Finite Group Databasebeta

← #14417644

Subgroups — #14417644

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#11754916C212yesmaximal, complemented
3C5×Dic3×D8C211yesmaximal, characteristic, complemented
4C3×D8×Dic5C211yesmaximal, characteristic, complemented
5#11749014C212yesmaximal, complemented
6#11749004C212yesmaximal, complemented
7#11748959C212yesmaximal, complemented
8#11747873C211yesmaximal, characteristic, complemented
9#11747851C211yesmaximal, characteristic, complemented
10#11747657C211yesmaximal, characteristic, complemented
11#11747636C211yesmaximal, characteristic, complemented
12#10611320—31nomaximal, Hall
13C2×#6819C2212yes—
14C2×C3×C5×D8C2211yescharacteristic
15C2×#6716C2212yes—
16#91801C418yescomplemented
17C2×Dic60C2211yescharacteristic
18C2×C8×D15C2211yescharacteristic
19C5×D4×Dic3C2212yes—
20C3×D4×Dic5C2212yes—
21#91556—22no—
22#91552—22no—
23C2×#6669—22no—
24#91532—22no—
25#91437C2212yes—
26#91386C2211yescharacteristic
27#91340C2212yes—
28#91333C2212yes—
29C2×#6651C2211yescharacteristic
30C5×#832C2212yes—
31C5×#818C2211yescharacteristic
32C5×C8×Dic3C2211yescharacteristic
33C3×#3964C2212yes—
34C3×#3950C2211yescharacteristic
35C3×C8×Dic5C2211yescharacteristic
36#90989C2212yes—
37#90975C2212yes—
38#90974C2212yes—
39#90953C2211yescharacteristic
40#90952C2211yescharacteristic
41#79589—51nomaximal, Hall
42C2×#4058—31no—
43#65880—32no—
44C4×C5×D8—31no—
45D8×Dic5D311yescharacteristic, complemented
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—
54C2×#1220—22no—
55C22×Dic15—22no—
56#6819—24no—
57#6819C2×C418yescomplemented
58C2×C4×D15C2311yescharacteristic
59C2×Dic30C2312yes—
60C22×C5×Dic3—22no—
61C22×C3×Dic5—22no—
62C2×#1200—22no—
63C3×C5×D8C2×C414yescomplemented
64C2×C3×C5×C8C2311yescharacteristic
65#6716C2×C418yescomplemented
66C2×C3⋊#168C2311yescharacteristic
67Dic60C2×C414yescomplemented
68C8×D15C2×C414yescomplemented
69C5×#217—22no—
70C5×C4⋊Dic3C2312yes—
71C4×C5×Dic3C2311yescharacteristic
72C2×C5×C3⋊C8C2311yescharacteristic
73C3×C22⋊Dic5—22no—
74C3×C4⋊Dic5C2312yes—
75C3×C4×Dic5C2311yescharacteristic
76C2×C3×#168C2311yescharacteristic
77#6669—22no—
78#6669—22no—
79#6669—22no—
80#6669D411yescharacteristic
81#6669D411yescharacteristic
82#6667D411yescharacteristic
83#6667D411yescharacteristic
84Dic3×Dic5—22no—
85Dic3×Dic5—22no—
86#6651—22no—
87C2×#912—51no—
88#5546—52no—
89C3×C4×D8—51no—
90Dic3×D8D511yescharacteristic, complemented
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×D4—32no—
101D4×Dic5C2×D312yes—
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×#107—31no—
116C5×#102—32no—
117C4×C5×C8—31no—
118#3964C2×D312yes—
119#3950C2×D311yescharacteristic
120#3948—32no—
121#3947—31no—
122C8×Dic5C2×D311yescharacteristic
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×C5C2411yescharacteristic
132#1220—28no—
133C2×Dic15—22no—
134C2×Dic15—28no—
135C2×Dic15C2×D411yescharacteristic
136C4×D15C22×C412yes—
137C4×D15#4112yes—
138Dic30—22no—
139Dic30C22×C414yes—
140C2×C5×Dic3—22no—
141C2×C5×Dic3—82no—
142C2×C5×Dic3C2×D411yescharacteristic
143C2×C5×Dic3C2×D411yescharacteristic
144C2×C3×Dic5—22no—
