Finite Group Databasebeta

← #14513704

Subgroups — #14513704

Order 1920.

638 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 638 conjugacy classes of subgroups — too many to draw. Only its 87 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×#91948C211yesmaximal, characteristic
2C5×A4×C4⋊C4C211yesmaximal, characteristic
3#11752130C212yesmaximal
4C4×A4⋊Dic5C211yesmaximal, characteristic
5C4×A4⋊Dic5C212yesmaximal
6#10613893—31nomaximal, Hall
7C2×C4×C5×A4C2212yes—
8C2×C4×C5×A4C2211yescharacteristic
9C2×A4⋊Dic5C2211yescharacteristic
10C2×A4⋊Dic5C2212yes—
11C2×A4⋊Dic5C2211yescharacteristic
12#91948C414yescomplemented
13#91776—41nomaximal
14#85302—51nomaximal, Hall
15C22×C5×C4⋊C4D311yescharacteristic
16C2×#4070—31no—
17C2×#4033—31no—
18#65499—32no—
19C4×C22⋊Dic5—32no—
20C4×C22⋊Dic5—31no—
21#65267—32no—
22C4⋊C4×Dic5—31no—
23#65263—31no—
24#65262—31no—
25#65261—32no—
26C22×C5×A4C2311yescharacteristic
27C2×Dic30—41no—
28C4×C5×A4—22no—
29C4×C5×A4C2×C412yes—
30A4⋊Dic5—21no—
31A4⋊Dic5C2×C414yes—
32A4⋊Dic5Q812yescomplemented
33C3×C5×C4⋊C4—41no—
34#6712—42no—
35C4×Dic15—42no—
36C4×Dic15—41no—
37C2×A4⋊Q8—51no—
38A4×C4⋊C4D511yescharacteristic
39SL(2,ℤ/4)⋊C4—52no—
40C4×SL(2,ℤ/4)—52no—
41C4×SL(2,ℤ/4)—51no—
42C23×C4×C5C2×D312yes—
43C23×C4×C5C2×D311yescharacteristic
44C22×Dic10—31no—
45C2×C5×C4⋊C4—31no—
46C2×C5×C4⋊C4—32no—
47C2×C5×C4⋊C4—31no—
48C2×C22⋊Dic5—32no—
49C2×C22⋊Dic5—31no—
50C2×C22⋊Dic5—31no—
51C2×C4⋊Dic5—31no—
52#4070—34no—
53#4070—34no—
54C2×#683—32no—
55C2×#683—32no—
56C2×#683—32no—
57C2×C4×Dic5—31no—
58C2×C4×Dic5—32no—
59C2×C4×Dic5—31no—
60C2×C4×Dic5—32no—
61#4033—61no—
62#4033—62no—
63#4033—61no—
64#3963—31no—
65#3963—32no—
66#3963—32no—
67#3963—31no—
68#3963—32no—
69#3963—32no—
70#2360—151noSylow
71C2×C5×A4C22×C411yescharacteristic
72C2×C5×A4C2×Q811yescharacteristic
73C2×C5×A4#4111yescharacteristic
74C2×C3×C4×C5—41no—
75C2×C3×C4×C5—42no—
76C2×Dic15—41no—
77C2×Dic15—42no—
78C2×Dic15—41no—
79Dic30—44no—
80C2×C4×A4C2×D512yes—
81C2×C4×A4C2×D511yescharacteristic
82C2×SL(2,ℤ/4)—52no—
83C2×SL(2,ℤ/4)—51no—
84C2×SL(2,ℤ/4)—51no—
85A4⋊Q8—54no—
86#887—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×C5C4×D312yes—
96C22×Dic5—32no—
97C22×Dic5—31no—
98C22×Dic5—31no—
99C22×Dic5—32no—
100C22×Dic5—31no—
101C22×Dic5—31no—
102C2×Dic10—34no—
103C2×Dic10—62no—
104C2×Dic10—61no—
105C2×Dic10—61no—
106C5×C4⋊C4—32no—
107C5×C4⋊C4—31no—
108C5×C4⋊C4—61no—
109C5×C4⋊C4S411yescharacteristic
110C22⋊Dic5—32no—
111C22⋊Dic5—34no—
112C22⋊Dic5—34no—
113C22⋊Dic5—32no—
114C22⋊Dic5—61no—
115C22⋊Dic5—61no—
116C4⋊Dic5—34no—
117#683—38no—
118#683—62no—
119#683—62no—
120#683—122no—
121C4×Dic5—62no—
122C4×Dic5—61no—
