Finite Group Databasebeta

← #14439849

Subgroups — #14439849

Order 1920.

712 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66062C211yesmaximal, characteristic
2#11752506C211yesmaximal, characteristic
3#11751179C211yesmaximal, characteristic, complemented
4C5×#5080C211yesmaximal, characteristic, complemented
5#11747433C214yesmaximal
6#11747144C214yesmaximal, complemented
7C4×D5×C3⋊C8C211yesmaximal, characteristic
8#11746962C211yesmaximal, characteristic, complemented
9#11746948C211yesmaximal, characteristic, complemented
10#10613622—31nomaximal, Hall
11C3×C5×C4⋊Q8C2211yescharacteristic
12#91758C2211yescharacteristic
13C5×#869C2211yescharacteristic
14C3×#4092—21no—
15C3×Q8×Dic5—21no—
16C3×#4043—21no—
17C3×#4038C2212yes—
18C3×#4036C2212yes—
19C3×#4033—21no—
20C3×C42×D5C2211yescharacteristic
21C3×#4015C2211yescharacteristic
22#91388C2212yes—
23#91360—21no—
24#91359—21no—
25#91358C2212yes—
26#91333—21no—
27Dic5×Dic6—21no—
28C2×D5×C3⋊C8C2212yes—
29#91091C2214yes—
30C4×C3⋊#168C2211yescharacteristic
31C5×#808C2214yes—
32C4×C5×C3⋊C8C2211yescharacteristic
33#90989C2214yes—
34#90987C2214yes—
35Dic5×C3⋊C8C2212yes—
36#83339—51nomaximal, Hall
37#66062—31no—
38#66062D311yescharacteristic
39C5×#498—31no—
40#65367—31no—
41#65367—31no—
42#65149—34no—
43#65147—34no—
44C4×C8×D5—31no—
45#64969—31no—
46C2×C3×C5×Q8—21no—
47C2×Dic30—21no—
48C2×C5×Dic6—21no—
49C2×C3×C4×D5D411yescharacteristic
50C2×C3×C4×D5D411yescharacteristic
51C2×C3×C4×D5C2311yescharacteristic
52C2×C3×Dic10—21no—
53C3×C5×C4⋊C4—21no—
54C3×C5×C4⋊C4C2312yes—
55C3×C42×C5C2311yescharacteristic
56C4⋊Dic15—21no—
57C4⋊Dic15C2312yes—
58C2×C3⋊#168C2312yes—
59C5×C4⋊Dic3—21no—
60C5×C4⋊Dic3C2312yes—
61C2×C5×C3⋊C8C2312yes—
62C3×#685—22no—
63C3×C4⋊Dic5—21no—
64C3×C4⋊Dic5—22no—
65C3×C4⋊Dic5C2312yes—
66C3×#683—22no—
67C3×C4×Dic5—22no—
68C3×C4×Dic5D411yescharacteristic
69C3×C4×Dic5D411yescharacteristic
70C3×C4×Dic5C2311yescharacteristic
71Dic3⋊Dic5—22no—
72#6669—22no—
73#6665—22no—
74Dic3×Dic5—22no—
75D5×C3⋊C8Q818yescomplemented
76C3×#533—51no—
77#5470—51no—
78#5080—51no—
79#5080D511yescharacteristic, complemented
80#5078—51no—
81#5078—51no—
82#5065—54no—
83#4998—54no—
84C2×C4×C3⋊C8—51no—
85C5×C4⋊Q8—31no—
86C5×C4⋊Q8C2×D311yescharacteristic
87#4092—21no—
88#4092—61no—
89Q8×Dic5—21no—
90Q8×Dic5—61no—
91C2×C8×D5—32no—
92#4043—21no—
93#4043—61no—
94#4038—32no—
95#4038C2×D312yes—
96#4036—32no—
97#4036C2×D312yes—
98#4033—21no—
99#4033—61no—
100C42×D5C2×D311yescharacteristic
101#4015—31no—
102#4015C2×D311yescharacteristic
103C5×#106—34no—
104C4×C5×C8—31no—
105#3949—34no—
106C8×Dic5—32no—
107#3939—34no—
108#3939—34no—
109C4×#168—31no—
110#3160—151noSylow
111C22×C3×D5C2×D411yescharacteristic
112C3×C5×Q8—42no—
113C2×C3×C4×C5—22no—
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5C2×D411yescharacteristic
116C2×C3×C4×C5C2411yescharacteristic
117C2×Dic15—22no—
118Dic30—42no—
119C2×C5×Dic3—22no—
120C5×Dic6—42no—
121C2×C3×Dic5—22no—
122C2×C3×Dic5C2×D411yescharacteristic
123C2×C3×Dic5C2×D411yescharacteristic
124C2×C3×Dic5C2×D411yescharacteristic
125C3×C4×D5—22no—
126C3×C4×D5—22no—
127C3×C4×D5C2×Q814yes—
128C3×Dic10—42no—
129C3⋊#168C2×Q814yes—
