Finite Group Databasebeta

← #14283043

Subgroups — #14283043

Order 1920.

544 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 94 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#11756355C211yesmaximal, characteristic
2#11748653C211yesmaximal, characteristic, complemented
3#11748338C211yesmaximal, characteristic, complemented
4C5×#4537C211yesmaximal, characteristic, complemented
5C3×#64757C211yesmaximal, characteristic, complemented
6#11745959C211yesmaximal, characteristic, complemented
7#11745958C211yesmaximal, characteristic, complemented
8#10599071—31nomaximal, Hall
9C2×#6819—21no—
10C3×C5×#121C2211yescharacteristic
11#91829C411yescharacteristic, complemented
12#91828—21no—
13D4×Dic15C411yescharacteristic, complemented
14#91819C2211yescharacteristic
15C2×C4×Dic15C2211yescharacteristic
16#91782C411yescharacteristic, complemented
17#91777C411yescharacteristic, complemented
18#91774—21no—
19#91770—21no—
20C2×Dic3×Dic5—21no—
21C5×C3⋊#95C2211yescharacteristic
22C5×#830C2211yescharacteristic
23C3×#3963C2211yescharacteristic
24C3×C22⋊#168C2211yescharacteristic
25#90994—21no—
26#90983—21no—
27#90954—21no—
28#68278—51nomaximal, Hall
29#65930—31no—
30#65008—31no—
31#64937—31no—
32C5×#327—31no—
33#64757D311yescharacteristic, complemented
34#64690—31no—
35#64671—31no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4C2×C411yescharacteristic
38C22×C3×C4×C5C2311yescharacteristic
39C2×#1220—21no—
40C2×#1220—21no—
41C2×#1220—21no—
42C22×Dic15—21no—
43C22×Dic15D411yescharacteristic
44C22×Dic15D411yescharacteristic
45#6819—42no—
46#6819—42no—
47C2×D60C2×C411yescharacteristic
48C2×C4×D15—21no—
49C2×Dic30—21no—
50C22×C5×Dic3—21no—
51C22×C3×Dic5—21no—
52C3×C5×C4⋊C4C2×C411yescharacteristic
53C3×C5×C22⋊C4—21no—
54#6719—21no—
55#6714—21no—
56#6714—21no—
57C4⋊Dic15C2×C411yescharacteristic
58#6712—21no—
59C4×Dic15C2×C411yescharacteristic
60C4×Dic15C2×C411yescharacteristic
61C4×Dic15D411yescharacteristic
62C4×Dic15D411yescharacteristic
63C2×C5×C3⋊C8—21no—
64C2×C3×#168—21no—
65Dic3×Dic5—24no—
66#5596—51no—
67#4719—51no—
68#4648—51no—
69C3×#327—51no—
70#4537D511yescharacteristic, complemented
71#4470—51no—
72#4451—51no—
73C2×#711—61no—
74C5×#121C2×D311yescharacteristic
75#4086—31no—
76#4085—61no—
77D4×Dic5—31no—
78#4076—31no—
79C2×C4×Dic5—31no—
80C2×C4×Dic5—61no—
81#4039—31no—
82#4034—31no—
83#4031—61no—
84#4027—61no—
85C5×C22⋊C8—31no—
86C5×#95—31no—
87#3963—61no—
88#3963C2×D311yescharacteristic
89C22⋊#168C2×D311yescharacteristic
90#3947—61no—
91#3946—61no—
92#1505—151noSylow
93C23×C3×C5—21no—
94C23×C3×C5C2×D411yescharacteristic
95C22×D15—21no—
96C3×C5×D4—41no—
97C3×C5×D4—41no—
