Finite Group Databasebeta

← #14302891

Subgroups — #14302891

Order 1920.

724 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 724 conjugacy classes of subgroups — too many to draw. Only its 117 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
1#11756987C211yesmaximal, characteristic, complemented
2C3×#66049C211yesmaximal, characteristic
3D5⋊#833C211yesmaximal, characteristic, complemented
4#11752428C212yesmaximal, complemented
5#11746734C212yesmaximal, complemented
6#10604615—31nomaximal, Hall
7C2×C3×#711C2211yescharacteristic
8C2×C3×D4×D5C2211yescharacteristic
9C2×#6763—22no—
10D4×ΓL(1,𝔽16)—24no—
11#91989C2212yes—
12D5⋊#208C2212yes—
13C3×C5×#127C411yescharacteristic, complemented
14C3×#4086C411yescharacteristic, complemented
15C3×#4085—22no—
16C3×#4083—22no—
17C3×#4082C411yescharacteristic, complemented
18C3×#4021C411yescharacteristic, complemented
19C3×#4018C2211yescharacteristic
20#91242—22no—
21#91237—24no—
22#71853—51nomaximal, Hall
23#66258—31no—
24#66049D311yescharacteristic
25D5⋊#100—31no—
26#65769—32no—
27#64863—32no—
28C23×C3×D5D412yes—
29C22×ΓL(1,𝔽16)—24no—
30C2×C3×C5×D4—22no—
31C2×C3×C5×D4C2×C411yescharacteristic
32C2×C3×C5×D4C2×C411yescharacteristic, complemented
33C2×C3×C22⋊D5—21no—
34C2×C3×C22⋊D5—22no—
35C2×C3×C22⋊D5D412yes—
36C22×C3×Dic5—21no—
37C3×#711—22no—
38C3×#711—22no—
39C3×D4×D5—22no—
40C3×D4×D5—22no—
41C2×C3×D20C2×C411yescharacteristic
42C2×C3×C4×D5C2311yescharacteristic
43C2×C3×Dic10C2×C411yescharacteristic, complemented
44#6763—24no—
45#6763—22no—
46#6762—22no—
47C4⋊ΓL(1,𝔽16)—22no—
48C4×ΓL(1,𝔽16)D414yescomplemented
49#6758—22no—
50D5⋊(C3⋊C8)—22no—
51C3×C42×C5C2×C411yescharacteristic, complemented
52C3×C22⋊Dic5—22no—
53C3×#685—22no—
54C3×#685—21no—
55C3×#683—21no—
56C3×C4×Dic5C2×C411yescharacteristic, complemented
57C3×#535—51no—
58#5798—51no—
59#5236—52no—
60C2×#833—51no—
61#4531—52no—
62C2×#711C2×D311yescharacteristic
63C2×D4×D5C2×D311yescharacteristic
64C2×C22⋊AGL(1,𝔽5)—62no—
65D4×AGL(1,𝔽5)—64no—
66#4130—32no—
67D5⋊M16—32no—
68C5×#127Dic311yescharacteristic, complemented
69#4086Dic311yescharacteristic, complemented
70#4085—22no—
71#4083—22no—
72#4082Dic311yescharacteristic, complemented
73#4021Dic311yescharacteristic, complemented
74#4018C2×D311yescharacteristic
75#4013—62no—
76#4008—64no—
77#1911—151noSylow
78C23×C3×C5—21no—
79C23×C3×C5C22⋊C412yes—
80C22×C3×D5—22no—
81C22×C3×D5—22no—
82C22×C3×D5—82no—
83C22×C3×D5C22⋊C412yes—
84C22×C3×D5C2×D411yescharacteristic
85C2×ΓL(1,𝔽16)—24no—
86C2×ΓL(1,𝔽16)—84no—
87C3×C5×D4—22no—
88C3×C5×D4—22no—
