Finite Group Databasebeta

← #14479149

Subgroups — #14479149

Order 1920.

3080 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#237C211yesmaximal, characteristic
2#11756557C211yesmaximal, characteristic, complemented
3C3×#66132C211yesmaximal, characteristic, complemented
4#11755410C214yesmaximal, complemented
5C2×#91529C214yesmaximal, complemented
6#11754920C218yesmaximal, complemented
7Dic5×#237C218yesmaximal, complemented
8D3×#4072C212yesmaximal, complemented
9#11754211C212yesmaximal, complemented
10#10619161—31nomaximal, Hall
11C22×C3×C5×D4C2211yescharacteristic
12C22×C5×#67C2212yes—
13C23×C5×Dic3C2212yes—
14C2×C5×#237C4116yescomplemented
15C2×C5×#237C2214yes—
16C2×C5×#237C2214yes—
17C22×C4×C5×D3C2211yescharacteristic
18C22×C5×Dic6C2211yescharacteristic
19C2×#6719C2214yes—
20D4×Dic15C2218yescomplemented
21#91815C2212yes—
22C2×C3×C22⋊Dic5C2214yes—
23C3×D4×Dic5C2218yescomplemented
24C3×#4072C2212yes—
25#67⋊Dic5C22116yescomplemented
26D3×C22⋊Dic5C2214yes—
27Dic5×#67C22116yescomplemented
28C2×Dic3⋊Dic5C2218yescomplemented
29#91529C2214yes—
30#91529C2218yes—
31#91529C2218yescomplemented
32#91529C2218yescomplemented
33C2×Dic3×Dic5C2218yescomplemented
34D3×C4⋊Dic5C2214yescomplemented
35C4×D3×Dic5C2214yescomplemented
36#91371C2214yescomplemented
37#91344C2218yescomplemented
38#91338C2214yescomplemented
39Dic5×Dic6C2218yescomplemented
40#85856—51nomaximal, Hall
41C22×C5×#41—31no—
42#66161—38no—
43#41×Dic5—38no—
44#66146—32no—
45#66132—31no—
46#66132—34no—
47#66132D311yescharacteristic, complemented
48C2×#4072—32no—
49C2×#4072—34no—
50C24×C3×C5C2312yes—
51C23×C5×D3C2311yescharacteristic
52C2×C3×C5×D4C2×C418yescomplemented
53C2×C3×C5×D4C2314yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15C2318yes—
56C2×C5×#67C2×C4116yescomplemented
57C2×C5×#67C2318yes—
58C22×C5×Dic3C2×C4116yescomplemented
59C22×C5×Dic3C2314yes—
60C22×C5×Dic3C2312yes—
61C22×C5×Dic3C2311yescharacteristic
62C22×C5×Dic3C2314yes—
63C5×#237C2×C4132yescomplemented
64C5×#237C2×C4132yescomplemented
65C2×C4×C5×D3C2×C418yescomplemented
66C2×C4×C5×D3C2312yes—
67C2×C4×C5×D3C2312yes—
68C2×C5×Dic6C2×C418yescomplemented
69C2×C5×Dic6C2314yes—
70C22×C3×Dic5C2318yes—
71C2×D3×Dic5C2318yes—
72#6719C2314yes—
73#6719C2318yes—
74C4⋊Dic15C2314yes—
75C4×Dic15C2314yes—
76C3×C22⋊Dic5C2318yes—
77C3×C22⋊Dic5C2314yes—
78C3×C4⋊Dic5C2314yes—
79C3×C4×Dic5C2314yes—
80Dic3⋊Dic5C2318yes—
81Dic3⋊Dic5C23116yes—
82(C2×D3)⋊Dic5C2318yes—
83Dic3×Dic5C2318yes—
