Finite Group Databasebeta

← #14512509

Subgroups — #14512509

Order 1920.

534 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 66 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
1C22×A4×Dic5C211yesmaximal, characteristic
2C2×A4⋊#170C212yesmaximal, complemented
3#10605025—31nomaximal, Hall
4C23×C5×A4C411yescharacteristic
5C2×A4×Dic5—22no—
6C2×A4×Dic5C411yescharacteristic
7C2×A4×Dic5C2211yescharacteristic
8A4⋊#170—22no—
9#91241—41nomaximal
10#73141—51nomaximal, Hall
11C24×Dic5D311yescharacteristic
12C2×C22⋊#170—32no—
13C2×C22⋊#170—31no—
14C2×C22⋊#170—31no—
15C2×C22⋊#170—32no—
16C22×C5×A4—21no—
17C22×C5×A4—21no—
18C22×C5×A4C812yescomplemented
19C22×C5×A4C2×C411yescharacteristic
20C22×C3×Dic5—41no—
21C2×C3⋊#170—42no—
22A4×Dic5—21no—
23A4×Dic5D412yes—
24C22×C4×A4—51no—
25C2×A4⋊C8—52no—
26C25×C5Dic311yescharacteristic
27C23×Dic5—22no—
28C23×Dic5—31no—
29C23×Dic5—31no—
30C23×Dic5—31no—
31C23×Dic5—31no—
32C23×Dic5—62no—
33C23×Dic5Dic311yescharacteristic
34C23×Dic5C2×D311yescharacteristic
35C22×#170—32no—
36C22×#170—32no—
37C22⋊#170—62no—
38C22⋊#170—64no—
39C22⋊#170—61no—
40C22⋊#170—61no—
41C22⋊#170—61no—
42C22⋊#170—62no—
43C22⋊#170—61no—
44#1779—151noSylow
45C23×C3×C5—41no—
46C2×C5×A4—22no—
47C2×C5×A4C22⋊C411yescharacteristic
48C2×C5×A4C2×C811yescharacteristic
49C2×C5×A4M1611yescharacteristic
50C2×C3×Dic5—41no—
51C2×C3×Dic5—41no—
52C2×C3×Dic5—82no—
53C3⋊#170—82no—
54C23×A4AGL(1,𝔽5)11yescharacteristic
55C2×C4×A4—51no—
56C2×C4×A4—51no—
57C2×C4×A4—102no—
58A4⋊C8—102no—
59#830—201no—
60C24×C5—21no—
61C24×C5—21no—
62C24×C5—31no—
63C24×C5—31no—
64C24×C5—32no—
65C24×C5—61no—
66C24×C5—61no—
67C24×C5C3⋊C812yescomplemented
68C24×C5C2×Dic311yescharacteristic
69C22×Dic5—21no—
70C22×Dic5—31no—
71C22×Dic5—31no—
72C22×Dic5—31no—
73C22×Dic5—32no—
74C22×Dic5—34no—
75C22×Dic5—31no—
76C22×Dic5—31no—
77C22×Dic5—31no—
78C22×Dic5—31no—
79C22×Dic5—62no—
80C22×Dic5—62no—
81C22×Dic5—61no—
82C22×Dic5—61no—
83C22×Dic5—62no—
84C22×Dic5—62no—
85C22×Dic5—62no—
86C22×Dic5—62no—
87C22×Dic5—62no—
88C22×Dic5#6712yes—
89C22×Dic5S411yescharacteristic
90C2×#170—62no—
91C2×#170—62no—
92C2×#170—62no—
93C2×#170—62no—
94C2×#170—62no—
95C2×#170—62no—
96C24×C4—51no—
97C2×C22⋊C8—152no—
98C2×C22⋊C8—151no—
99C2×C22⋊C8—151no—
100C2×C22⋊C8—152no—
101C22×C3×C5—42no—
102C22×C3×C5—41no—
103C22×C3×C5—81no—
104C22×C3×C5—81no—
105C5×A4C22⋊C811yescharacteristic, complemented
106C3×Dic5—42no—
107C3×Dic5—81no—
108C22×A4—21no—
109C22×A4—21no—
110C22×A4#17012yescomplemented
111C22×A4C2×AGL(1,𝔽5)11yescharacteristic
112C22×C3×C4—201no—
113C4×A4—52no—
114C4×A4—101no—
115C2×C3⋊C8—202no—
116C23×C5—22no—
