Finite Group Databasebeta

← #14289236

Subgroups — #14289236

Order 1920.

500 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 92 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#11752558C211yesmaximal, characteristic, complemented
2#11751176C211yesmaximal, characteristic, complemented
3C5×#5072C211yesmaximal, characteristic
4C3×#65359C211yesmaximal, characteristic, complemented
5#11745855C211yesmaximal, characteristic, complemented
6#11745845C211yesmaximal, characteristic, complemented
7#11745837C211yesmaximal, characteristic, complemented
8#10601807—31nomaximal, Hall
9C2×D3×Dic10—21no—
10C3×C5×#127C2211yescharacteristic
11C2×#6716—21no—
12C4×Dic30C2211yescharacteristic
13C2×C5×#213—21no—
14C4×C5×D12C2211yescharacteristic
15C3×#4015C2211yescharacteristic
16#91470—21no—
17#91436—22no—
18#91435—21no—
19#91369—21no—
20#91116—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C5×#832—21no—
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×#3964—22no—
25C3×C4×#168C2211yescharacteristic
26#71205—51nomaximal, Hall
27D4×Dic10—31no—
28C5×#459—31no—
29#65364—31no—
30#65359D311yescharacteristic, complemented
31D4⋊#168—31no—
32#64706—31no—
33#64704—31no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×Dic30D411yescharacteristic
38C2×C5×D12D411yescharacteristic
39C2×C4×C5×D3—21no—
40C2×C3×Dic10—21no—
41C2×#1204—22no—
42C2×D3×Dic5—22no—
43D3×Dic10—42no—
44D3×Dic10—42no—
45C3×C42×C5C2311yescharacteristic
46#6716—42no—
47C4⋊Dic15D411yescharacteristic
48#6712—21no—
49C4×Dic15—21no—
50C2×C3⋊#168—21no—
51C5×#213—42no—
52C5×(C2×D3)⋊C4—21no—
53C5×C4⋊Dic3D411yescharacteristic
54C2×C5×C3⋊C8—21no—
55C3×C4⋊Dic5—21no—
56C3×C4⋊Dic5D412yes—
57C2×C3×#168—21no—
58#6669—22no—
59(C2×D3)⋊Dic5—22no—
60#5727—51no—
61C3×#486—51no—
62#5075—51no—
63#5072D511yescharacteristic
64#4547—51no—
65#4459—51no—
66#4456—51no—
67C22×Dic10—61no—
68C2×C5×D8—61no—
69C5×#127C2×D311yescharacteristic
70C4×C5×D4—31no—
71D4×Dic5—61no—
72C2×#687—61no—
73#4070—61no—
74#4034—61no—
75#4024—62no—
76#4015C2×D311yescharacteristic
77C4×Dic10—31no—
78C5×C4⋊C8—31no—
79C5×#102—61no—
80#3964—22no—
81#3964—61no—
82C4⋊#168—31no—
83C4×#168C2×D311yescharacteristic
84#1627—151noSylow
85C23×C3×C5—41no—
86C22×C5×D3—21no—
87C3×C5×D4—42no—
88C3×C5×D4—41no—
89C3×C5×D4—41no—
90C3×C5×D4—41no—
91C3×C5×D4—41no—
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×Dic15—21no—
96C2×Dic15—21no—
97Dic30—21no—
98Dic30D812yescomplemented
99C2×C5×Dic3—21no—
100C5×D12—21no—
101C5×D12SD1612yescomplemented
102C4×C5×D3—41no—
103C4×C5×D3—41no—
104C2×C3×Dic5—22no—
105C3×Dic10—41no—
106C3×Dic10—41no—
107#1204—44no—
108D3×Dic5—44no—
109C3⋊#168—41no—
110C3×#168—41no—
111C5×C3⋊C8—41no—
112C2×D3×Q8—101no—
113C3×C4⋊Q8—51no—
114C3×#127C2×D511yescharacteristic
115#946—101no—
116C2×#214—101no—
117C2×#213—21no—
118#896—102no—
119#893—101no—
120#888—101no—
121C4×D12C2×D511yescharacteristic
122C4×Dic6—51no—
123C3×#102—102no—
124C3×C4×C8—51no—
125#832—21no—
126#832—101no—
127C4⋊(C3⋊C8)—51no—
128C4⋊(C3⋊C8)C2×D511yescharacteristic
