Finite Group Databasebeta

← #14281609

Subgroups — #14281609

Order 1920.

552 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11753398C211yesmaximal, characteristic
2C4×D3×#170C211yesmaximal, characteristic, complemented
3#11751754C211yesmaximal, characteristic, complemented
4#11746742C211yesmaximal, characteristic, complemented
5C3×#64871C211yesmaximal, characteristic, complemented
6#11746495C211yesmaximal, characteristic, complemented
7#11746494C211yesmaximal, characteristic, complemented
8#10604359—31nomaximal, Hall
9C2×#6765C411yescharacteristic
10C2×D3×#170—21no—
11#91776C411yescharacteristic
12C5×#892C411yescharacteristic
13C3×#4039C2211yescharacteristic
14#91442—21no—
15#91440—21no—
16#91434C411yescharacteristic
17C4×D3×Dic5C2211yescharacteristic
18#91393—21no—
19C4×D5×Dic3—21no—
20#91333C2211yescharacteristic
21C4⋊(C3⋊#170)C2211yescharacteristic
22C4×C3⋊#170C2211yescharacteristic
23C3×C4⋊#170C2211yescharacteristic
24C3×C4×#170C2211yescharacteristic
25(C2×D3)⋊#170—21no—
26Dic3×#170—21no—
27Dic3×#170—21no—
28#68165—51nomaximal, Hall
29#65856—31no—
30#65748—31no—
31C2×C4×#170—31no—
32#64872—31no—
33#64872—31no—
34#64871—31no—
35#64871D311yescharacteristic, complemented
36C2×Dic30C2×C411yescharacteristic
37C2×C4×C5×D3C2×C411yescharacteristic
38C2×C3×D20C2×C411yescharacteristic
39C2×C3×C4×D5—21no—
40C2×#1201—21no—
41C2×D3×Dic5D411yescharacteristic
42C2×D3×Dic5D411yescharacteristic
43C2×D5×Dic3—21no—
44C2×D5×Dic3—21no—
45#6765—22no—
46#6765C814yescomplemented
47C2×C3⋊#170—21no—
48C2×C3⋊#170—21no—
49C2×C3×#170—21no—
50C2×C3×#170—21no—
51D3×#170—24no—
52C3×C5×C4⋊C4C2×C411yescharacteristic
53#6712—21no—
54C4×Dic15—21no—
55C4×Dic15C2×C411yescharacteristic
56C5×(C2×D3)⋊C4—21no—
57C5×C4⋊Dic3C2×C411yescharacteristic
58C4×C5×Dic3—21no—
59C3×#685—21no—
60C3×C4×Dic5C2311yescharacteristic
61#6669—21no—
62#6665—21no—
63Dic3×Dic5—21no—
64Dic3×Dic5D411yescharacteristic
65Dic3×Dic5D411yescharacteristic
66C4×#237—51no—
67#4833—51no—
68C4×D3×C8—51no—
69C3×D4⋊C8—51no—
70D4⋊(C3⋊C8)—51no—
71#4484—51no—
72#4456—51no—
73C2×#709—31no—
74C22×#170—61no—
75C5×#117—31no—
76C2×C4×Dic5—31no—
77#4039—31no—
78#4039C2×D311yescharacteristic
79#4033—31no—
80#4033—31no—
81#4027—61no—
82#4027—61no—
83#4018—61no—
84C42×D5—61no—
85C22⋊#170—61no—
86C4⋊#170—31no—
87C4⋊#170C2×D311yescharacteristic
88C4×#170—31no—
89C4×#170—61no—
90C4×#170—61no—
91C4×#170C2×D311yescharacteristic
92#1476—151noSylow
93C22×C5×D3C22⋊C411yescharacteristic
94C22×C3×D5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5C22×C411yescharacteristic
97C2×Dic15—21no—
