Finite Group Databasebeta

← #14282423

Subgroups — #14282423

Order 1920.

464 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752497C211yesmaximal, characteristic
2C3×#65126C211yesmaximal, characteristic
3C4×D5×C3⋊C8C211yesmaximal, characteristic
4#11746305C211yesmaximal, characteristic, complemented
5C5×#4484C211yesmaximal, characteristic, complemented
6#11745844C211yesmaximal, characteristic, complemented
7#11745842C211yesmaximal, characteristic, complemented
8#10599033—31nomaximal, Hall
9C4×Dic30C2211yescharacteristic
10C4×C5×Dic6C2211yescharacteristic
11C2×C3×#676—21no—
12C3×C42×D5C2211yescharacteristic
13#91468C411yescharacteristic
14C4×#1204—21no—
15#91378—21no—
16#91376C411yescharacteristic
17#91360C411yescharacteristic
18#91359C411yescharacteristic
19#91357—21no—
20#91349—21no—
21C2×D5×C3⋊C8—21no—
22C3×C5×C4⋊C8C2211yescharacteristic
23C4×C3⋊#168C2211yescharacteristic
24C4×C5×C3⋊C8C2211yescharacteristic
25C3×#3946—21no—
26C3×C4⋊#168C2211yescharacteristic
27Dic5×C3⋊C8—21no—
28#70501—51nomaximal, Hall
29#65912—31no—
30#65126D311yescharacteristic
31C4×C8×D5—31no—
32C5×Q8⋊C8—31no—
33Q8⋊#168—31no—
34#64704—31no—
35#64676—31no—
36C2×Dic30C2×C411yescharacteristic
37C2×C5×Dic6C2×C411yescharacteristic
38C2×C3×C4×D5C2×C411yescharacteristic
39C2×C3×C4×D5D411yescharacteristic
40C2×C3×C4×D5D411yescharacteristic
41C2×#1204—21no—
42C2×C3×C5×C8—21no—
43C3×C42×C5C2311yescharacteristic
44C4⋊Dic15C2×C411yescharacteristic
45#6712—21no—
46C4×Dic15—21no—
47C2×C3⋊#168—21no—
48C5×C4⋊Dic3C2×C411yescharacteristic
49C5×Dic3⋊C4—21no—
50C4×C5×Dic3—21no—
51C2×C5×C3⋊C8—21no—
52C3×C4×Dic5C2×C411yescharacteristic
53C3×C4×Dic5D411yescharacteristic
54C3×C4×Dic5D411yescharacteristic
55C2×C3×#168—21no—
56C3×#676—42no—
57Dic3⋊Dic5—21no—
58#6669—21no—
59#6668—21no—
60#6668—21no—
61#6668—21no—
62#6665—21no—
63#6665—21no—
64D5×C3⋊C8—24no—
65#5470—51no—
66C3×#423—51no—
67C2×C4×C3⋊C8—51no—
68#4484—51no—
69#4484—51no—
70#4484—51no—
71#4484D511yescharacteristic, complemented
72C4×C5×Q8—31no—
73#4092—31no—
74#4090—31no—
75C2×#676—21no—
76C2×C8×D5—61no—
77#4043—31no—
78#4042—61no—
79#4035—61no—
80#4034—31no—
81#4018—61no—
82C42×D5C2×D311yescharacteristic
83C4×Dic10—31no—
84C4×Dic10—61no—
85C5×C4⋊C8C2×D311yescharacteristic
86C4×C5×C8—31no—
87#3946—21no—
88C8×Dic5—61no—
89C4⋊#168C2×D311yescharacteristic
90C4×#168—31no—
91#1493—151noSylow
92C22×C3×D5C22⋊C411yescharacteristic
93C2×C3×C4×C5C22×C411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×Dic15—21no—
97C2×Dic15—21no—
98Dic30—21no—
99Dic30—21no—
100C2×C5×Dic3—21no—
101C2×C5×Dic3—21no—
102C5×Dic6—21no—
103C5×Dic6—21no—
104C2×C3×Dic5C22⋊C411yescharacteristic
105C2×C3×Dic5C22⋊C411yescharacteristic
106C2×C3×Dic5C22⋊C411yescharacteristic
107C3×C4×D5—21no—
108C3×C4×D5—21no—
109C3×C4×D5—22no—
110C3×C4×D5SD1612yes—
111C3×C4×D5Q1612yes—
112#1204—42no—
113C3×C5×C8—41no—
114C3⋊#168—22no—
115C3×#168—41no—
116C5×C3⋊C8—22no—
117C2×C3×M16—101no—
118C2×C3×C42—51no—
119#926—101no—
120#924—51no—
121#924—51no—
122#924—101no—
123C22×C3⋊C8—101no—
124#870—101no—
125#869—51no—
126#869—51no—
127C4×Dic6—51no—
128C4×Dic6—101no—
129C4×Dic6C2×D511yescharacteristic
130C3×C4⋊C8—51no—
