Finite Group Databasebeta

← #14282935

Subgroups — #14282935

Order 1920.

480 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754176C211yesmaximal, characteristic
2C5×#4649C211yesmaximal, characteristic
3#11748329C211yesmaximal, characteristic
4#11746273C211yesmaximal, characteristic
5C3×#64672C211yesmaximal, characteristic
6#11745965C211yesmaximal, characteristic
7#11745961C211yesmaximal, characteristic
8#10600264—31nomaximal, Hall
9#91813C2211yescharacteristic
10C2×C5×Dic3⋊C4—21no—
11C2×C4×C5×Dic3—21no—
12C2×C4×C5×Dic3C2211yescharacteristic
13C3×#4070C2211yescharacteristic
14#91575—21no—
15#91529—21no—
16#91469C411yescharacteristic, complemented
17#91389C411yescharacteristic, complemented
18#91379—21no—
19#91340C411yescharacteristic, complemented
20Dic3×Dic10C411yescharacteristic, complemented
21#91324—21no—
22C3×C5×#95C2211yescharacteristic
23#91114C2211yescharacteristic
24C5×C3⋊#95C2211yescharacteristic
25C3×C22⋊#168C2211yescharacteristic
26Dic3⋊#168—21no—
27Dic3×#168—21no—
28#68309—51nomaximal, Hall
29#65804—31no—
30C4×C5×C4⋊C4—31no—
31#65214—31no—
32#64672—31no—
33#64672—31no—
34#64672—31no—
35#64672D311yescharacteristic
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C2×Dic30C2×C411yescharacteristic
39C22×C5×Dic3—21no—
40C22×C5×Dic3D411yescharacteristic
41C22×C5×Dic3D411yescharacteristic
42C2×C3×Dic10C2×C411yescharacteristic
43C2×#1204—21no—
44#6719—21no—
45C4⋊Dic15C2×C411yescharacteristic
46#6712—21no—
47C2×C3⋊#168—21no—
48C5×Dic3⋊C4—24no—
49C4×C5×Dic3—42no—
50C4×C5×Dic3C2×C411yescharacteristic
51C4×C5×Dic3C2×C411yescharacteristic
52C4×C5×Dic3D411yescharacteristic
53C4×C5×Dic3D411yescharacteristic
54C3×C22⋊Dic5—21no—
55C3×C4⋊Dic5C2×C411yescharacteristic
56C3×#683—21no—
57C2×C3×#168—21no—
58Dic3⋊Dic5—21no—
59Dic3⋊Dic5—21no—
60Dic3⋊Dic5—21no—
61#6669—21no—
62#6668—21no—
63Dic3×Dic5—21no—
64Dic3×Dic5—21no—
65#5622—51no—
66#4718—51no—
67#4649D511yescharacteristic
68C3×#328—51no—
69#4538—51no—
70#4467—51no—
71#4452—51no—
72C2×C5×C4⋊C4—61no—
73C2×C42×C5—31no—
74C2×C42×C5—61no—
75#4072—61no—
76#4070—31no—
77#4070—61no—
78#4070C2×D311yescharacteristic
79#4016—61no—
80#4015—31no—
81#4015—31no—
82C4×Dic10—31no—
83C4×Dic10—31no—
84C4×Dic10—61no—
85C5×#95—31no—
86C5×#95C2×D311yescharacteristic
87C22⋊#168—31no—
88C22⋊#168C2×D311yescharacteristic
89C4⋊#168—61no—
90C4×#168—61no—
91#1503—151noSylow
92C23×C3×C5C2×D411yescharacteristic
93C2×C3×C4×C5—22no—
94C2×C3×C4×C5—41no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×Dic15—21no—
100C2×Dic15—21no—
101Dic30—41no—
102C2×C5×Dic3—22no—
103C2×C5×Dic3—22no—
104C2×C5×Dic3—41no—
105C2×C5×Dic3—41no—
106C2×C5×Dic3C22⋊C411yescharacteristic
107C2×C5×Dic3C22⋊C411yescharacteristic
108C2×C5×Dic3C22⋊C411yescharacteristic
109C2×C5×Dic3C22⋊C411yescharacteristic
110C2×C5×Dic3SD1612yes—
111C2×C5×Dic3Q1612yes—
112C2×C3×Dic5—21no—
113C2×C3×Dic5—21no—
114C3×Dic10—41no—
115#1204—42no—
116C3⋊#168—41no—
117C3×#168—41no—
118C3×C22⋊Q8—51no—
119Q8×Dic3—51no—
120#944—51no—
121#924—51no—
122C2×Dic3⋊C4—21no—
123C2×C4×Dic3—21no—
124C2×C4×Dic3C2×D511yescharacteristic
125#889—101no—
126#888—51no—
127#887—51no—
128#887—101no—
129#878—101no—
130#877—101no—
131C3×C22⋊C8—51no—
132C3×#95C2×D511yescharacteristic
