Finite Group Databasebeta

← #14282844

Subgroups — #14282844

Order 1920.

608 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5791C211yesmaximal, characteristic
2C4×#6719C211yesmaximal, characteristic, complemented
3C2×C3×C22⋊#168C211yesmaximal, characteristic, complemented
4#11745963C212yesmaximal, complemented
5#11745957C212yesmaximal, complemented
6#10602500—31nomaximal, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C2×C5×#235C411yescharacteristic, complemented
9C2×#6719—21no—
10C2×C4×Dic15—21no—
11C5×#953—21no—
12C5×#930C411yescharacteristic, complemented
13C5×#930C2211yescharacteristic
14C5×#929—21no—
15C4×C5×#67—21no—
16C4×C5×#67—21no—
17C5×#926C411yescharacteristic, complemented
18C5×#924C411yescharacteristic, complemented
19C5×#924C2211yescharacteristic
20C22×C3×#168—21no—
21#91115C2212yes—
22C3×C22⋊#168—21no—
23C3×C22⋊#168C2212yes—
24#69942—51nomaximal, Hall
25C5×#525—31no—
26C4×C22⋊Dic5—31no—
27C2×C22⋊#168D311yescharacteristic, complemented
28#64758—32no—
29#64757—32no—
30C24×C3×C5D411yescharacteristic
31C22×C3×C4×C5—42no—
32C22×C3×C4×C5C2×C411yescharacteristic
33C22×C3×C4×C5C2×C411yescharacteristic
34C22×C3×C4×C5D411yescharacteristic
35C22×C3×C4×C5D411yescharacteristic
36C22×C3×C4×C5D411yescharacteristic
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15—22no—
39C2×C5×#67—21no—
40C2×C5×#67—21no—
41C2×C5×#67—21no—
42C5×#235—42no—
43C2×C5×D12C2×C411yescharacteristic
44C2×C4×C5×D3—21no—
45C2×C5×Dic6C2×C411yescharacteristic
46#6719—24no—
47C4×Dic15—42no—
48C5×#217—21no—
49C5×#217—21no—
50C5×#217—21no—
51C5×(C2×D3)⋊C4—21no—
52C5×(C2×D3)⋊C4—21no—
53C5×C4⋊Dic3C2×C411yescharacteristic
54C5×C4⋊Dic3C2×C411yescharacteristic
55C5×Dic3⋊C4—21no—
56C5×Dic3⋊C4—21no—
57C4×C5×Dic3—21no—
58C2×C3×#168—22no—
59C2×C3×#168—42no—
60#5791D511yescharacteristic
61C2×C3×C22⋊C8—51no—
62C4×#217—51no—
63#4470—52no—
64#4467—52no—
65C2×C5×#41—31no—
66C23×C4×C5C2×D311yescharacteristic
67C5×#123—61no—
68C5×C22⋊Q8—31no—
69C5×C22⋊Q8—31no—
70C5×#121—31no—
71C5×#121—31no—
72C5×#120—61no—
73C4×C5×D4—61no—
74C4×C5×D4—61no—
75C5×#117—31no—
76C2×C22⋊Dic5—61no—
77C2×C4×Dic5—61no—
78C22×#168—21no—
79#3963—32no—
80C22⋊#168—21no—
81C22⋊#168C2×D312yes—
82#1501—151noSylow
83C23×C3×C5—22no—
84C23×C3×C5—22no—
85C23×C3×C5—41no—
86C23×C3×C5C22⋊C411yescharacteristic
87C23×C3×C5C22⋊C411yescharacteristic
88C23×C3×C5C2×D411yescharacteristic
89C22×C5×D3—21no—
90C2×C3×C4×C5—22no—
91C2×C3×C4×C5—22no—
92C2×C3×C4×C5—22no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5—41no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5C22⋊C411yescharacteristic
97C2×C3×C4×C5C22⋊C411yescharacteristic
98C2×C3×C4×C5C22×C411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×Dic15—24no—
