Finite Group Databasebeta

← #14289235

Subgroups — #14289235

Order 1920.

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

normal subgroups only

This group has 500 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
1Dic6×D20C211yesmaximal, characteristic, complemented
2#11751171C211yesmaximal, characteristic, complemented
3C5×#5075C211yesmaximal, characteristic, complemented
4C3×#65361C211yesmaximal, characteristic
5#11745859C211yesmaximal, characteristic, complemented
6#11745842C211yesmaximal, characteristic, complemented
7#11745834C211yesmaximal, characteristic, complemented
8#10601828—31nomaximal, Hall
9C2×D5×Dic6—21no—
10C3×C5×#127C2211yescharacteristic
11#91758C2211yescharacteristic
12C2×C5×#214—21no—
13C4×C5×Dic6C2211yescharacteristic
14C2×C3×#686—21no—
15C3×C4×D20C2211yescharacteristic
16#91469—21no—
17Dic3×D20—21no—
18#91422—22no—
19#91360—21no—
20#91116—22no—
21C4×C3⋊#168C2211yescharacteristic
22C5×#832—21no—
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×#3964—21no—
25C3×C4⋊#168C2211yescharacteristic
26#71014—51nomaximal, Hall
27Q8×D20—31no—
28C5×#460—31no—
29#65361D311yescharacteristic
30#65359—31no—
31Q8⋊#168—31no—
32#64703—31no—
33#64702—31no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×Dic30—21no—
38C2×C5×Dic6D411yescharacteristic
39C2×C3×D20D411yescharacteristic
40C2×C3×C4×D5—21no—
41C2×#1204—22no—
42C2×D5×Dic3—22no—
43D5×Dic6—42no—
44D5×Dic6—42no—
45C3×C42×C5C2311yescharacteristic
46C4⋊Dic15—21no—
47C4⋊Dic15D412yes—
48C2×C3⋊#168—21no—
49C5×#214—42no—
50C5×C4⋊Dic3D411yescharacteristic
51C5×Dic3⋊C4—21no—
52C4×C5×Dic3—21no—
53C2×C5×C3⋊C8—21no—
54C3×#686—42no—
55C3×#685—21no—
56C3×C4⋊Dic5D411yescharacteristic
57C2×C3×#168—21no—
58Dic3⋊Dic5—22no—
59#6665—22no—
60D4×Dic6—51no—
61C3×#459—51no—
62#5075D511yescharacteristic, complemented
63#5070—51no—
64D4⋊(C3⋊C8)—51no—
65#4486—51no—
66#4484—51no—
67C2×Q8×D5—61no—
68C2×C5×SD16—61no—
69C5×#127C2×D311yescharacteristic
70C4×C5×Q8—31no—
71C2×#686—21no—
72#4043—62no—
73#4043—61no—
74C4×D20—61no—
75C4×D20C2×D311yescharacteristic
76#4015—31no—
77#4015—61no—
78C5×C4⋊C8—31no—
79C5×#102—61no—
80#3964—21no—
81#3964—62no—
82C4⋊#168C2×D311yescharacteristic
83C4×#168—31no—
84#1627—151noSylow
85C23×C3×C5—41no—
86C22×C3×D5—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—22no—
96Dic30—41no—
97Dic30—41no—
98C2×C5×Dic3—21no—
99C2×C5×Dic3—21no—
100C5×Dic6—21no—
101C5×Dic6D812yescomplemented
102C2×C3×Dic5—21no—
103C3×D20—21no—
104C3×D20SD1612yescomplemented
105C3×C4×D5—41no—
106C3×C4×D5—41no—
107#1204—44no—
108D5×Dic3—44no—
109C3⋊#168—41no—
110C3×#168—41no—
111C5×C3⋊C8—41no—
112C22×Dic6—101no—
113C2×C3×D8—101no—
114C3×#127C2×D511yescharacteristic
115C3×C4×D4—51no—
116D4×Dic3—101no—
117C2×#214—21no—
118#924—101no—
119#888—101no—
120#878—102no—
121#869—51no—
122C4×Dic6C2×D511yescharacteristic
123C3×C4⋊C8—51no—
124C3×#102—101no—
125#832—21no—
126#832—102no—
