Finite Group Databasebeta

← #14513706

Subgroups — #14513706

Order 1920.

622 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91948C212yesmaximal
2C5×A4×C4⋊C4C211yesmaximal, characteristic
3C4⋊(A4⋊Dic5)C211yesmaximal, characteristic
4#11752130C212yesmaximal
5C4×A4⋊Dic5C211yesmaximal, characteristic
6#10613902—31nomaximal, Hall
7C2×C4×C5×A4C2212yes—
8C2×C4×C5×A4C2211yescharacteristic
9C2×A4⋊Dic5C2212yes—
10C2×A4⋊Dic5C2211yescharacteristic
11C2×A4⋊Dic5C2211yescharacteristic
12#91948—24no—
13#91777—41nomaximal
14#85303—51nomaximal, Hall
15C22×C5×C4⋊C4D311yescharacteristic
16C2×#4070—32no—
17C2×#4034—31no—
18#65501—31no—
19#65499—32no—
20C4×C22⋊Dic5—31no—
21#65274—31no—
22#65273—32no—
23#65268—32no—
24#65265—31no—
25#65262—31no—
26C22×C5×A4C2311yescharacteristic
27C2×Dic30—42no—
28C4×C5×A4—22no—
29C4×C5×A4Q812yescomplemented
30A4⋊Dic5—22no—
31A4⋊Dic5D412yes—
32A4⋊Dic5Q812yescomplemented
33C3×C5×C4⋊C4—41no—
34C4⋊Dic15—41no—
35#6712—42no—
36C4×Dic15—41no—
37C2×A4⋊Q8—52no—
38A4×C4⋊C4D511yescharacteristic
39C4⋊SL(2,ℤ/4)—51no—
40SL(2,ℤ/4)⋊C4—52no—
41C4×SL(2,ℤ/4)—51no—
42C23×C4×C5C2×D312yes—
43C23×C4×C5C2×D311yescharacteristic
44C22×Dic10—32no—
45C2×C5×C4⋊C4—31no—
46C2×C5×C4⋊C4—31no—
47C2×C5×C4⋊C4—32no—
48C2×C22⋊Dic5—31no—
49C2×C22⋊Dic5—31no—
50C2×C22⋊Dic5—32no—
51C2×C4⋊Dic5—31no—
52C2×C4⋊Dic5—32no—
53C2×C4⋊Dic5—31no—
54#4070—64no—
55#4070—64no—
56C2×#683—32no—
57C2×#683—32no—
58C2×#683—32no—
59C2×#683—32no—
60C2×C4×Dic5—31no—
61C2×C4×Dic5—31no—
62#4034—62no—
63#4034—61no—
64#4034—61no—
65#3963—31no—
66#3963—31no—
67#3963—32no—
68#3963—32no—
69#3963—32no—
70#2440—151noSylow
71C2×C5×A4C2×D411yescharacteristic
72C2×C5×A4C2×Q811yescharacteristic
73C2×C5×A4C2×Q811yescharacteristic
74C2×C3×C4×C5—41no—
75C2×C3×C4×C5—42no—
76C2×Dic15—41no—
77C2×Dic15—41no—
78C2×Dic15—42no—
79Dic30—84no—
80C2×C4×A4C2×D512yes—
81C2×C4×A4C2×D511yescharacteristic
82C2×SL(2,ℤ/4)—51no—
83C2×SL(2,ℤ/4)—51no—
84C2×SL(2,ℤ/4)—52no—
85A4⋊Q8—104no—
86#888—201no—
87C24×C5C22×D311yescharacteristic
88C22×C4×C5—22no—
89C22×C4×C5—31no—
90C22×C4×C5—31no—
91C22×C4×C5—32no—
92C22×C4×C5—32no—
93C22×C4×C5—32no—
94C22×C4×C5—62no—
95C22×C4×C5Dic612yescomplemented
96C22×Dic5—31no—
97C22×Dic5—31no—
98C22×Dic5—31no—
99C22×Dic5—31no—
100C22×Dic5—32no—
101C22×Dic5—32no—
102C2×Dic10—64no—
103C2×Dic10—62no—
104C2×Dic10—62no—
105C2×Dic10—122no—
106C5×C4⋊C4—32no—
107C5×C4⋊C4—31no—
108C5×C4⋊C4—61no—
109C5×C4⋊C4S411yescharacteristic
110C22⋊Dic5—32no—
111C22⋊Dic5—32no—
112C22⋊Dic5—32no—
113C22⋊Dic5—32no—
114C22⋊Dic5—62no—
115C22⋊Dic5—62no—
116C4⋊Dic5—64no—
117C4⋊Dic5—61no—
118C4⋊Dic5—62no—
119C4⋊Dic5—61no—
120#683—64no—
121#683—64no—
122#683—62no—
123#683—62no—
124#683—122no—
125C4×Dic5—61no—
126C4×Dic5—62no—
127C4×Dic5—61no—
128C2×C4⋊Q8—151no—
129C2×C22⋊Q8—152no—
