Finite Group Databasebeta

← #14299531

Subgroups — #14299531

Order 1920.

556 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×M16C211yesmaximal, characteristic
2C2×C5×#822C211yesmaximal, characteristic, complemented
3C2×#90992C211yesmaximal, characteristic, complemented
4#11748341C211yesmaximal, characteristic
5C2×#90955C211yesmaximal, characteristic
6#11746379C211yesmaximal, characteristic, complemented
7#11745983C211yesmaximal, characteristic, complemented
8#10601506—31nomaximal, Hall
9C22×C3×C4×D5C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C2×#6710C2211yescharacteristic
12C22×C3⋊#168C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C22×C5×C3⋊C8C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16C3×D5×M16—22no—
17C3×D5×M16—22no—
18C2×C3×#676—21no—
19C2×C3×C8×D5—21no—
20C5×#822—22no—
21#90992—22no—
22#90955—21no—
23#90955—21no—
24#90955C412yes—
25#90955C412yes—
26#72001—51nomaximal, Hall
27C2×D5×M16D311yescharacteristic
28C2×C5×#108—31no—
29#65415—31no—
30C2×#3954—31no—
31C2×#3952—31no—
32#64778—31no—
33#64772—31no—
34C23×C3×D5Q811yescharacteristic
35C22×C3×C4×C5C2311yescharacteristic
36C22×C3×Dic5Q811yescharacteristic
37C2×C3×C4×D5—21no—
38C2×C3×C4×D5—21no—
39C2×C3×C4×D5—21no—
40C2×C3×C4×D5—21no—
41C2×C3×C4×D5C2×C411yescharacteristic
42C2×C3×C4×D5C2×C411yescharacteristic
43C2×C3×C4×D5D411yescharacteristic
44C2×C3×C4×D5D411yescharacteristic
45C3×C5×M16—21no—
46C3×C5×M16D412yes—
47C2×C3×C5×C8—21no—
48#6710—21no—
49#6710—21no—
50C2×C3⋊#168—21no—
51C2×C3⋊#168—21no—
52C2×C3⋊#168—21no—
53C2×C3⋊#168C2×C412yes—
54C5×#208—21no—
55C5×#208—21no—
56C2×C5×C3⋊C8—21no—
57C2×C5×C3⋊C8—21no—
58C2×C5×C3⋊C8—21no—
59C2×C5×C3⋊C8C2×C412yes—
60C3×#681—21no—
61C3×#681D412yes—
62C2×C3×#168—21no—
63C3×#676—24no—
64C3×C8×D5—24no—
65C22×C3×M16—51no—
66#5207—51no—
67C2×#830—51no—
68C2×#822—51no—
69C2×#822D511yescharacteristic, complemented
70#4558—51no—
71#4558—51no—
72C22×C4×D5C2×D311yescharacteristic
73C2×C5×M16—31no—
74C2×C5×M16C2×D311yescharacteristic
75C22×C5×C8—31no—
76C2×#681—31no—
77C2×#681C2×D311yescharacteristic
78C22×#168—31no—
79D5×M16—22no—
80D5×M16—22no—
81C2×#676—21no—
82C2×C8×D5—21no—
83C5×#108—62no—
84#3954—62no—
85#3952—32no—
86#3952—32no—
87#3952—61no—
88#3952—61no—
89#1855—151noSylow
90C23×C3×C5C2×Q811yescharacteristic
91C22×C3×D5—21no—
92C22×C3×D5—21no—
93C22×C3×D5—22no—
94C22×C3×D5—41no—
95C22×C3×D5C4⋊C411yescharacteristic
96C22×C3×D5C4⋊C411yescharacteristic
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5#4111yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×C3×Dic5—21no—
104C2×C3×Dic5—21no—
105C2×C3×Dic5C4⋊C411yescharacteristic
106C2×C3×Dic5C4⋊C411yescharacteristic
