Finite Group Databasebeta

← #14289445

Subgroups — #14289445

Order 1920.

512 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 96 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
1C5×#5718C211yesmaximal, characteristic
2#11751177C211yesmaximal, characteristic, complemented
3#11746961C211yesmaximal, characteristic, complemented
4#11746883C211yesmaximal, characteristic, complemented
5C3×#64764C211yesmaximal, characteristic, complemented
6#11745842C211yesmaximal, characteristic, complemented
7#11745836C211yesmaximal, characteristic, complemented
8#10602712—31nomaximal, Hall
9C2×C5×#237—21no—
10C3×C5×#127C2211yescharacteristic
11C2×#6716—22no—
12#91758C2211yescharacteristic
13C5×#940—21no—
14C5×#939—22no—
15C5×#938—21no—
16C5×D4×Dic3—21no—
17C4×C5×D12C2211yescharacteristic
18C4×C5×Dic6C2211yescharacteristic
19C4×C3⋊#168C2211yescharacteristic
20C3×C4⋊#168C2211yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22#90988—21no—
23#90985—21no—
24#90973—21no—
25#90967—21no—
26#68405—51nomaximal, Hall
27C5×#550—31no—
28#65365—31no—
29#65310—31no—
30#65297—31no—
31#64764D311yescharacteristic, complemented
32Q8⋊#168—31no—
33D4⋊#168—31no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4D412yes—
37C2×Dic30—21no—
38C2×C5×#67—22no—
39C2×C5×#67—22no—
40C22×C5×Dic3—22no—
41C5×#237—42no—
42C5×#237—42no—
43C2×C5×D12D411yescharacteristic
44C2×C4×C5×D3—21no—
45C2×C5×Dic6D411yescharacteristic
46C3×C42×C5C2311yescharacteristic
47#6716—44no—
48C4⋊Dic15—21no—
49C4⋊Dic15—21no—
50C2×C3⋊#168—21no—
51C5×#217—22no—
52C5×(C2×D3)⋊C4—21no—
53C5×C4⋊Dic3D411yescharacteristic
54C5×C4⋊Dic3D411yescharacteristic
55C5×Dic3⋊C4—21no—
56C4×C5×Dic3—21no—
57C2×C3×#168—21no—
58C2×C3×#168—21no—
59#5718D511yescharacteristic
60#5076—51no—
61#4850—51no—
62#4842—51no—
63C3×#331—51no—
64#4484—51no—
65#4483—51no—
66C2×C5×#41—61no—
67C5×#127—61no—
68C5×#127C2×D311yescharacteristic
69C5×#121—61no—
70C5×#121—62no—
71C4×C5×Q8—31no—
72C4×C5×D4—31no—
73C4×C5×D4—61no—
74C2×#687—62no—
75#4015—31no—
76#3967—61no—
77#3964—61no—
78#3940—61no—
79#3939—61no—
80C4⋊#168C2×D311yescharacteristic
81C4⋊#168C2×D311yescharacteristic
82C4×#168—31no—
83#1631—151noSylow
84C23×C3×C5—22no—
85C22×C5×D3—21no—
86C3×C5×D4—42no—
87C3×C5×D4—41no—
88C3×C5×D4—41no—
89C3×C5×D4—41no—
90C3×C5×D4—41no—
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×Dic15—41no—
95Dic30—42no—
96C5×#67—44no—
97C5×#67—82no—
98C2×C5×Dic3—21no—
99C2×C5×Dic3—21no—
100C2×C5×Dic3—21no—
101C2×C5×Dic3—44no—
102C5×D12—21no—
103C5×D12—21no—
104C4×C5×D3—41no—
105C4×C5×D3—41no—
106C5×Dic6—21no—
107C5×Dic6SD1612yescomplemented
108C3⋊#168—22no—
109C3×#168—41no—
110C3×#168—41no—
111C2×#237—21no—
112C3×#127C2×D511yescharacteristic
113#940—21no—
114#939—22no—
115#938—21no—
116D4×Dic3—21no—
117C2×#214—102no—
118C4×D12C2×D511yescharacteristic
119#869—51no—
120C4×Dic6C2×D511yescharacteristic
121C3×C4⋊C8—51no—
122C3×C4⋊C8—51no—
123#821—101no—
124#818—101no—
125#817—101no—
126#816—101no—
127C4×C3⋊C8—51no—
128C5×#41—122no—
