Finite Group Databasebeta

← #14283385

Subgroups — #14283385

Order 1920.

444 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 98 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#11754415C211yesmaximal, characteristic
2C3×#65008C211yesmaximal, characteristic, complemented
3#11748580C211yesmaximal, characteristic, complemented
4#11746291C211yesmaximal, characteristic
5C5×#4467C211yesmaximal, characteristic, complemented
6#11745963C211yesmaximal, characteristic, complemented
7#11745959C211yesmaximal, characteristic
8#10599105—31nomaximal, Hall
9#91819C2211yescharacteristic
10C5×#924C2211yescharacteristic
11C2×C3×C4×Dic5C2211yescharacteristic
12#91552—21no—
13#91546—21no—
14C2×#6668—21no—
15#91418C411yescharacteristic, complemented
16#91402—21no—
17#91388C411yescharacteristic, complemented
18#91387—21no—
19#91375C411yescharacteristic, complemented
20Dic5×Dic6C411yescharacteristic, complemented
21C3×C5×C22⋊C8C2211yescharacteristic
22#91115C2211yescharacteristic
23C5×C3⋊#95C2211yescharacteristic
24C3×C22⋊#168C2211yescharacteristic
25C3×#3947—21no—
26C3×#3946—21no—
27#90994—21no—
28#70834—51nomaximal, Hall
29#65958—31no—
30#65008D311yescharacteristic, complemented
31#64939—31no—
32C5×#328—31no—
33#64758—31no—
34#64690—31no—
35#64671—31no—
36C22×C3×C4×C5C2311yescharacteristic
37C2×#1220—21no—
38C22×Dic15—21no—
39C2×D60C2×C411yescharacteristic
40C22×C5×Dic3—21no—
41C2×C5×Dic6C2×C411yescharacteristic
42C22×C3×Dic5D411yescharacteristic
43C22×C3×Dic5D411yescharacteristic
44C2×#1200—21no—
45C2×C3×C5×C8—21no—
46#6714—21no—
47C4⋊Dic15C2×C411yescharacteristic
48C5×#217—21no—
49C5×C4⋊Dic3C2×C411yescharacteristic
50C5×Dic3⋊C4—21no—
51C3×C4×Dic5C2×C411yescharacteristic
52C3×C4×Dic5C2×C411yescharacteristic
53C3×C4×Dic5D411yescharacteristic
54C3×C4×Dic5D411yescharacteristic
55C2×C3×#168—21no—
56Dic3⋊Dic5—21no—
57Dic3⋊Dic5—21no—
58#6669—21no—
59#6668—42no—
60#6667—21no—
61#6667—21no—
62#6667—21no—
63Dic3×Dic5—21no—
64#5479—51no—
65C3×#432—51no—
66#4936—51no—
67#4470—51no—
68#4470—51no—
69#4467—51no—
70#4467D511yescharacteristic, complemented
71C5×C22⋊Q8—31no—
72#4093—31no—
73Q8×Dic5—31no—
74#4076—31no—
75C2×#683—61no—
76C2×C4×Dic5C2×D311yescharacteristic
77#4044—61no—
78#4039—31no—
79#4038—61no—
80#4036—31no—
81#4032—61no—
82#4027—61no—
83C5×C22⋊C8C2×D311yescharacteristic
84C5×#95—31no—
85#3963—31no—
86#3963—61no—
87C22⋊#168C2×D311yescharacteristic
88#3947—21no—
89#3946—21no—
90#1512—151noSylow
91C23×C3×C5C2×D411yescharacteristic
92C22×D15—21no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5C22×C411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96#1220—41no—
97#1220—41no—
98C2×Dic15—21no—
99C2×Dic15—41no—
100C2×Dic15—41no—
101C2×Dic15—41no—
102D60—41no—
103C2×C5×Dic3—21no—
104C2×C5×Dic3—21no—
105C2×C5×Dic3—41no—
106C2×C5×Dic3—41no—
107C2×C5×Dic3—41no—
108C5×Dic6—41no—
109C2×C3×Dic5—21no—
110C2×C3×Dic5—21no—
111C2×C3×Dic5—41no—
112C2×C3×Dic5C22⋊C411yescharacteristic
113C2×C3×Dic5C22⋊C411yescharacteristic
114C2×C3×Dic5C22⋊C411yescharacteristic
115C2×C3×Dic5C22⋊C411yescharacteristic
116#1200—42no—
117C3×C5×C8—41no—
118C3×#168—41no—
119C2×C3×C42—51no—
120#930—51no—
121#929—101no—
122C4×#67—101no—
123C2×C4⋊Dic3—101no—
124#924C2×D511yescharacteristic
125#876—101no—
126#875—51no—
127C4×D12—51no—
128#872—101no—
129#870—51no—
130C4×Dic6—51no—
131C3×C4⋊C8—101no—
132C3×C22⋊C8—51no—
