Finite Group Databasebeta

← #14284216

Subgroups — #14284216

Order 1920.

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

normal subgroups only

This group has 512 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#11754572C211yesmaximal, characteristic
2C2×#91231C211yesmaximal, characteristic, complemented
3C3×#65757C211yesmaximal, characteristic, complemented
4#11746505C212yesmaximal, complemented
5#11746504C212yesmaximal, complemented
6#10604994—31nomaximal, Hall
7C2×#6817C411yescharacteristic
8C2×C5×#235C411yescharacteristic
9C22×C3⋊#170—21no—
10C2×C3×C4×Dic5C2211yescharacteristic
11#91566—21no—
12#91566—21no—
13#91451C411yescharacteristic
14C4×#1203—21no—
15C4×#1203—21no—
16#91376C411yescharacteristic
17#91375C2211yescharacteristic
18#91373C2211yescharacteristic
19#91231—21no—
20#91231C2212yes—
21C3×C22⋊#170—21no—
22C3×#4004—21no—
23C3×#4002C2212yes—
24#70806—51nomaximal, Hall
25#66166—31no—
26#65757D311yescharacteristic, complemented
27C2×#4002—31no—
28#64927—32no—
29#64921—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C2×#1220—21no—
32#6817—42no—
33C2×D60C2×C411yescharacteristic
34C2×C4×D15—21no—
35C2×Dic30C2×C411yescharacteristic
36C2×C5×#67—21no—
37C5×#235—42no—
38C2×C5×D12C2×C411yescharacteristic
39C2×C4×C5×D3—21no—
40C2×C5×Dic6C2×C411yescharacteristic
41C22×C3×Dic5D411yescharacteristic
42C22×C3×Dic5D411yescharacteristic
43C2×#1203—21no—
44C2×#1203—21no—
45C2×C3⋊#170—24no—
46C2×C3⋊#170—22no—
47C2×C3×#170—22no—
48C3×C4×Dic5C2×C411yescharacteristic
49C3×C4×Dic5D411yescharacteristic
50C3×C4×Dic5D411yescharacteristic
51C3×C4×Dic5C2311yescharacteristic
52#6668—21no—
53#6668—21no—
54#6667—21no—
55#6667—21no—
56(C2×D3)⋊Dic5—21no—
57(C2×D3)⋊Dic5—21no—
58#5477—51no—
59C3×#432—51no—
60C2×#803—51no—
61#4464—52no—
62#4464—52no—
63C2×C5×#41—31no—
64C2×#709—31no—
65C22×#170—61no—
66#4093—31no—
67#4090—31no—
68#4086—31no—
69#4085—61no—
70#4085—61no—
71#4082—31no—
72C4×C22⋊D5—61no—
73C4×C22⋊D5—61no—
74C2×C4×Dic5C2×D311yescharacteristic
75C22⋊#170—21no—
76#4004—21no—
77#4002—32no—
78#4002—61no—
79#4002C2×D312yes—
80#1530—151noSylow
81C23×C3×C5C22⋊C411yescharacteristic
82C22×D15—21no—
83C22×C5×D3—21no—
84C2×C3×C4×C5—22no—
85C2×C3×C4×C5C22⋊C411yescharacteristic
86C2×C3×C4×C5C22×C411yescharacteristic
87#1220—42no—
88C2×Dic15—21no—
89D60—41no—
90C4×D15—42no—
91Dic30—41no—
92C5×#67—42no—
93C2×C5×Dic3—21no—
94C5×D12—41no—
95C4×C5×D3—42no—
96C5×Dic6—41no—
97C2×C3×Dic5—22no—
98C2×C3×Dic5—41no—
99C2×C3×Dic5C22⋊C411yescharacteristic
100C2×C3×Dic5C22⋊C411yescharacteristic
101C2×C3×Dic5C2×D411yescharacteristic
102C2×C3×Dic5C2×D411yescharacteristic
103#1203—42no—
104#1203—42no—
105C3⋊#170—24no—
106C3×#170—42no—
107C2×#235—51no—
108C2×#235AGL(1,𝔽5)11yescharacteristic
109C2×C3×C42—51no—
110#930—101no—
111#930—101no—
112C22×C3⋊C8—101no—
113#875—51no—
114#875—51no—
115#874—51no—
116C4×D12—101no—
117C4×D12—101no—
118#869—51no—
119C3×C4⋊C8—101no—
120C3×C22⋊C8—101no—
121C3×#97—52no—
122#803—52no—
123#803—101no—
124C5×#41—122no—
125C2×C5×Q8—31no—
126C2×C5×D4—31no—
127C2×C5×D4—61no—
128C22×C4×C5—61no—