89C3×C5×D4—82no—
90C2×C3×C4×C5—21no—
91C2×C3×C4×C5C22×C411yescharacteristic
92C3×C22⋊D5—24no—
93C3×C22⋊D5—41no—
94C3×C22⋊D5—41no—
95C3×C22⋊D5—82no—
96C2×C3×Dic5—21no—
97C2×C3×Dic5—21no—
98C2×C3×Dic5—42no—
99C2×C3×Dic5C2×D411yescharacteristic
100C3×D20—22no—
101C3×C4×D5C2×D412yes—
102C3×C4×D5#4112yes—
103C3×Dic10—22no—
104C3⋊#170—42no—
105C2×C3×#41—51no—
106C22×C3×D4—51no—
107C3×#127—51no—
108C3×#127AGL(1,𝔽5)11yescharacteristic, complemented
109C3×#124—51no—
110C3×#124—51no—
111C3×#121—102no—
112C3×#120—102no—
113C3×#117—51no—
114C2×#217—102no—
115D4×Dic3—104no—
116#926—52no—
117C2×#208—52no—
118#837—104no—
119#833—102no—
120C23×D5#6712yes—
121C22×AGL(1,𝔽5)—64no—
122C2×C5×D4—22no—
123C2×C5×D4C2×Dic311yescharacteristic
124C2×C5×D4C2×Dic311yescharacteristic, complemented
125C2×C22⋊D5—21no—
126C2×C22⋊D5—22no—
127C2×C22⋊D5#6712yes—
128C22×Dic5—21no—
129#711—22no—
130#711—22no—
131D4×D5—22no—
132D4×D5—22no—
133C2×D20C2×Dic311yescharacteristic
134C2×C4×D5C22×D311yescharacteristic
135C2×Dic10C2×Dic311yescharacteristic, complemented
136C22⋊AGL(1,𝔽5)—64no—
137C22⋊AGL(1,𝔽5)—62no—
138#704—62no—
139C4⋊AGL(1,𝔽5)—62no—
140C4×AGL(1,𝔽5)—34no—
141#700—62no—
142D5⋊C8—62no—
143C42×C5C2×Dic311yescharacteristic, complemented
144C22⋊Dic5—22no—
145#685—22no—
146#685—21no—
147#683—21no—
148C4×Dic5C2×Dic311yescharacteristic, complemented
149#535—51no—
150#518—151no—
151#421—152no—
152C2×#100—151no—
153H(3,ℤ/4)—152no—
154C22×C3×C5—22no—
155C22×C3×C5—42no—
156C22×C3×C5—42no—
157C22×C3×C5—41no—
158C22×C3×C5C2×C22⋊C411yescharacteristic
159C2×C3×D5—22no—
160C2×C3×D5—41no—
161C2×C3×D5—44no—
162C2×C3×D5—42no—
163C2×C3×D5—82no—
164C2×C3×D5#12011yescharacteristic
165C2×C3×D5#12311yescharacteristic
166ΓL(1,𝔽16)—44no—
167C3×C4×C5—41no—
168C3×C4×C5C4×D412yes—
169C3×Dic5—41no—
170C3×Dic5—41no—
171C3×Dic5#12112yes—
172C24×C3—52no—
173C3×#41—102no—
174C3×#41—102no—
175C2×C3×Q8—51no—
176C2×C3×D4—22no—
177C2×C3×D4—52no—
178C2×C3×D4—51no—
179C2×C3×D4—102no—
180C2×C3×D4—102no—
181C2×C3×D4—101no—
182C2×C3×D4—102no—
183C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
184C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic, complemented
185C22×C3×C4—51no—
186C22×C3×C4—101no—
187C22×Dic3—104no—
188C3×C4⋊C4—101no—
189C3×C22⋊C4—101no—
190C3×C22⋊C4—102no—
191C3×C22⋊C4—102no—
192C3×C42—51no—
193C3×C42C2×AGL(1,𝔽5)11yescharacteristic, complemented
194#217—102no—
195#217—104no—
196C4⋊Dic3—102no—
197C4×Dic3—54no—
198#208—102no—
199#208—102no—
200C2×C3⋊C8—102no—
201C23×C5—21no—
202C23×C5#21712yes—
203C22×D5—22no—
204C22×D5—22no—
