Finite Group Databasebeta

← #14277199

Subgroups — #14277199

Order 1920.

492 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C4×#6763C211yesmaximal, characteristic
2C3×#65756C211yesmaximal, characteristic
3#11748702C211yesmaximal, characteristic
4#10598507—31nomaximal, Hall
5C22×C3×C4×D5C2211yescharacteristic
6C2×#6763—21no—
7C2×C4×ΓL(1,𝔽16)—21no—
8C2×C3×#700C412yescomplemented
9C2×#6665—21no—
10C2×Dic3×Dic5—21no—
11#91235C412yescomplemented
12C3×C22⋊#170—21no—
13C3×#4003—21no—
14#91115C411yescharacteristic, complemented
15C5×C3⋊#95C411yescharacteristic, complemented
16#67683—51nomaximal, Hall
17C4×C22⋊AGL(1,𝔽5)—31no—
18#65756D311yescharacteristic
19#64955—31no—
20C23×C3×D5D411yescharacteristic
21C22×ΓL(1,𝔽16)—22no—
22C22×C3×C4×C5C2×C411yescharacteristic
23C22×Dic15—21no—
24C22×C5×Dic3—21no—
25C22×C3×Dic5D411yescharacteristic
26C2×C3×C4×D5—42no—
27C2×C3×C4×D5C2×C411yescharacteristic
28C2×C3×C4×D5C2×C411yescharacteristic
29C2×C3×C4×D5D411yescharacteristic
30C2×C3×C4×D5Q811yescharacteristic
31#6763—22no—
32#6763—22no—
33C4×ΓL(1,𝔽16)—42no—
34C2×C3×#170—22no—
35C3×#700—42no—
36#6665—24no—
37Dic3×Dic5—42no—
38C3×#407—51no—
39C4×#217—51no—
40C4×#217—51no—
41C22×C4×D5C2×D311yescharacteristic
42C2×C22⋊AGL(1,𝔽5)—61no—
43C2×C4×AGL(1,𝔽5)—61no—
44C2×#700Dic312yescomplemented
45C2×#685—61no—
46C2×C4×Dic5—61no—
47C22⋊#170—21no—
48(C2×AGL(1,𝔽5))⋊C4—32no—
49#4003—21no—
50C5×#95—31no—
51#3963—31no—
52#1297—151noSylow
53C23×C3×C5C22⋊C411yescharacteristic
54C22×C3×D5—21no—
55C22×C3×D5—21no—
56C22×C3×D5—22no—
57C22×C3×D5—41no—
58C22×C3×D5C22⋊C411yescharacteristic
59C22×C3×D5C4⋊C411yescharacteristic
60C2×ΓL(1,𝔽16)—24no—
61C2×ΓL(1,𝔽16)—42no—
62C2×ΓL(1,𝔽16)—42no—
63C2×C3×C4×C5—41no—
64C2×C3×C4×C5C4211yescharacteristic
65C2×C3×C4×C5C4⋊C411yescharacteristic
66C2×Dic15—22no—
67C2×Dic15—41no—
68C2×Dic15—41no—
69C2×C5×Dic3—22no—
70C2×C5×Dic3—41no—
71C2×C5×Dic3—41no—
72C2×C3×Dic5—22no—
73C2×C3×Dic5C22⋊C411yescharacteristic
74C2×C3×Dic5C4⋊C411yescharacteristic
75C3×C4×D5—22no—
76C3×C4×D5—22no—
77C3×C4×D5—41no—
78C3×C4×D5—41no—
79C3×#170—42no—
80C23×C3×C4—51no—
81C2×C3×M16—52no—
82C2×#217—101no—
83C2×#217—101no—
84C2×C4×Dic3—101no—
85C2×C4×Dic3—101no—
86C3×C22⋊C8—101no—
87C3×C22⋊C8—101no—
88C3⋊#95—52no—
89C3⋊#95—51no—
90C3⋊#95AGL(1,𝔽5)11yescharacteristic, complemented
91C23×D5D1211yescharacteristic
92C22×AGL(1,𝔽5)—62no—
93C22×C4×C5—61no—
94C22×C4×C5C4×D311yescharacteristic
95C22×Dic5—61no—
96C22×Dic5#6711yescharacteristic
97C2×C4×D5—42no—
98C2×C4×D5Dic611yescharacteristic
99C2×C4×D5C4×D311yescharacteristic
100C2×C4×D5C2×Dic311yescharacteristic
101C2×C4×D5#6711yescharacteristic
102C22⋊AGL(1,𝔽5)—62no—
103C22⋊AGL(1,𝔽5)—62no—
104C2×#170—22no—
105C4×AGL(1,𝔽5)—122no—
106#700—42no—
107#685—64no—
108C4×Dic5—122no—
109#407—51no—
110C4×C22⋊C4—151no—
