Finite Group Databasebeta

← #14282874

Subgroups — #14282874

Order 1920.

568 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756355C211yesmaximal, characteristic
2#11750819C211yesmaximal, characteristic, complemented
3#11750750C211yesmaximal, characteristic, complemented
4C3×C5×#327C211yesmaximal, characteristic, complemented
5#11746358C211yesmaximal, characteristic, complemented
6#11746291C211yesmaximal, characteristic, complemented
7#11746272C211yesmaximal, characteristic, complemented
8#10599070—31nomaximal, Hall
9C2×#6819—21no—
10C3×C5×#121C2211yescharacteristic
11#91829C411yescharacteristic, complemented
12#91828—21no—
13D4×Dic15C411yescharacteristic, complemented
14#91819C2211yescharacteristic
15C2×#6712—21no—
16C2×C4×Dic15—21no—
17C2×C4×Dic15C2211yescharacteristic
18#91782C411yescharacteristic, complemented
19#91777C411yescharacteristic, complemented
20#91774—21no—
21#91770—21no—
22C3×C5×C22⋊C8C2211yescharacteristic
23C3×C5×#95C2211yescharacteristic
24#91115C2211yescharacteristic
25#91114C2211yescharacteristic
26#91098—21no—
27C8×Dic15—21no—
28#68277—51nomaximal, Hall
29#65930—31no—
30#65007—31no—
31#64938—31no—
32C5×#327D311yescharacteristic, complemented
33#64757—31no—
34#64690—31no—
35#64671—31no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4C2×C411yescharacteristic
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5C2311yescharacteristic
40C2×#1220—21no—
41C2×#1220—21no—
42C2×#1220—21no—
43C22×Dic15—21no—
44C22×Dic15—21no—
45C22×Dic15D411yescharacteristic
46C22×Dic15D411yescharacteristic
47#6819—42no—
48#6819—42no—
49C2×D60C2×C411yescharacteristic
50C2×C4×D15—21no—
51C2×Dic30—21no—
52C2×C3×C5×C8—21no—
53C3×C5×C4⋊C4C2×C411yescharacteristic
54C3×C5×C22⋊C4—21no—
55#6719—21no—
56#6714—21no—
57#6714—21no—
58C4⋊Dic15C2×C411yescharacteristic
59#6712—24no—
60#6712—21no—
61C4×Dic15—42no—
62C4×Dic15C2×C411yescharacteristic
63C4×Dic15C2×C411yescharacteristic
64C4×Dic15D411yescharacteristic
65C4×Dic15D411yescharacteristic
66C2×C3⋊#168—21no—
67#5596—51no—
68#4718—51no—
69#4649—51no—
70C3×#327D511yescharacteristic, complemented
71#4537—51no—
72#4470—51no—
73#4451—51no—
74C2×#711—61no—
75C5×#121C2×D311yescharacteristic
76#4086—31no—
77#4085—61no—
78D4×Dic5—31no—
79#4076—31no—
80C2×#683—61no—
81C2×C4×Dic5—31no—
82C2×C4×Dic5—61no—
83#4039—31no—
84#4034—31no—
85#4031—61no—
86#4027—61no—
87C5×C22⋊C8C2×D311yescharacteristic
88C5×#95C2×D311yescharacteristic
89#3963—31no—
90C22⋊#168—31no—
91#3946—61no—
92C8×Dic5—61no—
93#1502—151noSylow
94C23×C3×C5—21no—
95C23×C3×C5C2×D411yescharacteristic
96C22×D15—21no—
97C3×C5×D4—41no—
98C3×C5×D4—41no—
99C3×C5×D4—41no—
100C2×C3×C4×C5—22no—
