Finite Group Databasebeta

← #14417613

Subgroups — #14417613

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91801C211yesmaximal, characteristic
2#11756305C212yesmaximal, complemented
3C3×C4×C5×D8C211yesmaximal, characteristic, complemented
4D8×Dic15C211yesmaximal, characteristic, complemented
5#11751119C212yesmaximal, complemented
6D15×#107C211yesmaximal, characteristic, complemented
7#11750974C211yesmaximal, characteristic, complemented
8#11750872C212yesmaximal, complemented
9#11750858C212yesmaximal, complemented
10C4×Dic60C211yesmaximal, characteristic, complemented
11#11750790C211yesmaximal, characteristic, complemented
12#10611320—31nomaximal, Hall
13C2×#6819C2212yes—
14C2×C3×C5×D8C2211yescharacteristic
15C3×C4×C5×D4C2212yes—
16D4×Dic15C2212yes—
17C2×#6716C2212yes—
18C4×#1220—22no—
19C2×#6712—22no—
20#91801C418yescomplemented
21C2×Dic60C2211yescharacteristic
22C2×#6705C2211yescharacteristic
23C2×C8×D15C2211yescharacteristic
24C4⋊C4×D15C2212yes—
25#91776C2212yes—
26#91770—22no—
27#91766—22no—
28#91761C2211yescharacteristic
29C4×Dic30C2212yes—
30C3×C5×#107C2211yescharacteristic
31C3×C5×#102C2212yes—
32C3×C4×C5×C8C2211yescharacteristic
33#91116C2212yes—
34#91102C2211yescharacteristic
35#91100C2212yes—
36#91099C2211yescharacteristic
37C8×Dic15C2211yescharacteristic
38#91094C2212yes—
39#91091C2212yes—
40#91087C2211yescharacteristic
41#79589—51nomaximal, Hall
42C2×#4058—31no—
43#65880—32no—
44C4×C5×D8D311yescharacteristic, complemented
45D8×Dic5—31no—
46#65307—32no—
47D5×#107—31no—
48#65162—31no—
49#65060—32no—
50#65046—32no—
51C4×Dic20—31no—
52#64978—31no—
53C2×C3×C5×D4C2312yes—
54C22×C3×C4×C5—22no—
55C2×#1220—22no—
56C22×Dic15—22no—
57C22×Dic15—22no—
58#6819—24no—
59#6819C2×C418yescomplemented
60C2×C4×D15—22no—
61C2×C4×D15C2311yescharacteristic
62C2×Dic30C2312yes—
63C3×C5×D8C2×C414yescomplemented
64C2×C3×C5×C8C2311yescharacteristic
65C2×C3×C5×C8C2311yescharacteristic
66C3×C5×C4⋊C4C2312yes—
67C3×C5×C22⋊C4—22no—
68C3×C42×C5C2311yescharacteristic
69#6719—22no—
70#6716C2×C418yescomplemented
71#6714D411yescharacteristic
72#6714D411yescharacteristic
73C4⋊Dic15C2312yes—
74#6712—22no—
75#6712—22no—
76#6712—22no—
77#6712D411yescharacteristic
78#6712D411yescharacteristic
79C4×Dic15—22no—
80C4×Dic15—22no—
81C4×Dic15C2311yescharacteristic
82C2×C3⋊#168C2311yescharacteristic
83C2×C3⋊#168C2311yescharacteristic
84Dic60C2×C414yescomplemented
85#6705—22no—
86C8×D15C2×C414yescomplemented
87C2×#912—51no—
88#5546—52no—
89C3×C4×D8D511yescharacteristic, complemented
90Dic3×D8—51no—
91#5018—52no—
92D3×#107—51no—
93#4873—51no—
94#4771—52no—
95#4757—52no—
96C4×Dic12—51no—
97#4689—51no—
98C2×#711—32no—
99C2×C5×D8C2×D311yescharacteristic
100C4×C5×D4C2×D312yes—
101D4×Dic5—32no—
102C2×#687—32no—
103C4×C22⋊D5—62no—
104C2×#683—62no—
105#4058—38no—
106C2×Dic20—31no—
107C2×#676—31no—
108C2×C8×D5—31no—
109D5×C4⋊C4—32no—
110#4033—32no—
