Finite Group Databasebeta

← #14305913

Subgroups — #14305913

Order 1920.

688 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4082C211yesmaximal, characteristic
2C2×#91116C211yesmaximal, characteristic
3C2×C5×#832C211yesmaximal, characteristic
4#11748834C211yesmaximal, characteristic, complemented
5C2×#90971C211yesmaximal, characteristic, complemented
6C2×#90970C211yesmaximal, characteristic, complemented
7C2×#90952C211yesmaximal, characteristic, complemented
8#10600952—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×C3×Dic10C2211yescharacteristic
11C2×C4⋊Dic15C2211yescharacteristic
12C22×C3⋊#168C2211yescharacteristic
13C2×C5×C4⋊Dic3C2211yescharacteristic
14C22×C5×C3⋊C8C2211yescharacteristic
15C2×C3×C22⋊Dic5—22no—
16C3×#4082—22no—
17C3×#4082C414yescomplemented
18C2×C3×C4×Dic5C2211yescharacteristic
19C2×#6668—22no—
20#91116—22no—
21C5×#832—22no—
22#90971—22no—
23#90970—22no—
24#90952—22no—
25#71726—51nomaximal, Hall
26C2×#4082D311yescharacteristic
27C2×C5×#102—31no—
28C2×#3964—31no—
29C2×#3948—31no—
30C2×#3947—31no—
31#65265—31no—
32C2×#3942—31no—
33C24×C3×C5—21no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4C2×C412yes—
40C22×C3×C4×C5C2311yescharacteristic
41C22×Dic15—21no—
42C22×C5×Dic3—21no—
43C22×C3×Dic5—21no—
44C22×C3×Dic5D412yes—
45C2×C3×Dic10—21no—
46C2×C3×Dic10—21no—
47C2×C3×Dic10—21no—
48C2×C3×Dic10—21no—
49C2×C3×Dic10—21no—
50C2×C3×Dic10C2×C412yes—
51C4⋊Dic15—21no—
52C4⋊Dic15—21no—
53C2×C3⋊#168—21no—
54C2×C3⋊#168—21no—
55C2×C3⋊#168D412yes—
56C5×C4⋊Dic3—21no—
57C5×C4⋊Dic3—21no—
58C2×C5×C3⋊C8—21no—
59C2×C5×C3⋊C8—21no—
60C2×C5×C3⋊C8D412yes—
61C3×C22⋊Dic5—28no—
62C3×C4×Dic5C2×C412yes—
63C3×C4×Dic5D412yes—
64#6668—44no—
65C2×C3×#124—51no—
66C2×#835—51no—
67C2×#835—51no—
68C2×#832—51no—
69C2×#832D511yescharacteristic
70#4935—51no—
71C2×#803—51no—
72C22×C5×D4C2×D311yescharacteristic
73C22×Dic10C2×D311yescharacteristic
74C22×C5×C8—31no—
75C2×C5×C4⋊C4—31no—
76C2×C22⋊Dic5—22no—
77#4082—22no—
78#4082Dic314yescomplemented
79C2×C4⋊Dic5—31no—
80C2×#683—62no—
81C2×C4×Dic5C2×D311yescharacteristic
82C22×#168—31no—
83C5×#102—62no—
84#3964—62no—
85#3948—62no—
86#3947—62no—
87#3942—62no—
88#1959—151noSylow
89C23×C3×C5—22no—
90C23×C3×C5—41no—
91C23×C3×C5—41no—
92C23×C3×C5—42no—
93C23×C3×C5—42no—
94C23×C3×C5C2×D411yescharacteristic
95C3×C5×D4—22no—
96C3×C5×D4—22no—
97C3×C5×D4—41no—
98C3×C5×D4—41no—
99C2×C3×C4×C5C22×C411yescharacteristic
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
105C2×Dic15—41no—
106C2×Dic15—42no—
107C2×C5×Dic3—41no—
108C2×C5×Dic3—42no—
109C2×C3×Dic5—22no—
110C2×C3×Dic5—22no—
111C2×C3×Dic5—22no—
