Finite Group Databasebeta

← #14313480

Subgroups — #14313480

Order 1920.

572 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5805C211yesmaximal, characteristic
2C2×#91118C211yesmaximal, characteristic, complemented
3C2×C3×#3966C211yesmaximal, characteristic, complemented
4#11746010C212yesmaximal, complemented
5#11746007C212yesmaximal, complemented
6#10602653—31nomaximal, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C2×C5×#235C411yescharacteristic, complemented
9C2×#6719—21no—
10C5×#953—21no—
11C5×#953—21no—
12C5×#940C411yescharacteristic, complemented
13C5×#940C2211yescharacteristic
14C5×#938—21no—
15C5×#938—21no—
16C5×#936C411yescharacteristic, complemented
17C5×#936C2211yescharacteristic
18C5×#926C411yescharacteristic, complemented
19C2×C3×C22⋊Dic5—21no—
20#91118—21no—
21#91118C2212yes—
22C3×#3966—21no—
23C3×#3966C2212yes—
24#70019—51nomaximal, Hall
25C5×#535—31no—
26C2×#3966—31no—
27C2×#3966D311yescharacteristic, complemented
28#64765—32no—
29#64761—32no—
30C24×C3×C5D411yescharacteristic
31C24×C3×C5D411yescharacteristic
32C2×C3×C5×D4—41no—
33C2×C3×C5×D4—41no—
34C2×C3×C5×D4C2×C411yescharacteristic
35C2×C3×C5×D4D411yescharacteristic
36C2×C3×C5×D4D411yescharacteristic
37C2×C3×C5×D4C2311yescharacteristic
38C22×C3×C4×C5C2×C411yescharacteristic
39C22×Dic15—41no—
40C2×C5×#67—21no—
41C2×C5×#67—21no—
42C2×C5×#67—21no—
43C2×C5×#67—21no—
44C2×C5×#67—21no—
45C5×#235—41no—
46C5×#235—41no—
47C2×C5×D12C2×C411yescharacteristic, complemented
48C2×C4×C5×D3—21no—
49C2×C5×Dic6C2×C411yescharacteristic, complemented
50C22×C3×Dic5—41no—
51#6719—22no—
52#6719—41no—
53C5×#217—21no—
54C5×#217—21no—
55C5×#217—21no—
56C5×#217—21no—
57C5×#217—21no—
58C5×C4⋊Dic3—21no—
59C4×C5×Dic3C2×C411yescharacteristic, complemented
60C4×C5×Dic3C2×C411yescharacteristic, complemented
61C3×C22⋊Dic5—22no—
62C3×C22⋊Dic5—41no—
63#5805D511yescharacteristic
64C2×C3×#99—51no—
65C2×#834—51no—
66#4474—52no—
67#4473—52no—
68C2×C5×#41—31no—
69C22×C5×D4C2×D311yescharacteristic
70C5×#127—31no—
71C5×#127—31no—
72C5×#124—31no—
73C5×#124—31no—
74C5×#121—61no—
75C5×#121—61no—
76C5×#120—61no—
77C5×#120—61no—
78C5×#117—31no—
79C2×C22⋊Dic5—21no—
80C2×C22⋊Dic5—61no—
81#3966—21no—
82#3966—32no—
83#3966—61no—
84#3966C2×D312yes—
85#2127—151noSylow
86C23×C3×C5—21no—
87C23×C3×C5—21no—
88C23×C3×C5—21no—
89C23×C3×C5—21no—
90C23×C3×C5—81no—
91C23×C3×C5—81no—
92C23×C3×C5C22⋊C411yescharacteristic
93C23×C3×C5C22⋊C411yescharacteristic
94C23×C3×C5C22⋊C411yescharacteristic
95C23×C3×C5C2×D411yescharacteristic
96C23×C3×C5C2×D411yescharacteristic
97C22×C5×D3—21no—
98C3×C5×D4—41no—
99C3×C5×D4—41no—
100C3×C5×D4—41no—
101C3×C5×D4—41no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—21no—
104C2×C3×C4×C5C22⋊C411yescharacteristic
105C2×C3×C4×C5C22×C411yescharacteristic
106C2×Dic15—42no—
107C2×Dic15—82no—
108C5×#67—41no—
109C5×#67—41no—
110C5×#67—81no—
111C5×#67—81no—
112C5×#67—81no—
113C5×#67—81no—
114C2×C5×Dic3—21no—
115C2×C5×Dic3—21no—
116C2×C5×Dic3—21no—
117C5×D12—41no—