111#4027—62no—
112#4023—62no—
113#4018—31no—
114C4×Dic10—32no—
115C5×#107C2×D311yescharacteristic
116C5×#102C2×D312yes—
117C4×C5×C8C2×D311yescharacteristic
118#3964—32no—
119#3950—31no—
120#3948—32no—
121#3947—31no—
122C8×Dic5—31no—
123#3942—32no—
124#3939—32no—
125#3935—31no—
126#2951—151noSylow
127C23×C3×C5—22no—
128C22×D15C2×D411yescharacteristic
129C3×C5×D4—22no—
130C3×C5×D4C22×C414yes—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—82no—
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2411yescharacteristic
136#1220—28no—
137C2×Dic15—22no—
138C2×Dic15—28no—
139C2×Dic15—22no—
140C2×Dic15—82no—
141C2×Dic15C2×D411yescharacteristic
142C2×Dic15C2×D411yescharacteristic
143C2×Dic15C2×D411yescharacteristic
144C4×D15—82no—
145C4×D15C22×C412yes—
146C4×D15#4112yes—
147Dic30—22no—
148Dic30C22×C414yes—
149C3×C5×C8—21no—
150C3×C5×C8C22×C412yes—
151C3⋊#168—21no—
152C3⋊#168C22×C412yes—
153C2×#237—52no—
154C2×C3×D8C2×D511yescharacteristic
155C3×C4×D4C2×D512yes—
156D4×Dic3—52no—
157C2×#214—52no—
158C4×#67—102no—
159C2×Dic3⋊C4—102no—
160#912—58no—
161C2×Dic12—51no—
162C2×ΓL(1,𝔽25)—51no—
163C2×D3×C8—51no—
164D3×C4⋊C4—52no—
165#887—52no—
166#67⋊C4—102no—
167#877—102no—
168#872—51no—
169C4×Dic6—52no—
170C3×#107C2×D511yescharacteristic
171C3×#102C2×D512yes—
172C3×C4×C8C2×D511yescharacteristic
173#832—52no—
174#818—51no—
175#816—52no—
176#815—51no—
177C8×Dic3—51no—
178#810—52no—
179#807—52no—
180#803—51no—
181C2×C5×D4C22×D312yes—
182C22×C4×C5—22no—
183C2×C22⋊D5—62no—
184C22×Dic5—62no—
185C22×Dic5—62no—
186#711—38no—
187#711—64no—
188C2×C4×D5—31no—
189C2×C4×D5—62no—
190C2×Dic10—32no—
191C5×D8C4×D314yescomplemented
192C2×C5×C8C22×D311yescharacteristic
193C2×C5×C8C22×D311yescharacteristic
194C5×C4⋊C4C22×D312yes—
195C5×C22⋊C4—22no—
196C42×C5C22×D311yescharacteristic
197C22⋊Dic5—62no—
198#687—38no—
199#685—31no—
200#685—31no—
201C4⋊Dic5—32no—
202#683—31no—
203#683—31no—
204#683—62no—
205#683—62no—
206#683—62no—
207C4×Dic5—31no—
208C4×Dic5—62no—
209C4×Dic5—62no—
210C2×#168—31no—
211C2×#168—31no—
212Dic20—34no—
213#676—62no—
214C8×D5—34no—
215C2×#135—151no—
216#520—152no—
217#440—152no—
218#440—152no—
219C4×Q16—151no—
220C4×Q16—151no—
221C4×D8—151no—
222C4×D8D1511yescharacteristic, complemented
223C2×#107—151no—
224#417—152no—
225#405—151no—
226C22×C3×C5—24no—
227C22×C3×C5—42no—
228C22×C3×C5—42no—
229C22×C3×C5C22×D411yescharacteristic
230C2×D15—21no—
231C2×D15—21no—
232C2×D15C4×D412yes—
233C3×C4×C5—21no—
234C3×C4×C5—21no—
235C3×C4×C5—42no—
236C3×C4×C5C23×C411yescharacteristic
237C3×C4×C5C2×#4111yescharacteristic
238Dic15—24no—
239Dic15—21no—
240Dic15—21no—
241Dic15—42no—
242Dic15C4×D412yes—
243C2×C3×D4C22×D512yes—
244C22×C3×C4—22no—
245C2×#67—102no—
246C22×Dic3—102no—
247C22×Dic3—102no—
248#237—58no—
249#237—104no—
250C2×C4×D3—51no—
251C2×C4×D3—102no—
252C2×Dic6—52no—
253C3×D8C4×D514yescomplemented
