Finite Group Databasebeta

← #14305868

Subgroups — #14305868

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 448 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#11748613C211yesmaximal, characteristic, complemented
5C2×#90971C211yesmaximal, characteristic, complemented
6C2×#90970C211yesmaximal, characteristic, complemented
7C2×Dic5×C3⋊C8C211yesmaximal, characteristic, complemented
8#10600951—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
19#91116—22no—
20C5×#832—22no—
21#90994—22no—
22#90971—22no—
23#90970—22no—
24Dic5×C3⋊C8—22no—
25#71725—51nomaximal, Hall
26C2×#4082D311yescharacteristic
27C2×C5×#102—31no—
28C2×#3964—31no—
29C2×#3948—31no—
30C2×C8×Dic5—31no—
31#65266—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—
64C2×C3×#124—51no—
65C2×#835—51no—
66C2×#835—51no—
67C2×#832—51no—
68C2×#832D511yescharacteristic
69#4936—51no—
70C2×C4×C3⋊C8—51no—
71C22×C5×D4C2×D311yescharacteristic
72C22×Dic10C2×D311yescharacteristic
73C22×C5×C8—31no—
74C2×C5×C4⋊C4—31no—
75C2×C22⋊Dic5—22no—
76#4082—22no—
77#4082Dic314yescomplemented
78C2×C4⋊Dic5—31no—
79C2×C4×Dic5C2×D311yescharacteristic
80C22×#168—31no—
81C5×#102—62no—
82#3964—62no—
83#3963—62no—
84#3948—62no—
85C8×Dic5—62no—
86#3942—62no—
87#1958—151noSylow
88C23×C3×C5—22no—
89C23×C3×C5—41no—
90C23×C3×C5—41no—
91C23×C3×C5—42no—
92C23×C3×C5—42no—
93C23×C3×C5C2×D411yescharacteristic
94C3×C5×D4—22no—
95C3×C5×D4—22no—
96C3×C5×D4—41no—
97C3×C5×D4—41no—
98C2×C3×C4×C5C22×C411yescharacteristic
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—41no—
105C2×Dic15—42no—
106C2×C5×Dic3—41no—
107C2×C5×Dic3—42no—
108C2×C3×Dic5—22no—
109C2×C3×Dic5—22no—
110C2×C3×Dic5—22no—
111C2×C3×Dic5—41no—
112C2×C3×Dic5—41no—
113C2×C3×Dic5C22⋊C414yes—
114C3×Dic10—22no—
115C3×Dic10—22no—
116C3×Dic10—41no—
117C3×Dic10—41no—
118C3⋊#168—22no—
119C5×C3⋊C8—22no—
120C22×C3×Q8—51no—
121C22×C3×D4C2×D511yescharacteristic
122C3×#124—54no—
123C3×#124—102no—
124C2×C3×C22⋊C4—102no—
125C2×C3×C42—51no—
126C2×C4⋊Dic3—51no—
127C2×C4⋊Dic3C2×D511yescharacteristic
128C22×C3⋊C8—51no—
129C22×C3⋊C8C2×D511yescharacteristic
130#835—102no—
131#835—102no—
132#832—22no—
133#832—102no—
134C3⋊#95—102no—
135C4×C3⋊C8—102no—
136C24×C5—21no—
137C2×C5×D4—21no—
138C2×C5×D4—21no—
139C2×C5×D4—21no—
140C2×C5×D4—21no—
141C2×C5×D4—21no—
142C2×C5×D4C2×Dic312yes—
143C22×C4×C5—61no—
144C22×C4×C5C22×D311yescharacteristic
145C22×Dic5—21no—
146C22×Dic5—61no—
147C22×Dic5#6712yes—
148C2×Dic10—21no—
149C2×Dic10—21no—
150C2×Dic10—21no—
151C2×Dic10—21no—
152C2×Dic10—21no—
153C2×Dic10C2×Dic312yes—
154C2×C5×C8—32no—
155C2×C5×C8—61no—
156C2×C5×C8—61no—
157C5×C4⋊C4—61no—
158C5×C4⋊C4—61no—
159C22⋊Dic5—28no—
160C4⋊Dic5—61no—
161C4⋊Dic5—61no—
162C4×Dic5C2×Dic312yes—
163C4×Dic5#6712yes—
164C2×#168—32no—
165C2×#168—61no—
166C2×#168—61no—
167C2×#124—51no—
168C2×#103—151no—
169C2×#103—151no—
170C2×#102—31no—
171C2×#102—151no—
172C2×C4×C8—151no—
173#382—151no—
174C22×C3×C5—42no—
175C22×C3×C5—44no—
176C22×C3×C5—82no—
177C22×C3×C5—81no—
178C22×C3×C5—81no—
179C22×C3×C5C2×C22⋊C411yescharacteristic
