Finite Group Databasebeta

← #14298650

Subgroups — #14298650

Order 1920.

592 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5486C211yesmaximal, characteristic
2C2×#90996C211yesmaximal, characteristic
3C2×#90996C211yesmaximal, characteristic
4#11746348C211yesmaximal, characteristic, complemented
5C3×#64747C211yesmaximal, characteristic, complemented
6#11746020C211yesmaximal, characteristic, complemented
7#11746019C211yesmaximal, characteristic, complemented
8#10602446—31nomaximal, Hall
9C22×C5×#67C2211yescharacteristic
10C2×C3×C5×C22⋊C4C2211yescharacteristic
11C2×#6719C2211yescharacteristic
12C2×#6719C2211yescharacteristic
13C2×C5×#217C2211yescharacteristic
14C4×C5×#67—22no—
15C5×#67⋊C4—22no—
16C5×D3×C22⋊C4C412yescomplemented
17C5×#877C412yescomplemented
18C2×C3×C22⋊Dic5C2211yescharacteristic
19C2×C3×C22⋊Dic5C2211yescharacteristic
20#90996—22no—
21#90996—22no—
22#68960—51nomaximal, Hall
23C5×#518—31no—
24C2×#3966—31no—
25C2×#3966—31no—
26#64747—31no—
27#64747—31no—
28#64747—31no—
29#64747D311yescharacteristic, complemented
30C24×C3×C5C2311yescharacteristic
31C23×C5×D3C2×C411yescharacteristic
32C22×C3×C4×C5—21no—
33C22×Dic15—21no—
34C22×Dic15—21no—
35C2×C5×#67—21no—
36C2×C5×#67—21no—
37C2×C5×#67—21no—
38C2×C5×#67—21no—
39C2×C5×#67D412yes—
40C2×C5×#67D412yes—
41C22×C5×Dic3—21no—
42C22×C5×Dic3C2×C411yescharacteristic
43C2×C4×C5×D3—22no—
44C22×C3×Dic5—21no—
45C22×C3×Dic5—21no—
46C3×C5×C22⋊C4—21no—
47C3×C5×C22⋊C4C2×C412yes—
48#6719—21no—
49#6719—21no—
50#6719—21no—
51#6719—21no—
52C5×#217—21no—
53C5×#217C2×C412yes—
54C5×(C2×D3)⋊C4—22no—
55C5×Dic3⋊C4—22no—
56C4×C5×Dic3—22no—
57C3×C22⋊Dic5—21no—
58C3×C22⋊Dic5—21no—
59C3×C22⋊Dic5—21no—
60C3×C22⋊Dic5—21no—
61#5486D511yescharacteristic
62C2×#806—51no—
63C2×#806—51no—
64C3×#342—51no—
65#4527—51no—
66#4527—51no—
67#4526—51no—
68C22×C5×D4—31no—
69C4×C5×D4—62no—
70C4×C5×D4—62no—
71C5×#117—32no—
72C2×C5×C22⋊C4—31no—
73C2×C5×C22⋊C4—32no—
74C2×C5×C22⋊C4C2×D311yescharacteristic
75C2×C22⋊Dic5—31no—
76C2×C22⋊Dic5—31no—
77C2×C22⋊Dic5C2×D311yescharacteristic
78C2×C22⋊Dic5C2×D311yescharacteristic
79#3966—62no—
80#3966—62no—
81#1828—151noSylow
82C23×C3×C5—81no—
83C23×C3×C5C22×C411yescharacteristic
84C23×C3×C5C2×D411yescharacteristic
85C23×C3×C5C2×D411yescharacteristic
86C23×C3×C5#4111yescharacteristic
87C23×C3×C5#4111yescharacteristic
88C23×C3×C5#4111yescharacteristic
89C23×C3×C5#4111yescharacteristic
90C22×C5×D3—21no—
91C22×C5×D3—21no—
92C22×C5×D3—81no—
93C22×C5×D3C22⋊C412yes—
94C2×C3×C4×C5—22no—
95C2×C3×C4×C5—81no—
96C2×Dic15—41no—
97C2×Dic15—41no—
98C2×Dic15—81no—
99C2×Dic15—81no—
100C5×#67—22no—
101C5×#67—22no—
102C5×#67—22no—
103C5×#67—22no—
104C2×C5×Dic3—21no—
105C2×C5×Dic3—21no—