118C4×C5×D3—42no—
119C5×Dic6—41no—
120C2×C3×Dic5—42no—
121C2×C3×Dic5—82no—
122C22×C3×D4C2×D511yescharacteristic
123C2×#235Dic511yescharacteristic, complemented
124C2×C3×C22⋊C4—101no—
125#953—21no—
126#953—21no—
127C2×#217—101no—
128#940Dic511yescharacteristic, complemented
129#940C2×D511yescharacteristic
130#938—21no—
131#938—21no—
132#936Dic511yescharacteristic, complemented
133#936C2×D511yescharacteristic
134#926Dic511yescharacteristic, complemented
135C3×#99—52no—
136C3×#99—101no—
137#834—52no—
138#834—101no—
139C24×C5D1211yescharacteristic
140C24×C5#6711yescharacteristic
141C5×#41—121no—
142C5×#41—121no—
143C2×C5×Q8—31no—
144C2×C5×D4—31no—
145C2×C5×D4—41no—
146C2×C5×D4—41no—
147C2×C5×D4—61no—
148C2×C5×D4—61no—
149C2×C5×D4—61no—
150C2×C5×D4—61no—
151C2×C5×D4—61no—
152C2×C5×D4C4×D311yescharacteristic
153C2×C5×D4D1211yescharacteristic
154C2×C5×D4#6711yescharacteristic
155C2×C5×D4C22×D311yescharacteristic
156C22×C4×C5—61no—
157C22×C4×C5C4×D311yescharacteristic
158C22×Dic5—41no—
159C22×Dic5—121no—
160C5×C4⋊C4—61no—
161C5×C22⋊C4—61no—
162C5×C22⋊C4—61no—
163C5×C22⋊C4—61no—
164C5×C22⋊C4—61no—
165C5×C22⋊C4—61no—
166C42×C5—31no—
167C42×C5—31no—
168C22⋊Dic5—22no—
169C22⋊Dic5—41no—
170C22⋊Dic5—62no—
171C22⋊Dic5—121no—
172#535—31no—
173C2×#99—51no—
174C2×#99—151no—
175#354—152no—
176#353—152no—
177C22×C3×C5—21no—
178C22×C3×C5—21no—
179C22×C3×C5—21no—
180C22×C3×C5—21no—
181C22×C3×C5—41no—
182C22×C3×C5—41no—
183C22×C3×C5—41no—
184C22×C3×C5—41no—
185C22×C3×C5—41no—
186C22×C3×C5—42no—
187C22×C3×C5—42no—
188C22×C3×C5—81no—
189C22×C3×C5—81no—
190C22×C3×C5#9911yescharacteristic
191C22×C3×C5#9911yescharacteristic
192C22×C3×C5C2×C22⋊C411yescharacteristic
193C2×C5×D3—41no—
194C2×C5×D3—41no—
195C2×C5×D3—41no—
196C3×C4×C5—21no—
197C3×C4×C5—21no—
198Dic15—82no—
199C3×Dic5—82no—
200C5×Dic3—41no—
201C5×Dic3—41no—
202C5×Dic3—41no—
203C24×C3C22⋊D511yescharacteristic
204C24×C3C22⋊D511yescharacteristic
205C2×C3×D4—41no—
206C2×C3×D4—41no—
207C2×C3×D4C2×Dic511yescharacteristic
208C2×C3×D4C22⋊D511yescharacteristic
209C2×C3×D4C22⋊D511yescharacteristic
210C2×C3×D4C22×D511yescharacteristic
211C22×C3×C4—201no—
212C22×C3×C4C2×Dic511yescharacteristic
213C2×#67—21no—
214C2×#67—21no—
215C2×#67—21no—
216C2×#67—21no—
217C2×#67—21no—
218C22×Dic3—201no—
219#235—41no—
220#235—41no—
221C2×D12C2×Dic511yescharacteristic, complemented
222C2×C4×D3—21no—
223C2×Dic6C2×Dic511yescharacteristic, complemented
224C3×C22⋊C4—102no—
225C3×C22⋊C4—201no—
226#217—21no—
227#217—21no—
228#217—21no—
229#217—21no—
230#217—21no—
231#217—102no—
232#217—201no—
233C4⋊Dic3—21no—
234C4×Dic3C2×Dic511yescharacteristic, complemented
235C4×Dic3C2×Dic511yescharacteristic, complemented
236C23×C5—21no—
237C23×C5—21no—
238C23×C5—21no—
239C23×C5—21no—
240C23×C5—61no—
241C23×C5—81no—
242C23×C5—81no—
243C23×C5(C2×D3)⋊C411yescharacteristic
244C23×C5(C2×D3)⋊C411yescharacteristic
245C23×C5(C2×D3)⋊C411yescharacteristic
246C23×C5C2×D1211yescharacteristic
247C23×C5C2×#6711yescharacteristic
248C5×Q8—121no—
