Finite Group Databasebeta

← #14283967

Subgroups — #14283967

Order 1920.

468 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 98 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#11754410C211yesmaximal, characteristic
2C4×#6762C211yesmaximal, characteristic, complemented
3C2×C3×#4002C211yesmaximal, characteristic, complemented
4#11746506C212yesmaximal, complemented
5#11746504C212yesmaximal, complemented
6#10604473—31nomaximal, Hall
7C2×#6762—21no—
8C22×C3×#170—21no—
9#91813C411yescharacteristic
10C5×#930C411yescharacteristic
11C2×C3×C4×Dic5C2211yescharacteristic
12Dic5×#67—21no—
13#91539—21no—
14Dic5×D12C411yescharacteristic
15#91398—21no—
16#91388C2211yescharacteristic
17#91373C2211yescharacteristic
18#91372—21no—
19#91333C411yescharacteristic
20#91231C2212yes—
21C4×C3⋊#170—21no—
22C3×#4002—21no—
23C3×#4002C2212yes—
24#69797—51nomaximal, Hall
25#65934—31no—
26C4×#704—31no—
27C2×#4002D311yescharacteristic, complemented
28#64921—32no—
29#64870—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C2×Dic30C2×C411yescharacteristic
32C2×C5×#67—21no—
33C2×C5×D12C2×C411yescharacteristic
34C22×C3×Dic5D411yescharacteristic
35C22×C3×Dic5D411yescharacteristic
36C2×D3×Dic5—21no—
37#6762—24no—
38C2×C3⋊#170—22no—
39C2×C3×#170—24no—
40C2×C3×#170—22no—
41#6719—21no—
42C4⋊Dic15C2×C411yescharacteristic
43#6712—21no—
44C5×(C2×D3)⋊C4—21no—
45C5×C4⋊Dic3C2×C411yescharacteristic
46C3×C4×Dic5C2×C411yescharacteristic
47C3×C4×Dic5D411yescharacteristic
48C3×C4×Dic5D411yescharacteristic
49C3×C4×Dic5C2311yescharacteristic
50Dic3⋊Dic5—21no—
51#6669—21no—
52#6669—21no—
53(C2×D3)⋊Dic5—21no—
54(C2×D3)⋊Dic5—21no—
55(C2×D3)⋊Dic5—21no—
56Dic3×Dic5—21no—
57#5479—51no—
58C2×C3×#97—51no—
59C4×#208—51no—
60#4465—52no—
61#4464—52no—
62C2×#704—61no—
63C22×#170—21no—
64C5×#121—31no—
65#4082—31no—
66#4081—61no—
67D4×Dic5—31no—
68D4×Dic5—61no—
69#4070—31no—
70C2×C4×Dic5C2×D311yescharacteristic
71#4036—31no—
72#4033—31no—
73#4025—61no—
74#4023—61no—
75#4002—21no—
76#4002—32no—
77#4002C2×D312yes—
78C4×#170—61no—
79#1524—151noSylow
80C23×C3×C5C22⋊C411yescharacteristic
81C22×C5×D3—21no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5C22⋊C411yescharacteristic
84C2×C3×C4×C5C22×C411yescharacteristic
85C2×Dic15—21no—
86C2×Dic15—21no—
87Dic30—41no—
88C5×#67—42no—
89C2×C5×Dic3—21no—
90C5×D12—41no—
91C2×C3×Dic5—22no—
92C2×C3×Dic5—22no—
93C2×C3×Dic5C22⋊C411yescharacteristic
94C2×C3×Dic5C22⋊C411yescharacteristic
95C2×C3×Dic5C2×D411yescharacteristic
96C2×C3×Dic5C2×D411yescharacteristic
97D3×Dic5—42no—
98C3⋊#170—24no—
99C3×#170—24no—
100C22×C3×C8—101no—
101C2×C3×C42—51no—
102#930AGL(1,𝔽5)11yescharacteristic
103#929—101no—
104C4×#67—101no—
105#924—51no—
106C2×#208—101no—
107#876—101no—
108#875—51no—
109C4×D12—51no—
110#872—101no—
111#870—51no—
112C4×Dic6—51no—
113C3×#97—52no—
114C3×#97—101no—
115#803—52no—
116C4×C3⋊C8—101no—
117C2×C5×D4—31no—
