Finite Group Databasebeta

← #14471555

Subgroups — #14471555

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
1D4×Dic30C211yesmaximal, characteristic
2#11752481C211yesmaximal, characteristic, complemented
3C4×C5×#214C211yesmaximal, characteristic
4C3×#65308C211yesmaximal, characteristic
5#11749118C212yesmaximal
6#11749017C212yesmaximal
7#11747428C212yesmaximal, complemented
8#11747304C212yesmaximal, complemented
9#11746945C211yesmaximal, characteristic, complemented
10#11746920C211yesmaximal, characteristic, complemented
11#11746855C211yesmaximal, characteristic, complemented
12#10611350—31nomaximal, Hall
13C22×Dic30—21no—
14C3×C4×C5×D4C2211yescharacteristic
15D4×Dic15C2212yes—
16#91813—21no—
17#91777C2212yes—
18#91767—22no—
19#91758C2211yescharacteristic
20C4×Dic30C2211yescharacteristic
21C2×C5×#214C2211yescharacteristic
22C4×C5×Dic6C2211yescharacteristic
23C2×C3×#687C2212yes—
24C3×#4015C2211yescharacteristic
25#91385C2212yes—
26#91381—21no—
27#91340—21no—
28#91339—22no—
29#91331C2212yes—
30C5×#832C2211yescharacteristic
31C5×#810C2211yescharacteristic
32C5×#808C2211yescharacteristic
33C4×C5×C3⋊C8C2211yescharacteristic
34C3×#3942C2212yes—
35C3×C4⋊#168C2211yescharacteristic
36#90985C2212yes—
37#90983C2212yes—
38#90973C2212yes—
39#90971C2212yes—
40#90971C2212yes—
41#90951C2212yes—
42#80414—51nomaximal, Hall
43#65901—31no—
44D4×Dic10—31no—
45C4×C5×SD16—31no—
46#65451—32no—
47#65309—31no—
48#65308D311yescharacteristic
49#65143—32no—
50#65081—32no—
51#65047—32no—
52#64970—31no—
53C8×Dic10—31no—
54C2×C3×C5×D4C2311yescharacteristic
55C22×C3×C4×C5—21no—
56C22×Dic15—22no—
57C2×Dic30—21no—
58C2×Dic30—22no—
59C2×Dic30—44no—
60C2×Dic30D411yescharacteristic
61C2×C5×Dic6C2311yescharacteristic
62C2×C3×Dic10C2312yes—
63C3×C5×C4⋊C4C2311yescharacteristic
64C3×C5×C22⋊C4—21no—
65C3×C42×C5C2311yescharacteristic
66#6719—22no—
67C4⋊Dic15—21no—
68C4⋊Dic15D411yescharacteristic
69C4⋊Dic15C2312yes—
70#6712—22no—
71#6712D412yes—
72C4×Dic15C2312yes—
73C5×#214—22no—
74C5×C4⋊Dic3C2311yescharacteristic
75C5×Dic3⋊C4—21no—
76C4×C5×Dic3—21no—
77C2×C5×C3⋊C8C2311yescharacteristic
78C2×C5×C3⋊C8C2311yescharacteristic
79C3×#687—24no—
80C3×C4⋊Dic5—21no—
81C3×C4⋊Dic5—21no—
82C2×C3×#168C2312yes—
83#6669—22no—
84#6669—22no—
85#6668—22no—
86Dic3×Dic5—22no—
87#5721—51no—
88D4×Dic6—51no—
89C3×#461—51no—
90#5162—52no—
91Dic3×SD16—52no—
92#5079—51no—
93C4×#214D511yescharacteristic
94#4851—51no—
95#4830—51no—
96#4792—52no—
97#4791—52no—
98C22×Dic10—61no—
99C2×C5×SD16—31no—
100C4×C5×Q8—31no—
101C4×C5×D4C2×D311yescharacteristic
102#4090—32no—
103D4×Dic5—32no—
104C2×#687C2×D312yes—
105#4070—61no—
106#4035—62no—
107#4034—32no—
108#4033—32no—
109#4024—62no—
110#4016—61no—
111#4015—31no—
112#4015C2×D311yescharacteristic
113C4×Dic10—31no—
114C4×Dic10—61no—
115C5×#106—31no—
116C5×#103—31no—
117C5×#102—31no—
118C4×C5×C8—31no—
119#3967—32no—
120#3948—32no—
121#3948—32no—
122#3946—32no—
123C8×Dic5—32no—
124#3942C2×D312yes—
125#3940—32no—
126C4⋊#168C2×D311yescharacteristic
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—22no—
137C2×Dic15—44no—
138C2×Dic15C2×D412yes—
139C2×Dic15C2×D412yes—
140Dic30—42no—
141Dic30—44no—
142Dic30SD1614yescomplemented
143C2×C5×Dic3—21no—
144C2×C5×Dic3—21no—
145C5×Dic6—21no—
146C5×Dic6—21no—
147C2×C3×Dic5—22no—
