Finite Group Databasebeta

← #14284611

Subgroups — #14284611

Order 1920.

512 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×#66059C211yesmaximal, characteristic
2D5×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
3#11746869C211yesmaximal, characteristic, complemented
4#11746368C211yesmaximal, characteristic, complemented
5C5×#4547C211yesmaximal, characteristic, complemented
6#11745852C211yesmaximal, characteristic, complemented
7#11745852C211yesmaximal, characteristic, complemented
8#10599210—31nomaximal, Hall
9C2×C3×#713—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×#4093—21no—
12C3×#4041—21no—
13C3×#4041C412yes—
14C3×#4039—21no—
15C3×#4039C412yes—
16C3×#4020C2211yescharacteristic
17C3×C42×D5C2211yescharacteristic
18C2×D5×C3⋊C8—21no—
19C4⋊(C3⋊#168)C2211yescharacteristic
20C4⋊(C3⋊#168)C2211yescharacteristic
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23#90982—21no—
24#90955—21no—
25Dic5×C3⋊C8—21no—
26#71804—51nomaximal, Hall
27#66059D311yescharacteristic
28#65122—31no—
29D5×C4⋊C8—31no—
30C5×#332—31no—
31#64767—31no—
32#64705—31no—
33#64705—31no—
34C2×C3×C5×Q8—21no—
35C3×#713—42no—
36C3×#713—42no—
37C2×C3×D20—22no—
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C2×C3×D20C2×C412yes—
41C2×C3×C4×D5—22no—
42C2×C3×C4×D5C2×C411yescharacteristic
43C2×C3×C4×D5D411yescharacteristic
44C2×C3×C4×D5D411yescharacteristic
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4C2×C412yes—
47C3×C42×C5C2311yescharacteristic
48C2×C3⋊#168—21no—
49C2×C3⋊#168—21no—
50C2×C5×C3⋊C8—21no—
51C2×C5×C3⋊C8—21no—
52C3×#685—22no—
53C3×#685—22no—
54C3×C4×Dic5C2×C411yescharacteristic
55C3×C4×Dic5D411yescharacteristic
56C3×C4×Dic5D411yescharacteristic
57D5×C3⋊C8—42no—
58C3×#532—51no—
59#4925—51no—
60C2×C4⋊(C3⋊C8)—51no—
61#4547—51no—
62#4547D511yescharacteristic, complemented
63#4544—51no—
64#4544—51no—
65C2×#713—21no—
66C5×C4⋊Q8C2×D311yescharacteristic
67#4093—21no—
68C2×C8×D5—61no—
69#4041—21no—
70#4041Dic312yes—
71#4039—21no—
72#4039Dic312yes—
73#4020C2×D311yescharacteristic
74C42×D5C2×D311yescharacteristic
75C5×C4⋊C8—31no—
76C5×C4⋊C8—31no—
77#3952—61no—
78#3946—61no—
79C8×Dic5—61no—
80C4⋊#168—31no—
81C4⋊#168—31no—
82#1540—151noSylow
83C22×C3×D5—22no—
84C22×C3×D5C22⋊C411yescharacteristic
85C3×C5×Q8—41no—
86C3×C5×Q8—41no—
87C2×C3×C4×C5—22no—
88C2×C3×C4×C5C22×C411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×Dic5C22⋊C411yescharacteristic
92C2×C3×Dic5C22⋊C411yescharacteristic
93C2×C3×Dic5C22⋊C411yescharacteristic
94C3×D20—42no—
95C3×D20—44no—
96C3×D20—41no—
97C3×D20—41no—
98C3×D20—41no—
99C3×D20—41no—
100C3×C4×D5—21no—
101C3×C4×D5—21no—
102C3×C4×D5—41no—
103C3×C4×D5—44no—
104C3×C4×D5D812yes—
105C3×C4×D5SD1612yes—
106C3⋊#168—41no—
107C3⋊#168—41no—
108C5×C3⋊C8—41no—
109C5×C3⋊C8—41no—
110C2×C3×#41—101no—
111C3×C4⋊Q8C2×D511yescharacteristic
112C3×#127—51no—
113C3×#124—101no—
114C3×#121—52no—
115C3×#121—101no—
116C3×C4×D4—52no—
117C3×C4×D4—101no—
118C2×C3×C42—51no—
119C22×C3⋊C8—101no—
120#830—101no—
121C4⋊(C3⋊C8)—51no—
122C4⋊(C3⋊C8)—51no—
123C4⋊(C3⋊C8)—101no—
124C4⋊(C3⋊C8)C2×D511yescharacteristic
