Finite Group Databasebeta

← #14284418

Subgroups — #14284418

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
1C5×#5680C211yesmaximal, characteristic
2#11746878C211yesmaximal, characteristic, complemented
3#11746878C211yesmaximal, characteristic, complemented
4#11746361C211yesmaximal, characteristic, complemented
5C3×#64760C211yesmaximal, characteristic, complemented
6#11745850C211yesmaximal, characteristic, complemented
7#11745850C211yesmaximal, characteristic, complemented
8#10602542—31nomaximal, Hall
9C3×C5×#124C2211yescharacteristic
10C5×#946C411yescharacteristic
11C5×Q8×Dic3C411yescharacteristic
12C5×#938C411yescharacteristic
13C5×D4×Dic3C411yescharacteristic
14C5×#883—21no—
15C5×#67⋊C4—21no—
16C5×#879—21no—
17C5×#877—21no—
18C42×C5×D3C2211yescharacteristic
19C5×#870C2211yescharacteristic
20#91087C2211yescharacteristic
21#91087C2211yescharacteristic
22C3×#3935C2211yescharacteristic
23C3×#3935C2211yescharacteristic
24Dic3⋊#168—21no—
25Dic3⋊#168—21no—
26(C2×D3)⋊#168—21no—
27(C2×D3)⋊#168—21no—
28#68348—51nomaximal, Hall
29C5×#529—31no—
30#65215—31no—
31#65215—31no—
32#64763—31no—
33#64763—31no—
34#64760—31no—
35#64760D311yescharacteristic, complemented
36C2×C3×C5×Q8C2×C411yescharacteristic
37C2×C3×C5×D4C2×C411yescharacteristic
38C2×C5×#67—21no—
39C22×C5×Dic3—21no—
40C2×C4×C5×D3C2×C411yescharacteristic
41C2×C4×C5×D3D411yescharacteristic
42C2×C4×C5×D3D411yescharacteristic
43C3×C5×C22⋊C4—21no—
44C3×C5×C22⋊C4—21no—
45C3×C42×C5C2311yescharacteristic
46C2×C3⋊#168—21no—
47C2×C3⋊#168—21no—
48C5×#217—21no—
49C5×#217—21no—
50C5×(C2×D3)⋊C4—21no—
51C5×C4⋊Dic3—21no—
52C5×C4⋊Dic3C2×C411yescharacteristic
53C5×C4⋊Dic3C2×C411yescharacteristic
54C5×Dic3⋊C4—21no—
55C5×Dic3⋊C4—21no—
56C5×Dic3⋊C4—21no—
57C4×C5×Dic3—21no—
58C4×C5×Dic3C2×C411yescharacteristic
59C4×C5×Dic3D411yescharacteristic
60C4×C5×Dic3D411yescharacteristic
61C2×C3×#168—21no—
62C2×C3×#168—21no—
63#5680D511yescharacteristic
64#4705—51no—
65#4705—51no—
66C3×#329—51no—
67#4540—51no—
68#4465—51no—
69#4465—51no—
70C5×#126—61no—
71C5×#125—31no—
72C5×#124C2×D311yescharacteristic
73C5×#123—61no—
74C5×C22⋊Q8—31no—
75C5×#121—31no—
76C4×C5×Q8—31no—
77C4×C5×D4—31no—
78C4×C5×D4—61no—
79C5×#117—61no—
80C2×C42×C5—31no—
81C22⋊#168—61no—
82C22⋊#168—61no—
83C4⋊#168—61no—
84C4⋊#168—61no—
85#3935—31no—
86#3935—31no—
87#3935C2×D311yescharacteristic
88#3935C2×D311yescharacteristic
89#1535—151noSylow
90C23×C3×C5—21no—
91C22×C5×D3C22⋊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
98C5×#67—42no—
99C2×C5×Dic3—21no—
100C2×C5×Dic3—21no—
101C2×C5×Dic3—42no—
102C2×C5×Dic3C22⋊C411yescharacteristic
103C2×C5×Dic3C22⋊C411yescharacteristic
104C2×C5×Dic3C22⋊C411yescharacteristic
105C4×C5×D3—41no—
106C4×C5×D3—41no—
107C4×C5×D3—41no—
108C3⋊#168—41no—
109C3⋊#168—41no—
110C3×#168—41no—
111C3×#168—41no—
112C3×#124C2×D511yescharacteristic
113#946Dic511yescharacteristic
114Q8×Dic3Dic511yescharacteristic
115#938Dic511yescharacteristic
116D4×Dic3Dic511yescharacteristic
117#883—21no—
118#67⋊C4—21no—