101C2×Dic15—42no—
102C2×Dic15—42no—
103C5×#67—42no—
104C5×#67—42no—
105C5×#67—42no—
106C2×C5×Dic3—21no—
107C2×C5×Dic3—21no—
108C2×C5×Dic3—21no—
109C5×D12—41no—
110C4×C5×D3—42no—
111C5×Dic6—41no—
112C3×#168—42no—
113C23×C3×C4C2×D511yescharacteristic
114C2×#235Dic511yescharacteristic, complemented
115C22×C3×C8—101no—
116#953—21no—
117C2×#217—101no—
118#930Dic511yescharacteristic, complemented
119#930C2×D511yescharacteristic
120#929—21no—
121C4×#67—21no—
122C4×#67—21no—
123#926Dic511yescharacteristic, complemented
124#924Dic511yescharacteristic, complemented
125#924C2×D511yescharacteristic
126C2×C4×Dic3—101no—
127C3×C22⋊C8—52no—
128C3×C22⋊C8—101no—
129C3⋊#95—52no—
130C24×C5D1211yescharacteristic
131C5×#41—122no—
132C2×C5×Q8—31no—
133C2×C5×D4—31no—
134C2×C5×D4—61no—
135C2×C5×D4—61no—
136C2×C5×D4—61no—
137C22×C4×C5—42no—
138C22×C4×C5—61no—
139C22×C4×C5C4×D311yescharacteristic
140C22×C4×C5C4×D311yescharacteristic
141C22×C4×C5D1211yescharacteristic
142C22×C4×C5#6711yescharacteristic
143C22×C4×C5#6711yescharacteristic
144C22×C4×C5C22×D311yescharacteristic
145C22×Dic5—62no—
146C5×C4⋊C4—31no—
147C5×C4⋊C4—31no—
148C5×C4⋊C4—61no—
149C5×C4⋊C4—61no—
150C5×C22⋊C4—61no—
151C5×C22⋊C4—61no—
152C5×C22⋊C4—61no—
153C5×C22⋊C4—61no—
154C5×C22⋊C4—61no—
155C42×C5—61no—
156C22⋊Dic5—64no—
157C4×Dic5—122no—
158C2×#168—22no—
159C2×#168—42no—
160#525—31no—
161C2×C22⋊C8—51no—
162C4×C22⋊C4—151no—
163#328—152no—
164#327—152no—
165C22×C3×C5—21no—
166C22×C3×C5—21no—
167C22×C3×C5—21no—
168C22×C3×C5—21no—
169C22×C3×C5—21no—
170C22×C3×C5—21no—
171C22×C3×C5—21no—
172C22×C3×C5—44no—
173C22×C3×C5#10412yes—
174C22×C3×C5C2×C22⋊C411yescharacteristic
175C22×C3×C5#13512yes—
176C2×C5×D3—41no—
177C2×C5×D3—41no—
178C2×C5×D3—41no—
179C3×C4×C5—21no—
180C3×C4×C5—21no—
181C3×C4×C5—21no—
182C3×C4×C5#9912yes—
183Dic15—44no—
184C5×Dic3—41no—
185C5×Dic3—41no—
186C5×Dic3—41no—
187C24×C3C22⋊D511yescharacteristic
188C22×C3×C4—42no—
189C22×C3×C4C2×Dic511yescharacteristic
190C22×C3×C4C2×Dic511yescharacteristic
191C22×C3×C4C22⋊D511yescharacteristic
192C22×C3×C4C22⋊D511yescharacteristic
193C22×C3×C4C22⋊D511yescharacteristic
194C22×C3×C4C22×D511yescharacteristic
195C2×#67—21no—
196C2×#67—21no—
197C2×#67—21no—
198C22×Dic3—102no—
199#235—42no—
200C2×D12C2×Dic511yescharacteristic
201C2×C4×D3—21no—
202C2×Dic6C2×Dic511yescharacteristic
203C2×C3×C8—102no—
204C2×C3×C8—202no—
205#217—21no—
206#217—21no—
207#217—21no—
208#217—104no—
209(C2×D3)⋊C4—21no—
210(C2×D3)⋊C4—21no—
211C4⋊Dic3C2×Dic511yescharacteristic
212C4⋊Dic3C2×Dic511yescharacteristic
213Dic3⋊C4—21no—
214Dic3⋊C4—21no—
215C4×Dic3—21no—
216C4×Dic3—202no—
217C23×C5—22no—
218C23×C5—22no—
219C23×C5—41no—
