Finite Group Databasebeta

← #14299560

Subgroups — #14299560

Order 1920.

556 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5⋊#208C211yesmaximal, characteristic
2C3×#65756C211yesmaximal, characteristic
3C2×#91162C211yesmaximal, characteristic, complemented
4C2×#91161C211yesmaximal, characteristic, complemented
5D5×#830C211yesmaximal, characteristic
6#11746532C211yesmaximal, characteristic, complemented
7#11746532C211yesmaximal, characteristic, complemented
8#10603918—31nomaximal, Hall
9C22×C3×C4×D5C2211yescharacteristic
10C2×#6762—21no—
11D5⋊#208—22no—
12D5⋊#208—22no—
13C2×#6758C2211yescharacteristic
14C2×#6758C2211yescharacteristic
15C2×D5⋊(C3⋊C8)—21no—
16C2×C3×#700C2211yescharacteristic
17C2×C3×#700C2211yescharacteristic
18C2×D5×C3⋊C8C2211yescharacteristic
19C2×D5×C3⋊C8C2211yescharacteristic
20C3×C22⋊#170—21no—
21C3×#4003—21no—
22#91162—22no—
23#91161—22no—
24#91114C411yescharacteristic
25C5×#830C411yescharacteristic
26#90955C411yescharacteristic
27#90955C411yescharacteristic
28#69984—51nomaximal, Hall
29C2×D5⋊M16—31no—
30#65756D311yescharacteristic
31C2×#3996—31no—
32C2×#3995—31no—
33D5×C22⋊C8—31no—
34#64896—31no—
35#64896—31no—
36C23×C3×D5Q811yescharacteristic
37C22×C3×C4×C5C2×C411yescharacteristic
38C22×C3×Dic5D411yescharacteristic
39C2×C3×C4×D5—21no—
40C2×C3×C4×D5—21no—
41C2×C3×C4×D5—21no—
42C2×C3×C4×D5—21no—
43C2×C3×C4×D5C2×C411yescharacteristic
44C2×C3×C4×D5D411yescharacteristic
45C2×C3×C4×D5Q811yescharacteristic
46C2×C3×C4×D5C2311yescharacteristic
47#6762—24no—
48C2×C3⋊#170—21no—
49C2×C3⋊#170—21no—
50#6758—21no—
51#6758—21no—
52#6758D412yes—
53#6758D412yes—
54D5⋊(C3⋊C8)—24no—
55C2×C3×#170—21no—
56C2×C3×#170—21no—
57C3×#700—21no—
58C3×#700—21no—
59C3×#700—21no—
60C3×#700—21no—
61C2×C3⋊#168C2×C411yescharacteristic
62C2×C3⋊#168C2×C411yescharacteristic
63C2×C5×C3⋊C8C2×C411yescharacteristic
64C2×C5×C3⋊C8C2×C411yescharacteristic
65D5×C3⋊C8—21no—
66D5×C3⋊C8—21no—
67D5×C3⋊C8—21no—
68D5×C3⋊C8—21no—
69C22×#208—51no—
70C3×#407—51no—
71C2×#830—51no—
72C2×#822—51no—
73C2×#822—51no—
74#4558—51no—
75#4558—51no—
76C22×C4×D5C2×D311yescharacteristic
77C2×#704—61no—
78D5⋊M16—62no—
79D5⋊M16—62no—
80C2×#700—31no—
81C2×#700—31no—
82C2×#700C2×D311yescharacteristic
83C2×#700C2×D311yescharacteristic
84C2×D5⋊C8—61no—
85C2×C8×D5—31no—
86C2×C8×D5—31no—
87C22⋊#170—21no—
88#4003—21no—
89#3996—62no—
90#3995—62no—
91C5×C22⋊C8—31no—
92C22⋊#168—31no—
93#3952—31no—
94#3952—31no—
95#1855—151noSylow
96C23×C3×C5C4⋊C411yescharacteristic
97C22×C3×D5—22no—
98C22×C3×D5—21no—
99C22×C3×D5—21no—
100C22×C3×D5—41no—
101C22×C3×D5C4⋊C411yescharacteristic
102C22×C3×D5C2×Q811yescharacteristic
103C2×C3×C4×C5—21no—
104C2×C3×C4×C5—21no—
105C2×C3×C4×C5C4⋊C411yescharacteristic
106C2×C3×C4×C5C22×C411yescharacteristic
