Finite Group Databasebeta

← #14298651

Subgroups — #14298651

Order 1920.

592 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11755406C211yesmaximal, characteristic
2C2×#91240C211yesmaximal, characteristic
3C2×C3×#4011C211yesmaximal, characteristic
4#11746572C212yesmaximal, complemented
5#11746571C212yesmaximal, complemented
6#10604219—31nomaximal, Hall
7C22×C3×C22⋊D5C2211yescharacteristic
8C2×#6763C2212yes—
9C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
10C2×#6719C411yescharacteristic, complemented
11C2×C5×#217C411yescharacteristic, complemented
12#91559—21no—
13#91559—21no—
14Dic3×C22⋊D5—21no—
15Dic3×C22⋊D5—21no—
16D5×#217C2211yescharacteristic
17D5×#217C2211yescharacteristic
18#91528C411yescharacteristic, complemented
19#91528C411yescharacteristic, complemented
20#91240—21no—
21#91240—21no—
22C3×#4011—21no—
23C3×#4011—21no—
24#70020—51nomaximal, Hall
25#65820—31no—
26C2×#4011—31no—
27C2×#4011D311yescharacteristic
28#64866—32no—
29#64866—32no—
30C24×C3×C5C2×C411yescharacteristic
31C23×C3×D5C2311yescharacteristic
32C22×ΓL(1,𝔽16)—22no—
33C22×C3×AGL(1,𝔽5)—22no—
34C22×Dic15—21no—
35C22×C5×Dic3—21no—
36C2×C3×C22⋊D5—22no—
37C2×C3×C22⋊D5—22no—
38C2×C3×C22⋊D5D411yescharacteristic
39C2×C3×C22⋊D5D411yescharacteristic
40C2×C3×C22⋊D5D411yescharacteristic
41C2×C3×C22⋊D5D411yescharacteristic
42C22×C3×Dic5C2×C411yescharacteristic
43C2×D5×Dic3—21no—
44C2×D5×Dic3—21no—
45#6763—22no—
46#6763—22no—
47C3×C22⋊AGL(1,𝔽5)—22no—
48C3×C22⋊AGL(1,𝔽5)—22no—
49#6719—21no—
50#6719C2×C411yescharacteristic
51#6719C2×C411yescharacteristic
52C5×#217—21no—
53C5×#217C2×C411yescharacteristic
54C5×#217C2×C411yescharacteristic
55#6668—21no—
56#6668—21no—
57#6665—21no—
58#6665—21no—
59Dic3×Dic5—21no—
60Dic3×Dic5—21no—
61#5798—51no—
62C2×C3×#99—51no—
63C2×#834—51no—
64#4527—52no—
65#4526—52no—
66C22×C22⋊D5C2×D311yescharacteristic
67C2×C22⋊AGL(1,𝔽5)—32no—
68C2×C22⋊AGL(1,𝔽5)C2×D312yes—
69C2×C5×C22⋊C4—31no—
70C2×C22⋊Dic5—31no—
71C4×C22⋊D5—61no—
72C4×C22⋊D5—61no—
73#4027—61no—
74#4027—61no—
75D5×C22⋊C4—31no—
76D5×C22⋊C4—31no—
77#4023—31no—
78#4023—31no—
79#4011—21no—
80#4011—21no—
81#4011—61no—
82#4011—61no—
83#1828—151noSylow
84C23×C3×C5—21no—
85C23×C3×C5—21no—
86C23×C3×C5—81no—
87C23×C3×C5C22⋊C411yescharacteristic
88C23×C3×C5C22⋊C411yescharacteristic
89C23×C3×C5C22×C411yescharacteristic
90C22×C3×D5—81no—
91C22×C3×D5C2×D411yescharacteristic
92C22×C3×D5C2×D411yescharacteristic
93C22×C3×D5#4112yes—
94C22×C3×D5#4112yes—
95C2×ΓL(1,𝔽16)—42no—
96C2×ΓL(1,𝔽16)—82no—
97C2×C3×AGL(1,𝔽5)—42no—
98C2×C3×AGL(1,𝔽5)—82no—
99C2×Dic15—21no—
100C2×Dic15—21no—
101C2×Dic15—81no—
102C2×C5×Dic3—21no—
103C2×C5×Dic3—21no—
104C2×C5×Dic3—81no—
