Finite Group Databasebeta

← #14417604

Subgroups — #14417604

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×Dic20C211yesmaximal, characteristic
2#11753405C212yesmaximal
3#11750954C211yesmaximal, characteristic, complemented
4C5×#4860C211yesmaximal, characteristic
5C3×#65142C211yesmaximal, characteristic, complemented
6#11747884C211yesmaximal, characteristic, complemented
7#11747854C211yesmaximal, characteristic, complemented
8#11747665C211yesmaximal, characteristic
9#11747489C212yesmaximal
10#11747271C212yesmaximal, complemented
11#11747270C212yesmaximal, complemented
12#10610900—31nomaximal, Hall
13C2×D3×Dic10C2212yes—
14C2×Dic60C2211yescharacteristic
15#91776C2212yes—
16C2×C5×D3×C8C2211yescharacteristic
17C5×#892C2212yes—
18C2×C3×Dic20C2211yescharacteristic
19C3×#4033C2212yes—
20C4×#1204—22no—
21#91400—22no—
22#91398—22no—
23#91371C2211yescharacteristic
24#91333C2212yes—
25#91331C2212yes—
26#91324—22no—
27C2×#6662C2212yes—
28C2×#6650C2211yescharacteristic
29D3×Dic20C418yescomplemented
30C3×C5×#106C2211yescharacteristic
31#91099C2211yescharacteristic
32#91094C2212yes—
33C5×#817C2211yescharacteristic
34C5×#807C2212yes—
35C3×#3947C2211yescharacteristic
36C3×#3942C2212yes—
37#90975C2212yes—
38#90970C2212yes—
39#90951C2211yescharacteristic
40Dic5×C3⋊C8C2211yescharacteristic
41#79831—51nomaximal, Hall
42C22×Dic20—31no—
43#65850—32no—
44C5×#427—31no—
45#65390—31no—
46#65293—32no—
47#65162—32no—
48#65162—32no—
49#65142—31no—
50#65142—31no—
51#65142—31no—
52#65142D311yescharacteristic, complemented
53C2×Dic30C2312yes—
54C2×C4×C5×D3C2311yescharacteristic
55C2×C3×Dic10C2312yes—
56C2×#1204—22no—
57C2×D3×Dic5—22no—
58D3×Dic10—24no—
59D3×Dic10C2×C418yes—
60C2×C3×C5×C8C2311yescharacteristic
61C3×C5×C4⋊C4C2312yes—
62#6712—22no—
63C4×Dic15—22no—
64C4×Dic15C2311yescharacteristic
65C2×C3⋊#168C2311yescharacteristic
66Dic60C2×C414yes—
67C5×(C2×D3)⋊C4—22no—
68C5×C4⋊Dic3C2312yes—
69C4×C5×Dic3—22no—
70C2×C5×C3⋊C8C2311yescharacteristic
71C5×D3×C8C2×C414yes—
72C3×#683—22no—
73C3×C4×Dic5—22no—
74C3×C4×Dic5C2311yescharacteristic
75C2×C3×#168C2311yescharacteristic
76C3×Dic20C2×C414yes—
77Dic3⋊Dic5D412yes—
78#6669—22no—
79#6668—22no—
80(C2×D3)⋊Dic5D412yes—
81Dic3×Dic5—22no—
82Dic3×Dic5—22no—
83#6662C2×C418yes—
84#6650—22no—
85C2×D3×Q16—51no—
86#5572—52no—
87C3×#441—51no—
88#5184—51no—
89C4×#216—52no—
90#4860D511yescharacteristic
91#4853—51no—
92#4802—52no—
93#4790—52no—
94#4716—51no—
95#4708—51no—
96C22×Dic10—32no—
97C22×C5×C8—31no—
98C5×#117—32no—
99#4072—31no—
100C2×#681—31no—
101C2×Dic20—32no—
102C2×Dic20—31no—
103C2×Dic20—38no—
104C2×Dic20C2×D311yescharacteristic
105#4033—32no—
106#4033—32no—
107#4033—32no—
108#4033C2×D312yes—
109#4023—62no—
110#4023—62no—
111C4×Dic10—62no—
112C4×Dic10—62no—
113C5×#107—32no—
114C5×#106—31no—
115C5×#106C2×D311yescharacteristic
116#3947—31no—
117#3947C2×D311yescharacteristic
118C8×Dic5—31no—
119C8×Dic5—31no—
120#3942—32no—
121#3942—32no—
122#3942—32no—
123#3942C2×D312yes—
124#2950—151noSylow
125C22×C5×D3C2×D411yescharacteristic
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5C2411yescharacteristic
128C2×Dic15—22no—
129C2×Dic15C2×D412yes—
130Dic30—22no—
131Dic30C22×C414yes—
132C2×C5×Dic3—22no—
133C2×C5×Dic3C2×D411yescharacteristic
