Finite Group Databasebeta

← #14471672

Subgroups — #14471672

Order 1920.

700 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
1C5×#5543C211yesmaximal, characteristic, complemented
2#11752483C211yesmaximal, characteristic, complemented
3C4×#6715C211yesmaximal, characteristic
4C3×#65308C211yesmaximal, characteristic, complemented
5#11749080C212yesmaximal
6Dic3×#687C212yesmaximal, complemented
7#11747379C212yesmaximal, complemented
8#11747296C212yesmaximal, complemented
9#11746924C211yesmaximal, characteristic, complemented
10#11746885C211yesmaximal, characteristic, complemented
11#11746857C211yesmaximal, characteristic, complemented
12#10615368—31nomaximal, Hall
13C3×C4×C5×D4C2211yescharacteristic
14C2×#6715C2211yescharacteristic
15C4×D60C2211yescharacteristic
16C5×D4×Dic3C2212yes—
17C2×C5×C4⋊Dic3—21no—
18C5×#924—21no—
19C5×#890C2212yes—
20C5×#878—22no—
21C5×#869C2211yescharacteristic
22C4×C5×Dic6C2211yescharacteristic
23C2×C3×#687C2212yes—
24C3×#4015C2211yescharacteristic
25#91383—21no—
26#91374C2212yes—
27#91347—21no—
28#91345—22no—
29Dic3×Dic10C2212yes—
30#91116C2211yescharacteristic
31#91093C2211yescharacteristic
32#91091C2211yescharacteristic
33C4×C3⋊#168C2211yescharacteristic
34C3×#3942C2212yes—
35C3×C4⋊#168C2211yescharacteristic
36#90985C2212yes—
37Dic3⋊#168C2212yes—
38#90970C2212yes—
39#90970C2212yes—
40#90969C2212yes—
41Dic3×#168C2212yes—
42#80415—51nomaximal, Hall
43C5×#554—31no—
44#65918—31no—
45#65382—31no—
46#65373—31no—
47#65357—32no—
48#65352—32no—
49Q8×#168—31no—
50#65308D311yescharacteristic, complemented
51C4×#687—32no—
52#65305—32no—
53C4×#686—31no—
54C2×C3×C5×D4C2311yescharacteristic
55C22×C3×C4×C5—21no—
56C2×D60C2311yescharacteristic
57C2×C4×D15—21no—
58C22×C5×Dic3—22no—
59C2×C5×Dic6—21no—
60C2×C5×Dic6D411yescharacteristic
61C2×C3×Dic10C2312yes—
62C3×C5×C4⋊C4C2311yescharacteristic
63C3×C5×C22⋊C4—21no—
64C3×C42×C5C2311yescharacteristic
65#6715—22no—
66#6714—21no—
67C4⋊Dic15C2311yescharacteristic
68C2×C3⋊#168C2311yescharacteristic
69C2×C3⋊#168C2311yescharacteristic
70C5×#217—22no—
71C5×C4⋊Dic3—21no—
72C5×C4⋊Dic3—22no—
73C5×C4⋊Dic3D411yescharacteristic
74C5×C4⋊Dic3C2312yes—
75C5×Dic3⋊C4—22no—
76C5×Dic3⋊C4D412yes—
77C4×C5×Dic3C2312yes—
78C3×#687—24no—
79C3×C4⋊Dic5—21no—
80C3×C4⋊Dic5—21no—
81C2×C3×#168C2312yes—
82#6668—22no—
83#6667—22no—
84#6667—22no—
85Dic3×Dic5—22no—
86#5732—51no—
87#5543D511yescharacteristic, complemented
88C3×#461—51no—
89#5165—52no—
90Dic3×SD16—52no—
91#5079—51no—
92C4×#213—51no—
93#4842—51no—
94#4830—51no—
95#4800—52no—
96#4799—52no—
97C5×C4⋊Q8—31no—
98C5×#125—32no—
99C5×C22⋊Q8—62no—
100C5×C22⋊Q8—61no—
101C4×C5×Q8—31no—
102C4×C5×D4—32no—
103C4×C5×D4C2×D311yescharacteristic
