Finite Group Databasebeta

← #14282195

Subgroups — #14282195

Order 1920.

492 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#6821C211yesmaximal, characteristic
2#11746937C211yesmaximal, characteristic, complemented
3#11746867C211yesmaximal, characteristic, complemented
4C5×#4535C211yesmaximal, characteristic, complemented
5C3×Q8⋊#168C211yesmaximal, characteristic, complemented
6#11745839C211yesmaximal, characteristic, complemented
7#11745838C211yesmaximal, characteristic, complemented
8#10599030—31nomaximal, Hall
9C2×#6821C411yescharacteristic
10C3×C4×C5×Q8C2211yescharacteristic
11Q8×Dic15C411yescharacteristic
12#91782—21no—
13#91782C411yescharacteristic
14#91781—21no—
15#91781C411yescharacteristic
16C4×D60—21no—
17C4×D60C2211yescharacteristic
18C42×D15—21no—
19C42×D15C2211yescharacteristic
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C4×C5×C3⋊C8C2211yescharacteristic
22C3×C4⋊#168C2211yescharacteristic
23C3×C4×#168C2211yescharacteristic
24#90983—21no—
25#90957—21no—
26#90957—21no—
27#90954—21no—
28#68237—51nomaximal, Hall
29C4×#713—31no—
30#65124—31no—
31#64974—31no—
32C5×Q8⋊C8—31no—
33Q8⋊#168D311yescharacteristic, complemented
34#64703—31no—
35#64679—31no—
36C2×C3×C5×Q8C2×C411yescharacteristic
37#6821—22no—
38#6821—22no—
39C2×D60—21no—
40C2×D60C2×C411yescharacteristic
41C2×C4×D15—21no—
42C2×C4×D15—21no—
43C2×C4×D15—21no—
44C2×C4×D15C2×C411yescharacteristic
45C2×C4×D15D411yescharacteristic
46C2×C4×D15D411yescharacteristic
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4C2×C411yescharacteristic
49C3×C42×C5—21no—
50C3×C42×C5C2311yescharacteristic
51#6714—21no—
52#6714—21no—
53#6714—21no—
54C4⋊Dic15—21no—
55C4⋊Dic15C2×C411yescharacteristic
56C4×Dic15—21no—
57C4×Dic15—21no—
58C4×Dic15C2×C411yescharacteristic
59C4×Dic15D411yescharacteristic
60C4×Dic15D411yescharacteristic
61C2×C5×C3⋊C8—21no—
62C2×C5×C3⋊C8—21no—
63C2×C3×#168—21no—
64C2×C3×#168—21no—
65C4×#239—51no—
66#4835—51no—
67#4685—51no—
68C3×Q8⋊C8—51no—
69#4535D511yescharacteristic, complemented
70#4483—51no—
71#4459—51no—
72C2×#713—31no—
73C4×C5×Q8C2×D311yescharacteristic
74Q8×Dic5—31no—
75#4039—31no—
76#4039—61no—
77#4038—31no—
78#4038—61no—
79C4×D20—31no—
80C4×D20—61no—
81C42×D5—31no—
82C42×D5—61no—
83C5×C4⋊C8—31no—
84C4×C5×C8—31no—
85#3952—61no—
86#3952—61no—
87#3947—61no—
88#3946—61no—
89C4⋊#168C2×D311yescharacteristic
90C4×#168C2×D311yescharacteristic
91#1488—151noSylow
92C22×D15—21no—
93C22×D15C22⋊C411yescharacteristic
94C3×C5×Q8—21no—
95C3×C5×Q8M1612yes—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5C22×C411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×Dic15—21no—
102C2×Dic15C22⋊C411yescharacteristic
103C2×Dic15C22⋊C411yescharacteristic
104C2×Dic15C22⋊C411yescharacteristic
105D60—24no—
106D60—21no—
107D60M1612yes—
108C4×D15—24no—
109C4×D15—21no—
110C4×D15—21no—
111C4×D15—21no—
112C4×D15—21no—
113C4×D15—41no—
114C4×D15—42no—
115C4×D15—41no—
116C4×D15—41no—
117C3×#168—41no—
118C3×#168—41no—
119C5×C3⋊C8—41no—
120C5×C3⋊C8—41no—
121C2×#239—51no—
122C3×C4×Q8C2×D511yescharacteristic
123Q8×Dic3—51no—
124#893—51no—
125#893—101no—
126#892—51no—
127#892—101no—
128C4×D12—51no—
129C4×D12—101no—
130C42×D3—51no—
131C42×D3—101no—
132C3×C4⋊C8—51no—
133C3×C4×C8—51no—
134(C2×D3)⋊C8—101no—
135(C2×D3)⋊C8—101no—
136#815—101no—