180C22×C3×C5#12411yescharacteristic
181C22×C3×C5#12711yescharacteristic
182C22×C3×C5#13512yes—
183C22×C3×C5#13512yes—
184C3×C4×C5C4×D411yescharacteristic
185C3×C4×C5C4×D411yescharacteristic
186C3×C4×C5#12111yescharacteristic
187C3×C4×C5#12111yescharacteristic
188Dic15—81no—
189C3×Dic5—24no—
190C3×Dic5—42no—
191C5×Dic3—81no—
192C24×C3—21no—
193C2×C3×Q8—52no—
194C2×C3×Q8—101no—
195C2×C3×Q8—101no—
196C2×C3×Q8—101no—
197C2×C3×Q8—101no—
198C2×C3×Q8—101no—
199C2×C3×D4—21no—
200C2×C3×D4—21no—
201C2×C3×D4—21no—
202C2×C3×D4—21no—
203C2×C3×D4—21no—
204C2×C3×D4C4×D512yes—
205C22×C3×C4—52no—
206C22×C3×C4—101no—
207C22×C3×C4C22×D511yescharacteristic
208C22×Dic3—21no—
209C22×Dic3—101no—
210C3×C22⋊C4—108no—
211C3×C42—52no—
212C3×C42—52no—
213C4⋊Dic3—21no—
214C4⋊Dic3—21no—
215C4⋊Dic3—101no—
216C4⋊Dic3—101no—
217C2×C3⋊C8—21no—
218C2×C3⋊C8—21no—
219C2×C3⋊C8—52no—
220C2×C3⋊C8—101no—
221C2×C3⋊C8—101no—
222C2×C3⋊C8C22⋊D512yes—
223C23×C5—22no—
224C23×C5—41no—
225C23×C5—41no—
226C23×C5—42no—
227C23×C5—42no—
228C23×C5C2×#6711yescharacteristic
229C5×D4—22no—
230C5×D4—22no—
231C5×D4—41no—
232C5×D4—41no—
233C2×C4×C5—121no—
234C2×C4×C5—122no—
235C2×C4×C5D3×D411yescharacteristic
236C2×C4×C5D3×D411yescharacteristic
237C2×C4×C5#23711yescharacteristic
238C2×C4×C5#23711yescharacteristic
239C2×C4×C5C22×Dic311yescharacteristic
240C2×C4×C5C2×#6711yescharacteristic
241C2×Dic5—22no—
242C2×Dic5—22no—
243C2×Dic5—22no—
244C2×Dic5—41no—
245C2×Dic5—41no—
246C2×Dic5—121no—
247C2×Dic5—122no—
248C2×Dic5#21714yes—
249Dic10—22no—
250Dic10—22no—
251Dic10—41no—
252Dic10—41no—
253C5×C8—62no—
254#168—62no—
255C22×Q8—51no—
256C22×D4D3×D511yescharacteristic
257C22×C8—31no—
258C22×C8—151no—
259#124—54no—
260#124—102no—
261C2×C4⋊C4—31no—
262C2×C4⋊C4—151no—
263C2×C22⋊C4—102no—
264C2×C42—51no—
265#103—302no—
266#103—302no—
267#102—62no—
268#102—302no—
269C4×C8—302no—
270#95—302no—
271C2×C3×C5—82no—
272C2×C3×C5#39011yescharacteristic
273C2×C3×C5#41612yes—
274C2×C3×C5#48812yes—
275C2×C3×C5#49511yescharacteristic
276C2×C3×C5#49511yescharacteristic
277C23×C3—22no—
278C23×C3—41no—
279C23×C3—42no—
280C23×C3—42no—
281C23×C3—41no—
282C23×C3D4×D511yescharacteristic
283C3×Q8—102no—
284C3×Q8—102no—
285C3×Q8—201no—
286C3×Q8—201no—
287C3×D4—22no—
288C3×D4—22no—
289C3×D4—41no—
290C3×D4—41no—
291C2×C3×C4—54no—
292C2×C3×C4—102no—
293C2×C3×C4—102no—
294C2×C3×C4—102no—
295C2×C3×C4—201no—
296C2×C3×C4—201no—
297C2×C3×C4C2×C4×D511yescharacteristic
298C2×C3×C4#70911yescharacteristic
299C2×C3×C4D4×D511yescharacteristic
300C2×C3×C4D4×D511yescharacteristic
301C2×C3×C4#71111yescharacteristic
302C2×C3×C4C2×C22⋊D511yescharacteristic
303C2×Dic3—42no—
304C2×Dic3—41no—
305C2×Dic3—202no—
306C2×Dic3—201no—
307C3⋊C8—22no—
308C3⋊C8—102no—
309C22×C5—42no—
310C22×C5—44no—
311C22×C5—82no—
312C22×C5—81no—
313C22×C5—81no—
314C22×C5#93611yescharacteristic
315C22×C5#94011yescharacteristic
316C22×C5#95012yes—
317C22×C5#95012yes—
318C22×C5C2×#21711yescharacteristic
319C4×C5—241no—
320C4×C5D4×Dic311yescharacteristic
321C4×C5D4×Dic311yescharacteristic
322C4×C5#93811yescharacteristic
