Finite Group Databasebeta

← #14297486

Subgroups — #14297486

Order 1920.

624 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4018C211yesmaximal, characteristic
2C2×C4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
3C2×C5×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4C2×#90955C212yesmaximal
5#11745966C212yesmaximal, complemented
6#10601269—31nomaximal, Hall
7C22×C3×C4×D5C2211yescharacteristic
8C2×C3×C42×C5C2211yescharacteristic
9C22×C3⋊#168C2212yes—
10C22×C5×C3⋊C8C2212yes—
11C2×C3×#685C411yescharacteristic
12C2×C3×#685C411yescharacteristic
13C2×C3×#683C411yescharacteristic
14C2×C3×#683C411yescharacteristic
15C2×C3×C4×Dic5C2211yescharacteristic
16C3×#4018—22no—
17C3×#4018—22no—
18C4⋊(C3⋊#168)—22no—
19C5×C4⋊(C3⋊C8)—22no—
20#90955—24no—
21#71583—51nomaximal, Hall
22C2×#4018D311yescharacteristic
23C2×C5×C4⋊C8—31no—
24C2×#3952—32no—
25C2×C4⋊#168—31no—
26#64770—32no—
27C23×C3×D5C2×C411yescharacteristic
28C22×C3×C4×C5C2×C411yescharacteristic
29C22×C3×C4×C5C2×C411yescharacteristic
30C22×C3×C4×C5C2311yescharacteristic
31C22×C3×Dic5C2×C411yescharacteristic
32C22×C3×Dic5C2×C411yescharacteristic
33C22×C3×Dic5C2×C411yescharacteristic
34C2×C3×C4×D5—21no—
35C2×C3×C4×D5—21no—
36C2×C3×C4×D5—21no—
37C2×C3×C4×D5—21no—
38C2×C3×C4×D5D412yes—
39C2×C3×C4×D5Q812yes—
40C3×C42×C5D412yes—
41C3×C42×C5D412yes—
42C2×C3⋊#168—22no—
43C2×C3⋊#168—22no—
44C2×C3⋊#168—22no—
45C2×C5×C3⋊C8—22no—
46C2×C5×C3⋊C8—22no—
47C2×C5×C3⋊C8—22no—
48C3×#685—22no—
49C3×#685—22no—
50C3×#683—22no—
51C3×#683—22no—
52C3×C4×Dic5—21no—
53C3×C4×Dic5—21no—
54C2×C3×#117—51no—
55C2×#830—52no—
56C2×C4⋊(C3⋊C8)—51no—
57C2×C4⋊(C3⋊C8)D511yescharacteristic, complemented
58#4524—52no—
59C22×C4×D5C2×D311yescharacteristic
60C22×C5×C8—32no—
61C2×C42×C5C2×D311yescharacteristic
62C2×#685Dic311yescharacteristic
63C2×#685Dic311yescharacteristic
64C2×#683Dic311yescharacteristic
65C2×#683Dic311yescharacteristic
66C2×C4×Dic5C2×D311yescharacteristic
67C22×#168—32no—
68#4018—22no—
69#4018—22no—
70C5×C4⋊C8—62no—
71#3952—64no—
72C4⋊#168—62no—
73#1798—151noSylow
74C23×C3×C5C22×C411yescharacteristic
75C22×C3×D5—21no—
76C22×C3×D5—21no—
77C22×C3×D5—22no—
78C22×C3×D5—22no—
79C22×C3×D5C4⋊C412yes—
80C2×C3×C4×C5—22no—
81C2×C3×C4×C5—22no—
82C2×C3×C4×C5C22⋊C412yes—
83C2×C3×C4×C5C22⋊C412yes—
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×Q811yescharacteristic
88C2×C3×C4×C5#4111yescharacteristic
89C2×C3×C4×C5#4111yescharacteristic
90C2×C3×Dic5—21no—
91C2×C3×Dic5—21no—
92C2×C3×Dic5—21no—
93C2×C3×Dic5—21no—
94C2×C3×Dic5—22no—