137Dic3⋊C8—101no—
138C4⋊(C3⋊C8)C2×D511yescharacteristic
139C4×C3⋊C8C2×D511yescharacteristic
140C2×C5×Q8C4×D311yescharacteristic
141#713—62no—
142#713—62no—
143C2×D20—31no—
144C2×D20—61no—
145C2×C4×D5—31no—
146C2×C4×D5—31no—
147C2×C4×D5—31no—
148C2×C4×D5—61no—
149C2×C4×D5—61no—
150C2×C4×D5—61no—
151C2×C5×C8—61no—
152C2×C5×C8—61no—
153C5×C4⋊C4—21no—
154C5×C4⋊C4C4×D311yescharacteristic
155C42×C5—21no—
156C42×C5C22×D311yescharacteristic
157#685—61no—
158#685—61no—
159#685—61no—
160C4⋊Dic5—31no—
161C4⋊Dic5—61no—
162C4×Dic5—31no—
163C4×Dic5—31no—
164C4×Dic5—31no—
165C4×Dic5—61no—
166C4×Dic5—61no—
167C2×#168—21no—
168C2×#168—21no—
169C4×#41—151no—
170#432—151no—
171#431—151no—
172Q8⋊C8—31no—
173Q8⋊C8—51no—
174D4⋊C8—151no—
175D4⋊C8—151no—
176C22×C3×C5C2×C22⋊C411yescharacteristic
177C2×D15—21no—
178C2×D15—22no—
179C2×D15—21no—
180C2×D15—21no—
181C2×D15—41no—
182C2×D15—41no—
183C3×C4×C5—22no—
184C3×C4×C5—21no—
185C3×C4×C5—41no—
186C3×C4×C5C2×M1611yescharacteristic
187C3×C4×C5C2×M1611yescharacteristic
188C3×C4×C5#13511yescharacteristic
189C3×C4×C5#13511yescharacteristic
190Dic15—21no—
191Dic15—21no—
192Dic15—21no—
193Dic15—41no—
194C2×C3×Q8C4×D511yescharacteristic
195#239—102no—
196#239—102no—
197C2×D12—51no—
198C2×D12—101no—
199C2×C4×D3—51no—
200C2×C4×D3—51no—
201C2×C4×D3—51no—
202C2×C4×D3—101no—
203C2×C4×D3—101no—
204C2×C4×D3—101no—
205C2×C3×C8—101no—
206C2×C3×C8—101no—
207C3×C4⋊C4—21no—
208C3×C4⋊C4C4×D511yescharacteristic
209C3×C42—21no—
210C3×C42C22×D511yescharacteristic
211(C2×D3)⋊C4—101no—
212(C2×D3)⋊C4—101no—
213(C2×D3)⋊C4—101no—
214C4⋊Dic3—51no—
215C4⋊Dic3—101no—
216C4×Dic3—51no—
217C4×Dic3—51no—
218C4×Dic3—51no—
219C4×Dic3—101no—
220C4×Dic3—101no—
221C2×C3⋊C8—21no—
222C2×C3⋊C8—21no—
223C22×D5—31no—
224C22×D5—61no—
225C5×Q8—21no—
226C5×Q8ΓL(1,𝔽25)12yes—
227C2×C4×C5—21no—
228C2×C4×C5—21no—
229C2×C4×C5C2×C4×D311yescharacteristic
230C2×C4×C5D3×D411yescharacteristic
231C2×C4×C5D3×D411yescharacteristic
232C2×Dic5—31no—
233C2×Dic5—31no—
234C2×Dic5—31no—
235C2×Dic5—61no—
236D20—32no—
237D20—64no—
238D20—61no—
239C4×D5—64no—
240C4×D5—61no—
241C4×D5—61no—
242C4×D5—61no—
243C4×D5—61no—
244C4×D5—121no—
245C4×D5—122no—
246C4×D5—121no—
247C4×D5—121no—
248C5×C8—121no—
249C5×C8—121no—
250#168—41no—
251#168—41no—
252C2×#41—151no—
253C4×Q8—151no—
254C4×Q8D3×D511yescharacteristic
255C4×D4—151no—
256C4×D4—151no—
257C4×D4—301no—
258C4×D4—301no—
259#117—151no—
260#117—301no—
261C2×C42—151no—
262C2×C42—301no—
263C4⋊C8—31no—
264C4⋊C8—51no—
265C4⋊C8—301no—
266C22⋊C8—301no—
267C22⋊C8—301no—
268#97—301no—
269C4×C8—31no—
270C4×C8—51no—
271C2×C3×C5#40711yescharacteristic
272C2×C3×C5#41611yescharacteristic
273C2×C3×C5#42111yescharacteristic
274D15—41no—
275D15—42no—
276C22×D3—51no—
277C22×D3—101no—
278C3×Q8—21no—
279C3×Q8#67612yes—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4C2×C4×D511yescharacteristic
283C2×C3×C4D4×D511yescharacteristic
284C2×C3×C4D4×D511yescharacteristic
285C2×Dic3—51no—
286C2×Dic3—51no—
287C2×Dic3—51no—
288C2×Dic3—101no—
289D12—52no—
290D12—104no—
291D12—101no—
292C4×D3—104no—
293C4×D3—101no—
294C4×D3—101no—
295C4×D3—101no—
296C4×D3—101no—
297C4×D3—201no—
298C4×D3—202no—
299C4×D3—201no—
300C4×D3—201no—
301C3×C8—201no—
302C3×C8—201no—
303C3⋊C8—41no—
304C3⋊C8—41no—
305C22×C5D3×C22⋊C411yescharacteristic