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5C22×C411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107#1220—41no—
108#1220—41no—
109#1220—42no—
110#1220—42no—
111C2×Dic15—22no—
112C2×Dic15—22no—
113C2×Dic15—21no—
114C2×Dic15—41no—
115C2×Dic15—41no—
116C2×Dic15—42no—
117C2×Dic15C22⋊C411yescharacteristic
118C2×Dic15C22⋊C411yescharacteristic
119C2×Dic15C22⋊C411yescharacteristic
120C2×Dic15C22⋊C411yescharacteristic
121C2×Dic15D812yes—
122C2×Dic15SD1612yes—
123D60—41no—
124C4×D15—42no—
125Dic30—42no—
126C3×C5×C8—41no—
127C3⋊#168—41no—
128C2×#237—101no—
129C3×#121C2×D511yescharacteristic
130#940—51no—
131#939—101no—
132D4×Dic3—51no—
133#930—51no—
134C2×Dic3⋊C4—101no—
135C2×C4×Dic3—51no—
136C2×C4×Dic3—101no—
137#893—51no—
138#888—51no—
139#885—101no—
140#67⋊C4—101no—
141C3×C22⋊C8C2×D511yescharacteristic
142C3×#95C2×D511yescharacteristic
143C3⋊#95—51no—
144#830—51no—
145Dic3⋊C8—101no—
146C8×Dic3—101no—
147C2×C5×D4—21no—
148C2×C5×D4C4×D311yescharacteristic
149C22×C4×C5—21no—
150C22×C4×C5C22×D311yescharacteristic
151C2×C22⋊D5—61no—
152C2×C22⋊D5—61no—
153C2×C22⋊D5—61no—
154C22×Dic5—31no—
155C22×Dic5—31no—
156C22×Dic5—61no—
157C22×Dic5—61no—
158#711—122no—
159#711—122no—
160C2×D20—31no—
161C2×C4×D5—61no—
162C2×Dic10—61no—
163C2×C5×C8—21no—
164C5×C4⋊C4C4×D311yescharacteristic
165C5×C22⋊C4—21no—
166C22⋊Dic5—61no—
167#685—61no—
168#685—61no—
169C4⋊Dic5—31no—
170#683—61no—
171#683—64no—
172C4×Dic5—31no—
173C4×Dic5—31no—
174C4×Dic5—31no—
175C4×Dic5—31no—
176C4×Dic5—122no—
177C2×#168—61no—
178#532—151no—
179#431—151no—
180C4×C4⋊C4—151no—
181#327—151no—
182#327—151no—
183#327—151no—
184#327D1511yescharacteristic, complemented
185C22×C3×C5—21no—
186C22×C3×C5—21no—
187C22×C3×C5—41no—
188C22×C3×C5—41no—
189C22×C3×C5—41no—
190C22×C3×C5C2×C22⋊C411yescharacteristic
191C22×C3×C5C2×D811yescharacteristic
192C22×C3×C5C2×SD1611yescharacteristic
193C2×D15—41no—
194C2×D15—41no—
195C2×D15—41no—
196C3×C4×C5—21no—
197C3×C4×C5—21no—
198C3×C4×C5—42no—
199C3×C4×C5—41no—
200Dic15—21no—
201Dic15—42no—
202Dic15—41no—
203Dic15#10212yes—
204Dic15#10212yes—
205Dic15#10412yes—
206C2×C3×D4—21no—
207C2×C3×D4C4×D511yescharacteristic
208C22×C3×C4—21no—
209C22×C3×C4C22×D511yescharacteristic
210C2×#67—101no—
211C2×#67—101no—
212C2×#67—101no—
213C22×Dic3—51no—
214C22×Dic3—51no—
215C22×Dic3—101no—
216C22×Dic3—101no—
217#237—202no—
218#237—202no—
219C2×D12—51no—
220C2×C4×D3—101no—
221C2×Dic6—101no—
222C2×C3×C8—21no—
223C3×C4⋊C4C4×D511yescharacteristic
224C3×C22⋊C4—21no—
225#217—101no—
226(C2×D3)⋊C4—101no—
227(C2×D3)⋊C4—101no—
228C4⋊Dic3—51no—
229Dic3⋊C4—101no—
230Dic3⋊C4—104no—
231C4×Dic3—51no—
232C4×Dic3—51no—
233C4×Dic3—51no—
234C4×Dic3—51no—
235C4×Dic3—202no—
236C2×C3⋊C8—101no—
237C23×C5—21no—
238C23×C5D3×D411yescharacteristic
