Finite Group Databasebeta

← #14288883

Subgroups — #14288883

Order 1920.

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

normal subgroups only

This group has 556 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, complemented
2C3×C5×#493C211yesmaximal, characteristic, complemented
3#11751176C211yesmaximal, characteristic, complemented
4#11751173C211yesmaximal, characteristic, complemented
5#11746365C211yesmaximal, characteristic, complemented
6#11746280C211yesmaximal, characteristic, complemented
7#11746277C211yesmaximal, characteristic, complemented
8#10602078—31nomaximal, Hall
9C2×#6819—21no—
10C2×C3×C5×D8—22no—
11C3×C5×#127C2211yescharacteristic
12C3×C5×#127C2211yescharacteristic
13#91829—21no—
14#91828—22no—
15#91827—21no—
16D4×Dic15—21no—
17C2×#6716—21no—
18C2×#6715—21no—
19C4×D60C2211yescharacteristic
20C4×Dic30C2211yescharacteristic
21C3×C4×C5×C8C2211yescharacteristic
22#91116—21no—
23#91116—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4⋊(C3⋊#168)C2211yescharacteristic
26#71285—51nomaximal, Hall
27#66052—31no—
28C5×#493D311yescharacteristic, complemented
29#65364—31no—
30#65361—31no—
31#64764—31no—
32#64679—31no—
33#64676—31no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4D412yes—
40C2×#1220—22no—
41C2×#1220—22no—
42C22×Dic15—22no—
43#6819—42no—
44#6819—42no—
45C2×D60D411yescharacteristic
46C2×C4×D15—21no—
47C2×Dic30D411yescharacteristic
48C3×C5×D8—44no—
49C2×C3×C5×C8—21no—
50C3×C42×C5C2311yescharacteristic
51#6719—22no—
52#6716—42no—
53#6715—42no—
54#6714—21no—
55C4⋊Dic15D411yescharacteristic
56C4⋊Dic15D411yescharacteristic
57#6712—21no—
58C4×Dic15—21no—
59C2×C3⋊#168—21no—
60C2×C3⋊#168—21no—
61#5718—51no—
62C3×#493D511yescharacteristic, complemented
63#5075—51no—
64#5072—51no—
65#4544—51no—
66#4459—51no—
67#4456—51no—
68C2×#711—61no—
69C2×C5×D8—22no—
70C5×#127C2×D311yescharacteristic
71C5×#127C2×D311yescharacteristic
72#4086—61no—
73#4085—62no—
74#4084—61no—
75D4×Dic5—61no—
76C2×#687—61no—
77C2×#686—61no—
78C4×D20—31no—
79C4×Dic10—31no—
80C4×C5×C8C2×D311yescharacteristic
81#3964—61no—
82#3964—61no—
83C4⋊#168—31no—
84C4⋊#168—31no—
85#1621—151noSylow
86C23×C3×C5—22no—
87C23×C3×C5—41no—
88C22×D15—21no—
89C3×C5×D4—42no—
90C3×C5×D4—42no—
91C3×C5×D4—41no—
92C3×C5×D4—41no—
93C3×C5×D4—41no—
94C3×C5×D4—41no—
95C3×C5×D4—41no—
96C3×C5×D4—41no—
97C3×C5×D4—41no—
98C3×C5×D4—41no—
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102#1220—44no—
103#1220—82no—
104C2×Dic15—21no—
105C2×Dic15—21no—
106C2×Dic15—21no—
107C2×Dic15—44no—
108D60—21no—
109D60—21no—
110C4×D15—41no—
111C4×D15—41no—
112Dic30—21no—
113Dic30D812yescomplemented
114C3×C5×C8—22no—
115C3⋊#168—41no—
116C3⋊#168—41no—
117C2×#237—101no—
118C2×C3×D8—22no—
119C3×#127C2×D511yescharacteristic
120C3×#127C2×D511yescharacteristic
121#940—101no—
122#939—102no—
123#938—101no—
124D4×Dic3—101no—
125C2×#214—101no—
126C2×#213—101no—
127C4×D12—51no—
128C4×Dic6—51no—
129C3×C4×C8C2×D511yescharacteristic
130#832—101no—
131#832—101no—
132C4⋊(C3⋊C8)—51no—
133C4⋊(C3⋊C8)—51no—
134C2×C5×D4—21no—
135C2×C5×D4—21no—
136C2×C5×D4—21no—
137C2×C5×D4—21no—
138C2×C5×D4—21no—
139C2×C5×D4#6712yes—