145C2×C3×Dic5—82no—
146C2×C3×Dic5C2×D411yescharacteristic
147C2×C3×Dic5C2×D411yescharacteristic
148#1200—82no—
149C3×C5×C8C22×C412yes—
150C3⋊#168C22×C412yes—
151C3×#168—21no—
152C5×C3⋊C8—21no—
153C2×#237—52no—
154C2×C3×D8C2×D511yescharacteristic
155C3×C4×D4—52no—
156D4×Dic3C2×D512yes—
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×#107—51no—
171C3×#102—52no—
172C3×C4×C8—51no—
173#832C2×D512yes—
174#818C2×D511yescharacteristic
175#816—52no—
176#815—51no—
177C8×Dic3C2×D511yescharacteristic
178#810—52no—
179#807—52no—
180#803—51no—
181C2×C5×D4C22×D312yes—
182C22×C4×C5—62no—
183C2×C22⋊D5—62no—
184C22×Dic5—22no—
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×C8—31no—
193C2×C5×C8C22×D311yescharacteristic
194C5×C4⋊C4—32no—
195C5×C22⋊C4—62no—
196C42×C5—31no—
197C22⋊Dic5—22no—
198#687—38no—
199#685—31no—
200#685—31no—
201C4⋊Dic5C22×D312yes—
202#683—31no—
203#683—31no—
204#683—62no—
205#683—62no—
206#683—62no—
207C4×Dic5—62no—
208C4×Dic5—62no—
209C4×Dic5C22×D311yescharacteristic
210C2×#168—31no—
211C2×#168C22×D311yescharacteristic
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—31no—
222C4×D8—51no—
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×C5C23×C411yescharacteristic
234C3×C4×C5C2×#4111yescharacteristic
235Dic15—24no—
236Dic15C4×D412yes—
237C3×Dic5—21no—
238C3×Dic5—21no—
239C3×Dic5—42no—
240C5×Dic3—21no—
241C5×Dic3—21no—
242C5×Dic3—42no—
243C2×C3×D4C22×D512yes—
244C22×C3×C4—102no—
245C2×#67—102no—
246C22×Dic3—22no—
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×C8—51no—
255C2×C3×C8C22×D511yescharacteristic
256C3×C4⋊C4—52no—
257C3×C22⋊C4—102no—
258C3×C42—51no—
259#217—22no—
260#214—58no—
261(C2×D3)⋊C4—51no—
262(C2×D3)⋊C4—51no—
263C4⋊Dic3C22×D512yes—
264Dic3⋊C4—51no—
265Dic3⋊C4—51no—
266Dic3⋊C4—102no—
267Dic3⋊C4—102no—
268Dic3⋊C4—102no—
269C4×Dic3—102no—
270C4×Dic3—102no—
271C4×Dic3C22×D511yescharacteristic
272C2×C3⋊C8—51no—
273C2×C3⋊C8C22×D511yescharacteristic
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—31no—
282C2×C4×C5—31no—
283C2×C4×C5—62no—
284C2×C4×C5—242no—
285C2×C4×C5C23×D311yescharacteristic
286C22⋊D5—68no—
287C2×Dic5—22no—
288C2×Dic5—31no—
289C2×Dic5—68no—
290C2×Dic5—62no—
291C2×Dic5—82no—
292C2×Dic5D3×D411yescharacteristic
293C2×Dic5D3×D411yescharacteristic
294C4×D5—32no—
295C4×D5—32no—
296C4×D5—242no—
297Dic10—34no—
298Dic10—62no—
299C5×C8—61no—
300C5×C8C2×C4×D312yes—
301#168—21no—
302#168—32no—
303C2×#41—152no—
304#135—158no—
305C2×Q16—151no—
306C2×SD16—152no—
307C2×D8D3×D511yescharacteristic
308C2×M16—151no—
309C22×C8—151no—
310C4×Q8—152no—
311C4×Q8—152no—
312C4×D4—32no—
313C4×D4—52no—
314C4×D4—302no—
315C4×D4—302no—
316#117—151no—
317#117—302no—
318C2×C4⋊C4—152no—
319C2×C4⋊C4—302no—
320#107—31no—
321#107—51no—
322#107—152no—
323#103—152no—
324#103—152no—
325#102—32no—
326#102—52no—
327#97—151no—
328#97—151no—
329C4×C8—31no—
330C4×C8—51no—
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—51no—
341C2×C3×C4—51no—
342C2×C3×C4—102no—
343C2×C3×C4—402no—
344C2×C3×C4C23×D511yescharacteristic
345#67—108no—
346C2×Dic3—22no—
347C2×Dic3—51no—
348C2×Dic3—82no—
349C2×Dic3—108no—
