Finite Group Databasebeta

← #14282426

Subgroups — #14282426

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
1C3×#65912C211yesmaximal, characteristic
2#11747007C211yesmaximal, characteristic
3C4×D5×C3⋊C8C211yesmaximal, characteristic
4#11746356C211yesmaximal, characteristic, complemented
5C5×#4535C211yesmaximal, characteristic, complemented
6#11745841C211yesmaximal, characteristic, complemented
7#11745840C211yesmaximal, characteristic, complemented
8#10599033—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10C3×#4092C411yescharacteristic
11C3×#4090C411yescharacteristic
12C3×#4043C411yescharacteristic
13C3×#4042—21no—
14C3×#4035—21no—
15C3×#4034C411yescharacteristic
16C3×#4018—21no—
17C3×C42×D5C2211yescharacteristic
18C3×C4×Dic10—21no—
19C3×C4×Dic10C2211yescharacteristic
20C2×#6649—21no—
21C2×D5×C3⋊C8—21no—
22C4⋊(C3⋊#168)C2211yescharacteristic
23C4×C3⋊#168C2211yescharacteristic
24C5×C4⋊(C3⋊C8)C2211yescharacteristic
25C4×C5×C3⋊C8C2211yescharacteristic
26#90982—21no—
27Dic5×C3⋊C8—21no—
28#71826—51nomaximal, Hall
29#65912D311yescharacteristic
30#65126—31no—
31C4×C8×D5—31no—
32C5×Q8⋊C8—31no—
33Q8⋊#168—31no—
34#64704—31no—
35#64676—31no—
36C2×C3×C5×Q8C2×C411yescharacteristic
37C2×C3×C4×D5C2×C411yescharacteristic
38C2×C3×C4×D5D411yescharacteristic
39C2×C3×C4×D5D411yescharacteristic
40C2×C3×Dic10—21no—
41C2×C3×Dic10C2×C411yescharacteristic
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4C2×C411yescharacteristic
44C3×C42×C5—21no—
45C3×C42×C5C2311yescharacteristic
46C2×C3⋊#168—21no—
47C2×C3⋊#168—21no—
48C2×C5×C3⋊C8—21no—
49C2×C5×C3⋊C8—21no—
50C3×#685—21no—
51C3×#685—21no—
52C3×C4⋊Dic5—21no—
53C3×C4⋊Dic5C2×C411yescharacteristic
54C3×#683—21no—
55C3×#683—21no—
56C3×#683—21no—
57C3×#683—21no—
58C3×#683—21no—
59C3×C4×Dic5—21no—
60C3×C4×Dic5C2×C411yescharacteristic
61C3×C4×Dic5D411yescharacteristic
62C3×C4×Dic5D411yescharacteristic
63#6649—42no—
64D5×C3⋊C8—24no—
65C3×#533—51no—
66#4924—51no—
67C2×C4×C3⋊C8—51no—
68#4535—51no—
69#4535—51no—
70#4535—51no—
71#4535D511yescharacteristic, complemented
72C4×C5×Q8C2×D311yescharacteristic
73#4092Dic311yescharacteristic
74#4090Dic311yescharacteristic
75C2×#676—61no—
76C2×C8×D5—61no—
77#4043Dic311yescharacteristic
78#4042—21no—
79#4035—21no—
80#4034Dic311yescharacteristic
81#4018—21no—
82C42×D5C2×D311yescharacteristic
83C4×Dic10—21no—
84C4×Dic10C2×D311yescharacteristic
85C5×C4⋊C8—31no—
86C4×C5×C8—31no—
87#3946—61no—
88C8×Dic5—61no—
89C4⋊#168—31no—
90C4×#168—31no—
91#1493—151noSylow
92C22×C3×D5C22⋊C411yescharacteristic
93C3×C5×Q8—21no—
94C3×C5×Q8—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×Dic5—21no—
101C2×C3×Dic5—21no—
102C2×C3×Dic5C22⋊C411yescharacteristic
103C2×C3×Dic5C22⋊C411yescharacteristic
104C2×C3×Dic5C22⋊C411yescharacteristic
105C3×C4×D5—21no—
106C3×C4×D5—21no—
107C3×C4×D5—22no—
108C3×C4×D5SD1612yes—
109C3×C4×D5Q1612yes—
110C3×Dic10—21no—
111C3×Dic10—21no—
112C3×Dic10—42no—
113C3⋊#168—22no—
114C3⋊#168—41no—
115C5×C3⋊C8—22no—
116C5×C3⋊C8—41no—
117C3×C4⋊Q8—51no—
118C3×C4⋊Q8—51no—
119C3×#125—101no—
120C3×C22⋊Q8—51no—
121C3×C22⋊Q8—51no—
