Finite Group Databasebeta

← #14282312

Subgroups — #14282312

Order 1920.

632 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 110 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
1C2×#91418C211yesmaximal, characteristic
2C4×#6762C211yesmaximal, characteristic, complemented
3C3×#65759C211yesmaximal, characteristic, complemented
4#11746490C214yesmaximal, complemented
5#10604274—31nomaximal, Hall
6C22×D60C411yescharacteristic
7C22×#1200—21no—
8C2×#6762—21no—
9C2×C5×C4⋊Dic3C411yescharacteristic
10C2×C3×C4×Dic5C2211yescharacteristic
11C2×#6667—21no—
12#91418—21no—
13#91418—21no—
14#91418C412yes—
15#91418C2212yes—
16#91231—21no—
17C4×C3⋊#170C2212yescomplemented
18C3×C22⋊#170—21no—
19C3×#4002—21no—
20C3×C4⋊#170C2212yescomplemented
21#70799—51nomaximal, Hall
22C2×#4039—31no—
23#65759D311yescharacteristic, complemented
24C4×#704—31no—
25#64871—34no—
26C23×D15—21no—
27C22×C3×C4×C5C2×C411yescharacteristic
28C2×D60—21no—
29C2×D60—24no—
30C2×D60C2×C412yes—
31C22×C5×Dic3—21no—
32C22×C3×Dic5D411yescharacteristic
33C22×C3×Dic5D411yescharacteristic
34C2×#1200—22no—
35C2×#1200—22no—
36C2×#1200—44no—
37#6762—24no—
38C2×C3⋊#170—22no—
39C2×C3×#170—22no—
40C5×C4⋊Dic3—21no—
41C5×C4⋊Dic3C2×C412yes—
42C3×C4×Dic5C2×C411yescharacteristic
43C3×C4×Dic5D411yescharacteristic
44C3×C4×Dic5D411yescharacteristic
45C3×C4×Dic5C2311yescharacteristic
46#6667—22no—
47#6667—22no—
48C2×C4×D12—51no—
49C3×#432—51no—
50C4×#208—51no—
51#4483—54no—
52C22×D20—31no—
53C22×C4×D5—61no—
54C2×#704—61no—
55C2×C5×C4⋊C4—31no—
56C2×#685—61no—
57C2×C4×Dic5C2×D311yescharacteristic
58#4039—32no—
59#4039—32no—
60#4039—61no—
61#4039—61no—
62C22⋊#170—21no—
63#4002—21no—
64#4002—61no—
65C4⋊#170C2×D312yescomplemented
66C4×#170—32no—
67#1490—151noSylow
68C23×C3×C5C22⋊C411yescharacteristic
69C22×D15—24no—
70C22×D15—22no—
71C22×D15—42no—
72C22×D15—42no—
73C2×C3×C4×C5—22no—
74C2×C3×C4×C5C22⋊C411yescharacteristic
75C2×C3×C4×C5C22×C411yescharacteristic
76D60—24no—
77D60—22no—
78D60M1614yescomplemented
79C2×C5×Dic3—22no—
80C2×C5×Dic3—42no—
81C2×C3×Dic5—22no—
82C2×C3×Dic5—22no—
83C2×C3×Dic5C22⋊C411yescharacteristic
84C2×C3×Dic5C22⋊C411yescharacteristic
85C2×C3×Dic5C2×D411yescharacteristic
86C2×C3×Dic5C2×D411yescharacteristic
87#1200—44no—
88#1200—44no—
89C3⋊#170—24no—
90C3×#170—42no—
91C22×D12—51no—
92C22×C4×D3—101no—
93C2×C3×C42—51no—
94C2×(C2×D3)⋊C4—101no—
95C2×C4⋊Dic3AGL(1,𝔽5)11yescharacteristic
96C2×#208—101no—
97C4×D12—52no—
98C4×D12—52no—
99C4×D12—101no—
100C4×D12—101no—
101C3×C4⋊C8—52no—
102C3×C22⋊C8—101no—
103C3×#97—101no—
104#803—101no—
105C4×C3⋊C8—52no—
106C23×D5—61no—
107C22×C4×C5—61no—
108C22×C4×C5C4×D311yescharacteristic
109C22×Dic5D1211yescharacteristic
110C22×Dic5#6711yescharacteristic
