Finite Group Databasebeta

← #14284062

Subgroups — #14284062

Order 1920.

528 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 86 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#11752751C211yesmaximal, characteristic
2#11750806C211yesmaximal, characteristic, complemented
3#11746844C211yesmaximal, characteristic, complemented
4C5×#4464C211yesmaximal, characteristic, complemented
5C3×#64684C211yesmaximal, characteristic, complemented
6#11745847C211yesmaximal, characteristic, complemented
7#11745846C211yesmaximal, characteristic, complemented
8#10599136—31nomaximal, Hall
9C2×#6777C411yescharacteristic
10C2×D15⋊Q8C411yescharacteristic
11C42×D15C2211yescharacteristic
12C5×#875C2211yescharacteristic
13C3×#4021C2211yescharacteristic
14#91473—21no—
15#91473—21no—
16#91464—21no—
17#91464—21no—
18#91370C411yescharacteristic
19#91368C411yescharacteristic
20C2×#6651—21no—
21C3×C5×#97C2211yescharacteristic, complemented
22#91104—21no—
23#91098—21no—
24#91087C2211yescharacteristic, complemented
25C5×#803C2211yescharacteristic, complemented
26C3×#3935C2211yescharacteristic, complemented
27#90951—21no—
28#68343—51nomaximal, Hall
29D5×#124—31no—
30#64996—31no—
31#64994—31no—
32C5×#329—31no—
33#64760—31no—
34#64684—31no—
35#64684D311yescharacteristic, complemented
36C22×D3×D5—21no—
37C2×C4×D15C2×C411yescharacteristic
38C2×C4×D15D411yescharacteristic
39C2×C4×D15D411yescharacteristic
40C2×C5×D12C2×C411yescharacteristic
41C2×C5×Dic6C2×C411yescharacteristic
42C2×C3×D20C2×C411yescharacteristic
43C2×C3×Dic10C2×C411yescharacteristic
44C2×#1204—21no—
45C2×#1201—21no—
46C2×#1200—21no—
47#6777—42no—
48D15⋊Q8—42no—
49C2×C3×C5×C8—21no—
50C3×C42×C5C2311yescharacteristic
51C4×Dic15C2×C411yescharacteristic
52C4×Dic15D411yescharacteristic
53C4×Dic15D411yescharacteristic
54C2×C3⋊#168—21no—
55C5×(C2×D3)⋊C4—21no—
56C5×(C2×D3)⋊C4—21no—
57C2×C5×C3⋊C8—21no—
58C3×#685—21no—
59C3×#685—21no—
60C2×C3×#168—21no—
61(C2×D3)⋊Dic5—21no—
62(C2×D3)⋊Dic5—21no—
63#6665—21no—
64#6665—21no—
65#6651—24no—
66D3×#124—51no—
67#4707—51no—
68#4705—51no—
69C3×#329—51no—
70#4540—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#4021C2×D311yescharacteristic
84C42×D5—31no—
85C5×#97—31no—
86C5×#97C2×D311yescharacteristic, complemented
87#3952—61no—
88#3946—61no—
89C8×Dic5—61no—
90#3935—31no—
91#3935C2×D311yescharacteristic, complemented
92#1527—151noSylow
93C22×D15C22⋊C411yescharacteristic
94C22×C5×D3—21no—
95C22×C3×D5—21no—
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×Dic15C22⋊C411yescharacteristic
103C2×Dic15C22⋊C411yescharacteristic
104C2×Dic15C22⋊C411yescharacteristic
105C4×D15—22no—
106C4×D15—22no—
107C4×D15—41no—
108C2×C5×Dic3—21no—
109C5×D12—41no—
110C5×Dic6—41no—
111C2×C3×Dic5—21no—
112C3×D20—41no—
113C3×Dic10—41no—
114#1204—42no—
115#1201—42no—
116#1200—42no—
117C3×C5×C8—41no—
118C3⋊#168—41no—
119C3×#168—22no—
120C5×C3⋊C8—22no—
121C2×D3×Q8—51no—
122C2×D3×D4—51no—
123C3×#124—51no—
124#947—51no—
125#936—51no—
126C2×ΓL(1,𝔽25)—101no—
127#885—101no—
128#885—101no—
129D3×C22⋊C4—101no—
130D3×C22⋊C4—101no—
131#875C2×D511yescharacteristic
132C42×D3—51no—
133C3×#97—51no—
134C3×#97C2×D511yescharacteristic, complemented