122C3×C22⋊Q8—101no—
123C3×C4×Q8—51no—
124C3×C4×Q8—101no—
125C3×C4×Q8C2×D511yescharacteristic
126C3×#117—101no—
127C2×C3×C42—51no—
128C2×#208—101no—
129C22×C3⋊C8—101no—
130C4⋊(C3⋊C8)—51no—
131C4⋊(C3⋊C8)—101no—
132C4⋊(C3⋊C8)C2×D511yescharacteristic
133C4×C3⋊C8—51no—
134C4×C3⋊C8—101no—
135C4×C3⋊C8C2×D511yescharacteristic
136C2×C5×Q8C2×Dic311yescharacteristic
137C2×C4×D5C2×Dic311yescharacteristic
138C2×C4×D5#6711yescharacteristic
139C2×C4×D5#6711yescharacteristic
140C2×Dic10—21no—
141C2×Dic10C2×Dic311yescharacteristic
142C2×C5×C8—61no—
143C2×C5×C8—61no—
144C5×C4⋊C4—21no—
145C5×C4⋊C4C2×Dic311yescharacteristic
146C42×C5—21no—
147C42×C5C22×D311yescharacteristic
148#685—21no—
149#685—21no—
150C4⋊Dic5—21no—
151C4⋊Dic5C2×Dic311yescharacteristic
152#683—21no—
153#683—21no—
154#683—21no—
155#683—21no—
156#683—21no—
157C4×Dic5—21no—
158C4×Dic5C2×Dic311yescharacteristic
159C4×Dic5#6711yescharacteristic
160C4×Dic5#6711yescharacteristic
161C2×#168—61no—
162C2×#168—61no—
163#676—122no—
164C8×D5—64no—
165#533—51no—
166#423—151no—
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—41no—
178C3×C4×C5—41no—
179C3×C4×C5#13111yescharacteristic
180C3×C4×C5#13111yescharacteristic
181C3×C4×C5C2×SD1611yescharacteristic
182C3×C4×C5C2×Q1611yescharacteristic
183C3×Dic5—21no—
184C3×Dic5—41no—
185C3×Dic5—41no—
186C3×Dic5#10312yes—
187C3×Dic5#10412yes—
188C2×C3×Q8—51no—
189C2×C3×Q8—101no—
190C2×C3×Q8C4×D511yescharacteristic
191C22×C3×C4—51no—
192C22×C3×C4—51no—
193C22×C3×C4—51no—
194C3×C4⋊C4—21no—
195C3×C4⋊C4—51no—
196C3×C4⋊C4—101no—
197C3×C4⋊C4—101no—
198C3×C4⋊C4—101no—
199C3×C4⋊C4—101no—
200C3×C4⋊C4—101no—
201C3×C4⋊C4—101no—
202C3×C4⋊C4C4×D511yescharacteristic
203C3×C22⋊C4—101no—
204C3×C22⋊C4—101no—
205C3×C42—21no—
206C3×C42—51no—
207C3×C42—51no—
208C3×C42—51no—
209C3×C42—101no—
210C3×C42C22×D511yescharacteristic
211#208—202no—
212C2×C3⋊C8—21no—
213C2×C3⋊C8—21no—
214C2×C3⋊C8—104no—
215C2×C3⋊C8—101no—
216C2×C3⋊C8—101no—
217C22×D5#21711yescharacteristic
218C5×Q8—21no—
219C5×Q8—21no—
220C2×C4×C5—21no—
221C2×C4×C5—21no—
222C2×C4×C5C22×Dic311yescharacteristic
223C2×C4×C5C2×#6711yescharacteristic
224C2×C4×C5C2×#6711yescharacteristic
225C2×Dic5—21no—
226C2×Dic5—21no—
227C2×Dic5#21711yescharacteristic
228C2×Dic5#21711yescharacteristic
229C2×Dic5#21711yescharacteristic
230C4×D5—21no—
231C4×D5—21no—
232C4×D5—22no—
233C4×D5#21512yes—
234C4×D5#21612yes—
235Dic10—21no—
236Dic10—21no—
237Dic10—42no—
238C5×C8—62no—
239C5×C8—121no—
240#168—62no—
241#168—121no—
242C2×M16—301no—
243C22×C8—301no—
244C4⋊Q8—51no—
245C4⋊Q8—51no—
246#125—101no—
247C22⋊Q8—51no—
248C22⋊Q8—51no—
249C22⋊Q8—101no—
250C4×Q8—51no—
251C4×Q8—101no—
252C4×Q8D3×D511yescharacteristic
253#117—101no—
254C2×C42—51no—
255C4⋊C8—31no—
256C4⋊C8—151no—
257C4⋊C8—301no—
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—
266C3×Q8—21no—
267C3×Q8—21no—
268C3×Q8—101no—
269C3×Q8—101no—
270C3×Q8—202no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—51no—
274C2×C3×C4—51no—
275C2×C3×C4—52no—
276C2×C3×C4—52no—
277C2×C3×C4—51no—
278C2×C3×C4—102no—
279C2×C3×C4—101no—
280C2×C3×C4—101no—
281C2×C3×C4—101no—