98C3×C5×D4—41no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5C22×C411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103#1220—42no—
104#1220—41no—
105#1220—41no—
106#1220—42no—
107C2×Dic15—21no—
108C2×Dic15—21no—
109C2×Dic15—22no—
110C2×Dic15—21no—
111C2×Dic15—42no—
112C2×Dic15C22⋊C411yescharacteristic
113C2×Dic15C22⋊C411yescharacteristic
114C2×Dic15C22⋊C411yescharacteristic
115C2×Dic15C22⋊C411yescharacteristic
116D60—41no—
117C4×D15—42no—
118Dic30—42no—
119C2×C5×Dic3—22no—
120C2×C5×Dic3—41no—
121C2×C5×Dic3—41no—
122C2×C3×Dic5—22no—
123C2×C3×Dic5—41no—
124C2×C3×Dic5—41no—
125C3×#168—41no—
126C5×C3⋊C8—41no—
127C2×#237—101no—
128C3×#121C2×D511yescharacteristic
129#940—51no—
130#939—101no—
131D4×Dic3—51no—
132#930—51no—
133C2×C4×Dic3—51no—
134C2×C4×Dic3—101no—
135#893—51no—
136#888—51no—
137#885—101no—
138#67⋊C4—101no—
139C3×C22⋊C8—51no—
140C3×#95—51no—
141C3⋊#95—101no—
142C3⋊#95C2×D511yescharacteristic
143#830C2×D511yescharacteristic
144#815—101no—
145Dic3⋊C8—101no—
146C2×C5×D4—21no—
147C2×C5×D4C4×D311yescharacteristic
148C22×C4×C5—61no—
149C22×C4×C5C22×D311yescharacteristic
150C2×C22⋊D5—61no—
151C2×C22⋊D5—61no—
152C2×C22⋊D5—61no—
153C22×Dic5—21no—
154C22×Dic5—31no—
155C22×Dic5—31no—
156C22×Dic5—61no—
157#711—122no—
158#711—122no—
159C2×D20—31no—
160C2×C4×D5—61no—
161C2×Dic10—61no—
162C2×C5×C8—61no—
163C5×C4⋊C4C4×D311yescharacteristic
164C5×C22⋊C4—21no—
165C22⋊Dic5—61no—
166#685—61no—
167#685—61no—
168C4⋊Dic5—31no—
169#683—61no—
170C4×Dic5—31no—
171C4×Dic5—31no—
172C4×Dic5—31no—
173C4×Dic5—31no—
174C4×Dic5—64no—
175C2×#168—21no—
176#532—151no—
177#432—151no—
178#376—151no—
179#327—31no—
180#327—51no—
181#327—151no—
182#327—151no—
183C22×C3×C5—21no—
184C22×C3×C5—21no—
185C22×C3×C5—41no—
186C22×C3×C5—41no—
187C22×C3×C5—41no—
188C22×C3×C5C2×C22⋊C411yescharacteristic
189C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
190C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
191C2×D15—41no—
192C2×D15—41no—
193C2×D15—41no—
194C3×C4×C5—21no—
195C3×C4×C5—21no—
196C3×C4×C5—41no—
197Dic15—21no—
198Dic15—21no—
199Dic15—21no—
200Dic15—41no—
201Dic15#10412yes—
202C3×Dic5—42no—
203C5×Dic3—42no—
204C2×C3×D4—21no—
205C2×C3×D4C4×D511yescharacteristic
206C22×C3×C4—101no—
207C22×C3×C4C22×D511yescharacteristic
208C2×#67—101no—
209C2×#67—101no—
210C2×#67—101no—
211C22×Dic3—21no—
212C22×Dic3—51no—
213C22×Dic3—51no—
214C22×Dic3—101no—
215#237—202no—
216#237—202no—
217C2×D12—51no—
218C2×C4×D3—101no—
219C2×Dic6—101no—
220C2×C3×C8—101no—
221C3×C4⋊C4C4×D511yescharacteristic
222C3×C22⋊C4—21no—
223#217—101no—
224(C2×D3)⋊C4—101no—
225(C2×D3)⋊C4—101no—
226C4⋊Dic3—51no—
227Dic3⋊C4—101no—
228C4×Dic3—51no—
229C4×Dic3—51no—
230C4×Dic3—51no—
231C4×Dic3—51no—
232C4×Dic3—104no—
233C2×C3⋊C8—21no—
234C23×C5—21no—
