Finite Group Databasebeta

← #14283939

Subgroups — #14283939

Order 1920.

468 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66014C211yesmaximal, characteristic
2#11747003C211yesmaximal, characteristic, complemented
3D5×#803C211yesmaximal, characteristic, complemented
4#11746361C211yesmaximal, characteristic, complemented
5C5×#4540C211yesmaximal, characteristic, complemented
6#11745849C211yesmaximal, characteristic, complemented
7#11745849C211yesmaximal, characteristic, complemented
8#10599134—31nomaximal, Hall
9C3×C5×#124C2211yescharacteristic
10C3×#4092C411yescharacteristic
11C3×Q8×Dic5C411yescharacteristic
12C3×#4084C411yescharacteristic
13C3×D4×Dic5C411yescharacteristic
14C3×#4029—21no—
15C3×#4027—21no—
16C3×#4025—21no—
17C3×#4023—21no—
18C3×C42×D5C2211yescharacteristic
19C3×#4016C2211yescharacteristic
20C2×#6649—21no—
21C2×D5×C3⋊C8—21no—
22#91087C2211yescharacteristic
23#91087C2211yescharacteristic
24C5×#803C2211yescharacteristic
25C5×#803C2211yescharacteristic
26#90952—21no—
27Dic5×C3⋊C8—21no—
28#71746—51nomaximal, Hall
29#66014D311yescharacteristic
30#64996—31no—
31D5×#97—31no—
32C5×#329—31no—
33#64760—31no—
34#64685—31no—
35#64685—31no—
36C2×C3×C5×Q8C2×C411yescharacteristic
37C2×C3×C5×D4C2×C411yescharacteristic
38C2×C3×C22⋊D5—21no—
39C22×C3×Dic5—21no—
40C2×C3×C4×D5C2×C411yescharacteristic
41C2×C3×C4×D5D411yescharacteristic
42C2×C3×C4×D5D411yescharacteristic
43C3×C5×C22⋊C4—21no—
44C3×C5×C22⋊C4—21no—
45C3×C42×C5C2311yescharacteristic
46C2×C3⋊#168—21no—
47C2×C3⋊#168—21no—
48C2×C5×C3⋊C8—21no—
49C2×C5×C3⋊C8—21no—
50C3×C22⋊Dic5—21no—
51C3×C22⋊Dic5—21no—
52C3×#685—21no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5C2×C411yescharacteristic
55C3×C4⋊Dic5C2×C411yescharacteristic
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—24no—
64D5×C3⋊C8—24no—
65C3×#529—51no—
66C4×#208—51no—
67C2×#803—51no—
68#4543—51no—
69#4543—51no—
70#4540—51no—
71#4540D511yescharacteristic, complemented
72C5×#124C2×D311yescharacteristic
73#4092Dic311yescharacteristic
74Q8×Dic5Dic311yescharacteristic
75#4084Dic311yescharacteristic
76D4×Dic5Dic311yescharacteristic
77C2×#676—61no—
78C2×C8×D5—61no—
79#4029—21no—
80#4027—21no—
81#4025—21no—
82#4023—21no—
83C42×D5C2×D311yescharacteristic
84#4016C2×D311yescharacteristic
85C5×#97—31no—
86C5×#97—31no—
87#3947—61no—
88C8×Dic5—61no—
89#3935—31no—
90#3935—31no—
91#1524—151noSylow
92C23×C3×C5—21no—
93C22×C3×D5C22⋊C411yescharacteristic
94C3×C5×Q8—41no—
95C3×C5×D4—41no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C3×C22⋊D5—42no—
101C2×C3×Dic5—21no—
102C2×C3×Dic5—21no—
103C2×C3×Dic5—42no—
104C2×C3×Dic5C22⋊C411yescharacteristic
105C2×C3×Dic5C22⋊C411yescharacteristic
106C2×C3×Dic5C22⋊C411yescharacteristic
107C3×C4×D5—22no—
108C3×C4×D5—22no—
109C3×C4×D5—41no—
110C3⋊#168—22no—
111C3⋊#168—22no—
112C5×C3⋊C8—22no—
113C5×C3⋊C8—22no—
114C3×#126—101no—
115C3×#125—51no—
116C3×#124C2×D511yescharacteristic
117C3×#123—101no—
118C3×C22⋊Q8—51no—
119C3×#121—51no—
120C3×C4×Q8—51no—
121C3×C4×D4—51no—
122C3×C4×D4—101no—
123C3×#117—101no—