134C4×C5×D3C22×C412yes—
135C4×C5×D3#4112yes—
136C2×C3×Dic5—22no—
137C2×C3×Dic5C2×D412yes—
138C3×Dic10—22no—
139C3×Dic10C22×C414yes—
140#1204—28no—
141D3×Dic5—28no—
142C3×C5×C8C22×C412yes—
143C3⋊#168—21no—
144C3×#168—21no—
145C5×C3⋊C8C22×C412yes—
146C2×D3×Q8—52no—
147C2×C3×Q16—51no—
148C3×C4×Q8—52no—
149Q8×Dic3—52no—
150C2×#216—52no—
151D3×Q16—58no—
152C2×Dic12—51no—
153C2×ΓL(1,𝔽25)—51no—
154C2×D3×C8C2×D511yescharacteristic
155#892—102no—
156#892C2×D512yes—
157#887—52no—
158#887—102no—
159#872—51no—
160#872—102no—
161C4×Dic6—52no—
162C4×Dic6—102no—
163C3×#106C2×D511yescharacteristic
164C3×#103—52no—
165C3×#97—51no—
166#835—52no—
167#817C2×D511yescharacteristic
168#816—52no—
169#815—51no—
170C8×Dic3—51no—
171#810—52no—
172#807C2×D512yes—
173C4×C3⋊C8—51no—
174C22×C4×C5—31no—
175C22×Dic5—62no—
176C2×Dic10—32no—
177C2×Dic10—38no—
178C2×Dic10—64no—
179C2×Dic10—62no—
180C2×Dic10C22×D312yes—
181C2×C5×C8—31no—
182C2×C5×C8—34no—
183C2×C5×C8C22×D311yescharacteristic
184C5×C4⋊C4—32no—
185C5×C4⋊C4C22×D312yes—
186C5×C22⋊C4—62no—
187C42×C5—62no—
188C22⋊Dic5—32no—
189C4⋊Dic5—32no—
190#683—22no—
191#683—62no—
192#683—62no—
193#683—62no—
194C4×Dic5—22no—
195C4×Dic5—31no—
196C4×Dic5—62no—
197C4×Dic5—62no—
198C4×Dic5—62no—
199C4×Dic5C22×D311yescharacteristic
200#681—62no—
201C2×#168—31no—
202C2×#168C22×D311yescharacteristic
203Dic20—38no—
204Dic20—34no—
205Dic20C4×D314yes—
206C22×Q16—151no—
207#519—152no—
208#441—51no—
209#441—151no—
210#441—151no—
211#441—151no—
212C4×Q16—152no—
213C4×Q16—152no—
214#427—31no—
215#419—152no—
216#405—151no—
217C22×C3×C5C22×D411yescharacteristic
218C2×C5×D3—22no—
219C2×C5×D3C4×D412yes—
220C3×C4×C5—42no—
221C3×C4×C5C23×C411yescharacteristic
222C3×C4×C5C2×#4111yescharacteristic
223Dic15—24no—
224Dic15—22no—
225C3×Dic5—24no—
226C3×Dic5—22no—
227C5×Dic3—42no—
228C5×Dic3C4×D412yes—
229C2×C3×Q8—52no—
230D3×Q8—58no—
231D3×Q8—104no—
232C2×C4×D3—102no—
233C2×C4×D3C22×D511yescharacteristic
234C2×Dic6—52no—
235C2×Dic6—102no—
236C3×Q16—54no—
237C2×C3×C8—51no—
238C2×C3×C8C22×D511yescharacteristic
239C3×C4⋊C4—102no—
240C3×C4⋊C4C22×D512yes—
241C3×C42—51no—
242C3×C42—102no—
243#216—58no—
244(C2×D3)⋊C4—22no—
245(C2×D3)⋊C4—52no—
246C4⋊Dic3—102no—
247C4⋊Dic3C22×D512yes—
248Dic3⋊C4—52no—
249Dic3⋊C4—102no—
250Dic3⋊C4—102no—
251C4×Dic3—22no—
252C4×Dic3—51no—
253C4×Dic3—102no—
254C4×Dic3—102no—
255C4×Dic3—102no—
256C2×C3⋊C8—51no—
257C2×C3⋊C8C22×D511yescharacteristic
258Dic12—54no—
259ΓL(1,𝔽25)—102no—
260D3×C8C4×D514yes—
261C23×C5—31no—
262C2×C4×C5—22no—
263C2×C4×C5—31no—
264C2×C4×C5—32no—
265C2×C4×C5—32no—
266C2×C4×C5—62no—
267C2×C4×C5C23×D311yescharacteristic
268C2×Dic5—22no—
269C2×Dic5—32no—
270C2×Dic5—68no—
271C2×Dic5—62no—
272C2×Dic5D3×D412yes—
273Dic10—22no—
274Dic10—34no—
275Dic10—68no—
276Dic10—62no—
277Dic10C2×C4×D314yes—
278C5×C8—32no—
279C5×C8C2×C4×D312yes—
280#168—21no—
281#168—61no—
282C22×Q8—152no—
283C2×Q16—51no—
284C2×Q16—158no—
285C2×Q16—152no—
286C2×Q16—151no—
287C2×M16—151no—
288C22×C8—31no—
289C4×Q8—52no—
290C4×Q8—152no—
291C4×Q8—152no—
292C4×Q8—152no—
293C4×Q8—302no—
294C4×Q8—302no—
295#117—32no—
296#117—151no—
297#117—302no—
298#117—302no—
299#107—32no—
300#106—31no—
301#106D3×D511yescharacteristic
302#103—52no—
303#103—152no—
304#103—152no—
305#103—152no—
