Finite Group Databasebeta

← #14439876

Subgroups — #14439876

Order 1920.

712 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66022C211yesmaximal, characteristic
2#11752498C211yesmaximal, characteristic
3#11751166C211yesmaximal, characteristic, complemented
4C5×#5065C211yesmaximal, characteristic, complemented
5#11747433C212yesmaximal
6#11747432C212yesmaximal
7#11747141C212yesmaximal, complemented
8#11747139C212yesmaximal, complemented
9C4×D5×C3⋊C8C211yesmaximal, characteristic
10#11746968C211yesmaximal, characteristic, complemented
11#11746950C211yesmaximal, characteristic, complemented
12#10613647—31nomaximal, Hall
13C3×C5×#125C2211yescharacteristic
14#91759C2211yescharacteristic
15C5×#870C2211yescharacteristic
16C3×#4042—22no—
17C3×#4038C2212yes—
18C3×#4034C2212yes—
19C3×#4033—22no—
20C3×C42×D5C2211yescharacteristic
21C3×#4016C2211yescharacteristic
22#91468C2212yes—
23#91358C2212yes—
24#91349—22no—
25#91323—22no—
26C2×D5×C3⋊C8C2211yescharacteristic
27C2×D5×C3⋊C8C2211yescharacteristic
28#91092C2212yes—
29#91091C2212yes—
30C4×C3⋊#168C2211yescharacteristic
31C5×#808C2212yes—
32C5×#807C2212yes—
33C4×C5×C3⋊C8C2211yescharacteristic
34#90990C2212yes—
35#90989C2212yes—
36#90987C2212yes—
37#90986C2212yes—
38Dic5×C3⋊C8C2211yescharacteristic
39Dic5×C3⋊C8C2211yescharacteristic
40#83339—51nomaximal, Hall
41#66022—31no—
42#66022D311yescharacteristic
43C5×#499—31no—
44#65353—31no—
45#65353—31no—
46#65169—32no—
47#65163—32no—
48#65149—32no—
49#65144—32no—
50C4×C8×D5—31no—
51#64972—31no—
52C2×C3×C4×D5D412yes—
53C2×C3×C4×D5C2311yescharacteristic
54C2×C3×Dic10—22no—
55C2×#1204—22no—
56C3×C5×C4⋊C4—22no—
57C3×C5×C4⋊C4C2312yes—
58C3×C42×C5C2311yescharacteristic
59C4⋊Dic15C2312yes—
60#6712—22no—
61C2×C3⋊#168C2311yescharacteristic
62C2×C3⋊#168C2311yescharacteristic
63C5×C4⋊Dic3C2312yes—
64C5×Dic3⋊C4—22no—
65C2×C5×C3⋊C8C2311yescharacteristic
66C2×C5×C3⋊C8C2311yescharacteristic
67C3×#685—22no—
68C3×C4⋊Dic5C2312yes—
69C3×#683—22no—
70C3×#683—22no—
71C3×C4×Dic5—22no—
72C3×C4×Dic5D412yes—
73C3×C4×Dic5C2311yescharacteristic
74#6668—22no—
75#6665—22no—
76Dic3×Dic5—22no—
77D5×C3⋊C8Q814yescomplemented
78D5×C3⋊C8Q814yescomplemented
79C3×#533—51no—
80#5470—51no—
81#5080—52no—
82#5078—52no—
83#5065—51no—
84#5065—51no—
85#5065—51no—
86#5065D511yescharacteristic, complemented
87#4998—52no—
88#4998—52no—
89C2×C4×C3⋊C8—51no—
90C5×#125—31no—
91C5×#125C2×D311yescharacteristic
92C2×C8×D5—31no—
93C2×C8×D5—31no—
94#4042—22no—
95#4042—62no—
96#4038—32no—
97#4038C2×D312yes—
98#4034—32no—
99#4034C2×D312yes—
100#4033—22no—
101#4033—62no—
102C42×D5C2×D311yescharacteristic
103#4016—31no—
104#4016C2×D311yescharacteristic
105C5×#107—32no—
106C5×#106—32no—
107C4×C5×C8—31no—
108#3950—32no—
109#3949—32no—
110C8×Dic5—31no—
111C8×Dic5—31no—
112#3940—32no—
113#3940—32no—
114#3939—32no—
115#3939—32no—
116C4×#168—31no—
117#3160—151noSylow
118C22×C3×D5C2×D411yescharacteristic
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5C2×D412yes—
121C2×C3×C4×C5C2411yescharacteristic
122C2×Dic15—22no—
123C2×C5×Dic3—22no—
