Finite Group Databasebeta

← #14313267

Subgroups — #14313267

Order 1920.

532 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C3×#66139C211yesmaximal, characteristic
2#11752420C211yesmaximal, characteristic, complemented
3#11752404C211yesmaximal, characteristic, complemented
4#11746805C214yesmaximal, complemented
5#10604940—31nomaximal, Hall
6C22×C3×C5×D4C411yescharacteristic, complemented
7C2×C3×#709C2211yescharacteristic
8#91989—21no—
9D5⋊#208—21no—
10C3×#4099C412yescomplemented
11C3×#4099C2212yes—
12C3×#4086—21no—
13C3×#4084—21no—
14C3×#4084—21no—
15C3×#4082—21no—
16C3×#4072C411yescharacteristic, complemented
17#91242C2212yes—
18#91240C2212yes—
19#91234—21no—
20#91228—21no—
21#71859—51nomaximal, Hall
22#66139D311yescharacteristic
23#65761—31no—
24#65745—31no—
25#64934—34no—
26C24×C3×C5C2×C412yes—
27C2×C3×C5×D4—21no—
28C2×C3×C5×D4—21no—
29C2×C3×C5×D4—41no—
30C2×C3×C5×D4—41no—
31C22×C3×C4×C5C2×C411yescharacteristic
32C2×C3×C22⋊D5—22no—
33C2×C3×C22⋊D5—22no—
34C2×C3×C22⋊D5C2×C411yescharacteristic
35C2×C3×C22⋊D5C2311yescharacteristic
36C3×#709—41no—
37C3×#709—41no—
38C2×C3×D20D411yescharacteristic
39C2×C3×C4×D5D411yescharacteristic
40C2×C3×C4×D5D411yescharacteristic
41C2×C3×Dic10D411yescharacteristic
42#6763—22no—
43#6762—22no—
44C4⋊ΓL(1,𝔽16)—41no—
45C4×ΓL(1,𝔽16)—41no—
46#6758—41no—
47D5⋊(C3⋊C8)—41no—
48C3×C22⋊Dic5—22no—
49C3×C22⋊Dic5—22no—
50C3×C22⋊Dic5C2×C412yes—
51C3×C4⋊Dic5—21no—
52C3×C4×Dic5—21no—
53C3×#535—51no—
54#5240—51no—
55#5237—51no—
56#4536—54no—
57C22×C5×D4Dic311yescharacteristic, complemented
58C2×#709C2×D311yescharacteristic
59#4130—61no—
60D5⋊M16—61no—
61#4099Dic312yescomplemented
62#4099C2×D312yes—
63#4086—21no—
64#4084—21no—
65#4084—21no—
66#4082—21no—
67#4072Dic311yescharacteristic, complemented
68#4013—32no—
69#4011—32no—
70#4005—61no—
71#3999—61no—
72#2122—151noSylow
73C23×C3×C5—22no—
74C23×C3×C5—42no—
75C23×C3×C5—82no—
76C23×C3×C5C22×C411yescharacteristic
77C22×C3×D5C22⋊C411yescharacteristic
78C22×C3×D5C2×D411yescharacteristic
79C2×ΓL(1,𝔽16)—42no—
80C3×C5×D4—42no—
81C3×C5×D4—41no—
82C3×C5×D4—41no—
83C2×C3×C4×C5—21no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5C22⋊C411yescharacteristic
86C2×C3×C4×C5C22⋊C411yescharacteristic
87C3×C22⋊D5—41no—
88C3×C22⋊D5—41no—
89C3×C22⋊D5—82no—
90C3×C22⋊D5—82no—
91C2×C3×Dic5—22no—
92C2×C3×Dic5C22⋊C411yescharacteristic
93C2×C3×Dic5C2×D411yescharacteristic
94C3×D20—41no—
95C3×C4×D5—21no—
96C3×C4×D5—21no—
97C3×C4×D5—21no—
98C3×C4×D5—21no—
99C3×Dic10—41no—
100C3⋊#170—42no—
101C2×C3×#41—51no—
102C22×C3×D4AGL(1,𝔽5)11yescharacteristic, complemented
103C3×#127—101no—
104C3×#124—101no—
105C3×#121—101no—
106C3×#121—101no—
107C3×#120—52no—
108C3×#120—52no—
109C3×#117—51no—
110#926—101no—
111C2×#208—101no—
112#836—101no—
113#834—52no—
114#834—101no—
115#833—52no—
116C24×C5C2×Dic312yes—
117C2×C5×D4—21no—
118C2×C5×D4—21no—
119C2×C5×D4—41no—
120C2×C5×D4—41no—
121C22×C4×C5C2×Dic311yescharacteristic
122C2×C22⋊D5—22no—
123C2×C22⋊D5—22no—
124C2×C22⋊D5C2×Dic311yescharacteristic
125C2×C22⋊D5C22×D311yescharacteristic
126#709—41no—
