Finite Group Databasebeta

← #14279054

Subgroups — #14279054

Order 1920.

468 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 81 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×#91242C211yesmaximal, characteristic
2C2×#91240C211yesmaximal, characteristic
3C3×#65502C211yesmaximal, characteristic
4#10598822—31nomaximal, Hall
5C23×C3×C4×C5C411yescharacteristic, complemented
6C22×C3×C22⋊D5C2211yescharacteristic
7C2×#6763—21no—
8C2×#6762—21no—
9C2×C3×C22⋊Dic5C411yescharacteristic, complemented
10C2×C3×#685—21no—
11#91242—21no—
12#91242C412yescomplemented
13#91240—21no—
14#91240C412yescomplemented
15C3×#3963—21no—
16#67637—51nomaximal, Hall
17C2×#4013—31no—
18C2×#4011—31no—
19#65502D311yescharacteristic
20C24×C3×C5C2×C411yescharacteristic
21C23×C3×D5D411yescharacteristic
22C22×ΓL(1,𝔽16)—41no—
23C22×C3×C4×C5—21no—
24C22×C3×C4×C5—42no—
25C22×C3×C4×C5—41no—
26C2×C3×C22⋊D5—41no—
27C2×C3×C22⋊D5—41no—
28C2×C3×C22⋊D5C2×C411yescharacteristic
29C2×C3×C22⋊D5C2×C411yescharacteristic
30C2×C3×C22⋊D5D411yescharacteristic
31C2×C3×C22⋊D5Q811yescharacteristic
32C22×C3×Dic5—21no—
33C22×C3×Dic5D411yescharacteristic
34#6763—22no—
35#6763—41no—
36#6762—22no—
37#6762—41no—
38C2×C3⋊#170—41no—
39C3×C22⋊Dic5—41no—
40C3×#685—42no—
41C3×#386—51no—
42C2×#834—51no—
43C2×#833—51no—
44C23×C4×C5Dic311yescharacteristic, complemented
45C22×C22⋊D5C2×D311yescharacteristic
46C2×C22⋊AGL(1,𝔽5)—61no—
47C2×#704—61no—
48C2×C22⋊Dic5Dic311yescharacteristic, complemented
49C2×#685—21no—
50#4013—32no—
51#4013—61no—
52#4011—32no—
53#4011—61no—
54#3963—21no—
55#1390—151noSylow
56C23×C3×C5—21no—
57C23×C3×C5—21no—
58C23×C3×C5—41no—
59C23×C3×C5—41no—
60C23×C3×C5C4211yescharacteristic
61C23×C3×C5C22⋊C411yescharacteristic
62C23×C3×C5C4⋊C411yescharacteristic
63C22×C3×D5—21no—
64C22×C3×D5—21no—
65C22×C3×D5—41no—
66C22×C3×D5—41no—
67C22×C3×D5C22⋊C411yescharacteristic
68C22×C3×D5C4⋊C411yescharacteristic
69C2×ΓL(1,𝔽16)—42no—
70C2×ΓL(1,𝔽16)—81no—
71C2×ΓL(1,𝔽16)—81no—
72C2×C3×C4×C5—22no—
73C2×C3×C4×C5—41no—
74C2×C3×C4×C5—42no—
75C2×C3×C4×C5—41no—
76C2×C3×C4×C5—42no—
77C3×C22⋊D5—41no—
78C3×C22⋊D5—41no—
79C3×C22⋊D5—41no—
80C3×C22⋊D5—41no—
81C2×C3×Dic5—21no—
82C2×C3×Dic5—21no—
83C2×C3×Dic5—41no—
84C2×C3×Dic5—41no—
85C2×C3×Dic5—41no—
86C2×C3×Dic5C22⋊C411yescharacteristic
87C2×C3×Dic5C4⋊C411yescharacteristic
88C3⋊#170—42no—
89C22×C3×D4—51no—
90C23×C3×C4AGL(1,𝔽5)11yescharacteristic, complemented
91C2×C3×C22⋊C4—51no—
92C2×C3×C22⋊C4—101no—
93C2×#217—101no—
94C2×#208—101no—
95C3×#95—101no—
96#834—52no—
97#834—101no—
98#833—52no—
99#833—101no—
100C24×C5C2×Dic311yescharacteristic
101C23×D5#6711yescharacteristic
102C22×AGL(1,𝔽5)—121no—
103C22×C4×C5—21no—
104C22×C4×C5—42no—
105C22×C4×C5—41no—
106C2×C22⋊D5—41no—
107C2×C22⋊D5—41no—
108C2×C22⋊D5Dic611yescharacteristic
109C2×C22⋊D5C4×D311yescharacteristic
110C2×C22⋊D5C4×D311yescharacteristic
111C2×C22⋊D5D1211yescharacteristic
112C22×Dic5—21no—
113C22×Dic5#6711yescharacteristic
114C22⋊AGL(1,𝔽5)—62no—
115C22⋊AGL(1,𝔽5)—121no—
116#704—62no—
117#704—121no—
118C2×#170—121no—
119C22⋊Dic5—41no—
120#685—42no—
121C2×#100—151no—
122C2×#99—151no—
123#386—51no—
124C22×C3×C5—21no—
