Finite Group Databasebeta

← #14304591

Subgroups — #14304591

Order 1920.

584 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11751322C211yesmaximal, characteristic
2C2×C5×#832C211yesmaximal, characteristic
3C2×C3×#3964C211yesmaximal, characteristic
4#11748868C211yesmaximal, characteristic, complemented
5C2×#90951C211yesmaximal, characteristic, complemented
6#11745981C211yesmaximal, characteristic, complemented
7#11745980C211yesmaximal, characteristic, complemented
8#10600978—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C2×#6719—21no—
11C2×#6719—21no—
12C2×C4⋊Dic15C2211yescharacteristic
13C2×C4×Dic15C2211yescharacteristic
14C2×C5×C4⋊Dic3C2211yescharacteristic
15C22×C5×C3⋊C8C2211yescharacteristic
16C2×C3×C4⋊Dic5C2211yescharacteristic
17C22×C3×#168C2211yescharacteristic
18C2×Dic3⋊Dic5—21no—
19C5×#832C414yescomplemented
20C3×#3964—22no—
21#90994—21no—
22#90951—22no—
23#70186—51nomaximal, Hall
24C2×C5×#102—31no—
25#65510—31no—
26C2×#3964D311yescharacteristic
27C2×C8×Dic5—31no—
28#65274—31no—
29#64771—31no—
30#64749—31no—
31C24×C3×C5—21no—
32C2×C3×C5×D4—21no—
33C2×C3×C5×D4—21no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4C2×C412yes—
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15—21no—
40C22×Dic15D411yescharacteristic
41C22×Dic15D411yescharacteristic
42C22×C5×Dic3—21no—
43C22×C3×Dic5—21no—
44#6719—42no—
45#6719—42no—
46C4⋊Dic15—21no—
47C4⋊Dic15—21no—
48C4×Dic15—21no—
49C4×Dic15—21no—
50C5×C4⋊Dic3—21no—
51C5×C4⋊Dic3C2×C412yes—
52C2×C5×C3⋊C8—21no—
53C2×C5×C3⋊C8—21no—
54C2×C5×C3⋊C8C2×C412yes—
55C3×C4⋊Dic5—21no—
56C3×C4⋊Dic5—21no—
57C2×C3×#168—21no—
58C2×C3×#168—21no—
59C2×C3×#168D412yes—
60Dic3⋊Dic5—42no—
61C2×C3×#102—51no—
62#5221—51no—
63C2×#832D511yescharacteristic
64C2×C8×Dic3—51no—
65#4972—51no—
66#4551—51no—
67#4529—51no—
68C22×C5×D4C2×D311yescharacteristic
69C22×C5×C8—31no—
70C2×C5×C4⋊C4—31no—
71C2×C22⋊Dic5—61no—
72C2×C22⋊Dic5—61no—
73C2×C4⋊Dic5—31no—
74C2×C4⋊Dic5—61no—
75C2×C4⋊Dic5C2×D311yescharacteristic
76C2×C4×Dic5—31no—
77C22×#168C2×D311yescharacteristic
78C5×#102—34no—
79#3964—22no—
80#3963—61no—
81C8×Dic5—62no—
82#1934—151noSylow
83C23×C3×C5—22no—
84C23×C3×C5—41no—
85C23×C3×C5—41no—
86C23×C3×C5—41no—
87C23×C3×C5—41no—
88C23×C3×C5—41no—
89C23×C3×C5—41no—
90C23×C3×C5C2×D411yescharacteristic
91C3×C5×D4—22no—
92C3×C5×D4—22no—
93C3×C5×D4—41no—
94C3×C5×D4—41no—
95C2×C3×C4×C5C22×C411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×C4×C5#4111yescharacteristic
98C2×C3×C4×C5#4111yescharacteristic
99C2×C3×C4×C5#4111yescharacteristic
100C2×C3×C4×C5#4111yescharacteristic
101C2×Dic15—21no—
102C2×Dic15—21no—
103C2×Dic15—21no—
104C2×Dic15—21no—
105C2×Dic15—41no—
106C2×Dic15—41no—
107C2×Dic15—41no—
108C2×Dic15D812yes—
109C2×Dic15SD1612yes—
110C2×C5×Dic3—22no—
111C2×C5×Dic3—41no—
112C2×C5×Dic3—41no—
113C2×C3×Dic5—41no—
114C2×C3×Dic5—41no—
115C2×C3×Dic5—41no—