84Dic3×Dic5C23116yes—
85C22×#237D511yescharacteristic
86C3×#518—51no—
87#5798—51no—
88#5546—58no—
89C4×#237—58no—
90D3×#117—52no—
91#5516—52no—
92#5486—54no—
93C2×#877—54no—
94C2×C5×#41—316no—
95C2×C5×#41—34no—
96C2×C5×#41—34no—
97C22×C5×Q8—31no—
98C22×C5×D4—32no—
99C22×C5×D4C2×D311yescharacteristic
100C23×C4×C5—32no—
101C23×C4×C5—31no—
102C2×C22⋊Dic5—34no—
103C2×C22⋊Dic5—34no—
104C2×C22⋊Dic5C2×D314yes—
105Q8×Dic5—38no—
106Q8×Dic5—38no—
107D4×Dic5—38no—
108D4×Dic5—316no—
109D4×Dic5—316no—
110D4×Dic5C2×D318yescomplemented
111#4072—32no—
112#4072—34no—
113#4072—38no—
114#4072—38no—
115#4072—38no—
116#4072—34no—
117#4072—34no—
118#4072C2×D312yes—
119C2×C4⋊Dic5—38no—
120C2×C4⋊Dic5—34no—
121C2×C4×Dic5—38no—
122C2×C4×Dic5—34no—
123#3428—151noSylow
124C23×C3×C5—44no—
125C23×C3×C5C22×C418yes—
126C23×C3×C5C2411yescharacteristic
127C23×C3×C5C2414yes—
128C22×C5×D3—42no—
129C22×C5×D3C22×C414yes—
130C22×C5×D3C2412yes—
131C3×C5×D4C22×C4116yes—
132C2×C3×C4×C5C22×C414yes—
133C2×C3×C4×C5C2412yes—
134C2×Dic15—48no—
135C2×Dic15C2418yes—
136C5×#67C22×C4132yes—
137C2×C5×Dic3C22×C418yes—
138C2×C5×Dic3C22×C414yes—
139C2×C5×Dic3C22×C4116yes—
140C2×C5×Dic3C22×C4116yes—
141C2×C5×Dic3C2411yescharacteristic
142C2×C5×Dic3C2414yes—
143C2×C5×Dic3C2411yescharacteristic
144C4×C5×D3C22×C418yes—
145C4×C5×D3C22×C418yes—
146C5×Dic6C22×C4116yes—
147C2×C3×Dic5—48no—
148C2×C3×Dic5C2418yes—
149D3×Dic5—48no—
150C22×C3×D4C2×D511yescharacteristic
151C22×#67C2×D512yes—
152C23×Dic3C2×D512yes—
153C2×#237Dic5116yescomplemented
154C2×#237C2×D514yes—
155C2×#237C2×D514yes—
156C22×C4×D3C2×D511yescharacteristic
157C22×Dic6C2×D511yescharacteristic
158C3×C4×D4—58no—
159C3×#117—52no—
160C2×C3×C22⋊C4—54no—
161C2×#217—54no—
162D4×Dic3—58no—
163C4×#67—516no—
164#926—52no—
165C2×Dic3⋊C4—58no—
166C2×C4×Dic3—58no—
167#892—54no—
168D3×C4⋊C4—54no—
169#887—58no—
170#67⋊C4—516no—
171D3×C22⋊C4—54no—
172#877—54no—
173#877—58no—
174#877—58no—
175#877—58no—
176#872—54no—
177C42×D3—54no—
178C4×Dic6—58no—
179C24×C5—31no—
180C24×C5C22×D312yes—
181C5×#41—332no—
182C5×#41—332no—
183C2×C5×Q8—38no—
184C2×C5×Q8—34no—
185C2×C5×D4—316no—
186C2×C5×D4—38no—
187C2×C5×D4C4×D318yescomplemented
188C2×C5×D4C22×D314yes—
189C22×C4×C5—316no—
190C22×C4×C5—31no—
191C22×C4×C5—32no—
192C22×C4×C5—34no—
193C22×C4×C5—34no—
194C22×C4×C5—38no—
195C22×C4×C5—32no—
196C22×C4×C5—32no—
197C22×C4×C5C22×D311yescharacteristic
198C22×Dic5—38no—
199C22×Dic5—38no—
200C22×Dic5C22×D318yes—
