Finite Group Databasebeta

← #14284698

Subgroups — #14284698

Order 1920.

424 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754174C211yesmaximal, characteristic
2#11752413C211yesmaximal, characteristic
3C2×C3×#4004C211yesmaximal, characteristic
4#11746511C212yesmaximal, complemented
5#11746510C212yesmaximal, complemented
6#10604517—31nomaximal, Hall
7C22×C3×#170—21no—
8#91813C411yescharacteristic
9C5×#924C411yescharacteristic
10C2×C3×C4×Dic5C2211yescharacteristic
11#91574—21no—
12#91528—21no—
13#91468C2211yescharacteristic
14#91378—21no—
15#91376C2211yescharacteristic
16#91333C411yescharacteristic
17Dic5×Dic6C411yescharacteristic
18#91323—21no—
19#91241—21no—
20#91233C2212yes—
21C4×C3⋊#170—21no—
22C3×#4004—21no—
23C3×#4004C2212yes—
24#70437—51nomaximal, Hall
25#65956—31no—
26#65754—31no—
27C2×#4004D311yescharacteristic
28#64931—32no—
29#64873—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C2×Dic30C2×C411yescharacteristic
32C2×C5×Dic6C2×C411yescharacteristic
33C22×C3×Dic5D411yescharacteristic
34C22×C3×Dic5D411yescharacteristic
35C2×#1204—21no—
36C2×C3⋊#170—22no—
37C2×C3×#170—22no—
38C2×C3×#170—42no—
39#6719—21no—
40C4⋊Dic15C2×C411yescharacteristic
41#6712—21no—
42C5×#217—21no—
43C5×C4⋊Dic3C2×C411yescharacteristic
44C5×Dic3⋊C4—21no—
45C3×C4×Dic5C2×C411yescharacteristic
46C3×C4×Dic5D411yescharacteristic
47C3×C4×Dic5D411yescharacteristic
48C3×C4×Dic5C2311yescharacteristic
49Dic3⋊Dic5—21no—
50#6669—21no—
51#6668—21no—
52#6668—21no—
53#6668—21no—
54Dic3×Dic5—21no—
55Dic3×Dic5—21no—
56#5470—51no—
57C2×C3×C4⋊C8—51no—
58#4925—51no—
59#4486—52no—
60#4481—52no—
61C22×#170—21no—
62C5×C22⋊Q8—31no—
63Q8×Dic5—31no—
64#4090—31no—
65#4070—31no—
66C2×C4×Dic5C2×D311yescharacteristic
67#4035—61no—
68#4034—31no—
69#4033—31no—
70#4033—61no—
71#4024—61no—
72#4023—61no—
73C22⋊#170—61no—
74#4004—21no—
75#4004—32no—
76#4004C2×D312yes—
77C4×#170—61no—
78#1542—151noSylow
79C23×C3×C5C22⋊C411yescharacteristic
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5C22⋊C411yescharacteristic
82C2×C3×C4×C5C22×C411yescharacteristic
83C2×Dic15—21no—
84C2×Dic15—21no—
85Dic30—41no—
86C2×C5×Dic3—21no—
87C2×C5×Dic3—21no—
88C5×Dic6—41no—
89C2×C3×Dic5—22no—
90C2×C3×Dic5C22⋊C411yescharacteristic
91C2×C3×Dic5C22⋊C411yescharacteristic
92C2×C3×Dic5SD1612yes—
93C2×C3×Dic5Q1612yes—
94C2×C3×Dic5C2×D411yescharacteristic
95C2×C3×Dic5C2×D411yescharacteristic
96#1204—42no—
97C3⋊#170—42no—
98C3×#170—42no—
99C22×C3×C8—101no—
100C2×C3×C42—51no—
101#926—101no—
102#924—51no—
103#924—101no—
104#924AGL(1,𝔽5)11yescharacteristic
105#870—101no—
106#869—51no—
107#869—51no—
108C4×Dic6—51no—
109C4×Dic6—51no—
110C4×Dic6—101no—
111C3×C4⋊C8—52no—
112C3×C4⋊C8—101no—
113#830—101no—
114C4⋊(C3⋊C8)—52no—
115C4×C3⋊C8—101no—
116C2×C5×Q8—31no—
