Finite Group Databasebeta

← #14281278

Subgroups — #14281278

Order 1920.

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

normal subgroups only

This group has 408 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
1C2×#91778C211yesmaximal, characteristic
2#11750820C211yesmaximal, characteristic
3#11750819C211yesmaximal, characteristic
4C3×C5×#324C211yesmaximal, characteristic
5#11746349C211yesmaximal, characteristic
6#11746290C211yesmaximal, characteristic
7#11746290C211yesmaximal, characteristic
8#10598921—31nomaximal, Hall
9C2×C3×C5×C4⋊C4C2211yescharacteristic
10C2×C4⋊Dic15C411yescharacteristic
11C2×#6712C411yescharacteristic
12C2×#6712C411yescharacteristic
13C2×#6712C411yescharacteristic
14C2×#6712C2211yescharacteristic
15C2×C4×Dic15C2211yescharacteristic
16#91778—21no—
17#91778—21no—
18#91778—21no—
19#91778—21no—
20C3×C5×C22⋊C8C2211yescharacteristic
21C3×C5×C22⋊C8C2211yescharacteristic
22#91114C2211yescharacteristic
23#91114C2211yescharacteristic
24#91099—21no—
25#91098—21no—
26#91098—21no—
27C8×Dic15—21no—
28#68128—51nomaximal, Hall
29C2×#4035—31no—
30#65008—31no—
31#65007—31no—
32C5×#324D311yescharacteristic
33#64748—31no—
34#64689—31no—
35#64689—31no—
36C22×C3×C4×C5C2×C411yescharacteristic
37C22×C3×C4×C5C2×C411yescharacteristic
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15C2×C411yescharacteristic
40C22×Dic15C2×C411yescharacteristic
41C22×Dic15C2×C411yescharacteristic
42C22×Dic15C2×C411yescharacteristic
43C2×C3×C5×C8—21no—
44C2×C3×C5×C8—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47C4⋊Dic15—21no—
48C4⋊Dic15—21no—
49#6712—21no—
50#6712—21no—
51#6712—21no—
52#6712—21no—
53#6712—21no—
54#6712—21no—
55#6712—21no—
56#6712—21no—
57C4×Dic15D411yescharacteristic
58C4×Dic15D411yescharacteristic
59C4×Dic15D411yescharacteristic
60C4×Dic15D411yescharacteristic
61C2×C3⋊#168—21no—
62C2×C3⋊#168—21no—
63C2×#889—51no—
64#4719—51no—
65#4718—51no—
66C3×#324D511yescharacteristic
67#4528—51no—
68#4469—51no—
69#4469—51no—
70C2×C5×C4⋊C4C2×D311yescharacteristic
71C2×C4⋊Dic5—31no—
72C2×#683—31no—
73C2×#683—31no—
74C2×#683—31no—
75C2×#683—31no—
76C2×C4×Dic5—31no—
77#4035—61no—
78#4035—61no—
79#4035—61no—
80#4035—61no—
81C5×C22⋊C8C2×D311yescharacteristic
82C5×C22⋊C8C2×D311yescharacteristic
83C22⋊#168—31no—
84C22⋊#168—31no—
85#3947—61no—
86#3946—61no—
87#3946—61no—
88C8×Dic5—61no—
89#1470—151noSylow
90C23×C3×C5C22×C411yescharacteristic
91C2×C3×C4×C5—21no—
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×Dic15—21no—
100C2×Dic15—21no—
101C2×Dic15—22no—
102C2×Dic15—21no—
103C2×Dic15—21no—
104C2×Dic15—21no—
105C2×Dic15—21no—
106C2×Dic15—41no—
107C2×Dic15C22⋊C411yescharacteristic
108C2×Dic15C22⋊C411yescharacteristic
109C2×Dic15C22⋊C411yescharacteristic
110C2×Dic15C22⋊C411yescharacteristic
111C3×C5×C8—41no—
112C3×C5×C8—41no—
113C3⋊#168—41no—
114C3⋊#168—41no—
115C2×C3×C4⋊C4C2×D511yescharacteristic
116C2×C4⋊Dic3—51no—
117C2×Dic3⋊C4—51no—
118C2×Dic3⋊C4—51no—
119C2×Dic3⋊C4—51no—
120C2×Dic3⋊C4—51no—
121C2×C4×Dic3—51no—
122#889—101no—
