Finite Group Databasebeta

← #14282799

Subgroups — #14282799

Order 1920.

476 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 84 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#11753528C211yesmaximal, characteristic
2#11751832C211yesmaximal, characteristic, complemented
3#11751762C211yesmaximal, characteristic, complemented
4#11746740C211yesmaximal, characteristic, complemented
5C3×#64869C211yesmaximal, characteristic, complemented
6#11746498C211yesmaximal, characteristic
7#11746496C211yesmaximal, characteristic
8#10604388—31nomaximal, Hall
9C2×Dic3×AGL(1,𝔽5)—21no—
10#91779C411yescharacteristic, complemented
11C5×#893C411yescharacteristic, complemented
12C3×#4043C2211yescharacteristic
13#91449C2211yescharacteristic
14#91441—21no—
15#91414—21no—
16C4×D5×Dic3C2211yescharacteristic
17#91370C411yescharacteristic, complemented
18#91341—21no—
19#91338—21no—
20Dic3×Dic10C411yescharacteristic, complemented
21#91235C2211yescharacteristic
22#91232C2211yescharacteristic
23C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
24C3×#4003C2211yescharacteristic
25Dic3⋊#170—21no—
26Dic3×#170—21no—
27(C2×AGL(1,𝔽5))⋊Dic3—21no—
28#68308—51nomaximal, Hall
29#65891—31no—
30#65686—31no—
31#65680—31no—
32#64920—31no—
33#64920—31no—
34#64869—31no—
35#64869D311yescharacteristic, complemented
36C22×ΓL(1,𝔽16)—21no—
37C22×C3×AGL(1,𝔽5)—21no—
38C2×C5×D12C2×C411yescharacteristic
39C2×C4×C5×D3—21no—
40C2×C3×C4×D5C2311yescharacteristic
41C2×C3×Dic10C2×C411yescharacteristic
42C2×#1201—21no—
43C2×D5×Dic3D411yescharacteristic
44C2×D5×Dic3D411yescharacteristic
45C2×C3⋊#170—21no—
46C2×C3×#170—21no—
47Dic3×AGL(1,𝔽5)—24no—
48C3×C5×C4⋊C4C2×C411yescharacteristic
49C4⋊Dic15—21no—
50C4⋊Dic15C2×C411yescharacteristic
51#6712—21no—
52C4×Dic15C2×C411yescharacteristic
53C5×(C2×D3)⋊C4—21no—
54C4×C5×Dic3C2×C411yescharacteristic
55C3×#685—21no—
56C3×C4⋊Dic5—21no—
57#6668—21no—
58(C2×D3)⋊Dic5—21no—
59(C2×D3)⋊Dic5—21no—
60(C2×D3)⋊Dic5—21no—
61Dic3×Dic5—21no—
62Dic3×Dic5D411yescharacteristic
63Dic3×Dic5D411yescharacteristic
64#5624—51no—
65#4718—51no—
66#4648—51no—
67C3×#328—51no—
68#4538—51no—
69#4470—51no—
70#4451—51no—
71C2×C4×AGL(1,𝔽5)—61no—
72C4×C5×D4—31no—
73#4084—31no—
74#4082—31no—
75C4×C22⋊D5—61no—
76#4072—61no—
77#4043C2×D311yescharacteristic
78#4036—31no—
79#4029—61no—
80#4025—61no—
81C42×D5—31no—
82C4×Dic10—31no—
83(C2×AGL(1,𝔽5))⋊C4—31no—
84(C2×AGL(1,𝔽5))⋊C4—61no—
85(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
86#4003—31no—
87#4003C2×D311yescharacteristic
88C4⋊#170—61no—
89C4×#170—61no—
90#1500—151noSylow
91C22×C5×D3—21no—
92C22×C3×D5C2×D411yescharacteristic
93C2×ΓL(1,𝔽16)—22no—
94C2×ΓL(1,𝔽16)—41no—
95C2×ΓL(1,𝔽16)—41no—
96C2×C3×AGL(1,𝔽5)—22no—
97C2×C3×AGL(1,𝔽5)—41no—
98C2×C3×AGL(1,𝔽5)—41no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5C22×C411yescharacteristic
101C2×Dic15—21no—
102C2×Dic15C22⋊C411yescharacteristic
103C2×Dic15C22⋊C411yescharacteristic
104C2×C5×Dic3C22⋊C411yescharacteristic
105C2×C5×Dic3C22⋊C411yescharacteristic
106C5×D12—41no—
107C4×C5×D3—42no—
108C2×C3×Dic5—21no—
109C2×C3×Dic5C2×D411yescharacteristic
110C3×C4×D5—41no—
111C3×Dic10—41no—
112#1201—41no—
113#1201—41no—
114D5×Dic3—21no—
115D5×Dic3—21no—
116D5×Dic3—22no—
117C3⋊#170—41no—
118C3×#170—41no—
119C3×C22⋊Q8—51no—
120#947—51no—
121Q8×Dic3—51no—
122#930—51no—
123C2×C4×Dic3—51no—
124C2×C4×Dic3—101no—
125#898—101no—
126#893AGL(1,𝔽5)11yescharacteristic, complemented