235C23×C5D3×D411yescharacteristic
236C22×D5—61no—
237C5×D4—41no—
238C5×D4—41no—
239C5×D4—41no—
240C2×C4×C5—21no—
241C2×C4×C5—41no—
242C2×C4×C5—62no—
243C2×C4×C5—121no—
244C2×C4×C5—121no—
245C2×C4×C5C2×C4×D311yescharacteristic
246C2×C4×C5D3×D411yescharacteristic
247C22⋊D5—122no—
248C22⋊D5—122no—
249C22⋊D5—121no—
250C22⋊D5—121no—
251C2×Dic5—22no—
252C2×Dic5—31no—
253C2×Dic5—31no—
254C2×Dic5—31no—
255C2×Dic5—31no—
256C2×Dic5—41no—
257C2×Dic5—41no—
258C2×Dic5—62no—
259C2×Dic5—61no—
260C2×Dic5—61no—
261C2×Dic5—61no—
262C2×Dic5—122no—
263D20—121no—
264C4×D5—122no—
265Dic10—122no—
266C5×C8—121no—
267#168—41no—
268C2×#41—301no—
269C4⋊Q8—151no—
270#127—151no—
271#124—301no—
272#121—151no—
273#121—301no—
274#121D3×D511yescharacteristic
275C4×D4—151no—
276C4×D4—151no—
277C4×D4—301no—
278C2×C42—151no—
279C2×C42—301no—
280C4⋊C8—301no—
281C22⋊C8—31no—
282C22⋊C8—51no—
283#97—301no—
284#95—31no—
285#95—51no—
286#95—301no—
287C2×C3×C5—21no—
288C2×C3×C5—21no—
289C2×C3×C5—81no—
290C2×C3×C5#41011yescharacteristic
291C2×C3×C5#41811yescharacteristic
292C2×C3×C5C2×#10411yescharacteristic
293D15—81no—
294C23×C3—21no—
295C23×C3D4×D511yescharacteristic
296C22×D3—101no—
297C3×D4—41no—
298C3×D4—41no—
299C3×D4—41no—
300C2×C3×C4—21no—
301C2×C3×C4—41no—
302C2×C3×C4—102no—
303C2×C3×C4—201no—
304C2×C3×C4—201no—
305C2×C3×C4C2×C4×D511yescharacteristic
306C2×C3×C4D4×D511yescharacteristic
307#67—202no—
308#67—202no—
309#67—201no—
310#67—201no—
311C2×Dic3—22no—
312C2×Dic3—41no—
313C2×Dic3—41no—
314C2×Dic3—51no—
315C2×Dic3—51no—
316C2×Dic3—51no—
317C2×Dic3—51no—
318C2×Dic3—102no—
319C2×Dic3—101no—
320C2×Dic3—101no—
321C2×Dic3—101no—
322C2×Dic3—202no—
323D12—201no—
324C4×D3—202no—
325Dic6—202no—
326C3×C8—201no—
327C3⋊C8—41no—
328C22×C5—21no—
329C22×C5—21no—
330C22×C5—41no—
331C22×C5—41no—
332C22×C5—41no—
333C22×C5D3×C22⋊C411yescharacteristic
334C22×C5#91111yescharacteristic
335C22×C5#91411yescharacteristic
336C2×D5—121no—
337C2×D5—121no—
338C2×D5—121no—
339C4×C5—21no—
340C4×C5—21no—
341C4×C5—41no—
342C4×C5—122no—
343Dic5—32no—
344Dic5—42no—
345Dic5—61no—
346Dic5—61no—
347Dic5—61no—
348Dic5—121no—
349#41—602no—
350#41—602no—
351C2×Q8—301no—
352C2×D4—21no—
353C2×D4—151no—
354C2×D4—301no—
355C2×D4—301no—
356C2×D4—301no—
357C2×D4#120011yescharacteristic
358C22×C4—61no—
359C22×C4—101no—
360C22×C4—151no—
361C22×C4—151no—
362C22×C4—301no—
363C22×C4—301no—
364C22×C4C2×D3×D511yescharacteristic
365C2×C8—61no—
366C2×C8—101no—
367C4⋊C4—151no—
368C4⋊C4—301no—
369C4⋊C4#120011yescharacteristic
370C22⋊C4—21no—
371C22⋊C4—301no—
372C22⋊C4—301no—
373C22⋊C4—301no—
374C42—151no—
375C42—151no—
376C42—151no—
377C42—151no—
378C42—304no—
379C3×C5#150511yescharacteristic, complemented, Hall
