Finite Group Databasebeta

← #14471669

Subgroups — #14471669

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
1C3×#65877C211yesmaximal, characteristic, complemented
2#11752491C211yesmaximal, characteristic, complemented
3#11751120C211yesmaximal, characteristic, complemented
4C4×C5×#213C211yesmaximal, characteristic
5#11749065C212yesmaximal
6#11748998C212yesmaximal, complemented
7#11747288C212yesmaximal, complemented
8#11747142C212yesmaximal, complemented
9#11746921C211yesmaximal, characteristic, complemented
10#11746882C211yesmaximal, characteristic, complemented
11C3⋊C8×Dic10C211yesmaximal, characteristic, complemented
12#10611299—31nomaximal, Hall
13C3×C4×C5×D4C2211yescharacteristic
14C2×#6716C2212yes—
15#91758C2211yescharacteristic
16C2×C5×#213C2211yescharacteristic
17C4×C5×D12C2211yescharacteristic
18C3×D4×Dic5C2212yes—
19C2×C3×C4⋊Dic5—21no—
20C3×#4070—21no—
21C3×#4036C2212yes—
22C3×#4024—22no—
23C3×#4015C2211yescharacteristic
24C3×C4×Dic10C2211yescharacteristic
25#91373C2212yes—
26#91369—21no—
27#91342—22no—
28#91338—21no—
29#91333C2212yes—
30#91094C2212yes—
31C4⋊(C3⋊#168)C2211yescharacteristic
32C5×#832C2211yescharacteristic
33C5×#809C2211yescharacteristic
34C5×#807C2211yescharacteristic
35C4×C5×C3⋊C8C2211yescharacteristic
36#90986C2212yes—
37#90982C2212yes—
38#90974C2212yes—
39#90974C2212yes—
40#90966C2212yes—
41Dic5×C3⋊C8C2212yes—
42#83637—51nomaximal, Hall
43#65877D311yescharacteristic, complemented
44#65876—31no—
45C4×C5×D8—31no—
46#65442—32no—
47#65308—31no—
48#65297—31no—
49#65166—32no—
50#65057—32no—
51#65047—32no—
52#64970—31no—
53C8×Dic10—31no—
54C2×C3×C5×D4C2311yescharacteristic
55C22×C3×C4×C5—21no—
56C2×Dic30C2312yes—
57C2×C5×D12C2311yescharacteristic
58C2×C4×C5×D3—21no—
59C22×C3×Dic5—22no—
60C2×C3×Dic10—21no—
61C2×C3×Dic10D411yescharacteristic
62C3×C5×C4⋊C4C2311yescharacteristic
63C3×C5×C22⋊C4—21no—
64C3×C42×C5C2311yescharacteristic
65#6716—24no—
66C4⋊Dic15—21no—
67C4⋊Dic15—21no—
68C2×C3⋊#168C2312yes—
69C5×#213—22no—
70C5×(C2×D3)⋊C4—21no—
71C5×C4⋊Dic3C2311yescharacteristic
72C2×C5×C3⋊C8C2311yescharacteristic
73C2×C5×C3⋊C8C2311yescharacteristic
74C3×C22⋊Dic5—22no—
75C3×C4⋊Dic5—21no—
76C3×C4⋊Dic5—22no—
77C3×C4⋊Dic5D411yescharacteristic
78C3×C4⋊Dic5C2312yes—
79C3×#683—22no—
80C3×#683D412yes—
81C3×C4×Dic5C2312yes—
82#6669—22no—
83(C2×D3)⋊Dic5—22no—
84(C2×D3)⋊Dic5—22no—
85Dic3×Dic5—22no—
86C3×#554—51no—
87#5584—51no—
88#5093—51no—
89#5084—51no—
90#5068—52no—
91#5063—52no—
92Q8×C3⋊C8—51no—
93#5019—51no—
94C4×#214—52no—
95#5016—52no—
96C4×#213D511yescharacteristic
97C2×C5×D8—31no—
98C4×C5×D4—31no—
99C4×C5×D4C2×D311yescharacteristic
100#4082—32no—
101D4×Dic5C2×D312yes—
102C2×#687—32no—
