Finite Group Databasebeta

← #14282189

Subgroups — #14282189

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×#6768C211yesmaximal, characteristic
2#11750786C211yesmaximal, characteristic, complemented
3#11746867C211yesmaximal, characteristic, complemented
4C5×#4459C211yesmaximal, characteristic, complemented
5C3×#64676C211yesmaximal, characteristic, complemented
6#11745840C211yesmaximal, characteristic, complemented
7#11745836C211yesmaximal, characteristic, complemented
8#10598966—31nomaximal, Hall
9C2×#6768C411yescharacteristic
10C42×D15C2211yescharacteristic
11C4×C5×D12C2211yescharacteristic
12C3×C4×Dic10C2211yescharacteristic
13C4×#1203—21no—
14#91435C411yescharacteristic
15#91406—21no—
16#91400—21no—
17C4×D3×Dic5—21no—
18#91347C411yescharacteristic
19#91331C411yescharacteristic
20C3×C4×C5×C8C2211yescharacteristic
21#91104—21no—
22#91098—21no—
23C4×C3⋊#168C2211yescharacteristic
24C5×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×C4⋊#168C2211yescharacteristic
26#90957—21no—
27#90954—21no—
28#68237—51nomaximal, Hall
29C4×#711—31no—
30#65124—31no—
31#64974—31no—
32C5×D4⋊C8—31no—
33D4⋊#168—31no—
34#64704—31no—
35#64676D311yescharacteristic, complemented
36C2×C4×D15C2×C411yescharacteristic
37C2×C4×D15D411yescharacteristic
38C2×C4×D15D411yescharacteristic
39C2×C5×D12C2×C411yescharacteristic
40C2×C4×C5×D3—21no—
41C2×C3×Dic10C2×C411yescharacteristic
42C2×#1203—21no—
43C2×D3×Dic5—21no—
44C2×D3×Dic5—21no—
45#6768—22no—
46#6768—22no—
47C2×C3×C5×C8—21no—
48C3×C42×C5C2311yescharacteristic
49C4×Dic15C2×C411yescharacteristic
50C4×Dic15D411yescharacteristic
51C4×Dic15D411yescharacteristic
52C2×C3⋊#168—21no—
53C5×(C2×D3)⋊C4—21no—
54C5×C4⋊Dic3C2×C411yescharacteristic
55C2×C5×C3⋊C8—21no—
56C3×C4⋊Dic5C2×C411yescharacteristic
57C3×#683—21no—
58C3×C4×Dic5—21no—
59C2×C3×#168—21no—
60#6668—21no—
61#6667—21no—
62(C2×D3)⋊Dic5—21no—
63Dic3×Dic5—21no—
64Dic3×Dic5—21no—
65C4×#239—51no—
66#4835—51no—
67#4685—51no—
68C3×Q8⋊C8—51no—
69#4535—51no—
70#4483—51no—
71#4459D511yescharacteristic, complemented
72C2×#711—31no—
73C4×C5×D4—31no—
74D4×Dic5—31no—
75C4×C22⋊D5—61no—
76C2×C4×Dic5—61no—
77#4038—31no—
78#4033—31no—
79#4027—61no—
80#4023—61no—
81C42×D5—31no—
82C4×Dic10C2×D311yescharacteristic
83C5×C4⋊C8—31no—
84C4×C5×C8C2×D311yescharacteristic
85#3952—61no—
86#3952—61no—
87#3947—61no—
88#3946—61no—
89C4⋊#168C2×D311yescharacteristic
90C4×#168—31no—
91#1488—151noSylow
92C22×D15C22⋊C411yescharacteristic
93C22×C5×D3—21no—
94C2×C3×C4×C5C22×C411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×Dic15C22⋊C411yescharacteristic
98C2×Dic15C22⋊C411yescharacteristic
99C2×Dic15C22⋊C411yescharacteristic
100C4×D15—21no—
101C4×D15—21no—
102C4×D15—21no—
103C4×D15—21no—
104C4×D15—41no—
105C2×C5×Dic3—21no—
106C5×D12—21no—
107C5×D12M1612yes—
108C4×C5×D3—41no—
109C4×C5×D3—41no—
110C2×C3×Dic5—21no—
111C2×C3×Dic5—21no—
112C3×Dic10—21no—
113C3×Dic10M1612yes—
114#1203—24no—
115D3×Dic5—24no—
116D3×Dic5—42no—
117C3×C5×C8—41no—
118C3⋊#168—41no—
119C3×#168—41no—
120C5×C3⋊C8—41no—
121C2×#239—51no—
122C3×C4×Q8—51no—
123Q8×Dic3—51no—
124#893—51no—
125#893—101no—
126#892—51no—
127#892—101no—
128C4×D12—101no—
129C4×D12C2×D511yescharacteristic
130C42×D3—51no—
131C42×D3—101no—
132C3×C4⋊C8—51no—
