Finite Group Databasebeta

← #14282384

Subgroups — #14282384

Order 1920.

552 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756307C211yesmaximal, characteristic
2#11747015C211yesmaximal, characteristic, complemented
3C4×#6648C211yesmaximal, characteristic, complemented
4C5×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
5C3×D4⋊#168C211yesmaximal, characteristic, complemented
6#11745839C211yesmaximal, characteristic, complemented
7#11745838C211yesmaximal, characteristic, complemented
8#10598969—31nomaximal, Hall
9C2×#6817—21no—
10C3×C4×C5×D4C2211yescharacteristic
11#91829C411yescharacteristic
12#91827C411yescharacteristic
13C4×#1220—21no—
14#91784C411yescharacteristic
15#91777C411yescharacteristic
16#91774—21no—
17#91773—21no—
18C4×D60C2211yescharacteristic
19C42×D15C2211yescharacteristic
20C2×#6651—21no—
21C2×#6648—21no—
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C4×C5×C3⋊C8C2211yescharacteristic
24C3×C4⋊#168C2211yescharacteristic
25C3×C4×#168C2211yescharacteristic
26#90983—21no—
27#90951—21no—
28#68176—51nomaximal, Hall
29#65882—31no—
30#65126—31no—
31C4×C8×D5—31no—
32C5×D4⋊C8—31no—
33D4⋊#168D311yescharacteristic, complemented
34#64703—31no—
35#64679—31no—
36C2×C3×C5×D4C2×C411yescharacteristic
37C22×C3×C4×C5—21no—
38C2×#1220—21no—
39C2×#1220—21no—
40C2×#1220—21no—
41#6817—42no—
42#6817—42no—
43C2×D60—21no—
44C2×D60C2×C411yescharacteristic
45C2×C4×D15—21no—
46C2×C4×D15C2×C411yescharacteristic
47C2×C4×D15D411yescharacteristic
48C2×C4×D15D411yescharacteristic
49C2×Dic30—21no—
50C3×C5×C4⋊C4C2×C411yescharacteristic
51C3×C5×C22⋊C4—21no—
52C3×C42×C5C2311yescharacteristic
53#6719—21no—
54#6714—21no—
55#6714—21no—
56C4⋊Dic15C2×C411yescharacteristic
57#6712—21no—
58C4×Dic15C2×C411yescharacteristic
59C4×Dic15D411yescharacteristic
60C4×Dic15D411yescharacteristic
61C2×C5×C3⋊C8—21no—
62C2×C5×C3⋊C8—21no—
63C2×C3×#168—21no—
64C2×C3×#168—21no—
65#6651—42no—
66#6648—24no—
67#5548—51no—
68#4837—51no—
69C4×D3×C8—51no—
70C3×D4⋊C8—51no—
71D4⋊(C3⋊C8)D511yescharacteristic, complemented
72#4483—51no—
73#4459—51no—
74C2×#709—61no—
75C4×C5×D4C2×D311yescharacteristic
76#4086—31no—
77#4084—31no—
78C4×C22⋊D5—61no—
79C2×#676—61no—
80C2×C8×D5—61no—
81#4041—31no—
82#4034—31no—
83#4031—61no—
84#4030—61no—
85C4×D20—31no—
86C42×D5—31no—
87C5×C4⋊C8—31no—
88C4×C5×C8—31no—
89#3946—61no—
90C8×Dic5—61no—
91C4⋊#168C2×D311yescharacteristic
92C4×#168C2×D311yescharacteristic
93#1492—151noSylow
94C23×C3×C5—21no—
95C22×D15—21no—
96C22×D15C22⋊C411yescharacteristic
97C3×C5×D4—21no—
98C3×C5×D4—21no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5C22×C411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105#1220—42no—
