Finite Group Databasebeta

← #14512477

Subgroups — #14512477

Order 1920.

534 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 60 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×C4×D5×A4C211yesmaximal, characteristic
2C2×A4⋊#170C212yesmaximal, complemented
3#10604898—31nomaximal, Hall
4C22×D5×A4C411yescharacteristic
5C2×C4×C5×A4C411yescharacteristic
6C2×A4×Dic5C2211yescharacteristic
7C4×D5×A4—22no—
8A4⋊#170—22no—
9#91232—41nomaximal
10#73141—51nomaximal, Hall
11C23×C4×D5D311yescharacteristic
12C2×C22⋊#170—32no—
13C2×#4003—32no—
14C2×#4003—31no—
15C2×#4003—31no—
16C22×C5×A4C2×C411yescharacteristic
17C2×D5×A4—21no—
18C2×D5×A4—21no—
19C2×D5×A4C812yescomplemented
20C2×C3×C4×D5—41no—
21C4×C5×A4—21no—
22C2×C3⋊#170—42no—
23A4×Dic5D412yes—
24C22×C4×A4—51no—
25C2×A4⋊C8—52no—
26C24×D5Dic311yescharacteristic
27C23×C4×C5Dic311yescharacteristic
28C23×Dic5C2×D311yescharacteristic
29C22×C4×D5—22no—
30C22×C4×D5—31no—
31C22×C4×D5—31no—
32C22×C4×D5—31no—
33C22×C4×D5—31no—
34C22×C4×D5—62no—
35C22×#170—32no—
36C22×#170—32no—
37C22⋊#170—62no—
38C22⋊#170—62no—
39#4003—64no—
40#4003—61no—
41#4003—61no—
42#4003—61no—
43#4003—61no—
44#1779—151noSylow
45C22×C3×D5—41no—
46C2×C5×A4C22⋊C411yescharacteristic
47C2×C5×A4C2×C811yescharacteristic
48C2×C5×A4M1611yescharacteristic
49D5×A4—22no—
50C2×C3×C4×C5—41no—
51C2×C3×Dic5—41no—
52C3×C4×D5—82no—
53C3⋊#170—82no—
54C23×A4—51no—
55C2×C4×A4—51no—
56C2×C4×A4—102no—
57C2×C4×A4AGL(1,𝔽5)11yescharacteristic
58A4⋊C8—102no—
59#830—201no—
60C24×C5C2×Dic311yescharacteristic
61C23×D5—21no—
62C23×D5—21no—
63C23×D5—31no—
64C23×D5—31no—
65C23×D5—32no—
66C23×D5—61no—
67C23×D5—61no—
68C23×D5C3⋊C812yescomplemented
69C22×C4×C5—21no—
70C22×C4×C5—31no—
71C22×C4×C5—31no—
72C22×C4×C5—61no—
73C22×Dic5—31no—
74C22×Dic5—31no—
75C22×Dic5—32no—
76C22×Dic5#6712yes—
77C2×C4×D5—34no—
78C2×C4×D5—31no—
79C2×C4×D5—31no—
80C2×C4×D5—31no—
81C2×C4×D5—62no—
82C2×C4×D5—62no—
83C2×C4×D5—61no—
84C2×C4×D5—62no—
85C2×C4×D5—62no—
86C2×C4×D5—62no—
87C2×C4×D5—62no—
88C2×C4×D5—62no—
89C2×C4×D5S411yescharacteristic
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—41no—
102C2×C3×D5—42no—
103C2×C3×D5—81no—
104C2×C3×D5—81no—
105C5×A4C22⋊C811yescharacteristic, complemented
106C3×C4×C5—81no—
107C3×Dic5—42no—
108C22×A4—52no—
109C22×A4—101no—
110C22×A4—101no—
111C22×A4C2×AGL(1,𝔽5)11yescharacteristic
112C22×C3×C4—201no—
113C4×A4—21no—
114C4×A4—52no—
115C2×C3⋊C8—202no—
116C23×C5—31no—
117C23×C5—31no—