130C22×C4⋊C4D1511yescharacteristic
131#398—152no—
132#395—152no—
133#389—151no—
134#389—151no—
135#385—152no—
136#384—151no—
137#380—151no—
138C4×C22⋊C4—151no—
139C22×C3×C5—41no—
140C5×A4C4⋊Q811yescharacteristic, complemented
141C3×C4×C5—42no—
142C3×C4×C5—82no—
143Dic15—42no—
144Dic15—42no—
145Dic15—82no—
146C22×A4C22×D511yescharacteristic
147C2×Dic6—202no—
148C4×A4—22no—
149C4×A4Dic1012yescomplemented
150SL(2,ℤ/4)—52no—
151SL(2,ℤ/4)—52no—
152SL(2,ℤ/4)—102no—
153C3×C4⋊C4—41no—
154C4⋊Dic3—201no—
155Dic3⋊C4—202no—
156C4×Dic3—201no—
157C23×C5—31no—
158C23×C5—31no—
159C23×C5—31no—
160C23×C5—31no—
161C23×C5C2×Dic611yescharacteristic
162C23×C5D3×D411yescharacteristic
163C23×C5D3×Q811yescharacteristic
164C2×C4×C5—31no—
165C2×C4×C5—32no—
166C2×C4×C5—32no—
167C2×C4×C5—32no—
168C2×C4×C5—32no—
169C2×C4×C5—62no—
170C2×C4×C5—62no—
171C2×C4×C5—61no—
172C2×C4×C5—62no—
173C2×C4×C5—62no—
174C2×C4×C5C2×S412yes—
175C2×C4×C5C2×S411yescharacteristic
176C2×Dic5—32no—
177C2×Dic5—32no—
178C2×Dic5—32no—
179C2×Dic5—32no—
180C2×Dic5—61no—
181C2×Dic5—61no—
182C2×Dic5—61no—
183C2×Dic5—61no—
184C2×Dic5—61no—
185C2×Dic5—61no—
186C2×Dic5—61no—
187C2×Dic5—61no—
188C2×Dic5—62no—
189C2×Dic5—62no—
190C2×Dic5—62no—
191C2×Dic5—62no—
192C2×Dic5—62no—
193C2×Dic5—62no—
194Dic10—124no—
195Dic10—124no—
196C22×Q8—152no—
197C23×C4C2×D1512yes—
198C23×C4C2×D1511yescharacteristic
199C4⋊Q8—302no—
200C4⋊Q8—301no—
201C4⋊Q8—301no—
202C22⋊Q8—304no—
203C22⋊Q8—304no—
204C2×C4⋊C4—31no—
205C2×C4⋊C4—31no—
206C2×C4⋊C4—32no—
207C2×C4⋊C4—152no—
208C2×C4⋊C4—152no—
209C2×C4⋊C4—152no—
210C2×C4⋊C4—151no—
211C2×C4⋊C4—152no—
212C2×C4⋊C4—151no—
213C2×C4⋊C4—152no—
214C2×C22⋊C4—151no—
215C2×C22⋊C4—151no—
216C2×C22⋊C4—152no—
217C2×C42—151no—
218C2×C42—151no—
219#95—151no—
220#95—151no—
221#95—152no—
222#95—152no—
223#95—152no—
224C2×C3×C5—41no—
225C2×C3×C5—41no—
226C2×C3×C5—41no—
227C2×A4C2×Dic1011yescharacteristic
228C2×A4D4×D511yescharacteristic
229C2×A4Q8×D511yescharacteristic
230C2×C3×C4—41no—
231C2×C3×C4—42no—
232C2×Dic3—201no—
233C2×Dic3—201no—
234C2×Dic3—202no—
235Dic6—404no—
236C22×C5—31no—
237C22×C5—31no—
238C22×C5—31no—
239C22×C5—31no—
240C22×C5—31no—
241C22×C5—31no—
242C22×C5—31no—
243C22×C5—31no—
244C22×C5—31no—
245C22×C5—61no—
246C22×C5#88811yescharacteristic, complemented
247C22×C5C22×S411yescharacteristic
248C4×C5—22no—
249C4×C5—32no—
250C4×C5—62no—
251C4×C5A4⋊Q812yescomplemented
252Dic5—62no—
253Dic5—62no—
254Dic5—62no—
255Dic5—62no—
256Dic5—122no—
257Dic5—122no—
258C24C22×D1511yescharacteristic
259C2×Q8—302no—
260C2×Q8—304no—
261C2×Q8—302no—
262C2×Q8—602no—
263C22×C4—22no—
264C22×C4—31no—
265C22×C4—31no—
266C22×C4—32no—
267C22×C4—32no—
268C22×C4—32no—
269C22×C4—62no—
270C22×C4—151no—
271C22×C4—151no—
272C22×C4—151no—
273C22×C4—151no—
274C22×C4—152no—
