Finite Group Databasebeta

← #14285111

Subgroups — #14285111

Order 1920.

416 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 102 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#11754615C211yesmaximal, characteristic
2#11752416C211yesmaximal, characteristic
3C2×C3×#4004C211yesmaximal, characteristic
4#11746510C212yesmaximal, complemented
5#11746509C212yesmaximal, complemented
6#10604364—31nomaximal, Hall
7C22×C3×#170—21no—
8#91815C411yescharacteristic
9C5×#926C411yescharacteristic
10C2×C3×C4×Dic5C2211yescharacteristic
11#91574—21no—
12#91574—21no—
13#91468C2211yescharacteristic
14#91468C2211yescharacteristic
15C4×#1204—21no—
16C4×#1204—21no—
17#91388C411yescharacteristic
18#91388C411yescharacteristic
19#91241—21no—
20#91233C2212yes—
21#91231—21no—
22C3×#4004—21no—
23C3×#4004C2212yes—
24#70439—51nomaximal, Hall
25#65851—31no—
26#65757—31no—
27C2×#4004D311yescharacteristic
28#64873—32no—
29#64873—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C22×C3×Dic5D411yescharacteristic
32C22×C3×Dic5D411yescharacteristic
33C2×#1204—21no—
34C2×#1204—21no—
35C2×C3⋊#170—22no—
36C2×C3×#170—22no—
37C2×C3×#170—42no—
38#6719—21no—
39C4⋊Dic15C2×C411yescharacteristic
40C4⋊Dic15C2×C411yescharacteristic
41C4×Dic15—21no—
42C5×#217—21no—
43C5×C4⋊Dic3C2×C411yescharacteristic
44C5×C4⋊Dic3C2×C411yescharacteristic
45C4×C5×Dic3—21no—
46C3×C4×Dic5C2×C411yescharacteristic
47C3×C4×Dic5D411yescharacteristic
48C3×C4×Dic5D411yescharacteristic
49C3×C4×Dic5C2311yescharacteristic
50Dic3⋊Dic5—21no—
51Dic3⋊Dic5—21no—
52#6669—21no—
53#6669—21no—
54#6668—21no—
55#6668—21no—
56#5470—51no—
57C2×C3×C4⋊C8—51no—
58#4926—51no—
59#4486—52no—
60#4482—52no—
61C22×#170—21no—
62C5×#117—31no—
63#4072—31no—
64C2×C4×Dic5C2×D311yescharacteristic
65#4036—31no—
66#4036—31no—
67#4034—31no—
68#4034—31no—
69#4024—61no—
70#4024—61no—
71C4×Dic10—61no—
72C4×Dic10—61no—
73C22⋊#170—61no—
74#4004—21no—
75#4004—32no—
76#4004C2×D312yes—
77#4002—61no—
78#1552—151noSylow
79C23×C3×C5C22⋊C411yescharacteristic
80C2×C3×C4×C5—22no—
81C2×C3×C4×C5C22⋊C411yescharacteristic
82C2×C3×C4×C5C22×C411yescharacteristic
83C2×Dic15—21no—
84C2×Dic15—21no—
85C2×C5×Dic3—21no—
86C2×C5×Dic3—21no—
87C2×C3×Dic5—22no—
88C2×C3×Dic5—21no—
89C2×C3×Dic5—21no—
90C2×C3×Dic5C22⋊C411yescharacteristic
91C2×C3×Dic5C22⋊C411yescharacteristic
92C2×C3×Dic5C2×D411yescharacteristic
93C2×C3×Dic5C2×D411yescharacteristic
94#1204—42no—
95#1204—41no—
96#1204—41no—
97C3⋊#170—42no—
98C3×#170—42no—
99C22×C3×C8—101no—
100C2×C3×C42—51no—
101#926—51no—
102#926AGL(1,𝔽5)11yescharacteristic
103#924—101no—
104#924—101no—
105#870—51no—
106#870—51no—
107#869—51no—
108#869—51no—
109C4×Dic6—101no—
110C4×Dic6—101no—
111C3×C4⋊C8—52no—
112C3×C4⋊C8—101no—
113#830—101no—
114C4⋊(C3⋊C8)—52no—
115#803—101no—
116C22×C4×C5C4×D311yescharacteristic
117C22×Dic5D1211yescharacteristic
118C22×Dic5#6711yescharacteristic
119C2×Dic10—61no—
120C2×Dic10—61no—
121C2×#170—22no—
122C2×#170—42no—
123C2×#170—62no—
124C5×C4⋊C4—31no—
125C5×C4⋊C4—31no—
126C5×C22⋊C4—61no—
127C42×C5—61no—
128C22⋊Dic5—61no—
129C4⋊Dic5—31no—
130C4⋊Dic5—31no—
131C4⋊Dic5—61no—
132C4⋊Dic5—61no—
133#683—61no—
134#683—61no—
135#683—61no—
136#683—61no—
137C4×Dic5—61no—
138C4×Dic5C4×D311yescharacteristic
139C4×Dic5D1211yescharacteristic
140C4×Dic5#6711yescharacteristic
141C4×Dic5C22×D311yescharacteristic
142#533—151no—
143#432—151no—
144C2×C4⋊C8—51no—
145#332—152no—
146#332—152no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5#10112yes—
150C22×C3×C5C2×C22⋊C411yescharacteristic
151C3×C4×C5—21no—
152C3×C4×C5—21no—
153Dic15—41no—
154Dic15—41no—
155C3×Dic5—21no—
156C3×Dic5—21no—
157C3×Dic5#13512yes—
158C3×Dic5AGL(1,ℤ/8)11yescharacteristic
159C3×Dic5#13711yescharacteristic
160C5×Dic3—41no—
161C5×Dic3—41no—
162C22×C3×C4—51no—
163C22×C3×C4—51no—
164C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
165C2×Dic6—101no—
166C2×Dic6—101no—
167C2×C3×C8—102no—
