Finite Group Databasebeta

← #14281184

Subgroups — #14281184

Order 1920.

560 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×#91818C211yesmaximal, characteristic
2C3×C5×#407C211yesmaximal, characteristic, complemented
3C2×#91114C211yesmaximal, characteristic, complemented
4#11746290C212yesmaximal, complemented
5#11746289C212yesmaximal, complemented
6#10600762—31nomaximal, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C22×#1220C411yescharacteristic
9C2×C3×C5×M16—21no—
10C2×#6719C411yescharacteristic
11#91818—21no—
12#91818—21no—
13#91818—21no—
14#91818—21no—
15C2×#6714C411yescharacteristic
16C2×#6714C2211yescharacteristic
17C2×#6712C411yescharacteristic
18C2×#6712C2211yescharacteristic
19C22×C3⋊#168—21no—
20C3×C5×C22⋊C8—21no—
21C3×C5×C22⋊C8C2212yes—
22#91114—21no—
23#91114C2212yes—
24#69969—51nomaximal, Hall
25C2×#4075—31no—
26C5×#407D311yescharacteristic, complemented
27C2×C22⋊#168—31no—
28#64689—32no—
29#64688—32no—
30C24×C3×C5C2×C411yescharacteristic
31C23×D15C2×C411yescharacteristic
32C22×C3×C4×C5—42no—
33C22×C3×C4×C5C2×C411yescharacteristic
34C22×C3×C4×C5D411yescharacteristic
35C22×C3×C4×C5D411yescharacteristic
36C22×C3×C4×C5D411yescharacteristic
37C22×C3×C4×C5D411yescharacteristic
38C22×C3×C4×C5C2311yescharacteristic
39C2×#1220—21no—
40C2×#1220—21no—
41C2×#1220—42no—
42C22×Dic15C2×C411yescharacteristic
43C22×Dic15C2×C411yescharacteristic
44C22×Dic15C2×C411yescharacteristic
45C3×C5×M16—42no—
46C2×C3×C5×C8—22no—
47#6719—21no—
48#6719—21no—
49#6714—21no—
50#6714—21no—
51#6714—21no—
52#6714—21no—
53#6712—21no—
54#6712—21no—
55#6712—21no—
56#6712—21no—
57C2×C3⋊#168—22no—
58C2×C3⋊#168—42no—
59C2×#929—51no—
60C3×#407D511yescharacteristic, complemented
61C2×#830—51no—
62#4469—52no—
63#4468—52no—
64C23×C4×C5C2×D311yescharacteristic
65C22×C22⋊D5—31no—
66C2×C5×M16—21no—
67C2×C22⋊Dic5—31no—
68#4075—61no—
69#4075—61no—
70#4075—61no—
71#4075—61no—
72C2×#685—31no—
73C2×#685—31no—
74C2×#683—31no—
75C2×#683—31no—
76C22×#168—61no—
77C5×C22⋊C8—21no—
78C5×C22⋊C8C2×D312yes—
79C22⋊#168—32no—
80C22⋊#168—61no—
81#1468—151noSylow
82C23×C3×C5—22no—
83C23×C3×C5—22no—
84C23×C3×C5—41no—
85C23×C3×C5C22⋊C411yescharacteristic
86C23×C3×C5C22⋊C411yescharacteristic
87C23×C3×C5C22×C411yescharacteristic
88C22×D15—21no—
89C22×D15—22no—
90C22×D15—41no—
91C22×D15—41no—
92C2×C3×C4×C5—22no—
93C2×C3×C4×C5—22no—
94C2×C3×C4×C5—41no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5C22⋊C411yescharacteristic
99C2×C3×C4×C5C22⋊C411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102#1220—42no—
103#1220—42no—
104C2×Dic15—21no—
105C2×Dic15—21no—
106C2×Dic15—21no—
107C2×Dic15—22no—
108C2×Dic15—41no—
109C2×Dic15—41no—
110C3×C5×C8—42no—
111C3⋊#168—42no—
112C23×C3×C4C2×D511yescharacteristic
113C22×#67—51no—
114C2×C3×M16—21no—
115C2×#217—51no—
116#929—101no—
117#929—101no—
118#929—101no—
119#929—101no—
120C2×(C2×D3)⋊C4—51no—
121C2×(C2×D3)⋊C4—51no—
122C2×Dic3⋊C4—51no—
123C2×Dic3⋊C4—51no—
124C22×C3⋊C8—101no—
125C3×C22⋊C8—21no—
126C3×C22⋊C8C2×D512yes—
127#830—52no—
128#830—101no—
129C24×C5C4×D311yescharacteristic
130C23×D5—31no—
131C22×C4×C5—42no—
132C22×C4×C5C4×D311yescharacteristic
133C22×C4×C5D1211yescharacteristic
134C22×C4×C5D1211yescharacteristic
135C22×C4×C5#6711yescharacteristic
136C22×C4×C5#6711yescharacteristic
137C22×C4×C5C22×D311yescharacteristic
138C2×C22⋊D5—61no—
139C2×C22⋊D5—61no—
