Finite Group Databasebeta

← #14280820

Subgroups — #14280820

Order 1920.

528 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 110 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
1C2×#91394C211yesmaximal, characteristic
2#11750819C211yesmaximal, characteristic, complemented
3#11748331C211yesmaximal, characteristic, complemented
4C5×#4469C211yesmaximal, characteristic, complemented
5C3×#64688C211yesmaximal, characteristic
6#11745952C211yesmaximal, characteristic, complemented
7#11745948C211yesmaximal, characteristic
8#10598917—31nomaximal, Hall
9C22×D5×Dic3C411yescharacteristic
10C2×C4×Dic15C2211yescharacteristic
11C2×C5×Dic3⋊C4C2211yescharacteristic
12C2×C3×#685C2211yescharacteristic
13C2×Dic3⋊Dic5C411yescharacteristic
14C2×#6665C411yescharacteristic
15C2×Dic3×Dic5C411yescharacteristic
16#91394—21no—
17#91394—21no—
18#91394—21no—
19#91394—21no—
20C3×C5×C22⋊C8C2211yescharacteristic
21#91114C2211yescharacteristic
22#91098—21no—
23C8×Dic15—21no—
24C5×#830C2211yescharacteristic
25C3×C22⋊#168C2211yescharacteristic
26#90983—21no—
27#90951—21no—
28#68100—51nomaximal, Hall
29C2×#4038—31no—
30#65007—31no—
31#65007—31no—
32C5×#324—31no—
33#64748—31no—
34#64688—31no—
35#64688D311yescharacteristic
36C23×C3×D5C2×C411yescharacteristic
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15C2×C411yescharacteristic
39C22×Dic15C2×C411yescharacteristic
40C22×C5×Dic3C2×C411yescharacteristic
41C22×C5×Dic3C2×C411yescharacteristic
42C22×C3×Dic5C2×C411yescharacteristic
43C2×D5×Dic3—21no—
44C2×D5×Dic3—21no—
45C2×D5×Dic3—22no—
46C2×D5×Dic3C814yescomplemented
47C2×C3×C5×C8—21no—
48C4×Dic15D411yescharacteristic
49C4×Dic15D411yescharacteristic
50C4×Dic15D411yescharacteristic
51C4×Dic15D411yescharacteristic
52C2×C3⋊#168—21no—
53C5×Dic3⋊C4—21no—
54C5×Dic3⋊C4—21no—
55C2×C5×C3⋊C8—21no—
56C3×#685—21no—
57C3×#685—21no—
58C2×C3×#168—21no—
59Dic3⋊Dic5—21no—
60Dic3⋊Dic5—21no—
61#6665—21no—
62#6665—21no—
63Dic3×Dic5—21no—
64Dic3×Dic5—21no—
65C2×#877—51no—
66#4718—51no—
67#4718—51no—
68C3×#323—51no—
69#4525—51no—
70#4469—51no—
71#4469D511yescharacteristic, complemented
72C22×C4×D5—31no—
73C2×C5×C4⋊C4—31no—
74C2×#685—31no—
75C2×#685C2×D311yescharacteristic
76C2×C4⋊Dic5—31no—
77C2×C4×Dic5—31no—
78C2×C4×Dic5—31no—
79#4038—61no—
80#4038—61no—
81#4038—61no—
82#4038—61no—
83C5×C22⋊C8—31no—
84C5×C22⋊C8C2×D311yescharacteristic
85C22⋊#168—31no—
86C22⋊#168C2×D311yescharacteristic
87#3946—61no—
88#3946—61no—
89C8×Dic5—61no—
90C8×Dic5—61no—
91#1458—151noSylow
92C23×C3×C5C22×C411yescharacteristic
