Finite Group Databasebeta

← #14471675

Subgroups — #14471675

Order 1920.

700 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5732C211yesmaximal, characteristic, complemented
2#11752657C211yesmaximal, characteristic, complemented
3#11751180C211yesmaximal, characteristic, complemented
4C3×#65372C211yesmaximal, characteristic, complemented
5#11749333C212yesmaximal, complemented
6Dic3×#688C212yesmaximal, complemented
7#11749228C212yesmaximal
8#11749188C212yesmaximal, complemented
9C4×#6652C211yesmaximal, characteristic
10#11746883C211yesmaximal, characteristic, complemented
11#11746857C211yesmaximal, characteristic, complemented
12#10615398—31nomaximal, Hall
13C3×C5×C4⋊Q8C2211yescharacteristic
14#91758C2211yescharacteristic
15C5×#947C2212yes—
16C5×Q8×Dic3C2212yes—
17C5×#898—22no—
18C5×#897—21no—
19C5×#892—21no—
20C4×C5×D12C2211yescharacteristic
21C4×C5×Dic6C2211yescharacteristic
22C2×C3×#688C2212yes—
23C3×C4×D20C2211yescharacteristic
24#91431—22no—
25Dic3×D20C2212yes—
26D5×C4⋊Dic3—21no—
27#91381C2212yes—
28#91359—21no—
29C2×#6652C2211yescharacteristic
30#91119C2212yes—
31#91119C2212yes—
32C4×C3⋊#168C2211yescharacteristic
33C3×#3967C2212yes—
34C3×C4⋊#168C2211yescharacteristic
35#90989C2211yescharacteristic
36#90985C2212yes—
37Dic3⋊#168C2212yes—
38#90967C2212yes—
39#90966C2211yescharacteristic
40#90964C2211yescharacteristic
41Dic3×#168C2212yes—
42#80415—51nomaximal, Hall
43C5×#556—31no—
44#65913—31no—
45#65372D311yescharacteristic, complemented
46#65370—31no—
47#65346—32no—
48#65345—32no—
49C4×#688—32no—
50Q8×#168—31no—
51#65311—32no—
52C4×#686—31no—
53#65297—31no—
54C2×C3×C5×Q8C2312yes—
55C2×Dic30—21no—
56C2×C5×D12C2311yescharacteristic
57C2×C4×C5×D3—21no—
58C2×C5×Dic6D411yescharacteristic
59C2×C3×D20C2311yescharacteristic
60C2×C3×C4×D5—21no—
61C2×D5×Dic3—22no—
62C3×C5×C4⋊C4—21no—
63C3×C5×C4⋊C4—21no—
64C3×C42×C5C2311yescharacteristic
65C4⋊Dic15—21no—
66C4⋊Dic15C2312yes—
67C2×C3⋊#168C2311yescharacteristic
68C2×C3⋊#168C2311yescharacteristic
69C5×(C2×D3)⋊C4—21no—
70C5×(C2×D3)⋊C4—22no—
71C5×(C2×D3)⋊C4—22no—
72C5×C4⋊Dic3—22no—
73C5×C4⋊Dic3D411yescharacteristic
74C5×C4⋊Dic3C2311yescharacteristic
75C5×Dic3⋊C4D412yes—
76C4×C5×Dic3—22no—
77C4×C5×Dic3C2312yes—
78C3×#688—24no—
79C3×#685—21no—
80C3×C4⋊Dic5C2311yescharacteristic
81C2×C3×#168C2312yes—
82#6669—22no—
83#6668—22no—
84#6665—22no—
85#6652—22no—
86#5732D511yescharacteristic, complemented
87#5543—51no—
88C3×#461—51no—
89#5165—52no—
90Dic3×SD16—52no—
91#5079—51no—
92C4×#213—51no—
93#4842—51no—
94#4830—51no—
95#4800—52no—
96#4799—52no—
97C5×C4⋊Q8C2×D311yescharacteristic
98C5×#126—62no—
99C5×#124—32no—
