Finite Group Databasebeta

← #14284309

Subgroups — #14284309

Order 1920.

436 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 94 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#11752685C211yesmaximal, characteristic
2C3×#64994C211yesmaximal, characteristic, complemented
3D5×#803C211yesmaximal, characteristic, complemented
4#11746285C211yesmaximal, characteristic, complemented
5C5×#4465C211yesmaximal, characteristic, complemented
6#11745850C211yesmaximal, characteristic, complemented
7#11745848C211yesmaximal, characteristic, complemented
8#10599159—31nomaximal, Hall
9#91764C2211yescharacteristic
10C5×#870C2211yescharacteristic
11C3×C42×D5C2211yescharacteristic
12#91450C411yescharacteristic
13#91444—21no—
14#91418C411yescharacteristic
15#91402—21no—
16#91387—21no—
17#91360C411yescharacteristic
18#91348—21no—
19#91333C411yescharacteristic
20C2×D5×C3⋊C8—21no—
21C3×C5×#97C2211yescharacteristic
22#91087C2211yescharacteristic
23C5×#803C2211yescharacteristic
24C3×#3952—21no—
25C3×#3946—21no—
26C3×#3935C2211yescharacteristic
27#90952—21no—
28#70807—51nomaximal, Hall
29#66025—31no—
30#64994D311yescharacteristic, complemented
31D5×#97—31no—
32C5×#330—31no—
33#64763—31no—
34#64684—31no—
35#64684—31no—
36C2×D60C2×C411yescharacteristic
37C2×Dic30C2×C411yescharacteristic
38C2×C3×C4×D5C2×C411yescharacteristic
39C2×C3×C4×D5D411yescharacteristic
40C2×C3×C4×D5D411yescharacteristic
41C2×#1202—21no—
42C2×#1200—21no—
43C2×C3×C5×C8—21no—
44C3×C42×C5C2311yescharacteristic
45#6714—21no—
46#6714—21no—
47C2×C3⋊#168—21no—
48C5×C4⋊Dic3C2×C411yescharacteristic
49C5×C4⋊Dic3C2×C411yescharacteristic
50C5×Dic3⋊C4—21no—
51C5×Dic3⋊C4—21no—
52C2×C5×C3⋊C8—21no—
53C3×C4×Dic5C2×C411yescharacteristic
54C3×C4×Dic5D411yescharacteristic
55C3×C4×Dic5D411yescharacteristic
56C2×C3×#168—21no—
57Dic3⋊Dic5—21no—
58#6669—21no—
59#6667—21no—
60#6667—21no—
61#6665—21no—
62Dic3×Dic5—21no—
63D5×C3⋊C8—24no—
64#5479—51no—
65C3×#432—51no—
66C2×#803—51no—
67#4465—51no—
68#4465D511yescharacteristic, complemented
69#4464—51no—
70#4464—51no—
71C5×#125—31no—
72C2×C8×D5—61no—
73#4044—61no—
74#4043—31no—
75#4041—31no—
76#4040—61no—
77#4039—31no—
78#4039—61no—
79#4038—61no—
80#4033—31no—
81#4021—31no—
82C42×D5C2×D311yescharacteristic
83C5×#97—31no—
84C5×#97C2×D311yescharacteristic
85#3952—21no—
86#3947—61no—
87#3946—21no—
88#3935—31no—
89#3935C2×D311yescharacteristic
90#1532—151noSylow
91C22×D15—21no—
92C22×C3×D5C22⋊C411yescharacteristic
93C2×C3×C4×C5C22×C411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×Dic15—21no—
97D60—41no—
98Dic30—41no—
99C2×C5×Dic3—21no—
100C2×C5×Dic3—21no—
101C2×C3×Dic5C22⋊C411yescharacteristic
102C2×C3×Dic5C22⋊C411yescharacteristic
103C2×C3×Dic5C22⋊C411yescharacteristic
104C3×C4×D5—22no—
105C3×C4×D5—41no—
106C3×C4×D5—41no—
107#1202—42no—
108#1200—42no—
109C3×C5×C8—41no—
110C3⋊#168—22no—
111C3×#168—41no—
112C5×C3⋊C8—22no—
113C2×C3×C42—51no—
114#930—51no—
115#929—101no—
116C4×#67—101no—
117#924—51no—
118C22×C3⋊C8—101no—
119#876—101no—
120#875—51no—
