Finite Group Databasebeta

← #14283952

Subgroups — #14283952

Order 1920.

468 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 86 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#11752620C211yesmaximal, characteristic
2#11750808C211yesmaximal, characteristic, complemented
3#11746983C211yesmaximal, characteristic, complemented
4C5×#4465C211yesmaximal, characteristic, complemented
5C3×#64684C211yesmaximal, characteristic, complemented
6#11745850C211yesmaximal, characteristic, complemented
7#11745846C211yesmaximal, characteristic, complemented
8#10599154—31nomaximal, Hall
9C2×#6705—21no—
10C42×D15C2211yescharacteristic
11C5×#870C2211yescharacteristic
12C3×#4021C2211yescharacteristic
13#91465C411yescharacteristic
14#91434C411yescharacteristic
15#91396—21no—
16#91394—21no—
17#91390C411yescharacteristic
18#91366—21no—
19#91354—21no—
20#91331C411yescharacteristic
21C2×#6648—21no—
22C3×C5×#97C2211yescharacteristic
23C8×Dic15—21no—
24#91087C2211yescharacteristic
25C5×#803C2211yescharacteristic
26C3×#3935C2211yescharacteristic
27#90954—21no—
28#68341—51nomaximal, Hall
29#66025—31no—
30#64996—31no—
31D5×#97—31no—
32C5×#330—31no—
33#64763—31no—
34#64684—31no—
35#64684D311yescharacteristic, complemented
36C2×C4×D15C2×C411yescharacteristic
37C2×C4×D15D411yescharacteristic
38C2×C4×D15D411yescharacteristic
39C2×C3×D20C2×C411yescharacteristic
40C2×C3×Dic10C2×C411yescharacteristic
41C2×#1202—21no—
42C2×D5×Dic3—21no—
43C2×C3×C5×C8—21no—
44C3×C42×C5C2311yescharacteristic
45C4×Dic15C2×C411yescharacteristic
46C4×Dic15D411yescharacteristic
47C4×Dic15D411yescharacteristic
48C2×C3⋊#168—21no—
49#6705—24no—
50C5×C4⋊Dic3C2×C411yescharacteristic
51C5×C4⋊Dic3C2×C411yescharacteristic
52C5×Dic3⋊C4—21no—
53C5×Dic3⋊C4—21no—
54C2×C5×C3⋊C8—21no—
55C3×#685—21no—
56C3×#685—21no—
57C2×C3×#168—21no—
58Dic3⋊Dic5—21no—
59#6668—21no—
60#6667—21no—
61#6665—21no—
62#6665—21no—
63Dic3×Dic5—21no—
64#6648—24no—
65#5680—51no—
66#4707—51no—
67D3×#97—51no—
68C3×#329—51no—
69#4540—51no—
70#4465—51no—
71#4465D511yescharacteristic, complemented
72C5×#125—31no—
73C2×#676—61no—
74C2×C8×D5—61no—
75#4044—61no—
76#4043—31no—
77#4041—31no—
78#4040—61no—
79#4039—31no—
80#4039—61no—
81#4038—61no—
82#4033—31no—
83#4021C2×D311yescharacteristic
84C42×D5—31no—
85C5×#97—31no—
86C5×#97C2×D311yescharacteristic
87#3947—61no—
88C8×Dic5—61no—
89#3935—31no—
90#3935C2×D311yescharacteristic
91#1524—151noSylow
92C22×D15C22⋊C411yescharacteristic
93C22×C3×D5—21no—
94C2×C3×C4×C5C22×C411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×Dic15C22⋊C411yescharacteristic
98C2×Dic15C22⋊C411yescharacteristic
99C2×Dic15C22⋊C411yescharacteristic
100C4×D15—22no—
101C4×D15—22no—
102C4×D15—41no—
103C2×C5×Dic3—21no—
104C2×C5×Dic3—21no—
105C2×C3×Dic5—21no—
106C3×D20—41no—
107C3×Dic10—41no—
108#1202—42no—
109D5×Dic3—42no—
110C3×C5×C8—22no—
111C3⋊#168—22no—
112C3×#168—22no—
113C5×C3⋊C8—22no—
114C3×#124—51no—
115#946—51no—
116Q8×Dic3—51no—
117#938—51no—
