Finite Group Databasebeta

← #14439907

Subgroups — #14439907

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D15×C4⋊Q8C211yesmaximal, characteristic
2#11752631C211yesmaximal, characteristic
3C5×#5081C211yesmaximal, characteristic, complemented
4C3×#65369C211yesmaximal, characteristic, complemented
5#11747441C212yesmaximal
6#11747438C212yesmaximal
7#11747398C212yesmaximal, complemented
8#11747397C212yesmaximal, complemented
9#11746983C211yesmaximal, characteristic
10#11746958C211yesmaximal, characteristic, complemented
11#11746953C211yesmaximal, characteristic, complemented
12D5×#501—31nomaximal, Hall
13C2×Q8×D15—21no—
14C3×C5×C4⋊Q8C2211yescharacteristic
15#91833—21no—
16C4⋊C4×D15—21no—
17C4⋊C4×D15C2212yes—
18#91777—21no—
19#91777C2212yes—
20C42×D15C2211yescharacteristic
21#91758C2211yescharacteristic
22C5×#870C2211yescharacteristic
23C3×#4016C2211yescharacteristic
24#91437C2211yescharacteristic
25#91437C2211yescharacteristic
26#91404—21no—
27#91404—21no—
28#91384C2211yescharacteristic
29#91384C2211yescharacteristic
30#91382—21no—
31#91382—21no—
32C2×#6648C2212yes—
33C5×#808C2212yes—
34C5×#807C2212yes—
35C5×#803C2211yescharacteristic
36C3×#3940C2212yes—
37C3×#3939C2212yes—
38C3×#3935C2211yescharacteristic
39#90990C2212yes—
40#90988C2212yes—
41#90987C2212yes—
42#90985C2212yes—
43#90954C2212yes—
44D3×#501—51nomaximal, Hall
45D5×C4⋊Q8—31no—
46D5×#125—31no—
47C5×#501—31no—
48#65369D311yescharacteristic, complemented
49#65354—31no—
50D5×#107—32no—
51#65165—32no—
52D5×#106—32no—
53#65145—32no—
54D5×#97—31no—
55#64991—31no—
56C2×C3×C5×Q8—21no—
57Q8×D15—44no—
58C2×C4×D15—22no—
59C2×C4×D15D411yescharacteristic
60C2×C4×D15D411yescharacteristic
61C2×C4×D15C2311yescharacteristic
62C2×Dic30—21no—
63C2×Dic30—22no—
64C2×#1200—21no—
65C2×#1200—21no—
66C3×C5×C4⋊C4—21no—
67C3×C5×C4⋊C4C2312yes—
68C3×C42×C5C2311yescharacteristic
69C4⋊Dic15—21no—
70C4⋊Dic15C2312yes—
71#6712—22no—
72#6712—22no—
73C4×Dic15D411yescharacteristic
74C4×Dic15D411yescharacteristic
75C4×Dic15C2311yescharacteristic
76C5×C4⋊Dic3C2311yescharacteristic
77C5×C4⋊Dic3C2311yescharacteristic
78C5×Dic3⋊C4—21no—
79C5×Dic3⋊C4—21no—
80C2×C5×C3⋊C8C2312yes—
81C3×C4⋊Dic5C2311yescharacteristic
82C3×C4⋊Dic5C2311yescharacteristic
83C3×#683—21no—
84C3×#683—21no—
85C2×C3×#168C2312yes—
86Dic3⋊Dic5—21no—
87Dic3⋊Dic5—21no—
88#6669—21no—
89#6669—21no—
90#6668—21no—
91#6668—21no—
92#6648Q818yescomplemented
93D3×C4⋊Q8—51no—
94D3×#125—51no—
95C3×#501—51no—
96#5081D511yescharacteristic, complemented
97#5064—51no—
98D3×#107—52no—
99#4876—52no—
100D3×#106—52no—
101#4856—52no—
102D3×#97—51no—
103#4702—51no—
104C2×Q8×D5—61no—
105C5×C4⋊Q8C2×D311yescharacteristic
106C5×#125—31no—
107#4090—61no—
108C2×C8×D5—32no—
109D5×C4⋊C4—32no—
110D5×C4⋊C4—31no—
111D5×C4⋊C4—31no—