127#892—101no—
128#890—51no—
129#886—101no—
130#67⋊C4—101no—
131C3×C22⋊C8—51no—
132C3×#95—51no—
133C3⋊#95—51no—
134C3⋊#95—101no—
135#830—51no—
136Dic3⋊C8—101no—
137C8×Dic3—101no—
138C22×AGL(1,𝔽5)—21no—
139C22×AGL(1,𝔽5)—61no—
140C2×C5×D4—31no—
141C22×C4×C5—61no—
142C2×C22⋊D5—61no—
143C2×C4×D5—31no—
144C2×C4×D5—31no—
145C2×C4×D5C22×D311yescharacteristic
146C2×Dic10C4×D311yescharacteristic
147C2×#170—21no—
148C2×#170—61no—
149C4×AGL(1,𝔽5)—64no—
150C5×C4⋊C4C4×D311yescharacteristic
151C5×C22⋊C4—61no—
152C42×C5—31no—
153C22⋊Dic5—61no—
154C22⋊Dic5—61no—
155C22⋊Dic5—61no—
156#685—21no—
157C4⋊Dic5—21no—
158C4⋊Dic5—31no—
159C4⋊Dic5—61no—
160#683—61no—
161#683—61no—
162C4×Dic5—31no—
163C4×Dic5—31no—
164C4×Dic5—31no—
165C4×Dic5—61no—
166#529—151no—
167#431—151no—
168#376—151no—
169#328—51no—
170#328—151no—
171#327—151no—
172#327—151no—
173C22×C3×C5C2×C22⋊C411yescharacteristic
174C2×C5×D3—41no—
175C2×C5×D3—41no—
176C2×C5×D3—41no—
177C2×C3×D5—21no—
178C2×C3×D5—21no—
179C2×C3×D5#13511yescharacteristic
180C2×C3×D5#13511yescharacteristic
181ΓL(1,𝔽16)—42no—
182C3×AGL(1,𝔽5)—42no—
183C3×C4×C5—21no—
184C3×C4×C5—41no—
185Dic15—21no—
186Dic15—21no—
187Dic15—41no—
188C3×Dic5—21no—
189C3×Dic5—41no—
190C5×Dic3—21no—
191C5×Dic3#10412yes—
192C2×C3×Q8—51no—
193C22×C3×C4—51no—
194C22×C3×C4—101no—
195C2×#67—101no—
196C22×Dic3—51no—
197C22×Dic3—51no—
198C22×Dic3—101no—
199C2×D12C2×AGL(1,𝔽5)11yescharacteristic
200C2×C4×D3—21no—
201C2×C3×C8—101no—
202C3×C4⋊C4—101no—
203C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
204C3×C22⋊C4—101no—
205(C2×D3)⋊C4—21no—
206(C2×D3)⋊C4—101no—
207(C2×D3)⋊C4—101no—
208(C2×D3)⋊C4—101no—
209C4⋊Dic3—51no—
210C4⋊Dic3—101no—
211C4⋊Dic3—101no—
212Dic3⋊C4—101no—
213C4×Dic3—51no—
214C4×Dic3—51no—
215C4×Dic3—51no—
216C4×Dic3—104no—
217C4×Dic3—101no—
218C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
219C2×C3⋊C8—101no—
220C23×C5—61no—
221C22×D5D3×D411yescharacteristic
222C2×AGL(1,𝔽5)—22no—
223C2×AGL(1,𝔽5)—41no—
224C2×AGL(1,𝔽5)—41no—
225C2×AGL(1,𝔽5)—62no—
226C2×AGL(1,𝔽5)—121no—
227C2×AGL(1,𝔽5)—121no—
228C5×D4—121no—
229C2×C4×C5—21no—
230C2×C4×C5—31no—
231C2×C4×C5—31no—
232C2×C4×C5—122no—
233C2×C4×C5C2×C4×D311yescharacteristic
234C22⋊D5—121no—
235C22⋊D5—121no—
236C2×Dic5—21no—
237C2×Dic5—31no—
238C2×Dic5—31no—
239C2×Dic5—61no—
240C2×Dic5D3×D411yescharacteristic
241C4×D5—41no—
242C4×D5—62no—
243C4×D5—61no—
244C4×D5—61no—
245Dic10—41no—
246#170—41no—
247#170—121no—
248#126—301no—
249#125—151no—
250#124—151no—
251#123—301no—
252C22⋊Q8—51no—
253#121—151no—
254C4×Q8—151no—
255C4×D4—31no—
256C4×D4—301no—
257#117—301no—
258C2×C42—151no—
259C2×C42—301no—
260C4⋊C8—301no—
261C22⋊C8—51no—
262C22⋊C8—151no—
263C4×C8—301no—
264#95—51no—
265#95—151no—
266#95—301no—
267C2×C3×C5#41011yescharacteristic
268C2×C3×C5#41611yescharacteristic
269C2×C3×C5C2×#10411yescharacteristic
270C3×D5—21no—
271C3×D5—21no—
272C5×D3—81no—
273C23×C3—51no—
274C22×D3—21no—
275C3×Q8—201no—
276C2×C3×C4—21no—
277C2×C3×C4—51no—
278C2×C3×C4—102no—
279C2×C3×C4—101no—
280C2×C3×C4—201no—
281C2×C3×C4—201no—
282C2×C3×C4—201no—
283C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
284#67—201no—
285#67—201no—
286C2×Dic3—51no—
287C2×Dic3—51no—
288C2×Dic3—101no—
289C2×Dic3—101no—
290C2×Dic3—102no—
291C2×Dic3—102no—
292C2×Dic3—101no—
293C2×Dic3—201no—
294C2×Dic3—201no—
295C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