121C4×D12—51no—
122#872—101no—
123#870C2×D511yescharacteristic
124C4×Dic6—51no—
125C3×C4⋊C8—101no—
126C3×C22⋊C8—101no—
127C3×#97—51no—
128C3×#97C2×D511yescharacteristic
129#803—51no—
130#803—101no—
131#803C2×D511yescharacteristic
132C2×D20—31no—
133C2×D20—61no—
134C2×C4×D5—61no—
135C2×C4×D5C4×D311yescharacteristic
136C2×C4×D5D1211yescharacteristic
137C2×C4×D5#6711yescharacteristic
138C2×Dic10—31no—
139C2×C5×C8—21no—
140C2×C5×C8—61no—
141C5×C4⋊C4—31no—
142C5×C4⋊C4—31no—
143C5×C4⋊C4—61no—
144C5×C4⋊C4—61no—
145C42×C5C22×D311yescharacteristic
146#685—61no—
147#685—61no—
148#685—61no—
149#685—61no—
150#685—61no—
151C4⋊Dic5—61no—
152#683—61no—
153C4×Dic5—61no—
154C4×Dic5C4×D311yescharacteristic
155C4×Dic5D1211yescharacteristic
156C4×Dic5#6711yescharacteristic
157C2×#168—21no—
158C2×#168—61no—
159C8×D5—64no—
160#529—151no—
161#432—51no—
162C2×#97—151no—
163#330—31no—
164#330—151no—
165#329—151no—
166#329—151no—
167C22×C3×C5C2×C22⋊C411yescharacteristic
168C2×D15—41no—
169C2×D15—41no—
170C2×D15—41no—
171C2×C3×D5—21no—
172C2×C3×D5—21no—
173C2×C3×D5#10412yes—
174C3×C4×C5—21no—
175C3×C4×C5—21no—
176C3×C4×C5—21no—
177Dic15—41no—
178C3×Dic5—21no—
179C3×Dic5—21no—
180C3×Dic5—21no—
181C5×Dic3—41no—
182C5×Dic3—41no—
183C22×C3×C4—51no—
184C22×C3×C4—51no—
185C22×C3×C4—51no—
186C2×#67—101no—
187C2×D12—51no—
188C2×C4×D3—101no—
189C2×Dic6—51no—
190C2×C3×C8—21no—
191C2×C3×C8—101no—
192C3×C42—51no—
193C3×C42—51no—
194C3×C42—51no—
195C3×C42C22×D511yescharacteristic
196#217—101no—
197(C2×D3)⋊C4—101no—
198(C2×D3)⋊C4—101no—
199(C2×D3)⋊C4—101no—
200(C2×D3)⋊C4—101no—
201C4⋊Dic3C4×D511yescharacteristic
202C4⋊Dic3C4×D511yescharacteristic
203Dic3⋊C4—21no—
204Dic3⋊C4—21no—
205Dic3⋊C4—101no—
206Dic3⋊C4—101no—
207C4×Dic3—101no—
208C2×C3⋊C8—21no—
209C2×C3⋊C8—104no—
210C2×C3⋊C8—101no—
211C22×D5—61no—
212C22×D5(C2×D3)⋊C411yescharacteristic
213C2×C4×C5—61no—
214C2×C4×C5—61no—
215C2×C4×C5C2×C4×D311yescharacteristic
216C2×C4×C5C2×D1211yescharacteristic
217C2×C4×C5C2×#6711yescharacteristic
218C2×Dic5—61no—
219C2×Dic5(C2×D3)⋊C411yescharacteristic
220C2×Dic5(C2×D3)⋊C411yescharacteristic
221C2×Dic5(C2×D3)⋊C411yescharacteristic
222D20—121no—
223D20—122no—
224C4×D5—22no—
225C4×D5—41no—
226C4×D5—41no—
227C4×D5—122no—
228Dic10—121no—
229C5×C8—41no—
230C5×C8—62no—
231#168—41no—
232#168—62no—
233C22×C8—301no—
234#126—301no—
235#125—31no—
236#124—151no—
237#123—301no—
238C22⋊Q8—151no—
239#121—151no—
240C4×Q8—151no—
241C4×D4—151no—
242C4×D4—301no—
243#117—301no—
244C2×C42—51no—
245C4⋊C8—101no—
246C22⋊C8—101no—
247#97—31no—
248#97—51no—
249#97—151no—
250#97—301no—
251#97D3×D511yescharacteristic
252C2×C3×C5#41311yescharacteristic
253C2×C3×C5C2×#10411yescharacteristic
254C2×C3×C5#42111yescharacteristic
255D15—81no—
256C3×D5—22no—
257C23×C3—51no—
258C22×D3—101no—
259C2×C3×C4—51no—
260C2×C3×C4—51no—
261C2×C3×C4—51no—
262C2×C3×C4—102no—
263C2×C3×C4—201no—
264C2×C3×C4—201no—
265C2×C3×C4C2×C4×D511yescharacteristic
266C2×C3×C4D4×D511yescharacteristic
267C2×C3×C4D4×D511yescharacteristic
268#67—202no—