275C22×C4—152no—
276C22×C4Dic3012yescomplemented
277C4⋊C4—32no—
278C4⋊C4—31no—
279C4⋊C4—61no—
280C4⋊C4—302no—
281C4⋊C4—301no—
282C4⋊C4—302no—
283C4⋊C4—304no—
284C4⋊C4—304no—
285C4⋊C4—304no—
286C4⋊C4—302no—
287C4⋊C4—301no—
288C4⋊C4—602no—
289C4⋊C4C5⋊S411yescharacteristic
290C22⋊C4—152no—
291C22⋊C4—152no—
292C22⋊C4—152no—
293C22⋊C4—152no—
294C22⋊C4—302no—
295C22⋊C4—302no—
296C42—301no—
297C42—302no—
298C42—301no—
299C3×C5—41noHall
300C22×C3—41no—
301A4#403411yescharacteristic, complemented
302C3×C4—42no—
303C3×C4—82no—
304Dic3—202no—
305Dic3—202no—
306Dic3—402no—
307C2×C5—31no—
308C2×C5—31no—
309C2×C5—31no—
310C2×C5—31no—
311C2×C5C2×A4⋊Q811yescharacteristic
312C2×C5D4×S411yescharacteristic
313C2×C5Q8×S411yescharacteristic
314C23—31no—
315C23—31no—
316C23—31no—
317C23—31no—
318C23C2×Dic3011yescharacteristic
319C23D4×D1511yescharacteristic
320C23Q8×D1511yescharacteristic
321Q8—604no—
322Q8—604no—
323C2×C4—31no—
324C2×C4—32no—
325C2×C4—32no—
326C2×C4—32no—
327C2×C4—32no—
328C2×C4—62no—
329C2×C4—62no—
330C2×C4—61no—
331C2×C4—62no—
332C2×C4—62no—
333C2×C4—152no—
334C2×C4—152no—
335C2×C4—152no—
336C2×C4—152no—
337C2×C4—301no—
338C2×C4—301no—
339C2×C4—301no—
340C2×C4—301no—
341C2×C4—301no—
342C2×C4—301no—
343C2×C4—301no—
344C2×C4—301no—
345C2×C4—302no—
346C2×C4—302no—
347C2×C4—302no—
348C2×C4—302no—
349C2×C4—302no—
350C2×C4—302no—
351C2×C4C2×C5⋊S412yes—
352C2×C4C2×C5⋊S411yescharacteristic
353C2×C3—41no—
354C2×C3—41no—
355C2×C3—41no—
356C5#8530311yescharacteristic, complemented, Sylow
357C22—31no—
358C22—31no—
359C22—31no—
360C22—31no—
361C22—31no—
362C22—31no—
363C22—31no—
364C22—31no—
365C22—31no—
366C22—61no—
367C22#9177711yescharacteristic, complemented
368C22C22×C5⋊S411yescharacteristic
369C4—22no—
370C4—32no—
371C4—62no—
372C4—302no—
373C4—302no—
374C4—302no—
375C4—302no—
376C4—602no—
377C4—602no—
378C4#9194812yescomplemented
379C3—41noSylow
380C2—31no—
381C2—31no—
382C2—31no—
383C2—31no—
384C2C2×#9194811yescharacteristic
385C2D4×C5⋊S411yescharacteristic
386C2Q8×C5⋊S411yescharacteristic
subgroupG/H
center, FrattiniC22C22×C5⋊S4
commutator, prime radical, cosocleC22×C5×A4C23
FittingC22×C5×C4⋊C4D3
socleC24×C5C22×D3
hypercenterC4⋊C4C5⋊S4
hypocenterC5×A4C4⋊Q8
LCSG ▷ C22×C5×A4 ▷ C5×A4
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
29. C4×C5×A4Q8semidirect
32. A4⋊Dic5Q8semidirect
95. C22×C4×C5Dic6semidirect
140. C5×A4C4⋊Q8semidirect
149. C4×A4Dic10semidirect
246. C22×C5#888semidirect
251. C4×C5A4⋊Q8semidirect
276. C22×C4Dic30semidirect
301. A4#4034semidirect
356. C5#85303semidirect
367. C22#91777semidirect
378. C4#91948semidirect

Maximal subgroups

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

subgroupindex
C2×#919482
C5×A4×C4⋊C42
C4⋊(A4⋊Dic5)2
#117521302
C4×A4⋊Dic52
#106139023
#917774
#853035