Finite Group Databasebeta

← #14289429

Subgroups — #14289429

Order 1920.

512 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 93 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#11756477C211yesmaximal, characteristic
2#11751177C211yesmaximal, characteristic, complemented
3#11750951C211yesmaximal, characteristic, complemented
4#11750943C211yesmaximal, characteristic, complemented
5C3×C5×#331C211yesmaximal, characteristic, complemented
6#11746305C211yesmaximal, characteristic, complemented
7#11746304C211yesmaximal, characteristic, complemented
8#10599198—31nomaximal, Hall
9C2×#6819—21no—
10C3×C5×#127C2211yescharacteristic
11#91829—21no—
12#91828—22no—
13#91827—21no—
14D4×Dic15—21no—
15C2×#6716—22no—
16C4×D60C2211yescharacteristic
17#91758C2211yescharacteristic
18C4×Dic30C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×C5×C4⋊C8C2211yescharacteristic
21#91105—21no—
22#91102—21no—
23#91101—21no—
24#91100—21no—
25C4×C3⋊#168C2211yescharacteristic
26#68405—51nomaximal, Hall
27#66052—31no—
28#65365—31no—
29#65139—31no—
30#65131—31no—
31C5×#331D311yescharacteristic, complemented
32#64704—31no—
33#64703—31no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4D412yes—
37C2×#1220—22no—
38C2×#1220—22no—
39C22×Dic15—22no—
40#6819—42no—
41#6819—42no—
42C2×D60D411yescharacteristic
43C2×C4×D15—21no—
44C2×Dic30—21no—
45C2×Dic30D411yescharacteristic
46C2×C3×C5×C8—21no—
47C2×C3×C5×C8—21no—
48C3×C42×C5C2311yescharacteristic
49#6719—22no—
50#6716—44no—
51#6714—21no—
52C4⋊Dic15—21no—
53C4⋊Dic15—21no—
54C4⋊Dic15D411yescharacteristic
55C4⋊Dic15D411yescharacteristic
56#6712—21no—
57C4×Dic15—21no—
58C2×C3⋊#168—21no—
59#5718—51no—
60#5076—51no—
61#4850—51no—
62#4842—51no—
63C3×#331D511yescharacteristic, complemented
64#4484—51no—
65#4483—51no—
66C2×#711—61no—
67C5×#127C2×D311yescharacteristic
68#4086—61no—
69#4085—62no—
70#4084—61no—
71D4×Dic5—61no—
72C2×#687—62no—
73C4×D20—31no—
74#4015—31no—
75C4×Dic10—31no—
76C5×C4⋊C8C2×D311yescharacteristic
77C5×C4⋊C8C2×D311yescharacteristic
78#3953—61no—
79#3950—61no—
80#3949—61no—
81#3948—61no—
82C4×#168—31no—
83#1631—151noSylow
84C23×C3×C5—22no—
85C22×D15—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
94#1220—44no—
95#1220—82no—
96C2×Dic15—21no—
97C2×Dic15—21no—
98C2×Dic15—21no—
99C2×Dic15—44no—
100C2×Dic15—41no—
101D60—21no—
102D60—21no—
103C4×D15—41no—
104C4×D15—41no—
105Dic30—21no—
106Dic30—42no—
107Dic30SD1612yescomplemented
108C3×C5×C8—41no—
109C3×C5×C8—41no—
110C3⋊#168—22no—
111C2×#237—101no—
112C3×#127C2×D511yescharacteristic
113#940—101no—
114#939—102no—
115#938—101no—
116D4×Dic3—101no—
117C2×#214—102no—
118C4×D12—51no—
119#869—51no—
120C4×Dic6—51no—
121C3×C4⋊C8C2×D511yescharacteristic
122C3×C4⋊C8C2×D511yescharacteristic
123#821—101no—
124#818—101no—
125#817—101no—
126#816—101no—
127C4×C3⋊C8—51no—
128C2×C5×D4—21no—