130C5×C3⋊C8C2×Q814yes—
131C3×C4⋊Q8—51no—
132C3×C4⋊Q8C2×D511yescharacteristic
133C3×#125—52no—
134C3×C22⋊Q8—101no—
135C3×C22⋊Q8—101no—
136C3×C4×Q8—101no—
137C3×C4×Q8—101no—
138C3×#117—52no—
139C2×C3×C42—51no—
140#926—52no—
141#924—101no—
142#924—101no—
143C22×C3⋊C8—52no—
144#870—52no—
145#869—51no—
146#869C2×D511yescharacteristic
147C4×Dic6—101no—
148C4×Dic6—101no—
149#808—54no—
150#808C2×D514yes—
151#807—54no—
152#807—54no—
153C4×C3⋊C8—51no—
154C4×C3⋊C8—52no—
155C4×C3⋊C8C2×D511yescharacteristic
156C2×C5×Q8—21no—
157C2×C5×Q8—61no—
158C2×C4×D5#6711yescharacteristic
159C2×C4×D5#6711yescharacteristic
160C2×C4×D5C22×D311yescharacteristic
161C2×Dic10—21no—
162C2×Dic10—61no—
163C2×C5×C8—32no—
164C5×C4⋊C4—21no—
165C5×C4⋊C4—32no—
166C5×C4⋊C4—61no—
167C5×C4⋊C4C22×D312yes—
168C42×C5C22×D311yescharacteristic
169#685—22no—
170#685—62no—
171C4⋊Dic5—21no—
172C4⋊Dic5—22no—
173C4⋊Dic5—32no—
174C4⋊Dic5—61no—
175C4⋊Dic5—62no—
176C4⋊Dic5C22×D312yes—
177#683—22no—
178#683—62no—
179C4×Dic5—22no—
180C4×Dic5—62no—
181C4×Dic5#6711yescharacteristic
182C4×Dic5#6711yescharacteristic
183C4×Dic5C22×D311yescharacteristic
184C2×#168—32no—
185C8×D5—38no—
186#533—51no—
187#533—151no—
188#500—151no—
189#500—151no—
190#499—154no—
191#498—31no—
192#498—151no—
193#427—154no—
194C2×C4×C8—151no—
195C22×C3×C5C22×D411yescharacteristic
196C2×C3×D5—21no—
197C2×C3×D5—21no—
198C2×C3×D5C4⋊Q812yes—
199C3×C4×C5—42no—
200C3×C4×C5#13512yes—
201C3×C4×C5#13512yes—
202C3×C4×C5C22×Q812yes—
203Dic15—42no—
204C3×Dic5—21no—
205C3×Dic5—21no—
206C3×Dic5—42no—
207C3×Dic5C4⋊Q812yes—
208C5×Dic3—42no—
209C2×C3×Q8—21no—
210C2×C3×Q8—101no—
211C22×C3×C4—51no—
212C22×C3×C4—51no—
213C22×C3×C4—51no—
214C2×Dic6—21no—
215C2×Dic6—101no—
216C3×C4⋊C4—21no—
217C3×C4⋊C4—52no—
218C3×C4⋊C4—102no—
219C3×C4⋊C4—102no—
220C3×C4⋊C4—101no—
221C3×C4⋊C4C22×D512yes—
222C3×C22⋊C4—102no—
223C3×C42—51no—
224C3×C42—51no—
225C3×C42—51no—
226C3×C42—102no—
227C3×C42C22×D511yescharacteristic
228#217—102no—
229C4⋊Dic3—21no—
230C4⋊Dic3—52no—
231C4⋊Dic3—101no—
232C4⋊Dic3C22×D512yes—
233Dic3⋊C4—102no—
234Dic3⋊C4—102no—
235C4×Dic3—102no—
236C2×C3⋊C8—52no—
237C2×C3⋊C8—58no—
238C2×C3⋊C8C22×D512yes—
239C22×D5C2×#6711yescharacteristic
240C5×Q8—42no—
241C5×Q8—122no—
242C2×C4×C5—22no—
243C2×C4×C5—62no—
244C2×C4×C5C2×#6711yescharacteristic
245C2×C4×C5C2×#6711yescharacteristic
246C2×C4×C5C23×D311yescharacteristic
247C2×Dic5—22no—
248C2×Dic5—62no—
249C2×Dic5C2×#6711yescharacteristic
250C2×Dic5C2×#6711yescharacteristic
251C2×Dic5C2×#6711yescharacteristic
252C4×D5—22no—
253C4×D5—22no—
254C4×D5D3×Q814yes—
255Dic10—42no—
256Dic10—122no—
257C5×C8—34no—
258#168—34no—
259C22×C8—152no—
260C4⋊Q8—31no—
261C4⋊Q8—51no—
262C4⋊Q8—151no—
263C4⋊Q8D3×D511yescharacteristic
264#125—52no—
265#125—152no—
266C22⋊Q8—101no—
267C22⋊Q8—101no—
268C22⋊Q8—301no—
269C22⋊Q8—301no—
270C4×Q8—101no—
271C4×Q8—101no—
272C4×Q8—301no—
273C4×Q8—301no—
274#117—52no—
275#117—152no—
276C2×C42—51no—
277#107—154no—
278#107—154no—
279#106—34no—
280#106—154no—
281C4×C8—31no—
282C4×C8—152no—
283C4×C8—151no—
284C2×C3×C5C2×C4⋊Q811yescharacteristic
285C2×C3×C5C2×#13511yescharacteristic
286C2×C3×C5C2×#13511yescharacteristic
