Finite Group Databasebeta

← #14283918

Subgroups — #14283918

Order 1920.

468 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 91 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#11756450C211yesmaximal, characteristic
2#11750808C211yesmaximal, characteristic, complemented
3D15×#97C211yesmaximal, characteristic, complemented
4C3×C5×#330C211yesmaximal, characteristic, complemented
5#11746364C211yesmaximal, characteristic, complemented
6#11746285C211yesmaximal, characteristic, complemented
7#11746285C211yesmaximal, characteristic, complemented
8#10599154—31nomaximal, Hall
9C3×C5×#125C2211yescharacteristic
10C2×#6705—21no—
11C2×C8×D15—21no—
12#91787—21no—
13#91786C411yescharacteristic
14#91784C411yescharacteristic
15#91783—21no—
16#91782—21no—
17#91782C411yescharacteristic
18#91781—21no—
19#91776C411yescharacteristic
20#91764C2211yescharacteristic
21C42×D15C2211yescharacteristic
22C3×C5×#97C2211yescharacteristic
23C3×C5×#97C2211yescharacteristic
24#91099—21no—
25C8×Dic15—21no—
26#91087C2211yescharacteristic
27#91087C2211yescharacteristic
28#68361—51nomaximal, Hall
29#66025—31no—
30#64996—31no—
31D5×#97—31no—
32C5×#330D311yescharacteristic, complemented
33#64763—31no—
34#64684—31no—
35#64684—31no—
36C2×D60—21no—
37C2×D60C2×C411yescharacteristic
38C2×C4×D15—21no—
39C2×C4×D15C2×C411yescharacteristic
40C2×C4×D15D411yescharacteristic
41C2×C4×D15D411yescharacteristic
42C2×Dic30C2×C411yescharacteristic
43C2×C3×C5×C8—21no—
44C2×C3×C5×C8—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4C2×C411yescharacteristic
48C3×C5×C4⋊C4C2×C411yescharacteristic
49C3×C42×C5C2311yescharacteristic
50#6714—21no—
51#6714—21no—
52#6714—21no—
53#6714—21no—
54#6714—21no—
55C4⋊Dic15—21no—
56#6712—21no—
57C4×Dic15—21no—
58C4×Dic15C2×C411yescharacteristic
59C4×Dic15D411yescharacteristic
60C4×Dic15D411yescharacteristic
61C2×C3⋊#168—21no—
62C2×C3⋊#168—21no—
63#6705—24no—
64C8×D15—24no—
65#5691—51no—
66#4707—51no—
67D3×#97—51no—
68C3×#330D511yescharacteristic, complemented
69#4543—51no—
70#4464—51no—
71#4464—51no—
72C5×#125C2×D311yescharacteristic
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#4021—31no—
84C42×D5—31no—
85C5×#97C2×D311yescharacteristic
86C5×#97C2×D311yescharacteristic
87#3947—61no—
88C8×Dic5—61no—
89#3935—31no—
90#3935—31no—
91#1524—151noSylow
92C22×D15—21no—
93C22×D15C22⋊C411yescharacteristic
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5C22×C411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×Dic15—21no—
100C2×Dic15C22⋊C411yescharacteristic
101C2×Dic15C22⋊C411yescharacteristic
102C2×Dic15C22⋊C411yescharacteristic
103D60—41no—
104D60—42no—
105C4×D15—22no—
106C4×D15—22no—
107C4×D15—41no—
108C4×D15—42no—
109Dic30—41no—
110C3×C5×C8—22no—
111C3×C5×C8—22no—
112C3⋊#168—22no—
113C3⋊#168—22no—
114C3×#125C2×D511yescharacteristic
115C2×ΓL(1,𝔽25)—101no—
116C2×D3×C8—101no—
117#898—101no—
118#897—51no—
119#895—51no—
120#894—101no—
121#893—51no—
