Finite Group Databasebeta

← #14282102

Subgroups — #14282102

Order 1920.

624 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 122 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
2#11752417C211yesmaximal, characteristic, complemented
3C3×#65754C211yesmaximal, characteristic, complemented
4#11746491C214yesmaximal, complemented
5#10604272—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#91233—21no—
17C4⋊(C3⋊#170)C2212yescomplemented
18C3×C22⋊#170—21no—
19C3×#4004—21no—
20C3×C4×#170C2212yescomplemented
21#70762—51nomaximal, Hall
22C2×#4039—31no—
23#65758—31no—
24#65754D311yescharacteristic, complemented
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—42no—
37C2×#1200—42no—
38#6762—42no—
39C2×C3⋊#170—22no—
40C2×C3×#170—22no—
41C5×C4⋊Dic3—21no—
42C5×C4⋊Dic3C2×C412yes—
43C3×C4×Dic5C2×C411yescharacteristic
44C3×C4×Dic5D411yescharacteristic
45C3×C4×Dic5D411yescharacteristic
46C3×C4×Dic5C2311yescharacteristic
47#6667—22no—
48#6667—22no—
49C2×C4×D12—51no—
50C3×#431—51no—
51#4924—51no—
52#4459—54no—
53C22×D20—31no—
54C22×C4×D5—61no—
55C2×#704—61no—
56C2×C5×C4⋊C4—31no—
57C2×#685—61no—
58C2×C4×Dic5C2×D311yescharacteristic
59#4039—32no—
60#4039—32no—
61#4039—61no—
62#4039—61no—
63C22⋊#170—21no—
64#4004—21no—
65#4004—61no—
66C4⋊#170—32no—
67C4×#170C2×D312yescomplemented
68#1486—151noSylow
69C23×C3×C5C22⋊C411yescharacteristic
70C22×D15—24no—
71C22×D15—22no—
72C22×D15—42no—
73C22×D15—42no—
74C2×C3×C4×C5—22no—
75C2×C3×C4×C5C22⋊C411yescharacteristic
76C2×C3×C4×C5C22×C411yescharacteristic
77D60—24no—
78D60—22no—
79D60M1614yescomplemented
80C2×C5×Dic3—22no—
81C2×C5×Dic3—42no—
82C2×C3×Dic5—41no—
83C2×C3×Dic5C22⋊C411yescharacteristic
84C2×C3×Dic5C22⋊C411yescharacteristic
85C2×C3×Dic5D812yes—
86C2×C3×Dic5SD1612yes—
87C2×C3×Dic5C2×D411yescharacteristic
88C2×C3×Dic5C2×D411yescharacteristic
89#1200—44no—
90#1200—42no—
91#1200—42no—
92C3⋊#170—42no—
93C3×#170—42no—
94C22×D12—51no—
95C22×C4×D3—101no—
96C2×C3×C42—51no—
97C2×(C2×D3)⋊C4—101no—
98C2×C4⋊Dic3AGL(1,𝔽5)11yescharacteristic
99C2×#208—101no—
100C4×D12—52no—
101C4×D12—52no—
102C4×D12—101no—
103C4×D12—101no—
104C3×C4⋊C8—101no—
105C3×C22⋊C8—101no—
106C3×C4×C8—52no—
107C4⋊(C3⋊C8)—52no—
108C4⋊(C3⋊C8)—101no—
109C23×D5—61no—
110C22×C4×C5—61no—
111C22×C4×C5C4×D311yescharacteristic
112C22×Dic5D1211yescharacteristic
113C22×Dic5#6711yescharacteristic
114C2×D20—32no—
115C2×D20—64no—
116C2×D20—61no—
117C2×C4×D5—62no—
118C2×C4×D5—62no—
119C2×C4×D5—122no—
120C2×C4×D5—122no—
121#704—122no—
122C2×#170—22no—
123C2×#170—62no—
124C5×C4⋊C4—32no—
125C5×C4⋊C4—61no—
126#685—62no—
127#685—62no—
128C4×Dic5C4×D311yescharacteristic
129C4×Dic5D1211yescharacteristic
