Finite Group Databasebeta

← #14298649

Subgroups — #14298649

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
1#11756245C211yesmaximal, characteristic
2C2×#90997C211yesmaximal, characteristic
3C2×#90997C211yesmaximal, characteristic
4C5×#4527C211yesmaximal, characteristic, complemented
5C3×#64747C211yesmaximal, characteristic, complemented
6#11746019C211yesmaximal, characteristic, complemented
7#11746018C211yesmaximal, characteristic, complemented
8#10599753—31nomaximal, Hall
9C22×#1220C2211yescharacteristic
10C2×C3×C5×C22⋊C4C2211yescharacteristic
11C2×#6719C2211yescharacteristic
12C4×#1220—22no—
13#91770—22no—
14C22⋊C4×D15C412yescomplemented
15#91766C412yescomplemented
16C2×C5×#217C2211yescharacteristic
17C2×C5×#217C2211yescharacteristic
18C2×C3×C22⋊Dic5C2211yescharacteristic
19C2×C3×C22⋊Dic5C2211yescharacteristic
20#90997—22no—
21#90997—22no—
22#68960—51nomaximal, Hall
23#65820—31no—
24C2×#3938—31no—
25C2×#3938—31no—
26C5×#342—31no—
27#64747—31no—
28#64747D311yescharacteristic, complemented
29#64746—31no—
30C24×C3×C5C2311yescharacteristic
31C23×D15C2×C411yescharacteristic
32C22×C3×C4×C5—21no—
33C2×#1220—21no—
34C2×#1220—21no—
35C2×#1220—21no—
36C2×#1220—21no—
37C2×#1220D412yes—
38C2×#1220D412yes—
39C22×Dic15—21no—
40C22×Dic15C2×C411yescharacteristic
41C2×C4×D15—22no—
42C22×C5×Dic3—21no—
43C22×C5×Dic3—21no—
44C22×C3×Dic5—21no—
45C22×C3×Dic5—21no—
46C3×C5×C22⋊C4—21no—
47C3×C5×C22⋊C4C2×C412yes—
48#6719—21no—
49#6719C2×C412yes—
50#6714—22no—
51#6712—22no—
52C4×Dic15—22no—
53C5×#217—21no—
54C5×#217—21no—
55C5×#217—21no—
56C5×#217—21no—
57C3×C22⋊Dic5—21no—
58C3×C22⋊Dic5—21no—
59C3×C22⋊Dic5—21no—
60C3×C22⋊Dic5—21no—
61#5486—51no—
62C2×#806—51no—
63C2×#806—51no—
64C3×#342—51no—
65#4527—51no—
66#4527D511yescharacteristic, complemented
67#4526—51no—
68C22×C22⋊D5—31no—
69C2×C5×C22⋊C4—31no—
70C2×C5×C22⋊C4—31no—
71C2×C5×C22⋊C4C2×D311yescharacteristic
72C2×C22⋊Dic5—31no—
73C2×C22⋊Dic5C2×D311yescharacteristic
74C2×C22⋊Dic5C2×D311yescharacteristic
75C4×C22⋊D5—62no—
76#4027—62no—
77D5×C22⋊C4—32no—
78#4023—32no—
79#3938—62no—
80#3938—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×D15—21no—
91C22×D15—21no—
92C22×D15—81no—
93C22×D15C22⋊C412yes—
94C2×C3×C4×C5—22no—
95C2×C3×C4×C5—81no—
96#1220—22no—
97#1220—22no—
98#1220—22no—
99#1220—22no—
100C2×Dic15—21no—
101C2×Dic15—21no—
102C2×Dic15—22no—
103C2×Dic15—81no—
104C2×Dic15C22⋊C412yes—
105C4×D15—82no—
106C2×C5×Dic3—41no—
107C2×C5×Dic3—41no—
108C2×C5×Dic3—81no—
109C2×C5×Dic3—81no—
110C2×C3×Dic5—41no—
111C2×C3×Dic5—41no—
112C2×C3×Dic5—81no—
113C2×C3×Dic5—81no—
114C22×#67—51no—
115C2×C3×C22⋊C4—51no—
116C2×C3×C22⋊C4—51no—
117C2×C3×C22⋊C4C2×D511yescharacteristic
118C2×#217—51no—
119C2×#217C2×D511yescharacteristic
120C2×#217C2×D511yescharacteristic
121C4×#67—102no—
122#67⋊C4—102no—
123D3×C22⋊C4—52no—
124#877—52no—
125#806—102no—
126#806—102no—
127C24×C5C22×D311yescharacteristic
128C23×D5—31no—
129C22×C4×C5—21no—
130C22×C4×C5—61no—
131C22×C4×C5—61no—
132C2×C22⋊D5—32no—
133C2×C22⋊D5—32no—
134C2×C22⋊D5—61no—
135C2×C22⋊D5—61no—
136C2×C22⋊D5—61no—
137C2×C22⋊D5—61no—
138C22×Dic5—21no—
139C22×Dic5—21no—
140C22×Dic5—31no—
141C22×Dic5—61no—
142C2×C4×D5—62no—