125C22×C3×C5—21no—
126C22×C3×C5—21no—
127C22×C3×C5—21no—
128C22×C3×C5—41no—
129C22×C3×C5—41no—
130C22×C3×C5—42no—
131C22×C3×C5—41no—
132C22×C3×C5—41no—
133C22×C3×C5#9511yescharacteristic
134C22×C3×C5#9911yescharacteristic
135C22×C3×C5#9911yescharacteristic
136C2×C3×D5—21no—
137C2×C3×D5—21no—
138C2×C3×D5—41no—
139C2×C3×D5—41no—
140C2×C3×D5—41no—
141C2×C3×D5—41no—
142C2×C3×D5—81no—
143ΓL(1,𝔽16)—82no—
144C3×C4×C5—42no—
145C3×Dic5—21no—
146C3×Dic5—21no—
147C3×Dic5—81no—
148C24×C3—51no—
149C24×C3C2×AGL(1,𝔽5)11yescharacteristic
150C2×C3×D4—51no—
151C2×C3×D4—51no—
152C2×C3×D4—51no—
153C2×C3×D4—51no—
154C2×C3×D4—201no—
155C2×C3×D4—201no—
156C22×C3×C4—21no—
157C22×C3×C4—42no—
158C22×C3×C4—41no—
159C22×C3×C4—51no—
160C22×C3×C4—101no—
161C22×Dic3—201no—
162C3×C22⋊C4—202no—
163C3×C22⋊C4—201no—
164#217—102no—
165#217—201no—
166#208—102no—
167#208—201no—
168C2×C3⋊C8—201no—
169C23×C5—21no—
170C23×C5—21no—
171C23×C5—41no—
172C23×C5—41no—
173C23×C5C4×Dic311yescharacteristic
174C23×C5C4⋊Dic311yescharacteristic
175C23×C5#21711yescharacteristic
176C22×D5—21no—
177C22×D5—21no—
178C22×D5—41no—
179C22×D5—41no—
180C22×D5Dic3⋊C411yescharacteristic
181C22×D5(C2×D3)⋊C411yescharacteristic
182C2×AGL(1,𝔽5)—122no—
183C2×AGL(1,𝔽5)—241no—
184C2×AGL(1,𝔽5)—241no—
185C2×C4×C5—22no—
186C2×C4×C5—41no—
187C2×C4×C5—42no—
188C2×C4×C5—41no—
189C2×C4×C5—42no—
190C22⋊D5—41no—
191C22⋊D5—41no—
192C22⋊D5—41no—
193C22⋊D5—41no—
194C2×Dic5—21no—
195C2×Dic5—21no—
196C2×Dic5—41no—
197C2×Dic5—41no—
198C2×Dic5—41no—
199C2×Dic5Dic3⋊C411yescharacteristic
200C2×Dic5(C2×D3)⋊C411yescharacteristic
201#170—122no—
202C22×D4—51no—
203C23×C4ΓL(1,𝔽16)11yescharacteristic, complemented
204C2×M16—301no—
205C2×C22⋊C4—51no—
206C2×C22⋊C4—101no—
207C2×C22⋊C4—301no—
208#100—152no—
209#100—301no—
210#99—152no—
211#99—301no—
212#95—101no—
213C2×C3×C5—21no—
214C2×C3×C5—21no—
215C2×C3×C5—41no—
216C2×C3×C5—41no—
217C2×C3×C5#34211yescharacteristic
218C2×C3×C5AΣL(1,𝔽16)11yescharacteristic
219C2×C3×C5#35211yescharacteristic
220C3×D5—41no—
221C3×D5—41no—
222C23×C3—21no—
223C23×C3—21no—
224C23×C3—41no—
225C23×C3—41no—
226C23×C3—51no—
227C23×C3—51no—
228C23×C3—101no—
229C23×C3—101no—
230C23×C3—201no—
231C23×C3—201no—
232C23×C3C4×AGL(1,𝔽5)11yescharacteristic
233C23×C3C4⋊AGL(1,𝔽5)11yescharacteristic
234C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
235C3×D4—201no—
236C3×D4—201no—
237C3×D4—201no—
238C3×D4—201no—
239C2×C3×C4—22no—
240C2×C3×C4—41no—
241C2×C3×C4—42no—
242C2×C3×C4—41no—
243C2×C3×C4—42no—
244C2×C3×C4—51no—
245C2×C3×C4—51no—
246C2×C3×C4—101no—
247C2×C3×C4—101no—
248C2×C3×C4—201no—
249C2×C3×C4—201no—
250C2×C3×C4—201no—
251C2×Dic3—202no—
252C2×Dic3—401no—
253C2×Dic3—401no—
254C3⋊C8—202no—
255C22×C5—21no—
256C22×C5—21no—
257C22×C5—21no—
258C22×C5—21no—
259C22×C5—41no—
260C22×C5—41no—
261C22×C5—42no—
262C22×C5—41no—
263C22×C5—41no—
264C22×C5C3⋊#9511yescharacteristic
265C22×C5#83411yescharacteristic
266C22×C5#83411yescharacteristic
267C2×D5—21no—
268C2×D5—21no—
269C2×D5—41no—
270C2×D5—41no—
271C2×D5—41no—
272C2×D5—41no—
273C2×D5—81no—
274AGL(1,𝔽5)—242no—
275C4×C5—42no—
276Dic5—21no—
277Dic5—21no—
278Dic5—81no—
279C24—51no—