133C3⋊#95C2×D511yescharacteristic
134#830—51no—
135Dic3⋊C8—101no—
136C8×Dic3—101no—
137C22×C4×C5—21no—
138C22×C4×C5—31no—
139C22×C4×C5—31no—
140C22×C4×C5—61no—
141C22×C4×C5C22×D311yescharacteristic
142C2×Dic10—31no—
143C2×Dic10—61no—
144C2×Dic10C4×D311yescharacteristic
145C5×C4⋊C4—64no—
146C42×C5—31no—
147C42×C5—31no—
148C42×C5—31no—
149C42×C5—31no—
150C42×C5—122no—
151C22⋊Dic5—21no—
152C22⋊Dic5—61no—
153C4⋊Dic5—31no—
154C4⋊Dic5—61no—
155C4⋊Dic5—61no—
156C4⋊Dic5—61no—
157C4⋊Dic5C4×D311yescharacteristic
158#683—21no—
159#683—61no—
160#683—61no—
161#683—61no—
162C4×Dic5—61no—
163C4×Dic5—61no—
164C2×#168—21no—
165C2×#168—61no—
166#533—151no—
167#431—151no—
168C4×C4⋊C4—31no—
169#328—51no—
170#328—151no—
171#328—151no—
172#328—151no—
173C22×C3×C5—21no—
174C22×C3×C5—21no—
175C22×C3×C5C2×C22⋊C411yescharacteristic
176C22×C3×C5C2×SD1611yescharacteristic
177C22×C3×C5C2×Q1611yescharacteristic
178C3×C4×C5—21no—
179C3×C4×C5—21no—
180C3×C4×C5—42no—
181Dic15—41no—
182Dic15—41no—
183C3×Dic5—41no—
184C3×Dic5—41no—
185C5×Dic3—21no—
186C5×Dic3—42no—
187C5×Dic3#10312yes—
188C5×Dic3#10312yes—
189C5×Dic3#10412yes—
190C2×C3×Q8—51no—
191C22×C3×C4—21no—
192C22×C3×C4C22×D511yescharacteristic
193C22×Dic3—21no—
194C22×Dic3C22⋊D511yescharacteristic
195C22×Dic3C22⋊D511yescharacteristic
196C2×Dic6—51no—
197C2×Dic6—101no—
198C2×C3×C8—101no—
199C3×C4⋊C4—51no—
200C3×C4⋊C4—101no—
201C3×C22⋊C4—101no—
202#217—101no—
203C4⋊Dic3—51no—
204C4⋊Dic3—101no—
205Dic3⋊C4—24no—
206Dic3⋊C4—101no—
207Dic3⋊C4—101no—
208Dic3⋊C4—101no—
209Dic3⋊C4—101no—
210Dic3⋊C4—101no—
211C4×Dic3—42no—
212C4×Dic3—101no—
213C4×Dic3—101no—
214C4×Dic3C4×D511yescharacteristic
215C4×Dic3C4×D511yescharacteristic
216C4×Dic3D2011yescharacteristic
217C4×Dic3D2011yescharacteristic
218C2×C3⋊C8—101no—
219C23×C5D3×D411yescharacteristic
220C2×C4×C5—22no—
221C2×C4×C5—31no—
222C2×C4×C5—31no—
223C2×C4×C5—31no—
224C2×C4×C5—32no—
225C2×C4×C5—32no—
226C2×C4×C5—31no—
227C2×C4×C5—41no—
228C2×C4×C5—41no—
229C2×C4×C5—41no—
230C2×C4×C5—62no—
231C2×C4×C5—62no—
232C2×C4×C5—121no—
233C2×C4×C5—121no—
234C2×C4×C5C2×C4×D311yescharacteristic
235C2×C4×C5D3×D411yescharacteristic
236C2×Dic5—21no—
237C2×Dic5—21no—
238C2×Dic5—61no—
239C2×Dic5—61no—
240Dic10—41no—
241Dic10—122no—
242Dic10—121no—
243#168—41no—
244#168—121no—
245C4⋊Q8—151no—
246C4⋊Q8—151no—
247#125—301no—
248C22⋊Q8—51no—
249C22⋊Q8—151no—
250C22⋊Q8—301no—
251C4×Q8—151no—
252C4×Q8—151no—
253C4×Q8—301no—
254#117—301no—
255C2×C4⋊C4—61no—
256C2×C42—31no—
257C2×C42—61no—
258C4⋊C8—301no—
259C22⋊C8—51no—
260C22⋊C8—151no—
261C4×C8—301no—
262#95—31no—
263#95D3×D511yescharacteristic
264C2×C3×C5—21no—
265C2×C3×C5—21no—
266C2×C3×C5#41011yescharacteristic
267C2×C3×C5C2×#10311yescharacteristic
268C2×C3×C5C2×#10411yescharacteristic
269C23×C3C2×C22⋊D511yescharacteristic
270C3×Q8—201no—
271C2×C3×C4—22no—
272C2×C3×C4—41no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—101no—
276C2×C3×C4—101no—
277C2×C3×C4C2×C4×D511yescharacteristic
278C2×C3×C4C2×D2011yescharacteristic
279C2×Dic3—22no—
280C2×Dic3—22no—
281C2×Dic3—41no—
282C2×Dic3—41no—
283C2×Dic3—101no—
284C2×Dic3—101no—
285C2×Dic3#68511yescharacteristic
286C2×Dic3#68511yescharacteristic
287C2×Dic3#68511yescharacteristic
