Finite Group Databasebeta

← #14284241

Subgroups — #14284241

Order 1920.

424 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 98 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×D5×#97C211yesmaximal, characteristic
3#11746870C211yesmaximal, characteristic
4#11746286C211yesmaximal, characteristic, complemented
5C5×#4465C211yesmaximal, characteristic, complemented
6#11745851C211yesmaximal, characteristic, complemented
7#11745850C211yesmaximal, characteristic, complemented
8#10599158—31nomaximal, Hall
9#91759C2211yescharacteristic
10C5×#870C2211yescharacteristic
11C2×C3×C8×D5—21no—
12C3×C42×D5C2211yescharacteristic
13#91468C411yescharacteristic
14#91468C411yescharacteristic
15#91358C411yescharacteristic
16#91358C411yescharacteristic
17#91349—21no—
18#91349—21no—
19#91323—21no—
20#91323—21no—
21C3×C5×#97C2211yescharacteristic
22#91087C2211yescharacteristic
23C5×#803C2211yescharacteristic
24C3×#3947—21no—
25C3×#3935C2211yescharacteristic
26#90982—21no—
27#90955—21no—
28#69801—51nomaximal, Hall
29#66022—31no—
30#64994—31no—
31D5×#97D311yescharacteristic
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—
57C3×C8×D5—24no—
58#6668—21no—
59#6668—21no—
60#6665—21no—
61#6665—21no—
62Dic3×Dic5—21no—
63Dic3×Dic5—21no—
64#5470—51no—
65C2×C3×#97—51no—
66#4926—51no—
67#4465—51no—
68#4465—51no—
69#4465—51no—
70#4465D511yescharacteristic, complemented
71C5×#125—31no—
72C2×C8×D5—21no—
73#4042—61no—
74#4042—61no—
75#4038—31no—
76#4038—31no—
77#4034—31no—
78#4034—31no—
79#4033—61no—
80#4033—61no—
81C42×D5C2×D311yescharacteristic
82#4016—31no—
83C5×#97—31no—
84C5×#97C2×D311yescharacteristic
85#3952—61no—
86#3947—21no—
87#3946—61no—
88#3935—31no—
89#3935C2×D311yescharacteristic
90#1531—151noSylow
91C22×C3×D5C22⋊C411yescharacteristic
92C2×C3×C4×C5C22×C411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×Dic15—21no—
96C2×Dic15—21no—
97C2×C5×Dic3—21no—
98C2×C5×Dic3—21no—
99C2×C3×Dic5C22⋊C411yescharacteristic
100C2×C3×Dic5C22⋊C411yescharacteristic
101C2×C3×Dic5C22⋊C411yescharacteristic
102C3×C4×D5—22no—
103C3×C4×D5—22no—
104C3×C4×D5—41no—
105#1204—42no—
106#1204—42no—
107C3×C5×C8—22no—
108C3⋊#168—41no—
109C3×#168—22no—
110C5×C3⋊C8—41no—
111C22×C3×C8—101no—
112C2×C3×C42—51no—
113#926—51no—
114#926—51no—
115#924—101no—
116#924—101no—
117#870—51no—
118#870C2×D511yescharacteristic
119#869—51no—
120#869—51no—
121C4×Dic6—101no—
122C4×Dic6—101no—
123C3×#97—51no—
124C3×#97—101no—
125C3×#97C2×D511yescharacteristic
126#830—101no—
127C4⋊(C3⋊C8)—101no—
128#803—51no—
129#803C2×D511yescharacteristic
130C2×C4×D5C4×D311yescharacteristic