103#4072—61no—
104C2×C4⋊Dic5—21no—
105#4070—21no—
106#4070—61no—
107#4036C2×D312yes—
108#4033—32no—
109#4025—62no—
110#4024—22no—
111#4015—31no—
112#4015C2×D311yescharacteristic
113C4×Dic10C2×D311yescharacteristic
114C5×#107—31no—
115C5×#102—31no—
116C5×#102—31no—
117C4×C5×C8—31no—
118#3964—32no—
119#3948—32no—
120#3948—32no—
121#3946—32no—
122C8×Dic5—32no—
123#3942—32no—
124#3940—32no—
125C4⋊#168—31no—
126#3360—151noSylow
127C23×C3×C5—21no—
128C22×C5×D3—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—22no—
137Dic30—22no—
138Dic30—22no—
139C2×C5×Dic3—21no—
140C5×D12—21no—
141C5×D12—21no—
142C4×C5×D3—42no—
143C2×C3×Dic5—22no—
144C2×C3×Dic5—82no—
145C2×C3×Dic5C2×D412yes—
146C2×C3×Dic5C2×D412yes—
147C3×Dic10—22no—
148C3×Dic10—81no—
149C3⋊#168—22no—
150C5×C3⋊C8—21no—
151C5×C3⋊C8—21no—
152C3×C4⋊Q8—51no—
153C3×#125—52no—
154C3×C22⋊Q8—102no—
155C3×C22⋊Q8—101no—
156C3×C4×Q8—51no—
157C3×C4×D4—52no—
158C3×C4×D4C2×D511yescharacteristic
159C2×C3×C4⋊C4—101no—
160#946—101no—
161C2×#214—52no—
162C2×#213C2×D511yescharacteristic
163#898—102no—
164#892—101no—
165#875—52no—
166C4×D12C2×D511yescharacteristic
167#869—51no—
168C4×Dic6—52no—
169#832C2×D511yescharacteristic
170#810—52no—
171#810—52no—
172#810—52no—
173#809—52no—
174#809C2×D511yescharacteristic
175#808—52no—
176#807C2×D511yescharacteristic
177C4⋊(C3⋊C8)—51no—
178C4⋊(C3⋊C8)—52no—
179C4×C3⋊C8—52no—
180C4×C3⋊C8C2×D511yescharacteristic
181C2×C5×D4—31no—
182C2×C5×D4C22×D311yescharacteristic
183C22×C4×C5—21no—
184C22×C4×C5—61no—
185C22×Dic5—22no—
186C2×Dic10—21no—
187C2×Dic10—32no—
188C2×Dic10#6711yescharacteristic
189C5×D8—62no—
190C2×C5×C8—31no—
191C2×C5×C8—31no—
192C5×C4⋊C4—31no—
193C5×C4⋊C4C22×D311yescharacteristic
194C5×C22⋊C4—21no—
195C5×C22⋊C4—61no—
196C42×C5C22×D311yescharacteristic
197C22⋊Dic5—22no—
198C22⋊Dic5—62no—
199C22⋊Dic5—62no—
200#687—64no—
201C4⋊Dic5—21no—
202C4⋊Dic5—22no—
203C4⋊Dic5—61no—
204C4⋊Dic5—61no—
205C4⋊Dic5#6711yescharacteristic
206C4⋊Dic5C22×D312yes—
207#683—22no—
208#683—62no—
209#683#6712yes—
210C4×Dic5—62no—
211C4×Dic5C22×D312yes—
212C2×#168—32no—
213#556—151no—
214#554—51no—
215#488—152no—
216#487—151no—
217#479—152no—
218#476—151no—
219#463—152no—
220#461—151no—
221C8×Q8—151no—
222C4×SD16—152no—
223C4×D8—31no—
224C22×C3×C5—22no—
225C22×C3×C5—41no—
226C22×C3×C5—41no—
227C22×C3×C5C22×D411yescharacteristic
228C2×C5×D3—41no—
229C2×C5×D3—41no—
230C2×C5×D3—41no—
231C3×C4×C5—21no—
232C3×C4×C5—41no—
233C3×C4×C5#13512yes—
234C3×C4×C5C2×#4111yescharacteristic
235C3×C4×C52−1+411yescharacteristic
236Dic15—42no—
237C3×Dic5—22no—
238C3×Dic5—22no—
239C3×Dic5—42no—
240C5×Dic3—41no—
241C2×C3×Q8—51no—
242C2×C3×Q8—101no—
243C2×C3×D4C22×D511yescharacteristic