100C5×C22⋊Q8—61no—
101C4×C5×Q8—31no—
102C4×C5×Q8—32no—
103C4×C5×D4—31no—
104C5×#117—61no—
105#4092—61no—
106C2×#688C2×D312yes—
107C2×#686—31no—
108#4042—62no—
109D5×C4⋊C4—61no—
110C4×D20—32no—
111C4×D20C2×D311yescharacteristic
112#4016—32no—
113#4015—31no—
114#3967—32no—
115#3967—32no—
116#3967C2×D312yes—
117#3964—31no—
118#3964—32no—
119#3941—31no—
120#3940—32no—
121#3939—31no—
122C4⋊#168—32no—
123C4⋊#168C2×D311yescharacteristic
124C4×#168—31no—
125C4×#168—32no—
126#3360—151noSylow
127C22×C5×D3—21no—
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—81no—
137C2×C5×Dic3—21no—
138C2×C5×Dic3C2×D412yes—
139C2×C5×Dic3C2×D412yes—
140C5×D12—21no—
141C5×D12—21no—
142C4×C5×D3—42no—
143C5×Dic6—22no—
144C2×C3×Dic5—21no—
145C3×D20—21no—
146C3×D20#4112yes—
147C3×C4×D5—42no—
148D5×Dic3—82no—
149C3⋊#168—21no—
150C3⋊#168—21no—
151C3×#168—22no—
152C2×C3×SD16—52no—
153C3×C4⋊Q8C2×D511yescharacteristic
154C3×C4×D4—51no—
155#947C2×D512yes—
156Q8×Dic3C2×D512yes—
157D4×Dic3—52no—
158C2×#213—51no—
159C2×C4⋊Dic3—101no—
160#924—101no—
161#898—22no—
162#897—21no—
163#892—21no—
164#890—52no—
165#878—102no—
166C4×D12C2×D511yescharacteristic
167#869—51no—
168C4×Dic6C2×D511yescharacteristic
169C3×C4⋊C8—51no—
170C3×#103—52no—
171#835—52no—
172#835—52no—
173#832—51no—
174#821—52no—
175#817—52no—
176Dic3⋊C8—52no—
177C8×Dic3—52no—
178#809—51no—
179#807—51no—
180C4×C3⋊C8—51no—
181C2×C5×Q8—31no—
182C2×C5×Q8C22×D312yes—
183C2×C5×D4—31no—
184C22×C4×C5—61no—
185C2×D20C22×D311yescharacteristic
186C2×C4×D5—21no—
187C2×C4×D5—62no—
188C2×Dic10—61no—
189C5×C4⋊C4—21no—
190C5×C4⋊C4—21no—
191C5×C4⋊C4—31no—
192C5×C4⋊C4—32no—
193C5×C4⋊C4—31no—
194C5×C4⋊C4—62no—
195C5×C22⋊C4—62no—
196C5×C22⋊C4—62no—
197C5×C22⋊C4—61no—
198C42×C5—32no—
199C42×C5—62no—
200C42×C5C22×D311yescharacteristic
201#688—24no—
202#686—62no—
203#685—21no—
204#685—62no—
205C4⋊Dic5—32no—
206C4⋊Dic5—61no—
207C4⋊Dic5C22×D311yescharacteristic
208#683—62no—
209#683—62no—
210C2×#168—31no—
211C2×#168—31no—
212C2×#168C22×D312yes—
213#556—31no—
214#554—151no—
215#488—152no—
216#487—151no—
217#479—152no—
218#476—151no—
219#463—152no—
220#461—51no—
221C8×Q8—151no—
222C4×SD16—152no—
223C4×D8—151no—
224C22×C3×C5C22×D411yescharacteristic
225C2×C5×D3—41no—
226C2×C5×D3—41no—
227C2×C5×D3—41no—
228C2×C3×D5—22no—
229C2×C3×D5—41no—
230C2×C3×D5—41no—
231C3×C4×C5—21no—
232C3×C4×C5—42no—
233C3×C4×C5#13512yes—
234C3×C4×C5C2×#4111yescharacteristic
235C3×C4×C52−1+411yescharacteristic
236Dic15—42no—
237C3×Dic5—41no—
238C5×Dic3—22no—
239C5×Dic3—22no—
240C5×Dic3—41no—
241C2×C3×Q8C22×D512yes—
242C2×C3×D4—51no—
243C22×C3×C4—101no—
244C22×Dic3—102no—
