Finite Group Databasebeta

← #14302918

Subgroups — #14302918

Order 1920.

724 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 724 conjugacy classes of subgroups — too many to draw. Only its 106 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
2#11754935C211yesmaximal, characteristic
3C3×D5⋊#100C211yesmaximal, characteristic, complemented
4#11751718C212yesmaximal, complemented
5#11746520C212yesmaximal, complemented
6#10604615—31nomaximal, Hall
7C2×C3×D4×D5C2211yescharacteristic
8C2×#6772C2211yescharacteristic
9C2×#6763—22no—
10D4×ΓL(1,𝔽16)—24no—
11#91989C2212yes—
12C3×D5⋊M16C2212yes—
13#91825C411yescharacteristic, complemented
14C5×#940C411yescharacteristic, complemented
15#91565—22no—
16#91563—22no—
17#91463C411yescharacteristic, complemented
18#91364C411yescharacteristic, complemented
19#91357C2211yescharacteristic
20C3×#4013—22no—
21#91155—24no—
22#70071—51nomaximal, Hall
23#66258—31no—
24#66049—31no—
25D5⋊#100D311yescharacteristic, complemented
26#65769—32no—
27#64863—32no—
28C23×C3×D5D412yes—
29C22×ΓL(1,𝔽16)—24no—
30C2×C3×C5×D4C2×C411yescharacteristic
31C2×Dic30C2×C411yescharacteristic, complemented
32C2×C5×#67—22no—
33C2×C5×D12C2×C411yescharacteristic, complemented
34C2×C3×C22⋊D5D412yes—
35C3×D4×D5—22no—
36C3×D4×D5—22no—
37C2×C3×D20C2×C411yescharacteristic
38C2×C3×C4×D5C2311yescharacteristic
39C2×#1201—21no—
40C2×#1201—22no—
41C2×D3×Dic5—21no—
42#6772—22no—
43#6772—22no—
44#6763—24no—
45#6763—22no—
46C4⋊ΓL(1,𝔽16)—22no—
47C4×ΓL(1,𝔽16)D414yescomplemented
48C3×#704—22no—
49C3×#700—22no—
50C3×D5⋊C8—22no—
51#6719—22no—
52C4×Dic15C2×C411yescharacteristic, complemented
53C4×C5×Dic3C2×C411yescharacteristic, complemented
54#6668—21no—
55#6665—22no—
56#6665—21no—
57#5805—51no—
58#5798—51no—
59C2×C3×#100—51no—
60#5139—52no—
61#4557—52no—
62C2×#711—31no—
63C2×D4×D5C2×D311yescharacteristic
64C2×C22⋊AGL(1,𝔽5)—62no—
65D4×AGL(1,𝔽5)—64no—
66#4130—32no—
67D5⋊M16C2×D312yes—
68C5×#127—31no—
69#4086—31no—
70#4085—62no—
71#4083—62no—
72#4082—31no—
73#4021—31no—
74#4018—31no—
75#4013—22no—
76#4008—64no—
77#1911—151noSylow
78C23×C3×C5C22⋊C412yes—
79C22×C5×D3—21no—
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—
88C2×C3×C4×C5C22×C411yescharacteristic
89C2×Dic15—21no—
90C2×Dic15—21no—
91Dic30—22no—
92C5×#67—82no—
93C2×C5×Dic3—21no—
94C5×D12—22no—
95C3×C22⋊D5—24no—
96C2×C3×Dic5C2×D411yescharacteristic
97C3×D20—22no—
98C3×C4×D5C2×D412yes—
99C3×C4×D5#4112yes—
100#1201—41no—
101#1201—41no—
102#1201—82no—
103D3×Dic5—42no—
104C3×#170—42no—
105C22×C3×D4—51no—
106C2×#235—51no—
107C2×C3×M16—52no—
108#953—102no—
109C2×#217—102no—
110#940—51no—
111#940AGL(1,𝔽5)11yescharacteristic, complemented
112#938—102no—
113#936—51no—
114#936—51no—
115D4×Dic3—104no—
116#926—52no—
117#926—51no—
118C3×#100—102no—
119#825—104no—
120C23×D5D1212yes—
121C22×AGL(1,𝔽5)—64no—
122C2×C5×D4—31no—
123C2×C5×D4—62no—
124C2×C5×D4C4×D311yescharacteristic
125C2×C22⋊D5—61no—
126C2×C22⋊D5—62no—
127C2×C22⋊D5#6712yes—
128C22×Dic5—61no—
129#711—62no—
130#711—62no—
131D4×D5—22no—
132D4×D5—22no—
