Finite Group Databasebeta

← #14303111

Subgroups — #14303111

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×#65860C211yesmaximal, characteristic
2#11754120C211yesmaximal, characteristic
3C2×#90961C211yesmaximal, characteristic, complemented
4C2×#90961C211yesmaximal, characteristic, complemented
5#11748353C211yesmaximal, characteristic
6#11746354C211yesmaximal, characteristic, complemented
7C5×#4533C211yesmaximal, characteristic, complemented
8#10599834—31nomaximal, Hall
9C2×C3×#709C2211yescharacteristic
10C22×C3×Dic10C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C2×C5×#208C2211yescharacteristic
16C3×#4043—22no—
17C3×#4032C414yes—
18C3×#4021—21no—
19C3×#4015—21no—
20#91284—22no—
21#91283—22no—
22D5×#208—22no—
23#90961—21no—
24#90961—22no—
25#90961—22no—
26#90958—21no—
27#71866—51nomaximal, Hall
28#66079—31no—
29#65860D311yescharacteristic
30C2×#3956—31no—
31C2×#3956—31no—
32#65421—31no—
33C5×#344—31no—
34#64753—31no—
35C22×C3×C4×C5C2311yescharacteristic
36C2×C3×C22⋊D5C2×C412yes—
37C22×C3×Dic5C2×C412yes—
38C3×#709—21no—
39C3×#709—21no—
40C3×#709—21no—
41C3×#709—21no—
42C2×C3×D20D411yescharacteristic
43C2×C3×C4×D5D412yes—
44C2×C3×Dic10—21no—
45C2×C3×Dic10—21no—
46C2×C3×Dic10—21no—
47C2×C3×Dic10—21no—
48C2×C3×Dic10—21no—
49C2×C3×Dic10—21no—
50C2×C3×Dic10D411yescharacteristic
51C3×C5×C4⋊C4—21no—
52C3×C5×C22⋊C4C2×C412yes—
53C3×C42×C5—21no—
54#6710—21no—
55#6710—21no—
56#6710—21no—
57#6710D412yes—
58C2×C3⋊#168—21no—
59C2×C3⋊#168—21no—
60C5×#208—21no—
61C5×#208—21no—
62C5×#208—21no—
63C5×#208D412yes—
64C2×C5×C3⋊C8—21no—
65C2×C5×C3⋊C8—21no—
66C3×#685—24no—
67C3×C4⋊Dic5—24no—
68#6649—24no—
69D5×C3⋊C8—24no—
70C3×#536—51no—
71#5819—51no—
72#5237—51no—
73C2×#836—51no—
74C2×#836—51no—
75#4533—51no—
76#4533D511yescharacteristic, complemented
77C2×#709C2×D311yescharacteristic
78C22×Dic10C2×D311yescharacteristic
79C2×C5×M16—31no—
80C2×C5×M16—31no—
81C5×#117C2×D311yescharacteristic
82C2×#681—31no—
83C2×#681—31no—
84#4053—62no—
85D5×M16—62no—
86#4047—62no—
87#4043—22no—
88#4032Dic314yes—
89#4021—21no—
90#4015—21no—
91#3956—62no—
92#3956—62no—
93#3956—61no—
94#3955—61no—
95#1915—151noSylow
96C23×C3×C5C22×C411yescharacteristic
97C22×C3×D5C22⋊C412yes—
98C2×C3×C4×C5—22no—
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5#4111yescharacteristic
104C2×C3×C4×C5#4111yescharacteristic
105C3×C22⋊D5—22no—
106C3×C22⋊D5—22no—
107C2×C3×Dic5—22no—
108C2×C3×Dic5—22no—
109C2×C3×Dic5—22no—
110C2×C3×Dic5C22⋊C412yes—
111C3×D20—21no—
112C3×D20—21no—
113C3×C4×D5—22no—
114C3×C4×D5—22no—
115C3×Dic10—21no—
116C3×Dic10—21no—
117C3×Dic10—41no—
118C3×Dic10—41no—
119C3×Dic10—41no—
120C3×Dic10—41no—
121C3⋊#168—22no—
122C3⋊#168—41no—
123C5×C3⋊C8—22no—
124C5×C3⋊C8—41no—
125C2×C3×#41—51no—
126C22×C3×Q8—51no—
127C3×C4⋊Q8—101no—
128C3×#124—101no—
129C3×#123—54no—
130C3×C22⋊Q8—102no—
131C3×#117C2×D511yescharacteristic
132#948—102no—
133#948—102no—
134C2×#208—51no—
135C2×#208—51no—
136C2×#208—102no—
137C2×#208C2×D511yescharacteristic
138C2×#208C2×D511yescharacteristic