323C4×C5#93811yescharacteristic
324Dic5—24no—
325Dic5—42no—
326Dic5—241no—
327C24—21no—
328C2×Q8—52no—
329C2×Q8—101no—
330C2×Q8—101no—
331C2×Q8—101no—
332C2×Q8—101no—
333C2×Q8—101no—
334C2×D4—21no—
335C2×D4—21no—
336C2×D4—21no—
337C2×D4—21no—
338C2×D4—21no—
339C2×D4D5×Dic312yes—
340C22×C4—52no—
341C22×C4—61no—
342C22×C4—101no—
343C22×C4—301no—
344C22×C4C2×D3×D511yescharacteristic
345C2×C8—32no—
346C2×C8—61no—
347C2×C8—61no—
348C2×C8—152no—
349C2×C8—301no—
350C2×C8—301no—
351C4⋊C4—61no—
352C4⋊C4—61no—
353C4⋊C4—301no—
354C4⋊C4—301no—
355C22⋊C4—108no—
356C42—52no—
357C42—52no—
358C3×C5#195811yescharacteristic, complemented, Hall
359C22×C3—44no—
360C22×C3—42no—
361C22×C3—82no—
362C22×C3—81no—
363C22×C3—81no—
364C22×C3D5×C22⋊C411yescharacteristic
365C22×C3#403111yescharacteristic
366C22×C3#405812yes—
367C22×C3#406212yes—
368C22×C3#408611yescharacteristic
369C3×C4—104no—
370C3×C4—202no—
371C3×C4#402711yescharacteristic
372C3×C4#403011yescharacteristic
373C3×C4C4×C22⋊D511yescharacteristic
374C3×C4#408511yescharacteristic
375Dic3—81no—
376Dic3—401no—
377C2×C5—82no—
378C2×C5#505612yes—
379C2×C5#505911yescharacteristic
380C2×C5#505911yescharacteristic
381C2×C5#522111yescharacteristic
382C2×C5#523312yes—
383C23—22no—
384C23—42no—
385C23—42no—
386C23—41no—
387C23—41no—
388C23D5×#6711yescharacteristic
389Q8—102no—
390Q8—102no—
391Q8—201no—
392Q8—201no—
393D4—22no—
394D4—22no—
395D4—41no—
396D4—41no—
397C2×C4—54no—
398C2×C4—102no—
399C2×C4—102no—
400C2×C4—102no—
401C2×C4—122no—
402C2×C4—121no—
403C2×C4—201no—
404C2×C4—201no—
405C2×C4—602no—
406C2×C4—601no—
407C2×C4C2×D5×Dic311yescharacteristic
408C2×C4#677911yescharacteristic
409C2×C4#678011yescharacteristic
410C2×C4D5×#6711yescharacteristic
411C2×C4D3×C22⋊D511yescharacteristic
412C2×C4#679011yescharacteristic
413C8—62no—
414C8—302no—
415C2×C3—82no—
416C2×C3#6505712yes—
417C2×C3#6506112yes—
418C2×C3#6524611yescharacteristic
419C2×C3#6544411yescharacteristic
420C2×C3#6545711yescharacteristic
421C5#7172511yescharacteristic, complemented, Sylow
422C22—44no—
423C22—42no—
424C22—81no—
425C22—81no—
426C22—82no—
427C22#9149012yes—
428C22#9149212yes—
429C22#9153411yescharacteristic
430C22D5×#21711yescharacteristic
431C22#9156711yescharacteristic
432C4—104no—
433C4—202no—
434C4—241no—
435C4—1201no—
436C4#9153311yescharacteristic
437C4Dic3×C22⋊D511yescharacteristic
438C4#9155911yescharacteristic
439C4#9156511yescharacteristic
440C3#1060095111yescharacteristic, complemented, Sylow
441C2—82no—
442C2#1174896112yes—
443C2#1174906711yescharacteristic
444C2#1174907011yescharacteristic
445C2#1174908512yes—
446C2#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#1958
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. #11748613C2semidirect
5. C2×#90971C2semidirect
6. C2×#90970C2semidirect
7. C2×Dic5×C3⋊C8C2semidirect
17. C3×#4082C4semidirect
77. #4082Dic3semidirect
358. C3×C5#1958semidirect
421. C5#71725semidirect
440. C3#10600951semidirect

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
#117486132
C2×#909712
C2×#909702
C2×Dic5×C3⋊C82
#106009513
#717255