Finite Group Databasebeta

← #14283222

Subgroups — #14283222

Order 1920.

484 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65934C211yesmaximal, characteristic
2#11748638C211yesmaximal, characteristic, complemented
3#11748333C211yesmaximal, characteristic, complemented
4#11746358C211yesmaximal, characteristic
5C5×#4537C211yesmaximal, characteristic
6#11745961C211yesmaximal, characteristic, complemented
7#11745960C211yesmaximal, characteristic, complemented
8#10599072—31nomaximal, Hall
9C3×C5×#121C2211yescharacteristic
10C3×#4082C411yescharacteristic, complemented
11C3×#4081—21no—
12C3×D4×Dic5—21no—
13C3×D4×Dic5C411yescharacteristic, complemented
14C3×#4070C2211yescharacteristic
15C2×C3×C4×Dic5C2211yescharacteristic
16C3×#4036C411yescharacteristic, complemented
17C3×#4033C411yescharacteristic, complemented
18C3×#4025—21no—
19C3×#4023—21no—
20C2×#6668—21no—
21C2×Dic3×Dic5—21no—
22#91115C2211yescharacteristic
23#91114C2211yescharacteristic
24C5×C3⋊#95C2211yescharacteristic
25C5×#830C2211yescharacteristic
26#90982—21no—
27#90952—21no—
28#71755—51nomaximal, Hall
29#65934D311yescharacteristic
30#65008—31no—
31#64938—31no—
32C5×#327—31no—
33#64757—31no—
34#64687—31no—
35#64672—31no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4C2×C411yescharacteristic
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15—21no—
40C22×C5×Dic3—21no—
41C22×C3×Dic5—21no—
42C22×C3×Dic5D411yescharacteristic
43C22×C3×Dic5D411yescharacteristic
44C2×C3×Dic10C2×C411yescharacteristic
45C3×C5×C4⋊C4C2×C411yescharacteristic
46C3×C5×C22⋊C4—21no—
47C2×C3⋊#168—21no—
48C2×C5×C3⋊C8—21no—
49C3×C22⋊Dic5—21no—
50C3×C22⋊Dic5—21no—
51C3×C22⋊Dic5—21no—
52C3×C22⋊Dic5—21no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5C2×C411yescharacteristic
55C3×#683—21no—
56C3×#683—21no—
57C3×#683—21no—
58C3×C4×Dic5—21no—
59C3×C4×Dic5C2×C411yescharacteristic
60C3×C4×Dic5C2×C411yescharacteristic
61C3×C4×Dic5D411yescharacteristic
62C3×C4×Dic5D411yescharacteristic
63#6668—24no—
64Dic3×Dic5—42no—
65C3×#529—51no—
66C4×C4⋊Dic3—51no—
67#4926—51no—
68#4538—51no—
69#4538—51no—
70#4537—51no—
71#4537D511yescharacteristic
72C5×#121C2×D311yescharacteristic
73#4082Dic311yescharacteristic, complemented
74#4081—21no—
75D4×Dic5—21no—
76D4×Dic5Dic311yescharacteristic, complemented
77#4070C2×D311yescharacteristic
78C2×#683—61no—
79C2×C4×Dic5—61no—
80C2×C4×Dic5C2×D311yescharacteristic
81#4036Dic311yescharacteristic, complemented
82#4033Dic311yescharacteristic, complemented
83#4025—21no—
84#4023—21no—
85C5×C22⋊C8—31no—
86C5×#95—31no—
87#3963—31no—
88C22⋊#168—31no—
89#3947—61no—
90#3946—61no—
91#1509—151noSylow
92C23×C3×C5—21no—
