117460072
#106026123
#700605