Finite Group Databasebeta

← #14284494

Subgroups — #14284494

Order 1920.

388 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 94 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#11752498C211yesmaximal, characteristic
2C3×#64994C211yesmaximal, characteristic
3#11746870C211yesmaximal, characteristic
4#11746286C211yesmaximal, characteristic, complemented
5C5×#4465C211yesmaximal, characteristic, complemented
6#11745851C211yesmaximal, characteristic, complemented
7#11745850C211yesmaximal, characteristic, complemented
8#10599162—31nomaximal, Hall
9#91759C2211yescharacteristic
10C5×#870C2211yescharacteristic
11C3×C42×D5C2211yescharacteristic
12#91468C411yescharacteristic
13#91468C411yescharacteristic
14#91358C411yescharacteristic
15#91358C411yescharacteristic
16#91349—21no—
17#91349—21no—
18#91323—21no—
19#91323—21no—
20C3×C5×#97C2211yescharacteristic
21#91087C2211yescharacteristic
22C5×#803C2211yescharacteristic
23C3×#3952—21no—
24C3×#3946—21no—
25C3×#3935C2211yescharacteristic
26#90982—21no—
27#90955—21no—
28#70815—51nomaximal, Hall
29#66022—31no—
30#64994—31no—
31#64994D311yescharacteristic
32C5×#330—31no—
33#64763—31no—
34#64685—31no—
35#64685—31no—
36C2×C3×C4×D5C2×C411yescharacteristic
37C2×C3×C4×D5D411yescharacteristic
38C2×C3×C4×D5D411yescharacteristic
39C2×#1204—21no—
40C2×#1204—21no—
41C2×C3×C5×C8—21no—
42C3×C42×C5C2311yescharacteristic
43C4⋊Dic15C2×C411yescharacteristic
44C4⋊Dic15C2×C411yescharacteristic
45#6712—21no—
46#6712—21no—
47C2×C3⋊#168—21no—
48C5×C4⋊Dic3C2×C411yescharacteristic
49C5×C4⋊Dic3C2×C411yescharacteristic
50C5×Dic3⋊C4—21no—
51C5×Dic3⋊C4—21no—
52C2×C5×C3⋊C8—21no—
53C3×C4×Dic5C2×C411yescharacteristic
54C3×C4×Dic5D411yescharacteristic
55C3×C4×Dic5D411yescharacteristic
56C2×C3×#168—21no—
57#6668—21no—
58#6668—21no—
59#6665—21no—
60#6665—21no—
61Dic3×Dic5—21no—
62Dic3×Dic5—21no—
63#5470—51no—
64C3×#432—51no—
65#4926—51no—
66#4465—51no—
67#4465—51no—
68#4465—51no—
69#4465D511yescharacteristic, complemented
70C5×#125—31no—
71#4042—61no—
72#4042—61no—
73#4038—31no—
74#4038—31no—
75#4034—31no—
76#4034—31no—
77#4033—61no—
78#4033—61no—
79C42×D5C2×D311yescharacteristic
80#4016—31no—
81C5×#97—31no—
82C5×#97C2×D311yescharacteristic
83#3952—21no—
84#3952—61no—
85#3946—21no—
86#3946—61no—
87#3935—31no—
88#3935C2×D311yescharacteristic
89#1537—151noSylow
90C22×C3×D5C22⋊C411yescharacteristic
91C2×C3×C4×C5C22×C411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×Dic15—21no—
95C2×Dic15—21no—
96C2×C5×Dic3—21no—
97C2×C5×Dic3—21no—
98C2×C3×Dic5C22⋊C411yescharacteristic
99C2×C3×Dic5C22⋊C411yescharacteristic
100C2×C3×Dic5C22⋊C411yescharacteristic
101C3×C4×D5—22no—
102C3×C4×D5—41no—
103C3×C4×D5—41no—
104#1204—42no—
105#1204—42no—
106C3×C5×C8—41no—
107C3⋊#168—41no—
108C3×#168—41no—
109C5×C3⋊C8—41no—
110C2×C3×C42—51no—
111#926—51no—
112#926—51no—
113#924—101no—
114#924—101no—
115#870—51no—
