Finite Group Databasebeta

← #14297775

Subgroups — #14297775

Order 1920.

584 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×Q8×D5C211yesmaximal, characteristic
2C2×#91238C212yesmaximal
3#11752348C211yesmaximal, characteristic
4D5⋊(C4⋊(C3⋊C8))C211yesmaximal, characteristic
5#11746745C212yesmaximal
6#10604452—31nomaximal, Hall
7C2×C3×Q8×D5C2211yescharacteristic
8C2×C4⋊ΓL(1,𝔽16)C2212yes—
9C2×D5⋊(C3⋊C8)C2212yes—
10C3×C4×C5×Q8C411yescharacteristic, complemented
11C3×Q8×Dic5C411yescharacteristic, complemented
12C3×D5×C4⋊C4—21no—
13C3×D5×C4⋊C4C2211yescharacteristic
14C3×#4033—21no—
15C3×#4033C411yescharacteristic, complemented
16C3×C42×D5—21no—
17C3×C42×D5C2211yescharacteristic
18C3×C4×Dic10—21no—
19C3×C4×Dic10C411yescharacteristic, complemented
20#91238—24no—
21#91235—21no—
22#91235—21no—
23#91233—21no—
24C4⋊(C3⋊#170)—21no—
25#71627—51nomaximal, Hall
26C4×Q8×D5D311yescharacteristic
27C2×#4009—32no—
28#65689—31no—
29D5⋊(C4⋊C8)—31no—
30#64874—32no—
31C22×ΓL(1,𝔽16)—22no—
32C2×C3×C5×Q8C2×C411yescharacteristic
33C3×Q8×D5—21no—
34C3×Q8×D5—21no—
35C3×Q8×D5D412yes—
36C3×Q8×D5Q812yes—
37C2×C3×C4×D5—21no—
38C2×C3×C4×D5—21no—
39C2×C3×C4×D5D411yescharacteristic
40C2×C3×C4×D5D411yescharacteristic
41C2×C3×C4×D5C2311yescharacteristic
42C2×C3×Dic10—21no—
43C2×C3×Dic10C2×C411yescharacteristic
44C2×C3⋊#170—22no—
45C4⋊ΓL(1,𝔽16)—22no—
46C4⋊ΓL(1,𝔽16)—22no—
47D5⋊(C3⋊C8)—22no—
48D5⋊(C3⋊C8)—22no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4C2×C411yescharacteristic
51C3×C42×C5—21no—
52C3×C42×C5C2×C411yescharacteristic
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5C2×C411yescharacteristic
55C3×#683—21no—
56C3×#683—21no—
57C3×#683—21no—
58C3×C4×Dic5—21no—
59C3×C4×Dic5—21no—
60C3×C4×Dic5—21no—
61C3×C4×Dic5C2×C411yescharacteristic
62C3×C4×Dic5D411yescharacteristic
63C3×C4×Dic5D411yescharacteristic
64C2×C3×C4×Q8—51no—
65C2×#835—52no—
66#4936—51no—
67C2×C4⋊(C3⋊C8)—51no—
68#4529—52no—
69C2×Q8×D5C2×D311yescharacteristic
70C2×C4⋊AGL(1,𝔽5)—32no—
71C2×D5⋊C8—32no—
72C4×C5×Q8Dic311yescharacteristic, complemented
73Q8×Dic5Dic311yescharacteristic, complemented
74D5×C4⋊C4—21no—
75D5×C4⋊C4C2×D311yescharacteristic
76#4033—21no—
77#4033Dic311yescharacteristic, complemented
78C42×D5—21no—
79C42×D5C2×D311yescharacteristic
80C4×Dic10—21no—
81C4×Dic10Dic311yescharacteristic, complemented
82#4009—64no—
83(C2×AGL(1,𝔽5))⋊C4—61no—
84(C2×AGL(1,𝔽5))⋊C4—61no—
85#4004—61no—
86C4⋊#170—61no—
87#1805—151noSylow
88C22×C3×D5C2×D411yescharacteristic
89C2×ΓL(1,𝔽16)—42no—
90C2×ΓL(1,𝔽16)—42no—
91C2×ΓL(1,𝔽16)—42no—
92C3×C5×Q8—21no—
93C3×C5×Q8C4⋊C412yes—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5C22⋊C411yescharacteristic
97C2×C3×C4×C5C22⋊C411yescharacteristic
98C2×C3×C4×C5C22×C411yescharacteristic
99C2×C3×Dic5—21no—
100C2×C3×Dic5—21no—
