Finite Group Databasebeta

← #14295131

Subgroups — #14295131

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91358C211yesmaximal, characteristic
2C2×#91232C211yesmaximal, characteristic
3C2×C3×#4003C211yesmaximal, characteristic
4C2×#91169C211yesmaximal, characteristic, complemented
5C2×Dic3×#170C211yesmaximal, characteristic, complemented
6#11746570C211yesmaximal, characteristic, complemented
7#11746570C211yesmaximal, characteristic, complemented
8#10604313—31nomaximal, Hall
9C22×C3×C4×D5C2211yescharacteristic
10C22×C3⋊#170C2211yescharacteristic
11C22×C3⋊#170C2211yescharacteristic
12C22×C3×#170C2211yescharacteristic
13C22×C3×#170C2211yescharacteristic
14C2×C4⋊Dic15C411yescharacteristic
15C2×C5×C4⋊Dic3C411yescharacteristic
16C2×#6665C411yescharacteristic
17C2×#6665C411yescharacteristic
18C2×Dic3×Dic5C2211yescharacteristic
19C2×Dic3×Dic5C2211yescharacteristic
20#91358—22no—
21#91358—22no—
22#91232C414yescomplemented
23C3×#4003C414yescomplemented
24#91169—22no—
25Dic3×#170—22no—
26#69907—51nomaximal, Hall
27C2×#4038—31no—
28C2×#4003—31no—
29C2×#4003D311yescharacteristic
30C2×#4002—31no—
31C2×C4×#170—31no—
32#64918—31no—
33#64918—31no—
34C23×C3×D5C2×C411yescharacteristic
35C22×C3×C4×C5C2×C411yescharacteristic
36C22×Dic15C2×C411yescharacteristic
37C22×Dic15C2×C411yescharacteristic
38C22×C5×Dic3C2×C411yescharacteristic
39C22×C5×Dic3C2×C411yescharacteristic
40C22×C3×Dic5C2311yescharacteristic
41C2×C3×C4×D5—21no—
42C2×C3×C4×D5—21no—
43C2×C3×C4×D5—21no—
44C2×C3×C4×D5—21no—
45C2×C3×C4×D5C2×C412yes—
46C2×C3×C4×D5C2×C412yes—
47C2×C3⋊#170—21no—
48C2×C3⋊#170—21no—
49C2×C3⋊#170—21no—
50C2×C3⋊#170—21no—
51C2×C3⋊#170C2×C412yes—
52C2×C3⋊#170C2×C412yes—
53C2×C3×#170—21no—
54C2×C3×#170—21no—
55C2×C3×#170—21no—
56C2×C3×#170—21no—
57C2×C3×#170C2×C412yes—
58C2×C3×#170C2×C412yes—
59C4⋊Dic15—22no—
60C5×C4⋊Dic3—22no—
61#6665—22no—
62#6665—22no—
63Dic3×Dic5—21no—
64Dic3×Dic5—21no—
65Dic3×Dic5D412yes—
66Dic3×Dic5D412yes—
67C2×#926—51no—
68C2×C3×C22⋊C8—51no—
69C2×#830—51no—
70C2×#815—51no—
71C2×C8×Dic3—51no—
72#4550—51no—
73#4550—51no—
74C22×C4×D5C2×D311yescharacteristic
75C22×#170—31no—
76C22×#170—31no—
77C22×#170C2×D311yescharacteristic
78C22×#170C2×D311yescharacteristic
79C2×C5×C4⋊C4—31no—
80C2×#685—31no—
81C2×#685—31no—
82C2×C4⋊Dic5—31no—
83C2×C4×Dic5—31no—
84C2×C4×Dic5—31no—
85#4038—62no—
86#4038—62no—
87#4003—34no—
88#4003Dic314yescomplemented
89#4002—62no—
90C4×#170—62no—
91#1750—151noSylow
92C23×C3×C5C22×C411yescharacteristic
93C22×C3×D5—21no—
94C22×C3×D5—21no—
95C22×C3×D5—21no—
96C22×C3×D5—21no—
97C22×C3×D5—21no—
98C22×C3×D5—21no—
99C22×C3×D5C4212yes—
100C2×C3×C4×C5—21no—
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5C4212yes—
103C2×Dic15—21no—
104C2×Dic15—21no—
105C2×Dic15—21no—
106C2×Dic15—21no—
107C2×Dic15—21no—
108C2×Dic15C22⋊C412yes—
109C2×C5×Dic3—21no—
110C2×C5×Dic3—21no—
111C2×C5×Dic3—21no—
112C2×C5×Dic3—21no—
113C2×C5×Dic3—21no—
114C2×C5×Dic3C22⋊C412yes—
115C2×C3×Dic5C22×C411yescharacteristic
116C2×C3×Dic5C22×C411yescharacteristic
117C2×C3×Dic5C2×D411yescharacteristic
