Finite Group Databasebeta

← #14282383

Subgroups — #14282383

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
1C3×#65882C211yesmaximal, characteristic
2#11747007C211yesmaximal, characteristic, complemented
3C4×D5×C3⋊C8C211yesmaximal, characteristic, complemented
4D4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
5C5×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#11745835C211yesmaximal, characteristic, complemented
7#11745834C211yesmaximal, characteristic, complemented
8#10598969—31nomaximal, Hall
9C2×C3×#709—21no—
10C3×C4×C5×D4C2211yescharacteristic
11C3×#4086C411yescharacteristic
12C3×#4084C411yescharacteristic
13C3×C4×C22⋊D5—21no—
14C3×#4041C411yescharacteristic
15C3×#4034C411yescharacteristic
16C3×#4031—21no—
17C3×#4030—21no—
18C3×C4×D20C2211yescharacteristic
19C3×C42×D5C2211yescharacteristic
20C2×#6649—21no—
21C2×D5×C3⋊C8—21no—
22C4⋊(C3⋊#168)C2211yescharacteristic
23C4×C3⋊#168C2211yescharacteristic
24C5×C4⋊(C3⋊C8)C2211yescharacteristic
25C4×C5×C3⋊C8C2211yescharacteristic
26#90982—21no—
27Dic5×C3⋊C8—21no—
28#71802—51nomaximal, Hall
29#65882D311yescharacteristic
30#65126—31no—
31C4×C8×D5—31no—
32C5×D4⋊C8—31no—
33D4⋊#168—31no—
34#64703—31no—
35#64679—31no—
36C2×C3×C5×D4C2×C411yescharacteristic
37C22×C3×C4×C5—21no—
38C2×C3×C22⋊D5—21no—
39C2×C3×C22⋊D5—21no—
40C2×C3×C22⋊D5—21no—
41C3×#709—42no—
42C3×#709—42no—
43C2×C3×D20—21no—
44C2×C3×D20C2×C411yescharacteristic
45C2×C3×C4×D5—21no—
46C2×C3×C4×D5C2×C411yescharacteristic
47C2×C3×C4×D5D411yescharacteristic
48C2×C3×C4×D5D411yescharacteristic
49C2×C3×Dic10—21no—
50C3×C5×C4⋊C4C2×C411yescharacteristic
51C3×C5×C22⋊C4—21no—
52C3×C42×C5C2311yescharacteristic
53C2×C3⋊#168—21no—
54C2×C3⋊#168—21no—
55C2×C5×C3⋊C8—21no—
56C2×C5×C3⋊C8—21no—
57C3×C22⋊Dic5—21no—
58C3×#685—21no—
59C3×#685—21no—
60C3×C4⋊Dic5C2×C411yescharacteristic
61C3×#683—21no—
62C3×C4×Dic5C2×C411yescharacteristic
63C3×C4×Dic5D411yescharacteristic
64C3×C4×Dic5D411yescharacteristic
65#6649—42no—
66D5×C3⋊C8—24no—
67C3×#532—51no—
68#4924—51no—
69C2×C4×C3⋊C8—51no—
70D4⋊(C3⋊C8)—51no—
71D4⋊(C3⋊C8)—51no—
72D4⋊(C3⋊C8)—51no—
73D4⋊(C3⋊C8)D511yescharacteristic, complemented
74C2×#709—21no—
75C4×C5×D4C2×D311yescharacteristic
76#4086Dic311yescharacteristic
77#4084Dic311yescharacteristic
78C4×C22⋊D5—21no—
79C2×#676—61no—
80C2×C8×D5—61no—
81#4041Dic311yescharacteristic
82#4034Dic311yescharacteristic
83#4031—21no—
84#4030—21no—
85C4×D20C2×D311yescharacteristic
86C42×D5C2×D311yescharacteristic
87C5×C4⋊C8—31no—
88C4×C5×C8—31no—
89#3946—61no—
90C8×Dic5—61no—
91C4⋊#168—31no—
92C4×#168—31no—
93#1492—151noSylow
94C23×C3×C5—21no—
95C22×C3×D5—21no—
96C22×C3×D5C22⋊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