119#879—21no—
120#877—21no—
121C42×D3C2×D511yescharacteristic
122#870C2×D511yescharacteristic
123C3×#97—51no—
124C3×#97—51no—
125(C2×D3)⋊C8—101no—
126(C2×D3)⋊C8—101no—
127Dic3⋊C8—101no—
128Dic3⋊C8—101no—
129#803—51no—
130#803—51no—
131C2×C5×Q8C4×D311yescharacteristic
132C2×C5×D4—61no—
133C2×C5×D4C4×D311yescharacteristic
134C22×C4×C5—31no—
135C22×C4×C5—31no—
136C22×C4×C5—31no—
137C22×C4×C5—61no—
138C5×C4⋊C4—31no—
139C5×C4⋊C4—31no—
140C5×C4⋊C4—61no—
141C5×C4⋊C4—61no—
142C5×C4⋊C4—61no—
143C5×C4⋊C4—61no—
144C5×C22⋊C4—21no—
145C5×C22⋊C4—21no—
146C5×C22⋊C4—61no—
147C5×C22⋊C4—61no—
148C5×C22⋊C4—61no—
149C42×C5—31no—
150C42×C5—31no—
151C42×C5—31no—
152C42×C5—61no—
153C42×C5C22×D311yescharacteristic
154C2×#168—21no—
155C2×#168—21no—
156C2×#168—61no—
157C2×#168—61no—
158#529—31no—
159#432—151no—
160#432—151no—
161#330—151no—
162#330—151no—
163#329—51no—
164#329—151no—
165C22×C3×C5—41no—
166C22×C3×C5—41no—
167C22×C3×C5—41no—
168C22×C3×C5C2×C22⋊C411yescharacteristic
169C2×C5×D3—21no—
170C2×C5×D3—21no—
171C2×C5×D3—21no—
172C3×C4×C5—21no—
173C3×C4×C5—21no—
174C3×C4×C5—21no—
175C3×C4×C5—41no—
176C5×Dic3—21no—
177C5×Dic3—21no—
178C5×Dic3—21no—
179C5×Dic3—41no—
180C5×Dic3—41no—
181C2×C3×Q8C2×Dic511yescharacteristic
182C2×C3×D4C2×Dic511yescharacteristic
183C2×#67—21no—
184C22×Dic3—21no—
185C2×C4×D3C2×Dic511yescharacteristic
186C2×C4×D3C22⋊D511yescharacteristic
187C2×C4×D3C22⋊D511yescharacteristic
188C2×C3×C8—101no—
189C2×C3×C8—101no—
190C3×C22⋊C4—21no—
191C3×C22⋊C4—21no—
192C3×C42C22×D511yescharacteristic
193#217—21no—
194#217—21no—
195(C2×D3)⋊C4—21no—
196C4⋊Dic3—21no—
197C4⋊Dic3C2×Dic511yescharacteristic
198C4⋊Dic3C2×Dic511yescharacteristic
199Dic3⋊C4—21no—
200Dic3⋊C4—21no—
201Dic3⋊C4—21no—
202C4×Dic3—21no—
203C4×Dic3C2×Dic511yescharacteristic
204C4×Dic3C22⋊D511yescharacteristic
205C4×Dic3C22⋊D511yescharacteristic
206C2×C3⋊C8—101no—
207C2×C3⋊C8—101no—
208C23×C5—21no—
209C23×C5—31no—
210C5×Q8—41no—
211C5×D4—41no—
212C5×D4—122no—
213C2×C4×C5—21no—
214C2×C4×C5—31no—
215C2×C4×C5—31no—
216C2×C4×C5—31no—
217C2×C4×C5—61no—
218C2×C4×C5—61no—
219C2×C4×C5—121no—
220C2×C4×C5—121no—
221C2×C4×C5—121no—
222C2×C4×C5—122no—
223C2×C4×C5C2×C4×D311yescharacteristic
224C2×C4×C5D3×D411yescharacteristic
225C2×C4×C5D3×D411yescharacteristic
226#168—41no—
227#168—41no—
228#168—121no—
229#168—121no—
230#126—61no—
231#125—31no—
232#124D3×D511yescharacteristic
233#123—61no—
234C22⋊Q8—31no—
235#121—31no—
236C4×Q8—31no—
237C4×D4—31no—
238C4×D4—61no—
239#117—61no—
240C2×C42—31no—
241C4⋊C8—301no—
242C4⋊C8—301no—
243C22⋊C8—301no—
244C22⋊C8—301no—
245#97—51no—
246#97—51no—
247#97—151no—
248#97—151no—
249C2×C3×C5—81no—
250C2×C3×C5#41311yescharacteristic
251C2×C3×C5#42111yescharacteristic
252C2×C3×C5#42111yescharacteristic
253C5×D3—41no—
254C23×C3—21no—
255C22×D3C22⋊Dic511yescharacteristic
256C3×Q8—41no—
257C3×D4—41no—
258C2×C3×C4—21no—
259C2×C3×C4C22×Dic511yescharacteristic
260C2×C3×C4C2×C22⋊D511yescharacteristic
261C2×C3×C4C2×C22⋊D511yescharacteristic
262#67—42no—