244C22×C3×C4—21no—
245C22×C3×C4—102no—
246C2×D12C22×D511yescharacteristic
247C2×C4×D3—21no—
248C2×Dic6—52no—
249C3×C4⋊C4—52no—
250C3×C4⋊C4—51no—
251C3×C4⋊C4—52no—
252C3×C4⋊C4—102no—
253C3×C4⋊C4—102no—
254C3×C4⋊C4—101no—
255C3×C4⋊C4C22×D511yescharacteristic
256C3×C22⋊C4—21no—
257C3×C22⋊C4—102no—
258C3×C42—52no—
259C3×C42C22×D511yescharacteristic
260#214—104no—
261#213—22no—
262(C2×D3)⋊C4—21no—
263(C2×D3)⋊C4—102no—
264(C2×D3)⋊C4—102no—
265C4⋊Dic3—101no—
266C4⋊Dic3—101no—
267C4⋊Dic3C22×D511yescharacteristic
268Dic3⋊C4—102no—
269C4×Dic3—102no—
270C2×C3⋊C8—52no—
271C2×C3⋊C8C22×D511yescharacteristic
272C2×C3⋊C8C22×D511yescharacteristic
273C23×C5—21no—
274C23×C5—61no—
275C5×D4—21no—
276C5×D4—61no—
277C5×D4—61no—
278C5×D4#23912yes—
279C2×C4×C5—21no—
280C2×C4×C5—42no—
281C2×C4×C5—61no—
282C2×C4×C5—122no—
283C2×C4×C5C2×#6711yescharacteristic
284C2×C4×C5C2×#6711yescharacteristic
285C2×C4×C5C23×D311yescharacteristic
286C2×Dic5—22no—
287C2×Dic5—62no—
288C2×Dic5—82no—
289C2×Dic5C2×#6712yes—
290C2×Dic5C2×#6712yes—
291Dic10—22no—
292Dic10—62no—
293Dic10—62no—
294Dic10—81no—
295C5×C8—61no—
296C5×C8—61no—
297#168—62no—
298C2×SD16—152no—
299C2×D8—31no—
300C4⋊Q8—51no—
301C4⋊Q8—151no—
302#126—302no—
303#125—52no—
304#124—152no—
305C22⋊Q8—102no—
306C22⋊Q8—101no—
307C22⋊Q8—301no—
308C4×Q8—51no—
309C4×Q8—152no—
310C4×D4—31no—
311C4×D4—52no—
312C4×D4D3×D511yescharacteristic
313#117—301no—
314C2×C4⋊C4—101no—
315#107—31no—
316#106—152no—
317C4⋊C8—152no—
318C4⋊C8—151no—
319#103—152no—
320#103—152no—
321#103—152no—
322#102—31no—
323#102—31no—
324#102—152no—
325C4×C8—31no—
326C4×C8—152no—
327C2×C3×C5—42no—
328C2×C3×C5#54811yescharacteristic
329C2×C3×C5C2×#13511yescharacteristic
330C2×C3×C5#57711yescharacteristic
331C5×D3—81no—
332C23×C3—21no—
333C22×D3—21no—
334C3×Q8—102no—
335C3×Q8—401no—
336C3×D4—21no—
337C3×D4#70912yes—
338C2×C3×C4—21no—
339C2×C3×C4—42no—
340C2×C3×C4—52no—
341C2×C3×C4—52no—
342C2×C3×C4—102no—
343C2×C3×C4—402no—
344C2×C3×C4D4×D511yescharacteristic
345C2×C3×C4D4×D511yescharacteristic
346C2×C3×C4C23×D511yescharacteristic
347C2×Dic3—21no—
348C2×Dic3—102no—
349D12—21no—
350D12—21no—
351C4×D3—42no—
352Dic6—102no—
353Dic6—102no—
354C3⋊C8—21no—
355C3⋊C8—21no—
356C3⋊C8—102no—
357C22×C5—22no—
358C22×C5—41no—
359C22×C5—41no—
360C22×C5—121no—
361C22×C5—121no—
362C22×C5—121no—
363C22×C5C22×#6711yescharacteristic
364C4×C5—21no—
365C4×C5—41no—
366C4×C5—121no—
367C4×C5#95012yes—
368C4×C5C2×#23911yescharacteristic
369C4×C5#100711yescharacteristic
370Dic5—22no—
371Dic5—22no—
372Dic5—42no—
373Dic5—122no—
374C2×Q8—51no—
375C2×Q8—101no—
376C2×Q8—152no—
377C2×D4—31no—
378C2×D4C2×D3×D511yescharacteristic
379C22×C4—21no—
380C22×C4—61no—
