Finite Group Databasebeta

← #14289448

Subgroups — #14289448

Order 1920.

512 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C3×#65911C211yesmaximal, characteristic
2C5×#5021C211yesmaximal, characteristic, complemented
3#11747079C211yesmaximal, characteristic, complemented
4#11746880C211yesmaximal, characteristic, complemented
5#11746356C211yesmaximal, characteristic, complemented
6#11745852C211yesmaximal, characteristic, complemented
7#11745834C211yesmaximal, characteristic, complemented
8#10601953—31nomaximal, Hall
9C2×C3×#713—21no—
10C3×C4×C5×Q8C2211yescharacteristic
11C5×#869C2211yescharacteristic
12C3×#4041—22no—
13C3×#4041—21no—
14C3×#4020—21no—
15C3×#4020C2211yescharacteristic
16C3×C4×D20—21no—
17C3×C4×D20C2211yescharacteristic
18C2×#6655—22no—
19C4⋊(C3⋊#168)C2211yescharacteristic
20C4×C3⋊#168C2211yescharacteristic
21C5×#835—21no—
22C5×#807—21no—
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24#90986—21no—
25#90964—21no—
26#71919—51nomaximal, Hall
27#65911D311yescharacteristic
28C5×#477—31no—
29#65374—31no—
30#65373—31no—
31Q8⋊#168—31no—
32#64705—31no—
33#64703—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×C5×Dic6—21no—
36C3×#713—42no—
37C3×#713—42no—
38C2×C3×D20—22no—
39C2×C3×D20—21no—
40C2×C3×D20—21no—
41C2×C3×D20—22no—
42C2×C3×D20D411yescharacteristic
43C2×C3×D20D412yes—
44C2×C3×C4×D5—22no—
45C2×C3×C4×D5—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4D411yescharacteristic
48C3×C42×C5—21no—
49C3×C42×C5C2311yescharacteristic
50C2×C3⋊#168—21no—
51C2×C3⋊#168—21no—
52C5×C4⋊Dic3—21no—
53C5×C4⋊Dic3—21no—
54C2×C5×C3⋊C8—21no—
55C3×#685—22no—
56C3×#685—21no—
57C3×C4⋊Dic5D411yescharacteristic
58#6655—44no—
59C3×#550—51no—
60#5076—51no—
61#5021D511yescharacteristic, complemented
62#5008—51no—
63#4544—51no—
64#4535—51no—
65D4⋊(C3⋊C8)—51no—
66C2×#713—21no—
67C5×C4⋊Q8—31no—
68C4×C5×Q8C2×D311yescharacteristic
69C2×#688—62no—
70#4041—22no—
71#4041—21no—
72#4020—21no—
73#4020C2×D311yescharacteristic
74C4×D20—21no—
75C4×D20C2×D311yescharacteristic
76C5×#107—61no—
77C5×C4⋊C8—31no—
78C5×#103—61no—
79#3941—61no—
80#3940—61no—
81C4⋊#168—31no—
82C4×#168—31no—
83#1631—151noSylow
84C22×C3×D5—21no—
85C22×C3×D5—22no—
86C3×C5×Q8—21no—
87C3×C5×Q8SD1612yescomplemented
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C5×Dic3—41no—
94C5×Dic6—42no—
95C2×C3×Dic5—21no—
96C3×D20—21no—
97C3×D20—21no—
98C3×D20—44no—
99C3×D20—42no—
100C3×D20—41no—
101C3×D20—41no—
102C3×D20—41no—
103C3×D20—41no—
104C3×D20—82no—
105C3×C4×D5—44no—
106C3×C4×D5—41no—
107C3×C4×D5—41no—
108C3⋊#168—22no—
109C3⋊#168—41no—
110C5×C3⋊C8—41no—
111C2×C3×#41—101no—
112C3×#127—51no—
113C3×#127—101no—
114C3×#121—102no—
115C3×#121—101no—
116C3×C4×Q8C2×D511yescharacteristic
117C3×C4×D4—51no—
118C3×C4×D4—101no—
119C2×#214—102no—
120#869C2×D511yescharacteristic
121#835—21no—
122#832—101no—
123#808—101no—
124#807—21no—
125C4⋊(C3⋊C8)—51no—
126C4⋊(C3⋊C8)C2×D511yescharacteristic
127C4×C3⋊C8—51no—
128C2×C5×Q8—61no—
129C2×C5×Q8#6711yescharacteristic
130#713—42no—
131#713—42no—
132C2×D20—22no—