263C2×Dic3—21no—
264C2×Dic3—21no—
265C2×Dic3—42no—
266C2×Dic3C22⋊Dic511yescharacteristic
267C2×Dic3C22⋊Dic511yescharacteristic
268C2×Dic3C22⋊Dic511yescharacteristic
269C4×D3—41no—
270C4×D3—41no—
271C4×D3—41no—
272C3×C8—201no—
273C3×C8—201no—
274C3⋊C8—201no—
275C3⋊C8—201no—
276C22×C5—41no—
277C22×C5—41no—
278C22×C5—41no—
279C22×C5—61no—
280C22×C5—61no—
281C22×C5—61no—
282C22×C5D3×C22⋊C411yescharacteristic
283C4×C5—21no—
284C4×C5—21no—
285C4×C5—21no—
286C4×C5—41no—
287C4×C5—61no—
288C4×C5—61no—
289C4×C5—61no—
290C4×C5—121no—
291C4×C5—121no—
292C2×Q8D3×Dic511yescharacteristic
293C2×D4—61no—
294C2×D4D3×Dic511yescharacteristic
295C22×C4—31no—
296C22×C4—31no—
297C22×C4—31no—
298C22×C4—61no—
299C2×C8—101no—
300C2×C8—101no—
301C2×C8—301no—
302C2×C8—301no—
303C4⋊C4—31no—
304C4⋊C4—31no—
305C4⋊C4—61no—
306C4⋊C4—61no—
307C4⋊C4—61no—
308C4⋊C4—61no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—61no—
312C22⋊C4—61no—
313C22⋊C4—61no—
314C42—31no—
315C42—31no—
316C42—31no—
317C42—61no—
318C42C2×D3×D511yescharacteristic
319C3×C5#153511yescharacteristic, complemented, Hall
320C22×C3—41no—
321C22×C3—41no—
322C22×C3—41no—
323C22×C3C2×C22⋊Dic511yescharacteristic
324C2×D3—21no—
325C2×D3—21no—
326C2×D3—21no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—41no—
331Dic3—21no—
332Dic3—21no—
333Dic3—21no—
334Dic3—41no—
335Dic3—41no—
336C2×C5—81no—
337C2×C5—121no—
338C2×C5#474511yescharacteristic
339C2×C5#482111yescharacteristic
340C2×C5#482111yescharacteristic
341C23—21no—
342C23—31no—
343Q8—41no—
344D4—41no—
345D4—122no—
346C2×C4—21no—
347C2×C4—31no—
348C2×C4—31no—
349C2×C4—31no—
350C2×C4—61no—
351C2×C4—61no—
352C2×C4—121no—
353C2×C4—121no—
354C2×C4—121no—
355C2×C4—122no—
356C2×C4C2×D3×Dic511yescharacteristic
357C2×C4D3×C22⋊D511yescharacteristic
358C2×C4D3×C22⋊D511yescharacteristic
359C8—201no—
360C8—201no—
361C8—601no—
362C8—601no—
363C2×C3—81no—
364C2×C3#6552511yescharacteristic
365C2×C3#6552511yescharacteristic
366C2×C3#6552611yescharacteristic
367D3—41no—
368C5#6834811yescharacteristic, complemented, Sylow
369C22—41no—
370C22—41no—
371C22—41no—
372C22—61no—
373C22—61no—
374C22—61no—
375C22D3×C22⋊Dic511yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—61no—
381C4—61no—
382C4—61no—
383C4—121no—
384C4—121no—
385C3#1060254211yescharacteristic, complemented, Sylow
386C2—81no—
387C2—121no—
388C2#1174912611yescharacteristic
389C2#1174942911yescharacteristic
390C2#1174942911yescharacteristic
subgroupG/H
centerC22D3×C22⋊Dic5
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#938C4
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. #11746878C2semidirect
3. #11746878C2semidirect
4. #11746361C2semidirect
5. C3×#64760C2semidirect
6. #11745850C2semidirect
7. #11745850C2semidirect
35. #64760D3semidirect
319. C3×C5#1535semidirect
368. C5#68348semidirect
385. C3#10602542semidirect

Maximal subgroups

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

subgroupindex
C5×#56802
#117468782
#117463612
C3×#647602
#117458502
#106025423
#683485