107C3×C4×D5—21no—
108C3×C4×D5—21no—
109C3×C4×D5—21no—
110C3×C4×D5—21no—
111C3×C4×D5—21no—
112C3×C4×D5—21no—
113C3×C4×D5—21no—
114C3×C4×D5—21no—
115C3×C5×C8—22no—
116C3⋊#168—22no—
117C3⋊#168—41no—
118C3×#168—22no—
119C5×C3⋊C8—22no—
120C5×C3⋊C8—41no—
121C23×C3×C4—51no—
122C2×C3×M16—51no—
123C2×C3×M16—101no—
124C2×C3×M16—102no—
125C2×C3×M16—102no—
126C2×C3×M16C2×D511yescharacteristic
127C22×C3×C8—101no—
128C2×#208—51no—
129C2×#208C2×D511yescharacteristic
130C22×C3⋊C8—51no—
131C22×C3⋊C8C2×D511yescharacteristic
132#830—52no—
133#830—52no—
134#830—101no—
135#830—101no—
136#822—22no—
137#822—102no—
138C23×D5Dic611yescharacteristic
139C22×C4×C5C22×D311yescharacteristic
140C22×Dic5Dic611yescharacteristic
141C2×C4×D5—21no—
142C2×C4×D5—21no—
143C2×C4×D5—21no—
144C2×C4×D5—21no—
145C2×C4×D5C4×D311yescharacteristic
146C2×C4×D5C4×D311yescharacteristic
147C2×C4×D5#6711yescharacteristic
148C2×C4×D5#6711yescharacteristic
149C5×M16—21no—
150C5×M16—61no—
151C5×M16—61no—
152C5×M16#6712yes—
153C2×C5×C8—21no—
154C2×C5×C8—32no—
155C2×C5×C8—61no—
156C2×C5×C8—61no—
157C2×C5×C8—61no—
158#681—21no—
159#681—61no—
160#681—61no—
161#681#6712yes—
162C2×#168—21no—
163C2×#168—32no—
164C2×#168—61no—
165C2×#168—61no—
166C2×#168—61no—
167#676—24no—
168C8×D5—24no—
169C22×M16—51no—
170C2×#108—31no—
171C2×#108—151no—
172#407—151no—
173C2×C22⋊C8—151no—
174#341—151no—
175#341—151no—
176C22×C3×C5—21no—
177C22×C3×C5—21no—
178C22×C3×C5C2×C4⋊C411yescharacteristic
179C22×C3×C5C22⋊Q811yescharacteristic
180C22×C3×C5C22⋊Q811yescharacteristic
181C2×C3×D5—21no—
182C2×C3×D5—21no—
183C2×C3×D5—21no—
184C2×C3×D5—21no—
185C2×C3×D5—21no—
186C2×C3×D5—42no—
187C2×C3×D5—42no—
188C2×C3×D5#10812yescomplemented
189C3×C4×C5C4×D411yescharacteristic
190C3×C4×C5C4×D411yescharacteristic
191C3×C4×C5#12011yescharacteristic
192C3×C4×C5#12311yescharacteristic
193C3×Dic5—21no—
194C3×Dic5—21no—
195C24×C3—51no—
196C22×C3×C4—51no—
197C22×C3×C4—51no—
198C22×C3×C4—51no—
199C22×C3×C4—51no—
200C22×C3×C4—51no—
201C22×C3×C4—101no—
202C22×C3×C4—101no—
203C22×C3×C4—101no—
204C22×C3×C4—101no—
205C22×C3×C4C22×D511yescharacteristic
206C3×M16—21no—
207C3×M16—52no—
208C3×M16—104no—
209C3×M16—101no—
210C3×M16C22⋊D512yes—
211C2×C3×C8—21no—
212C2×C3×C8—104no—
213C2×C3×C8—101no—
214#208—21no—
215#208—21no—
216#208—101no—
217#208—101no—
218C2×C3⋊C8—21no—
219C2×C3⋊C8—21no—
220C2×C3⋊C8—21no—
221C2×C3⋊C8—52no—
222C2×C3⋊C8—101no—
223C2×C3⋊C8—101no—
224C2×C3⋊C8—101no—
225C2×C3⋊C8C4×D512yes—
226C23×C5C2×Dic611yescharacteristic
227C22×D5—21no—
228C22×D5—21no—
229C22×D5—22no—
230C22×D5—41no—
231C22×D5Dic3⋊C411yescharacteristic
232C22×D5Dic3⋊C411yescharacteristic