133C2×D20C4×D311yescharacteristic
134C2×C4×D5C22×D311yescharacteristic
135C2×Dic10—31no—
136C22⋊AGL(1,𝔽5)—64no—
137C22⋊AGL(1,𝔽5)—62no—
138#704—22no—
139C4⋊AGL(1,𝔽5)—62no—
140C4×AGL(1,𝔽5)—34no—
141#700—22no—
142D5⋊C8—22no—
143C42×C5—31no—
144C22⋊Dic5—62no—
145#685—62no—
146#685—61no—
147#683—61no—
148C4×Dic5—31no—
149#535—151no—
150#518—151no—
151#421—152no—
152C2×#100—51no—
153H(3,ℤ/4)—152no—
154C22×C3×C5—22no—
155C22×C3×C5—42no—
156C22×C3×C5C2×C22⋊C411yescharacteristic
157C2×C5×D3—42no—
158C2×C5×D3—41no—
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×C5C4×D412yes—
168Dic15—41no—
169Dic15—41no—
170C3×Dic5#12112yes—
171C5×Dic3—41no—
172C24×C3—52no—
173C2×C3×D4—52no—
174C2×C3×D4—51no—
175C2×C3×D4—102no—
176C2×C3×D4—102no—
177C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
178C22×C3×C4—51no—
179C2×#67—22no—
180C2×#67—101no—
181C2×#67—102no—
182C22×Dic3—104no—
183#235—102no—
184#235—102no—
185C2×D12C2×AGL(1,𝔽5)11yescharacteristic, complemented
186C2×C4×D3—101no—
187C2×Dic6—51no—
188C3×M16—102no—
189C3×M16—102no—
190C2×C3×C8—102no—
191#217—101no—
192#217—102no—
193#217—102no—
194#217—104no—
195#217—102no—
196C4⋊Dic3—101no—
197C4⋊Dic3—102no—
198C4×Dic3—54no—
199C4×Dic3—51no—
200C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
201C23×C5—61no—
202C23×C5(C2×D3)⋊C412yes—
203C22×D5—22no—
204C22×D5—22no—
205C22×D5—82no—
206C22×D5(C2×D3)⋊C412yes—
207C22×D5C2×D1211yescharacteristic
208C2×AGL(1,𝔽5)—64no—
209C2×AGL(1,𝔽5)—244no—
210C5×D4—22no—
211C5×D4—62no—
212C5×D4—242no—
213C2×C4×C5—61no—
214C2×C4×C5C2×C4×D311yescharacteristic
215C22⋊D5—24no—
216C22⋊D5—121no—
217C22⋊D5—121no—
218C22⋊D5—242no—
219C2×Dic5—61no—
220C2×Dic5—61no—
221C2×Dic5—122no—
222C2×Dic5C2×#6711yescharacteristic
223D20—22no—
224C4×D5D3×D412yes—
225C4×D5#23712yes—
226Dic10—62no—
227#170—42no—
228C2×#41—151no—
229C22×D4—51no—
230C2×M16—52no—
231#127—31no—
232#127—151no—
233#124—151no—
234#124—151no—
235#121—302no—
236#120—302no—
237C4×D4—304no—
238#117—151no—
239#117—152no—
240C2×C22⋊C4—302no—
241#104—304no—
242#100—102no—
243C2×C3×C5—21no—
244C2×C3×C5—42no—
245C2×C3×C5#38611yescharacteristic
246C3×D5—21no—
247C3×D5—21no—
248C3×D5—42no—
249C5×D3—81no—
250C23×C3—51no—
251C23×C3—52no—
252C23×C3—102no—
253C23×C3—102no—
254C23×C3—402no—
255C23×C3C22⋊AGL(1,𝔽5)12yes—
256C22×D3—21no—
257C3×D4—22no—
258C3×D4—104no—
259C3×D4—102no—
260C2×C3×C4—51no—
261C2×C3×C4—52no—
262C2×C3×C4—52no—
263C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
264#67—82no—
265#67—201no—
266#67—201no—
267#67—402no—
268C2×Dic3—21no—
269C2×Dic3—104no—
270C2×Dic3—101no—
271C2×Dic3—101no—
272C2×Dic3—404no—
273D12—22no—
274C4×D3—202no—
275Dic6—102no—
276C3×C8—202no—
277C22×C5—22no—
278C22×C5—42no—
279C22×C5—122no—
280C22×C5—121no—
281C22×C5C2×(C2×D3)⋊C411yescharacteristic
282C2×D5—22no—
283C2×D5—41no—
284C2×D5—44no—
285C2×D5—42no—
286C2×D5—82no—
287C2×D5#88211yescharacteristic
288C2×D5#88611yescharacteristic
289AGL(1,𝔽5)—124no—
290C4×C5—121no—
291C4×C5#67⋊C412yes—
292Dic5—121no—
293Dic5—121no—
294Dic5#93912yes—
295C24—52no—
296#41—302no—