140C2×C22⋊D5—122no—
141C22×Dic5—31no—
142C22×Dic5—31no—
143C22×Dic5—31no—
144C5×M16—42no—
145C2×C5×C8—22no—
146C22⋊Dic5—61no—
147C22⋊Dic5—61no—
148#685—61no—
149#685—61no—
150#685—61no—
151#685—61no—
152#683—61no—
153#683—61no—
154#683—61no—
155#683—61no—
156C2×#168—62no—
157C2×#168—122no—
158C2×#123—151no—
159#407D1511yescharacteristic, complemented
160C2×C22⋊C8—151no—
161#324—152no—
162#323—152no—
163C22×C3×C5—21no—
164C22×C3×C5—21no—
165C22×C3×C5—21no—
166C22×C3×C5—21no—
167C22×C3×C5—21no—
168C22×C3×C5—21no—
169C22×C3×C5—21no—
170C22×C3×C5—44no—
171C22×C3×C5#9912yes—
172C22×C3×C5C2×C22⋊C411yescharacteristic
173C22×C3×C5#13112yes—
174C2×D15—41no—
175C2×D15—41no—
176C2×D15—41no—
177C2×D15—82no—
178C3×C4×C5—21no—
179C3×C4×C5—21no—
180C3×C4×C5—21no—
181C3×C4×C5—21no—
182Dic15—41no—
183Dic15—41no—
184Dic15—41no—
185C24×C3C4×D511yescharacteristic
186C23×D3—51no—
187C22×C3×C4—42no—
188C22×C3×C4C4×D511yescharacteristic
189C22×C3×C4D2011yescharacteristic
190C22×C3×C4D2011yescharacteristic
191C22×C3×C4C22⋊D511yescharacteristic
192C22×C3×C4C22⋊D511yescharacteristic
193C22×C3×C4C22×D511yescharacteristic
194C2×#67—101no—
195C2×#67—101no—
196C2×#67—202no—
197C22×Dic3—51no—
198C22×Dic3—51no—
199C22×Dic3—51no—
200C3×M16—42no—
201C2×C3×C8—22no—
202#217—101no—
203#217—101no—
204(C2×D3)⋊C4—101no—
205(C2×D3)⋊C4—101no—
206(C2×D3)⋊C4—101no—
207(C2×D3)⋊C4—101no—
208Dic3⋊C4—101no—
209Dic3⋊C4—101no—
210Dic3⋊C4—101no—
211Dic3⋊C4—101no—
212C2×C3⋊C8—102no—
213C2×C3⋊C8—202no—
214C23×C5—22no—
215C23×C5—22no—
216C23×C5—41no—
217C23×C5(C2×D3)⋊C411yescharacteristic
218C23×C5(C2×D3)⋊C411yescharacteristic
219C23×C5C2×C4×D311yescharacteristic
220C22×D5—61no—
221C22×D5—62no—
222C22×D5—121no—
223C22×D5—121no—
224C2×C4×C5—22no—
225C2×C4×C5—22no—
226C2×C4×C5—41no—
227C2×C4×C5—41no—
228C2×C4×C5—41no—
229C2×C4×C5—41no—
230C2×C4×C5(C2×D3)⋊C411yescharacteristic
231C2×C4×C5(C2×D3)⋊C411yescharacteristic
232C2×C4×C5C2×D1211yescharacteristic
233C2×C4×C5C2×#6711yescharacteristic
234C22⋊D5—122no—
235C22⋊D5—122no—
236C2×Dic5—62no—
237C2×Dic5—61no—
238C2×Dic5—61no—
239C2×Dic5—61no—
240C2×Dic5—121no—
241C2×Dic5—121no—
242C5×C8—42no—
243#168—122no—
244C22×D4—151no—
245C23×C4C2×D1511yescharacteristic
246C2×M16—21no—
247C22×C8—301no—
248#123—301no—
249#123—301no—
250#123—301no—
251#123—301no—
252C2×C4⋊C4—151no—
253C2×C4⋊C4—151no—
254C2×C22⋊C4—151no—
255C2×C22⋊C4—151no—
256C2×C22⋊C4—151no—
257C22⋊C8—21no—
258C22⋊C8—152no—
259C22⋊C8—301no—
260C22⋊C8C2×D1512yes—
261C2×C3×C5—22no—
262C2×C3×C5—22no—
263C2×C3×C5—41no—
264C2×C3×C5#40811yescharacteristic
265C2×C3×C5C2×#9911yescharacteristic
266C2×C3×C5#41311yescharacteristic
267D15—81no—
268C23×C3—22no—
269C23×C3—22no—
270C23×C3—41no—
271C23×C3#68511yescharacteristic
272C23×C3#68511yescharacteristic
273C23×C3C2×C4×D511yescharacteristic
274C22×D3—101no—
275C22×D3—102no—
276C22×D3—201no—
277C22×D3—201no—
278C2×C3×C4—22no—
279C2×C3×C4—22no—
280C2×C3×C4—41no—
281C2×C3×C4—41no—
282C2×C3×C4—41no—
283C2×C3×C4—41no—
284C2×C3×C4#68511yescharacteristic
285C2×C3×C4#68511yescharacteristic
286C2×C3×C4C2×D2011yescharacteristic
287C2×C3×C4C2×C22⋊D511yescharacteristic
288#67—202no—
289#67—202no—
290C2×Dic3—102no—
291C2×Dic3—101no—
292C2×Dic3—101no—
293C2×Dic3—101no—
294C2×Dic3—201no—
295C2×Dic3—201no—
296C3×C8—42no—
297C3⋊C8—202no—
298C22×C5—21no—
299C22×C5—21no—
300C22×C5—21no—