106#1220—42no—
107#1220—42no—
108C2×Dic15—21no—
109C2×Dic15C22⋊C411yescharacteristic
110C2×Dic15C22⋊C411yescharacteristic
111C2×Dic15C22⋊C411yescharacteristic
112D60—21no—
113D60—21no—
114D60—42no—
115C4×D15—21no—
116C4×D15—21no—
117C4×D15—22no—
118C4×D15—41no—
119C4×D15—41no—
120C4×D15D812yes—
121C4×D15SD1612yes—
122Dic30—42no—
123C3×#168—22no—
124C3×#168—41no—
125C5×C3⋊C8—22no—
126C5×C3⋊C8—41no—
127C2×#235—101no—
128C3×C4×D4C2×D511yescharacteristic
129#940—51no—
130#938—51no—
131C4×#67—101no—
132C2×ΓL(1,𝔽25)—101no—
133C2×D3×C8—101no—
134#895—51no—
135#888—51no—
136#885—101no—
137#884—101no—
138C4×D12—51no—
139C42×D3—51no—
140C3×C4⋊C8—51no—
141C3×C4×C8—51no—
142Dic3⋊C8—101no—
143C8×Dic3—101no—
144C4⋊(C3⋊C8)C2×D511yescharacteristic
145C4×C3⋊C8C2×D511yescharacteristic
146C2×C5×D4C4×D311yescharacteristic
147C22×C4×C5—21no—
148C2×C22⋊D5—61no—
149C2×C22⋊D5—61no—
150C2×C22⋊D5—61no—
151#709—122no—
152#709—122no—
153C2×D20—31no—
154C2×D20—61no—
155C2×C4×D5—31no—
156C2×C4×D5—31no—
157C2×C4×D5—31no—
158C2×C4×D5—61no—
159C2×Dic10—61no—
160C2×C5×C8—61no—
161C2×C5×C8—61no—
162C5×C4⋊C4C4×D311yescharacteristic
163C5×C22⋊C4—21no—
164C42×C5C22×D311yescharacteristic
165C22⋊Dic5—61no—
166#685—61no—
167#685—61no—
168C4⋊Dic5—31no—
169#683—61no—
170C4×Dic5—31no—
171C4×Dic5—31no—
172C4×Dic5—31no—
173C2×#168—21no—
174C2×#168—21no—
175#676—122no—
176C8×D5—64no—
177#532—151no—
178#423—151no—
179C2×C4×C8—151no—
180D4⋊C8—31no—
181D4⋊C8—51no—
182D4⋊C8—151no—
183D4⋊C8—151no—
184C22×C3×C5—41no—
185C22×C3×C5—41no—
186C22×C3×C5—41no—
187C22×C3×C5C2×C22⋊C411yescharacteristic
188C2×D15—21no—
189C2×D15—21no—
190C2×D15—41no—
191C2×D15—41no—
192C2×D15—41no—
193C2×D15#10212yes—
194C3×C4×C5—21no—
195C3×C4×C5—41no—
196C3×C4×C5#13111yescharacteristic
197C3×C4×C5#13111yescharacteristic
198C3×C4×C5C2×D811yescharacteristic
199C3×C4×C5C2×SD1611yescharacteristic
200Dic15—21no—
201Dic15—41no—
202Dic15#10212yes—
203Dic15#10412yes—
204C2×C3×D4C4×D511yescharacteristic
205C22×C3×C4—21no—
206C2×#67—101no—
207C2×#67—101no—
208C2×#67—101no—
209#235—202no—
210#235—202no—
211C2×D12—51no—
212C2×D12—101no—
213C2×C4×D3—51no—
214C2×C4×D3—51no—
215C2×C4×D3—51no—
216C2×C4×D3—101no—
217C2×Dic6—101no—
218C2×C3×C8—101no—
219C2×C3×C8—101no—
220C3×C4⋊C4C4×D511yescharacteristic
221C3×C22⋊C4—21no—
222C3×C42C22×D511yescharacteristic
223#217—101no—
224(C2×D3)⋊C4—101no—
225(C2×D3)⋊C4—101no—
226C4⋊Dic3—51no—
227Dic3⋊C4—101no—
228C4×Dic3—51no—
229C4×Dic3—51no—
230C4×Dic3—51no—
231C2×C3⋊C8—21no—
232C2×C3⋊C8—21no—
233ΓL(1,𝔽25)—202no—
234D3×C8—104no—
