Finite Group Databasebeta

← #14282178

Subgroups — #14282178

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×#6773C211yesmaximal, characteristic
2C3×#65124C211yesmaximal, characteristic, complemented
3#11746868C211yesmaximal, characteristic, complemented
4#11746304C211yesmaximal, characteristic, complemented
5C5×#4484C211yesmaximal, characteristic, complemented
6#11745842C211yesmaximal, characteristic, complemented
7#11745838C211yesmaximal, characteristic, complemented
8#10599030—31nomaximal, Hall
9C2×#6773C411yescharacteristic
10C4×D60C2211yescharacteristic
11C4×C5×Dic6C2211yescharacteristic
12C3×C42×D5C2211yescharacteristic
13#91444—21no—
14C4×#1202—21no—
15#91418C411yescharacteristic
16#91402—21no—
17C4×#1200—21no—
18#91358C411yescharacteristic
19Dic5×Dic6C411yescharacteristic
20C3×C5×C4⋊C8C2211yescharacteristic
21C4×C3⋊#168C2211yescharacteristic
22C4×C5×C3⋊C8C2211yescharacteristic
23C3×#3952—21no—
24C3×#3947—21no—
25C3×C4⋊#168C2211yescharacteristic
26#90982—21no—
27#90955—21no—
28#70798—51nomaximal, Hall
29C4×#713—31no—
30#65124D311yescharacteristic, complemented
31#64974—31no—
32C5×Q8⋊C8—31no—
33Q8⋊#168—31no—
34#64703—31no—
35#64679—31no—
36C2×D60C2×C411yescharacteristic
37C2×C4×D15—21no—
38C2×C5×Dic6C2×C411yescharacteristic
39C2×C3×C4×D5C2×C411yescharacteristic
40C2×C3×C4×D5D411yescharacteristic
41C2×C3×C4×D5D411yescharacteristic
42C2×#1202—21no—
43C2×#1200—21no—
44C2×#1200—21no—
45#6773—22no—
46#6773—22no—
47C2×C3×C5×C8—21no—
48C3×C42×C5C2311yescharacteristic
49#6714—21no—
50C4⋊Dic15C2×C411yescharacteristic
51C2×C3⋊#168—21no—
52C5×C4⋊Dic3C2×C411yescharacteristic
53C5×Dic3⋊C4—21no—
54C4×C5×Dic3—21no—
55C2×C5×C3⋊C8—21no—
56C3×C4×Dic5C2×C411yescharacteristic
57C3×C4×Dic5D411yescharacteristic
58C3×C4×Dic5D411yescharacteristic
59C2×C3×#168—21no—
60Dic3⋊Dic5—21no—
61#6667—21no—
62#6665—21no—
63Dic3×Dic5—21no—
64Dic3×Dic5—21no—
65C4×#235—51no—
66C3×#432—51no—
67#4925—51no—
68#4484—51no—
69#4484D511yescharacteristic, complemented
70#4483—51no—
71#4483—51no—
72C2×#713—31no—
73C4×C5×Q8—31no—
74Q8×Dic5—31no—
75#4039—31no—
76#4039—61no—
77#4038—31no—
78#4038—61no—
79C4×D20—31no—
80C4×D20—61no—
81C42×D5—61no—
82C42×D5C2×D311yescharacteristic
83C5×C4⋊C8C2×D311yescharacteristic
84C4×C5×C8—31no—
85#3952—21no—
86#3952—61no—
87#3947—21no—
88#3946—61no—
89C4⋊#168C2×D311yescharacteristic
90C4×#168—31no—
91#1488—151noSylow
92C22×D15—21no—
93C22×C3×D5C22⋊C411yescharacteristic
