Finite Group Databasebeta

← #14284416

Subgroups — #14284416

Order 1920.

400 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66014C211yesmaximal, characteristic
2#11746870C211yesmaximal, characteristic, complemented
3#11746870C211yesmaximal, characteristic, complemented
4#11746361C211yesmaximal, characteristic, complemented
5C5×#4540C211yesmaximal, characteristic, complemented
6#11745849C211yesmaximal, characteristic, complemented
7#11745849C211yesmaximal, characteristic, complemented
8#10599141—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
20#91087C2211yescharacteristic
21#91087C2211yescharacteristic
22C5×#803C2211yescharacteristic
23C5×#803C2211yescharacteristic
24#90982—21no—
25#90982—21no—
26#90955—21no—
27#90955—21no—
28#71749—51nomaximal, Hall
29#66014D311yescharacteristic
30#64994—31no—
31#64994—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
63C3×#529—51no—
64#4926—51no—
65#4926—51no—
66#4543—51no—
67#4543—51no—
68#4540—51no—
69#4540D511yescharacteristic, complemented
70C5×#124C2×D311yescharacteristic
71#4092Dic311yescharacteristic
72Q8×Dic5Dic311yescharacteristic
73#4084Dic311yescharacteristic
74D4×Dic5Dic311yescharacteristic
75#4029—21no—
76#4027—21no—
77#4025—21no—
78#4023—21no—
79C42×D5C2×D311yescharacteristic
80#4016C2×D311yescharacteristic
81C5×#97—31no—
82C5×#97—31no—
83#3952—61no—
84#3952—61no—
85#3946—61no—
86#3946—61no—
87#3935—31no—
88#3935—31no—
89#1535—151noSylow
90C23×C3×C5—21no—
91C22×C3×D5C22⋊C411yescharacteristic
92C3×C5×Q8—41no—
93C3×C5×D4—41no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5C22×C411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C3×C22⋊D5—42no—
99C2×C3×Dic5—21no—
100C2×C3×Dic5—21no—
101C2×C3×Dic5—42no—
102C2×C3×Dic5C22⋊C411yescharacteristic
103C2×C3×Dic5C22⋊C411yescharacteristic
104C2×C3×Dic5C22⋊C411yescharacteristic
105C3×C4×D5—41no—
106C3×C4×D5—41no—
107C3×C4×D5—41no—
108C3⋊#168—41no—
109C3⋊#168—41no—
110C5×C3⋊C8—41no—
111C5×C3⋊C8—41no—
112C3×#126—101no—
113C3×#125—51no—
114C3×#124C2×D511yescharacteristic
115C3×#123—101no—
116C3×C22⋊Q8—51no—
117C3×#121—51no—
118C3×C4×Q8—51no—
119C3×C4×D4—51no—
120C3×C4×D4—101no—
121C3×#117—101no—
122C2×C3×C42—51no—
123#830—101no—
124#830—101no—
125C4⋊(C3⋊C8)—101no—
126C4⋊(C3⋊C8)—101no—
127#803—51no—
128#803—51no—
129#803C2×D511yescharacteristic
130#803C2×D511yescharacteristic
131C2×C5×Q8C2×Dic311yescharacteristic
132C2×C5×D4C2×Dic311yescharacteristic
133C2×C22⋊D5—21no—
134C22×Dic5—21no—
135C2×C4×D5C2×Dic311yescharacteristic
136C2×C4×D5#6711yescharacteristic
137C2×C4×D5#6711yescharacteristic
138C2×C5×C8—61no—
139C2×C5×C8—61no—
140C5×C22⋊C4—21no—
141C5×C22⋊C4—21no—
142C42×C5C22×D311yescharacteristic
143C22⋊Dic5—21no—