111C2×D20—32no—
112C2×D20—64no—
113C2×D20—61no—
114C2×C4×D5—62no—
115C2×C4×D5—62no—
116C2×C4×D5—124no—
117#704—64no—
118C2×#170—22no—
119C2×#170—62no—
120C5×C4⋊C4—32no—
121C5×C4⋊C4—61no—
122#685—62no—
123#685—62no—
124C4×Dic5C4×D311yescharacteristic
125C4×Dic5D1211yescharacteristic
126C4×Dic5#6711yescharacteristic
127C4×Dic5C22×D311yescharacteristic
128C2×C4×D4—151no—
129#432—51no—
130C4×M16—151no—
131D4⋊C8—154no—
132C22×C3×C5—21no—
133C22×C3×C5—21no—
134C22×C3×C5#10412yes—
135C22×C3×C5C2×C22⋊C411yescharacteristic
136C2×D15—24no—
137C2×D15—48no—
138C2×D15—42no—
139C2×D15—42no—
140C3×C4×C5—21no—
141C3×C4×C5C2×M1612yes—
142C3×Dic5—21no—
143C3×Dic5—21no—
144C3×Dic5—21no—
145C3×Dic5AGL(1,ℤ/8)12yes—
146C5×Dic3—42no—
147C23×D3—101no—
148C22×C3×C4—51no—
149C22×C3×C4—51no—
150C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
151C22×Dic3—21no—
152C2×D12—52no—
153C2×D12—104no—
154C2×D12—101no—
155C2×C4×D3—102no—
156C2×C4×D3—102no—
157C2×C4×D3—204no—
158C2×C3×C8—102no—
159C3×C42—51no—
160C3×C42—51no—
161C3×C42—51no—
162C3×C42—51no—
163(C2×D3)⋊C4—102no—
164(C2×D3)⋊C4—102no—
165C4⋊Dic3—21no—
166C4⋊Dic3C2×AGL(1,𝔽5)12yes—
167#208—104no—
168C2×C3⋊C8—102no—
169C23×C5(C2×D3)⋊C411yescharacteristic
170C22×D5—64no—
171C22×D5—62no—
172C22×D5—122no—
173C22×D5—122no—
174C2×C4×C5—22no—
175C2×C4×C5—62no—
176C2×C4×C5—122no—
177C2×C4×C5(C2×D3)⋊C411yescharacteristic
178C2×C4×C5C2×C4×D311yescharacteristic
179C2×Dic5—22no—
180C2×Dic5—22no—
181C2×Dic5(C2×D3)⋊C411yescharacteristic
182C2×Dic5(C2×D3)⋊C411yescharacteristic
183C2×Dic5C2×D1211yescharacteristic
184C2×Dic5C2×#6711yescharacteristic
185D20—34no—
186D20—64no—
187D20—62no—
188C4×D5—124no—
189C4×D5—124no—
190#170—42no—
191#170—64no—
192C22×D4—151no—
193C23×C4—301no—
194C2×M16—301no—
195C4×D4—152no—
196C4×D4—152no—
197C4×D4—301no—
198C4×D4—301no—
199C2×C4⋊C4—31no—
200C2×C22⋊C4—301no—
201C2×C42—51no—
202C4⋊C8—52no—
203C22⋊C8—101no—
204#97—101no—
205#97—301no—
206C4×C8—152no—
207C2×C3×C5—22no—
208C2×C3×C5#40711yescharacteristic
209C2×C3×C5#41811yescharacteristic
210C2×C3×C5C2×#10411yescharacteristic
211D15—44no—
212C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
213C22×D3—104no—
214C22×D3—102no—
215C22×D3—202no—
216C22×D3—202no—
217C2×C3×C4—22no—
218C2×C3×C4—51no—
219C2×C3×C4—51no—
220C2×C3×C4—51no—
221C2×C3×C4—51no—
222C2×C3×C4—102no—
223C2×C3×C4—102no—
224C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
225C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
226C2×Dic3—22no—
227C2×Dic3—42no—
228D12—54no—
229D12—104no—
230D12—102no—
231C4×D3—204no—
232C4×D3—204no—
233C3×C8—202no—
234C3⋊C8—104no—
235C22×C5—21no—
236C22×C5—21no—
237C22×C5#82512yes—
238C22×C5C2×(C2×D3)⋊C411yescharacteristic
239C2×D5—64no—