122#893—101no—
123#892—101no—
124#887—51no—
125#875—51no—
126C42×D3—51no—
127C3×#97C2×D511yescharacteristic
128C3×#97C2×D511yescharacteristic
129#815—101no—
130C8×Dic3—101no—
131#803—51no—
132#803—51no—
133C2×D20—31no—
134C2×D20—61no—
135C2×C4×D5—31no—
136C2×C4×D5—31no—
137C2×C4×D5—31no—
138C2×C4×D5—61no—
139C2×Dic10—31no—
140C2×C5×C8—21no—
141C2×C5×C8—21no—
142C5×C4⋊C4—21no—
143C5×C4⋊C4—21no—
144C5×C4⋊C4C4×D311yescharacteristic
145C5×C4⋊C4C4×D311yescharacteristic
146C42×C5C22×D311yescharacteristic
147#685—61no—
148#685—61no—
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—61no—
159C2×#168—61no—
160#676—64no—
161C8×D5—64no—
162#529—151no—
163C4×M16—151no—
164C2×#97—151no—
165#330—151no—
166#330D1511yescharacteristic, complemented
167#329—151no—
168#329—151no—
169C22×C3×C5C2×C22⋊C411yescharacteristic
170C2×D15—21no—
171C2×D15—21no—
172C2×D15—41no—
173C2×D15—41no—
174C2×D15—41no—
175C2×D15#10412yes—
176C3×C4×C5—21no—
177C3×C4×C5—21no—
178C3×C4×C5—21no—
179C3×C4×C5—41no—
180C3×C4×C5—41no—
181Dic15—21no—
182Dic15—21no—
183Dic15—41no—
184Dic15#10412yes—
185C2×D12—51no—
186C2×D12—101no—
187C2×C4×D3—51no—
188C2×C4×D3—51no—
189C2×C4×D3—51no—
190C2×C4×D3—101no—
191C2×Dic6—51no—
192C2×C3×C8—21no—
193C2×C3×C8—21no—
194C3×C4⋊C4—21no—
195C3×C4⋊C4—21no—
196C3×C4⋊C4C4×D511yescharacteristic
197C3×C4⋊C4C4×D511yescharacteristic
198C3×C42C22×D511yescharacteristic
199(C2×D3)⋊C4—101no—
200(C2×D3)⋊C4—101no—
201(C2×D3)⋊C4—101no—
202(C2×D3)⋊C4—101no—
203(C2×D3)⋊C4—101no—
204C4⋊Dic3—101no—
205Dic3⋊C4—101no—
206C4×Dic3—51no—
207C4×Dic3—51no—
208C4×Dic3—51no—
209C4×Dic3—101no—
210C2×C3⋊C8—101no—
211C2×C3⋊C8—101no—
212ΓL(1,𝔽25)—104no—
213D3×C8—104no—
214C22×D5—31no—
215C22×D5—61no—
216C2×C4×C5—21no—
217C2×C4×C5—21no—
218C2×C4×C5C2×C4×D311yescharacteristic
219C2×C4×C5D3×D411yescharacteristic
220C2×C4×C5D3×D411yescharacteristic
221C2×Dic5—31no—
222C2×Dic5—31no—
223C2×Dic5—31no—
224C2×Dic5—61no—
225D20—121no—
226D20—122no—
227C4×D5—62no—
228C4×D5—62no—
229C4×D5—122no—
230C4×D5—121no—
231Dic10—121no—
232C5×C8—22no—
233C5×C8—22no—
234#168—62no—
235#168—62no—
236C2×M16—301no—
237C22×C8—301no—
238#126—301no—
239#125C2×D1511yescharacteristic
240#124—151no—
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—151no—
250#97—151no—
251#97—301no—
252#97C2×D1511yescharacteristic
253#97C2×D1511yescharacteristic
254C4×C8—301no—
255C2×C3×C5#41311yescharacteristic
256C2×C3×C5C2×#10411yescharacteristic
257C2×C3×C5C2×#10411yescharacteristic
258D15—22no—
259D15—81no—
260C22×D3—51no—
261C22×D3—101no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4C2×C4×D511yescharacteristic
265C2×C3×C4D4×D511yescharacteristic
266C2×C3×C4D4×D511yescharacteristic
267C2×Dic3—51no—
268C2×Dic3—51no—
269C2×Dic3—51no—
270C2×Dic3—101no—
271D12—201no—
272D12—202no—
273C4×D3—102no—
274C4×D3—102no—
275C4×D3—202no—
276C4×D3—201no—
277Dic6—201no—
278C3×C8—22no—
279C3×C8—22no—
280C3⋊C8—102no—
281C3⋊C8—102no—
