Finite Group Databasebeta

← #14320081

Subgroups — #14320081

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C42×D5C211yesmaximal, characteristic
2C4×C4⋊Dic15C211yesmaximal, characteristic, complemented
3C4×C5×C4⋊Dic3C211yesmaximal, characteristic, complemented
4#11748759C212yesmaximal
5#11748737C212yesmaximal
6C4×#6665C212yesmaximal
7#11748613C212yesmaximal, complemented
8#11748612C212yesmaximal, complemented
9#11748611C212yesmaximal, complemented
10#10605483—31nomaximal, Hall
11C22×C3×C4×D5C2211yescharacteristic
12C22×C3×C4×D5C2211yescharacteristic
13C22×C3×C4×D5C2211yescharacteristic
14C2×C3×C42×C5C2211yescharacteristic
15C2×C4⋊Dic15C2212yes—
16C2×C4×Dic15C2212yes—
17C2×C5×C4⋊Dic3C2212yes—
18C2×C4×C5×Dic3C2212yes—
19C2×C3×C4×Dic5C2211yescharacteristic
20C2×C3×C4×Dic5C2211yescharacteristic
21C2×C3×C4×Dic5C2211yescharacteristic
22C3×C42×D5C418yescomplemented
23C2×#6665C2214yes—
24#91115C2212yes—
25C5×C3⋊#95C2212yes—
26#90994C2214yes—
27#90994C2214yes—
28#90994C2214yes—
29#82060—51nomaximal, Hall
30C2×C42×D5D311yescharacteristic
31C4×C5×C4⋊C4—31no—
32#65276—32no—
33#65266—32no—
34C4×#685—32no—
35C4×C4⋊Dic5—31no—
36#65221—32no—
37#64953—32no—
38#64940—32no—
39C23×C3×D5C2311yescharacteristic
40C22×C3×C4×C5C2311yescharacteristic
41C22×C3×C4×C5C2311yescharacteristic
42C22×C3×C4×C5C2311yescharacteristic
43C22×Dic15C2314yes—
44C22×C5×Dic3C2314yes—
45C22×C3×Dic5C2311yescharacteristic
46C22×C3×Dic5C2311yescharacteristic
47C22×C3×Dic5C2311yescharacteristic
48C2×C3×C4×D5—24no—
49C2×C3×C4×D5—24no—
50C2×C3×C4×D5—22no—
51C2×C3×C4×D5—22no—
52C2×C3×C4×D5C2×C414yes—
53C2×C3×C4×D5C2×C414yes—
54C2×C3×C4×D5C2×C414yes—
55C3×C42×C5C2×C414yes—
56C4⋊Dic15—24no—
57C4×Dic15—24no—
58C5×C4⋊Dic3—24no—
59C4×C5×Dic3—24no—
60C3×C4×Dic5C2×C414yes—
61C3×C4×Dic5C2×C414yes—
62C3×C4×Dic5C2×C414yes—
63#6665—28no—
64C22×C3×C42—51no—
65#5212—52no—
66#5211—52no—
67C4×#217—52no—
68#4937—52no—
69#4936—52no—
70C4×C4⋊Dic3—51no—
71C4×C4⋊Dic3D511yescharacteristic, complemented
72#4932—52no—
73C22×C4×D5C2×D311yescharacteristic
74C22×C4×D5C2×D311yescharacteristic
75C22×C4×D5C2×D311yescharacteristic
76C2×C5×C4⋊C4—32no—
77C2×C42×C5—32no—
78C2×C42×C5C2×D311yescharacteristic
79C2×#685—34no—
80C2×C4⋊Dic5—32no—
81C2×C4×Dic5—32no—
82C2×C4×Dic5C2×D311yescharacteristic
83C2×C4×Dic5C2×D311yescharacteristic
84C2×C4×Dic5C2×D311yescharacteristic
85C42×D5Dic318yescomplemented
86C5×#95—32no—
87#3963—32no—
88#3963—34no—
89#3963—34no—
90#3963—34no—
91#2283—151noSylow
92C23×C3×C5C2411yescharacteristic
93C22×C3×D5—22no—
94C22×C3×D5—21no—
