Finite Group Databasebeta

← #14284164

Subgroups — #14284164

Order 1920.

432 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 80 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#11754878C211yesmaximal, characteristic
2#11751808C211yesmaximal, characteristic, complemented
3#11751756C211yesmaximal, characteristic, complemented
4#11746792C211yesmaximal, characteristic, complemented
5C3×#64921C211yesmaximal, characteristic, complemented
6#11746507C211yesmaximal, characteristic, complemented
7#11746506C211yesmaximal, characteristic, complemented
8#10604397—31nomaximal, Hall
9C2×#6740—21no—
10#91827C411yescharacteristic
11C5×D4×Dic3C411yescharacteristic
12C3×#4082C2211yescharacteristic
13#91562—21no—
14#91556—21no—
15#91531—21no—
16#91529—21no—
17C4×#1200C2211yescharacteristic
18#91390C411yescharacteristic
19#91388C2211yescharacteristic
20Dic3×Dic10C411yescharacteristic
21#91231C2211yescharacteristic
22#91231C2211yescharacteristic
23C3×#4002C2211yescharacteristic
24C3×#4002C2211yescharacteristic
25Dic3⋊#170—21no—
26#91171—21no—
27Dic3×#170—21no—
28#68344—51nomaximal, Hall
29#65891—31no—
30#65683—31no—
31C4×#700—31no—
32#64921—31no—
33#64921D311yescharacteristic, complemented
34#64870—31no—
35#64870—31no—
36C2×C3×C5×D4C2×C411yescharacteristic
37C2×#1220—21no—
38C2×C4×D15C2×C411yescharacteristic
39C22×C5×Dic3—21no—
40C2×C3×Dic10C2×C411yescharacteristic
41C2×#1200D411yescharacteristic
42C2×#1200D411yescharacteristic
43C2×C3⋊#170—21no—
44C2×C3⋊#170—21no—
45C2×C3×#170—21no—
46C2×C3×#170—21no—
47#6740—24no—
48#6719—21no—
49C4⋊Dic15C2×C411yescharacteristic
50C5×#217—21no—
51C5×C4⋊Dic3C2×C411yescharacteristic
52C4×C5×Dic3C2×C411yescharacteristic
53C3×C22⋊Dic5—21no—
54C3×C22⋊Dic5—21no—
55C3×C4×Dic5C2311yescharacteristic
56Dic3⋊Dic5—21no—
57Dic3⋊Dic5—21no—
58#6669—21no—
59#6668—21no—
60#6667—21no—
61Dic3×Dic5—21no—
62Dic3×Dic5D411yescharacteristic
63Dic3×Dic5D411yescharacteristic
64#5680—51no—
65#4707—51no—
66#4705—51no—
67C3×#329—51no—
68#4540—51no—
69#4465—51no—
70#4465—51no—
71C2×#700—61no—
72C4×C5×D4—31no—
73#4084—31no—
74#4082C2×D311yescharacteristic
75C4×C22⋊D5—61no—
76#4072—61no—
77#4043—31no—
78#4036—31no—
79#4029—61no—
80#4025—61no—
81C42×D5—31no—
82C4×Dic10—31no—
83#4003—61no—
84#4002—31no—
85#4002—31no—
86#4002C2×D311yescharacteristic
87#4002C2×D311yescharacteristic
88C4⋊#170—61no—
89C4×#170—61no—
90#1529—151noSylow
91C23×C3×C5—21no—
92C22×D15C22⋊C411yescharacteristic
93C3×C5×D4—41no—
94C2×C3×C4×C5C22×C411yescharacteristic
95#1220—42no—
96C2×Dic15—21no—
97C2×Dic15C22⋊C411yescharacteristic
98C4×D15—41no—
99C2×C5×Dic3—21no—
100C2×C5×Dic3—42no—
101C2×C5×Dic3C22⋊C411yescharacteristic
102C2×C5×Dic3C22⋊C411yescharacteristic
103C2×C3×Dic5—21no—
104C2×C3×Dic5C2×D411yescharacteristic
105C2×C3×Dic5C2×D411yescharacteristic
106C3×Dic10—41no—
107#1200—22no—
108#1200—41no—
109C3⋊#170—22no—
110C3⋊#170—41no—
111C3×#170—22no—
112C3×#170—41no—
113C3×#124—51no—
114#946—51no—
115Q8×Dic3—51no—
116#938—51no—
117D4×Dic3AGL(1,𝔽5)11yescharacteristic