127#709—41no—
128C2×D20#6711yescharacteristic
129C2×C4×D5#6711yescharacteristic
130C2×C4×D5#6711yescharacteristic
131C2×Dic10#6711yescharacteristic
132C22⋊AGL(1,𝔽5)—62no—
133#704—62no—
134C4⋊AGL(1,𝔽5)—121no—
135C4×AGL(1,𝔽5)—121no—
136#700—121no—
137D5⋊C8—121no—
138C22⋊Dic5—22no—
139C22⋊Dic5—22no—
140C22⋊Dic5C2×Dic312yes—
141C4⋊Dic5—21no—
142C4×Dic5—21no—
143#535—51no—
144#413—151no—
145#410—151no—
146AΣL(1,𝔽16)—154no—
147C22×C3×C5—21no—
148C22×C3×C5—41no—
149C22×C3×C5—42no—
150C22×C3×C5—42no—
151C22×C3×C5—42no—
152C22×C3×C5—84no—
153C22×C3×C5C2×C22⋊C411yescharacteristic
154C2×C3×D5—21no—
155C2×C3×D5—21no—
156C2×C3×D5—41no—
157C2×C3×D5—41no—
158ΓL(1,𝔽16)—82no—
159C3×C4×C5—21no—
160C3×C4×C5#9911yescharacteristic
161C3×C4×C5#9911yescharacteristic
162C3×Dic5—21no—
163C3×Dic5—21no—
164C3×Dic5—42no—
165C24×C3C2×AGL(1,𝔽5)12yes—
166C3×#41—201no—
167C3×#41—201no—
168C2×C3×Q8—51no—
169C2×C3×D4—21no—
170C2×C3×D4—21no—
171C2×C3×D4—41no—
172C2×C3×D4—41no—
173C2×C3×D4—51no—
174C2×C3×D4—51no—
175C2×C3×D4—51no—
176C2×C3×D4—102no—
177C2×C3×D4—102no—
178C22×C3×C4—51no—
179C22×C3×C4—51no—
180C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
181C3×C4⋊C4—101no—
182C3×C22⋊C4—52no—
183C3×C22⋊C4—102no—
184C3×C22⋊C4—102no—
185C3×C42—101no—
186#217—102no—
187C4⋊Dic3—201no—
188C4×Dic3—201no—
189#208—102no—
190#208—201no—
191C2×C3⋊C8—201no—
192C23×C5—22no—
193C23×C5—42no—
194C23×C5—82no—
195C23×C5C22×Dic311yescharacteristic
196C22×D5#21711yescharacteristic
197C22×D5C2×#6711yescharacteristic
198C2×AGL(1,𝔽5)—122no—
199C5×D4—42no—
200C5×D4—41no—
201C5×D4—41no—
202C2×C4×C5—21no—
203C2×C4×C5—21no—
204C2×C4×C5#21711yescharacteristic
205C2×C4×C5#21711yescharacteristic
206C22⋊D5—41no—
207C22⋊D5—41no—
208C22⋊D5—82no—
209C22⋊D5—82no—
210C2×Dic5—22no—
211C2×Dic5#21711yescharacteristic
212C2×Dic5C2×#6711yescharacteristic
213D20—41no—
214C4×D5—21no—
215C4×D5—21no—
216C4×D5—21no—
217C4×D5—21no—
218Dic10—41no—
219#170—122no—
220C2×#41—51no—
221C22×D4ΓL(1,𝔽16)11yescharacteristic, complemented
222C2×M16—301no—
223#127—101no—
224#124—101no—
225#121—101no—
226#121—101no—
227#120—52no—
228#120—52no—
229#117—51no—
230#117—301no—
231#101—301no—
232#100—152no—
233#99—152no—
234#99—301no—
235C2×C3×C5—21no—
236C2×C3×C5—41no—
237C2×C3×C5—82no—
238C2×C3×C5C2×#9911yescharacteristic
239C3×D5—41no—
240C3×D5—41no—
241C23×C3—22no—
242C23×C3—42no—
243C23×C3—51no—
244C23×C3—51no—
245C23×C3—82no—
246C23×C3C22×AGL(1,𝔽5)11yescharacteristic
247C3×Q8—201no—
248C3×D4—42no—
249C3×D4—41no—
250C3×D4—41no—
251C3×D4—201no—
252C3×D4—201no—
253C3×D4—201no—
254C3×D4—402no—
255C3×D4—402no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—51no—
259C2×C3×C4—51no—
260C2×C3×C4—101no—
261C2×C3×C4—101no—
262C2×C3×C4—101no—
263C2×C3×C4—101no—
264C2×C3×C4—102no—
265C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
266C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
267C2×Dic3—202no—
268C3⋊C8—202no—
269C22×C5—21no—
270C22×C5—41no—
271C22×C5—42no—
272C22×C5—42no—
273C22×C5—42no—
274C22×C5—84no—
275C22×C5C2×#21711yescharacteristic
276C2×D5—21no—
