Finite Group Databasebeta

← #14313146

Subgroups — #14313146

Order 1920.

528 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65858C211yesmaximal, characteristic
2#11752420C211yesmaximal, characteristic, complemented
3#11752404C211yesmaximal, characteristic, complemented
4#11746736C212yesmaximal, complemented
5#11746735C212yesmaximal, complemented
6#10604381—31nomaximal, Hall
7C2×C3×#709C2211yescharacteristic
8C22×C3×C4×D5C411yescharacteristic, complemented
9#91989—21no—
10D5⋊#208—21no—
11C3×C5×#117C411yescharacteristic, complemented
12C3×#4043—21no—
13C3×#4041—21no—
14C3×#4032C411yescharacteristic, complemented
15C3×#4032C2211yescharacteristic
16C3×#4028C411yescharacteristic, complemented
17C3×#4028C2211yescharacteristic
18C3×C4×D20—21no—
19C3×C4×D20—21no—
20#91242C2212yes—
21#91240C2212yes—
22#91234—21no—
23#91228—21no—
24#71716—51nomaximal, Hall
25#65858D311yescharacteristic
26#65761—31no—
27#65745—31no—
28#64865—32no—
29#64864—32no—
30C23×C3×D5C2×C411yescharacteristic
31C22×C3×C4×C5C2×C411yescharacteristic
32C2×C3×C22⋊D5C2×C411yescharacteristic
33C2×C3×C22⋊D5C2311yescharacteristic
34C22×C3×Dic5C2×C411yescharacteristic
35C3×#709—41no—
36C3×#709—41no—
37C2×C3×D20—21no—
38C2×C3×D20—21no—
39C2×C3×D20D411yescharacteristic
40C2×C3×C4×D5—21no—
41C2×C3×C4×D5—21no—
42C2×C3×C4×D5—41no—
43C2×C3×C4×D5—41no—
44C2×C3×C4×D5D411yescharacteristic
45C2×C3×C4×D5D411yescharacteristic
46C2×C3×Dic10D411yescharacteristic
47#6763—22no—
48#6762—22no—
49C4⋊ΓL(1,𝔽16)—41no—
50C4×ΓL(1,𝔽16)—41no—
51#6758—41no—
52D5⋊(C3⋊C8)—41no—
53C3×C5×C4⋊C4—21no—
54C3×C5×C22⋊C4C2×C411yescharacteristic
55C3×C5×C22⋊C4C2×C411yescharacteristic
56C3×C42×C5—21no—
57C3×#685—21no—
58C3×#685—21no—
59C3×#685—21no—
60C3×#685—21no—
61C3×C4⋊Dic5—21no—
62C3×C4⋊Dic5—21no—
63C3×#525—51no—
64#5240—51no—
65#5237—51no—
66#4539—52no—
67#4536—52no—
68C2×#709C2×D311yescharacteristic
69C22×C4×D5Dic311yescharacteristic, complemented
70#4130—61no—
71D5⋊M16—61no—
72C5×#117Dic311yescharacteristic, complemented
73#4043—21no—
74#4041—21no—
75#4032Dic311yescharacteristic, complemented
76#4032C2×D311yescharacteristic
77#4028Dic311yescharacteristic, complemented
78#4028C2×D311yescharacteristic
79C4×D20—21no—
80C4×D20—21no—
81#4013—32no—
82#4011—32no—
83#4005—61no—
84#3999—61no—
85#2120—151noSylow
86C23×C3×C5C22×C411yescharacteristic
87C22×C3×D5—21no—
88C22×C3×D5—42no—
89C22×C3×D5—41no—
90C22×C3×D5C22⋊C411yescharacteristic
91C22×C3×D5C2×D411yescharacteristic
92C2×ΓL(1,𝔽16)—42no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5C22⋊C411yescharacteristic
98C2×C3×C4×C5C22⋊C411yescharacteristic
99C3×C22⋊D5—41no—
100C3×C22⋊D5—41no—
101C2×C3×Dic5—21no—
