Finite Group Databasebeta

← #14305897

Subgroups — #14305897

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×#91373C211yesmaximal, characteristic
2C2×#91094C211yesmaximal, characteristic, complemented
3C2×C5×#809C211yesmaximal, characteristic
4C3×#65265C211yesmaximal, characteristic, complemented
5C2×#90974C211yesmaximal, characteristic, complemented
6C2×#90966C211yesmaximal, characteristic
7C2×#90952C211yesmaximal, characteristic, complemented
8#10600952—31nomaximal, Hall
9C22×Dic30C2211yescharacteristic
10C22×C5×D12C2211yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C22×C3⋊#168C2211yescharacteristic
13C22×C5×C3⋊C8C2211yescharacteristic
14C2×C3×C4⋊Dic5C2211yescharacteristic
15C2×C3×#683—22no—
16C2×C3×C4×Dic5C2211yescharacteristic
17C2×(C2×D3)⋊Dic5—22no—
18#91373—22no—
19#91373C414yescomplemented
20#91094—22no—
21C5×#809—22no—
22#90974—22no—
23#90966—22no—
24#90952—22no—
25#69581—51nomaximal, Hall
26C2×#4082—31no—
27C2×C5×#102—31no—
28C2×#3964—31no—
29C2×#3948—31no—
30C2×#3947—31no—
31#65265D311yescharacteristic, complemented
32C2×#3942—31no—
33C23×C5×D3—21no—
34C22×C3×C4×C5—21no—
35C22×C3×C4×C5C2311yescharacteristic
36C22×Dic15—21no—
37C2×Dic30—21no—
38C2×Dic30—21no—
39C2×Dic30—21no—
40C2×Dic30—21no—
41C2×Dic30—21no—
42C2×Dic30C2×C412yes—
43C2×C5×D12—21no—
44C2×C5×D12—21no—
45C2×C5×D12—21no—
46C2×C5×D12—21no—
47C2×C5×D12—21no—
48C2×C5×D12C2×C412yes—
49C22×C3×Dic5—21no—
50C22×C3×Dic5D412yes—
51C3×C5×C4⋊C4—21no—
52C3×C5×C4⋊C4—21no—
53C2×C3⋊#168—21no—
54C2×C3⋊#168—21no—
55C2×C3⋊#168D412yes—
56C2×C5×C3⋊C8—21no—
57C2×C5×C3⋊C8—21no—
58C2×C5×C3⋊C8D412yes—
59C3×C4⋊Dic5—21no—
60C3×C4⋊Dic5—21no—
61C3×#683—44no—
62C3×C4×Dic5C2×C412yes—
63C3×C4×Dic5D412yes—
64(C2×D3)⋊Dic5—28no—
65C2×#875—51no—
66C3×#384—51no—
67C2×#810—51no—
68C2×#810—51no—
69C2×#809—51no—
70C2×#809D511yescharacteristic
71C2×#803—51no—
72C22×C5×D4—31no—
73C22×Dic10—31no—
74C22×C5×C8—31no—
75C2×C5×C4⋊C4C2×D311yescharacteristic
76C2×C22⋊Dic5—62no—
77#4082—34no—
78#4082—62no—
79C2×C4⋊Dic5C2×D311yescharacteristic
80C2×#683—22no—
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×C5C2×D411yescharacteristic
90C22×C5×D3—22no—
91C22×C5×D3—41no—
92C22×C5×D3—41no—
93C22×C5×D3—42no—
94C22×C5×D3—42no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—42no—
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×Dic15—22no—
104C2×Dic15—41no—
105C2×Dic15—41no—
106Dic30—22no—
107Dic30—22no—
108Dic30—41no—
109Dic30—41no—
110C5×D12—22no—
111C5×D12—22no—
112C5×D12—41no—
113C5×D12—41no—
114C2×C3×Dic5—22no—
115C2×C3×Dic5—22no—
116C2×C3×Dic5—41no—
117C2×C3×Dic5—42no—
118C2×C3×Dic5C22⋊C414yes—
119C3⋊#168—22no—
120C5×C3⋊C8—22no—
121C22×D12C2×D511yescharacteristic
122C22×Dic6—51no—
123C2×C3×C4⋊C4—51no—
124C2×C3×C4⋊C4—102no—
125C2×C3×C4⋊C4C2×D511yescharacteristic
126C2×C3×C42—51no—
127C2×(C2×D3)⋊C4—102no—
128C22×C3⋊C8—51no—
129C22×C3⋊C8C2×D511yescharacteristic
130#875—54no—
131#875—102no—
132#810—102no—
133#810—102no—
134#809—22no—
135#809—102no—
136#803—102no—
137C24×C5—61no—
138C2×C5×D4—32no—
139C2×C5×D4—61no—
140C2×C5×D4—61no—
141C2×C5×D4—61no—
142C2×C5×D4—61no—
143C2×C5×D4—61no—
144C22×C4×C5—21no—
145C22×C4×C5C22×D311yescharacteristic
146C22×Dic5—21no—
147C22×Dic5—61no—
148C22×Dic5#6712yes—
149C2×Dic10—32no—
150C2×Dic10—61no—
151C2×Dic10—61no—
152C2×Dic10—61no—
153C2×Dic10—61no—
154C2×Dic10—61no—
