Finite Group Databasebeta

← #14471553

Subgroups — #14471553

Order 1920.

740 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×D4×Dic6C211yesmaximal, characteristic
2#11752482C211yesmaximal, characteristic, complemented
3C4×#6716C211yesmaximal, characteristic
4C3×#65308C211yesmaximal, characteristic
5#11749114C212yesmaximal
6Dic3×#687C212yesmaximal
7#11747422C212yesmaximal, complemented
8#11747293C212yesmaximal, complemented
9#11746946C211yesmaximal, characteristic, complemented
10#11746924C211yesmaximal, characteristic, complemented
11#11746857C211yesmaximal, characteristic, complemented
12#10615299—31nomaximal, Hall
13C22×C5×Dic6—21no—
14C3×C4×C5×D4C2211yescharacteristic
15C2×#6716C2211yescharacteristic
16C4×Dic30C2211yescharacteristic
17C5×D4×Dic3C2212yes—
18C5×#924—21no—
19C5×#888C2212yes—
20C5×#878—22no—
21C5×#869C2211yescharacteristic
22C4×C5×Dic6C2211yescharacteristic
23C2×C3×#687C2212yes—
24C3×#4015C2211yescharacteristic
25#91389C2212yes—
26#91384—21no—
27#91346—22no—
28#91344—21no—
29Dic3×Dic10C2212yes—
30#91116C2211yescharacteristic
31#91094C2211yescharacteristic
32#91092C2211yescharacteristic
33C4×C3⋊#168C2211yescharacteristic
34C3×#3942C2212yes—
35C3×C4⋊#168C2211yescharacteristic
36#90985C2212yes—
37Dic3⋊#168C2212yes—
38#90975C2212yes—
39#90970C2212yes—
40#90970C2212yes—
41Dic3×#168C2212yes—
42#80414—51nomaximal, Hall
43C5×D4×Q8—31no—
44#65904—31no—
45#65383—32no—
46#65383—31no—
47#65382—31no—
48#65382—32no—
49Q8×#168—31no—
50#65308—32no—
51#65308D311yescharacteristic
52C4×#687—32no—
53C4×#687—31no—
54C2×C3×C5×D4C2311yescharacteristic
55C22×C3×C4×C5—21no—
56C2×Dic30C2311yescharacteristic
57C22×C5×Dic3—22no—
58C2×C5×Dic6—21no—
59C2×C5×Dic6—22no—
60C2×C5×Dic6—44no—
61C2×C5×Dic6D411yescharacteristic
62C2×C3×Dic10C2312yes—
63C3×C5×C4⋊C4C2311yescharacteristic
64C3×C5×C22⋊C4—21no—
65C3×C42×C5C2311yescharacteristic
66#6716—22no—
67C4⋊Dic15C2311yescharacteristic
68#6712—21no—
69C4×Dic15—21no—
70C2×C3⋊#168C2311yescharacteristic
71C2×C3⋊#168C2311yescharacteristic
72C5×#217—22no—
73C5×C4⋊Dic3—21no—
74C5×C4⋊Dic3D411yescharacteristic
75C5×C4⋊Dic3C2312yes—
76C5×Dic3⋊C4—22no—
77C5×Dic3⋊C4D412yes—
78C4×C5×Dic3C2312yes—
79C3×#687—24no—
80C3×C4⋊Dic5—21no—
81C3×C4⋊Dic5—21no—
82C2×C3×#168C2312yes—
83Dic3⋊Dic5—22no—
84Dic3⋊Dic5—22no—
85#6668—22no—
86Dic3×Dic5—22no—
87#5721—51no—
88D4×Dic6D511yescharacteristic
89C3×#461—51no—
90#5162—52no—
91Dic3×SD16—52no—
92#5079—51no—
93C4×#214—51no—
94#4851—51no—
95#4830—51no—
96#4792—52no—
97#4791—52no—
98C22×C5×Q8—61no—
99C5×C4⋊Q8—32no—
100C5×C4⋊Q8—31no—
101C5×C22⋊Q8—62no—
102C5×C22⋊Q8—61no—
103C4×C5×Q8—31no—