117C23×C5—31no—
118C23×C5—31no—
119C23×C5—32no—
120C23×C5—31no—
121C23×C5—31no—
122C23×C5—32no—
123C23×C5—32no—
124C23×C5—32no—
125C23×C5—32no—
126C23×C5—31no—
127C23×C5—61no—
128C23×C5—61no—
129C23×C5—61no—
130C23×C5—61no—
131C23×C5—62no—
132C23×C5—61no—
133C23×C5—61no—
134C23×C5—62no—
135C23×C5—62no—
136C23×C5—61no—
137C23×C5—64no—
138C23×C5C2×C3⋊C811yescharacteristic
139C23×C5#20811yescharacteristic
140C23×C5#21711yescharacteristic
141C23×C5SL(2,ℤ/4)11yescharacteristic
142C2×Dic5—22no—
143C2×Dic5—31no—
144C2×Dic5—32no—
145C2×Dic5—32no—
146C2×Dic5—32no—
147C2×Dic5—32no—
148C2×Dic5—31no—
149C2×Dic5—62no—
150C2×Dic5—61no—
151C2×Dic5—61no—
152C2×Dic5—61no—
153C2×Dic5—62no—
154C2×Dic5—64no—
155C2×Dic5—62no—
156C2×Dic5—61no—
157C2×Dic5SL(2,ℤ/4)11yescharacteristic
158C2×Dic5C2×S411yescharacteristic
159#170—122no—
160#170—122no—
161C25ΓL(1,𝔽16)11yescharacteristic
162C23×C4—51no—
163C23×C4—51no—
164C23×C4—102no—
165C23×C4—151no—
166C23×C4—151no—
167C23×C4—151no—
168C23×C4—151no—
169C23×C4—302no—
170C22×C8—152no—
171C22×C8—152no—
172C22⋊C8—301no—
173C22⋊C8—302no—
174C22⋊C8—301no—
175C22⋊C8—301no—
176C22⋊C8—302no—
177C22⋊C8—304no—
178C22⋊C8—301no—
179C2×C3×C5—41no—
180C2×C3×C5—41no—
181C2×C3×C5—41no—
182C2×C3×C5—82no—
183C23×C3—41no—
184C2×A4—22no—
185C2×A4C2×#17011yescharacteristic
186C2×A4#70411yescharacteristic
187C2×A4C22⋊AGL(1,𝔽5)11yescharacteristic
188C2×C3×C4—201no—
189C2×C3×C4—201no—
190C2×C3×C4—402no—
191C3⋊C8—402no—
192C22×C5—21no—
193C22×C5—21no—
194C22×C5—31no—
195C22×C5—31no—
196C22×C5—31no—
197C22×C5—31no—
198C22×C5—31no—
199C22×C5—31no—
200C22×C5—31no—
201C22×C5—31no—
202C22×C5—31no—
203C22×C5—34no—
204C22×C5—32no—
205C22×C5—62no—
206C22×C5—62no—
207C22×C5—62no—
208C22×C5—62no—
209C22×C5—61no—
210C22×C5—62no—
211C22×C5—62no—
212C22×C5—62no—
213C22×C5—61no—
214C22×C5—61no—
215C22×C5#83011yescharacteristic, complemented
216C22×C5A4⋊C812yescomplemented
217C22×C5C2×SL(2,ℤ/4)11yescharacteristic
218Dic5—21no—
219Dic5—32no—
220Dic5—61no—
221Dic5GL(2,ℤ/4)12yes—
222C24—21no—
223C24—21no—
224C24—31no—
225C24—31no—
226C24—32no—
227C24—61no—
228C24—61no—
229C24C3⋊#17012yescomplemented
230C24C2×ΓL(1,𝔽16)11yescharacteristic
231C22×C4—51no—
232C22×C4—52no—
233C22×C4—101no—
234C22×C4—151no—
235C22×C4—151no—
236C22×C4—151no—
237C22×C4—151no—
238C22×C4—152no—
239C22×C4—151no—
240C22×C4—151no—
241C22×C4—154no—
242C22×C4—151no—
243C22×C4—302no—
244C22×C4—302no—
245C22×C4—301no—
246C22×C4—301no—
247C22×C4—302no—
248C22×C4—302no—
249C22×C4—302no—
250C22×C4—302no—
251C22×C4—302no—
252C2×C8—302no—
253C2×C8—302no—
254C2×C8—302no—
255C2×C8—302no—
256C2×C8—302no—