101C2×C3×Dic5C22⋊C411yescharacteristic
102C2×C3×Dic5C22⋊C411yescharacteristic
103C2×C3×Dic5C2×D411yescharacteristic
104C3×C4×D5—22no—
105C3×C4×D5—22no—
106C3×C4×D5—22no—
107C3×C4×D5—22no—
108C3×C4×D5—42no—
109C3×C4×D5C2×D411yescharacteristic
110C3×C4×D5C2×Q811yescharacteristic
111C3×C4×D5#4111yescharacteristic
112C3×C4×D5#4111yescharacteristic
113C3×Dic10—21no—
114C3×Dic10—22no—
115C3×Dic10—22no—
116C3×Dic10C4⋊C412yes—
117C3⋊#170—42no—
118C22×C3×Q8—51no—
119C3×C4×Q8—51no—
120C3×C4×Q8—51no—
121C3×C4×Q8—51no—
122C3×C4×Q8—101no—
123C3×C4×Q8—101no—
124C3×C4×Q8AGL(1,𝔽5)11yescharacteristic, complemented
125C2×C3×C4⋊C4—51no—
126C2×C3×C4⋊C4—101no—
127C2×C3×C42—51no—
128C2×C3×C42—101no—
129C2×C4⋊Dic3—52no—
130C22×C3⋊C8—52no—
131#835—104no—
132C3⋊#95—101no—
133C3⋊#95—101no—
134C4⋊(C3⋊C8)—101no—
135C4⋊(C3⋊C8)—101no—
136C22×AGL(1,𝔽5)—62no—
137C2×C5×Q8C2×Dic311yescharacteristic
138Q8×D5—21no—
139Q8×D5—21no—
140Q8×D5Dic612yes—
141Q8×D5D1212yes—
142C2×C4×D5—21no—
143C2×C4×D5—21no—
144C2×C4×D5#6711yescharacteristic
145C2×C4×D5#6711yescharacteristic
146C2×C4×D5C22×D311yescharacteristic
147C2×Dic10—21no—
148C2×Dic10C2×Dic311yescharacteristic
149C2×#170—62no—
150C4⋊AGL(1,𝔽5)—62no—
151C4⋊AGL(1,𝔽5)—62no—
152D5⋊C8—62no—
153D5⋊C8—62no—
154C5×C4⋊C4—21no—
155C5×C4⋊C4C2×Dic311yescharacteristic
156C42×C5—21no—
157C42×C5C2×Dic311yescharacteristic
158C4⋊Dic5—21no—
159C4⋊Dic5C2×Dic311yescharacteristic
160#683—21no—
161#683—21no—
162#683—21no—
163C4×Dic5—21no—
164C4×Dic5—21no—
165C4×Dic5—21no—
166C4×Dic5C2×Dic311yescharacteristic
167C4×Dic5#6711yescharacteristic
168C4×Dic5#6711yescharacteristic
169C2×C4×Q8—51no—
170C2×C4⋊C8—151no—
171C2×#103—152no—
172#382—151no—
173#340—152no—
174C22×C3×C5C2×C22⋊C411yescharacteristic
175C2×C3×D5#12111yescharacteristic
176C2×C3×D5C22⋊Q811yescharacteristic
177C2×C3×D5#13512yes—
178C2×C3×D5#13712yes—
179ΓL(1,𝔽16)—82no—
180C3×C4×C5—22no—
181C3×C4×C5—21no—
182C3×C4×C5—21no—
183C3×C4×C5—41no—
184C3×C4×C5C2×C4⋊C411yescharacteristic
185C3×C4×C5#11711yescharacteristic
186C3×Dic5—22no—
187C3×Dic5—21no—
188C3×Dic5—21no—
189C3×Dic5—41no—
190C3×Dic5#12111yescharacteristic
191C3×Dic5C22⋊Q811yescharacteristic
192C2×C3×Q8—52no—
193C2×C3×Q8—52no—
194C2×C3×Q8—51no—
195C2×C3×Q8—101no—
196C2×C3×Q8—101no—
197C2×C3×Q8—101no—
198C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
199C22×C3×C4—51no—
200C22×C3×C4—51no—
201C22×C3×C4—51no—
202C22×C3×C4—101no—
203C22×C3×C4—101no—
204C22×Dic3—102no—
205C3×C4⋊C4—21no—
206C3×C4⋊C4—51no—
207C3×C4⋊C4—101no—
208C3×C4⋊C4—101no—
209C3×C4⋊C4—101no—
210C3×C4⋊C4—101no—
211C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
212C3×C42—21no—
213C3×C42—51no—
214C3×C42—51no—
215C3×C42—51no—
216C3×C42—101no—
217C3×C42—101no—
218C3×C42—101no—
219C3×C42C2×AGL(1,𝔽5)11yescharacteristic
