Finite Group Databasebeta

← #14284424

Subgroups — #14284424

Order 1920.

400 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65813C211yesmaximal, characteristic
2#11751027C211yesmaximal, characteristic, complemented
3C5×#4926C211yesmaximal, characteristic, complemented
4#11745849C212yesmaximal, complemented
5#11745846C212yesmaximal, complemented
6#10601603—31nomaximal, Hall
7C2×C3×C42×C5C2211yescharacteristic
8C3×#4076C411yescharacteristic
9C3×#4075—21no—
10C3×C4×C22⋊D5—21no—
11C3×#4070C411yescharacteristic
12C3×#4022—21no—
13C3×#4021C2211yescharacteristic
14C3×C4×D20C411yescharacteristic
15C3×#4018—21no—
16C3×#4016C2211yescharacteristic
17C3×C4×Dic10C411yescharacteristic
18#91114—21no—
19C4⋊(C3⋊#168)—21no—
20#91087C2212yes—
21C5×#830—21no—
22C5×C4⋊(C3⋊C8)—21no—
23C5×#803C2212yes—
24#71749—51nomaximal, Hall
25#65813D311yescharacteristic
26C5×#432—31no—
27#65215—31no—
28#64685—32no—
29#64684—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5D411yescharacteristic
33C2×C3×C22⋊D5—21no—
34C2×C3×D20C2×C411yescharacteristic
35C2×C3×C4×D5—21no—
36C2×C3×Dic10C2×C411yescharacteristic
37C3×C42×C5C2×C411yescharacteristic
38C3×C42×C5D411yescharacteristic
39C3×C42×C5D411yescharacteristic
40C3×C42×C5C2311yescharacteristic
41C2×C3⋊#168—22no—
42C2×C5×C3⋊C8—22no—
43C3×C22⋊Dic5—21no—
44C3×#685—21no—
45C3×#685—21no—
46C3×#685—21no—
47C3×#685—21no—
48C3×C4⋊Dic5C2×C411yescharacteristic
49C3×C4⋊Dic5C2×C411yescharacteristic
50C3×#683—21no—
51C3×#683—21no—
52C3×#683—21no—
53C3×#683—21no—
54C3×C4×Dic5—21no—
55C3×#529—51no—
56#4926—51no—
57#4926D511yescharacteristic, complemented
58#4543—52no—
59#4540—52no—
60C2×C42×C5C2×D311yescharacteristic
61#4076Dic311yescharacteristic
62#4075—21no—
63C4×C22⋊D5—21no—
64#4070Dic311yescharacteristic
65#4022—21no—
66#4021C2×D311yescharacteristic
67C4×D20Dic311yescharacteristic
68#4018—21no—
69#4016C2×D311yescharacteristic
70C4×Dic10Dic311yescharacteristic
71C5×C4⋊C8—61no—
72C5×C22⋊C8—61no—
73C5×#97—32no—
74C22⋊#168—61no—
75C4⋊#168—61no—
76#3935—32no—
77#1535—151noSylow
78C23×C3×C5C22⋊C411yescharacteristic
79C22×C3×D5—21no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5—41no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5C22⋊C411yescharacteristic
84C2×C3×C4×C5C22⋊C411yescharacteristic
85C2×C3×C4×C5C22⋊C411yescharacteristic
86C2×C3×C4×C5C22×C411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C3×C22⋊D5—42no—
90C2×C3×Dic5—21no—
91C2×C3×Dic5—21no—
92C2×C3×Dic5—21no—
93C3×D20—41no—
94C3×C4×D5—42no—
95C3×Dic10—41no—
96C3⋊#168—42no—
97C5×C3⋊C8—42no—
98C3×#126—101no—
99C3×#125—51no—
100C3×#124—51no—
101C3×#123—101no—
102C3×C22⋊Q8—51no—
103C3×#121—51no—
104C3×C4×Q8—51no—
105C3×C4×D4—51no—
106C3×C4×D4—101no—
107C3×#117—101no—
108C2×C3×C42C2×D511yescharacteristic
109#830—21no—
110#830—101no—
111C4⋊(C3⋊C8)—21no—
112C4⋊(C3⋊C8)—101no—
113#803—52no—
114#803C2×D512yes—
