Finite Group Databasebeta

← #14282001

Subgroups — #14282001

Order 1920.

524 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5548C211yesmaximal, characteristic
2C4×#6650C211yesmaximal, characteristic, complemented
3#11746853C211yesmaximal, characteristic, complemented
4D4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
5C3×D4⋊#168C211yesmaximal, characteristic, complemented
6#11745837C211yesmaximal, characteristic, complemented
7#11745836C211yesmaximal, characteristic, complemented
8#10602594—31nomaximal, Hall
9C2×C5×#235—21no—
10C3×C4×C5×D4C2211yescharacteristic
11C5×#940C411yescharacteristic
12C5×#938C411yescharacteristic
13C4×C5×#67—21no—
14C5×#895C411yescharacteristic
15C5×#888C411yescharacteristic
16C5×#885—21no—
17C5×#884—21no—
18C4×C5×D12C2211yescharacteristic
19C42×C5×D3C2211yescharacteristic
20C2×#6650—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C4×C3⋊#168C2211yescharacteristic
23C3×C4⋊#168C2211yescharacteristic
24C3×C4×#168C2211yescharacteristic
25(C2×D3)⋊#168—21no—
26#90953—21no—
27Dic3×#168—21no—
28#68171—51nomaximal, Hall
29C5×#532—31no—
30#65214—31no—
31C4×#681—31no—
32D4⋊#168—31no—
33D4⋊#168—31no—
34D4⋊#168—31no—
35D4⋊#168D311yescharacteristic, complemented
36C2×C3×C5×D4C2×C411yescharacteristic
37C22×C3×C4×C5—21no—
38C2×C5×#67—21no—
39C2×C5×#67—21no—
40C2×C5×#67—21no—
41C5×#235—42no—
42C5×#235—42no—
43C2×C5×D12—21no—
44C2×C5×D12C2×C411yescharacteristic
45C2×C4×C5×D3—21no—
46C2×C4×C5×D3C2×C411yescharacteristic
47C2×C4×C5×D3D411yescharacteristic
48C2×C4×C5×D3D411yescharacteristic
49C2×C5×Dic6—21no—
50C3×C5×C4⋊C4C2×C411yescharacteristic
51C3×C5×C22⋊C4—21no—
52C3×C42×C5C2311yescharacteristic
53C2×C3⋊#168—21no—
54C2×C3⋊#168—21no—
55C5×#217—21no—
56C5×(C2×D3)⋊C4—21no—
57C5×(C2×D3)⋊C4—21no—
58C5×C4⋊Dic3C2×C411yescharacteristic
59C5×Dic3⋊C4—21no—
60C4×C5×Dic3C2×C411yescharacteristic
61C4×C5×Dic3D411yescharacteristic
62C4×C5×Dic3D411yescharacteristic
63C2×C3×#168—21no—
64C2×C3×#168—21no—
65#6650—24no—
66#5548D511yescharacteristic
67#4833—51no—
68C4×ΓL(1,𝔽25)—51no—
69C3×D4⋊C8—51no—
70D4⋊(C3⋊C8)—51no—
71#4483—51no—
72#4459—51no—
73C2×C5×#41—61no—
74C5×C4⋊Q8—31no—
75C5×#127—31no—
76C5×#124—61no—
77C5×#121—31no—
78C5×#121—31no—
79C5×#121—61no—
80C4×C5×D4—31no—
81C4×C5×D4—61no—
82C4×C5×D4C2×D311yescharacteristic
83C2×C42×C5—31no—
84C2×#681—61no—
85C22⋊#168—61no—
86C4⋊#168—31no—
87C4⋊#168C2×D311yescharacteristic
88#3935—61no—
89C4×#168—31no—
90C4×#168—61no—
91C4×#168C2×D311yescharacteristic
92#1484—151noSylow
93C23×C3×C5—21no—
94C22×C5×D3—21no—
95C22×C5×D3C22⋊C411yescharacteristic
96C3×C5×D4—21no—
97C3×C5×D4—21no—
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5C22×C411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C5×#67—42no—