107C2×C3×Dic5—21no—
108C2×C3×Dic5—21no—
109C2×C3×Dic5C4⋊C411yescharacteristic
110C2×C3×Dic5C2×D411yescharacteristic
111C3×C4×D5—21no—
112C3×C4×D5—21no—
113C3×C4×D5—21no—
114C3×C4×D5—21no—
115C3×C4×D5—21no—
116C3×C4×D5—21no—
117C3×C4×D5C2×D411yescharacteristic
118C3×C4×D5C2×D411yescharacteristic
119C3×C4×D5#4111yescharacteristic
120C3×C4×D5#4111yescharacteristic
121C3⋊#170—22no—
122C3⋊#170—22no—
123C3×#170—41no—
124C3×#170—41no—
125C3⋊#168—21no—
126C3⋊#168—21no—
127C5×C3⋊C8—21no—
128C5×C3⋊C8—21no—
129C23×C3×C4—51no—
130C2×C3×M16—51no—
131C2×C3×M16—51no—
132C2×#208—51no—
133C2×#208—51no—
134C2×#208—102no—
135C2×#208—102no—
136C2×#208—101no—
137C22×C3⋊C8—51no—
138C22×C3⋊C8—51no—
139C22×C3⋊C8—101no—
140C3×C22⋊C8—101no—
141C3×C22⋊C8—101no—
142#830—51no—
143#830—51no—
144#830—51no—
145#830AGL(1,𝔽5)11yescharacteristic
146#822—102no—
147#822—102no—
148C23×D5Dic611yescharacteristic
149C22×C4×C5C4×D311yescharacteristic
150C22×Dic5#6711yescharacteristic
151C2×C4×D5—21no—
152C2×C4×D5—21no—
153C2×C4×D5—21no—
154C2×C4×D5—21no—
155C2×C4×D5Dic611yescharacteristic
156C2×C4×D5C4×D311yescharacteristic
157C2×C4×D5#6711yescharacteristic
158C2×C4×D5C22×D311yescharacteristic
159#704—64no—
160C2×#170—21no—
161C2×#170—21no—
162C2×#170—61no—
163C2×#170—61no—
164#700—21no—
165#700—21no—
166#700—21no—
167#700—21no—
168#700—32no—
169#700—32no—
170#700—61no—
171#700—61no—
172D5⋊C8—64no—
173C2×C5×C8—31no—
174C2×C5×C8—31no—
175C2×#168—31no—
176C2×#168—31no—
177C8×D5—61no—
178C8×D5—61no—
179C8×D5—61no—
180C8×D5—61no—
181C22×M16—151no—
182C2×#108—151no—
183C2×#108—151no—
184#407—51no—
185C2×C22⋊C8—151no—
186#341—151no—
187#341—151no—
188C22×C3×C5—21no—
189C22×C3×C5—21no—
190C22×C3×C5—21no—
191C22×C3×C5C2×C4⋊C411yescharacteristic
192C2×C3×D5—21no—
193C2×C3×D5—21no—
194C2×C3×D5—21no—
195C2×C3×D5—21no—
196C2×C3×D5—42no—
197C2×C3×D5—42no—
198C2×C3×D5#10812yescomplemented
199C2×C3×D5C22⋊Q811yescharacteristic
200C2×C3×D5C22⋊Q811yescharacteristic
201C3×C4×C5—21no—
202C3×C4×C5C4×D411yescharacteristic
203C3×C4×C5C4×D411yescharacteristic
204C3×Dic5—21no—
205C3×Dic5#12011yescharacteristic
206C3×Dic5#12311yescharacteristic
207C24×C3—51no—
208C22×C3×C4—51no—
209C22×C3×C4—51no—
210C22×C3×C4—51no—
211C22×C3×C4—51no—
212C22×C3×C4—51no—
213C22×C3×C4—101no—
214C22×C3×C4—101no—
215C22×C3×C4—101no—
216C22×C3×C4—101no—
217C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
218C3×M16—101no—
219C3×M16—101no—
220C3×M16—101no—
221C3×M16—101no—
222C2×C3×C8—101no—
223C2×C3×C8—101no—
224#208—52no—
225#208—52no—
226#208—101no—
227#208—101no—
228#208—104no—
229C2×C3⋊C8—51no—
230C2×C3⋊C8—51no—
231C2×C3⋊C8—101no—
232C2×C3⋊C8—101no—
233C2×C3⋊C8—101no—
234C2×C3⋊C8—101no—
235C2×C3⋊C8—101no—
236C2×C3⋊C8—101no—
237C2×C3⋊C8—104no—
238C2×C3⋊C8C2×AGL(1,𝔽5)11yescharacteristic