201C22⋊Dic5—34no—
202C22⋊Dic5—38no—
203C22⋊Dic5—38no—
204C22⋊Dic5C22×D314yes—
205C22⋊Dic5C22×D318yes—
206C4⋊Dic5—34no—
207C4⋊Dic5—38no—
208C4⋊Dic5—316no—
209C4⋊Dic5C22×D314yes—
210C4×Dic5—34no—
211C4×Dic5—38no—
212C4×Dic5—316no—
213C4×Dic5C22×D314yes—
214C22×#41—31no—
215#520—158no—
216#519—152no—
217#518—51no—
218#518—154no—
219#518—151no—
220C4×#41—158no—
221C2×#117—154no—
222C2×#117—152no—
223C22×C3×C5—28no—
224C22×C3×C5—22no—
225C22×C3×C5—48no—
226C22×C3×C5C23×C412yes—
227C22×C3×C5C23×C418yes—
228C22×C3×C5C2511yescharacteristic
229C2×C5×D3—24no—
230C2×C5×D3—44no—
231C2×C5×D3C23×C414yes—
232C3×C4×C5C23×C414yes—
233Dic15—28no—
234C3×Dic5—28no—
235C5×Dic3C23×C418yes—
236C5×Dic3C23×C412yes—
237C5×Dic3C23×C412yes—
238C24×C3C22×D512yes—
239C23×D3C22×D511yescharacteristic
240C2×C3×D4C2×Dic518yescomplemented
241C2×C3×D4C22×D514yes—
242C22×C3×C4—58no—
243C22×C3×C4C22×D511yescharacteristic
244C2×#67C2×Dic5116yescomplemented
245C2×#67C22×D518yes—
246C22×Dic3—58no—
247C22×Dic3C2×Dic5116yescomplemented
248C22×Dic3C22×D512yes—
249C22×Dic3C22×D511yescharacteristic
250C22×Dic3C22×D514yes—
251C22×Dic3C22×D514yes—
252#237C2×Dic5132yescomplemented
253#237C2×Dic5132yescomplemented
254C2×C4×D3—58no—
255C2×C4×D3C2×Dic518yescomplemented
256C2×C4×D3C22×D512yes—
257C2×C4×D3C22×D512yes—
258C2×Dic6C2×Dic518yescomplemented
259C2×Dic6C22×D514yes—
260C3×C4⋊C4—54no—
261C3×C22⋊C4—54no—
262C3×C22⋊C4—58no—
263C3×C42—54no—
264#217—54no—
265#217—58no—
266(C2×D3)⋊C4—58no—
267C4⋊Dic3—54no—
268Dic3⋊C4—516no—
269Dic3⋊C4—58no—
270C4×Dic3—54no—
271C4×Dic3—516no—
272C4×Dic3—58no—
273C23×C5—32no—
274C23×C5—34no—
275C23×C5—44no—
276C23×C5—122no—
277C23×C5C2×C4×D318yes—
278C23×C5C23×D311yescharacteristic
279C23×C5C23×D314yes—
280C5×Q8—316no—
281C5×D4—332no—
282C5×D4C2×C4×D3116yes—
283C2×C4×C5—34no—
284C2×C4×C5—38no—
285C2×C4×C5—316no—
286C2×C4×C5—316no—
287C2×C4×C5—31no—
288C2×C4×C5—34no—
289C2×C4×C5—31no—
290C2×C4×C5—38no—
291C2×C4×C5—38no—
292C2×C4×C5C2×C4×D314yes—
293C2×C4×C5C23×D312yes—
294C2×Dic5—38no—
295C2×Dic5—48no—
296C2×Dic5—128no—
297C2×Dic5—128no—
298C2×Dic5C23×D318yes—
299C2×#41—316no—
300C2×#41—34no—
301C2×#41—34no—
302C22×Q8—31no—
303C22×D4—32no—
304C22×D4D3×D511yescharacteristic
305C23×C4—32no—
306C23×C4—31no—
307C4×Q8—158no—
308C4×Q8—158no—
309C4×D4—58no—
310C4×D4—1516no—
311C4×D4—1516no—
312C4×D4—158no—
313#117—52no—
314#117—154no—
315#117—154no—
316#117—158no—
317#117—158no—
318#117—158no—
319#117—154no—