98C2×Dic15C22⋊C411yescharacteristic
99C2×Dic15C22⋊C411yescharacteristic
100Dic30—21no—
101Dic30C2×C812yescomplemented
102C2×C5×Dic3—21no—
103C2×C5×Dic3C22⋊C411yescharacteristic
104C4×C5×D3C2×C812yes—
105C4×C5×D3M1612yes—
106C2×C3×Dic5C2×D411yescharacteristic
107C2×C3×Dic5C2×D411yescharacteristic
108C3×D20—21no—
109C3×D20C2×C812yescomplemented
110C3×C4×D5—41no—
111C3×C4×D5—41no—
112#1201—24no—
113D3×Dic5—22no—
114D3×Dic5—21no—
115D3×Dic5—21no—
116D5×Dic3—24no—
117D5×Dic3—42no—
118C3⋊#170—22no—
119C3⋊#170—41no—
120C3×#170—22no—
121C3×#170—41no—
122C2×#237—51no—
123C3×C4×D4—51no—
124D4×Dic3—51no—
125C4×#67—101no—
126C2×C4×Dic3—101no—
127C2×D3×C8—101no—
128#892AGL(1,𝔽5)11yescharacteristic
129#887—51no—
130#67⋊C4—101no—
131#877—101no—
132C42×D3—51no—
133C4×Dic6—51no—
134C3×C4⋊C8—51no—
135C3×C4×C8—51no—
136(C2×D3)⋊C8—101no—
137C8×Dic3—101no—
138C8×Dic3—101no—
139C4⋊(C3⋊C8)—51no—
140C4×C3⋊C8—51no—
141C22×C4×C5—31no—
142C2×C22⋊D5—61no—
143C22×Dic5—31no—
144C22×Dic5—31no—
145#709—34no—
146#709—62no—
147C2×D20C4×D311yescharacteristic
148C2×C4×D5—21no—
149C2×C4×D5—61no—
150C2×C4×D5—61no—
151C2×Dic10—31no—
152C2×#170—21no—
153C2×#170—21no—
154C2×#170—64no—
155C2×#170—61no—
156C2×#170—61no—
157C5×C4⋊C4—31no—
158C5×C4⋊C4C4×D311yescharacteristic
159C5×C22⋊C4—61no—
160C42×C5—61no—
161#685—21no—
162#685—61no—
163#683—61no—
164#683—61no—
165C4×Dic5—31no—
166C4×Dic5—31no—
167C4×Dic5—31no—
168C4×Dic5—61no—
169C4×Dic5—61no—
170C4×Dic5C22×D311yescharacteristic
171C4×#41—151no—
172#431—151no—
173C2×C4×C8—151no—
174Q8⋊C8—151no—
175Q8⋊C8—151no—
176D4⋊C8—51no—
177D4⋊C8—151no—
178C22×C3×C5C2×C22⋊C411yescharacteristic
179C2×C5×D3—21no—
180C2×C5×D3—21no—
181C2×C5×D3C22⋊C812yes—
182C2×C3×D5—22no—
183C2×C3×D5—41no—
184C2×C3×D5—41no—
185C3×C4×C5—41no—
186C3×C4×C5C22×C811yescharacteristic
187C3×C4×C5C2×M1611yescharacteristic
188Dic15—22no—
189Dic15—21no—
190Dic15#10412yes—
191C3×Dic5—21no—
192C3×Dic5#13511yescharacteristic
193C3×Dic5#13511yescharacteristic
194C5×Dic3—41no—
195C5×Dic3C22⋊C812yes—
196C2×C3×D4—51no—
197C22×C3×C4—101no—
198C2×#67—101no—
199C22×Dic3—101no—
200C22×Dic3—101no—
201#237—54no—
202#237—102no—
203C2×C4×D3—51no—
204C2×C4×D3—51no—
205C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
206C2×Dic6—51no—
207C2×C3×C8—101no—
208C2×C3×C8—101no—
209C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
210C3×C22⋊C4—101no—
211C3×C42—51no—
212#217—101no—
213(C2×D3)⋊C4—21no—
214C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
215Dic3⋊C4—101no—
216Dic3⋊C4—101no—
217C4×Dic3—21no—
218C4×Dic3—51no—
219C4×Dic3—51no—
220C4×Dic3—51no—