95C22×C3×D5—21no—
96C22×C3×D5C22×C412yes—
97C22×C3×D5#4114yes—
98C2×C3×C4×C5—22no—
99C2×C3×C4×C5C22×C412yes—
100C2×C3×C4×C5C22×C412yes—
101C2×C3×C4×C5C22×C412yes—
102C2×C3×C4×C5#4114yes—
103C2×C3×C4×C5#4112yes—
104C2×C3×C4×C5#4112yes—
105C2×Dic15—24no—
106C2×Dic15—24no—
107C2×Dic15—24no—
108C2×C5×Dic3—24no—
109C2×C5×Dic3—24no—
110C2×C5×Dic3—24no—
111C2×C3×Dic5—22no—
112C2×C3×Dic5—21no—
113C2×C3×Dic5—21no—
114C2×C3×Dic5—22no—
115C2×C3×Dic5C22×C412yes—
116C2×C3×Dic5C22×C412yes—
117C2×C3×Dic5C22×C412yes—
118C3×C4×D5—28no—
119C3×C4×D5—28no—
120C3×C4×D5—28no—
121C23×C3×C4—51no—
122C23×C3×C4—51no—
123C23×C3×C4—51no—
124C2×C3×C42—51no—
125C2×C3×C42—51no—
126C2×C3×C42—51no—
127C2×C3×C42—58no—
128C2×C3×C42C2×D511yescharacteristic
129C2×#217—54no—
130C2×C4⋊Dic3—52no—
131C2×C4⋊Dic3C2×D512yes—
132C2×C4×Dic3—52no—
133C2×C4×Dic3C2×D512yes—
134C3⋊#95—52no—
135C3⋊#95—54no—
136C3⋊#95—54no—
137C3⋊#95—54no—
138C3⋊#95C2×D512yes—
139C23×D5C22×D311yescharacteristic
140C22×C4×C5—34no—
141C22×C4×C5C22×D311yescharacteristic
142C22×C4×C5C22×D311yescharacteristic
143C22×C4×C5C22×D311yescharacteristic
144C22×Dic5—34no—
145C22×Dic5C22×D311yescharacteristic
146C22×Dic5C22×D311yescharacteristic
147C22×Dic5C22×D311yescharacteristic
148C2×C4×D5—24no—
149C2×C4×D5—24no—
150C2×C4×D5—22no—
151C2×C4×D5—22no—
152C2×C4×D5C2×Dic314yes—
153C2×C4×D5C2×Dic314yes—
154C2×C4×D5C2×Dic314yes—
155C5×C4⋊C4—64no—
156C42×C5—64no—
157C42×C5C2×Dic314yes—
158#685—68no—
159C4⋊Dic5—64no—
160C4×Dic5—64no—
161C4×Dic5C2×Dic314yes—
162C4×Dic5C2×Dic314yes—
163C4×Dic5C2×Dic314yes—
164C22×C42—51no—
165#383—152no—
166#382—152no—
167#381—152no—
168#380—152no—
169C4×C4⋊C4—31no—
170C4×C4⋊C4—151no—
171C4×C22⋊C4—152no—
172#376—152no—
173C22×C3×C5C23×C411yescharacteristic
174C22×C3×C5C2×#4112yes—
175C22×C3×C5C2×#4111yescharacteristic
176C22×C3×C5C2×#4111yescharacteristic
177C22×C3×C5C2×#4112yes—
178C2×C3×D5—22no—
179C2×C3×D5—22no—
180C2×C3×D5—24no—
181C2×C3×D5—24no—
182C2×C3×D5#11714yes—
183C3×C4×C5—22no—
184C3×C4×C5#11714yes—
185C3×C4×C5#11714yes—
186Dic15—44no—
187C3×Dic5—22no—
188C3×Dic5—22no—
189C3×Dic5—22no—
190C5×Dic3—44no—
191C24×C3—51no—
192C22×C3×C4—51no—
193C22×C3×C4—51no—
194C22×C3×C4—51no—
195C22×C3×C4—54no—
196C22×C3×C4—54no—
197C22×C3×C4—54no—
198C22×C3×C4—104no—
199C22×C3×C4—104no—
200C22×C3×C4—102no—
201C22×C3×C4—102no—
202C22×C3×C4C22×D511yescharacteristic
203C22×C3×C4C22×D511yescharacteristic
204C22×C3×C4C22×D511yescharacteristic
205C22×Dic3—54no—
206C22×Dic3C22×D514yes—
207C3×C42—54no—
208C3×C42—54no—
209C3×C42—54no—