129C2×C5×D4—21no—
130C2×C5×D4D1212yes—
131C2×C22⋊D5—62no—
132C2×C22⋊D5—62no—
133C22×Dic5—62no—
134#711—122no—
135#711—122no—
136C2×D20—31no—
137C2×C4×D5—61no—
138C2×Dic10—31no—
139C2×Dic10—61no—
140C2×C5×C8—21no—
141C2×C5×C8—21no—
142C42×C5C22×D311yescharacteristic
143C22⋊Dic5—62no—
144#687—124no—
145#685—61no—
146C4⋊Dic5—31no—
147C4⋊Dic5—31no—
148C4⋊Dic5—61no—
149C4⋊Dic5—61no—
150#683—61no—
151C4×Dic5—61no—
152C2×#168—61no—
153#550—151no—
154#492—151no—
155#477—151no—
156#476—151no—
157#331D1511yescharacteristic, complemented
158Q8⋊C8—151no—
159D4⋊C8—151no—
160C22×C3×C5—42no—
161C22×C3×C5—42no—
162C22×C3×C5—42no—
163C22×C3×C5#12011yescharacteristic
164C2×D15—41no—
165C2×D15—41no—
166C2×D15—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—22no—
173Dic15—41no—
174Dic15—41no—
175Dic15—81no—
176C2×C3×D4—21no—
177C2×C3×D4—21no—
178C2×C3×D4D2012yes—
179C2×#67—102no—
180C2×#67—102no—
181C22×Dic3—102no—
182#237—202no—
183#237—202no—
184C2×D12—51no—
185C2×C4×D3—101no—
186C2×Dic6—51no—
187C2×Dic6—101no—
188C2×C3×C8—21no—
189C2×C3×C8—21no—
190C3×C42C22×D511yescharacteristic
191#217—102no—
192#214—204no—
193(C2×D3)⋊C4—101no—
194C4⋊Dic3—51no—
195C4⋊Dic3—51no—
196C4⋊Dic3—101no—
197C4⋊Dic3—101no—
198Dic3⋊C4—101no—
199C4×Dic3—101no—
200C2×C3⋊C8—101no—
201C23×C5—22no—
202C22×D5—61no—
203C5×D4—42no—
204C5×D4—41no—
205C5×D4—41no—
206C5×D4—41no—
207C5×D4—41no—
208C2×C4×C5C2×D1211yescharacteristic
209C2×C4×C5D3×D411yescharacteristic
210C2×C4×C5D3×D411yescharacteristic
211C22⋊D5—124no—
212C22⋊D5—242no—
213C2×Dic5—61no—
214C2×Dic5—61no—
215C2×Dic5—61no—
216C2×Dic5—124no—
217C2×Dic5—121no—
218D20—61no—
219D20—61no—
220C4×D5—121no—
221C4×D5—121no—
222Dic10—32no—
223Dic10—61no—
224Dic10—122no—
225C5×C8—41no—
226C5×C8—41no—
227#168—62no—
228C2×#41—301no—
229C2×SD16—302no—
230C4⋊Q8—151no—
231#127—301no—
232#127C2×D1511yescharacteristic
233#121—301no—
234#121—302no—
235C4×Q8—151no—
236C4×D4—151no—
237C4×D4—301no—
238#107—301no—
239#106—301no—
240C4⋊C8C2×D1511yescharacteristic
241C4⋊C8C2×D1511yescharacteristic
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
249D15—81no—
250C23×C3—22no—
251C22×D3—101no—
252C3×D4—42no—
253C3×D4—41no—
254C3×D4—41no—
255C3×D4—41no—
256C3×D4—41no—
257C2×C3×C4C2×D2011yescharacteristic
258C2×C3×C4D4×D511yescharacteristic
259C2×C3×C4D4×D511yescharacteristic
260#67—204no—
261#67—402no—
262C2×Dic3—101no—
263C2×Dic3—101no—
264C2×Dic3—101no—
265C2×Dic3—204no—
266C2×Dic3—201no—
267D12—101no—
268D12—101no—
269C4×D3—201no—
270C4×D3—201no—
271Dic6—52no—
272Dic6—101no—
273Dic6—202no—
274C3×C8—41no—
275C3×C8—41no—
276C3⋊C8—102no—
277C22×C5—42no—
278C22×C5—42no—
279C22×C5—42no—
280C22×C5#88211yescharacteristic
281C2×D5—121no—
282C2×D5—121no—
283C2×D5—121no—
284C4×C5—21no—
285C4×C5#91111yescharacteristic
286C4×C5#91211yescharacteristic
287C4×C5D3×SD1611yescharacteristic
