Finite Group Databasebeta

← #14289117

Subgroups — #14289117

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
1C3×#66060C211yesmaximal, characteristic, complemented
2#11751189C211yesmaximal, characteristic, complemented
3#11747028C211yesmaximal, characteristic, complemented
4#11747028C211yesmaximal, characteristic, complemented
5C5×#4547C211yesmaximal, characteristic, complemented
6#11745834C211yesmaximal, characteristic, complemented
7#11745834C211yesmaximal, characteristic, complemented
8#10599225—31nomaximal, Hall
9C2×C3×#713—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11#91763C2211yescharacteristic
12C3×#4092—21no—
13C3×#4041—21no—
14C3×#4040—22no—
15C3×D5×C4⋊C4—21no—
16C3×C4×D20C2211yescharacteristic
17C3×C4×D20C2211yescharacteristic
18C2×#6653—21no—
19C2×#6653—21no—
20#91093—22no—
21C4×C3⋊#168C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24#90968—21no—
25#90968—21no—
26#71910—51nomaximal, Hall
27#66060D311yescharacteristic, complemented
28#65377—31no—
29#65132—31no—
30#65132—31no—
31C5×#332—31no—
32#64703—31no—
33#64703—31no—
34C2×C3×C5×Q8—21no—
35C2×D60—21no—
36C2×D60—21no—
37C2×D60—21no—
38C3×#713—42no—
39C3×#713—42no—
40C2×C3×D20—22no—
41C2×C3×D20D411yescharacteristic
42C2×C3×D20D411yescharacteristic
43C2×C3×C4×D5—22no—
44C2×C3×C4×D5—21no—
45C2×C3×C4×D5—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4D412yes—
48C3×C42×C5C2311yescharacteristic
49C2×C3⋊#168—21no—
50C2×C5×C3⋊C8—21no—
51C2×C5×C3⋊C8—21no—
52C3×#685—22no—
53C3×#685—21no—
54C3×#685—21no—
55C3×C4⋊Dic5D411yescharacteristic
56C3×C4⋊Dic5D411yescharacteristic
57C3×#683—22no—
58#6653—42no—
59#6653—42no—
60C3×#547—51no—
61#5088—51no—
62#5015—51no—
63#5015—51no—
64#4547D511yescharacteristic, complemented
65D4⋊(C3⋊C8)—51no—
66D4⋊(C3⋊C8)—51no—
67C2×#713—21no—
68C5×C4⋊Q8C2×D311yescharacteristic
69#4092—21no—
70C2×D40—61no—
71C2×D40—61no—
72#4041—21no—
73#4040—22no—
74D5×C4⋊C4—21no—
75#4020—31no—
76C4×D20C2×D311yescharacteristic
77C4×D20C2×D311yescharacteristic
78C5×C4⋊C8—31no—
79C5×C4⋊C8—31no—
80#3953—61no—
81#3953—61no—
82#3941—62no—
83C4×#168—31no—
84#1625—151noSylow
85C22×D15—41no—
86C22×C3×D5—21no—
87C22×C3×D5—21no—
88C3×C5×Q8—41no—
89C3×C5×Q8—41no—
90C2×C3×C4×C5—22no—
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94D60—42no—
95D60—41no—
96D60—41no—
97D60—41no—
98D60—41no—
99C2×C3×Dic5—21no—
100C2×C3×Dic5—21no—
101C3×D20—21no—
102C3×D20—21no—
103C3×D20—21no—
104C3×D20—44no—
105C3×D20D812yescomplemented
106C3×C4×D5—44no—
107C3×C4×D5—41no—
108C3×C4×D5—41no—
109C3×C4×D5—41no—
110C3×C4×D5—41no—
111C3⋊#168—41no—
112C5×C3⋊C8—41no—
113C5×C3⋊C8—41no—
114C2×C3×#41—101no—
115C3×C4⋊Q8C2×D511yescharacteristic
116C3×#123—102no—
117C3×C22⋊Q8—101no—
118C3×#121—101no—
119C3×C4×D4—51no—
120C3×C4×D4—51no—
121C2×C3×C4⋊C4—101no—
122C2×#213—101no—
123C2×#213—101no—
124#874—51no—
125#809—101no—
126#809—101no—
127#809—102no—
128C4⋊(C3⋊C8)C2×D511yescharacteristic
129C4⋊(C3⋊C8)C2×D511yescharacteristic
130C4×C3⋊C8—51no—
131C2×C5×Q8—21no—
132#713—42no—
133#713—42no—
134C2×D20—22no—
135C2×D20—61no—
136C2×D20—61no—
137C2×D20—61no—