106C2×C5×Dic3—22no—
107C2×C5×Dic3—81no—
108C2×C5×Dic3C22⋊C412yes—
109C4×C5×D3—82no—
110C2×C3×Dic5—41no—
111C2×C3×Dic5—41no—
112C2×C3×Dic5—81no—
113C2×C3×Dic5—81no—
114C22×#67C2×D511yescharacteristic
115C2×C3×C22⋊C4—51no—
116C2×C3×C22⋊C4—51no—
117C2×C3×C22⋊C4C2×D511yescharacteristic
118C2×#217—51no—
119C2×#217—51no—
120C2×#217C2×D511yescharacteristic
121C4×#67—22no—
122#67⋊C4—22no—
123D3×C22⋊C4Dic512yescomplemented
124#877Dic512yescomplemented
125#806—102no—
126#806—102no—
127C24×C5—31no—
128C24×C5C22×D311yescharacteristic
129C2×C5×D4—32no—
130C2×C5×D4—32no—
131C2×C5×D4—61no—
132C2×C5×D4—61no—
133C2×C5×D4—61no—
134C2×C5×D4—61no—
135C22×C4×C5—21no—
136C22×C4×C5—31no—
137C22×C4×C5—62no—
138C22×C4×C5—61no—
139C22×Dic5—21no—
140C22×Dic5—21no—
141C22×Dic5—61no—
142C22×Dic5—61no—
143C5×C4⋊C4—62no—
144C5×C22⋊C4—21no—
145C5×C22⋊C4—32no—
146C5×C22⋊C4—62no—
147C5×C22⋊C4—61no—
148C5×C22⋊C4C4×D312yes—
149C42×C5—62no—
150C22⋊Dic5—21no—
151C22⋊Dic5—21no—
152C22⋊Dic5—21no—
153C22⋊Dic5—21no—
154C22⋊Dic5—61no—
155C22⋊Dic5—61no—
156C22⋊Dic5—61no—
157C22⋊Dic5—61no—
158#518—31no—
159C2×#99—151no—
160C2×#99—151no—
161#342—51no—
162#342—151no—
163#342—151no—
164#342—151no—
165C22×C3×C5—41no—
166C22×C3×C5—41no—
167C22×C3×C5—41no—
168C22×C3×C5—41no—
169C22×C3×C5—41no—
170C22×C3×C5—41no—
171C22×C3×C5—41no—
172C22×C3×C5C2×C22⋊C411yescharacteristic
173C22×C3×C5#11711yescharacteristic
174C22×C3×C5#11711yescharacteristic
175C22×C3×C5#12311yescharacteristic
176C22×C3×C5#12311yescharacteristic
177C22×C3×C5#12311yescharacteristic
178C22×C3×C5#12311yescharacteristic
179C2×C5×D3—22no—
180C2×C5×D3—42no—
181C2×C5×D3—81no—
182C2×C5×D3—81no—
183C3×C4×C5—42no—
184Dic15—81no—
185Dic15—81no—
186C3×Dic5—81no—
187C3×Dic5—81no—
188C5×Dic3—22no—
189C5×Dic3—42no—
190C24×C3C22×D511yescharacteristic
191C23×D3C2×Dic511yescharacteristic
192C22×C3×C4—21no—
193C22×C3×C4—101no—
194C22×C3×C4—101no—
195C2×#67—21no—
196C2×#67—21no—
197C2×#67—21no—
198C2×#67—21no—
199C2×#67C22⋊D512yes—
200C2×#67C22⋊D512yes—
201C22×Dic3—21no—
202C22×Dic3—101no—
203C22×Dic3—101no—
204C22×Dic3C2×Dic511yescharacteristic
205C2×C4×D3—22no—
206C3×C22⋊C4—21no—
207C3×C22⋊C4—101no—
208C3×C22⋊C4—101no—
209C3×C22⋊C4—101no—
210C3×C22⋊C4—101no—
211C3×C22⋊C4C2×Dic512yes—
212#217—21no—
213#217—101no—
214#217—101no—
215#217—101no—
216#217—101no—
217#217C2×Dic512yes—
218(C2×D3)⋊C4—22no—
219Dic3⋊C4—22no—
220C4×Dic3—22no—
221C23×C5—32no—
222C23×C5—61no—
223C23×C5—61no—
224C23×C5—81no—
225C23×C5—241no—
226C23×C5C2×C4×D311yescharacteristic
227C23×C5#23511yescharacteristic
228C23×C5#23511yescharacteristic
229C23×C5D3×D411yescharacteristic
230C23×C5D3×D411yescharacteristic
231C23×C5#23711yescharacteristic
232C23×C5#23911yescharacteristic