116C3×#168—22no—
117C5×C3⋊C8—22no—
118C22×C3×D4C2×D511yescharacteristic
119C22×C3×C8—51no—
120C2×C3×C4⋊C4—51no—
121C2×#217—101no—
122C2×#217—101no—
123C2×C4⋊Dic3—51no—
124C2×C4⋊Dic3C2×D511yescharacteristic
125C2×Dic3⋊C4—101no—
126C2×C4×Dic3—51no—
127C22×C3⋊C8C2×D511yescharacteristic
128C3×#102—102no—
129#832Dic514yescomplemented
130C3⋊#95—101no—
131C8×Dic3—102no—
132C24×C5—21no—
133C2×C5×D4—21no—
134C2×C5×D4—21no—
135C2×C5×D4—21no—
136C2×C5×D4—21no—
137C2×C5×D4—21no—
138C2×C5×D4C4×D312yes—
139C22×C4×C5—61no—
140C22×C4×C5C22×D311yescharacteristic
141C22×Dic5—21no—
142C22×Dic5—31no—
143C22×Dic5—31no—
144C22×Dic5—61no—
145C2×C5×C8—32no—
146C2×C5×C8—61no—
147C2×C5×C8—61no—
148C5×C4⋊C4—32no—
149C5×C4⋊C4—61no—
150C22⋊Dic5—122no—
151C22⋊Dic5—122no—
152C4⋊Dic5—21no—
153C4⋊Dic5—21no—
154C4⋊Dic5—61no—
155C4⋊Dic5—61no—
156C4⋊Dic5—122no—
157C4×Dic5—61no—
158C4×Dic5—61no—
159C2×#168—21no—
160C2×#168—21no—
161C2×#168#6712yes—
162C2×#102—31no—
163C2×#102—51no—
164C2×C4×C8—151no—
165#390—151no—
166#389—151no—
167#340—151no—
168#340—151no—
169C22×C3×C5—42no—
170C22×C3×C5—42no—
171C22×C3×C5—42no—
172C22×C3×C5—81no—
173C22×C3×C5—81no—
174C22×C3×C5—81no—
175C22×C3×C5—81no—
176C22×C3×C5C4×D411yescharacteristic
177C22×C3×C5#12111yescharacteristic
178C22×C3×C5#12411yescharacteristic
179C22×C3×C5C2×D811yescharacteristic
180C22×C3×C5C2×SD1611yescharacteristic
181C22×C3×C5#13511yescharacteristic
182C22×C3×C5#13511yescharacteristic
183C3×C4×C5#11711yescharacteristic
184C3×C4×C5C4×D411yescharacteristic
185C3×C4×C5#12311yescharacteristic
186C3×C4×C5#12611yescharacteristic
187Dic15—22no—
188Dic15—22no—
189Dic15—81no—
190C3×Dic5—81no—
191C5×Dic3—42no—
192C24×C3—21no—
193C2×C3×D4—21no—
194C2×C3×D4—21no—
195C2×C3×D4—21no—
196C2×C3×D4—21no—
197C2×C3×D4—21no—
198C2×C3×D4C2×Dic512yes—
199C22×C3×C4—101no—
200C22×C3×C4C22×D511yescharacteristic
201C22×Dic3—21no—
202C22×Dic3—51no—
203C22×Dic3—51no—
204C22×Dic3—101no—
205C2×C3×C8—52no—
206C2×C3×C8—101no—
207C2×C3×C8—101no—
208C3×C4⋊C4—101no—
209C3×C4⋊C4—101no—
210#217—202no—
211#217—202no—
212C4⋊Dic3—21no—
213C4⋊Dic3—101no—
214C4⋊Dic3—101no—
215C4⋊Dic3C2×Dic512yes—
216Dic3⋊C4—202no—
217C4×Dic3—101no—
218C4×Dic3—101no—
219C2×C3⋊C8—21no—
220C2×C3⋊C8—21no—
221C2×C3⋊C8C2×Dic512yes—
222C23×C5—22no—
223C23×C5—41no—
224C23×C5—41no—
225C23×C5—41no—
226C23×C5—41no—
227C23×C5—41no—
228C23×C5—41no—
229C23×C5D3×D411yescharacteristic
230C5×D4—22no—
231C5×D4—22no—
232C5×D4—41no—
233C5×D4—41no—
234C2×C4×C5—62no—
235C2×C4×C5—121no—
236C2×C4×C5—121no—
237C2×C4×C5C2×C4×D311yescharacteristic
238C2×C4×C5#23511yescharacteristic
239C2×C4×C5#23711yescharacteristic
240C2×C4×C5#23711yescharacteristic
241C2×C4×C5#23711yescharacteristic
242C2×C4×C5C2×#6711yescharacteristic
243C2×Dic5—32no—
244C2×Dic5—32no—
245C2×Dic5—41no—
246C2×Dic5—41no—
247C2×Dic5—41no—
248C2×Dic5—61no—
249C2×Dic5—61no—
250C2×Dic5—61no—