282C2×C3×C4—101no—
283C2×C3×C4C2×C4×D511yescharacteristic
284C2×C3×C4D4×D511yescharacteristic
285C2×C3×C4D4×D511yescharacteristic
286C3⋊C8—22no—
287C3⋊C8—41no—
288C3⋊C8—102no—
289C3⋊C8—201no—
290C22×C5C2×#21711yescharacteristic
291C2×D5—21no—
292C2×D5—21no—
293C2×D5#83512yes—
294C4×C5—21no—
295C4×C5—41no—
296C4×C5—41no—
297C4×C5C2×#21511yescharacteristic
298C4×C5C2×#21611yescharacteristic
299C4×C5#94811yescharacteristic
300C4×C5#94811yescharacteristic
301Dic5—21no—
302Dic5—41no—
303Dic5—41no—
304Dic5#83512yes—
305Dic5#83712yes—
306C2×Q8—51no—
307C2×Q8—101no—
308C2×Q8D5×Dic311yescharacteristic
309C22×C4—51no—
310C22×C4—51no—
311C22×C4—51no—
312M16—602no—
313C2×C8—61no—
314C2×C8—61no—
315C2×C8—304no—
316C2×C8—301no—
317C2×C8—301no—
318C4⋊C4—21no—
319C4⋊C4—51no—
320C4⋊C4—101no—
321C4⋊C4—101no—
322C4⋊C4—101no—
323C4⋊C4—101no—
324C4⋊C4—101no—
325C4⋊C4—101no—
326C4⋊C4D5×Dic311yescharacteristic
327C22⋊C4—101no—
328C22⋊C4—101no—
329C42—21no—
330C42—51no—
331C42—51no—
332C42—51no—
333C42—101no—
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—41no—
342C3×C4—41no—
343C3×C4—52no—
344C3×C4—52no—
345C3×C4—101no—
346C3×C4—201no—
347C3×C4—201no—
348C3×C4#404711yescharacteristic
349C3×C4#405311yescharacteristic
350C3×C4D5×SD1611yescharacteristic
351C3×C4D5×Q1611yescharacteristic
352C2×C5C2×#83511yescharacteristic
353C2×C5#523411yescharacteristic
354C2×C5C2×#83711yescharacteristic
355D5—22no—
356C23—51no—
357Q8—21no—
358Q8—21no—
359Q8—101no—
360Q8—101no—
361Q8—202no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—51no—
365C2×C4—51no—
366C2×C4—52no—
367C2×C4—52no—
368C2×C4—51no—
369C2×C4—102no—
370C2×C4—101no—
371C2×C4—101no—
372C2×C4—101no—
373C2×C4—101no—
374C2×C4C2×D5×Dic311yescharacteristic
375C2×C4D5×#6711yescharacteristic
376C2×C4D5×#6711yescharacteristic
377C8—62no—
378C8—121no—
379C8—302no—
380C8—601no—
381C2×C3—102no—
382C2×C3#6501611yescharacteristic
383C2×C3D5×#10311yescharacteristic
384C2×C3D5×#10411yescharacteristic
385C5#7182611yescharacteristic, complemented, Sylow
386C22—52no—
387C22—101no—
388C22—101no—
389C22D5×#21711yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—52no—
394C4—52no—
395C4—101no—
396C4—201no—
397C4—201no—
398C4#9128311yescharacteristic
399C4#9128411yescharacteristic
400C4D5×#21511yescharacteristic
401C4D5×#21611yescharacteristic
402C3#1059903311yescharacteristic, complemented, Sylow
403C2—102no—
404C2#1174848211yescharacteristic
405C2D5×#83511yescharacteristic
406C2D5×#83711yescharacteristic
subgroupG/H
centerC2×C4D5×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C22⋊C4
cosocleC3×C42×C5C23
hypercenterC4×Q8D3×D5
hypocenterC3×C5#1493
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
4. #11746356C2semidirect
5. C5×#4535C2semidirect
6. #11745841C2semidirect
7. #11745840C2semidirect
71. #4535D5semidirect
335. C3×C5#1493semidirect
385. C5#71826semidirect
402. C3#10599033semidirect

Maximal subgroups

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

subgroupindex
C3×#659122
#117470072
C4×D5×C3⋊C82
#117463562
C5×#45352
#117458412
#117458402
#105990333
#718265