Finite Group Databasebeta

← #14283957

Subgroups — #14283957

Order 1920.

468 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 82 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#11751873C211yesmaximal, characteristic, complemented
3#11751756C211yesmaximal, characteristic, complemented
4#11746792C211yesmaximal, characteristic, complemented
5C3×#64921C211yesmaximal, characteristic, complemented
6#11746507C211yesmaximal, characteristic, complemented
7#11746506C211yesmaximal, characteristic, complemented
8#10604396—31nomaximal, Hall
9C2×#6740—21no—
10C2×#6738—21no—
11#91827C411yescharacteristic
12C5×D4×Dic3C411yescharacteristic
13C3×#4082C2211yescharacteristic
14#91562—21no—
15#91556—21no—
16#91531—21no—
17#91529—21no—
18C4×#1200C2211yescharacteristic
19#91390C411yescharacteristic
20#91388C2211yescharacteristic
21Dic3×Dic10C411yescharacteristic
22#91231C2211yescharacteristic
23#91231C2211yescharacteristic
24C3×#4002C2211yescharacteristic
25C3×#4002C2211yescharacteristic
26#91169—21no—
27Dic3×#170—21no—
28#68341—51nomaximal, Hall
29#65891—31no—
30C4×#700—31no—
31#65676—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#6738—24no—
49#6719—21no—
50C4⋊Dic15C2×C411yescharacteristic
51C5×#217—21no—
52C5×C4⋊Dic3C2×C411yescharacteristic
53C4×C5×Dic3C2×C411yescharacteristic
54C3×C22⋊Dic5—21no—
55C3×C22⋊Dic5—21no—
56C3×C4×Dic5C2311yescharacteristic
57Dic3⋊Dic5—21no—
58Dic3⋊Dic5—21no—
59#6669—21no—
60#6668—21no—
61#6667—21no—
62Dic3×Dic5—21no—
63Dic3×Dic5D411yescharacteristic
64Dic3×Dic5D411yescharacteristic
65#5680—51no—
66#4707—51no—
67D3×#97—51no—
68C3×#329—51no—
69#4540—51no—
70#4465—51no—
71#4465—51no—
72C2×#700—61no—
73C2×D5⋊C8—61no—
74C4×C5×D4—31no—
75#4084—31no—
76#4082C2×D311yescharacteristic
77C4×C22⋊D5—61no—
78#4072—61no—
79#4043—31no—
80#4036—31no—
81#4029—61no—
82#4025—61no—
83C42×D5—31no—
84C4×Dic10—31no—
85#4002—31no—
86#4002—31no—
87#4002—61no—
88#4002C2×D311yescharacteristic
89#4002C2×D311yescharacteristic
90C4×#170—61no—
91#1524—151noSylow
92C23×C3×C5—21no—
93C22×D15C22⋊C411yescharacteristic
94C3×C5×D4—41no—
95C2×C3×C4×C5C22×C411yescharacteristic
96#1220—42no—
97C2×Dic15—21no—
98C2×Dic15C22⋊C411yescharacteristic
99C4×D15—41no—
100C2×C5×Dic3—21no—
101C2×C5×Dic3—42no—
102C2×C5×Dic3C22⋊C411yescharacteristic
103C2×C5×Dic3C22⋊C411yescharacteristic
104C2×C3×Dic5—21no—
105C2×C3×Dic5C2×D411yescharacteristic
106C2×C3×Dic5C2×D411yescharacteristic
107C3×Dic10—41no—
108#1200—22no—
109#1200—22no—
110C3⋊#170—22no—
111C3⋊#170—22no—
112C3×#170—22no—
113C3×#170—22no—
114C3×#124—51no—
115#946—51no—
116Q8×Dic3—51no—
117#938—51no—
118D4×Dic3AGL(1,𝔽5)11yescharacteristic
119C2×ΓL(1,𝔽25)—101no—
120C2×D3×C8—101no—
121#883—101no—
122#67⋊C4—101no—
123#879—101no—
124#877—101no—
125C42×D3—51no—
126#870—51no—
127C3×#97—51no—
128C3×#97—51no—
129#815—101no—
130C8×Dic3—101no—
131#803—51no—
