Finite Group Databasebeta

← #14304698

Subgroups — #14304698

Order 1920.

568 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
1C3×C5×#389C211yesmaximal, characteristic, complemented
2C2×#91093C211yesmaximal, characteristic
3C2×#91093C211yesmaximal, characteristic
4#11751040C211yesmaximal, characteristic
5C2×#91087C211yesmaximal, characteristic, complemented
6#11746350C211yesmaximal, characteristic, complemented
7#11746350C211yesmaximal, characteristic, complemented
8#10600410—31nomaximal, Hall
9C22×D60C2211yescharacteristic
10C2×C3×C5×C4⋊C4—21no—
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13C2×C3×C42×C5C2211yescharacteristic
14C2×#6714—21no—
15C2×#6714—21no—
16C2×C4⋊Dic15C2211yescharacteristic
17C22×C3⋊#168C2211yescharacteristic
18C22×C3⋊#168C2211yescharacteristic
19C3×C5×#95—21no—
20#91093—22no—
21#91093C414yescomplemented
22#91087—22no—
23#69617—51nomaximal, Hall
24C5×#389D311yescharacteristic, complemented
25C2×#3941—31no—
26C2×#3941—31no—
27#65228—31no—
28C2×#3935—31no—
29#64749—31no—
30#64749—31no—
31C23×D15—21no—
32C22×C3×C4×C5—21no—
33C22×C3×C4×C5—21no—
34C22×C3×C4×C5D411yescharacteristic
35C22×C3×C4×C5D411yescharacteristic
36C22×C3×C4×C5C2311yescharacteristic
37C22×Dic15—21no—
38C2×D60—21no—
39C2×D60—21no—
40C2×D60—21no—
41C2×D60—21no—
42C2×D60—21no—
43C2×D60C2×C412yes—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4—42no—
48C3×C5×C4⋊C4C2×C412yes—
49C3×C42×C5—21no—
50C3×C42×C5—21no—
51#6714—42no—
52#6714—42no—
53C4⋊Dic15—21no—
54C4⋊Dic15—21no—
55C2×C3⋊#168—21no—
56C2×C3⋊#168—21no—
57C2×C3⋊#168—21no—
58C2×C3⋊#168—21no—
59C2×C3⋊#168C2×C412yes—
60C2×C3⋊#168D412yes—
61C3×#389D511yescharacteristic, complemented
62C2×#809—51no—
63C2×#809—51no—
64#4939—51no—
65C2×#803—51no—
66#4529—51no—
67#4529—51no—
68C22×D20—31no—
69C2×C5×C4⋊C4—21no—
70C2×C5×C4⋊C4C2×D311yescharacteristic
71C2×C5×C4⋊C4C2×D311yescharacteristic
72C2×C42×C5C2×D311yescharacteristic
73C2×#685—61no—
74C2×#685—61no—
75C2×C4⋊Dic5—31no—
76C22×#168—31no—
77C22×#168—31no—
78C5×#95—21no—
79#3941—34no—
80#3941—62no—
81#3935—62no—
82#1936—151noSylow
83C23×C3×C5C2×D411yescharacteristic
84C22×D15—22no—
85C22×D15—41no—
86C22×D15—41no—
87C22×D15—41no—
88C22×D15—41no—
89C22×D15—41no—
90C22×D15—41no—
91C2×C3×C4×C5—22no—
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5C22×C411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5#4111yescharacteristic
106C2×C3×C4×C5#4111yescharacteristic
107C2×C3×C4×C5#4111yescharacteristic
108C2×C3×C4×C5#4111yescharacteristic
109C2×Dic15—41no—
110C2×Dic15—41no—
111C2×Dic15—41no—
112D60—22no—
113D60—22no—
114D60—41no—
115D60—41no—
116C3⋊#168—22no—
117C3⋊#168—22no—
118C22×D12—51no—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4C2×D511yescharacteristic
121C2×C3×C4⋊C4C2×D511yescharacteristic