118C2×C3×Dic5C2×D411yescharacteristic
119C2×C3×Dic5#4111yescharacteristic
120C2×C3×Dic5#4111yescharacteristic
121C3×C4×D5—22no—
122C3×C4×D5—22no—
123C3×C4×D5—22no—
124C3×C4×D5—22no—
125C3⋊#170—22no—
126C3⋊#170—22no—
127C3×#170—22no—
128C3×#170—22no—
129C23×C3×C4—51no—
130C22×C3×C8—51no—
131C22×C3×C8—51no—
132C2×#217—51no—
133C2×#217—51no—
134#926—102no—
135#926—102no—
136C2×C4⋊Dic3—51no—
137C2×C4⋊Dic3AGL(1,𝔽5)11yescharacteristic
138C2×C4×Dic3—51no—
139C2×C4×Dic3—51no—
140C22×C3⋊C8—51no—
141C22×C3⋊C8—51no—
142C3×C22⋊C8—54no—
143#830—54no—
144#815—102no—
145C8×Dic3—102no—
146C23×D5C4×D311yescharacteristic
147C22×C4×C5—31no—
148C22×C4×C5—31no—
149C22×C4×C5C4×D311yescharacteristic
150C22×Dic5—31no—
151C22×Dic5—31no—
152C22×Dic5C22×D311yescharacteristic
153C2×C4×D5—21no—
154C2×C4×D5—21no—
155C2×C4×D5—21no—
156C2×C4×D5—21no—
157C2×C4×D5C4×D312yes—
158C2×C4×D5C2×Dic312yes—
159C2×#170—21no—
160C2×#170—21no—
161C2×#170—21no—
162C2×#170—21no—
163C2×#170—32no—
164C2×#170—32no—
165C2×#170—61no—
166C2×#170—61no—
167C2×#170—61no—
168C2×#170—61no—
169C2×#170C2×Dic312yes—
170C2×#170C2×Dic312yes—
171C5×C4⋊C4—62no—
172#685—62no—
173#685—62no—
174C4⋊Dic5—62no—
175C4×Dic5—32no—
176C4×Dic5—32no—
177C4×Dic5—61no—
178C4×Dic5—61no—
179C2×#117—151no—
180C2×C22⋊C8—51no—
181C2×C22⋊C8—151no—
182C2×#97—151no—
183C2×C4×C8—151no—
184#336—151no—
185#336—151no—
186C22×C3×C5C2×C4211yescharacteristic
187C22×C3×C5C2×C22⋊C411yescharacteristic
188C22×C3×C5#11711yescharacteristic
189C22×C3×C5#13111yescharacteristic
190C22×C3×C5#13111yescharacteristic
191C22×C3×C5#13111yescharacteristic
192C22×C3×C5#13111yescharacteristic
193C2×C3×D5—22no—
194C2×C3×D5—22no—
195C2×C3×D5—22no—
196C2×C3×D5—41no—
197C2×C3×D5—41no—
198C2×C3×D5—41no—
199C2×C3×D5—41no—
200C3×C4×C5—22no—
201Dic15—22no—
202Dic15—41no—
203C3×Dic5C4×D411yescharacteristic
204C3×Dic5C4×D411yescharacteristic
205C3×Dic5C4×D411yescharacteristic
206C3×Dic5C4×D411yescharacteristic
207C5×Dic3—22no—
208C5×Dic3—41no—
209C24×C3—51no—
210C22×C3×C4—51no—
211C22×C3×C4—52no—
212C22×C3×C4—52no—
213C22×C3×C4—101no—
214C22×C3×C4—101no—
215C22×C3×C4—101no—
216C22×C3×C4—101no—
217C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
218C22×Dic3—51no—
219C22×Dic3—51no—
220C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
221C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
222C2×C3×C8—52no—
223C2×C3×C8—52no—
224C2×C3×C8—101no—
225C2×C3×C8—101no—
226C2×C3×C8—101no—
227C2×C3×C8—101no—
228#217—102no—
229#217—102no—
230C4⋊Dic3—22no—
231C4⋊Dic3—102no—
232C4×Dic3—52no—
233C4×Dic3—52no—
234C4×Dic3—101no—
235C4×Dic3—101no—
236C2×C3⋊C8—52no—
237C2×C3⋊C8—52no—
238C2×C3⋊C8—101no—
239C2×C3⋊C8—101no—
240C2×C3⋊C8—101no—
241C2×C3⋊C8—101no—
242C23×C5C2×C4×D311yescharacteristic
243C22×D5—21no—
244C22×D5—21no—
245C22×D5—21no—
246C22×D5—21no—
247C22×D5—21no—
248C22×D5—21no—
249C22×D5C4×Dic312yes—
250C2×C4×C5—21no—
251C2×C4×C5—21no—
252C2×C4×C5—32no—
253C2×C4×C5—61no—
254C2×C4×C5—61no—
255C2×C4×C5—61no—
256C2×C4×C5—61no—
257C2×C4×C5—61no—
258C2×C4×C5C4×Dic312yes—