205C22×D5—82no—
206C22×D5#21712yes—
207C22×D5C2×#6711yescharacteristic
208C2×AGL(1,𝔽5)—64no—
209C2×AGL(1,𝔽5)—244no—
210C5×D4—22no—
211C5×D4—22no—
212C5×D4—82no—
213C2×C4×C5—21no—
214C2×C4×C5C22×Dic311yescharacteristic
215C22⋊D5—24no—
216C22⋊D5—41no—
217C22⋊D5—41no—
218C22⋊D5—82no—
219C2×Dic5—21no—
220C2×Dic5—21no—
221C2×Dic5—42no—
222C2×Dic5C2×#6711yescharacteristic
223D20—22no—
224C4×D5D3×D412yes—
225C4×D5#23712yes—
226Dic10—22no—
227#170—122no—
228C2×#41—51no—
229C22×D4—51no—
230C2×M16—152no—
231#127—51no—
232#127ΓL(1,𝔽16)11yescharacteristic, complemented
233#124—51no—
234#124—51no—
235#121—102no—
236#120—102no—
237C4×D4—304no—
238#117—51no—
239#117—152no—
240C2×C22⋊C4—302no—
241#104—304no—
242#100—302no—
243C2×C3×C5—21no—
244C2×C3×C5—42no—
245C2×C3×C5—81no—
246C2×C3×C5#38611yescharacteristic
247C3×D5—21no—
248C3×D5—21no—
249C3×D5—42no—
250C23×C3—21no—
251C23×C3—51no—
252C23×C3—52no—
253C23×C3—102no—
254C23×C3—102no—
255C23×C3—402no—
256C23×C3C22⋊AGL(1,𝔽5)12yes—
257C3×Q8—102no—
258C3×D4—22no—
259C3×D4—22no—
260C3×D4—82no—
261C3×D4—104no—
262C3×D4—102no—
263C3×D4—201no—
264C3×D4—201no—
265C3×D4—402no—
266C2×C3×C4—21no—
267C2×C3×C4—51no—
268C2×C3×C4—52no—
269C2×C3×C4—52no—
270C2×C3×C4—101no—
271C2×C3×C4—101no—
272C2×C3×C4—202no—
273C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
274C2×Dic3—104no—
275C2×Dic3—404no—
276C3⋊C8—202no—
277C22×C5—22no—
278C22×C5—42no—
279C22×C5—42no—
280C22×C5—41no—
281C22×C5C2×#21711yescharacteristic
282C2×D5—22no—
283C2×D5—41no—
284C2×D5—44no—
285C2×D5—42no—
286C2×D5—82no—
287C2×D5#93511yescharacteristic
288C2×D5#93711yescharacteristic
289AGL(1,𝔽5)—124no—
290C4×C5—41no—
291C4×C5D4×Dic312yes—
292Dic5—41no—
293Dic5—41no—
294Dic5#93912yes—
295C24—52no—
296#41—102no—
297#41—102no—
298C2×Q8—51no—
299C2×D4—22no—
300C2×D4—52no—
301C2×D4—51no—
302C2×D4—102no—
303C2×D4—102no—
304C2×D4—101no—
305C2×D4—102no—
306C2×D4C2×ΓL(1,𝔽16)11yescharacteristic
307C2×D4C2×ΓL(1,𝔽16)11yescharacteristic, complemented
308C22×C4—51no—
309C22×C4—101no—
310C22×C4—304no—
311M16—302no—
312M16—302no—
313C2×C8—302no—
314C4⋊C4—101no—
315C4⋊C4—302no—
316C22⋊C4—101no—
317C22⋊C4—102no—
318C22⋊C4—102no—
319C22⋊C4—302no—
320C22⋊C4—304no—
321C42—51no—
322C42—154no—
323C42C2×ΓL(1,𝔽16)11yescharacteristic, complemented
324C3×C5#191111yescharacteristic, complemented, Hall
325C22×C3—22no—
326C22×C3—42no—
327C22×C3—42no—
328C22×C3—41no—
329C22×C3—51no—
330C22×C3—51no—
331C22×C3—102no—
332C22×C3—201no—
333C22×C3—202no—
334C22×C3—204no—
335C22×C3—402no—
336C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