118C23×C5—31no—
119C23×C5—31no—
120C23×C5C2×C3⋊C811yescharacteristic
121C23×C5#20811yescharacteristic
122C23×C5#21711yescharacteristic
123C22×D5—22no—
124C22×D5—32no—
125C22×D5—32no—
126C22×D5—32no—
127C22×D5—31no—
128C22×D5—32no—
129C22×D5—32no—
130C22×D5—61no—
131C22×D5—61no—
132C22×D5—61no—
133C22×D5—61no—
134C22×D5—61no—
135C22×D5—62no—
136C22×D5—64no—
137C22×D5—61no—
138C22×D5—62no—
139C22×D5—62no—
140C22×D5—61no—
141C22×D5SL(2,ℤ/4)11yescharacteristic
142C2×C4×C5—32no—
143C2×C4×C5—31no—
144C2×C4×C5—61no—
145C2×C4×C5—61no—
146C2×C4×C5—61no—
147C2×C4×C5SL(2,ℤ/4)11yescharacteristic
148C2×Dic5—31no—
149C2×Dic5—32no—
150C2×Dic5—32no—
151C2×Dic5—32no—
152C2×Dic5—61no—
153C2×Dic5C2×S411yescharacteristic
154C4×D5—22no—
155C4×D5—62no—
156C4×D5—62no—
157C4×D5—64no—
158C4×D5—62no—
159#170—122no—
160#170—122no—
161C25—51no—
162C23×C4—51no—
163C23×C4—102no—
164C23×C4—151no—
165C23×C4—151no—
166C23×C4—151no—
167C23×C4—151no—
168C23×C4—302no—
169C23×C4ΓL(1,𝔽16)11yescharacteristic
170C22×C8—152no—
171C22×C8—152no—
172C22⋊C8—301no—
173C22⋊C8—302no—
174C22⋊C8—301no—
175C22⋊C8—301no—
176C22⋊C8—304no—
177C22⋊C8—301no—
178C22⋊C8—302no—
179C2×C3×C5—41no—
180C2×C3×C5—41no—
181C2×C3×C5—41no—
182C3×D5—82no—
183C23×C3—201no—
184C2×A4—102no—
185C2×A4D5⋊C811yescharacteristic
186C2×A4#70011yescharacteristic
187C2×A4C22⋊AGL(1,𝔽5)11yescharacteristic
188C2×C3×C4—41no—
189C2×C3×C4—201no—
190C2×C3×C4—402no—
191C3⋊C8—402no—
192C22×C5—31no—
193C22×C5—31no—
194C22×C5—31no—
195C22×C5—31no—
196C22×C5—31no—
197C22×C5—31no—
198C22×C5—31no—
199C22×C5—31no—
200C22×C5—31no—
201C22×C5—61no—
202C22×C5#83011yescharacteristic, complemented
203C22×C5C2×SL(2,ℤ/4)11yescharacteristic
204C2×D5—21no—
205C2×D5—21no—
206C2×D5—34no—
207C2×D5—32no—
208C2×D5—62no—
209C2×D5—62no—
210C2×D5—62no—
211C2×D5—62no—
212C2×D5—62no—
213C2×D5—62no—
214C2×D5—61no—
215C2×D5—61no—
216C2×D5—62no—
217C2×D5A4⋊C812yescomplemented
218C4×C5—21no—
219C4×C5—61no—
220Dic5—32no—
221Dic5GL(2,ℤ/4)12yes—
222C24—52no—
223C24—101no—
224C24—101no—
225C24—151no—
226C24—151no—
227C24—152no—
228C24—301no—
229C24—301no—
230C24C2×ΓL(1,𝔽16)11yescharacteristic
231C22×C4—21no—
232C22×C4—31no—
233C22×C4—31no—
234C22×C4—51no—
235C22×C4—52no—
236C22×C4—61no—
237C22×C4—151no—
238C22×C4—151no—
239C22×C4—154no—
240C22×C4—151no—
241C22×C4—152no—
242C22×C4—151no—
243C22×C4—151no—
244C22×C4—301no—
245C22×C4—302no—
246C22×C4—302no—
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—202no—