139#836—102no—
140#836—101no—
141#836—102no—
142#833—101no—
143C22×C4×C5C22×D311yescharacteristic
144C2×C22⋊D5C2×Dic312yes—
145C22×Dic5C2×Dic312yes—
146#709—21no—
147#709—21no—
148#709—21no—
149#709—21no—
150C2×D20#6711yescharacteristic
151C2×C4×D5#6712yes—
152C2×Dic10—21no—
153C2×Dic10—21no—
154C2×Dic10—21no—
155C2×Dic10—21no—
156C2×Dic10—21no—
157C2×Dic10—21no—
158C2×Dic10#6711yescharacteristic
159C5×M16—32no—
160C5×M16—61no—
161C5×M16—61no—
162C5×M16—61no—
163C2×C5×C8—61no—
164C2×C5×C8—61no—
165C5×C4⋊C4—21no—
166C5×C22⋊C4C2×Dic312yes—
167C42×C5—21no—
168#685—24no—
169C4⋊Dic5—24no—
170#681—32no—
171#681—61no—
172#681—61no—
173#681—61no—
174C2×#168—61no—
175C2×#168—61no—
176#676—64no—
177C8×D5—64no—
178#568—151no—
179#536—51no—
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—42no—
192C3×C4×C5#12011yescharacteristic
193C3×C4×C5#12111yescharacteristic
194C3×C4×C5#12111yescharacteristic
195C3×C4×C5#12311yescharacteristic
196C3×Dic5—22no—
197C3×Dic5—42no—
198C3×#41—101no—
199C3×#41—101no—
200C3×#41—101no—
201C3×#41—101no—
202C2×C3×Q8—51no—
203C2×C3×Q8—101no—
204C2×C3×Q8—101no—
205C2×C3×Q8—101no—
206C2×C3×Q8—101no—
207C2×C3×Q8—101no—
208C2×C3×Q8—101no—
209C2×C3×D4—52no—
210C2×C3×D4—51no—
211C22×C3×C4—52no—
212C22×C3×C4—52no—
213C22×C3×C4C22×D511yescharacteristic
214C3×C4⋊C4—21no—
215C3×C4⋊C4—104no—
216C3×C22⋊C4—104no—
217C3×C22⋊C4C4×D512yes—
218C3×C42—21no—
219#208—21no—
220#208—21no—
221#208—21no—
222#208—52no—
223#208—104no—
224#208—101no—
225#208—101no—
226#208—101no—
227#208D2012yes—
228C2×C3⋊C8—21no—
229C2×C3⋊C8—21no—
230C2×C3⋊C8—104no—
231C2×C3⋊C8—101no—
232C2×C3⋊C8—101no—
233C23×C5C22×Dic311yescharacteristic
234C22×D5#21712yes—
235C2×C4×C5—22no—
236C2×C4×C5D3×D411yescharacteristic
237C2×C4×C5D3×D411yescharacteristic
238C2×C4×C5#23711yescharacteristic
239C2×C4×C5#23711yescharacteristic
240C2×C4×C5C2×#6711yescharacteristic
241C2×C4×C5C2×#6711yescharacteristic
242C22⋊D5—22no—
243C22⋊D5—22no—
244C2×Dic5—22no—
245C2×Dic5—22no—
246C2×Dic5—22no—
247C2×Dic5#21712yes—
248D20—21no—
249D20—21no—
250C4×D5—22no—
251C4×D5—22no—
252Dic10—21no—
253Dic10—21no—
254Dic10—41no—
255Dic10—41no—
256Dic10—41no—
257Dic10—41no—
258C5×C8—62no—
259C5×C8—121no—
260#168—62no—
261#168—121no—
262C2×#41—51no—
263C22×Q8—51no—
264#131—302no—
265#131—302no—
266C2×M16—31no—
267C2×M16—31no—
268C2×M16—151no—
269C2×M16—151no—
270C2×M16—302no—
271C4⋊Q8—101no—
272#124—101no—
273#123—54no—
274C22⋊Q8—102no—
275#117D3×D511yescharacteristic
276#101—302no—
277#101—302no—
278#101—301no—
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×Q8—201no—
290C3×Q8—201no—
291C3×Q8—201no—
292C3×Q8—201no—
293C3×D4—102no—
294C3×D4—102no—
295C3×D4—101no—
296C3×D4—101no—
297C2×C3×C4—22no—
298C2×C3×C4—52no—
299C2×C3×C4—102no—
300C2×C3×C4—102no—
301C2×C3×C4—102no—
302C2×C3×C4—102no—
303C2×C3×C4—102no—
304C2×C3×C4C2×D2011yescharacteristic
305C2×C3×C4#70911yescharacteristic
306C2×C3×C4D4×D511yescharacteristic
307C2×C3×C4D4×D511yescharacteristic
308C2×C3×C4D4×D511yescharacteristic
309C2×C3×C4#71311yescharacteristic