123#889—101no—
124#889—101no—
125#889—101no—
126C3×C22⋊C8C2×D511yescharacteristic
127C3×C22⋊C8C2×D511yescharacteristic
128#830—51no—
129#830—51no—
130#815—101no—
131Dic3⋊C8—101no—
132Dic3⋊C8—101no—
133C8×Dic3—101no—
134C22×C4×C5C4×D311yescharacteristic
135C22×C4×C5C4×D311yescharacteristic
136C22×C4×C5C22×D311yescharacteristic
137C22×Dic5—31no—
138C22×Dic5—31no—
139C22×Dic5—31no—
140C22×Dic5—31no—
141C2×C5×C8—21no—
142C2×C5×C8—21no—
143C5×C4⋊C4—21no—
144C5×C4⋊C4—21no—
145C4⋊Dic5—61no—
146C4⋊Dic5—61no—
147#683—61no—
148#683—61no—
149#683—61no—
150#683—61no—
151#683—61no—
152#683—61no—
153#683—61no—
154#683—61no—
155C4×Dic5—31no—
156C4×Dic5—31no—
157C4×Dic5—31no—
158C4×Dic5—31no—
159C2×#168—61no—
160C2×#168—61no—
161C2×#125—151no—
162#432—151no—
163#431—151no—
164#324—151no—
165#324—151no—
166#324—151no—
167#324D1511yescharacteristic
168C22×C3×C5—21no—
169C22×C3×C5—21no—
170C22×C3×C5C2×C22⋊C411yescharacteristic
171C22×C3×C5#13111yescharacteristic
172C22×C3×C5#13111yescharacteristic
173C3×C4×C5—21no—
174C3×C4×C5—21no—
175C3×C4×C5—41no—
176C3×C4×C5—41no—
177Dic15—21no—
178Dic15—21no—
179Dic15—21no—
180Dic15—41no—
181Dic15—41no—
182Dic15#10112yes—
183C22×C3×C4C4×D511yescharacteristic
184C22×C3×C4C4×D511yescharacteristic
185C22×C3×C4C22×D511yescharacteristic
186C22×Dic3—51no—
187C22×Dic3—51no—
188C22×Dic3—51no—
189C22×Dic3—51no—
190C2×C3×C8—21no—
191C2×C3×C8—21no—
192C3×C4⋊C4—21no—
193C3×C4⋊C4—21no—
194C4⋊Dic3—101no—
195C4⋊Dic3—101no—
196Dic3⋊C4—101no—
197Dic3⋊C4—101no—
198Dic3⋊C4—101no—
199Dic3⋊C4—101no—
200Dic3⋊C4—101no—
201Dic3⋊C4—101no—
202Dic3⋊C4—101no—
203Dic3⋊C4—101no—
204C4×Dic3—51no—
205C4×Dic3—51no—
206C4×Dic3—51no—
207C4×Dic3—51no—
208C2×C3⋊C8—101no—
209C2×C3⋊C8—101no—
210C23×C5C2×C4×D311yescharacteristic
211C2×C4×C5—21no—
212C2×C4×C5—21no—
213C2×C4×C5—21no—
214C2×C4×C5—21no—
215C2×C4×C5—41no—
216C2×C4×C5—41no—
217C2×C4×C5D3×D411yescharacteristic
218C2×C4×C5D3×D411yescharacteristic
219C2×Dic5—31no—
220C2×Dic5—31no—
221C2×Dic5—31no—
222C2×Dic5—31no—
223C2×Dic5—62no—
224C2×Dic5—61no—
225C2×Dic5—61no—
226C2×Dic5—61no—
227C2×Dic5—61no—
228C2×Dic5—61no—
229C2×Dic5—61no—
230C2×Dic5—121no—
231C5×C8—41no—
232C5×C8—41no—
233#168—121no—
234#168—121no—
235#125—301no—
236#125—301no—
237#125—301no—
238#125—301no—
239C2×C4⋊C4—151no—
240C2×C4⋊C4—151no—
241C2×C4⋊C4—151no—
242C2×C4⋊C4—151no—
243C2×C4⋊C4—151no—
244C2×C4⋊C4C2×D1511yescharacteristic
245C2×C42—151no—
246C4⋊C8—301no—
247C4⋊C8—301no—
248C22⋊C8—151no—
249C22⋊C8—151no—
250C22⋊C8C2×D1511yescharacteristic
251C22⋊C8C2×D1511yescharacteristic
252#97—301no—
253C4×C8—301no—
254C2×C3×C5—21no—
255C2×C3×C5—21no—
256C2×C3×C5#40811yescharacteristic
257C2×C3×C5#41011yescharacteristic
258C2×C3×C5C2×#10111yescharacteristic
259C23×C3C2×C4×D511yescharacteristic
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—41no—
265C2×C3×C4—41no—
266C2×C3×C4D4×D511yescharacteristic
267C2×C3×C4D4×D511yescharacteristic
268C2×Dic3—51no—
269C2×Dic3—51no—
270C2×Dic3—51no—
271C2×Dic3—51no—
272C2×Dic3—102no—