337C3×C4—41no—
338C3×C4—52no—
339C3×C4—201no—
340C3×C4—201no—
341C3×C4D4×AGL(1,𝔽5)12yes—
342Dic3—204no—
343C2×C5—21no—
344C2×C5—42no—
345C2×C5—81no—
346C2×C5#522011yescharacteristic
347D5—21no—
348D5—21no—
349D5—42no—
350C23—21no—
351C23—51no—
352C23—52no—
353C23—102no—
354C23—102no—
355C23—402no—
356C23#676312yes—
357Q8—102no—
358D4—22no—
359D4—22no—
360D4—82no—
361D4—104no—
362D4—102no—
363D4—201no—
364D4—201no—
365D4—402no—
366C2×C4—21no—
367C2×C4—51no—
368C2×C4—52no—
369C2×C4—52no—
370C2×C4—101no—
371C2×C4—101no—
372C2×C4—202no—
373C2×C4—304no—
374C2×C4—1204no—
375C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
376C8—602no—
377C2×C3—21no—
378C2×C3—42no—
379C2×C3—81no—
380C2×C3—101no—
381C2×C3—101no—
382C2×C3—202no—
383C2×C3#6577911yescharacteristic
384C5#7185311yescharacteristic, complemented, Sylow
385C22—22no—
386C22—42no—
387C22—42no—
388C22—41no—
389C22—51no—
390C22—51no—
391C22—102no—
392C22—201no—
393C22—202no—
394C22—204no—
395C22—402no—
396C22C2×#676311yescharacteristic
397C4—41no—
398C4—52no—
399C4—201no—
400C4—201no—
401C4—604no—
402C4D4×ΓL(1,𝔽16)12yes—
403C3#1060461511yescharacteristic, complemented, Sylow
404C2—21no—
405C2—42no—
406C2—81no—
407C2—101no—
408C2—101no—
409C2—202no—
410C2#1175243811yescharacteristic
subgroupG/H
centerC2#11752438
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC3×C5×#127C4
socleC2×C3×C5#386
prime radicalC3×#66049C2
cosocleC2×C3×C4×D5C23
hypercenter#127ΓL(1,𝔽16)
hypocenterC3×C5#1911
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #11756987C2semidirect
3. D5⋊#833C2semidirect
4. #11752428C2semidirect
5. #11746734C2semidirect
13. C3×C5×#127C4semidirect
14. C3×#4086C4semidirect
17. C3×#4082C4semidirect
18. C3×#4021C4semidirect
32. C2×C3×C5×D4C2×C4semidirect
43. C2×C3×Dic10C2×C4semidirect
48. C4×ΓL(1,𝔽16)D4semidirect
51. C3×C42×C5C2×C4semidirect
56. C3×C4×Dic5C2×C4semidirect
68. C5×#127Dic3semidirect
69. #4086Dic3semidirect
72. #4082Dic3semidirect
73. #4021Dic3semidirect
108. C3×#127AGL(1,𝔽5)semidirect
124. C2×C5×D4C2×Dic3semidirect
135. C2×Dic10C2×Dic3semidirect
143. C42×C5C2×Dic3semidirect
148. C4×Dic5C2×Dic3semidirect
184. C2×C3×D4C2×AGL(1,𝔽5)semidirect
193. C3×C42C2×AGL(1,𝔽5)semidirect
232. #127ΓL(1,𝔽16)semidirect
307. C2×D4C2×ΓL(1,𝔽16)semidirect
323. C42C2×ΓL(1,𝔽16)semidirect
324. C3×C5#1911semidirect
384. C5#71853semidirect
403. C3#10604615semidirect

Maximal subgroups

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

subgroupindex
#117569872
C3×#660492
D5⋊#8332
#117524282
#117467342
#106046153
#718535