350C2×Dic3—102no—
351C2×Dic3D4×D511yescharacteristic
352C2×Dic3D4×D511yescharacteristic
353C4×D3—52no—
354C4×D3—52no—
355C4×D3—402no—
356Dic6—54no—
357Dic6—102no—
358C3×C8—101no—
359C3×C8C2×C4×D512yes—
360C3⋊C8—21no—
361C3⋊C8—52no—
362C22×C5—24no—
363C22×C5—42no—
364C22×C5—42no—
365C22×C5C2×D3×D411yescharacteristic
366C2×D5—32no—
367C2×D5—61no—
368C2×D5—61no—
369C4×C5—61no—
370C4×C5—61no—
371C4×C5—122no—
372C4×C5C22×C4×D311yescharacteristic
373C4×C5D3×#4111yescharacteristic
374Dic5—21no—
375Dic5—21no—
376Dic5—32no—
377Dic5—42no—
378Dic5—64no—
379#41—158no—
380#41—304no—
381C2×Q8—152no—
382C2×D4—302no—
383C2×D4C2×D3×D512yes—
384C22×C4—62no—
385C22×C4—102no—
386C22×C4—151no—
387C22×C4—302no—
388C22×C4—302no—
389Q16—154no—
390SD16—158no—
391D8#120014yescomplemented
392M16—302no—
393C2×C8—31no—
394C2×C8—51no—
395C2×C8—151no—
396C2×C8—154no—
397C2×C8C2×D3×D511yescharacteristic
398C4⋊C4—32no—
399C4⋊C4—52no—
400C4⋊C4—151no—
401C4⋊C4—151no—
402C4⋊C4—302no—
403C4⋊C4—302no—
404C4⋊C4—302no—
405C22⋊C4—62no—
406C22⋊C4—102no—
407C22⋊C4—151no—
408C22⋊C4—151no—
409C42—31no—
410C42—51no—
411C42—302no—
412C42—302no—
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—101no—
422C3×C4—101no—
423C3×C4—202no—
424C3×C4C22×C4×D511yescharacteristic
425C3×C4D5×#4111yescharacteristic
426Dic3—21no—
427Dic3—21no—
428Dic3—42no—
429Dic3—52no—
430Dic3—104no—
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×#120014yes—
443C2×C4—31no—
444C2×C4—31no—
445C2×C4—51no—
446C2×C4—51no—
447C2×C4—62no—
448C2×C4—102no—
449C2×C4—151no—
450C2×C4—152no—
451C2×C4—152no—
452C2×C4—242no—
453C2×C4—308no—
454C2×C4—302no—
455C2×C4—402no—
456C2×C4—1202no—
457C2×C4C22×D3×D511yescharacteristic
458C8—61no—
459C8—101no—
460C8—152no—
461C8C2×#120012yes—
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—
474C22D3×D4×D511yescharacteristic
475C4—61no—
476C4—61no—
477C4—101no—
478C4—101no—
479C4—122no—
480C4—152no—
481C4—202no—
482C4—304no—
483C4#9202411yescharacteristic
484C4C22×#120011yescharacteristic
485C3#1061132011yescharacteristic, complemented, Sylow
486C2—44no—
487C2—302no—
488C2#1175405411yescharacteristic
489C2#1175406311yescharacteristic
490C2D4×#120011yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×D8C22
socleC22×C3×C5C22×D4
prime radicalC2×#91801C2
cosocleC2×C3×C4×C5C24
hypercenterC2×D8D3×D5
hypocenterC3×C5#2951
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
2. #11754916C2semidirect
3. C5×Dic3×D8C2semidirect
4. C3×D8×Dic5C2semidirect
5. #11749014C2semidirect
6. #11749004C2semidirect
7. #11748959C2semidirect
8. #11747873C2semidirect
9. #11747851C2semidirect
10. #11747657C2semidirect
11. #11747636C2semidirect
16. #91801C4semidirect
45. D8×Dic5D3semidirect
57. #6819C2×C4semidirect
63. C3×C5×D8C2×C4semidirect
65. #6716C2×C4semidirect
67. Dic60C2×C4semidirect
68. C8×D15C2×C4semidirect
90. Dic3×D8D5semidirect
191. C5×D8C4×D3semidirect
253. C3×D8C4×D5semidirect
391. D8#1200semidirect
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
#117549162
C5×Dic3×D82
C3×D8×Dic52
#117490142
#117490042
#117489592
#117478732
#117478512
#117476572
#117476362
#106113203
#795895