Finite Group Databasebeta

← #14282754

Subgroups — #14282754

Order 1920.

476 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 97 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#11756383C211yesmaximal, characteristic
2#11750819C211yesmaximal, characteristic, complemented
3#11750749C211yesmaximal, characteristic, complemented
4C3×C5×#328C211yesmaximal, characteristic, complemented
5#11746359C211yesmaximal, characteristic, complemented
6#11746291C211yesmaximal, characteristic
7#11746272C211yesmaximal, characteristic
8#10599101—31nomaximal, Hall
9C3×C5×C22⋊Q8C2211yescharacteristic
10#91836C411yescharacteristic, complemented
11Q8×Dic15C411yescharacteristic, complemented
12#91819C2211yescharacteristic
13C2×C4×Dic15—21no—
14C2×C4×Dic15C2211yescharacteristic
15#91787—21no—
16#91782C411yescharacteristic, complemented
17#91781—21no—
18#91779C411yescharacteristic, complemented
19#91775—21no—
20#91770—21no—
21C3×C5×C22⋊C8C2211yescharacteristic
22C3×C5×#95C2211yescharacteristic
23#91115—21no—
24#91115C2211yescharacteristic
25#91114C2211yescharacteristic
26#91098—21no—
27C8×Dic15—21no—
28#68308—51nomaximal, Hall
29#65958—31no—
30#65007—31no—
31#64937—31no—
32C5×#328D311yescharacteristic, complemented
33#64758—31no—
34#64690—31no—
35#64671—31no—
36C2×C3×C5×Q8C2×C411yescharacteristic
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5C2311yescharacteristic
39C2×#1220—21no—
40C22×Dic15—21no—
41C22×Dic15D411yescharacteristic
42C22×Dic15D411yescharacteristic
43C2×D60C2×C411yescharacteristic
44C2×C4×D15—21no—
45C2×C3×C5×C8—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4C2×C411yescharacteristic
48C3×C5×C22⋊C4—21no—
49#6714—21no—
50#6714—21no—
51#6714—21no—
52#6714—21no—
53C4⋊Dic15—21no—
54C4⋊Dic15—21no—
55C4⋊Dic15C2×C411yescharacteristic
56#6712—21no—
57C4×Dic15—24no—
58C4×Dic15—21no—
59C4×Dic15C2×C411yescharacteristic
60C4×Dic15C2×C411yescharacteristic
61C4×Dic15D411yescharacteristic
62C4×Dic15D411yescharacteristic
63C2×C3⋊#168—21no—
64#5624—51no—
65#4718—51no—
66#4648—51no—
67C3×#328D511yescharacteristic, complemented
68#4538—51no—
69#4470—51no—
70#4451—51no—
71C5×C22⋊Q8C2×D311yescharacteristic
72#4093—31no—
73Q8×Dic5—31no—
74#4076—31no—
75C2×C4×Dic5—31no—
76C2×C4×Dic5—61no—
77#4044—61no—
78#4039—31no—
79#4038—61no—
80#4036—31no—
81#4032—61no—
82#4027—61no—
83C5×C22⋊C8C2×D311yescharacteristic
84C5×#95C2×D311yescharacteristic
85#3963—31no—
86#3963—61no—
87C22⋊#168—31no—
88#3946—61no—
89C8×Dic5—61no—
90#1500—151noSylow
91C23×C3×C5C2×D411yescharacteristic
92C22×D15—21no—
93C3×C5×Q8—41no—
94C2×C3×C4×C5—22no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5C22×C411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102#1220—41no—
103#1220—41no—
104C2×Dic15—21no—
105C2×Dic15—21no—
106C2×Dic15—22no—
107C2×Dic15—22no—
108C2×Dic15—21no—
109C2×Dic15—41no—
110C2×Dic15—41no—
111C2×Dic15C22⋊C411yescharacteristic
112C2×Dic15C22⋊C411yescharacteristic
113C2×Dic15C22⋊C411yescharacteristic
114C2×Dic15C22⋊C411yescharacteristic
115D60—41no—
116C4×D15—42no—
117C3×C5×C8—41no—
118C3⋊#168—41no—
119C3×C22⋊Q8C2×D511yescharacteristic
120#947—51no—
121Q8×Dic3—51no—
122#930—51no—
123C2×C4×Dic3—51no—
124C2×C4×Dic3—101no—
125#898—101no—
126#893—51no—
127#892—101no—
128#890—51no—
129#886—101no—
130#67⋊C4—101no—
131C3×C22⋊C8C2×D511yescharacteristic