220C4⋊Dic3—102no—
221C4⋊Dic3—102no—
222C2×C3⋊C8—102no—
223C2×C3⋊C8—102no—
224C2×C3⋊C8—102no—
225C22×D5C2×#6711yescharacteristic
226C2×AGL(1,𝔽5)—122no—
227C2×AGL(1,𝔽5)—122no—
228C2×AGL(1,𝔽5)—122no—
229C5×Q8—21no—
230C5×Q8C4⋊Dic312yes—
231C2×C4×C5—21no—
232C2×C4×C5—21no—
233C2×C4×C5#21711yescharacteristic
234C2×C4×C5#21711yescharacteristic
235C2×C4×C5C22×Dic311yescharacteristic
236C2×Dic5—21no—
237C2×Dic5—21no—
238C2×Dic5#21711yescharacteristic
239C2×Dic5#21711yescharacteristic
240C2×Dic5C2×#6711yescharacteristic
241C4×D5—22no—
242C4×D5—22no—
243C4×D5—22no—
244C4×D5—22no—
245C4×D5—42no—
246C4×D5C2×Dic611yescharacteristic
247C4×D5C2×D1211yescharacteristic
248C4×D5#23511yescharacteristic
249C4×D5#23511yescharacteristic
250Dic10—21no—
251Dic10—22no—
252Dic10—22no—
253Dic10C4⋊Dic312yes—
254#170—122no—
255C22×Q8—51no—
256C22×C8—152no—
257C4×Q8—51no—
258C4×Q8—51no—
259C4×Q8—51no—
260C4×Q8—101no—
261C4×Q8—101no—
262C4×Q8ΓL(1,𝔽16)11yescharacteristic, complemented
263C2×C4⋊C4—51no—
264C2×C4⋊C4—101no—
265C2×C4⋊C4—152no—
266C2×C42—51no—
267C2×C42—101no—
268C4⋊C8—301no—
269C4⋊C8—301no—
270#103—304no—
271#95—301no—
272#95—301no—
273C2×C3×C5#38011yescharacteristic
274C2×C3×C5#41611yescharacteristic
275C2×C3×C5#41911yescharacteristic
276C3×D5#46412yes—
277C3×D5#47912yes—
278C23×C3—51no—
279C3×Q8—21no—
280C3×Q8—52no—
281C3×Q8—102no—
282C3×Q8—102no—
283C3×Q8—101no—
284C3×Q8C4⋊AGL(1,𝔽5)12yes—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—51no—
288C2×C3×C4—51no—
289C2×C3×C4—51no—
290C2×C3×C4—51no—
291C2×C3×C4—51no—
292C2×C3×C4—51no—
293C2×C3×C4—51no—
294C2×C3×C4—102no—
295C2×C3×C4—102no—
296C2×C3×C4—102no—
297C2×C3×C4—102no—
298C2×C3×C4—101no—
299C2×C3×C4—101no—
300C2×C3×C4—202no—
301C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
302C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
303C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
304C2×Dic3—202no—
305C2×Dic3—202no—
306C2×Dic3—202no—
307C3⋊C8—202no—
308C22×C5C2×#21711yescharacteristic
309C2×D5#92411yescharacteristic
310C2×D5#93011yescharacteristic
311C2×D5#94212yes—
312C2×D5#95012yes—
313AGL(1,𝔽5)—242no—
314C4×C5—22no—
315C4×C5—21no—
316C4×C5—21no—
317C4×C5—41no—
318C4×C5C2×C4⋊Dic311yescharacteristic
319C4×C5#92611yescharacteristic
320Dic5—22no—
321Dic5—21no—
322Dic5—21no—
323Dic5—41no—
324Dic5#92411yescharacteristic
325Dic5#93011yescharacteristic
326C2×Q8—52no—
327C2×Q8—52no—
328C2×Q8—51no—
329C2×Q8—101no—
330C2×Q8—101no—
331C2×Q8—101no—
332C2×Q8C2×ΓL(1,𝔽16)11yescharacteristic
333C22×C4—51no—
334C22×C4—51no—
335C22×C4—51no—
336C22×C4—101no—
337C22×C4—101no—
338C22×C4—302no—
339C2×C8—302no—
340C2×C8—302no—
341C2×C8—302no—
342C4⋊C4—21no—
343C4⋊C4—51no—
344C4⋊C4—101no—
345C4⋊C4—101no—
346C4⋊C4—101no—
347C4⋊C4—101no—
348C4⋊C4—302no—