320#117—152no—
321C2×C4⋊C4—154no—
322C2×C4⋊C4—158no—
323C2×C22⋊C4—54no—
324C2×C22⋊C4—154no—
325C2×C22⋊C4—154no—
326C2×C42—154no—
327C2×C42—158no—
328C2×C3×C5—22no—
329C2×C3×C5—28no—
330C2×C3×C5C24×C411yescharacteristic
331C2×C3×C5#58512yes—
332C5×D3—24no—
333C23×C3—44no—
334C23×C3C22×Dic518yes—
335C23×C3C23×D511yescharacteristic
336C23×C3C23×D514yes—
337C22×D3—42no—
338C22×D3C22×Dic514yes—
339C22×D3C23×D512yes—
340C3×D4C22×Dic5116yes—
341C2×C3×C4—58no—
342C2×C3×C4—208no—
343C2×C3×C4C22×Dic514yes—
344C2×C3×C4C23×D512yes—
345#67C22×Dic5132yes—
346C2×Dic3—58no—
347C2×Dic3—208no—
348C2×Dic3C22×Dic518yes—
349C2×Dic3C22×Dic514yes—
350C2×Dic3C22×Dic5116yes—
351C2×Dic3C22×Dic5116yes—
352C2×Dic3C23×D511yescharacteristic
353C2×Dic3C23×D514yes—
354C2×Dic3C23×D511yescharacteristic
355C4×D3—208no—
356C4×D3C22×Dic518yes—
357C4×D3C22×Dic518yes—
358Dic6C22×Dic5116yes—
359C22×C5—28no—
360C22×C5—22no—
361C22×C5—34no—
362C22×C5—48no—
363C22×C5—64no—
364C22×C5—124no—
365C22×C5C22×C4×D312yes—
366C22×C5C22×C4×D318yes—
367C22×C5C24×D311yescharacteristic
368C4×C5—32no—
369C4×C5—32no—
370C4×C5—38no—
371C4×C5C22×C4×D314yes—
372Dic5—28no—
373Dic5—68no—
374C24—31no—
375C24C2×D3×D512yes—
376#41—332no—
377#41—332no—
378C2×Q8—38no—
379C2×Q8—34no—
380C2×D4—316no—
381C2×D4—38no—
382C2×D4D3×Dic518yescomplemented
383C2×D4C2×D3×D514yes—
384C22×C4—316no—
385C22×C4—34no—
386C22×C4—34no—
387C22×C4—31no—
388C22×C4—32no—
389C22×C4—38no—
390C22×C4—32no—
391C22×C4—32no—
392C22×C4—58no—
393C22×C4—158no—
394C22×C4—158no—
395C22×C4C2×D3×D511yescharacteristic
396C4⋊C4—54no—
397C4⋊C4—158no—
398C4⋊C4—1516no—
399C4⋊C4—154no—
400C22⋊C4—54no—
401C22⋊C4—58no—
402C22⋊C4—158no—
403C22⋊C4—154no—
404C22⋊C4—158no—
405C42—54no—
406C42—158no—
407C42—1516no—
408C42—154no—
409C3×C5#342811yescharacteristic, complemented, Hall
410C22×C3—28no—
411C22×C3—22no—
412C22×C3—48no—
413C22×C3C23×Dic512yes—
414C22×C3C23×Dic518yes—
415C22×C3C24×D511yescharacteristic
416C2×D3—24no—
417C2×D3—44no—
418C2×D3C23×Dic514yes—
419C3×C4—108no—
420C3×C4C23×Dic514yes—
421Dic3—108no—
422Dic3C23×Dic518yes—
423Dic3C23×Dic512yes—
424Dic3C23×Dic512yes—
425C2×C5—22no—
426C2×C5—28no—
427C2×C5—64no—
428C2×C5C23×C4×D311yescharacteristic
429C2×C5#596612yes—
430C23—32no—
431C23—34no—
432C23—44no—
433C23—122no—
434C23C2×D3×Dic518yes—
435C23C22×D3×D511yescharacteristic
436C23C22×D3×D514yes—
437Q8—316no—
438D4—332no—
439D4C2×D3×Dic5116yes—
440C2×C4—34no—
441C2×C4—38no—
442C2×C4—316no—
