Finite Group Databasebeta

← #14276910

Subgroups — #14276910

Order 1920.

452 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 85 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
2#11752415C211yesmaximal, characteristic
3C3×#64953C211yesmaximal, characteristic
4#10598503—31nomaximal, Hall
5C22×C3×C4×D5C2211yescharacteristic
6C2×#6763—21no—
7C2×C4×ΓL(1,𝔽16)C412yescomplemented
8C2×#6758—21no—
9C2×C3×#685—21no—
10#91241—21no—
11#91235—21no—
12#91232C412yescomplemented
13C3×C5×#95C411yescharacteristic, complemented
14C3×#3963—21no—
15C3×#3963C411yescharacteristic, complemented
16#67628—51nomaximal, Hall
17C4×C22⋊AGL(1,𝔽5)—31no—
18#65756—31no—
19#64953D311yescharacteristic
20C23×C3×D5D411yescharacteristic
21C22×ΓL(1,𝔽16)—22no—
22C22×C3×C4×C5—21no—
23C22×C3×C4×C5C2×C411yescharacteristic
24C22×C3×Dic5—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—
33C2×C3⋊#170—22no—
34C4×ΓL(1,𝔽16)—42no—
35#6758—42no—
36C3×#685—42no—
37C3×#381—51no—
38C4×#217—51no—
39#5207—51no—
40C22×C4×D5C2×D311yescharacteristic
41C2×C22⋊AGL(1,𝔽5)—61no—
42C2×C4×AGL(1,𝔽5)—32no—
43C2×#700—61no—
44C2×#685—21no—
45C22⋊#170—61no—
46(C2×AGL(1,𝔽5))⋊C4—61no—
47#4003—32no—
48C5×#95Dic311yescharacteristic, complemented
49#3963—21no—
50#3963Dic311yescharacteristic, complemented
51#1284—151noSylow
52C23×C3×C5C22⋊C411yescharacteristic
53C22×C3×D5—21no—
54C22×C3×D5—21no—
55C22×C3×D5—22no—
56C22×C3×D5—41no—
57C22×C3×D5C22⋊C411yescharacteristic
58C22×C3×D5C4⋊C411yescharacteristic
59C2×ΓL(1,𝔽16)—24no—
60C2×ΓL(1,𝔽16)—42no—
61C2×ΓL(1,𝔽16)—42no—
62C2×C3×C4×C5—41no—
63C2×C3×C4×C5—41no—
64C2×C3×C4×C5—41no—
65C2×C3×C4×C5—41no—
66C2×C3×C4×C5C4211yescharacteristic
67C2×C3×C4×C5C4⋊C411yescharacteristic
68C2×C3×Dic5—41no—
69C2×C3×Dic5—41no—
70C2×C3×Dic5—41no—
71C2×C3×Dic5—41no—
72C2×C3×Dic5C22⋊C411yescharacteristic
73C2×C3×Dic5C4⋊C411yescharacteristic
74C3×C4×D5—22no—
75C3×C4×D5—22no—
76C3×C4×D5—41no—
77C3×C4×D5—41no—
78C3⋊#170—42no—
79C23×C3×C4—51no—
80C2×C3×C22⋊C4—101no—
81C2×#217—101no—
82C2×C4×Dic3—52no—
83C2×#208—101no—
84C3×#95—51no—
85C3×#95—101no—
86C3×#95AGL(1,𝔽5)11yescharacteristic, complemented
87C3⋊#95—101no—
88#830—52no—
89#830—101no—
90C23×D5#6711yescharacteristic
91C22×AGL(1,𝔽5)—62no—
92C22×C4×C5—21no—
93C22×C4×C5C2×Dic311yescharacteristic
94C22×Dic5—21no—
95C22×Dic5#6711yescharacteristic
96C2×C4×D5—42no—
97C2×C4×D5Dic611yescharacteristic
98C2×C4×D5C4×D311yescharacteristic
99C2×C4×D5C4×D311yescharacteristic
100C2×C4×D5D1211yescharacteristic
101C22⋊AGL(1,𝔽5)—62no—
102C22⋊AGL(1,𝔽5)—62no—
103C2×#170—62no—
104C4×AGL(1,𝔽5)—122no—
105#700—122no—
106#685—42no—
107#407—151no—
108#381—51no—
109C4×C22⋊C4—151no—
110C22×C3×C5—21no—
111C22×C3×C5—21no—
112C22×C3×C5#9511yescharacteristic
113C22×C3×C5#10411yescharacteristic