117C22×C4×C5C4×D311yescharacteristic
118C22×Dic5D1211yescharacteristic
119C22×Dic5#6711yescharacteristic
120C2×Dic10—31no—
121C2×Dic10—61no—
122C2×#170—22no—
123C2×#170—42no—
124C2×#170—62no—
125C5×C4⋊C4—31no—
126C5×C4⋊C4—61no—
127C5×C22⋊C4—61no—
128C22⋊Dic5—61no—
129C4⋊Dic5—31no—
130C4⋊Dic5—61no—
131#683—61no—
132#683—61no—
133#683—61no—
134#683—61no—
135#683—61no—
136C4×Dic5—61no—
137C4×Dic5—61no—
138C4×Dic5C4×D311yescharacteristic
139C4×Dic5D1211yescharacteristic
140C4×Dic5#6711yescharacteristic
141C4×Dic5C22×D311yescharacteristic
142#533—151no—
143#431—151no—
144C2×C4⋊C8—51no—
145#333—152no—
146#332—152no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5#10312yes—
150C22×C3×C5C2×C22⋊C411yescharacteristic
151C3×C4×C5—21no—
152C3×C4×C5—21no—
153Dic15—41no—
154Dic15—41no—
155C3×Dic5—21no—
156C3×Dic5#10312yes—
157C3×Dic5C2×SD1611yescharacteristic
158C3×Dic5C2×Q1611yescharacteristic
159C3×Dic5#13512yes—
160C5×Dic3—41no—
161C5×Dic3—41no—
162C22×C3×C4—51no—
163C22×C3×C4—51no—
164C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
165C2×Dic6—51no—
166C2×Dic6—101no—
167C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
168C2×C3×C8—102no—
169C2×C3×C8—202no—
170C3×C42—51no—
171C3×C42—51no—
172C3×C42—51no—
173C3×C42—51no—
174#217—21no—
175#217—101no—
176C4⋊Dic3—51no—
177C4⋊Dic3—101no—
178C4⋊Dic3—101no—
179C4⋊Dic3—101no—
180C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
181Dic3⋊C4—21no—
182Dic3⋊C4—101no—
183Dic3⋊C4—101no—
184Dic3⋊C4—101no—
185C4×Dic3—101no—
186C4×Dic3—101no—
187C2×C3⋊C8—102no—
188C23×C5(C2×D3)⋊C411yescharacteristic
189C5×Q8—121no—
190C2×C4×C5—41no—
191C2×C4×C5—61no—
192C2×C4×C5—61no—
193C2×C4×C5(C2×D3)⋊C411yescharacteristic
194C2×C4×C5C2×C4×D311yescharacteristic
195C2×Dic5—22no—
196C2×Dic5—61no—
197C2×Dic5—61no—
198C2×Dic5(C2×D3)⋊C411yescharacteristic
199C2×Dic5(C2×D3)⋊C411yescharacteristic
200C2×Dic5#21412yes—
201C2×Dic5#21612yes—
202C2×Dic5C2×D1211yescharacteristic
203C2×Dic5C2×#6711yescharacteristic
204Dic10—122no—
205Dic10—121no—
206#170—42no—
207#170—122no—
208C22×C8—101no—
209C4⋊Q8—151no—
210C4⋊Q8—151no—
211#125—301no—
212C22⋊Q8—31no—
213C22⋊Q8—151no—
214C22⋊Q8—301no—
215C4×Q8—151no—
216C4×Q8—151no—
217C4×Q8—301no—
218#117—301no—
219C2×C42—51no—
220C4⋊C8—52no—
221C4⋊C8—101no—
222C4⋊C8—152no—
223C22⋊C8—301no—
224C4×C8—301no—
225C2×C3×C5—22no—
226C2×C3×C5#41311yescharacteristic
227C2×C3×C5C2×#10311yescharacteristic
228C2×C3×C5#41611yescharacteristic
229C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
230C2×C3×C4—41no—
231C2×C3×C4—51no—
232C2×C3×C4—51no—
233C2×C3×C4—51no—
234C2×C3×C4—52no—
235C2×C3×C4—52no—
236C2×C3×C4—51no—
237C2×C3×C4—102no—
238C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
239C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