220C23×C5—61no—
221C23×C5(C2×D3)⋊C411yescharacteristic
222C23×C5(C2×D3)⋊C411yescharacteristic
223C23×C5C2×D1211yescharacteristic
224C5×Q8—121no—
225C5×D4—121no—
226C5×D4—122no—
227C5×D4—122no—
228C5×D4—122no—
229C2×C4×C5—22no—
230C2×C4×C5—22no—
231C2×C4×C5—22no—
232C2×C4×C5—41no—
233C2×C4×C5—41no—
234C2×C4×C5—41no—
235C2×C4×C5—61no—
236C2×C4×C5—61no—
237C2×C4×C5—61no—
238C2×C4×C5—122no—
239C2×C4×C5(C2×D3)⋊C411yescharacteristic
240C2×C4×C5(C2×D3)⋊C411yescharacteristic
241C2×C4×C5C2×C4×D311yescharacteristic
242C2×C4×C5C2×#6711yescharacteristic
243C2×Dic5—64no—
244C2×Dic5—122no—
245C2×Dic5—122no—
246#168—42no—
247C2×#41—31no—
248C23×C4D3×D511yescharacteristic
249C22×C8—101no—
250#123—61no—
251C22⋊Q8—31no—
252C22⋊Q8—31no—
253#121—31no—
254#121—31no—
255#120—61no—
256C4×D4—61no—
257C4×D4—61no—
258#117—31no—
259C2×C22⋊C4—301no—
260C2×C42—301no—
261C22⋊C8—52no—
262C22⋊C8—101no—
263#95—152no—
264C2×C3×C5—22no—
265C2×C3×C5—22no—
266C2×C3×C5—41no—
267C2×C3×C5C2×#9911yescharacteristic
268C2×C3×C5#41611yescharacteristic
269C2×C3×C5C2×#10411yescharacteristic
270C5×D3—81no—
271C23×C3—22no—
272C23×C3—22no—
273C23×C3—41no—
274C23×C3C22⋊Dic511yescharacteristic
275C23×C3C22⋊Dic511yescharacteristic
276C23×C3C2×C22⋊D511yescharacteristic
277C22×D3—21no—
278C2×C3×C4—22no—
279C2×C3×C4—22no—
280C2×C3×C4—22no—
281C2×C3×C4—41no—
282C2×C3×C4—41no—
283C2×C3×C4—41no—
284C2×C3×C4C22⋊Dic511yescharacteristic
285C2×C3×C4C22⋊Dic511yescharacteristic
286C2×C3×C4C22×Dic511yescharacteristic
287C2×C3×C4C2×C22⋊D511yescharacteristic
288#67—42no—
289#67—42no—
290#67—42no—
291C2×Dic3—21no—
292C2×Dic3—21no—
293C2×Dic3—21no—
294C2×Dic3—104no—
295C2×Dic3—202no—
296C2×Dic3—202no—
297D12—41no—
298C4×D3—42no—
299Dic6—41no—
300C3×C8—202no—
301C22×C5—21no—
302C22×C5—21no—
303C22×C5—21no—
304C22×C5—21no—
305C22×C5—21no—
306C22×C5—21no—
307C22×C5—21no—
308C22×C5—44no—
309C22×C5—121no—
310C22×C5—121no—
311C22×C5—121no—
312C22×C5#82512yes—
313C22×C5#90412yes—
314C22×C5C2×(C2×D3)⋊C411yescharacteristic
315C4×C5—21no—
316C4×C5—21no—
317C4×C5—21no—
318C4×C5—121no—
319C4×C5—121no—
320C4×C5—121no—
321C4×C5#80612yes—
322Dic5—124no—
323C24#120311yescharacteristic
324#41—122no—
325C2×Q8—31no—
326C2×D4—31no—
327C2×D4—61no—
328C2×D4—61no—
329C2×D4—61no—
330C22×C4—42no—
331C22×C4—61no—
332C22×C4—302no—
333C22×C4D3×Dic511yescharacteristic
334C22×C4D3×Dic511yescharacteristic
335C22×C4#120111yescharacteristic
336C22×C4#120111yescharacteristic
337C22×C4#120311yescharacteristic
338C22×C4C2×D3×D511yescharacteristic
339C2×C8—102no—
340C2×C8—202no—
341C4⋊C4—31no—
342C4⋊C4—31no—
343C4⋊C4—61no—
344C4⋊C4—61no—
345C22⋊C4—61no—
346C22⋊C4—61no—
347C22⋊C4—61no—
348C22⋊C4—61no—
349C22⋊C4—61no—
350C22⋊C4—304no—