297#41—302no—
298C2×Q8—151no—
299C2×D4—31no—
300C2×D4—52no—
301C2×D4—51no—
302C2×D4—62no—
303C2×D4—102no—
304C2×D4—102no—
305C2×D4—301no—
306C2×D4—302no—
307C2×D4D3×AGL(1,𝔽5)11yescharacteristic
308C22×C4—51no—
309C22×C4—301no—
310C22×C4—304no—
311M16—102no—
312M16—102no—
313C2×C8—102no—
314C4⋊C4—301no—
315C4⋊C4—302no—
316C22⋊C4—301no—
317C22⋊C4—302no—
318C22⋊C4—302no—
319C22⋊C4—304no—
320C22⋊C4—302no—
321C42—31no—
322C42—154no—
323C42—151no—
324C3×C5#191111yescharacteristic, complemented, Hall
325C22×C3—22no—
326C22×C3—42no—
327C22×C3—51no—
328C22×C3—51no—
329C22×C3—102no—
330C22×C3—201no—
331C22×C3—202no—
332C22×C3—204no—
333C22×C3—402no—
334C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
335C2×D3—42no—
336C2×D3—41no—
337C3×C4—52no—
338C3×C4D4×AGL(1,𝔽5)12yes—
339Dic3—41no—
340Dic3—201no—
341Dic3—204no—
342Dic3—201no—
343C2×C5—21no—
344C2×C5—42no—
345C2×C5—241no—
346C2×C5#495811yescharacteristic
347D5—21no—
348D5—21no—
349D5—42no—
350C23—51no—
351C23—52no—
352C23—61no—
353C23—102no—
354C23—102no—
355C23—402no—
356C23(C2×D3)⋊AGL(1,𝔽5)12yes—
357Q8—302no—
358D4—22no—
359D4—62no—
360D4—104no—
361D4—102no—
362D4—242no—
363D4—601no—
364D4—601no—
365D4—1202no—
366C2×C4—51no—
367C2×C4—52no—
368C2×C4—52no—
369C2×C4—61no—
370C2×C4—304no—
371C2×C4—301no—
372C2×C4—301no—
373C2×C4—602no—
374C2×C4—1204no—
375C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
376C8—202no—
377C2×C3—21no—
378C2×C3—42no—
379C2×C3—101no—
380C2×C3—101no—
381C2×C3—202no—
382C2×C3#6577911yescharacteristic
383D3—81no—
384C5#7007111yescharacteristic, complemented, Sylow
385C22—22no—
386C22—42no—
387C22—51no—
388C22—51no—
389C22—102no—
390C22—122no—
391C22—121no—
392C22—201no—
393C22—202no—
394C22—204no—
395C22—402no—
396C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
397C4—52no—
398C4—121no—
399C4—601no—
400C4—604no—
401C4—601no—
402C4#67⋊AGL(1,𝔽5)12yes—
403C3#1060461511yescharacteristic, complemented, Sylow
404C2—21no—
405C2—42no—
406C2—101no—
407C2—101no—
408C2—202no—
409C2—241no—
410C2#1175202611yescharacteristic
subgroupG/H
centerC2#11752026
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC2×C3×C5×D4C2×C4
socleC2×C3×C5#386
prime radical#11754935C2
cosocleC2×C3×C4×D5C23
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5#1911
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. #11756987C2semidirect
3. C3×D5⋊#100C2semidirect
4. #11751718C2semidirect
5. #11746520C2semidirect
13. #91825C4semidirect
14. C5×#940C4semidirect
17. #91463C4semidirect
18. #91364C4semidirect
25. D5⋊#100D3semidirect
31. C2×Dic30C2×C4semidirect
33. C2×C5×D12C2×C4semidirect
47. C4×ΓL(1,𝔽16)D4semidirect
52. C4×Dic15C2×C4semidirect
53. C4×C5×Dic3C2×C4semidirect
111. #940AGL(1,𝔽5)semidirect
185. C2×D12C2×AGL(1,𝔽5)semidirect
200. C4×Dic3C2×AGL(1,𝔽5)semidirect
324. C3×C5#1911semidirect
384. C5#70071semidirect
403. C3#10604615semidirect

Maximal subgroups

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

subgroupindex
#117569872
#117549352
C3×D5⋊#1002
#117517182
#117465202
#106046153
#700715