Finite Group Databasebeta

← #14439851

Subgroups — #14439851

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
1C5×#5728C211yesmaximal, characteristic
2#11752478C211yesmaximal, characteristic
3#11751179C211yesmaximal, characteristic, complemented
4C3×#65368C211yesmaximal, characteristic, complemented
5#11747437C214yesmaximal
6#11747149C214yesmaximal, complemented
7C4×D3×#168C211yesmaximal, characteristic
8#11746962C211yesmaximal, characteristic, complemented
9#11746941C211yesmaximal, characteristic, complemented
10#10615070—31nomaximal, Hall
11C3×C5×C4⋊Q8C2211yescharacteristic
12#91758C2211yescharacteristic
13C5×#946—21no—
14C5×Q8×Dic3—21no—
15C5×#897—21no—
16C5×#892C2212yes—
17C5×#890C2212yes—
18C5×#887—21no—
19C42×C5×D3C2211yescharacteristic
20C5×#869C2211yescharacteristic
21C3×#4015C2211yescharacteristic
22#91381C2212yes—
23#91369—21no—
24#91365—21no—
25#91340—21no—
26#91338C2212yes—
27Dic3×Dic10—21no—
28C2×D3×#168C2212yes—
29#91091C2214yes—
30C4×C3⋊#168C2211yescharacteristic
31C3×#3940C2214yes—
32C3×C4×#168C2211yescharacteristic
33#90989C2214yes—
34#90985C2214yes—
35Dic3×#168C2212yes—
36#81891—51nomaximal, Hall
37C5×#533—31no—
38#65804—31no—
39#65368—31no—
40#65368D311yescharacteristic, complemented
41#65367—31no—
42#65367—31no—
43#65353—34no—
44#65287—34no—
45C2×C4×#168—31no—
46C2×C3×C5×Q8—21no—
47C2×Dic30—21no—
48C2×C4×C5×D3D411yescharacteristic
49C2×C4×C5×D3D411yescharacteristic
50C2×C4×C5×D3C2311yescharacteristic
51C2×C5×Dic6—21no—
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×(C2×D3)⋊C4—22no—
60C5×C4⋊Dic3—21no—
61C5×C4⋊Dic3—22no—
62C5×C4⋊Dic3C2312yes—
63C5×Dic3⋊C4—22no—
64C4×C5×Dic3—22no—
65C4×C5×Dic3D411yescharacteristic
66C4×C5×Dic3D411yescharacteristic
67C4×C5×Dic3C2311yescharacteristic
68C3×C4⋊Dic5—21no—
69C3×C4⋊Dic5C2312yes—
70C2×C3×#168C2312yes—
71#6669—22no—
72#6668—22no—
73(C2×D3)⋊Dic5—22no—
74Dic3×Dic5—22no—
75D3×#168Q818yescomplemented
76#5728—51no—
77#5728D511yescharacteristic
78C3×#498—51no—
79#5078—51no—
80#5078—51no—
81#4860—54no—
82#4858—54no—
83C4×D3×C8—51no—
84#4680—51no—
85C5×C4⋊Q8—31no—
86C5×C4⋊Q8C2×D311yescharacteristic
87C5×#125—32no—
88C5×C22⋊Q8—61no—
89C5×C22⋊Q8—61no—
90C4×C5×Q8—61no—
91C4×C5×Q8—61no—
92C5×#117—32no—
93C2×C42×C5—31no—
94#4072—32no—
95#4070—61no—
96#4070—61no—
97C22×#168—32no—
98#4016—32no—
99#4015—31no—
100#4015C2×D311yescharacteristic
101C4×Dic10—61no—
102C4×Dic10—61no—
103#3940—34no—
104#3940C2×D314yes—
105#3939—34no—
106#3939—34no—
107C4×#168—31no—
108C4×#168—32no—
109C4×#168C2×D311yescharacteristic
110#3160—151noSylow
111C22×C5×D3C2×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—
120C2×C5×Dic3C2×D411yescharacteristic
121C2×C5×Dic3C2×D411yescharacteristic
122C2×C5×Dic3C2×D411yescharacteristic
123C4×C5×D3—22no—
124C4×C5×D3—22no—
125C4×C5×D3C2×Q814yes—
126C5×Dic6—42no—
127C2×C3×Dic5—22no—
128C3×Dic10—42no—
129C3⋊#168C2×Q814yes—
130C3×#168C2×Q814yes—
131C3×C4⋊Q8—51no—
132C3×C4⋊Q8C2×D511yescharacteristic
133#946—21no—
134#946—101no—
135Q8×Dic3—21no—
136Q8×Dic3—101no—
137C2×D3×C8—52no—