127C4⋊(C3⋊C8)C2×D511yescharacteristic
128C4×C3⋊C8—51no—
129C2×C5×Q8—31no—
130C2×C5×D4—21no—
131C2×C5×D4—21no—
132C2×C5×D4—21no—
133Q8×D5—122no—
134Q8×D5—122no—
135C2×D20#6711yescharacteristic
136C2×C4×D5—21no—
137C2×C4×D5—62no—
138C2×Dic10—62no—
139C2×Dic10—61no—
140C5×SD16—122no—
141C2×C5×C8—61no—
142C5×C4⋊C4—31no—
143C5×C4⋊C4—61no—
144C42×C5—61no—
145C42×C5C22×D311yescharacteristic
146#686—42no—
147#685—21no—
148#685—62no—
149C4⋊Dic5—32no—
150C4⋊Dic5—62no—
151C4⋊Dic5—61no—
152C4⋊Dic5#6711yescharacteristic
153C2×#168—21no—
154C2×#168—61no—
155D4×Q8—151no—
156#486—151no—
157#460—31no—
158#459—51no—
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×C3×D5—22no—
167C2×C3×D5—41no—
168C2×C3×D5—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—42no—
175C3×Dic5—41no—
176C5×Dic3—22no—
177C5×Dic3—41no—
178C2×C3×D4—21no—
179C2×C3×D4—21no—
180C2×C3×D4—21no—
181C2×C3×D4—51no—
182C22×C3×C4—101no—
183C22×Dic3—102no—
184C2×Dic6—102no—
185C2×Dic6—101no—
186C2×Dic6—202no—
187C2×Dic6—202no—
188C2×Dic6C22⋊D511yescharacteristic
189C3×D8—202no—
190C2×C3×C8—101no—
191C3×C4⋊C4—51no—
192C3×C22⋊C4—101no—
193C3×C42C22×D511yescharacteristic
194#217—102no—
195#214—42no—
196C4⋊Dic3—52no—
197C4⋊Dic3—101no—
198C4⋊Dic3C22⋊D511yescharacteristic
199Dic3⋊C4—21no—
200Dic3⋊C4—102no—
201C4×Dic3—21no—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—101no—
204C23×C5—41no—
205C22×D5—21no—
206C5×Q8—32no—
207C5×Q8—61no—
208C5×D4—42no—
209C5×D4—41no—
210C5×D4—41no—
211C5×D4—41no—
212C5×D4—41no—
213C2×C4×C5—61no—
214C2×C4×C5—61no—
215C2×C4×C5D3×D411yescharacteristic
216C2×C4×C5D3×D411yescharacteristic
217C2×C4×C5C2×#6711yescharacteristic
218C2×Dic5—21no—
219C2×Dic5—62no—
220D20—21no—
221D20#21412yescomplemented
222C4×D5—41no—
223C4×D5—41no—
224C4×D5—124no—
225Dic10—124no—
226Dic10—121no—
227Dic10—121no—
228C5×C8—121no—
229#168—41no—
230#168—121no—
231C22×Q8—301no—
232C2×SD16—61no—
233C2×D8—101no—
234C4⋊Q8—151no—
235C4⋊Q8—301no—
236#127D3×D511yescharacteristic
237C22⋊Q8—302no—
238C22⋊Q8—301no—
239C4×Q8—31no—
240C4×D4—51no—
241C4×D4—301no—
242C4⋊C8—31no—
243C4⋊C8—51no—
244#102—61no—
245#102—101no—
246#102—302no—
247C4×C8—151no—
248C2×C3×C5—161no—
249C2×C3×C5#44711yescharacteristic
250C2×C3×C5#44811yescharacteristic
251C2×C3×C5#45411yescharacteristic
252C3×D5—42no—
253C23×C3—41no—
254C23×C3—101no—
255C3×D4—42no—
256C3×D4—41no—
257C3×D4—41no—
258C3×D4—41no—
259C3×D4—41no—
260C3×D4—52no—
261C3×D4—101no—
262C2×C3×C4—101no—
263C2×C3×C4—201no—
264C2×C3×C4—201no—
265C2×C3×C4D4×D511yescharacteristic
266C2×C3×C4D4×D511yescharacteristic
267C2×C3×C4C2×C22⋊D511yescharacteristic
268C2×Dic3—21no—
269C2×Dic3—21no—
270C2×Dic3—102no—
271C2×Dic3—204no—
272Dic6—21no—
273Dic6—204no—
274Dic6—201no—
275Dic6—201no—
276Dic6#68612yescomplemented
277C3×C8—201no—
278C3⋊C8—41no—
279C3⋊C8—201no—
280C22×C5—81no—
281C22×C5—81no—
282C22×C5—81no—
283C22×C5#93711yescharacteristic
284C2×D5—22no—
285C2×D5—41no—
286C2×D5—41no—