259C2×Dic5—32no—
260C2×Dic5—61no—
261C2×Dic5—61no—
262C2×Dic5—61no—
263C2×Dic5—61no—
264C2×Dic5—61no—
265C2×Dic5C2×C4×D311yescharacteristic
266C2×Dic5D3×D411yescharacteristic
267C2×Dic5D3×D411yescharacteristic
268C2×Dic5#23711yescharacteristic
269C2×Dic5#23711yescharacteristic
270C2×Dic5C22×Dic311yescharacteristic
271C4×D5—22no—
272C4×D5—22no—
273C4×D5—22no—
274C4×D5—22no—
275#170—22no—
276#170—22no—
277#170—62no—
278#170—62no—
279C23×C4—51no—
280C22×C8—51no—
281C22×C8—51no—
282C22×C8—151no—
283C22×C8—151no—
284#117—302no—
285#117—302no—
286C2×C4⋊C4—31no—
287C2×C4⋊C4—151no—
288C2×C22⋊C4—151no—
289C2×C22⋊C4—151no—
290C2×C42—151no—
291C2×C42—151no—
292C22⋊C8—54no—
293C22⋊C8—154no—
294#97—302no—
295C4×C8—302no—
296C2×C3×C5C4×C22⋊C411yescharacteristic
297C2×C3×C5#40511yescharacteristic
298C2×C3×C5#40511yescharacteristic
299C2×C3×C5#40811yescharacteristic
300C2×C3×C5#40811yescharacteristic
301C2×C3×C5#43311yescharacteristic
302C2×C3×C5#43311yescharacteristic
303C3×D5—42no—
304C23×C3—52no—
305C23×C3—101no—
306C23×C3—101no—
307C23×C3—101no—
308C23×C3—101no—
309C23×C3—101no—
310C23×C3—101no—
311C23×C3C22×AGL(1,𝔽5)11yescharacteristic
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—51no—
315C2×C3×C4—51no—
316C2×C3×C4—51no—
317C2×C3×C4—51no—
318C2×C3×C4—51no—
319C2×C3×C4—51no—
320C2×C3×C4—102no—
321C2×C3×C4—102no—
322C2×C3×C4—102no—
323C2×C3×C4—102no—
324C2×C3×C4C4×AGL(1,𝔽5)12yes—
325C2×Dic3—21no—
326C2×Dic3—21no—
327C2×Dic3—21no—
328C2×Dic3—21no—
329C2×Dic3—21no—
330C2×Dic3—52no—
331C2×Dic3—101no—
332C2×Dic3—101no—
333C2×Dic3—101no—
334C2×Dic3—101no—
335C2×Dic3—101no—
336C2×Dic3C22⋊AGL(1,𝔽5)12yes—
337C3×C8—102no—
338C3×C8—102no—
339C3⋊C8—102no—
340C3⋊C8—102no—
341C22×C5#87711yescharacteristic
342C22×C5D3×C22⋊C411yescharacteristic
343C22×C5#90111yescharacteristic
344C22×C5#90111yescharacteristic
345C22×C5#90711yescharacteristic
346C22×C5#90711yescharacteristic
347C22×C5C2×C4×Dic311yescharacteristic
348C2×D5—22no—
349C2×D5—22no—
350C2×D5—22no—
351C2×D5—41no—
352C2×D5—41no—
353C2×D5—41no—
354C2×D5—41no—
355C4×C5—22no—
356C4×C5—62no—
357C4×C5—121no—
358Dic5—62no—
359Dic5—121no—
360Dic5#67⋊C411yescharacteristic
361Dic5#67⋊C411yescharacteristic
362Dic5D4×Dic311yescharacteristic
363Dic5D4×Dic311yescharacteristic
364C24—51no—
365C22×C4—31no—
366C22×C4—31no—
367C22×C4—51no—
368C22×C4—52no—
369C22×C4—52no—
370C22×C4—101no—
371C22×C4—101no—
372C22×C4—101no—
373C22×C4—101no—
374C22×C4—151no—
375C22×C4—151no—
376C22×C4D3×AGL(1,𝔽5)11yescharacteristic
377C2×C8—52no—
378C2×C8—52no—
379C2×C8—101no—
380C2×C8—101no—
381C2×C8—101no—
382C2×C8—101no—
383C2×C8—152no—
384C2×C8—152no—
385C2×C8—301no—
386C2×C8—301no—
387C2×C8—301no—
388C2×C8—301no—
389C4⋊C4—62no—
390C4⋊C4—302no—
391C22⋊C4—302no—
392C22⋊C4—302no—
393C42—152no—
394C42—152no—
395C42—301no—
396C42—301no—
397C3×C5#175011yescharacteristic, complemented, Hall
398C22×C3—102no—
399C22×C3—102no—
400C22×C3—102no—
401C22×C3—201no—
402C22×C3—201no—
403C22×C3—201no—
404C22×C3—201no—
405C22×C3C2×C4×AGL(1,𝔽5)11yescharacteristic
