Finite Group Databasebeta

← #14471526

Subgroups — #14471526

Order 1920.

740 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5721C211yesmaximal, characteristic, complemented
2Dic6×D20C211yesmaximal, characteristic
3#11751180C211yesmaximal, characteristic, complemented
4C3×#65372C211yesmaximal, characteristic
5#11749358C212yesmaximal, complemented
6Dic3×#688C212yesmaximal
7#11749227C212yesmaximal
8#11749187C212yesmaximal, complemented
9C4×#6655C211yesmaximal, characteristic
10#11746945C211yesmaximal, characteristic, complemented
11#11746857C211yesmaximal, characteristic, complemented
12#10615419—31nomaximal, Hall
13C2×D5×Dic6—21no—
14C3×C5×C4⋊Q8C2211yescharacteristic
15#91758C2211yescharacteristic
16C5×Q8×Dic3C2212yes—
17C5×#944C2212yes—
18C5×#890—21no—
19C5×#889—22no—
20C5×#887—21no—
21C4×C5×Dic6C2211yescharacteristic
22C4×C5×Dic6C2211yescharacteristic
23C2×C3×#688C2212yes—
24C3×C4×D20C2211yescharacteristic
25#91469C2212yes—
26Dic3×D20C2212yes—
27#91422—22no—
28#91360—21no—
29C2×#6655C2211yescharacteristic
30#91119C2212yes—
31#91119C2212yes—
32C4×C3⋊#168C2211yescharacteristic
33C3×#3967C2212yes—
34C3×C4⋊#168C2211yescharacteristic
35#90986C2211yescharacteristic
36#90985C2212yes—
37Dic3⋊#168C2212yes—
38#90973C2212yes—
39#90972C2211yescharacteristic
40#90964C2211yescharacteristic
41Dic3×#168C2212yes—
42#80414—51nomaximal, Hall
43C5×#557—31no—
44Q8×D20—31no—
45#65372—32no—
46#65372D311yescharacteristic
47#65370—32no—
48#65370—31no—
49C4×#688—32no—
50C4×#688—31no—
51Q8×#168—31no—
52#65309—32no—
53#65309—31no—
54C2×C3×C5×Q8C2312yes—
55C2×Dic30—21no—
56C2×C5×Dic6D411yescharacteristic
57C2×C5×Dic6C2311yescharacteristic
58C2×C3×D20C2311yescharacteristic
59C2×C3×C4×D5—21no—
60C2×#1204—22no—
61C2×D5×Dic3—22no—
62D5×Dic6—44no—
63C3×C5×C4⋊C4—21no—
64C3×C5×C4⋊C4—21no—
65C3×C42×C5C2311yescharacteristic
66C4⋊Dic15—21no—
67C4⋊Dic15C2312yes—
68C2×C3⋊#168C2311yescharacteristic
69C2×C3⋊#168C2311yescharacteristic
70C5×C4⋊Dic3—22no—
71C5×C4⋊Dic3D411yescharacteristic
72C5×C4⋊Dic3C2311yescharacteristic
73C5×Dic3⋊C4—21no—
74C5×Dic3⋊C4—22no—
75C5×Dic3⋊C4—22no—
76C5×Dic3⋊C4D412yes—
77C4×C5×Dic3—21no—
78C4×C5×Dic3—22no—
79C4×C5×Dic3C2312yes—
80C3×#688—24no—
81C3×#685—21no—
82C3×C4⋊Dic5C2311yescharacteristic
83C2×C3×#168C2312yes—
84Dic3⋊Dic5—22no—
85#6665—22no—
86#6655—22no—
87#5721D511yescharacteristic, complemented
88D4×Dic6—51no—
89C3×#461—51no—
90#5162—52no—
91Dic3×SD16—52no—
92#5079—51no—
93C4×#214—51no—
94#4851—51no—
95#4830—51no—
96#4792—52no—
97#4791—52no—
98C2×Q8×D5—61no—
99C5×C4⋊Q8—32no—
100C5×C4⋊Q8C2×D311yescharacteristic
101C5×#125—62no—
102C5×#125—61no—
103C4×C5×Q8—31no—
