Finite Group Databasebeta

← #14472069

Subgroups — #14472069

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756329C211yesmaximal, characteristic, complemented
2#11756301C211yesmaximal, characteristic
3C3×C4×C5×SD16C211yesmaximal, characteristic
4#11751267C212yesmaximal
5#11751132C211yesmaximal, characteristic, complemented
6#11751108C211yesmaximal, characteristic
7#11750958C212yesmaximal, complemented
8#11750891C212yesmaximal, complemented
9#11750869C212yesmaximal
10#11750782C211yesmaximal, characteristic, complemented
11C8×Dic30C211yesmaximal, characteristic, complemented
12#10611354—31nomaximal, Hall
13C2×C3×C5×SD16C2211yescharacteristic
14C3×C4×C5×Q8C2211yescharacteristic
15C3×C4×C5×D4C2211yescharacteristic
16Q8×Dic15C2212yes—
17C2×#6718C2212yes—
18#91825C2212yes—
19#91815—21no—
20#91813—21no—
21#91779—22no—
22#91779C2212yes—
23#91776C2212yes—
24#91768—22no—
25#91758—21no—
26#91758C2211yescharacteristic
27#91758C2211yescharacteristic
28C4×Dic30—21no—
29C4×Dic30C2211yescharacteristic
30C3×C5×#106C2211yescharacteristic
31C3×C5×#103C2211yescharacteristic
32C3×C5×#102C2211yescharacteristic
33C3×C4×C5×C8C2211yescharacteristic
34#91116C2212yes—
35#91100C2212yes—
36#91100C2212yes—
37#91098C2212yes—
38C8×Dic15C2212yes—
39#91094C2212yes—
40#91091C2212yes—
41C4⋊(C3⋊#168)C2211yescharacteristic
42#79623—51nomaximal, Hall
43#65904—31no—
44#65876—31no—
45C4×C5×SD16D311yescharacteristic
46#65455—32no—
47#65320—31no—
48#65296—31no—
49#65146—32no—
50#65079—32no—
51#65057—32no—
52#64970—31no—
53C8×Dic10—31no—
54C2×C3×C5×Q8C2311yescharacteristic
55C2×C3×C5×D4C2311yescharacteristic
56C22×C3×C4×C5—21no—
57C2×Dic30—21no—
58C2×Dic30D411yescharacteristic
59C2×Dic30C2312yes—
60C3×C5×SD16—22no—
61C2×C3×C5×C8C2311yescharacteristic
62C2×C3×C5×C8C2311yescharacteristic
63C3×C5×C4⋊C4—21no—
64C3×C5×C4⋊C4C2311yescharacteristic
65C3×C5×C4⋊C4C2311yescharacteristic
66C3×C5×C22⋊C4—21no—
67C3×C42×C5—21no—
68C3×C42×C5C2311yescharacteristic
69#6719—22no—
70#6719—22no—
71#6718—24no—
72C4⋊Dic15—21no—
73C4⋊Dic15—21no—
74C4⋊Dic15—21no—
75C4⋊Dic15—22no—
76C4⋊Dic15—22no—
77C4⋊Dic15D411yescharacteristic
78C4⋊Dic15C2312yes—
79#6712—22no—
80#6712—22no—
81#6712D412yes—
82C4×Dic15—22no—
83C4×Dic15—22no—
84C4×Dic15C2312yes—
85C2×C3⋊#168C2312yes—
86#5570—51no—
87#5542—51no—
88C3×C4×SD16D511yescharacteristic
89#5166—52no—
90#5031—51no—
91#5007—51no—
92#4857—52no—
93#4790—52no—
94#4768—52no—
95#4681—51no—
96C8×Dic6—51no—
97C2×C5×SD16C2×D311yescharacteristic
98C4×C5×Q8C2×D311yescharacteristic
99C4×C5×D4C2×D311yescharacteristic
100Q8×Dic5—32no—
101C2×#689—32no—
102#4082—32no—
103#4072—61no—
104#4070—61no—
105#4036—32no—
106#4036—62no—
