Finite Group Databasebeta

← #14305170

Subgroups — #14305170

Order 1920.

480 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65712C211yesmaximal, characteristic
2#11751859C211yesmaximal, characteristic
3C2×#91159C211yesmaximal, characteristic
4C2×#91149C211yesmaximal, characteristic
5D5×#807C211yesmaximal, characteristic
6#11746745C211yesmaximal, characteristic
7#11746528C211yesmaximal, characteristic
8#10604076—31nomaximal, Hall
9C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
10C2×D5⋊(C3⋊C8)C2211yescharacteristic
11C2×C3×C4⋊AGL(1,𝔽5)—21no—
12C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
13C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
14C2×Dic3⋊AGL(1,𝔽5)—21no—
15C3×D5×C4⋊C4C2211yescharacteristic
16D5×C4⋊Dic3C2211yescharacteristic
17C2×D5×C3⋊C8C2211yescharacteristic
18C3×(C2×AGL(1,𝔽5))⋊C4—21no—
19(C2×AGL(1,𝔽5))⋊Dic3—21no—
20#91159—22no—
21#91149—22no—
22#91091C411yescharacteristic, complemented
23C5×#807C411yescharacteristic, complemented
24#90990C411yescharacteristic, complemented
25#90989C411yescharacteristic, complemented
26#69620—51nomaximal, Hall
27C2×#3993—31no—
28C2×#3992—31no—
29#65712—31no—
30#65712D311yescharacteristic
31D5×#107—31no—
32#64874—31no—
33#64874—31no—
34C22×ΓL(1,𝔽16)—21no—
35C22×C3×AGL(1,𝔽5)—21no—
36C22×C3×AGL(1,𝔽5)D411yescharacteristic
37C22×C3×AGL(1,𝔽5)D411yescharacteristic
38C2×C3×C4×D5—21no—
39C2×C3×C4×D5C2311yescharacteristic
40C2×D5×Dic3—21no—
41C2×C3⋊#170—21no—
42C4⋊ΓL(1,𝔽16)—21no—
43C4⋊ΓL(1,𝔽16)—21no—
44D5⋊(C3⋊C8)—21no—
45D5⋊(C3⋊C8)Q812yes—
46C3×C4⋊AGL(1,𝔽5)—21no—
47C3×C4⋊AGL(1,𝔽5)—21no—
48C3×C4⋊AGL(1,𝔽5)—42no—
49C3×C4×AGL(1,𝔽5)—21no—
50C3×C4×AGL(1,𝔽5)—21no—
51Dic3⋊AGL(1,𝔽5)—42no—
52C3×C5×C4⋊C4C2×C411yescharacteristic
53C4⋊Dic15C2×C411yescharacteristic
54C2×C3⋊#168C2×C411yescharacteristic
55C5×C4⋊Dic3C2×C411yescharacteristic
56C2×C5×C3⋊C8C2×C411yescharacteristic
57C3×C4⋊Dic5C2×C411yescharacteristic
58C3×#683—21no—
59#6668—21no—
60D5×C3⋊C8D412yes—
61D5×C3⋊C8Q812yes—
62C3×#389—51no—
63C2×#808—51no—
64C2×#807—51no—
65#4928—51no—
66C2×#803—51no—
67#4529—51no—
68#4529—51no—
69C2×C4⋊AGL(1,𝔽5)—21no—
70C2×C4⋊AGL(1,𝔽5)—31no—
71C2×C4⋊AGL(1,𝔽5)—61no—
72C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
73C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
74C2×D5⋊C8—31no—
75C2×C8×D5—31no—
76D5×C4⋊C4—31no—
77D5×C4⋊C4C2×D311yescharacteristic
78(C2×AGL(1,𝔽5))⋊C4—21no—
79(C2×AGL(1,𝔽5))⋊C4—61no—
80#3993—62no—
81#3992—62no—
82C5×#107—31no—
83#3950—31no—
84#3939—31no—
85#3939—31no—
86#1943—151noSylow
87C22×C3×D5C2×D411yescharacteristic
88C2×ΓL(1,𝔽16)—41no—
89C2×ΓL(1,𝔽16)—41no—
90C2×ΓL(1,𝔽16)—41no—
91C2×C3×AGL(1,𝔽5)—21no—
92C2×C3×AGL(1,𝔽5)—21no—
93C2×C3×AGL(1,𝔽5)—21no—
94C2×C3×AGL(1,𝔽5)—21no—
95C2×C3×AGL(1,𝔽5)—21no—
96C2×C3×AGL(1,𝔽5)—21no—