131C3×C4⋊C8—101no—
132C3×C4⋊C8C2×D511yescharacteristic
133C4×C3⋊C8—51no—
134C4×C3⋊C8—101no—
135C4×C3⋊C8C2×D511yescharacteristic
136C2×C5×Q8—31no—
137C2×C4×D5C4×D311yescharacteristic
138C2×C4×D5D1211yescharacteristic
139C2×C4×D5#6711yescharacteristic
140C2×Dic10—31no—
141C2×Dic10—61no—
142C2×C5×C8—21no—
143C2×C5×C8—61no—
144C5×C4⋊C4—31no—
145C5×C4⋊C4—61no—
146C42×C5—61no—
147C42×C5C22×D311yescharacteristic
148#685—61no—
149#685—61no—
150C4⋊Dic5—31no—
151C4⋊Dic5—61no—
152#683—61no—
153#683—61no—
154#683—61no—
155#683—61no—
156#683—61no—
157C4×Dic5—61no—
158C4×Dic5C4×D311yescharacteristic
159C4×Dic5D1211yescharacteristic
160C4×Dic5#6711yescharacteristic
161C2×#168—21no—
162C2×#168—61no—
163#676—42no—
164C8×D5—64no—
165#533—151no—
166#423—51no—
167C2×C4×C8—151no—
168Q8⋊C8—31no—
169Q8⋊C8—151no—
170Q8⋊C8—151no—
171Q8⋊C8—151no—
172C22×C3×C5C2×C22⋊C411yescharacteristic
173C2×C3×D5—21no—
174C2×C3×D5—21no—
175C2×C3×D5#10312yes—
176C3×C4×C5—21no—
177C3×C4×C5#13111yescharacteristic
178C3×C4×C5#13111yescharacteristic
179C3×C4×C5C2×SD1611yescharacteristic
180C3×C4×C5C2×Q1611yescharacteristic
181Dic15—41no—
182Dic15—41no—
183C3×Dic5—21no—
184C3×Dic5#10312yes—
185C3×Dic5#10412yes—
186C5×Dic3—41no—
187C5×Dic3—41no—
188C22×C3×C4—51no—
189C22×C3×C4—51no—
190C22×C3×C4—51no—
191C2×Dic6—51no—
192C2×Dic6—101no—
193C2×Dic6C4×D511yescharacteristic
194C3×M16—202no—
195C2×C3×C8—21no—
196C2×C3×C8—101no—
197C3×C42—51no—
198C3×C42—51no—
199C3×C42—51no—
200C3×C42C22×D511yescharacteristic
201#217—101no—
202#217—101no—
203C4⋊Dic3—51no—
204C4⋊Dic3—101no—
205C4⋊Dic3—101no—
206C4⋊Dic3—101no—
207C4⋊Dic3C4×D511yescharacteristic
208Dic3⋊C4—21no—
209Dic3⋊C4—101no—
210Dic3⋊C4—101no—
211Dic3⋊C4—101no—
212C4×Dic3—21no—
213C4×Dic3—101no—
214C2×C3⋊C8—21no—
215C2×C3⋊C8—104no—
216C2×C3⋊C8—101no—
217C22×D5(C2×D3)⋊C411yescharacteristic
218C5×Q8—61no—
219C5×Q8—61no—
220C2×C4×C5—61no—
221C2×C4×C5—61no—
222C2×C4×C5C2×C4×D311yescharacteristic
223C2×C4×C5C2×D1211yescharacteristic
224C2×C4×C5C2×#6711yescharacteristic
225C2×Dic5—61no—
226C2×Dic5—61no—
227C2×Dic5(C2×D3)⋊C411yescharacteristic
228C2×Dic5(C2×D3)⋊C411yescharacteristic
229C2×Dic5(C2×D3)⋊C411yescharacteristic
230C4×D5—21no—
231C4×D5—21no—
232C4×D5—22no—
233C4×D5#21412yes—
234C4×D5#21612yes—
235Dic10—61no—
236Dic10—61no—
237Dic10—122no—
238C5×C8—41no—
239C5×C8—62no—
240#168—41no—
241#168—62no—
242C2×M16—101no—
243C22×C8—301no—
244C4⋊Q8—151no—
245C4⋊Q8—151no—
246#125—301no—
247C22⋊Q8—151no—
248C22⋊Q8—151no—
249C22⋊Q8—301no—
250C4×Q8—31no—
251C4×Q8—151no—
252C4×Q8—301no—
253#117—301no—
254C2×C42—51no—
255C4⋊C8—51no—
256C4⋊C8—101no—
257C4⋊C8D3×D511yescharacteristic
258C4×C8—31no—
259C4×C8—151no—
260C4×C8—301no—
261C2×C3×C5#40811yescharacteristic
262C2×C3×C5C2×#10311yescharacteristic
263C2×C3×C5C2×#10411yescharacteristic
264C3×D5—22no—
265C23×C3—51no—
266C2×C3×C4—51no—
267C2×C3×C4—51no—
268C2×C3×C4—52no—
269C2×C3×C4—52no—
270C2×C3×C4—51no—
271C2×C3×C4—102no—
272C2×C3×C4—101no—
273C2×C3×C4—101no—
274C2×C3×C4C2×C4×D511yescharacteristic
275C2×C3×C4D4×D511yescharacteristic
276C2×C3×C4D4×D511yescharacteristic
277C2×Dic3—21no—
278C2×Dic3—21no—
279C2×Dic3—101no—
280C2×Dic3—101no—
