Finite Group Databasebeta

← #14282770

Subgroups — #14282770

Order 1920.

476 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 92 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#11754460C211yesmaximal, characteristic
2#11750749C211yesmaximal, characteristic, complemented
3#11748331C211yesmaximal, characteristic, complemented
4C5×#4451C211yesmaximal, characteristic
5C3×#64672C211yesmaximal, characteristic, complemented
6#11745960C211yesmaximal, characteristic, complemented
7#11745957C211yesmaximal, characteristic
8#10599069—31nomaximal, Hall
9C2×C4×Dic15—21no—
10C2×C4×Dic15C2211yescharacteristic
11C5×#930C2211yescharacteristic
12C3×#4070C2211yescharacteristic
13#67⋊Dic5—21no—
14#91543—21no—
15#91435C411yescharacteristic, complemented
16#91400—21no—
17#91384C411yescharacteristic, complemented
18#91370C411yescharacteristic, complemented
19#91367—21no—
20#91331C411yescharacteristic, complemented
21C3×C5×#95C2211yescharacteristic
22#91115—21no—
23#91115C2211yescharacteristic
24C5×#830C2211yescharacteristic
25C3×C22⋊#168C2211yescharacteristic
26#90983—21no—
27#90951—21no—
28#68308—51nomaximal, Hall
29#65934—31no—
30#65007—31no—
31#64937—31no—
32C5×#327—31no—
33#64757—31no—
34#64687—31no—
35#64672D311yescharacteristic, complemented
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15—21no—
39C22×Dic15D411yescharacteristic
40C22×Dic15D411yescharacteristic
41C2×C5×#67—21no—
42C2×C5×D12C2×C411yescharacteristic
43C2×C3×Dic10C2×C411yescharacteristic
44C2×D3×Dic5—21no—
45C4×Dic15—24no—
46C4×Dic15C2×C411yescharacteristic
47C4×Dic15C2×C411yescharacteristic
48C4×Dic15D411yescharacteristic
49C4×Dic15D411yescharacteristic
50C5×(C2×D3)⋊C4—21no—
51C5×C4⋊Dic3C2×C411yescharacteristic
52C2×C5×C3⋊C8—21no—
53C3×C22⋊Dic5—21no—
54C3×C4⋊Dic5C2×C411yescharacteristic
55C3×#683—21no—
56C2×C3×#168—21no—
57Dic3⋊Dic5—21no—
58#6668—21no—
59#6668—21no—
60(C2×D3)⋊Dic5—21no—
61(C2×D3)⋊Dic5—21no—
62(C2×D3)⋊Dic5—21no—
63Dic3×Dic5—21no—
64#5624—51no—
65#4718—51no—
66#4648—51no—
67C3×#328—51no—
68#4538—51no—
69#4470—51no—
70#4451D511yescharacteristic
71C5×#121—31no—
72#4082—31no—
73#4081—61no—
74D4×Dic5—31no—
75D4×Dic5—61no—
76#4070C2×D311yescharacteristic
77C2×C4×Dic5—31no—
78C2×C4×Dic5—61no—
79#4036—31no—
80#4033—31no—
81#4025—61no—
82#4023—61no—
83C5×C22⋊C8—31no—
84C5×#95C2×D311yescharacteristic
85#3963—31no—
86#3963—61no—
87C22⋊#168C2×D311yescharacteristic
88#3946—61no—
89C8×Dic5—61no—
90#1500—151noSylow
91C23×C3×C5C2×D411yescharacteristic
92C22×C5×D3—21no—
93C2×C3×C4×C5—22no—
94C2×C3×C4×C5—41no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×Dic15—21no—
100C2×Dic15—21no—
101C2×Dic15—22no—
102C2×Dic15—22no—
103C2×Dic15—41no—
104C2×Dic15—41no—
105C2×Dic15C22⋊C411yescharacteristic
106C2×Dic15C22⋊C411yescharacteristic
107C2×Dic15C22⋊C411yescharacteristic
108C2×Dic15C22⋊C411yescharacteristic
109C5×#67—41no—
110C5×#67—41no—
111C2×C5×Dic3—21no—
112C5×D12—41no—
113C2×C3×Dic5—21no—
114C2×C3×Dic5—21no—
115C3×Dic10—41no—
116D3×Dic5—42no—
117C3×#168—41no—
118C5×C3⋊C8—41no—
119C3×C22⋊Q8—51no—
120#947—51no—
121Q8×Dic3—51no—
122#930C2×D511yescharacteristic
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⋊C8—51no—
132C3×#95C2×D511yescharacteristic
133C3⋊#95—51no—
