Finite Group Databasebeta

← #14278081

Subgroups — #14278081

Order 1920.

444 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 57 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
1C3×#65512C211yesmaximal, characteristic
2#11746788C211yesmaximal, characteristic, complemented
3#11746786C211yesmaximal, characteristic, complemented
4#10598825—31nomaximal, Hall
5C22×C3×C5×D4C411yescharacteristic, complemented
6C22×C3×C22⋊D5—21no—
7C2×#6763—21no—
8C2×C3×C22⋊Dic5—21no—
9C2×C3×#685C2211yescharacteristic
10#91241—21no—
11C3×#3963C411yescharacteristic, complemented
12#67645—51nomaximal, Hall
13#65512D311yescharacteristic
14#64917—31no—
15#64915—31no—
16C24×C3×C5—21no—
17C23×C3×D5D411yescharacteristic
18C22×ΓL(1,𝔽16)—41no—
19C2×C3×C5×D4—41no—
20C2×C3×C5×D4—42no—
21C22×C3×C4×C5C2×C411yescharacteristic
22C2×C3×C22⋊D5—42no—
23C2×C3×C22⋊D5—42no—
24C2×C3×C22⋊D5—41no—
25C2×C3×C22⋊D5—41no—
26C22×C3×Dic5—21no—
27C22×C3×Dic5D411yescharacteristic
28#6763—22no—
29#6763—41no—
30C2×C3⋊#170—41no—
31C3×C22⋊Dic5—42no—
32C3×#685—41no—
33C3×#392—51no—
34#4526—51no—
35#4525—51no—
36C22×C5×D4Dic311yescharacteristic, complemented
37C22×C22⋊D5—21no—
38C2×C22⋊AGL(1,𝔽5)—61no—
39C2×C22⋊Dic5—21no—
40C2×#685C2×D311yescharacteristic
41C22⋊#170—61no—
42#3963Dic311yescharacteristic, complemented
43#1343—151noSylow
44C23×C3×C5—22no—
45C23×C3×C5—41no—
46C23×C3×C5—41no—
47C23×C3×C5—41no—
48C23×C3×C5—41no—
49C23×C3×C5—41no—
50C23×C3×C5—41no—
51C23×C3×C5C22⋊C411yescharacteristic
52C22×C3×D5—21no—
53C22×C3×D5—21no—
54C22×C3×D5—41no—
55C22×C3×D5—41no—
56C22×C3×D5D811yescharacteristic
57C22×C3×D5SD1611yescharacteristic
58C2×ΓL(1,𝔽16)—42no—
59C2×ΓL(1,𝔽16)—81no—
60C2×ΓL(1,𝔽16)—81no—
61C3×C5×D4—42no—
62C3×C5×D4—42no—
63C2×C3×C4×C5—21no—
64C2×C3×C4×C5—41no—
65C3×C22⋊D5—44no—
66C3×C22⋊D5—44no—
67C2×C3×Dic5—22no—
68C2×C3×Dic5—21no—
69C2×C3×Dic5—41no—
70C2×C3×Dic5—41no—
71C2×C3×Dic5—41no—
72C3⋊#170—81no—
73C22×C3×D4—101no—
74C22×C3×D4AGL(1,𝔽5)11yescharacteristic, complemented
75C2×C3×C22⋊C4—51no—
76C2×C3×C22⋊C4—101no—
77C2×#217—101no—
78C3×#95—51no—
79#830—101no—
80C24×C5—21no—
81C23×D5#6711yescharacteristic
82C22×AGL(1,𝔽5)—121no—
83C2×C5×D4—41no—
84C2×C5×D4—42no—
85C22×C4×C5C2×Dic311yescharacteristic
86C2×C22⋊D5—42no—
87C2×C22⋊D5—42no—
88C2×C22⋊D5—41no—
89C2×C22⋊D5—41no—
90C22×Dic5—21no—
91C22×Dic5#6711yescharacteristic
92C22⋊AGL(1,𝔽5)—62no—
93C22⋊AGL(1,𝔽5)—121no—
94C2×#170—121no—
95C22⋊Dic5—42no—
96#685—41no—
97#392—51no—
98#342—151no—
99#323—151no—
100C22×C3×C5—21no—
101C22×C3×C5—21no—
102C22×C3×C5—42no—
103C22×C3×C5—42no—
104C22×C3×C5—42no—
105C22×C3×C5—81no—
106C22×C3×C5—81no—
107C22×C3×C5—81no—
108C22×C3×C5—81no—
109C22×C3×C5#9911yescharacteristic
110C22×C3×C5#10211yescharacteristic