155C2×C5×C8—32no—
156C2×C5×C8—61no—
157C2×C5×C8—61no—
158C5×C4⋊C4—21no—
159C5×C4⋊C4—21no—
160C22⋊Dic5—68no—
161C4⋊Dic5—21no—
162C4⋊Dic5—21no—
163#683—44no—
164C4×Dic5C4×D312yes—
165C4×Dic5D1212yes—
166C2×#168—32no—
167C2×#168—61no—
168C2×#168—61no—
169C2×#124—151no—
170C2×#103—151no—
171C2×#103—151no—
172C2×#102—31no—
173C2×#102—151no—
174C2×#97—151no—
175#384—51no—
176C22×C3×C5C2×C22⋊C411yescharacteristic
177C22×C3×C5#12411yescharacteristic
178C22×C3×C5#12711yescharacteristic
179C22×C3×C5AGL(1,ℤ/8)12yes—
180C22×C3×C5#13712yes—
181C2×C5×D3—42no—
182C2×C5×D3—44no—
183C2×C5×D3—82no—
184C2×C5×D3—81no—
185C2×C5×D3—81no—
186C3×C4×C5—81no—
187C3×C4×C5C4×D411yescharacteristic
188C3×C4×C5C4×D411yescharacteristic
189C3×C4×C5#12111yescharacteristic
190C3×C4×C5#12111yescharacteristic
191Dic15—42no—
192C3×Dic5—24no—
193C3×Dic5—81no—
194C23×D3—21no—
195C22×C3×C4—21no—
196C22×C3×C4—52no—
197C22×C3×C4—101no—
198C22×C3×C4C22×D511yescharacteristic
199C22×Dic3—101no—
200C2×D12—21no—
201C2×D12—21no—
202C2×D12—21no—
203C2×D12—21no—
204C2×D12—21no—
205C2×D12C4×D512yes—
206C2×Dic6—52no—
207C2×Dic6—101no—
208C2×Dic6—101no—
209C2×Dic6—101no—
210C2×Dic6—101no—
211C2×Dic6—101no—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—21no—
214C3×C4⋊C4—101no—
215C3×C4⋊C4—101no—
216C3×C4⋊C4—204no—
217C3×C42—52no—
218C3×C42—52no—
219(C2×D3)⋊C4—108no—
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—62no—
227C23×C5—122no—
228C23×C5—121no—
229C23×C5—122no—
230C23×C5—121no—
231C23×C5C2×#6711yescharacteristic
232C5×D4—62no—
233C5×D4—62no—
234C5×D4—121no—
235C5×D4—121no—
236C2×C4×C5—42no—
237C2×C4×C5—41no—
238C2×C4×C5C2×C4×D311yescharacteristic
239C2×C4×C5C2×D1211yescharacteristic
240C2×C4×C5D3×D411yescharacteristic
241C2×C4×C5D3×D411yescharacteristic
242C2×C4×C5#23911yescharacteristic
243C2×C4×C5#23911yescharacteristic
244C2×Dic5—22no—
245C2×Dic5—22no—
246C2×Dic5—42no—
247C2×Dic5—41no—
248C2×Dic5—62no—
249C2×Dic5—121no—
250C2×Dic5—121no—
251C2×Dic5(C2×D3)⋊C414yes—
252Dic10—62no—
253Dic10—62no—
254Dic10—121no—
255Dic10—121no—
256C5×C8—62no—
257#168—62no—
258C22×Q8—151no—
259C22×D4—31no—
260C22×C8—31no—
261C22×C8—151no—
262#124—154no—
263#124—302no—
264C2×C4⋊C4—51no—
265C2×C4⋊C4—102no—
266C2×C4⋊C4D3×D511yescharacteristic
267C2×C22⋊C4—302no—
268C2×C42—51no—
269#103—302no—
270#103—302no—
271#102—62no—
272#102—302no—
273#97—302no—
274C2×C3×C5#39011yescharacteristic
275C2×C3×C5#41712yes—
276C2×C3×C5#48912yes—
277C2×C3×C5#49611yescharacteristic
278C2×C3×C5#49711yescharacteristic
279C5×D3—82no—
280C23×C3D4×D511yescharacteristic
281C22×D3—22no—
282C22×D3—41no—
283C22×D3—42no—
284C22×D3—42no—
285C22×D3—41no—
286C2×C3×C4—42no—
287C2×C3×C4—41no—
288C2×C3×C4—54no—
289C2×C3×C4—102no—
290C2×C3×C4—102no—
291C2×C3×C4—202no—
292C2×C3×C4—201no—
293C2×C3×C4C2×C4×D511yescharacteristic
294C2×C3×C4#70911yescharacteristic
295C2×C3×C4D4×D511yescharacteristic
296C2×C3×C4D4×D511yescharacteristic
297C2×C3×C4#71111yescharacteristic
298C2×C3×C4C2×C22⋊D511yescharacteristic
299C2×Dic3—102no—
300C2×Dic3—201no—
301C2×Dic3—201no—
302D12—22no—
303D12—22no—
304D12—41no—
305D12—41no—
306Dic6—102no—
307Dic6—102no—
308Dic6—201no—
309Dic6—201no—
310C3⋊C8—22no—
311C3⋊C8—102no—
312C22×C5—124no—
313C22×C5—122no—
314C22×C5—241no—
315C22×C5—241no—
316C22×C5—242no—
317C22×C5C2×(C2×D3)⋊C411yescharacteristic
318C22×C5#93212yes—