221C4×Dic3—101no—
222C4×Dic3—101no—
223C2×C3⋊C8—101no—
224C2×C3⋊C8—101no—
225D3×C8—104no—
226C23×C5—31no—
227C22×D5—21no—
228C2×C4×C5—21no—
229C2×C4×C5—31no—
230C2×C4×C5—32no—
231C2×C4×C5—32no—
232C2×C4×C5—61no—
233C2×C4×C5C2×C4×D311yescharacteristic
234C22⋊D5—64no—
235C2×Dic5—31no—
236C2×Dic5—31no—
237C2×Dic5—62no—
238C2×Dic5—61no—
239C2×Dic5—61no—
240C2×Dic5—61no—
241C2×Dic5D3×D411yescharacteristic
242C2×Dic5D3×D411yescharacteristic
243D20—21no—
244D20D3×C812yescomplemented
245C4×D5—41no—
246C4×D5—41no—
247C4×D5—64no—
248C4×D5—122no—
249Dic10—32no—
250Dic10—61no—
251#170—22no—
252#170—41no—
253#170—62no—
254#170—121no—
255C2×#41—151no—
256C22×C8—301no—
257C4×Q8—151no—
258C4×Q8—151no—
259C4×D4—51no—
260C4×D4—151no—
261C4×D4—301no—
262C4×D4—301no—
263#117—31no—
264#117—301no—
265C2×C42—151no—
266C2×C42—301no—
267C4⋊C8—51no—
268C4⋊C8—151no—
269C22⋊C8—301no—
270C4×C8—51no—
271C4×C8—151no—
272C4×C8—301no—
273C4×C8—301no—
274C2×C3×C5C2×C22⋊C811yescharacteristic
275C2×C3×C5#41611yescharacteristic
276C2×C3×C5C2×#10411yescharacteristic
277C3×D5—42no—
278C5×D3—22no—
279C23×C3—101no—
280C22×D3C22⋊AGL(1,𝔽5)11yescharacteristic
281C3×D4—52no—
282C3×D4—101no—
283C2×C3×C4—21no—
284C2×C3×C4—51no—
285C2×C3×C4—51no—
286C2×C3×C4—201no—
287C2×C3×C4—201no—
288C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
289#67—104no—
290C2×Dic3—21no—
291C2×Dic3—51no—
292C2×Dic3—51no—
293C2×Dic3—101no—
294C2×Dic3—104no—
295C2×Dic3—202no—
296C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
297C4×D3—102no—
298C4×D3—101no—
299C4×D3—101no—
300C4×D3D5⋊C812yes—
301C4×D3#70012yes—
302Dic6—52no—
303Dic6—101no—
304C3×C8—102no—
305C3×C8—201no—
306C3⋊C8—102no—
307C3⋊C8—201no—
308C22×C5—32no—
309C22×C5—61no—
310C22×C5—61no—
311C22×C5D3×C22⋊C411yescharacteristic
312C2×D5—22no—
313C2×D5—41no—
314C2×D5—41no—
315C4×C5—32no—
316C4×C5—41no—
317C4×C5—121no—
318C4×C5C2×D3×C811yescharacteristic
319C4×C5D3×M1611yescharacteristic
320Dic5—21no—
321Dic5—32no—
322Dic5—62no—
323Dic5—61no—
324Dic5#91211yescharacteristic
325Dic5#91611yescharacteristic
326#41—154no—
327#41—302no—
328C2×Q8—151no—
329C2×D4—51no—
330C2×D4—301no—
331C22×C4—31no—
332C22×C4—101no—
333C22×C4—151no—
334C22×C4—151no—
335C22×C4—301no—
336C22×C4—301no—
337C2×C8—101no—
338C2×C8—101no—
339C2×C8—304no—
340C2×C8—301no—
341C2×C8—301no—
342C4⋊C4—31no—
343C4⋊C4—301no—
344C4⋊C4—301no—
345C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
346C22⋊C4—61no—
347C22⋊C4—101no—
348C22⋊C4—301no—
349C42—51no—
350C42—61no—
351C42—151no—
352C42—151no—
353C42—151no—
354C42—301no—
355C42—301no—
