Finite Group Databasebeta

← #14303101

Subgroups — #14303101

Order 1920.

616 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
1C3×#66079C211yesmaximal, characteristic
2#11754252C211yesmaximal, characteristic
3C2×#91108C211yesmaximal, characteristic, complemented
4C2×#90963C211yesmaximal, characteristic, complemented
5#11748353C211yesmaximal, characteristic
6C5×#4559C211yesmaximal, characteristic, complemented
7#11745989C211yesmaximal, characteristic, complemented
8#10599834—31nomaximal, Hall
9C22×Dic30C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C5×#926C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16C3×#4053—22no—
17C3×D5×M16—22no—
18C3×#4047—22no—
19#91537C414yes—
20#91389—21no—
21#91364—21no—
22#91360—22no—
23#91108—22no—
24#90963—22no—
25#90961—21no—
26#90958—21no—
27#72031—51nomaximal, Hall
28#66079D311yescharacteristic
29#65860—31no—
30C2×#3956—31no—
31C2×#3956—31no—
32#65421—31no—
33C5×#344—31no—
34#64753—31no—
35C22×C3×C4×C5C2311yescharacteristic
36C22×Dic15C2×C412yes—
37C2×Dic30—21no—
38C2×Dic30—21no—
39C2×Dic30—21no—
40C2×Dic30—21no—
41C2×Dic30—21no—
42C2×Dic30—21no—
43C2×C3×C22⋊D5C2×C412yes—
44C3×#709—21no—
45C3×#709—21no—
46C3×#709—21no—
47C3×#709—21no—
48C2×C3×D20D411yescharacteristic
49C2×C3×C4×D5D412yes—
50C2×C3×Dic10D411yescharacteristic
51C3×C5×M16—21no—
52C3×C5×M16D412yes—
53C2×C3×C5×C8—21no—
54#6710—21no—
55#6710—21no—
56C2×C3⋊#168—21no—
57C5×#217C2×C412yes—
58C5×C4⋊Dic3—21no—
59C4×C5×Dic3—21no—
60C5×#208—21no—
61C5×#208—21no—
62C2×C5×C3⋊C8—21no—
63C3×#681—21no—
64C3×#681D412yes—
65C2×C3×#168—21no—
66C3×#676—24no—
67C3×C8×D5—24no—
68Dic3⋊Dic5—24no—
69#6665—24no—
70C3×#568—51no—
71#5825—51no—
72#5237—51no—
73C2×#824—51no—
74C2×#824—51no—
75#4559—51no—
76#4559D511yescharacteristic, complemented
77C2×#709C2×D311yescharacteristic
78C22×Dic10—31no—
79C2×C5×M16—31no—
80C2×C5×M16C2×D311yescharacteristic
81C5×#117—31no—
82C2×#681—31no—
83C2×#681C2×D311yescharacteristic
84#4053—22no—
85D5×M16—22no—
86#4047—22no—
87#4043—62no—
88#4032—34no—
89#4021—61no—
90#4015—61no—
91#3956—61no—
92#3956—62no—
93#3956—62no—
94#3955—61no—
95#1915—151noSylow
96C23×C3×C5C22×C411yescharacteristic
97C22×C3×D5C22⋊C412yes—
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×C3×C4×C5#4111yescharacteristic
104C2×Dic15—22no—
105C2×Dic15—22no—
106C2×Dic15—22no—
107Dic30—41no—
108Dic30—41no—
109Dic30—41no—
110Dic30—41no—
111C2×C5×Dic3—22no—
112C3×C22⋊D5—22no—
113C3×C22⋊D5—22no—
114C2×C3×Dic5C22⋊C412yes—
115C3×D20—21no—
116C3×D20—21no—
117C3×C4×D5—22no—
118C3×C4×D5—22no—
119C3×Dic10—21no—
120C3×Dic10—21no—
121C3×C5×C8—22no—
122C3⋊#168—41no—
123C3×#168—22no—
124C5×C3⋊C8—41no—
125C2×C3×#41—51no—
126C22×Dic6—51no—
127C3×#131—102no—
128C3×#131—102no—
129C2×C3×M16—51no—
130C2×C3×M16—102no—
131C2×C3×M16C2×D511yescharacteristic
132#944—101no—
133#936—101no—
134#935—54no—
135#926C2×D511yescharacteristic
136#924—102no—
137C2×#208—51no—
138C2×#208C2×D511yescharacteristic
139#836—101no—
140#833—101no—
141#824—102no—
142#824—102no—
143C22×C4×C5C22×D311yescharacteristic
144C2×C22⋊D5C4×D312yes—
145C22×Dic5—32no—
146#709—21no—
147#709—21no—
148#709—21no—
149#709—21no—
150C2×D20D1211yescharacteristic