249C5×D4—41no—
250C5×D4—41no—
251C5×D4—41no—
252C5×D4—41no—
253C5×D4—121no—
254C5×D4—121no—
255C5×D4—121no—
256C5×D4—241no—
257C5×D4—241no—
258C5×D4—241no—
259C5×D4—241no—
260C2×C4×C5—21no—
261C2×C4×C5—21no—
262C2×C4×C5—61no—
263C2×C4×C5—61no—
264C2×C4×C5—61no—
265C2×C4×C5—122no—
266C2×C4×C5(C2×D3)⋊C411yescharacteristic
267C2×C4×C5C2×C4×D311yescharacteristic
268C2×Dic5—42no—
269C2×Dic5—82no—
270C2×Dic5—122no—
271C2×Dic5—242no—
272C2×#41—31no—
273C22×D4D3×D511yescharacteristic
274#127—31no—
275#127—31no—
276#124—31no—
277#124—31no—
278#121—61no—
279#121—61no—
280#120—61no—
281#120—61no—
282#117—31no—
283C2×C22⋊C4—101no—
284C2×C22⋊C4—301no—
285#99—52no—
286#99—101no—
287#99—152no—
288#99—301no—
289C2×C3×C5—21no—
290C2×C3×C5—21no—
291C2×C3×C5—21no—
292C2×C3×C5—41no—
293C2×C3×C5—41no—
294C2×C3×C5—41no—
295C2×C3×C5—41no—
296C2×C3×C5C2×#9911yescharacteristic
297C5×D3—81no—
298C23×C3—21no—
299C23×C3—21no—
300C23×C3—21no—
301C23×C3—21no—
302C23×C3—81no—
303C23×C3—81no—
304C23×C3C22⋊Dic511yescharacteristic
305C23×C3C22⋊Dic511yescharacteristic
306C23×C3C22⋊Dic511yescharacteristic
307C23×C3C2×C22⋊D511yescharacteristic
308C23×C3C2×C22⋊D511yescharacteristic
309C22×D3—21no—
310C3×D4—41no—
311C3×D4—41no—
312C3×D4—41no—
313C3×D4—41no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—202no—
317C2×C3×C4—402no—
318C2×C3×C4C22⋊Dic511yescharacteristic
319C2×C3×C4C22×Dic511yescharacteristic
320#67—41no—
321#67—41no—
322#67—81no—
323#67—81no—
324#67—81no—
325#67—81no—
326C2×Dic3—21no—
327C2×Dic3—21no—
328C2×Dic3—21no—
329C2×Dic3—202no—
330C2×Dic3—402no—
331D12—41no—
332C4×D3—42no—
333Dic6—41no—
334C22×C5—21no—
335C22×C5—21no—
336C22×C5—21no—
337C22×C5—21no—
338C22×C5—41no—
339C22×C5—41no—
340C22×C5—41no—
341C22×C5—41no—
342C22×C5—41no—
343C22×C5—42no—
344C22×C5—42no—
345C22×C5—81no—
346C22×C5—81no—
347C22×C5—121no—
348C22×C5—121no—
349C22×C5—121no—
350C22×C5#80611yescharacteristic
351C22×C5#80611yescharacteristic
352C22×C5C2×(C2×D3)⋊C411yescharacteristic
353C4×C5—21no—
354C4×C5—21no—
355C4×C5—121no—
356C4×C5—121no—
357C4×C5—121no—
358Dic5—82no—
359Dic5—242no—
360C24#120111yescharacteristic
361C24#120311yescharacteristic
362#41—121no—
363#41—121no—
364C2×Q8—31no—
365C2×D4—31no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—61no—
369C2×D4—61no—
370C2×D4—61no—
371C2×D4—61no—
372C2×D4—61no—
373C2×D4D3×Dic511yescharacteristic
374C2×D4#120111yescharacteristic
375C2×D4#120311yescharacteristic
376C2×D4C2×D3×D511yescharacteristic
377C22×C4—61no—
378C22×C4—201no—
379C22×C4—601no—
380C22×C4D3×Dic511yescharacteristic
381C4⋊C4—61no—
382C22⋊C4—61no—
383C22⋊C4—61no—
384C22⋊C4—61no—
385C22⋊C4—61no—
386C22⋊C4—61no—
387C22⋊C4—102no—
388C22⋊C4—201no—
389C22⋊C4—302no—
390C22⋊C4—601no—
391C42—31no—
392C42—31no—
393C3×C5#212711yescharacteristic, complemented, Hall
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—41no—
399C22×C3—41no—
400C22×C3—41no—
401C22×C3—41no—
402C22×C3—41no—
403C22×C3—42no—
404C22×C3—42no—
405C22×C3—81no—
406C22×C3—81no—
