Finite Group Databasebeta

← #14284312

Subgroups — #14284312

Order 1920.

436 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5691C211yesmaximal, characteristic
2D3×#3935C211yesmaximal, characteristic, complemented
3#11746878C211yesmaximal, characteristic, complemented
4#11746364C211yesmaximal, characteristic, complemented
5C3×#64763C211yesmaximal, characteristic, complemented
6#11745847C211yesmaximal, characteristic, complemented
7#11745847C211yesmaximal, characteristic, complemented
8#10602541—31nomaximal, Hall
9C3×C5×#125C2211yescharacteristic
10C5×#898—21no—
11C5×#897C411yescharacteristic
12C5×#895C411yescharacteristic
13C5×#894—21no—
14C5×#893—21no—
15C5×#893C411yescharacteristic
16C5×#892—21no—
17C5×#887C411yescharacteristic
18C5×#875C2211yescharacteristic
19C42×C5×D3C2211yescharacteristic
20C2×D3×#168—21no—
21#91087C2211yescharacteristic
22#91087C2211yescharacteristic
23C3×#3935C2211yescharacteristic
24C3×#3935C2211yescharacteristic
25Dic3⋊#168—21no—
26(C2×D3)⋊#168—21no—
27#90953—21no—
28#68366—51nomaximal, Hall
29C5×#529—31no—
30#65215—31no—
31C2×#3935—31no—
32#64763—31no—
33#64763D311yescharacteristic, complemented
34#64760—31no—
35#64760—31no—
36C2×C5×D12—21no—
37C2×C5×D12C2×C411yescharacteristic
38C2×C4×C5×D3—21no—
39C2×C4×C5×D3C2×C411yescharacteristic
40C2×C4×C5×D3D411yescharacteristic
41C2×C4×C5×D3D411yescharacteristic
42C2×C5×Dic6C2×C411yescharacteristic
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4C2×C411yescharacteristic
46C3×C5×C4⋊C4C2×C411yescharacteristic
47C3×C42×C5C2311yescharacteristic
48C2×C3⋊#168—21no—
49C2×C3⋊#168—21no—
50C5×(C2×D3)⋊C4—21no—
51C5×(C2×D3)⋊C4—21no—
52C5×(C2×D3)⋊C4—21no—
53C5×(C2×D3)⋊C4—21no—
54C5×(C2×D3)⋊C4—21no—
55C5×C4⋊Dic3—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—
63D3×#168—24no—
64#5691D511yescharacteristic
65#4705—51no—
66D3×#97—51no—
67C3×#330—51no—
68#4543—51no—
69#4464—51no—
70#4464—51no—
71C5×#126—61no—
72C5×#125C2×D311yescharacteristic
73C5×#124—31no—
74C5×#123—61no—
75C5×C22⋊Q8—31no—
76C5×#121—31no—
77C4×C5×Q8—31no—
78C4×C5×D4—31no—
79C4×C5×D4—61no—
80C5×#117—61no—
81C2×C42×C5—31no—
82C22×#168—61no—
83C22⋊#168—61no—
84C4⋊#168—61no—
85#3935—31no—
86#3935—31no—
87#3935—61no—
88#3935C2×D311yescharacteristic
89#3935C2×D311yescharacteristic
90#1532—151noSylow
91C22×C5×D3—21no—
92C22×C5×D3C22⋊C411yescharacteristic
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5C22×C411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C5×Dic3—21no—
99C2×C5×Dic3C22⋊C411yescharacteristic
100C2×C5×Dic3C22⋊C411yescharacteristic
101C2×C5×Dic3C22⋊C411yescharacteristic
102C5×D12—41no—
103C5×D12—42no—
104C4×C5×D3—22no—
105C4×C5×D3—41no—
106C4×C5×D3—41no—
107C4×C5×D3—42no—
108C5×Dic6—41no—
109C3⋊#168—22no—
110C3⋊#168—41no—
111C3×#168—22no—
112C3×#168—41no—
113C3×#125C2×D511yescharacteristic
114C2×D3×C8—101no—
115#898—21no—
116#897Dic511yescharacteristic
117#895Dic511yescharacteristic
118#894—21no—
119#893—21no—
120#893Dic511yescharacteristic
121#892—21no—
122#887Dic511yescharacteristic
123#875C2×D511yescharacteristic