133C2×D20—21no—
134C2×D20—21no—
135C2×D20—22no—
136C2×D20#6711yescharacteristic
137C2×D20#6712yes—
138C2×C4×D5—22no—
139C2×C4×D5—21no—
140C2×C5×C8—61no—
141C5×C4⋊C4—21no—
142C5×C4⋊C4—61no—
143C5×C4⋊C4—61no—
144C5×C4⋊C4#6711yescharacteristic
145C42×C5—21no—
146C42×C5C22×D311yescharacteristic
147#688—124no—
148#685—22no—
149#685—21no—
150C4⋊Dic5#6711yescharacteristic
151C2×#168—61no—
152C2×#168—61no—
153#550—51no—
154#492—151no—
155#477—31no—
156#476—151no—
157#331—151no—
158Q8⋊C8—151no—
159D4⋊C8—151no—
160C22×C3×C5#12011yescharacteristic
161C2×C3×D5—42no—
162C2×C3×D5—41no—
163C2×C3×D5—41no—
164C2×C3×D5—42no—
165C2×C3×D5—42no—
166C2×C3×D5—41no—
167C3×C4×C5—22no—
168C3×C4×C5—21no—
169C3×C4×C5—41no—
170C3×C4×C5C2×SD1611yescharacteristic
171C3×C4×C5#13511yescharacteristic
172C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
173C3×C4×C5#13711yescharacteristic
174C3×Dic5—41no—
175C5×Dic3—81no—
176C3×#41—202no—
177C3×#41—202no—
178C2×C3×Q8C22⋊D511yescharacteristic
179C2×C3×D4—51no—
180C2×C3×D4—52no—
181C2×C3×D4—102no—
182C2×C3×D4—102no—
183C2×C3×D4—101no—
184C2×C3×D4—101no—
185C22×C3×C4—102no—
186C22×C3×C4—101no—
187C2×Dic6—21no—
188C3×C4⋊C4—21no—
189C3×C4⋊C4—51no—
190C3×C4⋊C4C22⋊D511yescharacteristic
191C3×C22⋊C4—102no—
192C3×C22⋊C4—101no—
193C3×C42—21no—
194C3×C42C22×D511yescharacteristic
195#214—204no—
196C4⋊Dic3—21no—
197C4⋊Dic3—21no—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—101no—
200C2×C3⋊C8—101no—
201C22×D5—21no—
202C22×D5—22no—
203C5×Q8—21no—
204C5×Q8—122no—
205C5×Q8#21412yescomplemented
206C2×C4×C5—21no—
207C2×C4×C5—21no—
208C2×C4×C5—121no—
209C2×C4×C5C2×#6711yescharacteristic
210C2×C4×C5C2×#6711yescharacteristic
211C2×C4×C5C2×#6711yescharacteristic
212C2×Dic5—21no—
213D20—21no—
214D20—21no—
215D20—42no—
216D20—44no—
217D20—41no—
218D20—41no—
219D20—41no—
220D20—41no—
221D20—82no—
222C4×D5—44no—
223C4×D5—41no—
224C4×D5—41no—
225C5×C8—121no—
226#168—62no—
227#168—121no—
228C2×#41—101no—
229C2×SD16—302no—
230C4⋊Q8—31no—
231#127—51no—
232#127—101no—
233#121—102no—
234#121—101no—
235C4×Q8D3×D511yescharacteristic
236C4×D4—51no—
237C4×D4—101no—
238#107—61no—
239#106—301no—
240C4⋊C8—31no—
241C4⋊C8—151no—
242#103—61no—
243#102—301no—
244C4×C8—151no—
245C2×C3×C5#45011yescharacteristic
246C2×C3×C5#45211yescharacteristic
247C2×C3×C5#45311yescharacteristic
248C3×D5—81no—
249C3×D5—82no—
250C23×C3—101no—
251C23×C3—102no—
252C3×Q8—21no—
253C3×Q8#68812yescomplemented
254C3×D4—101no—
255C3×D4—101no—
256C3×D4—202no—
257C3×D4—204no—
258C3×D4—201no—
259C3×D4—201no—
260C3×D4—201no—
261C3×D4—201no—
262C3×D4—402no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—101no—
266C2×C3×C4—204no—
267C2×C3×C4—201no—
268C2×C3×C4—201no—
269C2×C3×C4D4×D511yescharacteristic
270C2×C3×C4D4×D511yescharacteristic
271C2×C3×C4C2×C22⋊D511yescharacteristic
272C2×Dic3—41no—
273Dic6—42no—
274C3⋊C8—41no—
275C3⋊C8—102no—
276C3⋊C8—201no—
277C22×C5#95311yescharacteristic
278C2×D5—42no—
279C2×D5—41no—
280C2×D5—41no—
281C2×D5—42no—
282C2×D5—42no—
283C2×D5—41no—
284C4×C5—22no—
285C4×C5—21no—