239C22×D5—61no—
240C5×D4—41no—
241C5×D4—41no—
242C5×D4—41no—
243C2×C4×C5—22no—
244C2×C4×C5—21no—
245C2×C4×C5—41no—
246C2×C4×C5—41no—
247C2×C4×C5—41no—
248C2×C4×C5C2×C4×D311yescharacteristic
249C2×C4×C5D3×D411yescharacteristic
250C22⋊D5—122no—
251C22⋊D5—122no—
252C22⋊D5—121no—
253C22⋊D5—121no—
254C2×Dic5—31no—
255C2×Dic5—31no—
256C2×Dic5—31no—
257C2×Dic5—32no—
258C2×Dic5—32no—
259C2×Dic5—31no—
260C2×Dic5—62no—
261C2×Dic5—62no—
262C2×Dic5—61no—
263C2×Dic5—122no—
264C2×Dic5—121no—
265C2×Dic5—121no—
266D20—121no—
267C4×D5—122no—
268Dic10—122no—
269C5×C8—41no—
270#168—121no—
271C2×#41—301no—
272C4⋊Q8—151no—
273#127—151no—
274#124—301no—
275#121—151no—
276#121—301no—
277#121C2×D1511yescharacteristic
278C4×D4—151no—
279C4×D4—151no—
280C4×D4—301no—
281C2×C4⋊C4—301no—
282C2×C42—151no—
283C2×C42—301no—
284C4⋊C8—301no—
285C22⋊C8—151no—
286C22⋊C8C2×D1511yescharacteristic
287C4×C8—301no—
288#95—151no—
289#95C2×D1511yescharacteristic
290C2×C3×C5—21no—
291C2×C3×C5—21no—
292C2×C3×C5—81no—
293C2×C3×C5#41011yescharacteristic
294C2×C3×C5C2×#10211yescharacteristic
295C2×C3×C5C2×#10411yescharacteristic
296D15—81no—
297C23×C3—21no—
298C23×C3D4×D511yescharacteristic
299C22×D3—101no—
300C3×D4—41no—
301C3×D4—41no—
302C3×D4—41no—
303C2×C3×C4—22no—
304C2×C3×C4—21no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4C2×C4×D511yescharacteristic
309C2×C3×C4D4×D511yescharacteristic
310#67—202no—
311#67—202no—
312#67—201no—
313#67—201no—
314C2×Dic3—51no—
315C2×Dic3—51no—
316C2×Dic3—51no—
317C2×Dic3—52no—
318C2×Dic3—52no—
319C2×Dic3—51no—
320C2×Dic3—102no—
321C2×Dic3—102no—
322C2×Dic3—101no—
323C2×Dic3—202no—
324C2×Dic3—201no—
325C2×Dic3—201no—
326D12—201no—
327C4×D3—202no—
328Dic6—202no—
329C3×C8—41no—
330C3⋊C8—201no—
331C22×C5—21no—
332C22×C5—21no—
333C22×C5—41no—
334C22×C5—41no—
335C22×C5—41no—
336C22×C5D3×C22⋊C411yescharacteristic
337C22×C5D3×D811yescharacteristic
338C22×C5D3×SD1611yescharacteristic
339C2×D5—121no—
340C2×D5—121no—
341C2×D5—121no—
342C4×C5—21no—
343C4×C5—21no—
344C4×C5—42no—
345C4×C5—41no—
346Dic5—32no—
347Dic5—32no—
348Dic5—32no—
349Dic5—61no—
350Dic5—122no—
351Dic5—121no—
352#41—602no—
353#41—602no—
354C2×Q8—301no—
355C2×D4—21no—
356C2×D4—151no—
357C2×D4—301no—
358C2×D4—301no—
359C2×D4—301no—
360C2×D4C4×D1511yescharacteristic
361C22×C4—21no—
362C22×C4—151no—
363C22×C4—151no—
364C22×C4—301no—
365C22×C4—301no—
366C22×C4—301no—
367C22×C4C22×D1511yescharacteristic
368C2×C8—21no—
369C2×C8—301no—
370C4⋊C4—151no—
371C4⋊C4—301no—
372C4⋊C4—304no—
373C4⋊C4C4×D1511yescharacteristic
374C22⋊C4—21no—
375C22⋊C4—301no—
376C22⋊C4—301no—
377C22⋊C4—301no—
378C42—151no—
379C42—151no—
380C42—151no—
381C42—151no—
382C42—602no—
383C3×C5#150211yescharacteristic, complemented, Hall