254C2×C3×C8C22×D511yescharacteristic
255C2×C3×C8C22×D511yescharacteristic
256C3×C4⋊C4C22×D512yes—
257C3×C22⋊C4—22no—
258C3×C42C22×D511yescharacteristic
259#217—102no—
260#214—58no—
261(C2×D3)⋊C4—51no—
262(C2×D3)⋊C4—51no—
263C4⋊Dic3—52no—
264Dic3⋊C4—51no—
265Dic3⋊C4—51no—
266Dic3⋊C4—102no—
267Dic3⋊C4—102no—
268Dic3⋊C4—102no—
269C4×Dic3—51no—
270C4×Dic3—102no—
271C4×Dic3—102no—
272C2×C3⋊C8—51no—
273C2×C3⋊C8—51no—
274Dic12—54no—
275ΓL(1,𝔽25)—102no—
276D3×C8—54no—
277C23×C5—22no—
278C22×D5—31no—
279C5×D4—22no—
280C5×D4C2×C4×D314yes—
281C2×C4×C5—22no—
282C2×C4×C5—82no—
283C2×C4×C5D3×D411yescharacteristic
284C2×C4×C5D3×D411yescharacteristic
285C2×C4×C5C23×D311yescharacteristic
286C22⋊D5—68no—
287C2×Dic5—31no—
288C2×Dic5—31no—
289C2×Dic5—31no—
290C2×Dic5—68no—
291C2×Dic5—62no—
292C2×Dic5—62no—
293C2×Dic5—242no—
294C4×D5—32no—
295C4×D5—32no—
296C4×D5—242no—
297Dic10—34no—
298Dic10—62no—
299C5×C8—21no—
300C5×C8C2×C4×D312yes—
301#168—32no—
302#168—61no—
303C2×#41—152no—
304#135—158no—
305C2×Q16—151no—
306C2×SD16—152no—
307C2×D8C2×D1511yescharacteristic
308C2×M16—151no—
309C22×C8—151no—
310C4×Q8—152no—
311C4×Q8—152no—
312C4×D4—152no—
313C4×D4—302no—
314C4×D4—302no—
315C4×D4C2×D1512yes—
316#117—151no—
317#117—302no—
318C2×C4⋊C4—152no—
319C2×C4⋊C4—302no—
320#107—151no—
321#107—152no—
322#107C2×D1511yescharacteristic
323#103—152no—
324#103—152no—
325#102—152no—
326#102C2×D1512yes—
327#97—151no—
328#97—151no—
329C4×C8—151no—
330C4×C8C2×D1511yescharacteristic
331C2×C3×C5—44no—
332C2×C3×C5C2×C4×D411yescharacteristic
333C2×C3×C5#57611yescharacteristic
334C2×C3×C5#57811yescharacteristic
335D15—22no—
336C23×C3—22no—
337C22×D3—51no—
338C3×D4—22no—
339C3×D4C2×C4×D514yes—
340C2×C3×C4—22no—
341C2×C3×C4—82no—
342C2×C3×C4D4×D511yescharacteristic
343C2×C3×C4D4×D511yescharacteristic
344C2×C3×C4C23×D511yescharacteristic
345#67—108no—
346C2×Dic3—51no—
347C2×Dic3—51no—
348C2×Dic3—51no—
349C2×Dic3—108no—
350C2×Dic3—102no—
351C2×Dic3—102no—
352C2×Dic3—402no—
353C4×D3—52no—
354C4×D3—52no—
355C4×D3—402no—
356Dic6—54no—
357Dic6—102no—
358C3×C8—21no—
359C3×C8C2×C4×D512yes—
360C3⋊C8—52no—
361C3⋊C8—101no—
362C22×C5—24no—
363C22×C5—42no—
364C22×C5—42no—
365C22×C5C2×D3×D411yescharacteristic
366C2×D5—32no—
367C2×D5—61no—
368C2×D5—61no—
369C4×C5—21no—
370C4×C5—21no—
371C4×C5—42no—
372C4×C5C22×C4×D311yescharacteristic
373C4×C5D3×#4111yescharacteristic
374Dic5—32no—
375Dic5—61no—
376Dic5—61no—
377Dic5—64no—
378Dic5—122no—
379#41—158no—
380#41—304no—
381C2×Q8—152no—
382C2×D4—302no—
383C2×D4C22×D1512yes—
384C22×C4—22no—
385C22×C4—151no—
386C22×C4—302no—
387C22×C4—302no—
388C22×C4—302no—
389Q16—154no—
390SD16—158no—
391D8C4×D1514yescomplemented
392M16—302no—
393C2×C8—151no—
394C2×C8—154no—
395C2×C8—151no—
396C2×C8C22×D1511yescharacteristic
397C2×C8C22×D1511yescharacteristic
398C4⋊C4—151no—
399C4⋊C4—151no—
400C4⋊C4—152no—
401C4⋊C4—302no—
402C4⋊C4—302no—
403C4⋊C4—302no—