287C3×D5—22no—
288C23×C3—51no—
289C3×Q8—42no—
290C3×Q8—202no—
291C2×C3×C4—22no—
292C2×C3×C4—51no—
293C2×C3×C4—54no—
294C2×C3×C4—51no—
295C2×C3×C4—51no—
296C2×C3×C4—102no—
297C2×C3×C4—102no—
298C2×C3×C4—102no—
299C2×C3×C4D4×D511yescharacteristic
300C2×C3×C4D4×D511yescharacteristic
301C2×C3×C4C23×D511yescharacteristic
302C2×Dic3—22no—
303C2×Dic3—102no—
304Dic6—42no—
305Dic6—202no—
306C3⋊C8—54no—
307C3⋊C8Q8×D514yes—
308C22×C5C22×#6711yescharacteristic
309C2×D5—21no—
310C2×D5—21no—
311C2×D5#94412yes—
312C4×C5—42no—
313C4×C5—122no—
314C4×C5#95012yes—
315C4×C5#95012yes—
316C4×C5C2×D3×Q812yes—
317Dic5—21no—
318Dic5—21no—
319Dic5—42no—
320Dic5—122no—
321Dic5#94412yes—
322C2×Q8—21no—
323C2×Q8—61no—
324C2×Q8—101no—
325C2×Q8—301no—
326C22×C4—51no—
327C22×C4—51no—
328C22×C4—51no—
329C2×C8—32no—
330C2×C8—158no—
331C2×C8—152no—
332C4⋊C4—21no—
333C4⋊C4—32no—
334C4⋊C4—52no—
335C4⋊C4—61no—
336C4⋊C4—102no—
337C4⋊C4—102no—
338C4⋊C4—101no—
339C4⋊C4—152no—
340C4⋊C4—302no—
341C4⋊C4—302no—
342C4⋊C4—301no—
343C4⋊C4C2×D3×D512yes—
344C22⋊C4—102no—
345C22⋊C4—302no—
346C42—51no—
347C42—51no—
348C42—51no—
349C42—102no—
350C42—302no—
351C42C2×D3×D511yescharacteristic
352C3×C5#316011yescharacteristic, complemented, Hall
353C22×C3—52no—
354C22×C3—101no—
355C22×C3—101no—
356C22×C3C2×D4×D511yescharacteristic
357C3×C4—42no—
358C3×C4—52no—
359C3×C4—101no—
360C3×C4—101no—
361C3×C4—202no—
362C3×C4#406212yes—
363C3×C4#406212yes—
364C3×C4C2×Q8×D512yes—
365Dic3—42no—
366Dic3—202no—
367C2×C5C2×#94411yescharacteristic
368C2×C5C2×#95011yescharacteristic
369C2×C5C2×#95011yescharacteristic
370D5—22no—
371C23—51no—
372Q8—42no—
373Q8—122no—
374Q8—202no—
375Q8—602no—
376C2×C4—22no—
377C2×C4—51no—
378C2×C4—54no—
379C2×C4—51no—
380C2×C4—51no—
381C2×C4—62no—
382C2×C4—102no—
383C2×C4—102no—
384C2×C4—102no—
385C2×C4—302no—
386C2×C4D5×#6711yescharacteristic
387C2×C4D5×#6711yescharacteristic
388C2×C4C22×D3×D511yescharacteristic
389C8—34no—
390C8—154no—
391C2×C3—102no—
392C2×C3D5×C4⋊Q811yescharacteristic
393C2×C3C2×#406211yescharacteristic
394C2×C3C2×#406211yescharacteristic
395C5#8333911yescharacteristic, complemented, Sylow
396C22—52no—
397C22—101no—
398C22—101no—
399C22C2×D5×#6711yescharacteristic
400C4—42no—
401C4—52no—
402C4—101no—
403C4—101no—
404C4—122no—
405C4—202no—
406C4—602no—
407C4#9149212yes—
408C4#9151412yes—
409C4D3×Q8×D512yes—
410C3#1061362211yescharacteristic, complemented, Sylow
411C2—102no—
412C2C2×#9149211yescharacteristic
413C2C2×#9151411yescharacteristic
414C2D5×#94411yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC22×C3×D5C2×D4
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3160
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #11751179C2semidirect
4. C5×#5080C2semidirect
6. #11747144C2semidirect
8. #11746962C2semidirect
9. #11746948C2semidirect
75. D5×C3⋊C8Q8semidirect
79. #5080D5semidirect
352. C3×C5#3160semidirect
395. C5#83339semidirect
410. C3#10613622semidirect

Maximal subgroups

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

subgroupindex
C3×#660622
#117525062
#117511792
C5×#50802
#117474332
#117471442
C4×D5×C3⋊C82
#117469622
#117469482
#106136223
#833395