356C3×C5#147611yescharacteristic, complemented, Hall
357C22×C3—102no—
358C22×C3—201no—
359C22×C3—201no—
360C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
361C2×D3—21no—
362C2×D3—21no—
363C2×D3#400312yes—
364C3×C4—41no—
365C3×C4—51no—
366C3×C4—51no—
367C3×C4—101no—
368C3×C4C2×D5⋊C811yescharacteristic
369C3×C4C2×#70011yescharacteristic
370Dic3—41no—
371Dic3—52no—
372Dic3—101no—
373Dic3—102no—
374Dic3#400312yes—
375C2×C5—62no—
376C2×C5D3×C22⋊C811yescharacteristic
377C2×C5#477211yescharacteristic
378C2×C5D3×#10411yescharacteristic
379D5—42no—
380C23—31no—
381C23—101no—
382Q8—152no—
383Q8—301no—
384D4—52no—
385D4—101no—
386D4—304no—
387C2×C4—21no—
388C2×C4—31no—
389C2×C4—32no—
390C2×C4—32no—
391C2×C4—51no—
392C2×C4—51no—
393C2×C4—61no—
394C2×C4—151no—
395C2×C4—151no—
396C2×C4—201no—
397C2×C4—201no—
398C2×C4—304no—
399C2×C4—301no—
400C2×C4—301no—
401C2×C4—302no—
402C2×C4—301no—
403C2×C4—602no—
404C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
405C8—102no—
406C8—201no—
407C8—302no—
408C8—601no—
409C2×C3—202no—
410C2×C3C2×#400311yescharacteristic
411C2×C3D5⋊#10411yescharacteristic
412C2×C3#6579411yescharacteristic
413D3—22no—
414C5#6816511yescharacteristic, complemented, Sylow
415C22—32no—
416C22—61no—
417C22—61no—
418C22—102no—
419C22—201no—
420C22—201no—
421C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
422C4—32no—
423C4—41no—
424C4—51no—
425C4—51no—
426C4—101no—
427C4—121no—
428C4—152no—
429C4—301no—
430C4—302no—
431C4D3×D5⋊C811yescharacteristic
432C4D3×#70011yescharacteristic
433C3#1060435911yescharacteristic, complemented, Sylow
434C2—62no—
435C2—202no—
436C2D3×#400311yescharacteristic
437C2#1175194711yescharacteristic
438C2#1175195911yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC3×C4×C5C22×C8
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C5×C4⋊C4C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×#6765C4
cosocleC3×C4×Dic5C23
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1476
LCSG ▷ C3×C4×C5 ▷ C2×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. C4×D3×#170C2semidirect
3. #11751754C2semidirect
4. #11746742C2semidirect
5. C3×#64871C2semidirect
6. #11746495C2semidirect
7. #11746494C2semidirect
35. #64871D3semidirect
46. #6765C8semidirect
101. Dic30C2×C8semidirect
109. C3×D20C2×C8semidirect
244. D20D3×C8semidirect
356. C3×C5#1476semidirect
414. C5#68165semidirect
433. C3#10604359semidirect

Maximal subgroups

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

subgroupindex
#117533982
C4×D3×#1702
#117517542
#117467422
C3×#648712
#117464952
#117464942
#106043593
#681655