132C3×#95C2×D511yescharacteristic
133C3⋊#95—51no—
134C3⋊#95—101no—
135#830—51no—
136Dic3⋊C8—101no—
137C8×Dic3—101no—
138C2×C5×Q8C4×D311yescharacteristic
139C22×C4×C5—21no—
140C22×C4×C5C22×D311yescharacteristic
141C2×C22⋊D5—61no—
142C22×Dic5—31no—
143C22×Dic5—31no—
144C22×Dic5—61no—
145C2×D20—31no—
146C2×C4×D5—61no—
147C2×C5×C8—21no—
148C5×C4⋊C4—21no—
149C5×C4⋊C4C4×D311yescharacteristic
150C5×C22⋊C4—21no—
151#685—61no—
152#685—61no—
153#685—61no—
154#685—61no—
155C4⋊Dic5—31no—
156C4⋊Dic5—61no—
157C4⋊Dic5—61no—
158#683—61no—
159C4×Dic5—31no—
160C4×Dic5—31no—
161C4×Dic5—31no—
162C4×Dic5—31no—
163C4×Dic5—61no—
164C4×Dic5—64no—
165C2×#168—61no—
166#529—151no—
167#431—151no—
168#376—151no—
169#328—151no—
170#328D1511yescharacteristic, complemented
171#327—151no—
172#327—151no—
173C22×C3×C5—21no—
174C22×C3×C5—21no—
175C22×C3×C5C2×C22⋊C411yescharacteristic
176C22×C3×C5#13511yescharacteristic
177C22×C3×C5#13511yescharacteristic
178C2×D15—41no—
179C2×D15—41no—
180C2×D15—41no—
181C3×C4×C5—21no—
182C3×C4×C5—21no—
183C3×C4×C5—42no—
184C3×C4×C5—41no—
185C3×C4×C5—41no—
186Dic15—21no—
187Dic15—21no—
188Dic15—21no—
189Dic15—42no—
190Dic15—41no—
191Dic15#10412yes—
192C2×C3×Q8C4×D511yescharacteristic
193C22×C3×C4—21no—
194C22×C3×C4C22×D511yescharacteristic
195C2×#67—101no—
196C22×Dic3—51no—
197C22×Dic3—51no—
198C22×Dic3—101no—
199C2×D12—51no—
200C2×C4×D3—101no—
201C2×C3×C8—21no—
202C3×C4⋊C4—21no—
203C3×C4⋊C4C4×D511yescharacteristic
204C3×C22⋊C4—21no—
205(C2×D3)⋊C4—101no—
206(C2×D3)⋊C4—101no—
207(C2×D3)⋊C4—101no—
208(C2×D3)⋊C4—101no—
209C4⋊Dic3—51no—
210C4⋊Dic3—101no—
211C4⋊Dic3—101no—
212Dic3⋊C4—101no—
213C4×Dic3—51no—
214C4×Dic3—51no—
215C4×Dic3—51no—
216C4×Dic3—51no—
217C4×Dic3—101no—
218C4×Dic3—104no—
219C2×C3⋊C8—101no—
220C23×C5D3×D411yescharacteristic
221C22×D5—61no—
222C5×Q8—41no—
223C2×C4×C5—22no—
224C2×C4×C5—21no—
225C2×C4×C5—21no—
226C2×C4×C5—41no—
227C2×C4×C5—41no—
228C2×C4×C5—41no—
229C2×C4×C5C2×C4×D311yescharacteristic
230C2×C4×C5D3×D411yescharacteristic
231C22⋊D5—121no—
232C22⋊D5—121no—
233C2×Dic5—31no—
234C2×Dic5—31no—
235C2×Dic5—31no—
236C2×Dic5—31no—
237C2×Dic5—62no—
238C2×Dic5—61no—
239C2×Dic5—61no—
240C2×Dic5—62no—
241C2×Dic5—61no—
242C2×Dic5—121no—
243C2×Dic5—121no—
244D20—121no—
245C4×D5—122no—
246C5×C8—41no—
247#168—121no—
248#126—301no—
249#125—151no—
250#124—151no—
251#123—301no—
252C22⋊Q8C2×D1511yescharacteristic
253#121—151no—
254C4×Q8—151no—
255C4×D4—151no—
256C4×D4—301no—
257#117—301no—
258C2×C42—151no—
259C2×C42—301no—
260C4⋊C8—301no—
261C22⋊C8—151no—
262C22⋊C8C2×D1511yescharacteristic
263C4×C8—301no—
264#95—151no—
265#95—301no—
266#95C2×D1511yescharacteristic
267C2×C3×C5—21no—
268C2×C3×C5—21no—
269C2×C3×C5#41011yescharacteristic
270C2×C3×C5#41611yescharacteristic
271C2×C3×C5C2×#10411yescharacteristic
272D15—81no—
273C23×C3D4×D511yescharacteristic
274C22×D3—101no—
275C3×Q8—41no—
276C2×C3×C4—22no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—41no—
280C2×C3×C4—41no—
281C2×C3×C4—41no—
282C2×C3×C4C2×C4×D511yescharacteristic
283C2×C3×C4D4×D511yescharacteristic
284#67—201no—
285#67—201no—
286C2×Dic3—51no—
287C2×Dic3—51no—
288C2×Dic3—51no—
289C2×Dic3—51no—
290C2×Dic3—102no—
291C2×Dic3—101no—
292C2×Dic3—101no—
293C2×Dic3—102no—
294C2×Dic3—101no—
295C2×Dic3—201no—
296C2×Dic3—201no—
297D12—201no—
298C4×D3—202no—
299C3×C8—41no—
300C3⋊C8—201no—