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—41no—
387C22×C3—41no—
388C22×C3—41no—
389C22×C3D5×C22⋊C411yescharacteristic
390C22×C3D5×D811yescharacteristic
391C22×C3D5×SD1611yescharacteristic
392C2×D3—201no—
393C2×D3—201no—
394C2×D3—201no—
395C3×C4—21no—
396C3×C4—21no—
397C3×C4—42no—
398C3×C4—41no—
399Dic3—52no—
400Dic3—52no—
401Dic3—52no—
402Dic3—101no—
403Dic3—202no—
404Dic3—201no—
405C2×C5—21no—
406C2×C5—21no—
407C2×C5—81no—
408C2×C5#474011yescharacteristic
409C2×C5D3×#10211yescharacteristic
410C2×C5D3×#10411yescharacteristic
411D5—241no—
412C23—21no—
413C23—301no—
414C23D4×D1511yescharacteristic
415Q8—602no—
416D4—41no—
417D4—41no—
418D4—41no—
419D4—601no—
420D4—602no—
421D4—602no—
422D4—601no—
423D4—601no—
424C2×C4—22no—
425C2×C4—21no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—151no—
430C2×C4—151no—
431C2×C4—151no—
432C2×C4—152no—
433C2×C4—152no—
434C2×C4—151no—
435C2×C4—302no—
436C2×C4—302no—
437C2×C4—301no—
438C2×C4—602no—
439C2×C4—602no—
440C2×C4—601no—
441C2×C4—601no—
442C2×C4C2×C4×D1511yescharacteristic
443C2×C4D4×D1511yescharacteristic
444C8—41no—
445C8—601no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—81no—
449C2×C3#6502911yescharacteristic
450C2×C3D5×#10211yescharacteristic
451C2×C3D5×#10411yescharacteristic
452D3—401no—
453C5#6827711yescharacteristic, complemented, Sylow
454C22—21no—
455C22—21no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—601no—
460C22—601no—
461C22—601no—
462C22C22⋊C4×D1511yescharacteristic
463C22D8×D1511yescharacteristic
464C22SD16×D1511yescharacteristic
465C4—21no—
466C4—21no—
467C4—42no—
468C4—41no—
469C4—152no—
470C4—152no—
471C4—152no—
472C4—301no—
473C4—602no—
474C4—601no—
475C3#1059907011yescharacteristic, complemented, Sylow
476C2—21no—
477C2—21no—
478C2—81no—
479C2—1201no—
480C2#1175084111yescharacteristic
481C2D15×#10211yescharacteristic
482C2D15×#10411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#327C2
socleC22×C3×C5C2×C22⋊C4
prime radical#11756355C2
cosocleC22×C3×C4×C5C23
hypercenter#327D15
hypocenterC3×C5#1502
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #11750819C2semidirect
3. #11750750C2semidirect
4. C3×C5×#327C2semidirect
5. #11746358C2semidirect
6. #11746291C2semidirect
7. #11746272C2semidirect
11. #91829C4semidirect
13. D4×Dic15C4semidirect
18. #91782C4semidirect
19. #91777C4semidirect
32. C5×#327D3semidirect
70. C3×#327D5semidirect
184. #327D15semidirect
383. C3×C5#1502semidirect
453. C5#68277semidirect
475. C3#10599070semidirect

Maximal subgroups

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

subgroupindex
#117563552
#117508192
#117507502
C3×C5×#3272
#117463582
#117462912
#117462722
#105990703
#682775