269C2×Dic3—21no—
270C2×Dic3—21no—
271C2×Dic3—101no—
272D12—201no—
273C4×D3—202no—
274Dic6—201no—
275C3×C8—41no—
276C3×C8—201no—
277C3⋊C8—22no—
278C3⋊C8—102no—
279C22×C5C2×(C2×D3)⋊C411yescharacteristic
280C2×D5—21no—
281C2×D5—21no—
282C2×D5—121no—
283C2×D5—121no—
284C2×D5—121no—
285C2×D5#82512yes—
286C4×C5—21no—
287C4×C5—21no—
288C4×C5—21no—
289C4×C5—121no—
290C4×C5—121no—
291Dic5—21no—
292Dic5—21no—
293Dic5—21no—
294Dic5—121no—
295C2×Q8—151no—
296C2×D4—151no—
297C2×D4—301no—
298C22×C4—51no—
299C22×C4—51no—
300C22×C4—51no—
301C22×C4—301no—
302C2×C8—21no—
303C2×C8—61no—
304C2×C8—101no—
305C2×C8—304no—
306C2×C8—301no—
307C4⋊C4—31no—
308C4⋊C4—31no—
309C4⋊C4—61no—
310C4⋊C4—61no—
311C4⋊C4—301no—
312C4⋊C4—301no—
313C22⋊C4—301no—
314C22⋊C4—301no—
315C22⋊C4—301no—
316C22⋊C4—301no—
317C22⋊C4—301no—
318C42—51no—
319C42—51no—
320C42—51no—
321C42—301no—
322C42C2×D3×D511yescharacteristic
323C3×C5#153211yescharacteristic, complemented, Hall
324C22×C3—52no—
325C22×C3—101no—
326C22×C3—101no—
327C22×C3D5×C22⋊C411yescharacteristic
328C2×D3—201no—
329C2×D3—201no—
330C2×D3—201no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—101no—
335C3×C4—101no—
336C3×C4—101no—
337Dic3—41no—
338Dic3—41no—
339Dic3—201no—
340C2×C5#500511yescharacteristic
341C2×C5#513211yescharacteristic
342C2×C5C2×#82511yescharacteristic
343D5—22no—
344D5—241no—
345C23—51no—
346C23—301no—
347Q8—601no—
348D4—601no—
349D4—602no—
350C2×C4—51no—
351C2×C4—51no—
352C2×C4—51no—
353C2×C4—61no—
354C2×C4—61no—
355C2×C4—102no—
356C2×C4—201no—
357C2×C4—201no—
358C2×C4—301no—
359C2×C4—602no—
360C2×C4C4×D3×D511yescharacteristic
361C2×C4D5×D1211yescharacteristic
362C2×C4D5×#6711yescharacteristic
363C8—41no—
364C8—62no—
365C8—201no—
366C8—302no—
367C2×C3—102no—
368C2×C3#6504011yescharacteristic
369C2×C3D5×#10411yescharacteristic
370C2×C3#6511011yescharacteristic
371D3—401no—
372C5#7080711yescharacteristic, complemented, Sylow
373C22—52no—
374C22—101no—
375C22—101no—
376C22—601no—
377C22—601no—
378C22—601no—
379C22D5×(C2×D3)⋊C411yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—101no—
384C4—101no—
385C4—101no—
386C4—121no—
387C4—121no—
388C4—601no—
389C3#1059915911yescharacteristic, complemented, Sylow
390C2—102no—
391C2—1201no—
392C2#1174710911yescharacteristic
393C2D5×#82511yescharacteristic
394C2#1174823111yescharacteristic
subgroupG/H
centerC22D5×(C2×D3)⋊C4
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#97C22
socleC22×C3×C5C2×C22⋊C4
prime radical#91450C4
cosocleC3×C42×C5C23
hypercenter#97D3×D5
hypocenterC3×C5#1532
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. D5×#803C2semidirect
4. #11746285C2semidirect
5. C5×#4465C2semidirect
6. #11745850C2semidirect
7. #11745848C2semidirect
30. #64994D3semidirect
68. #4465D5semidirect
323. C3×C5#1532semidirect
372. C5#70807semidirect
389. C3#10599159semidirect

Maximal subgroups

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

subgroupindex
#117526852
C3×#649942
D5×#8032
#117462852
C5×#44652
#117458502
#117458482
#105991593
#708075