381C22×C4—102no—
382SD16—304no—
383D8—62no—
384C2×C8—31no—
385C2×C8—31no—
386C2×C8—152no—
387C4⋊C4—31no—
388C4⋊C4—51no—
389C4⋊C4—52no—
390C4⋊C4—52no—
391C4⋊C4—102no—
392C4⋊C4—102no—
393C4⋊C4—101no—
394C4⋊C4—302no—
395C4⋊C4—301no—
396C4⋊C4—301no—
397C4⋊C4C2×D3×D511yescharacteristic
398C22⋊C4—21no—
399C22⋊C4—61no—
400C22⋊C4—102no—
401C22⋊C4—302no—
402C22⋊C4—302no—
403C42—52no—
404C42—302no—
405C42C2×D3×D511yescharacteristic
406C3×C5#336011yescharacteristic, complemented, Hall
407C22×C3—22no—
408C22×C3—41no—
409C22×C3—41no—
410C22×C3C2×D4×D511yescharacteristic
411C2×D3—41no—
412C2×D3—41no—
413C2×D3—41no—
414C3×C4—21no—
415C3×C4—41no—
416C3×C4—102no—
417C3×C4—102no—
418C3×C4—202no—
419C3×C4#405812yes—
420C3×C4C2×#70911yescharacteristic
421C3×C4#415011yescharacteristic
422Dic3—41no—
423Dic3—202no—
424C2×C5—42no—
425C2×C5—241no—
426C2×C5#581711yescharacteristic
427C2×C5C2×#95011yescharacteristic
428C2×C5#583611yescharacteristic
429C23—21no—
430C23—61no—
431Q8—102no—
432Q8—302no—
433Q8—302no—
434Q8—401no—
435D4—21no—
436D4—61no—
437D4—61no—
438D4#676912yes—
439C2×C4—21no—
440C2×C4—42no—
441C2×C4—52no—
442C2×C4—52no—
443C2×C4—61no—
444C2×C4—102no—
445C2×C4—122no—
446C2×C4—302no—
447C2×C4—402no—
448C2×C4D5×#6711yescharacteristic
449C2×C4D5×#6711yescharacteristic
450C2×C4C22×D3×D511yescharacteristic
451C8—61no—
452C8—61no—
453C8—302no—
454C2×C3—42no—
455C2×C3#6588611yescharacteristic
456C2×C3C2×#405811yescharacteristic
457C2×C3#6610411yescharacteristic
458D3—81no—
459C5#8363711yescharacteristic, complemented, Sylow
460C22—22no—
461C22—41no—
462C22—41no—
463C22—121no—
464C22—121no—
465C22—121no—
466C22C2×D5×#6711yescharacteristic
467C4—21no—
468C4—41no—
469C4—102no—
470C4—102no—
471C4—121no—
472C4—202no—
473C4—602no—
474C4#9149012yes—
475C4#9200411yescharacteristic
476C4C2×#676911yescharacteristic
477C3#1061129911yescharacteristic, complemented, Sylow
478C2—42no—
479C2—241no—
480C2#1175432111yescharacteristic
481C2C2×#9149011yescharacteristic
482C2#1175533711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#213C22
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. C3×#65877C2semidirect
2. #11752491C2semidirect
3. #11751120C2semidirect
6. #11748998C2semidirect
7. #11747288C2semidirect
8. #11747142C2semidirect
9. #11746921C2semidirect
10. #11746882C2semidirect
11. C3⋊C8×Dic10C2semidirect
43. #65877D3semidirect
406. C3×C5#3360semidirect
459. C5#83637semidirect
477. C3#10611299semidirect

Maximal subgroups

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

subgroupindex
C3×#658772
#117524912
#117511202
C4×C5×#2132
#117490652
#117489982
#117472882
#117471422
#117469212
#117468822
C3⋊C8×Dic102
#106112993
#836375