132#803—51no—
133C2×C5×D4C4×D311yescharacteristic
134C22×C4×C5—61no—
135C2×C22⋊D5—61no—
136C2×C4×D5—31no—
137C2×C4×D5—31no—
138C2×C4×D5—31no—
139C2×Dic10C4×D311yescharacteristic
140C2×#170—21no—
141C2×#170—21no—
142C2×#170—61no—
143C2×#170—61no—
144#700—64no—
145D5⋊C8—64no—
146C5×C4⋊C4—31no—
147C5×C22⋊C4—61no—
148C42×C5—31no—
149C22⋊Dic5—21no—
150C22⋊Dic5—21no—
151C22⋊Dic5—61no—
152#685—61no—
153C4⋊Dic5—31no—
154C4⋊Dic5—61no—
155C4⋊Dic5—61no—
156#683—61no—
157#683—61no—
158C4×Dic5—31no—
159C4×Dic5—31no—
160C4×Dic5—61no—
161C4×Dic5C22×D311yescharacteristic
162#529—151no—
163C4×M16—151no—
164C2×#97—151no—
165#330—151no—
166#330—151no—
167#329—51no—
168#329—151no—
169C22×C3×C5—41no—
170C22×C3×C5—41no—
171C22×C3×C5—41no—
172C22×C3×C5C2×C22⋊C411yescharacteristic
173C2×D15—21no—
174C2×D15—21no—
175C2×D15#10412yes—
176C3×C4×C5—21no—
177Dic15—21no—
178Dic15—41no—
179C3×Dic5—21no—
180C3×Dic5—21no—
181C3×Dic5—41no—
182C5×Dic3—21no—
183C5×Dic3—41no—
184C5×Dic3#10412yes—
185C2×C3×Q8—51no—
186C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
187C2×#67—101no—
188C22×Dic3—21no—
189C2×C4×D3—51no—
190C2×C4×D3—51no—
191C2×C4×D3—51no—
192C2×C3×C8—101no—
193C2×C3×C8—101no—
194C3×C22⋊C4—101no—
195C3×C22⋊C4—101no—
196C3×C42—51no—
197#217—21no—
198#217—101no—
199(C2×D3)⋊C4—101no—
200C4⋊Dic3—51no—
201C4⋊Dic3—101no—
202C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
203Dic3⋊C4—101no—
204Dic3⋊C4—101no—
205Dic3⋊C4—101no—
206C4×Dic3—51no—
207C4×Dic3—51no—
208C4×Dic3—101no—
209C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
210C2×C3⋊C8—101no—
211C2×C3⋊C8—101no—
212ΓL(1,𝔽25)—104no—
213D3×C8—104no—
214C23×C5—21no—
215C22×D5—31no—
216C5×D4—41no—
217C2×C4×C5—31no—
218C2×C4×C5—31no—
219C2×C4×C5—61no—
220C2×C4×C5—122no—
221C2×C4×C5C2×C4×D311yescharacteristic
222C22⋊D5—122no—
223C2×Dic5—21no—
224C2×Dic5—31no—
225C2×Dic5—61no—
226C2×Dic5D3×D411yescharacteristic
227C2×Dic5D3×D411yescharacteristic
228C4×D5—62no—
229C4×D5—62no—
230C4×D5—121no—
231Dic10—41no—
232#170—22no—
233#170—22no—
234#170—62no—
235#170—62no—
236C2×M16—301no—
237C22×C8—301no—
238#126—301no—
239#125—151no—
240#124—51no—
241#123—301no—
242C22⋊Q8—151no—
243#121—151no—
244C4×Q8—151no—
245C4×D4—31no—
246C4×D4—301no—
247#117—301no—
248C2×C42—151no—
249#97—51no—
250#97—51no—
251#97—151no—
252#97—151no—
253#97—301no—
254C4×C8—301no—
255C2×C3×C5—81no—
256C2×C3×C5#41311yescharacteristic
257C2×C3×C5C2×#10411yescharacteristic
258C2×C3×C5C2×#10411yescharacteristic
259D15—22no—
260C23×C3—21no—
261C22×D3—51no—
262C3×Q8—201no—
263C3×D4—41no—
264C2×C3×C4—51no—
265C2×C3×C4—51no—
266C2×C3×C4—101no—
267C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
268#67—202no—
269C2×Dic3—21no—
270C2×Dic3—42no—
271C2×Dic3—51no—
272C2×Dic3—101no—
273C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
274C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