95C2×C3×Dic5—22no—
96C2×C3×Dic5C4⋊C412yes—
97C3×C4×D5—22no—
98C3×C4×D5—22no—
99C3×C4×D5—22no—
100C3×C4×D5—22no—
101C3⋊#168—42no—
102C5×C3⋊C8—42no—
103C23×C3×C4—51no—
104C3×#117—102no—
105C3×#117—102no—
106C2×C3×C4⋊C4—51no—
107C2×C3×C4⋊C4—51no—
108C2×C3×C22⋊C4—51no—
109C2×C3×C22⋊C4—51no—
110C2×C3×C42—51no—
111C2×C3×C42C2×D511yescharacteristic
112C22×C3⋊C8—52no—
113C22×C3⋊C8C2×D512yes—
114#830—104no—
115C4⋊(C3⋊C8)—22no—
116C4⋊(C3⋊C8)—102no—
117C23×D5C2×Dic311yescharacteristic
118C22×C4×C5C2×Dic311yescharacteristic
119C22×C4×C5C2×Dic311yescharacteristic
120C22×C4×C5C22×D311yescharacteristic
121C22×Dic5C2×Dic311yescharacteristic
122C22×Dic5C2×Dic311yescharacteristic
123C22×Dic5C2×Dic311yescharacteristic
124C2×C4×D5—21no—
125C2×C4×D5—21no—
126C2×C4×D5—21no—
127C2×C4×D5—21no—
128C2×C4×D5Dic612yes—
129C2×C4×D5D1212yes—
130C2×C5×C8—62no—
131C2×C5×C8—62no—
132C2×C5×C8—62no—
133C42×C5#6712yes—
134C42×C5#6712yes—
135#685—22no—
136#685—22no—
137#683—22no—
138#683—22no—
139C4×Dic5—21no—
140C4×Dic5—21no—
141C2×#168—62no—
142C2×#168—62no—
143C2×#168—62no—
144C2×#117—51no—
145C2×C4⋊C8—31no—
146C2×C4⋊C8—151no—
147C2×C22⋊C8—152no—
148#336—152no—
149C22×C3×C5C2×C22⋊C411yescharacteristic
150C22×C3×C5C2×C4⋊C411yescharacteristic
151C22×C3×C5#11711yescharacteristic
152C22×C3×C5#13112yes—
153C22×C3×C5#13112yes—
154C2×C3×D5—22no—
155C2×C3×D5—24no—
156C2×C3×D5—41no—
157C2×C3×D5—41no—
158C2×C3×D5—42no—
159C3×C4×C5—22no—
160C3×C4×C5—22no—
161C3×C4×C5#12111yescharacteristic
162C3×C4×C5#12111yescharacteristic
163C3×C4×C5C22⋊Q811yescharacteristic
164C3×C4×C5C22⋊Q811yescharacteristic
165C3×Dic5—22no—
166C3×Dic5—41no—
167C3×Dic5—41no—
168C24×C3—51no—
169C22×C3×C4—51no—
170C22×C3×C4—52no—
171C22×C3×C4—52no—
172C22×C3×C4—51no—
173C22×C3×C4—51no—
174C22×C3×C4—101no—
175C22×C3×C4—101no—
176C22×C3×C4—101no—
177C22×C3×C4—101no—
178C22×C3×C4C4×D511yescharacteristic
179C22×C3×C4C4×D511yescharacteristic
180C22×C3×C4C22×D511yescharacteristic
181C3×C4⋊C4—102no—
182C3×C4⋊C4—102no—
183C3×C22⋊C4—102no—
184C3×C22⋊C4—102no—
185C3×C42—101no—
186C3×C42—101no—
187C3×C42D2012yes—
188C3×C42C22⋊D512yes—
189C2×C3⋊C8—22no—
190C2×C3⋊C8—22no—
191C2×C3⋊C8—22no—
192C2×C3⋊C8—102no—
193C2×C3⋊C8—102no—
194C2×C3⋊C8—102no—
195C23×C5C22×Dic311yescharacteristic
196C22×D5—21no—
197C22×D5—22no—
198C22×D5—22no—
199C22×D5—21no—
200C22×D5C4⋊Dic312yes—
201C2×C4×C5—22no—
202C2×C4×C5—22no—
203C2×C4×C5#21712yes—
204C2×C4×C5#21712yes—
205C2×C4×C5C2×Dic611yescharacteristic
206C2×C4×C5C2×D1211yescharacteristic