134C3⋊#95—101no—
135#830C2×D511yescharacteristic
136Dic3⋊C8—101no—
137C8×Dic3—101no—
138C2×C5×D4—31no—
139C2×C5×D4—61no—
140C22×C4×C5—21no—
141C22×C4×C5C22×D311yescharacteristic
142C22×Dic5—31no—
143C22×Dic5—31no—
144C22×Dic5—61no—
145C22×Dic5—61no—
146C2×Dic10C4×D311yescharacteristic
147C2×C5×C8—61no—
148C5×C4⋊C4—31no—
149C5×C22⋊C4—61no—
150C22⋊Dic5—21no—
151C22⋊Dic5—61no—
152C22⋊Dic5—61no—
153C22⋊Dic5—61no—
154C4⋊Dic5—61no—
155C4⋊Dic5C4×D311yescharacteristic
156#683—21no—
157#683—61no—
158#683—61no—
159C4×Dic5—31no—
160C4×Dic5—31no—
161C4×Dic5—31no—
162C4×Dic5—31no—
163C4×Dic5—61no—
164C4×Dic5—64no—
165C2×#168—21no—
166#529—151no—
167#431—151no—
168#376—151no—
169#328—51no—
170#328—151no—
171#327—31no—
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×C5×D3—41no—
179C2×C5×D3—41no—
180C2×C5×D3—41no—
181C3×C4×C5—21no—
182C3×C4×C5—21no—
183C3×C4×C5—42no—
184Dic15—21no—
185Dic15—21no—
186Dic15—21no—
187Dic15—42no—
188Dic15#10412yes—
189C3×Dic5—41no—
190C3×Dic5—41no—
191C5×Dic3—41no—
192C2×C3×Q8—51no—
193C22×C3×C4—21no—
194C22×C3×C4C22×D511yescharacteristic
195C2×#67—21no—
196C22×Dic3—51no—
197C22×Dic3—51no—
198C22×Dic3—101no—
199C2×D12C4×D511yescharacteristic
200C2×C4×D3—101no—
201C2×C3×C8—101no—
202C3×C4⋊C4—51no—
203C3×C4⋊C4—101no—
204C3×C22⋊C4—101no—
205(C2×D3)⋊C4—21no—
206(C2×D3)⋊C4—101no—
207(C2×D3)⋊C4—101no—
208(C2×D3)⋊C4—101no—
209C4⋊Dic3—101no—
210C4⋊Dic3—101no—
211C4⋊Dic3C4×D511yescharacteristic
212Dic3⋊C4—101no—
213C4×Dic3—51no—
214C4×Dic3—51no—
215C4×Dic3—51no—
216C4×Dic3—51no—
217C4×Dic3—101no—
218C4×Dic3—104no—
219C2×C3⋊C8—21no—
220C23×C5—61no—
221C23×C5D3×D411yescharacteristic
222C5×D4—121no—
223C5×D4—121no—
224C5×D4—121no—
225C2×C4×C5—22no—
226C2×C4×C5—41no—
227C2×C4×C5—41no—
228C2×C4×C5—41no—
229C2×C4×C5—61no—
230C2×C4×C5C2×C4×D311yescharacteristic
231C2×C4×C5D3×D411yescharacteristic
232C2×Dic5—21no—
233C2×Dic5—21no—
234C2×Dic5—31no—
235C2×Dic5—31no—
236C2×Dic5—31no—
237C2×Dic5—31no—
238C2×Dic5—62no—
239C2×Dic5—61no—
240C2×Dic5—61no—
241C2×Dic5—62no—
242C2×Dic5—122no—
243C2×Dic5—121no—
244C2×Dic5—121no—
245Dic10—41no—
246C5×C8—121no—
247#168—41no—
248#126—301no—
249#125—151no—
250#124—151no—
251#123—301no—
252C22⋊Q8—51no—
253#121—31no—
254C4×Q8—151no—
255C4×D4—151no—
256C4×D4—301no—
257#117—301no—
258C2×C42—151no—
259C2×C42—301no—
260C4⋊C8—301no—
261C22⋊C8—31no—
262C22⋊C8—51no—
263C4×C8—301no—
264#95—151no—
265#95—301no—
266#95D3×D511yescharacteristic
267C2×C3×C5—21no—
268C2×C3×C5—21no—
269C2×C3×C5#41011yescharacteristic
270C2×C3×C5#41611yescharacteristic
271C2×C3×C5C2×#10411yescharacteristic
272C5×D3—81no—
273C23×C3D4×D511yescharacteristic
274C22×D3—21no—
275C3×Q8—201no—
276C2×C3×C4—22no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—41no—
280C2×C3×C4—101no—
281C2×C3×C4—101no—
282C2×C3×C4C2×C4×D511yescharacteristic
283C2×C3×C4D4×D511yescharacteristic
284#67—41no—
285#67—41no—
286C2×Dic3—21no—
287C2×Dic3—51no—
288C2×Dic3—51no—
289C2×Dic3—51no—
290C2×Dic3—51no—
291C2×Dic3—102no—
292C2×Dic3—101no—
293C2×Dic3—101no—
294C2×Dic3—102no—
295C2×Dic3—201no—
296C2×Dic3—201no—
297D12—41no—
298C4×D3—202no—
299C3×C8—201no—
300C3⋊C8—41no—
301C22×C5—21no—
302C22×C5—21no—
303C22×C5—121no—
304C22×C5—121no—
305C22×C5—121no—