124C2×C3×Dic5—22no—
125C2×C3×Dic5C2×D411yescharacteristic
126C2×C3×Dic5C2×D412yes—
127C3×C4×D5—24no—
128C3×C4×D5C2×Q812yes—
129C3×C4×D5C2×Q812yes—
130C3×Dic10—44no—
131#1204—44no—
132C3⋊#168C2×Q812yes—
133C3⋊#168C2×Q812yes—
134C5×C3⋊C8C2×Q812yes—
135C5×C3⋊C8C2×Q812yes—
136C3×C4⋊Q8—52no—
137C3×#125—51no—
138C3×#125C2×D511yescharacteristic
139C3×C22⋊Q8—102no—
140C3×C4×Q8—102no—
141C3×#117—52no—
142C2×C3×C42—51no—
143#926—52no—
144#924—102no—
145C22×C3⋊C8—51no—
146C22×C3⋊C8—51no—
147#870—51no—
148#870C2×D511yescharacteristic
149#869—52no—
150C4×Dic6—102no—
151#808—52no—
152#808—52no—
153#808—52no—
154#808C2×D512yes—
155#807—52no—
156#807—52no—
157#807—52no—
158#807C2×D512yes—
159C4×C3⋊C8—51no—
160C4×C3⋊C8—51no—
161C4×C3⋊C8—51no—
162C4×C3⋊C8C2×D511yescharacteristic
163C2×C4×D5#6712yes—
164C2×C4×D5C22×D311yescharacteristic
165C2×Dic10—22no—
166C2×Dic10—62no—
167C2×C5×C8—31no—
168C2×C5×C8—31no—
169C5×C4⋊C4—22no—
170C5×C4⋊C4—32no—
171C5×C4⋊C4—62no—
172C5×C4⋊C4C22×D312yes—
173C42×C5C22×D311yescharacteristic
174#685—22no—
175#685—62no—
176C4⋊Dic5—32no—
177C4⋊Dic5C22×D312yes—
178#683—22no—
179#683—22no—
180#683—62no—
181#683—62no—
182C4×Dic5—22no—
183C4×Dic5—62no—
184C4×Dic5#6712yes—
185C4×Dic5C22×D311yescharacteristic
186C2×#168—31no—
187C2×#168—31no—
188C8×D5—34no—
189C8×D5—34no—
190#533—51no—
191#533—151no—
192#500—152no—
193#499—31no—
194#499—151no—
195#499—151no—
196#499—151no—
197#498—152no—
198#427—152no—
199#427—152no—
200C2×C4×C8—151no—
201C22×C3×C5C22×D411yescharacteristic
202C2×C3×D5—22no—
203C2×C3×D5C4⋊Q812yes—
204C3×C4×C5—22no—
205C3×C4×C5—42no—
206C3×C4×C5C22×Q811yescharacteristic
207C3×C4×C5C22×Q811yescharacteristic
208Dic15—42no—
209C3×Dic5—42no—
210C3×Dic5C4⋊Q812yes—
211C3×Dic5#13514yes—
212C5×Dic3—42no—
213C2×C3×Q8—102no—
214C22×C3×C4—51no—
215C22×C3×C4—52no—
216C2×Dic6—102no—
217C3×C4⋊C4—22no—
218C3×C4⋊C4—52no—
219C3×C4⋊C4—102no—
220C3×C4⋊C4—102no—
221C3×C4⋊C4C22×D512yes—
222C3×C22⋊C4—102no—
223C3×C42—52no—
224C3×C42—51no—
225C3×C42—102no—
226C3×C42C22×D511yescharacteristic
227#217—102no—
228C4⋊Dic3—52no—
229C4⋊Dic3—102no—
230C4⋊Dic3C22×D512yes—
231Dic3⋊C4—22no—
232Dic3⋊C4—102no—
233C4×Dic3—102no—
234C2×C3⋊C8—51no—
235C2×C3⋊C8—51no—
236C2×C3⋊C8—54no—
237C2×C3⋊C8—54no—
238C2×C3⋊C8C22×D511yescharacteristic
239C2×C3⋊C8C22×D511yescharacteristic
240C22×D5C2×#6711yescharacteristic
241C2×C4×C5—22no—
242C2×C4×C5—62no—
243C2×C4×C5C2×#6712yes—
244C2×C4×C5C23×D311yescharacteristic
245C2×Dic5—22no—
246C2×Dic5—62no—
247C2×Dic5C2×#6711yescharacteristic
248C2×Dic5C2×#6712yes—
249C4×D5—24no—
250C4×D5D3×Q812yes—
251C4×D5D3×Q812yes—
252Dic10—44no—
253Dic10—124no—
254C5×C8—32no—
255C5×C8—32no—
256#168—32no—
257#168—32no—
258C22×C8—151no—
259C22×C8—151no—
260C4⋊Q8—52no—
261C4⋊Q8—152no—
262#125—31no—
263#125—51no—
264#125—151no—
265#125D3×D511yescharacteristic
266C22⋊Q8—102no—
267C22⋊Q8—302no—
268C4×Q8—102no—
269C4×Q8—302no—
270#117—52no—
271#117—152no—
272C2×C42—51no—
273#107—32no—
274#107—152no—
275#107—152no—
276#107—152no—
277#106—32no—
278#106—152no—
279#106—152no—