138C2×D20#6711yescharacteristic
139C2×D20#6711yescharacteristic
140C2×C4×D5—22no—
141C2×C4×D5—21no—
142C2×C4×D5—21no—
143C2×C5×C8—61no—
144C2×C5×C8—61no—
145C5×C4⋊C4—21no—
146C5×C4⋊C4#6712yes—
147C42×C5C22×D311yescharacteristic
148#685—22no—
149#685—21no—
150#685—21no—
151C4⋊Dic5#6711yescharacteristic
152C4⋊Dic5#6711yescharacteristic
153#683—22no—
154C2×#168—61no—
155D40—122no—
156D40—122no—
157#547—51no—
158#486—151no—
159#459—151no—
160#459—151no—
161#332—31no—
162D4⋊C8—151no—
163D4⋊C8—151no—
164C22×C3×C5#12011yescharacteristic
165C2×D15—81no—
166C2×D15—81no—
167C2×D15—81no—
168C2×C3×D5—22no—
169C2×C3×D5—41no—
170C2×C3×D5—41no—
171C2×C3×D5—41no—
172C2×C3×D5—41no—
173C2×C3×D5—41no—
174C3×C4×C5—21no—
175C3×C4×C5—42no—
176C3×C4×C5C2×D811yescharacteristic
177C3×C4×C5#13511yescharacteristic
178C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
179C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
180C3×Dic5—41no—
181C3×Dic5—41no—
182C3×#41—202no—
183C3×#41—202no—
184C2×C3×Q8—21no—
185C2×C3×D4—51no—
186C2×C3×D4—51no—
187C2×C3×D4—102no—
188C22×C3×C4—102no—
189C22×C3×C4—101no—
190C22×C3×C4—101no—
191C2×D12—101no—
192C2×D12—101no—
193C2×D12—101no—
194C3×C4⋊C4—21no—
195C3×C4⋊C4—51no—
196C3×C4⋊C4—51no—
197C3×C4⋊C4—102no—
198C3×C4⋊C4D2012yes—
199C3×C22⋊C4—102no—
200C3×C22⋊C4—101no—
201C3×C22⋊C4—101no—
202C3×C42C22×D511yescharacteristic
203#213—202no—
204#213—202no—
205C2×C3⋊C8—21no—
206C2×C3⋊C8—21no—
207C2×C3⋊C8—101no—
208C22×D5—21no—
209C22×D5—21no—
210C22×D5—121no—
211C5×Q8—41no—
212C5×Q8—41no—
213C2×C4×C5—22no—
214C2×C4×C5C2×#6711yescharacteristic
215C2×C4×C5C2×#6711yescharacteristic
216C2×C4×C5C2×#6711yescharacteristic
217C2×Dic5—21no—
218C2×Dic5—21no—
219D20—21no—
220D20—21no—
221D20—21no—
222D20—44no—
223D20—122no—
224D20—121no—
225D20—121no—
226D20—121no—
227D20—121no—
228D20#21312yescomplemented
229C4×D5—44no—
230C4×D5—41no—
231C4×D5—41no—
232C4×D5—41no—
233C4×D5—41no—
234C5×C8—121no—
235C5×C8—121no—
236#168—121no—
237C2×#41—101no—
238C2×D8—301no—
239C2×D8—301no—
240C4⋊Q8D3×D511yescharacteristic
241#127—151no—
242#123—102no—
243C22⋊Q8—101no—
244#121—101no—
245C4×D4—51no—
246C4×D4—51no—
247C2×C4⋊C4—101no—
248C4⋊C8—31no—
249C4⋊C8—31no—
250#102—301no—
251#102—301no—
252#102—302no—
253C4×C8—151no—
254C2×C3×C5#44711yescharacteristic
255C2×C3×C5#44911yescharacteristic
256C2×C3×C5#45411yescharacteristic
257D15—161no—
258C3×D5—42no—
259C3×D5—81no—
260C23×C3—101no—
261C23×C3—101no—
262C22×D3—201no—
263C3×Q8—41no—
264C3×Q8—41no—
265C3×D4—52no—
266C3×D4—101no—
267C3×D4—101no—
268C3×D4—101no—
269C3×D4—204no—
270C2×C3×C4—22no—
271C2×C3×C4—101no—
272C2×C3×C4—101no—
273C2×C3×C4—204no—
274C2×C3×C4—201no—
275C2×C3×C4—201no—
276C2×C3×C4—201no—
277C2×C3×C4—201no—
278C2×C3×C4C2×D2011yescharacteristic
279C2×C3×C4D4×D511yescharacteristic
280C2×C3×C4D4×D511yescharacteristic
281D12—202no—
282D12—201no—
283D12—201no—
284D12—201no—
285D12—201no—
286C3⋊C8—41no—
287C3⋊C8—41no—
288C3⋊C8—201no—
289C22×C5#95311yescharacteristic
290C2×D5—22no—
291C2×D5—41no—
292C2×D5—41no—
293C2×D5—41no—
294C2×D5—41no—
295C2×D5—41no—
296C2×D5—241no—