306C22×C5D3×C22⋊C411yescharacteristic
307C22×C5#91611yescharacteristic
308C22×C5#91911yescharacteristic
309C4×C5—21no—
310C4×C5—21no—
311C4×C5—42no—
312C4×C5—121no—
313Dic5—32no—
314Dic5—41no—
315Dic5—41no—
316Dic5—61no—
317Dic5—61no—
318Dic5—61no—
319Dic5—122no—
320C2×Q8—51no—
321C2×D4—31no—
322C2×D4—61no—
323C22×C4—21no—
324C22×C4—151no—
325C22×C4—151no—
326C22×C4—301no—
327C22×C4—301no—
328C22×C4C2×D3×D511yescharacteristic
329C2×C8—61no—
330C2×C8—101no—
331C4⋊C4—31no—
332C4⋊C4—51no—
333C4⋊C4—101no—
334C4⋊C4—301no—
335C4⋊C4—301no—
336C4⋊C4—301no—
337C22⋊C4—61no—
338C22⋊C4—101no—
339C22⋊C4—301no—
340C22⋊C4—301no—
341C22⋊C4—301no—
342C42—151no—
343C42—151no—
344C42—151no—
345C42—151no—
346C42—304no—
347C42—301no—
348C3×C5#150011yescharacteristic, complemented, Hall
349C22×C3—21no—
350C22×C3—21no—
351C22×C3D5×C22⋊C411yescharacteristic
352C22×C3#405811yescharacteristic
353C22×C3#406211yescharacteristic
354C2×D3—41no—
355C2×D3—41no—
356C2×D3—41no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—42no—
360C3×C4—201no—
361C3×C4—201no—
362Dic3—41no—
363Dic3—52no—
364Dic3—101no—
365Dic3—101no—
366Dic3—101no—
367Dic3—202no—
368C2×C5—21no—
369C2×C5—21no—
370C2×C5—241no—
371C2×C5#474011yescharacteristic
372C2×C5#480411yescharacteristic
373C2×C5D3×#10411yescharacteristic
374C23—61no—
375C23#679011yescharacteristic
376Q8—201no—
377D4—121no—
378D4—121no—
379D4—121no—
380C2×C4—22no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—61no—
385C2×C4—101no—
386C2×C4—101no—
387C2×C4—151no—
388C2×C4—151no—
389C2×C4—151no—
390C2×C4—151no—
391C2×C4—302no—
392C2×C4—301no—
393C2×C4—301no—
394C2×C4—302no—
395C2×C4—602no—
396C2×C4—601no—
397C2×C4—601no—
398C2×C4C4×D3×D511yescharacteristic
399C2×C4#677711yescharacteristic
400C8—121no—
401C8—201no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3#6502911yescharacteristic
405C2×C3#6506111yescharacteristic
406C2×C3D5×#10411yescharacteristic
407D3—81no—
408C5#6830811yescharacteristic, complemented, Sylow
409C22—21no—
410C22—21no—
411C22—121no—
412C22—121no—
413C22—121no—
414C22#9147311yescharacteristic
415C22#9149911yescharacteristic
416C22#9152311yescharacteristic
417C4—21no—
418C4—21no—
419C4—42no—
420C4—121no—
421C4—152no—
422C4—201no—
423C4—201no—
424C4—301no—
425C4—301no—
426C4—301no—
427C4—602no—
428C3#1059906911yescharacteristic, complemented, Sylow
429C2—21no—
430C2—21no—
431C2—241no—
432C2#1174711211yescharacteristic
433C2#1174713111yescharacteristic
434C2#1174750811yescharacteristic
subgroupG/H
centerC22#91473
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#95C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#930C22
cosocleC22×C3×C4×C5C23
hypercenter#95D3×D5
hypocenterC3×C5#1500
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #11750749C2semidirect
3. #11748331C2semidirect
5. C3×#64672C2semidirect
6. #11745960C2semidirect
15. #91435C4semidirect
17. #91384C4semidirect
18. #91370C4semidirect
20. #91331C4semidirect
35. #64672D3semidirect
348. C3×C5#1500semidirect
408. C5#68308semidirect
428. C3#10599069semidirect

Maximal subgroups

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

subgroupindex
#117544602
#117507492
#117483312
C5×#44512
C3×#646722
#117459602
#117459572
#105990693
#683085