407C22×C3#396611yescharacteristic
408C22×C3#396611yescharacteristic
409C22×C3C2×C22⋊Dic511yescharacteristic
410C2×D3—41no—
411C2×D3—41no—
412C2×D3—41no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—402no—
416Dic3—41no—
417Dic3—41no—
418Dic3—41no—
419Dic3—402no—
420C2×C5—21no—
421C2×C5—21no—
422C2×C5—21no—
423C2×C5—41no—
424C2×C5—41no—
425C2×C5—41no—
426C2×C5—41no—
427C2×C5—241no—
428C2×C5C2×#80611yescharacteristic
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—61no—
434C23—81no—
435C23—81no—
436C23(C2×D3)⋊Dic511yescharacteristic
437C23(C2×D3)⋊Dic511yescharacteristic
438C23(C2×D3)⋊Dic511yescharacteristic
439C23C2×#120111yescharacteristic
440C23C2×#120311yescharacteristic
441Q8—121no—
442D4—41no—
443D4—41no—
444D4—41no—
445D4—41no—
446D4—121no—
447D4—121no—
448D4—121no—
449D4—241no—
450D4—241no—
451D4—241no—
452D4—241no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—61no—
456C2×C4—61no—
457C2×C4—61no—
458C2×C4—122no—
459C2×C4—202no—
460C2×C4—402no—
461C2×C4—602no—
462C2×C4—1202no—
463C2×C4(C2×D3)⋊Dic511yescharacteristic
464C2×C4C2×D3×Dic511yescharacteristic
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—41no—
469C2×C3—41no—
470C2×C3—41no—
471C2×C3—41no—
472C2×C3C2×#396611yescharacteristic
473D3—81no—
474C5#7001911yescharacteristic, complemented, Sylow
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—41no—
480C22—41no—
481C22—41no—
482C22—41no—
483C22—41no—
484C22—42no—
485C22—42no—
486C22—81no—
487C22—81no—
488C22—121no—
489C22—121no—
490C22—121no—
491C22#9099611yescharacteristic
492C22#9099611yescharacteristic
493C22C2×(C2×D3)⋊Dic511yescharacteristic
494C4—21no—
495C4—21no—
496C4—121no—
497C4—121no—
498C4—121no—
499C4—402no—
500C4—1202no—
501C3#1060265311yescharacteristic, complemented, Sylow
502C2—21no—
503C2—21no—
504C2—21no—
505C2—41no—
506C2—41no—
507C2—41no—
508C2—41no—
509C2—241no—
510C2C2×#9099611yescharacteristic
subgroupG/H
centerC2C2×#90996
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×D4C2×D3×D5
FittingC22×C3×C5×D4C22
socleC2×C3×C5C2×#99
prime radicalC5×#5805C2
cosocleC2×C3×C5×D4C23
hypercenterC22×D4D3×D5
hypocenterC3×C5#2127
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#91118C2semidirect
3. C2×C3×#3966C2semidirect
4. #11746010C2semidirect
5. #11746007C2semidirect
8. C2×C5×#235C4semidirect
12. C5×#940C4semidirect
16. C5×#936C4semidirect
18. C5×#926C4semidirect
27. C2×#3966D3semidirect
47. C2×C5×D12C2×C4semidirect
49. C2×C5×Dic6C2×C4semidirect
59. C4×C5×Dic3C2×C4semidirect
60. C4×C5×Dic3C2×C4semidirect
123. C2×#235Dic5semidirect
128. #940Dic5semidirect
132. #936Dic5semidirect
134. #926Dic5semidirect
221. C2×D12C2×Dic5semidirect
223. C2×Dic6C2×Dic5semidirect
234. C4×Dic3C2×Dic5semidirect
235. C4×Dic3C2×Dic5semidirect
393. C3×C5#2127semidirect
474. C5#70019semidirect
501. C3#10602653semidirect

Maximal subgroups

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

subgroupindex
C5×#58052
C2×#911182
C2×C3×#39662
#117460102
#117460072
#106026533
#700195