273C2×Dic3—101no—
274C2×Dic3—101no—
275C2×Dic3—101no—
276C2×Dic3—101no—
277C2×Dic3—101no—
278C2×Dic3—101no—
279C2×Dic3—201no—
280C3×C8—41no—
281C3×C8—41no—
282C3⋊C8—201no—
283C3⋊C8—201no—
284C22×C5—21no—
285C22×C5—21no—
286C22×C5D3×C22⋊C411yescharacteristic
287C22×C5#90111yescharacteristic
288C22×C5#90711yescharacteristic
289C4×C5—21no—
290C4×C5—21no—
291C4×C5—41no—
292C4×C5—41no—
293Dic5—32no—
294Dic5—61no—
295Dic5—61no—
296Dic5—61no—
297Dic5—121no—
298Dic5—121no—
299C22×C4—151no—
300C22×C4—151no—
301C22×C4—151no—
302C22×C4—151no—
303C22×C4C4×D1511yescharacteristic
304C22×C4C4×D1511yescharacteristic
305C22×C4C22×D1511yescharacteristic
306C2×C8—21no—
307C2×C8—21no—
308C2×C8—301no—
309C2×C8—301no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—301no—
313C4⋊C4—301no—
314C4⋊C4—301no—
315C4⋊C4—301no—
316C4⋊C4—301no—
317C4⋊C4—301no—
318C4⋊C4—301no—
319C4⋊C4—301no—
320C4⋊C4—301no—
321C4⋊C4—301no—
322C42—151no—
323C42—151no—
324C42—151no—
325C42—151no—
326C3×C5#147011yescharacteristic, complemented, Hall
327C22×C3—21no—
328C22×C3—21no—
329C22×C3D5×C22⋊C411yescharacteristic
330C22×C3#404711yescharacteristic
331C22×C3#405311yescharacteristic
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—41no—
335C3×C4—41no—
336Dic3—52no—
337Dic3—101no—
338Dic3—101no—
339Dic3—101no—
340Dic3—201no—
341Dic3—201no—
342C2×C5—21no—
343C2×C5—21no—
344C2×C5#472711yescharacteristic
345C2×C5#474011yescharacteristic
346C2×C5D3×#10111yescharacteristic
347C23C2×C4×D1511yescharacteristic
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—151no—
355C2×C4—151no—
356C2×C4—151no—
357C2×C4—151no—
358C2×C4—302no—
359C2×C4—301no—
360C2×C4—301no—
361C2×C4—301no—
362C2×C4—301no—
363C2×C4—301no—
364C2×C4—301no—
365C2×C4—601no—
366C2×C4D4×D1511yescharacteristic
367C2×C4D4×D1511yescharacteristic
368C8—41no—
369C8—41no—
370C8—601no—
371C8—601no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3#6501611yescharacteristic
375C2×C3#6502911yescharacteristic
376C2×C3D5×#10111yescharacteristic
377C5#6812811yescharacteristic, complemented, Sylow
378C22—21no—
379C22—21no—
380C22C22⋊C4×D1511yescharacteristic
381C22#9179011yescharacteristic
382C22#9179611yescharacteristic
383C4—21no—
384C4—21no—
385C4—41no—
386C4—41no—
387C4—152no—
388C4—301no—
389C4—301no—
390C4—301no—
391C4—601no—
392C4—601no—
393C3#1059892111yescharacteristic, complemented, Sylow
394C2—21no—
395C2—21no—
396C2#1175082811yescharacteristic
397C2#1175084111yescharacteristic
398C2D15×#10111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D15
commutator, prime radicalC23×C3×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#324C2
socleC22×C3×C5C2×C22⋊C4
cosocleC22×C3×C4×C5C23
hypercenter#324D15
hypocenterC3×C5#1470
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
326. C3×C5#1470semidirect
377. C5#68128semidirect
393. C3#10598921semidirect

Maximal subgroups

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

subgroupindex
C2×#917782
#117508202
#117508192
C3×C5×#3242
#117463492
#117462902
#105989213
#681285