97C2×C3×AGL(1,𝔽5)—41no—
98C2×C3×AGL(1,𝔽5)—41no—
99C2×C3×AGL(1,𝔽5)—41no—
100C2×C3×C4×C5—21no—
101C2×C3×C4×C5C22×C411yescharacteristic
102C2×Dic15—21no—
103C2×C5×Dic3—21no—
104C2×C3×Dic5—21no—
105C2×C3×Dic5#4111yescharacteristic
106C3×C4×D5—41no—
107C3×C4×D5—41no—
108C3×C4×D5C2×D411yescharacteristic
109C3×C4×D5C2×Q811yescharacteristic
110C3×C4×D5C2×Q811yescharacteristic
111C3×C4×D5#4111yescharacteristic
112D5×Dic3—41no—
113D5×Dic3—41no—
114C3⋊#170—22no—
115C3⋊#168C4⋊C412yescomplemented
116C5×C3⋊C8C4⋊C412yescomplemented
117C2×C3×C4⋊C4—51no—
118C2×C3×C4⋊C4—51no—
119C2×C3×C4⋊C4—101no—
120C2×C3×C42—51no—
121C2×C4⋊Dic3—51no—
122C2×C4⋊Dic3—51no—
123C2×Dic3⋊C4—101no—
124C22×C3⋊C8—51no—
125C22×C3⋊C8—51no—
126C3×#95—101no—
127C3⋊#95—101no—
128#808—102no—
129#807—51no—
130#807—51no—
131#807—51no—
132#807AGL(1,𝔽5)11yescharacteristic, complemented
133#803—102no—
134C22×AGL(1,𝔽5)—21no—
135C22×AGL(1,𝔽5)—61no—
136C22×AGL(1,𝔽5)#6711yescharacteristic
137C22×AGL(1,𝔽5)#6711yescharacteristic
138C2×C4×D5—21no—
139C2×C4×D5—61no—
140C2×C4×D5C22×D311yescharacteristic
141C2×#170—61no—
142C4⋊AGL(1,𝔽5)—21no—
143C4⋊AGL(1,𝔽5)—21no—
144C4⋊AGL(1,𝔽5)—42no—
145C4⋊AGL(1,𝔽5)—61no—
146C4⋊AGL(1,𝔽5)—61no—
147C4⋊AGL(1,𝔽5)—122no—
148C4×AGL(1,𝔽5)—21no—
149C4×AGL(1,𝔽5)—21no—
150D5⋊C8—32no—
151D5⋊C8—61no—
152C2×C5×C8—31no—
153C5×C4⋊C4—31no—
154C5×C4⋊C4C4×D311yescharacteristic
155C4⋊Dic5—31no—
156C4⋊Dic5C4×D311yescharacteristic
157#683—21no—
158#683—61no—
159C2×#168—31no—
160C8×D5—32no—
161C8×D5—32no—
162C2×#107—151no—
163C2×#106—151no—
164C2×#97—151no—
165#389—51no—
166#389—151no—
167#340—151no—
168#340—151no—
169C22×C3×C5C4×D411yescharacteristic
170C2×C3×D5#12111yescharacteristic
171C2×C3×D5C4⋊Q811yescharacteristic
172C2×C3×D5AGL(1,ℤ/8)11yescharacteristic
173C2×C3×D5AGL(1,ℤ/8)11yescharacteristic
174C2×C3×D5#13711yescharacteristic
175C2×C3×D5#13711yescharacteristic
176ΓL(1,𝔽16)—81no—
177C3×AGL(1,𝔽5)—41no—
178C3×AGL(1,𝔽5)—41no—
179C3×AGL(1,𝔽5)—81no—
180C3×C4×C5—41no—
181C3×C4×C5C2×C4⋊C411yescharacteristic
182C3×C4×C5C4×Q811yescharacteristic
183Dic15—41no—
184C3×Dic5—41no—
185C3×Dic5C22⋊Q811yescharacteristic
186C3×Dic5#12511yescharacteristic
187C5×Dic3—41no—
188C22×C3×C4—51no—
189C22×C3×C4—51no—
190C22×C3×C4—51no—
191C22×C3×C4—101no—
192C22×C3×C4—101no—
193C22×Dic3—101no—
194C22×Dic3—101no—
195C3×C4⋊C4—51no—
196C3×C4⋊C4—101no—
197C3×C4⋊C4—101no—
198C3×C4⋊C4—101no—
199C3×C4⋊C4—202no—
200C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
201C3×C42—101no—
202C3×C42—101no—
203C4⋊Dic3—51no—
204C4⋊Dic3—101no—
205C4⋊Dic3—101no—
206C4⋊Dic3—101no—
207C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
208Dic3⋊C4—202no—
209C2×C3⋊C8—51no—
210C2×C3⋊C8—52no—
211C2×C3⋊C8—52no—
212C2×C3⋊C8—52no—
213C2×C3⋊C8—101no—
214C2×C3⋊C8—101no—