104C4×C5×D4—32no—
105C4×C5×D4C2×D311yescharacteristic
106Q8×Dic5—61no—
107C2×#687—31no—
108C2×#687C2×D312yes—
109#4036—62no—
110#4036—61no—
111#4015—32no—
112#4015C2×D311yescharacteristic
113C4×Dic10—32no—
114C4×Dic10—31no—
115#3964—31no—
116#3942—32no—
117#3942—32no—
118#3942—31no—
119#3942—32no—
120#3942C2×D312yes—
121#3940—31no—
122#3940—32no—
123C4⋊#168—32no—
124C4⋊#168C2×D311yescharacteristic
125C4×#168—31no—
126C4×#168—32no—
127#3359—151noSylow
128C23×C3×C5—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—
137C2×Dic15—21no—
138Dic30—21no—
139Dic30—21no—
140C2×C5×Dic3—22no—
141C2×C5×Dic3—44no—
142C2×C5×Dic3C2×D412yes—
143C2×C5×Dic3C2×D412yes—
144C5×Dic6—42no—
145C5×Dic6—44no—
146C5×Dic6SD1614yescomplemented
147C2×C3×Dic5—22no—
148C3×Dic10—22no—
149C3×Dic10—22no—
150C3⋊#168—21no—
151C3⋊#168—21no—
152C3×#168—22no—
153C22×Dic6—21no—
154C2×C3×SD16—52no—
155C3×C4⋊Q8—51no—
156C3×C4×D4C2×D511yescharacteristic
157Q8×Dic3—52no—
158#944—52no—
159D4×Dic3C2×D512yes—
160C2×#214—51no—
161#924—21no—
162#890—101no—
163#889—102no—
164#888C2×D512yes—
165#887—101no—
166#878—22no—
167#869C2×D511yescharacteristic
168C4×Dic6—51no—
169C4×Dic6C2×D511yescharacteristic
170C3×C4⋊C8—51no—
171C3×#103—52no—
172#835—52no—
173#835—52no—
174#832—51no—
175#817—52no—
176#816—52no—
177Dic3⋊C8—52no—
178C8×Dic3—52no—
179#810—51no—
180#808—51no—
181C4×C3⋊C8—51no—
182C2×C5×Q8—31no—
183C2×C5×Q8—62no—
184C2×C5×Q8—61no—
185C2×C5×Q8—124no—
186C2×C5×D4C22×D311yescharacteristic
187C22×C4×C5—21no—
188C22×C4×C5—62no—
189C2×Dic10—31no—
190C2×Dic10C22×D312yes—
191C5×C4⋊C4—32no—
192C5×C4⋊C4—31no—
193C5×C4⋊C4—32no—
194C5×C4⋊C4—62no—
195C5×C4⋊C4—61no—
196C5×C4⋊C4C22×D311yescharacteristic
197C5×C22⋊C4—21no—
198C5×C22⋊C4—62no—
199C42×C5—32no—
200C42×C5C22×D311yescharacteristic
201#687—24no—
202#687—62no—
203C4⋊Dic5—21no—
204C4⋊Dic5—21no—
205C4⋊Dic5—31no—
206C4⋊Dic5—62no—
207C4⋊Dic5—62no—
208#683—62no—
209#683—61no—
210C4×Dic5—62no—
211C4×Dic5—61no—
212C2×#168—31no—
213C2×#168—31no—
214C2×#168C22×D312yes—
215#557—151no—
216D4×Q8—31no—
217#487—152no—
218#487—151no—
219#475—152no—
220#475—151no—
221#461—51no—
222#461—152no—
223C8×Q8—151no—
224C4×SD16—152no—
225C4×SD16—151no—
226C22×C3×C5—22no—
227C22×C3×C5—41no—
228C22×C3×C5—41no—
229C22×C3×C5C22×D411yescharacteristic
230C3×C4×C5—21no—
231C3×C4×C5—41no—
232C3×C4×C5C2×SD1612yes—
233C3×C4×C5C2×#4111yescharacteristic
234C3×C4×C52−1+411yescharacteristic
235Dic15—41no—
236Dic15—41no—
237C3×Dic5—42no—
238C5×Dic3—22no—
239C5×Dic3—42no—
240C5×Dic3C2×SD1614yes—
241C2×C3×Q8—52no—
242C2×C3×D4C22×D511yescharacteristic
243C22×C3×C4—21no—
244C22×Dic3—22no—