105C3×C22⋊D5—22no—
106C3×C22⋊D5—22no—
107C3×C22⋊D5—22no—
108C3×C22⋊D5—22no—
109C2×C3×Dic5—21no—
110C2×C3×Dic5—21no—
111C2×C3×Dic5C22⋊C411yescharacteristic
112C2×C3×Dic5C22⋊C411yescharacteristic
113D5×Dic3—81no—
114D5×Dic3—81no—
115C22×C3×D4—51no—
116C2×C3×C22⋊C4—52no—
117C2×#217—51no—
118C2×#217—51no—
119C2×#217—51no—
120C2×#217—52no—
121C2×#217AGL(1,𝔽5)11yescharacteristic, complemented
122D4×Dic3—101no—
123D4×Dic3—101no—
124D4×Dic3—101no—
125D4×Dic3—101no—
126#926—51no—
127#926—51no—
128C3×#99—101no—
129C3×#99—101no—
130#834—101no—
131#834—101no—
132C24×C5C4×D311yescharacteristic
133C23×D5C22×D311yescharacteristic
134C22×AGL(1,𝔽5)—22no—
135C22×AGL(1,𝔽5)—62no—
136C22×C4×C5—61no—
137C2×C22⋊D5—22no—
138C2×C22⋊D5—22no—
139C2×C22⋊D5D1211yescharacteristic
140C2×C22⋊D5D1211yescharacteristic
141C2×C22⋊D5#6711yescharacteristic
142C2×C22⋊D5#6711yescharacteristic
143C22×Dic5—61no—
144C22×Dic5C4×D311yescharacteristic
145C2×C4×D5—61no—
146C2×C4×D5—61no—
147C22⋊AGL(1,𝔽5)—22no—
148C22⋊AGL(1,𝔽5)—22no—
149C22⋊AGL(1,𝔽5)—62no—
150C22⋊AGL(1,𝔽5)—62no—
151C5×C22⋊C4—31no—
152C5×C22⋊C4—31no—
153C5×C22⋊C4—61no—
154C22⋊Dic5—31no—
155C22⋊Dic5—31no—
156C22⋊Dic5—61no—
157#685—61no—
158#685—61no—
159#683—61no—
160#683—61no—
161C4×Dic5—61no—
162C4×Dic5—61no—
163#518—151no—
164C2×#99—51no—
165C2×#99—151no—
166#342—152no—
167#342—152no—
168C22×C3×C5—21no—
169C22×C3×C5—21no—
170C22×C3×C5—41no—
171C22×C3×C5—41no—
172C22×C3×C5—41no—
173C22×C3×C5—81no—
174C22×C3×C5—81no—
175C22×C3×C5C2×C22⋊C411yescharacteristic
176C22×C3×C5#11711yescharacteristic
177C22×C3×C5#11711yescharacteristic
178C2×C3×D5—41no—
179C2×C3×D5—41no—
180C2×C3×D5—42no—
181C2×C3×D5—42no—
182C2×C3×D5#12312yes—
183C2×C3×D5#12312yes—
184ΓL(1,𝔽16)—82no—
185C3×AGL(1,𝔽5)—82no—
186Dic15—41no—
187Dic15—41no—
188C3×Dic5—21no—
189C3×Dic5—21no—
190C5×Dic3—41no—
191C5×Dic3—41no—
192C24×C3—51no—
193C24×C3C2×AGL(1,𝔽5)11yescharacteristic
194C2×C3×D4—51no—
195C2×C3×D4—51no—
196C2×C3×D4—51no—
197C2×C3×D4—51no—
198C2×C3×D4—102no—
199C2×C3×D4—102no—
200C22×C3×C4—51no—
201C22×C3×C4—102no—
202C22×Dic3—21no—
203C22×Dic3—101no—
204C22×Dic3—101no—
205C22×Dic3—101no—
206C22×Dic3—102no—
207C3×C22⋊C4—102no—
208C3×C22⋊C4—102no—
209#217—21no—
210#217—51no—
211#217—51no—
212#217—101no—
213#217—101no—
214#217—101no—
215#217—102no—
216#217—102no—
217#217C2×AGL(1,𝔽5)11yescharacteristic
218#217C2×AGL(1,𝔽5)11yescharacteristic
219C4⋊Dic3—101no—
220C4⋊Dic3—101no—
221C4×Dic3—101no—
222C4×Dic3—101no—
223C23×C5—21no—
224C23×C5—21no—
225C23×C5—81no—
226C23×C5(C2×D3)⋊C411yescharacteristic
227C23×C5(C2×D3)⋊C411yescharacteristic
228C23×C5C2×C4×D311yescharacteristic
229C22×D5—81no—