151C2×C4×D5#6712yes—
152C2×Dic10—61no—
153C2×Dic10—61no—
154C2×Dic10—61no—
155C2×Dic10—61no—
156C2×Dic10—61no—
157C2×Dic10—61no—
158C2×Dic10D1211yescharacteristic
159C5×M16—21no—
160C5×M16—61no—
161C5×M16—61no—
162C5×M16#6712yes—
163C2×C5×C8—21no—
164C2×C5×C8—61no—
165C5×C4⋊C4—61no—
166C5×C22⋊C4—32no—
167C42×C5—61no—
168#685—64no—
169C4⋊Dic5—64no—
170#681—21no—
171#681—61no—
172#681—61no—
173#681#6712yes—
174C2×#168—21no—
175C2×#168—61no—
176#676—24no—
177C8×D5—24no—
178#568—51no—
179#536—151no—
180#413—151no—
181C2×#101—151no—
182C2×#101—151no—
183#344—31no—
184#344—151no—
185C22×C3×C5—41no—
186C22×C3×C5C2×C22⋊C411yescharacteristic
187C22×C3×C5C4×D411yescharacteristic
188C22×C3×C5C4×D411yescharacteristic
189C2×C3×D5—22no—
190C2×C3×D5—42no—
191C3×C4×C5#12011yescharacteristic
192C3×C4×C5#12111yescharacteristic
193C3×C4×C5#12111yescharacteristic
194C3×C4×C5#12311yescharacteristic
195Dic15—42no—
196C3×Dic5—22no—
197C5×Dic3—42no—
198C3×#41—101no—
199C3×#41—101no—
200C3×#41—101no—
201C3×#41—101no—
202C2×C3×Q8—51no—
203C2×C3×D4—52no—
204C2×C3×D4—51no—
205C22×C3×C4—52no—
206C22×C3×C4C22×D511yescharacteristic
207C22×Dic3—52no—
208C2×Dic6—101no—
209C2×Dic6—101no—
210C2×Dic6—101no—
211C2×Dic6—101no—
212C2×Dic6—101no—
213C2×Dic6—101no—
214C3×M16—21no—
215C3×M16—52no—
216C3×M16—104no—
217C3×M16—101no—
218C3×M16D2012yes—
219C2×C3×C8—21no—
220C2×C3×C8—104no—
221C2×C3×C8—101no—
222#217—104no—
223#217C4×D512yes—
224C4⋊Dic3—21no—
225Dic3⋊C4—104no—
226C4×Dic3—21no—
227#208—21no—
228#208—21no—
229#208—101no—
230#208—101no—
231C2×C3⋊C8—21no—
232C2×C3⋊C8—101no—
233C23×C5C2×C4×D311yescharacteristic
234C22×D5(C2×D3)⋊C412yes—
235C2×C4×C5—62no—
236C2×C4×C5C2×D1211yescharacteristic
237C2×C4×C5#23511yescharacteristic
238C2×C4×C5#23511yescharacteristic
239C2×C4×C5C2×#6711yescharacteristic
240C2×C4×C5C2×#6711yescharacteristic
241C2×C4×C5C2×#6711yescharacteristic
242C22⋊D5—22no—
243C22⋊D5—22no—
244C2×Dic5—62no—
245C2×Dic5—62no—
246C2×Dic5—62no—
247C2×Dic5(C2×D3)⋊C412yes—
248D20—21no—
249D20—21no—
250C4×D5—22no—
251C4×D5—22no—
252Dic10—21no—
253Dic10—21no—
254Dic10—121no—
255Dic10—121no—
256Dic10—121no—
257Dic10—121no—
258C5×C8—22no—
259C5×C8—121no—
260#168—22no—
261#168—121no—
262C2×#41—51no—
263C22×Q8—151no—
264#131—102no—
265#131—102no—
266C2×M16—31no—
267C2×M16—51no—
268C2×M16—102no—
269C2×M16—151no—
270C2×M16D3×D511yescharacteristic
271C4⋊Q8—301no—
272#124—301no—
273#123—154no—
274C22⋊Q8—302no—
275#117—31no—
276#101—302no—
277#101—301no—
278#101—302no—
279#100—301no—
280C2×C3×C5—21no—
281C2×C3×C5—21no—
282C2×C3×C5—21no—
283C2×C3×C5#38611yescharacteristic
284C3×D5—42no—
285C23×C3—52no—
286C23×C3C2×C4×D511yescharacteristic
287C3×Q8—101no—
288C3×Q8—101no—
289C3×D4—102no—
290C3×D4—102no—
291C3×D4—101no—
292C3×D4—101no—
293C2×C3×C4—52no—
294C2×C3×C4—102no—
295C2×C3×C4—102no—
296C2×C3×C4C2×D2011yescharacteristic
297C2×C3×C4#70911yescharacteristic
298C2×C3×C4D4×D511yescharacteristic
299C2×C3×C4D4×D511yescharacteristic
300C2×C3×C4D4×D511yescharacteristic
301C2×C3×C4#71311yescharacteristic
302C2×Dic3—22no—
303C2×Dic3—102no—
304C2×Dic3—102no—
305C2×Dic3—102no—
306Dic6—201no—
307Dic6—201no—
308Dic6—201no—
309Dic6—201no—
310C3×C8—22no—