443C2×C4—316no—
444C2×C4—31no—
445C2×C4—34no—
446C2×C4—31no—
447C2×C4—38no—
448C2×C4—38no—
449C2×C4—58no—
450C2×C4—158no—
451C2×C4—208no—
452C2×C4—608no—
453C2×C4—608no—
454C2×C4C2×D3×Dic514yes—
455C2×C4C22×D3×D512yes—
456C2×C3—22no—
457C2×C3—28no—
458C2×C3#6628312yes—
459C2×C3C24×Dic511yescharacteristic
460D3—24no—
461C5#8585611yescharacteristic, complemented, Sylow
462C22—28no—
463C22—22no—
464C22—34no—
465C22—48no—
466C22—64no—
467C22—124no—
468C22C22×D3×Dic512yes—
469C22C22×D3×Dic518yes—
470C22C23×D3×D511yescharacteristic
471C4—32no—
472C4—32no—
473C4—38no—
474C4—108no—
475C4—308no—
476C4C22×D3×Dic514yes—
477C3#1061916111yescharacteristic, complemented, Sylow
478C2—22no—
479C2—28no—
480C2—64no—
481C2#1175703512yes—
482C2C23×D3×Dic511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutatorC2×C3×C5C24×C4
FittingC22×C3×C5×D4C22
socle, cosocleC22×C3×C5C25
prime radicalC22×C5×#237C2
hypercenterC22×D4D3×D5
hypocenterC3×C5#3428
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #11756557C2semidirect
3. C3×#66132C2semidirect
4. #11755410C2semidirect
5. C2×#91529C2semidirect
6. #11754920C2semidirect
7. Dic5×#237C2semidirect
8. D3×#4072C2semidirect
9. #11754211C2semidirect
14. C2×C5×#237C4semidirect
20. D4×Dic15C22semidirect
23. C3×D4×Dic5C22semidirect
25. #67⋊Dic5C22semidirect
27. Dic5×#67C22semidirect
28. C2×Dic3⋊Dic5C22semidirect
31. #91529C22semidirect
32. #91529C22semidirect
33. C2×Dic3×Dic5C22semidirect
34. D3×C4⋊Dic5C22semidirect
35. C4×D3×Dic5C22semidirect
36. #91371C22semidirect
37. #91344C22semidirect
38. #91338C22semidirect
39. Dic5×Dic6C22semidirect
47. #66132D3semidirect
52. C2×C3×C5×D4C2×C4semidirect
56. C2×C5×#67C2×C4semidirect
58. C22×C5×Dic3C2×C4semidirect
63. C5×#237C2×C4semidirect
64. C5×#237C2×C4semidirect
65. C2×C4×C5×D3C2×C4semidirect
68. C2×C5×Dic6C2×C4semidirect
110. D4×Dic5C2×D3semidirect
153. C2×#237Dic5semidirect
187. C2×C5×D4C4×D3semidirect
240. C2×C3×D4C2×Dic5semidirect
244. C2×#67C2×Dic5semidirect
247. C22×Dic3C2×Dic5semidirect
252. #237C2×Dic5semidirect
253. #237C2×Dic5semidirect
255. C2×C4×D3C2×Dic5semidirect
258. C2×Dic6C2×Dic5semidirect
382. C2×D4D3×Dic5semidirect
409. C3×C5#3428semidirect
461. C5#85856semidirect
477. C3#10619161semidirect

Maximal subgroups

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

subgroupindex
C22×C5×#2372
#117565572
C3×#661322
#117554102
C2×#915292
#117549202
Dic5×#2372
D3×#40722
#117542112
#106191613
#858565