122C2×C3×C42C2×D511yescharacteristic
123C2×(C2×D3)⋊C4—101no—
124C2×(C2×D3)⋊C4—101no—
125C2×C4⋊Dic3—51no—
126C22×C3⋊C8—51no—
127C22×C3⋊C8—51no—
128C3×#95—21no—
129#809—54no—
130#809—102no—
131#803—102no—
132C23×D5—61no—
133C22×C4×C5—21no—
134C22×C4×C5—21no—
135C22×C4×C5#6711yescharacteristic
136C22×C4×C5#6711yescharacteristic
137C22×C4×C5C22×D311yescharacteristic
138C22×Dic5—61no—
139C2×D20—32no—
140C2×D20—61no—
141C2×D20—61no—
142C2×D20—61no—
143C2×D20—61no—
144C2×D20—61no—
145C5×C4⋊C4—21no—
146C5×C4⋊C4—21no—
147C5×C4⋊C4—21no—
148C5×C4⋊C4—42no—
149C5×C4⋊C4C4×D312yes—
150C42×C5—21no—
151C42×C5—21no—
152#685—122no—
153#685—122no—
154C4⋊Dic5—61no—
155C4⋊Dic5—61no—
156C2×#168—32no—
157C2×#168—32no—
158C2×#168—61no—
159C2×#168—61no—
160C2×#168—61no—
161C2×#168—61no—
162C2×#102—151no—
163C2×#102—151no—
164C2×#97—151no—
165#390—151no—
166#389D1511yescharacteristic, complemented
167#340—151no—
168#340—151no—
169C22×C3×C5C4×D411yescharacteristic
170C22×C3×C5#12111yescharacteristic
171C22×C3×C5#12411yescharacteristic
172C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
173C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
174C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
175C22×C3×C5#13711yescharacteristic
176C2×D15—42no—
177C2×D15—42no—
178C2×D15—42no—
179C2×D15—81no—
180C2×D15—81no—
181C2×D15—81no—
182C2×D15—81no—
183C3×C4×C5—42no—
184C3×C4×C5—41no—
185C3×C4×C5—41no—
186C3×C4×C5—81no—
187C3×C4×C5#11711yescharacteristic
188C3×C4×C5C4×D411yescharacteristic
189C3×C4×C5#12311yescharacteristic
190C3×C4×C5#12611yescharacteristic
191Dic15—81no—
192C23×D3—101no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4C22⋊D511yescharacteristic
196C22×C3×C4C22⋊D511yescharacteristic
197C22×C3×C4C22×D511yescharacteristic
198C22×Dic3—101no—
199C2×D12—52no—
200C2×D12—101no—
201C2×D12—101no—
202C2×D12—101no—
203C2×D12—101no—
204C2×D12—101no—
205C3×C4⋊C4—21no—
206C3×C4⋊C4—21no—
207C3×C4⋊C4—21no—
208C3×C4⋊C4—42no—
209C3×C4⋊C4C4×D512yes—
210C3×C42—21no—
211C3×C42—21no—
212(C2×D3)⋊C4—202no—
213(C2×D3)⋊C4—202no—
214C4⋊Dic3—101no—
215C4⋊Dic3—101no—
216C2×C3⋊C8—52no—
217C2×C3⋊C8—52no—
218C2×C3⋊C8—101no—
219C2×C3⋊C8—101no—
220C2×C3⋊C8—101no—
221C2×C3⋊C8—101no—
222C23×C5C2×#6711yescharacteristic
223C22×D5—62no—
224C22×D5—121no—
225C22×D5—121no—
226C22×D5—121no—
227C22×D5—121no—
228C22×D5—121no—
229C22×D5—121no—
230C2×C4×C5—22no—
231C2×C4×C5—21no—
232C2×C4×C5—21no—
233C2×C4×C5—21no—
234C2×C4×C5—21no—
235C2×C4×C5—21no—
236C2×C4×C5—21no—
237C2×C4×C5—41no—
238C2×C4×C5—41no—
239C2×C4×C5—41no—
240C2×C4×C5—41no—
241C2×C4×C5—41no—
242C2×C4×C5C2×C4×D311yescharacteristic
243C2×C4×C5#23511yescharacteristic
244C2×C4×C5D3×D411yescharacteristic
245C2×C4×C5#23711yescharacteristic
246C2×C4×C5#23911yescharacteristic
247C2×C4×C5#23911yescharacteristic
248C2×Dic5—121no—
249C2×Dic5—121no—