104C4×C5×Q8—32no—
105C4×C5×Q8—31no—
106C4×C5×Q8—61no—
107C2×#688—31no—
108C2×#688C2×D312yes—
109#4043—62no—
110#4043—61no—
111C4×D20—32no—
112C4×D20C2×D311yescharacteristic
113#4015—31no—
114#4015—32no—
115#3967—32no—
116#3967—32no—
117#3967—31no—
118#3967—32no—
119#3967C2×D312yes—
120#3941—31no—
121#3940—31no—
122#3940—32no—
123C4⋊#168—32no—
124C4⋊#168C2×D311yescharacteristic
125C4×#168—31no—
126C4×#168—32no—
127#3359—151noSylow
128C22×C3×D5—21no—
129C3×C5×Q8—22no—
130C3×C5×Q8—22no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2411yescharacteristic
135C2×Dic15—22no—
136Dic30—42no—
137C2×C5×Dic3—21no—
138C2×C5×Dic3—21no—
139C2×C5×Dic3C2×D412yes—
140C2×C5×Dic3C2×D412yes—
141C5×Dic6—21no—
142C5×Dic6—21no—
143C5×Dic6SD1614yescomplemented
144C2×C3×Dic5—21no—
145C3×D20—21no—
146C3×D20#4112yes—
147C3×C4×D5—42no—
148#1204—44no—
149D5×Dic3—44no—
150C3⋊#168—21no—
151C3⋊#168—21no—
152C3×#168—22no—
153C22×Dic6—101no—
154C2×C3×SD16—52no—
155C3×C4⋊Q8C2×D511yescharacteristic
156C3×C4×D4—51no—
157Q8×Dic3C2×D512yes—
158#944C2×D512yes—
159D4×Dic3—52no—
160C2×#214—51no—
161#924—101no—
162#890—21no—
163#889—22no—
164#888—52no—
165#887—21no—
166#878—102no—
167#869—51no—
168C4×Dic6C2×D511yescharacteristic
169C4×Dic6C2×D511yescharacteristic
170C3×C4⋊C8—51no—
171C3×#103—52no—
172#835—52no—
173#835—52no—
174#832—51no—
175#817—52no—
176#816—52no—
177Dic3⋊C8—52no—
178C8×Dic3—52no—
179#810—51no—
180#808—51no—
181C4×C3⋊C8—51no—
182C2×C5×Q8—31no—
183C2×C5×Q8—31no—
184C2×C5×Q8C22×D312yes—
185Q8×D5—124no—
186C2×D20C22×D311yescharacteristic
187C2×C4×D5—21no—
188C2×C4×D5—62no—
189C2×Dic10—62no—
190C2×Dic10—61no—
191C5×C4⋊C4—21no—
192C5×C4⋊C4—21no—
193C5×C4⋊C4—32no—
194C5×C4⋊C4—31no—
195C5×C4⋊C4—31no—
196C5×C4⋊C4—62no—
197C5×C4⋊C4—62no—
198C5×C4⋊C4—62no—
199C5×C4⋊C4—61no—
200C42×C5—32no—
201C42×C5—62no—
202C42×C5—61no—
203C42×C5C22×D311yescharacteristic
204#688—24no—
205#688—62no—
206#685—21no—
207#685—62no—
208C4⋊Dic5—32no—
209C4⋊Dic5—62no—
210C4⋊Dic5—61no—
211C4⋊Dic5C22×D311yescharacteristic
212C2×#168—31no—
213C2×#168—31no—
214C2×#168C22×D312yes—
215#557—31no—
216D4×Q8—151no—
217#487—152no—
218#487—151no—
219#475—152no—
220#475—151no—
221#461—51no—
222#461—152no—
223C8×Q8—151no—
224C4×SD16—151no—
225C4×SD16—152no—
226C22×C3×C5C22×D411yescharacteristic
227C2×C3×D5—22no—
228C2×C3×D5—41no—
229C2×C3×D5—41no—
230C3×C4×C5—21no—
231C3×C4×C5—42no—
232C3×C4×C5C2×SD1612yes—
233C3×C4×C5C2×#4111yescharacteristic
234C3×C4×C52−1+411yescharacteristic
235Dic15—42no—
236C3×Dic5—41no—
237C5×Dic3—22no—
238C5×Dic3—41no—
239C5×Dic3—41no—
240C5×Dic3C2×SD1614yes—
241C2×C3×Q8C22×D512yes—
242C2×C3×D4—51no—