144C22⋊Dic5—21no—
145#685—21no—
146C4⋊Dic5—21no—
147C4⋊Dic5C2×Dic311yescharacteristic
148C4⋊Dic5C2×Dic311yescharacteristic
149#683—21no—
150#683—21no—
151#683—21no—
152C4×Dic5—21no—
153C4×Dic5C2×Dic311yescharacteristic
154C4×Dic5#6711yescharacteristic
155C4×Dic5#6711yescharacteristic
156C2×#168—61no—
157C2×#168—61no—
158#529—51no—
159#432—151no—
160#432—151no—
161#330—151no—
162#330—151no—
163#329—31no—
164#329—151no—
165C22×C3×C5—41no—
166C22×C3×C5—41no—
167C22×C3×C5—41no—
168C22×C3×C5C2×C22⋊C411yescharacteristic
169C2×C3×D5—21no—
170C2×C3×D5—21no—
171C2×C3×D5—21no—
172C3×C4×C5—21no—
173C3×C4×C5—21no—
174C3×C4×C5—21no—
175C3×C4×C5—41no—
176C3×Dic5—21no—
177C3×Dic5—21no—
178C3×Dic5—21no—
179C3×Dic5—41no—
180C3×Dic5—41no—
181C2×C3×Q8C4×D511yescharacteristic
182C2×C3×D4—101no—
183C2×C3×D4C4×D511yescharacteristic
184C22×C3×C4—51no—
185C22×C3×C4—51no—
186C22×C3×C4—51no—
187C22×C3×C4—101no—
188C3×C4⋊C4—51no—
189C3×C4⋊C4—51no—
190C3×C4⋊C4—101no—
191C3×C4⋊C4—101no—
192C3×C4⋊C4—101no—
193C3×C4⋊C4—101no—
194C3×C22⋊C4—21no—
195C3×C22⋊C4—21no—
196C3×C22⋊C4—101no—
197C3×C22⋊C4—101no—
198C3×C22⋊C4—101no—
199C3×C42—51no—
200C3×C42—51no—
201C3×C42—51no—
202C3×C42—101no—
203C3×C42C22×D511yescharacteristic
204C2×C3⋊C8—21no—
205C2×C3⋊C8—21no—
206C2×C3⋊C8—101no—
207C2×C3⋊C8—101no—
208C23×C5—21no—
209C22×D5#21711yescharacteristic
210C5×Q8—41no—
211C5×D4—41no—
212C2×C4×C5—21no—
213C2×C4×C5C22×Dic311yescharacteristic
214C2×C4×C5C2×#6711yescharacteristic
215C2×C4×C5C2×#6711yescharacteristic
216C22⋊D5—42no—
217C2×Dic5—21no—
218C2×Dic5—21no—
219C2×Dic5—42no—
220C2×Dic5#21711yescharacteristic
221C2×Dic5#21711yescharacteristic
222C2×Dic5#21711yescharacteristic
223C4×D5—41no—
224C4×D5—41no—
225C4×D5—41no—
226C5×C8—121no—
227C5×C8—121no—
228#168—121no—
229#168—121no—
230#126—101no—
231#125—51no—
232#124D3×D511yescharacteristic
233#123—101no—
234C22⋊Q8—51no—
235#121—51no—
236C4×Q8—51no—
237C4×D4—51no—
238C4×D4—101no—
239#117—101no—
240C2×C42—51no—
241C4⋊C8—301no—
242C4⋊C8—301no—
243C22⋊C8—301no—
244C22⋊C8—301no—
245#97—31no—
246#97—31no—
247#97—151no—
248#97—151no—
249C2×C3×C5—81no—
250C2×C3×C5#41311yescharacteristic
251C2×C3×C5#42111yescharacteristic
252C2×C3×C5#42111yescharacteristic
253C3×D5—41no—
254C23×C3—21no—
255C23×C3—51no—
256C3×Q8—41no—
257C3×D4—41no—
258C3×D4—202no—
259C2×C3×C4—21no—
260C2×C3×C4—51no—
261C2×C3×C4—51no—
262C2×C3×C4—51no—
263C2×C3×C4—101no—
264C2×C3×C4—101no—
265C2×C3×C4—201no—
266C2×C3×C4—201no—
267C2×C3×C4—201no—
268C2×C3×C4—202no—
269C2×C3×C4C2×C4×D511yescharacteristic
270C2×C3×C4D4×D511yescharacteristic
271C2×C3×C4D4×D511yescharacteristic
272C3⋊C8—41no—
273C3⋊C8—41no—
274C3⋊C8—201no—
275C3⋊C8—201no—
276C22×C5—41no—