118D4×Dic3—51no—
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#870C2×D511yescharacteristic
127C3×#97—51no—
128C3×#97C2×D511yescharacteristic
129#815—101no—
130C8×Dic3—101no—
131#803—51no—
132#803C2×D511yescharacteristic
133C2×D20—61no—
134C2×D20C4×D311yescharacteristic
135C2×C4×D5—31no—
136C2×C4×D5—31no—
137C2×C4×D5—31no—
138C2×C4×D5—61no—
139C2×Dic10C4×D311yescharacteristic
140C2×C5×C8—21no—
141C2×C5×C8—61no—
142C5×C4⋊C4—31no—
143C5×C4⋊C4—31no—
144C5×C4⋊C4—61no—
145C5×C4⋊C4—61no—
146C42×C5C22×D311yescharacteristic
147#685—21no—
148#685—21no—
149#685—61no—
150#685—61no—
151#685—61no—
152C4⋊Dic5—61no—
153#683—61no—
154C4×Dic5—31no—
155C4×Dic5—31no—
156C4×Dic5—31no—
157C4×Dic5—61no—
158C2×#168—21no—
159C2×#168—61no—
160#676—64no—
161C8×D5—64no—
162#529—151no—
163C4×M16—151no—
164C2×#97—151no—
165#330—31no—
166#330—151no—
167#329—51no—
168#329—151no—
169C22×C3×C5C2×C22⋊C411yescharacteristic
170C2×D15—21no—
171C2×D15—21no—
172C2×D15#10412yes—
173C2×C3×D5—41no—
174C2×C3×D5—41no—
175C2×C3×D5—41no—
176C3×C4×C5—21no—
177C3×C4×C5—21no—
178C3×C4×C5—21no—
179Dic15—21no—
180Dic15—21no—
181Dic15#10412yes—
182C3×Dic5—41no—
183C5×Dic3—41no—
184C5×Dic3—41no—
185C2×C3×Q8—51no—
186C2×C3×D4—51no—
187C2×#67—101no—
188C22×Dic3—101no—
189C2×C4×D3—51no—
190C2×C4×D3—51no—
191C2×C4×D3—51no—
192C2×C3×C8—21no—
193C2×C3×C8—101no—
194C3×C22⋊C4—101no—
195C3×C22⋊C4—101no—
196C3×C42C22×D511yescharacteristic
197#217—101no—
198#217—101no—
199(C2×D3)⋊C4—101no—
200C4⋊Dic3—101no—
201C4⋊Dic3C4×D511yescharacteristic
202C4⋊Dic3C4×D511yescharacteristic
203Dic3⋊C4—21no—
204Dic3⋊C4—21no—
205Dic3⋊C4—101no—
206C4×Dic3—51no—
207C4×Dic3—51no—
208C4×Dic3—51no—
209C4×Dic3—101no—
210C2×C3⋊C8—21no—
211C2×C3⋊C8—101no—
212ΓL(1,𝔽25)—104no—
213D3×C8—104no—
214C22×D5—21no—
215C22×D5—31no—
216C2×C4×C5—61no—
217C2×C4×C5—61no—
218C2×C4×C5C2×C4×D311yescharacteristic
219C2×C4×C5D3×D411yescharacteristic
220C2×C4×C5D3×D411yescharacteristic
221C2×Dic5—21no—
222C2×Dic5—31no—
223C2×Dic5—31no—
224C2×Dic5—31no—
225D20—41no—
226D20—122no—
227C4×D5—62no—
228C4×D5—62no—
229C4×D5—122no—
230C4×D5—121no—
231Dic10—41no—
232C5×C8—22no—
233C5×C8—62no—
234#168—22no—
235#168—62no—
236C2×M16—301no—
237C22×C8—301no—
238#126—301no—
239#125—31no—
240#124—51no—
241#123—301no—
242C22⋊Q8—151no—
243#121—151no—
244C4×Q8—151no—
245C4×D4—151no—
246C4×D4—301no—
247#117—301no—
248C2×C42—151no—
249#97—31no—
250#97—51no—
251#97—151no—
252#97—301no—
253#97D3×D511yescharacteristic
254C4×C8—301no—
255C2×C3×C5#41311yescharacteristic
256C2×C3×C5C2×#10411yescharacteristic
257C2×C3×C5C2×#10411yescharacteristic
258D15—22no—
259C3×D5—81no—
260C23×C3—101no—
261C22×D3—51no—
262C3×Q8—201no—
263C3×D4—201no—
264C2×C3×C4—101no—
265C2×C3×C4C2×C4×D511yescharacteristic
266C2×C3×C4D4×D511yescharacteristic
267C2×C3×C4D4×D511yescharacteristic
268#67—202no—
269C2×Dic3—21no—
270C2×Dic3—21no—
271C2×Dic3—51no—
272C2×Dic3—51no—
273C2×Dic3—51no—
274C2×Dic3—202no—
275C4×D3—102no—
276C4×D3—102no—