243C22×C3×C4—101no—
244C22×Dic3—102no—
245C2×Dic6—101no—
246C2×Dic6—102no—
247C2×Dic6—204no—
248C2×Dic6C22⋊D511yescharacteristic
249C2×Dic6C22×D511yescharacteristic
250C3×SD16—104no—
251C2×C3×C8—52no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—51no—
255C3×C22⋊C4—101no—
256C3×C42C22×D511yescharacteristic
257#217—102no—
258#214—102no—
259C4⋊Dic3—22no—
260C4⋊Dic3—52no—
261C4⋊Dic3—101no—
262C4⋊Dic3C22⋊D511yescharacteristic
263C4⋊Dic3C22×D511yescharacteristic
264Dic3⋊C4—21no—
265Dic3⋊C4—22no—
266Dic3⋊C4—22no—
267Dic3⋊C4—102no—
268Dic3⋊C4C22⋊D512yes—
269C4×Dic3—21no—
270C4×Dic3—22no—
271C4×Dic3C22×D512yes—
272C2×C3⋊C8—51no—
273C2×C3⋊C8—51no—
274C22×D5—21no—
275C5×Q8—22no—
276C5×Q8—22no—
277C5×Q8—34no—
278C5×Q8—61no—
279C5×Q8—61no—
280C2×C4×C5—22no—
281C2×C4×C5—32no—
282C2×C4×C5—32no—
283C2×C4×C5—61no—
284C2×C4×C5—61no—
285C2×C4×C5D3×D411yescharacteristic
286C2×C4×C5D3×D411yescharacteristic
287C2×C4×C5C23×D311yescharacteristic
288C2×Dic5—21no—
289C2×Dic5—62no—
290D20—21no—
291D20#23712yes—
292C4×D5—42no—
293C4×D5—124no—
294Dic10—124no—
295Dic10—122no—
296#168—22no—
297#168—61no—
298#168—61no—
299C22×Q8—301no—
300C2×SD16—52no—
301C2×SD16—151no—
302C4⋊Q8—32no—
303C4⋊Q8—152no—
304C4⋊Q8—151no—
305C4⋊Q8D3×D511yescharacteristic
306#125—62no—
307#125—61no—
308C22⋊Q8—302no—
309C22⋊Q8—301no—
310C4×Q8—31no—
311C4×Q8—32no—
312C4×Q8—31no—
313C4×Q8—61no—
314C4×D4—51no—
315C4×D4—152no—
316#106—151no—
317#106—152no—
318C4⋊C8—51no—
319C4⋊C8—152no—
320#103—52no—
321#103—151no—
322#103—152no—
323#103—152no—
324#103—152no—
325#102—151no—
326C4×C8—152no—
327C4×C8—151no—
328C2×C3×C5#54811yescharacteristic
329C2×C3×C5C22×SD1611yescharacteristic
330C2×C3×C5#57811yescharacteristic
331C3×D5—42no—
332C23×C3—101no—
333C3×Q8—22no—
334C3×Q8—22no—
335C3×D4—52no—
336C3×D4—101no—
337C2×C3×C4—22no—
338C2×C3×C4—101no—
339C2×C3×C4—202no—
340C2×C3×C4C2×C22⋊D511yescharacteristic
341C2×C3×C4C2×C22⋊D511yescharacteristic
342C2×C3×C4C23×D511yescharacteristic
343C2×Dic3—21no—
344C2×Dic3—21no—
345C2×Dic3—102no—
346C2×Dic3—204no—
347C2×Dic3C2×C22⋊D512yes—
348C2×Dic3C2×C22⋊D512yes—
349Dic6—21no—
350Dic6—21no—
351Dic6—202no—
352Dic6—204no—
353Dic6#68814yescomplemented
354C3×C8—102no—
355C3⋊C8—101no—
356C3⋊C8—101no—
357C22×C5C2×D3×D411yescharacteristic
358C2×D5—22no—
359C2×D5—41no—
360C2×D5—41no—
361C4×C5—21no—
362C4×C5—34no—
363C4×C5—42no—
364C4×C5—62no—
365C4×C5—121no—
366C4×C5—121no—
367C4×C5D3×SD1612yes—
368C4×C5C2×#23711yescharacteristic
369C4×C5#101011yescharacteristic
370Dic5—41no—
371Dic5—122no—
372C2×Q8—31no—
373C2×Q8—31no—
374C2×Q8—302no—
375C2×Q8—301no—
376C2×Q8—604no—
377C2×Q8C2×D3×D512yes—