240C2×Dic3—21no—
241C2×Dic3—21no—
242C2×Dic3—101no—
243C2×Dic3—101no—
244Dic6—41no—
245Dic6—202no—
246Dic6—201no—
247C3×C8—202no—
248C3⋊C8—202no—
249C22×C5—21no—
250C22×C5—21no—
251C22×C5#81012yes—
252C22×C5C2×(C2×D3)⋊C411yescharacteristic
253C4×C5—21no—
254C4×C5—21no—
255C4×C5—121no—
256C4×C5—121no—
257Dic5—21no—
258Dic5—121no—
259Dic5—121no—
260Dic5#81012yes—
261Dic5#90412yes—
262Dic5C2×#21411yescharacteristic
263Dic5C2×#21611yescharacteristic
264C2×Q8—31no—
265C2×Q8—151no—
266C2×Q8—301no—
267C22×C4—51no—
268C22×C4—51no—
269C22×C4D3×AGL(1,𝔽5)11yescharacteristic
270C2×C8—102no—
271C2×C8—202no—
272C2×C8—302no—
273C4⋊C4—31no—
274C4⋊C4—61no—
275C4⋊C4—151no—
276C4⋊C4—301no—
277C4⋊C4—301no—
278C4⋊C4—301no—
279C4⋊C4—301no—
280C4⋊C4—301no—
281C4⋊C4—301no—
282C22⋊C4—61no—
283C22⋊C4—301no—
284C42—51no—
285C42—51no—
286C42—51no—
287C42—51no—
288C42—301no—
289C42—301no—
290C3×C5#154211yescharacteristic, complemented, Hall
291C22×C3—21no—
292C22×C3—21no—
293C22×C3#400912yes—
294C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—52no—
298C3×C4—52no—
299C3×C4—51no—
300C3×C4—51no—
301C3×C4—101no—
302Dic3—41no—
303Dic3—41no—
304Dic3—201no—
305Dic3—201no—
306C2×C5—22no—
307C2×C5C2×#81011yescharacteristic
308C2×C5#511311yescharacteristic
309C2×C5#513211yescharacteristic
310C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
311Q8—121no—
312Q8—601no—
313Q8—602no—
314C2×C4—41no—
315C2×C4—52no—
316C2×C4—52no—
317C2×C4—51no—
318C2×C4—51no—
319C2×C4—51no—
320C2×C4—51no—
321C2×C4—61no—
322C2×C4—61no—
323C2×C4—102no—
324C2×C4—301no—
325C2×C4—301no—
326C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
327C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
328C8—202no—
329C8—602no—
330C2×C3—22no—
331C2×C3#6577711yescharacteristic
332C2×C3C2×#400911yescharacteristic
333C2×C3#6579411yescharacteristic
334C5#7043711yescharacteristic, complemented, Sylow
335C22—21no—
336C22—21no—
337C22#9115312yes—
338C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
339C4—21no—
340C4—21no—
341C4—52no—
342C4—51no—
343C4—52no—
344C4—51no—
345C4—101no—
346C4—121no—
347C4—121no—
348C4—601no—
349C4—601no—
350C3#1060451711yescharacteristic, complemented, Sylow
351C2—22no—
352C2#1175170411yescharacteristic
353C2C2×#9115311yescharacteristic
354C2#1175200811yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C22⋊C4
cosocleC3×C4×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1542
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #11746511C2semidirect
5. #11746510C2semidirect
290. C3×C5#1542semidirect
334. C5#70437semidirect
350. C3#10604517semidirect

Maximal subgroups

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

subgroupindex
#117541742
#117524132
C2×C3×#40042
#117465112
#117465102
#106045173
#704375