306C2×D5—62no—
307C2×D5—61no—
308C2×D5—61no—
309C2×D5—61no—
310C2×D5—121no—
311C2×D5—121no—
312C4×C5—22no—
313C4×C5—21no—
314C4×C5—41no—
315C4×C5C2×ΓL(1,𝔽25)11yescharacteristic
316C4×C5D3×M1611yescharacteristic
317C4×C5#91611yescharacteristic
318C4×C5#91911yescharacteristic
319Dic5—61no—
320Dic5—61no—
321Dic5—61no—
322Dic5—121no—
323#41—302no—
324#41—302no—
325C2×Q8#120011yescharacteristic
326C2×D4—151no—
327C2×D4—301no—
328C22×C4—151no—
329C22×C4—151no—
330C22×C4—151no—
331C22×C4—301no—
332C22×C4—301no—
333C22×C4—301no—
334C2×C8—61no—
335C2×C8—61no—
336C2×C8—101no—
337C2×C8—101no—
338C4⋊C4—21no—
339C4⋊C4—151no—
340C4⋊C4—301no—
341C4⋊C4#120011yescharacteristic
342C22⋊C4—301no—
343C22⋊C4—301no—
344C22⋊C4—301no—
345C42—21no—
346C42—151no—
347C42—151no—
348C42—151no—
349C42—301no—
350C42—301no—
351C42C2×D3×D511yescharacteristic
352C3×C5#148811yescharacteristic, complemented, Hall
353C22×C3D5×C22⋊C411yescharacteristic
354C2×D3—101no—
355C2×D3—101no—
356C2×D3—102no—
357C2×D3—101no—
358C2×D3—201no—
359C2×D3—201no—
360C3×C4—21no—
361C3×C4—22no—
362C3×C4—41no—
363C3×C4C2×#67611yescharacteristic
364C3×C4D5×M1611yescharacteristic
365C3×C4#406211yescharacteristic
366C3×C4#406511yescharacteristic
367Dic3—101no—
368Dic3—101no—
369Dic3—101no—
370Dic3—201no—
371C2×C5#472611yescharacteristic
372C2×C5#480411yescharacteristic
373C2×C5#482111yescharacteristic
374D5—121no—
375D5—122no—
376C23—151no—
377C23—301no—
378Q8—21no—
379Q8#665112yes—
380D4—152no—
381D4—304no—
382D4—301no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—151no—
386C2×C4—151no—
387C2×C4—151no—
388C2×C4—304no—
389C2×C4—301no—
390C2×C4—301no—
391C2×C4—301no—
392C2×C4—301no—
393C2×C4—301no—
394C2×C4—601no—
395C2×C4—602no—
396C2×C4—601no—
397C2×C4—601no—
398C2×C4C2×#120011yescharacteristic
399C2×C4#679011yescharacteristic
400C2×C4#679011yescharacteristic
401C8—121no—
402C8—121no—
403C8—201no—
404C8—201no—
405C2×C3#6501511yescharacteristic
406C2×C3#6509311yescharacteristic
407C2×C3#6511011yescharacteristic
408D3—201no—
409D3—202no—
410C5#6823711yescharacteristic, complemented, Sylow
411C22—301no—
412C22—301no—
413C22—302no—
414C22—301no—
415C22—601no—
416C22—601no—
417C22#9156111yescharacteristic
418C4—21no—
419C4—22no—
420C4—41no—
421C4—301no—
422C4—301no—
423C4—301no—
424C4—601no—
425C4#9129211yescharacteristic
426C4C2×#665111yescharacteristic
427C4#9152111yescharacteristic
428C4#9152311yescharacteristic
429C3#1059903011yescharacteristic, complemented, Sylow
430C2—601no—
431C2—602no—
432C2#1174850911yescharacteristic
433C2#1174921511yescharacteristic
434C2#1174943111yescharacteristic
subgroupG/H
centerC2×C4#6790
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×#6821C4
cosocleC3×C42×C5C23
hypercenterC4×Q8D3×D5
hypocenterC3×C5#1488
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. #11746937C2semidirect
3. #11746867C2semidirect
4. C5×#4535C2semidirect
5. C3×Q8⋊#168C2semidirect
6. #11745839C2semidirect
7. #11745838C2semidirect
33. Q8⋊#168D3semidirect
69. #4535D5semidirect
352. C3×C5#1488semidirect
410. C5#68237semidirect
429. C3#10599030semidirect

Maximal subgroups

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

subgroupindex
C4×#68212
#117469372
#117468672
C5×#45352
C3×Q8⋊#1682
#117458392
#117458382
#105990303
#682375