138#897—21no—
139#897—101no—
140#892—52no—
141#892C2×D512yes—
142#890—52no—
143#890C2×D512yes—
144#887—21no—
145#887—101no—
146C42×D3C2×D511yescharacteristic
147#869—51no—
148#869C2×D511yescharacteristic
149C3×#106—54no—
150C3×C4×C8—51no—
151#817—54no—
152C8×Dic3—52no—
153#807—54no—
154#807—54no—
155C4×C3⋊C8—51no—
156C2×C5×Q8—21no—
157C2×C5×Q8—61no—
158C22×C4×C5—31no—
159C22×C4×C5—31no—
160C22×C4×C5—31no—
161C2×Dic10—21no—
162C2×Dic10—61no—
163C5×C4⋊C4—21no—
164C5×C4⋊C4—32no—
165C5×C4⋊C4—62no—
166C5×C4⋊C4—62no—
167C5×C4⋊C4—61no—
168C5×C4⋊C4C22×D312yes—
169C5×C22⋊C4—62no—
170C42×C5—31no—
171C42×C5—31no—
172C42×C5—31no—
173C42×C5—62no—
174C42×C5C22×D311yescharacteristic
175C22⋊Dic5—62no—
176C4⋊Dic5—21no—
177C4⋊Dic5—32no—
178C4⋊Dic5—61no—
179C4⋊Dic5C22×D312yes—
180#683—62no—
181#683—62no—
182C4×Dic5—62no—
183C2×#168—32no—
184C2×#168—38no—
185C2×#168C22×D312yes—
186#533—31no—
187#533—151no—
188#500—151no—
189#500—151no—
190#499—154no—
191#498—51no—
192#498—151no—
193#427—154no—
194C2×C4×C8—151no—
195C22×C3×C5C22×D411yescharacteristic
196C2×C5×D3—21no—
197C2×C5×D3—21no—
198C2×C5×D3C4⋊Q812yes—
199C3×C4×C5—42no—
200C3×C4×C5#13512yes—
201C3×C4×C5#13512yes—
202C3×C4×C5C22×Q812yes—
203Dic15—42no—
204C3×Dic5—42no—
205C5×Dic3—21no—
206C5×Dic3—21no—
207C5×Dic3—42no—
208C5×Dic3C4⋊Q812yes—
209C2×C3×Q8—21no—
210C2×C3×Q8—101no—
211C2×C4×D3C22⋊D511yescharacteristic
212C2×C4×D3C22⋊D511yescharacteristic
213C2×C4×D3C22×D511yescharacteristic
214C2×Dic6—21no—
215C2×Dic6—101no—
216C2×C3×C8—52no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—52no—
219C3×C4⋊C4—101no—
220C3×C4⋊C4C22×D512yes—
221C3×C42C22×D511yescharacteristic
222(C2×D3)⋊C4—22no—
223(C2×D3)⋊C4—102no—
224C4⋊Dic3—21no—
225C4⋊Dic3—22no—
226C4⋊Dic3—52no—
227C4⋊Dic3—101no—
228C4⋊Dic3—102no—
229C4⋊Dic3C22×D512yes—
230Dic3⋊C4—22no—
231Dic3⋊C4—102no—
232C4×Dic3—22no—
233C4×Dic3—102no—
234C4×Dic3C22⋊D511yescharacteristic
235C4×Dic3C22⋊D511yescharacteristic
236C4×Dic3C22×D511yescharacteristic
237C2×C3⋊C8—52no—
238D3×C8—58no—
239C23×C5—31no—
240C5×Q8—42no—
241C5×Q8—122no—
242C2×C4×C5—22no—
243C2×C4×C5—31no—
244C2×C4×C5—34no—
245C2×C4×C5—31no—
246C2×C4×C5—31no—
247C2×C4×C5—62no—
248C2×C4×C5—62no—
249C2×C4×C5—62no—
250C2×C4×C5D3×D411yescharacteristic
251C2×C4×C5D3×D411yescharacteristic
252C2×C4×C5C23×D311yescharacteristic
253C2×Dic5—22no—
254C2×Dic5—62no—
255Dic10—42no—
256Dic10—122no—
257#168—34no—
258#168D3×Q814yes—
259C22×C8—152no—
260C4⋊Q8—31no—
261C4⋊Q8—51no—
262C4⋊Q8—151no—
263C4⋊Q8D3×D511yescharacteristic
264#125—32no—
265#125—152no—
266C22⋊Q8—61no—
267C22⋊Q8—61no—
268C22⋊Q8—301no—
269C22⋊Q8—301no—
270C4×Q8—61no—
271C4×Q8—61no—
272C4×Q8—301no—
273C4×Q8—301no—
274#117—32no—
275#117—152no—
276C2×C42—31no—
277#107—154no—
278#107—154no—
279#106—54no—
280#106—154no—
281C4×C8—51no—
282C4×C8—152no—
283C4×C8—151no—
284C2×C3×C5C2×C4⋊Q811yescharacteristic
285C2×C3×C5C2×#13511yescharacteristic
286C2×C3×C5C2×#13511yescharacteristic
287C5×D3—22no—
288C22×D3C2×C22⋊D511yescharacteristic
289C3×Q8—42no—
290C3×Q8—202no—
291C2×C3×C4—22no—