105C5×#67—42no—
106C5×#67—42no—
107C2×C5×Dic3—21no—
108C2×C5×Dic3C22⋊C411yescharacteristic
109C2×C5×Dic3C22⋊C411yescharacteristic
110C2×C5×Dic3C22⋊C411yescharacteristic
111C5×D12—21no—
112C5×D12—21no—
113C5×D12—42no—
114C4×C5×D3—21no—
115C4×C5×D3—21no—
116C4×C5×D3—21no—
117C4×C5×D3—21no—
118C4×C5×D3—22no—
119C4×C5×D3—41no—
120C4×C5×D3—41no—
121C5×Dic6—42no—
122C3⋊#168—22no—
123C3⋊#168—41no—
124C3×#168—22no—
125C3×#168—41no—
126C2×#235—21no—
127C3×C4×D4C2×D511yescharacteristic
128#940Dic511yescharacteristic
129#938Dic511yescharacteristic
130C4×#67—21no—
131C2×ΓL(1,𝔽25)—101no—
132#895Dic511yescharacteristic
133#888Dic511yescharacteristic
134#885—21no—
135#884—21no—
136C4×D12C2×D511yescharacteristic
137C42×D3C2×D511yescharacteristic
138C3×C4⋊C8—51no—
139C3×C4×C8—51no—
140(C2×D3)⋊C8—101no—
141#815—101no—
142C8×Dic3—101no—
143C4⋊(C3⋊C8)—51no—
144C4×C3⋊C8—51no—
145C5×#41—122no—
146C5×#41—122no—
147C2×C5×Q8—61no—
148C2×C5×D4—31no—
149C2×C5×D4—61no—
150C2×C5×D4—61no—
151C2×C5×D4—61no—
152C2×C5×D4—61no—
153C2×C5×D4C4×D311yescharacteristic
154C22×C4×C5—21no—
155C22×C4×C5—31no—
156C22×C4×C5—31no—
157C22×C4×C5—31no—
158C22×C4×C5—61no—
159C5×C4⋊C4—31no—
160C5×C4⋊C4—61no—
161C5×C4⋊C4C4×D311yescharacteristic
162C5×C22⋊C4—21no—
163C5×C22⋊C4—61no—
164C5×C22⋊C4—61no—
165C5×C22⋊C4—61no—
166C42×C5—31no—
167C42×C5—31no—
168C42×C5—31no—
169C42×C5C22×D311yescharacteristic
170#681—64no—
171C2×#168—21no—
172C2×#168—21no—
173C2×#168—61no—
174C2×#168—61no—
175#532—31no—
176#431—151no—
177C4×M16—151no—
178D4⋊C8—51no—
179D4⋊C8—151no—
180D4⋊C8—151no—
181D4⋊C8—151no—
182C22×C3×C5—41no—
183C22×C3×C5—41no—
184C22×C3×C5—41no—
185C22×C3×C5C2×C22⋊C411yescharacteristic
186C2×C5×D3—21no—
187C2×C5×D3—21no—
188C2×C5×D3—21no—
189C2×C5×D3—41no—
190C2×C5×D3—41no—
191C2×C5×D3—41no—
192C3×C4×C5—21no—
193C3×C4×C5—41no—
194C3×C4×C5#13111yescharacteristic
195C3×C4×C5#13111yescharacteristic
196C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
197C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
198C5×Dic3—21no—
199C5×Dic3—21no—
200C5×Dic3—41no—
201C5×Dic3#10412yes—
202C2×C3×D4C2×Dic511yescharacteristic
203C22×C3×C4—21no—
204C2×#67—21no—
205C2×#67—21no—
206C2×#67—21no—
207#235—42no—
208#235—42no—
209C2×D12—21no—
210C2×D12C2×Dic511yescharacteristic
211C2×C4×D3—21no—
212C2×C4×D3C2×Dic511yescharacteristic
213C2×C4×D3C22⋊D511yescharacteristic
214C2×C4×D3C22⋊D511yescharacteristic
215C2×Dic6—21no—
216C2×C3×C8—101no—
217C2×C3×C8—101no—
218C3×C4⋊C4C2×Dic511yescharacteristic
219C3×C22⋊C4—21no—
220C3×C42C22×D511yescharacteristic
221#217—21no—
222(C2×D3)⋊C4—21no—
223(C2×D3)⋊C4—21no—
224C4⋊Dic3C2×Dic511yescharacteristic
225Dic3⋊C4—21no—