250C2×Dic5—121no—
251D20—62no—
252D20—62no—
253D20—121no—
254D20—121no—
255#168—62no—
256#168—62no—
257C22×D4—151no—
258C22×C8—151no—
259C22×C8—151no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—151no—
262C2×C4⋊C4C2×D1511yescharacteristic
263C2×C4⋊C4C2×D1511yescharacteristic
264C2×C22⋊C4—301no—
265C2×C22⋊C4—301no—
266C2×C42C2×D1511yescharacteristic
267#102—154no—
268#102—302no—
269#97—302no—
270#95—21no—
271C2×C3×C5#38811yescharacteristic
272C2×C3×C5#44011yescharacteristic
273C2×C3×C5#44211yescharacteristic
274C2×C3×C5#46811yescharacteristic
275C2×C3×C5#46911yescharacteristic
276C2×C3×C5#48911yescharacteristic
277C2×C3×C5#49011yescharacteristic
278D15—82no—
279C23×C3C2×C22⋊D511yescharacteristic
280C22×D3—102no—
281C22×D3—201no—
282C22×D3—201no—
283C22×D3—201no—
284C22×D3—201no—
285C22×D3—201no—
286C22×D3—201no—
287C2×C3×C4—22no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—41no—
295C2×C3×C4—41no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4C2×C4×D511yescharacteristic
300C2×C3×C4#70911yescharacteristic
301C2×C3×C4D4×D511yescharacteristic
302C2×C3×C4#71111yescharacteristic
303C2×C3×C4#71311yescharacteristic
304C2×C3×C4#71311yescharacteristic
305C2×Dic3—201no—
306C2×Dic3—201no—
307C2×Dic3—201no—
308D12—102no—
309D12—102no—
310D12—201no—
311D12—201no—
312C3⋊C8—102no—
313C3⋊C8—102no—
314C22×C5C4×#6711yescharacteristic
315C22×C5#93211yescharacteristic
316C22×C5#93911yescharacteristic
317C22×C5#94211yescharacteristic
318C22×C5#94711yescharacteristic
319C22×C5#94911yescharacteristic
320C22×C5#94911yescharacteristic
321C2×D5—122no—
322C2×D5—122no—
323C2×D5—122no—
324C2×D5—241no—
325C2×D5—241no—
326C2×D5—241no—
327C2×D5—241no—
328C4×C5—42no—
329C4×C5—41no—
330C4×C5—41no—
331C4×C5—81no—
332C4×C5#89211yescharacteristic
333C4×C5#89311yescharacteristic
334C4×C5#89411yescharacteristic
335C4×C5#89811yescharacteristic
336Dic5—241no—
337C24—301no—
338C2×D4—152no—
339C2×D4—301no—
340C2×D4—301no—
341C2×D4—301no—
342C2×D4—301no—
343C2×D4—301no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—301no—
347C22×C4#122011yescharacteristic
348C22×C4#122011yescharacteristic
349C22×C4C22×D1511yescharacteristic
350C2×C8—152no—
351C2×C8—152no—
352C2×C8—301no—
353C2×C8—301no—
354C2×C8—301no—
355C2×C8—301no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—42no—
360C4⋊C4—301no—
361C4⋊C4—301no—
362C4⋊C4C4×D1512yes—
363C22⋊C4—602no—
364C22⋊C4—602no—
365C42—21no—
366C42—21no—
367C3×C5#193611yescharacteristic, complemented, Hall
368C22×C3C4×C22⋊D511yescharacteristic
369C22×C3#407811yescharacteristic
370C22×C3#408511yescharacteristic
371C22×C3#408811yescharacteristic
372C22×C3#409311yescharacteristic
373C22×C3#409511yescharacteristic
374C22×C3#409511yescharacteristic
375C2×D3—202no—
376C2×D3—202no—
377C2×D3—202no—
378C2×D3—401no—
