Finite Group Databasebeta

← #14283276

Subgroups — #14283276

Order 1920.

652 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#4076C211yesmaximal, characteristic
2C5×#4664C211yesmaximal, characteristic, complemented
3#11748505C211yesmaximal, characteristic, complemented
4#11746272C211yesmaximal, characteristic, complemented
5C3×#64671C211yesmaximal, characteristic, complemented
6#11745959C211yesmaximal, characteristic, complemented
7#11745954C211yesmaximal, characteristic, complemented
8#10600324—31nomaximal, Hall
9C22×C4×C5×D3C2211yescharacteristic
10C2×D3×C22⋊D5—21no—
11C2×D3×D20C411yescharacteristic, complemented
12#91819C2211yescharacteristic
13C2×C5×(C2×D3)⋊C4—21no—
14C3×#4076C2211yescharacteristic
15#91569—21no—
16D3×#685—21no—
17#91460C411yescharacteristic, complemented
18#91456C411yescharacteristic, complemented
19#91454—21no—
20D3×C4⋊Dic5C411yescharacteristic, complemented
21C2×#6650—21no—
22C3×C5×#95C2211yescharacteristic, complemented
23#91114C2211yescharacteristic, complemented
24C5×C3⋊#95—21no—
25C5×C3⋊#95C2211yescharacteristic, complemented
26C3×C22⋊#168C2211yescharacteristic, complemented
27(C2×D3)⋊#168—21no—
28#68304—51nomaximal, Hall
29C2×#4076—31no—
30C5×#381—31no—
31#65496—31no—
32#64671—31no—
33#64671—31no—
34#64671—31no—
35#64671D311yescharacteristic, complemented
36C23×C5×D3D411yescharacteristic
37C22×D3×D5—21no—
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5C2311yescharacteristic
40C2×#1220—21no—
41C2×D60C2×C411yescharacteristic
42C22×C5×Dic3—21no—
43C22×C5×Dic3D411yescharacteristic
44C2×C4×C5×D3—42no—
45C2×C4×C5×D3C2×C411yescharacteristic
46C2×C4×C5×D3C2×C411yescharacteristic
47C2×C4×C5×D3D411yescharacteristic
48C2×C4×C5×D3D411yescharacteristic
49C2×C3×C22⋊D5—21no—
50C2×C3×D20C2×C411yescharacteristic
51D3×C22⋊D5—42no—
52D3×C22⋊D5—42no—
53C2×#1203—21no—
54C2×#1202—21no—
55C2×#1201—21no—
56C2×D3×Dic5—21no—
57D3×D20—42no—
58#6714—21no—
59C4⋊Dic15C2×C411yescharacteristic
60C2×C3⋊#168—21no—
61C5×(C2×D3)⋊C4—42no—
62C3×#685—21no—
63C3×C4⋊Dic5C2×C411yescharacteristic
64C2×C3×#168—21no—
65Dic3⋊Dic5—21no—
66#6667—21no—
67#6665—21no—
68#6650—42no—
69D3×#121—51no—
70#4726—51no—
71#4664D511yescharacteristic, complemented
72C3×#327—51no—
73#4537—51no—
74#4470—51no—
75#4451—51no—
76C23×C4×C5—31no—
77C22×C22⋊D5—61no—
78C22×D20—31no—
79C2×C5×C22⋊C4—61no—
80#4076—31no—
81#4076—31no—
82#4076—31no—
83#4076—61no—
84#4076—61no—
85#4076C2×D311yescharacteristic
86C2×#685—61no—
87C2×C4⋊Dic5—31no—
88C2×#681—61no—
89C5×#95—31no—
90C5×#95—61no—
91C5×#95C2×D311yescharacteristic, complemented
92C22⋊#168—31no—
93C22⋊#168—61no—
94C22⋊#168C2×D311yescharacteristic, complemented
95#1510—151noSylow
96C23×C3×C5C2×D411yescharacteristic
97C22×D15—21no—
98C22×C5×D3—21no—
99C22×C5×D3—21no—
100C22×C5×D3—22no—
101C22×C5×D3—41no—
102C22×C5×D3C22⋊C411yescharacteristic
103C22×C5×D3C22⋊C411yescharacteristic
104C22×C3×D5—21no—
105C2×D3×D5—42no—
106C2×D3×D5—42no—
107C2×D3×D5—42no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5—41no—
112C2×C3×C4×C5C22×C411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114#1220—41no—
115#1220—41no—
116C2×Dic15—21no—
117D60—41no—