118C2×C5×D4—61no—
119C22×C4×C5C4×D311yescharacteristic
120C22×Dic5—61no—
121C22×Dic5D1211yescharacteristic
122C22×Dic5#6711yescharacteristic
123C2×Dic10—31no—
124#704—64no—
125C2×#170—24no—
126C2×#170—22no—
127C2×#170—62no—
128C5×C4⋊C4—31no—
129C5×C22⋊C4—61no—
130C22⋊Dic5—61no—
131C22⋊Dic5—61no—
132C22⋊Dic5—61no—
133C22⋊Dic5—61no—
134C4⋊Dic5—31no—
135C4⋊Dic5—61no—
136#683—61no—
137#683—61no—
138#683—61no—
139C4×Dic5—61no—
140C4×Dic5C4×D311yescharacteristic
141C4×Dic5D1211yescharacteristic
142C4×Dic5#6711yescharacteristic
143C4×Dic5C22×D311yescharacteristic
144#529—151no—
145C4×M16—151no—
146C2×#97—51no—
147#330—152no—
148#329—152no—
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5#10412yes—
152C22×C3×C5C2×C22⋊C411yescharacteristic
153C2×C5×D3—41no—
154C2×C5×D3—41no—
155C2×C5×D3—41no—
156C3×C4×C5—21no—
157C3×C4×C5—21no—
158Dic15—41no—
159Dic15—41no—
160C3×Dic5—21no—
161C3×Dic5—21no—
162C3×Dic5—21no—
163C3×Dic5#10412yes—
164C5×Dic3—41no—
165C22×C3×C4—51no—
166C22×C3×C4—51no—
167C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
168C2×#67—21no—
169C2×D12C2×AGL(1,𝔽5)11yescharacteristic
170C2×C4×D3—101no—
171C2×Dic6—51no—
172C2×C3×C8—102no—
173C2×C3×C8—104no—
174C3×C42—51no—
175C3×C42—51no—
176C3×C42—51no—
177C3×C42—51no—
178#217—101no—
179(C2×D3)⋊C4—21no—
180(C2×D3)⋊C4—101no—
181(C2×D3)⋊C4—101no—
182(C2×D3)⋊C4—101no—
183C4⋊Dic3—51no—
184C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
185Dic3⋊C4—101no—
186Dic3⋊C4—101no—
187Dic3⋊C4—101no—
188Dic3⋊C4—101no—
189C4×Dic3—101no—
190#208—104no—
191C2×C3⋊C8—102no—
192C23×C5—61no—
193C23×C5(C2×D3)⋊C411yescharacteristic
194C5×D4—121no—
195C5×D4—122no—
196C2×C4×C5—41no—
197C2×C4×C5—61no—
198C2×C4×C5(C2×D3)⋊C411yescharacteristic
199C2×C4×C5C2×C4×D311yescharacteristic
200C2×Dic5—22no—
201C2×Dic5—22no—
202C2×Dic5—61no—
203C2×Dic5—61no—
204C2×Dic5—122no—
205C2×Dic5(C2×D3)⋊C411yescharacteristic
206C2×Dic5(C2×D3)⋊C411yescharacteristic
207C2×Dic5C2×D1211yescharacteristic
208C2×Dic5C2×#6711yescharacteristic
209Dic10—121no—
210#170—24no—
211#170—64no—
212C2×M16—301no—
213C22×C8—101no—
214#126—301no—
215#125—151no—
216#124—151no—
217#123—301no—
218C22⋊Q8—151no—
219#121—31no—
220C4×Q8—151no—
221C4×D4—151no—
222C4×D4—301no—
223#117—301no—
224C2×C42—51no—
225#97—52no—
226#97—101no—
227#97—152no—
228C4×C8—301no—
229C2×C3×C5—22no—
230C2×C3×C5#41311yescharacteristic
231C2×C3×C5C2×#10411yescharacteristic
232C2×C3×C5C2×#10411yescharacteristic
233C5×D3—81no—
234C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
235C22×D3—21no—
236C2×C3×C4—41no—
237C2×C3×C4—51no—
238C2×C3×C4—51no—
239C2×C3×C4—51no—
240C2×C3×C4—51no—
241C2×C3×C4—102no—
242C2×C3×C4—102no—
243C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
244C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
245#67—42no—
246C2×Dic3—21no—
247C2×Dic3—101no—
248C2×Dic3—101no—
249D12—41no—
250C4×D3—202no—