233C2×C4×C5C2×C4×D311yescharacteristic
234C2×C4×C5#23511yescharacteristic
235C2×C4×C5#23511yescharacteristic
236C2×C4×C5C2×#6711yescharacteristic
237C2×C4×C5C2×#6711yescharacteristic
238C2×C4×C5C2×#6711yescharacteristic
239C2×Dic5—21no—
240C2×Dic5—21no—
241C2×Dic5Dic3⋊C411yescharacteristic
242C2×Dic5Dic3⋊C411yescharacteristic
243C4×D5—21no—
244C4×D5—21no—
245C4×D5—21no—
246C4×D5—21no—
247C4×D5—21no—
248C4×D5—21no—
249C4×D5—21no—
250C4×D5—21no—
251C5×C8—22no—
252C5×C8—62no—
253C5×C8—121no—
254#168—22no—
255#168—62no—
256#168—121no—
257C23×C4—51no—
258C2×M16—31no—
259C2×M16—51no—
260C2×M16—101no—
261C2×M16—102no—
262C2×M16—102no—
263C2×M16—151no—
264C2×M16D3×D511yescharacteristic
265C22×C8—31no—
266C22×C8—101no—
267C22×C8—151no—
268#108—62no—
269#108—302no—
270C22⋊C8—152no—
271C22⋊C8—152no—
272C22⋊C8—301no—
273C22⋊C8—301no—
274C2×C3×C5—21no—
275C2×C3×C5—21no—
276C2×C3×C5#38511yescharacteristic
277C2×C3×C5C2×#10811yescharacteristic
278C2×C3×C5#43011yescharacteristic
279C3×D5—22no—
280C3×D5—41no—
281C23×C3—51no—
282C23×C3—51no—
283C23×C3—102no—
284C23×C3—101no—
285C23×C3—101no—
286C23×C3—201no—
287C23×C3Q8×D511yescharacteristic
288C2×C3×C4—51no—
289C2×C3×C4—51no—
290C2×C3×C4—101no—
291C2×C3×C4—101no—
292C2×C3×C4—101no—
293C2×C3×C4—101no—
294C2×C3×C4—101no—
295C2×C3×C4—101no—
296C2×C3×C4—101no—
297C2×C3×C4—101no—
298C2×C3×C4—101no—
299C2×C3×C4—101no—
300C2×C3×C4C2×C4×D511yescharacteristic
301C2×C3×C4#70911yescharacteristic
302C2×C3×C4D4×D511yescharacteristic
303C2×C3×C4D4×D511yescharacteristic
304C2×C3×C4#71311yescharacteristic
305C2×C3×C4C2×C22⋊D511yescharacteristic
306C3×C8—22no—
307C3×C8—102no—
308C3⋊C8—22no—
309C3⋊C8—41no—
310C3⋊C8—102no—
311C3⋊C8—201no—
312C22×C5—21no—
313C22×C5—21no—
314C22×C5C2×Dic3⋊C411yescharacteristic
315C22×C5#92411yescharacteristic
316C22×C5#92411yescharacteristic
317C2×D5—21no—
318C2×D5—21no—
319C2×D5—21no—
320C2×D5—21no—
321C2×D5—21no—
322C2×D5—42no—
323C2×D5—42no—
324C2×D5#82212yescomplemented
325C4×C5C4×#6711yescharacteristic
326C4×C5C4×#6711yescharacteristic
327C4×C5#92911yescharacteristic
328C4×C5#95311yescharacteristic
329Dic5—21no—
330Dic5—21no—
331C24—51no—
332C22×C4—51no—
333C22×C4—51no—
334C22×C4—51no—
335C22×C4—51no—
336C22×C4—51no—
337C22×C4—101no—
338C22×C4—101no—
339C22×C4—101no—
340C22×C4—101no—
341C22×C4C2×D3×D511yescharacteristic
342M16—21no—
343M16—52no—
344M16—61no—
345M16—61no—
346M16—104no—
347M16—101no—
348M16—301no—
349M16—301no—
350M16#120112yes—
351C2×C8—21no—
352C2×C8—32no—
353C2×C8—61no—
354C2×C8—61no—
355C2×C8—61no—
356C2×C8—104no—
357C2×C8—101no—
358C2×C8—152no—
359C2×C8—301no—
360C2×C8—301no—
361C2×C8—301no—
362C3×C5#185511yescharacteristic, complemented, Hall