140C2×C22⋊D5—62no—
141C2×C22⋊D5—62no—
142C22×Dic5—62no—
143#711—122no—
144#711—122no—
145C2×D20—31no—
146C2×C4×D5—61no—
147C2×Dic10—31no—
148C5×D8—44no—
149C2×C5×C8—21no—
150C42×C5C22×D311yescharacteristic
151C22⋊Dic5—62no—
152#687—122no—
153#686—122no—
154#685—61no—
155C4⋊Dic5—31no—
156C4⋊Dic5—31no—
157#683—61no—
158C4×Dic5—61no—
159C2×#168—61no—
160C2×#168—61no—
161#550—151no—
162#493D1511yescharacteristic, complemented
163#460—151no—
164#459—151no—
165#331—151no—
166Q8⋊C8—151no—
167D4⋊C8—151no—
168C22×C3×C5—42no—
169C22×C3×C5—42no—
170C22×C3×C5—42no—
171C22×C3×C5—81no—
172C22×C3×C5—81no—
173C22×C3×C5—81no—
174C22×C3×C5#12011yescharacteristic
175C2×D15—41no—
176C2×D15—41no—
177C2×D15—41no—
178C3×C4×C5—21no—
179C3×C4×C5C2×D811yescharacteristic
180C3×C4×C5#13511yescharacteristic
181C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
182C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
183Dic15—22no—
184Dic15—41no—
185Dic15—41no—
186C2×C3×D4—21no—
187C2×C3×D4—21no—
188C2×C3×D4—21no—
189C2×C3×D4—21no—
190C2×C3×D4—21no—
191C2×C3×D4C22⋊D512yes—
192C2×#67—102no—
193C2×#67—102no—
194C22×Dic3—102no—
195#237—202no—
196#237—202no—
197C2×D12—51no—
198C2×C4×D3—101no—
199C2×Dic6—51no—
200C3×D8—44no—
201C2×C3×C8—21no—
202C3×C42C22×D511yescharacteristic
203#217—102no—
204#214—202no—
205#213—202no—
206(C2×D3)⋊C4—101no—
207C4⋊Dic3—51no—
208C4⋊Dic3—51no—
209Dic3⋊C4—101no—
210C4×Dic3—101no—
211C2×C3⋊C8—101no—
212C2×C3⋊C8—101no—
213C23×C5—22no—
214C23×C5—41no—
215C22×D5—61no—
216C5×D4—42no—
217C5×D4—42no—
218C5×D4—41no—
219C5×D4—41no—
220C5×D4—41no—
221C5×D4—41no—
222C5×D4—41no—
223C5×D4—41no—
224C5×D4—41no—
225C5×D4—41no—
226C2×C4×C5D3×D411yescharacteristic
227C2×C4×C5D3×D411yescharacteristic
228C2×C4×C5C2×#6711yescharacteristic
229C22⋊D5—124no—
230C22⋊D5—242no—
231C2×Dic5—61no—
232C2×Dic5—61no—
233C2×Dic5—61no—
234C2×Dic5—124no—
235D20—61no—
236D20—61no—
237C4×D5—121no—
238C4×D5—121no—
239Dic10—32no—
240Dic10—61no—
241C5×C8—22no—
242#168—121no—
243#168—121no—
244C2×#41—301no—
245C2×SD16—301no—
246C2×D8—22no—
247C2×D8—301no—
248#127—301no—
249#127C2×D1511yescharacteristic
250#127C2×D1511yescharacteristic
251#121—301no—
252#121—302no—
253C4×Q8—151no—
254C4×D4—151no—
255C4×D4—301no—
256C4⋊C8—151no—
257C4⋊C8—151no—
258#102—301no—
259#102—301no—
260C4×C8C2×D1511yescharacteristic
261C2×C3×C5—82no—
262C2×C3×C5—161no—
263C2×C3×C5#44711yescharacteristic
264C2×C3×C5#44911yescharacteristic
265C2×C3×C5#45311yescharacteristic
266D15—81no—
267C23×C3—22no—
268C23×C3—41no—
269C22×D3—101no—
270C3×D4—42no—
271C3×D4—42no—
272C3×D4—41no—
273C3×D4—41no—
274C3×D4—41no—
275C3×D4—41no—
276C3×D4—41no—
277C3×D4—41no—
278C3×D4—41no—
279C3×D4—41no—
280C2×C3×C4D4×D511yescharacteristic
281C2×C3×C4D4×D511yescharacteristic
282C2×C3×C4C2×C22⋊D511yescharacteristic
283#67—204no—
284#67—402no—
285C2×Dic3—101no—
286C2×Dic3—101no—
287C2×Dic3—101no—
288C2×Dic3—204no—
289D12—101no—
290D12—101no—
291C4×D3—201no—
292C4×D3—201no—
293Dic6—52no—
294Dic6—101no—
295C3×C8—22no—
296C3⋊C8—201no—
297C3⋊C8—201no—
298C22×C5—42no—
299C22×C5—42no—
300C22×C5—42no—
301C22×C5—81no—
302C22×C5—81no—
303C22×C5—81no—
