Finite Group Databasebeta

← #14438033

Subgroups — #14438033

Order 1920.

784 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5832C211yesmaximal, characteristic
2#11754616C211yesmaximal, characteristic, complemented
3#11751334C211yesmaximal, characteristic, complemented
4C3×#65522C211yesmaximal, characteristic, complemented
5#11749192C212yesmaximal, complemented
6#11749191C212yesmaximal, complemented
7#11748946C212yesmaximal, complemented
8#11748945C212yesmaximal, complemented
9#11748388C211yesmaximal, characteristic, complemented
10#11748382C211yesmaximal, characteristic, complemented
11C2×#90953C211yesmaximal, characteristic, complemented
12#10615013—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15#91815C2211yescharacteristic
16C22×C3⋊#168C2211yescharacteristic
17C5×#947C2211yescharacteristic
18C5×#944C2211yescharacteristic
19C5×#940C2211yescharacteristic
20C5×#939—22no—
21C5×#936C2211yescharacteristic
22C4×C5×#67—22no—
23C2×C4×C5×Dic3C2211yescharacteristic
24C3×#4072C2211yescharacteristic
25C22×C3×#168C2211yescharacteristic
26#91575—22no—
27#91469C2212yes—
28C4×#1204—22no—
29#91381C2212yes—
30#91119C2212yes—
31#91116C2212yes—
32C3×#3967C2212yes—
33C3×#3964C2212yes—
34#90973C2212yes—
35#90972C2212yes—
36#90967C2212yes—
37#90966C2212yes—
38#90953C2212yes—
39#90953C2212yes—
40#78826—51nomaximal, Hall
41C5×#532—31no—
42#65804—31no—
43#65522—31no—
44#65522—31no—
45#65522—31no—
46#65522D311yescharacteristic, complemented
47#65371—32no—
48#65360—32no—
49#65344—32no—
50#65344—32no—
51C2×#3935—31no—
52C3×C5×#41—22no—
53C3×C5×#41—22no—
54C2×C3×C5×Q8C2311yescharacteristic
55C2×C3×C5×D4—21no—
56C2×C3×C5×D4C2311yescharacteristic
57C22×C3×C4×C5—21no—
58C22×C3×C4×C5C2311yescharacteristic
59C2×C5×#67—21no—
60C2×C5×#67—22no—
61C22×C5×Dic3D412yes—
62C5×#235—22no—
63C5×#235—22no—
64C2×C5×D12C2311yescharacteristic
65C2×C4×C5×D3—21no—
66C2×C5×Dic6C2311yescharacteristic
67C2×#1204—22no—
68#6719—21no—
69C4⋊Dic15C2312yes—
70C4×Dic15—21no—
71C2×C3⋊#168—22no—
72C2×C3⋊#168C2312yes—
73C5×#217—22no—
74C5×(C2×D3)⋊C4—22no—
75C5×Dic3⋊C4—22no—
76C4×C5×Dic3D412yes—
77C4×C5×Dic3C2311yescharacteristic
78C4×C5×Dic3C2311yescharacteristic
79C3×C22⋊Dic5—21no—
80C3×C4⋊Dic5C2312yes—
81C3×C4×Dic5—21no—
82C2×C3×#168—22no—
83C2×C3×#168C2312yes—
84Dic3⋊Dic5—22no—
85#6669—22no—
86#6668—22no—
87#5832D511yescharacteristic
88#5517—51no—
89C3×#416—51no—
90#5233—51no—
91#5113—51no—
92C2×#815—51no—
93#5002—51no—
94#4797—52no—
95#4794—52no—
96#4765—52no—
97#4764—52no—
98C2×C5×#41—31no—
99C2×C5×#41C2×D311yescharacteristic
100C5×C4⋊Q8—31no—
101C5×#127—31no—
102C5×#124—31no—
103C5×#124—31no—
104C5×#121—62no—
105C4×C5×D4—62no—
106C2×C42×C5—31no—
107#4072—31no—
108#4072C2×D311yescharacteristic
109#4070—62no—
110C22×#168—31no—