130C4×Dic5#6711yescharacteristic
131C4×Dic5C22×D311yescharacteristic
132C2×C4×D4—151no—
133#431—51no—
134#423—151no—
135D4⋊C8—154no—
136C22×C3×C5—21no—
137C22×C3×C5—21no—
138C22×C3×C5#10212yes—
139C22×C3×C5C2×C22⋊C411yescharacteristic
140C2×D15—24no—
141C2×D15—48no—
142C2×D15—42no—
143C2×D15—42no—
144C3×C4×C5—21no—
145C3×C4×C5C2×M1612yes—
146C3×Dic5—21no—
147C3×Dic5—21no—
148C3×Dic5#10212yes—
149C3×Dic5C2×D811yescharacteristic
150C3×Dic5C2×SD1611yescharacteristic
151C5×Dic3—42no—
152C23×D3—101no—
153C22×C3×C4—51no—
154C22×C3×C4—51no—
155C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
156C22×Dic3—21no—
157C2×D12—52no—
158C2×D12—104no—
159C2×D12—101no—
160C2×C4×D3—102no—
161C2×C4×D3—102no—
162C2×C4×D3—202no—
163C2×C4×D3—202no—
164C2×C3×C8—102no—
165C3×C42—51no—
166C3×C42—51no—
167C3×C42—51no—
168C3×C42—51no—
169(C2×D3)⋊C4—102no—
170(C2×D3)⋊C4—102no—
171C4⋊Dic3—21no—
172C4⋊Dic3C2×AGL(1,𝔽5)12yes—
173#208—202no—
174C2×C3⋊C8—102no—
175C23×C5(C2×D3)⋊C411yescharacteristic
176C22×D5—64no—
177C22×D5—62no—
178C22×D5—122no—
179C22×D5—122no—
180C2×C4×C5—22no—
181C2×C4×C5—62no—
182C2×C4×C5—122no—
183C2×C4×C5(C2×D3)⋊C411yescharacteristic
184C2×C4×C5C2×C4×D311yescharacteristic
185C2×Dic5—41no—
186C2×Dic5#20412yes—
187C2×Dic5D2412yes—
188C2×Dic5(C2×D3)⋊C411yescharacteristic
189C2×Dic5(C2×D3)⋊C411yescharacteristic
190C2×Dic5C2×D1211yescharacteristic
191C2×Dic5C2×#6711yescharacteristic
192D20—34no—
193D20—64no—
194D20—62no—
195C4×D5—124no—
196C4×D5—122no—
197C4×D5—122no—
198#170—42no—
199#170—122no—
200C22×D4—151no—
201C23×C4—301no—
202C2×M16—301no—
203C4×D4—152no—
204C4×D4—152no—
205C4×D4—301no—
206C4×D4—301no—
207C2×C4⋊C4—31no—
208C2×C22⋊C4—301no—
209C2×C42—51no—
210C4⋊C8—101no—
211C4⋊C8—152no—
212C4⋊C8—301no—
213C22⋊C8—101no—
214C4×C8—52no—
215C2×C3×C5—22no—
216C2×C3×C5#40711yescharacteristic
217C2×C3×C5C2×#10211yescharacteristic
218C2×C3×C5#42111yescharacteristic
219D15—44no—
220C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
221C22×D3—104no—
222C22×D3—102no—
223C22×D3—202no—
224C22×D3—202no—
225C2×C3×C4—22no—
226C2×C3×C4—51no—
227C2×C3×C4—51no—
228C2×C3×C4—52no—
229C2×C3×C4—52no—
230C2×C3×C4—51no—
231C2×C3×C4—51no—
232C2×C3×C4—201no—
233C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
234C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
235C2×Dic3—22no—
236C2×Dic3—42no—
237D12—54no—
238D12—104no—
239D12—102no—
240C4×D3—204no—
241C4×D3—202no—
242C4×D3—202no—
243C3×C8—202no—
244C3⋊C8—202no—
245C22×C5—21no—
246C22×C5—21no—
247C22×C5#82112yes—
248C22×C5C2×(C2×D3)⋊C411yescharacteristic
249C2×D5—64no—
250C2×D5—128no—
251C2×D5—122no—
252C2×D5—122no—
253C4×C5—21no—
254C4×C5—122no—