129C2×C5×D4—21no—
130C2×C5×D4—21no—
131C2×C5×D4—21no—
132C2×C5×D4—31no—
133C22×C4×C5—61no—
134C22×Dic5—62no—
135C2×Dic10—21no—
136C2×Dic10—31no—
137C2×Dic10—62no—
138C2×Dic10—122no—
139C2×Dic10—122no—
140C5×D8—122no—
141C2×C5×C8—61no—
142C5×C4⋊C4—31no—
143C5×C22⋊C4—61no—
144C42×C5C22×D311yescharacteristic
145C22⋊Dic5—62no—
146#687—122no—
147C4⋊Dic5—21no—
148C4⋊Dic5—31no—
149C4⋊Dic5#6712yes—
150#683—62no—
151#683—61no—
152C4×Dic5—61no—
153C2×#168—21no—
154C2×#168—61no—
155D4×Q8—151no—
156#486—51no—
157#460—151no—
158#459—31no—
159#332—151no—
160Q8⋊C8—151no—
161D4⋊C8—151no—
162C22×C3×C5—81no—
163C22×C3×C5—81no—
164C22×C3×C5—81no—
165C22×C3×C5#12011yescharacteristic
166C2×C5×D3—22no—
167C2×C5×D3—41no—
168C2×C5×D3—41no—
169C3×C4×C5—21no—
170C3×C4×C5C2×D811yescharacteristic
171C3×C4×C5C2×SD1611yescharacteristic
172C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
173C3×C4×C5#13711yescharacteristic
174Dic15—22no—
175Dic15—41no—
176C3×Dic5—42no—
177C5×Dic3—41no—
178C2×C3×Q8—101no—
179C2×C3×D4—21no—
180C2×C3×D4—21no—
181C2×C3×D4—21no—
182D3×Q8—202no—
183D3×Q8—202no—
184C2×D12C22⋊D511yescharacteristic
185C2×C4×D3—21no—
186C2×C4×D3—102no—
187C2×Dic6—51no—
188C2×Dic6—102no—
189C2×C3×C8—101no—
190C3×C4⋊C4—52no—
191C3×C4⋊C4—101no—
192C3×C42C22×D511yescharacteristic
193#214—202no—
194#213—42no—
195(C2×D3)⋊C4—21no—
196(C2×D3)⋊C4—102no—
197C4⋊Dic3—51no—
198C4⋊Dic3C22⋊D511yescharacteristic
199Dic3⋊C4—102no—
200Dic3⋊C4—101no—
201C4×Dic3—101no—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—101no—
204C23×C5—41no—
205C23×C5—61no—
206C5×D4—32no—
207C5×D4—42no—
208C5×D4—41no—
209C5×D4—41no—
210C5×D4—41no—
211C5×D4—41no—
212C5×D4—61no—
213C2×C4×C5—61no—
214C2×C4×C5—121no—
215C2×C4×C5—121no—
216C2×C4×C5D3×D411yescharacteristic
217C2×C4×C5D3×D411yescharacteristic
218C2×C4×C5C2×#6711yescharacteristic
219C2×Dic5—22no—
220C2×Dic5—61no—
221C2×Dic5—61no—
222C2×Dic5—124no—
223Dic10—32no—
224Dic10—41no—
225Dic10—41no—
226Dic10—61no—
227Dic10—124no—
228C5×C8—121no—
229#168—41no—
230#168—121no—
231C22×Q8—301no—
232C2×SD16—301no—
233C2×D8—61no—
234C4⋊Q8—51no—
235C4⋊Q8—301no—
236#127D3×D511yescharacteristic
237C22⋊Q8—302no—
238C22⋊Q8—301no—
239C4×Q8—151no—
240C4×D4—31no—
241C4×D4—301no—
242C4⋊C8—31no—
243C4⋊C8—151no—
244#102—61no—
245#102—102no—
246#102—301no—
247C4×C8—51no—
248C2×C3×C5—161no—
249C2×C3×C5#44711yescharacteristic
250C2×C3×C5#44811yescharacteristic
251C2×C3×C5#45411yescharacteristic
252C5×D3—42no—
253C23×C3—41no—
254C22×D3—21no—
255C3×Q8—201no—
256C3×Q8—201no—
257C3×D4—42no—
258C3×D4—41no—
259C3×D4—41no—
260C3×D4—41no—
261C3×D4—41no—
262C2×C3×C4—102no—
263C2×C3×C4D4×D511yescharacteristic
264C2×C3×C4D4×D511yescharacteristic
265C2×C3×C4C2×C22⋊D511yescharacteristic
266C2×Dic3—21no—
267C2×Dic3—101no—
268C2×Dic3—101no—
269D12—21no—
270D12#68712yescomplemented
271C4×D3—41no—
272C4×D3—41no—
273C4×D3—204no—
274Dic6—52no—
275Dic6—101no—
276Dic6—204no—
277C3×C8—201no—
278C3⋊C8—41no—
279C3⋊C8—201no—
280C22×C5—62no—
281C22×C5—81no—
282C22×C5—81no—