245C2×D12C22×D511yescharacteristic
246C2×C4×D3—21no—
247C2×Dic6—101no—
248C2×Dic6C22⋊D511yescharacteristic
249C3×SD16—104no—
250C2×C3×C8—52no—
251C3×C4⋊C4—21no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—51no—
254C3×C22⋊C4—101no—
255C3×C42C22×D511yescharacteristic
256#217—102no—
257#213—102no—
258(C2×D3)⋊C4—21no—
259(C2×D3)⋊C4—22no—
260(C2×D3)⋊C4—22no—
261C4⋊Dic3—22no—
262C4⋊Dic3—52no—
263C4⋊Dic3—101no—
264C4⋊Dic3—102no—
265C4⋊Dic3C22⋊D511yescharacteristic
266C4⋊Dic3C22×D511yescharacteristic
267Dic3⋊C4—102no—
268Dic3⋊C4C22⋊D512yes—
269C4×Dic3—22no—
270C4×Dic3C22×D512yes—
271C2×C3⋊C8—51no—
272C2×C3⋊C8—51no—
273C23×C5—61no—
274C22×D5—21no—
275C5×Q8—22no—
276C5×Q8—22no—
277C5×Q8—62no—
278C5×D4—61no—
279C5×D4—61no—
280C2×C4×C5—22no—
281C2×C4×C5—32no—
282C2×C4×C5—32no—
283C2×C4×C5—61no—
284C2×C4×C5—122no—
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—242no—
294Dic10—241no—
295#168—22no—
296#168—61no—
297#168—61no—
298C2×SD16—52no—
299C2×D8—151no—
300C4⋊Q8—151no—
301C4⋊Q8D3×D511yescharacteristic
302#126—62no—
303#125—152no—
304#124—32no—
305C22⋊Q8—61no—
306C22⋊Q8—302no—
307C22⋊Q8—301no—
308C4×Q8—31no—
309C4×Q8—32no—
310C4×D4—31no—
311C4×D4—51no—
312C4×D4—152no—
313#117—61no—
314C2×C4⋊C4—301no—
315#107—151no—
316#106—152no—
317C4⋊C8—51no—
318C4⋊C8—152no—
319#103—52no—
320#103—152no—
321#103—152no—
322#102—151no—
323#102—151no—
324#102—152no—
325C4×C8—152no—
326C4×C8—151no—
327C2×C3×C5#54811yescharacteristic
328C2×C3×C5C2×#13511yescharacteristic
329C2×C3×C5#57711yescharacteristic
330C3×D5—42no—
331C5×D3—81no—
332C23×C3—101no—
333C22×D3—21no—
334C3×Q8—22no—
335C3×Q8—22no—
336C3×D4—52no—
337C3×D4—101no—
338C2×C3×C4—22no—
339C2×C3×C4—101no—
340C2×C3×C4—202no—
341C2×C3×C4C2×C22⋊D511yescharacteristic
342C2×C3×C4C2×C22⋊D511yescharacteristic
343C2×C3×C4C23×D511yescharacteristic
344C2×Dic3—21no—
345C2×Dic3—102no—
346C2×Dic3—402no—
347C2×Dic3C2×C22⋊D512yes—
348C2×Dic3C2×C22⋊D512yes—
349D12—21no—
350D12—21no—
351C4×D3—42no—
352Dic6—22no—
353Dic6—401no—
354C3×C8—102no—
355C3⋊C8—101no—
356C3⋊C8—101no—
357C22×C5—121no—
358C22×C5—121no—
359C22×C5—121no—
360C22×C5C2×D3×D411yescharacteristic
361C2×D5—22no—
362C2×D5—41no—
363C2×D5—41no—
364C4×C5—21no—
365C4×C5—42no—
366C4×C5—62no—
367C4×C5—62no—
368C4×C5—121no—
369C4×C5#91612yes—
370C4×C5C2×#23711yescharacteristic
371C4×C5#101011yescharacteristic
372Dic5—41no—
373Dic5—122no—
374C2×Q8—31no—
375C2×Q8—301no—
376C2×Q8C2×D3×D512yes—
377C2×D4—31no—
378C2×D4—51no—
379C22×C4—61no—
380C22×C4—101no—
381C22×C4—302no—
382SD16—104no—
383D8—302no—
384C2×C8—52no—
385C2×C8—151no—
386C2×C8—151no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—31no—