124C42×D3C2×D511yescharacteristic
125C3×#97—51no—
126C3×#97—51no—
127(C2×D3)⋊C8—101no—
128#815—101no—
129Dic3⋊C8—101no—
130#803—51no—
131#803—51no—
132C2×C5×Q8—31no—
133C2×C5×D4—31no—
134C2×C5×D4—61no—
135C22×C4×C5—31no—
136C22×C4×C5—31no—
137C22×C4×C5—31no—
138C22×C4×C5—61no—
139C5×C4⋊C4—21no—
140C5×C4⋊C4—21no—
141C5×C4⋊C4—61no—
142C5×C4⋊C4—61no—
143C5×C4⋊C4C4×D311yescharacteristic
144C5×C4⋊C4C4×D311yescharacteristic
145C5×C22⋊C4—61no—
146C5×C22⋊C4—61no—
147C5×C22⋊C4—61no—
148C5×C22⋊C4—61no—
149C5×C22⋊C4—61no—
150C42×C5—31no—
151C42×C5—31no—
152C42×C5—31no—
153C42×C5—61no—
154C42×C5C22×D311yescharacteristic
155C2×#168—21no—
156C2×#168—21no—
157C2×#168—64no—
158C2×#168—61no—
159C2×#168—61no—
160#529—31no—
161#432—151no—
162C2×#97—151no—
163#330—51no—
164#330—151no—
165#329—151no—
166#329—151no—
167C22×C3×C5C2×C22⋊C411yescharacteristic
168C2×C5×D3—21no—
169C2×C5×D3—21no—
170C2×C5×D3—41no—
171C2×C5×D3—41no—
172C2×C5×D3—41no—
173C2×C5×D3#10412yes—
174C3×C4×C5—21no—
175C3×C4×C5—21no—
176C3×C4×C5—21no—
177C3×C4×C5—41no—
178C3×C4×C5—41no—
179C5×Dic3—21no—
180C5×Dic3—21no—
181C5×Dic3—21no—
182C5×Dic3—41no—
183C2×D12—21no—
184C2×D12C2×Dic511yescharacteristic
185C2×C4×D3—21no—
186C2×C4×D3C2×Dic511yescharacteristic
187C2×C4×D3C22⋊D511yescharacteristic
188C2×C4×D3C22⋊D511yescharacteristic
189C2×Dic6C2×Dic511yescharacteristic
190C2×C3×C8—101no—
191C2×C3×C8—101no—
192C3×C4⋊C4—21no—
193C3×C4⋊C4—21no—
194C3×C4⋊C4C2×Dic511yescharacteristic
195C3×C4⋊C4C2×Dic511yescharacteristic
196C3×C42C22×D511yescharacteristic
197(C2×D3)⋊C4—21no—
198(C2×D3)⋊C4—21no—
199(C2×D3)⋊C4—21no—
200(C2×D3)⋊C4—21no—
201(C2×D3)⋊C4—21no—
202C4⋊Dic3—21no—
203Dic3⋊C4—21no—
204C4×Dic3—21no—
205C4×Dic3C2×Dic511yescharacteristic
206C4×Dic3C22⋊D511yescharacteristic
207C4×Dic3C22⋊D511yescharacteristic
208C2×C3⋊C8—101no—
209C2×C3⋊C8—101no—
210D3×C8—104no—
211C23×C5—31no—
212C23×C5—61no—
213C5×Q8—121no—
214C5×D4—121no—
215C5×D4—122no—
216C2×C4×C5—21no—
217C2×C4×C5—21no—
218C2×C4×C5—31no—
219C2×C4×C5—31no—
220C2×C4×C5—31no—
221C2×C4×C5—62no—
222C2×C4×C5—61no—
223C2×C4×C5—121no—
224C2×C4×C5—121no—
225C2×C4×C5—122no—
226C2×C4×C5C2×C4×D311yescharacteristic
227C2×C4×C5D3×D411yescharacteristic
228C2×C4×C5D3×D411yescharacteristic
229#168—22no—
230#168—41no—
231#168—62no—
232#168—121no—
233C22×C8—301no—
234#126—61no—
235#125D3×D511yescharacteristic
236#124—31no—
237#123—61no—
238C22⋊Q8—31no—
239#121—31no—
240C4×Q8—31no—
241C4×D4—31no—
242C4×D4—61no—
243#117—61no—
244C2×C42—31no—
245C4⋊C8—301no—
246C22⋊C8—301no—
247#97—51no—
248#97—51no—
249#97—151no—
250#97—151no—
251#97—301no—
252C2×C3×C5#41311yescharacteristic
253C2×C3×C5C2×#10411yescharacteristic
254C2×C3×C5#42111yescharacteristic
255C5×D3—22no—
256C5×D3—81no—
257C22×D3—21no—
258C22×D3C22⋊Dic511yescharacteristic
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4C22×Dic511yescharacteristic
262C2×C3×C4C2×C22⋊D511yescharacteristic
263C2×C3×C4C2×C22⋊D511yescharacteristic
264C2×Dic3—21no—
265C2×Dic3C22⋊Dic511yescharacteristic
266C2×Dic3C22⋊Dic511yescharacteristic