107#4033—32no—
108#4025—62no—
109#4015—31no—
110#4015—31no—
111#4015—61no—
112C4×Dic10—31no—
113C4×Dic10—61no—
114C5×#106C2×D311yescharacteristic
115C5×#103C2×D311yescharacteristic
116C5×#102C2×D311yescharacteristic
117C4×C5×C8C2×D311yescharacteristic
118#3964—32no—
119#3948—32no—
120#3948—32no—
121#3946—32no—
122C8×Dic5—32no—
123#3942—32no—
124#3939—32no—
125C4⋊#168—31no—
126#3364—151noSylow
127C23×C3×C5—21no—
128C3×C5×Q8—21no—
129C3×C5×Q8#4112yes—
130C3×C5×D4—21no—
131C3×C5×D4—21no—
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5—21no—
134C2×C3×C4×C5—21no—
135C2×C3×C4×C5—42no—
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2411yescharacteristic
139C2×Dic15—22no—
140C2×Dic15—22no—
141C2×Dic15C2×D412yes—
142C2×Dic15C2×D412yes—
143Dic30—22no—
144Dic30—22no—
145Dic30—22no—
146Dic30—42no—
147C3×C5×C8—21no—
148C3×C5×C8—21no—
149C3⋊#168—22no—
150C2×C3×SD16C2×D511yescharacteristic
151C3×C4×Q8C2×D511yescharacteristic
152C3×C4×D4C2×D511yescharacteristic
153Q8×Dic3—52no—
154C2×#216—52no—
155#936—52no—
156#926—101no—
157#924—101no—
158#890—52no—
159#890—102no—
160#887—52no—
161#879—102no—
162#869—51no—
163#869—51no—
164#869—101no—
165C4×Dic6—51no—
166C4×Dic6—101no—
167C3×#106C2×D511yescharacteristic
168C3×#103C2×D511yescharacteristic
169C3×#102C2×D511yescharacteristic
170C3×C4×C8C2×D511yescharacteristic
171#832—52no—
172#816—52no—
173#816—52no—
174Dic3⋊C8—52no—
175C8×Dic3—52no—
176#810—52no—
177#807—52no—
178C4⋊(C3⋊C8)—51no—
179C2×C5×Q8C22×D311yescharacteristic
180C2×C5×D4C22×D311yescharacteristic
181C22×C4×C5—21no—
182C2×Dic10—31no—
183C2×Dic10—32no—
184C2×Dic10—61no—
185C5×SD16—22no—
186C2×C5×C8C22×D311yescharacteristic
187C2×C5×C8C22×D311yescharacteristic
188C5×C4⋊C4—21no—
189C5×C4⋊C4C22×D311yescharacteristic
190C5×C4⋊C4C22×D311yescharacteristic
191C5×C22⋊C4—21no—
192C42×C5—21no—
193C42×C5C22×D311yescharacteristic
194C22⋊Dic5—62no—
195C22⋊Dic5—62no—
196#689—64no—
197C4⋊Dic5—31no—
198C4⋊Dic5—32no—
199C4⋊Dic5—62no—
200C4⋊Dic5—62no—
201C4⋊Dic5—61no—
202C4⋊Dic5—61no—
203C4⋊Dic5—61no—
204#683—32no—
205#683—62no—
206#683—62no—
207C4×Dic5—32no—
208C4×Dic5—62no—
209C4×Dic5—62no—
210C2×#168—32no—
211#557—151no—
212#556—151no—
213#488—152no—
214#487—151no—
215#479—152no—
216#474—151no—
217#464—152no—
218#462—151no—
219C8×Q8—151no—
220C4×Q16—152no—
221C4×SD16D1511yescharacteristic
222C22×C3×C5—41no—
223C22×C3×C5—41no—
224C22×C3×C5—41no—
225C22×C3×C5C22×D411yescharacteristic
226C3×C4×C5—22no—
227C3×C4×C5—21no—
228C3×C4×C5—41no—
229C3×C4×C5—41no—
230C3×C4×C5#13512yes—
231C3×C4×C5C2×#4111yescharacteristic
232C3×C4×C52−1+411yescharacteristic
233Dic15—22no—
234Dic15—22no—
235Dic15—42no—