116#870C2×D511yescharacteristic
117#869—51no—
118#869—51no—
119C4×Dic6—101no—
120C4×Dic6—101no—
121C3×C4⋊C8—101no—
122C3×C22⋊C8—101no—
123C3×#97—51no—
124C3×#97C2×D511yescharacteristic
125#830—101no—
126C4⋊(C3⋊C8)—101no—
127#803—51no—
128#803C2×D511yescharacteristic
129C2×C4×D5C4×D311yescharacteristic
130C2×C4×D5D1211yescharacteristic
131C2×C4×D5#6711yescharacteristic
132C2×Dic10—61no—
133C2×Dic10—61no—
134C2×C5×C8—21no—
135C2×C5×C8—61no—
136C5×C4⋊C4—31no—
137C5×C4⋊C4—31no—
138C5×C4⋊C4—61no—
139C5×C4⋊C4—61no—
140C42×C5C22×D311yescharacteristic
141#685—61no—
142#685—61no—
143C4⋊Dic5—31no—
144C4⋊Dic5—31no—
145#683—61no—
146#683—61no—
147#683—61no—
148#683—61no—
149C4×Dic5—61no—
150C4×Dic5—61no—
151C4×Dic5C4×D311yescharacteristic
152C4×Dic5D1211yescharacteristic
153C4×Dic5#6711yescharacteristic
154C2×#168—21no—
155C2×#168—61no—
156#533—151no—
157#432—51no—
158#432—151no—
159#330—31no—
160#330—151no—
161#330—151no—
162#330—151no—
163C22×C3×C5C2×C22⋊C411yescharacteristic
164C2×C3×D5—21no—
165C2×C3×D5—21no—
166C2×C3×D5—21no—
167C3×C4×C5—21no—
168C3×C4×C5—21no—
169C3×C4×C5—21no—
170Dic15—41no—
171Dic15—41no—
172C3×Dic5—21no—
173C3×Dic5—21no—
174C3×Dic5#10112yes—
175C5×Dic3—41no—
176C5×Dic3—41no—
177C22×C3×C4—51no—
178C22×C3×C4—51no—
179C22×C3×C4—51no—
180C2×Dic6—101no—
181C2×Dic6—101no—
182C2×C3×C8—21no—
183C2×C3×C8—101no—
184C3×C42—51no—
185C3×C42—51no—
186C3×C42—51no—
187C3×C42C22×D511yescharacteristic
188#217—101no—
189#217—101no—
190C4⋊Dic3—51no—
191C4⋊Dic3—51no—
192C4⋊Dic3—101no—
193C4⋊Dic3—101no—
194C4⋊Dic3C4×D511yescharacteristic
195C4⋊Dic3C4×D511yescharacteristic
196Dic3⋊C4—21no—
197Dic3⋊C4—21no—
198Dic3⋊C4—101no—
199Dic3⋊C4—101no—
200C4×Dic3—101no—
201C4×Dic3—101no—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—101no—
204C22×D5(C2×D3)⋊C411yescharacteristic
205C2×C4×C5—61no—
206C2×C4×C5—61no—
207C2×C4×C5C2×C4×D311yescharacteristic
208C2×C4×C5C2×D1211yescharacteristic
209C2×C4×C5C2×#6711yescharacteristic
210C2×Dic5—61no—
211C2×Dic5—61no—
212C2×Dic5(C2×D3)⋊C411yescharacteristic
213C2×Dic5(C2×D3)⋊C411yescharacteristic
214C2×Dic5(C2×D3)⋊C411yescharacteristic
215C4×D5—22no—
216C4×D5—41no—
217C4×D5—41no—
218Dic10—122no—
219Dic10—122no—
220C5×C8—41no—
221C5×C8—121no—
222#168—41no—
223#168—121no—
224C4⋊Q8—151no—
225C4⋊Q8—151no—
226#125—31no—
227#125—151no—
228C22⋊Q8—301no—
229C22⋊Q8—301no—
230C4×Q8—301no—
231C4×Q8—301no—
232#117—151no—
233#117—151no—
234C2×C42—51no—
235C4⋊C8—101no—
236C4⋊C8—301no—
237C22⋊C8—101no—
238C22⋊C8—301no—
239#97—31no—
240#97—51no—
241#97—151no—
242#97D3×D511yescharacteristic
243C2×C3×C5C2×#10111yescharacteristic
244C2×C3×C5#42111yescharacteristic
245C2×C3×C5#42111yescharacteristic
246C3×D5—41no—
247C23×C3—51no—
248C2×C3×C4—51no—
249C2×C3×C4—51no—
250C2×C3×C4—51no—
251C2×C3×C4—102no—
252C2×C3×C4—201no—
253C2×C3×C4—201no—
254C2×C3×C4C2×C4×D511yescharacteristic