245C2×Dic6—21no—
246C2×Dic6—22no—
247C2×Dic6—44no—
248C2×Dic6—51no—
249C2×Dic6C22⋊D511yescharacteristic
250C3×SD16—104no—
251C2×C3×C8—52no—
252C3×C4⋊C4—101no—
253C3×C4⋊C4—101no—
254C3×C4⋊C4C22×D511yescharacteristic
255C3×C22⋊C4—21no—
256C3×C42C22×D511yescharacteristic
257#217—22no—
258#214—102no—
259C4⋊Dic3—21no—
260C4⋊Dic3—51no—
261C4⋊Dic3—102no—
262C4⋊Dic3C22⋊D511yescharacteristic
263C4⋊Dic3C22×D512yes—
264Dic3⋊C4—22no—
265Dic3⋊C4—101no—
266Dic3⋊C4—102no—
267Dic3⋊C4—102no—
268Dic3⋊C4C22⋊D512yes—
269C4×Dic3—101no—
270C4×Dic3—102no—
271C4×Dic3C22×D512yes—
272C2×C3⋊C8—51no—
273C2×C3⋊C8—51no—
274C23×C5—21no—
275C5×Q8—34no—
276C5×Q8—124no—
277C5×Q8—122no—
278C5×D4—21no—
279C5×D4#23712yes—
280C2×C4×C5—21no—
281C2×C4×C5—32no—
282C2×C4×C5—32no—
283C2×C4×C5—42no—
284C2×C4×C5—62no—
285C2×C4×C5—124no—
286C2×C4×C5D3×D411yescharacteristic
287C2×C4×C5D3×D411yescharacteristic
288C2×C4×C5C23×D311yescharacteristic
289C2×Dic5—22no—
290C2×Dic5—61no—
291C2×Dic5—61no—
292Dic10—22no—
293Dic10—22no—
294Dic10—61no—
295Dic10—61no—
296#168—22no—
297#168—61no—
298#168—61no—
299C22×Q8—61no—
300C2×SD16—52no—
301C2×SD16—151no—
302C4⋊Q8—32no—
303C4⋊Q8—31no—
304C4⋊Q8—51no—
305C4⋊Q8—152no—
306#125—302no—
307#125—301no—
308C22⋊Q8—62no—
309C22⋊Q8—61no—
310C4×Q8—31no—
311C4×Q8—152no—
312C4×Q8—151no—
313C4×Q8—301no—
314C4×D4—32no—
315C4×D4D3×D511yescharacteristic
316#106—152no—
317#106—151no—
318C4⋊C8—51no—
319C4⋊C8—152no—
320#103—52no—
321#103—152no—
322#103—152no—
323#103—152no—
324#103—151no—
325#102—151no—
326C4×C8—152no—
327C4×C8—151no—
328C2×C3×C5—42no—
329C2×C3×C5#54811yescharacteristic
330C2×C3×C5C22×SD1611yescharacteristic
331C2×C3×C5#57811yescharacteristic
332C23×C3—21no—
333C3×Q8—102no—
334C3×Q8—102no—
335C3×D4—21no—
336C3×D4#71312yes—
337C2×C3×C4—21no—
338C2×C3×C4—42no—
339C2×C3×C4—102no—
340C2×C3×C4C2×C22⋊D511yescharacteristic
341C2×C3×C4C2×C22⋊D511yescharacteristic
342C2×C3×C4C23×D511yescharacteristic
343C2×Dic3—22no—
344C2×Dic3—44no—
345C2×Dic3—101no—
346C2×Dic3—101no—
347C2×Dic3C2×C22⋊D512yes—
348C2×Dic3C2×C22⋊D512yes—
349Dic6—42no—
350Dic6—44no—
351Dic6—101no—
352Dic6—101no—
353Dic6#68714yescomplemented
354C3×C8—102no—
355C3⋊C8—101no—
356C3⋊C8—101no—
357C22×C5—22no—
358C22×C5—41no—
359C22×C5—41no—
360C22×C5C2×D3×D411yescharacteristic
361C4×C5—21no—
362C4×C5—34no—
363C4×C5—41no—
364C4×C5—62no—
365C4×C5—122no—
366C4×C5D3×SD1612yes—
367C4×C5C2×#23711yescharacteristic
368C4×C5#101011yescharacteristic
369Dic5—42no—
370Dic5—121no—
371Dic5—121no—
372C2×Q8—31no—
373C2×Q8—52no—
374C2×Q8—62no—
375C2×Q8—61no—
376C2×Q8—124no—
377C2×Q8—151no—
378C2×D4C2×D3×D511yescharacteristic
379C22×C4—21no—