111C4×C22⋊C4—151no—
112C22×C3×C5—21no—
113C22×C3×C5—21no—
114C22×C3×C5#9511yescharacteristic
115C22×C3×C5#10411yescharacteristic
116C22×C3×C5#10411yescharacteristic
117C2×C3×D5—21no—
118C2×C3×D5—21no—
119C2×C3×D5—21no—
120C2×C3×D5—21no—
121C2×C3×D5—21no—
122C2×C3×D5—42no—
123C2×C3×D5—42no—
124C2×C3×D5#10412yes—
125ΓL(1,𝔽16)—44no—
126C3×C4×C5—21no—
127C3×C4×C5—21no—
128Dic15—42no—
129C3×Dic5—21no—
130C3×Dic5#9912yes—
131C5×Dic3—42no—
132C24×C3—51no—
133C22×C3×C4—51no—
134C22×C3×C4—51no—
135C22×C3×C4—51no—
136C22×C3×C4—51no—
137C22×C3×C4—51no—
138C22×C3×C4—202no—
139C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
140C22×Dic3—21no—
141C22×Dic3—102no—
142C22×Dic3—101no—
143C3×M16—202no—
144C2×C3×C8—102no—
145#217—104no—
146#217—102no—
147#217—102no—
148C4×Dic3—202no—
149C4×Dic3—202no—
150C23×C5(C2×D3)⋊C411yescharacteristic
151C22×D5—21no—
152C22×D5—21no—
153C22×D5—22no—
154C22×D5—41no—
155C22×D5C4⋊Dic311yescharacteristic
156C22×D5(C2×D3)⋊C411yescharacteristic
157C2×AGL(1,𝔽5)—64no—
158C2×AGL(1,𝔽5)—122no—
159C2×AGL(1,𝔽5)—122no—
160C2×C4×C5—41no—
161C2×C4×C5—62no—
162C2×C4×C5—121no—
163C2×C4×C5—121no—
164C2×C4×C5C4×Dic311yescharacteristic
165C2×C4×C5Dic3⋊C411yescharacteristic
166C2×Dic5—22no—
167C2×Dic5—62no—
168C2×Dic5—121no—
169C2×Dic5—121no—
170C2×Dic5Dic3⋊C411yescharacteristic
171C2×Dic5#21711yescharacteristic
172C4×D5—22no—
173C4×D5—22no—
174C4×D5—41no—
175C4×D5—41no—
176#170—42no—
177C23×C4—51no—
178C2×M16—52no—
179C2×C22⋊C4—301no—
180C2×C22⋊C4—301no—
181C2×C42—301no—
182C2×C42—301no—
183C22⋊C8—101no—
184C22⋊C8—101no—
185#95—31no—
186#95—152no—
187#95—151no—
188C2×C3×C5—21no—
189C2×C3×C5—21no—
190C2×C3×C5#33911yescharacteristic
191C2×C3×C5#33911yescharacteristic
192C2×C3×C5#34211yescharacteristic
193C3×D5—22no—
194C3×D5—41no—
195C23×C3—51no—
196C23×C3—51no—
197C23×C3—102no—
198C23×C3—101no—
199C23×C3—101no—
200C23×C3—201no—
201C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
202C2×C3×C4—41no—
203C2×C3×C4—51no—
204C2×C3×C4—51no—
205C2×C3×C4—102no—
206C2×C3×C4—102no—
207C2×C3×C4—102no—
208C2×C3×C4—201no—
209C2×C3×C4—201no—
210C2×C3×C4C4×AGL(1,𝔽5)11yescharacteristic
211C2×C3×C4C4⋊AGL(1,𝔽5)11yescharacteristic
212C2×Dic3—22no—
213C2×Dic3—41no—
214C2×Dic3—41no—
215C2×Dic3—102no—
216C2×Dic3—104no—
217C2×Dic3—201no—
218C2×Dic3—202no—
219C2×Dic3—202no—
220C2×Dic3—201no—
221C3×C8—202no—
222C22×C5—21no—
223C22×C5—21no—
224C22×C5#82511yescharacteristic
225C22×C5#82511yescharacteristic
226C22×C5C3⋊#9511yescharacteristic
227C2×D5—21no—
228C2×D5—21no—
229C2×D5—21no—
230C2×D5—21no—
231C2×D5—21no—
232C2×D5—42no—
233C2×D5—42no—
234C2×D5#82512yes—
235AGL(1,𝔽5)—124no—
236C4×C5—21no—
237C4×C5—21no—
238C4×C5—122no—
239Dic5—21no—
240Dic5—122no—
241Dic5#83412yes—
242C24—51no—
243C22×C4—51no—
244C22×C4—51no—
245C22×C4—51no—
246C22×C4—51no—