215C2×C3⋊C8C2×AGL(1,𝔽5)11yescharacteristic
216C22×D5C2×#6711yescharacteristic
217C2×AGL(1,𝔽5)—21no—
218C2×AGL(1,𝔽5)—21no—
219C2×AGL(1,𝔽5)—21no—
220C2×AGL(1,𝔽5)—21no—
221C2×AGL(1,𝔽5)—21no—
222C2×AGL(1,𝔽5)—21no—
223C2×AGL(1,𝔽5)—41no—
224C2×AGL(1,𝔽5)—41no—
225C2×AGL(1,𝔽5)—41no—
226C2×AGL(1,𝔽5)—121no—
227C2×AGL(1,𝔽5)—121no—
228C2×AGL(1,𝔽5)—121no—
229C2×C4×C5—21no—
230C2×C4×C5—61no—
231C2×C4×C5C2×C4×D311yescharacteristic
232C2×Dic5—21no—
233C2×Dic5—61no—
234C2×Dic5#23511yescharacteristic
235C4×D5—41no—
236C4×D5—41no—
237C4×D5—121no—
238C4×D5—121no—
239C4×D5D3×D411yescharacteristic
240C4×D5#23711yescharacteristic
241C4×D5D3×Q811yescharacteristic
242C4×D5D3×Q811yescharacteristic
243#170—62no—
244C5×C8—32no—
245#168—32no—
246C22×C8—151no—
247C22×C8—151no—
248C2×C4⋊C4—51no—
249C2×C4⋊C4—51no—
250C2×C4⋊C4—101no—
251C2×C4⋊C4—151no—
252C2×C4⋊C4—151no—
253C2×C4⋊C4—301no—
254C2×C42—51no—
255#107—31no—
256#107—151no—
257#107—151no—
258#107—151no—
259#106—302no—
260#97—302no—
261#95—101no—
262#95—301no—
263C2×C3×C5#38911yescharacteristic
264C2×C3×C5#44111yescharacteristic
265C2×C3×C5#44211yescharacteristic
266C3×D5#46811yescharacteristic
267C3×D5#46811yescharacteristic
268C3×D5#50111yescharacteristic
269C3×D5#50111yescharacteristic
270C23×C3—51no—
271C2×C3×C4—21no—
272C2×C3×C4—51no—
273C2×C3×C4—51no—
274C2×C3×C4—51no—
275C2×C3×C4—51no—
276C2×C3×C4—51no—
277C2×C3×C4—101no—
278C2×C3×C4—101no—
279C2×C3×C4—101no—
280C2×C3×C4—101no—
281C2×C3×C4—101no—
282C2×C3×C4—101no—
283C2×C3×C4—101no—
284C2×C3×C4—201no—
285C2×C3×C4—201no—
286C2×C3×C4—201no—
287C2×C3×C4—201no—
288C2×C3×C4—201no—
289C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
290C2×Dic3—21no—
291C2×Dic3—101no—
292C2×Dic3—201no—
293C2×Dic3—201no—
294C2×Dic3—201no—
295C2×Dic3—201no—
296C2×Dic3—201no—
297C3⋊C8—52no—
298C3⋊C8—102no—
299C3⋊C8C4⋊AGL(1,𝔽5)12yescomplemented
300C22×C5C4×#6711yescharacteristic
301C2×D5#93211yescharacteristic
302C2×D5#93911yescharacteristic
303C2×D5#94211yescharacteristic
304C2×D5#94411yescharacteristic
305C2×D5#94911yescharacteristic
306C2×D5#95111yescharacteristic
307AGL(1,𝔽5)—41no—
308AGL(1,𝔽5)—41no—
309AGL(1,𝔽5)—81no—
310AGL(1,𝔽5)—241no—
311C4×C5—41no—
312C4×C5—121no—
313C4×C5#88711yescharacteristic
314C4×C5D3×C4⋊C411yescharacteristic
315Dic5—41no—
316Dic5—121no—
317Dic5#88911yescharacteristic
318Dic5#89611yescharacteristic
319C22×C4—51no—
320C22×C4—51no—
321C22×C4—51no—
322C22×C4—101no—
323C22×C4—101no—
324C22×C4—301no—
325C22×C4—301no—
326C2×C8—31no—
327C2×C8—152no—
328C2×C8—152no—
329C2×C8—151no—
330C2×C8—152no—
331C2×C8—301no—
332C2×C8—301no—
333C4⋊C4—31no—
334C4⋊C4—51no—
335C4⋊C4—101no—
336C4⋊C4—101no—
337C4⋊C4—101no—
338C4⋊C4—151no—
339C4⋊C4—202no—
340C4⋊C4—301no—
341C4⋊C4—301no—
342C4⋊C4—301no—
343C4⋊C4—602no—