125C4⋊(C3⋊C8)C2×D511yescharacteristic
126C4×C3⋊C8—101no—
127C2×C5×Q8—21no—
128#713—42no—
129#713—42no—
130C2×D20—22no—
131C2×D20—21no—
132C2×D20—21no—
133C2×D20C2×Dic312yes—
134C2×C4×D5—22no—
135C2×C4×D5C2×Dic311yescharacteristic
136C2×C4×D5#6711yescharacteristic
137C2×C4×D5#6711yescharacteristic
138C2×C5×C8—61no—
139C2×C5×C8—61no—
140C5×C4⋊C4—21no—
141C5×C4⋊C4C2×Dic312yes—
142C42×C5C22×D311yescharacteristic
143#685—22no—
144#685—22no—
145C4×Dic5C2×Dic311yescharacteristic
146C4×Dic5#6711yescharacteristic
147C4×Dic5#6711yescharacteristic
148C2×#168—61no—
149C2×#168—61no—
150C8×D5—122no—
151#532—51no—
152#431—151no—
153C2×C4⋊C8—151no—
154#332—31no—
155#332—151no—
156#331—151no—
157#331—151no—
158C22×C3×C5C2×C22⋊C411yescharacteristic
159C2×C3×D5—21no—
160C2×C3×D5—21no—
161C2×C3×D5—42no—
162C2×C3×D5—42no—
163C2×C3×D5—42no—
164C2×C3×D5#10212yes—
165C3×C4×C5—21no—
166C3×C4×C5—42no—
167C3×C4×C5C2×D811yescharacteristic
168C3×C4×C5C2×SD1611yescharacteristic
169C3×C4×C5#13511yescharacteristic
170C3×C4×C5#13511yescharacteristic
171C3×Dic5—21no—
172C3×Dic5—21no—
173C3×Dic5#10212yes—
174C3×#41—202no—
175C3×#41—202no—
176C2×C3×Q8—21no—
177C2×C3×D4—52no—
178C2×C3×D4—102no—
179C2×C3×D4—101no—
180C2×C3×D4—101no—
181C22×C3×C4—51no—
182C22×C3×C4—51no—
183C22×C3×C4—51no—
184C22×C3×C4—102no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4C4×D512yes—
187C3×C22⋊C4—102no—
188C3×C22⋊C4—102no—
189C3×C42—51no—
190C3×C42—51no—
191C3×C42—51no—
192C3×C42C22×D511yescharacteristic
193C2×C3⋊C8—21no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—101no—
196C2×C3⋊C8—101no—
197C2×C3⋊C8—202no—
198C22×D5—22no—
199C22×D5#21711yescharacteristic
200C5×Q8—41no—
201C5×Q8—41no—
202C2×C4×C5—22no—
203C2×C4×C5C22×Dic311yescharacteristic
204C2×C4×C5C2×#6711yescharacteristic
205C2×C4×C5C2×#6711yescharacteristic
206C2×Dic5#21711yescharacteristic
207C2×Dic5#21711yescharacteristic
208C2×Dic5#21711yescharacteristic
209D20—42no—
210D20—44no—
211D20—41no—
212D20—41no—
213D20—41no—
214D20—41no—
215C4×D5—21no—
216C4×D5—21no—
217C4×D5—41no—
218C4×D5—44no—
219C4×D5#21312yes—
220C4×D5#21412yes—
221C5×C8—121no—
222C5×C8—121no—
223#168—121no—
224#168—121no—
225C2×#41—101no—
226C22×C8—301no—
227C4⋊Q8D3×D511yescharacteristic
228#127—51no—
229#124—101no—
230#121—52no—
231#121—101no—
232C4×D4—52no—
233C4×D4—101no—
234C2×C42—51no—
235C4⋊C8—31no—
236C4⋊C8—31no—
237C4⋊C8—151no—
238C4⋊C8—151no—
239C4⋊C8—301no—
240C22⋊C8—301no—
241C4×C8—301no—
242C2×C3×C5#41311yescharacteristic
243C2×C3×C5C2×#10211yescharacteristic
244C2×C3×C5#41611yescharacteristic
245C3×D5—22no—
246C3×D5—82no—
247C23×C3—51no—
248C23×C3—102no—
249C3×Q8—41no—
250C3×Q8—41no—
251C3×D4—202no—
252C3×D4—204no—
253C3×D4—201no—
254C3×D4—201no—
255C3×D4—201no—
256C3×D4—201no—
257C2×C3×C4—22no—
258C2×C3×C4—51no—
259C2×C3×C4—52no—
260C2×C3×C4—52no—
261C2×C3×C4—51no—
262C2×C3×C4—51no—
263C2×C3×C4—101no—
264C2×C3×C4—101no—
265C2×C3×C4—201no—
266C2×C3×C4—204no—
267C2×C3×C4C2×C4×D511yescharacteristic
268C2×C3×C4D4×D511yescharacteristic
269C2×C3×C4D4×D511yescharacteristic