311C3×C8—102no—
312C3⋊C8—41no—
313C3⋊C8—201no—
314C22×C5—41no—
315C22×C5C2×(C2×D3)⋊C411yescharacteristic
316C22×C5C4×#6711yescharacteristic
317C22×C5C4×#6711yescharacteristic
318C2×D5—22no—
319C2×D5—42no—
320C4×C5—122no—
321C4×C5#92911yescharacteristic
322C4×C5#93011yescharacteristic
323C4×C5#93011yescharacteristic
324C4×C5#95311yescharacteristic
325Dic5—22no—
326Dic5—122no—
327#41—101no—
328#41—101no—
329#41—101no—
330#41—101no—
331C2×Q8—51no—
332C2×Q8—301no—
333C2×Q8—301no—
334C2×Q8—301no—
335C2×Q8—301no—
336C2×Q8—301no—
337C2×Q8—301no—
338C2×D4—52no—
339C2×D4—51no—
340C22×C4—52no—
341C22×C4—152no—
342C22×C4C2×D3×D511yescharacteristic
343M16—21no—
344M16—52no—
345M16—61no—
346M16—61no—
347M16—104no—
348M16—101no—
349M16—301no—
350M16—301no—
351M16#120212yes—
352C2×C8—21no—
353C2×C8—61no—
354C2×C8—104no—
355C2×C8—101no—
356C2×C8—301no—
357C4⋊C4—61no—
358C4⋊C4—304no—
359C22⋊C4—32no—
360C22⋊C4—304no—
361C42—61no—
362C3×C5#191511yescharacteristic, complemented, Hall
363C22×C3—41no—
364C22×C3—102no—
365C22×C3—202no—
366C22×C3C4×D2011yescharacteristic
367C22×C3D5×C22⋊C411yescharacteristic
368C22×C3#403911yescharacteristic
369C3×C4—102no—
370C3×C4#402811yescharacteristic
371C3×C4#403011yescharacteristic
372C3×C4#404011yescharacteristic
373C3×C4#404111yescharacteristic
374Dic3—42no—
375Dic3—202no—
376C2×C5—21no—
377C2×C5—21no—
378C2×C5—21no—
379C2×C5#521311yescharacteristic
380D5—42no—
381C23—52no—
382C23C4×D3×D511yescharacteristic
383Q8—101no—
384Q8—101no—
385Q8—601no—
386Q8—601no—
387Q8—601no—
388Q8—601no—
389D4—102no—
390D4—102no—
391D4—101no—
392D4—101no—
393C2×C4—52no—
394C2×C4—62no—
395C2×C4—102no—
396C2×C4—102no—
397C2×C4—302no—
398C2×C4—302no—
399C2×C4—302no—
400C2×C4#677111yescharacteristic
401C2×C4#677311yescharacteristic
402C2×C4D5×D1211yescharacteristic
403C2×C4C2×#120211yescharacteristic
404C2×C4D5×#6711yescharacteristic
405C2×C4D5×#6711yescharacteristic
406C8—22no—
407C8—102no—
408C8—121no—
409C8—601no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—202no—
414C2×C3#6495411yescharacteristic
415C5#7203111yescharacteristic, complemented, Sylow
416C22—41no—
417C22—102no—
418C22—202no—
419C22C4×#120211yescharacteristic
420C22#9144411yescharacteristic
421C22D5×(C2×D3)⋊C411yescharacteristic
422C4—102no—
423C4—122no—
424C4—602no—
425C4#9134811yescharacteristic
426C4#9144811yescharacteristic
427C4#9145011yescharacteristic
428C4#9156411yescharacteristic
429C3#1059983411yescharacteristic, complemented, Sylow
430C2—21no—
431C2—21no—
432C2—21no—
433C2—202no—
434C2#1174890711yescharacteristic
subgroupG/H
centerC2#11748907
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#386
prime radicalC2×C3×#709C22
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1915
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. C2×#91108C2semidirect
4. C2×#90963C2semidirect
6. C5×#4559C2semidirect
7. #11745989C2semidirect
76. #4559D5semidirect
362. C3×C5#1915semidirect
415. C5#72031semidirect
429. C3#10599834semidirect

Maximal subgroups

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

subgroupindex
C3×#660792
#117542522
C2×#911082
C2×#909632
#117483532
C5×#45592
#117459892
#105998343
#720315