104C2×C5×C4⋊C4—61no—
105#4092—61no—
106C2×#687C2×D312yes—
107C2×#686—31no—
108#4044—62no—
109#4038—61no—
110#4021—32no—
111C4×D20—31no—
112#4015C2×D311yescharacteristic
113C4×Dic10—32no—
114#3964—31no—
115#3942—32no—
116#3942—32no—
117#3942C2×D312yes—
118#3941—31no—
119#3941—32no—
120#3940—32no—
121#3939—31no—
122C4⋊#168—32no—
123C4⋊#168C2×D311yescharacteristic
124C4×#168—31no—
125C4×#168—32no—
126#3360—151noSylow
127C23×C3×C5—21no—
128C22×D15—21no—
129C3×C5×D4—21no—
130C3×C5×D4#4112yes—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5—42no—
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2411yescharacteristic
136C2×Dic15—21no—
137D60—21no—
138D60—21no—
139C4×D15—42no—
140C2×C5×Dic3—22no—
141C2×C5×Dic3—82no—
142C2×C5×Dic3C2×D412yes—
143C2×C5×Dic3C2×D412yes—
144C5×Dic6—22no—
145C5×Dic6—81no—
146C2×C3×Dic5—22no—
147C3×Dic10—22no—
148C3×Dic10—22no—
149C3⋊#168—21no—
150C3⋊#168—21no—
151C3×#168—22no—
152C2×C3×SD16—52no—
153C3×C4⋊Q8—51no—
154C3×C4×D4C2×D511yescharacteristic
155#947—52no—
156Q8×Dic3—52no—
157D4×Dic3C2×D512yes—
158C2×#213—51no—
159C2×C4⋊Dic3—21no—
160#924—21no—
161#898—102no—
162#897—101no—
163#892—101no—
164#890C2×D512yes—
165#878—22no—
166C4×D12—51no—
167#869C2×D511yescharacteristic
168C4×Dic6C2×D511yescharacteristic
169C3×C4⋊C8—51no—
170C3×#103—52no—
171#835—52no—
172#835—52no—
173#832—51no—
174#821—52no—
175#817—52no—
176Dic3⋊C8—52no—
177C8×Dic3—52no—
178#809—51no—
179#807—51no—
180C4×C3⋊C8—51no—
181C2×C5×Q8—31no—
182C2×C5×Q8—61no—
183C2×C5×D4C22×D311yescharacteristic
184C22×C4×C5—21no—
185C22×C4×C5—62no—
186C2×D20—31no—
187C2×C4×D5—61no—
188C2×Dic10C22×D312yes—
189C5×C4⋊C4—31no—
190C5×C4⋊C4—32no—
191C5×C4⋊C4—32no—
192C5×C4⋊C4—62no—
193C5×C4⋊C4—62no—
194C5×C4⋊C4—61no—
195C5×C4⋊C4C22×D311yescharacteristic
196C5×C22⋊C4—21no—
197C5×C22⋊C4—62no—
198C42×C5—32no—
199C42×C5C22×D311yescharacteristic
200#687—24no—
201#686—62no—
202#685—62no—
203#685—62no—
204#685—61no—
205C4⋊Dic5—21no—
206C4⋊Dic5—21no—
207C4⋊Dic5—31no—
208#683—62no—
209C4×Dic5—62no—
210C2×#168—31no—
211C2×#168—31no—
212C2×#168C22×D312yes—
213#556—151no—
214#554—31no—
215#488—152no—
216#487—151no—
217#479—152no—
218#476—151no—
219#463—152no—
220#461—51no—
221C8×Q8—151no—
222C4×SD16—152no—
223C4×D8—151no—
224C22×C3×C5—22no—
225C22×C3×C5—41no—
226C22×C3×C5—41no—
227C22×C3×C5C22×D411yescharacteristic
228C2×D15—41no—
229C2×D15—41no—
230C2×D15—41no—
231C3×C4×C5—21no—
232C3×C4×C5—41no—
233C3×C4×C5#13512yes—
234C3×C4×C5C2×#4111yescharacteristic
235C3×C4×C52−1+411yescharacteristic
236Dic15—41no—
237C3×Dic5—42no—
238C5×Dic3—22no—
239C5×Dic3—22no—
240C5×Dic3—42no—
241C2×C3×Q8—52no—
242C2×C3×D4C22×D511yescharacteristic
243C22×C3×C4—21no—
244C22×Dic3—22no—