296C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
297D12—41no—
298C4×D3—42no—
299C3×C8—201no—
300C3⋊C8—201no—
301C22×C5—121no—
302C22×C5—121no—
303C22×C5—121no—
304C22×C5D3×C22⋊C411yescharacteristic
305C2×D5—21no—
306C2×D5—21no—
307C2×D5#91611yescharacteristic
308C2×D5#91911yescharacteristic
309AGL(1,𝔽5)—42no—
310AGL(1,𝔽5)—122no—
311C4×C5—21no—
312C4×C5—32no—
313C4×C5—41no—
314C4×C5—61no—
315Dic5—21no—
316Dic5—41no—
317Dic5—61no—
318Dic5—61no—
319Dic5—121no—
320C2×Q8—51no—
321C2×D4—31no—
322C2×D4—301no—
323C22×C4—51no—
324C22×C4—61no—
325C22×C4—101no—
326C22×C4—151no—
327C22×C4—151no—
328C22×C4—301no—
329C2×C8—101no—
330C2×C8—301no—
331C4⋊C4—101no—
332C4⋊C4—151no—
333C4⋊C4—301no—
334C4⋊C4—301no—
335C4⋊C4—301no—
336C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
337C22⋊C4—61no—
338C22⋊C4—101no—
339C22⋊C4—301no—
340C22⋊C4—301no—
341C22⋊C4—301no—
342C42—31no—
343C42—151no—
344C42—151no—
345C42—151no—
346C42—301no—
347C42—304no—
348C3×C5#150011yescharacteristic, complemented, Hall
349C22×C3—51no—
350C22×C3—51no—
351C22×C3—101no—
352C22×C3—101no—
353C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
354C2×D3—41no—
355C2×D3—41no—
356C2×D3—41no—
357C3×C4—21no—
358C3×C4—41no—
359C3×C4—101no—
360C3×C4—202no—
361C3×C4—201no—
362Dic3—21no—
363Dic3—101no—
364Dic3—101no—
365Dic3—202no—
366Dic3—201no—
367Dic3#400812yes—
368C2×C5—241no—
369C2×C5#474011yescharacteristic
370C2×C5#480411yescharacteristic
371C2×C5D3×#10411yescharacteristic
372D5—21no—
373D5—21no—
374C23—51no—
375C23—61no—
376Q8—201no—
377D4—121no—
378D4—601no—
379D4—601no—
380C2×C4—21no—
381C2×C4—31no—
382C2×C4—31no—
383C2×C4—51no—
384C2×C4—102no—
385C2×C4—101no—
386C2×C4—122no—
387C2×C4—151no—
388C2×C4—151no—
389C2×C4—201no—
390C2×C4—201no—
391C2×C4—201no—
392C2×C4—302no—
393C2×C4—301no—
394C2×C4—301no—
395C2×C4—302no—
396C2×C4—301no—
397C2×C4—601no—
398C2×C4—601no—
399C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
400C8—201no—
401C8—601no—
402C2×C3—101no—
403C2×C3—101no—
404C2×C3#6574511yescharacteristic
405C2×C3C2×#400811yescharacteristic
406C2×C3#6579411yescharacteristic
407D3—81no—
408C5#6830811yescharacteristic, complemented, Sylow
409C22—51no—
410C22—51no—
411C22—101no—
412C22—101no—
413C22—121no—
414C22—121no—
415C22—121no—
416C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
417C4—21no—
418C4—32no—
419C4—41no—
420C4—61no—
421C4—101no—
422C4—202no—
423C4—201no—
424C4—301no—
425C4—301no—
426C4—602no—
427C4—601no—
428C3#1060438811yescharacteristic, complemented, Sylow
429C2—101no—
430C2—101no—
431C2—241no—
432C2#1175186211yescharacteristic
433C2D3×#400811yescharacteristic
434C2#1175197111yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C5×C4⋊C4C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radical#91449C22
cosocleC2×C3×C4×D5C23
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1500
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11751832C2semidirect
3. #11751762C2semidirect
4. #11746740C2semidirect
5. C3×#64869C2semidirect
10. #91779C4semidirect
11. C5×#893C4semidirect
17. #91370C4semidirect
20. Dic3×Dic10C4semidirect
35. #64869D3semidirect
126. #893AGL(1,𝔽5)semidirect
348. C3×C5#1500semidirect
408. C5#68308semidirect
428. C3#10604388semidirect

Maximal subgroups

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

subgroupindex
#117535282
#117518322
#117517622
#117467402
C3×#648692
#117464982
#117464962
#106043883
#683085