Finite Group Databasebeta

← #14282098

Subgroups — #14282098

Order 1920.

624 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 108 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
1D4×#1200C211yesmaximal, characteristic
2#11751922C211yesmaximal, characteristic, complemented
3#11751797C211yesmaximal, characteristic, complemented
4D4⋊(C3⋊#170)C211yesmaximal, characteristic, complemented
5C3×D4⋊#170C211yesmaximal, characteristic, complemented
6#11746491C211yesmaximal, characteristic, complemented
7#11746490C211yesmaximal, characteristic, complemented
8#10604404—31nomaximal, Hall
9C2×D4×D15C411yescharacteristic
10C22×#1200—21no—
11C2×#6740—21no—
12C5×D4×Dic3C411yescharacteristic
13C3×D4×Dic5C2211yescharacteristic
14#91561—21no—
15#91556—21no—
16#91552—21no—
17#91437C411yescharacteristic
18#91428C411yescharacteristic
19#91418C2211yescharacteristic
20C4×#1200C2211yescharacteristic
21C4⋊(C3⋊#170)C2211yescharacteristic, complemented
22C4×C3⋊#170C2211yescharacteristic, complemented
23C3×C4⋊#170C2211yescharacteristic, complemented
24C3×C4×#170C2211yescharacteristic, complemented
25Dic3⋊#170—21no—
26Dic3⋊#170—21no—
27#91171—21no—
28#68172—51nomaximal, Hall
29C4×D4×D5—31no—
30#65681—31no—
31#65680—31no—
32D4⋊#170—31no—
33D4⋊#170D311yescharacteristic, complemented
34#64871—31no—
35#64871—31no—
36C23×D15—21no—
37C2×C3×C5×D4C2×C411yescharacteristic
38C2×#1220—21no—
39D4×D15—22no—
40D4×D15—22no—
41C2×D60C2×C411yescharacteristic
42C2×C4×D15C2×C411yescharacteristic
43C22×C5×Dic3—21no—
44C22×C3×Dic5—21no—
45C2×#1200—21no—
46C2×#1200—21no—
47C2×#1200—21no—
48C2×#1200—42no—
49C2×#1200—42no—
50C2×#1200D411yescharacteristic
51C2×#1200D411yescharacteristic
52C2×C3⋊#170—21no—
53C2×C3⋊#170—21no—
54C2×C3×#170—21no—
55C2×C3×#170—21no—
56#6740—42no—
57C5×#217—21no—
58C5×C4⋊Dic3C2×C411yescharacteristic
59C4×C5×Dic3C2×C411yescharacteristic
60C3×C22⋊Dic5—21no—
61C3×C4⋊Dic5C2×C411yescharacteristic
62C3×C4×Dic5C2311yescharacteristic
63#6669—21no—
64#6667—21no—
65#6667—21no—
66Dic3×Dic5D411yescharacteristic
67Dic3×Dic5D411yescharacteristic
68C4×D3×D4—51no—
69#4837—51no—
70#4685—51no—
71C3×D4⋊C8—51no—
72D4⋊(C3⋊C8)—51no—
73#4483—51no—
74#4459—51no—
75C2×D4×D5—31no—
76C22×C4×D5—61no—
77C2×#700—61no—
78C4×C5×D4—31no—
79D4×Dic5C2×D311yescharacteristic
80C4×C22⋊D5—61no—
81#4039—31no—
82D5×C4⋊C4—31no—
83#4027—61no—
84D5×C22⋊C4—61no—
85C4×D20—31no—
86C42×D5—31no—
87#4003—61no—
88C4⋊#170—31no—
89C4⋊#170—61no—
90C4⋊#170—61no—
91C4⋊#170C2×D311yescharacteristic, complemented
92C4×#170—31no—
93C4×#170C2×D311yescharacteristic, complemented
94#1486—151noSylow
95C23×C3×C5—21no—
96C22×D15—24no—
97C22×D15—21no—
98C22×D15—42no—
99C22×D15—42no—
100C22×D15C22⋊C411yescharacteristic
101C3×C5×D4—21no—
102C3×C5×D4M1612yescomplemented
103C2×C3×C4×C5C22×C411yescharacteristic
104#1220—24no—
105C2×Dic15C22⋊C411yescharacteristic