287C4×C5—21no—
288C4×C5—62no—
289C4×C5—121no—
290C4×C5D3×D811yescharacteristic
291C4×C5#91111yescharacteristic
292C4×C5C2×#21411yescharacteristic
293C4×C5#95111yescharacteristic
294Dic5—41no—
295Dic5—122no—
296C2×Q8—31no—
297C2×Q8—302no—
298C2×Q8—301no—
299C2×Q8—602no—
300C2×Q8—602no—
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—51no—
305C22×C4—101no—
306C22×C4—302no—
307SD16—122no—
308D8—202no—
309C2×C8—61no—
310C2×C8—101no—
311C2×C8—301no—
312C4⋊C4—31no—
313C4⋊C4—51no—
314C4⋊C4—61no—
315C4⋊C4—152no—
316C4⋊C4—302no—
317C4⋊C4—301no—
318C22⋊C4—101no—
319C22⋊C4—302no—
320C42—61no—
321C42C2×D3×D511yescharacteristic
322C3×C5#162711yescharacteristic, complemented, Hall
323C22×C3—81no—
324C22×C3—81no—
325C22×C3—81no—
326C22×C3—102no—
327C22×C3—201no—
328C22×C3—201no—
329C22×C3#408311yescharacteristic
330C3×C4—21no—
331C3×C4—201no—
332C3×C4D5×SD1611yescharacteristic
333C3×C4#406111yescharacteristic
334C3×C4C2×#68611yescharacteristic
335C3×C4#409511yescharacteristic
336Dic3—22no—
337Dic3—41no—
338Dic3—202no—
339C2×C5—161no—
340C2×C5#504011yescharacteristic
341C2×C5#515611yescharacteristic
342C2×C5#520111yescharacteristic
343D5—42no—
344C23—41no—
345C23—101no—
346Q8—32no—
347Q8—61no—
348Q8—604no—
349Q8—601no—
350Q8—601no—
351D4—42no—
352D4—41no—
353D4—41no—
354D4—41no—
355D4—41no—
356D4—52no—
357D4—101no—
358C2×C4—61no—
359C2×C4—61no—
360C2×C4—101no—
361C2×C4—201no—
362C2×C4—201no—
363C2×C4—302no—
364C2×C4—604no—
365C2×C4D5×#6711yescharacteristic
366C2×C4D3×C22⋊D511yescharacteristic
367C2×C4#679011yescharacteristic
368C8—121no—
369C8—201no—
370C8—601no—
371C2×C3—161no—
372C2×C3—202no—
373C2×C3#6532511yescharacteristic
374C2×C3#6545911yescharacteristic
375C2×C3#6549011yescharacteristic
376C5#7101411yescharacteristic, complemented, Sylow
377C22—81no—
378C22—81no—
379C22—81no—
380C22—102no—
381C22—201no—
382C22—201no—
383C22#9157711yescharacteristic
384C4—21no—
385C4—62no—
386C4—121no—
387C4—201no—
388C4—602no—
389C4D3×#68611yescharacteristic
390C4#9148011yescharacteristic
391C4D5×#21411yescharacteristic
392C4#9148411yescharacteristic
393C3#1060182811yescharacteristic, complemented, Sylow
394C2—161no—
395C2—202no—
396C2#1174915211yescharacteristic
397C2#1174915411yescharacteristic
398C2#1174916611yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5#120
prime radicalC3×#65361C2
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. Dic6×D20C2semidirect
2. #11751171C2semidirect
3. C5×#5075C2semidirect
5. #11745859C2semidirect
6. #11745842C2semidirect
7. #11745834C2semidirect
62. #5075D5semidirect
101. C5×Dic6D8semidirect
104. C3×D20SD16semidirect
221. D20#214semidirect
276. Dic6#686semidirect
322. C3×C5#1627semidirect
376. C5#71014semidirect
393. C3#10601828semidirect

Maximal subgroups

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

subgroupindex
Dic6×D202
#117511712
C5×#50752
C3×#653612
#117458592
#117458422
#117458342
#106018283
#710145