235C23×C5—21no—
236C22×D5—31no—
237C22×D5—61no—
238C5×D4—21no—
239C5×D4—21no—
240C2×C4×C5—21no—
241C2×C4×C5—41no—
242C2×C4×C5—41no—
243C2×C4×C5C2×C4×D311yescharacteristic
244C2×C4×C5D3×D411yescharacteristic
245C2×C4×C5D3×D411yescharacteristic
246C22⋊D5—122no—
247C22⋊D5—122no—
248C22⋊D5—122no—
249C2×Dic5—31no—
250C2×Dic5—31no—
251C2×Dic5—31no—
252C2×Dic5—61no—
253D20—61no—
254D20—61no—
255D20—122no—
256C4×D5—32no—
257C4×D5—32no—
258C4×D5—62no—
259C4×D5—61no—
260C4×D5—61no—
261C4×D5—121no—
262C4×D5—121no—
263Dic10—122no—
264C5×C8—62no—
265C5×C8—121no—
266#168—22no—
267#168—41no—
268C2×#41—301no—
269C2×M16—301no—
270C22×C8—301no—
271C4⋊Q8—151no—
272#127—151no—
273#124—301no—
274#121—151no—
275#121—151no—
276#121—301no—
277C4×D4—151no—
278C4×D4—301no—
279C4×D4D3×D511yescharacteristic
280C2×C42—151no—
281C4⋊C8—31no—
282C4⋊C8—51no—
283C4⋊C8—301no—
284C4×C8—31no—
285C4×C8—51no—
286C4×C8—301no—
287C2×C3×C5—81no—
288C2×C3×C5#40811yescharacteristic
289C2×C3×C5C2×#10211yescharacteristic
290C2×C3×C5C2×#10411yescharacteristic
291D15—22no—
292D15—81no—
293C23×C3—21no—
294C22×D3—51no—
295C22×D3—101no—
296C3×D4—21no—
297C3×D4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—41no—
300C2×C3×C4—41no—
301C2×C3×C4C2×C4×D511yescharacteristic
302C2×C3×C4D4×D511yescharacteristic
303C2×C3×C4D4×D511yescharacteristic
304#67—202no—
305#67—202no—
306#67—202no—
307C2×Dic3—51no—
308C2×Dic3—51no—
309C2×Dic3—51no—
310C2×Dic3—101no—
311D12—101no—
312D12—101no—
313D12—202no—
314C4×D3—52no—
315C4×D3—52no—
316C4×D3—102no—
317C4×D3—101no—
318C4×D3—101no—
319C4×D3—201no—
320C4×D3—201no—
321Dic6—202no—
322C3×C8—102no—
323C3×C8—201no—
324C3⋊C8—22no—
325C3⋊C8—41no—
326C22×C5—41no—
327C22×C5—41no—
328C22×C5—41no—
329C22×C5D3×C22⋊C411yescharacteristic
330C2×D5—32no—
331C2×D5—61no—
332C2×D5—61no—
333C2×D5—121no—
334C2×D5—121no—
335C2×D5—121no—
336C4×C5—21no—
337C4×C5—41no—
338C4×C5#90111yescharacteristic
339C4×C5#90711yescharacteristic
340C4×C5D3×D811yescharacteristic
341C4×C5D3×SD1611yescharacteristic
342Dic5—32no—
343Dic5—32no—
344Dic5—61no—
345Dic5—121no—
346#41—602no—
347#41—602no—
348C2×Q8—301no—
349C2×D4—151no—
350C2×D4—301no—
351C2×D4—301no—
352C2×D4—301no—
353C2×D4—301no—
354C2×D4#120011yescharacteristic
355C22×C4—21no—
356C22×C4—151no—
357C22×C4—151no—
358C22×C4—151no—
359C22×C4—301no—
360M16—602no—
361C2×C8—61no—
362C2×C8—61no—
363C2×C8—101no—
364C2×C8—101no—
365C2×C8—304no—
366C4⋊C4—151no—
367C4⋊C4—301no—
368C4⋊C4#120011yescharacteristic
369C22⋊C4—21no—
370C22⋊C4—301no—
371C22⋊C4—301no—
372C22⋊C4—301no—
373C42—151no—
374C42—151no—
375C42—151no—
376C42C2×D3×D511yescharacteristic