257C2×C8—302no—
258C3×C5—41noHall
259C22×C3—41no—
260C22×C3—42no—
261C22×C3—81no—
262C22×C3—81no—
263A4C22⋊#17011yescharacteristic, complemented
264C3×C4—202no—
265C3×C4—401no—
266C2×C5—22no—
267C2×C5—31no—
268C2×C5—31no—
269C2×C5—31no—
270C2×C5—31no—
271C2×C5—62no—
272C2×C5C2×A4⋊C811yescharacteristic
273C2×C5#540911yescharacteristic
274C2×C5#543211yescharacteristic
275C23—22no—
276C23—31no—
277C23—31no—
278C23—32no—
279C23—31no—
280C23—31no—
281C23—32no—
282C23—32no—
283C23—31no—
284C23—32no—
285C23—32no—
286C23—61no—
287C23—61no—
288C23—61no—
289C23—61no—
290C23—62no—
291C23—61no—
292C23—61no—
293C23—62no—
294C23—62no—
295C23—61no—
296C23—64no—
297C23C2×C3⋊#17011yescharacteristic
298C23#676211yescharacteristic
299C23#676311yescharacteristic
300C23A4⋊AGL(1,𝔽5)11yescharacteristic
301C2×C4—51no—
302C2×C4—51no—
303C2×C4—102no—
304C2×C4—152no—
305C2×C4—152no—
306C2×C4—151no—
307C2×C4—152no—
308C2×C4—152no—
309C2×C4—151no—
310C2×C4—302no—
311C2×C4—302no—
312C2×C4—301no—
313C2×C4—301no—
314C2×C4—301no—
315C2×C4—302no—
316C2×C4—304no—
317C2×C4—301no—
318C8—602no—
319C8—602no—
320C2×C3—41no—
321C2×C3—41no—
322C2×C3—41no—
323C2×C3—82no—
324C5#7314111yescharacteristic, complemented, Sylow
325C22—21no—
326C22—21no—
327C22—31no—
328C22—31no—
329C22—31no—
330C22—31no—
331C22—31no—
332C22—31no—
333C22—31no—
334C22—31no—
335C22—31no—
336C22—34no—
337C22—32no—
338C22—62no—
339C22—62no—
340C22—62no—
341C22—62no—
342C22—61no—
343C22—62no—
344C22—62no—
345C22—62no—
346C22—61no—
347C22—61no—
348C22#9124111yescharacteristic, complemented
349C22A4⋊#17012yescomplemented
350C22C2×A4⋊AGL(1,𝔽5)11yescharacteristic
351C4—52no—
352C4—101no—
353C4—152no—
354C4—301no—
355C3—41noSylow
356C2—22no—
357C2—31no—
358C2—31no—
359C2—31no—
360C2—31no—
361C2—62no—
362C2C2×A4⋊#17011yescharacteristic
363C2#1175672811yescharacteristic
364C2#1175672911yescharacteristic
subgroupG/H
center, FrattiniC22C2×A4⋊AGL(1,𝔽5)
commutatorC2×C5×A4C2×C8
FittingC25×C5Dic3
socleC24×C5C2×Dic3
prime radicalC23×C5×A4C4
cosocleC2×A4×Dic5C22
hypercenterC23A4⋊AGL(1,𝔽5)
hypocenterC5×A4C22⋊C8
LCSG ▷ C2×C5×A4 ▷ C5×A4
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
2. C2×A4⋊#170C2semidirect
18. C22×C5×A4C8semidirect
67. C24×C5C3⋊C8semidirect
105. C5×A4C22⋊C8semidirect
110. C22×A4#170semidirect
215. C22×C5#830semidirect
216. C22×C5A4⋊C8semidirect
229. C24C3⋊#170semidirect
263. A4C22⋊#170semidirect
324. C5#73141semidirect
348. C22#91241semidirect
349. C22A4⋊#170semidirect

Maximal subgroups

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

subgroupindex
C22×A4×Dic52
C2×A4⋊#1702
#106050253
#912414
#731415