319C22×C5#94011yescharacteristic
320C22×C5#94212yes—
321C22×C5#94711yescharacteristic
322C4×C5—81no—
323C4×C5#89311yescharacteristic
324C4×C5#89311yescharacteristic
325C4×C5#89511yescharacteristic
326C4×C5#89511yescharacteristic
327Dic5—24no—
328Dic5—81no—
329Dic5—122no—
330C24—61no—
331C2×Q8—152no—
332C2×Q8—301no—
333C2×Q8—301no—
334C2×Q8—301no—
335C2×Q8—301no—
336C2×Q8—301no—
337C2×D4—32no—
338C2×D4—61no—
339C2×D4—61no—
340C2×D4—61no—
341C2×D4—61no—
342C2×D4—61no—
343C22×C4—21no—
344C22×C4—52no—
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—21no—
355C4⋊C4—21no—
356C4⋊C4—101no—
357C4⋊C4—101no—
358C4⋊C4—204no—
359C22⋊C4—308no—
360C42—52no—
361C42—52no—
362C3×C5#195911yescharacteristic, complemented, Hall
363C22×C3D5×C22⋊C411yescharacteristic
364C22×C3#403111yescharacteristic
365C22×C3#405712yes—
366C22×C3#406112yes—
367C22×C3#408611yescharacteristic
368C2×D3—44no—
369C2×D3—42no—
370C2×D3—82no—
371C2×D3—81no—
372C2×D3—81no—
373C3×C4—81no—
374C3×C4—104no—
375C3×C4—401no—
376C3×C4#402711yescharacteristic
377C3×C4#403011yescharacteristic
378C3×C4C4×C22⋊D511yescharacteristic
379C3×C4#408511yescharacteristic
380Dic3—202no—
381C2×C5—242no—
382C2×C5#496612yes—
383C2×C5#498811yescharacteristic
384C2×C5#507411yescharacteristic
385C2×C5#508611yescharacteristic
386C2×C5#508912yes—
387C23—62no—
388C23—122no—
389C23—122no—
390C23—121no—
391C23—121no—
392C23D5×#6711yescharacteristic
393Q8—302no—
394Q8—302no—
395Q8—601no—
396Q8—601no—
397D4—62no—
398D4—62no—
399D4—121no—
400D4—121no—
401C2×C4—42no—
402C2×C4—41no—
403C2×C4—54no—
404C2×C4—102no—
405C2×C4—102no—
406C2×C4—202no—
407C2×C4—201no—
408C2×C4—302no—
409C2×C4—601no—
410C2×C4—601no—
411C2×C4#676811yescharacteristic
412C2×C4#676911yescharacteristic
413C2×C4C4×D3×D511yescharacteristic
414C2×C4D5×D1211yescharacteristic
415C2×C4D3×C22⋊D511yescharacteristic
416C2×C4#679011yescharacteristic
417C8—62no—
418C8—302no—
419C2×C3#6505412yes—
420C2×C3#6506012yes—
421C2×C3#6524611yescharacteristic
422C2×C3#6544311yescharacteristic
423C2×C3#6545611yescharacteristic
424D3—82no—
425C5#6958111yescharacteristic, complemented, Sylow
426C22—122no—
427C22—124no—
428C22—242no—
429C22—241no—
430C22—241no—
431C22#9132611yescharacteristic
432C22D5×(C2×D3)⋊C411yescharacteristic
433C22#9148912yes—
434C22#9151312yes—
435C22#9156711yescharacteristic
436C4—81no—
437C4—104no—
438C4—401no—
439C4—602no—
440C4#9140611yescharacteristic
441C4#9141611yescharacteristic
442C4#9142011yescharacteristic
443C4#9144611yescharacteristic
444C3#1060095211yescharacteristic, complemented, Sylow
445C2—242no—
446C2#1174736912yes—
447C2#1174749812yes—
448C2#1174890911yescharacteristic
449C2#1174906611yescharacteristic
450C2#1174931211yescharacteristic
subgroupG/H
centerC23D5×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC22×C5×D12C22
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1959
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#91094C2semidirect
4. C3×#65265C2semidirect
5. C2×#90974C2semidirect
7. C2×#90952C2semidirect
19. #91373C4semidirect
31. #65265D3semidirect
362. C3×C5#1959semidirect
425. C5#69581semidirect
444. C3#10600952semidirect

Maximal subgroups

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

subgroupindex
C2×#913732
C2×#910942
C2×C5×#8092
C3×#652652
C2×#909742
C2×#909662
C2×#909522
#106009523
#695815