236Dic15—42no—
237C2×C3×Q8C22×D511yescharacteristic
238C2×C3×D4C22×D511yescharacteristic
239C22×C3×C4—21no—
240C2×Dic6—51no—
241C2×Dic6—52no—
242C2×Dic6—101no—
243C3×SD16—22no—
244C2×C3×C8C22×D511yescharacteristic
245C2×C3×C8C22×D511yescharacteristic
246C3×C4⋊C4—21no—
247C3×C4⋊C4C22×D511yescharacteristic
248C3×C4⋊C4C22×D511yescharacteristic
249C3×C22⋊C4—21no—
250C3×C42—21no—
251C3×C42C22×D511yescharacteristic
252#217—102no—
253#217—102no—
254#216—104no—
255C4⋊Dic3—51no—
256C4⋊Dic3—52no—
257C4⋊Dic3—102no—
258C4⋊Dic3—102no—
259C4⋊Dic3—101no—
260C4⋊Dic3—101no—
261C4⋊Dic3—101no—
262Dic3⋊C4—52no—
263Dic3⋊C4—102no—
264Dic3⋊C4—102no—
265C4×Dic3—52no—
266C4×Dic3—102no—
267C4×Dic3—102no—
268C2×C3⋊C8—52no—
269C23×C5—21no—
270C5×Q8—21no—
271C5×Q8#23512yes—
272C5×D4—21no—
273C5×D4—21no—
274C2×C4×C5—21no—
275C2×C4×C5—21no—
276C2×C4×C5—21no—
277C2×C4×C5—42no—
278C2×C4×C5D3×D411yescharacteristic
279C2×C4×C5D3×D411yescharacteristic
280C2×C4×C5C23×D311yescharacteristic
281C2×Dic5—32no—
282C2×Dic5—32no—
283C2×Dic5—62no—
284C2×Dic5—62no—
285Dic10—62no—
286Dic10—62no—
287Dic10—62no—
288Dic10—122no—
289C5×C8—21no—
290C5×C8—21no—
291#168—62no—
292C2×Q16—152no—
293C2×SD16C2×D1511yescharacteristic
294C4⋊Q8—151no—
295C4⋊Q8—151no—
296C4⋊Q8—301no—
297#126—302no—
298#125—152no—
299#125—302no—
300#124—152no—
301C22⋊Q8—301no—
302C4×Q8—151no—
303C4×Q8—152no—
304C4×Q8—152no—
305C4×Q8—301no—
306C4×Q8C2×D1511yescharacteristic
307C4×D4C2×D1511yescharacteristic
308#117—301no—
309#107—152no—
310#106C2×D1511yescharacteristic
311C4⋊C8—152no—
312C4⋊C8—151no—
313#103—152no—
314#103—152no—
315#103—152no—
316#103C2×D1511yescharacteristic
317#102—152no—
318#102C2×D1511yescharacteristic
319C4×C8—152no—
320C4×C8C2×D1511yescharacteristic
321C2×C3×C5—81no—
322C2×C3×C5#54811yescharacteristic
323C2×C3×C5C2×#13511yescharacteristic
324C2×C3×C5#57811yescharacteristic
325C23×C3—21no—
326C3×Q8—21no—
327C3×Q8#70912yes—
328C3×D4—21no—
329C3×D4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—42no—
334C2×C3×C4D4×D511yescharacteristic
335C2×C3×C4D4×D511yescharacteristic
336C2×C3×C4C23×D511yescharacteristic
337C2×Dic3—52no—
338C2×Dic3—52no—
339C2×Dic3—102no—
340C2×Dic3—102no—
341Dic6—102no—
342Dic6—102no—
343Dic6—102no—
344Dic6—202no—
345C3×C8—21no—
346C3×C8—21no—
347C3⋊C8—102no—
348C22×C5—41no—
349C22×C5—41no—
350C22×C5—41no—
351C22×C5C2×D3×D411yescharacteristic
352C4×C5—21no—
353C4×C5—22no—
354C4×C5—41no—
355C4×C5—41no—
356C4×C5#91612yes—
357C4×C5C2×#23511yescharacteristic
358C4×C5#101011yescharacteristic
359Dic5—62no—
360Dic5—62no—
361Dic5—122no—
362Dic5—122no—
363C2×Q8—151no—
364C2×Q8—152no—
365C2×Q8—301no—
366C2×Q8C22×D1511yescharacteristic