112C2×C3×Dic5—41no—
113C2×C3×Dic5—41no—
114C2×C3×Dic5C22⋊C414yes—
115C3×Dic10—22no—
116C3×Dic10—22no—
117C3×Dic10—41no—
118C3×Dic10—41no—
119C3⋊#168—22no—
120C5×C3⋊C8—22no—
121C22×C3×Q8—51no—
122C22×C3×D4C2×D511yescharacteristic
123C3×#124—54no—
124C3×#124—102no—
125C2×C3×C22⋊C4—102no—
126C2×C3×C42—51no—
127C2×C4⋊Dic3—51no—
128C2×C4⋊Dic3—102no—
129C2×C4⋊Dic3C2×D511yescharacteristic
130C22×C3⋊C8—51no—
131C22×C3⋊C8C2×D511yescharacteristic
132#835—102no—
133#835—102no—
134#832—22no—
135#832—102no—
136#803—102no—
137C24×C5—21no—
138C2×C5×D4—21no—
139C2×C5×D4—21no—
140C2×C5×D4—21no—
141C2×C5×D4—21no—
142C2×C5×D4—21no—
143C2×C5×D4C2×Dic312yes—
144C22×C4×C5—61no—
145C22×C4×C5C22×D311yescharacteristic
146C22×Dic5—21no—
147C22×Dic5—61no—
148C22×Dic5#6712yes—
149C2×Dic10—21no—
150C2×Dic10—21no—
151C2×Dic10—21no—
152C2×Dic10—21no—
153C2×Dic10—21no—
154C2×Dic10C2×Dic312yes—
155C2×C5×C8—32no—
156C2×C5×C8—61no—
157C2×C5×C8—61no—
158C5×C4⋊C4—61no—
159C5×C4⋊C4—61no—
160C22⋊Dic5—28no—
161C4⋊Dic5—61no—
162C4⋊Dic5—61no—
163#683—124no—
164C4×Dic5C2×Dic312yes—
165C4×Dic5#6712yes—
166C2×#168—32no—
167C2×#168—61no—
168C2×#168—61no—
169C2×#124—51no—
170C2×#103—151no—
171C2×#103—151no—
172C2×#102—31no—
173C2×#102—151no—
174C2×#97—151no—
175#384—151no—
176C22×C3×C5—42no—
177C22×C3×C5—44no—
178C22×C3×C5—82no—
179C22×C3×C5—81no—
180C22×C3×C5—81no—
181C22×C3×C5C2×C22⋊C411yescharacteristic
182C22×C3×C5#12411yescharacteristic
183C22×C3×C5#12711yescharacteristic
184C22×C3×C5AGL(1,ℤ/8)12yes—
185C22×C3×C5#13712yes—
186C3×C4×C5C4×D411yescharacteristic
187C3×C4×C5C4×D411yescharacteristic
188C3×C4×C5#12111yescharacteristic
189C3×C4×C5#12111yescharacteristic
190Dic15—81no—
191C3×Dic5—24no—
192C3×Dic5—42no—
193C5×Dic3—81no—
194C24×C3—21no—
195C2×C3×Q8—52no—
196C2×C3×Q8—101no—
197C2×C3×Q8—101no—
198C2×C3×Q8—101no—
199C2×C3×Q8—101no—
200C2×C3×Q8—101no—
201C2×C3×D4—21no—
202C2×C3×D4—21no—
203C2×C3×D4—21no—
204C2×C3×D4—21no—
205C2×C3×D4—21no—
206C2×C3×D4C4×D512yes—
207C22×C3×C4—52no—
208C22×C3×C4—101no—
209C22×C3×C4C22×D511yescharacteristic
210C22×Dic3—21no—
211C22×Dic3—101no—
212C3×C22⋊C4—108no—
213C3×C42—52no—
214C3×C42—52no—
215C4⋊Dic3—21no—
216C4⋊Dic3—21no—
217C4⋊Dic3—101no—
218C4⋊Dic3—101no—
219C4⋊Dic3—204no—
220C2×C3⋊C8—21no—
221C2×C3⋊C8—21no—
222C2×C3⋊C8—52no—
223C2×C3⋊C8—101no—
224C2×C3⋊C8—101no—
225C2×C3⋊C8C22⋊D512yes—
226C23×C5—22no—
227C23×C5—41no—
228C23×C5—41no—
229C23×C5—42no—
230C23×C5—42no—
231C23×C5C2×#6711yescharacteristic
232C5×D4—22no—
233C5×D4—22no—
234C5×D4—41no—
235C5×D4—41no—
236C2×C4×C5—121no—
237C2×C4×C5—122no—
238C2×C4×C5D3×D411yescharacteristic