115C22×C4×C5C2×Dic311yescharacteristic
116C22×C4×C5#6711yescharacteristic
117C22×C4×C5#6711yescharacteristic
118C2×C22⋊D5—21no—
119C2×D20C2×Dic311yescharacteristic
120C2×C4×D5—21no—
121C2×Dic10C2×Dic311yescharacteristic
122C2×C5×C8—62no—
123C42×C5C2×Dic311yescharacteristic
124C42×C5#6711yescharacteristic
125C42×C5#6711yescharacteristic
126C42×C5C22×D311yescharacteristic
127C22⋊Dic5—21no—
128#685—21no—
129#685—21no—
130#685—21no—
131#685—21no—
132C4⋊Dic5C2×Dic311yescharacteristic
133C4⋊Dic5C2×Dic311yescharacteristic
134#683—21no—
135#683—21no—
136#683—21no—
137#683—21no—
138C4×Dic5—21no—
139C2×#168—62no—
140#529—51no—
141#432—31no—
142#432—151no—
143#330—152no—
144#329—152no—
145C22×C3×C5—21no—
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5C2×C22⋊C411yescharacteristic
149C2×C3×D5—41no—
150C2×C3×D5—41no—
151C2×C3×D5—41no—
152C3×C4×C5—21no—
153C3×C4×C5—21no—
154C3×C4×C5—21no—
155C3×C4×C5—21no—
156C3×C4×C5—21no—
157C3×C4×C5—21no—
158C3×Dic5—41no—
159C3×Dic5—41no—
160C3×Dic5—41no—
161C2×C3×Q8—51no—
162C2×C3×D4—51no—
163C2×C3×D4—101no—
164C22×C3×C4—101no—
165C22×C3×C4C4×D511yescharacteristic
166C22×C3×C4D2011yescharacteristic
167C22×C3×C4C22⋊D511yescharacteristic
168C3×C4⋊C4—51no—
169C3×C4⋊C4—51no—
170C3×C4⋊C4—101no—
171C3×C4⋊C4—101no—
172C3×C4⋊C4—101no—
173C3×C4⋊C4—101no—
174C3×C22⋊C4—101no—
175C3×C22⋊C4—101no—
176C3×C22⋊C4—101no—
177C3×C22⋊C4—101no—
178C3×C22⋊C4—101no—
179C3×C42—101no—
180C3×C42C4×D511yescharacteristic
181C3×C42D2011yescharacteristic
182C3×C42C22⋊D511yescharacteristic
183C3×C42C22×D511yescharacteristic
184C2×C3⋊C8—22no—
185C2×C3⋊C8—102no—
186C23×C5#21711yescharacteristic
187C22×D5—21no—
188C2×C4×C5—41no—
189C2×C4×C5—41no—
190C2×C4×C5—41no—
191C2×C4×C5#21711yescharacteristic
192C2×C4×C5#21711yescharacteristic
193C2×C4×C5#21711yescharacteristic
194C2×C4×C5C22×Dic311yescharacteristic
195C2×C4×C5C2×#6711yescharacteristic
196C2×C4×C5C2×#6711yescharacteristic
197C22⋊D5—42no—
198C2×Dic5—21no—
199C2×Dic5—21no—
200C2×Dic5—21no—
201D20—41no—
202C4×D5—42no—
203Dic10—41no—
204C5×C8—122no—
205#168—122no—
206#126—101no—
207#125—51no—
208#124—51no—
209#123—101no—
210C22⋊Q8—51no—
211#121—51no—
212C4×Q8—51no—
213C4×D4—51no—
214C4×D4—101no—
215#117—101no—
216C2×C42D3×D511yescharacteristic
217C4⋊C8—61no—
218C4⋊C8—301no—
219C22⋊C8—61no—
220C22⋊C8—301no—
221#97—32no—
222#97—152no—
223C2×C3×C5—41no—
224C2×C3×C5#41311yescharacteristic
225C2×C3×C5#42111yescharacteristic
226C2×C3×C5#42111yescharacteristic
227C3×D5—81no—
228C23×C3—101no—
229C23×C3#68511yescharacteristic
230C3×Q8—201no—
231C3×D4—201no—
232C3×D4—202no—
233C2×C3×C4—41no—
234C2×C3×C4—41no—
235C2×C3×C4—41no—
236C2×C3×C4—101no—
237C2×C3×C4—101no—
238C2×C3×C4—101no—
239C2×C3×C4—202no—
240C2×C3×C4#68511yescharacteristic
241C2×C3×C4#68511yescharacteristic
242C2×C3×C4#68511yescharacteristic
243C2×C3×C4C2×C4×D511yescharacteristic
