Finite Group Databasebeta

← #14284061

Subgroups — #14284061

Order 1920.

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

normal subgroups only

This group has 528 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
1D5×#875C211yesmaximal, characteristic
2C3×#64994C211yesmaximal, characteristic, complemented
3#11747003C211yesmaximal, characteristic, complemented
4#11746285C211yesmaximal, characteristic, complemented
5C5×#4464C211yesmaximal, characteristic, complemented
6#11745848C211yesmaximal, characteristic, complemented
7#11745847C211yesmaximal, characteristic, complemented
8#10599136—31nomaximal, Hall
9C2×D5×D12C411yescharacteristic
10C2×D5×Dic6C411yescharacteristic
11#91764C2211yescharacteristic
12C5×#875C2211yescharacteristic
13C3×C42×D5C2211yescharacteristic
14D5×(C2×D3)⋊C4—21no—
15D5×(C2×D3)⋊C4—21no—
16#91375C411yescharacteristic
17#91373C411yescharacteristic
18#91350—21no—
19#91350—21no—
20C2×#6649—21no—
21C3×C5×#97C2211yescharacteristic, complemented
22#91087C2211yescharacteristic, complemented
23C5×#803C2211yescharacteristic, complemented
24C3×#3952—21no—
25C3×#3946—21no—
26C3×#3935C2211yescharacteristic, complemented
27Dic5×C3⋊C8—21no—
28#70804—51nomaximal, Hall
29D5×#124—31no—
30#64996—31no—
31#64994D311yescharacteristic, complemented
32C5×#329—31no—
33#64760—31no—
34#64684—31no—
35#64684—31no—
36C22×D3×D5—21no—
37C2×D60C2×C411yescharacteristic
38C2×Dic30C2×C411yescharacteristic
39C2×C5×D12C2×C411yescharacteristic
40C2×C5×Dic6C2×C411yescharacteristic
41C2×C3×C4×D5C2×C411yescharacteristic
42C2×C3×C4×D5D411yescharacteristic
43C2×C3×C4×D5D411yescharacteristic
44C2×#1204—21no—
45C2×#1203—21no—
46C2×D5×Dic3—21no—
47D5×D12—42no—
48D5×Dic6—42no—
49C2×C3×C5×C8—21no—
50C3×C42×C5C2311yescharacteristic
51#6714—21no—
52#6714—21no—
53C2×C3⋊#168—21no—
54C5×(C2×D3)⋊C4—21no—
55C5×(C2×D3)⋊C4—21no—
56C2×C5×C3⋊C8—21no—
57C3×C4×Dic5C2×C411yescharacteristic
58C3×C4×Dic5D411yescharacteristic
59C3×C4×Dic5D411yescharacteristic
60C2×C3×#168—21no—
61#6667—21no—
62#6667—21no—
63(C2×D3)⋊Dic5—21no—
64(C2×D3)⋊Dic5—21no—
65#6649—24no—
66C2×#875—51no—
67C3×#432—51no—
68C4×#208—51no—
69#4464—51no—
70#4464—51no—
71#4464—51no—
72#4464D511yescharacteristic, complemented
73C2×Q8×D5—31no—
74C2×D4×D5—31no—
75C5×#124—31no—
76#4093—31no—
77#4082—31no—
78C2×#676—61no—
79#4031—61no—
80#4031—61no—
81D5×C22⋊C4—61no—
82D5×C22⋊C4—61no—
83#4021—31no—
84C42×D5C2×D311yescharacteristic
85C5×#97—31no—
86C5×#97C2×D311yescharacteristic, complemented
87#3952—21no—
88#3946—21no—
89C8×Dic5—61no—
90#3935—31no—
91#3935C2×D311yescharacteristic, complemented