111C22×#168C2×D311yescharacteristic
112#4016—32no—
113#4015—32no—
114C4×Dic10—62no—
115#3967—32no—
116#3967—32no—
117#3967—32no—
118#3967C2×D312yes—
119#3964—32no—
120#3964—32no—
121#3964—32no—
122#3964C2×D312yes—
123#3935—32no—
124#3935—32no—
125#3135—151noSylow
126C23×C3×C5—21no—
127C23×C3×C5C2×D411yescharacteristic
128C22×C5×D3—21no—
129C3×C5×Q8—21no—
130C3×C5×Q8—21no—
131C3×C5×D4—21no—
132C3×C5×D4—21no—
133C3×C5×D4—42no—
134C2×C3×C4×C5—21no—
135C2×C3×C4×C5—42no—
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5#4112yes—
138C2×C3×C4×C5#4112yes—
139C2×C3×C4×C5C2411yescharacteristic
140C2×Dic15—22no—
141C5×#67—44no—
142C5×#67—42no—
143C2×C5×Dic3—21no—
144C2×C5×Dic3—42no—
145C2×C5×Dic3C2×D412yes—
146C2×C5×Dic3C2×D412yes—
147C5×D12—21no—
148C5×D12—21no—
149C4×C5×D3—42no—
150C5×Dic6—21no—
151C5×Dic6—21no—
152C2×C3×Dic5—22no—
153#1204—44no—
154C3⋊#168—22no—
155C3×#168—22no—
156C2×C3×#41C2×D511yescharacteristic
157C2×#235C2×D511yescharacteristic
158C22×C3×C8—51no—
159C3×#117—51no—
160#947C2×D511yescharacteristic
161#944C2×D511yescharacteristic
162#940C2×D511yescharacteristic
163#939—22no—
164#936C2×D511yescharacteristic
165C4×#67—22no—
166#926—51no—
167C2×C4×Dic3C2×D511yescharacteristic
168C22×C3⋊C8—51no—
169#890—52no—
170#888—52no—
171#878—102no—
172C4×Dic6—102no—
173C3×#103—52no—
174C3×#102—52no—
175#835—52no—
176#832—52no—
177#821—52no—
178#816—52no—
179#815—52no—
180#815—52no—
181#810—52no—
182#809—52no—
183C5×#41—22no—
184C5×#41—22no—
185C5×#41—62no—
186C5×#41—62no—
187C2×C5×Q8—31no—
188C2×C5×Q8C22×D311yescharacteristic
189C2×C5×D4—21no—
190C2×C5×D4—31no—
191C2×C5×D4—62no—
192C2×C5×D4—61no—
193C2×C5×D4C22×D311yescharacteristic
194C22×C4×C5—21no—
195C22×C4×C5—32no—
196C22×C4×C5—61no—
197C22×C4×C5C22×D311yescharacteristic
198C2×Dic10—62no—
199C5×C4⋊C4—62no—
200C5×C22⋊C4—62no—
201C5×C22⋊C4—62no—
202C42×C5—32no—
203C42×C5—31no—
204C42×C5—31no—
205C22⋊Dic5—21no—
206C22⋊Dic5—61no—
207C4⋊Dic5—32no—
208C4⋊Dic5—62no—
209C4⋊Dic5C22×D312yes—
210#683—62no—
211#683—62no—
212C4×Dic5—21no—
213C4×Dic5—61no—
214C2×#168—22no—
215C2×#168—32no—
216C2×#168—62no—
217C2×#168C22×D312yes—
218#533—151no—
219#532—31no—
220#491—152no—
221#490—152no—
222#489—152no—
223#489—152no—
224#416—51no—
225#416—151no—
226#416—151no—
227#416—151no—
228C2×#97—151no—
229C22×C3×C5—22no—
230C22×C3×C5—41no—
231C22×C3×C5—42no—
232C22×C3×C5#12412yes—
233C22×C3×C5C22×D411yescharacteristic
234C2×C5×D3—41no—
235C2×C5×D3—42no—
236C3×C4×C5—41no—
237C3×C4×C5#12412yes—
238C3×C4×C5C2×#4111yescharacteristic
239C3×C4×C5C2×#4111yescharacteristic
240Dic15—42no—
241C3×Dic5—42no—
242C5×Dic3—22no—
243C5×Dic3—22no—
244C5×Dic3—41no—
245C3×#41—22no—
246C3×#41—22no—
247C2×C3×Q8C22×D511yescharacteristic
248C2×C3×D4—21no—
249C2×C3×D4C22×D511yescharacteristic