112D5×C4⋊C4—61no—
113D5×C4⋊C4—61no—
114D5×C4⋊C4—61no—
115#4036—31no—
116#4036—31no—
117#4035—61no—
118#4035—61no—
119#4034—32no—
120#4034—61no—
121C42×D5—31no—
122#4016C2×D311yescharacteristic
123#4015—31no—
124C5×#107—32no—
125C5×#106—32no—
126C5×#97—31no—
127#3950—32no—
128#3949—32no—
129#3947—32no—
130#3940—32no—
131#3940C2×D312yes—
132#3939—32no—
133#3939C2×D312yes—
134#3935C2×D311yescharacteristic
135C2×#501—151noSylow
136C22×D15C2×D411yescharacteristic
137C3×C5×Q8—42no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2411yescharacteristic
142C2×Dic15—22no—
143C2×Dic15C2×D411yescharacteristic
144C2×Dic15C2×D411yescharacteristic
145C2×Dic15C2×D411yescharacteristic
146C4×D15—22no—
147C4×D15—22no—
148C4×D15—44no—
149C4×D15C2×Q814yes—
150Dic30—44no—
151Dic30—42no—
152C2×C5×Dic3—21no—
153C2×C5×Dic3—21no—
154C2×C3×Dic5—21no—
155C2×C3×Dic5—21no—
156#1200—42no—
157#1200—42no—
158C3×#168C2×Q814yescomplemented
159C5×C3⋊C8C2×Q814yescomplemented
160C2×D3×Q8—101no—
161C3×C4⋊Q8C2×D511yescharacteristic
162C3×#125—51no—
163#944—101no—
164C2×D3×C8—52no—
165D3×C4⋊C4—52no—
166D3×C4⋊C4—51no—
167D3×C4⋊C4—51no—
168D3×C4⋊C4—101no—
169D3×C4⋊C4—101no—
170D3×C4⋊C4—101no—
171#890—51no—
172#890—51no—
173#889—101no—
174#889—101no—
175#888—52no—
176#888—101no—
177C42×D3—51no—
178#870C2×D511yescharacteristic
179#869—51no—
180C3×#107—52no—
181C3×#106—52no—
182C3×#97—51no—
183#818—52no—
184#817—52no—
185#815—52no—
186#808—52no—
187#808C2×D512yes—
188#807—52no—
189#807C2×D512yes—
190#803C2×D511yescharacteristic
191C2×C5×Q8—21no—
192Q8×D5—124no—
193C2×C4×D5—31no—
194C2×C4×D5—31no—
195C2×C4×D5—31no—
196C2×C4×D5—61no—
197C2×C4×D5—61no—
198C2×C4×D5—62no—
199C2×Dic10—62no—
200C2×Dic10—61no—
201C2×C5×C8—32no—
202C5×C4⋊C4—21no—
203C5×C4⋊C4—31no—
204C5×C4⋊C4—31no—
205C5×C4⋊C4—61no—
206C5×C4⋊C4—61no—
207C5×C4⋊C4C22×D312yes—
208C42×C5C22×D311yescharacteristic
209C4⋊Dic5—32no—
210C4⋊Dic5—61no—
211C4⋊Dic5—61no—
212C4⋊Dic5—61no—
213C4⋊Dic5C22×D311yescharacteristic
214C4⋊Dic5C22×D311yescharacteristic
215#683—21no—
216#683—21no—
217#683—61no—
218#683—61no—
219#683—61no—
220#683—61no—
221#683—62no—
222#683—62no—
223C4×Dic5—31no—
224C4×Dic5—31no—
225C4×Dic5—31no—
226C2×#168C22×D312yes—
227C8×D5—38no—
228C2×C4⋊Q8—151no—
229C2×#125—151no—
230#501—31no—
231#501—51no—
232#501—151no—
233#501—151no—
234#501—152no—
235#501—152no—
236C2×#107—152no—
237C2×#106—152no—
238C2×#97—151no—
239C22×C3×C5C22×D411yescharacteristic
240C2×D15C4⋊Q812yes—
241C2×D15AGL(1,ℤ/8)12yes—
242C2×D15#13712yes—
243C3×C4×C5—21no—
244C3×C4×C5—21no—
245C3×C4×C5—42no—
246C3×C4×C5C22×Q812yes—
247Dic15—21no—
248Dic15—21no—
249Dic15—42no—
250Dic15C4⋊Q812yes—
251C3×Dic5—41no—
252C3×Dic5—41no—
253C5×Dic3—41no—
254C5×Dic3—41no—
255C2×C3×Q8—21no—
256D3×Q8—204no—