210C3×C42C4×D514yes—
211#217—108no—
212C4⋊Dic3—24no—
213C4⋊Dic3—104no—
214C4×Dic3—24no—
215C4×Dic3—104no—
216C23×C5C23×D311yescharacteristic
217C22×D5—22no—
218C22×D5—21no—
219C22×D5—21no—
220C22×D5#23514yes—
221C22×D5C22×Dic312yes—
222C2×C4×C5—22no—
223C2×C4×C5—64no—
224C2×C4×C5—64no—
225C2×C4×C5—64no—
226C2×C4×C5#23514yes—
227C2×C4×C5#23512yes—
228C2×C4×C5#23512yes—
229C2×C4×C5C22×Dic312yes—
230C2×C4×C5C22×Dic312yes—
231C2×C4×C5C22×Dic312yes—
232C2×Dic5—22no—
233C2×Dic5—21no—
234C2×Dic5—21no—
235C2×Dic5—22no—
236C2×Dic5—64no—
237C2×Dic5—64no—
238C2×Dic5—64no—
239C2×Dic5C22×Dic312yes—
240C2×Dic5C22×Dic312yes—
241C2×Dic5C22×Dic312yes—
242C4×D5—28no—
243C4×D5—28no—
244C4×D5—28no—
245C23×C4—51no—
246C23×C4—51no—
247C23×C4—51no—
248C2×C4⋊C4—32no—
249C2×C4⋊C4—152no—
250C2×C22⋊C4—154no—
251C2×C42—32no—
252C2×C42—51no—
253C2×C42—51no—
254C2×C42—51no—
255C2×C42—58no—
256C2×C42—152no—
257C2×C42D3×D511yescharacteristic
258#95—32no—
259#95—154no—
260#95—154no—
261#95—154no—
262#95—152no—
263C2×C3×C5C2×#11711yescharacteristic
264C2×C3×C5C2×#11711yescharacteristic
265C2×C3×C5C2×#11711yescharacteristic
266C2×C3×C5#52912yes—
267C2×C3×C5#52912yes—
268C3×D5—24no—
269C23×C3—52no—
270C23×C3—54no—
271C23×C3—102no—
272C23×C3—101no—
273C23×C3—101no—
274C23×C3C23×D511yescharacteristic
275C2×C3×C4—22no—
276C2×C3×C4—52no—
277C2×C3×C4—52no—
278C2×C3×C4—52no—
279C2×C3×C4—108no—
280C2×C3×C4—102no—
281C2×C3×C4—101no—
282C2×C3×C4—101no—
283C2×C3×C4—102no—
284C2×C3×C4—108no—
285C2×C3×C4—108no—
286C2×C3×C4C2×C4×D512yes—
287C2×C3×C4C2×C4×D512yes—
288C2×C3×C4C2×C4×D512yes—
289C2×C3×C4#70914yes—
290C2×C3×C4#71112yes—
291C2×C3×C4#71312yes—
292C2×Dic3—24no—
293C2×Dic3—24no—
294C2×Dic3—24no—
295C2×Dic3—104no—
296C2×Dic3—104no—
297C2×Dic3—104no—
298C22×C5C2×#23512yes—
299C22×C5C2×#23511yescharacteristic
300C22×C5C2×#23511yescharacteristic
301C22×C5C2×#23512yes—
302C22×C5C23×Dic311yescharacteristic
303C2×D5—24no—
304C2×D5—24no—
305C2×D5—22no—
306C2×D5—22no—
307C2×D5#92614yes—
308C4×C5—22no—
309C4×C5—124no—
310C4×C5#92614yes—
311C4×C5#92614yes—
312Dic5—22no—
313Dic5—22no—
314Dic5—22no—
315Dic5—124no—
316C24—51no—
317C22×C4—34no—
318C22×C4—51no—
319C22×C4—51no—
320C22×C4—51no—
321C22×C4—54no—
322C22×C4—54no—
323C22×C4—54no—
324C22×C4—104no—
325C22×C4—104no—
326C22×C4—102no—
327C22×C4—102no—
328C22×C4—154no—
329C22×C4C2×D3×D511yescharacteristic
330C22×C4C2×D3×D511yescharacteristic
331C22×C4C2×D3×D511yescharacteristic
332C4⋊C4—64no—
333C4⋊C4—304no—
334C22⋊C4—308no—
335C42—54no—
336C42—54no—
337C42—54no—
338C42—64no—
