Finite Group Databasebeta

← #14301685

Subgroups — #14301685

Order 1920.

772 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91824C211yesmaximal, characteristic
2C5×#5798C211yesmaximal, characteristic
3C2×C3×#3966C211yesmaximal, characteristic
4#11749473C212yesmaximal, complemented
5#11746018C212yesmaximal, complemented
6#10602448—31nomaximal, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C23×Dic15C2211yescharacteristic
9C2×#6719—21no—
10C2×#6719C2211yescharacteristic
11#91824—22no—
12#91824C414yescomplemented
13C2×#6712—21no—
14C2×C5×#217—21no—
15C2×C5×#217C2212yes—
16C5×D4×Dic3—24no—
17C5×#926—21no—
18C2×C3×C22⋊Dic5C2212yes—
19C3×#3966—22no—
20#90994—24no—
21#70023—51nomaximal, Hall
22C5×#518—31no—
23C2×#4081—31no—
24C2×#3966D311yescharacteristic
25#65232—32no—
26#64746—32no—
27C24×C3×C5D411yescharacteristic
28C24×C3×C5C2311yescharacteristic
29C2×C3×C5×D4—22no—
30C2×C3×C5×D4—22no—
31C2×C3×C5×D4C2×C412yes—
32C2×C3×C5×D4D412yes—
33C22×C3×C4×C5D411yescharacteristic
34C22×Dic15—22no—
35C22×Dic15—21no—
36C22×Dic15—21no—
37C22×Dic15—21no—
38C22×Dic15—22no—
39C22×Dic15C2×C412yescomplemented
40C22×C5×Dic3—22no—
41C22×C5×Dic3D414yes—
42C22×C3×Dic5—22no—
43#6719—24no—
44#6719—21no—
45#6719C2×C412yescomplemented
46#6712—24no—
47C5×#217—22no—
48C5×#217—22no—
49C5×#217—22no—
50C5×C4⋊Dic3—22no—
51C4×C5×Dic3—22no—
52C3×C22⋊Dic5—22no—
53C3×C22⋊Dic5—22no—
54#5798D511yescharacteristic
55C2×#935—51no—
56C2×C3×#99—51no—
57#4943—52no—
58#4527—52no—
59C22×C5×D4C2×D311yescharacteristic
60C23×Dic5—31no—
61C4×C5×D4—64no—
62C5×#117—61no—
63C2×C5×C22⋊C4—32no—
64C2×C5×C22⋊C4—61no—
65C2×C22⋊Dic5—31no—
66C2×C22⋊Dic5—61no—
67C2×C22⋊Dic5C2×D312yes—
68#4081—34no—
69#4081—62no—
70C2×#683—61no—
71#3966—22no—
72#3963—64no—
73#1890—151noSylow
74C23×C3×C5—21no—
75C23×C3×C5—21no—
76C23×C3×C5—42no—
77C23×C3×C5—42no—
78C23×C3×C5C22⋊C412yes—
79C23×C3×C5C22×C411yescharacteristic
80C23×C3×C5C2×D411yescharacteristic
81C23×C3×C5C2×D412yes—
82C23×C3×C5C2×D411yescharacteristic
83C23×C3×C5#4112yes—
84C3×C5×D4—24no—
85C3×C5×D4—24no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5C22⋊C412yes—
89C2×Dic15—22no—
90C2×Dic15—22no—
91C2×Dic15—24no—
92C2×Dic15—42no—
93C2×Dic15—41no—
94C2×Dic15—42no—
95C2×Dic15—41no—
96C2×C5×Dic3—24no—
97C2×C5×Dic3—44no—
98C2×C5×Dic3—82no—
99C2×C3×Dic5—44no—
100C2×C3×Dic5—42no—
101C22×C3×D4C2×D511yescharacteristic
102C23×Dic3—51no—
103C2×C3×C22⋊C4—52no—
104C2×#217—21no—
105C2×#217—51no—
106C2×#217—101no—
107C2×#217C2×D512yes—
108#935—54no—
109#935—102no—
110D4×Dic3—24no—
111#926—21no—
112C2×Dic3⋊C4—101no—
113C3×#99—102no—
114C3⋊#95—104no—
115C24×C5D1211yescharacteristic
116C24×C5C22×D311yescharacteristic
117C2×C5×D4—22no—
118C2×C5×D4—22no—
119C2×C5×D4C4×D312yes—
120C2×C5×D4#6712yes—
121C22×C4×C5—34no—
122C22×C4×C5—62no—
123C22×C4×C5D1211yescharacteristic
124C22×Dic5—22no—
125C22×Dic5—32no—
126C22×Dic5—61no—
127C22×Dic5—61no—
128C22×Dic5—62no—
129C22×Dic5—62no—
130C22×Dic5—61no—
131C5×C4⋊C4—62no—