230C22×D5C2×D1211yescharacteristic
231C22×D5#23712yes—
232C22×D5#23712yes—
233C22×D5C2×#6711yescharacteristic
234C2×AGL(1,𝔽5)—42no—
235C2×AGL(1,𝔽5)—82no—
236C2×AGL(1,𝔽5)—122no—
237C2×AGL(1,𝔽5)—242no—
238C2×C4×C5—61no—
239C2×C4×C5—61no—
240C2×C4×C5—241no—
241C22⋊D5—22no—
242C22⋊D5—22no—
243C22⋊D5—22no—
244C22⋊D5—22no—
245C2×Dic5—21no—
246C2×Dic5—21no—
247C2×Dic5—61no—
248C2×Dic5—61no—
249C2×Dic5—241no—
250C2×Dic5(C2×D3)⋊C411yescharacteristic
251C2×Dic5(C2×D3)⋊C411yescharacteristic
252C4×D5—241no—
253C4×D5—241no—
254C22×D4—51no—
255C4×D4—301no—
256C4×D4—301no—
257C4×D4—301no—
258C4×D4—301no—
259#117—151no—
260#117—151no—
261C2×C22⋊C4—31no—
262C2×C22⋊C4—52no—
263C2×C22⋊C4—151no—
264C2×C22⋊C4—151no—
265C2×C22⋊C4—151no—
266C2×C22⋊C4—152no—
267#99—101no—
268#99—101no—
269#99—301no—
270#99—301no—
271C2×C3×C5—21no—
272C2×C3×C5—21no—
273C2×C3×C5—21no—
274C2×C3×C5—41no—
275C2×C3×C5—41no—
276C2×C3×C5#38111yescharacteristic
277C3×D5—22no—
278C3×D5—22no—
279C23×C3—21no—
280C23×C3—21no—
281C23×C3—52no—
282C23×C3—52no—
283C23×C3—51no—
284C23×C3—51no—
285C23×C3—81no—
286C23×C3—401no—
287C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
288C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
289C23×C3C22×AGL(1,𝔽5)11yescharacteristic
290C3×D4—102no—
291C3×D4—102no—
292C3×D4—102no—
293C3×D4—102no—
294C2×C3×C4—51no—
295C2×C3×C4—51no—
296C2×C3×C4—101no—
297C2×C3×C4—101no—
298C2×C3×C4—202no—
299C2×C3×C4—402no—
300C2×Dic3—21no—
301C2×Dic3—21no—
302C2×Dic3—81no—
303C2×Dic3—101no—
304C2×Dic3—101no—
305C2×Dic3—202no—
306C2×Dic3—401no—
307C2×Dic3—401no—
308C2×Dic3—401no—
309C2×Dic3—402no—
310C22×C5—21no—
311C22×C5—21no—
312C22×C5—41no—
313C22×C5—41no—
314C22×C5—41no—
315C22×C5—81no—
316C22×C5—81no—
317C22×C5#87711yescharacteristic
318C22×C5#87711yescharacteristic
319C22×C5C2×(C2×D3)⋊C411yescharacteristic
320C2×D5—41no—
321C2×D5—41no—
322C2×D5—42no—
323C2×D5—42no—
324C2×D5#88612yes—
325C2×D5#93512yes—
326AGL(1,𝔽5)—82no—
327AGL(1,𝔽5)—242no—
328C4×C5—121no—
329C4×C5—121no—
330Dic5—21no—
331Dic5—21no—
332Dic5—121no—
333Dic5—121no—
334C24—51no—
335C24D3×AGL(1,𝔽5)11yescharacteristic
336C2×D4—51no—
337C2×D4—51no—
338C2×D4—51no—
339C2×D4—51no—
340C2×D4—102no—
341C2×D4—102no—
342C22×C4—51no—
343C22×C4—61no—
344C22×C4—102no—
345C22×C4—301no—
346C22×C4—301no—
347C22×C4—301no—
348C22×C4—302no—
349C4⋊C4—301no—
350C4⋊C4—301no—
351C22⋊C4—31no—
352C22⋊C4—31no—
353C22⋊C4—61no—
354C22⋊C4—102no—
355C22⋊C4—102no—
356C22⋊C4—151no—
357C22⋊C4—151no—
358C22⋊C4—301no—
359C22⋊C4—301no—
360C22⋊C4—301no—
361C22⋊C4—302no—
362C22⋊C4—302no—
363C42—301no—
364C42—301no—
365C3×C5#182811yescharacteristic, complemented, Hall