94C2×C3×C4×C5C22×C411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×Dic15—21no—
98D60—21no—
99D60M1612yes—
100C4×D15—41no—
101C4×D15—41no—
102C2×C5×Dic3—21no—
103C2×C5×Dic3—21no—
104C5×Dic6—21no—
105C5×Dic6M1612yes—
106C2×C3×Dic5C22⋊C411yescharacteristic
107C2×C3×Dic5C22⋊C411yescharacteristic
108C2×C3×Dic5C22⋊C411yescharacteristic
109C3×C4×D5—21no—
110C3×C4×D5—21no—
111C3×C4×D5—21no—
112C3×C4×D5—21no—
113C3×C4×D5—41no—
114#1202—24no—
115#1200—24no—
116#1200—42no—
117C3×C5×C8—41no—
118C3⋊#168—41no—
119C3×#168—41no—
120C5×C3⋊C8—41no—
121C2×#235—51no—
122C2×C3×C42—51no—
123C4×#67—101no—
124C4×#67—101no—
125#926—51no—
126C4×D12—51no—
127C4×D12—51no—
128#872—101no—
129C42×D3—101no—
130C4×Dic6—51no—
131C4×Dic6C2×D511yescharacteristic
132C3×C4⋊C8—51no—
133C3×C4⋊C8C2×D511yescharacteristic
134C3×C22⋊C8—101no—
135C3×#97—101no—
136#830—101no—
137C4⋊(C3⋊C8)—101no—
138C4×C3⋊C8—51no—
139C4×C3⋊C8C2×D511yescharacteristic
140C2×C5×Q8—31no—
141#713—62no—
142#713—62no—
143C2×D20—31no—
144C2×D20—61no—
145C2×C4×D5—61no—
146C2×C4×D5—61no—
147C2×C4×D5—61no—
148C2×C4×D5C4×D311yescharacteristic
149C2×C4×D5D1211yescharacteristic
150C2×C4×D5#6711yescharacteristic
151C2×C5×C8—21no—
152C2×C5×C8—61no—
153C5×C4⋊C4—31no—
154C5×C4⋊C4—61no—
155C42×C5—61no—
156C42×C5C22×D311yescharacteristic
157#685—61no—
158#685—61no—
159#685—61no—
160C4⋊Dic5—31no—
161C4⋊Dic5—61no—
162C4×Dic5—61no—
163C4×Dic5—61no—
164C4×Dic5C4×D311yescharacteristic
165C4×Dic5D1211yescharacteristic
166C4×Dic5#6711yescharacteristic
167C2×#168—21no—
168C2×#168—61no—
169C4×#41—151no—
170#432—51no—
171#431—151no—
172Q8⋊C8—31no—
173Q8⋊C8—151no—
174D4⋊C8—151no—
175D4⋊C8—151no—
176C22×C3×C5C2×C22⋊C411yescharacteristic
177C2×D15—22no—
178C2×D15—41no—
179C2×D15—41no—
180C2×C3×D5—21no—
181C2×C3×D5—21no—
182C2×C3×D5—21no—
183C3×C4×C5—21no—
184C3×C4×C5C2×M1611yescharacteristic
185C3×C4×C5C2×M1611yescharacteristic
186C3×C4×C5#13511yescharacteristic
187C3×C4×C5#13511yescharacteristic
188Dic15—41no—
189C3×Dic5—21no—
190C3×Dic5—21no—
191C3×Dic5—21no—
192C5×Dic3—22no—
193C5×Dic3—41no—
194C22×C3×C4—51no—
195C22×C3×C4—51no—
196C22×C3×C4—51no—
197C2×#67—101no—
198#235—102no—
199#235—102no—
200C2×D12—51no—
201C2×C4×D3—101no—
202C2×C4×D3—101no—
203C2×C4×D3—101no—
204C2×Dic6C4×D511yescharacteristic
205C2×C3×C8—21no—
206C2×C3×C8—101no—
207C3×C42—51no—
208C3×C42—51no—
209C3×C42—51no—
210C3×C42C22×D511yescharacteristic
211#217—101no—
212(C2×D3)⋊C4—101no—
213(C2×D3)⋊C4—101no—
214C4⋊Dic3—51no—
215C4⋊Dic3C4×D511yescharacteristic