93C23×C3×C5C2×D411yescharacteristic
94C3×C5×D4—41no—
95C3×C5×D4—41no—
96C3×C5×D4—41no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5C22×C411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×Dic15—22no—
102C2×Dic15—41no—
103C2×Dic15—41no—
104C2×C5×Dic3—22no—
105C2×C5×Dic3—41no—
106C2×C5×Dic3—41no—
107C2×C3×Dic5—21no—
108C2×C3×Dic5—21no—
109C2×C3×Dic5—22no—
110C2×C3×Dic5—21no—
111C2×C3×Dic5—21no—
112C2×C3×Dic5—42no—
113C2×C3×Dic5C22⋊C411yescharacteristic
114C2×C3×Dic5C22⋊C411yescharacteristic
115C2×C3×Dic5C22⋊C411yescharacteristic
116C2×C3×Dic5C22⋊C411yescharacteristic
117C3×Dic10—41no—
118C3⋊#168—41no—
119C5×C3⋊C8—41no—
120C3×#126—101no—
121C3×#125—51no—
122C3×#124—51no—
123C3×#123—101no—
124C3×C22⋊Q8—51no—
125C3×#121C2×D511yescharacteristic
126C3×C4×Q8—51no—
127C3×C4×D4—51no—
128C3×C4×D4—101no—
129C3×#117—101no—
130C2×C3×C42—51no—
131C2×C4⋊Dic3—101no—
132C2×C4×Dic3—101no—
133C3⋊#95—51no—
134C3⋊#95C2×D511yescharacteristic
135#830—51no—
136#830C2×D511yescharacteristic
137C4⋊(C3⋊C8)—101no—
138#803—101no—
139C2×C5×D4—21no—
140C2×C5×D4C2×Dic311yescharacteristic
141C22×C4×C5—61no—
142C22×C4×C5C22×D311yescharacteristic
143C22×Dic5—21no—
144C22×Dic5—61no—
145C22×Dic5#6711yescharacteristic
146C22×Dic5#6711yescharacteristic
147C2×Dic10C2×Dic311yescharacteristic
148C2×C5×C8—61no—
149C5×C4⋊C4C2×Dic311yescharacteristic
150C5×C22⋊C4—21no—
151C22⋊Dic5—21no—
152C22⋊Dic5—21no—
153C22⋊Dic5—21no—
154C22⋊Dic5—21no—
155C4⋊Dic5—21no—
156C4⋊Dic5C2×Dic311yescharacteristic
157#683—21no—
158#683—21no—
159#683—21no—
160#683—64no—
161C4×Dic5—21no—
162C4×Dic5—122no—
163C4×Dic5C2×Dic311yescharacteristic
164C4×Dic5C2×Dic311yescharacteristic
165C4×Dic5#6711yescharacteristic
166C4×Dic5#6711yescharacteristic
167C2×#168—61no—
168#529—51no—
169#432—151no—
170C4×C4⋊C4—151no—
171#328—151no—
172#328—151no—
173#327—31no—
174#327—151no—
175C22×C3×C5—21no—
176C22×C3×C5—21no—
177C22×C3×C5—41no—
178C22×C3×C5—41no—
179C22×C3×C5—41no—
180C22×C3×C5C2×C22⋊C411yescharacteristic
181C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
182C22×C3×C5#13711yescharacteristic
183C3×C4×C5—21no—
184C3×C4×C5—21no—
185C3×C4×C5—41no—
186Dic15—42no—
187C3×Dic5—21no—
188C3×Dic5—21no—
189C3×Dic5—21no—
190C3×Dic5—41no—
191C3×Dic5—41no—
192C3×Dic5#10412yes—
193C5×Dic3—42no—
194C2×C3×Q8—51no—
195C2×C3×D4—21no—
196C2×C3×D4C4×D511yescharacteristic
197C22×C3×C4—51no—
198C22×C3×C4—51no—
199C22×C3×C4—101no—
200C22×C3×C4C22×D511yescharacteristic
201C22×Dic3—21no—
202C22×Dic3—101no—
203C3×C4⋊C4—51no—
204C3×C4⋊C4—101no—
205C3×C4⋊C4—101no—
206C3×C4⋊C4—101no—
207C3×C4⋊C4—101no—
208C3×C4⋊C4C4×D511yescharacteristic
209C3×C22⋊C4—21no—