118C2×C5×Dic3—41no—
119C2×C5×Dic3—41no—
120C2×C5×Dic3—41no—
121C2×C5×Dic3—41no—
122C2×C5×Dic3C22⋊C411yescharacteristic
123C2×C5×Dic3C22⋊C411yescharacteristic
124C4×C5×D3—22no—
125C4×C5×D3—22no—
126C4×C5×D3—41no—
127C4×C5×D3—41no—
128C3×C22⋊D5—41no—
129C3×C22⋊D5—41no—
130C2×C3×Dic5—21no—
131C3×D20—41no—
132#1203—42no—
133#1202—42no—
134#1201—42no—
135D3×Dic5—42no—
136C3⋊#168—41no—
137C3×#168—41no—
138C2×D3×D4—51no—
139C2×D3×D4—101no—
140C22×C4×D3C2×D511yescharacteristic
141C3×#121—51no—
142#939—101no—
143#938—51no—
144#930—51no—
145C2×(C2×D3)⋊C4—21no—
146C2×ΓL(1,𝔽25)—101no—
147#895—51no—
148D3×C4⋊C4—51no—
149#884—101no—
150D3×C22⋊C4—101no—
151C3×C22⋊C8—51no—
152C3×#95C2×D511yescharacteristic, complemented
153C3⋊#95—21no—
154C3⋊#95C2×D511yescharacteristic, complemented
155#830—51no—
156(C2×D3)⋊C8—101no—
157C24×C5—31no—
158C23×D5—61no—
159C22×C4×C5—21no—
160C22×C4×C5—31no—
161C22×C4×C5—31no—
162C22×C4×C5—31no—
163C22×C4×C5—31no—
164C22×C4×C5—31no—
165C22×C4×C5—61no—
166C22×C4×C5—122no—
167C22×C4×C5C22×D311yescharacteristic
168C2×C22⋊D5—21no—
169C2×C22⋊D5—61no—
170C2×C22⋊D5—61no—
171C2×C22⋊D5—61no—
172C2×C22⋊D5—122no—
173C2×C22⋊D5—122no—
174C22×Dic5—61no—
175C2×D20—31no—
176C2×D20—61no—
177C2×D20—122no—
178C2×D20C4×D311yescharacteristic
179C5×C22⋊C4—122no—
180#685—21no—
181#685—61no—
182#685—61no—
183#685—61no—
184C4⋊Dic5—31no—
185C4⋊Dic5—61no—
186C4⋊Dic5C4×D311yescharacteristic
187#681—122no—
188C2×#168—21no—
189C2×#168—61no—
190C2×#121—151no—
191#407—151no—
192#381—31no—
193#327—51no—
194#327—151no—
195#327—151no—
196#327—151no—
197C22×C3×C5—21no—
198C22×C3×C5—21no—
199C22×C3×C5C2×C22⋊C411yescharacteristic
200C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
201C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
202C2×D15—41no—
203C2×D15—41no—
204C2×D15—41no—
205C2×C5×D3—21no—
206C2×C5×D3—21no—
207C2×C5×D3—21no—
208C2×C5×D3—21no—
209C2×C5×D3—21no—
210C2×C5×D3—42no—
211C2×C5×D3—42no—
212C2×C5×D3#9912yes—
213C2×C3×D5—41no—
214C2×C3×D5—41no—
215C2×C3×D5—41no—
216D3×D5—84no—
217C3×C4×C5—21no—
218C3×C4×C5—21no—
219C3×C4×C5—81no—
220Dic15—41no—
221C3×Dic5—41no—
222C5×Dic3—21no—
223C5×Dic3—21no—
224C5×Dic3—81no—
225C23×D3—101no—
226C23×D3C22⋊D511yescharacteristic
227C2×C3×D4—51no—
228C2×C3×D4—101no—
229C22×C3×C4—21no—
230C22×C3×C4C22×D511yescharacteristic
231C2×#67—101no—
232C2×#67—101no—
233C2×#67—101no—
234C22×Dic3—21no—
235C22×Dic3C22⋊D511yescharacteristic
236D3×D4—202no—
237D3×D4—202no—
238D3×D4—202no—
239C2×D12—51no—
240C2×D12—101no—
241C2×C4×D3—42no—
242C2×C4×D3—101no—
243C2×C4×D3C4×D511yescharacteristic
244C2×C4×D3C4×D511yescharacteristic
245C2×C4×D3D2011yescharacteristic
246C2×C4×D3D2011yescharacteristic
247C2×C3×C8—101no—
248C3×C4⋊C4—51no—
249C3×C22⋊C4—101no—
250#217—101no—
251(C2×D3)⋊C4—42no—
252(C2×D3)⋊C4—101no—
253(C2×D3)⋊C4—101no—
254C4⋊Dic3—51no—
255Dic3⋊C4—101no—
256C2×C3⋊C8—101no—
257ΓL(1,𝔽25)—202no—
258C23×C5—31no—
259C23×C5—31no—
260C23×C5—62no—
261C23×C5—61no—
262C23×C5—61no—
263C23×C5—121no—
264C23×C5D3×D411yescharacteristic
265C22×D5—21no—
266C22×D5—61no—
267C22×D5—122no—
268C22×D5—122no—
269C22×D5—122no—
270C2×C4×C5—31no—
271C2×C4×C5—31no—