123C4×Dic5—62no—
124C4×Dic5—62no—
125C4×Dic5—61no—
126C4×Dic5—122no—
127C2×C22⋊Q8—151no—
128C2×C4×Q8—151no—
129C22×C4⋊C4D1511yescharacteristic
130#391—151no—
131#389—152no—
132#389—151no—
133#387—152no—
134#385—152no—
135C4×C4⋊C4—151no—
136C4×C22⋊C4—151no—
137C4×C22⋊C4—152no—
138C22×C3×C5—41no—
139C5×A4C4×Q811yescharacteristic, complemented
140C3×C4×C5—42no—
141C3×C4×C5—82no—
142Dic15—44no—
143Dic15—42no—
144Dic15—81no—
145C22×A4C22×D511yescharacteristic
146C2×Dic6—201no—
147C4×A4—22no—
148C4×A4C4×D512yes—
149SL(2,ℤ/4)—54no—
150SL(2,ℤ/4)—52no—
151SL(2,ℤ/4)—101no—
152C3×C4⋊C4—41no—
153Dic3⋊C4—202no—
154C4×Dic3—202no—
155C4×Dic3—201no—
156C23×C5—31no—
157C23×C5—31no—
158C23×C5—31no—
159C23×C5—31no—
160C23×C5C2×C4×D311yescharacteristic
161C23×C5#23711yescharacteristic
162C23×C5D3×Q811yescharacteristic
163C2×C4×C5—31no—
164C2×C4×C5—32no—
165C2×C4×C5—32no—
166C2×C4×C5—32no—
167C2×C4×C5—32no—
168C2×C4×C5—62no—
169C2×C4×C5—62no—
170C2×C4×C5—61no—
171C2×C4×C5—62no—
172C2×C4×C5—62no—
173C2×C4×C5C2×S412yes—
174C2×C4×C5C2×S411yescharacteristic
175C2×Dic5—34no—
176C2×Dic5—34no—
177C2×Dic5—32no—
178C2×Dic5—32no—
179C2×Dic5—61no—
180C2×Dic5—61no—
181C2×Dic5—62no—
182C2×Dic5—62no—
183C2×Dic5—62no—
184C2×Dic5—61no—
185C2×Dic5—61no—
186C2×Dic5—62no—
187C2×Dic5—61no—
188C2×Dic5—61no—
189C2×Dic5—61no—
190C2×Dic5—61no—
191C2×Dic5—61no—
192C2×Dic5—61no—
193Dic10—64no—
194Dic10—64no—
195C22×Q8—151no—
196C23×C4C2×D1512yes—
197C23×C4C2×D1511yescharacteristic
198C22⋊Q8—154no—
199C22⋊Q8—154no—
200C4×Q8—301no—
201C4×Q8—302no—
202C4×Q8—301no—
203C2×C4⋊C4—31no—
204C2×C4⋊C4—32no—
205C2×C4⋊C4—31no—
206C2×C4⋊C4—151no—
207C2×C4⋊C4—152no—
208C2×C4⋊C4—152no—
209C2×C4⋊C4—152no—
210C2×C22⋊C4—152no—
211C2×C22⋊C4—151no—
212C2×C22⋊C4—151no—
213C2×C42—152no—
214C2×C42—151no—
215C2×C42—151no—
216C2×C42—152no—
217#95—151no—
218#95—152no—
219#95—151no—
220#95—152no—
221#95—152no—
222#95—152no—
223C2×C3×C5—41no—
224C2×C3×C5—41no—
225C2×C3×C5—41no—
226C2×A4C2×C4×D511yescharacteristic
227C2×A4#71111yescharacteristic
228C2×A4Q8×D511yescharacteristic
229C2×C3×C4—41no—
230C2×C3×C4—42no—
231C2×Dic3—201no—
232C2×Dic3—202no—
233C2×Dic3—201no—
234Dic6—204no—
235C22×C5—31no—
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—61no—
245C22×C5#88711yescharacteristic, complemented
246C22×C5C22×S411yescharacteristic
247C4×C5—22no—
248C4×C5—32no—
249C4×C5—62no—
250C4×C5C4×S412yes—
251Dic5—64no—
252Dic5—62no—
253Dic5—64no—
254Dic5—62no—
255Dic5—121no—
256Dic5—121no—
257C24C22×D1511yescharacteristic
258C2×Q8—154no—
259C2×Q8—301no—
260C2×Q8—302no—
261C2×Q8—301no—
262C22×C4—22no—
263C22×C4—31no—
264C22×C4—31no—
265C22×C4—32no—
266C22×C4—32no—