102C2×C3×Dic5—41no—
103C2×C3×Dic5C22⋊C411yescharacteristic
104C2×C3×Dic5C2×D411yescharacteristic
105C3×D20—41no—
106C3×D20—42no—
107C3×D20—42no—
108C3×C4×D5—21no—
109C3×C4×D5—21no—
110C3×C4×D5—21no—
111C3×C4×D5—21no—
112C3×C4×D5—42no—
113C3×C4×D5—41no—
114C3×C4×D5—41no—
115C3×Dic10—41no—
116C3⋊#170—42no—
117C2×C3×#41—51no—
118C23×C3×C4—51no—
119C3×#123—51no—
120C3×#123—51no—
121C3×C22⋊Q8—101no—
122C3×#121—101no—
123C3×#120—51no—
124C3×#120—51no—
125C3×C4×D4—101no—
126C3×C4×D4—101no—
127C3×#117AGL(1,𝔽5)11yescharacteristic, complemented
128#926—101no—
129C2×#208—101no—
130#836—101no—
131#834—52no—
132#834—101no—
133#833—52no—
134C23×D5C2×Dic311yescharacteristic
135C22×C4×C5C2×Dic311yescharacteristic
136C2×C22⋊D5C2×Dic311yescharacteristic
137C2×C22⋊D5C22×D311yescharacteristic
138C22×Dic5C2×Dic311yescharacteristic
139#709—41no—
140#709—41no—
141C2×D20—21no—
142C2×D20—21no—
143C2×D20#6711yescharacteristic
144C2×C4×D5—21no—
145C2×C4×D5—21no—
146C2×C4×D5—41no—
147C2×C4×D5—41no—
148C2×C4×D5#6711yescharacteristic
149C2×C4×D5#6711yescharacteristic
150C2×Dic10#6711yescharacteristic
151C22⋊AGL(1,𝔽5)—62no—
152#704—62no—
153C4⋊AGL(1,𝔽5)—121no—
154C4×AGL(1,𝔽5)—121no—
155#700—121no—
156D5⋊C8—121no—
157C5×C4⋊C4—21no—
158C5×C22⋊C4C2×Dic311yescharacteristic
159C5×C22⋊C4C2×Dic311yescharacteristic
160C42×C5—21no—
161#685—21no—
162#685—21no—
163#685—21no—
164#685—21no—
165C4⋊Dic5—21no—
166C4⋊Dic5—21no—
167#525—51no—
168#413—151no—
169#410—151no—
170#352—152no—
171AΣL(1,𝔽16)—152no—
172C22×C3×C5—21no—
173C22×C3×C5—41no—
174C22×C3×C5C2×C22⋊C411yescharacteristic
175C2×C3×D5—22no—
176C2×C3×D5—21no—
177C2×C3×D5—21no—
178C2×C3×D5—41no—
179C2×C3×D5—42no—
180C2×C3×D5—41no—
181C2×C3×D5—41no—
182C2×C3×D5—41no—
183C2×C3×D5—42no—
184ΓL(1,𝔽16)—82no—
185C3×C4×C5—21no—
186C3×C4×C5—41no—
187C3×C4×C5—41no—
188C3×C4×C5#9911yescharacteristic
189C3×C4×C5#9911yescharacteristic
190C3×Dic5—21no—
191C3×Dic5—21no—
192C3×Dic5—41no—
193C24×C3—51no—
194C3×#41—201no—
195C3×#41—201no—
196C2×C3×Q8—51no—
197C2×C3×D4—51no—
198C2×C3×D4—51no—
199C2×C3×D4—51no—
200C2×C3×D4—101no—
201C2×C3×D4—101no—
202C22×C3×C4—51no—
203C22×C3×C4—51no—
204C22×C3×C4—51no—
205C22×C3×C4—101no—
206C22×C3×C4—101no—
207C22×C3×C4—201no—
208C22×C3×C4—201no—
209C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
210C3×C4⋊C4—21no—
211C3×C4⋊C4—101no—
212C3×C4⋊C4—101no—
213C3×C22⋊C4—101no—
214C3×C22⋊C4—101no—
215C3×C22⋊C4—101no—
216C3×C22⋊C4—101no—
217C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
218C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
219C3×C42—21no—
220#217—102no—
221C4⋊Dic3—201no—
222C4×Dic3—201no—
223#208—102no—
224#208—201no—