267C2×Dic3C22⋊Dic511yescharacteristic
268D12—41no—
269D12—42no—
270C4×D3—22no—
271C4×D3—41no—
272C4×D3—41no—
273C4×D3—42no—
274Dic6—41no—
275C3×C8—102no—
276C3×C8—201no—
277C3⋊C8—102no—
278C3⋊C8—201no—
279C22×C5—32no—
280C22×C5—61no—
281C22×C5—61no—
282C22×C5—121no—
283C22×C5—121no—
284C22×C5—121no—
285C22×C5D3×C22⋊C411yescharacteristic
286C4×C5—21no—
287C4×C5—21no—
288C4×C5—21no—
289C4×C5—41no—
290C4×C5—41no—
291C4×C5—61no—
292C4×C5—61no—
293C4×C5—61no—
294C4×C5—121no—
295C2×Q8—31no—
296C2×D4—31no—
297C2×D4—61no—
298C22×C4—31no—
299C22×C4—31no—
300C22×C4—31no—
301C22×C4—61no—
302C2×C8—101no—
303C2×C8—101no—
304C2×C8—304no—
305C2×C8—301no—
306C2×C8—301no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—61no—
310C4⋊C4—61no—
311C4⋊C4D3×Dic511yescharacteristic
312C4⋊C4D3×Dic511yescharacteristic
313C22⋊C4—61no—
314C22⋊C4—61no—
315C22⋊C4—61no—
316C22⋊C4—61no—
317C22⋊C4—61no—
318C42—31no—
319C42—31no—
320C42—31no—
321C42—61no—
322C42C2×D3×D511yescharacteristic
323C3×C5#153211yescharacteristic, complemented, Hall
324C22×C3C2×C22⋊Dic511yescharacteristic
325C2×D3—21no—
326C2×D3—21no—
327C2×D3—41no—
328C2×D3—41no—
329C2×D3—41no—
330C2×D3#396912yes—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—41no—
335C3×C4—41no—
336Dic3—21no—
337Dic3—21no—
338Dic3—21no—
339Dic3—41no—
340C2×C5—62no—
341C2×C5—241no—
342C2×C5#475111yescharacteristic
343C2×C5D3×#10411yescharacteristic
344C2×C5#482111yescharacteristic
345C23—31no—
346C23—61no—
347Q8—121no—
348D4—121no—
349D4—122no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—31no—
353C2×C4—31no—
354C2×C4—31no—
355C2×C4—62no—
356C2×C4—61no—
357C2×C4—121no—
358C2×C4—121no—
359C2×C4—122no—
360C2×C4C2×D3×Dic511yescharacteristic
361C2×C4D3×C22⋊D511yescharacteristic
362C2×C4D3×C22⋊D511yescharacteristic
363C8—102no—
364C8—201no—
365C8—302no—
366C8—601no—
367C2×C3C2×#396911yescharacteristic
368C2×C3#6552511yescharacteristic
369C2×C3#6552611yescharacteristic
370D3—22no—
371D3—81no—
372C5#6836611yescharacteristic, complemented, Sylow
373C22—32no—
374C22—61no—
375C22—61no—
376C22—121no—
377C22—121no—
378C22—121no—
379C22D3×C22⋊Dic511yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—41no—
384C4—41no—
385C4—61no—
386C4—61no—
387C4—61no—
388C4—121no—
389C3#1060254111yescharacteristic, complemented, Sylow
390C2—62no—
391C2—241no—
392C2#1174937211yescharacteristic
393C2D3×#396911yescharacteristic
394C2#1174942911yescharacteristic
subgroupG/H
centerC22D3×C22⋊Dic5
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#895C4
cosocleC3×C42×C5C23
hypercenter#125D3×D5
hypocenterC3×C5#1532
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
2. D3×#3935C2semidirect
3. #11746878C2semidirect
4. #11746364C2semidirect
5. C3×#64763C2semidirect
6. #11745847C2semidirect
7. #11745847C2semidirect
33. #64763D3semidirect
323. C3×C5#1532semidirect
372. C5#68366semidirect
389. C3#10602541semidirect

Maximal subgroups

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

subgroupindex
C5×#56912
D3×#39352
#117468782
#117463642
C3×#647632
#117458472
#106025413
#683665