Finite Group Databasebeta

← #14283953

Subgroups — #14283953

Order 1920.

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

normal subgroups only

This group has 468 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
1#11752685C211yesmaximal, characteristic
2C3×#64996C211yesmaximal, characteristic, complemented
3D5×#803C211yesmaximal, characteristic, complemented
4#11746285C211yesmaximal, characteristic, complemented
5C5×#4465C211yesmaximal, characteristic, complemented
6#11745850C211yesmaximal, characteristic, complemented
7#11745848C211yesmaximal, characteristic, complemented
8#10599154—31nomaximal, Hall
9#91764C2211yescharacteristic
10C5×#870C2211yescharacteristic
11C2×C3×#676—21no—
12C3×C42×D5C2211yescharacteristic
13#91450C411yescharacteristic
14#91444—21no—
15#91418C411yescharacteristic
16#91402—21no—
17#91387—21no—
18#91360C411yescharacteristic
19#91348—21no—
20#91333C411yescharacteristic
21C2×D5×C3⋊C8—21no—
22C3×C5×#97C2211yescharacteristic
23#91087C2211yescharacteristic
24C5×#803C2211yescharacteristic
25C3×C8×Dic5—21no—
26C3×#3935C2211yescharacteristic
27#90952—21no—
28#69858—51nomaximal, Hall
29#66025—31no—
30#64996D311yescharacteristic, 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—
57C3×#676—24no—
58Dic3⋊Dic5—21no—
59#6669—21no—
60#6667—21no—
61#6667—21no—
62#6665—21no—
63Dic3×Dic5—21no—
64D5×C3⋊C8—24no—
65#5479—51no—
66C3×C4×M16—51no—
67C2×#803—51no—
68#4465—51no—
69#4465D511yescharacteristic, complemented
70#4464—51no—
71#4464—51no—
72C5×#125—31no—
73C2×#676—21no—
74C2×C8×D5—61no—
75#4044—61no—
76#4043—31no—
77#4041—31no—
78#4040—61no—
79#4039—31no—
80#4039—61no—
81#4038—61no—
82#4033—31no—
83#4021—31no—
84C42×D5C2×D311yescharacteristic
85C5×#97—31no—
86C5×#97C2×D311yescharacteristic
87#3947—61no—
88C8×Dic5—21no—
89#3935—31no—
90#3935C2×D311yescharacteristic
91#1524—151noSylow
92C22×D15—21no—
93C22×C3×D5C22⋊C411yescharacteristic
94C2×C3×C4×C5C22×C411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×Dic15—21no—
98D60—41no—
99Dic30—41no—
100C2×C5×Dic3—21no—
101C2×C5×Dic3—21no—
102C2×C3×Dic5C22⋊C411yescharacteristic
103C2×C3×Dic5C22⋊C411yescharacteristic
104C2×C3×Dic5C22⋊C411yescharacteristic
105C3×C4×D5—22no—
106C3×C4×D5—22no—
107C3×C4×D5—41no—
108#1202—42no—
109#1200—42no—
110C3×C5×C8—22no—
111C3⋊#168—22no—
112C3×#168—22no—
113C5×C3⋊C8—22no—
114C2×C3×M16—101no—
115C2×C3×C42—51no—
116#930—51no—
117#929—101no—
118C4×#67—101no—
119#924—51no—
120C22×C3⋊C8—101no—
121#876—101no—
122#875—51no—
123C4×D12—51no—
124#872—101no—
125#870C2×D511yescharacteristic
126C4×Dic6—51no—
127C3×#97—51no—
128C3×#97C2×D511yescharacteristic
129C3×C4×C8—101no—
130#803—51no—
131#803—101no—
132#803C2×D511yescharacteristic
133C2×D20—31no—
134C2×D20—61no—
135C2×C4×D5—61no—
136C2×C4×D5C4×D311yescharacteristic