239C2×C3⋊C8C2×AGL(1,𝔽5)11yescharacteristic
240C23×C5Dic3⋊C411yescharacteristic
241C22×D5—22no—
242C22×D5—21no—
243C22×D5—21no—
244C22×D5—41no—
245C22×D5Dic3⋊C411yescharacteristic
246C22×D5C2×Dic611yescharacteristic
247C2×C4×C5—21no—
248C2×C4×C5—21no—
249C2×C4×C5Dic3⋊C411yescharacteristic
250C2×C4×C5C2×C4×D311yescharacteristic
251C2×Dic5—21no—
252C2×Dic5—21no—
253C2×Dic5Dic3⋊C411yescharacteristic
254C2×Dic5C2×#6711yescharacteristic
255C4×D5—21no—
256C4×D5—21no—
257C4×D5—21no—
258C4×D5—21no—
259C4×D5—21no—
260C4×D5—21no—
261C4×D5D3×D411yescharacteristic
262C4×D5D3×D411yescharacteristic
263C4×D5#23711yescharacteristic
264C4×D5#23711yescharacteristic
265#170—41no—
266#170—41no—
267#170—62no—
268#170—62no—
269C5×C8—61no—
270C5×C8—61no—
271#168—61no—
272#168—61no—
273C23×C4—51no—
274C2×M16—51no—
275C2×M16—51no—
276C2×M16—151no—
277C2×M16—151no—
278C2×M16—302no—
279C2×M16—302no—
280C2×M16—301no—
281C22×C8—151no—
282C22×C8—151no—
283C22×C8—301no—
284#108—302no—
285#108—302no—
286C22⋊C8—31no—
287C22⋊C8—101no—
288C22⋊C8—101no—
289C22⋊C8—151no—
290C22⋊C8—151no—
291C22⋊C8—151no—
292C2×C3×C5—41no—
293C2×C3×C5#38511yescharacteristic
294C2×C3×C5C2×#10811yescharacteristic
295C2×C3×C5#43011yescharacteristic
296C3×D5—22no—
297C3×D5—21no—
298C3×D5—21no—
299C23×C3—51no—
300C23×C3—51no—
301C23×C3—101no—
302C23×C3—101no—
303C23×C3—102no—
304C23×C3—201no—
305C23×C3C4⋊AGL(1,𝔽5)11yescharacteristic
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—51no—
309C2×C3×C4—51no—
310C2×C3×C4—51no—
311C2×C3×C4—51no—
312C2×C3×C4—51no—
313C2×C3×C4—51no—
314C2×C3×C4—101no—
315C2×C3×C4—101no—
316C2×C3×C4—101no—
317C2×C3×C4—101no—
318C2×C3×C4—101no—
319C2×C3×C4—101no—
320C2×C3×C4—101no—
321C2×C3×C4—101no—
322C2×C3×C4C4⋊AGL(1,𝔽5)11yescharacteristic
323C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
324C3×C8—201no—
325C3×C8—201no—
326C3⋊C8—21no—
327C3⋊C8—21no—
328C3⋊C8—102no—
329C3⋊C8—102no—
330C3⋊C8—101no—
331C3⋊C8—101no—
332C22×C5—21no—
333C22×C5—21no—
334C22×C5—21no—
335C22×C5C2×Dic3⋊C411yescharacteristic
336C2×D5—21no—
337C2×D5—21no—
338C2×D5—21no—
339C2×D5—21no—
340C2×D5—42no—
341C2×D5—42no—
342C2×D5#82212yescomplemented
343C2×D5#87811yescharacteristic
344C2×D5#87811yescharacteristic
345C4×C5—21no—
346C4×C5#67⋊C411yescharacteristic
347C4×C5#67⋊C411yescharacteristic
348Dic5—21no—
349Dic5#93511yescharacteristic
350Dic5#93711yescharacteristic
351C24—51no—
352C22×C4—51no—
353C22×C4—51no—
354C22×C4—51no—
355C22×C4—51no—
356C22×C4—51no—
357C22×C4—101no—
358C22×C4—101no—
359C22×C4—101no—
360C22×C4—101no—
361C22×C4D3×AGL(1,𝔽5)11yescharacteristic
362M16—101no—
363M16—101no—
364M16—101no—
365M16—101no—
366M16—152no—
367M16—152no—
368M16—301no—
369M16—301no—
370M16—304no—
371C2×C8—31no—
372C2×C8—31no—
373C2×C8—101no—