143C5×C22⋊C4—21no—
144C5×C22⋊C4—61no—
145C5×C22⋊C4—61no—
146C5×C22⋊C4—61no—
147C5×C22⋊C4—61no—
148C5×C22⋊C4C4×D312yes—
149C22⋊Dic5—21no—
150C22⋊Dic5—21no—
151C22⋊Dic5—21no—
152C22⋊Dic5—21no—
153C22⋊Dic5—32no—
154C22⋊Dic5—61no—
155#685—62no—
156#683—62no—
157C4×Dic5—62no—
158#518—151no—
159C2×#99—151no—
160C2×#99—151no—
161#342—31no—
162#342—51no—
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×D15—22no—
180C2×D15—42no—
181C2×D15—81no—
182C2×D15—81no—
183C3×C4×C5—42no—
184Dic15—22no—
185Dic15—42no—
186C3×Dic5—81no—
187C3×Dic5—81no—
188C5×Dic3—81no—
189C5×Dic3—81no—
190C24×C3C22×D511yescharacteristic
191C23×D3—51no—
192C22×C3×C4—21no—
193C22×C3×C4—101no—
194C22×C3×C4—101no—
195C2×#67—52no—
196C2×#67—52no—
197C2×#67—101no—
198C2×#67—101no—
199C2×#67—101no—
200C2×#67—101no—
201C22×Dic3—21no—
202C22×Dic3—21no—
203C22×Dic3—51no—
204C22×Dic3—101no—
205C2×C4×D3—102no—
206C3×C22⋊C4—21no—
207C3×C22⋊C4—101no—
208C3×C22⋊C4—101no—
209C3×C22⋊C4—101no—
210C3×C22⋊C4—101no—
211C3×C22⋊C4C4×D512yes—
212#217—21no—
213#217—21no—
214#217—21no—
215#217—21no—
216#217—52no—
217#217—101no—
218(C2×D3)⋊C4—102no—
219Dic3⋊C4—102no—
220C4×Dic3—102no—
221C23×C5—81no—
222C23×C5C2×C4×D311yescharacteristic
223C23×C5#23511yescharacteristic
224C23×C5#23511yescharacteristic
225C23×C5D3×D411yescharacteristic
226C23×C5D3×D411yescharacteristic
227C23×C5#23711yescharacteristic
228C23×C5#23911yescharacteristic
229C22×D5—32no—
230C22×D5—61no—
231C22×D5—61no—
232C22×D5—241no—
233C2×C4×C5—22no—
234C2×C4×C5—81no—
235C2×C4×C5—121no—
236C2×C4×C5—121no—
237C2×C4×C5—241no—
238C2×C4×C5—241no—
239C22⋊D5—62no—
240C22⋊D5—62no—
241C22⋊D5—62no—
242C22⋊D5—62no—
243C2×Dic5—32no—
244C2×Dic5—41no—
245C2×Dic5—41no—
246C2×Dic5—61no—
247C2×Dic5—61no—
248C2×Dic5—62no—
249C2×Dic5—81no—
250C2×Dic5—81no—
251C2×Dic5—241no—
252C4×D5—242no—
253C22×D4—151no—
254C4×D4—302no—
255C4×D4—302no—
256#117—152no—
257C2×C22⋊C4—31no—
258C2×C22⋊C4—31no—
259C2×C22⋊C4—51no—
260C2×C22⋊C4—51no—
261C2×C22⋊C4—151no—
262C2×C22⋊C4—152no—
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
274D15—42no—
275C23×C3—81no—
276C23×C3C2×C4×D511yescharacteristic
277C23×C3#70911yescharacteristic
278C23×C3#70911yescharacteristic
279C23×C3D4×D511yescharacteristic
280C23×C3D4×D511yescharacteristic
281C23×C3#71111yescharacteristic
282C23×C3#71311yescharacteristic
283C22×D3—52no—
284C22×D3—101no—
285C22×D3—101no—
286C22×D3—401no—
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—102no—
294#67—102no—
295#67—102no—
296#67—102no—
297C2×Dic3—41no—
298C2×Dic3—41no—
299C2×Dic3—52no—
300C2×Dic3—81no—
301C2×Dic3—81no—
302C2×Dic3—101no—
303C2×Dic3—101no—
304C2×Dic3—102no—
305C2×Dic3—401no—
306C4×D3—402no—
307C22×C5—41no—
308C22×C5—41no—
309C22×C5—41no—
310C22×C5—41no—
311C22×C5—41no—
312C22×C5—41no—
313C22×C5—41no—
314C22×C5#87211yescharacteristic
315C22×C5D3×C22⋊C411yescharacteristic
316C22×C5#88311yescharacteristic
317C22×C5#88311yescharacteristic
318C22×C5#89211yescharacteristic
319C22×C5#89411yescharacteristic
320C22×C5#89411yescharacteristic
321C2×D5—62no—
322C2×D5—122no—
323C2×D5—241no—
324C2×D5—241no—
325C4×C5—42no—
326C4×C5—241no—
327C4×C5—241no—
328Dic5—62no—
329Dic5—81no—