93C22×C3×D5—21no—
94C22×C3×D5—21no—
95C22×C3×D5—41no—
96C22×C3×D5—41no—
97C22×C3×D5C2×C812yes—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×Dic15—41no—
102C2×Dic15C22⋊C411yescharacteristic
103C2×Dic15C22⋊C411yescharacteristic
104C2×Dic15C22⋊C411yescharacteristic
105C2×Dic15C22⋊C411yescharacteristic
106C2×Dic15C2×C812yes—
107C2×Dic15M1612yes—
108C2×C5×Dic3—21no—
109C2×C5×Dic3—21no—
110C2×C5×Dic3—21no—
111C2×C5×Dic3—41no—
112C2×C5×Dic3C2×C812yes—
113C2×C3×Dic5—21no—
114C2×C3×Dic5—41no—
115D5×Dic3—24no—
116D5×Dic3—24no—
117C3×C5×C8—41no—
118C3⋊#168—41no—
119C3×#168—41no—
120C5×C3⋊C8—41no—
121C23×Dic3—51no—
122C2×C3×C22⋊C4—51no—
123C2×#217—51no—
124C2×Dic3⋊C4—51no—
125C2×Dic3⋊C4C2×D511yescharacteristic
126C2×C4×Dic3—51no—
127C2×C4×Dic3—51no—
128#877—101no—
129#877—101no—
130#877—101no—
131#877—101no—
132C3×C22⋊C8—51no—
133C3×C22⋊C8C2×D511yescharacteristic
134#830—51no—
135#830C2×D511yescharacteristic
136Dic3⋊C8—101no—
137Dic3⋊C8—101no—
138C8×Dic3—101no—
139C8×Dic3—101no—
140C23×D5C4×D311yescharacteristic
141C22×C4×C5—31no—
142C22×C4×C5—31no—
143C22×C4×C5C22×D311yescharacteristic
144C22×Dic5—31no—
145C22×Dic5—31no—
146C22×Dic5C4×D311yescharacteristic
147C2×C4×D5—34no—
148C2×C4×D5—62no—
149C2×C4×D5—61no—
150C2×C4×D5—61no—
151C2×C5×C8—21no—
152C2×C5×C8—61no—
153C5×C4⋊C4—61no—
154C5×C4⋊C4—61no—
155#685—21no—
156#685—21no—
157#685—61no—
158#685—61no—
159C4⋊Dic5—61no—
160C4⋊Dic5—61no—
161C4×Dic5—31no—
162C4×Dic5—31no—
163C4×Dic5—31no—
164C4×Dic5—31no—
165C4×Dic5—61no—
166C4×Dic5—61no—
167C2×#168—21no—
168C2×#168—61no—
169C2×#117—151no—
170#431—151no—
171#431—151no—
172#324—31no—
173#324—151no—
174#323—51no—
175#323—151no—
176C22×C3×C5—21no—
177C22×C3×C5—21no—
178C22×C3×C5C2×C22⋊C411yescharacteristic
179C22×C3×C5C22×C811yescharacteristic
180C22×C3×C5C2×M1611yescharacteristic
181C2×C3×D5—22no—
182C2×C3×D5—42no—
183C2×C3×D5—41no—
184C2×C3×D5—41no—
185C2×C3×D5—42no—
186C3×C4×C5—21no—
187C3×C4×C5—21no—
188Dic15—21no—
189Dic15—21no—
190Dic15C22⋊C812yes—
191Dic15C22⋊C812yes—
192C3×Dic5—41no—
193C5×Dic3—22no—
194C5×Dic3—41no—
195C24×C3—51no—
196C22×C3×C4—51no—
197C22×C3×C4C22×D511yescharacteristic
198C22×Dic3—51no—
199C22×Dic3—51no—
200C22×Dic3—54no—
201C22×Dic3—101no—
202C22×Dic3—101no—
203C22×Dic3—102no—
204C22×Dic3C4×D511yescharacteristic
205C22×Dic3C4×D511yescharacteristic
206C2×C3×C8—21no—
207C2×C3×C8—101no—
208C3×C22⋊C4—101no—
209C3×C22⋊C4—101no—
210#217—101no—
211#217—101no—
212Dic3⋊C4—21no—
213Dic3⋊C4—21no—
214Dic3⋊C4—101no—
215Dic3⋊C4—101no—
216C4×Dic3—51no—