306#97—51no—
307#97—151no—
308C4×C8—151no—
309C4×C8—151no—
310C2×C3×C5C2×C4×D411yescharacteristic
311C2×C3×C5#57812yes—
312C5×D3—22no—
313C22×D3D4×D511yescharacteristic
314C3×Q8—54no—
315C3×Q8—102no—
316C2×C3×C4—22no—
317C2×C3×C4—52no—
318C2×C3×C4—102no—
319C2×C3×C4C23×D511yescharacteristic
320C2×Dic3—22no—
321C2×Dic3—52no—
322C2×Dic3—102no—
323C2×Dic3D4×D511yescharacteristic
324C4×D3—108no—
325C4×D3C2×C4×D512yes—
326C4×D3#71312yes—
327Dic6—54no—
328Dic6—102no—
329Dic6—108no—
330C3×C8—101no—
331C3×C8C2×C4×D512yes—
332C3⋊C8—101no—
333C3⋊C8C2×C4×D512yes—
334C22×C5—32no—
335C22×C5—62no—
336C22×C5C2×D3×D411yescharacteristic
337C4×C5—32no—
338C4×C5—42no—
339C4×C5—122no—
340C4×C5C22×C4×D311yescharacteristic
341C4×C5D3×#4111yescharacteristic
342Dic5—22no—
343Dic5—24no—
344Dic5—62no—
345Dic5—64no—
346C2×Q8—52no—
347C2×Q8—158no—
348C2×Q8—152no—
349C2×Q8—302no—
350C2×Q8—304no—
351C22×C4—31no—
352C22×C4—302no—
353Q16—54no—
354Q16—158no—
355Q16—154no—
356M16—302no—
357C2×C8—31no—
358C2×C8—34no—
359C2×C8—51no—
360C2×C8—151no—
361C2×C8C2×D3×D511yescharacteristic
362C4⋊C4—32no—
363C4⋊C4—102no—
364C4⋊C4—152no—
365C4⋊C4—302no—
366C4⋊C4—302no—
367C4⋊C4—302no—
368C4⋊C4C2×D3×D512yes—
369C22⋊C4—62no—
370C22⋊C4—152no—
371C42—51no—
372C42—62no—
373C42—102no—
374C42—151no—
375C42—302no—
376C42—302no—
377C42—302no—
378C3×C5#295011yescharacteristic, complemented, Hall
379C22×C3C2×D4×D511yescharacteristic
380C2×D3—22no—
381C2×D3#403912yes—
382C3×C4—42no—
383C3×C4—104no—
384C3×C4—102no—
385C3×C4C22×C4×D511yescharacteristic
386C3×C4C2×#71311yescharacteristic
387Dic3—42no—
388Dic3—104no—
389Dic3—102no—
390Dic3#403912yes—
391C2×C5—62no—
392C2×C5C4×D3×D411yescharacteristic
393C2×C5#577912yes—
394C23—31no—
395Q8—54no—
396Q8—102no—
397Q8—154no—
398Q8—308no—
399Q8—302no—
400C2×C4—22no—
401C2×C4—31no—
402C2×C4—32no—
403C2×C4—32no—
404C2×C4—52no—
405C2×C4—62no—
406C2×C4—102no—
407C2×C4—152no—
408C2×C4—308no—
409C2×C4—302no—
410C2×C4C22×D3×D511yescharacteristic
411C8—32no—
412C8—101no—
413C8—301no—
414C8C4×D3×D512yes—
415C2×C3C2×#403911yescharacteristic
416C2×C3#6610512yes—
417D3—22no—
418C5#7983111yescharacteristic, complemented, Sylow
419C22—32no—
420C22—62no—
421C22D3×D4×D511yescharacteristic
422C4—32no—
423C4—42no—
424C4—102no—
425C4—104no—
426C4—122no—
427C4—302no—
428C4—304no—
429C4C2×C4×D3×D511yescharacteristic
430C4D3×#71311yescharacteristic
431C3#1061090011yescharacteristic, complemented, Sylow
432C2—62no—
433C2D3×#403911yescharacteristic
434C2#1175409112yes—
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#106C22
socleC22×C3×C5C22×D4
prime radicalC22×C5×D3C2×D4
cosocleC2×C3×C4×C5C24
hypercenter#106D3×D5
hypocenterC3×C5#2950
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
3. #11750954C2semidirect
5. C3×#65142C2semidirect
6. #11747884C2semidirect
7. #11747854C2semidirect
10. #11747271C2semidirect
11. #11747270C2semidirect
29. D3×Dic20C4semidirect
52. #65142D3semidirect
378. C3×C5#2950semidirect
418. C5#79831semidirect
431. C3#10610900semidirect

Maximal subgroups

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

subgroupindex
C2×D3×Dic202
#117534052
#117509542
C5×#48602
C3×#651422
#117478842
#117478542
#117476652
#117474892
#117472712
#117472702
#106109003
#798315