404C4⋊C4C22×D1512yes—
405C22⋊C4—22no—
406C22⋊C4—151no—
407C22⋊C4—151no—
408C22⋊C4—302no—
409C42—151no—
410C42—302no—
411C42—302no—
412C42C22×D1511yescharacteristic
413C3×C5#295111yescharacteristic, complemented, Hall
414C22×C3—24no—
415C22×C3—42no—
416C22×C3—42no—
417C22×C3C2×D4×D511yescharacteristic
418C2×D3—52no—
419C2×D3—101no—
420C2×D3—101no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—42no—
424C3×C4C22×C4×D511yescharacteristic
425C3×C4D5×#4111yescharacteristic
426Dic3—52no—
427Dic3—101no—
428Dic3—101no—
429Dic3—104no—
430Dic3—202no—
431C2×C5—44no—
432C2×C5C4×D3×D411yescharacteristic
433C2×C5#575711yescharacteristic
434C2×C5#577111yescharacteristic
435D5—62no—
436C23—22no—
437C23—151no—
438Q8—154no—
439Q8—302no—
440D4—22no—
441D4—308no—
442D4C2×C4×D1514yes—
443C2×C4—22no—
444C2×C4—82no—
445C2×C4—151no—
446C2×C4—152no—
447C2×C4—152no—
448C2×C4—151no—
449C2×C4—151no—
450C2×C4—308no—
451C2×C4—302no—
452C2×C4—302no—
453C2×C4—1202no—
454C2×C4—1202no—
455C2×C4D4×D1511yescharacteristic
456C2×C4D4×D1511yescharacteristic
457C2×C4C23×D1511yescharacteristic
458C8—21no—
459C8—152no—
460C8—301no—
461C8C2×C4×D1512yes—
462C2×C3—44no—
463C2×C3C4×D4×D511yescharacteristic
464C2×C3#6609111yescharacteristic
465C2×C3#6610511yescharacteristic
466D3—102no—
467C5#7958911yescharacteristic, complemented, Sylow
468C22—24no—
469C22—42no—
470C22—42no—
471C22—152no—
472C22—301no—
473C22—301no—
474C22C2×D4×D1511yescharacteristic
475C4—21no—
476C4—21no—
477C4—42no—
478C4—152no—
479C4—304no—
480C4—301no—
481C4—301no—
482C4—602no—
483C4C22×C4×D1511yescharacteristic
484C4#41×D1511yescharacteristic
485C3#1061132011yescharacteristic, complemented, Sylow
486C2—44no—
487C2—302no—
488C2C4×D4×D1511yescharacteristic
489C2#1175651611yescharacteristic
490C2#1175653011yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC3×C4×C5×D8C2
socleC22×C3×C5C22×D4
prime radicalC2×#91801C2
cosocleC2×C3×C4×C5C24
hypercenterC4×D8D15
hypocenterC3×C5#2951
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
2. #11756305C2semidirect
3. C3×C4×C5×D8C2semidirect
4. D8×Dic15C2semidirect
5. #11751119C2semidirect
6. D15×#107C2semidirect
7. #11750974C2semidirect
8. #11750872C2semidirect
9. #11750858C2semidirect
10. C4×Dic60C2semidirect
11. #11750790C2semidirect
20. #91801C4semidirect
44. C4×C5×D8D3semidirect
59. #6819C2×C4semidirect
63. C3×C5×D8C2×C4semidirect
70. #6716C2×C4semidirect
84. Dic60C2×C4semidirect
86. C8×D15C2×C4semidirect
89. C3×C4×D8D5semidirect
191. C5×D8C4×D3semidirect
222. C4×D8D15semidirect
253. C3×D8C4×D5semidirect
391. D8C4×D15semidirect
413. C3×C5#2951semidirect
467. C5#79589semidirect
485. C3#10611320semidirect

Maximal subgroups

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

subgroupindex
C2×#918012
#117563052
C3×C4×C5×D82
D8×Dic152
#117511192
D15×#1072
#117509742
#117508722
#117508582
C4×Dic602
#117507902
#106113203
#795895