217C4×Dic3—51no—
218C4×Dic3—51no—
219C4×Dic3—51no—
220C4×Dic3—101no—
221C4×Dic3—101no—
222C2×C3⋊C8—21no—
223C2×C3⋊C8—101no—
224C23×C5C2×C4×D311yescharacteristic
225C22×D5—21no—
226C22×D5—21no—
227C22×D5—41no—
228C22×D5—41no—
229C22×D5D3×C812yes—
230C2×C4×C5—32no—
231C2×C4×C5—41no—
232C2×C4×C5—61no—
233C2×C4×C5—61no—
234C2×C4×C5—61no—
235C2×C4×C5—121no—
236C2×C4×C5D3×D411yescharacteristic
237C2×C4×C5D3×D411yescharacteristic
238C2×Dic5—21no—
239C2×Dic5—31no—
240C2×Dic5—31no—
241C2×Dic5—32no—
242C2×Dic5—32no—
243C2×Dic5—31no—
244C2×Dic5—31no—
245C2×Dic5—41no—
246C2×Dic5—121no—
247C4×D5—64no—
248C4×D5—64no—
249C5×C8—41no—
250C5×C8—121no—
251#168—41no—
252#168—121no—
253C23×C4—151no—
254#117—301no—
255#117—301no—
256#117—301no—
257#117—301no—
258C2×C4⋊C4—31no—
259C2×C4⋊C4—151no—
260C2×C22⋊C4—51no—
261C2×C22⋊C4—151no—
262C2×C42—151no—
263C2×C42—151no—
264C4⋊C8—301no—
265C4⋊C8—301no—
266C22⋊C8—31no—
267C22⋊C8—51no—
268C22⋊C8—151no—
269C22⋊C8D3×D511yescharacteristic
270C4×C8—301no—
271C4×C8—301no—
272C2×C3×C5—21no—
273C2×C3×C5—21no—
274C2×C3×C5C2×C22⋊C811yescharacteristic
275C2×C3×C5#41011yescharacteristic
276C2×C3×C5#41311yescharacteristic
277C3×D5—42no—
278C23×C3—52no—
279C23×C3—101no—
280C23×C3—101no—
281C23×C3—201no—
282C23×C3—201no—
283C23×C3C2×C4×D511yescharacteristic
284C2×C3×C4—41no—
285C2×C3×C4—101no—
286C2×C3×C4—201no—
287C2×C3×C4D4×D511yescharacteristic
288C2×C3×C4D4×D511yescharacteristic
289C2×Dic3—21no—
290C2×Dic3—21no—
291C2×Dic3—21no—
292C2×Dic3—41no—
293C2×Dic3—51no—
294C2×Dic3—51no—
295C2×Dic3—52no—
296C2×Dic3—52no—
297C2×Dic3—51no—
298C2×Dic3—51no—
299C2×Dic3—104no—
300C2×Dic3—104no—
301C2×Dic3—201no—
302C2×Dic3C8×D512yes—
303C3×C8—41no—
304C3×C8—201no—
305C3⋊C8—41no—
306C3⋊C8—201no—
307C22×C5—21no—
308C22×C5—21no—
309C22×C5D3×C22⋊C411yescharacteristic
310C22×C5C2×D3×C811yescharacteristic
311C22×C5D3×M1611yescharacteristic
312C2×D5—22no—
313C2×D5—42no—
314C2×D5—41no—
315C2×D5—41no—
316C2×D5—42no—
317C4×C5—21no—
318C4×C5—21no—
319C4×C5—62no—
320C4×C5—121no—
321Dic5—32no—
322Dic5—32no—
323Dic5—41no—
324Dic5—61no—
325Dic5—61no—
326C24—51no—
327C22×C4—31no—
328C22×C4—31no—
329C22×C4—51no—
330C22×C4—154no—
331C22×C4—151no—
332C22×C4—151no—
333C22×C4—301no—
334C22×C4—301no—
335C22×C4—302no—
336C22×C4C2×D3×D511yescharacteristic
337C2×C8—21no—
338C2×C8—61no—
339C2×C8—101no—
340C2×C8—301no—
341C4⋊C4—61no—
342C4⋊C4—61no—
343C4⋊C4—301no—
344C4⋊C4—301no—
345C22⋊C4—101no—
346C22⋊C4—101no—
347C22⋊C4—301no—
348C22⋊C4—301no—
349C42—151no—
350C42—151no—
351C42—151no—