379C2×D3—401no—
380C2×D3—401no—
381C2×D3—401no—
382C3×C4—42no—
383C3×C4—41no—
384C3×C4—41no—
385C3×C4—81no—
386C3×C4#403811yescharacteristic
387C3×C4#403911yescharacteristic
388C3×C4#404011yescharacteristic
389C3×C4#404411yescharacteristic
390Dic3—401no—
391C2×C5#499011yescharacteristic
392C2×C5#501411yescharacteristic
393C2×C5#502611yescharacteristic
394C2×C5#503911yescharacteristic
395C2×C5#504911yescharacteristic
396C2×C5#506711yescharacteristic
397C2×C5#508911yescharacteristic
398D5—242no—
399C23—302no—
400C23—601no—
401C23—601no—
402C23—601no—
403C23—601no—
404C23—601no—
405C23—601no—
406C23C2×#122011yescharacteristic
407D4—302no—
408D4—302no—
409D4—601no—
410D4—601no—
411C2×C4—22no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—601no—
424C2×C4—601no—
425C2×C4—601no—
426C2×C4C2×C4×D1511yescharacteristic
427C2×C4#681711yescharacteristic
428C2×C4D4×D1511yescharacteristic
429C2×C4#681911yescharacteristic
430C2×C4#682111yescharacteristic
431C2×C4#682111yescharacteristic
432C8—302no—
433C8—302no—
434C2×C3#6527911yescharacteristic
435C2×C3#6530311yescharacteristic
436C2×C3#6531511yescharacteristic
437C2×C3#6532811yescharacteristic
438C2×C3#6533811yescharacteristic
439C2×C3#6535611yescharacteristic
440C2×C3#6537811yescharacteristic
441D3—402no—
442C5#6961711yescharacteristic, complemented, Sylow
443C22—602no—
444C22—602no—
445C22—602no—
446C22—1201no—
447C22—1201no—
448C22—1201no—
449C22—1201no—
450C22C4×#122011yescharacteristic
451C22#9182111yescharacteristic
452C22#9182811yescharacteristic
453C22#9183111yescharacteristic
454C22#9183611yescharacteristic
455C22#9183811yescharacteristic
456C22#9183811yescharacteristic
457C4—42no—
458C4—41no—
459C4—41no—
460C4—81no—
461C4—1201no—
462C4#9178111yescharacteristic
463C4#9178211yescharacteristic
464C4#9178311yescharacteristic
465C4#9178711yescharacteristic
466C3#1060041011yescharacteristic, complemented, Sylow
467C2—1202no—
468C2#1175109111yescharacteristic
469C2#1175111511yescharacteristic
470C2#1175112711yescharacteristic
471C2#1175114011yescharacteristic
472C2#1175115011yescharacteristic
473C2#1175116811yescharacteristic
474C2#1175119011yescharacteristic
subgroupG/H
centerC23C2×#1220
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#389C2
socleC23×C3×C5C2×D4
prime radicalC22×D60C22
cosocleC22×C3×C4×C5C23
hypercenter#389D15
hypocenterC3×C5#1936
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C3×C5×#389C2semidirect
5. C2×#91087C2semidirect
6. #11746350C2semidirect
7. #11746350C2semidirect
21. #91093C4semidirect
24. C5×#389D3semidirect
61. C3×#389D5semidirect
166. #389D15semidirect
367. C3×C5#1936semidirect
442. C5#69617semidirect
466. C3#10600410semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#3892
C2×#910932
#117510402
C2×#910872
#117463502
#106004103
#696175