Finite Group Databasebeta

← #14303100

Subgroups — #14303100

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
1#11756504C211yesmaximal, characteristic
2#11754278C211yesmaximal, characteristic
3C2×C3×#3956C211yesmaximal, characteristic, complemented
4C2×#90961C211yesmaximal, characteristic, complemented
5#11748357C211yesmaximal, characteristic
6C5×#4559C211yesmaximal, characteristic, complemented
7#11745988C211yesmaximal, characteristic, complemented
8#10599834—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C22×C3×Dic10C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13#91796—22no—
14M16×D15—22no—
15#91790—22no—
16C5×#926C2211yescharacteristic
17C2×C5×#208C2211yescharacteristic
18C2×C3×#681C2211yescharacteristic
19#91546C414yes—
20#91390—22no—
21#91389—21no—
22#91374—21no—
23C3×#3956—22no—
24#90963—21no—
25#90961—22no—
26#90960—21no—
27#70124—51nomaximal, Hall
28#66079—31no—
29#65860—31no—
30C2×#3956—31no—
31C2×#3956D311yescharacteristic, complemented
32#65421—31no—
33C5×#344—31no—
34#64753—31no—
35C22×C3×C4×C5C2311yescharacteristic
36C2×#1220C2×C412yes—
37#6817—21no—
38#6817—21no—
39#6817—21no—
40#6817—21no—
41C2×D60D411yescharacteristic
42C2×C4×D15D412yes—
43C2×Dic30D411yescharacteristic
44C22×C3×Dic5C2×C412yes—
45C2×C3×Dic10—21no—
46C2×C3×Dic10—21no—
47C2×C3×Dic10—21no—
48C2×C3×Dic10—21no—
49C2×C3×Dic10—21no—
50C2×C3×Dic10—21no—
51C3×C5×M16—21no—
52C3×C5×M16D412yes—
53C2×C3×C5×C8—21no—
54#6710—21no—
55#6710D412yes—
56C2×C3⋊#168—21no—
57#6705—24no—
58C8×D15—24no—
59C5×#217C2×C412yes—
60C5×C4⋊Dic3—21no—
61C4×C5×Dic3—21no—
62C5×#208—21no—
63C5×#208—21no—
64C2×C5×C3⋊C8—21no—
65C3×#681—21no—
66C3×#681—21no—
67C2×C3×#168—21no—
68Dic3⋊Dic5—24no—
69#6667—24no—
70#5816—51no—
71#5745—51no—
72C2×C3×#101—51no—
73C2×#836—51no—
74#5132—51no—
75#4559D511yescharacteristic, complemented
76#4556—51no—
77C2×#709—31no—
78C22×Dic10C2×D311yescharacteristic
79C2×C5×M16—31no—
80C2×C5×M16C2×D311yescharacteristic
81C5×#117—31no—
82C2×#681—31no—
83C2×#681C2×D311yescharacteristic
84#4053—62no—
85D5×M16—62no—
86#4047—62no—
87#4043—62no—
88#4032—34no—
89#4021—61no—
90#4015—61no—
91#3956—22no—
92#3956—61no—
93#3956—62no—
94#3955—61no—
95#1915—151noSylow
96C23×C3×C5C22×C411yescharacteristic
97C22×D15C22⋊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
104#1220—22no—
105#1220—22no—
106C2×Dic15C22⋊C412yes—
107D60—21no—
108D60—21no—
109C4×D15—22no—
110C4×D15—22no—
111Dic30—21no—
112Dic30—21no—
113C2×C5×Dic3—22no—
114C2×C3×Dic5—22no—
115C2×C3×Dic5—22no—
116C2×C3×Dic5—22no—
117C3×Dic10—41no—
118C3×Dic10—41no—
119C3×Dic10—41no—
120C3×Dic10—41no—
121C3×C5×C8—22no—
122C3⋊#168—22no—
123C3×#168—41no—
124C5×C3⋊C8—41no—
125C22×C3×Q8—51no—
126C2×#235—51no—
127C2×C3×M16—51no—
128C2×C3×M16C2×D511yescharacteristic
129#947—101no—
130#946—102no—
131#944—101no—
132#929—54no—
133#926C2×D511yescharacteristic
134C2×#208—51no—
135C2×#208C2×D511yescharacteristic
136#907—102no—
137D3×M16—102no—
138#901—102no—
139C3×#101—102no—
