Finite Group Databasebeta

← #14290011

Subgroups — #14290011

Order 1920.

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

normal subgroups only

This group has 500 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#11751171C211yesmaximal, characteristic, complemented
3#11750950C211yesmaximal, characteristic, complemented
4#11750947C211yesmaximal, characteristic, complemented
5C3×C5×#331C211yesmaximal, characteristic, complemented
6#11746305C211yesmaximal, characteristic, complemented
7#11746304C211yesmaximal, characteristic, complemented
8#10599200—31nomaximal, Hall
9C2×#6819—21no—
10C3×C5×#127C2211yescharacteristic
11#91829—21no—
12#91828—22no—
13#91827—21no—
14D4×Dic15—21no—
15C2×Dic60—21no—
16C4×D60C2211yescharacteristic
17#91758C2211yescharacteristic
18C4×Dic30C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×C5×C4⋊C8C2211yescharacteristic
21#91116—22no—
22#91105—21no—
23#91102—21no—
24#91100—21no—
25C4×C3⋊#168C2211yescharacteristic
26#68407—51nomaximal, Hall
27#66052—31no—
28#65359—31no—
29#65138—31no—
30#65135—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#6714—21no—
51C4⋊Dic15—21no—
52C4⋊Dic15—21no—
53C4⋊Dic15D411yescharacteristic
54C4⋊Dic15D411yescharacteristic
55#6712—21no—
56C4×Dic15—21no—
57C2×C3⋊#168—21no—
58Dic60—42no—
59#5718—51no—
60#5070—51no—
61#4849—51no—
62#4846—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×Dic20—61no—
73C4×D20—31no—
74#4015—31no—
75C4×Dic10—31no—
76C5×C4⋊C8C2×D311yescharacteristic
77C5×C4⋊C8C2×D311yescharacteristic
78#3964—62no—
79#3953—61no—
80#3950—61no—
81#3948—61no—
82C4×#168—31no—
83#1641—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—41no—
107Dic30—41no—
108Dic30D812yes—
109C3×C5×C8—41no—
110C3×C5×C8—41no—
111C3⋊#168—41no—
112C2×#237—101no—
113C3×#127C2×D511yescharacteristic
114#940—101no—
115#939—102no—
116#938—101no—
117D4×Dic3—101no—
118C2×Dic12—101no—
119C4×D12—51no—
120#869—51no—
121C4×Dic6—51no—
122C3×C4⋊C8C2×D511yescharacteristic
123C3×C4⋊C8C2×D511yescharacteristic
124#832—102no—
125#821—101no—
126#818—101no—
127#816—101no—
128C4×C3⋊C8—51no—
129C2×C5×D4—21no—
130C2×C5×D4—21no—
131C2×C5×D4D1212yes—
132C2×C22⋊D5—62no—
133C2×C22⋊D5—62no—
134C22×Dic5—62no—
135#711—122no—
136#711—122no—
137C2×D20—31no—
138C2×C4×D5—61no—
139C2×Dic10—31no—
140C2×Dic10—61no—
141C2×C5×C8—21no—
142C2×C5×C8—21no—
143C42×C5C22×D311yescharacteristic
144C22⋊Dic5—62no—
145#685—61no—
146C4⋊Dic5—31no—
147C4⋊Dic5—31no—
148C4⋊Dic5—61no—
149C4⋊Dic5—61no—
150#683—61no—
151C4×Dic5—61no—
152C2×#168—61no—
153Dic20—122no—
154#550—151no—
155#486—151no—
156#474—151no—
157#462—151no—
158#331D1511yescharacteristic, complemented
159Q8⋊C8—151no—
160D4⋊C8—151no—
161C22×C3×C5—42no—
162C22×C3×C5—42no—
163C22×C3×C5—42no—
164C22×C3×C5#12011yescharacteristic
165C2×D15—41no—
166C2×D15—41no—
167C2×D15—41no—
168C3×C4×C5—21no—
169C3×C4×C5C2×D811yescharacteristic
170C3×C4×C5#13511yescharacteristic
171C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
172C3×C4×C5#13711yescharacteristic
173Dic15—22no—
174Dic15—41no—
175Dic15—41no—
176Dic15—81no—
177C2×C3×D4—21no—
178C2×C3×D4—21no—
179C2×C3×D4D2012yes—
180C2×#67—102no—
181C2×#67—102no—
182C22×Dic3—102no—
183#237—202no—
184#237—202no—
185C2×D12—51no—
186C2×C4×D3—101no—
187C2×Dic6—51no—
188C2×Dic6—101no—
189C2×C3×C8—21no—
190C2×C3×C8—21no—
191C3×C42C22×D511yescharacteristic
192#217—102no—
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—
201Dic12—202no—
202C23×C5—22no—
203C22×D5—61no—
204C5×D4—42no—
205C5×D4—41no—
206C5×D4—41no—
207C5×D4—41no—
208C5×D4—41no—
209C2×C4×C5C2×D1211yescharacteristic
210C2×C4×C5D3×D411yescharacteristic
211C2×C4×C5D3×D411yescharacteristic
212C22⋊D5—124no—
213C22⋊D5—242no—
214C2×Dic5—61no—
215C2×Dic5—61no—
216C2×Dic5—61no—
217C2×Dic5—124no—
218C2×Dic5—121no—
219D20—61no—
220D20—61no—
221C4×D5—121no—
222C4×D5—121no—
223Dic10—32no—
224Dic10—61no—
225Dic10—121no—
226Dic10—121no—
227C5×C8—41no—
228C5×C8—41no—
229#168—121no—
230C2×#41—301no—