137C2×C4×D5D1211yescharacteristic
138C2×C4×D5#6711yescharacteristic
139C2×Dic10—31no—
140C2×C5×C8—21no—
141C2×C5×C8—61no—
142C5×C4⋊C4—31no—
143C5×C4⋊C4—31no—
144C5×C4⋊C4—61no—
145C5×C4⋊C4—61no—
146C42×C5C22×D311yescharacteristic
147#685—61no—
148#685—61no—
149#685—61no—
150#685—61no—
151#685—61no—
152C4⋊Dic5—61no—
153#683—61no—
154C4×Dic5—61no—
155C4×Dic5C4×D311yescharacteristic
156C4×Dic5D1211yescharacteristic
157C4×Dic5#6711yescharacteristic
158C2×#168—21no—
159C2×#168—61no—
160#676—24no—
161C8×D5—64no—
162#529—151no—
163C4×M16—51no—
164C2×#97—151no—
165#330—31no—
166#330—151no—
167#329—151no—
168#329—151no—
169C22×C3×C5C2×C22⋊C411yescharacteristic
170C2×D15—41no—
171C2×D15—41no—
172C2×D15—41no—
173C2×C3×D5—21no—
174C2×C3×D5—21no—
175C2×C3×D5#10412yes—
176C3×C4×C5—21no—
177C3×C4×C5—21no—
178C3×C4×C5—21no—
179Dic15—41no—
180C3×Dic5—21no—
181C3×Dic5—21no—
182C3×Dic5#10412yes—
183C5×Dic3—41no—
184C5×Dic3—41no—
185C22×C3×C4—51no—
186C22×C3×C4—51no—
187C22×C3×C4—51no—
188C2×#67—101no—
189C2×D12—51no—
190C2×C4×D3—101no—
191C2×Dic6—51no—
192C3×M16—104no—
193C2×C3×C8—21no—
194C2×C3×C8—101no—
195C3×C42—51no—
196C3×C42—51no—
197C3×C42—51no—
198C3×C42C22×D511yescharacteristic
199#217—101no—
200(C2×D3)⋊C4—101no—
201(C2×D3)⋊C4—101no—
202(C2×D3)⋊C4—101no—
203(C2×D3)⋊C4—101no—
204C4⋊Dic3C4×D511yescharacteristic
205C4⋊Dic3C4×D511yescharacteristic
206Dic3⋊C4—21no—
207Dic3⋊C4—21no—
208Dic3⋊C4—101no—
209Dic3⋊C4—101no—
210C4×Dic3—101no—
211C2×C3⋊C8—21no—
212C2×C3⋊C8—104no—
213C2×C3⋊C8—101no—
214C22×D5—61no—
215C22×D5(C2×D3)⋊C411yescharacteristic
216C2×C4×C5—61no—
217C2×C4×C5—61no—
218C2×C4×C5C2×C4×D311yescharacteristic
219C2×C4×C5C2×D1211yescharacteristic
220C2×C4×C5C2×#6711yescharacteristic
221C2×Dic5—61no—
222C2×Dic5(C2×D3)⋊C411yescharacteristic
223C2×Dic5(C2×D3)⋊C411yescharacteristic
224C2×Dic5(C2×D3)⋊C411yescharacteristic
225D20—121no—
226D20—122no—
227C4×D5—22no—
228C4×D5—22no—
229C4×D5—41no—
230C4×D5—122no—
231Dic10—121no—
232C5×C8—22no—
233C5×C8—62no—
234#168—22no—
235#168—62no—
236C2×M16—101no—
237C22×C8—301no—
238#126—301no—
239#125—31no—
240#124—151no—
241#123—301no—
242C22⋊Q8—151no—
243#121—151no—
244C4×Q8—151no—
245C4×D4—151no—
246C4×D4—301no—
247#117—301no—
248C2×C42—51no—
249#97—31no—
250#97—51no—
251#97—151no—
252#97—301no—
253#97D3×D511yescharacteristic
254C4×C8—101no—
255C2×C3×C5#41311yescharacteristic
256C2×C3×C5C2×#10411yescharacteristic
257C2×C3×C5C2×#10411yescharacteristic
258D15—81no—
259C3×D5—22no—
260C23×C3—51no—
261C22×D3—101no—
262C2×C3×C4—51no—
263C2×C3×C4—51no—
264C2×C3×C4—51no—
265C2×C3×C4—102no—
266C2×C3×C4—102no—
267C2×C3×C4—201no—
268C2×C3×C4C2×C4×D511yescharacteristic
269C2×C3×C4D4×D511yescharacteristic
270C2×C3×C4D4×D511yescharacteristic
271#67—202no—
272C2×Dic3—21no—
273C2×Dic3—21no—
274C2×Dic3—101no—
275D12—201no—
276C4×D3—202no—