133C3×C4×C8C2×D511yescharacteristic
134(C2×D3)⋊C8—101no—
135(C2×D3)⋊C8—101no—
136#815—101no—
137Dic3⋊C8—101no—
138C4⋊(C3⋊C8)C2×D511yescharacteristic
139C4×C3⋊C8—51no—
140C2×C5×D4—31no—
141C22×C4×C5—61no—
142C2×C22⋊D5—61no—
143C22×Dic5—61no—
144C22×Dic5—61no—
145#711—62no—
146#711—62no—
147C2×C4×D5—31no—
148C2×C4×D5—31no—
149C2×C4×D5—31no—
150C2×Dic10C4×D311yescharacteristic
151C2×C5×C8—21no—
152C2×C5×C8—61no—
153C5×C4⋊C4—31no—
154C5×C22⋊C4—61no—
155C42×C5C22×D311yescharacteristic
156C22⋊Dic5—61no—
157#685—61no—
158C4⋊Dic5C4×D311yescharacteristic
159#683—21no—
160#683—61no—
161C4×Dic5—21no—
162C4×Dic5—31no—
163C4×Dic5—31no—
164C4×Dic5—31no—
165C4×Dic5—61no—
166C4×Dic5—61no—
167C2×#168—21no—
168C2×#168—61no—
169C4×#41—151no—
170#432—151no—
171#431—151no—
172Q8⋊C8—51no—
173Q8⋊C8—151no—
174D4⋊C8—31no—
175D4⋊C8—151no—
176C22×C3×C5C2×C22⋊C411yescharacteristic
177C2×D15—21no—
178C2×D15—21no—
179C2×D15—21no—
180C2×C5×D3—22no—
181C2×C5×D3—41no—
182C2×C5×D3—41no—
183C3×C4×C5—21no—
184C3×C4×C5C2×M1611yescharacteristic
185C3×C4×C5C2×M1611yescharacteristic
186C3×C4×C5#13511yescharacteristic
187C3×C4×C5#13511yescharacteristic
188Dic15—21no—
189Dic15—21no—
190Dic15—21no—
191C3×Dic5—22no—
192C3×Dic5—41no—
193C5×Dic3—41no—
194C2×C3×Q8—51no—
195#239—102no—
196#239—102no—
197C2×D12—101no—
198C2×D12C4×D511yescharacteristic
199C2×C4×D3—21no—
200C2×C4×D3—51no—
201C2×C4×D3—51no—
202C2×C4×D3—51no—
203C2×C4×D3—101no—
204C2×C4×D3—101no—
205C2×C3×C8—21no—
206C2×C3×C8—101no—
207C3×C4⋊C4—51no—
208C3×C4⋊C4—101no—
209C3×C42—101no—
210C3×C42C22×D511yescharacteristic
211(C2×D3)⋊C4—21no—
212(C2×D3)⋊C4—101no—
213(C2×D3)⋊C4—101no—
214C4⋊Dic3—101no—
215C4⋊Dic3C4×D511yescharacteristic
216C4×Dic3—51no—
217C4×Dic3—51no—
218C4×Dic3—51no—
219C4×Dic3—101no—
220C4×Dic3—101no—
221C2×C3⋊C8—21no—
222C2×C3⋊C8—101no—
223C23×C5—61no—
224C22×D5—31no—
225C5×D4—32no—
226C5×D4—61no—
227C2×C4×C5—61no—
228C2×C4×C5—121no—
229C2×C4×C5—121no—
230C2×C4×C5C2×C4×D311yescharacteristic
231C2×C4×C5D3×D411yescharacteristic
232C2×C4×C5D3×D411yescharacteristic
233C22⋊D5—64no—
234C2×Dic5—21no—
235C2×Dic5—21no—
236C2×Dic5—31no—
237C2×Dic5—31no—
238C2×Dic5—31no—
239C2×Dic5—64no—
240C2×Dic5—122no—
241C4×D5—61no—
242C4×D5—61no—
243C4×D5—61no—
244C4×D5—61no—
245C4×D5—121no—
246Dic10—21no—
247Dic10ΓL(1,𝔽25)12yes—
248C5×C8—41no—
249C5×C8—121no—
250#168—41no—
251#168—121no—
252C2×#41—151no—
253C4×Q8—51no—
254C4×Q8—151no—
255C4×D4—31no—
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—151no—
270C4×C8D3×D511yescharacteristic
271C2×C3×C5#40711yescharacteristic
272C2×C3×C5#41611yescharacteristic
273C2×C3×C5#42111yescharacteristic
274D15—41no—
275C5×D3—42no—
276C22×D3—21no—
277C22×D3—51no—
278C3×Q8—52no—
279C3×Q8—101no—
280C2×C3×C4—101no—
281C2×C3×C4—101no—
282C2×C3×C4C2×C4×D511yescharacteristic
283C2×C3×C4D4×D511yescharacteristic
284C2×C3×C4D4×D511yescharacteristic
285C2×Dic3—21no—
286C2×Dic3—51no—
287C2×Dic3—51no—
288C2×Dic3—51no—
289D12—21no—
290D12—104no—
291D12#67612yes—
292C4×D3—41no—
293C4×D3—41no—
294C4×D3—104no—
295C4×D3—101no—
296C4×D3—101no—
297C4×D3—101no—
298C4×D3—101no—
299C4×D3—201no—
300C4×D3—202no—
301C3×C8—41no—
302C3×C8—201no—
303C3⋊C8—41no—
304C3⋊C8—201no—
305C22×C5—62no—
306C22×C5—121no—