349C4⋊C4—302no—
350C4⋊C4C2×ΓL(1,𝔽16)11yescharacteristic
351C42—21no—
352C42—51no—
353C42—51no—
354C42—51no—
355C42—101no—
356C42—101no—
357C42—101no—
358C42C2×ΓL(1,𝔽16)11yescharacteristic
359C3×C5#180511yescharacteristic, complemented, Hall
360C22×C3—52no—
361C22×C3—51no—
362C22×C3—51no—
363C22×C3—52no—
364C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
365C3×C4—21no—
366C3×C4—22no—
367C3×C4—21no—
368C3×C4—41no—
369C3×C4—51no—
370C3×C4—51no—
371C3×C4—101no—
372C3×C4—102no—
373C3×C4—101no—
374C3×C4—201no—
375C3×C4C2×C4⋊AGL(1,𝔽5)11yescharacteristic
376C3×C4#413011yescharacteristic
377Dic3—402no—
378C2×C5#521211yescharacteristic
379C2×C5#522511yescharacteristic
380C2×C5#523311yescharacteristic
381D5#502212yes—
382D5#502812yes—
383C23—51no—
384Q8—21no—
385Q8—52no—
386Q8—102no—
387Q8—102no—
388Q8—101no—
389Q8C4⋊ΓL(1,𝔽16)12yes—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—51no—
393C2×C4—51no—
394C2×C4—51no—
395C2×C4—51no—
396C2×C4—51no—
397C2×C4—51no—
398C2×C4—51no—
399C2×C4—102no—
400C2×C4—102no—
401C2×C4—102no—
402C2×C4—102no—
403C2×C4—101no—
404C2×C4—101no—
405C2×C4—202no—
406C2×C4—602no—
407C2×C4—602no—
408C2×C4—602no—
409C2×C4#676311yescharacteristic
410C2×C4#676311yescharacteristic
411C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
412C8—602no—
413C2×C3—52no—
414C2×C3—52no—
415C2×C3#6576511yescharacteristic
416C2×C3#6578211yescharacteristic
417C2×C3#6579411yescharacteristic
418C5#7162711yescharacteristic, complemented, Sylow
419C22—52no—
420C22—51no—
421C22—51no—
422C22—52no—
423C22C2×#676311yescharacteristic
424C4—21no—
425C4—22no—
426C4—21no—
427C4—41no—
428C4—51no—
429C4—51no—
430C4—101no—
431C4—102no—
432C4—101no—
433C4—201no—
434C4—1202no—
435C4C2×C4⋊ΓL(1,𝔽16)11yescharacteristic
436C4#9198911yescharacteristic
437C3#1060445211yescharacteristic, complemented, Sylow
438C2—52no—
439C2—52no—
440C2#1175242411yescharacteristic
441C2#1175244111yescharacteristic
442C2#1175245311yescharacteristic
subgroupG/H
centerC22C2×#6763
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC3×C4×C5×Q8C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C2×D4
cosocleC2×C3×C4×D5C23
hypercenterC4×Q8ΓL(1,𝔽16)
hypocenterC3×C5#1805
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
10. C3×C4×C5×Q8C4semidirect
11. C3×Q8×Dic5C4semidirect
15. C3×#4033C4semidirect
19. C3×C4×Dic10C4semidirect
72. C4×C5×Q8Dic3semidirect
73. Q8×Dic5Dic3semidirect
77. #4033Dic3semidirect
81. C4×Dic10Dic3semidirect
124. C3×C4×Q8AGL(1,𝔽5)semidirect
262. C4×Q8ΓL(1,𝔽16)semidirect
359. C3×C5#1805semidirect
418. C5#71627semidirect
437. C3#10604452semidirect

Maximal subgroups

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

subgroupindex
C3×C4×Q8×D52
C2×#912382
#117523482
D5⋊(C4⋊(C3⋊C8))2
#117467452
#106044523
#716275