277C22×C5—41no—
278C22×C5—41no—
279C22×C5C2×#21711yescharacteristic
280C2×D5—21no—
281C2×D5—21no—
282C2×D5—21no—
283C4×C5—21no—
284C4×C5—21no—
285C4×C5—21no—
286C4×C5—41no—
287Dic5—21no—
288Dic5—21no—
289Dic5—21no—
290Dic5—41no—
291Dic5—41no—
292C2×Q8D5×Dic311yescharacteristic
293C2×D4—101no—
294C2×D4D5×Dic311yescharacteristic
295C22×C4—51no—
296C22×C4—51no—
297C22×C4—51no—
298C22×C4—101no—
299C2×C8—61no—
300C2×C8—61no—
301C2×C8—301no—
302C2×C8—301no—
303C4⋊C4—51no—
304C4⋊C4—51no—
305C4⋊C4—101no—
306C4⋊C4—101no—
307C4⋊C4—101no—
308C4⋊C4—101no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—101no—
312C22⋊C4—101no—
313C22⋊C4—101no—
314C42—51no—
315C42—51no—
316C42—51no—
317C42—101no—
318C42C2×D3×D511yescharacteristic
319C3×C5#153511yescharacteristic, complemented, Hall
320C22×C3—41no—
321C22×C3—41no—
322C22×C3—41no—
323C22×C3—101no—
324C22×C3—101no—
325C22×C3—101no—
326C22×C3D5×C22⋊C411yescharacteristic
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—41no—
331C3×C4—101no—
332C3×C4—101no—
333C3×C4—101no—
334C3×C4—201no—
335C3×C4—201no—
336C2×C5—81no—
337C2×C5#523611yescharacteristic
338C2×C5#523611yescharacteristic
339C2×C5#523711yescharacteristic
340D5—41no—
341C23—21no—
342C23—51no—
343Q8—41no—
344D4—41no—
345D4—202no—
346C2×C4—21no—
347C2×C4—51no—
348C2×C4—51no—
349C2×C4—51no—
350C2×C4—101no—
351C2×C4—101no—
352C2×C4—201no—
353C2×C4—201no—
354C2×C4—201no—
355C2×C4—202no—
356C2×C4C2×D5×Dic311yescharacteristic
357C2×C4D5×#6711yescharacteristic
358C2×C4D5×#6711yescharacteristic
359C8—121no—
360C8—121no—
361C8—601no—
362C8—601no—
363C2×C3—81no—
364C2×C3—201no—
365C2×C3#6503411yescharacteristic
366C2×C3#6511011yescharacteristic
367C2×C3#6511011yescharacteristic
368C5#7174911yescharacteristic, complemented, Sylow
369C22—41no—
370C22—41no—
371C22—41no—
372C22—101no—
373C22—101no—
374C22—101no—
375C22D5×#21711yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—101no—
381C4—101no—
382C4—101no—
383C4—201no—
384C4—201no—
385C3#1059914111yescharacteristic, complemented, Sylow
386C2—81no—
387C2—201no—
388C2#1174912311yescharacteristic
389C2#1174942711yescharacteristic
390C2#1174942711yescharacteristic
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#1535
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. #11746870C2semidirect
3. #11746870C2semidirect
4. #11746361C2semidirect
5. C5×#4540C2semidirect
6. #11745849C2semidirect
7. #11745849C2semidirect
69. #4540D5semidirect
319. C3×C5#1535semidirect
368. C5#71749semidirect
385. C3#10599141semidirect

Maximal subgroups

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

subgroupindex
C3×#660142
#117468702
#117463612
C5×#45402
#117458492
#105991413
#717495