245C2×D12—51no—
246C2×C4×D3—101no—
247C2×Dic6—21no—
248C2×Dic6C22⋊D511yescharacteristic
249C3×SD16—104no—
250C2×C3×C8—52no—
251C3×C4⋊C4—101no—
252C3×C4⋊C4—101no—
253C3×C4⋊C4C22×D511yescharacteristic
254C3×C22⋊C4—21no—
255C3×C42C22×D511yescharacteristic
256#217—22no—
257#213—102no—
258(C2×D3)⋊C4—101no—
259(C2×D3)⋊C4—102no—
260(C2×D3)⋊C4—102no—
261C4⋊Dic3—21no—
262C4⋊Dic3—22no—
263C4⋊Dic3—51no—
264C4⋊Dic3—102no—
265C4⋊Dic3C22⋊D511yescharacteristic
266C4⋊Dic3C22×D512yes—
267Dic3⋊C4—22no—
268Dic3⋊C4C22⋊D512yes—
269C4×Dic3—102no—
270C4×Dic3C22×D512yes—
271C2×C3⋊C8—51no—
272C2×C3⋊C8—51no—
273C23×C5—21no—
274C22×D5—61no—
275C5×Q8—62no—
276C5×Q8—241no—
277C5×D4—21no—
278C5×D4#23712yes—
279C2×C4×C5—21no—
280C2×C4×C5—32no—
281C2×C4×C5—32no—
282C2×C4×C5—42no—
283C2×C4×C5—62no—
284C2×C4×C5—242no—
285C2×C4×C5D3×D411yescharacteristic
286C2×C4×C5D3×D411yescharacteristic
287C2×C4×C5C23×D311yescharacteristic
288C2×Dic5—22no—
289C2×Dic5—61no—
290D20—61no—
291D20—61no—
292C4×D5—122no—
293Dic10—22no—
294Dic10—22no—
295#168—22no—
296#168—61no—
297#168—61no—
298C2×SD16—52no—
299C2×D8—151no—
300C4⋊Q8—31no—
301C4⋊Q8—51no—
302#126—302no—
303#125—32no—
304#124—152no—
305C22⋊Q8—62no—
306C22⋊Q8—61no—
307C22⋊Q8—301no—
308C4×Q8—31no—
309C4×Q8—152no—
310C4×D4—32no—
311C4×D4—151no—
312C4×D4D3×D511yescharacteristic
313#117—301no—
314C2×C4⋊C4—61no—
315#107—151no—
316#106—152no—
317C4⋊C8—51no—
318C4⋊C8—152no—
319#103—52no—
320#103—152no—
321#103—152no—
322#102—152no—
323#102—151no—
324#102—151no—
325C4×C8—152no—
326C4×C8—151no—
327C2×C3×C5—42no—
328C2×C3×C5#54811yescharacteristic
329C2×C3×C5C2×#13511yescharacteristic
330C2×C3×C5#57711yescharacteristic
331D15—81no—
332C23×C3—21no—
333C22×D3—101no—
334C3×Q8—102no—
335C3×Q8—102no—
336C3×D4—21no—
337C3×D4#71312yes—
338C2×C3×C4—21no—
339C2×C3×C4—42no—
340C2×C3×C4—102no—
341C2×C3×C4C2×C22⋊D511yescharacteristic
342C2×C3×C4C2×C22⋊D511yescharacteristic
343C2×C3×C4C23×D511yescharacteristic
344C2×Dic3—22no—
345C2×Dic3—82no—
346C2×Dic3—101no—
347C2×Dic3C2×C22⋊D512yes—
348C2×Dic3C2×C22⋊D512yes—
349D12—101no—
350D12—101no—
351C4×D3—202no—
352Dic6—22no—
353Dic6—81no—
354C3×C8—102no—
355C3⋊C8—101no—
356C3⋊C8—101no—
357C22×C5—22no—
358C22×C5—41no—
359C22×C5—41no—
360C22×C5C2×D3×D411yescharacteristic
361C2×D5—121no—
362C2×D5—121no—
363C2×D5—121no—
364C4×C5—21no—
365C4×C5—41no—
366C4×C5—62no—
367C4×C5—62no—
368C4×C5—122no—
369C4×C5#91612yes—
370C4×C5C2×#23711yescharacteristic
371C4×C5#101011yescharacteristic
372Dic5—42no—
373Dic5—121no—
374C2×Q8—31no—
375C2×Q8—52no—
376C2×Q8—61no—
377C2×D4—151no—
378C2×D4C2×D3×D511yescharacteristic
379C22×C4—21no—
380C22×C4—62no—
381C22×C4—301no—
382SD16—104no—
383D8—302no—
384C2×C8—52no—