105C3×C22⋊D5—42no—
106C3×C22⋊D5—42no—
107C3×C22⋊D5—42no—
108C2×C3×Dic5—21no—
109C2×C3×Dic5C22⋊C411yescharacteristic
110C2×C3×Dic5C22⋊C411yescharacteristic
111C2×C3×Dic5C22⋊C411yescharacteristic
112C3×D20—21no—
113C3×D20—21no—
114C3×D20—42no—
115C3×C4×D5—21no—
116C3×C4×D5—21no—
117C3×C4×D5—22no—
118C3×C4×D5—41no—
119C3×C4×D5—41no—
120C3×C4×D5D812yes—
121C3×C4×D5SD1612yes—
122C3×Dic10—42no—
123C3⋊#168—22no—
124C3⋊#168—41no—
125C5×C3⋊C8—22no—
126C5×C3⋊C8—41no—
127C2×C3×#41—101no—
128C3×C4⋊Q8—51no—
129C3×#127—51no—
130C3×#124—101no—
131C3×#121—51no—
132C3×#121—51no—
133C3×#121—101no—
134C3×C4×D4—51no—
135C3×C4×D4—101no—
136C3×C4×D4C2×D511yescharacteristic
137C2×C3×C42—51no—
138C2×#208—101no—
139C22×C3⋊C8—101no—
140C4⋊(C3⋊C8)—51no—
141C4⋊(C3⋊C8)—101no—
142C4⋊(C3⋊C8)C2×D511yescharacteristic
143C4×C3⋊C8—51no—
144C4×C3⋊C8—101no—
145C4×C3⋊C8C2×D511yescharacteristic
146C2×C5×D4C2×Dic311yescharacteristic
147C22×C4×C5—21no—
148C2×C22⋊D5—21no—
149C2×C22⋊D5—21no—
150C2×C22⋊D5—21no—
151#709—42no—
152#709—42no—
153C2×D20—21no—
154C2×D20C2×Dic311yescharacteristic
155C2×C4×D5—21no—
156C2×C4×D5C2×Dic311yescharacteristic
157C2×C4×D5#6711yescharacteristic
158C2×C4×D5#6711yescharacteristic
159C2×Dic10—21no—
160C2×C5×C8—61no—
161C2×C5×C8—61no—
162C5×C4⋊C4C2×Dic311yescharacteristic
163C5×C22⋊C4—21no—
164C42×C5C22×D311yescharacteristic
165C22⋊Dic5—21no—
166#685—21no—
167#685—21no—
168C4⋊Dic5C2×Dic311yescharacteristic
169#683—21no—
170C4×Dic5C2×Dic311yescharacteristic
171C4×Dic5#6711yescharacteristic
172C4×Dic5#6711yescharacteristic
173C2×#168—61no—
174C2×#168—61no—
175#676—122no—
176C8×D5—64no—
177#532—51no—
178#423—151no—
179C2×C4×C8—151no—
180D4⋊C8—31no—
181D4⋊C8—151no—
182D4⋊C8—151no—
183D4⋊C8—151no—
184C22×C3×C5—41no—
185C22×C3×C5—41no—
186C22×C3×C5—41no—
187C22×C3×C5C2×C22⋊C411yescharacteristic
188C2×C3×D5—21no—
189C2×C3×D5—21no—
190C2×C3×D5—41no—
191C2×C3×D5—41no—
192C2×C3×D5—41no—
193C2×C3×D5#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
200C3×Dic5—21no—
201C3×Dic5—41no—
202C3×Dic5#10212yes—
203C3×Dic5#10412yes—
204C3×#41—202no—
205C3×#41—202no—
206C2×C3×Q8—101no—
207C2×C3×D4—51no—
208C2×C3×D4—101no—
209C2×C3×D4—101no—
210C2×C3×D4—101no—
211C2×C3×D4—101no—
212C2×C3×D4C4×D511yescharacteristic
213C22×C3×C4—21no—
214C22×C3×C4—51no—
215C22×C3×C4—51no—
216C22×C3×C4—51no—
217C22×C3×C4—101no—
218C3×C4⋊C4—51no—
219C3×C4⋊C4—101no—
220C3×C4⋊C4C4×D511yescharacteristic
221C3×C22⋊C4—21no—
222C3×C22⋊C4—101no—
223C3×C22⋊C4—101no—
224C3×C22⋊C4—101no—
225C3×C42—51no—
226C3×C42—51no—
227C3×C42—51no—
228C3×C42C22×D511yescharacteristic
229#208—202no—
230C2×C3⋊C8—21no—
231C2×C3⋊C8—21no—