216Dic3⋊C4—21no—
217Dic3⋊C4—101no—
218C4×Dic3—21no—
219C4×Dic3—101no—
220C4×Dic3—101no—
221C2×C3⋊C8—21no—
222C2×C3⋊C8—101no—
223C22×D5—61no—
224C22×D5(C2×D3)⋊C411yescharacteristic
225C5×Q8—32no—
226C5×Q8—61no—
227C2×C4×C5—61no—
228C2×C4×C5—61no—
229C2×C4×C5C2×C4×D311yescharacteristic
230C2×C4×C5C2×D1211yescharacteristic
231C2×C4×C5C2×#6711yescharacteristic
232C2×Dic5—61no—
233C2×Dic5(C2×D3)⋊C411yescharacteristic
234C2×Dic5(C2×D3)⋊C411yescharacteristic
235C2×Dic5(C2×D3)⋊C411yescharacteristic
236D20—32no—
237D20—64no—
238D20—61no—
239C4×D5—21no—
240C4×D5—21no—
241C4×D5—21no—
242C4×D5—21no—
243C4×D5—41no—
244C4×D5—64no—
245C4×D5—122no—
246C4×D5—121no—
247C4×D5—121no—
248C5×C8—41no—
249C5×C8—121no—
250#168—41no—
251#168—121no—
252C2×#41—151no—
253C4×Q8—31no—
254C4×Q8—151no—
255C4×D4—151no—
256C4×D4—151no—
257C4×D4—301no—
258C4×D4—301no—
259#117—151no—
260#117—301no—
261C2×C42—51no—
262C2×C42—301no—
263C4⋊C8—51no—
264C4⋊C8—301no—
265C4⋊C8D3×D511yescharacteristic
266C22⋊C8—101no—
267C22⋊C8—301no—
268#97—101no—
269C4×C8—31no—
270C4×C8—151no—
271C2×C3×C5#40711yescharacteristic
272C2×C3×C5#41611yescharacteristic
273C2×C3×C5#42111yescharacteristic
274D15—42no—
275C3×D5—41no—
276C23×C3—51no—
277C22×D3—101no—
278C2×C3×C4—51no—
279C2×C3×C4—51no—
280C2×C3×C4—51no—
281C2×C3×C4—101no—
282C2×C3×C4—101no—
283C2×C3×C4—101no—
284C2×C3×C4—101no—
285C2×C3×C4—201no—
286C2×C3×C4C2×C4×D511yescharacteristic
287C2×C3×C4D4×D511yescharacteristic
288C2×C3×C4D4×D511yescharacteristic
289#67—104no—
290C2×Dic3—21no—
291C2×Dic3—21no—
292C2×Dic3—101no—
293D12—52no—
294D12—101no—
295C4×D3—104no—
296C4×D3—202no—
297C4×D3—201no—
298C4×D3—201no—
299Dic6—21no—
300Dic6#67612yes—
301C3×C8—41no—
302C3×C8—201no—
303C3⋊C8—41no—
304C3⋊C8—201no—
305C22×C5C2×(C2×D3)⋊C411yescharacteristic
306C2×D5—21no—
307C2×D5—21no—
308C2×D5—21no—
309C2×D5—62no—
310C2×D5—121no—
311C2×D5—121no—
312C4×C5—21no—
313C4×C5—62no—
314C4×C5—121no—
315C4×C5D3×M1611yescharacteristic
316C4×C5D3×M1611yescharacteristic
317C4×C5#95011yescharacteristic
318C4×C5#95011yescharacteristic
319Dic5—21no—
320Dic5—21no—
321Dic5—21no—
322Dic5—121no—
323#41—302no—
324#41—302no—
325C2×Q8—31no—
326C2×D4—151no—
327C2×D4—301no—
328C22×C4—51no—
329C22×C4—51no—
330C22×C4—51no—
331C22×C4—301no—
332C22×C4—301no—
333C22×C4—301no—
334C2×C8—21no—
335C2×C8—61no—
336C2×C8—101no—
337C2×C8—301no—
338C4⋊C4—31no—
339C4⋊C4—61no—
340C4⋊C4—151no—
341C4⋊C4—301no—
342C22⋊C4—301no—
343C22⋊C4—301no—
344C22⋊C4—301no—