207C2×C4×C5#23511yescharacteristic
208C2×C4×C5#23511yescharacteristic
209C2×C4×C5C2×#6711yescharacteristic
210C2×C4×C5C2×#6711yescharacteristic
211C2×Dic5—21no—
212C2×Dic5—21no—
213C2×Dic5—22no—
214C2×Dic5—22no—
215C2×Dic5—21no—
216C2×Dic5—21no—
217C2×Dic5C4⋊Dic312yes—
218C4×D5—22no—
219C4×D5—22no—
220C4×D5—22no—
221C4×D5—22no—
222C5×C8—122no—
223#168—122no—
224C23×C4—51no—
225C22×C8—32no—
226C22×C8—152no—
227#117—102no—
228#117—102no—
229C2×C4⋊C4—51no—
230C2×C4⋊C4—51no—
231C2×C22⋊C4—51no—
232C2×C22⋊C4—51no—
233C2×C42—51no—
234C2×C42D3×D511yescharacteristic
235C4⋊C8—62no—
236C4⋊C8—302no—
237C22⋊C8—304no—
238C2×C3×C5#38011yescharacteristic
239C2×C3×C5#40811yescharacteristic
240C2×C3×C5#40811yescharacteristic
241C2×C3×C5#42412yes—
242C2×C3×C5#43312yes—
243C3×D5—42no—
244C23×C3—52no—
245C23×C3—101no—
246C23×C3—102no—
247C23×C3—102no—
248C23×C3—101no—
249C23×C3C2×C4×D511yescharacteristic
250C2×C3×C4—22no—
251C2×C3×C4—22no—
252C2×C3×C4—52no—
253C2×C3×C4—101no—
254C2×C3×C4—101no—
255C2×C3×C4—102no—
256C2×C3×C4—102no—
257C2×C3×C4—102no—
258C2×C3×C4—102no—
259C2×C3×C4—102no—
260C2×C3×C4—102no—
261C2×C3×C4—101no—
262C2×C3×C4—101no—
263C2×C3×C4#68512yes—
264C2×C3×C4#68512yes—
265C2×C3×C4C2×D2011yescharacteristic
266C2×C3×C4D4×D511yescharacteristic
267C2×C3×C4#71111yescharacteristic
268C2×C3×C4Q8×D511yescharacteristic
269C2×C3×C4#71311yescharacteristic
270C2×C3×C4C2×C22⋊D511yescharacteristic
271C3⋊C8—42no—
272C3⋊C8—202no—
273C22×C5C2×C4⋊Dic311yescharacteristic
274C22×C5#92611yescharacteristic
275C22×C5#94812yes—
276C22×C5#94812yes—
277C22×C5C2×#21711yescharacteristic
278C2×D5—22no—
279C2×D5—24no—
280C2×D5—41no—
281C2×D5—41no—
282C2×D5—42no—
283C4×C5—22no—
284C4×C5—22no—
285C4×C5#92411yescharacteristic
286C4×C5#92411yescharacteristic
287C4×C5#93011yescharacteristic
288C4×C5#93011yescharacteristic
289Dic5—22no—
290Dic5—41no—
291Dic5—41no—
292C24—51no—
293C22×C4—51no—
294C22×C4—52no—
295C22×C4—52no—
296C22×C4—51no—
297C22×C4—51no—
298C22×C4—101no—
299C22×C4—101no—
300C22×C4—101no—
301C22×C4—101no—
302C22×C4D5×Dic311yescharacteristic
303C22×C4D5×Dic311yescharacteristic
304C22×C4C2×D3×D511yescharacteristic
305C2×C8—62no—
306C2×C8—62no—
307C2×C8—62no—
308C2×C8—302no—
309C2×C8—302no—
310C2×C8—302no—
311C4⋊C4—102no—
312C4⋊C4—102no—
313C22⋊C4—102no—
314C22⋊C4—102no—
315C42—101no—
316C42—101no—
317C42#120112yes—
318C42#120212yes—
319C3×C5#179811yescharacteristic, complemented, Hall
320C22×C3—104no—
321C22×C3—102no—
322C22×C3—202no—
323C22×C3—201no—
324C22×C3—201no—