270C3⋊C8—41no—
271C3⋊C8—41no—
272C3⋊C8—201no—
273C3⋊C8—201no—
274C22×C5C2×#21711yescharacteristic
275C2×D5—21no—
276C2×D5—21no—
277C2×D5—42no—
278C2×D5—42no—
279C2×D5—42no—
280C2×D5#83212yes—
281C4×C5—21no—
282C4×C5—42no—
283C4×C5C2×#21311yescharacteristic
284C4×C5C2×#21411yescharacteristic
285C4×C5#95011yescharacteristic
286C4×C5#95011yescharacteristic
287Dic5—21no—
288Dic5—21no—
289Dic5#83212yes—
290#41—202no—
291#41—202no—
292C2×Q8—21no—
293C2×D4—52no—
294C2×D4—102no—
295C2×D4—101no—
296C2×D4—101no—
297C22×C4—51no—
298C22×C4—51no—
299C22×C4—51no—
300C22×C4—102no—
301C2×C8—61no—
302C2×C8—61no—
303C2×C8—301no—
304C2×C8—301no—
305C2×C8—602no—
306C4⋊C4—21no—
307C4⋊C4D5×Dic312yes—
308C22⋊C4—102no—
309C22⋊C4—102no—
310C42—51no—
311C42—51no—
312C42—51no—
313C42C2×D3×D511yescharacteristic
314C3×C5#154011yescharacteristic, complemented, Hall
315C22×C3—52no—
316C22×C3—101no—
317C22×C3—101no—
318C22×C3—202no—
319C22×C3—202no—
320C22×C3—202no—
321C22×C3D5×C22⋊C411yescharacteristic
322C3×C4—21no—
323C3×C4—42no—
324C3×C4—52no—
325C3×C4—101no—
326C3×C4—101no—
327C3×C4D5×D811yescharacteristic
328C3×C4D5×SD1611yescharacteristic
329C3×C4#406211yescharacteristic
330C3×C4#406511yescharacteristic
331C2×C5C2×#83211yescharacteristic
332C2×C5#523311yescharacteristic
333C2×C5#523711yescharacteristic
334D5—22no—
335D5—82no—
336C23—51no—
337C23—102no—
338Q8—41no—
339Q8—41no—
340D4—202no—
341D4—204no—
342D4—201no—
343D4—201no—
344D4—201no—
345D4—201no—
346C2×C4—22no—
347C2×C4—51no—
348C2×C4—52no—
349C2×C4—52no—
350C2×C4—51no—
351C2×C4—51no—
352C2×C4—101no—
353C2×C4—101no—
354C2×C4—201no—
355C2×C4—204no—
356C2×C4C2×D5×Dic311yescharacteristic
357C2×C4D5×#6711yescharacteristic
358C2×C4D5×#6711yescharacteristic
359C8—121no—
360C8—121no—
361C8—601no—
362C8—601no—
363C2×C3—102no—
364C2×C3—402no—
365C2×C3#6504011yescharacteristic
366C2×C3D5×#10211yescharacteristic
367C2×C3#6509311yescharacteristic
368C5#7180411yescharacteristic, complemented, Sylow
369C22—52no—
370C22—101no—
371C22—101no—
372C22—202no—
373C22—202no—
374C22—202no—
375C22D5×#21711yescharacteristic
376C4—21no—
377C4—42no—
378C4—52no—
379C4—101no—
380C4—101no—
381C4D5×#21311yescharacteristic
382C4D5×#21411yescharacteristic
383C4#9151411yescharacteristic
384C4#9151611yescharacteristic
385C3#1059921011yescharacteristic, complemented, Sylow
386C2—102no—
387C2—402no—
388C2D5×#83211yescharacteristic
389C2#1174920711yescharacteristic
390C2#1174936911yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#66059C2
cosocleC3×C42×C5C23
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1540
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. D5×C4⋊(C3⋊C8)C2semidirect
3. #11746869C2semidirect
4. #11746368C2semidirect
5. C5×#4547C2semidirect
6. #11745852C2semidirect
7. #11745852C2semidirect
62. #4547D5semidirect
314. C3×C5#1540semidirect
368. C5#71804semidirect
385. C3#10599210semidirect

Maximal subgroups

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

subgroupindex
C3×#660592
D5×C4⋊(C3⋊C8)2
#117468692
#117463682
C5×#45472
#117458522
#105992103
#718045