233C5×D4—62no—
234C5×D4—62no—
235C5×D4—62no—
236C5×D4—62no—
237C2×C4×C5—22no—
238C2×C4×C5—32no—
239C2×C4×C5—61no—
240C2×C4×C5—61no—
241C2×C4×C5—62no—
242C2×C4×C5—81no—
243C2×C4×C5—242no—
244C2×C4×C5—241no—
245C2×Dic5—41no—
246C2×Dic5—41no—
247C2×Dic5—81no—
248C2×Dic5—81no—
249C2×Dic5—121no—
250C2×Dic5—121no—
251C2×Dic5—241no—
252C2×Dic5—241no—
253C22×D4—31no—
254C4×D4—62no—
255C4×D4—62no—
256#117—32no—
257C2×C22⋊C4—31no—
258C2×C22⋊C4—32no—
259C2×C22⋊C4—51no—
260C2×C22⋊C4—51no—
261C2×C22⋊C4—151no—
262C2×C22⋊C4—151no—
263C2×C22⋊C4D3×D511yescharacteristic
264#99—302no—
265#99—302no—
266C2×C3×C5—21no—
267C2×C3×C5—21no—
268C2×C3×C5—21no—
269C2×C3×C5—21no—
270C2×C3×C5—21no—
271C2×C3×C5—21no—
272C2×C3×C5—21no—
273C2×C3×C5#38111yescharacteristic
274C5×D3—42no—
275C23×C3—81no—
276C23×C3#70911yescharacteristic
277C23×C3#70911yescharacteristic
278C23×C3#70911yescharacteristic
279C23×C3#70911yescharacteristic
280C23×C3C22×Dic511yescharacteristic
281C23×C3C2×C22⋊D511yescharacteristic
282C23×C3C2×C22⋊D511yescharacteristic
283C22×D3—21no—
284C22×D3—21no—
285C22×D3—81no—
286C22×D3C22⋊Dic512yes—
287C2×C3×C4—22no—
288C2×C3×C4—81no—
289C2×C3×C4—201no—
290C2×C3×C4—201no—
291C2×C3×C4—401no—
292C2×C3×C4—401no—
293#67—22no—
294#67—22no—
295#67—22no—
296#67—22no—
297C2×Dic3—21no—
298C2×Dic3—21no—
299C2×Dic3—22no—
300C2×Dic3—81no—
301C2×Dic3—201no—
302C2×Dic3—201no—
303C2×Dic3—401no—
304C2×Dic3—401no—
305C2×Dic3C22⋊Dic512yes—
306C4×D3—82no—
307C22×C5—41no—
308C22×C5—41no—
309C22×C5—41no—
310C22×C5—41no—
311C22×C5—41no—
312C22×C5—41no—
313C22×C5—41no—
314C22×C5—62no—
315C22×C5—122no—
316C22×C5—241no—
317C22×C5—241no—
318C22×C5#87211yescharacteristic
319C22×C5D3×C22⋊C411yescharacteristic
320C22×C5#88311yescharacteristic
321C22×C5#88311yescharacteristic
322C22×C5#89211yescharacteristic
323C22×C5#89411yescharacteristic
324C22×C5#89411yescharacteristic
325C4×C5—42no—
326C4×C5—62no—
327C4×C5—122no—
328Dic5—81no—
329Dic5—81no—
330Dic5—241no—
331Dic5—241no—
332C24—31no—
333C24C2×D3×D511yescharacteristic
334C2×D4—32no—
335C2×D4—32no—
336C2×D4—61no—
337C2×D4—61no—
338C2×D4—61no—
339C2×D4—61no—
340C22×C4—21no—
341C22×C4—31no—
342C22×C4—62no—
343C22×C4—61no—
344C22×C4—101no—
345C22×C4—101no—
346C22×C4—301no—
347C22×C4—301no—
348C4⋊C4—62no—
349C22⋊C4—21no—
350C22⋊C4—32no—
351C22⋊C4—62no—
352C22⋊C4—61no—
353C22⋊C4—101no—
354C22⋊C4—101no—
355C22⋊C4—101no—
356C22⋊C4—101no—
357C22⋊C4—301no—
358C22⋊C4—301no—
359C22⋊C4—301no—
360C22⋊C4—301no—
361C22⋊C4D3×Dic512yes—
362C42—62no—
363C3×C5#182811yescharacteristic, complemented, Hall
364C22×C3—41no—
365C22×C3—41no—
366C22×C3—41no—
367C22×C3—41no—
368C22×C3—41no—
369C22×C3—41no—
370C22×C3—41no—