131C2×C4×D5D1211yescharacteristic
132C2×C4×D5#6711yescharacteristic
133C2×Dic10—61no—
134C2×Dic10—61no—
135C2×C5×C8—21no—
136C2×C5×C8—61no—
137C5×C4⋊C4—31no—
138C5×C4⋊C4—31no—
139C5×C4⋊C4—61no—
140C5×C4⋊C4—61no—
141C42×C5C22×D311yescharacteristic
142#685—61no—
143#685—61no—
144C4⋊Dic5—31no—
145C4⋊Dic5—31no—
146#683—61no—
147#683—61no—
148#683—61no—
149#683—61no—
150C4×Dic5—61no—
151C4×Dic5—61no—
152C4×Dic5C4×D311yescharacteristic
153C4×Dic5D1211yescharacteristic
154C4×Dic5#6711yescharacteristic
155C2×#168—21no—
156C2×#168—61no—
157C8×D5—24no—
158#533—151no—
159#432—151no—
160C2×#97—51no—
161#330—31no—
162#330—151no—
163#330—151no—
164#330—151no—
165C22×C3×C5C2×C22⋊C411yescharacteristic
166C2×C3×D5—21no—
167C2×C3×D5—21no—
168C2×C3×D5#10112yes—
169C3×C4×C5—21no—
170C3×C4×C5—21no—
171C3×C4×C5—21no—
172Dic15—41no—
173Dic15—41no—
174C3×Dic5—21no—
175C3×Dic5—21no—
176C3×Dic5#10412yes—
177C5×Dic3—41no—
178C5×Dic3—41no—
179C22×C3×C4—51no—
180C22×C3×C4—51no—
181C22×C3×C4—51no—
182C2×Dic6—101no—
183C2×Dic6—101no—
184C2×C3×C8—21no—
185C2×C3×C8—104no—
186C2×C3×C8—101no—
187C3×C42—51no—
188C3×C42—51no—
189C3×C42—51no—
190C3×C42C22×D511yescharacteristic
191#217—101no—
192#217—101no—
193C4⋊Dic3—51no—
194C4⋊Dic3—51no—
195C4⋊Dic3—101no—
196C4⋊Dic3—101no—
197C4⋊Dic3C4×D511yescharacteristic
198C4⋊Dic3C4×D511yescharacteristic
199Dic3⋊C4—21no—
200Dic3⋊C4—21no—
201Dic3⋊C4—101no—
202Dic3⋊C4—101no—
203C4×Dic3—101no—
204C4×Dic3—101no—
205C2×C3⋊C8—21no—
206C2×C3⋊C8—101no—
207C22×D5(C2×D3)⋊C411yescharacteristic
208C2×C4×C5—61no—
209C2×C4×C5—61no—
210C2×C4×C5C2×C4×D311yescharacteristic
211C2×C4×C5C2×D1211yescharacteristic
212C2×C4×C5C2×#6711yescharacteristic
213C2×Dic5—61no—
214C2×Dic5—61no—
215C2×Dic5(C2×D3)⋊C411yescharacteristic
216C2×Dic5(C2×D3)⋊C411yescharacteristic
217C2×Dic5(C2×D3)⋊C411yescharacteristic
218C4×D5—22no—
219C4×D5—22no—
220C4×D5—41no—
221Dic10—122no—
222Dic10—122no—
223C5×C8—22no—
224C5×C8—121no—
225#168—22no—
226#168—121no—
227C22×C8—101no—
228C4⋊Q8—151no—
229C4⋊Q8—151no—
230#125—31no—
231#125—151no—
232C22⋊Q8—301no—
233C22⋊Q8—301no—
234C4×Q8—301no—
235C4×Q8—301no—
236#117—151no—
237#117—151no—
238C2×C42—51no—
239C4⋊C8—301no—
240C22⋊C8—301no—
241#97—31no—
242#97—51no—
243#97—101no—
244#97—151no—
245#97D3×D511yescharacteristic
246C2×C3×C5C2×#10111yescharacteristic
247C2×C3×C5C2×#10411yescharacteristic
248C2×C3×C5#42111yescharacteristic
249C3×D5—22no—
250C23×C3—51no—
251C2×C3×C4—51no—
252C2×C3×C4—51no—
253C2×C3×C4—51no—
254C2×C3×C4—102no—
255C2×C3×C4—102no—
256C2×C3×C4—201no—
257C2×C3×C4C2×C4×D511yescharacteristic
258C2×C3×C4D4×D511yescharacteristic