210C3×C22⋊C4—101no—
211C3×C22⋊C4—101no—
212C3×C22⋊C4—101no—
213C3×C22⋊C4—101no—
214C3×C42—51no—
215C3×C42—51no—
216C3×C42—51no—
217C3×C42—51no—
218C3×C42—101no—
219C4⋊Dic3—104no—
220C4×Dic3—202no—
221C2×C3⋊C8—21no—
222C2×C3⋊C8—101no—
223C23×C5—21no—
224C23×C5C2×#6711yescharacteristic
225C5×D4—41no—
226C5×D4—41no—
227C5×D4—41no—
228C2×C4×C5—21no—
229C2×C4×C5—41no—
230C2×C4×C5—62no—
231C2×C4×C5—121no—
232C2×C4×C5—121no—
233C2×C4×C5C22×Dic311yescharacteristic
234C2×C4×C5C2×#6711yescharacteristic
235C2×Dic5—21no—
236C2×Dic5—21no—
237C2×Dic5—22no—
238C2×Dic5—21no—
239C2×Dic5—21no—
240C2×Dic5—42no—
241C2×Dic5—62no—
242C2×Dic5—121no—
243C2×Dic5—121no—
244C2×Dic5#21711yescharacteristic
245C2×Dic5#21711yescharacteristic
246C2×Dic5#21711yescharacteristic
247C2×Dic5#21711yescharacteristic
248Dic10—41no—
249C5×C8—121no—
250#168—121no—
251#126—101no—
252#125—51no—
253#124—51no—
254#123—101no—
255C22⋊Q8—51no—
256#121D3×D511yescharacteristic
257C4×Q8—51no—
258C4×D4—51no—
259C4×D4—101no—
260#117—101no—
261C2×C4⋊C4—301no—
262C2×C42—51no—
263C2×C42—301no—
264C4⋊C8—301no—
265C22⋊C8—31no—
266C22⋊C8—151no—
267#97—301no—
268#95—31no—
269#95—151no—
270C2×C3×C5—21no—
271C2×C3×C5—21no—
272C2×C3×C5—81no—
273C2×C3×C5#41011yescharacteristic
274C2×C3×C5#41711yescharacteristic
275C2×C3×C5C2×#10411yescharacteristic
276C23×C3—21no—
277C23×C3D4×D511yescharacteristic
278C3×Q8—201no—
279C3×D4—41no—
280C3×D4—41no—
281C3×D4—41no—
282C2×C3×C4—21no—
283C2×C3×C4—41no—
284C2×C3×C4—51no—
285C2×C3×C4—51no—
286C2×C3×C4—51no—
287C2×C3×C4—51no—
288C2×C3×C4—102no—
289C2×C3×C4—101no—
290C2×C3×C4—101no—
291C2×C3×C4—101no—
292C2×C3×C4—101no—
293C2×C3×C4—202no—
294C2×C3×C4C2×C4×D511yescharacteristic
295C2×C3×C4D4×D511yescharacteristic
296C2×Dic3—22no—
297C2×Dic3—41no—
298C2×Dic3—41no—
299C2×Dic3—102no—
300C2×Dic3—201no—
301C2×Dic3—201no—
302C3⋊C8—41no—
303C3⋊C8—201no—
304C22×C5—21no—
305C22×C5—21no—
306C22×C5—41no—
307C22×C5—41no—
308C22×C5—41no—
309C22×C5#94911yescharacteristic
310C22×C5#95111yescharacteristic
311C22×C5C2×#21711yescharacteristic
312C4×C5—21no—
313C4×C5—21no—
314C4×C5—41no—
315C4×C5—122no—
316Dic5—21no—
317Dic5—21no—
318Dic5—21no—
319Dic5—41no—
320Dic5—41no—
321Dic5—122no—
322Dic5#83712yes—
323C2×Q8—51no—
324C2×D4—21no—
325C2×D4D5×Dic311yescharacteristic
326C22×C4—51no—
327C22×C4—51no—
328C22×C4—61no—
329C22×C4—101no—
330C22×C4—301no—
331C22×C4C2×D3×D511yescharacteristic
332C2×C8—61no—
333C2×C8—301no—
334C4⋊C4—51no—
335C4⋊C4—101no—
336C4⋊C4—101no—
337C4⋊C4—101no—
338C4⋊C4—101no—
339C4⋊C4—304no—
340C4⋊C4D5×Dic311yescharacteristic
341C22⋊C4—21no—
342C22⋊C4—101no—
343C22⋊C4—101no—
344C22⋊C4—101no—
345C22⋊C4—101no—