133C3×C22⋊C8C2×D511yescharacteristic
134C3×#97—101no—
135C3⋊#95—51no—
136C3⋊#95—101no—
137C3⋊#95C2×D511yescharacteristic
138C2×C5×Q8—31no—
139C22×C4×C5—61no—
140C22×C4×C5C22×D311yescharacteristic
141C2×C22⋊D5—61no—
142C22×Dic5—61no—
143C22×Dic5D1211yescharacteristic
144C22×Dic5D1211yescharacteristic
145C2×D20—31no—
146C2×C4×D5—61no—
147C2×C5×C8—21no—
148C5×C4⋊C4—31no—
149C5×C4⋊C4—61no—
150C5×C22⋊C4—61no—
151#685—61no—
152#685—61no—
153#685—61no—
154#685—61no—
155C4⋊Dic5—31no—
156C4⋊Dic5—61no—
157C4⋊Dic5—61no—
158#683—61no—
159#683—122no—
160C4×Dic5—61no—
161C4×Dic5C4×D311yescharacteristic
162C4×Dic5C4×D311yescharacteristic
163C4×Dic5#6711yescharacteristic
164C4×Dic5#6711yescharacteristic
165C2×#168—21no—
166#529—151no—
167#432—51no—
168#382—151no—
169#328—31no—
170#328—151no—
171#327—151no—
172#327—151no—
173C22×C3×C5—21no—
174C22×C3×C5—21no—
175C22×C3×C5C2×C22⋊C411yescharacteristic
176C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
177C22×C3×C5#13711yescharacteristic
178C2×D15—41no—
179C2×D15—41no—
180C2×D15—41no—
181C3×C4×C5—21no—
182C3×C4×C5—21no—
183Dic15—41no—
184Dic15—81no—
185C3×Dic5—21no—
186C3×Dic5—21no—
187C3×Dic5—21no—
188C3×Dic5—21no—
189C5×Dic3—41no—
190C5×Dic3—41no—
191C5×Dic3—81no—
192C22×C3×C4—51no—
193C22×C3×C4—51no—
194C22×C3×C4C22×D511yescharacteristic
195C2×#67—101no—
196C22×Dic3—21no—
197C22×Dic3—101no—
198C2×D12—51no—
199C2×C4×D3—101no—
200C2×Dic6C4×D511yescharacteristic
201C2×C3×C8—21no—
202C2×C3×C8—101no—
203C3×C42—51no—
204C3×C42—51no—
205C3×C42—51no—
206C3×C42—51no—
207#217—21no—
208(C2×D3)⋊C4—101no—
209(C2×D3)⋊C4—101no—
210(C2×D3)⋊C4—101no—
211(C2×D3)⋊C4—101no—
212C4⋊Dic3—51no—
213C4⋊Dic3—202no—
214C4⋊Dic3C4×D511yescharacteristic
215Dic3⋊C4—21no—
216Dic3⋊C4—101no—
217Dic3⋊C4—101no—
218Dic3⋊C4—101no—
219C4×Dic3—101no—
220C23×C5C2×D1211yescharacteristic
221C22×D5—61no—
222C5×Q8—121no—
223C2×C4×C5—41no—
224C2×C4×C5—61no—
225C2×C4×C5—61no—
226C2×C4×C5—121no—
227C2×C4×C5—121no—
228C2×C4×C5—121no—
229C2×C4×C5C2×C4×D311yescharacteristic
230C2×C4×C5C2×#6711yescharacteristic
231C22⋊D5—121no—
232C22⋊D5—121no—
233C2×Dic5—21no—
234C2×Dic5—21no—
235C2×Dic5—41no—
236C2×Dic5—61no—
237C2×Dic5—121no—
238C2×Dic5—121no—
239C2×Dic5—121no—
240C2×Dic5(C2×D3)⋊C411yescharacteristic
241C2×Dic5(C2×D3)⋊C411yescharacteristic
242C2×Dic5(C2×D3)⋊C411yescharacteristic
243C2×Dic5(C2×D3)⋊C411yescharacteristic
244D20—121no—
245C4×D5—122no—
246C5×C8—41no—
247#168—41no—
248#126—301no—
249#125—151no—
250#124—151no—
251#123—301no—
252C22⋊Q8—31no—
253#121—151no—
254C4×Q8—151no—
255C4×D4—151no—
256C4×D4—301no—
257#117—301no—
258C2×C4⋊C4—301no—
259C2×C42—51no—
260C4⋊C8—101no—
261C22⋊C8—51no—
262C22⋊C8D3×D511yescharacteristic
263#97—101no—
264#95—31no—
265#95—151no—
266#95—301no—
267C2×C3×C5—21no—
268C2×C3×C5—21no—
269C2×C3×C5#41011yescharacteristic
270C2×C3×C5#41711yescharacteristic
271C2×C3×C5#42111yescharacteristic
272D15—81no—
273C23×C3D4×D511yescharacteristic
274C22×D3—101no—
275C2×C3×C4—41no—
276C2×C3×C4—51no—
277C2×C3×C4—51no—
278C2×C3×C4—51no—
279C2×C3×C4—51no—
280C2×C3×C4—101no—
281C2×C3×C4—101no—
282C2×C3×C4—201no—
283C2×C3×C4C2×C4×D511yescharacteristic
284C2×C3×C4D4×D511yescharacteristic
285#67—201no—
286#67—201no—
287C2×Dic3—21no—
288C2×Dic3—21no—
289C2×Dic3—41no—
290C2×Dic3—41no—
291C2×Dic3—41no—
292C2×Dic3—101no—
293C2×Dic3—201no—
294C2×Dic3—201no—
295C2×Dic3—201no—
296D12—201no—
297C4×D3—202no—