106D60—21no—
107D60M1612yescomplemented
108C4×D15—21no—
109C4×D15—21no—
110C2×C5×Dic3—21no—
111C2×C5×Dic3—42no—
112C2×C5×Dic3C22⋊C411yescharacteristic
113C2×C5×Dic3C22⋊C411yescharacteristic
114C2×C3×Dic5—21no—
115C2×C3×Dic5—41no—
116C2×C3×Dic5—41no—
117C2×C3×Dic5C2×D411yescharacteristic
118C2×C3×Dic5C2×D411yescharacteristic
119#1200—41no—
120#1200—42no—
121#1200—41no—
122#1200—41no—
123#1200—42no—
124#1200D812yes—
125#1200SD1612yes—
126C3⋊#170—41no—
127C3⋊#170—41no—
128C3×#170—41no—
129C3×#170—41no—
130C2×D3×D4—51no—
131C22×C4×D3—101no—
132C3×C4×D4—51no—
133D4×Dic3AGL(1,𝔽5)11yescharacteristic
134C4×#67—101no—
135C2×ΓL(1,𝔽25)—101no—
136#893—51no—
137D3×C4⋊C4—51no—
138#67⋊C4—101no—
139D3×C22⋊C4—101no—
140C4×D12—51no—
141C42×D3—51no—
142C3×C4⋊C8—51no—
143C3×C4×C8—51no—
144(C2×D3)⋊C8—101no—
145Dic3⋊C8—101no—
146Dic3⋊C8—101no—
147C4⋊(C3⋊C8)—51no—
148C4×C3⋊C8—51no—
149C23×D5—61no—
150C2×C5×D4C4×D311yescharacteristic
151C22×C4×C5—61no—
152C2×C22⋊D5—61no—
153C22×Dic5—21no—
154D4×D5—62no—
155D4×D5—62no—
156C2×D20—31no—
157C2×C4×D5—31no—
158C2×C4×D5—31no—
159C2×C4×D5—31no—
160C2×C4×D5—61no—
161C2×C4×D5—61no—
162C2×C4×D5—61no—
163C2×C4×D5—122no—
164C2×C4×D5—122no—
165C2×#170—21no—
166C2×#170—21no—
167C2×#170—61no—
168C2×#170—61no—
169#700—122no—
170C5×C4⋊C4—31no—
171C5×C22⋊C4—61no—
172C42×C5—31no—
173C22⋊Dic5—21no—
174#685—61no—
175#685—61no—
176C4⋊Dic5C4×D311yescharacteristic
177#683—61no—
178C4×Dic5—31no—
179C4×Dic5—31no—
180C4×Dic5C22×D311yescharacteristic
181C2×C4×D4—151no—
182#431—151no—
183#423—151no—
184D4⋊C8—51no—
185D4⋊C8—151no—
186D4⋊C8—151no—
187D4⋊C8—151no—
188C22×C3×C5—22no—
189C22×C3×C5—41no—
190C22×C3×C5—41no—
191C22×C3×C5C2×C22⋊C411yescharacteristic
192C2×D15—21no—
193C2×D15—21no—
194C2×D15—22no—
195C2×D15—48no—
196C2×D15—41no—
197C2×D15—41no—
198C2×D15#10212yes—
199C3×C4×C5C2×M1611yescharacteristic
200C3×C4×C5C2×M1611yescharacteristic
201Dic15—21no—
202C3×Dic5—21no—
203C3×Dic5—41no—
204C3×Dic5C2×D811yescharacteristic
205C3×Dic5C2×SD1611yescharacteristic
206C5×Dic3—21no—
207C5×Dic3—41no—
208C5×Dic3#10212yes—
209C23×D3—101no—
210C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
211C22×C3×C4—101no—
212C2×#67—101no—
213C22×Dic3—21no—
214D3×D4—102no—
215D3×D4—102no—
216C2×D12—51no—
217C2×C4×D3—51no—
218C2×C4×D3—51no—
219C2×C4×D3—51no—
220C2×C4×D3—101no—
221C2×C4×D3—101no—
222C2×C4×D3—101no—
223C2×C4×D3—202no—
224C2×C4×D3—202no—
225C2×C3×C8—101no—
226C2×C3×C8—101no—
227C3×C4⋊C4—51no—
228C3×C22⋊C4—101no—
229C3×C42—51no—
230#217—21no—
231(C2×D3)⋊C4—101no—
232(C2×D3)⋊C4—101no—
233C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
234Dic3⋊C4—101no—
235C4×Dic3—51no—
236C4×Dic3—51no—
237C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
238C2×C3⋊C8—101no—
239C2×C3⋊C8—101no—
240ΓL(1,𝔽25)—202no—
241C23×C5—21no—
242C22×D5—31no—
243C22×D5—64no—