345C42—51no—
346C42—51no—
347C42—51no—
348C42—61no—
349C42—301no—
350C42—301no—
351C42C2×D3×D511yescharacteristic
352C3×C5#148811yescharacteristic, complemented, Hall
353C22×C3—101no—
354C22×C3—101no—
355C22×C3—101no—
356C22×C3D5×C22⋊C411yescharacteristic
357C2×D3—102no—
358C2×D3—201no—
359C2×D3—201no—
360C3×C4—21no—
361C3×C4—101no—
362C3×C4—101no—
363C3×C4—101no—
364C3×C4C2×#67611yescharacteristic
365C3×C4D5×M1611yescharacteristic
366C3×C4#406211yescharacteristic
367C3×C4#406511yescharacteristic
368Dic3—22no—
369Dic3—41no—
370Dic3—201no—
371C2×C5#500211yescharacteristic
372C2×C5#512611yescharacteristic
373C2×C5#513911yescharacteristic
374D5—41no—
375D5—122no—
376C23—51no—
377C23—301no—
378Q8—32no—
379Q8—61no—
380D4—152no—
381D4—304no—
382D4—301no—
383C2×C4—51no—
384C2×C4—51no—
385C2×C4—51no—
386C2×C4—61no—
387C2×C4—61no—
388C2×C4—101no—
389C2×C4—101no—
390C2×C4—101no—
391C2×C4—101no—
392C2×C4—201no—
393C2×C4—304no—
394C2×C4—301no—
395C2×C4—602no—
396C2×C4—601no—
397C2×C4—601no—
398C2×C4C4×D3×D511yescharacteristic
399C2×C4D5×D1211yescharacteristic
400C2×C4D5×#6711yescharacteristic
401C8—41no—
402C8—121no—
403C8—201no—
404C8—601no—
405C2×C3—201no—
406C2×C3#6501511yescharacteristic
407C2×C3#6509311yescharacteristic
408C2×C3#6511011yescharacteristic
409D3—202no—
410C5#7079811yescharacteristic, complemented, Sylow
411C22—101no—
412C22—101no—
413C22—101no—
414C22—302no—
415C22—601no—
416C22—601no—
417C22D5×(C2×D3)⋊C411yescharacteristic
418C4—21no—
419C4—62no—
420C4—101no—
421C4—101no—
422C4—101no—
423C4—121no—
424C4—601no—
425C4D3×#67611yescharacteristic
426C4#9124611yescharacteristic
427C4#9149211yescharacteristic
428C4#9151611yescharacteristic
429C3#1059903011yescharacteristic, complemented, Sylow
430C2—201no—
431C2—602no—
432C2#1174750111yescharacteristic
433C2#1174810111yescharacteristic
434C2#1174822911yescharacteristic
subgroupG/H
centerC2×C4D5×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×#6773C4
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. C3×#65124C2semidirect
3. #11746868C2semidirect
4. #11746304C2semidirect
5. C5×#4484C2semidirect
6. #11745842C2semidirect
7. #11745838C2semidirect
30. #65124D3semidirect
69. #4484D5semidirect
352. C3×C5#1488semidirect
410. C5#70798semidirect
429. C3#10599030semidirect

Maximal subgroups

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

subgroupindex
C4×#67732
C3×#651242
#117468682
#117463042
C5×#44842
#117458422
#117458382
#105990303
#707985