135(C2×D3)⋊C8—101no—
136Dic3⋊C8—101no—
137C8×Dic3—101no—
138#803—51no—
139#803C2×D511yescharacteristic, complemented
140C23×D5—61no—
141C2×C5×Q8—31no—
142C2×C5×D4—31no—
143C2×C22⋊D5—61no—
144Q8×D5—122no—
145D4×D5—122no—
146C2×D20C4×D311yescharacteristic
147C2×C4×D5—31no—
148C2×C4×D5—31no—
149C2×C4×D5—31no—
150C2×C4×D5—61no—
151C2×Dic10—61no—
152C2×Dic10C4×D311yescharacteristic
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—21no—
161#685—21no—
162#685—61no—
163#685—61no—
164C4×Dic5—31no—
165C4×Dic5—31no—
166C4×Dic5—31no—
167C2×#168—21no—
168C2×#168—61no—
169#676—64no—
170C2×#124—151no—
171#432—151no—
172C4×M16—151no—
173#329—31no—
174#329—51no—
175#329—151no—
176#329—151no—
177C22×C3×C5C2×C22⋊C411yescharacteristic
178C2×D15—21no—
179C2×D15—21no—
180C2×D15#10412yes—
181C2×C5×D3—41no—
182C2×C5×D3—41no—
183C2×C5×D3—41no—
184C2×C3×D5—41no—
185C2×C3×D5—41no—
186C2×C3×D5—41no—
187D3×D5—84no—
188C3×C4×C5—21no—
189C3×C4×C5—21no—
190C3×C4×C5—21no—
191Dic15—21no—
192Dic15—21no—
193Dic15#10012yes—
194C3×Dic5—41no—
195C5×Dic3—41no—
196C23×D3—101no—
197C2×C3×Q8—51no—
198C2×C3×D4—51no—
199C2×#67—101no—
200D3×Q8—202no—
201D3×D4—202no—
202C2×D12C4×D511yescharacteristic
203C2×C4×D3—51no—
204C2×C4×D3—51no—
205C2×C4×D3—51no—
206C2×C4×D3—101no—
207C2×Dic6—101no—
208C2×Dic6C4×D511yescharacteristic
209C2×C3×C8—21no—
210C2×C3×C8—101no—
211C3×C22⋊C4—101no—
212C3×C22⋊C4—101no—
213C3×C42C22×D511yescharacteristic
214#217—101no—
215#217—101no—
216(C2×D3)⋊C4—21no—
217(C2×D3)⋊C4—21no—
218(C2×D3)⋊C4—101no—
219(C2×D3)⋊C4—101no—
220C4×Dic3—51no—
221C4×Dic3—51no—
222C4×Dic3—51no—
223C2×C3⋊C8—21no—
224C2×C3⋊C8—101no—
225ΓL(1,𝔽25)—104no—
226C23×C5—61no—
227C22×D5—21no—
228C22×D5—31no—
229C22×D5—122no—
230C22×D5—122no—
231C22×D5—122no—
232C5×Q8—121no—
233C5×D4—121no—
234C2×C4×C5—61no—
235C2×C4×C5C2×C4×D311yescharacteristic
236C2×C4×C5D3×D411yescharacteristic
237C2×C4×C5D3×D411yescharacteristic
238C22⋊D5—122no—
239C2×Dic5—21no—
240C2×Dic5—31no—
241C2×Dic5—31no—
242C2×Dic5—31no—
243D20—41no—
244C4×D5—62no—
245C4×D5—62no—
246C4×D5—122no—
247C4×D5—121no—
248Dic10—41no—
249Dic10—122no—
250C5×C8—41no—
251C5×C8—62no—
252#168—22no—
253#168—121no—
254C22×Q8—151no—
255C22×D4—151no—
256C2×M16—301no—
257#124—31no—
258#124—51no—
259#124—151no—
260#124—151no—
261#124—301no—
262#124—301no—
263C2×C22⋊C4—301no—
264C2×C22⋊C4—301no—
265C2×C42—151no—
266C4⋊C8—301no—
267C22⋊C8—301no—
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—22no—
277C3×D5—81no—
278C5×D3—81no—
279C23×C3—101no—
280C22×D3—21no—
281C22×D3—51no—
282C22×D3—202no—
283C22×D3—202no—
284C22×D3—202no—
285C3×Q8—201no—
286C3×D4—201no—
287C2×C3×C4—101no—
288C2×C3×C4C2×C4×D511yescharacteristic
289C2×C3×C4D4×D511yescharacteristic
290C2×C3×C4D4×D511yescharacteristic
291#67—202no—
292C2×Dic3—21no—
293C2×Dic3—51no—
294C2×Dic3—51no—
295C2×Dic3—51no—
296D12—41no—
297C4×D3—102no—
298C4×D3—102no—
299C4×D3—202no—
300C4×D3—201no—
301Dic6—41no—
302Dic6—202no—
303C3×C8—41no—
304C3×C8—102no—
305C3⋊C8—22no—
306C3⋊C8—201no—
307C22×C5—121no—
308C22×C5—121no—
309C22×C5—121no—
310C22×C5D3×C22⋊C411yescharacteristic
311C2×D5—32no—
312C2×D5—41no—