92#1527—151noSylow
93C22×D15—21no—
94C22×C5×D3—21no—
95C22×C3×D5C22⋊C411yescharacteristic
96C2×D3×D5—42no—
97C2×D3×D5—42no—
98C2×D3×D5—42no—
99C2×C3×C4×C5C22×C411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×Dic15—21no—
103D60—41no—
104Dic30—41no—
105C2×C5×Dic3—21no—
106C5×D12—41no—
107C5×Dic6—41no—
108C2×C3×Dic5C22⋊C411yescharacteristic
109C2×C3×Dic5C22⋊C411yescharacteristic
110C2×C3×Dic5C22⋊C411yescharacteristic
111C3×C4×D5—22no—
112C3×C4×D5—22no—
113C3×C4×D5—41no—
114#1204—42no—
115#1203—42no—
116D5×Dic3—42no—
117C3×C5×C8—41no—
118C3⋊#168—22no—
119C3×#168—41no—
120C5×C3⋊C8—22no—
121C22×D12—51no—
122C22×Dic6—51no—
123C2×C3×C42—51no—
124C2×(C2×D3)⋊C4—101no—
125C2×(C2×D3)⋊C4—101no—
126C2×#208—101no—
127#875—51no—
128#875—51no—
129#875—51no—
130#875—101no—
131#875—101no—
132#875C2×D511yescharacteristic
133C3×C4⋊C8—101no—
134C3×C22⋊C8—101no—
135C3×#97—51no—
136C3×#97C2×D511yescharacteristic, complemented
137#803—51no—
138#803C2×D511yescharacteristic, complemented
139C4×C3⋊C8—101no—
140C23×D5—61no—
141C2×C5×Q8—31no—
142C2×C5×D4—31no—
143C2×C22⋊D5—61no—
144Q8×D5—122no—
145D4×D5—122no—
146C2×D20—31no—
147C2×C4×D5—61no—
148C2×C4×D5C4×D311yescharacteristic
149C2×C4×D5D1211yescharacteristic
150C2×C4×D5#6711yescharacteristic
151C2×Dic10—31no—
152C2×Dic10—61no—
153C2×C5×C8—21no—
154C2×C5×C8—61no—
155C5×C22⋊C4—61no—
156C5×C22⋊C4—61no—
157C42×C5C22×D311yescharacteristic
158C22⋊Dic5—61no—
159C22⋊Dic5—61no—
160#685—61no—
161#685—61no—
162#685—61no—
163#685—61no—
164C4×Dic5C4×D311yescharacteristic
165C4×Dic5D1211yescharacteristic
166C4×Dic5#6711yescharacteristic
167C2×#168—21no—
168C2×#168—61no—
169#676—64no—
170C2×#124—151no—
171#432—51no—
172C4×M16—151no—
173#329—31no—
174#329—151no—
175#329—151no—
176#329—151no—
177C22×C3×C5C2×C22⋊C411yescharacteristic
178C2×D15—41no—
179C2×D15—41no—
180C2×D15—41no—
181C2×C5×D3—41no—
182C2×C5×D3—41no—
183C2×C5×D3—41no—
184C2×C3×D5—21no—
185C2×C3×D5—21no—
186C2×C3×D5#10412yes—
187D3×D5—84no—
188C3×C4×C5—21no—
189C3×C4×C5—21no—
190C3×C4×C5—21no—
191Dic15—41no—
192C3×Dic5—21no—
193C3×Dic5—21no—
194C3×Dic5#10012yes—
195C5×Dic3—41no—
196C23×D3—101no—
197C22×C3×C4—51no—
198C22×C3×C4—51no—
199C22×C3×C4—51no—
200C22×Dic3—101no—
201C2×D12—51no—
202C2×D12—101no—
203C2×D12—202no—
204C2×D12C4×D511yescharacteristic
205C2×Dic6—51no—
206C2×Dic6—101no—
207C2×Dic6—202no—
208C2×Dic6C4×D511yescharacteristic
209C2×C3×C8—21no—
210C2×C3×C8—101no—
211C3×C42—51no—
212C3×C42—51no—
213C3×C42—51no—
214C3×C42C22×D511yescharacteristic
215(C2×D3)⋊C4—21no—
216(C2×D3)⋊C4—21no—
217(C2×D3)⋊C4—101no—
218(C2×D3)⋊C4—101no—