275C4×D3—102no—
276C4×D3—102no—
277C4×D3—201no—
278C3×C8—102no—
279C3×C8—102no—
280C3⋊C8—102no—
281C3⋊C8—102no—
282C22×C5—41no—
283C22×C5—41no—
284C22×C5—41no—
285C22×C5D3×C22⋊C411yescharacteristic
286C2×D5—32no—
287C2×D5—61no—
288C2×D5—61no—
289C4×C5—21no—
290C4×C5—32no—
291C4×C5—61no—
292C4×C5—121no—
293Dic5—21no—
294Dic5—21no—
295Dic5—41no—
296Dic5—61no—
297Dic5—121no—
298C2×Q8—51no—
299C2×D4—301no—
300C2×D4D3×AGL(1,𝔽5)11yescharacteristic
301C22×C4—61no—
302C22×C4—151no—
303C22×C4—151no—
304C22×C4—151no—
305M16—304no—
306C2×C8—101no—
307C2×C8—101no—
308C2×C8—304no—
309C2×C8—301no—
310C2×C8—301no—
311C4⋊C4—31no—
312C4⋊C4—151no—
313C4⋊C4—301no—
314C4⋊C4—301no—
315C4⋊C4—301no—
316C4⋊C4—301no—
317C22⋊C4—61no—
318C22⋊C4—101no—
319C22⋊C4—101no—
320C22⋊C4—301no—
321C22⋊C4—301no—
322C42—31no—
323C42—51no—
324C42—151no—
325C42—151no—
326C42—301no—
327C3×C5#152411yescharacteristic, complemented, Hall
328C22×C3—41no—
329C22×C3—41no—
330C22×C3—41no—
331C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
332C2×D3—52no—
333C2×D3—101no—
334C2×D3—101no—
335C3×C4—21no—
336C3×C4—101no—
337C3×C4—101no—
338C3×C4—201no—
339Dic3—21no—
340Dic3—41no—
341Dic3—101no—
342Dic3—201no—
343Dic3#400812yes—
344C2×C5—81no—
345C2×C5#474511yescharacteristic
346C2×C5D3×#10411yescharacteristic
347C2×C5D3×#10411yescharacteristic
348D5—62no—
349C23—21no—
350C23—151no—
351Q8—201no—
352D4—41no—
353D4—602no—
354C2×C4—31no—
355C2×C4—31no—
356C2×C4—51no—
357C2×C4—51no—
358C2×C4—61no—
359C2×C4—101no—
360C2×C4—122no—
361C2×C4—151no—
362C2×C4—302no—
363C2×C4—302no—
364C2×C4—301no—
365C2×C4—601no—
366C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
367C8—102no—
368C8—102no—
369C8—302no—
370C8—302no—
371C2×C3—81no—
372C2×C3#6576111yescharacteristic
373C2×C3C2×#400811yescharacteristic
374C2×C3D5⋊#10411yescharacteristic
375D3—102no—
376C5#6834111yescharacteristic, complemented, Sylow
377C22—41no—
378C22—41no—
379C22—41no—
380C22—152no—
381C22—301no—
382C22—301no—
383C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
384C4—21no—
385C4—32no—
386C4—61no—
387C4—101no—
388C4—101no—
389C4—121no—
390C4—201no—
391C4—301no—
392C4—601no—
393C3#1060439611yescharacteristic, complemented, Sylow
394C2—81no—
395C2—302no—
396C2#1175193511yescharacteristic
397C2D3×#400811yescharacteristic
398C2#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#1524
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. #11751873C2semidirect
3. #11751756C2semidirect
4. #11746792C2semidirect
5. C3×#64921C2semidirect
6. #11746507C2semidirect
7. #11746506C2semidirect
33. #64921D3semidirect
327. C3×C5#1524semidirect
376. C5#68341semidirect
393. C3#10604396semidirect

Maximal subgroups

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

subgroupindex
#117548782
#117518732
#117517562
#117467922
C3×#649212
#117465072
#117465062
#106043963
#683415