114C22×C3×C5#10411yescharacteristic
115C2×C3×D5—21no—
116C2×C3×D5—21no—
117C2×C3×D5—21no—
118C2×C3×D5—21no—
119C2×C3×D5—21no—
120C2×C3×D5—42no—
121C2×C3×D5—42no—
122C2×C3×D5#9912yes—
123ΓL(1,𝔽16)—44no—
124C3×C4×C5—21no—
125C3×C4×C5—21no—
126C3×C4×C5—81no—
127C3×Dic5—21no—
128C3×Dic5—21no—
129C3×Dic5—81no—
130C24×C3—51no—
131C22×C3×C4—21no—
132C22×C3×C4—51no—
133C22×C3×C4—51no—
134C22×C3×C4—51no—
135C22×C3×C4—51no—
136C22×C3×C4—51no—
137C22×C3×C4—101no—
138C22×C3×C4—202no—
139C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
140C22×Dic3—102no—
141C3×C22⋊C4—202no—
142#217—102no—
143#217—102no—
144C4×Dic3—202no—
145#208—202no—
146C2×C3⋊C8—102no—
147C23×C5#21711yescharacteristic
148C22×D5—21no—
149C22×D5—21no—
150C22×D5—22no—
151C22×D5—41no—
152C22×D5Dic3⋊C411yescharacteristic
153C22×D5(C2×D3)⋊C411yescharacteristic
154C2×AGL(1,𝔽5)—64no—
155C2×AGL(1,𝔽5)—122no—
156C2×AGL(1,𝔽5)—122no—
157C2×C4×C5—41no—
158C2×C4×C5—41no—
159C2×C4×C5—41no—
160C2×C4×C5—41no—
161C2×C4×C5C4×Dic311yescharacteristic
162C2×C4×C5C4⋊Dic311yescharacteristic
163C2×Dic5—41no—
164C2×Dic5—41no—
165C2×Dic5—41no—
166C2×Dic5—41no—
167C2×Dic5Dic3⋊C411yescharacteristic
168C2×Dic5(C2×D3)⋊C411yescharacteristic
169C4×D5—22no—
170C4×D5—22no—
171C4×D5—41no—
172C4×D5—41no—
173#170—122no—
174C23×C4—51no—
175C2×M16—301no—
176C2×C22⋊C4—101no—
177C2×C22⋊C4—301no—
178C2×C42—152no—
179C22⋊C8—152no—
180C22⋊C8—301no—
181#95—51no—
182#95—101no—
183#95—301no—
184#95ΓL(1,𝔽16)11yescharacteristic, complemented
185C2×C3×C5—21no—
186C2×C3×C5—21no—
187C2×C3×C5H(3,ℤ/4)11yescharacteristic
188C2×C3×C5#33911yescharacteristic
189C2×C3×C5#34211yescharacteristic
190C3×D5—22no—
191C3×D5—41no—
192C23×C3—51no—
193C23×C3—51no—
194C23×C3—102no—
195C23×C3—101no—
196C23×C3—101no—
197C23×C3—201no—
198C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
199C2×C3×C4—41no—
200C2×C3×C4—41no—
201C2×C3×C4—41no—
202C2×C3×C4—41no—
203C2×C3×C4—51no—
204C2×C3×C4—51no—
205C2×C3×C4—102no—
206C2×C3×C4—102no—
207C2×C3×C4—201no—
208C2×C3×C4—201no—
209C2×C3×C4—201no—
210C2×C3×C4—201no—
211C2×C3×C4—201no—
212C2×C3×C4—201no—
213C2×C3×C4C4×AGL(1,𝔽5)11yescharacteristic
214C2×C3×C4C4⋊AGL(1,𝔽5)11yescharacteristic
215C2×Dic3—104no—
216C2×Dic3—202no—
217C2×Dic3—202no—
218C3⋊C8—202no—
219C22×C5—21no—
220C22×C5—21no—
221C22×C5C3⋊#9511yescharacteristic
222C22×C5#83711yescharacteristic
223C22×C5#83711yescharacteristic
224C2×D5—21no—
225C2×D5—21no—
226C2×D5—21no—
227C2×D5—21no—
228C2×D5—21no—
229C2×D5—42no—
230C2×D5—42no—
231C2×D5#80612yes—
232AGL(1,𝔽5)—124no—
233C4×C5—21no—
234C4×C5—21no—
235C4×C5—81no—
236Dic5—21no—
237Dic5—21no—
238Dic5—81no—
239C24—51no—
240C22×C4—21no—
241C22×C4—51no—
242C22×C4—51no—
243C22×C4—51no—
244C22×C4—51no—
245C22×C4—51no—