351C42—61no—
352C42—602no—
353C3×C5#150111yescharacteristic, complemented, Hall
354C22×C3—21no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—44no—
362C22×C3#396912yes—
363C22×C3#409612yes—
364C22×C3C2×C22⋊Dic511yescharacteristic
365C2×D3—41no—
366C2×D3—41no—
367C2×D3—41no—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4#396612yes—
372Dic3—41no—
373Dic3—41no—
374Dic3—41no—
375Dic3—204no—
376C2×C5—22no—
377C2×C5—22no—
378C2×C5—41no—
379C2×C5—241no—
380C2×C5C2×#80611yescharacteristic
381C2×C5#511311yescharacteristic
382C2×C5C2×#82511yescharacteristic
383C23—22no—
384C23—22no—
385C23—41no—
386C23—61no—
387C23(C2×D3)⋊Dic511yescharacteristic
388C23(C2×D3)⋊Dic511yescharacteristic
389C23C2×#120311yescharacteristic
390Q8—121no—
391D4—121no—
392D4—122no—
393D4—122no—
394D4—122no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—61no—
402C2×C4—61no—
403C2×C4—61no—
404C2×C4—122no—
405C2×C4—304no—
406C2×C4—602no—
407C2×C4—602no—
408C2×C4(C2×D3)⋊Dic511yescharacteristic
409C2×C4(C2×D3)⋊Dic511yescharacteristic
410C2×C4C2×D3×Dic511yescharacteristic
411C2×C4C2×#120111yescharacteristic
412C8—202no—
413C2×C3—22no—
414C2×C3—22no—
415C2×C3—41no—
416C2×C3C2×#396611yescharacteristic
417C2×C3#6552211yescharacteristic
418C2×C3C2×#396911yescharacteristic
419D3—81no—
420C5#6994211yescharacteristic, complemented, Sylow
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—44no—
429C22—121no—
430C22—121no—
431C22—121no—
432C22#9097812yes—
433C22#9130312yes—
434C22C2×(C2×D3)⋊Dic511yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—121no—
439C4—121no—
440C4—121no—
441C4—604no—
442C4#9099612yes—
443C3#1060250011yescharacteristic, complemented, Sylow
444C2—22no—
445C2—22no—
446C2—41no—
447C2—241no—
448C2#1174838811yescharacteristic
449C2C2×#9097811yescharacteristic
450C2C2×#9099611yescharacteristic
subgroupG/H
centerC2×C4(C2×D3)⋊Dic5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC23×C3×C4×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#5791C2
cosocleC22×C3×C4×C5C23
hypercenterC23×C4D3×D5
hypocenterC3×C5#1501
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C4×#6719C2semidirect
3. C2×C3×C22⋊#168C2semidirect
4. #11745963C2semidirect
5. #11745957C2semidirect
8. C2×C5×#235C4semidirect
12. C5×#930C4semidirect
17. C5×#926C4semidirect
18. C5×#924C4semidirect
27. C2×C22⋊#168D3semidirect
114. C2×#235Dic5semidirect
118. #930Dic5semidirect
123. #926Dic5semidirect
124. #924Dic5semidirect
353. C3×C5#1501semidirect
420. C5#69942semidirect
443. C3#10602500semidirect

Maximal subgroups

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

subgroupindex
C5×#57912
C4×#67192
C2×C3×C22⋊#1682
#117459632
#117459572
#106025003
#699425