257C2×C4×D3—51no—
258C2×C4×D3—51no—
259C2×C4×D3—51no—
260C2×C4×D3—101no—
261C2×C4×D3—101no—
262C2×C4×D3—102no—
263C2×Dic6—102no—
264C2×Dic6—101no—
265C2×C3×C8—52no—
266C3×C4⋊C4—21no—
267C3×C4⋊C4—51no—
268C3×C4⋊C4—51no—
269C3×C4⋊C4—101no—
270C3×C4⋊C4—101no—
271C3×C4⋊C4C22×D512yes—
272C3×C42C22×D511yescharacteristic
273C4⋊Dic3—52no—
274C4⋊Dic3—101no—
275C4⋊Dic3—101no—
276C4⋊Dic3—101no—
277C4⋊Dic3C22×D511yescharacteristic
278C4⋊Dic3C22×D511yescharacteristic
279Dic3⋊C4—21no—
280Dic3⋊C4—21no—
281Dic3⋊C4—101no—
282Dic3⋊C4—101no—
283Dic3⋊C4—101no—
284Dic3⋊C4—101no—
285Dic3⋊C4—102no—
286Dic3⋊C4—102no—
287C4×Dic3—51no—
288C4×Dic3—51no—
289C4×Dic3—51no—
290C2×C3⋊C8C22×D512yes—
291D3×C8—58no—
292C22×D5—31no—
293C5×Q8—42no—
294C2×C4×C5—22no—
295C2×C4×C5—61no—
296C2×C4×C5—61no—
297C2×C4×C5D3×D411yescharacteristic
298C2×C4×C5D3×D411yescharacteristic
299C2×C4×C5C23×D311yescharacteristic
300C2×Dic5—21no—
301C2×Dic5—21no—
302C2×Dic5—31no—
303C2×Dic5—31no—
304C2×Dic5—31no—
305C2×Dic5—62no—
306C4×D5—34no—
307C4×D5—62no—
308C4×D5—62no—
309C4×D5—122no—
310C4×D5—122no—
311C4×D5—124no—
312Dic10—124no—
313Dic10—122no—
314C5×C8—34no—
315#168D3×Q814yescomplemented
316C22×Q8—301no—
317C22×C8—152no—
318C4⋊Q8—152no—
319C4⋊Q8—151no—
320C4⋊Q8—301no—
321C4⋊Q8—301no—
322C4⋊Q8D3×D511yescharacteristic
323#125—31no—
324#125—51no—
325#125—151no—
326#125—151no—
327#125—301no—
328#125—301no—
329C2×C4⋊C4—151no—
330C2×C4⋊C4—151no—
331C2×C4⋊C4—152no—
332C2×C4⋊C4—301no—
333C2×C4⋊C4—301no—
334C2×C4⋊C4—301no—
335C2×C42—151no—
336#107—32no—
337#107—52no—
338#107—152no—
339#107—152no—
340#106—32no—
341#106—52no—
342#106—152no—
343#106—152no—
344#97—31no—
345#97—51no—
346#97—152no—
347C2×C3×C5C2×C4⋊Q811yescharacteristic
348C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
349C2×C3×C5C2×#13711yescharacteristic
350D15#50114yescomplemented
351C22×D3—51no—
352C3×Q8—42no—
353C2×C3×C4—22no—
354C2×C3×C4—101no—
355C2×C3×C4—101no—
356C2×C3×C4D4×D511yescharacteristic
357C2×C3×C4D4×D511yescharacteristic
358C2×C3×C4C23×D511yescharacteristic
359C2×Dic3—21no—
360C2×Dic3—21no—
361C2×Dic3—51no—
362C2×Dic3—51no—
363C2×Dic3—51no—
364C2×Dic3—102no—
365C4×D3—54no—
366C4×D3—102no—
367C4×D3—102no—
368C4×D3—202no—
369C4×D3—202no—
370C4×D3—204no—
371Dic6—204no—
372Dic6—202no—
373C3×C8—54no—
374C3⋊C8Q8×D514yescomplemented
375C22×C5C2×D3×D411yescharacteristic
376C2×D5—32no—
377C2×D5—32no—
378C2×D5—32no—
379C4×C5—21no—
380C4×C5—21no—
381C4×C5—42no—
382C4×C5—121no—
383C4×C5—121no—
384C4×C5C2×D3×Q812yes—
385Dic5—32no—
386Dic5—41no—
387Dic5—41no—
388Dic5—61no—
389Dic5—61no—
390Dic5—122no—
391C2×Q8—21no—
392C2×Q8—302no—
393C2×Q8—301no—
394C2×Q8—604no—
395C22×C4—151no—
396C22×C4—151no—
397C22×C4—151no—
398C22×C4—302no—
399C22×C4—301no—
400C22×C4—301no—
401C2×C8—32no—