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—41no—
383C22×C3—41no—
384C22×C3—41no—
385C22×C3D5×C22⋊C411yescharacteristic
386C22×C3#405711yescharacteristic
387C22×C3#406011yescharacteristic
388C2×D3—201no—
389C2×D3—201no—
390C2×D3—201no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—41no—
394C3×C4—202no—
395Dic3—42no—
396Dic3—52no—
397Dic3—101no—
398Dic3—101no—
399Dic3—101no—
400Dic3—201no—
401C2×C5—21no—
402C2×C5—21no—
403C2×C5—81no—
404C2×C5#474011yescharacteristic
405C2×C5#477011yescharacteristic
406C2×C5D3×#10411yescharacteristic
407D5—241no—
408C23—21no—
409C23—301no—
410C23#679011yescharacteristic
411Q8—602no—
412D4—41no—
413D4—41no—
414D4—41no—
415D4—601no—
416D4—602no—
417D4—602no—
418D4—601no—
419D4—601no—
420C2×C4—21no—
421C2×C4—41no—
422C2×C4—62no—
423C2×C4—102no—
424C2×C4—121no—
425C2×C4—121no—
426C2×C4—151no—
427C2×C4—151no—
428C2×C4—151no—
429C2×C4—151no—
430C2×C4—201no—
431C2×C4—201no—
432C2×C4—302no—
433C2×C4—301no—
434C2×C4—301no—
435C2×C4—301no—
436C2×C4—602no—
437C2×C4—602no—
438C2×C4C2×#120011yescharacteristic
439C2×C4#679011yescharacteristic
440C8—121no—
441C8—201no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—81no—
445C2×C3#6502911yescharacteristic
446C2×C3#6505911yescharacteristic
447C2×C3D5×#10411yescharacteristic
448D3—401no—
449C5#6827811yescharacteristic, complemented, Sylow
450C22—21no—
451C22—21no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—601no—
456C22—601no—
457C22—601no—
458C22#9149811yescharacteristic
459C22#9150011yescharacteristic
460C22#9156111yescharacteristic
461C4—21no—
462C4—21no—
463C4—41no—
464C4—122no—
465C4—152no—
466C4—202no—
467C4—301no—
468C4—301no—
469C4—301no—
470C4—601no—
471C3#1059907111yescharacteristic, complemented, Sylow
472C2—21no—
473C2—21no—
474C2—81no—
475C2—1201no—
476C2#1174897211yescharacteristic
477C2#1174917411yescharacteristic
478C2#1174943011yescharacteristic
subgroupG/H
centerC22#91561
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#121C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11756355C2
cosocleC22×C3×C4×C5C23
hypercenter#121D3×D5
hypocenterC3×C5#1505
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. #11748653C2semidirect
3. #11748338C2semidirect
4. C5×#4537C2semidirect
5. C3×#64757C2semidirect
6. #11745959C2semidirect
7. #11745958C2semidirect
11. #91829C4semidirect
13. D4×Dic15C4semidirect
16. #91782C4semidirect
17. #91777C4semidirect
33. #64757D3semidirect
70. #4537D5semidirect
379. C3×C5#1505semidirect
449. C5#68278semidirect
471. C3#10599071semidirect

Maximal subgroups

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

subgroupindex
#117563552
#117486532
#117483382
C5×#45372
C3×#647572
#117459592
#117459582
#105990713
#682785