129C5×#41—122no—
130C2×C5×Q8—31no—
131C2×C5×D4—21no—
132C2×C5×D4—21no—
133C2×C5×D4—31no—
134C2×C5×D4—62no—
135C2×C5×D4—62no—
136C2×C5×D4D1212yes—
137C22×C4×C5—62no—
138C22×C4×C5—61no—
139C2×Dic10—61no—
140C5×C4⋊C4—31no—
141C5×C4⋊C4—31no—
142C5×C4⋊C4—61no—
143C5×C22⋊C4—62no—
144C5×C22⋊C4—61no—
145C42×C5—61no—
146C42×C5C22×D311yescharacteristic
147#687—124no—
148C4⋊Dic5—61no—
149C4⋊Dic5—61no—
150C2×#168—21no—
151C2×#168—21no—
152C2×#168—61no—
153#550—31no—
154#492—151no—
155#477—151no—
156#476—151no—
157#331—51no—
158Q8⋊C8—151no—
159D4⋊C8—151no—
160C22×C3×C5—42no—
161C22×C3×C5—42no—
162C22×C3×C5—42no—
163C22×C3×C5#12011yescharacteristic
164C2×C5×D3—41no—
165C2×C5×D3—41no—
166C2×C5×D3—41no—
167C3×C4×C5—21no—
168C3×C4×C5C2×SD1611yescharacteristic
169C3×C4×C5#13511yescharacteristic
170C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
171C3×C4×C5#13711yescharacteristic
172Dic15—81no—
173C5×Dic3—22no—
174C5×Dic3—41no—
175C5×Dic3—41no—
176C2×C3×D4—21no—
177C2×C3×D4—21no—
178C2×C3×D4C22⋊D512yes—
179C2×#67—22no—
180C2×#67—22no—
181C22×Dic3—22no—
182#237—42no—
183#237—42no—
184C2×D12C22⋊D511yescharacteristic
185C2×C4×D3—21no—
186C2×Dic6—101no—
187C2×Dic6C22⋊D511yescharacteristic
188C2×C3×C8—101no—
189C2×C3×C8—101no—
190C3×C42C22×D511yescharacteristic
191#217—22no—
192#214—204no—
193(C2×D3)⋊C4—21no—
194C4⋊Dic3—101no—
195C4⋊Dic3—101no—
196C4⋊Dic3C22⋊D511yescharacteristic
197C4⋊Dic3C22⋊D511yescharacteristic
198Dic3⋊C4—21no—
199C4×Dic3—21no—
200C2×C3⋊C8—101no—
201C23×C5—22no—
202C23×C5—61no—
203C5×Q8—32no—
204C5×Q8—61no—
205C5×D4—42no—
206C5×D4—41no—
207C5×D4—41no—
208C5×D4—41no—
209C5×D4—41no—
210C5×D4—61no—
211C5×D4—61no—
212C5×D4—124no—
213C5×D4—242no—
214C2×C4×C5—61no—
215C2×C4×C5—61no—
216C2×C4×C5—61no—
217C2×C4×C5—124no—
218C2×C4×C5—121no—
219C2×C4×C5—121no—
220C2×C4×C5C2×D1211yescharacteristic
221C2×C4×C5D3×D411yescharacteristic
222C2×C4×C5D3×D411yescharacteristic
223C2×Dic5—121no—
224Dic10—122no—
225#168—41no—
226#168—41no—
227#168—62no—
228C2×#41—61no—
229C2×SD16—302no—
230C4⋊Q8—151no—
231#127—61no—
232#127D3×D511yescharacteristic
233#121—61no—
234#121—62no—
235C4×Q8—31no—
236C4×D4—31no—
237C4×D4—61no—
238#107—301no—
239#106—301no—
240C4⋊C8—51no—
241C4⋊C8—51no—
242#103—301no—
243#102—301no—
244C4×C8—151no—
245C2×C3×C5—82no—
246C2×C3×C5#45011yescharacteristic
247C2×C3×C5#45211yescharacteristic
248C2×C3×C5#45311yescharacteristic
249C5×D3—81no—
250C23×C3—22no—
251C22×D3—21no—
252C3×D4—42no—
253C3×D4—41no—
254C3×D4—41no—
255C3×D4—41no—
256C3×D4—41no—
257C2×C3×C4C2×C22⋊D511yescharacteristic
258C2×C3×C4C2×C22⋊D511yescharacteristic
259C2×C3×C4C2×C22⋊D511yescharacteristic
260#67—44no—
261#67—82no—
262C2×Dic3—21no—
263C2×Dic3—21no—
264C2×Dic3—21no—
265C2×Dic3—44no—
266C2×Dic3—201no—
267D12—21no—
268D12—21no—
269C4×D3—41no—
270C4×D3—41no—
271Dic6—21no—
272Dic6—202no—
273Dic6#68712yescomplemented
274C3×C8—201no—
275C3×C8—201no—
276C3⋊C8—102no—
277C22×C5—42no—
278C22×C5—42no—
279C22×C5—42no—
280C22×C5—121no—
281C22×C5—121no—