251C2×Dic5—61no—
252C2×Dic5—121no—
253C2×Dic5—121no—
254C2×Dic5—121no—
255C5×C8—62no—
256#168—22no—
257C22×D4D3×D511yescharacteristic
258C22×C8—31no—
259C22×C8—51no—
260C2×C4⋊C4—31no—
261C2×C4⋊C4—51no—
262C2×C4⋊C4—151no—
263C2×C4⋊C4—301no—
264C2×C22⋊C4—301no—
265C2×C22⋊C4—301no—
266C2×C42—151no—
267#102—34no—
268#102—102no—
269C4×C8—302no—
270#95—301no—
271C2×C3×C5—82no—
272C2×C3×C5#38811yescharacteristic
273C2×C3×C5C4×D811yescharacteristic
274C2×C3×C5C4×SD1611yescharacteristic
275C2×C3×C5#46511yescharacteristic
276C2×C3×C5#46611yescharacteristic
277C2×C3×C5#48611yescharacteristic
278C2×C3×C5#48811yescharacteristic
279C23×C3—22no—
280C23×C3—41no—
281C23×C3—41no—
282C23×C3—41no—
283C23×C3—41no—
284C23×C3—41no—
285C23×C3—41no—
286C23×C3D4×D511yescharacteristic
287C3×D4—22no—
288C3×D4—22no—
289C3×D4—41no—
290C3×D4—41no—
291C2×C3×C4—201no—
292C2×C3×C4—201no—
293C2×C3×C4—201no—
294C2×C3×C4#70911yescharacteristic
295C2×C3×C4#70911yescharacteristic
296C2×C3×C4D4×D511yescharacteristic
297C2×C3×C4#71111yescharacteristic
298C2×C3×C4#71111yescharacteristic
299C2×C3×C4C22×Dic511yescharacteristic
300C2×Dic3—22no—
301C2×Dic3—41no—
302C2×Dic3—41no—
303C2×Dic3—52no—
304C2×Dic3—52no—
305C2×Dic3—101no—
306C2×Dic3—101no—
307C2×Dic3—101no—
308C2×Dic3—101no—
309C2×Dic3—201no—
310C2×Dic3—201no—
311C2×Dic3—201no—
312C3×C8—102no—
313C3⋊C8—22no—
314C22×C5—42no—
315C22×C5—42no—
316C22×C5—42no—
317C22×C5—81no—
318C22×C5—81no—
319C22×C5—81no—
320C22×C5—81no—
321C22×C5#67⋊C411yescharacteristic
322C22×C5#88511yescharacteristic
323C22×C5D3×D811yescharacteristic
324C22×C5#91211yescharacteristic
325C22×C5D3×SD1611yescharacteristic
326C22×C5#91611yescharacteristic
327C22×C5#93811yescharacteristic
328C4×C5—122no—
329C4×C5#87711yescharacteristic
330C4×C5#87911yescharacteristic
331C4×C5C4×#6711yescharacteristic
332C4×C5#93511yescharacteristic
333Dic5—62no—
334Dic5—62no—
335Dic5—81no—
336Dic5—241no—
337C24—21no—
338C2×D4—21no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—21no—
342C2×D4—21no—
343C2×D4D3×Dic512yes—
344C22×C4—61no—
345C22×C4—101no—
346C22×C4—151no—
347C22×C4—151no—
348C22×C4—301no—
349C22×C4C2×D3×D511yescharacteristic
350C2×C8—32no—
351C2×C8—52no—
352C2×C8—61no—
353C2×C8—61no—
354C2×C8—101no—
355C2×C8—101no—
356C4⋊C4—32no—
357C4⋊C4—61no—
358C4⋊C4—101no—
359C4⋊C4—101no—
360C4⋊C4—301no—
361C4⋊C4—301no—
362C4⋊C4—602no—
363C22⋊C4—602no—
364C22⋊C4—602no—
365C42—301no—
366C42—301no—
367C3×C5#193411yescharacteristic, complemented, Hall
368C22×C3—42no—
369C22×C3—42no—
370C22×C3—42no—
371C22×C3—81no—
372C22×C3—81no—
373C22×C3—81no—
374C22×C3—81no—
375C22×C3#403011yescharacteristic
376C22×C3#403111yescharacteristic
377C22×C3D5×D811yescharacteristic
378C22×C3#405811yescharacteristic
379C22×C3D5×SD1611yescharacteristic
380C22×C3#406211yescharacteristic
381C22×C3D4×Dic511yescharacteristic
382C3×C4—401no—