250C22×C3×C4—21no—
251C22×C3×C4C22×D511yescharacteristic
252C2×#67—21no—
253C2×#67—22no—
254C22×Dic3C22⋊D512yes—
255#235—22no—
256#235—22no—
257C2×D12C22×D511yescharacteristic
258C2×C4×D3—21no—
259C2×Dic6—102no—
260C2×Dic6C22×D511yescharacteristic
261C2×C3×C8—52no—
262C2×C3×C8—102no—
263C3×C4⋊C4—52no—
264C3×C22⋊C4—101no—
265C3×C42—101no—
266#217—22no—
267#217—101no—
268(C2×D3)⋊C4—22no—
269C4⋊Dic3—52no—
270C4⋊Dic3—102no—
271Dic3⋊C4—22no—
272Dic3⋊C4—102no—
273Dic3⋊C4—102no—
274C4×Dic3—101no—
275C4×Dic3C22⋊D512yes—
276C4×Dic3C22×D511yescharacteristic
277C4×Dic3C22×D511yescharacteristic
278C2×C3⋊C8—52no—
279C2×C3⋊C8—102no—
280C23×C5—21no—
281C23×C5—61no—
282C23×C5D3×D411yescharacteristic
283C5×Q8—21no—
284C5×Q8—21no—
285C5×Q8—61no—
286C5×Q8—61no—
287C5×D4—21no—
288C5×D4—21no—
289C5×D4—42no—
290C5×D4—61no—
291C5×D4—61no—
292C5×D4—124no—
293C5×D4—122no—
294C2×C4×C5—21no—
295C2×C4×C5—32no—
296C2×C4×C5—32no—
297C2×C4×C5—42no—
298C2×C4×C5—61no—
299C2×C4×C5—122no—
300C2×C4×C5—122no—
301C2×C4×C5#23512yes—
302C2×C4×C5D3×D411yescharacteristic
303C2×C4×C5#23712yes—
304C2×C4×C5C23×D311yescharacteristic
305C2×Dic5—22no—
306C2×Dic5—62no—
307Dic10—124no—
308#168—22no—
309#168—62no—
310C2×#41—31no—
311C2×#41D3×D511yescharacteristic
312C22×C8—51no—
313C22×C8—151no—
314C4⋊Q8—31no—
315C4⋊Q8—152no—
316#127—31no—
317#125—152no—
318#124—31no—
319#124—31no—
320C22⋊Q8—302no—
321#121—62no—
322C4×Q8—302no—
323C4×D4—62no—
324#117—51no—
325#117—151no—
326C2×C42—31no—
327#103—52no—
328#103—152no—
329#103—152no—
330#103—152no—
331#102—52no—
332#102—152no—
333#102—152no—
334#102—152no—
335#97—152no—
336#97—152no—
337C2×C3×C5—22no—
338C2×C3×C5—81no—
339C2×C3×C5C2×#12411yescharacteristic
340C2×C3×C5#57512yes—
341C5×D3—81no—
342C23×C3—21no—
343C23×C3C2×C22⋊D511yescharacteristic
344C22×D3—21no—
345C3×Q8—21no—
346C3×Q8—21no—
347C3×D4—21no—
348C3×D4—21no—
349C3×D4—42no—
350C2×C3×C4—21no—
351C2×C3×C4—42no—
352C2×C3×C4—102no—
353C2×C3×C4#71112yes—
354C2×C3×C4#71112yes—
355C2×C3×C4C2×C22⋊D511yescharacteristic
356C2×C3×C4C23×D511yescharacteristic
357#67—44no—
358#67—42no—
359C2×Dic3—21no—
360C2×Dic3—42no—
361C2×Dic3—102no—
362C2×Dic3C2×C22⋊D512yes—
363C2×Dic3C2×C22⋊D512yes—
364D12—21no—
365D12—21no—
366C4×D3—42no—
367Dic6—21no—
368Dic6—21no—
369Dic6—204no—
370C3×C8—102no—
371C3⋊C8—102no—
372C22×C5—22no—
373C22×C5—41no—
374C22×C5—42no—
375C22×C5—121no—
376C22×C5—122no—
377C22×C5#88512yes—
378C22×C5C2×D3×D411yescharacteristic
379C4×C5—41no—
380C4×C5—62no—
381C4×C5—62no—
382C4×C5—121no—
383C4×C5#88512yes—
384C4×C5C2×#23511yescharacteristic
385C4×C5C2×#23711yescharacteristic
386Dic5—42no—
387Dic5—122no—
388#41—22no—
389#41—22no—
390#41—62no—
391#41—62no—
392C2×Q8—31no—
393C2×Q8—302no—
394C2×Q8C2×D3×D511yescharacteristic
395C2×D4—21no—
396C2×D4—31no—