367C2×D4C22×D1511yescharacteristic
368C22×C4—21no—
369Q16—304no—
370SD16—22no—
371C2×C8—152no—
372C2×C8C22×D1511yescharacteristic
373C2×C8C22×D1511yescharacteristic
374C4⋊C4—21no—
375C4⋊C4—151no—
376C4⋊C4—152no—
377C4⋊C4—152no—
378C4⋊C4—302no—
379C4⋊C4—302no—
380C4⋊C4—302no—
381C4⋊C4—302no—
382C4⋊C4—301no—
383C4⋊C4—301no—
384C4⋊C4—301no—
385C4⋊C4C22×D1511yescharacteristic
386C4⋊C4C22×D1511yescharacteristic
387C22⋊C4—21no—
388C22⋊C4—302no—
389C22⋊C4—302no—
390C42—21no—
391C42—152no—
392C42—302no—
393C42—302no—
394C42C22×D1511yescharacteristic
395C3×C5#336411yescharacteristic, complemented, Hall
396C22×C3—41no—
397C22×C3—41no—
398C22×C3—41no—
399C22×C3C2×D4×D511yescharacteristic
400C3×C4—21no—
401C3×C4—22no—
402C3×C4—41no—
403C3×C4—41no—
404C3×C4#406212yes—
405C3×C4C2×#70911yescharacteristic
406C3×C4#415011yescharacteristic
407Dic3—102no—
408Dic3—102no—
409Dic3—202no—
410Dic3—202no—
411C2×C5—81no—
412C2×C5#555211yescharacteristic
413C2×C5C2×#91611yescharacteristic
414C2×C5#577111yescharacteristic
415C23—21no—
416Q8—21no—
417Q8—302no—
418Q8—302no—
419Q8—302no—
420Q8—602no—
421Q8#681712yes—
422D4—21no—
423D4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—42no—
428C2×C4—152no—
429C2×C4—152no—
430C2×C4—302no—
431C2×C4—302no—
432C2×C4D4×D1511yescharacteristic
433C2×C4D4×D1511yescharacteristic
434C2×C4C23×D1511yescharacteristic
435C8—21no—
436C8—21no—
437C8—302no—
438C2×C3—81no—
439C2×C3#6588611yescharacteristic
440C2×C3C2×#406211yescharacteristic
441C2×C3#6610511yescharacteristic
442C5#7962311yescharacteristic, complemented, Sylow
443C22—41no—
444C22—41no—
445C22—41no—
446C22C2×D4×D1511yescharacteristic
447C4—22no—
448C4—21no—
449C4—41no—
450C4—41no—
451C4—302no—
452C4—302no—
453C4—602no—
454C4—602no—
455C4#9180512yes—
456C4C2×#681711yescharacteristic
457C4#9210111yescharacteristic
458C3#1061135411yescharacteristic, complemented, Sylow
459C2—81no—
460C2#1175631111yescharacteristic
461C2C2×#9180511yescharacteristic
462C2#1175653011yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C4×C5×SD16C2
socleC22×C3×C5C22×D4
prime radicalC2×C3×C5×D4C23
hypercenterC4×SD16D15
hypocenterC3×C5#3364
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #11756329C2semidirect
5. #11751132C2semidirect
7. #11750958C2semidirect
8. #11750891C2semidirect
10. #11750782C2semidirect
11. C8×Dic30C2semidirect
395. C3×C5#3364semidirect
442. C5#79623semidirect
458. C3#10611354semidirect

Maximal subgroups

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

subgroupindex
#117563292
#117563012
C3×C4×C5×SD162
#117512672
#117511322
#117511082
#117509582
#117508912
#117508692
#117507822
C8×Dic302
#106113543
#796235