385C2×C8—151no—
386C2×C8—151no—
387C4⋊C4—31no—
388C4⋊C4—32no—
389C4⋊C4—32no—
390C4⋊C4—62no—
391C4⋊C4—62no—
392C4⋊C4—61no—
393C4⋊C4—101no—
394C4⋊C4—101no—
395C4⋊C4—151no—
396C4⋊C4—302no—
397C4⋊C4C2×D3×D511yescharacteristic
398C22⋊C4—21no—
399C22⋊C4—62no—
400C22⋊C4—302no—
401C22⋊C4—302no—
402C22⋊C4—301no—
403C42—32no—
404C42—302no—
405C42C2×D3×D511yescharacteristic
406C3×C5#336011yescharacteristic, complemented, Hall
407C22×C3—22no—
408C22×C3—41no—
409C22×C3—41no—
410C22×C3C22×C22⋊D511yescharacteristic
411C2×D3—201no—
412C2×D3—201no—
413C2×D3—201no—
414C3×C4—21no—
415C3×C4—41no—
416C3×C4—202no—
417C3×C4#409612yes—
418C3×C4C2×#71311yescharacteristic
419C3×C4#414711yescharacteristic
420Dic3—22no—
421Dic3—22no—
422Dic3—42no—
423Dic3—201no—
424C2×C5—42no—
425C2×C5#559811yescharacteristic
426C2×C5C2×#91611yescharacteristic
427C2×C5#577811yescharacteristic
428D5—241no—
429C23—21no—
430C23—301no—
431Q8—62no—
432Q8—102no—
433Q8—102no—
434Q8—241no—
435D4—21no—
436D4—301no—
437D4—301no—
438D4#676612yes—
439C2×C4—21no—
440C2×C4—32no—
441C2×C4—32no—
442C2×C4—42no—
443C2×C4—62no—
444C2×C4—102no—
445C2×C4—242no—
446C2×C4—301no—
447C2×C4—602no—
448C2×C4D3×C22⋊D511yescharacteristic
449C2×C4D3×C22⋊D511yescharacteristic
450C2×C4C22×D3×D511yescharacteristic
451C8—102no—
452C8—301no—
453C8—301no—
454C2×C3—42no—
455C2×C3#6615111yescharacteristic
456C2×C3C2×#409611yescharacteristic
457C2×C3#6617011yescharacteristic
458D3—401no—
459C5#8041511yescharacteristic, complemented, Sylow
460C22—22no—
461C22—41no—
462C22—41no—
463C22—601no—
464C22—601no—
465C22—601no—
466C22C2×D3×C22⋊D511yescharacteristic
467C4—21no—
468C4—41no—
469C4—62no—
470C4—62no—
471C4—122no—
472C4—202no—
473C4—601no—
474C4#9149512yes—
475C4C2×#676611yescharacteristic
476C4#9200011yescharacteristic
477C3#1061536811yescharacteristic, complemented, Sylow
478C2—42no—
479C2—1201no—
480C2#1175434411yescharacteristic
481C2C2×#9149511yescharacteristic
482C2#1175534011yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×#6715C22
hypercenterC4×D4D3×D5
hypocenterC3×C5#3360
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C5×#5543C2semidirect
2. #11752483C2semidirect
4. C3×#65308C2semidirect
6. Dic3×#687C2semidirect
7. #11747379C2semidirect
8. #11747296C2semidirect
9. #11746924C2semidirect
10. #11746885C2semidirect
11. #11746857C2semidirect
50. #65308D3semidirect
87. #5543D5semidirect
406. C3×C5#3360semidirect
459. C5#80415semidirect
477. C3#10615368semidirect

Maximal subgroups

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

subgroupindex
C5×#55432
#117524832
C4×#67152
C3×#653082
#117490802
Dic3×#6872
#117473792
#117472962
#117469242
#117468852
#117468572
#106153683
#804155