286C4×C5—41no—
287C4×C5—241no—
288C4×C5#93211yescharacteristic
289C4×C5C2×#21411yescharacteristic
290C4×C5#95011yescharacteristic
291C4×C5#95111yescharacteristic
292Dic5—41no—
293#41—202no—
294#41—202no—
295C2×Q8—61no—
296C2×Q8#120111yescharacteristic
297C2×D4—51no—
298C2×D4—52no—
299C2×D4—102no—
300C2×D4—102no—
301C2×D4—101no—
302C2×D4—101no—
303C22×C4—102no—
304C22×C4—101no—
305SD16—604no—
306C2×C8—61no—
307C2×C8—301no—
308C2×C8—301no—
309C4⋊C4—21no—
310C4⋊C4—51no—
311C4⋊C4—61no—
312C4⋊C4—61no—
313C4⋊C4#120111yescharacteristic
314C22⋊C4—102no—
315C22⋊C4—101no—
316C42—21no—
317C42C2×D3×D511yescharacteristic
318C3×C5#163111yescharacteristic, complemented, Hall
319C22×C3—202no—
320C22×C3—201no—
321C22×C3—201no—
322C22×C3—202no—
323C22×C3—202no—
324C22×C3—201no—
325C22×C3#408311yescharacteristic
326C3×C4—22no—
327C3×C4—21no—
328C3×C4—41no—
329C3×C4—201no—
330C3×C4#406411yescharacteristic
331C3×C4#406511yescharacteristic
332C3×C4C2×#68811yescharacteristic
333C3×C4#409511yescharacteristic
334Dic3—81no—
335C2×C5#521811yescharacteristic
336C2×C5#523911yescharacteristic
337C2×C5#524111yescharacteristic
338D5—81no—
339D5—82no—
340C23—102no—
341C23—101no—
342Q8—21no—
343Q8—122no—
344Q8#665512yescomplemented
345D4—101no—
346D4—101no—
347D4—202no—
348D4—204no—
349D4—201no—
350D4—201no—
351D4—201no—
352D4—201no—
353D4—402no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—101no—
357C2×C4—121no—
358C2×C4—204no—
359C2×C4—201no—
360C2×C4—201no—
361C2×C4C2×#120111yescharacteristic
362C2×C4D5×#6711yescharacteristic
363C2×C4D5×#6711yescharacteristic
364C8—121no—
365C8—302no—
366C8—601no—
367C2×C3—401no—
368C2×C3—402no—
369C2×C3#6533511yescharacteristic
370C2×C3#6547611yescharacteristic
371C2×C3#6548711yescharacteristic
372C5#7191911yescharacteristic, complemented, Sylow
373C22—202no—
374C22—201no—
375C22—201no—
376C22—202no—
377C22—202no—
378C22—201no—
379C22#9156311yescharacteristic
380C4—21no—
381C4—22no—
382C4—41no—
383C4—201no—
384C4—241no—
385C4#9129811yescharacteristic
386C4C2×#665511yescharacteristic
387C4#9150811yescharacteristic
388C4#9151611yescharacteristic
389C3#1060195311yescharacteristic, complemented, Sylow
390C2—402no—
391C2—401no—
392C2#1174852711yescharacteristic
393C2#1174929411yescharacteristic
394C2#1174941711yescharacteristic
subgroupG/H
centerC22#91563
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5#120
prime radicalC3×#65911C2
hypercenterC4×Q8D3×D5
hypocenterC3×C5#1631
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C5×#5021C2semidirect
3. #11747079C2semidirect
4. #11746880C2semidirect
5. #11746356C2semidirect
6. #11745852C2semidirect
7. #11745834C2semidirect
61. #5021D5semidirect
87. C3×C5×Q8SD16semidirect
205. C5×Q8#214semidirect
253. C3×Q8#688semidirect
318. C3×C5#1631semidirect
344. Q8#6655semidirect
372. C5#71919semidirect
389. C3#10601953semidirect

Maximal subgroups

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

subgroupindex
C3×#659112
C5×#50212
#117470792
#117468802
#117463562
#117458522
#117458342
#106019533
#719195