124C2×C3×C42—51no—
125C2×#208—101no—
126C22×C3⋊C8—101no—
127#803—51no—
128#803—51no—
129#803—101no—
130#803C2×D511yescharacteristic
131#803C2×D511yescharacteristic
132C4×C3⋊C8—101no—
133C2×C5×Q8C2×Dic311yescharacteristic
134C2×C5×D4C2×Dic311yescharacteristic
135C2×C22⋊D5—21no—
136C22×Dic5—21no—
137C2×C4×D5C2×Dic311yescharacteristic
138C2×C4×D5#6711yescharacteristic
139C2×C4×D5#6711yescharacteristic
140C2×C5×C8—61no—
141C2×C5×C8—61no—
142C5×C22⋊C4—21no—
143C5×C22⋊C4—21no—
144C42×C5C22×D311yescharacteristic
145C22⋊Dic5—21no—
146C22⋊Dic5—21no—
147#685—21no—
148C4⋊Dic5—21no—
149C4⋊Dic5C2×Dic311yescharacteristic
150C4⋊Dic5C2×Dic311yescharacteristic
151#683—21no—
152#683—21no—
153#683—21no—
154C4×Dic5—21no—
155C4×Dic5C2×Dic311yescharacteristic
156C4×Dic5#6711yescharacteristic
157C4×Dic5#6711yescharacteristic
158C2×#168—61no—
159C2×#168—61no—
160#676—64no—
161C8×D5—64no—
162#529—51no—
163C4×M16—151no—
164C2×#97—151no—
165#330—151no—
166#330—151no—
167#329—31no—
168#329—151no—
169C22×C3×C5—41no—
170C22×C3×C5—41no—
171C22×C3×C5—41no—
172C22×C3×C5C2×C22⋊C411yescharacteristic
173C2×C3×D5—21no—
174C2×C3×D5—21no—
175C2×C3×D5#10412yes—
176C3×C4×C5—21no—
177C3×C4×C5—21no—
178C3×C4×C5—21no—
179C3×C4×C5—41no—
180C3×Dic5—21no—
181C3×Dic5—21no—
182C3×Dic5—41no—
183C3×Dic5—41no—
184C3×Dic5#10412yes—
185C2×C3×Q8C4×D511yescharacteristic
186C2×C3×D4—101no—
187C2×C3×D4C4×D511yescharacteristic
188C22×C3×C4—51no—
189C22×C3×C4—51no—
190C22×C3×C4—51no—
191C22×C3×C4—101no—
192C3×C4⋊C4—51no—
193C3×C4⋊C4—51no—
194C3×C4⋊C4—101no—
195C3×C4⋊C4—101no—
196C3×C4⋊C4—101no—
197C3×C4⋊C4—101no—
198C3×C22⋊C4—21no—
199C3×C22⋊C4—21no—
200C3×C22⋊C4—101no—
201C3×C22⋊C4—101no—
202C3×C22⋊C4—101no—
203C3×C42—51no—
204C3×C42—51no—
205C3×C42—51no—
206C3×C42—101no—
207C3×C42C22×D511yescharacteristic
208#208—104no—
209C2×C3⋊C8—21no—
210C2×C3⋊C8—21no—
211C2×C3⋊C8—104no—
212C2×C3⋊C8—101no—
213C2×C3⋊C8—101no—
214C23×C5—21no—
215C22×D5#21711yescharacteristic
216C5×Q8—41no—
217C5×D4—41no—
218C2×C4×C5—21no—
219C2×C4×C5C22×Dic311yescharacteristic
220C2×C4×C5C2×#6711yescharacteristic
221C2×C4×C5C2×#6711yescharacteristic
222C22⋊D5—42no—
223C2×Dic5—21no—
224C2×Dic5—21no—
225C2×Dic5—42no—
226C2×Dic5#21711yescharacteristic
227C2×Dic5#21711yescharacteristic
228C2×Dic5#21711yescharacteristic
229C4×D5—22no—
230C4×D5—22no—
231C4×D5—41no—
232C5×C8—62no—
233C5×C8—62no—
234#168—62no—
235#168—62no—
236C2×M16—301no—
237C22×C8—301no—
238#126—101no—
239#125—51no—
240#124D3×D511yescharacteristic
241#123—101no—
242C22⋊Q8—51no—
243#121—51no—
244C4×Q8—51no—
245C4×D4—51no—
246C4×D4—101no—
247#117—101no—
248C2×C42—51no—
249#97—31no—
250#97—31no—
251#97—151no—
252#97—151no—
253#97—301no—
254C4×C8—301no—
255C2×C3×C5—81no—
256C2×C3×C5#41311yescharacteristic
257C2×C3×C5C2×#10411yescharacteristic
258C2×C3×C5C2×#10411yescharacteristic
259C3×D5—22no—
260C23×C3—21no—
261C23×C3—51no—
262C3×Q8—41no—
263C3×D4—41no—
264C3×D4—202no—
265C2×C3×C4—21no—
266C2×C3×C4—51no—
267C2×C3×C4—51no—
268C2×C3×C4—51no—
269C2×C3×C4—102no—
270C2×C3×C4—102no—