148C3×Dic10—22no—
149C3×Dic10—22no—
150C3×#168—22no—
151C5×C3⋊C8—21no—
152C5×C3⋊C8—21no—
153C22×Dic6—101no—
154C2×C3×SD16—52no—
155C3×C4⋊Q8—51no—
156C3×C4×D4C2×D511yescharacteristic
157Q8×Dic3—52no—
158#944—52no—
159D4×Dic3—52no—
160C2×#214C2×D511yescharacteristic
161#924—101no—
162#890—101no—
163#889—102no—
164#888—52no—
165#887—101no—
166#878—102no—
167#869—51no—
168C4×Dic6—51no—
169C4×Dic6C2×D511yescharacteristic
170C3×C4⋊C8—51no—
171C3×#103—52no—
172#835—52no—
173#835—52no—
174#832C2×D511yescharacteristic
175#817—52no—
176#816—52no—
177Dic3⋊C8—52no—
178C8×Dic3—52no—
179#810C2×D511yescharacteristic
180#808C2×D511yescharacteristic
181C4×C3⋊C8C2×D511yescharacteristic
182C2×C5×Q8—31no—
183C2×C5×D4C22×D311yescharacteristic
184C22×C4×C5—21no—
185C22×Dic5—62no—
186C2×Dic10—31no—
187C2×Dic10—62no—
188C2×Dic10—61no—
189C2×Dic10—124no—
190C2×Dic10C22×D312yes—
191C5×SD16—62no—
192C2×C5×C8—31no—
193C2×C5×C8—31no—
194C5×C4⋊C4—31no—
195C5×C4⋊C4—61no—
196C5×C4⋊C4C22×D311yescharacteristic
197C5×C22⋊C4—21no—
198C42×C5—61no—
199C42×C5C22×D311yescharacteristic
200C22⋊Dic5—62no—
201#687—24no—
202C4⋊Dic5—21no—
203C4⋊Dic5—21no—
204C4⋊Dic5—31no—
205C4⋊Dic5—32no—
206C4⋊Dic5—61no—
207#683—32no—
208#683—62no—
209#683—62no—
210#683—62no—
211#683—62no—
212C4×Dic5—32no—
213C4×Dic5—62no—
214C2×#168C22×D312yes—
215#557—151no—
216D4×Q8—151no—
217#487—151no—
218#487—152no—
219#475—152no—
220#475—151no—
221#461—51no—
222#461—152no—
223C8×Q8—151no—
224C4×SD16—31no—
225C4×SD16—152no—
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—22no—
236Dic15—42no—
237Dic15C2×SD1614yes—
238C3×Dic5—42no—
239C5×Dic3—41no—
240C5×Dic3—41no—
241C2×C3×Q8—52no—
242C2×C3×D4C22×D511yescharacteristic
243C22×C3×C4—21no—
244C22×Dic3—102no—
245C2×Dic6—51no—
246C2×Dic6—102no—
247C2×Dic6—101no—
248C2×Dic6—204no—
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—102no—
258#214—22no—
259C4⋊Dic3—51no—
260C4⋊Dic3—52no—
261C4⋊Dic3—102no—
262C4⋊Dic3—101no—
263C4⋊Dic3C22×D511yescharacteristic
264Dic3⋊C4—21no—
265Dic3⋊C4—52no—
266Dic3⋊C4—102no—
267Dic3⋊C4—102no—
268Dic3⋊C4—102no—
269C4×Dic3—21no—
270C4×Dic3—52no—
271C4×Dic3—102no—
272C2×C3⋊C8C22×D511yescharacteristic
273C2×C3⋊C8C22×D511yescharacteristic
274C23×C5—21no—
275C5×Q8—61no—
276C5×Q8—61no—
277C5×D4—21no—
278C5×D4#23712yes—
279C2×C4×C5—21no—
280C2×C4×C5—42no—
281C2×C4×C5—61no—
282C2×C4×C5—61no—
283C2×C4×C5D3×D411yescharacteristic
284C2×C4×C5D3×D411yescharacteristic
285C2×C4×C5C23×D311yescharacteristic
286C2×Dic5—22no—
287C2×Dic5—32no—
288C2×Dic5—32no—
289C2×Dic5—62no—
290C2×Dic5—124no—
291Dic10—22no—
292Dic10—22no—
293Dic10—34no—
294Dic10—124no—
295Dic10—122no—
296C5×C8—61no—
297C5×C8—61no—
298#168—22no—
299C22×Q8—301no—
300C2×SD16—31no—
301C2×SD16—52no—
302C4⋊Q8—51no—
303C4⋊Q8—152no—
304C4⋊Q8—152no—
305C4⋊Q8—151no—
306#125—301no—
307#125—302no—
308C22⋊Q8—302no—
309C22⋊Q8—301no—
310C4×Q8—31no—
311C4×Q8—151no—
312C4×Q8—152no—
313C4×Q8—301no—
314C4×D4—152no—
315C4×D4D3×D511yescharacteristic
316#106—31no—
317#106—152no—
318C4⋊C8—51no—
319C4⋊C8—152no—
320#103—31no—
321#103—52no—
322#103—152no—
323#103—152no—
324#103—152no—
325#102—31no—
326C4×C8—31no—
327C4×C8—152no—
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#70912yes—
337C2×C3×C4—21no—
338C2×C3×C4—42no—
339C2×C3×C4—102no—