244C22×D5—61no—
245C22×D5—122no—
246C22×D5—122no—
247C5×D4—21no—
248C5×D4ΓL(1,𝔽25)12yescomplemented
249C2×C4×C5—31no—
250C2×C4×C5—31no—
251C2×C4×C5—61no—
252C2×C4×C5—122no—
253C2×C4×C5C2×C4×D311yescharacteristic
254C22⋊D5—64no—
255C2×Dic5—21no—
256C2×Dic5—31no—
257C2×Dic5—41no—
258C2×Dic5—41no—
259C2×Dic5D3×D411yescharacteristic
260C2×Dic5D3×D411yescharacteristic
261D20—32no—
262D20—61no—
263C4×D5—32no—
264C4×D5—32no—
265C4×D5—61no—
266C4×D5—61no—
267C4×D5—121no—
268C4×D5—122no—
269C4×D5—122no—
270C4×D5—121no—
271C4×D5—121no—
272#170—41no—
273#170—41no—
274#170—121no—
275#170—121no—
276C22×D4—151no—
277C23×C4—301no—
278C2×M16—301no—
279C4×D4—31no—
280C4×D4—51no—
281C4×D4—151no—
282C4×D4—151no—
283C4×D4—301no—
284C4×D4—301no—
285C2×C4⋊C4—151no—
286C2×C22⋊C4—301no—
287C2×C42—151no—
288C4⋊C8—51no—
289C4⋊C8—151no—
290C4⋊C8—301no—
291C4⋊C8—301no—
292C22⋊C8—301no—
293C4×C8—51no—
294C4×C8—151no—
295C2×C3×C5—42no—
296C2×C3×C5#40711yescharacteristic
297C2×C3×C5C2×#10211yescharacteristic
298C2×C3×C5#42111yescharacteristic
299D15—22no—
300D15—42no—
301C23×C3—21no—
302C22×D3—51no—
303C22×D3—104no—
304C22×D3—101no—
305C22×D3—202no—
306C22×D3—202no—
307C3×D4—21no—
308C3×D4#70012yescomplemented
309C2×C3×C4—51no—
310C2×C3×C4—51no—
311C2×C3×C4—101no—
312C2×C3×C4—201no—
313C2×C3×C4—201no—
314C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
315#67—104no—
316C2×Dic3—21no—
317C2×Dic3—42no—
318C2×Dic3—51no—
319C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
320C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
321D12—52no—
322D12—101no—
323C4×D3—52no—
324C4×D3—52no—
325C4×D3—101no—
326C4×D3—101no—
327C4×D3—201no—
328C4×D3—201no—
329C4×D3—201no—
330C4×D3—202no—
331C4×D3—202no—
332C3×C8—201no—
333C3×C8—201no—
334C3⋊C8—201no—
335C3⋊C8—201no—
336C22×C5—22no—
337C22×C5—41no—
338C22×C5—41no—
339C22×C5D3×C22⋊C411yescharacteristic
340C2×D5—32no—
341C2×D5—61no—
342C2×D5—61no—
343C2×D5—62no—
344C2×D5—128no—
345C2×D5—121no—
346C2×D5—121no—
347C4×C5—32no—
348C4×C5—61no—
349C4×C5—121no—
350C4×C5C2×ΓL(1,𝔽25)11yescharacteristic
351C4×C5D3×M1611yescharacteristic
352Dic5—21no—
353Dic5—41no—
354Dic5—61no—
355Dic5D3×D811yescharacteristic
356Dic5D3×SD1611yescharacteristic
357C24—301no—
358C2×D4—151no—
359C2×D4—301no—
360C2×D4—302no—
361C2×D4—302no—
362C2×D4D3×AGL(1,𝔽5)11yescharacteristic
363C22×C4—61no—
364C22×C4—101no—
365C22×C4—151no—
366C22×C4—151no—
367C22×C4—151no—
368C22×C4—301no—
369C22×C4—301no—
370C22×C4—301no—
371C22×C4—602no—
372C22×C4—602no—
373M16—602no—
374C2×C8—101no—
375C2×C8—101no—
376C2×C8—301no—
377C2×C8—301no—
378C4⋊C4—31no—
379C4⋊C4—51no—
380C4⋊C4—301no—
381C22⋊C4—61no—
382C22⋊C4—101no—
383C22⋊C4—301no—
384C22⋊C4—301no—
385C42—31no—
386C42—51no—
387C42—151no—
388C42—151no—
389C3×C5#148611yescharacteristic, complemented, Hall
390C22×C3—22no—
391C22×C3—41no—