277C4×D3—201no—
278C3×C8—22no—
279C3×C8—102no—
280C3⋊C8—22no—
281C3⋊C8—102no—
282C22×C5D3×C22⋊C411yescharacteristic
283C2×D5—32no—
284C2×D5—41no—
285C2×D5—41no—
286C2×D5—41no—
287C2×D5—61no—
288C2×D5—61no—
289C4×C5—21no—
290C4×C5—21no—
291C4×C5—21no—
292C4×C5—121no—
293C4×C5—121no—
294Dic5—32no—
295Dic5—41no—
296Dic5—61no—
297Dic5—61no—
298C2×Q8—51no—
299C2×D4—51no—
300C2×D4—301no—
301C22×C4—151no—
302C22×C4—151no—
303C22×C4—151no—
304C22×C4—301no—
305M16—304no—
306C2×C8—21no—
307C2×C8—61no—
308C2×C8—101no—
309C2×C8—304no—
310C2×C8—301no—
311C4⋊C4—31no—
312C4⋊C4—31no—
313C4⋊C4—61no—
314C4⋊C4—61no—
315C4⋊C4—301no—
316C4⋊C4—301no—
317C22⋊C4—101no—
318C22⋊C4—101no—
319C22⋊C4—301no—
320C22⋊C4—301no—
321C22⋊C4—301no—
322C42—151no—
323C42—151no—
324C42—151no—
325C42—301no—
326C42C2×D3×D511yescharacteristic
327C3×C5#152411yescharacteristic, complemented, Hall
328C22×C3—201no—
329C22×C3—201no—
330C22×C3—201no—
331C22×C3D5×C22⋊C411yescharacteristic
332C2×D3—52no—
333C2×D3—101no—
334C2×D3—101no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—201no—
339Dic3—41no—
340Dic3—41no—
341Dic3—52no—
342Dic3—101no—
343Dic3—101no—
344C2×C5#474511yescharacteristic
345C2×C5D3×#10411yescharacteristic
346C2×C5D3×#10411yescharacteristic
347D5—62no—
348D5—81no—
349C23—101no—
350C23—151no—
351Q8—201no—
352D4—201no—
353D4—602no—
354C2×C4—61no—
355C2×C4—61no—
356C2×C4—101no—
357C2×C4—151no—
358C2×C4—151no—
359C2×C4—151no—
360C2×C4—302no—
361C2×C4—302no—
362C2×C4—601no—
363C2×C4—602no—
364C2×C4C4×D3×D511yescharacteristic
365C2×C4#677711yescharacteristic
366C2×C4#679011yescharacteristic
367C8—22no—
368C8—62no—
369C8—102no—
370C8—302no—
371C2×C3—401no—
372C2×C3#6504011yescharacteristic
373C2×C3D5×#10411yescharacteristic
374C2×C3D5×#10411yescharacteristic
375D3—102no—
376C5#6834111yescharacteristic, complemented, Sylow
377C22—152no—
378C22—201no—
379C22—201no—
380C22—201no—
381C22—301no—
382C22—301no—
383C22#9147311yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—121no—
388C4—121no—
389C4—152no—
390C4—201no—
391C4—301no—
392C4—301no—
393C3#1059915411yescharacteristic, complemented, Sylow
394C2—302no—
395C2—401no—
396C2#1174711211yescharacteristic
397C2#1174823611yescharacteristic
398C2#1174823811yescharacteristic
subgroupG/H
centerC22#91473
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#97C22
socleC22×C3×C5C2×C22⋊C4
prime radical#91465C4
cosocleC3×C42×C5C23
hypercenter#97D3×D5
hypocenterC3×C5#1524
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
2. #11750808C2semidirect
3. #11746983C2semidirect
4. C5×#4465C2semidirect
5. C3×#64684C2semidirect
6. #11745850C2semidirect
7. #11745846C2semidirect
35. #64684D3semidirect
71. #4465D5semidirect
327. C3×C5#1524semidirect
376. C5#68341semidirect
393. C3#10599154semidirect

Maximal subgroups

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

subgroupindex
#117526202
#117508082
#117469832
C5×#44652
C3×#646842
#117458502
#117458462
#105991543
#683415