307C22×C5—121no—
308C22×C5D3×C22⋊C411yescharacteristic
309C2×D5—61no—
310C2×D5—61no—
311C2×D5—61no—
312C4×C5—21no—
313C4×C5—121no—
314C4×C5C2×ΓL(1,𝔽25)11yescharacteristic
315C4×C5D3×M1611yescharacteristic
316C4×C5#91611yescharacteristic
317C4×C5#91911yescharacteristic
318Dic5—22no—
319Dic5—41no—
320Dic5—61no—
321Dic5—61no—
322Dic5—61no—
323#41—302no—
324#41—302no—
325C2×Q8—51no—
326C2×D4—31no—
327C2×D4—301no—
328C22×C4—61no—
329C22×C4—151no—
330C22×C4—151no—
331C22×C4—151no—
332C22×C4—301no—
333C22×C4—301no—
334C2×C8—21no—
335C2×C8—61no—
336C2×C8—101no—
337C2×C8—301no—
338C4⋊C4—31no—
339C4⋊C4—51no—
340C4⋊C4—101no—
341C4⋊C4—301no—
342C22⋊C4—61no—
343C22⋊C4—301no—
344C22⋊C4—301no—
345C42—101no—
346C42—151no—
347C42—151no—
348C42—151no—
349C42—301no—
350C42—301no—
351C42C2×D3×D511yescharacteristic
352C3×C5#148811yescharacteristic, complemented, Hall
353C22×C3D5×C22⋊C411yescharacteristic
354C2×D3—22no—
355C2×D3—41no—
356C2×D3—41no—
357C2×D3—101no—
358C2×D3—101no—
359C2×D3—101no—
360C3×C4—21no—
361C3×C4—102no—
362C3×C4—201no—
363C3×C4C2×#67611yescharacteristic
364C3×C4D5×M1611yescharacteristic
365C3×C4#405811yescharacteristic
366C3×C4#406211yescharacteristic
367Dic3—41no—
368Dic3—101no—
369Dic3—101no—
370Dic3—101no—
371C2×C5—122no—
372C2×C5#472611yescharacteristic
373C2×C5#480411yescharacteristic
374C2×C5#482111yescharacteristic
375D5—121no—
376C23—61no—
377C23—151no—
378Q8—52no—
379Q8—101no—
380D4—32no—
381D4—61no—
382D4—304no—
383C2×C4—61no—
384C2×C4—101no—
385C2×C4—101no—
386C2×C4—121no—
387C2×C4—121no—
388C2×C4—151no—
389C2×C4—151no—
390C2×C4—151no—
391C2×C4—304no—
392C2×C4—301no—
393C2×C4—301no—
394C2×C4—301no—
395C2×C4—301no—
396C2×C4—601no—
397C2×C4—602no—
398C2×C4C4×D3×D511yescharacteristic
399C2×C4#677711yescharacteristic
400C2×C4#679011yescharacteristic
401C8—41no—
402C8—121no—
403C8—201no—
404C8—601no—
405C2×C3#6501511yescharacteristic
406C2×C3#6506111yescharacteristic
407C2×C3#6511011yescharacteristic
408D3—42no—
409D3—201no—
410C5#6823711yescharacteristic, complemented, Sylow
411C22—62no—
412C22—121no—
413C22—121no—
414C22—301no—
415C22—301no—
416C22—301no—
417C22#9147311yescharacteristic
418C4—21no—
419C4—102no—
420C4—121no—
421C4—201no—
422C4—301no—
423C4—301no—
424C4—301no—
425C4D5×ΓL(1,𝔽25)11yescharacteristic
426C4D3×#67611yescharacteristic
427C4#9127611yescharacteristic
428C4#9127911yescharacteristic
429C3#1059896611yescharacteristic, complemented, Sylow
430C2—122no—
431C2—601no—
432C2#1174711311yescharacteristic
433C2#1174810311yescharacteristic
434C2#1174814511yescharacteristic
subgroupG/H
centerC2×C4#6777
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×#6768C4
cosocleC3×C42×C5C23
hypercenterC4×C8D3×D5
hypocenterC3×C5#1488
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #11750786C2semidirect
3. #11746867C2semidirect
4. C5×#4459C2semidirect
5. C3×#64676C2semidirect
6. #11745840C2semidirect
7. #11745836C2semidirect
35. #64676D3semidirect
71. #4459D5semidirect
352. C3×C5#1488semidirect
410. C5#68237semidirect
429. C3#10598966semidirect

Maximal subgroups

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

subgroupindex
C4×#67682
#117507862
#117468672
C5×#44592
C3×#646762
#117458402
#117458362
#105989663
#682375