392C22×C3—41no—
393C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
394C2×D3—52no—
395C2×D3—101no—
396C2×D3—101no—
397C2×D3—102no—
398C2×D3—208no—
399C2×D3—201no—
400C2×D3—201no—
401C3×C4—51no—
402C3×C4—51no—
403C3×C4—101no—
404C3×C4—201no—
405C3×C4C2×#70011yescharacteristic
406C3×C4D5⋊M1611yescharacteristic
407Dic3—21no—
408Dic3—41no—
409Dic3—101no—
410Dic3#400712yes—
411C2×C5—42no—
412C2×C5#472611yescharacteristic
413C2×C5D3×#10211yescharacteristic
414C2×C5#482111yescharacteristic
415D5—62no—
416D5—122no—
417C23—21no—
418C23—151no—
419C23—304no—
420C23—301no—
421C23—602no—
422C23—602no—
423D4—21no—
424D4—152no—
425D4—304no—
426D4—301no—
427D4#674012yescomplemented
428C2×C4—31no—
429C2×C4—31no—
430C2×C4—51no—
431C2×C4—51no—
432C2×C4—61no—
433C2×C4—101no—
434C2×C4—122no—
435C2×C4—152no—
436C2×C4—152no—
437C2×C4—151no—
438C2×C4—201no—
439C2×C4—201no—
440C2×C4—301no—
441C2×C4—301no—
442C2×C4—602no—
443C2×C4—601no—
444C2×C4—601no—
445C2×C4—601no—
446C2×C4—602no—
447C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
448C8—201no—
449C8—201no—
450C8—601no—
451C8—601no—
452C2×C3—42no—
453C2×C3#6575611yescharacteristic
454C2×C3C2×#400711yescharacteristic
455C2×C3#6579511yescharacteristic
456D3—102no—
457D3—202no—
458C5#6817211yescharacteristic, complemented, Sylow
459C22—22no—
460C22—41no—
461C22—41no—
462C22—152no—
463C22—301no—
464C22—301no—
465C22—302no—
466C22—608no—
467C22—601no—
468C22—601no—
469C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
470C4—32no—
471C4—51no—
472C4—51no—
473C4—61no—
474C4—101no—
475C4—121no—
476C4—201no—
477C4—301no—
478C4#9193111yescharacteristic
479C4C2×#674011yescharacteristic
480C3#1060440411yescharacteristic, complemented, Sylow
481C2—42no—
482C2—302no—
483C2—602no—
484C2D3×#400711yescharacteristic
485C2#1175194911yescharacteristic
486C2#1175205211yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC2×C3×C5×D4C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×D4×D15C4
cosocleC3×C4×Dic5C23
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5#1486
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #11751922C2semidirect
3. #11751797C2semidirect
4. D4⋊(C3⋊#170)C2semidirect
5. C3×D4⋊#170C2semidirect
6. #11746491C2semidirect
7. #11746490C2semidirect
21. C4⋊(C3⋊#170)C22semidirect
22. C4×C3⋊#170C22semidirect
23. C3×C4⋊#170C22semidirect
24. C3×C4×#170C22semidirect
33. D4⋊#170D3semidirect
91. C4⋊#170C2×D3semidirect
93. C4×#170C2×D3semidirect
102. C3×C5×D4M16semidirect
107. D60M16semidirect
248. C5×D4ΓL(1,𝔽25)semidirect
308. C3×D4#700semidirect
389. C3×C5#1486semidirect
427. D4#6740semidirect
458. C5#68172semidirect
480. C3#10604404semidirect

Maximal subgroups

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

subgroupindex
D4×#12002
#117519222
#117517972
D4⋊(C3⋊#170)2
C3×D4⋊#1702
#117464912
#117464902
#106044043
#681725