377C3×C5#149211yescharacteristic, complemented, Hall
378C22×C3—41no—
379C22×C3—41no—
380C22×C3—41no—
381C22×C3D5×C22⋊C411yescharacteristic
382C2×D3—52no—
383C2×D3—101no—
384C2×D3—101no—
385C2×D3—201no—
386C2×D3—201no—
387C2×D3—201no—
388C3×C4—21no—
389C3×C4—41no—
390C3×C4#404711yescharacteristic
391C3×C4#405311yescharacteristic
392C3×C4D5×D811yescharacteristic
393C3×C4D5×SD1611yescharacteristic
394Dic3—52no—
395Dic3—52no—
396Dic3—101no—
397Dic3—201no—
398C2×C5—81no—
399C2×C5#472711yescharacteristic
400C2×C5D3×#10211yescharacteristic
401C2×C5D3×#10411yescharacteristic
402D5—62no—
403D5—241no—
404C23—21no—
405C23—151no—
406C23—301no—
407Q8—602no—
408D4—21no—
409D4—21no—
410D4—301no—
411D4—301no—
412D4—602no—
413D4—602no—
414D4—602no—
415D4—602no—
416C2×C4—21no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—151no—
420C2×C4—151no—
421C2×C4—152no—
422C2×C4—152no—
423C2×C4—151no—
424C2×C4—302no—
425C2×C4—301no—
426C2×C4—301no—
427C2×C4—301no—
428C2×C4—601no—
429C2×C4—601no—
430C2×C4C2×#120011yescharacteristic
431C2×C4#679011yescharacteristic
432C2×C4#679011yescharacteristic
433C8—62no—
434C8—102no—
435C8—121no—
436C8—201no—
437C2×C3—81no—
438C2×C3#6501611yescharacteristic
439C2×C3D5×#10211yescharacteristic
440C2×C3D5×#10411yescharacteristic
441D3—102no—
442D3—401no—
443C5#6817611yescharacteristic, complemented, Sylow
444C22—41no—
445C22—41no—
446C22—41no—
447C22—152no—
448C22—301no—
449C22—301no—
450C22—601no—
451C22—601no—
452C22—601no—
453C22#9156111yescharacteristic
454C4—21no—
455C4—41no—
456C4—152no—
457C4—152no—
458C4—301no—
459C4—601no—
460C4#9129011yescharacteristic
461C4#9129111yescharacteristic
462C4#9148111yescharacteristic
463C4#9148711yescharacteristic
464C3#1059896911yescharacteristic, complemented, Sylow
465C2—81no—
466C2—302no—
467C2—1201no—
468C2#1174849811yescharacteristic
469C2#1174895711yescharacteristic
470C2#1174943011yescharacteristic
subgroupG/H
centerC2×C4#6790
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11756307C2
cosocleC3×C42×C5C23
hypercenterC4×D4D3×D5
hypocenterC3×C5#1492
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #11747015C2semidirect
3. C4×#6648C2semidirect
4. C5×D4⋊(C3⋊C8)C2semidirect
5. C3×D4⋊#168C2semidirect
6. #11745839C2semidirect
7. #11745838C2semidirect
33. D4⋊#168D3semidirect
71. D4⋊(C3⋊C8)D5semidirect
377. C3×C5#1492semidirect
443. C5#68176semidirect
464. C3#10598969semidirect

Maximal subgroups

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

subgroupindex
#117563072
#117470152
C4×#66482
C5×D4⋊(C3⋊C8)2
C3×D4⋊#1682
#117458392
#117458382
#105989693
#681765