339C42—304no—
340C42D5×Dic314yes—
341C3×C5#228311yescharacteristic, complemented, Hall
342C22×C3—54no—
343C22×C3—102no—
344C22×C3—102no—
345C22×C3—104no—
346C22×C3—104no—
347C22×C3C22×C4×D511yescharacteristic
348C22×C3C2×#70912yes—
349C22×C3C2×#71111yescharacteristic
350C22×C3C2×#71311yescharacteristic
351C22×C3D5×#4112yes—
352C3×C4—22no—
353C3×C4—102no—
354C3×C4—102no—
355C3×C4—102no—
356C3×C4#401814yes—
357C3×C4#403814yes—
358Dic3—44no—
359Dic3—204no—
360C2×C5#547912yes—
361C2×C5#547912yes—
362C2×C5C2×#92611yescharacteristic
363C2×C5C2×#92611yescharacteristic
364C2×C5C2×#92611yescharacteristic
365D5—24no—
366C23—54no—
367C23—52no—
368C23—102no—
369C23—101no—
370C23—101no—
371C23C22×D3×D511yescharacteristic
372C2×C4—22no—
373C2×C4—52no—
374C2×C4—52no—
375C2×C4—52no—
376C2×C4—64no—
377C2×C4—64no—
378C2×C4—64no—
379C2×C4—108no—
380C2×C4—102no—
381C2×C4—101no—
382C2×C4—101no—
383C2×C4—102no—
384C2×C4—108no—
385C2×C4—108no—
386C2×C4—304no—
387C2×C4—304no—
388C2×C4—304no—
389C2×C4#677114yes—
390C2×C4#677212yes—
391C2×C4#677312yes—
392C2×C4C2×D5×Dic312yes—
393C2×C4C2×D5×Dic312yes—
394C2×C4C2×D5×Dic312yes—
395C2×C3—104no—
396C2×C3C2×#401811yescharacteristic
397C2×C3C2×#403811yescharacteristic
398C2×C3D5×#11711yescharacteristic
399C2×C3#6589112yes—
400C2×C3#6591412yes—
401C5#8206011yescharacteristic, complemented, Sylow
402C22—54no—
403C22—104no—
404C22—104no—
405C22—102no—
406C22—102no—
407C22C2×#677112yes—
408C22C2×#677211yescharacteristic
409C22C2×#677311yescharacteristic
410C22D5×#23512yes—
411C22C22×D5×Dic311yescharacteristic
412C4—22no—
413C4—102no—
414C4—102no—
415C4—102no—
416C4—124no—
417C4—604no—
418C4#9135714yes—
419C4#9135814yes—
420C3#1060548311yescharacteristic, complemented, Sylow
421C2—104no—
422C2#1175249412yes—
423C2#1175268212yes—
424C2C2×#9135711yescharacteristic
425C2C2×#9135811yescharacteristic
426C2D5×#92611yescharacteristic
subgroupG/H
centerC22×C4C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C3×D5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#2283
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C4×C4⋊Dic15C2semidirect
3. C4×C5×C4⋊Dic3C2semidirect
7. #11748613C2semidirect
8. #11748612C2semidirect
9. #11748611C2semidirect
22. C3×C42×D5C4semidirect
71. C4×C4⋊Dic3D5semidirect
85. C42×D5Dic3semidirect
341. C3×C5#2283semidirect
401. C5#82060semidirect
420. C3#10605483semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C42×D52
C4×C4⋊Dic152
C4×C5×C4⋊Dic32
#117487592
#117487372
C4×#66652
#117486132
#117486122
#117486112
#106054833
#820605