251Dic6—201no—
252C3×C8—104no—
253C3⋊C8—104no—
254C22×C5—21no—
255C22×C5—21no—
256C22×C5—121no—
257C22×C5—121no—
258C22×C5—121no—
259C22×C5#82512yes—
260C22×C5C2×(C2×D3)⋊C411yescharacteristic
261C4×C5—21no—
262C4×C5—21no—
263C4×C5—121no—
264Dic5—21no—
265Dic5—21no—
266Dic5—21no—
267Dic5—121no—
268Dic5—121no—
269Dic5#80512yes—
270C2×Q8—151no—
271C2×D4—31no—
272C2×D4—61no—
273C22×C4—51no—
274C22×C4—51no—
275C22×C4—301no—
276C22×C4D3×AGL(1,𝔽5)11yescharacteristic
277M16—304no—
278C2×C8—102no—
279C2×C8—104no—
280C2×C8—302no—
281C4⋊C4—31no—
282C4⋊C4—151no—
283C4⋊C4—301no—
284C4⋊C4—301no—
285C4⋊C4—301no—
286C4⋊C4—301no—
287C22⋊C4—61no—
288C22⋊C4—301no—
289C22⋊C4—301no—
290C22⋊C4—301no—
291C22⋊C4—301no—
292C42—51no—
293C42—51no—
294C42—51no—
295C42—51no—
296C42—301no—
297C3×C5#152411yescharacteristic, complemented, Hall
298C22×C3—21no—
299C22×C3—21no—
300C22×C3#400812yes—
301C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
302C2×D3—41no—
303C2×D3—41no—
304C2×D3—41no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—52no—
308C3×C4—101no—
309C3×C4—101no—
310C3×C4—101no—
311Dic3—41no—
312Dic3—201no—
313Dic3—201no—
314C2×C5—22no—
315C2×C5—241no—
316C2×C5C2×#80511yescharacteristic
317C2×C5#513211yescharacteristic
318C2×C5C2×#82511yescharacteristic
319C23—61no—
320C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
321Q8—601no—
322D4—121no—
323D4—122no—
324C2×C4—41no—
325C2×C4—51no—
326C2×C4—51no—
327C2×C4—51no—
328C2×C4—51no—
329C2×C4—61no—
330C2×C4—102no—
331C2×C4—102no—
332C2×C4—301no—
333C2×C4—301no—
334C2×C4—602no—
335C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
336C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
337C8—104no—
338C8—304no—
339C2×C3—22no—
340C2×C3C2×#400811yescharacteristic
341C2×C3#6577711yescharacteristic
342C2×C3D5⋊#10411yescharacteristic
343D3—81no—
344C5#6979711yescharacteristic, complemented, Sylow
345C22—21no—
346C22—21no—
347C22—121no—
348C22—121no—
349C22—121no—
350C22#9115512yes—
351C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
352C4—21no—
353C4—21no—
354C4—52no—
355C4—101no—
356C4—101no—
357C4—101no—
358C4—121no—
359C4—601no—
360C4—601no—
361C3#1060447311yescharacteristic, complemented, Sylow
362C2—22no—
363C2—241no—
364C2C2×#9115511yescharacteristic
365C2D5⋊#80511yescharacteristic
366C2#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 radicalC5×#930C4
cosocleC3×C4×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1524
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
2. C4×#6762C2semidirect
3. C2×C3×#4002C2semidirect
4. #11746506C2semidirect
5. #11746504C2semidirect
27. C2×#4002D3semidirect
297. C3×C5#1524semidirect
344. C5#69797semidirect
361. C3#10604473semidirect

Maximal subgroups

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

subgroupindex
#117544102
C4×#67622
C2×C3×#40022
#117465062
#117465042
#106044733
#697975