140#836—102no—
141#824—101no—
142#823—101no—
143C22×C4×C5C22×D311yescharacteristic
144C2×C22⋊D5—32no—
145C22×Dic5C4×D312yes—
146#709—61no—
147#709—61no—
148#709—61no—
149#709—61no—
150C2×D20—31no—
151C2×C4×D5—32no—
152C2×Dic10—21no—
153C2×Dic10—21no—
154C2×Dic10—21no—
155C2×Dic10—21no—
156C2×Dic10—21no—
157C2×Dic10—21no—
158C2×Dic10—31no—
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—21no—
172#681—32no—
173#681—61no—
174C2×#168—21no—
175C2×#168—61no—
176#676—64no—
177C8×D5—64no—
178#568—151no—
179#536—151no—
180#413—151no—
181C2×#101—51no—
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×D15—22no—
190C2×D15—42no—
191C3×C4×C5#12011yescharacteristic
192C3×C4×C5#12111yescharacteristic
193C3×C4×C5#12111yescharacteristic
194C3×C4×C5#12311yescharacteristic
195Dic15—22no—
196C3×Dic5—42no—
197C5×Dic3—42no—
198C2×C3×Q8—101no—
199C2×C3×Q8—101no—
200C2×C3×Q8—101no—
201C2×C3×Q8—101no—
202C2×C3×Q8—101no—
203C2×C3×Q8—101no—
204C22×C3×C4—52no—
205C22×C3×C4C22×D511yescharacteristic
206C2×#67—52no—
207#235—101no—
208#235—101no—
209#235—101no—
210#235—101no—
211C2×D12—51no—
212C2×C4×D3—52no—
213C2×Dic6—51no—
214C3×M16—21no—
215C3×M16—101no—
216C3×M16—101no—
217C3×M16D2012yes—
218C2×C3×C8—21no—
219C2×C3×C8—101no—
220#217C4×D512yes—
221(C2×D3)⋊C4—104no—
222C4⋊Dic3—21no—
223Dic3⋊C4—104no—
224C4×Dic3—21no—
225#208—21no—
226#208—21no—
227#208—52no—
228#208—101no—
229C2×C3⋊C8—21no—
230C2×C3⋊C8—101no—
231ΓL(1,𝔽25)—104no—
232D3×C8—104no—
233C23×C5C2×C4×D311yescharacteristic
234C22×D5—32no—
235C2×C4×C5—62no—
236C2×C4×C5#23511yescharacteristic
237C2×C4×C5D3×D411yescharacteristic
238C2×C4×C5D3×D411yescharacteristic
239C2×C4×C5D3×D411yescharacteristic
240C2×C4×C5#23711yescharacteristic
241C2×C4×C5C2×#6711yescharacteristic
242C22⋊D5—62no—
243C22⋊D5—62no—
244C2×Dic5—22no—
245C2×Dic5—22no—
246C2×Dic5—22no—
247C2×Dic5—32no—
248D20—61no—
249D20—61no—
250C4×D5—62no—
251C4×D5—62no—
252Dic10—41no—
253Dic10—41no—
254Dic10—41no—
255Dic10—41no—
256Dic10—61no—
257Dic10—61no—
258C5×C8—22no—
259C5×C8—121no—
260#168—41no—
261#168—62no—
262C2×#41—151no—
263C22×Q8—51no—
264#131—302no—
265#131—302no—
266C2×M16—31no—
267C2×M16—51no—
268C2×M16—151no—
269C2×M16—302no—
270C2×M16D3×D511yescharacteristic
271C4⋊Q8—301no—
272#124—301no—
273#123—154no—
274C22⋊Q8—302no—
275#117—31no—
276#101—102no—
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
284D15—42no—
285C23×C3C2×C4×D511yescharacteristic
286C22×D3—52no—
287C3×Q8—201no—
288C3×Q8—201no—
289C3×Q8—201no—
290C3×Q8—201no—
291C2×C3×C4—102no—
292C2×C3×C4—102no—
293C2×C3×C4—102no—
294C2×C3×C4C2×D2011yescharacteristic
295C2×C3×C4#70911yescharacteristic
296C2×C3×C4D4×D511yescharacteristic
297C2×C3×C4D4×D511yescharacteristic
298C2×C3×C4D4×D511yescharacteristic
299C2×C3×C4#71311yescharacteristic
300#67—102no—
301#67—102no—
302C2×Dic3—22no—
303C2×Dic3—52no—
304D12—101no—
305D12—101no—
306C4×D3—102no—
307C4×D3—102no—
308Dic6—101no—
309Dic6—101no—
310C3×C8—22no—
311C3×C8—201no—
312C3⋊C8—41no—