301C22×C5—21no—
302C22×C5—21no—
303C22×C5—21no—
304C22×C5—21no—
305C22×C5—44no—
306C22×C5#80612yes—
307C22×C5#90712yes—
308C22×C5C2×(C2×D3)⋊C411yescharacteristic
309C2×D5—121no—
310C2×D5—121no—
311C2×D5—121no—
312C2×D5—242no—
313C4×C5—21no—
314C4×C5—21no—
315C4×C5—21no—
316C4×C5—21no—
317Dic5—121no—
318Dic5—121no—
319Dic5—121no—
320C24—151no—
321C24C4×D1511yescharacteristic
322C2×D4—301no—
323C2×D4—301no—
324C2×D4—602no—
325C22×C4—42no—
326C22×C4—151no—
327C22×C4—151no—
328C22×C4—151no—
329C22×C4C4×D1511yescharacteristic
330C22×C4D6011yescharacteristic
331C22×C4D6011yescharacteristic
332C22×C4#122011yescharacteristic
333C22×C4#122011yescharacteristic
334C22×C4C22×D1511yescharacteristic
335M16—42no—
336C2×C8—22no—
337C2×C8—302no—
338C2×C8—602no—
339C4⋊C4—301no—
340C4⋊C4—301no—
341C4⋊C4—301no—
342C4⋊C4—301no—
343C22⋊C4—301no—
344C22⋊C4—301no—
345C22⋊C4—301no—
346C22⋊C4—301no—
347C22⋊C4—301no—
348C22⋊C4—301no—
349C3×C5#146811yescharacteristic, complemented, Hall
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—44no—
358C22×C3#393812yes—
359C22×C3#405312yes—
360C22×C3C2×#68511yescharacteristic
361C2×D3—201no—
362C2×D3—201no—
363C2×D3—201no—
364C2×D3—402no—
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—21no—
369Dic3—201no—
370Dic3—201no—
371Dic3—201no—
372C2×C5—22no—
373C2×C5—22no—
374C2×C5—41no—
375C2×C5C2×#80611yescharacteristic
376C2×C5#512911yescharacteristic
377C2×C5#513211yescharacteristic
378D5—241no—
379C23—22no—
380C23—22no—
381C23—41no—
382C23—301no—
383C23—302no—
384C23—601no—
385C23—601no—
386C23#671411yescharacteristic
387C23#671411yescharacteristic
388C23C2×C4×D1511yescharacteristic
389D4—602no—
390D4—602no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—302no—
398C2×C4—301no—
399C2×C4—301no—
400C2×C4—301no—
401C2×C4—601no—
402C2×C4—601no—
403C2×C4#671411yescharacteristic
404C2×C4#671411yescharacteristic
405C2×C4C2×D6011yescharacteristic
406C2×C4C2×#122011yescharacteristic
407C8—42no—
408C8—602no—
409C2×C3—22no—
410C2×C3—22no—
411C2×C3—41no—
412C2×C3C2×#393811yescharacteristic
413C2×C3#6541811yescharacteristic
414C2×C3#6542111yescharacteristic
415D3—401no—
416C5#6996911yescharacteristic, complemented, Sylow
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—44no—
425C22—601no—
426C22—601no—
427C22—601no—
428C22—1202no—
429C22#9109012yes—
430C22#9179612yes—
431C22C2×#671411yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—601no—
437C4—601no—
438C4—601no—
439C3#1060076211yescharacteristic, complemented, Sylow
440C2—22no—
441C2—22no—
442C2—41no—
443C2—1201no—
444C2C2×#9109011yescharacteristic
445C2#1175123011yescharacteristic
446C2#1175123311yescharacteristic
subgroupG/H
centerC22C2×#6714
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#407C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×#1220C4
cosocleC22×C3×C4×C5C23
hypercenter#407D15
hypocenterC3×C5#1468
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C3×C5×#407C2semidirect
3. C2×#91114C2semidirect
4. #11746290C2semidirect
5. #11746289C2semidirect
26. C5×#407D3semidirect
60. C3×#407D5semidirect
159. #407D15semidirect
349. C3×C5#1468semidirect
416. C5#69969semidirect
439. C3#10600762semidirect

Maximal subgroups

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

subgroupindex
C2×#918182
C3×C5×#4072
C2×#911142
#117462902
#117462892
#106007623
#699695