340C2×C3×C4D4×D511yescharacteristic
341C2×C3×C4D4×D511yescharacteristic
342C2×C3×C4C23×D511yescharacteristic
343C2×Dic3—21no—
344C2×Dic3—21no—
345C2×Dic3—52no—
346C2×Dic3—52no—
347C2×Dic3—102no—
348C2×Dic3—204no—
349Dic6—21no—
350Dic6—21no—
351Dic6—54no—
352Dic6—204no—
353Dic6—202no—
354C3×C8—102no—
355C3⋊C8—21no—
356C3⋊C8—21no—
357C22×C5—22no—
358C22×C5—41no—
359C22×C5—41no—
360C22×C5C2×D3×D411yescharacteristic
361C4×C5—21no—
362C4×C5—41no—
363C4×C5—121no—
364C4×C5—121no—
365C4×C5D3×SD1612yes—
366C4×C5C2×#23711yescharacteristic
367C4×C5#101011yescharacteristic
368Dic5—34no—
369Dic5—42no—
370Dic5—62no—
371Dic5—122no—
372C2×Q8—31no—
373C2×Q8—52no—
374C2×Q8—151no—
375C2×Q8—302no—
376C2×Q8—301no—
377C2×Q8—604no—
378C2×D4C2×D3×D511yescharacteristic
379C22×C4—21no—
380C22×C4—302no—
381SD16—62no—
382SD16—104no—
383C2×C8—31no—
384C2×C8—31no—
385C2×C8—52no—
386C4⋊C4—31no—
387C4⋊C4—61no—
388C4⋊C4—101no—
389C4⋊C4—101no—
390C4⋊C4—152no—
391C4⋊C4—151no—
392C4⋊C4—152no—
393C4⋊C4—302no—
394C4⋊C4—302no—
395C4⋊C4—302no—
396C4⋊C4—302no—
397C4⋊C4—301no—
398C4⋊C4C2×D3×D511yescharacteristic
399C22⋊C4—21no—
400C22⋊C4—302no—
401C42—61no—
402C42—152no—
403C42—302no—
404C42C2×D3×D511yescharacteristic
405C3×C5#335911yescharacteristic, complemented, Hall
406C22×C3—22no—
407C22×C3—41no—
408C22×C3—41no—
409C22×C3C2×D4×D511yescharacteristic
410C3×C4—21no—
411C3×C4—41no—
412C3×C4—202no—
413C3×C4D5×SD1612yes—
414C3×C4C2×#70911yescharacteristic
415C3×C4#415011yescharacteristic
416Dic3—41no—
417Dic3—41no—
418Dic3—54no—
419Dic3—102no—
420Dic3—202no—
421C2×C5—42no—
422C2×C5#559811yescharacteristic
423C2×C5C2×D3×SD1611yescharacteristic
424C2×C5#577911yescharacteristic
425C23—21no—
426Q8—61no—
427Q8—61no—
428Q8—102no—
429Q8—102no—
430Q8—154no—
431Q8—604no—
432Q8—602no—
433D4—21no—
434D4#676512yes—
435C2×C4—21no—
436C2×C4—42no—
437C2×C4—61no—
438C2×C4—61no—
439C2×C4—102no—
440C2×C4—152no—
441C2×C4—152no—
442C2×C4—302no—
443C2×C4—604no—
444C2×C4#679011yescharacteristic
445C2×C4#679011yescharacteristic
446C2×C4C22×D3×D511yescharacteristic
447C8—61no—
448C8—61no—
449C8—102no—
450C2×C3—42no—
451C2×C3#6588611yescharacteristic
452C2×C3C2×D5×SD1611yescharacteristic
453C2×C3#6610511yescharacteristic
454C5#8041411yescharacteristic, complemented, Sylow
455C22—22no—
456C22—41no—
457C22—41no—
458C22C2×#679011yescharacteristic
459C4—21no—
460C4—41no—
461C4—121no—
462C4—121no—
463C4—154no—
464C4—202no—
465C4—302no—
466C4—602no—
467C4#9148712yes—
468C4C2×#676511yescharacteristic
469C4#9200111yescharacteristic
470C3#1061135011yescharacteristic, complemented, Sylow
471C2—42no—
472C2#1175436911yescharacteristic
473C2C2×#9148711yescharacteristic
474C2#1175535311yescharacteristic
subgroupG/H
centerC22C2×#6790
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. #11752481C2semidirect
7. #11747428C2semidirect
8. #11747304C2semidirect
9. #11746945C2semidirect
10. #11746920C2semidirect
11. #11746855C2semidirect
142. Dic30SD16semidirect
405. C3×C5#3359semidirect
454. C5#80414semidirect
470. C3#10611350semidirect

Maximal subgroups

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

subgroupindex
D4×Dic302
#117524812
C4×C5×#2142
C3×#653082
#117491182
#117490172
#117474282
#117473042
#117469452
#117469202
#117468552
#106113503
#804145