288C2×Dic3#68511yescharacteristic
289C2×Dic3#68712yes—
290C2×Dic3#68912yes—
291Dic6—202no—
292Dic6—201no—
293C3×C8—201no—
294C3⋊C8—201no—
295C22×C5—21no—
296C22×C5—21no—
297C22×C5D3×C22⋊C411yescharacteristic
298C22×C5D3×SD1611yescharacteristic
299C22×C5D3×Q1611yescharacteristic
300C4×C5—21no—
301C4×C5—21no—
302C4×C5—32no—
303C4×C5—32no—
304C4×C5—32no—
305C4×C5—42no—
306C4×C5—61no—
307C4×C5—122no—
308Dic5—41no—
309Dic5—41no—
310Dic5—121no—
311Dic5—121no—
312C2×Q8—51no—
313C2×Q8—151no—
314C2×Q8—301no—
315C22×C4—21no—
316C22×C4—31no—
317C22×C4—31no—
318C22×C4—61no—
319C22×C4C2×D3×D511yescharacteristic
320C2×C8—101no—
321C2×C8—301no—
322C4⋊C4—51no—
323C4⋊C4—64no—
324C4⋊C4—101no—
325C4⋊C4—151no—
326C4⋊C4—301no—
327C4⋊C4—301no—
328C4⋊C4—301no—
329C4⋊C4—301no—
330C4⋊C4—301no—
331C4⋊C4—301no—
332C22⋊C4—101no—
333C22⋊C4—301no—
334C42—31no—
335C42—31no—
336C42—31no—
337C42—31no—
338C42—122no—
339C42—301no—
340C42—301no—
341C3×C5#150311yescharacteristic, complemented, Hall
342C22×C3—21no—
343C22×C3—21no—
344C22×C3C2×#68511yescharacteristic
345C22×C3C2×#68711yescharacteristic
346C22×C3C2×#68911yescharacteristic
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—42no—
350C3×C4—201no—
351C3×C4—201no—
352Dic3—21no—
353Dic3—42no—
354Dic3—201no—
355Dic3—201no—
356Dic3#393712yes—
357Dic3#394212yes—
358Dic3#394212yes—
359C2×C5—21no—
360C2×C5—21no—
361C2×C5#474011yescharacteristic
362C2×C5D3×#10311yescharacteristic
363C2×C5D3×#10411yescharacteristic
364C23D3×C22⋊D511yescharacteristic
365Q8—201no—
366Q8—601no—
367Q8—602no—
368C2×C4—22no—
369C2×C4—31no—
370C2×C4—31no—
371C2×C4—31no—
372C2×C4—32no—
373C2×C4—32no—
374C2×C4—31no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—62no—
379C2×C4—62no—
380C2×C4—101no—
381C2×C4—101no—
382C2×C4—121no—
383C2×C4—121no—
384C2×C4—301no—
385C2×C4—301no—
386C2×C4C4×D3×D511yescharacteristic
387C2×C4D3×D2011yescharacteristic
388C8—201no—
389C8—601no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3C2×#393711yescharacteristic
393C2×C3C2×#394211yescharacteristic
394C2×C3#6529511yescharacteristic
395C5#6830911yescharacteristic, complemented, Sylow
396C22—21no—
397C22—21no—
398C22D3×#68511yescharacteristic
399C22D3×#68711yescharacteristic
400C22D3×#68911yescharacteristic
401C4—21no—
402C4—21no—
403C4—32no—
404C4—32no—
405C4—32no—
406C4—42no—
407C4—61no—
408C4—122no—
409C4—201no—
410C4—201no—
411C4—601no—
412C4—601no—
413C3#1060026411yescharacteristic, complemented, Sylow
414C2—21no—
415C2—21no—
416C2D3×#393711yescharacteristic
417C2#1174713011yescharacteristic
418C2D3×#394211yescharacteristic
subgroupG/H
centerC22D3×#685
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#95C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C2×D4
cosocleC22×C3×C4×C5C23
hypercenter#95D3×D5
hypocenterC3×C5#1503
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
16. #91469C4semidirect
17. #91389C4semidirect
19. #91340C4semidirect
20. Dic3×Dic10C4semidirect
341. C3×C5#1503semidirect
395. C5#68309semidirect
413. C3#10600264semidirect

Maximal subgroups

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

subgroupindex
#117541762
C5×#46492
#117483292
#117462732
C3×#646722
#117459652
#117459612
#106002643
#683095