406C22×C3#413011yescharacteristic
407C22×C3#413111yescharacteristic
408C22×C3#413111yescharacteristic
409C22×C3#413311yescharacteristic
410C22×C3#413311yescharacteristic
411C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
412C3×C4—22no—
413C3×C4—51no—
414C3×C4—51no—
415C3×C4—51no—
416C3×C4—51no—
417Dic3—22no—
418Dic3—41no—
419Dic3—102no—
420Dic3—201no—
421C2×C5#472011yescharacteristic
422C2×C5#472011yescharacteristic
423C2×C5#472711yescharacteristic
424C2×C5#472711yescharacteristic
425C2×C5Dic3×C22⋊C411yescharacteristic
426C2×C5#510111yescharacteristic
427C2×C5#512211yescharacteristic
428D5—42no—
429C23—52no—
430C23—101no—
431C23—101no—
432C23—101no—
433C23—101no—
434C23—101no—
435C23—101no—
436C23C2×D3×AGL(1,𝔽5)11yescharacteristic
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—32no—
440C2×C4—51no—
441C2×C4—51no—
442C2×C4—51no—
443C2×C4—51no—
444C2×C4—51no—
445C2×C4—51no—
446C2×C4—61no—
447C2×C4—61no—
448C2×C4—61no—
449C2×C4—61no—
450C2×C4—61no—
451C2×C4—102no—
452C2×C4—102no—
453C2×C4—102no—
454C2×C4—102no—
455C2×C4—152no—
456C2×C4—301no—
457C2×C4—301no—
458C2×C4—301no—
459C2×C4—301no—
460C2×C4—301no—
461C2×C4Dic3×AGL(1,𝔽5)12yes—
462C8—102no—
463C8—102no—
464C8—302no—
465C8—302no—
466C2×C3—202no—
467C2×C3#6570111yescharacteristic
468C2×C3#6570111yescharacteristic
469C2×C3#6570611yescharacteristic
470C2×C3#6570611yescharacteristic
471C2×C3C4×C22⋊AGL(1,𝔽5)11yescharacteristic
472C2×C3#6577511yescharacteristic
473C2×C3#6578711yescharacteristic
474C5#6990711yescharacteristic, complemented, Sylow
475C22—102no—
476C22—102no—
477C22—102no—
478C22—201no—
479C22—201no—
480C22—201no—
481C22—201no—
482C22#9191111yescharacteristic
483C22#9191311yescharacteristic
484C22#9191411yescharacteristic
485C22#9191611yescharacteristic
486C22C2×Dic3×AGL(1,𝔽5)11yescharacteristic
487C22#9192311yescharacteristic
488C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
489C4—22no—
490C4—51no—
491C4—51no—
492C4—51no—
493C4—51no—
494C4—62no—
495C4—121no—
496C4—302no—
497C4—601no—
498C3#1060431311yescharacteristic, complemented, Sylow
499C2—202no—
500C2#1175176711yescharacteristic
501C2#1175176911yescharacteristic
502C2#1175177011yescharacteristic
503C2#1175178211yescharacteristic
504C2#1175189611yescharacteristic
505C2#1175190011yescharacteristic
506C2Dic3×C22⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC23C2×D3×AGL(1,𝔽5)
commutatorC22×C3×C5C2×C42
FittingC22×C3×C4×C5C2×C4
socleC23×C3×C5C22×C4
prime radicalC23×C3×D5C2×C4
cosocleC22×C3×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1750
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. C2×#91169C2semidirect
5. C2×Dic3×#170C2semidirect
6. #11746570C2semidirect
7. #11746570C2semidirect
22. #91232C4semidirect
23. C3×#4003C4semidirect
88. #4003Dic3semidirect
397. C3×C5#1750semidirect
474. C5#69907semidirect
498. C3#10604313semidirect

Maximal subgroups

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

subgroupindex
C2×#913582
C2×#912322
C2×C3×#40032
C2×#911692
C2×Dic3×#1702
#117465702
#106043133
#699075