267C22×C4—32no—
268C22×C4—62no—
269C22×C4—151no—
270C22×C4—151no—
271C22×C4—152no—
272C22×C4—152no—
273C22×C4—151no—
274C22×C4—151no—
275C22×C4C4×D1512yes—
276C4⋊C4—32no—
277C4⋊C4—31no—
278C4⋊C4—61no—
279C4⋊C4—158no—
280C4⋊C4—154no—
281C4⋊C4—302no—
282C4⋊C4—302no—
283C4⋊C4—602no—
284C4⋊C4C5⋊S411yescharacteristic
285C22⋊C4—154no—
286C22⋊C4—152no—
287C22⋊C4—154no—
288C22⋊C4—152no—
289C22⋊C4—301no—
290C22⋊C4—301no—
291C42—301no—
292C42—302no—
293C42—302no—
294C42—302no—
295C42—301no—
296C42—602no—
297C3×C5—41noHall
298C22×C3—41no—
299A4#403311yescharacteristic, complemented
300C3×C4—42no—
301C3×C4—82no—
302Dic3—204no—
303Dic3—202no—
304Dic3—401no—
305C2×C5—31no—
306C2×C5—31no—
307C2×C5—31no—
308C2×C5—31no—
309C2×C5C2×C4×S411yescharacteristic
310C2×C5#591411yescharacteristic
311C2×C5Q8×S411yescharacteristic
312C23—31no—
313C23—31no—
314C23—31no—
315C23—31no—
316C23C2×C4×D1511yescharacteristic
317C23#681911yescharacteristic
318C23Q8×D1511yescharacteristic
319Q8—304no—
320Q8—304no—
321C2×C4—31no—
322C2×C4—32no—
323C2×C4—32no—
324C2×C4—32no—
325C2×C4—32no—
326C2×C4—62no—
327C2×C4—62no—
328C2×C4—61no—
329C2×C4—62no—
330C2×C4—62no—
331C2×C4—154no—
332C2×C4—154no—
333C2×C4—152no—
334C2×C4—152no—
335C2×C4—301no—
336C2×C4—301no—
337C2×C4—302no—
338C2×C4—302no—
339C2×C4—302no—
340C2×C4—301no—
341C2×C4—301no—
342C2×C4—302no—
343C2×C4—301no—
344C2×C4—301no—
345C2×C4—301no—
346C2×C4—301no—
347C2×C4—301no—
348C2×C4—301no—
349C2×C4C2×C5⋊S412yes—
350C2×C4C2×C5⋊S411yescharacteristic
351C2×C3—41no—
352C2×C3—41no—
353C2×C3—41no—
354C5#8530211yescharacteristic, complemented, Sylow
355C22—31no—
356C22—31no—
357C22—31no—
358C22—31no—
359C22—31no—
360C22—31no—
361C22—31no—
362C22—31no—
363C22—31no—
364C22—61no—
365C22#9177611yescharacteristic, complemented
366C22C22×C5⋊S411yescharacteristic
367C4—22no—
368C4—32no—
369C4—62no—
370C4—304no—
371C4—302no—
372C4—304no—
373C4—302no—
374C4—601no—
375C4—601no—
376C4C4×C5⋊S412yes—
377C3—41noSylow
378C2—31no—
379C2—31no—
380C2—31no—
381C2—31no—
382C2C2×C4×C5⋊S411yescharacteristic
383C2#1175689811yescharacteristic
384C2Q8×C5⋊S411yescharacteristic
subgroupG/H
center, FrattiniC22C22×C5⋊S4
commutatorC2×C5×A4C22×C4
FittingC22×C5×C4⋊C4D3
socleC24×C5C22×D3
prime radical, cosocleC22×C5×A4C23
hypercenterC4⋊C4C5⋊S4
hypocenterC5×A4C4×Q8
LCSG ▷ C2×C5×A4 ▷ C5×A4
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
12. #91948C4semidirect
32. A4⋊Dic5Q8semidirect
139. C5×A4C4×Q8semidirect
245. C22×C5#887semidirect
299. A4#4033semidirect
354. C5#85302semidirect
365. C22#91776semidirect

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
#117521302
C4×A4⋊Dic52
#106138933
#917764
#853025