313C3⋊C8—102no—
314C22×C5—41no—
315C22×C5D3×C22⋊C411yescharacteristic
316C22×C5#67⋊C411yescharacteristic
317C22×C5C4×#6711yescharacteristic
318C2×D5—62no—
319C2×D5—122no—
320C4×C5—122no—
321C4×C5#88311yescharacteristic
322C4×C5#88411yescharacteristic
323C4×C5#93711yescharacteristic
324C4×C5#93811yescharacteristic
325Dic5—42no—
326Dic5—62no—
327#41—301no—
328#41—301no—
329#41—301no—
330#41—301no—
331C2×Q8—101no—
332C2×Q8—101no—
333C2×Q8—101no—
334C2×Q8—101no—
335C2×Q8—101no—
336C2×Q8—101no—
337C2×Q8—151no—
338C2×D4—152no—
339C2×D4—151no—
340C22×C4—52no—
341C22×C4—152no—
342C22×C4C2×D3×D511yescharacteristic
343M16—21no—
344M16—61no—
345M16—61no—
346M16—101no—
347M16—101no—
348M16—152no—
349M16—304no—
350M16—301no—
351M16#120212yes—
352C2×C8—21no—
353C2×C8—61no—
354C2×C8—101no—
355C2×C8—304no—
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×C3C4×D2011yescharacteristic
365C22×C3D5×C22⋊C411yescharacteristic
366C22×C3#403911yescharacteristic
367C2×D3—102no—
368C2×D3—202no—
369C3×C4—202no—
370C3×C4#402811yescharacteristic
371C3×C4#403011yescharacteristic
372C3×C4#404011yescharacteristic
373C3×C4#404111yescharacteristic
374Dic3—42no—
375Dic3—102no—
376C2×C5—21no—
377C2×C5—21no—
378C2×C5—21no—
379C2×C5#495611yescharacteristic
380D5—122no—
381C23—152no—
382C23C4×D3×D511yescharacteristic
383Q8—201no—
384Q8—201no—
385Q8—201no—
386Q8—201no—
387Q8—301no—
388Q8—301no—
389D4—302no—
390D4—302no—
391D4—301no—
392D4—301no—
393C2×C4—62no—
394C2×C4—102no—
395C2×C4—102no—
396C2×C4—102no—
397C2×C4—152no—
398C2×C4—302no—
399C2×C4—302no—
400C2×C4#676611yescharacteristic
401C2×C4#677111yescharacteristic
402C2×C4#677711yescharacteristic
403C2×C4C2×#120211yescharacteristic
404C2×C4#679011yescharacteristic
405C2×C4#679011yescharacteristic
406C8—22no—
407C8—121no—
408C8—201no—
409C8—302no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3#6495411yescharacteristic
414D3—202no—
415C5#7012411yescharacteristic, complemented, Sylow
416C22—41no—
417C22—302no—
418C22—602no—
419C22#9139611yescharacteristic
420C22C4×#120211yescharacteristic
421C22#9147311yescharacteristic
422C4—122no—
423C4—202no—
424C4—302no—
425C4#9135411yescharacteristic
426C4#9146111yescharacteristic
427C4#9146511yescharacteristic
428C4#9157211yescharacteristic
429C3#1059983411yescharacteristic, complemented, Sylow
430C2—21no—
431C2—21no—
432C2—21no—
433C2—602no—
434C2#1174891711yescharacteristic
subgroupG/H
centerC2#11748917
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#386
prime radicalC2×#6817C22
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×C3×#3956C2semidirect
4. C2×#90961C2semidirect
6. C5×#4559C2semidirect
7. #11745988C2semidirect
31. C2×#3956D3semidirect
75. #4559D5semidirect
362. C3×C5#1915semidirect
415. C5#70124semidirect
429. C3#10599834semidirect

Maximal subgroups

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

subgroupindex
#117565042
#117542782
C2×C3×#39562
C2×#909612
#117483572
C5×#45592
#117459882
#105998343
#701245