397C2×D4—62no—
398C2×D4—61no—
399C2×D4C2×D3×D511yescharacteristic
400C22×C4—21no—
401C22×C4—32no—
402C22×C4—61no—
403C22×C4C2×D3×D511yescharacteristic
404C2×C8—52no—
405C2×C8—102no—
406C2×C8—152no—
407C2×C8—302no—
408C4⋊C4—52no—
409C4⋊C4—62no—
410C4⋊C4—152no—
411C4⋊C4—302no—
412C4⋊C4—302no—
413C4⋊C4—302no—
414C22⋊C4—62no—
415C22⋊C4—62no—
416C22⋊C4—101no—
417C22⋊C4—301no—
418C42—32no—
419C42—31no—
420C42—31no—
421C42—101no—
422C42—301no—
423C3×C5#313511yescharacteristic, complemented, Hall
424C22×C3—22no—
425C22×C3—41no—
426C22×C3—42no—
427C22×C3#408212yes—
428C22×C3C22×C22⋊D511yescharacteristic
429C2×D3—41no—
430C2×D3—42no—
431C3×C4—41no—
432C3×C4—202no—
433C3×C4#408212yes—
434C3×C4C2×#71111yescharacteristic
435C3×C4C2×#71111yescharacteristic
436Dic3—22no—
437Dic3—22no—
438Dic3—41no—
439Dic3—202no—
440C2×C5—22no—
441C2×C5—81no—
442C2×C5—241no—
443C2×C5C2×#88511yescharacteristic
444C2×C5#576812yes—
445C23—21no—
446C23—61no—
447C23D3×C22⋊D511yescharacteristic
448Q8—21no—
449Q8—21no—
450Q8—61no—
451Q8—61no—
452Q8—604no—
453D4—21no—
454D4—21no—
455D4—42no—
456D4—61no—
457D4—61no—
458D4—124no—
459D4—122no—
460C2×C4—21no—
461C2×C4—32no—
462C2×C4—32no—
463C2×C4—42no—
464C2×C4—61no—
465C2×C4—102no—
466C2×C4—122no—
467C2×C4—122no—
468C2×C4—302no—
469C2×C4#678012yes—
470C2×C4#678212yes—
471C2×C4D3×C22⋊D511yescharacteristic
472C2×C4C22×D3×D511yescharacteristic
473C8—102no—
474C8—302no—
475C2×C3—22no—
476C2×C3—81no—
477C2×C3C2×#408211yescharacteristic
478C2×C3#6615612yes—
479D3—81no—
480C5#7882611yescharacteristic, complemented, Sylow
481C22—22no—
482C22—42no—
483C22—41no—
484C22—122no—
485C22—121no—
486C22#9152512yes—
487C22C2×D3×C22⋊D511yescharacteristic
488C4—41no—
489C4—62no—
490C4—62no—
491C4—121no—
492C4—202no—
493C4—602no—
494C4#9152512yes—
495C4C2×#678011yescharacteristic
496C4C2×#678211yescharacteristic
497C3#1061501311yescharacteristic, complemented, Sylow
498C2—22no—
499C2—81no—
500C2—241no—
501C2#1175532212yes—
502C2C2×#9152511yescharacteristic
subgroupG/H
centerC2×C4D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radicalC5×#5832C2
hypercenterC2×#41D3×D5
hypocenterC3×C5#3135
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #11754616C2semidirect
3. #11751334C2semidirect
4. C3×#65522C2semidirect
5. #11749192C2semidirect
6. #11749191C2semidirect
7. #11748946C2semidirect
8. #11748945C2semidirect
9. #11748388C2semidirect
10. #11748382C2semidirect
11. C2×#90953C2semidirect
46. #65522D3semidirect
423. C3×C5#3135semidirect
480. C5#78826semidirect
497. C3#10615013semidirect

Maximal subgroups

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

subgroupindex
C5×#58322
#117546162
#117513342
C3×#655222
#117491922
#117491912
#117489462
#117489452
#117483882
#117483822
C2×#909532
#106150133
#788265