255C4×C5D3×M1612yes—
256Dic5—21no—
257Dic5—21no—
258Dic5#82112yes—
259Dic5C2×#20411yescharacteristic
260Dic5C2×D2411yescharacteristic
261C24—301no—
262C2×D4—152no—
263C2×D4—304no—
264C2×D4—301no—
265C22×C4—51no—
266C22×C4—51no—
267C22×C4—61no—
268C22×C4—302no—
269C22×C4—302no—
270C22×C4—602no—
271C22×C4—602no—
272C22×C4D3×AGL(1,𝔽5)11yescharacteristic
273M16—602no—
274C2×C8—102no—
275C2×C8—302no—
276C4⋊C4—32no—
277C4⋊C4—61no—
278C22⋊C4—302no—
279C22⋊C4—302no—
280C42—51no—
281C42—51no—
282C42—51no—
283C42—51no—
284C3×C5#148611yescharacteristic, complemented, Hall
285C22×C3—21no—
286C22×C3—21no—
287C22×C3#400712yes—
288C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
289C2×D3—104no—
290C2×D3—208no—
291C2×D3—202no—
292C2×D3—202no—
293C3×C4—21no—
294C3×C4—52no—
295C3×C4—51no—
296C3×C4—51no—
297C3×C4—101no—
298C3×C4—101no—
299C3×C4D5⋊M1612yes—
300Dic3—42no—
301C2×C5—22no—
302C2×C5#500511yescharacteristic
303C2×C5C2×#82111yescharacteristic
304C2×C5#512611yescharacteristic
305D5—124no—
306C23—304no—
307C23—302no—
308C23—602no—
309C23—602no—
310C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
311D4—154no—
312D4—304no—
313D4—302no—
314C2×C4—22no—
315C2×C4—52no—
316C2×C4—52no—
317C2×C4—51no—
318C2×C4—51no—
319C2×C4—51no—
320C2×C4—51no—
321C2×C4—62no—
322C2×C4—122no—
323C2×C4—201no—
324C2×C4—602no—
325C2×C4—604no—
326C2×C4—602no—
327C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
328C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
329C8—202no—
330C8—602no—
331C2×C3—22no—
332C2×C3#6575511yescharacteristic
333C2×C3C2×#400711yescharacteristic
334C2×C3#6578411yescharacteristic
335D3—204no—
336C5#7076211yescharacteristic, complemented, Sylow
337C22—21no—
338C22—21no—
339C22—304no—
340C22—608no—
341C22—602no—
342C22—602no—
343C22#9115212yes—
344C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
345C4—21no—
346C4—51no—
347C4—52no—
348C4—51no—
349C4—101no—
350C4—101no—
351C4—122no—
352C4#9193112yes—
353C3#1060427211yescharacteristic, complemented, Sylow
354C2—22no—
355C2—604no—
356C2C2×#9115211yescharacteristic
357C2#1175172411yescharacteristic
358C2#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#1486
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. #11752417C2semidirect
3. C3×#65754C2semidirect
4. #11746491C2semidirect
17. C4⋊(C3⋊#170)C22semidirect
20. C3×C4×#170C22semidirect
24. #65754D3semidirect
67. C4×#170C2×D3semidirect
79. D60M16semidirect
284. C3×C5#1486semidirect
336. C5#70762semidirect
353. C3#10604272semidirect

Maximal subgroups

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

subgroupindex
C2×#914182
#117524172
C3×#657542
#117464912
#106042723
#707625