272C2×C4×C5—41no—
273C2×C4×C5—41no—
274C2×C4×C5—41no—
275C2×C4×C5—41no—
276C2×C4×C5—62no—
277C2×C4×C5—62no—
278C2×C4×C5—121no—
279C2×C4×C5—121no—
280C2×C4×C5—121no—
281C2×C4×C5—121no—
282C2×C4×C5—121no—
283C2×C4×C5—121no—
284C2×C4×C5C2×C4×D311yescharacteristic
285C2×C4×C5D3×D411yescharacteristic
286C22⋊D5—41no—
287C22⋊D5—41no—
288C22⋊D5—122no—
289C22⋊D5—122no—
290C22⋊D5—121no—
291C22⋊D5—121no—
292C2×Dic5—21no—
293C2×Dic5—61no—
294C2×Dic5—122no—
295D20—41no—
296D20—121no—
297D20—122no—
298#168—41no—
299#168—121no—
300C22×D4—151no—
301C22×D4—301no—
302C23×C4—31no—
303C2×M16—301no—
304#121—51no—
305#121—151no—
306#121—151no—
307#121—151no—
308#121—301no—
309#121—301no—
310C2×C4⋊C4—151no—
311C2×C22⋊C4—61no—
312C2×C22⋊C4—301no—
313C22⋊C8—51no—
314C22⋊C8—151no—
315C22⋊C8—301no—
316#95—31no—
317#95—61no—
318#95D3×D511yescharacteristic, complemented
319C2×C3×C5—21no—
320C2×C3×C5—21no—
321C2×C3×C5C2×#9911yescharacteristic
322C2×C3×C5#41811yescharacteristic
323C2×C3×C5#42111yescharacteristic
324D15—81no—
325C3×D5—81no—
326C5×D3—22no—
327C5×D3—41no—
328C23×C3—101no—
329C23×C3C2×C22⋊D511yescharacteristic
330C22×D3—21no—
331C22×D3—21no—
332C22×D3—22no—
333C22×D3—41no—
334C22×D3—101no—
335C22×D3—202no—
336C22×D3—202no—
337C22×D3—202no—
338C22×D3#68511yescharacteristic
339C22×D3#68511yescharacteristic
340C3×D4—201no—
341C3×D4—201no—
342C3×D4—201no—
343C2×C3×C4—41no—
344C2×C3×C4—41no—
345C2×C3×C4—41no—
346C2×C3×C4—41no—
347C2×C3×C4—101no—
348C2×C3×C4C2×C4×D511yescharacteristic
349C2×C3×C4C2×D2011yescharacteristic
350#67—202no—
351#67—202no—
352#67—201no—
353#67—201no—
354C2×Dic3—41no—
355C2×Dic3—41no—
356C2×Dic3—41no—
357C2×Dic3—41no—
358C2×Dic3—101no—
359C2×Dic3#68511yescharacteristic
360C2×Dic3#68511yescharacteristic
361D12—201no—
362D12—202no—
363C4×D3—22no—
364C4×D3—22no—
365C4×D3—41no—
366C4×D3—41no—
367C4×D3—202no—
368C3×C8—201no—
369C3⋊C8—201no—
370C22×C5—21no—
371C22×C5—21no—
372C22×C5—32no—
373C22×C5—61no—
374C22×C5—61no—
375C22×C5—61no—
376C22×C5—61no—
377C22×C5—61no—
378C22×C5—122no—
379C22×C5—122no—
380C22×C5D3×C22⋊C411yescharacteristic
381C22×C5#91111yescharacteristic
382C22×C5#91411yescharacteristic
383C2×D5—41no—
384C2×D5—41no—
385C2×D5—41no—
386C2×D5—121no—
387C2×D5—121no—
388C2×D5—121no—
389C2×D5—244no—
390C4×C5—21no—
391C4×C5—21no—
392C4×C5—61no—
393C4×C5—61no—
394C4×C5—81no—
395C4×C5—241no—
396Dic5—41no—
397Dic5—121no—
398C24—31no—
399C24—301no—
400C2×D4—51no—
401C2×D4—101no—
402C2×D4—151no—
403C2×D4—301no—
404C2×D4—301no—
405C2×D4—301no—
406C2×D4—301no—
407C2×D4—602no—
408C2×D4—602no—
409C2×D4—602no—
410C22×C4—21no—
411C22×C4—31no—
412C22×C4—31no—
413C22×C4—31no—
414C22×C4—31no—
415C22×C4—31no—
416C22×C4—61no—
417C22×C4—122no—
418C22×C4—301no—
419C22×C4C2×D3×D511yescharacteristic
420M16—602no—
421C2×C8—101no—
422C2×C8—301no—
423C4⋊C4—51no—
424C4⋊C4—151no—
425C4⋊C4—301no—
426C22⋊C4—101no—
427C22⋊C4—122no—
428C22⋊C4—301no—
429C22⋊C4—301no—
430C22⋊C4—301no—
431C3×C5#151011yescharacteristic, complemented, Hall
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—201no—
435C22×C3—201no—
436C22×C3—201no—
437C22×C3C2×#68511yescharacteristic
438C22×C3#409511yescharacteristic