281Dic6—21no—
282Dic6—21no—
283Dic6—101no—
284Dic6—101no—
285Dic6—202no—
286C3×C8—41no—
287C3×C8—201no—
288C3⋊C8—22no—
289C3⋊C8—102no—
290C22×C5C2×(C2×D3)⋊C411yescharacteristic
291C2×D5—21no—
292C2×D5—21no—
293C2×D5#81012yes—
294C4×C5—21no—
295C4×C5—121no—
296C4×C5—121no—
297C4×C5#90711yescharacteristic
298C4×C5#90711yescharacteristic
299C4×C5C2×#21411yescharacteristic
300C4×C5C2×#21611yescharacteristic
301Dic5—21no—
302Dic5—121no—
303Dic5—121no—
304Dic5#81012yes—
305Dic5#82512yes—
306C2×Q8—31no—
307C2×Q8—151no—
308C2×Q8—301no—
309C22×C4—51no—
310C22×C4—51no—
311C22×C4—51no—
312M16—202no—
313C2×C8—21no—
314C2×C8—61no—
315C2×C8—101no—
316C2×C8—304no—
317C2×C8—301no—
318C4⋊C4—31no—
319C4⋊C4—61no—
320C4⋊C4—151no—
321C4⋊C4—301no—
322C4⋊C4—301no—
323C4⋊C4—301no—
324C4⋊C4—301no—
325C4⋊C4—301no—
326C4⋊C4—301no—
327C22⋊C4—301no—
328C22⋊C4—301no—
329C42—51no—
330C42—51no—
331C42—51no—
332C42—61no—
333C42—301no—
334C42C2×D3×D511yescharacteristic
335C3×C5#149311yescharacteristic, complemented, Hall
336C22×C3—52no—
337C22×C3—101no—
338C22×C3—101no—
339C22×C3D5×C22⋊C411yescharacteristic
340C3×C4—21no—
341C3×C4—52no—
342C3×C4—52no—
343C3×C4—101no—
344C3×C4#404711yescharacteristic
345C3×C4#405311yescharacteristic
346C3×C4D5×SD1611yescharacteristic
347C3×C4D5×Q1611yescharacteristic
348Dic3—41no—
349Dic3—41no—
350Dic3—201no—
351Dic3—201no—
352C2×C5C2×#81011yescharacteristic
353C2×C5#512911yescharacteristic
354C2×C5C2×#82511yescharacteristic
355D5—22no—
356C23—51no—
357Q8—61no—
358Q8—61no—
359Q8—301no—
360Q8—301no—
361Q8—602no—
362C2×C4—51no—
363C2×C4—51no—
364C2×C4—52no—
365C2×C4—52no—
366C2×C4—51no—
367C2×C4—61no—
368C2×C4—61no—
369C2×C4—102no—
370C2×C4—101no—
371C2×C4—101no—
372C2×C4—301no—
373C2×C4—301no—
374C2×C4C4×D3×D511yescharacteristic
375C2×C4D5×D1211yescharacteristic
376C2×C4D5×#6711yescharacteristic
377C8—41no—
378C8—62no—
379C8—201no—
380C8—302no—
381C2×C3—102no—
382C2×C3#6501611yescharacteristic
383C2×C3D5×#10311yescharacteristic
384C2×C3D5×#10411yescharacteristic
385C5#7050111yescharacteristic, complemented, Sylow
386C22—52no—
387C22—101no—
388C22—101no—
389C22D5×(C2×D3)⋊C411yescharacteristic
390C4—21no—
391C4—52no—
392C4—52no—
393C4—101no—
394C4—121no—
395C4—121no—
396C4—601no—
397C4—601no—
398C4#9126711yescharacteristic
399C4#9126811yescharacteristic
400C4D5×#21411yescharacteristic
401C4D5×#21611yescharacteristic
402C3#1059903311yescharacteristic, complemented, Sylow
403C2—102no—
404C2D5×#81011yescharacteristic
405C2#1174813611yescharacteristic
406C2D5×#82511yescharacteristic
subgroupG/H
centerC2×C4D5×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C22⋊C4
cosocleC3×C42×C5C23
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1493
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
4. #11746305C2semidirect
5. C5×#4484C2semidirect
6. #11745844C2semidirect
7. #11745842C2semidirect
71. #4484D5semidirect
335. C3×C5#1493semidirect
385. C5#70501semidirect
402. C3#10599033semidirect

Maximal subgroups

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

subgroupindex
#117524972
C3×#651262
C4×D5×C3⋊C82
#117463052
C5×#44842
#117458442
#117458422
#105990333
#705015