244C2×C3×C4C2×D2011yescharacteristic
245C2×C3×C4C2×C22⋊D511yescharacteristic
246C3⋊C8—42no—
247C3⋊C8—202no—
248C22×C5—21no—
249C22×C5—21no—
250C22×C5—21no—
251C22×C5C2×#21711yescharacteristic
252C2×D5—41no—
253C2×D5—41no—
254C2×D5—41no—
255C4×C5—21no—
256C4×C5—21no—
257C4×C5—21no—
258C4×C5—21no—
259C4×C5—21no—
260C4×C5—21no—
261Dic5—41no—
262Dic5—41no—
263Dic5—41no—
264C2×Q8—51no—
265C2×D4—51no—
266C2×D4—101no—
267C22×C4—101no—
268C22×C4D5×Dic311yescharacteristic
269C22×C4#120111yescharacteristic
270C22×C4#120211yescharacteristic
271C2×C8—62no—
272C2×C8—302no—
273C4⋊C4—51no—
274C4⋊C4—51no—
275C4⋊C4—101no—
276C4⋊C4—101no—
277C4⋊C4—101no—
278C4⋊C4—101no—
279C22⋊C4—101no—
280C22⋊C4—101no—
281C22⋊C4—101no—
282C22⋊C4—101no—
283C22⋊C4—101no—
284C42—101no—
285C42D5×Dic311yescharacteristic
286C42#120111yescharacteristic
287C42#120211yescharacteristic
288C42C2×D3×D511yescharacteristic
289C3×C5#153511yescharacteristic, complemented, Hall
290C22×C3—21no—
291C22×C3—21no—
292C22×C3—21no—
293C22×C3—201no—
294C22×C3—201no—
295C22×C3—201no—
296C22×C3C2×#68511yescharacteristic
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—201no—
304C3×C4—201no—
305C3×C4—201no—
306C2×C5—41no—
307C2×C5#523611yescharacteristic
308C2×C5#523611yescharacteristic
309C2×C5#523711yescharacteristic
310D5—81no—
311C23—101no—
312C23#666511yescharacteristic
313Q8—201no—
314D4—201no—
315D4—202no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—101no—
320C2×C4—101no—
321C2×C4—101no—
322C2×C4—202no—
323C2×C4#666511yescharacteristic
324C2×C4#666511yescharacteristic
325C2×C4#666511yescharacteristic
326C2×C4C2×D5×Dic311yescharacteristic
327C2×C4C2×#120111yescharacteristic
328C2×C4C2×#120211yescharacteristic
329C8—122no—
330C8—602no—
331C2×C3—41no—
332C2×C3—401no—
333C2×C3#6529411yescharacteristic
334C2×C3#6542111yescharacteristic
335C2×C3#6542811yescharacteristic
336C5#7174911yescharacteristic, complemented, Sylow
337C22—21no—
338C22—21no—
339C22—21no—
340C22—201no—
341C22—201no—
342C22—201no—
343C22C2×#666511yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—201no—
351C4—201no—
352C4—201no—
353C3#1060160311yescharacteristic, complemented, Sylow
354C2—41no—
355C2—401no—
356C2#1174835311yescharacteristic
357C2#1174842011yescharacteristic
358C2#1174842111yescharacteristic
subgroupG/H
centerC22C2×#6665
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#4076C4
cosocleC3×C42×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1535
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #11751027C2semidirect
3. C5×#4926C2semidirect
4. #11745849C2semidirect
5. #11745846C2semidirect
57. #4926D5semidirect
289. C3×C5#1535semidirect
336. C5#71749semidirect
353. C3#10601603semidirect

Maximal subgroups

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

subgroupindex
C3×#658132
#117510272
C5×#49262
#117458492
#117458462
#106016033
#717495