Finite Group Databasebeta

← #14284429

Subgroups — #14284429

Order 1920.

400 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 82 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#11750806C211yesmaximal, characteristic, complemented
3#11746940C211yesmaximal, characteristic, complemented
4C5×#4465C211yesmaximal, characteristic, complemented
5C3×#64684C211yesmaximal, characteristic, complemented
6#11745850C211yesmaximal, characteristic, complemented
7#11745846C211yesmaximal, characteristic, complemented
8#10599161—31nomaximal, Hall
9C42×D15C2211yescharacteristic
10C5×#870C2211yescharacteristic
11C3×#4021C2211yescharacteristic
12#91465C411yescharacteristic
13#91434C411yescharacteristic
14#91396—21no—
15#91394—21no—
16#91390C411yescharacteristic
17#91366—21no—
18#91354—21no—
19#91331C411yescharacteristic
20C3×C5×#97C2211yescharacteristic
21#91104—21no—
22#91098—21no—
23#91087C2211yescharacteristic
24C5×#803C2211yescharacteristic
25C3×#3935C2211yescharacteristic
26#90983—21no—
27#90957—21no—
28#68348—51nomaximal, Hall
29#66025—31no—
30#64994—31no—
31#64994—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—
49C5×C4⋊Dic3C2×C411yescharacteristic
50C5×C4⋊Dic3C2×C411yescharacteristic
51C5×Dic3⋊C4—21no—
52C5×Dic3⋊C4—21no—
53C2×C5×C3⋊C8—21no—
54C3×#685—21no—
55C3×#685—21no—
56C2×C3×#168—21no—
57Dic3⋊Dic5—21no—
58#6668—21no—
59#6667—21no—
60#6665—21no—
61#6665—21no—
62Dic3×Dic5—21no—
63#5680—51no—
64#4705—51no—
65#4705—51no—
66C3×#329—51no—
67#4540—51no—
68#4465—51no—
69#4465D511yescharacteristic, complemented
70C5×#125—31no—
71#4044—61no—
72#4043—31no—
73#4041—31no—
74#4040—61no—
75#4039—31no—
76#4039—61no—
77#4038—61no—
78#4033—31no—
79#4021C2×D311yescharacteristic
80C42×D5—31no—
81C5×#97—31no—
82C5×#97C2×D311yescharacteristic
83#3952—61no—
84#3952—61no—
85#3946—61no—
86#3946—61no—
87#3935—31no—
88#3935C2×D311yescharacteristic
89#1535—151noSylow
90C22×D15C22⋊C411yescharacteristic
91C22×C3×D5—21no—
92C2×C3×C4×C5C22×C411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×Dic15C22⋊C411yescharacteristic
96C2×Dic15C22⋊C411yescharacteristic
97C2×Dic15C22⋊C411yescharacteristic
98C4×D15—41no—
99C4×D15—41no—
100C4×D15—41no—
101C2×C5×Dic3—21no—
102C2×C5×Dic3—21no—
103C2×C3×Dic5—21no—
104C3×D20—41no—
105C3×Dic10—41no—
106#1202—42no—
107D5×Dic3—42no—
108C3×C5×C8—41no—
109C3⋊#168—41no—
110C3×#168—41no—
111C5×C3⋊C8—41no—
112C3×#124—51no—
113#946—51no—
114Q8×Dic3—51no—
115#938—51no—
116D4×Dic3—51no—
117#883—101no—
118#67⋊C4—101no—
119#879—101no—
120#877—101no—
121C42×D3—51no—
122#870C2×D511yescharacteristic
123C3×#97—51no—
124C3×#97C2×D511yescharacteristic
125(C2×D3)⋊C8—101no—
126(C2×D3)⋊C8—101no—
127Dic3⋊C8—101no—
128Dic3⋊C8—101no—
129#803—51no—