239C2×C4×C5D3×D411yescharacteristic
240C2×C4×C5#23711yescharacteristic
241C2×C4×C5#23711yescharacteristic
242C2×C4×C5C22×Dic311yescharacteristic
243C2×C4×C5C2×#6711yescharacteristic
244C2×Dic5—22no—
245C2×Dic5—22no—
246C2×Dic5—22no—
247C2×Dic5—41no—
248C2×Dic5—41no—
249C2×Dic5—121no—
250C2×Dic5—122no—
251C2×Dic5#21714yes—
252Dic10—22no—
253Dic10—22no—
254Dic10—41no—
255Dic10—41no—
256C5×C8—62no—
257#168—62no—
258C22×Q8—51no—
259C22×D4D3×D511yescharacteristic
260C22×C8—31no—
261C22×C8—151no—
262#124—54no—
263#124—102no—
264C2×C4⋊C4—31no—
265C2×C4⋊C4—151no—
266C2×C4⋊C4—302no—
267C2×C22⋊C4—102no—
268C2×C42—51no—
269#103—302no—
270#103—302no—
271#102—62no—
272#102—302no—
273#97—302no—
274C2×C3×C5—82no—
275C2×C3×C5#39011yescharacteristic
276C2×C3×C5#41712yes—
277C2×C3×C5#48912yes—
278C2×C3×C5#49611yescharacteristic
279C2×C3×C5#49711yescharacteristic
280C23×C3—22no—
281C23×C3—41no—
282C23×C3—42no—
283C23×C3—42no—
284C23×C3—41no—
285C23×C3D4×D511yescharacteristic
286C3×Q8—102no—
287C3×Q8—102no—
288C3×Q8—201no—
289C3×Q8—201no—
290C3×D4—22no—
291C3×D4—22no—
292C3×D4—41no—
293C3×D4—41no—
294C2×C3×C4—54no—
295C2×C3×C4—102no—
296C2×C3×C4—102no—
297C2×C3×C4—102no—
298C2×C3×C4—201no—
299C2×C3×C4—201no—
300C2×C3×C4C2×C4×D511yescharacteristic
301C2×C3×C4#70911yescharacteristic
302C2×C3×C4D4×D511yescharacteristic
303C2×C3×C4D4×D511yescharacteristic
304C2×C3×C4#71111yescharacteristic
305C2×C3×C4C2×C22⋊D511yescharacteristic
306C2×Dic3—42no—
307C2×Dic3—41no—
308C2×Dic3—202no—
309C2×Dic3—201no—
310C3⋊C8—22no—
311C3⋊C8—102no—
312C22×C5—42no—
313C22×C5—44no—
314C22×C5—82no—
315C22×C5—81no—
316C22×C5—81no—
317C22×C5#93611yescharacteristic
318C22×C5#94011yescharacteristic
319C22×C5#94912yes—
320C22×C5#95112yes—
321C22×C5C2×#21711yescharacteristic
322C4×C5—241no—
323C4×C5D4×Dic311yescharacteristic
324C4×C5D4×Dic311yescharacteristic
325C4×C5#93811yescharacteristic
326C4×C5#93811yescharacteristic
327Dic5—24no—
328Dic5—42no—
329Dic5—241no—
330C24—21no—
331C2×Q8—52no—
332C2×Q8—101no—
333C2×Q8—101no—
334C2×Q8—101no—
335C2×Q8—101no—
336C2×Q8—101no—
337C2×D4—21no—
338C2×D4—21no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—21no—
342C2×D4D5×Dic312yes—
343C22×C4—52no—
344C22×C4—61no—
345C22×C4—101no—
346C22×C4—301no—
347C22×C4C2×D3×D511yescharacteristic
348C2×C8—32no—
349C2×C8—61no—
350C2×C8—61no—
351C2×C8—152no—
352C2×C8—301no—
353C2×C8—301no—
354C4⋊C4—61no—
355C4⋊C4—61no—
356C4⋊C4—301no—
357C4⋊C4—301no—
358C4⋊C4—604no—
359C22⋊C4—108no—
360C42—52no—
361C42—52no—
362C3×C5#195911yescharacteristic, complemented, Hall
363C22×C3—44no—