344C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
345C42—101no—
346C42—101no—
347C3×C5#194311yescharacteristic, complemented, Hall
348C22×C3—51no—
349C22×C3—51no—
350C22×C3—51no—
351C22×C3—51no—
352C22×C3—51no—
353C22×C3—51no—
354C22×C3D4×AGL(1,𝔽5)11yescharacteristic
355C3×C4—41no—
356C3×C4—51no—
357C3×C4—51no—
358C3×C4—201no—
359C3×C4—201no—
360C3×C4—201no—
361C3×C4—401no—
362C3×C4C2×C4⋊AGL(1,𝔽5)11yescharacteristic
363C3×C4Q8×AGL(1,𝔽5)11yescharacteristic
364Dic3—41no—
365Dic3—201no—
366Dic3—401no—
367C2×C5#497611yescharacteristic
368C2×C5#501411yescharacteristic
369C2×C5#503011yescharacteristic
370D5#504211yescharacteristic
371D5#504911yescharacteristic
372D5#506411yescharacteristic
373D5#508111yescharacteristic
374C23—51no—
375C2×C4—21no—
376C2×C4—51no—
377C2×C4—51no—
378C2×C4—51no—
379C2×C4—51no—
380C2×C4—51no—
381C2×C4—61no—
382C2×C4—101no—
383C2×C4—101no—
384C2×C4—101no—
385C2×C4—101no—
386C2×C4—101no—
387C2×C4—101no—
388C2×C4—101no—
389C2×C4—201no—
390C2×C4—201no—
391C2×C4—201no—
392C2×C4—201no—
393C2×C4—201no—
394C2×C4—301no—
395C2×C4—601no—
396C2×C4—601no—
397C2×C4—601no—
398C2×C4—601no—
399C2×C4—601no—
400C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
401C8—32no—
402C8—152no—
403C8—302no—
404C2×C3—51no—
405C2×C3—51no—
406C2×C3—51no—
407C2×C3—51no—
408C2×C3#6571211yescharacteristic
409C2×C3#6573111yescharacteristic
410C2×C3#6573911yescharacteristic
411C5#6962011yescharacteristic, complemented, Sylow
412C22—51no—
413C22—51no—
414C22—51no—
415C22—51no—
416C22—51no—
417C22—51no—
418C22AGL(1,𝔽5)×#6711yescharacteristic
419C4—41no—
420C4—51no—
421C4—51no—
422C4—121no—
423C4—201no—
424C4—201no—
425C4—201no—
426C4—401no—
427C4—601no—
428C4—1201no—
429C4ΓL(1,𝔽16)⋊Q811yescharacteristic
430C4D3×C4⋊AGL(1,𝔽5)11yescharacteristic
431C3#1060407611yescharacteristic, complemented, Sylow
432C2—51no—
433C2—51no—
434C2—51no—
435C2—51no—
436C2#1175183711yescharacteristic
437C2#1175194011yescharacteristic
438C2#1175196811yescharacteristic
subgroupG/H
centerC22AGL(1,𝔽5)×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C5×C4⋊C4C2×C4
socleC22×C3×C5C4×D4
prime radicalC22×C3×D5C2×D4
cosocleC2×C3×C4×D5C23
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1943
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
22. #91091C4semidirect
23. C5×#807C4semidirect
24. #90990C4semidirect
25. #90989C4semidirect
115. C3⋊#168C4⋊C4semidirect
116. C5×C3⋊C8C4⋊C4semidirect
132. #807AGL(1,𝔽5)semidirect
299. C3⋊C8C4⋊AGL(1,𝔽5)semidirect
347. C3×C5#1943semidirect
411. C5#69620semidirect
431. C3#10604076semidirect

Maximal subgroups

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

subgroupindex
C3×#657122
#117518592
C2×#911592
C2×#911492
D5×#8072
#117467452
#117465282
#106040763
#696205