371C22×C3#407211yescharacteristic
372C22×C3#407211yescharacteristic
373C22×C3#407511yescharacteristic
374C22×C3#407511yescharacteristic
375C22×C3#407511yescharacteristic
376C22×C3#407511yescharacteristic
377C22×C3C2×C22⋊Dic511yescharacteristic
378C2×D3—22no—
379C2×D3—42no—
380C2×D3—81no—
381C2×D3—81no—
382C3×C4—42no—
383C3×C4—401no—
384C3×C4—401no—
385Dic3—22no—
386Dic3—42no—
387Dic3—401no—
388Dic3—401no—
389C2×C5—21no—
390C2×C5—21no—
391C2×C5—21no—
392C2×C5—21no—
393C2×C5—21no—
394C2×C5—21no—
395C2×C5—21no—
396C2×C5—122no—
397C2×C5#466411yescharacteristic
398C23—32no—
399C23—61no—
400C23—61no—
401C23—81no—
402C23—241no—
403C23#676511yescharacteristic
404C23#676911yescharacteristic
405C23#677111yescharacteristic
406C23#677111yescharacteristic
407C23C2×D3×Dic511yescharacteristic
408C23D3×C22⋊D511yescharacteristic
409C23D3×C22⋊D511yescharacteristic
410D4—62no—
411D4—62no—
412D4—62no—
413D4—62no—
414C2×C4—22no—
415C2×C4—32no—
416C2×C4—61no—
417C2×C4—61no—
418C2×C4—62no—
419C2×C4—81no—
420C2×C4—201no—
421C2×C4—201no—
422C2×C4—242no—
423C2×C4—241no—
424C2×C4—401no—
425C2×C4—401no—
426C2×C4—601no—
427C2×C4—601no—
428C2×C4—1201no—
429C2×C4—1201no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3#6550011yescharacteristic
438D3—42no—
439C5#6896011yescharacteristic, complemented, Sylow
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—62no—
448C22—122no—
449C22—241no—
450C22—241no—
451C22#9133811yescharacteristic
452C22#9135111yescharacteristic
453C22#9135111yescharacteristic
454C22#9137111yescharacteristic
455C22#9145211yescharacteristic
456C22#9145211yescharacteristic
457C22D3×C22⋊Dic511yescharacteristic
458C4—42no—
459C4—62no—
460C4—122no—
461C4—401no—
462C4—401no—
463C4—1201no—
464C4—1201no—
465C3#1060244611yescharacteristic, complemented, Sylow
466C2—21no—
467C2—21no—
468C2—21no—
469C2—21no—
470C2—21no—
471C2—21no—
472C2—21no—
473C2—122no—
474C2#1174877711yescharacteristic
subgroupG/H
centerC2#11748777
commutatorC23×C3×C5C22×C4
FrattiniC24C2×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC2×C3×C5#381
prime radicalC22×C5×#67C22
cosocleC24×C3×C5C23
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#1828
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. #11746348C2semidirect
5. C3×#64747C2semidirect
6. #11746020C2semidirect
7. #11746019C2semidirect
16. C5×D3×C22⋊C4C4semidirect
17. C5×#877C4semidirect
29. #64747D3semidirect
123. D3×C22⋊C4Dic5semidirect
124. #877Dic5semidirect
363. C3×C5#1828semidirect
439. C5#68960semidirect
465. C3#10602446semidirect

Maximal subgroups

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

subgroupindex
C5×#54862
C2×#909962
#117463482
C3×#647472
#117460202
#117460192
#106024463
#689605