282C22×C5D3×C22⋊C411yescharacteristic
283C2×D5—32no—
284C2×D5—61no—
285C2×D5—61no—
286C2×D5—121no—
287C2×D5—121no—
288C2×D5—121no—
289C4×C5—21no—
290C4×C5—21no—
291C4×C5—21no—
292C4×C5—41no—
293C4×C5—41no—
294Dic5—32no—
295Dic5—61no—
296Dic5—61no—
297Dic5—121no—
298C2×Q8—151no—
299C2×D4—151no—
300C2×D4—301no—
301C22×C4—151no—
302C22×C4—151no—
303C22×C4—151no—
304C22×C4—301no—
305M16—304no—
306C2×C8—21no—
307C2×C8—21no—
308C2×C8—304no—
309C2×C8—301no—
310C2×C8—301no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—301no—
314C4⋊C4—301no—
315C4⋊C4C4×D1511yescharacteristic
316C4⋊C4C4×D1511yescharacteristic
317C22⋊C4—301no—
318C22⋊C4—301no—
319C22⋊C4—301no—
320C22⋊C4—301no—
321C22⋊C4—301no—
322C42—151no—
323C42—151no—
324C42—151no—
325C42—301no—
326C42C22×D1511yescharacteristic
327C3×C5#152411yescharacteristic, complemented, Hall
328C22×C3D5×C22⋊C411yescharacteristic
329C2×D3—52no—
330C2×D3—101no—
331C2×D3—101no—
332C2×D3—201no—
333C2×D3—201no—
334C2×D3—201no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—41no—
339C3×C4—41no—
340Dic3—52no—
341Dic3—101no—
342Dic3—101no—
343Dic3—201no—
344C2×C5#475111yescharacteristic
345C2×C5D3×#10411yescharacteristic
346C2×C5D3×#10411yescharacteristic
347D5—62no—
348D5—241no—
349C23—151no—
350C23—301no—
351Q8—601no—
352D4—601no—
353D4—602no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—151no—
357C2×C4—151no—
358C2×C4—151no—
359C2×C4—302no—
360C2×C4—302no—
361C2×C4—301no—
362C2×C4—601no—
363C2×C4—602no—
364C2×C4C2×C4×D1511yescharacteristic
365C2×C4D4×D1511yescharacteristic
366C2×C4D4×D1511yescharacteristic
367C8—22no—
368C8—22no—
369C8—302no—
370C8—302no—
371C2×C3#6504011yescharacteristic
372C2×C3D5×#10411yescharacteristic
373C2×C3D5×#10411yescharacteristic
374D3—102no—
375D3—401no—
376C5#6836111yescharacteristic, complemented, Sylow
377C22—152no—
378C22—301no—
379C22—301no—
380C22—601no—
381C22—601no—
382C22—601no—
383C22C22⋊C4×D1511yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—41no—
388C4—41no—
389C4—152no—
390C4—301no—
391C4—301no—
392C4—601no—
393C3#1059915411yescharacteristic, complemented, Sylow
394C2—302no—
395C2—1201no—
396C2#1175085211yescharacteristic
397C2D15×#10411yescharacteristic
398C2D15×#10411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C22×D15
FittingC3×C5×#330C2
socleC22×C3×C5C2×C22⋊C4
prime radical#91784C4
cosocleC3×C42×C5C23
hypercenter#330D15
hypocenterC3×C5#1524
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #11750808C2semidirect
3. D15×#97C2semidirect
4. C3×C5×#330C2semidirect
5. #11746364C2semidirect
6. #11746285C2semidirect
7. #11746285C2semidirect
32. C5×#330D3semidirect
68. C3×#330D5semidirect
166. #330D15semidirect
327. C3×C5#1524semidirect
376. C5#68361semidirect
393. C3#10599154semidirect

Maximal subgroups

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

subgroupindex
#117564502
#117508082
D15×#972
C3×C5×#3302
#117463642
#117462852
#105991543
#683615