374C2×C8—101no—
375C2×C8—151no—
376C2×C8—151no—
377C2×C8—301no—
378C2×C8—301no—
379C2×C8—301no—
380C2×C8—301no—
381C2×C8—301no—
382C2×C8—301no—
383C2×C8—304no—
384C3×C5#185511yescharacteristic, complemented, Hall
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—51no—
389C22×C3—51no—
390C22×C3—52no—
391C22×C3—101no—
392C22×C3—101no—
393C22×C3—101no—
394C22×C3—101no—
395C22×C3—202no—
396C22×C3—202no—
397C22×C3C2×C4⋊AGL(1,𝔽5)11yescharacteristic
398C3×C4—21no—
399C3×C4—51no—
400C3×C4—51no—
401C3×C4—101no—
402C3×C4D4×AGL(1,𝔽5)11yescharacteristic
403C3×C4D4×AGL(1,𝔽5)11yescharacteristic
404C2×C5—41no—
405C2×C5#494611yescharacteristic
406C2×C5C2×#82211yescharacteristic
407C2×C5#512411yescharacteristic
408D5—22no—
409D5—21no—
410D5—21no—
411C23—51no—
412C23—51no—
413C23—101no—
414C23—101no—
415C23—102no—
416C23—201no—
417C23Dic3⋊AGL(1,𝔽5)11yescharacteristic
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—51no—
421C2×C4—51no—
422C2×C4—51no—
423C2×C4—51no—
424C2×C4—51no—
425C2×C4—51no—
426C2×C4—101no—
427C2×C4—101no—
428C2×C4—101no—
429C2×C4—101no—
430C2×C4—101no—
431C2×C4—101no—
432C2×C4—101no—
433C2×C4—101no—
434C2×C4Dic3⋊AGL(1,𝔽5)11yescharacteristic
435C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
436C8—61no—
437C8—61no—
438C8—201no—
439C8—201no—
440C8—302no—
441C8—302no—
442C8—301no—
443C8—301no—
444C2×C3—41no—
445C2×C3—101no—
446C2×C3—101no—
447C2×C3—102no—
448C2×C3#6569911yescharacteristic
449C2×C3D5⋊#10811yescharacteristic
450C2×C3#6572911yescharacteristic
451C5#6998411yescharacteristic, complemented, Sylow
452C22—21no—
453C22—21no—
454C22—21no—
455C22—52no—
456C22—51no—
457C22—51no—
458C22—101no—
459C22—101no—
460C22—101no—
461C22—101no—
462C22—202no—
463C22—202no—
464C22C2×Dic3⋊AGL(1,𝔽5)11yescharacteristic
465C4—21no—
466C4—51no—
467C4—51no—
468C4—101no—
469C4#67⋊AGL(1,𝔽5)11yescharacteristic
470C4#67⋊AGL(1,𝔽5)11yescharacteristic
471C3#1060391811yescharacteristic, complemented, Sylow
472C2—41no—
473C2—102no—
474C2—101no—
475C2—101no—
476C2D5⋊#82211yescharacteristic
477C2#1175173211yescharacteristic
478C2#1175202911yescharacteristic
subgroupG/H
centerC22C2×Dic3⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C4⋊C4
prime radicalC23×C3×D5Q8
cosocleC2×C3×C4×D5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1855
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. C2×#91162C2semidirect
4. C2×#91161C2semidirect
6. #11746532C2semidirect
7. #11746532C2semidirect
198. C2×C3×D5#108semidirect
342. C2×D5#822semidirect
384. C3×C5#1855semidirect
451. C5#69984semidirect
471. C3#10603918semidirect

Maximal subgroups

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

subgroupindex
C2×D5⋊#2082
C3×#657562
C2×#911622
C2×#911612
D5×#8302
#117465322
#106039183
#699845