277Dic6—201no—
278C3×C8—22no—
279C3×C8—102no—
280C3⋊C8—22no—
281C3⋊C8—102no—
282C22×C5C2×(C2×D3)⋊C411yescharacteristic
283C2×D5—21no—
284C2×D5—21no—
285C2×D5—121no—
286C2×D5—121no—
287C2×D5—121no—
288C2×D5#80512yes—
289C4×C5—21no—
290C4×C5—21no—
291C4×C5—21no—
292C4×C5—121no—
293C4×C5—121no—
294Dic5—21no—
295Dic5—21no—
296Dic5—121no—
297Dic5#82512yes—
298C2×Q8—151no—
299C2×D4—151no—
300C2×D4—301no—
301C22×C4—51no—
302C22×C4—51no—
303C22×C4—51no—
304C22×C4—301no—
305M16—104no—
306C2×C8—21no—
307C2×C8—61no—
308C2×C8—101no—
309C2×C8—304no—
310C2×C8—301no—
311C4⋊C4—31no—
312C4⋊C4—31no—
313C4⋊C4—61no—
314C4⋊C4—61no—
315C4⋊C4—301no—
316C4⋊C4—301no—
317C22⋊C4—301no—
318C22⋊C4—301no—
319C22⋊C4—301no—
320C22⋊C4—301no—
321C22⋊C4—301no—
322C42—51no—
323C42—51no—
324C42—51no—
325C42—301no—
326C42C2×D3×D511yescharacteristic
327C3×C5#152411yescharacteristic, complemented, Hall
328C22×C3—52no—
329C22×C3—101no—
330C22×C3—101no—
331C22×C3D5×C22⋊C411yescharacteristic
332C2×D3—201no—
333C2×D3—201no—
334C2×D3—201no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—52no—
339C3×C4—101no—
340C3×C4—101no—
341Dic3—41no—
342Dic3—41no—
343Dic3—201no—
344C2×C5C2×#80511yescharacteristic
345C2×C5#513211yescharacteristic
346C2×C5C2×#82511yescharacteristic
347D5—22no—
348D5—241no—
349C23—51no—
350C23—301no—
351Q8—601no—
352D4—601no—
353D4—602no—
354C2×C4—51no—
355C2×C4—51no—
356C2×C4—51no—
357C2×C4—61no—
358C2×C4—61no—
359C2×C4—102no—
360C2×C4—102no—
361C2×C4—201no—
362C2×C4—301no—
363C2×C4—602no—
364C2×C4C4×D3×D511yescharacteristic
365C2×C4D5×D1211yescharacteristic
366C2×C4D5×#6711yescharacteristic
367C8—22no—
368C8—62no—
369C8—102no—
370C8—302no—
371C2×C3—102no—
372C2×C3#6504011yescharacteristic
373C2×C3D5×#10411yescharacteristic
374C2×C3D5×#10411yescharacteristic
375D3—401no—
376C5#6985811yescharacteristic, complemented, Sylow
377C22—52no—
378C22—101no—
379C22—101no—
380C22—601no—
381C22—601no—
382C22—601no—
383C22D5×(C2×D3)⋊C411yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—52no—
388C4—101no—
389C4—101no—
390C4—121no—
391C4—121no—
392C4—601no—
393C3#1059915411yescharacteristic, complemented, Sylow
394C2—102no—
395C2—1201no—
396C2D5×#80511yescharacteristic
397C2D5×#82511yescharacteristic
398C2#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#1524
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×#64996C2semidirect
3. D5×#803C2semidirect
4. #11746285C2semidirect
5. C5×#4465C2semidirect
6. #11745850C2semidirect
7. #11745848C2semidirect
30. #64996D3semidirect
69. #4465D5semidirect
327. C3×C5#1524semidirect
376. C5#69858semidirect
393. C3#10599154semidirect

Maximal subgroups

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

subgroupindex
#117526852
C3×#649962
D5×#8032
#117462852
C5×#44652
#117458502
#117458482
#105991543
#698585