219(C2×D3)⋊C4—101no—
220(C2×D3)⋊C4—101no—
221(C2×D3)⋊C4—101no—
222(C2×D3)⋊C4—101no—
223#208—104no—
224C2×C3⋊C8—21no—
225C2×C3⋊C8—101no—
226C23×C5—61no—
227C22×D5—61no—
228C22×D5—122no—
229C22×D5—122no—
230C22×D5—122no—
231C22×D5(C2×D3)⋊C411yescharacteristic
232C5×Q8—121no—
233C5×D4—121no—
234C2×C4×C5—61no—
235C2×C4×C5C2×C4×D311yescharacteristic
236C2×C4×C5C2×D1211yescharacteristic
237C2×C4×C5C2×#6711yescharacteristic
238C22⋊D5—122no—
239C2×Dic5—61no—
240C2×Dic5(C2×D3)⋊C411yescharacteristic
241C2×Dic5(C2×D3)⋊C411yescharacteristic
242C2×Dic5(C2×D3)⋊C411yescharacteristic
243D20—121no—
244C4×D5—22no—
245C4×D5—22no—
246C4×D5—41no—
247C4×D5—122no—
248Dic10—122no—
249Dic10—121no—
250C5×C8—41no—
251C5×C8—62no—
252#168—41no—
253#168—62no—
254C22×Q8—151no—
255C22×D4—151no—
256C2×M16—301no—
257#124—31no—
258#124—151no—
259#124—151no—
260#124—151no—
261#124—301no—
262#124—301no—
263C2×C22⋊C4—301no—
264C2×C22⋊C4—301no—
265C2×C42—51no—
266C4⋊C8—101no—
267C22⋊C8—101no—
268#97—31no—
269#97—51no—
270#97—151no—
271#97D3×D511yescharacteristic, complemented
272C4×C8—301no—
273C2×C3×C5C2×#10011yescharacteristic
274C2×C3×C5C2×#10411yescharacteristic
275C2×C3×C5#42111yescharacteristic
276D15—81no—
277C3×D5—22no—
278C5×D3—81no—
279C23×C3—51no—
280C22×D3—21no—
281C22×D3—101no—
282C22×D3—202no—
283C22×D3—202no—
284C22×D3—202no—
285C2×C3×C4—51no—
286C2×C3×C4—51no—
287C2×C3×C4—51no—
288C2×C3×C4—102no—
289C2×C3×C4—102no—
290C2×C3×C4—201no—
291C2×C3×C4C2×C4×D511yescharacteristic
292C2×C3×C4D4×D511yescharacteristic
293C2×C3×C4D4×D511yescharacteristic
294C2×Dic3—21no—
295C2×Dic3—101no—
296C2×Dic3—202no—
297D12—41no—
298D12—201no—
299D12—202no—
300Dic6—41no—
301Dic6—202no—
302Dic6—201no—
303C3×C8—41no—
304C3×C8—201no—
305C3⋊C8—22no—
306C3⋊C8—102no—
307C22×C5—121no—
308C22×C5—121no—
309C22×C5—121no—
310C22×C5C2×(C2×D3)⋊C411yescharacteristic
311C2×D5—21no—
312C2×D5—21no—
313C2×D5—121no—
314C2×D5—121no—
315C2×D5—121no—
316C2×D5—244no—
317C2×D5#82512yes—
318C4×C5—21no—
319C4×C5—21no—
320C4×C5—21no—
321C4×C5—121no—
322Dic5—21no—
323Dic5—21no—
324Dic5—121no—
325Dic5#82312yes—
326C24—301no—
327C2×Q8—31no—
328C2×Q8—151no—
329C2×Q8—301no—
330C2×Q8—602no—
331C2×D4—31no—
332C2×D4—151no—
333C2×D4—301no—
334C2×D4—602no—
335C22×C4—51no—
336C22×C4—51no—
337C22×C4—51no—
338C22×C4—301no—
339M16—304no—
340C2×C8—21no—
341C2×C8—61no—
342C2×C8—101no—
343C2×C8—301no—
344C22⋊C4—61no—
345C22⋊C4—61no—
346C22⋊C4—301no—
347C22⋊C4—301no—
348C22⋊C4—301no—
349C22⋊C4—301no—
350C22⋊C4—301no—
351C22⋊C4—301no—
352C42—51no—
353C42—51no—
354C42—51no—
355C42C2×D3×D511yescharacteristic