313C2×D5—41no—
314C2×D5—41no—
315C2×D5—61no—
316C2×D5—61no—
317C2×D5—244no—
318C4×C5—21no—
319C4×C5—21no—
320C4×C5—21no—
321C4×C5—121no—
322Dic5—32no—
323Dic5—41no—
324Dic5—61no—
325Dic5—61no—
326C24—301no—
327C2×Q8—31no—
328C2×Q8—51no—
329C2×Q8—301no—
330C2×Q8—602no—
331C2×D4—31no—
332C2×D4—51no—
333C2×D4—301no—
334C2×D4—602no—
335C22×C4—151no—
336C22×C4—151no—
337C22×C4—151no—
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—101no—
347C22⋊C4—101no—
348C22⋊C4—301no—
349C22⋊C4—301no—
350C22⋊C4—301no—
351C22⋊C4—301no—
352C42—151no—
353C42—151no—
354C42—151no—
355C42C2×D3×D511yescharacteristic
356C3×C5#152711yescharacteristic, complemented, Hall
357C22×C3—201no—
358C22×C3—201no—
359C22×C3—201no—
360C22×C3D5×C22⋊C411yescharacteristic
361C2×D3—41no—
362C2×D3—41no—
363C2×D3—41no—
364C2×D3—52no—
365C2×D3—101no—
366C2×D3—101no—
367C2×D3—404no—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—201no—
372Dic3—41no—
373Dic3—52no—
374Dic3—101no—
375Dic3—101no—
376C2×C5—241no—
377C2×C5D3×#10011yescharacteristic
378C2×C5D3×#10411yescharacteristic
379C2×C5#482111yescharacteristic
380D5—62no—
381D5—81no—
382C23—61no—
383C23—101no—
384C23—151no—
385C23—602no—
386C23—602no—
387C23—602no—
388Q8—121no—
389Q8—201no—
390Q8—602no—
391D4—121no—
392D4—201no—
393D4—602no—
394C2×C4—61no—
395C2×C4—101no—
396C2×C4—151no—
397C2×C4—151no—
398C2×C4—151no—
399C2×C4—302no—
400C2×C4—302no—
401C2×C4—601no—
402C2×C4—602no—
403C2×C4C4×D3×D511yescharacteristic
404C2×C4#677711yescharacteristic
405C2×C4#679011yescharacteristic
406C8—41no—
407C8—62no—
408C8—102no—
409C8—601no—
410C2×C3—401no—
411C2×C3D5×#10011yescharacteristic
412C2×C3D5×#10411yescharacteristic
413C2×C3#6511011yescharacteristic
414D3—81no—
415D3—102no—
416C5#6834311yescharacteristic, complemented, Sylow
417C22—121no—
418C22—121no—
419C22—121no—
420C22—152no—
421C22—201no—
422C22—201no—
423C22—201no—
424C22—301no—
425C22—301no—
426C22—1204no—
427C22#9147311yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—121no—
432C4—152no—
433C4—201no—
434C4—301no—
435C4—301no—
436C3#1059913611yescharacteristic, complemented, Sylow
437C2—241no—
438C2—302no—
439C2—401no—
440C2#1174711311yescharacteristic
441C2#1174822411yescharacteristic
442C2#1174823611yescharacteristic
subgroupG/H
centerC22#91473
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#97C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×#6777C4
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. #11750806C2semidirect
3. #11746844C2semidirect
4. C5×#4464C2semidirect
5. C3×#64684C2semidirect
6. #11745847C2semidirect
7. #11745846C2semidirect
21. C3×C5×#97C22semidirect
24. #91087C22semidirect
25. C5×#803C22semidirect
26. C3×#3935C22semidirect
35. #64684D3semidirect
72. #4464D5semidirect
86. C5×#97C2×D3semidirect
91. #3935C2×D3semidirect
134. C3×#97C2×D5semidirect
139. #803C2×D5semidirect
271. #97D3×D5semidirect
356. C3×C5#1527semidirect
416. C5#68343semidirect
436. C3#10599136semidirect

Maximal subgroups

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

subgroupindex
#117527512
#117508062
#117468442
C5×#44642
C3×#646842
#117458472
#117458462
#105991363
#683435