352C42—151no—
353C42—301no—
354C42—301no—
355C3×C5#145811yescharacteristic, complemented, Hall
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—102no—
359C22×C3—202no—
360C22×C3—202no—
361C22×C3—201no—
362C22×C3—201no—
363C22×C3D5×C22⋊C411yescharacteristic
364C22×C3C2×C8×D511yescharacteristic
365C22×C3D5×M1611yescharacteristic
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—201no—
369Dic3—22no—
370Dic3—41no—
371Dic3—52no—
372Dic3—52no—
373Dic3—101no—
374Dic3—101no—
375C2×C5—21no—
376C2×C5—21no—
377C2×C5D3×C22⋊C811yescharacteristic
378C2×C5#474011yescharacteristic
379C2×C5#474511yescharacteristic
380D5—42no—
381C23—52no—
382C23—101no—
383C23—101no—
384C23—201no—
385C23—201no—
386C23C4×D3×D511yescharacteristic
387C2×C4—32no—
388C2×C4—41no—
389C2×C4—61no—
390C2×C4—61no—
391C2×C4—61no—
392C2×C4—101no—
393C2×C4—121no—
394C2×C4—151no—
395C2×C4—151no—
396C2×C4—152no—
397C2×C4—152no—
398C2×C4—151no—
399C2×C4—151no—
400C2×C4—201no—
401C2×C4—304no—
402C2×C4—304no—
403C2×C4—601no—
404C2×C4#677711yescharacteristic
405C2×C4#679011yescharacteristic
406C8—41no—
407C8—121no—
408C8—201no—
409C8—601no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—202no—
413C2×C3D5×C22⋊C811yescharacteristic
414C2×C3#6502911yescharacteristic
415C2×C3#6504011yescharacteristic
416C5#6810011yescharacteristic, complemented, Sylow
417C22—21no—
418C22—21no—
419C22—102no—
420C22—202no—
421C22—202no—
422C22—201no—
423C22—201no—
424C22D3×C8×D511yescharacteristic
425C22#9124611yescharacteristic
426C22#9147311yescharacteristic
427C4—21no—
428C4—21no—
429C4—62no—
430C4—121no—
431C4—152no—
432C4—152no—
433C4—201no—
434C4—301no—
435C4—301no—
436C3#1059891711yescharacteristic, complemented, Sylow
437C2—21no—
438C2—21no—
439C2—202no—
440C2#1174713111yescharacteristic
441C2#1174810011yescharacteristic
442C2#1174823811yescharacteristic
subgroupG/H
centerC22#91473
commutatorC22×C3×C5C22×C8
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×D5C2×C4
cosocleC22×C3×C4×C5C23
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#1458
LCSG ▷ C22×C3×C5 ▷ C2×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. #11750819C2semidirect
3. #11748331C2semidirect
4. C5×#4469C2semidirect
6. #11745952C2semidirect
46. C2×D5×Dic3C8semidirect
71. #4469D5semidirect
355. C3×C5#1458semidirect
416. C5#68100semidirect
436. C3#10598917semidirect

Maximal subgroups

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

subgroupindex
C2×#913942
#117508192
#117483312
C5×#44692
C3×#646882
#117459522
#117459482
#105989173
#681005