132C5×C22⋊C4—62no—
133C5×C22⋊C4—62no—
134C5×C22⋊C4—62no—
135C42×C5—62no—
136C22⋊Dic5—22no—
137C22⋊Dic5—22no—
138C22⋊Dic5—32no—
139C22⋊Dic5—64no—
140C22⋊Dic5—61no—
141#683—64no—
142C2×#123—151no—
143#518—31no—
144C2×#99—51no—
145#381—152no—
146#342—152no—
147C22×C3×C5—24no—
148C22×C3×C5—22no—
149C22×C3×C5—22no—
150C22×C3×C5—41no—
151C22×C3×C5—41no—
152C22×C3×C5—42no—
153C22×C3×C5—42no—
154C22×C3×C5—42no—
155C22×C3×C5—81no—
156C22×C3×C5C2×C22⋊C411yescharacteristic
157C22×C3×C5C4×D412yes—
158C22×C3×C5#12011yescharacteristic
159C22×C3×C5#12112yes—
160C22×C3×C5#12311yescharacteristic
161C3×C4×C5—22no—
162Dic15—42no—
163Dic15—42no—
164C3×Dic5—82no—
165C5×Dic3—44no—
166C24×C3C22⋊D511yescharacteristic
167C24×C3C22×D511yescharacteristic
168C2×C3×D4—22no—
169C2×C3×D4—22no—
170C2×C3×D4C4×D512yes—
171C2×C3×D4D2012yes—
172C22×C3×C4—102no—
173C22×C3×C4C22⋊D511yescharacteristic
174C22×Dic3—22no—
175C22×Dic3—52no—
176C22×Dic3—101no—
177C22×Dic3—102no—
178C22×Dic3—102no—
179C22×Dic3—101no—
180C22×Dic3—101no—
181C22×Dic3C22⋊D514yes—
182C3×C22⋊C4—102no—
183C3×C22⋊C4—102no—
184#217—22no—
185#217—22no—
186#217—22no—
187#217—52no—
188#217—104no—
189#217—101no—
190C4⋊Dic3—22no—
191Dic3⋊C4—104no—
192C4×Dic3—22no—
193C23×C5—21no—
194C23×C5—21no—
195C23×C5—42no—
196C23×C5—42no—
197C23×C5(C2×D3)⋊C412yes—
198C23×C5C2×C4×D311yescharacteristic
199C23×C5C2×D1211yescharacteristic
200C23×C5D3×D412yes—
201C23×C5#23712yes—
202C23×C5C2×#6711yescharacteristic
203C5×D4—24no—
204C5×D4—24no—
205C2×C4×C5—21no—
206C2×C4×C5—21no—
207C2×C4×C5—64no—
208C2×C4×C5—124no—
209C2×C4×C5—242no—
210C2×C4×C5(C2×D3)⋊C412yes—
211C2×Dic5—44no—
212C2×Dic5—42no—
213C2×Dic5—64no—
214C2×Dic5—62no—
215C2×Dic5—62no—
216C2×Dic5—122no—
217C2×Dic5—121no—
218C2×Dic5—121no—
219C2×Dic5—122no—
220C22×D4D3×D511yescharacteristic
221C23×C4—151no—
222#123—154no—
223#123—302no—
224C4×D4—64no—
225#117—61no—
226C2×C4⋊C4—301no—
227C2×C22⋊C4—32no—
228C2×C22⋊C4—52no—
229C2×C22⋊C4—61no—
230C2×C22⋊C4—151no—
231C2×C22⋊C4—301no—
232#99—102no—
233#95—304no—
234C2×C3×C5—22no—
235C2×C3×C5—21no—
236C2×C3×C5—21no—
237C2×C3×C5—22no—
238C2×C3×C5—42no—
239C2×C3×C5#38611yescharacteristic
240C2×C3×C5#45812yes—
241C23×C3—21no—
242C23×C3—21no—
243C23×C3—42no—
244C23×C3—42no—
245C23×C3#68512yes—
246C23×C3C2×C4×D511yescharacteristic
247C23×C3C2×D2011yescharacteristic
248C23×C3#70912yes—
249C23×C3C2×C22⋊D511yescharacteristic
250C23×C3C2×C22⋊D512yes—
251C3×D4—24no—
252C3×D4—24no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—204no—
256C2×C3×C4—202no—
257C2×C3×C4#68512yes—
258C2×Dic3—24no—
259C2×Dic3—44no—
260C2×Dic3—82no—
261C2×Dic3—102no—
262C2×Dic3—102no—
263C2×Dic3—104no—
264C2×Dic3—202no—
265C2×Dic3—201no—
266C2×Dic3—201no—
267C2×Dic3—202no—
268C22×C5—24no—
269C22×C5—22no—
270C22×C5—22no—
271C22×C5—41no—
272C22×C5—42no—
273C22×C5—41no—
274C22×C5—42no—
275C22×C5—42no—
276C22×C5—81no—
277C22×C5#67⋊C412yes—
278C22×C5#88211yescharacteristic
279C22×C5#88611yescharacteristic