232C2×C3⋊C8—104no—
233C2×C3⋊C8—101no—
234C2×C3⋊C8—101no—
235C23×C5—21no—
236C22×D5—21no—
237C22×D5#21711yescharacteristic
238C5×D4—21no—
239C5×D4—21no—
240C2×C4×C5—21no—
241C2×C4×C5—41no—
242C2×C4×C5—41no—
243C2×C4×C5C22×Dic311yescharacteristic
244C2×C4×C5C2×#6711yescharacteristic
245C2×C4×C5C2×#6711yescharacteristic
246C22⋊D5—42no—
247C22⋊D5—42no—
248C22⋊D5—42no—
249C2×Dic5—21no—
250C2×Dic5#21711yescharacteristic
251C2×Dic5#21711yescharacteristic
252C2×Dic5#21711yescharacteristic
253D20—21no—
254D20—21no—
255D20—42no—
256C4×D5—21no—
257C4×D5—21no—
258C4×D5—22no—
259C4×D5—41no—
260C4×D5—41no—
261C4×D5#21312yes—
262C4×D5#21412yes—
263Dic10—42no—
264C5×C8—62no—
265C5×C8—121no—
266#168—62no—
267#168—121no—
268C2×#41—101no—
269C2×M16—301no—
270C22×C8—301no—
271C4⋊Q8—51no—
272#127—51no—
273#124—101no—
274#121—51no—
275#121—51no—
276#121—101no—
277C4×D4—51no—
278C4×D4—101no—
279C4×D4D3×D511yescharacteristic
280C2×C42—51no—
281C4⋊C8—31no—
282C4⋊C8—151no—
283C4⋊C8—301no—
284C4×C8—31no—
285C4×C8—151no—
286C4×C8—301no—
287C2×C3×C5—81no—
288C2×C3×C5#40811yescharacteristic
289C2×C3×C5C2×#10211yescharacteristic
290C2×C3×C5C2×#10411yescharacteristic
291C3×D5—22no—
292C3×D5—81no—
293C23×C3—21no—
294C23×C3—51no—
295C23×C3—101no—
296C3×Q8—202no—
297C3×D4—21no—
298C3×D4—21no—
299C3×D4—101no—
300C3×D4—101no—
301C3×D4—202no—
302C3×D4—202no—
303C3×D4—202no—
304C3×D4—202no—
305C2×C3×C4—21no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—51no—
309C2×C3×C4—51no—
310C2×C3×C4—52no—
311C2×C3×C4—52no—
312C2×C3×C4—51no—
313C2×C3×C4—102no—
314C2×C3×C4—101no—
315C2×C3×C4—101no—
316C2×C3×C4—101no—
317C2×C3×C4—201no—
318C2×C3×C4—201no—
319C2×C3×C4C2×C4×D511yescharacteristic
320C2×C3×C4D4×D511yescharacteristic
321C2×C3×C4D4×D511yescharacteristic
322C3⋊C8—22no—
323C3⋊C8—41no—
324C3⋊C8—102no—
325C3⋊C8—201no—
326C22×C5—41no—
327C22×C5—41no—
328C22×C5—41no—
329C22×C5C2×#21711yescharacteristic
330C2×D5—21no—
331C2×D5—21no—
332C2×D5—41no—
333C2×D5—41no—
334C2×D5—41no—
335C2×D5#83212yes—
336C4×C5—21no—
337C4×C5—41no—
338C4×C5C2×#21311yescharacteristic
339C4×C5C2×#21411yescharacteristic
340C4×C5#94811yescharacteristic
341C4×C5#94811yescharacteristic
342Dic5—21no—
343Dic5—41no—
344Dic5#83212yes—
345Dic5#83712yes—
346#41—202no—
347#41—202no—
348C2×Q8—101no—
349C2×D4—51no—
350C2×D4—101no—
351C2×D4—101no—
352C2×D4—101no—
353C2×D4—101no—
354C2×D4D5×Dic311yescharacteristic
355C22×C4—21no—
356C22×C4—51no—
357C22×C4—51no—
358C22×C4—51no—
359C22×C4—101no—
360M16—602no—
361C2×C8—61no—
362C2×C8—61no—
363C2×C8—304no—
364C2×C8—301no—
365C2×C8—301no—
366C4⋊C4—51no—
367C4⋊C4—101no—
368C4⋊C4D5×Dic311yescharacteristic