255C2×C3×C4D4×D511yescharacteristic
256C2×C3×C4D4×D511yescharacteristic
257C2×Dic3—21no—
258C2×Dic3—21no—
259C2×Dic3—101no—
260C2×Dic3—101no—
261Dic6—202no—
262Dic6—202no—
263C3×C8—41no—
264C3×C8—201no—
265C3⋊C8—41no—
266C3⋊C8—201no—
267C22×C5C2×(C2×D3)⋊C411yescharacteristic
268C2×D5—21no—
269C2×D5—21no—
270C2×D5—21no—
271C4×C5—21no—
272C4×C5—21no—
273C4×C5—21no—
274C4×C5—121no—
275C4×C5—121no—
276Dic5—21no—
277Dic5—21no—
278Dic5—121no—
279Dic5—121no—
280Dic5#82412yes—
281C2×Q8—301no—
282C2×Q8—301no—
283C22×C4—51no—
284C22×C4—51no—
285C22×C4—51no—
286C2×C8—21no—
287C2×C8—61no—
288C2×C8—101no—
289C2×C8—301no—
290C4⋊C4—31no—
291C4⋊C4—31no—
292C4⋊C4—61no—
293C4⋊C4—61no—
294C4⋊C4—151no—
295C4⋊C4—151no—
296C4⋊C4—301no—
297C4⋊C4—301no—
298C4⋊C4—301no—
299C4⋊C4—301no—
300C22⋊C4—301no—
301C22⋊C4—301no—
302C42—51no—
303C42—51no—
304C42—51no—
305C42—301no—
306C42—301no—
307C42C2×D3×D511yescharacteristic
308C3×C5#153711yescharacteristic, complemented, Hall
309C22×C3—101no—
310C22×C3—101no—
311C22×C3—101no—
312C22×C3D5×C22⋊C411yescharacteristic
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—52no—
317C3×C4—101no—
318C3×C4—101no—
319Dic3—41no—
320Dic3—41no—
321Dic3—201no—
322Dic3—201no—
323C2×C5#500511yescharacteristic
324C2×C5C2×#82411yescharacteristic
325C2×C5#513911yescharacteristic
326D5—41no—
327C23—51no—
328Q8—602no—
329Q8—602no—
330C2×C4—51no—
331C2×C4—51no—
332C2×C4—51no—
333C2×C4—61no—
334C2×C4—61no—
335C2×C4—102no—
336C2×C4—201no—
337C2×C4—201no—
338C2×C4—301no—
339C2×C4—301no—
340C2×C4C4×D3×D511yescharacteristic
341C2×C4D5×D1211yescharacteristic
342C2×C4D5×#6711yescharacteristic
343C8—41no—
344C8—121no—
345C8—201no—
346C8—601no—
347C2×C3—201no—
348C2×C3D5×#10111yescharacteristic
349C2×C3#6511011yescharacteristic
350C2×C3#6511011yescharacteristic
351C5#7081511yescharacteristic, complemented, Sylow
352C22—101no—
353C22—101no—
354C22—101no—
355C22D5×(C2×D3)⋊C411yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—52no—
360C4—101no—
361C4—101no—
362C4—121no—
363C4—121no—
364C4—601no—
365C4—601no—
366C3#1059916211yescharacteristic, complemented, Sylow
367C2—201no—
368C2#1174710911yescharacteristic
369C2D5×#82411yescharacteristic
370C2#1174822911yescharacteristic
subgroupG/H
centerC22D5×(C2×D3)⋊C4
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#97C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C22⋊C4
cosocleC3×C42×C5C23
hypercenter#97D3×D5
hypocenterC3×C5#1537
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
4. #11746286C2semidirect
5. C5×#4465C2semidirect
6. #11745851C2semidirect
7. #11745850C2semidirect
69. #4465D5semidirect
308. C3×C5#1537semidirect
351. C5#70815semidirect
366. C3#10599162semidirect

Maximal subgroups

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

subgroupindex
#117524982
C3×#649942
#117468702
#117462862
C5×#44652
#117458512
#117458502
#105991623
#708155