129C22×C4×C5C4×D311yescharacteristic
130C2×C22⋊D5—61no—
131C2×C22⋊D5—61no—
132C2×C22⋊D5—61no—
133C22×Dic5D1211yescharacteristic
134C22×Dic5#6711yescharacteristic
135#709—122no—
136C2×D20—31no—
137C2×C4×D5—61no—
138C2×Dic10—31no—
139C2×#170—22no—
140C2×#170—64no—
141C2×#170—62no—
142C22⋊Dic5—61no—
143C22⋊Dic5—61no—
144#685—61no—
145#685—61no—
146#683—61no—
147#683—61no—
148C4×Dic5C4×D311yescharacteristic
149C4×Dic5D1211yescharacteristic
150C4×Dic5#6711yescharacteristic
151C4×Dic5C22×D311yescharacteristic
152#532—151no—
153#432—51no—
154C2×#97—151no—
155#329—152no—
156#329—152no—
157C22×C3×C5—21no—
158C22×C3×C5—21no—
159C22×C3×C5#10012yes—
160C22×C3×C5C2×C22⋊C411yescharacteristic
161C2×D15—41no—
162C2×D15—41no—
163C2×D15—41no—
164C2×C5×D3—41no—
165C2×C5×D3—41no—
166C2×C5×D3—41no—
167C3×C4×C5—21no—
168C3×C4×C5—21no—
169Dic15—41no—
170C3×Dic5—21no—
171C3×Dic5—21no—
172C3×Dic5—21no—
173C3×Dic5#10412yes—
174C5×Dic3—41no—
175C22×C3×C4—51no—
176C22×C3×C4—51no—
177C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
178C2×#67—21no—
179C2×#67—101no—
180#235—42no—
181#235—202no—
182C2×D12—51no—
183C2×D12—101no—
184C2×D12—101no—
185C2×D12C2×AGL(1,𝔽5)11yescharacteristic
186C2×C4×D3—21no—
187C2×C4×D3—101no—
188C2×Dic6—51no—
189C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
190C2×C3×C8—102no—
191C3×C42—51no—
192C3×C42—51no—
193C3×C42—51no—
194C3×C42—51no—
195(C2×D3)⋊C4—101no—
196(C2×D3)⋊C4—101no—
197(C2×D3)⋊C4—101no—
198(C2×D3)⋊C4—101no—
199C4⋊Dic3—101no—
200C4⋊Dic3—101no—
201C2×C3⋊C8—102no—
202C2×C3⋊C8—104no—
203C23×C5—61no—
204C23×C5(C2×D3)⋊C411yescharacteristic
205C22×D5—61no—
206C5×Q8—121no—
207C5×D4—121no—
208C5×D4—122no—
209C2×C4×C5—22no—
210C2×C4×C5—61no—
211C2×C4×C5—122no—
212C2×C4×C5(C2×D3)⋊C411yescharacteristic
213C2×C4×C5C2×C4×D311yescharacteristic
214C22⋊D5—122no—
215C22⋊D5—122no—
216C22⋊D5—122no—
217C2×Dic5—22no—
218C2×Dic5—41no—
219C2×Dic5—61no—
220C2×Dic5(C2×D3)⋊C411yescharacteristic
221C2×Dic5(C2×D3)⋊C411yescharacteristic
222C2×Dic5C2×D1211yescharacteristic
223C2×Dic5C2×#6711yescharacteristic
224D20—121no—
225C4×D5—122no—
226Dic10—121no—
227#170—42no—
228#170—64no—
229C2×#41—31no—
230C2×#41—151no—
231C22×C8—301no—
232C4⋊Q8—151no—
233#127—151no—
234#124—151no—
235#124—151no—
236#121—301no—
237#121—301no—
238C4×D4—301no—
239C4×D4—301no—
240C2×C42—51no—
241C4⋊C8—101no—
242C22⋊C8—101no—
243#97—52no—
244#97—152no—
245#97—301no—
246C2×C3×C5—22no—
247C2×C3×C5C2×#10011yescharacteristic
248C2×C3×C5C2×#10411yescharacteristic
249C2×C3×C5#42111yescharacteristic
250D15—81no—
251C5×D3—81no—
252C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
253C22×D3—21no—
254C22×D3—101no—
255C2×C3×C4—22no—
256C2×C3×C4—51no—
257C2×C3×C4—51no—
258C2×C3×C4—51no—
259C2×C3×C4—51no—
260C2×C3×C4—102no—
261C2×C3×C4—201no—
262C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
263C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
264#67—42no—
265#67—202no—
266C2×Dic3—21no—
267C2×Dic3—101no—
268D12—41no—
269D12—201no—
270D12—202no—
271D12—202no—
272C4×D3—42no—
273C4×D3—202no—
274Dic6—41no—
275Dic6—201no—
276C3×C8—202no—