111C22×C3×C5#10411yescharacteristic
112C2×C3×D5—21no—
113C2×C3×D5—21no—
114C2×C3×D5—41no—
115C2×C3×D5—41no—
116C2×C3×D5—41no—
117C2×C3×D5—41no—
118C2×C3×D5—81no—
119ΓL(1,𝔽16)—82no—
120C3×C4×C5—41no—
121C3×Dic5—42no—
122C3×Dic5—41no—
123C24×C3—21no—
124C24×C3—51no—
125C2×C3×D4—41no—
126C2×C3×D4—42no—
127C2×C3×D4—202no—
128C2×C3×D4—202no—
129C2×C3×D4—201no—
130C2×C3×D4—201no—
131C22×C3×C4—51no—
132C22×C3×C4—101no—
133C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
134C22×Dic3—201no—
135C3×C22⋊C4—201no—
136C3×C22⋊C4—202no—
137#217—102no—
138#217—201no—
139C2×C3⋊C8—201no—
140C23×C5—22no—
141C23×C5—41no—
142C23×C5—41no—
143C23×C5—41no—
144C23×C5—41no—
145C23×C5—41no—
146C23×C5—41no—
147C23×C5#21711yescharacteristic
148C22×D5—21no—
149C22×D5—21no—
150C22×D5—41no—
151C22×D5—41no—
152C22×D5#21311yescharacteristic
153C22×D5#21411yescharacteristic
154C2×AGL(1,𝔽5)—122no—
155C2×AGL(1,𝔽5)—241no—
156C2×AGL(1,𝔽5)—241no—
157C5×D4—42no—
158C5×D4—42no—
159C2×C4×C5—21no—
160C2×C4×C5—41no—
161C22⋊D5—44no—
162C22⋊D5—44no—
163C2×Dic5—22no—
164C2×Dic5—21no—
165C2×Dic5—41no—
166C2×Dic5—41no—
167C2×Dic5—41no—
168#170—241no—
169C22×D4—101no—
170C22×D4ΓL(1,𝔽16)11yescharacteristic, complemented
171C2×C22⋊C4—51no—
172C2×C22⋊C4—101no—
173C2×C22⋊C4—301no—
174C22⋊C8—301no—
175#95—51no—
176C2×C3×C5—21no—
177C2×C3×C5—21no—
178C2×C3×C5—82no—
179C2×C3×C5#32711yescharacteristic
180C2×C3×C5AΣL(1,𝔽16)11yescharacteristic
181C2×C3×C5#35311yescharacteristic
182C3×D5—41no—
183C3×D5—41no—
184C23×C3—22no—
185C23×C3—41no—
186C23×C3—41no—
187C23×C3—41no—
188C23×C3—41no—
189C23×C3—41no—
190C23×C3—41no—
191C23×C3—51no—
192C23×C3—51no—
193C23×C3—101no—
194C23×C3—101no—
195C23×C3—201no—
196C23×C3—201no—
197C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
198C3×D4—42no—
199C3×D4—42no—
200C3×D4—204no—
201C3×D4—204no—
202C2×C3×C4—21no—
203C2×C3×C4—41no—
204C2×C3×C4—102no—
205C2×C3×C4—101no—
206C2×C3×C4—201no—
207C2×C3×C4—201no—
208C2×C3×C4—201no—
209C2×Dic3—202no—
210C2×Dic3—401no—
211C2×Dic3—401no—
212C3⋊C8—401no—
213C22×C5—21no—
214C22×C5—21no—
215C22×C5—42no—
216C22×C5—42no—
217C22×C5—42no—
218C22×C5—81no—
219C22×C5—81no—
220C22×C5—81no—
221C22×C5—81no—
222C22×C5#83211yescharacteristic
223C22×C5#83411yescharacteristic
224C22×C5#83711yescharacteristic
225C2×D5—21no—
226C2×D5—21no—
227C2×D5—41no—
228C2×D5—41no—
229C2×D5—41no—
230C2×D5—41no—
231C2×D5—81no—
232AGL(1,𝔽5)—242no—
233C4×C5—41no—
234Dic5—42no—
235Dic5—41no—
236C24—21no—
237C24—51no—
238C2×D4—41no—
239C2×D4—42no—
240C2×D4—202no—
241C2×D4—202no—
242C2×D4—201no—
243C2×D4—201no—
244C22×C4—51no—
245C22×C4—101no—
246C22×C4—601no—
247C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
248C2×C8—601no—