226C4×Dic3C2×Dic511yescharacteristic
227C4×Dic3C22⋊D511yescharacteristic
228C4×Dic3C22⋊D511yescharacteristic
229C2×C3⋊C8—101no—
230C2×C3⋊C8—101no—
231ΓL(1,𝔽25)—104no—
232C23×C5—21no—
233C23×C5—31no—
234C23×C5—61no—
235C5×Q8—122no—
236C5×D4—21no—
237C5×D4—21no—
238C5×D4—61no—
239C5×D4—61no—
240C5×D4—122no—
241C5×D4—122no—
242C5×D4—122no—
243C5×D4—122no—
244C2×C4×C5—21no—
245C2×C4×C5—31no—
246C2×C4×C5—31no—
247C2×C4×C5—31no—
248C2×C4×C5—41no—
249C2×C4×C5—41no—
250C2×C4×C5—62no—
251C2×C4×C5—61no—
252C2×C4×C5—61no—
253C2×C4×C5—61no—
254C2×C4×C5—61no—
255C2×C4×C5—61no—
256C2×C4×C5—121no—
257C2×C4×C5—121no—
258C2×C4×C5C2×C4×D311yescharacteristic
259C2×C4×C5D3×D411yescharacteristic
260C2×C4×C5D3×D411yescharacteristic
261#168—22no—
262#168—41no—
263#168—62no—
264#168—121no—
265C2×#41—61no—
266C2×M16—301no—
267C4⋊Q8—31no—
268#127—31no—
269#124—61no—
270#121—31no—
271#121—31no—
272#121—61no—
273C4×D4—31no—
274C4×D4—61no—
275C4×D4D3×D511yescharacteristic
276C2×C42—31no—
277C4⋊C8—51no—
278C4⋊C8—151no—
279C22⋊C8—301no—
280#97—301no—
281C4×C8—51no—
282C4×C8—151no—
283C4×C8—301no—
284C2×C3×C5—81no—
285C2×C3×C5#40811yescharacteristic
286C2×C3×C5#41811yescharacteristic
287C2×C3×C5C2×#10411yescharacteristic
288C5×D3—41no—
289C5×D3—81no—
290C23×C3—21no—
291C22×D3—21no—
292C22×D3C22⋊Dic511yescharacteristic
293C3×D4—21no—
294C3×D4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4C22×Dic511yescharacteristic
299C2×C3×C4C2×C22⋊D511yescharacteristic
300C2×C3×C4C2×C22⋊D511yescharacteristic
301#67—42no—
302#67—42no—
303#67—42no—
304C2×Dic3—21no—
305C2×Dic3C22⋊Dic511yescharacteristic
306C2×Dic3C22⋊Dic511yescharacteristic
307C2×Dic3C22⋊Dic511yescharacteristic
308D12—21no—
309D12—21no—
310D12—42no—
311C4×D3—21no—
312C4×D3—21no—
313C4×D3—21no—
314C4×D3—21no—
315C4×D3—22no—
316C4×D3—41no—
317C4×D3—41no—
318Dic6—42no—
319C3×C8—102no—
320C3×C8—201no—
321C3⋊C8—102no—
322C3⋊C8—201no—
323C22×C5—41no—
324C22×C5—41no—
325C22×C5—41no—
326C22×C5—61no—
327C22×C5—61no—
328C22×C5—61no—
329C22×C5—121no—
330C22×C5—121no—
331C22×C5—121no—
332C22×C5D3×C22⋊C411yescharacteristic
333C4×C5—21no—
334C4×C5—32no—
335C4×C5—41no—
336C4×C5—61no—
337C4×C5—61no—
338C4×C5—121no—
339C4×C5#90111yescharacteristic
340C4×C5#90711yescharacteristic
341C4×C5#91111yescharacteristic
342C4×C5#91411yescharacteristic
343#41—122no—
344#41—122no—
345C2×Q8—61no—
346C2×D4—31no—
347C2×D4—61no—
348C2×D4—61no—
349C2×D4—61no—
350C2×D4—61no—
351C2×D4D3×Dic511yescharacteristic
352C22×C4—21no—
353C22×C4—31no—
354C22×C4—31no—
355C22×C4—31no—
356C22×C4—61no—
357M16—304no—
358C2×C8—101no—
359C2×C8—101no—
360C2×C8—301no—
361C2×C8—301no—
362C4⋊C4—31no—
363C4⋊C4—61no—
364C4⋊C4D3×Dic511yescharacteristic