225C2×C3⋊C8—201no—
226C23×C5C22×Dic311yescharacteristic
227C22×D5—21no—
228C22×D5—42no—
229C22×D5—41no—
230C22×D5#21711yescharacteristic
231C22×D5C2×#6711yescharacteristic
232C2×AGL(1,𝔽5)—122no—
233C2×C4×C5—21no—
234C2×C4×C5—21no—
235C2×C4×C5—21no—
236C2×C4×C5—21no—
237C2×C4×C5#21711yescharacteristic
238C2×C4×C5#21711yescharacteristic
239C22⋊D5—41no—
240C22⋊D5—41no—
241C2×Dic5—21no—
242C2×Dic5—41no—
243C2×Dic5#21711yescharacteristic
244C2×Dic5C2×#6711yescharacteristic
245D20—41no—
246D20—42no—
247D20—42no—
248C4×D5—21no—
249C4×D5—21no—
250C4×D5—21no—
251C4×D5—21no—
252C4×D5—42no—
253C4×D5—41no—
254C4×D5—41no—
255Dic10—41no—
256#170—122no—
257C2×#41—51no—
258C23×C4—51no—
259C2×M16—301no—
260#123—51no—
261#123—51no—
262C22⋊Q8—101no—
263#121—101no—
264#120—51no—
265#120—51no—
266C4×D4—101no—
267C4×D4—101no—
268#117—301no—
269#117ΓL(1,𝔽16)11yescharacteristic, complemented
270#101—301no—
271#100—152no—
272#99—152no—
273#99—301no—
274C2×C3×C5—21no—
275C2×C3×C5—41no—
276C2×C3×C5C2×#9911yescharacteristic
277C3×D5—41no—
278C3×D5—41no—
279C3×D5—42no—
280C23×C3—51no—
281C23×C3—51no—
282C23×C3—101no—
283C23×C3—201no—
284C23×C3—202no—
285C23×C3C22×AGL(1,𝔽5)11yescharacteristic
286C3×Q8—201no—
287C3×D4—201no—
288C3×D4—202no—
289C3×D4—202no—
290C3×D4—201no—
291C3×D4—201no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—51no—
297C2×C3×C4—51no—
298C2×C3×C4—101no—
299C2×C3×C4—101no—
300C2×C3×C4—101no—
301C2×C3×C4—101no—
302C2×C3×C4—101no—
303C2×C3×C4—202no—
304C2×C3×C4—201no—
305C2×C3×C4—201no—
306C2×C3×C4—201no—
307C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
308C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
309C2×Dic3—202no—
310C3⋊C8—202no—
311C22×C5—21no—
312C22×C5—41no—
313C22×C5C2×#21711yescharacteristic
314C2×D5—22no—
315C2×D5—21no—
316C2×D5—21no—
317C2×D5—41no—
318C2×D5—42no—
319C2×D5—41no—
320C2×D5—41no—
321C2×D5—41no—
322C2×D5—42no—
323AGL(1,𝔽5)—242no—
324C4×C5—21no—
325C4×C5—41no—
326C4×C5—41no—
327C4×C5#83411yescharacteristic
328C4×C5#83411yescharacteristic
329Dic5—21no—
330Dic5—21no—
331Dic5—41no—
332C24—51no—
333#41—201no—
334#41—201no—
335C2×Q8—51no—
336C2×D4—51no—
337C2×D4—51no—
338C2×D4—51no—
339C2×D4—101no—
340C2×D4—101no—
341C22×C4—51no—
342C22×C4—51no—
343C22×C4—51no—
344C22×C4—101no—
345C22×C4—101no—
346C22×C4—201no—
347C22×C4—201no—
348C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
349M16—302no—
350M16—601no—
351C2×C8—601no—
352C4⋊C4—21no—
353C4⋊C4—101no—
354C4⋊C4—101no—
355C4⋊C4—601no—
356C22⋊C4—101no—
357C22⋊C4—101no—
358C22⋊C4—101no—
359C22⋊C4—101no—
360C22⋊C4—302no—
361C22⋊C4C2×ΓL(1,𝔽16)11yescharacteristic
362C22⋊C4C2×ΓL(1,𝔽16)11yescharacteristic