231C2×Q16—301no—
232C4⋊Q8—151no—
233#127—301no—
234#127C2×D1511yescharacteristic
235#121—301no—
236#121—302no—
237C4×Q8—151no—
238C4×D4—151no—
239C4×D4—301no—
240#107—301no—
241C4⋊C8C2×D1511yescharacteristic
242C4⋊C8C2×D1511yescharacteristic
243#103—301no—
244#102—301no—
245#102—302no—
246C4×C8—151no—
247C2×C3×C5—82no—
248C2×C3×C5#44711yescharacteristic
249C2×C3×C5#45211yescharacteristic
250C2×C3×C5#45511yescharacteristic
251D15—81no—
252C23×C3—22no—
253C22×D3—101no—
254C3×D4—42no—
255C3×D4—41no—
256C3×D4—41no—
257C3×D4—41no—
258C3×D4—41no—
259C2×C3×C4C2×D2011yescharacteristic
260C2×C3×C4D4×D511yescharacteristic
261C2×C3×C4D4×D511yescharacteristic
262#67—204no—
263#67—402no—
264C2×Dic3—101no—
265C2×Dic3—101no—
266C2×Dic3—101no—
267C2×Dic3—204no—
268C2×Dic3—201no—
269D12—101no—
270D12—101no—
271C4×D3—201no—
272C4×D3—201no—
273Dic6—52no—
274Dic6—101no—
275Dic6—201no—
276Dic6—201no—
277C3×C8—41no—
278C3×C8—41no—
279C3⋊C8—201no—
280C22×C5—42no—
281C22×C5—42no—
282C22×C5—42no—
283C22×C5#88211yescharacteristic
284C2×D5—121no—
285C2×D5—121no—
286C2×D5—121no—
287C4×C5—21no—
288C4×C5D3×D811yescharacteristic
289C4×C5#91211yescharacteristic
290C4×C5#91411yescharacteristic
291C4×C5#91511yescharacteristic
292Dic5—62no—
293Dic5—121no—
294Dic5—121no—
295Dic5—241no—
296#41—602no—
297#41—602no—
298C2×Q8—151no—
299C2×Q8—301no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—151no—
303C2×D4—302no—
304C2×D4—302no—
305C2×D4D6012yes—
306C22×C4—302no—
307C22×C4—301no—
308Q16—602no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—301no—
312C4⋊C4—151no—
313C4⋊C4—151no—
314C4⋊C4—301no—
315C4⋊C4—301no—
316C4⋊C4—301no—
317C22⋊C4—302no—
318C22⋊C4—301no—
319C42—301no—
320C42C22×D1511yescharacteristic
321C3×C5#164111yescharacteristic, complemented, Hall
322C22×C3—42no—
323C22×C3—42no—
324C22×C3—42no—
325C22×C3#402811yescharacteristic
326C2×D3—201no—
327C2×D3—201no—
328C2×D3—201no—
329C3×C4—21no—
330C3×C4D5×D811yescharacteristic
331C3×C4#405811yescharacteristic
332C3×C4#406011yescharacteristic
333C3×C4#406111yescharacteristic
334Dic3—102no—
335Dic3—201no—
336Dic3—201no—
337Dic3—401no—
338C2×C5—82no—
339C2×C5#474611yescharacteristic
340C2×C5#477311yescharacteristic
341C2×C5#478311yescharacteristic
342D5—241no—
343C23—22no—
344C23—301no—
345Q8—152no—
346Q8—301no—
347Q8—601no—
348Q8—601no—
349D4—42no—
350D4—41no—
351D4—41no—
352D4—41no—
353D4—41no—
354D4—301no—
355D4—301no—
356D4—604no—
357D4—1202no—
358C2×C4—301no—
359C2×C4—301no—
360C2×C4—301no—
361C2×C4—604no—
362C2×C4—601no—
363C2×C4—601no—
364C2×C4—601no—
365C2×C4C2×D6011yescharacteristic
366C2×C4D4×D1511yescharacteristic
367C2×C4D4×D1511yescharacteristic
368C8—41no—
369C8—41no—
370C8—601no—
371C2×C3—82no—
372C2×C3#6503511yescharacteristic
373C2×C3#6506211yescharacteristic
374C2×C3#6507211yescharacteristic
375D3—401no—
376C5#6840711yescharacteristic, complemented, Sylow
377C22—42no—
378C22—42no—
379C22—42no—
380C22—601no—
381C22—601no—
382C22—601no—
383C22#9177111yescharacteristic
384C4—21no—
385C4—302no—
386C4—601no—
387C4—601no—
388C4—1201no—
389C4D8×D1511yescharacteristic
390C4#9180111yescharacteristic
391C4#9180311yescharacteristic
392C4#9180411yescharacteristic
393C3#1059920011yescharacteristic, complemented, Sylow
394C2—82no—
395C2—1201no—
396C2#1175084711yescharacteristic
397C2#1175087411yescharacteristic
398C2#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#1641
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. #11751171C2semidirect
3. #11750950C2semidirect
4. #11750947C2semidirect
5. C3×C5×#331C2semidirect
6. #11746305C2semidirect
7. #11746304C2semidirect
31. C5×#331D3semidirect
63. C3×#331D5semidirect
158. #331D15semidirect
321. C3×C5#1641semidirect
376. C5#68407semidirect
393. C3#10599200semidirect

Maximal subgroups

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

subgroupindex
#117564772
#117511712
#117509502
#117509472
C3×C5×#3312
#117463052
#117463042
#105992003
#684075