365C22⋊C4—21no—
366C22⋊C4—61no—
367C22⋊C4—61no—
368C22⋊C4—61no—
369C42—31no—
370C42—31no—
371C42—31no—
372C42C2×D3×D511yescharacteristic
373C3×C5#148411yescharacteristic, complemented, Hall
374C22×C3—41no—
375C22×C3—41no—
376C22×C3—41no—
377C22×C3C2×C22⋊Dic511yescharacteristic
378C2×D3—21no—
379C2×D3—21no—
380C2×D3—21no—
381C2×D3—41no—
382C2×D3—41no—
383C2×D3—41no—
384C3×C4—21no—
385C3×C4—41no—
386C3×C4#407811yescharacteristic
387C3×C4#407811yescharacteristic
388C3×C4#409411yescharacteristic
389C3×C4#409411yescharacteristic
390Dic3—21no—
391Dic3—21no—
392Dic3—41no—
393Dic3#396912yes—
394C2×C5—81no—
395C2×C5—121no—
396C2×C5—241no—
397C2×C5#472711yescharacteristic
398C2×C5#477011yescharacteristic
399C2×C5D3×#10411yescharacteristic
400C23—21no—
401C23—31no—
402C23—61no—
403Q8—122no—
404D4—21no—
405D4—21no—
406D4—61no—
407D4—61no—
408D4—122no—
409D4—122no—
410D4—122no—
411D4—122no—
412C2×C4—21no—
413C2×C4—31no—
414C2×C4—31no—
415C2×C4—31no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—62no—
419C2×C4—61no—
420C2×C4—61no—
421C2×C4—61no—
422C2×C4—61no—
423C2×C4—61no—
424C2×C4—121no—
425C2×C4—121no—
426C2×C4C2×D3×Dic511yescharacteristic
427C2×C4D3×C22⋊D511yescharacteristic
428C2×C4D3×C22⋊D511yescharacteristic
429C8—102no—
430C8—201no—
431C8—302no—
432C8—601no—
433C2×C3—81no—
434C2×C3#6550411yescharacteristic
435C2×C3#6552311yescharacteristic
436C2×C3C2×#396911yescharacteristic
437D3—41no—
438D3—81no—
439C5#6817111yescharacteristic, complemented, Sylow
440C22—41no—
441C22—41no—
442C22—41no—
443C22—61no—
444C22—61no—
445C22—61no—
446C22—121no—
447C22—121no—
448C22—121no—
449C22D3×C22⋊Dic511yescharacteristic
450C4—21no—
451C4—32no—
452C4—41no—
453C4—61no—
454C4—61no—
455C4—121no—
456C4#9128611yescharacteristic
457C4#9128811yescharacteristic
458C4#9149411yescharacteristic
459C4#9149611yescharacteristic
460C3#1060259411yescharacteristic, complemented, Sylow
461C2—81no—
462C2—121no—
463C2—241no—
464C2#1174849011yescharacteristic
465C2#1174896711yescharacteristic
466C2D3×#396911yescharacteristic
subgroupG/H
centerC2×C4D3×C22⋊D5
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#5548C2
cosocleC3×C42×C5C23
hypercenterC4×D4D3×D5
hypocenterC3×C5#1484
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C4×#6650C2semidirect
3. #11746853C2semidirect
4. D4⋊(C3⋊#168)C2semidirect
5. C3×D4⋊#168C2semidirect
6. #11745837C2semidirect
7. #11745836C2semidirect
35. D4⋊#168D3semidirect
373. C3×C5#1484semidirect
439. C5#68171semidirect
460. C3#10602594semidirect

Maximal subgroups

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

subgroupindex
C5×#55482
C4×#66502
#117468532
D4⋊(C3⋊#168)2
C3×D4⋊#1682
#117458372
#117458362
#106025943
#681715