280C24C2×ΓL(1,𝔽16)11yescharacteristic
281C2×D4—51no—
282C2×D4—51no—
283C2×D4—51no—
284C2×D4—51no—
285C2×D4—201no—
286C2×D4—201no—
287C22×C4—21no—
288C22×C4—42no—
289C22×C4—41no—
290C22×C4—51no—
291C22×C4—101no—
292C22×C4—601no—
293M16—302no—
294M16—601no—
295C2×C8—601no—
296C22⋊C4—202no—
297C22⋊C4—201no—
298C22⋊C4—302no—
299C22⋊C4—601no—
300C3×C5#139011yescharacteristic, complemented, Hall
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—21no—
305C22×C3—41no—
306C22×C3—41no—
307C22×C3—42no—
308C22×C3—41no—
309C22×C3—41no—
310C22×C3—101no—
311C22×C3—101no—
312C22×C3—201no—
313C22×C3—201no—
314C22×C3—201no—
315C22×C3—201no—
316C22×C3—401no—
317C22×C3#399911yescharacteristic
318C22×C3(C2×AGL(1,𝔽5))⋊C411yescharacteristic
319C22×C3#401111yescharacteristic
320C3×C4—42no—
321C3×C4—101no—
322C3×C4—101no—
323C3×C4—401no—
324Dic3—402no—
325C2×C5—21no—
326C2×C5—21no—
327C2×C5—41no—
328C2×C5—41no—
329C2×C5#452611yescharacteristic
330C2×C5#453611yescharacteristic
331C2×C5#453911yescharacteristic
332D5—41no—
333D5—41no—
334C23—21no—
335C23—21no—
336C23—41no—
337C23—41no—
338C23—51no—
339C23—51no—
340C23—101no—
341C23—101no—
342C23—201no—
343C23—201no—
344C23C4×ΓL(1,𝔽16)11yescharacteristic
345C23C4⋊ΓL(1,𝔽16)11yescharacteristic
346C23#676311yescharacteristic
347D4—201no—
348D4—201no—
349D4—201no—
350D4—201no—
351C2×C4—22no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—51no—
357C2×C4—51no—
358C2×C4—101no—
359C2×C4—101no—
360C2×C4—201no—
361C2×C4—201no—
362C2×C4—201no—
363C2×C4—602no—
364C2×C4—1201no—
365C2×C4—1201no—
366C8—602no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—41no—
370C2×C3—41no—
371C2×C3—201no—
372C2×C3—201no—
373C2×C3#6491611yescharacteristic
374C2×C3#6491711yescharacteristic
375C2×C3#6493411yescharacteristic
376C5#6763711yescharacteristic, complemented, Sylow
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—41no—
382C22—41no—
383C22—42no—
384C22—41no—
385C22—41no—
386C22—101no—
387C22—101no—
388C22—201no—
389C22—201no—
390C22—201no—
391C22—201no—
392C22—401no—
393C22#9122811yescharacteristic
394C22#9123511yescharacteristic
395C22#9124011yescharacteristic
396C4—42no—
397C4—101no—
398C4—101no—
399C4—401no—
400C4—1202no—
401C3#1059882211yescharacteristic, complemented, Sylow
402C2—21no—
403C2—21no—
404C2—41no—
405C2—41no—
406C2—201no—
407C2—201no—
408C2#1174678711yescharacteristic
409C2#1174678811yescharacteristic
410C2#1174680511yescharacteristic
subgroupG/H
centerC22#91240
commutatorC23×C3×C5C42
FrattiniC24C2×ΓL(1,𝔽16)
FittingC23×C3×C4×C5C4
socleC22×C3×C5#99
prime radical, cosocleC22×C3×C22⋊D5C22
hypercenterC23×C4ΓL(1,𝔽16)
hypocenterC3×C5#1390
LCSG ▷ C23×C3×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
5. C23×C3×C4×C5C4semidirect
9. C2×C3×C22⋊Dic5C4semidirect
12. #91242C4semidirect
14. #91240C4semidirect
44. C23×C4×C5Dic3semidirect
48. C2×C22⋊Dic5Dic3semidirect
90. C23×C3×C4AGL(1,𝔽5)semidirect
203. C23×C4ΓL(1,𝔽16)semidirect
300. C3×C5#1390semidirect
376. C5#67637semidirect
401. C3#10598822semidirect

Maximal subgroups

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

subgroupindex
C2×#912422
C2×#912402
C3×#655022
#105988223
#676375