246C22×C4—101no—
247C22×C4—202no—
248C22×C4—302no—
249C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
250M16—602no—
251C2×C8—302no—
252C22⋊C4—202no—
253C22⋊C4—302no—
254C22⋊C4—302no—
255C42—602no—
256C3×C5#128411yescharacteristic, complemented, Hall
257C22×C3—21no—
258C22×C3—21no—
259C22×C3—52no—
260C22×C3—101no—
261C22×C3—101no—
262C22×C3—101no—
263C22×C3—101no—
264C22×C3—101no—
265C22×C3—202no—
266C22×C3—202no—
267C22×C3(C2×AGL(1,𝔽5))⋊C411yescharacteristic
268C22×C3#400811yescharacteristic
269C22×C3#401011yescharacteristic
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—81no—
273C3×C4—101no—
274C3×C4—101no—
275C3×C4—401no—
276Dic3—204no—
277C2×C5—21no—
278C2×C5—21no—
279C2×C5#452711yescharacteristic
280C2×C5#453111yescharacteristic
281C2×C5#453211yescharacteristic
282D5—22no—
283D5—41no—
284C23—51no—
285C23—51no—
286C23—102no—
287C23—101no—
288C23—101no—
289C23—201no—
290C23#676311yescharacteristic
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—51no—
296C2×C4—51no—
297C2×C4—102no—
298C2×C4—102no—
299C2×C4—201no—
300C2×C4—201no—
301C2×C4—201no—
302C2×C4—201no—
303C2×C4—201no—
304C2×C4—201no—
305C2×C4—304no—
306C2×C4—602no—
307C2×C4—602no—
308C2×C4C4×ΓL(1,𝔽16)11yescharacteristic
309C2×C4C4⋊ΓL(1,𝔽16)11yescharacteristic
310C8—602no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—102no—
314C2×C3—201no—
315C2×C3#6486311yescharacteristic
316C2×C3#6486611yescharacteristic
317C2×C3#6487511yescharacteristic
318C5#6762811yescharacteristic, complemented, Sylow
319C22—21no—
320C22—21no—
321C22—52no—
322C22—101no—
323C22—101no—
324C22—101no—
325C22—101no—
326C22—101no—
327C22—202no—
328C22—202no—
329C22#9123511yescharacteristic
330C22#9123711yescharacteristic
331C22#9123911yescharacteristic
332C4—21no—
333C4—21no—
334C4—81no—
335C4—101no—
336C4—101no—
337C4—401no—
338C4—604no—
339C3#1059850311yescharacteristic, complemented, Sylow
340C2—21no—
341C2—21no—
342C2—102no—
343C2—201no—
344C2#1174673411yescharacteristic
345C2#1174673711yescharacteristic
346C2#1174674611yescharacteristic
subgroupG/H
centerC22#91235
commutatorC2×C3×C4×C5C42
FrattiniC22×C4C2×ΓL(1,𝔽16)
FittingC3×C5×#95C4
socleC22×C3×C5#95
prime radicalC23×C3×D5D4
cosocleC22×C3×C4×D5C22
hypercenter#95ΓL(1,𝔽16)
hypocenterC3×C5#1284
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
7. C2×C4×ΓL(1,𝔽16)C4semidirect
12. #91232C4semidirect
13. C3×C5×#95C4semidirect
15. C3×#3963C4semidirect
48. C5×#95Dic3semidirect
50. #3963Dic3semidirect
86. C3×#95AGL(1,𝔽5)semidirect
184. #95ΓL(1,𝔽16)semidirect
256. C3×C5#1284semidirect
318. C5#67628semidirect
339. C3#10598503semidirect

Maximal subgroups

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

subgroupindex
C4×#67632
#117524152
C3×#649532
#105985033
#676285