297C2×D5—241no—
298C2×D5—241no—
299C4×C5—21no—
300C4×C5—42no—
301C4×C5C2×#21311yescharacteristic
302C4×C5#93211yescharacteristic
303C4×C5#94911yescharacteristic
304C4×C5#95011yescharacteristic
305Dic5—41no—
306Dic5—41no—
307#41—202no—
308#41—202no—
309C2×Q8—21no—
310C2×D4—51no—
311C2×D4—51no—
312C2×D4—102no—
313C2×D4—301no—
314C2×D4—301no—
315C2×D4—301no—
316C22×C4—102no—
317C22×C4—101no—
318C22×C4—101no—
319D8—602no—
320D8—602no—
321C2×C8—61no—
322C2×C8—61no—
323C2×C8—301no—
324C4⋊C4—21no—
325C4⋊C4—51no—
326C4⋊C4—51no—
327C4⋊C4—102no—
328C4⋊C4#120212yes—
329C22⋊C4—102no—
330C22⋊C4—101no—
331C22⋊C4—101no—
332C42C2×D3×D511yescharacteristic
333C3×C5#162511yescharacteristic, complemented, Hall
334C22×C3—102no—
335C22×C3—201no—
336C22×C3—201no—
337C22×C3—201no—
338C22×C3—201no—
339C22×C3—201no—
340C22×C3#402811yescharacteristic
341C2×D3—401no—
342C2×D3—401no—
343C2×D3—401no—
344C3×C4—21no—
345C3×C4—42no—
346C3×C4—201no—
347C3×C4—201no—
348C3×C4D5×D811yescharacteristic
349C3×C4#406011yescharacteristic
350C3×C4#406011yescharacteristic
351C3×C4#406511yescharacteristic
352C2×C5#521711yescharacteristic
353C2×C5#523811yescharacteristic
354C2×C5#524511yescharacteristic
355D5—42no—
356D5—81no—
357D5—481no—
358C23—101no—
359C23—101no—
360C23—601no—
361Q8—41no—
362Q8—41no—
363D4—52no—
364D4—101no—
365D4—101no—
366D4—101no—
367D4—204no—
368D4—602no—
369D4—601no—
370D4—601no—
371D4—601no—
372D4—601no—
373C2×C4—22no—
374C2×C4—101no—
375C2×C4—101no—
376C2×C4—204no—
377C2×C4—201no—
378C2×C4—201no—
379C2×C4—201no—
380C2×C4—201no—
381C2×C4C2×#120211yescharacteristic
382C2×C4D5×#6711yescharacteristic
383C2×C4D5×#6711yescharacteristic
384C8—121no—
385C8—121no—
386C8—601no—
387C2×C3—202no—
388C2×C3—401no—
389C2×C3#6504211yescharacteristic
390C2×C3#6506211yescharacteristic
391C2×C3#6510011yescharacteristic
392D3—801no—
393C5#7191011yescharacteristic, complemented, Sylow
394C22—102no—
395C22—201no—
396C22—201no—
397C22—201no—
398C22—201no—
399C22—201no—
400C22—1201no—
401C22—1201no—
402C22—1201no—
403C22#9156411yescharacteristic
404C4—21no—
405C4—42no—
406C4—201no—
407C4—201no—
408C4D5×#21311yescharacteristic
409C4#9149111yescharacteristic
410C4#9150211yescharacteristic
411C4#9151611yescharacteristic
412C3#1059922511yescharacteristic, complemented, Sylow
413C2—202no—
414C2—401no—
415C2—2401no—
416C2#1174902211yescharacteristic
417C2#1174927211yescharacteristic
418C2#1174938411yescharacteristic
subgroupG/H
centerC22#91564
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1625
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
1. C3×#66060C2semidirect
2. #11751189C2semidirect
3. #11747028C2semidirect
4. #11747028C2semidirect
5. C5×#4547C2semidirect
6. #11745834C2semidirect
7. #11745834C2semidirect
27. #66060D3semidirect
64. #4547D5semidirect
105. C3×D20D8semidirect
228. D20#213semidirect
333. C3×C5#1625semidirect
393. C5#71910semidirect
412. C3#10599225semidirect

Maximal subgroups

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

subgroupindex
C3×#660602
#117511892
#117470282
C5×#45472
#117458342
#105992253
#719105