310C3⋊C8—22no—
311C3⋊C8—41no—
312C3⋊C8—102no—
313C3⋊C8—201no—
314C22×C5—41no—
315C22×C5D4×Dic311yescharacteristic
316C22×C5D4×Dic311yescharacteristic
317C22×C5C2×#21711yescharacteristic
318C2×D5—22no—
319C2×D5—42no—
320C4×C5—42no—
321C4×C5#93511yescharacteristic
322C4×C5#93711yescharacteristic
323C4×C5#93911yescharacteristic
324C4×C5#93911yescharacteristic
325Dic5—22no—
326Dic5—42no—
327#41—101no—
328#41—101no—
329#41—101no—
330#41—101no—
331C2×Q8—51no—
332C2×Q8—101no—
333C2×Q8—101no—
334C2×Q8—101no—
335C2×Q8—101no—
336C2×Q8—101no—
337C2×Q8—101no—
338C2×D4—52no—
339C2×D4—51no—
340C22×C4—52no—
341C22×C4—52no—
342C22×C4C2×D3×D511yescharacteristic
343M16—32no—
344M16—61no—
345M16—61no—
346M16—61no—
347M16—152no—
348M16—304no—
349M16—301no—
350M16—301no—
351M16—301no—
352C2×C8—61no—
353C2×C8—61no—
354C2×C8—304no—
355C2×C8—301no—
356C2×C8—301no—
357C4⋊C4—21no—
358C4⋊C4—104no—
359C22⋊C4—104no—
360C22⋊C4D5×Dic312yes—
361C42—21no—
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—42no—
370C3×C4—102no—
371C3×C4—202no—
372C3×C4#402811yescharacteristic
373C3×C4#403011yescharacteristic
374C3×C4#404011yescharacteristic
375C3×C4#404111yescharacteristic
376C2×C5—21no—
377C2×C5—21no—
378C2×C5—21no—
379C2×C5#522011yescharacteristic
380D5—42no—
381C23—52no—
382C23C2×D5×Dic311yescharacteristic
383Q8—101no—
384Q8—101no—
385Q8—201no—
386Q8—201no—
387Q8—201no—
388Q8—201no—
389D4—102no—
390D4—102no—
391D4—101no—
392D4—101no—
393C2×C4—22no—
394C2×C4—52no—
395C2×C4—102no—
396C2×C4—102no—
397C2×C4—102no—
398C2×C4—102no—
399C2×C4—102no—
400C2×C4#676511yescharacteristic
401C2×C4#676611yescharacteristic
402C2×C4D3×D2011yescharacteristic
403C2×C4#677711yescharacteristic
404C2×C4D5×#6711yescharacteristic
405C2×C4D5×#6711yescharacteristic
406C8—62no—
407C8—121no—
408C8—302no—
409C8—601no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—202no—
414C2×C3#6495411yescharacteristic
415C5#7186611yescharacteristic, complemented, Sylow
416C22—41no—
417C22—102no—
418C22—202no—
419C22Dic3×D2011yescharacteristic
420C22#9143411yescharacteristic
421C22D5×#21711yescharacteristic
422C4—42no—
423C4—102no—
424C4—202no—
425C4#9140711yescharacteristic
426C4#9140811yescharacteristic
427C4#9140911yescharacteristic
428C4#9147411yescharacteristic
429C3#1059983411yescharacteristic, complemented, Sylow
430C2—21no—
431C2—21no—
432C2—21no—
433C2—202no—
434C2#1174889611yescharacteristic
subgroupG/H
centerC2#11748896
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5#386
prime radicalC2×C3×#709C22
cosocleC22×C3×C4×C5C23
hypercenter#117D3×D5
hypocenterC3×C5#1915
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
3. C2×#90961C2semidirect
4. C2×#90961C2semidirect
6. #11746354C2semidirect
7. C5×#4533C2semidirect
76. #4533D5semidirect
362. C3×C5#1915semidirect
415. C5#71866semidirect
429. C3#10599834semidirect

Maximal subgroups

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

subgroupindex
C3×#658602
#117541202
C2×#909612
#117483532
#117463542
C5×#45332
#105998343
#718665