Finite Group Databasebeta

← #14288895

Subgroups — #14288895

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
2#11751174C211yesmaximal, characteristic, complemented
3#11750949C211yesmaximal, characteristic, complemented
4#11750944C211yesmaximal, characteristic, complemented
5C3×C5×#331C211yesmaximal, characteristic, complemented
6#11746305C211yesmaximal, characteristic, complemented
7#11746304C211yesmaximal, characteristic, complemented
8#10599196—31nomaximal, Hall
9C2×#6819—21no—
10C3×C5×#127C2211yescharacteristic
11#91829—21no—
12#91828—22no—
13#91827—21no—
14D4×Dic15—21no—
15C2×#6715—22no—
16C2×D120—21no—
17C2×#6706—21no—
18#91763C2211yescharacteristic
19C4×D60C2211yescharacteristic
20C4×Dic30C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic
22C3×C5×C4⋊C8C2211yescharacteristic
23#91105—21no—
24#91105—21no—
25C4×C3⋊#168C2211yescharacteristic
26#68403—51nomaximal, Hall
27#66052—31no—
28#65362—31no—
29#65137—31no—
30#65132—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×D60—21no—
43C2×D60—21no—
44C2×D60—21no—
45C2×D60D411yescharacteristic
46C2×C4×D15—21no—
47C2×Dic30D411yescharacteristic
48C2×C3×C5×C8—21no—
49C2×C3×C5×C8—21no—
50C3×C42×C5C2311yescharacteristic
51#6719—22no—
52#6715—44no—
53#6714—21no—
54C4⋊Dic15D411yescharacteristic
55C4⋊Dic15D411yescharacteristic
56#6712—21no—
57C4×Dic15—21no—
58C2×C3⋊#168—21no—
59D120—42no—
60#6706—42no—
61#5718—51no—
62#5073—51no—
63#4848—51no—
64#4843—51no—
65C3×#331D511yescharacteristic, complemented
66#4484—51no—
67#4483—51no—
68C2×#711—61no—
69C5×#127C2×D311yescharacteristic
70#4086—61no—
71#4085—62no—
72#4084—61no—
73D4×Dic5—61no—
74C2×#686—62no—
75C2×D40—61no—
76C2×#677—61no—
77#4020—31no—
78C4×D20—31no—
79C4×Dic10—31no—
80C5×C4⋊C8C2×D311yescharacteristic
81C5×C4⋊C8C2×D311yescharacteristic
82#3953—61no—
83#3953—61no—
84C4×#168—31no—
85#1621—151noSylow
86C23×C3×C5—22no—
87C22×D15—21no—
88C22×D15—41no—
89C3×C5×D4—42no—
90C3×C5×D4—41no—
91C3×C5×D4—41no—
92C3×C5×D4—41no—
93C3×C5×D4—41no—
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97#1220—44no—
98#1220—82no—
99C2×Dic15—21no—
100C2×Dic15—21no—
101C2×Dic15—21no—
102C2×Dic15—44no—
103D60—21no—
104D60—21no—
105D60—42no—
106D60—41no—
107D60—41no—
108D60—41no—
109D60—41no—
110C4×D15—41no—
111C4×D15—41no—
112Dic30—21no—
113Dic30D812yescomplemented
114C3×C5×C8—41no—
115C3×C5×C8—41no—
116C3⋊#168—22no—
117C2×#237—101no—
118C3×#127C2×D511yescharacteristic
119#940—101no—
120#939—102no—
121#938—101no—
122D4×Dic3—101no—
123C2×#213—102no—
124C2×D24—101no—
125C2×#204—101no—
126#874—51no—
127C4×D12—51no—
128C4×Dic6—51no—
129C3×C4⋊C8C2×D511yescharacteristic
130C3×C4⋊C8C2×D511yescharacteristic
131#821—101no—
132#821—101no—
133C4×C3⋊C8—51no—
134C2×C5×D4—21no—
135C2×C5×D4—21no—
136C2×C5×D4D1212yes—
137C2×C22⋊D5—62no—
138C2×C22⋊D5—62no—
139C22×Dic5—62no—
140#711—122no—
141#711—122no—
142C2×D20—31no—
143C2×D20—61no—
144C2×D20—61no—
145C2×D20—61no—
146C2×C4×D5—61no—
147C2×Dic10—31no—
148C2×C5×C8—21no—
149C2×C5×C8—21no—
150C42×C5C22×D311yescharacteristic
151C22⋊Dic5—62no—
152#686—124no—
153#685—61no—
154C4⋊Dic5—31no—
155C4⋊Dic5—31no—
156#683—61no—
157C4×Dic5—61no—
158C2×#168—61no—
159D40—122no—
160#677—122no—
161#550—151no—
162#493—151no—
163#460—151no—
164#459—151no—
165#331D1511yescharacteristic, complemented
166Q8⋊C8—151no—
167D4⋊C8—151no—
168C22×C3×C5—42no—
169C22×C3×C5—42no—
170C22×C3×C5—42no—
171C22×C3×C5#12011yescharacteristic
172C2×D15—41no—
173C2×D15—41no—
174C2×D15—41no—
175C2×D15—81no—