330Dic5—81no—
331Dic5—122no—
332C24—151no—
333C24C2×D3×D511yescharacteristic
334C2×D4—152no—
335C2×D4—152no—
336C2×D4—301no—
337C2×D4—301no—
338C2×D4—301no—
339C2×D4—301no—
340C22×C4—21no—
341C22×C4—61no—
342C22×C4—61no—
343C22×C4—101no—
344C22×C4—101no—
345C22×C4—151no—
346C22×C4—302no—
347C22×C4—301no—
348C4⋊C4—302no—
349C22⋊C4—21no—
350C22⋊C4—61no—
351C22⋊C4—61no—
352C22⋊C4—61no—
353C22⋊C4—61no—
354C22⋊C4—101no—
355C22⋊C4—101no—
356C22⋊C4—101no—
357C22⋊C4—101no—
358C22⋊C4—152no—
359C22⋊C4—302no—
360C22⋊C4—301no—
361C22⋊C4#120012yes—
362C42—302no—
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#401811yescharacteristic
372C22×C3D5×C22⋊C411yescharacteristic
373C22×C3#402911yescharacteristic
374C22×C3#402911yescharacteristic
375C22×C3#403811yescharacteristic
376C22×C3#404011yescharacteristic
377C22×C3#404011yescharacteristic
378C2×D3—102no—
379C2×D3—202no—
380C2×D3—401no—
381C2×D3—401no—
382C3×C4—42no—
383C3×C4—401no—
384C3×C4—401no—
385Dic3—81no—
386Dic3—81no—
387Dic3—102no—
388Dic3—202no—
389C2×C5—21no—
390C2×C5—21no—
391C2×C5—21no—
392C2×C5—21no—
393C2×C5—21no—
394C2×C5—21no—
395C2×C5—21no—
396C2×C5#466411yescharacteristic
397D5—122no—
398C23—81no—
399C23—152no—
400C23—301no—
401C23—301no—
402C23—1201no—
403C23#676611yescharacteristic
404C23#676811yescharacteristic
405C23#677111yescharacteristic
406C23#677111yescharacteristic
407C23C2×#120011yescharacteristic
408C23#679011yescharacteristic
409C23#679011yescharacteristic
410D4—302no—
411D4—302no—
412D4—302no—
413D4—302no—
414C2×C4—22no—
415C2×C4—81no—
416C2×C4—121no—
417C2×C4—121no—
418C2×C4—152no—
419C2×C4—201no—
420C2×C4—201no—
421C2×C4—241no—
422C2×C4—241no—
423C2×C4—301no—
424C2×C4—301no—
425C2×C4—302no—
426C2×C4—401no—
427C2×C4—401no—
428C2×C4—1202no—
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#6495311yescharacteristic
438D3—202no—
439C5#6896011yescharacteristic, complemented, Sylow
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—302no—
448C22—602no—
449C22—1201no—
450C22—1201no—
451C22#9134711yescharacteristic
452C22#9135411yescharacteristic
453C22#9135411yescharacteristic
454C22#9135511yescharacteristic
455C22#9135511yescharacteristic
456C22#9138611yescharacteristic
457C22#9156111yescharacteristic
458C4—42no—
459C4—241no—
460C4—241no—
461C4—302no—
462C4—401no—
463C4—401no—
464C4—602no—
465C3#1059975311yescharacteristic, complemented, Sylow
466C2—21no—
467C2—21no—
468C2—21no—
469C2—21no—
470C2—21no—
471C2—21no—
472C2—21no—
473C2—602no—
474C2#1174860611yescharacteristic
subgroupG/H
centerC2#11748606
commutatorC23×C3×C5C22×C4
FrattiniC24C2×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC2×C3×C5#381
prime radicalC22×#1220C22
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. C5×#4527C2semidirect
5. C3×#64747C2semidirect
6. #11746019C2semidirect
7. #11746018C2semidirect
14. C22⋊C4×D15C4semidirect
15. #91766C4semidirect
28. #64747D3semidirect
66. #4527D5semidirect
363. C3×C5#1828semidirect
439. C5#68960semidirect
465. C3#10599753semidirect

Maximal subgroups

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

subgroupindex
#117562452
C2×#909972
C5×#45272
C3×#647472
#117460192
#117460182
#105997533
#689605