378C2×D4—51no—
379C22×C4—101no—
380C22×C4—302no—
381SD16—104no—
382SD16—302no—
383C2×C8—52no—
384C2×C8—151no—
385C2×C8—151no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—32no—
389C4⋊C4—31no—
390C4⋊C4—31no—
391C4⋊C4—51no—
392C4⋊C4—62no—
393C4⋊C4—62no—
394C4⋊C4—62no—
395C4⋊C4—61no—
396C4⋊C4—152no—
397C4⋊C4—302no—
398C4⋊C4—301no—
399C22⋊C4—101no—
400C22⋊C4—302no—
401C42—32no—
402C42—62no—
403C42—61no—
404C42C2×D3×D511yescharacteristic
405C3×C5#335911yescharacteristic, complemented, Hall
406C22×C3—102no—
407C22×C3—201no—
408C22×C3—201no—
409C22×C3C22×C22⋊D511yescharacteristic
410C3×C4—21no—
411C3×C4—42no—
412C3×C4—201no—
413C3×C4C2×#68812yes—
414C3×C4D5×#4111yescharacteristic
415C3×C4#415011yescharacteristic
416Dic3—22no—
417Dic3—41no—
418Dic3—41no—
419Dic3—202no—
420Dic3C2×#68814yes—
421C2×C5#559811yescharacteristic
422C2×C5C2×D3×SD1611yescharacteristic
423C2×C5#577911yescharacteristic
424D5—42no—
425C23—101no—
426Q8—22no—
427Q8—22no—
428Q8—34no—
429Q8—61no—
430Q8—61no—
431Q8—604no—
432Q8—602no—
433D4—52no—
434D4—101no—
435C2×C4—22no—
436C2×C4—32no—
437C2×C4—32no—
438C2×C4—61no—
439C2×C4—61no—
440C2×C4—101no—
441C2×C4—202no—
442C2×C4—302no—
443C2×C4—604no—
444C2×C4D3×C22⋊D511yescharacteristic
445C2×C4D3×C22⋊D511yescharacteristic
446C2×C4C22×D3×D511yescharacteristic
447C8—102no—
448C8—301no—
449C8—301no—
450C2×C3—202no—
451C2×C3C22×#68811yescharacteristic
452C2×C3#6616511yescharacteristic
453C2×C3#6617211yescharacteristic
454C5#8041411yescharacteristic, complemented, Sylow
455C22—102no—
456C22—201no—
457C22—201no—
458C22C2×D3×C22⋊D511yescharacteristic
459C4—21no—
460C4—34no—
461C4—42no—
462C4—62no—
463C4—121no—
464C4—121no—
465C4—201no—
466C4—602no—
467C4D3×#68812yes—
468C4#9202011yescharacteristic
469C4D5×#23711yescharacteristic
470C3#1061541911yescharacteristic, complemented, Sylow
471C2—202no—
472C2#1175480211yescharacteristic
473C2C2×D3×#68811yescharacteristic
474C2#1175511411yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×D20C23
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3359
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C5×#5721C2semidirect
3. #11751180C2semidirect
5. #11749358C2semidirect
8. #11749187C2semidirect
10. #11746945C2semidirect
11. #11746857C2semidirect
87. #5721D5semidirect
143. C5×Dic6SD16semidirect
353. Dic6#688semidirect
405. C3×C5#3359semidirect
454. C5#80414semidirect
470. C3#10615419semidirect

Maximal subgroups

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

subgroupindex
C5×#57212
Dic6×D202
#117511802
C3×#653722
#117493582
Dic3×#6882
#117492272
#117491872
C4×#66552
#117469452
#117468572
#106154193
#804145