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—52no—
366C22×C3—101no—
367C22×C3—101no—
368C22×C3—101no—
369C22×C3—101no—
370C22×C3—101no—
371C22×C3—202no—
372C22×C3—202no—
373C22×C3D5×C4⋊C411yescharacteristic
374C22×C3#404211yescharacteristic
375C22×C3#409211yescharacteristic
376C3×C4—101no—
377C3×C4—101no—
378C3×C4#403911yescharacteristic
379C3×C4#404011yescharacteristic
380C3×C4C4×C22⋊D511yescharacteristic
381C3×C4#408311yescharacteristic
382C2×C5—21no—
383C2×C5—21no—
384C2×C5C2×#82211yescharacteristic
385C2×C5#512411yescharacteristic
386C2×C5#521011yescharacteristic
387D5—22no—
388D5—41no—
389C23—51no—
390C23—51no—
391C23—102no—
392C23—101no—
393C23—101no—
394C23—201no—
395C23D5×Dic611yescharacteristic
396C2×C4—51no—
397C2×C4—51no—
398C2×C4—101no—
399C2×C4—101no—
400C2×C4—101no—
401C2×C4—101no—
402C2×C4—101no—
403C2×C4—101no—
404C2×C4—101no—
405C2×C4—101no—
406C2×C4—101no—
407C2×C4—101no—
408C2×C4#677111yescharacteristic
409C2×C4#677311yescharacteristic
410C2×C4C4×D3×D511yescharacteristic
411C2×C4C2×#120111yescharacteristic
412C2×C4D5×#6711yescharacteristic
413C2×C4D5×#6711yescharacteristic
414C8—22no—
415C8—62no—
416C8—102no—
417C8—121no—
418C8—302no—
419C8—601no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—102no—
423C2×C3—201no—
424C2×C3D5×#10811yescharacteristic
425C2×C3#6518211yescharacteristic
426C2×C3#6527811yescharacteristic
427C5#7200111yescharacteristic, complemented, Sylow
428C22—21no—
429C22—21no—
430C22—52no—
431C22—101no—
432C22—101no—
433C22—101no—
434C22—101no—
435C22—101no—
436C22—202no—
437C22—202no—
438C22#9134911yescharacteristic
439C22#9135911yescharacteristic
440C22D5×Dic3⋊C411yescharacteristic
441C4—101no—
442C4—101no—
443C4#9134811yescharacteristic
444C4C4×#120111yescharacteristic
445C4#9144411yescharacteristic
446C4#9156311yescharacteristic
447C3#1060150611yescharacteristic, complemented, Sylow
448C2—21no—
449C2—21no—
450C2—102no—
451C2—201no—
452C2D5×#82211yescharacteristic
453C2#1174817111yescharacteristic
454C2#1174870311yescharacteristic
subgroupG/H
centerC2×C4D5×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C2×C4⋊C4
prime radicalC23×C3×D5Q8
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1855
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×C5×#822C2semidirect
3. C2×#90992C2semidirect
6. #11746379C2semidirect
7. #11745983C2semidirect
69. C2×#822D5semidirect
188. C2×C3×D5#108semidirect
324. C2×D5#822semidirect
362. C3×C5#1855semidirect
427. C5#72001semidirect
447. C3#10601506semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×M162
C2×C5×#8222
C2×#909922
#117483412
C2×#909552
#117463792
#117459832
#106015063
#720015