288C4×C5#91511yescharacteristic
289Dic5—62no—
290Dic5—121no—
291Dic5—121no—
292Dic5—241no—
293#41—602no—
294#41—602no—
295C2×Q8—151no—
296C2×Q8—301no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—151no—
300C2×D4—302no—
301C2×D4—302no—
302C2×D4D6012yes—
303C22×C4—302no—
304C22×C4—301no—
305SD16—604no—
306C2×C8—21no—
307C2×C8—21no—
308C2×C8—301no—
309C4⋊C4—151no—
310C4⋊C4—151no—
311C4⋊C4—301no—
312C4⋊C4—301no—
313C4⋊C4—301no—
314C22⋊C4—302no—
315C22⋊C4—301no—
316C42—301no—
317C42C22×D1511yescharacteristic
318C3×C5#163111yescharacteristic, complemented, Hall
319C22×C3—42no—
320C22×C3—42no—
321C22×C3—42no—
322C22×C3#402811yescharacteristic
323C2×D3—201no—
324C2×D3—201no—
325C2×D3—201no—
326C3×C4—21no—
327C3×C4#405711yescharacteristic
328C3×C4#405811yescharacteristic
329C3×C4D5×SD1611yescharacteristic
330C3×C4#406111yescharacteristic
331Dic3—102no—
332Dic3—201no—
333Dic3—201no—
334Dic3—401no—
335C2×C5—82no—
336C2×C5#474711yescharacteristic
337C2×C5#477611yescharacteristic
338C2×C5#478311yescharacteristic
339D5—241no—
340C23—22no—
341C23—301no—
342Q8—152no—
343Q8—301no—
344Q8—602no—
345D4—42no—
346D4—41no—
347D4—41no—
348D4—41no—
349D4—41no—
350D4—301no—
351D4—301no—
352D4—604no—
353D4—1202no—
354C2×C4—301no—
355C2×C4—301no—
356C2×C4—301no—
357C2×C4—604no—
358C2×C4—601no—
359C2×C4—601no—
360C2×C4—601no—
361C2×C4C2×D6011yescharacteristic
362C2×C4D4×D1511yescharacteristic
363C2×C4D4×D1511yescharacteristic
364C8—41no—
365C8—41no—
366C8—302no—
367C2×C3—82no—
368C2×C3#6503611yescharacteristic
369C2×C3#6506511yescharacteristic
370C2×C3#6507211yescharacteristic
371D3—401no—
372C5#6840511yescharacteristic, complemented, Sylow
373C22—42no—
374C22—42no—
375C22—42no—
376C22—601no—
377C22—601no—
378C22—601no—
379C22#9177111yescharacteristic
380C4—21no—
381C4—302no—
382C4—601no—
383C4—601no—
384C4—1201no—
385C4#9180011yescharacteristic
386C4#9180111yescharacteristic
387C4SD16×D1511yescharacteristic
388C4#9180411yescharacteristic
389C3#1059919811yescharacteristic, complemented, Sylow
390C2—82no—
391C2—1201no—
392C2#1175084811yescharacteristic
393C2#1175087711yescharacteristic
394C2#1175088411yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#331C2
socleC22×C3×C5#120
prime radical#11756477C2
hypercenter#331D15
hypocenterC3×C5#1631
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #11751177C2semidirect
3. #11750951C2semidirect
4. #11750943C2semidirect
5. C3×C5×#331C2semidirect
6. #11746305C2semidirect
7. #11746304C2semidirect
31. C5×#331D3semidirect
63. C3×#331D5semidirect
107. Dic30SD16semidirect
157. #331D15semidirect
318. C3×C5#1631semidirect
372. C5#68405semidirect
389. C3#10599198semidirect

Maximal subgroups

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

subgroupindex
#117564772
#117511772
#117509512
#117509432
C3×C5×#3312
#117463052
#117463042
#105991983
#684055