280#106—152no—
281C4×C8—31no—
282C4×C8—151no—
283C4×C8—151no—
284C4×C8—151no—
285C2×C3×C5C2×C4⋊Q811yescharacteristic
286C2×C3×C5C2×#13512yes—
287C3×D5—22no—
288C23×C3—51no—
289C3×Q8—204no—
290C2×C3×C4—22no—
291C2×C3×C4—51no—
292C2×C3×C4—52no—
293C2×C3×C4—52no—
294C2×C3×C4—52no—
295C2×C3×C4—104no—
296C2×C3×C4—102no—
297C2×C3×C4D4×D512yes—
298C2×C3×C4C23×D511yescharacteristic
299C2×Dic3—22no—
300C2×Dic3—102no—
301Dic6—204no—
302C3⋊C8—52no—
303C3⋊C8—52no—
304C3⋊C8Q8×D512yes—
305C3⋊C8Q8×D512yes—
306C22×C5C22×#6711yescharacteristic
307C2×D5—22no—
308C2×D5#94412yes—
309C4×C5—22no—
310C4×C5—42no—
311C4×C5—122no—
312C4×C5C2×D3×Q811yescharacteristic
313C4×C5C2×D3×Q811yescharacteristic
314Dic5—42no—
315Dic5—122no—
316Dic5#94412yes—
317Dic5#95014yes—
318C2×Q8—102no—
319C2×Q8—302no—
320C22×C4—51no—
321C22×C4—52no—
322C2×C8—31no—
323C2×C8—31no—
324C2×C8—154no—
325C2×C8—154no—
326C2×C8—151no—
327C2×C8—151no—
328C4⋊C4—22no—
329C4⋊C4—32no—
330C4⋊C4—52no—
331C4⋊C4—62no—
332C4⋊C4—102no—
333C4⋊C4—102no—
334C4⋊C4—152no—
335C4⋊C4—302no—
336C4⋊C4—302no—
337C4⋊C4C2×D3×D512yes—
338C22⋊C4—102no—
339C22⋊C4—302no—
340C42—52no—
341C42—51no—
342C42—102no—
343C42—302no—
344C42C2×D3×D511yescharacteristic
345C3×C5#316011yescharacteristic, complemented, Hall
346C22×C3—52no—
347C22×C3—102no—
348C22×C3C2×D4×D511yescharacteristic
349C3×C4—22no—
350C3×C4—42no—
351C3×C4—52no—
352C3×C4—54no—
353C3×C4—202no—
354C3×C4C2×Q8×D511yescharacteristic
355C3×C4C2×Q8×D511yescharacteristic
356Dic3—42no—
357Dic3—202no—
358C2×C5C2×#94411yescharacteristic
359C2×C5C2×#95012yes—
360D5—22no—
361C23—51no—
362Q8—204no—
363Q8—604no—
364C2×C4—22no—
365C2×C4—51no—
366C2×C4—52no—
367C2×C4—52no—
368C2×C4—52no—
369C2×C4—62no—
370C2×C4—104no—
371C2×C4—102no—
372C2×C4—302no—
373C2×C4D5×#6712yes—
374C2×C4C22×D3×D511yescharacteristic
375C8—32no—
376C8—32no—
377C8—152no—
378C8—152no—
379C2×C3—102no—
380C2×C3D5×C4⋊Q811yescharacteristic
381C2×C3D5×#13512yes—
382C5#8333911yescharacteristic, complemented, Sylow
383C22—52no—
384C22—102no—
385C22C2×D5×#6711yescharacteristic
386C4—22no—
387C4—42no—
388C4—54no—
389C4—52no—
390C4—122no—
391C4—202no—
392C4—602no—
393C4D3×Q8×D511yescharacteristic
394C4D3×Q8×D511yescharacteristic
395C3#1061364711yescharacteristic, complemented, Sylow
396C2—102no—
397C2D5×#94411yescharacteristic
398C2D5×#95012yes—
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5C22×D4
prime radicalC22×C3×D5C2×D4
hypercenter#125D3×D5
hypocenterC3×C5#3160
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
3. #11751166C2semidirect
4. C5×#5065C2semidirect
7. #11747141C2semidirect
8. #11747139C2semidirect
10. #11746968C2semidirect
11. #11746950C2semidirect
77. D5×C3⋊C8Q8semidirect
78. D5×C3⋊C8Q8semidirect
86. #5065D5semidirect
345. C3×C5#3160semidirect
382. C5#83339semidirect
395. C3#10613647semidirect

Maximal subgroups

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

subgroupindex
C3×#660222
#117524982
#117511662
C5×#50652
#117474332
#117474322
#117471412
#117471392
C4×D5×C3⋊C82
#117469682
#117469502
#106136473
#833395