346C42—51no—
347C42—51no—
348C42—51no—
349C42—51no—
350C42—101no—
351C42—602no—
352C3×C5#150911yescharacteristic, complemented, Hall
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—41no—
356C22×C3—41no—
357C22×C3—41no—
358C22×C3D5×C22⋊C411yescharacteristic
359C22×C3#405711yescharacteristic
360C22×C3#406111yescharacteristic
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—41no—
364C3×C4—52no—
365C3×C4—101no—
366C3×C4—101no—
367C3×C4—101no—
368C3×C4—201no—
369C3×C4—201no—
370Dic3—42no—
371Dic3—202no—
372C2×C5—21no—
373C2×C5—21no—
374C2×C5—81no—
375C2×C5#523211yescharacteristic
376C2×C5C2×#83711yescharacteristic
377C2×C5#524011yescharacteristic
378C23—21no—
379C23D5×#6711yescharacteristic
380Q8—201no—
381D4—41no—
382D4—41no—
383D4—41no—
384C2×C4—21no—
385C2×C4—41no—
386C2×C4—51no—
387C2×C4—51no—
388C2×C4—51no—
389C2×C4—51no—
390C2×C4—62no—
391C2×C4—102no—
392C2×C4—101no—
393C2×C4—101no—
394C2×C4—101no—
395C2×C4—101no—
396C2×C4—121no—
397C2×C4—121no—
398C2×C4—202no—
399C2×C4—302no—
400C2×C4—601no—
401C2×C4—601no—
402C2×C4C2×D5×Dic311yescharacteristic
403C2×C4D5×#6711yescharacteristic
404C8—121no—
405C8—601no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—81no—
409C2×C3#6502911yescharacteristic
410C2×C3#6506011yescharacteristic
411C2×C3D5×#10411yescharacteristic
412C5#7175511yescharacteristic, complemented, Sylow
413C22—21no—
414C22—21no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22#9147811yescharacteristic
419C22#9148411yescharacteristic
420C22D5×#21711yescharacteristic
421C4—21no—
422C4—21no—
423C4—41no—
424C4—52no—
425C4—101no—
426C4—101no—
427C4—101no—
428C4—122no—
429C4—201no—
430C4—201no—
431C4—602no—
432C3#1059907211yescharacteristic, complemented, Sylow
433C2—21no—
434C2—21no—
435C2—81no—
436C2#1174895111yescharacteristic
437C2#1174917211yescharacteristic
438C2D5×#83711yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
Fitting, prime radicalC3×C5×#121C22
socleC22×C3×C5C2×C22⋊C4
cosocleC22×C3×C4×C5C23
hypercenter#121D3×D5
hypocenterC3×C5#1509
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. #11748638C2semidirect
3. #11748333C2semidirect
6. #11745961C2semidirect
7. #11745960C2semidirect
10. C3×#4082C4semidirect
13. C3×D4×Dic5C4semidirect
16. C3×#4036C4semidirect
17. C3×#4033C4semidirect
73. #4082Dic3semidirect
76. D4×Dic5Dic3semidirect
81. #4036Dic3semidirect
82. #4033Dic3semidirect
352. C3×C5#1509semidirect
412. C5#71755semidirect
432. C3#10599072semidirect

Maximal subgroups

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

subgroupindex
C3×#659342
#117486382
#117483332
#117463582
C5×#45372
#117459612
#117459602
#105990723
#717555