277C2×D5—21no—
278C2×D5—41no—
279C2×D5—41no—
280AGL(1,𝔽5)—242no—
281C4×C5—21no—
282C4×C5#83411yescharacteristic
283C4×C5#83411yescharacteristic
284Dic5—21no—
285Dic5—21no—
286Dic5—42no—
287C24C2×ΓL(1,𝔽16)12yes—
288#41—201no—
289#41—201no—
290C2×Q8—51no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—51no—
296C2×D4—51no—
297C2×D4—51no—
298C2×D4—102no—
299C2×D4—102no—
300C22×C4—51no—
301C22×C4—51no—
302C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
303M16—302no—
304M16—601no—
305C2×C8—601no—
306C4⋊C4—101no—
307C4⋊C4—601no—
308C22⋊C4—52no—
309C22⋊C4—102no—
310C22⋊C4—102no—
311C22⋊C4—302no—
312C42—101no—
313C42—601no—
314C3×C5#212211yescharacteristic, complemented, Hall
315C22×C3—21no—
316C22×C3—41no—
317C22×C3—42no—
318C22×C3—42no—
319C22×C3—42no—
320C22×C3—84no—
321C22×C3—101no—
322C22×C3—101no—
323C22×C3—201no—
324C22×C3—201no—
325C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
326C3×C4—21no—
327C3×C4—101no—
328C3×C4—101no—
329C3×C4—202no—
330C3×C4#401111yescharacteristic
331C3×C4#401111yescharacteristic
332Dic3—402no—
333C2×C5—21no—
334C2×C5—41no—
335C2×C5—82no—
336C2×C5C2×#83411yescharacteristic
337D5—41no—
338D5—41no—
339C23—22no—
340C23—42no—
341C23—51no—
342C23—51no—
343C23—82no—
344C23C22×ΓL(1,𝔽16)11yescharacteristic
345Q8—201no—
346D4—42no—
347D4—41no—
348D4—41no—
349D4—201no—
350D4—201no—
351D4—201no—
352D4—402no—
353D4—402no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—51no—
357C2×C4—51no—
358C2×C4—101no—
359C2×C4—101no—
360C2×C4—101no—
361C2×C4—101no—
362C2×C4—102no—
363C2×C4—602no—
364C2×C4#676311yescharacteristic
365C2×C4#676311yescharacteristic
366C8—602no—
367C2×C3—21no—
368C2×C3—41no—
369C2×C3—82no—
370C2×C3—201no—
371C2×C3—201no—
372C2×C3C2×#401111yescharacteristic
373C5#7185911yescharacteristic, complemented, Sylow
374C22—21no—
375C22—41no—
376C22—42no—
377C22—42no—
378C22—42no—
379C22—84no—
380C22—101no—
381C22—101no—
382C22—201no—
383C22—201no—
384C22C2×#676311yescharacteristic
385C4—21no—
386C4—101no—
387C4—101no—
388C4—202no—
389C4—1202no—
390C4#9124011yescharacteristic
391C4#9124011yescharacteristic
392C3#1060494011yescharacteristic, complemented, Sylow
393C2—21no—
394C2—41no—
395C2—82no—
396C2—201no—
397C2—201no—
398C2C2×#9124011yescharacteristic
subgroupG/H
centerC2C2×#91240
commutatorC23×C3×C5C22×C4
FrattiniC23C22×ΓL(1,𝔽16)
FittingC22×C3×C5×D4C4
socleC2×C3×C5C2×#99
prime radicalC3×#66139C2
cosocleC2×C3×C22⋊D5C23
hypercenterC22×D4ΓL(1,𝔽16)
hypocenterC3×C5#2122
LCSG ▷ C23×C3×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #11752420C2semidirect
3. #11752404C2semidirect
4. #11746805C2semidirect
6. C22×C3×C5×D4C4semidirect
10. C3×#4099C4semidirect
16. C3×#4072C4semidirect
57. C22×C5×D4Dic3semidirect
61. #4099Dic3semidirect
67. #4072Dic3semidirect
102. C22×C3×D4AGL(1,𝔽5)semidirect
221. C22×D4ΓL(1,𝔽16)semidirect
314. C3×C5#2122semidirect
373. C5#71859semidirect
392. C3#10604940semidirect

Maximal subgroups

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

subgroupindex
C3×#661392
#117524202
#117524042
#117468052
#106049403
#718595