439C22×C3#409511yescharacteristic
440C2×D3—21no—
441C2×D3—21no—
442C2×D3—21no—
443C2×D3—21no—
444C2×D3—21no—
445C2×D3—42no—
446C2×D3—42no—
447C2×D3—201no—
448C2×D3—201no—
449C2×D3—201no—
450C2×D3—404no—
451C2×D3#393812yes—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—81no—
455C3×C4—201no—
456Dic3—21no—
457Dic3—21no—
458Dic3—81no—
459Dic3—201no—
460C2×C5—21no—
461C2×C5—21no—
462C2×C5—62no—
463C2×C5—121no—
464C2×C5D3×#9911yescharacteristic
465C2×C5#477011yescharacteristic
466C2×C5#482111yescharacteristic
467D5—81no—
468D5—241no—
469C23—31no—
470C23—31no—
471C23—62no—
472C23—61no—
473C23—61no—
474C23—101no—
475C23—121no—
476C23—301no—
477C23—602no—
478C23—602no—
479C23—602no—
480C23D3×C22⋊D511yescharacteristic
481D4—201no—
482D4—201no—
483D4—201no—
484D4—601no—
485D4—602no—
486D4—602no—
487D4—602no—
488D4—601no—
489D4—601no—
490C2×C4—31no—
491C2×C4—31no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—101no—
499C2×C4—121no—
500C2×C4—121no—
501C2×C4—121no—
502C2×C4—121no—
503C2×C4—121no—
504C2×C4—121no—
505C2×C4—301no—
506C2×C4—602no—
507C2×C4C4×D3×D511yescharacteristic
508C2×C4D3×D2011yescharacteristic
509C8—201no—
510C8—601no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—401no—
514C2×C3C2×#393811yescharacteristic
515C2×C3#6529011yescharacteristic
516C2×C3#6529411yescharacteristic
517D3—22no—
518D3—41no—
519D3—401no—
520C5#6830411yescharacteristic, complemented, Sylow
521C22—21no—
522C22—21no—
523C22—32no—
524C22—61no—
525C22—61no—
526C22—61no—
527C22—61no—
528C22—61no—
529C22—122no—
530C22—122no—
531C22—201no—
532C22—201no—
533C22—201no—
534C22—601no—
535C22—601no—
536C22—601no—
537C22—1204no—
538C22D3×#68511yescharacteristic
539C22#9148011yescharacteristic
540C22#9150411yescharacteristic
541C4—21no—
542C4—21no—
543C4—61no—
544C4—61no—
545C4—81no—
546C4—201no—
547C4—241no—
548C4—601no—
549C3#1060032411yescharacteristic, complemented, Sylow
550C2—21no—
551C2—21no—
552C2—62no—
553C2—121no—
554C2—401no—
555C2—1201no—
556C2#1174711111yescharacteristic
557C2D3×#393811yescharacteristic
558C2#1174747711yescharacteristic
subgroupG/H
centerC22D3×#685
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#95C22
socleC22×C3×C5C2×C22⋊C4
prime radicalD3×#4076C2
cosocleC22×C3×C4×C5C23
hypercenter#95D3×D5
hypocenterC3×C5#1510
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C5×#4664C2semidirect
3. #11748505C2semidirect
4. #11746272C2semidirect
5. C3×#64671C2semidirect
6. #11745959C2semidirect
7. #11745954C2semidirect
11. C2×D3×D20C4semidirect
17. #91460C4semidirect
18. #91456C4semidirect
20. D3×C4⋊Dic5C4semidirect
22. C3×C5×#95C22semidirect
23. #91114C22semidirect
25. C5×C3⋊#95C22semidirect
26. C3×C22⋊#168C22semidirect
35. #64671D3semidirect
71. #4664D5semidirect
91. C5×#95C2×D3semidirect
94. C22⋊#168C2×D3semidirect
152. C3×#95C2×D5semidirect
154. C3⋊#95C2×D5semidirect
318. #95D3×D5semidirect
431. C3×C5#1510semidirect
520. C5#68304semidirect
549. C3#10600324semidirect

Maximal subgroups

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

subgroupindex
D3×#40762
C5×#46642
#117485052
#117462722
C3×#646712
#117459592
#117459542
#106003243
#683045