130#803C2×D511yescharacteristic
131C2×D20—61no—
132C2×D20C4×D311yescharacteristic
133C2×C4×D5—31no—
134C2×C4×D5—31no—
135C2×C4×D5—31no—
136C2×C4×D5—61no—
137C2×Dic10C4×D311yescharacteristic
138C2×C5×C8—21no—
139C2×C5×C8—61no—
140C5×C4⋊C4—31no—
141C5×C4⋊C4—31no—
142C5×C4⋊C4—61no—
143C5×C4⋊C4—61no—
144C42×C5C22×D311yescharacteristic
145#685—21no—
146#685—21no—
147#685—61no—
148#685—61no—
149#685—61no—
150C4⋊Dic5—61no—
151#683—61no—
152C4×Dic5—31no—
153C4×Dic5—31no—
154C4×Dic5—31no—
155C4×Dic5—61no—
156C2×#168—21no—
157C2×#168—61no—
158#529—151no—
159#432—151no—
160#432—151no—
161#330—31no—
162#330—151no—
163#329—51no—
164#329—151no—
165C22×C3×C5C2×C22⋊C411yescharacteristic
166C2×D15—21no—
167C2×D15—21no—
168C2×D15—21no—
169C2×C3×D5—41no—
170C2×C3×D5—41no—
171C2×C3×D5—41no—
172C3×C4×C5—21no—
173C3×C4×C5—21no—
174C3×C4×C5—21no—
175Dic15—21no—
176Dic15—21no—
177Dic15—21no—
178C3×Dic5—41no—
179C5×Dic3—41no—
180C5×Dic3—41no—
181C2×C3×Q8—51no—
182C2×C3×D4—51no—
183C2×#67—101no—
184C22×Dic3—101no—
185C2×C4×D3—51no—
186C2×C4×D3—51no—
187C2×C4×D3—51no—
188C2×C3×C8—21no—
189C2×C3×C8—101no—
190C3×C22⋊C4—101no—
191C3×C22⋊C4—101no—
192C3×C42C22×D511yescharacteristic
193#217—101no—
194#217—101no—
195(C2×D3)⋊C4—101no—
196C4⋊Dic3—101no—
197C4⋊Dic3C4×D511yescharacteristic
198C4⋊Dic3C4×D511yescharacteristic
199Dic3⋊C4—21no—
200Dic3⋊C4—21no—
201Dic3⋊C4—101no—
202C4×Dic3—51no—
203C4×Dic3—51no—
204C4×Dic3—51no—
205C4×Dic3—101no—
206C2×C3⋊C8—21no—
207C2×C3⋊C8—101no—
208C22×D5—21no—
209C22×D5—31no—
210C2×C4×C5—61no—
211C2×C4×C5—61no—
212C2×C4×C5C2×C4×D311yescharacteristic
213C2×C4×C5D3×D411yescharacteristic
214C2×C4×C5D3×D411yescharacteristic
215C2×Dic5—21no—
216C2×Dic5—31no—
217C2×Dic5—31no—
218C2×Dic5—31no—
219D20—41no—
220D20—122no—
221C4×D5—121no—
222C4×D5—121no—
223C4×D5—121no—
224C4×D5—122no—
225Dic10—41no—
226C5×C8—41no—
227C5×C8—121no—
228#168—41no—
229#168—121no—
230#126—301no—
231#125—31no—
232#124—51no—
233#123—301no—
234C22⋊Q8—151no—
235#121—151no—
236C4×Q8—151no—
237C4×D4—151no—
238C4×D4—301no—
239#117—301no—
240C2×C42—151no—
241C4⋊C8—301no—
242C4⋊C8—301no—
243C22⋊C8—301no—
244C22⋊C8—301no—
245#97—31no—
246#97—51no—
247#97—151no—
248#97D3×D511yescharacteristic
249C2×C3×C5#41311yescharacteristic
250C2×C3×C5#42111yescharacteristic
251C2×C3×C5#42111yescharacteristic
252D15—41no—
253C3×D5—81no—
254C23×C3—101no—
255C22×D3—51no—
256C3×Q8—201no—
257C3×D4—201no—
258C2×C3×C4—101no—
259C2×C3×C4C2×C4×D511yescharacteristic
260C2×C3×C4D4×D511yescharacteristic
261C2×C3×C4D4×D511yescharacteristic
262#67—202no—
263C2×Dic3—21no—
264C2×Dic3—21no—
265C2×Dic3—51no—
266C2×Dic3—51no—
267C2×Dic3—51no—
268C2×Dic3—202no—
269C4×D3—201no—
270C4×D3—201no—
271C4×D3—201no—
272C3×C8—41no—
273C3×C8—201no—