240C2×D5—128no—
241C2×D5—122no—
242C2×D5—122no—
243C4×C5—21no—
244C4×C5—122no—
245C4×C5D3×M1612yes—
246Dic5—21no—
247Dic5—21no—
248Dic5—21no—
249Dic5#94912yes—
250C24—301no—
251C2×D4—152no—
252C2×D4—304no—
253C2×D4—301no—
254C22×C4—51no—
255C22×C4—51no—
256C22×C4—61no—
257C22×C4—302no—
258C22×C4—302no—
259C22×C4—604no—
260C22×C4D3×AGL(1,𝔽5)11yescharacteristic
261M16—304no—
262C2×C8—102no—
263C2×C8—302no—
264C4⋊C4—32no—
265C4⋊C4—61no—
266C22⋊C4—302no—
267C22⋊C4—302no—
268C42—51no—
269C42—51no—
270C42—51no—
271C42—51no—
272C3×C5#149011yescharacteristic, complemented, Hall
273C22×C3—21no—
274C22×C3—21no—
275C22×C3#401012yes—
276C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
277C2×D3—104no—
278C2×D3—208no—
279C2×D3—202no—
280C2×D3—202no—
281C3×C4—21no—
282C3×C4—52no—
283C3×C4—101no—
284C3×C4—101no—
285C3×C4—101no—
286C3×C4D5⋊M1612yes—
287Dic3—42no—
288C2×C5—22no—
289C2×C5#500111yescharacteristic
290C2×C5#512611yescharacteristic
291C2×C5C2×#82511yescharacteristic
292D5—124no—
293C23—304no—
294C23—302no—
295C23—602no—
296C23—602no—
297C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
298D4—154no—
299D4—304no—
300D4—302no—
301C2×C4—22no—
302C2×C4—51no—
303C2×C4—51no—
304C2×C4—51no—
305C2×C4—51no—
306C2×C4—62no—
307C2×C4—102no—
308C2×C4—102no—
309C2×C4—122no—
310C2×C4—604no—
311C2×C4—604no—
312C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
313C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
314C8—202no—
315C8—304no—
316C2×C3—22no—
317C2×C3#6575511yescharacteristic
318C2×C3#6576711yescharacteristic
319C2×C3C2×#401011yescharacteristic
320D3—204no—
321C5#7079911yescharacteristic, complemented, Sylow
322C22—21no—
323C22—21no—
324C22—304no—
325C22—608no—
326C22—602no—
327C22—602no—
328C22#9115712yes—
329C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
330C4—21no—
331C4—52no—
332C4—101no—
333C4—101no—
334C4—101no—
335C4—122no—
336C4#9193112yes—
337C3#1060427411yescharacteristic, complemented, Sylow
338C2—22no—
339C2—604no—
340C2#1175170611yescharacteristic
341C2C2×#9115711yescharacteristic
342C2#1175200311yescharacteristic
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 radicalC22×D60C4
cosocleC3×C4×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1490
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C4×#6762C2semidirect
3. C3×#65759C2semidirect
4. #11746490C2semidirect
17. C4×C3⋊#170C22semidirect
20. C3×C4⋊#170C22semidirect
23. #65759D3semidirect
65. C4⋊#170C2×D3semidirect
78. D60M16semidirect
272. C3×C5#1490semidirect
321. C5#70799semidirect
337. C3#10604274semidirect

Maximal subgroups

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

subgroupindex
C2×#914182
C4×#67622
C3×#657592
#117464902
#106042743
#707995