364C22×C3—42no—
365C22×C3—82no—
366C22×C3—81no—
367C22×C3—81no—
368C22×C3D5×C22⋊C411yescharacteristic
369C22×C3#403111yescharacteristic
370C22×C3#405712yes—
371C22×C3#406112yes—
372C22×C3#408611yescharacteristic
373C3×C4—104no—
374C3×C4—202no—
375C3×C4#402711yescharacteristic
376C3×C4#403011yescharacteristic
377C3×C4C4×C22⋊D511yescharacteristic
378C3×C4#408511yescharacteristic
379Dic3—81no—
380Dic3—401no—
381C2×C5—82no—
382C2×C5#505512yes—
383C2×C5#505811yescharacteristic
384C2×C5#506011yescharacteristic
385C2×C5#522111yescharacteristic
386C2×C5#523212yes—
387C23—22no—
388C23—42no—
389C23—42no—
390C23—41no—
391C23—41no—
392C23D5×#6711yescharacteristic
393Q8—102no—
394Q8—102no—
395Q8—201no—
396Q8—201no—
397D4—22no—
398D4—22no—
399D4—41no—
400D4—41no—
401C2×C4—54no—
402C2×C4—102no—
403C2×C4—102no—
404C2×C4—102no—
405C2×C4—122no—
406C2×C4—121no—
407C2×C4—201no—
408C2×C4—201no—
409C2×C4—602no—
410C2×C4—601no—
411C2×C4C2×D5×Dic311yescharacteristic
412C2×C4#677911yescharacteristic
413C2×C4#678011yescharacteristic
414C2×C4D5×#6711yescharacteristic
415C2×C4D3×C22⋊D511yescharacteristic
416C2×C4#679011yescharacteristic
417C8—62no—
418C8—302no—
419C2×C3—82no—
420C2×C3#6505412yes—
421C2×C3#6506012yes—
422C2×C3#6524611yescharacteristic
423C2×C3#6544311yescharacteristic
424C2×C3#6545611yescharacteristic
425C5#7172611yescharacteristic, complemented, Sylow
426C22—44no—
427C22—42no—
428C22—81no—
429C22—82no—
430C22—81no—
431C22#9147812yes—
432C22#9148412yes—
433C22#9153411yescharacteristic
434C22D5×#21711yescharacteristic
435C22#9156711yescharacteristic
436C4—104no—
437C4—202no—
438C4—241no—
439C4—1201no—
440C4#9153311yescharacteristic
441C4Dic3×C22⋊D511yescharacteristic
442C4#9155911yescharacteristic
443C4#9156511yescharacteristic
444C3#1060095211yescharacteristic, complemented, Sylow
445C2—82no—
446C2#1174895112yes—
447C2#1174909411yescharacteristic
448C2#1174910512yes—
449C2#1174910711yescharacteristic
450C2#1174948911yescharacteristic
subgroupG/H
centerC23D5×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
Fitting, prime radicalC22×C3×C5×D4C22
socleC23×C3×C5C2×D4
cosocleC22×C3×C4×C5C23
hypercenterC22×D4D3×D5
hypocenterC3×C5#1959
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #11748834C2semidirect
5. C2×#90971C2semidirect
6. C2×#90970C2semidirect
7. C2×#90952C2semidirect
17. C3×#4082C4semidirect
78. #4082Dic3semidirect
362. C3×C5#1959semidirect
425. C5#71726semidirect
444. C3#10600952semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40822
C2×#911162
C2×C5×#8322
#117488342
C2×#909712
C2×#909702
C2×#909522
#106009523
#717265