274C3⋊C8—41no—
275C3⋊C8—201no—
276C22×C5D3×C22⋊C411yescharacteristic
277C2×D5—41no—
278C2×D5—41no—
279C2×D5—41no—
280C2×D5—61no—
281C2×D5—61no—
282C2×D5—61no—
283C4×C5—21no—
284C4×C5—21no—
285C4×C5—21no—
286C4×C5—121no—
287C4×C5—121no—
288Dic5—41no—
289Dic5—61no—
290Dic5—61no—
291Dic5—61no—
292C2×Q8—51no—
293C2×D4—51no—
294C2×D4—301no—
295C22×C4—151no—
296C22×C4—151no—
297C22×C4—151no—
298C22×C4—301no—
299C2×C8—21no—
300C2×C8—61no—
301C2×C8—101no—
302C2×C8—301no—
303C4⋊C4—31no—
304C4⋊C4—31no—
305C4⋊C4—61no—
306C4⋊C4—61no—
307C4⋊C4—301no—
308C4⋊C4—301no—
309C22⋊C4—101no—
310C22⋊C4—101no—
311C22⋊C4—301no—
312C22⋊C4—301no—
313C22⋊C4—301no—
314C42—151no—
315C42—151no—
316C42—151no—
317C42—301no—
318C42C2×D3×D511yescharacteristic
319C3×C5#153511yescharacteristic, complemented, Hall
320C22×C3—201no—
321C22×C3—201no—
322C22×C3—201no—
323C22×C3D5×C22⋊C411yescharacteristic
324C2×D3—101no—
325C2×D3—101no—
326C2×D3—101no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—201no—
331Dic3—41no—
332Dic3—41no—
333Dic3—101no—
334Dic3—101no—
335Dic3—101no—
336C2×C5#474511yescharacteristic
337C2×C5#482111yescharacteristic
338C2×C5#482111yescharacteristic
339D5—81no—
340D5—121no—
341C23—101no—
342C23—151no—
343Q8—201no—
344D4—201no—
345D4—602no—
346C2×C4—61no—
347C2×C4—61no—
348C2×C4—101no—
349C2×C4—151no—
350C2×C4—151no—
351C2×C4—151no—
352C2×C4—601no—
353C2×C4—601no—
354C2×C4—601no—
355C2×C4—602no—
356C2×C4C4×D3×D511yescharacteristic
357C2×C4#677711yescharacteristic
358C2×C4#679011yescharacteristic
359C8—41no—
360C8—121no—
361C8—201no—
362C8—601no—
363C2×C3—401no—
364C2×C3#6504011yescharacteristic
365C2×C3#6511011yescharacteristic
366C2×C3#6511011yescharacteristic
367D3—201no—
368C5#6834811yescharacteristic, complemented, Sylow
369C22—201no—
370C22—201no—
371C22—201no—
372C22—301no—
373C22—301no—
374C22—301no—
375C22#9147311yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—121no—
380C4—121no—
381C4—201no—
382C4—301no—
383C4—301no—
384C4—301no—
385C3#1059916111yescharacteristic, complemented, Sylow
386C2—401no—
387C2—601no—
388C2#1174711311yescharacteristic
389C2#1174823711yescharacteristic
390C2#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#1535
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. #11750806C2semidirect
3. #11746940C2semidirect
4. C5×#4465C2semidirect
5. C3×#64684C2semidirect
6. #11745850C2semidirect
7. #11745846C2semidirect
35. #64684D3semidirect
69. #4465D5semidirect
319. C3×C5#1535semidirect
368. C5#68348semidirect
385. C3#10599161semidirect

Maximal subgroups

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

subgroupindex
#117526202
#117508062
#117469402
C5×#44652
C3×#646842
#117458502
#117458462
#105991613
#683485