283C22×C5—81no—
284C22×C5—121no—
285C22×C5—121no—
286C22×C5#93711yescharacteristic
287C4×C5—21no—
288C4×C5—121no—
289C4×C5D3×D811yescharacteristic
290C4×C5#91111yescharacteristic
291C4×C5D3×SD1611yescharacteristic
292C4×C5#91511yescharacteristic
293Dic5—42no—
294Dic5—62no—
295Dic5—121no—
296C2×Q8—101no—
297C2×Q8—151no—
298C2×Q8—302no—
299C2×Q8—602no—
300C2×Q8—602no—
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—31no—
305C22×C4—61no—
306C22×C4—302no—
307SD16—602no—
308D8—122no—
309C2×C8—61no—
310C2×C8—101no—
311C2×C8—301no—
312C4⋊C4—31no—
313C4⋊C4—52no—
314C4⋊C4—101no—
315C4⋊C4—151no—
316C4⋊C4—302no—
317C4⋊C4—301no—
318C22⋊C4—61no—
319C22⋊C4—302no—
320C42—301no—
321C42C2×D3×D511yescharacteristic
322C3×C5#162711yescharacteristic, complemented, Hall
323C22×C3—81no—
324C22×C3—81no—
325C22×C3—81no—
326C22×C3#408311yescharacteristic
327C2×D3—22no—
328C2×D3—41no—
329C2×D3—41no—
330C3×C4—21no—
331C3×C4—202no—
332C3×C4D5×D811yescharacteristic
333C3×C4#405711yescharacteristic
334C3×C4C2×#68711yescharacteristic
335C3×C4#409711yescharacteristic
336Dic3—41no—
337Dic3—102no—
338Dic3—201no—
339C2×C5—122no—
340C2×C5—161no—
341C2×C5#506211yescharacteristic
342C2×C5#515611yescharacteristic
343C2×C5#517011yescharacteristic
344C23—41no—
345C23—61no—
346Q8—152no—
347Q8—201no—
348Q8—201no—
349Q8—301no—
350Q8—604no—
351D4—32no—
352D4—42no—
353D4—41no—
354D4—41no—
355D4—41no—
356D4—41no—
357D4—61no—
358C2×C4—61no—
359C2×C4—102no—
360C2×C4—121no—
361C2×C4—121no—
362C2×C4—301no—
363C2×C4—301no—
364C2×C4—604no—
365C2×C4D5×#6711yescharacteristic
366C2×C4D3×C22⋊D511yescharacteristic
367C2×C4#679011yescharacteristic
368C8—121no—
369C8—201no—
370C8—601no—
371C2×C3—161no—
372C2×C3#6532911yescharacteristic
373C2×C3#6544511yescharacteristic
374C2×C3#6549011yescharacteristic
375D3—42no—
376C5#7120511yescharacteristic, complemented, Sylow
377C22—62no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22—121no—
382C22—121no—
383C22#9157711yescharacteristic
384C4—21no—
385C4—121no—
386C4—202no—
387C4—302no—
388C4—601no—
389C4#9148111yescharacteristic
390C4#9148211yescharacteristic
391C4D3×#68711yescharacteristic
392C4#9148611yescharacteristic
393C3#1060180711yescharacteristic, complemented, Sylow
394C2—122no—
395C2—161no—
396C2#1174915311yescharacteristic
397C2#1174915511yescharacteristic
398C2#1174916811yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5#120
prime radicalC5×#5072C2
hypercenter#127D3×D5
hypocenterC3×C5#1627
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
1. #11752558C2semidirect
2. #11751176C2semidirect
4. C3×#65359C2semidirect
5. #11745855C2semidirect
6. #11745845C2semidirect
7. #11745837C2semidirect
30. #65359D3semidirect
98. Dic30D8semidirect
101. C5×D12SD16semidirect
270. D12#687semidirect
322. C3×C5#1627semidirect
376. C5#71205semidirect
393. C3#10601807semidirect

Maximal subgroups

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

subgroupindex
#117525582
#117511762
C5×#50722
C3×#653592
#117458552
#117458452
#117458372
#106018073
#712055