280C22×C5C2×(C2×D3)⋊C411yescharacteristic
281C22×C5#93912yes—
282C4×C5—22no—
283C4×C5—124no—
284Dic5—82no—
285Dic5—122no—
286Dic5—122no—
287C24#120311yescharacteristic
288C24C2×D3×D511yescharacteristic
289C2×D4—22no—
290C2×D4—22no—
291C2×D4#120012yes—
292C2×D4#120212yes—
293C22×C4—34no—
294C22×C4—62no—
295C22×C4—102no—
296C22×C4—152no—
297C22×C4—302no—
298C22×C4—301no—
299C22×C4—301no—
300C22×C4—301no—
301C22×C4—302no—
302C22×C4#120311yescharacteristic
303C4⋊C4—62no—
304C4⋊C4—304no—
305C22⋊C4—62no—
306C22⋊C4—62no—
307C22⋊C4—62no—
308C22⋊C4—102no—
309C22⋊C4—102no—
310C22⋊C4—152no—
311C22⋊C4—304no—
312C22⋊C4—301no—
313C42—62no—
314C3×C5#189011yescharacteristic, complemented, Hall
315C22×C3—24no—
316C22×C3—22no—
317C22×C3—22no—
318C22×C3—41no—
319C22×C3—41no—
320C22×C3—42no—
321C22×C3—42no—
322C22×C3—42no—
323C22×C3—81no—
324C22×C3C2×#68511yescharacteristic
325C22×C3C4×C22⋊D512yes—
326C22×C3#407511yescharacteristic
327C22×C3#407612yes—
328C22×C3#409911yescharacteristic
329C3×C4—22no—
330C3×C4—402no—
331Dic3—44no—
332Dic3—202no—
333Dic3—202no—
334C2×C5—22no—
335C2×C5—21no—
336C2×C5—21no—
337C2×C5—22no—
338C2×C5—42no—
339C2×C5#474212yes—
340C2×C5#495811yescharacteristic
341C23—21no—
342C23—21no—
343C23—42no—
344C23—42no—
345C23#666712yes—
346C23#677912yes—
347C23C2×#120011yescharacteristic
348C23C2×#120211yescharacteristic
349C23C2×#120311yescharacteristic
350C23D3×C22⋊D512yes—
351D4—24no—
352D4—24no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—64no—
356C2×C4—124no—
357C2×C4—204no—
358C2×C4—202no—
359C2×C4—242no—
360C2×C4—302no—
361C2×C4—302no—
362C2×C4—304no—
363C2×C4—602no—
364C2×C4—601no—
365C2×C4—602no—
366C2×C4—601no—
367C2×C4#666712yes—
368C2×C3—21no—
369C2×C3—22no—
370C2×C3—21no—
371C2×C3—22no—
372C2×C3—42no—
373C2×C3#6550211yescharacteristic
374C2×C3#6553212yes—
375C5#7002311yescharacteristic, complemented, Sylow
376C22—24no—
377C22—22no—
378C22—22no—
379C22—42no—
380C22—41no—
381C22—41no—
382C22—42no—
383C22—42no—
384C22—81no—
385C22C2×#666711yescharacteristic
386C22#9154211yescharacteristic
387C22#9155612yes—
388C22#9156912yes—
389C22#9157011yescharacteristic
390C4—22no—
391C4—124no—
392C4—402no—
393C4—602no—
394C4—602no—
395C3#1060244811yescharacteristic, complemented, Sylow
396C2—22no—
397C2—21no—
398C2—21no—
399C2—22no—
400C2—42no—
401C2#1174918412yes—
402C2#1174949811yescharacteristic
subgroupG/H
centerC22#91570
commutatorC23×C3×C5C22×C4
FrattiniC24C2×D3×D5
Fitting, prime radicalC22×C3×C5×D4C22
socleC22×C3×C5#120
cosocleC24×C3×C5C23
hypercenterC22×D4D3×D5
hypocenterC3×C5#1890
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #11749473C2semidirect
5. #11746018C2semidirect
12. #91824C4semidirect
39. C22×Dic15C2×C4semidirect
45. #6719C2×C4semidirect
314. C3×C5#1890semidirect
375. C5#70023semidirect
395. C3#10602448semidirect

Maximal subgroups

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

subgroupindex
C2×#918242
C5×#57982
C2×C3×#39662
#117494732
#117460182
#106024483
#700235