402C2×C8—52no—
403C2×C8—158no—
404C4⋊C4—21no—
405C4⋊C4—31no—
406C4⋊C4—31no—
407C4⋊C4—51no—
408C4⋊C4—51no—
409C4⋊C4—61no—
410C4⋊C4—61no—
411C4⋊C4—101no—
412C4⋊C4—101no—
413C4⋊C4—152no—
414C4⋊C4—302no—
415C4⋊C4—302no—
416C4⋊C4—301no—
417C4⋊C4—301no—
418C4⋊C4—301no—
419C4⋊C4—301no—
420C4⋊C4—301no—
421C4⋊C4—301no—
422C4⋊C4—301no—
423C4⋊C4C2×D3×D512yes—
424C42—151no—
425C42—151no—
426C42—151no—
427C42C2×D3×D511yescharacteristic
428C3×C5C2×#50111yescharacteristic, complemented, Hall
429C22×C3C2×D4×D511yescharacteristic
430C2×D3—52no—
431C2×D3—52no—
432C2×D3—52no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—42no—
436C3×C4—201no—
437C3×C4—201no—
438C3×C4C2×Q8×D512yes—
439Dic3—41no—
440Dic3—41no—
441Dic3—52no—
442Dic3—101no—
443Dic3—101no—
444Dic3—202no—
445C2×C5D3×C4⋊Q811yescharacteristic
446C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
447C2×C5D3×#13711yescharacteristic
448D5—34no—
449C23—151no—
450Q8—42no—
451Q8—602no—
452Q8—604no—
453C2×C4—22no—
454C2×C4—61no—
455C2×C4—61no—
456C2×C4—101no—
457C2×C4—101no—
458C2×C4—151no—
459C2×C4—154no—
460C2×C4—151no—
461C2×C4—151no—
462C2×C4—302no—
463C2×C4—302no—
464C2×C4—302no—
465C2×C4—604no—
466C2×C4—602no—
467C2×C4—602no—
468C2×C4#679011yescharacteristic
469C2×C4#679011yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—34no—
472C8—54no—
473C2×C3D5×C4⋊Q811yescharacteristic
474C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
475C2×C3D5×#13711yescharacteristic
476D3—54no—
477C5D3×#50111yescharacteristic, complemented, Sylow
478C22—152no—
479C22—152no—
480C22—152no—
481C22C2×#679011yescharacteristic
482C4—21no—
483C4—21no—
484C4—42no—
485C4—121no—
486C4—121no—
487C4—152no—
488C4—201no—
489C4—201no—
490C4—301no—
491C4—301no—
492C4—602no—
493C4D3×Q8×D512yes—
494C3D5×#50111yescharacteristic, complemented, Sylow
495C2—154no—
496C2#1175470111yescharacteristic
497C2#1175509511yescharacteristic
498C2#1175515311yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC22×D15C2×D4
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5C2×#501
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. C5×#5081C2semidirect
4. C3×#65369C2semidirect
7. #11747398C2semidirect
8. #11747397C2semidirect
10. #11746958C2semidirect
11. #11746953C2semidirect
48. #65369D3semidirect
92. #6648Q8semidirect
96. #5081D5semidirect
158. C3×#168C2×Q8semidirect
159. C5×C3⋊C8C2×Q8semidirect
315. #168D3×Q8semidirect
350. D15#501semidirect
374. C3⋊C8Q8×D5semidirect
428. C3×C5C2×#501semidirect
477. C5D3×#501semidirect
494. C3D5×#501semidirect

Maximal subgroups

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

subgroupindex
D15×C4⋊Q82
#117526312
C5×#50812
C3×#653692
#117474412
#117474382
#117473982
#117473972
#117469832
#117469582
#117469532
D5×#5013
D3×#5015