292C2×C3×C4—102no—
293C2×C3×C4C2×C22⋊D511yescharacteristic
294C2×C3×C4C2×C22⋊D511yescharacteristic
295C2×C3×C4C23×D511yescharacteristic
296C2×Dic3—22no—
297C2×Dic3—102no—
298C2×Dic3C2×C22⋊D511yescharacteristic
299C2×Dic3C2×C22⋊D511yescharacteristic
300C2×Dic3C2×C22⋊D511yescharacteristic
301C4×D3—22no—
302C4×D3—22no—
303C4×D3Q8×D514yes—
304Dic6—42no—
305Dic6—202no—
306C3×C8—54no—
307C3⋊C8—54no—
308C22×C5—32no—
309C22×C5—61no—
310C22×C5—61no—
311C22×C5C2×D3×D411yescharacteristic
312C4×C5—32no—
313C4×C5—42no—
314C4×C5—61no—
315C4×C5—61no—
316C4×C5—122no—
317C4×C5#91612yes—
318C4×C5#91612yes—
319C4×C5C2×D3×Q812yes—
320Dic5—42no—
321Dic5—122no—
322C2×Q8—21no—
323C2×Q8—61no—
324C2×Q8—101no—
325C2×Q8—301no—
326C22×C4—31no—
327C22×C4—31no—
328C22×C4—31no—
329C2×C8—52no—
330C2×C8—158no—
331C2×C8—152no—
332C4⋊C4—21no—
333C4⋊C4—32no—
334C4⋊C4—52no—
335C4⋊C4—62no—
336C4⋊C4—62no—
337C4⋊C4—61no—
338C4⋊C4—101no—
339C4⋊C4—152no—
340C4⋊C4—302no—
341C4⋊C4—302no—
342C4⋊C4—301no—
343C4⋊C4C2×D3×D512yes—
344C22⋊C4—62no—
345C22⋊C4—302no—
346C42—31no—
347C42—31no—
348C42—31no—
349C42—62no—
350C42—302no—
351C42C2×D3×D511yescharacteristic
352C3×C5#316011yescharacteristic, complemented, Hall
353C22×C3C22×C22⋊D511yescharacteristic
354C2×D3—21no—
355C2×D3—21no—
356C2×D3#409012yes—
357C3×C4—42no—
358C3×C4—202no—
359C3×C4#409612yes—
360C3×C4#409612yes—
361C3×C4C2×Q8×D512yes—
362Dic3—21no—
363Dic3—21no—
364Dic3—42no—
365Dic3—202no—
366Dic3#409012yes—
367C2×C5—62no—
368C2×C5D3×C4⋊Q811yescharacteristic
369C2×C5C2×#91611yescharacteristic
370C2×C5C2×#91611yescharacteristic
371C23—31no—
372Q8—42no—
373Q8—122no—
374Q8—202no—
375Q8—602no—
376C2×C4—22no—
377C2×C4—31no—
378C2×C4—34no—
379C2×C4—31no—
380C2×C4—31no—
381C2×C4—62no—
382C2×C4—62no—
383C2×C4—62no—
384C2×C4—102no—
385C2×C4—302no—
386C2×C4D3×C22⋊D511yescharacteristic
387C2×C4D3×C22⋊D511yescharacteristic
388C2×C4C22×D3×D511yescharacteristic
389C8—54no—
390C8—154no—
391C2×C3C2×#409011yescharacteristic
392C2×C3C2×#409611yescharacteristic
393C2×C3C2×#409611yescharacteristic
394D3—22no—
395C5#8189111yescharacteristic, complemented, Sylow
396C22—32no—
397C22—61no—
398C22—61no—
399C22C2×D3×C22⋊D511yescharacteristic
400C4—32no—
401C4—42no—
402C4—61no—
403C4—61no—
404C4—122no—
405C4—202no—
406C4—602no—
407C4#9149512yes—
408C4#9151712yes—
409C4D3×Q8×D512yes—
410C3#1061507011yescharacteristic, complemented, Sylow
411C2—62no—
412C2C2×#9149511yescharacteristic
413C2C2×#9151711yescharacteristic
414C2D3×#409011yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC22×C5×D3C2×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. C3×#65368C2semidirect
6. #11747149C2semidirect
8. #11746962C2semidirect
9. #11746941C2semidirect
40. #65368D3semidirect
75. D3×#168Q8semidirect
352. C3×C5#3160semidirect
395. C5#81891semidirect
410. C3#10615070semidirect

Maximal subgroups

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

subgroupindex
C5×#57282
#117524782
#117511792
C3×#653682
#117474372
#117471492
C4×D3×#1682
#117469622
#117469412
#106150703
#818915