301C22×C5—21no—
302C22×C5—21no—
303C22×C5D3×C22⋊C411yescharacteristic
304C22×C5#91611yescharacteristic
305C22×C5#91911yescharacteristic
306C2×D5—121no—
307C2×D5—121no—
308C2×D5—121no—
309C4×C5—21no—
310C4×C5—21no—
311C4×C5—42no—
312C4×C5—41no—
313C4×C5—41no—
314Dic5—32no—
315Dic5—61no—
316Dic5—61no—
317Dic5—61no—
318Dic5—122no—
319Dic5—121no—
320C2×Q8C4×D1511yescharacteristic
321C2×D4—151no—
322C2×D4—301no—
323C22×C4—21no—
324C22×C4—151no—
325C22×C4—151no—
326C22×C4—301no—
327C22×C4—301no—
328C22×C4C22×D1511yescharacteristic
329C2×C8—21no—
330C2×C8—301no—
331C4⋊C4—21no—
332C4⋊C4—151no—
333C4⋊C4—301no—
334C4⋊C4—301no—
335C4⋊C4—301no—
336C4⋊C4C4×D1511yescharacteristic
337C22⋊C4—21no—
338C22⋊C4—301no—
339C22⋊C4—301no—
340C22⋊C4—301no—
341C22⋊C4—301no—
342C42—151no—
343C42—151no—
344C42—151no—
345C42—151no—
346C42—301no—
347C42—304no—
348C3×C5#150011yescharacteristic, complemented, Hall
349C22×C3—21no—
350C22×C3—21no—
351C22×C3D5×C22⋊C411yescharacteristic
352C22×C3#406211yescharacteristic
353C22×C3#406511yescharacteristic
354C2×D3—201no—
355C2×D3—201no—
356C2×D3—201no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—42no—
360C3×C4—41no—
361C3×C4—41no—
362Dic3—52no—
363Dic3—101no—
364Dic3—101no—
365Dic3—101no—
366Dic3—202no—
367Dic3—201no—
368C2×C5—21no—
369C2×C5—21no—
370C2×C5#474011yescharacteristic
371C2×C5#480411yescharacteristic
372C2×C5D3×#10411yescharacteristic
373D5—241no—
374C23—301no—
375C23D4×D1511yescharacteristic
376Q8—41no—
377D4—601no—
378D4—601no—
379D4—601no—
380C2×C4—22no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—151no—
387C2×C4—151no—
388C2×C4—151no—
389C2×C4—151no—
390C2×C4—302no—
391C2×C4—301no—
392C2×C4—301no—
393C2×C4—302no—
394C2×C4—301no—
395C2×C4—602no—
396C2×C4—601no—
397C2×C4—601no—
398C2×C4C2×C4×D1511yescharacteristic
399C2×C4D4×D1511yescharacteristic
400C8—41no—
401C8—601no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3#6502911yescharacteristic
405C2×C3#6509311yescharacteristic
406C2×C3D5×#10411yescharacteristic
407D3—401no—
408C5#6830811yescharacteristic, complemented, Sylow
409C22—21no—
410C22—21no—
411C22—601no—
412C22—601no—
413C22—601no—
414C22C22⋊C4×D1511yescharacteristic
415C22#9180511yescharacteristic
416C22#9180811yescharacteristic
417C4—21no—
418C4—21no—
419C4—42no—
420C4—41no—
421C4—41no—
422C4—152no—
423C4—301no—
424C4—301no—
425C4—301no—
426C4—602no—
427C4—601no—
428C3#1059910111yescharacteristic, complemented, Sylow
429C2—21no—
430C2—21no—
431C2—1201no—
432C2#1175084111yescharacteristic
433C2#1175090511yescharacteristic
434C2D15×#10411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#328C2
socleC22×C3×C5C2×C22⋊C4
prime radical#91819C22
cosocleC22×C3×C4×C5C23
hypercenter#328D15
hypocenterC3×C5#1500
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #11750819C2semidirect
3. #11750749C2semidirect
4. C3×C5×#328C2semidirect
5. #11746359C2semidirect
10. #91836C4semidirect
11. Q8×Dic15C4semidirect
16. #91782C4semidirect
18. #91779C4semidirect
32. C5×#328D3semidirect
67. C3×#328D5semidirect
170. #328D15semidirect
348. C3×C5#1500semidirect
408. C5#68308semidirect
428. C3#10599101semidirect

Maximal subgroups

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

subgroupindex
#117563832
#117508192
#117507492
C3×C5×#3282
#117463592
#117462912
#117462722
#105991013
#683085