390C4⋊C4—32no—
391C4⋊C4—31no—
392C4⋊C4—51no—
393C4⋊C4—62no—
394C4⋊C4—152no—
395C4⋊C4—302no—
396C4⋊C4—302no—
397C4⋊C4—301no—
398C22⋊C4—62no—
399C22⋊C4—62no—
400C22⋊C4—61no—
401C22⋊C4—101no—
402C22⋊C4—302no—
403C42—32no—
404C42—62no—
405C42C2×D3×D511yescharacteristic
406C3×C5#336011yescharacteristic, complemented, Hall
407C22×C3—102no—
408C22×C3—201no—
409C22×C3—201no—
410C22×C3C22×C22⋊D511yescharacteristic
411C2×D3—41no—
412C2×D3—41no—
413C2×D3—41no—
414C3×C4—21no—
415C3×C4—42no—
416C3×C4—201no—
417C3×C4#409612yes—
418C3×C4D5×#4111yescharacteristic
419C3×C4#415011yescharacteristic
420Dic3—22no—
421Dic3—22no—
422Dic3—41no—
423Dic3—202no—
424C2×C5—241no—
425C2×C5#559811yescharacteristic
426C2×C5C2×#91611yescharacteristic
427C2×C5#577811yescharacteristic
428D5—42no—
429C23—61no—
430C23—101no—
431Q8—22no—
432Q8—22no—
433Q8—62no—
434Q8—1201no—
435D4—52no—
436D4—61no—
437D4—61no—
438D4—101no—
439C2×C4—22no—
440C2×C4—32no—
441C2×C4—32no—
442C2×C4—61no—
443C2×C4—101no—
444C2×C4—122no—
445C2×C4—202no—
446C2×C4—302no—
447C2×C4—1202no—
448C2×C4D3×C22⋊D511yescharacteristic
449C2×C4D3×C22⋊D511yescharacteristic
450C2×C4C22×D3×D511yescharacteristic
451C8—102no—
452C8—301no—
453C8—301no—
454C2×C3—202no—
455C2×C3C2×#409611yescharacteristic
456C2×C3#6616511yescharacteristic
457C2×C3#6617111yescharacteristic
458D3—81no—
459C5#8041511yescharacteristic, complemented, Sylow
460C22—102no—
461C22—121no—
462C22—121no—
463C22—121no—
464C22—201no—
465C22—201no—
466C22C2×D3×C22⋊D511yescharacteristic
467C4—21no—
468C4—42no—
469C4—62no—
470C4—62no—
471C4—121no—
472C4—201no—
473C4—602no—
474C4#9151712yes—
475C4#9202011yescharacteristic
476C4D5×#23711yescharacteristic
477C3#1061539811yescharacteristic, complemented, Sylow
478C2—202no—
479C2—241no—
480C2#1175480211yescharacteristic
481C2#1175509211yescharacteristic
482C2C2×#9151711yescharacteristic
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×#6652C22
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3360
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×#5732C2semidirect
2. #11752657C2semidirect
3. #11751180C2semidirect
4. C3×#65372C2semidirect
5. #11749333C2semidirect
6. Dic3×#688C2semidirect
8. #11749188C2semidirect
10. #11746883C2semidirect
11. #11746857C2semidirect
45. #65372D3semidirect
86. #5732D5semidirect
406. C3×C5#3360semidirect
459. C5#80415semidirect
477. C3#10615398semidirect

Maximal subgroups

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

subgroupindex
C5×#57322
#117526572
#117511802
C3×#653722
#117493332
Dic3×#6882
#117492282
#117491882
C4×#66522
#117468832
#117468572
#106153983
#804155