363C42—21no—
364C42—601no—
365C3×C5#212011yescharacteristic, complemented, Hall
366C22×C3—21no—
367C22×C3—41no—
368C22×C3—102no—
369C22×C3—101no—
370C22×C3—101no—
371C22×C3—201no—
372C22×C3—201no—
373C22×C3—201no—
374C22×C3—202no—
375C22×C3—202no—
376C22×C3—201no—
377C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
378C3×C4—21no—
379C3×C4—41no—
380C3×C4—41no—
381C3×C4—101no—
382C3×C4—101no—
383C3×C4—201no—
384C3×C4#399911yescharacteristic
385C3×C4#399911yescharacteristic
386Dic3—402no—
387C2×C5—21no—
388C2×C5—41no—
389C2×C5C2×#83411yescharacteristic
390D5—41no—
391D5—42no—
392D5—41no—
393C23—51no—
394C23—51no—
395C23—101no—
396C23—201no—
397C23—202no—
398C23C22×ΓL(1,𝔽16)11yescharacteristic
399Q8—201no—
400D4—201no—
401D4—202no—
402D4—202no—
403D4—201no—
404D4—201no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—51no—
410C2×C4—51no—
411C2×C4—101no—
412C2×C4—101no—
413C2×C4—101no—
414C2×C4—101no—
415C2×C4—101no—
416C2×C4—202no—
417C2×C4—201no—
418C2×C4—201no—
419C2×C4—201no—
420C2×C4—602no—
421C2×C4#676311yescharacteristic
422C2×C4#676311yescharacteristic
423C8—602no—
424C2×C3—21no—
425C2×C3—41no—
426C2×C3—201no—
427C2×C3—202no—
428C2×C3—201no—
429C2×C3C2×#399911yescharacteristic
430C5#7171611yescharacteristic, complemented, Sylow
431C22—21no—
432C22—41no—
433C22—102no—
434C22—101no—
435C22—101no—
436C22—201no—
437C22—201no—
438C22—201no—
439C22—202no—
440C22—202no—
441C22—201no—
442C22C2×#676311yescharacteristic
443C4—21no—
444C4—41no—
445C4—41no—
446C4—101no—
447C4—101no—
448C4—201no—
449C4—1202no—
450C4#9122811yescharacteristic
451C4#9122811yescharacteristic
452C3#1060438111yescharacteristic, complemented, Sylow
453C2—21no—
454C2—41no—
455C2—201no—
456C2—202no—
457C2—201no—
458C2C2×#9122811yescharacteristic
subgroupG/H
centerC4#91228
commutatorC23×C3×C5C22×C4
FrattiniC23C22×ΓL(1,𝔽16)
FittingC3×C5×#117C4
socleC2×C3×C5C2×#99
prime radicalC3×#65858C2
cosocleC2×C3×C22⋊D5C23
hypercenter#117ΓL(1,𝔽16)
hypocenterC3×C5#2120
LCSG ▷ C23×C3×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #11752420C2semidirect
3. #11752404C2semidirect
4. #11746736C2semidirect
5. #11746735C2semidirect
8. C22×C3×C4×D5C4semidirect
11. C3×C5×#117C4semidirect
14. C3×#4032C4semidirect
16. C3×#4028C4semidirect
69. C22×C4×D5Dic3semidirect
72. C5×#117Dic3semidirect
75. #4032Dic3semidirect
77. #4028Dic3semidirect
127. C3×#117AGL(1,𝔽5)semidirect
269. #117ΓL(1,𝔽16)semidirect
365. C3×C5#2120semidirect
430. C5#71716semidirect
452. C3#10604381semidirect

Maximal subgroups

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

subgroupindex
C3×#658582
#117524202
#117524042
#117467362
#117467352
#106043813
#717165