298Dic6—41no—
299C3×C8—41no—
300C3×C8—201no—
301C22×C5—21no—
302C22×C5—21no—
303C22×C5#90811yescharacteristic
304C22×C5#90911yescharacteristic
305C22×C5C2×(C2×D3)⋊C411yescharacteristic
306C2×D5—121no—
307C2×D5—121no—
308C2×D5—121no—
309C4×C5—21no—
310C4×C5—21no—
311C4×C5—121no—
312C4×C5—121no—
313C4×C5—241no—
314Dic5—21no—
315Dic5—21no—
316Dic5—21no—
317Dic5—21no—
318Dic5—121no—
319Dic5—241no—
320C2×Q8—31no—
321C2×D4—151no—
322C2×D4—301no—
323C22×C4—51no—
324C22×C4—51no—
325C22×C4—61no—
326C22×C4—301no—
327C22×C4—301no—
328C22×C4C2×D3×D511yescharacteristic
329C2×C8—21no—
330C2×C8—101no—
331C4⋊C4—31no—
332C4⋊C4—61no—
333C4⋊C4—151no—
334C4⋊C4—301no—
335C4⋊C4—301no—
336C4⋊C4—301no—
337C4⋊C4—602no—
338C22⋊C4—61no—
339C22⋊C4—301no—
340C22⋊C4—301no—
341C22⋊C4—301no—
342C22⋊C4—301no—
343C42—51no—
344C42—51no—
345C42—51no—
346C42—51no—
347C42—301no—
348C3×C5#151211yescharacteristic, complemented, Hall
349C22×C3—21no—
350C22×C3—21no—
351C22×C3D5×C22⋊C411yescharacteristic
352C22×C3#406011yescharacteristic
353C22×C3#406411yescharacteristic
354C2×D3—201no—
355C2×D3—201no—
356C2×D3—201no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—101no—
360C3×C4—101no—
361C3×C4—101no—
362C3×C4—101no—
363Dic3—41no—
364Dic3—41no—
365Dic3—81no—
366Dic3—201no—
367Dic3—401no—
368C2×C5—21no—
369C2×C5—21no—
370C2×C5#500611yescharacteristic
371C2×C5#513311yescharacteristic
372C2×C5#513911yescharacteristic
373D5—241no—
374C23—301no—
375C23D5×D1211yescharacteristic
376Q8—121no—
377D4—601no—
378D4—601no—
379D4—601no—
380C2×C4—41no—
381C2×C4—51no—
382C2×C4—51no—
383C2×C4—51no—
384C2×C4—51no—
385C2×C4—61no—
386C2×C4—61no—
387C2×C4—101no—
388C2×C4—101no—
389C2×C4—121no—
390C2×C4—121no—
391C2×C4—121no—
392C2×C4—201no—
393C2×C4—301no—
394C2×C4—602no—
395C2×C4—601no—
396C2×C4—601no—
397C2×C4—601no—
398C2×C4C4×D3×D511yescharacteristic
399C2×C4D5×#6711yescharacteristic
400C8—41no—
401C8—201no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3#6502911yescharacteristic
405C2×C3#6509211yescharacteristic
406C2×C3#6511011yescharacteristic
407D3—401no—
408C5#7083411yescharacteristic, complemented, Sylow
409C22—21no—
410C22—21no—
411C22—601no—
412C22—601no—
413C22—601no—
414C22#9124911yescharacteristic
415C22#9126111yescharacteristic
416C22D5×(C2×D3)⋊C411yescharacteristic
417C4—21no—
418C4—21no—
419C4—101no—
420C4—101no—
421C4—101no—
422C4—101no—
423C4—121no—
424C4—121no—
425C4—241no—
426C4—601no—
427C4—1201no—
428C3#1059910511yescharacteristic, complemented, Sylow
429C2—21no—
430C2—21no—
431C2—1201no—
432C2#1174712911yescharacteristic
433C2#1174760611yescharacteristic
434C2#1174822911yescharacteristic
subgroupG/H
centerC22D5×(C2×D3)⋊C4
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radical#91819C22
cosocleC22×C3×C4×C5C23
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#1512
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#65008C2semidirect
3. #11748580C2semidirect
5. C5×#4467C2semidirect
6. #11745963C2semidirect
15. #91418C4semidirect
17. #91388C4semidirect
19. #91375C4semidirect
20. Dic5×Dic6C4semidirect
30. #65008D3semidirect
70. #4467D5semidirect
348. C3×C5#1512semidirect
408. C5#70834semidirect
428. C3#10599105semidirect

Maximal subgroups

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

subgroupindex
#117544152
C3×#650082
#117485802
#117462912
C5×#44672
#117459632
#117459592
#105991053
#708345