356C3×C5#152711yescharacteristic, complemented, Hall
357C22×C3—52no—
358C22×C3—101no—
359C22×C3—101no—
360C22×C3D5×C22⋊C411yescharacteristic
361C2×D3—41no—
362C2×D3—41no—
363C2×D3—41no—
364C2×D3—201no—
365C2×D3—201no—
366C2×D3—201no—
367C2×D3—404no—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—52no—
372C3×C4—101no—
373C3×C4—101no—
374Dic3—41no—
375Dic3—201no—
376C2×C5—241no—
377C2×C5#500511yescharacteristic
378C2×C5C2×#82311yescharacteristic
379C2×C5C2×#82511yescharacteristic
380D5—22no—
381D5—241no—
382C23—51no—
383C23—61no—
384C23—301no—
385C23—602no—
386C23—602no—
387C23—602no—
388Q8—121no—
389Q8—601no—
390Q8—602no—
391D4—121no—
392D4—601no—
393D4—602no—
394C2×C4—51no—
395C2×C4—51no—
396C2×C4—51no—
397C2×C4—61no—
398C2×C4—102no—
399C2×C4—102no—
400C2×C4—201no—
401C2×C4—301no—
402C2×C4—602no—
403C2×C4C4×D3×D511yescharacteristic
404C2×C4D5×D1211yescharacteristic
405C2×C4D5×#6711yescharacteristic
406C8—41no—
407C8—62no—
408C8—201no—
409C8—302no—
410C2×C3—102no—
411C2×C3D5×#10011yescharacteristic
412C2×C3D5×#10411yescharacteristic
413C2×C3#6511011yescharacteristic
414D3—81no—
415D3—401no—
416C5#7080411yescharacteristic, complemented, Sylow
417C22—52no—
418C22—101no—
419C22—101no—
420C22—121no—
421C22—121no—
422C22—121no—
423C22—601no—
424C22—601no—
425C22—601no—
426C22—1204no—
427C22D5×(C2×D3)⋊C411yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—52no—
432C4—101no—
433C4—101no—
434C4—121no—
435C4—601no—
436C3#1059913611yescharacteristic, complemented, Sylow
437C2—102no—
438C2—241no—
439C2—1201no—
440C2#1174710911yescharacteristic
441C2D5×#82311yescharacteristic
442C2D5×#82511yescharacteristic
subgroupG/H
centerC22D5×(C2×D3)⋊C4
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#97C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×D5×D12C4
cosocleC3×C42×C5C23
hypercenter#97D3×D5
hypocenterC3×C5#1527
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
2. C3×#64994C2semidirect
3. #11747003C2semidirect
4. #11746285C2semidirect
5. C5×#4464C2semidirect
6. #11745848C2semidirect
7. #11745847C2semidirect
21. C3×C5×#97C22semidirect
22. #91087C22semidirect
23. C5×#803C22semidirect
26. C3×#3935C22semidirect
31. #64994D3semidirect
72. #4464D5semidirect
86. C5×#97C2×D3semidirect
91. #3935C2×D3semidirect
136. C3×#97C2×D5semidirect
138. #803C2×D5semidirect
271. #97D3×D5semidirect
356. C3×C5#1527semidirect
416. C5#70804semidirect
436. C3#10599136semidirect

Maximal subgroups

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

subgroupindex
D5×#8752
C3×#649942
#117470032
#117462852
C5×#44642
#117458482
#117458472
#105991363
#708045