118C2×ΓL(1,𝔽25)—101no—
119#883—101no—
120#67⋊C4—101no—
121#879—101no—
122#877—101no—
123C42×D3—51no—
124#870—51no—
125C3×#97—51no—
126C3×#97—51no—
127(C2×D3)⋊C8—101no—
128Dic3⋊C8—101no—
129C8×Dic3—101no—
130#803—51no—
131#803—51no—
132C2×C5×D4C4×D311yescharacteristic
133C22×C4×C5—61no—
134C2×C22⋊D5—61no—
135C2×C4×D5—31no—
136C2×C4×D5—31no—
137C2×C4×D5—31no—
138C2×Dic10C4×D311yescharacteristic
139C2×#170—21no—
140C2×#170—21no—
141C2×#170—61no—
142C2×#170—61no—
143#700—64no—
144C5×C4⋊C4—31no—
145C5×C22⋊C4—61no—
146C42×C5—31no—
147C22⋊Dic5—21no—
148C22⋊Dic5—21no—
149C22⋊Dic5—61no—
150#685—61no—
151C4⋊Dic5—31no—
152C4⋊Dic5—61no—
153C4⋊Dic5—61no—
154#683—61no—
155#683—61no—
156C4×Dic5—31no—
157C4×Dic5—31no—
158C4×Dic5—61no—
159C4×Dic5C22×D311yescharacteristic
160#529—151no—
161#432—151no—
162C4×M16—151no—
163#330—151no—
164#330—151no—
165#329—51no—
166#329—151no—
167C22×C3×C5—41no—
168C22×C3×C5—41no—
169C22×C3×C5—41no—
170C22×C3×C5C2×C22⋊C411yescharacteristic
171C2×D15—21no—
172C2×D15—21no—
173C2×D15—21no—
174C3×C4×C5—21no—
175Dic15—21no—
176Dic15—41no—
177C3×Dic5—21no—
178C3×Dic5—21no—
179C3×Dic5—41no—
180C5×Dic3—21no—
181C5×Dic3—41no—
182C5×Dic3#10412yes—
183C2×C3×Q8—51no—
184C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
185C2×#67—101no—
186C22×Dic3—21no—
187C2×C4×D3—51no—
188C2×C4×D3—51no—
189C2×C4×D3—51no—
190C2×C3×C8—101no—
191C2×C3×C8—101no—
192C3×C22⋊C4—101no—
193C3×C22⋊C4—101no—
194C3×C42—51no—
195#217—21no—
196#217—101no—
197(C2×D3)⋊C4—101no—
198C4⋊Dic3—51no—
199C4⋊Dic3—101no—
200C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
201Dic3⋊C4—101no—
202Dic3⋊C4—101no—
203Dic3⋊C4—101no—
204C4×Dic3—51no—
205C4×Dic3—51no—
206C4×Dic3—101no—
207C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
208C2×C3⋊C8—101no—
209C2×C3⋊C8—101no—
210ΓL(1,𝔽25)—104no—
211C23×C5—21no—
212C22×D5—31no—
213C5×D4—41no—
214C2×C4×C5—31no—
215C2×C4×C5—31no—
216C2×C4×C5—61no—
217C2×C4×C5—122no—
218C2×C4×C5C2×C4×D311yescharacteristic
219C22⋊D5—122no—
220C2×Dic5—21no—
221C2×Dic5—31no—
222C2×Dic5—61no—
223C2×Dic5D3×D411yescharacteristic
224C2×Dic5D3×D411yescharacteristic
225C4×D5—62no—
226C4×D5—121no—
227C4×D5—121no—
228Dic10—41no—
229#170—22no—
230#170—41no—
231#170—62no—
232#170—121no—
233C2×M16—301no—
234#126—301no—
235#125—151no—
236#124—51no—
237#123—301no—
238C22⋊Q8—151no—
239#121—151no—
240C4×Q8—151no—
241C4×D4—31no—
242C4×D4—301no—
243#117—301no—
244C2×C42—151no—
245C4⋊C8—301no—
246C22⋊C8—301no—
247#97—51no—
248#97—51no—
249#97—151no—
250#97—151no—
251C4×C8—301no—
252C2×C3×C5—81no—
253C2×C3×C5#41311yescharacteristic
254C2×C3×C5C2×#10411yescharacteristic
255C2×C3×C5#42111yescharacteristic
256D15—41no—
257C23×C3—21no—
258C22×D3—51no—
259C3×Q8—201no—
260C3×D4—41no—
261C2×C3×C4—51no—
262C2×C3×C4—51no—
263C2×C3×C4—101no—
264C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
265#67—202no—
266C2×Dic3—21no—
267C2×Dic3—42no—
268C2×Dic3—51no—
269C2×Dic3—101no—
270C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
271C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