259C2×C3×C4D4×D511yescharacteristic
260C2×Dic3—21no—
261C2×Dic3—21no—
262C2×Dic3—101no—
263C2×Dic3—101no—
264Dic6—202no—
265Dic6—202no—
266C3×C8—22no—
267C3×C8—102no—
268C3⋊C8—41no—
269C3⋊C8—201no—
270C22×C5C2×(C2×D3)⋊C411yescharacteristic
271C2×D5—21no—
272C2×D5—21no—
273C2×D5#82412yes—
274C4×C5—21no—
275C4×C5—21no—
276C4×C5—21no—
277C4×C5—121no—
278C4×C5—121no—
279Dic5—21no—
280Dic5—21no—
281Dic5—121no—
282Dic5—121no—
283Dic5#80512yes—
284C2×Q8—301no—
285C2×Q8—301no—
286C22×C4—51no—
287C22×C4—51no—
288C22×C4—51no—
289C2×C8—21no—
290C2×C8—61no—
291C2×C8—104no—
292C2×C8—101no—
293C2×C8—301no—
294C4⋊C4—31no—
295C4⋊C4—31no—
296C4⋊C4—61no—
297C4⋊C4—61no—
298C4⋊C4—151no—
299C4⋊C4—151no—
300C4⋊C4—301no—
301C4⋊C4—301no—
302C4⋊C4—301no—
303C4⋊C4—301no—
304C22⋊C4—301no—
305C22⋊C4—301no—
306C42—51no—
307C42—51no—
308C42—51no—
309C42—301no—
310C42—301no—
311C42C2×D3×D511yescharacteristic
312C3×C5#153111yescharacteristic, complemented, Hall
313C22×C3—52no—
314C22×C3—101no—
315C22×C3—101no—
316C22×C3D5×C22⋊C411yescharacteristic
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—21no—
320C3×C4—52no—
321C3×C4—101no—
322C3×C4—101no—
323Dic3—41no—
324Dic3—41no—
325Dic3—201no—
326Dic3—201no—
327C2×C5C2×#80511yescharacteristic
328C2×C5C2×#82411yescharacteristic
329C2×C5#513911yescharacteristic
330D5—22no—
331C23—51no—
332Q8—602no—
333Q8—602no—
334C2×C4—51no—
335C2×C4—51no—
336C2×C4—51no—
337C2×C4—61no—
338C2×C4—61no—
339C2×C4—102no—
340C2×C4—102no—
341C2×C4—201no—
342C2×C4—301no—
343C2×C4—301no—
344C2×C4C4×D3×D511yescharacteristic
345C2×C4D5×D1211yescharacteristic
346C2×C4D5×#6711yescharacteristic
347C8—22no—
348C8—102no—
349C8—121no—
350C8—601no—
351C2×C3—102no—
352C2×C3D5×#10111yescharacteristic
353C2×C3D5×#10411yescharacteristic
354C2×C3#6511011yescharacteristic
355C5#6980111yescharacteristic, complemented, Sylow
356C22—52no—
357C22—101no—
358C22—101no—
359C22D5×(C2×D3)⋊C411yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—52no—
364C4—101no—
365C4—101no—
366C4—121no—
367C4—121no—
368C4—601no—
369C4—601no—
370C3#1059915811yescharacteristic, complemented, Sylow
371C2—102no—
372C2D5×#80511yescharacteristic
373C2D5×#82411yescharacteristic
374C2#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#1531
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
70. #4465D5semidirect
312. C3×C5#1531semidirect
355. C5#69801semidirect
370. C3#10599158semidirect

Maximal subgroups

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

subgroupindex
#117524982
C3×D5×#972
#117468702
#117462862
C5×#44652
#117458512
#117458502
#105991583
#698015