304C22×C5#93711yescharacteristic
305C2×D5—121no—
306C2×D5—121no—
307C2×D5—121no—
308C4×C5—21no—
309C4×C5D3×D811yescharacteristic
310C4×C5#91111yescharacteristic
311C4×C5#91111yescharacteristic
312C4×C5#91211yescharacteristic
313Dic5—62no—
314Dic5—121no—
315Dic5—121no—
316#41—602no—
317#41—602no—
318C2×Q8—151no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—151no—
325C2×D4—302no—
326C2×D4—302no—
327C2×D4#122012yes—
328C22×C4—302no—
329C22×C4—301no—
330SD16—602no—
331D8—44no—
332D8—602no—
333C2×C8—21no—
334C2×C8—301no—
335C2×C8—301no—
336C4⋊C4—151no—
337C4⋊C4—151no—
338C4⋊C4—301no—
339C22⋊C4—302no—
340C22⋊C4—301no—
341C42—301no—
342C42C22×D1511yescharacteristic
343C3×C5#162111yescharacteristic, complemented, Hall
344C22×C3—42no—
345C22×C3—42no—
346C22×C3—42no—
347C22×C3—81no—
348C22×C3—81no—
349C22×C3—81no—
350C22×C3#408311yescharacteristic
351C2×D3—201no—
352C2×D3—201no—
353C2×D3—201no—
354C3×C4—21no—
355C3×C4D5×D811yescharacteristic
356C3×C4#405711yescharacteristic
357C3×C4#405711yescharacteristic
358C3×C4#405811yescharacteristic
359Dic3—102no—
360Dic3—201no—
361Dic3—201no—
362C2×C5—82no—
363C2×C5—161no—
364C2×C5#507711yescharacteristic
365C2×C5#515611yescharacteristic
366C2×C5#515811yescharacteristic
367D5—241no—
368C23—22no—
369C23—41no—
370C23—301no—
371Q8—152no—
372Q8—301no—
373D4—42no—
374D4—42no—
375D4—41no—
376D4—41no—
377D4—41no—
378D4—41no—
379D4—41no—
380D4—41no—
381D4—41no—
382D4—41no—
383D4—301no—
384D4—301no—
385D4—604no—
386D4—1202no—
387C2×C4—301no—
388C2×C4—301no—
389C2×C4—301no—
390C2×C4—604no—
391C2×C4—601no—
392C2×C4—601no—
393C2×C4D4×D1511yescharacteristic
394C2×C4D4×D1511yescharacteristic
395C2×C4C2×#122011yescharacteristic
396C8—22no—
397C8—601no—
398C8—601no—
399C2×C3—82no—
400C2×C3—161no—
401C2×C3#6536611yescharacteristic
402C2×C3#6544511yescharacteristic
403C2×C3#6544711yescharacteristic
404D3—401no—
405C5#7128511yescharacteristic, complemented, Sylow
406C22—42no—
407C22—42no—
408C22—42no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—601no—
413C22—601no—
414C22—601no—
415C22#9182611yescharacteristic
416C4—21no—
417C4—302no—
418C4—601no—
419C4—601no—
420C4D8×D1511yescharacteristic
421C4#9180011yescharacteristic
422C4#9180011yescharacteristic
423C4#9180111yescharacteristic
424C3#1060207811yescharacteristic, complemented, Sylow
425C2—82no—
426C2—161no—
427C2—1201no—
428C2#1175117811yescharacteristic
429C2#1175125711yescharacteristic
430C2#1175125911yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#493C2
socleC22×C3×C5#120
hypercenter#493D15
hypocenterC3×C5#1621
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #11756477C2semidirect
2. C3×C5×#493C2semidirect
3. #11751176C2semidirect
4. #11751173C2semidirect
5. #11746365C2semidirect
6. #11746280C2semidirect
7. #11746277C2semidirect
28. C5×#493D3semidirect
62. C3×#493D5semidirect
113. Dic30D8semidirect
162. #493D15semidirect
343. C3×C5#1621semidirect
405. C5#71285semidirect
424. C3#10602078semidirect

Maximal subgroups

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

subgroupindex
#117564772
C3×C5×#4932
#117511762
#117511732
#117463652
#117462802
#117462772
#106020783
#712855