325C22×C3D5×C4⋊C411yescharacteristic
326C22×C3#403811yescharacteristic
327C22×C3#404712yes—
328C22×C3#405312yes—
329C22×C3C2×#68511yescharacteristic
330C3×C4—22no—
331C3×C4—22no—
332C3×C4—102no—
333C3×C4—201no—
334C3×C4—201no—
335C3×C4#404111yescharacteristic
336C3×C4#404311yescharacteristic
337C3×C4#408411yescharacteristic
338C3×C4#409211yescharacteristic
339C2×C5#499912yes—
340C2×C5#500012yes—
341C2×C5#521211yescharacteristic
342C2×C5#523411yescharacteristic
343C2×C5#523411yescharacteristic
344D5—42no—
345C23—52no—
346C23—101no—
347C23—102no—
348C23—102no—
349C23—101no—
350C23C2×D5×Dic311yescharacteristic
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—52no—
354C2×C4—101no—
355C2×C4—101no—
356C2×C4—102no—
357C2×C4—102no—
358C2×C4—102no—
359C2×C4—102no—
360C2×C4—101no—
361C2×C4—101no—
362C2×C4—102no—
363C2×C4—102no—
364C2×C4#666512yes—
365C2×C4#666512yes—
366C2×C4D5×Dic611yescharacteristic
367C2×C4#677211yescharacteristic
368C2×C4#677311yescharacteristic
369C2×C4D5×D1211yescharacteristic
370C2×C4C2×#120111yescharacteristic
371C2×C4C2×#120211yescharacteristic
372C8—122no—
373C8—602no—
374C2×C3—202no—
375C2×C3#6512812yes—
376C2×C3#6512912yes—
377C2×C3#6527611yescharacteristic
378C2×C3#6539911yescharacteristic
379C2×C3#6541811yescharacteristic
380C5#7158311yescharacteristic, complemented, Sylow
381C22—102no—
382C22—104no—
383C22—202no—
384C22—201no—
385C22—201no—
386C22#9128312yes—
387C22#9128412yes—
388C22#9135811yescharacteristic
389C22D5×C4⋊Dic311yescharacteristic
390C22C2×#666511yescharacteristic
391C4—22no—
392C4—22no—
393C4—102no—
394C4—201no—
395C4—201no—
396C4#9135911yescharacteristic
397C4#9136011yescharacteristic
398C4#9144911yescharacteristic
399C4#9145011yescharacteristic
400C3#1060126911yescharacteristic, complemented, Sylow
401C2—202no—
402C2#1174687312yes—
403C2#1174698512yes—
404C2#1174834211yescharacteristic
405C2#1174834311yescharacteristic
406C2#1174875911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D3×D5
commutator, socleC23×C3×C5C22×C4
FittingC2×C3×C42×C5C22
prime radicalC23×C3×D5C2×C4
cosocleC22×C3×C4×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1798
LCSG ▷ C23×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊(C3⋊#168)C2semidirect
3. C2×C5×C4⋊(C3⋊C8)C2semidirect
5. #11745966C2semidirect
57. C2×C4⋊(C3⋊C8)D5semidirect
319. C3×C5#1798semidirect
380. C5#71583semidirect
400. C3#10601269semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40182
C2×C4⋊(C3⋊#168)2
C2×C5×C4⋊(C3⋊C8)2
C2×#909552
#117459662
#106012693
#715835