383C3×C4#402511yescharacteristic
384C3×C4#402911yescharacteristic
385C3×C4#407211yescharacteristic
386C3×C4D4×Dic511yescharacteristic
387Dic3—42no—
388Dic3—102no—
389Dic3—102no—
390Dic3—401no—
391C2×C5—82no—
392C2×C5#475611yescharacteristic
393C2×C5#475811yescharacteristic
394C2×C5#476011yescharacteristic
395C2×C5#476811yescharacteristic
396C2×C5#494411yescharacteristic
397C2×C5#515711yescharacteristic
398C2×C5#517111yescharacteristic
399C23—22no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23#679011yescharacteristic
407D4—22no—
408D4—22no—
409D4—41no—
410D4—41no—
411C2×C4—62no—
412C2×C4—121no—
413C2×C4—121no—
414C2×C4—152no—
415C2×C4—152no—
416C2×C4—201no—
417C2×C4—201no—
418C2×C4—201no—
419C2×C4—301no—
420C2×C4—301no—
421C2×C4—301no—
422C2×C4—301no—
423C2×C4—601no—
424C2×C4—601no—
425C2×C4—601no—
426C2×C4#677911yescharacteristic
427C2×C4#677911yescharacteristic
428C2×C4#678011yescharacteristic
429C2×C4C2×D3×Dic511yescharacteristic
430C2×C4#678211yescharacteristic
431C2×C4D5×#6711yescharacteristic
432C8—62no—
433C8—102no—
434C2×C3—82no—
435C2×C3#6504911yescharacteristic
436C2×C3#6505711yescharacteristic
437C2×C3#6506411yescharacteristic
438C2×C3#6506711yescharacteristic
439C2×C3#6524011yescharacteristic
440C2×C3D8×Dic511yescharacteristic
441C2×C3SD16×Dic511yescharacteristic
442C5#7018611yescharacteristic, complemented, Sylow
443C22—42no—
444C22—42no—
445C22—42no—
446C22—81no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22#9148111yescharacteristic
451C22#9148711yescharacteristic
452C22#9149711yescharacteristic
453C22#9149911yescharacteristic
454C22#9152611yescharacteristic
455C22#9153311yescharacteristic
456C22#67⋊Dic511yescharacteristic
457C4—122no—
458C4—302no—
459C4—302no—
460C4—401no—
461C4—1201no—
462C4#9152911yescharacteristic
463C4#9153111yescharacteristic
464C4#9154811yescharacteristic
465C4Dic5×#6711yescharacteristic
466C3#1060097811yescharacteristic, complemented, Sylow
467C2—82no—
468C2#1174894311yescharacteristic
469C2#1174894411yescharacteristic
470C2#1174899411yescharacteristic
471C2#1174901911yescharacteristic
472C2#1174903111yescharacteristic
473C2#1174905311yescharacteristic
474C2#1174947811yescharacteristic
subgroupG/H
centerC23#6790
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
Fitting, prime radicalC22×C3×C5×D4C22
socleC23×C3×C5C2×D4
cosocleC22×C3×C4×C5C23
hypercenterC22×D4D3×D5
hypocenterC3×C5#1934
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #11748868C2semidirect
5. C2×#90951C2semidirect
6. #11745981C2semidirect
7. #11745980C2semidirect
19. C5×#832C4semidirect
129. #832Dic5semidirect
367. C3×C5#1934semidirect
442. C5#70186semidirect
466. C3#10600978semidirect

Maximal subgroups

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

subgroupindex
#117513222
C2×C5×#8322
C2×C3×#39642
#117488682
C2×#909512
#117459812
#117459802
#106009783
#701865