271C2×C3×C4—101no—
272C2×C3×C4—101no—
273C2×C3×C4—201no—
274C2×C3×C4—202no—
275C2×C3×C4C2×C4×D511yescharacteristic
276C2×C3×C4D4×D511yescharacteristic
277C2×C3×C4D4×D511yescharacteristic
278C3⋊C8—22no—
279C3⋊C8—22no—
280C3⋊C8—102no—
281C3⋊C8—102no—
282C22×C5—41no—
283C22×C5—41no—
284C22×C5—41no—
285C22×C5C2×#21711yescharacteristic
286C2×D5—21no—
287C2×D5—21no—
288C2×D5#83712yes—
289C4×C5—21no—
290C4×C5—21no—
291C4×C5—21no—
292C4×C5—41no—
293Dic5—21no—
294Dic5—21no—
295Dic5—41no—
296Dic5—41no—
297Dic5#83712yes—
298C2×Q8D5×Dic311yescharacteristic
299C2×D4—101no—
300C2×D4D5×Dic311yescharacteristic
301C22×C4—51no—
302C22×C4—51no—
303C22×C4—51no—
304C22×C4—101no—
305M16—304no—
306C2×C8—61no—
307C2×C8—61no—
308C2×C8—304no—
309C2×C8—301no—
310C2×C8—301no—
311C4⋊C4—51no—
312C4⋊C4—51no—
313C4⋊C4—101no—
314C4⋊C4—101no—
315C4⋊C4—101no—
316C4⋊C4—101no—
317C22⋊C4—21no—
318C22⋊C4—21no—
319C22⋊C4—101no—
320C22⋊C4—101no—
321C22⋊C4—101no—
322C42—51no—
323C42—51no—
324C42—51no—
325C42—101no—
326C42C2×D3×D511yescharacteristic
327C3×C5#152411yescharacteristic, complemented, Hall
328C22×C3—41no—
329C22×C3—41no—
330C22×C3—41no—
331C22×C3—52no—
332C22×C3—101no—
333C22×C3—101no—
334C22×C3D5×C22⋊C411yescharacteristic
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—41no—
339C3×C4—52no—
340C3×C4—101no—
341C3×C4—101no—
342C3×C4—201no—
343C3×C4—201no—
344C2×C5—81no—
345C2×C5C2×#83711yescharacteristic
346C2×C5C2×#83711yescharacteristic
347C2×C5#523711yescharacteristic
348D5—22no—
349C23—21no—
350C23—51no—
351Q8—41no—
352D4—41no—
353D4—202no—
354C2×C4—21no—
355C2×C4—51no—
356C2×C4—51no—
357C2×C4—51no—
358C2×C4—102no—
359C2×C4—102no—
360C2×C4—101no—
361C2×C4—101no—
362C2×C4—201no—
363C2×C4—202no—
364C2×C4C2×D5×Dic311yescharacteristic
365C2×C4D5×#6711yescharacteristic
366C2×C4D5×#6711yescharacteristic
367C8—62no—
368C8—62no—
369C8—302no—
370C8—302no—
371C2×C3—81no—
372C2×C3—102no—
373C2×C3#6503411yescharacteristic
374C2×C3D5×#10411yescharacteristic
375C2×C3D5×#10411yescharacteristic
376C5#7174611yescharacteristic, complemented, Sylow
377C22—41no—
378C22—41no—
379C22—41no—
380C22—52no—
381C22—101no—
382C22—101no—
383C22D5×#21711yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—41no—
388C4—52no—
389C4—101no—
390C4—101no—
391C4—201no—
392C4—201no—
393C3#1059913411yescharacteristic, complemented, Sylow
394C2—81no—
395C2—102no—
396C2#1174912311yescharacteristic
397C2D5×#83711yescharacteristic
398C2D5×#83711yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#4084C4
cosocleC3×C42×C5C23
hypercenter#124D3×D5
hypocenterC3×C5#1524
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #11747003C2semidirect
3. D5×#803C2semidirect
4. #11746361C2semidirect
5. C5×#4540C2semidirect
6. #11745849C2semidirect
7. #11745849C2semidirect
71. #4540D5semidirect
327. C3×C5#1524semidirect
376. C5#71746semidirect
393. C3#10599134semidirect

Maximal subgroups

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

subgroupindex
C3×#660142
#117470032
D5×#8032
#117463612
C5×#45402
#117458492
#105991343
#717465