272C4×D3—102no—
273C4×D3—201no—
274C4×D3—201no—
275C3×C8—102no—
276C3×C8—201no—
277C3⋊C8—102no—
278C3⋊C8—201no—
279C22×C5—41no—
280C22×C5—41no—
281C22×C5—41no—
282C22×C5D3×C22⋊C411yescharacteristic
283C2×D5—61no—
284C2×D5—61no—
285C2×D5—61no—
286C4×C5—21no—
287C4×C5—32no—
288C4×C5—61no—
289C4×C5—121no—
290Dic5—21no—
291Dic5—21no—
292Dic5—41no—
293Dic5—61no—
294Dic5—121no—
295C2×Q8—51no—
296C2×D4—301no—
297C2×D4D3×AGL(1,𝔽5)11yescharacteristic
298C22×C4—61no—
299C22×C4—151no—
300C22×C4—151no—
301C22×C4—151no—
302M16—304no—
303C2×C8—101no—
304C2×C8—101no—
305C2×C8—301no—
306C2×C8—301no—
307C4⋊C4—31no—
308C4⋊C4—151no—
309C4⋊C4—301no—
310C4⋊C4—301no—
311C4⋊C4—301no—
312C4⋊C4—301no—
313C22⋊C4—61no—
314C22⋊C4—101no—
315C22⋊C4—101no—
316C22⋊C4—301no—
317C22⋊C4—301no—
318C42—31no—
319C42—51no—
320C42—151no—
321C42—151no—
322C42—301no—
323C3×C5#152911yescharacteristic, complemented, Hall
324C22×C3—41no—
325C22×C3—41no—
326C22×C3—41no—
327C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
328C2×D3—101no—
329C2×D3—101no—
330C2×D3—101no—
331C3×C4—21no—
332C3×C4—101no—
333C3×C4—101no—
334C3×C4—201no—
335Dic3—21no—
336Dic3—41no—
337Dic3—101no—
338Dic3—201no—
339Dic3#400812yes—
340C2×C5—81no—
341C2×C5#474511yescharacteristic
342C2×C5D3×#10411yescharacteristic
343C2×C5#482111yescharacteristic
344D5—121no—
345C23—21no—
346C23—151no—
347Q8—201no—
348D4—41no—
349D4—602no—
350C2×C4—31no—
351C2×C4—31no—
352C2×C4—51no—
353C2×C4—51no—
354C2×C4—61no—
355C2×C4—101no—
356C2×C4—122no—
357C2×C4—151no—
358C2×C4—302no—
359C2×C4—301no—
360C2×C4—601no—
361C2×C4—601no—
362C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
363C8—102no—
364C8—201no—
365C8—302no—
366C8—601no—
367C2×C3—81no—
368C2×C3#6576111yescharacteristic
369C2×C3C2×#400811yescharacteristic
370C2×C3#6579511yescharacteristic
371D3—201no—
372C5#6834411yescharacteristic, complemented, Sylow
373C22—41no—
374C22—41no—
375C22—41no—
376C22—301no—
377C22—301no—
378C22—301no—
379C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
380C4—21no—
381C4—32no—
382C4—61no—
383C4—101no—
384C4—101no—
385C4—121no—
386C4—201no—
387C4—301no—
388C4—601no—
389C3#1060439711yescharacteristic, complemented, Sylow
390C2—81no—
391C2—601no—
392C2D3×#400811yescharacteristic
393C2#1175194911yescharacteristic
394C2#1175204911yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC2×C3×C5×D4C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radical#91827C4
cosocleC3×C4×Dic5C23
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5#1529
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #11751808C2semidirect
3. #11751756C2semidirect
4. #11746792C2semidirect
5. C3×#64921C2semidirect
6. #11746507C2semidirect
7. #11746506C2semidirect
33. #64921D3semidirect
323. C3×C5#1529semidirect
372. C5#68344semidirect
389. C3#10604397semidirect

Maximal subgroups

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

subgroupindex
#117548782
#117518082
#117517562
#117467922
C3×#649212
#117465072
#117465062
#106043973
#683445