247C22×C4—51no—
248C22×C4—61no—
249C22×C4—202no—
250C22×C4—302no—
251C22×C4—301no—
252C22×C4D3×AGL(1,𝔽5)11yescharacteristic
253M16—202no—
254C2×C8—102no—
255C22⋊C4—304no—
256C22⋊C4—302no—
257C22⋊C4—302no—
258C42—602no—
259C42—602no—
260C3×C5#129711yescharacteristic, complemented, Hall
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—52no—
264C22×C3—101no—
265C22×C3—101no—
266C22×C3—101no—
267C22×C3—101no—
268C22×C3—101no—
269C22×C3—202no—
270C22×C3—202no—
271C22×C3(C2×AGL(1,𝔽5))⋊C411yescharacteristic
272C22×C3#400811yescharacteristic
273C22×C3#401011yescharacteristic
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—52no—
277C3×C4—101no—
278Dic3—42no—
279Dic3—202no—
280Dic3—204no—
281C2×C5—21no—
282C2×C5—21no—
283C2×C5#452611yescharacteristic
284C2×C5#455511yescharacteristic
285C2×C5#455511yescharacteristic
286D5—22no—
287D5—41no—
288C23—51no—
289C23—51no—
290C23—102no—
291C23—101no—
292C23—101no—
293C23—201no—
294C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
295C2×C4—41no—
296C2×C4—51no—
297C2×C4—51no—
298C2×C4—62no—
299C2×C4—102no—
300C2×C4—102no—
301C2×C4—102no—
302C2×C4—121no—
303C2×C4—121no—
304C2×C4—201no—
305C2×C4—201no—
306C2×C4—302no—
307C2×C4—304no—
308C2×C4—601no—
309C2×C4—602no—
310C2×C4—602no—
311C2×C4—601no—
312C2×C4Dic3×AGL(1,𝔽5)11yescharacteristic
313C2×C4Dic3⋊AGL(1,𝔽5)11yescharacteristic
314C8—202no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—102no—
318C2×C3—201no—
319C2×C3#6486211yescharacteristic
320C2×C3#6486611yescharacteristic
321C2×C3#6487511yescharacteristic
322C5#6768311yescharacteristic, complemented, Sylow
323C22—21no—
324C22—21no—
325C22—52no—
326C22—101no—
327C22—101no—
328C22—101no—
329C22—101no—
330C22—101no—
331C22—202no—
332C22—202no—
333C22#9115511yescharacteristic
334C22#9115711yescharacteristic
335C22(C2×AGL(1,𝔽5))⋊Dic311yescharacteristic
336C4—21no—
337C4—21no—
338C4—52no—
339C4—101no—
340C4—122no—
341C4—602no—
342C4—604no—
343C3#1059850711yescharacteristic, complemented, Sylow
344C2—21no—
345C2—21no—
346C2—102no—
347C2—201no—
348C2#1174652411yescharacteristic
349C2#1174652511yescharacteristic
350C2#1174657111yescharacteristic
subgroupG/H
centerC22(C2×AGL(1,𝔽5))⋊Dic3
commutatorC2×C3×C4×C5C42
Frattini, hypercenterC22×C4D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5#95
prime radicalC23×C3×D5D4
cosocleC22×C3×C4×D5C22
hypocenterC3×C5#1297
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
8. C2×C3×#700C4semidirect
11. #91235C4semidirect
14. #91115C4semidirect
15. C5×C3⋊#95C4semidirect
44. C2×#700Dic3semidirect
90. C3⋊#95AGL(1,𝔽5)semidirect
260. C3×C5#1297semidirect
322. C5#67683semidirect
343. C3#10598507semidirect

Maximal subgroups

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

subgroupindex
C4×#67632
C3×#657562
#117487022
#105985073
#676835