261C22×C3—401no—
262C22×C3—401no—
263A4#400311yescharacteristic, complemented
264C3×C4—81no—
265C3×C4—202no—
266C2×C5—31no—
267C2×C5—31no—
268C2×C5—31no—
269C2×C5—31no—
270C2×C5C2×A4⋊C811yescharacteristic
271C2×C5#540911yescharacteristic
272C2×C5#543211yescharacteristic
273D5—22no—
274D5—62no—
275C23—31no—
276C23—31no—
277C23—31no—
278C23—31no—
279C23—51no—
280C23—102no—
281C23—152no—
282C23—152no—
283C23—152no—
284C23—152no—
285C23—152no—
286C23—151no—
287C23—301no—
288C23—301no—
289C23—301no—
290C23—301no—
291C23—302no—
292C23—301no—
293C23—301no—
294C23—302no—
295C23—302no—
296C23—301no—
297C23—304no—
298C23D5⋊(C3⋊C8)11yescharacteristic
299C23#675811yescharacteristic
300C23#676311yescharacteristic
301C2×C4—32no—
302C2×C4—31no—
303C2×C4—51no—
304C2×C4—61no—
305C2×C4—61no—
306C2×C4—61no—
307C2×C4—102no—
308C2×C4—152no—
309C2×C4—152no—
310C2×C4—151no—
311C2×C4—152no—
312C2×C4—302no—
313C2×C4—302no—
314C2×C4—302no—
315C2×C4—304no—
316C2×C4—301no—
317C2×C4A4⋊AGL(1,𝔽5)11yescharacteristic
318C8—602no—
319C8—602no—
320C2×C3—41no—
321C2×C3—41no—
322C2×C3—41no—
323C2×C3—402no—
324C5#7314111yescharacteristic, complemented, Sylow
325C22—31no—
326C22—31no—
327C22—31no—
328C22—31no—
329C22—31no—
330C22—31no—
331C22—31no—
332C22—31no—
333C22—31no—
334C22—52no—
335C22—61no—
336C22—101no—
337C22—101no—
338C22—154no—
339C22—152no—
340C22—302no—
341C22—302no—
342C22—302no—
343C22—302no—
344C22—302no—
345C22—302no—
346C22—302no—
347C22—301no—
348C22—301no—
349C22#9123211yescharacteristic, complemented
350C22C2×A4⋊AGL(1,𝔽5)11yescharacteristic
351C4—21no—
352C4—52no—
353C4—61no—
354C4—152no—
355C3—41noSylow
356C2—31no—
357C2—31no—
358C2—31no—
359C2—31no—
360C2—102no—
361C2—302no—
362C2D5⋊(A4⋊C8)11yescharacteristic
363C2#1175671611yescharacteristic
364C2#1175672911yescharacteristic
subgroupG/H
center, FrattiniC22C2×A4⋊AGL(1,𝔽5)
commutatorC2×C5×A4C2×C8
FittingC23×C4×C5Dic3
socleC24×C5C2×Dic3
prime radicalC22×D5×A4C4
cosocleC2×A4×Dic5C22
hypercenterC2×C4A4⋊AGL(1,𝔽5)
hypocenterC5×A4C22⋊C8
LCSG ▷ C2×C5×A4 ▷ C5×A4
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×A4⋊#170C2semidirect
19. C2×D5×A4C8semidirect
68. C23×D5C3⋊C8semidirect
105. C5×A4C22⋊C8semidirect
202. C22×C5#830semidirect
217. C2×D5A4⋊C8semidirect
263. A4#4003semidirect
324. C5#73141semidirect
349. C22#91232semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D5×A42
C2×A4⋊#1702
#106048983
#912324
#731415