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—41no—
369C22×C3—41no—
370C22×C3—41no—
371C22×C3—52no—
372C22×C3—52no—
373C22×C3—81no—
374C22×C3—81no—
375C22×C3—201no—
376C22×C3—201no—
377C22×C3—202no—
378C22×C3—202no—
379C22×C3#413011yescharacteristic
380C22×C3#413011yescharacteristic
381C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
382C3×C4—101no—
383C3×C4—101no—
384C3×C4—402no—
385Dic3—41no—
386Dic3—41no—
387Dic3—201no—
388Dic3—201no—
389Dic3—402no—
390C2×C5—21no—
391C2×C5—21no—
392C2×C5—21no—
393C2×C5—41no—
394C2×C5—41no—
395C2×C5#494311yescharacteristic
396D5—22no—
397D5—22no—
398C23—21no—
399C23—21no—
400C23—52no—
401C23—52no—
402C23—51no—
403C23—51no—
404C23—81no—
405C23—401no—
406C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
407C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
408C23C2×D3×AGL(1,𝔽5)11yescharacteristic
409D4—102no—
410D4—102no—
411D4—102no—
412D4—102no—
413C2×C4—51no—
414C2×C4—51no—
415C2×C4—61no—
416C2×C4—61no—
417C2×C4—101no—
418C2×C4—101no—
419C2×C4—202no—
420C2×C4—241no—
421C2×C4—301no—
422C2×C4—301no—
423C2×C4—402no—
424C2×C4—602no—
425C2×C4—1201no—
426C2×C4—1201no—
427C2×C4—1201no—
428C2×C4—1202no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—41no—
433C2×C3—41no—
434C2×C3—102no—
435C2×C3—102no—
436C2×C3#6576411yescharacteristic
437C5#7002011yescharacteristic, complemented, Sylow
438C22—21no—
439C22—21no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—52no—
444C22—52no—
445C22—81no—
446C22—81no—
447C22—202no—
448C22—201no—
449C22—201no—
450C22—202no—
451C22#9192311yescharacteristic
452C22#9192311yescharacteristic
453C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
454C4—101no—
455C4—101no—
456C4—121no—
457C4—121no—
458C4—402no—
459C4—601no—
460C4—601no—
461C4—1202no—
462C3#1060421911yescharacteristic, complemented, Sylow
463C2—21no—
464C2—21no—
465C2—21no—
466C2—41no—
467C2—41no—
468C2—102no—
469C2—102no—
470C2#1175198411yescharacteristic
subgroupG/H
centerC2#11751984
commutatorC23×C3×C5C22×C4
FrattiniC23C2×D3×AGL(1,𝔽5)
FittingC24×C3×C5C2×C4
socleC2×C3×C5#381
prime radicalC22×C3×C22⋊D5C22
cosocleC23×C3×D5C23
hypercenterC24D3×AGL(1,𝔽5)
hypocenterC3×C5#1828
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
4. #11746572C2semidirect
5. #11746571C2semidirect
10. C2×#6719C4semidirect
11. C2×C5×#217C4semidirect
18. #91528C4semidirect
19. #91528C4semidirect
121. C2×#217AGL(1,𝔽5)semidirect
365. C3×C5#1828semidirect
437. C5#70020semidirect
462. C3#10604219semidirect

Maximal subgroups

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

subgroupindex
#117554062
C2×#912402
C2×C3×#40112
#117465722
#117465712
#106042193
#700205