369C22⋊C4—21no—
370C22⋊C4—101no—
371C22⋊C4—101no—
372C22⋊C4—101no—
373C42—51no—
374C42—51no—
375C42—51no—
376C42C2×D3×D511yescharacteristic
377C3×C5#149211yescharacteristic, complemented, Hall
378C22×C3—41no—
379C22×C3—41no—
380C22×C3—41no—
381C22×C3—52no—
382C22×C3—101no—
383C22×C3—101no—
384C22×C3—201no—
385C22×C3—201no—
386C22×C3—201no—
387C22×C3D5×C22⋊C411yescharacteristic
388C3×C4—21no—
389C3×C4—41no—
390C3×C4—52no—
391C3×C4—52no—
392C3×C4—101no—
393C3×C4—201no—
394C3×C4#404711yescharacteristic
395C3×C4#405311yescharacteristic
396C3×C4D5×D811yescharacteristic
397C3×C4D5×SD1611yescharacteristic
398C2×C5—81no—
399C2×C5C2×#83211yescharacteristic
400C2×C5#523411yescharacteristic
401C2×C5C2×#83711yescharacteristic
402D5—22no—
403D5—81no—
404C23—21no—
405C23—51no—
406C23—101no—
407Q8—202no—
408D4—21no—
409D4—21no—
410D4—101no—
411D4—101no—
412D4—202no—
413D4—202no—
414D4—202no—
415D4—202no—
416C2×C4—21no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—51no—
420C2×C4—51no—
421C2×C4—52no—
422C2×C4—52no—
423C2×C4—51no—
424C2×C4—102no—
425C2×C4—101no—
426C2×C4—101no—
427C2×C4—101no—
428C2×C4—201no—
429C2×C4—201no—
430C2×C4C2×D5×Dic311yescharacteristic
431C2×C4D5×#6711yescharacteristic
432C2×C4D5×#6711yescharacteristic
433C8—62no—
434C8—121no—
435C8—302no—
436C8—601no—
437C2×C3—81no—
438C2×C3—102no—
439C2×C3—401no—
440C2×C3#6501611yescharacteristic
441C2×C3D5×#10211yescharacteristic
442C2×C3D5×#10411yescharacteristic
443C5#7180211yescharacteristic, complemented, Sylow
444C22—41no—
445C22—41no—
446C22—41no—
447C22—52no—
448C22—101no—
449C22—101no—
450C22—201no—
451C22—201no—
452C22—201no—
453C22D5×#21711yescharacteristic
454C4—21no—
455C4—41no—
456C4—52no—
457C4—52no—
458C4—101no—
459C4—201no—
460C4#9128311yescharacteristic
461C4#9128411yescharacteristic
462C4D5×#21311yescharacteristic
463C4D5×#21411yescharacteristic
464C3#1059896911yescharacteristic, complemented, Sylow
465C2—81no—
466C2—102no—
467C2—401no—
468C2#1174848211yescharacteristic
469C2D5×#83211yescharacteristic
470C2D5×#83711yescharacteristic
subgroupG/H
centerC2×C4D5×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#65882C2
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. #11747007C2semidirect
3. C4×D5×C3⋊C8C2semidirect
4. D4⋊(C3⋊#168)C2semidirect
5. C5×D4⋊(C3⋊C8)C2semidirect
6. #11745835C2semidirect
7. #11745834C2semidirect
73. D4⋊(C3⋊C8)D5semidirect
377. C3×C5#1492semidirect
443. C5#71802semidirect
464. C3#10598969semidirect

Maximal subgroups

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

subgroupindex
C3×#658822
#117470072
C4×D5×C3⋊C82
D4⋊(C3⋊#168)2
C5×D4⋊(C3⋊C8)2
#117458352
#117458342
#105989693
#718025