380C22×C4—62no—
381SD16—104no—
382SD16—302no—
383C2×C8—52no—
384C2×C8—151no—
385C2×C8—151no—
386C4⋊C4—32no—
387C4⋊C4—31no—
388C4⋊C4—32no—
389C4⋊C4—62no—
390C4⋊C4—61no—
391C4⋊C4—101no—
392C4⋊C4—101no—
393C4⋊C4—151no—
394C4⋊C4—302no—
395C4⋊C4—302no—
396C4⋊C4—302no—
397C4⋊C4—301no—
398C4⋊C4C2×D3×D511yescharacteristic
399C22⋊C4—21no—
400C22⋊C4—62no—
401C42—32no—
402C42—302no—
403C42—301no—
404C42C2×D3×D511yescharacteristic
405C3×C5#335911yescharacteristic, complemented, Hall
406C22×C3—22no—
407C22×C3—41no—
408C22×C3—41no—
409C22×C3C22×C22⋊D511yescharacteristic
410C3×C4—21no—
411C3×C4—41no—
412C3×C4—202no—
413C3×C4C2×#68712yes—
414C3×C4C2×#71311yescharacteristic
415C3×C4#414711yescharacteristic
416Dic3—22no—
417Dic3—42no—
418Dic3—201no—
419Dic3—201no—
420Dic3C2×#68714yes—
421C2×C5—42no—
422C2×C5#559811yescharacteristic
423C2×C5C2×D3×SD1611yescharacteristic
424C2×C5#577911yescharacteristic
425C23—21no—
426Q8—34no—
427Q8—102no—
428Q8—102no—
429Q8—124no—
430Q8—122no—
431Q8—301no—
432Q8—301no—
433D4—21no—
434D4#676612yes—
435C2×C4—21no—
436C2×C4—32no—
437C2×C4—32no—
438C2×C4—42no—
439C2×C4—62no—
440C2×C4—102no—
441C2×C4—124no—
442C2×C4—301no—
443C2×C4—301no—
444C2×C4D3×C22⋊D511yescharacteristic
445C2×C4D3×C22⋊D511yescharacteristic
446C2×C4C22×D3×D511yescharacteristic
447C8—102no—
448C8—301no—
449C8—301no—
450C2×C3—42no—
451C2×C3C22×#68711yescharacteristic
452C2×C3#6615111yescharacteristic
453C2×C3#6617211yescharacteristic
454C5#8041411yescharacteristic, complemented, Sylow
455C22—22no—
456C22—41no—
457C22—41no—
458C22C2×D3×C22⋊D511yescharacteristic
459C4—21no—
460C4—34no—
461C4—41no—
462C4—62no—
463C4—122no—
464C4—202no—
465C4—601no—
466C4—601no—
467C4D3×#68712yes—
468C4C2×#676611yescharacteristic
469C4#9200011yescharacteristic
470C3#1061529911yescharacteristic, complemented, Sylow
471C2—42no—
472C2#1175434411yescharacteristic
473C2C2×D3×#68711yescharacteristic
474C2#1175534111yescharacteristic
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×C3×C5×D4C23
hypercenterC4×D4D3×D5
hypocenterC3×C5#3359
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
2. #11752482C2semidirect
7. #11747422C2semidirect
8. #11747293C2semidirect
9. #11746946C2semidirect
10. #11746924C2semidirect
11. #11746857C2semidirect
146. C5×Dic6SD16semidirect
353. Dic6#687semidirect
405. C3×C5#3359semidirect
454. C5#80414semidirect
470. C3#10615299semidirect

Maximal subgroups

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

subgroupindex
C5×D4×Dic62
#117524822
C4×#67162
C3×#653082
#117491142
Dic3×#6872
#117474222
#117472932
#117469462
#117469242
#117468572
#106152993
#804145