277C3⋊C8—104no—
278C22×C5—21no—
279C22×C5—21no—
280C22×C5—121no—
281C22×C5—121no—
282C22×C5—121no—
283C22×C5#82312yes—
284C22×C5C2×(C2×D3)⋊C411yescharacteristic
285C2×D5—121no—
286C2×D5—121no—
287C2×D5—121no—
288C4×C5—21no—
289C4×C5—21no—
290C4×C5—121no—
291Dic5—21no—
292Dic5—21no—
293Dic5—21no—
294Dic5—121no—
295Dic5#82512yes—
296#41—122no—
297#41—602no—
298C2×Q8—31no—
299C2×Q8—151no—
300C2×D4—31no—
301C2×D4—61no—
302C2×D4—151no—
303C2×D4—301no—
304C2×D4—301no—
305C2×D4—301no—
306C22×C4—51no—
307C22×C4—51no—
308C22×C4—61no—
309C22×C4—301no—
310C22×C4D3×AGL(1,𝔽5)11yescharacteristic
311C2×C8—102no—
312C2×C8—302no—
313C2×C8—304no—
314C4⋊C4—301no—
315C4⋊C4—301no—
316C22⋊C4—301no—
317C22⋊C4—301no—
318C22⋊C4—301no—
319C22⋊C4—301no—
320C42—51no—
321C42—51no—
322C42—51no—
323C42—51no—
324C3×C5#153011yescharacteristic, complemented, Hall
325C22×C3—21no—
326C22×C3—21no—
327C22×C3#401312yes—
328C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
329C2×D3—41no—
330C2×D3—41no—
331C2×D3—41no—
332C2×D3—201no—
333C2×D3—201no—
334C2×D3—201no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—52no—
338C3×C4—101no—
339C3×C4—101no—
340C3×C4—101no—
341Dic3—41no—
342Dic3—201no—
343C2×C5—22no—
344C2×C5—241no—
345C2×C5#500511yescharacteristic
346C2×C5C2×#82311yescharacteristic
347C2×C5C2×#82511yescharacteristic
348D5—241no—
349C23—61no—
350C23—301no—
351C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
352Q8—121no—
353Q8—601no—
354D4—121no—
355D4—122no—
356D4—601no—
357D4—602no—
358D4—602no—
359D4—602no—
360C2×C4—22no—
361C2×C4—51no—
362C2×C4—51no—
363C2×C4—51no—
364C2×C4—51no—
365C2×C4—61no—
366C2×C4—102no—
367C2×C4—122no—
368C2×C4—201no—
369C2×C4—301no—
370C2×C4—602no—
371C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
372C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
373C8—202no—
374C8—304no—
375C2×C3—22no—
376C2×C3D5⋊#10411yescharacteristic
377C2×C3#6579511yescharacteristic
378C2×C3C2×#401311yescharacteristic
379D3—81no—
380D3—401no—
381C5#7080611yescharacteristic, complemented, Sylow
382C22—21no—
383C22—21no—
384C22—121no—
385C22—121no—
386C22—121no—
387C22—601no—
388C22—601no—
389C22—601no—
390C22#9117412yes—
391C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
392C4—21no—
393C4—21no—
394C4—52no—
395C4—101no—
396C4—101no—
397C4—101no—
398C4—121no—
399C4—601no—
400C3#1060499411yescharacteristic, complemented, Sylow
401C2—22no—
402C2—241no—
403C2—1201no—
404C2D5⋊#82511yescharacteristic
405C2#1175172011yescharacteristic
406C2C2×#9117411yescharacteristic
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 radical#11754572C2
cosocleC3×C4×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1530
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. C2×#91231C2semidirect
3. C3×#65757C2semidirect
4. #11746505C2semidirect
5. #11746504C2semidirect
26. #65757D3semidirect
324. C3×C5#1530semidirect
381. C5#70806semidirect
400. C3#10604994semidirect

Maximal subgroups

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

subgroupindex
#117545722
C2×#912312
C3×#657572
#117465052
#117465042
#106049943
#708065