249C22⋊C4—201no—
250C22⋊C4—202no—
251C22⋊C4—302no—
252C22⋊C4—601no—
253C3×C5#134311yescharacteristic, complemented, Hall
254C22×C3—21no—
255C22×C3—21no—
256C22×C3—42no—
257C22×C3—42no—
258C22×C3—42no—
259C22×C3—81no—
260C22×C3—81no—
261C22×C3—81no—
262C22×C3—81no—
263C22×C3—101no—
264C22×C3—101no—
265C22×C3—201no—
266C22×C3—201no—
267C22×C3—201no—
268C22×C3—201no—
269C22×C3—401no—
270C22×C3#400711yescharacteristic
271C22×C3#400811yescharacteristic
272C22×C3#401111yescharacteristic
273C3×C4—41no—
274C3×C4—202no—
275C3×C4—201no—
276Dic3—402no—
277C2×C5—21no—
278C2×C5—21no—
279C2×C5—82no—
280C2×C5#453611yescharacteristic
281C2×C5#453711yescharacteristic
282C2×C5#454511yescharacteristic
283D5—41no—
284D5—41no—
285C23—22no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23—51no—
293C23—51no—
294C23—101no—
295C23—101no—
296C23—201no—
297C23—201no—
298C23#676311yescharacteristic
299D4—42no—
300D4—42no—
301D4—204no—
302D4—204no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—102no—
306C2×C4—101no—
307C2×C4—201no—
308C2×C4—201no—
309C2×C4—201no—
310C2×C4—602no—
311C2×C4—1201no—
312C2×C4—1201no—
313C8—1201no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—82no—
317C2×C3—201no—
318C2×C3—201no—
319C2×C3#6492011yescharacteristic
320C2×C3#6492211yescharacteristic
321C2×C3#6493411yescharacteristic
322C5#6764511yescharacteristic, complemented, Sylow
323C22—21no—
324C22—21no—
325C22—42no—
326C22—42no—
327C22—42no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—81no—
332C22—101no—
333C22—101no—
334C22—201no—
335C22—201no—
336C22—201no—
337C22—201no—
338C22—401no—
339C22#9123611yescharacteristic
340C22#9123711yescharacteristic
341C22#9124011yescharacteristic
342C4—41no—
343C4—202no—
344C4—201no—
345C4—1202no—
346C3#1059882511yescharacteristic, complemented, Sylow
347C2—21no—
348C2—21no—
349C2—82no—
350C2—201no—
351C2—201no—
352C2#1174679111yescharacteristic
353C2#1174679311yescharacteristic
354C2#1174680511yescharacteristic
subgroupG/H
centerC22#91240
commutatorC22×C3×C4×C5C2×C4
FrattiniC22×C4C2×ΓL(1,𝔽16)
FittingC22×C3×C5×D4C4
socleC22×C3×C5#99
prime radicalC3×#65512C2
cosocleC2×C3×#685C22
hypercenterC22×D4ΓL(1,𝔽16)
hypocenterC3×C5#1343
LCSG ▷ C22×C3×C4×C5 ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #11746788C2semidirect
3. #11746786C2semidirect
5. C22×C3×C5×D4C4semidirect
11. C3×#3963C4semidirect
36. C22×C5×D4Dic3semidirect
42. #3963Dic3semidirect
74. C22×C3×D4AGL(1,𝔽5)semidirect
170. C22×D4ΓL(1,𝔽16)semidirect
253. C3×C5#1343semidirect
322. C5#67645semidirect
346. C3#10598825semidirect

Maximal subgroups

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

subgroupindex
C3×#655122
#117467882
#117467862
#105988253
#676455