282C22×C5—121no—
283C22×C5#88211yescharacteristic
284C4×C5—21no—
285C4×C5—62no—
286C4×C5—121no—
287C4×C5—121no—
288C4×C5#91111yescharacteristic
289C4×C5#91211yescharacteristic
290C4×C5D3×SD1611yescharacteristic
291C4×C5#91511yescharacteristic
292Dic5—241no—
293#41—122no—
294#41—122no—
295C2×Q8—31no—
296C2×Q8—301no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—31no—
300C2×D4—62no—
301C2×D4—62no—
302C2×D4#120312yes—
303C22×C4—62no—
304C22×C4—61no—
305SD16—604no—
306C2×C8—101no—
307C2×C8—101no—
308C2×C8—301no—
309C4⋊C4—31no—
310C4⋊C4—31no—
311C4⋊C4—61no—
312C4⋊C4—301no—
313C4⋊C4—301no—
314C22⋊C4—62no—
315C22⋊C4—61no—
316C42—61no—
317C42C2×D3×D511yescharacteristic
318C3×C5#163111yescharacteristic, complemented, Hall
319C22×C3—42no—
320C22×C3—42no—
321C22×C3—42no—
322C22×C3#409911yescharacteristic
323C2×D3—41no—
324C2×D3—41no—
325C2×D3—41no—
326C3×C4—21no—
327C3×C4#407811yescharacteristic
328C3×C4C2×#68711yescharacteristic
329C3×C4#409611yescharacteristic
330C3×C4#409711yescharacteristic
331Dic3—22no—
332Dic3—41no—
333Dic3—41no—
334Dic3—401no—
335C2×C5—82no—
336C2×C5—241no—
337C2×C5#474711yescharacteristic
338C2×C5#477611yescharacteristic
339C2×C5#478311yescharacteristic
340C23—22no—
341C23—61no—
342Q8—32no—
343Q8—61no—
344Q8—602no—
345D4—42no—
346D4—41no—
347D4—41no—
348D4—41no—
349D4—41no—
350D4—61no—
351D4—61no—
352D4—124no—
353D4—242no—
354C2×C4—61no—
355C2×C4—61no—
356C2×C4—61no—
357C2×C4—124no—
358C2×C4—121no—
359C2×C4—121no—
360C2×C4—601no—
361C2×C4C2×#120311yescharacteristic
362C2×C4D3×C22⋊D511yescharacteristic
363C2×C4D3×C22⋊D511yescharacteristic
364C8—201no—
365C8—201no—
366C8—302no—
367C2×C3—82no—
368C2×C3#6550711yescharacteristic
369C2×C3#6552811yescharacteristic
370C2×C3#6553011yescharacteristic
371D3—81no—
372C5#6840511yescharacteristic, complemented, Sylow
373C22—42no—
374C22—42no—
375C22—42no—
376C22—121no—
377C22—121no—
378C22—121no—
379C22#9157011yescharacteristic
380C4—21no—
381C4—62no—
382C4—121no—
383C4—121no—
384C4—1201no—
385C4D3×#68711yescharacteristic
386C4#9148611yescharacteristic
387C4#9149311yescharacteristic
388C4#9149411yescharacteristic
389C3#1060271211yescharacteristic, complemented, Sylow
390C2—82no—
391C2—241no—
392C2#1174905411yescharacteristic
393C2#1174905611yescharacteristic
394C2#1174914111yescharacteristic
subgroupG/H
centerC22#91570
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5#120
prime radicalC5×#5718C2
hypercenter#127D3×D5
hypocenterC3×C5#1631
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #11751177C2semidirect
3. #11746961C2semidirect
4. #11746883C2semidirect
5. C3×#64764C2semidirect
6. #11745842C2semidirect
7. #11745836C2semidirect
31. #64764D3semidirect
107. C5×Dic6SD16semidirect
273. Dic6#687semidirect
318. C3×C5#1631semidirect
372. C5#68405semidirect
389. C3#10602712semidirect

Maximal subgroups

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

subgroupindex
C5×#57182
#117511772
#117469612
#117468832
C3×#647642
#117458422
#117458362
#106027123
#684055