168C2×C3×C8—202no—
169C3×C42—51no—
170C3×C42—51no—
171C3×C42—51no—
172C3×C42—51no—
173#217—21no—
174#217—101no—
175C4⋊Dic3—51no—
176C4⋊Dic3—51no—
177C4⋊Dic3—101no—
178C4⋊Dic3—101no—
179C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
180C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
181Dic3⋊C4—101no—
182Dic3⋊C4—101no—
183Dic3⋊C4—101no—
184Dic3⋊C4—101no—
185C4×Dic3—21no—
186C4×Dic3—101no—
187C2×C3⋊C8—102no—
188C23×C5(C2×D3)⋊C411yescharacteristic
189C2×C4×C5—22no—
190C2×C4×C5—61no—
191C2×C4×C5—61no—
192C2×C4×C5(C2×D3)⋊C411yescharacteristic
193C2×C4×C5C2×C4×D311yescharacteristic
194C2×Dic5—22no—
195C2×Dic5—21no—
196C2×Dic5—21no—
197C2×Dic5—61no—
198C2×Dic5—61no—
199C2×Dic5(C2×D3)⋊C411yescharacteristic
200C2×Dic5(C2×D3)⋊C411yescharacteristic
201C2×Dic5C2×D1211yescharacteristic
202C2×Dic5C2×#6711yescharacteristic
203Dic10—122no—
204Dic10—121no—
205Dic10—121no—
206#170—42no—
207#170—122no—
208C22×C8—101no—
209C4⋊Q8—151no—
210C4⋊Q8—151no—
211#125—151no—
212#125—151no—
213C22⋊Q8—301no—
214C22⋊Q8—301no—
215C4×Q8—301no—
216C4×Q8—301no—
217#117—31no—
218#117—151no—
219C2×C42—51no—
220C4⋊C8—52no—
221C4⋊C8—101no—
222C4⋊C8—152no—
223C22⋊C8—301no—
224#97—301no—
225C2×C3×C5—22no—
226C2×C3×C5C2×#10111yescharacteristic
227C2×C3×C5#41611yescharacteristic
228C2×C3×C5#41711yescharacteristic
229C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
230C2×C3×C4—22no—
231C2×C3×C4—51no—
232C2×C3×C4—51no—
233C2×C3×C4—51no—
234C2×C3×C4—51no—
235C2×C3×C4—101no—
236C2×C3×C4—101no—
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—201no—
245Dic6—201no—
246Dic6—202no—
247C3×C8—202no—
248C3⋊C8—202no—
249C22×C5—21no—
250C22×C5—21no—
251C22×C5#82412yes—
252C22×C5C2×(C2×D3)⋊C411yescharacteristic
253C4×C5—21no—
254C4×C5—21no—
255C4×C5—121no—
256C4×C5—121no—
257Dic5—21no—
258Dic5—21no—
259Dic5—121no—
260Dic5—121no—
261Dic5#90412yes—
262Dic5#93211yescharacteristic
263Dic5#94211yescharacteristic
264C2×Q8—301no—
265C2×Q8—301no—
266C22×C4—51no—
267C22×C4—51no—
268C22×C4D3×AGL(1,𝔽5)11yescharacteristic
269C2×C8—102no—
270C2×C8—202no—
271C2×C8—302no—
272C4⋊C4—31no—
273C4⋊C4—31no—
274C4⋊C4—151no—
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—61no—
289C42—301no—
290C3×C5#155211yescharacteristic, complemented, Hall
291C22×C3—21no—
292C22×C3—21no—
293C22×C3#400512yes—
294C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—51no—
298C3×C4—51no—
299C3×C4—52no—
300C3×C4—101no—
301C3×C4—101no—
302Dic3—41no—
303Dic3—41no—
304Dic3—201no—
305Dic3—201no—
306C2×C5—22no—
307C2×C5#496611yescharacteristic
308C2×C5#511311yescharacteristic
309C2×C5C2×#82411yescharacteristic
310C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
311Q8—602no—
312Q8—601no—
313Q8—601no—
314C2×C4—22no—
315C2×C4—51no—
316C2×C4—51no—
317C2×C4—51no—
318C2×C4—51no—
319C2×C4—61no—
320C2×C4—61no—
321C2×C4—101no—
322C2×C4—102no—
323C2×C4—101no—
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×C3C2×#400511yescharacteristic
332C2×C3#6579311yescharacteristic
333C2×C3#6579411yescharacteristic
334C5#7043911yescharacteristic, complemented, Sylow
335C22—21no—
336C22—21no—
337C22#9117512yes—
338C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
339C4—21no—
340C4—21no—
341C4—52no—
342C4—51no—
343C4—51no—
344C4—101no—
345C4—101no—
346C4—121no—
347C4—121no—
348C4—601no—
349C4—601no—
350C3#1060436411yescharacteristic, complemented, Sylow
351C2—22no—
352C2#1175170411yescharacteristic
353C2#1175170511yescharacteristic
354C2C2×#9117511yescharacteristic
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#1552
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. #11746510C2semidirect
5. #11746509C2semidirect
290. C3×C5#1552semidirect
334. C5#70439semidirect
350. C3#10604364semidirect

Maximal subgroups

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

subgroupindex
#117546152
#117524162
C2×C3×#40042
#117465102
#117465092
#106043643
#704395