176C2×D15—81no—
177C2×D15—81no—
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×D4D2012yes—
189C2×#67—102no—
190C2×#67—102no—
191C22×Dic3—102no—
192#237—202no—
193#237—202no—
194C2×D12—51no—
195C2×D12—101no—
196C2×D12—101no—
197C2×D12—101no—
198C2×C4×D3—101no—
199C2×Dic6—51no—
200C2×C3×C8—21no—
201C2×C3×C8—21no—
202C3×C42C22×D511yescharacteristic
203#217—102no—
204#213—204no—
205(C2×D3)⋊C4—101no—
206C4⋊Dic3—51no—
207C4⋊Dic3—51no—
208Dic3⋊C4—101no—
209C4×Dic3—101no—
210C2×C3⋊C8—101no—
211D24—202no—
212#204—202no—
213C23×C5—22no—
214C22×D5—61no—
215C22×D5—121no—
216C5×D4—42no—
217C5×D4—41no—
218C5×D4—41no—
219C5×D4—41no—
220C5×D4—41no—
221C2×C4×C5C2×D1211yescharacteristic
222C2×C4×C5D3×D411yescharacteristic
223C2×C4×C5D3×D411yescharacteristic
224C22⋊D5—124no—
225C22⋊D5—242no—
226C2×Dic5—61no—
227C2×Dic5—61no—
228C2×Dic5—61no—
229C2×Dic5—124no—
230D20—61no—
231D20—61no—
232D20—122no—
233D20—121no—
234D20—121no—
235D20—121no—
236D20—121no—
237C4×D5—121no—
238C4×D5—121no—
239Dic10—32no—
240Dic10—61no—
241C5×C8—41no—
242C5×C8—41no—
243#168—62no—
244C2×#41—301no—
245C2×SD16—301no—
246C2×D8—301no—
247C2×D8—302no—
248#127—151no—
249#127—301no—
250#127C2×D1511yescharacteristic
251#121—301no—
252#121—302no—
253C4×Q8—151no—
254C4×D4—151no—
255C4×D4—301no—
256C4⋊C8C2×D1511yescharacteristic
257C4⋊C8C2×D1511yescharacteristic
258#102—301no—
259#102—301no—
260C4×C8—151no—
261C2×C3×C5—82no—
262C2×C3×C5#44711yescharacteristic
263C2×C3×C5#44911yescharacteristic
264C2×C3×C5#45311yescharacteristic
265D15—81no—
266D15—161no—
267C23×C3—22no—
268C22×D3—101no—
269C22×D3—201no—
270C3×D4—42no—
271C3×D4—41no—
272C3×D4—41no—
273C3×D4—41no—
274C3×D4—41no—
275C2×C3×C4C2×D2011yescharacteristic
276C2×C3×C4D4×D511yescharacteristic
277C2×C3×C4D4×D511yescharacteristic
278#67—204no—
279#67—402no—
280C2×Dic3—101no—
281C2×Dic3—101no—
282C2×Dic3—101no—
283C2×Dic3—204no—
284D12—101no—
285D12—101no—
286D12—202no—
287D12—201no—
288D12—201no—
289D12—201no—
290D12—201no—
291C4×D3—201no—
292C4×D3—201no—
293Dic6—52no—
294Dic6—101no—
295C3×C8—41no—
296C3×C8—41no—
297C3⋊C8—102no—
298C22×C5—42no—
299C22×C5—42no—
300C22×C5—42no—
301C22×C5#88211yescharacteristic
302C2×D5—121no—
303C2×D5—121no—
304C2×D5—121no—
305C2×D5—241no—
306C2×D5—241no—
307C2×D5—241no—
308C4×C5—21no—
309C4×C5D3×D811yescharacteristic
310C4×C5#91111yescharacteristic
311C4×C5#91411yescharacteristic
312C4×C5#91611yescharacteristic
313Dic5—62no—
314Dic5—121no—
315Dic5—121no—
316#41—602no—
317#41—602no—
318C2×Q8—151no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—151no—
322C2×D4—302no—
323C2×D4—302no—
324C2×D4—301no—
325C2×D4—301no—
326C2×D4—301no—
327C2×D4D6012yes—
328C22×C4—302no—
329C22×C4—301no—
330SD16—602no—
331D8—602no—
332D8—604no—
333C2×C8—21no—
334C2×C8—21no—
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#402811yescharacteristic
348C2×D3—201no—
349C2×D3—201no—
350C2×D3—201no—
351C2×D3—401no—
352C2×D3—401no—
353C2×D3—401no—
354C3×C4—21no—
355C3×C4D5×D811yescharacteristic
356C3×C4#405711yescharacteristic
357C3×C4#406011yescharacteristic
358C3×C4#406211yescharacteristic
359Dic3—102no—
360Dic3—201no—
361Dic3—201no—
362C2×C5—82no—
363C2×C5#474711yescharacteristic
364C2×C5#477311yescharacteristic
365C2×C5#478111yescharacteristic
366D5—241no—
367D5—481no—
368C23—22no—
369C23—301no—
370C23—601no—
371Q8—152no—
372Q8—301no—
373D4—42no—
374D4—41no—
375D4—41no—
376D4—41no—
377D4—41no—
378D4—301no—
379D4—301no—
380D4—602no—
381D4—604no—
382D4—601no—
383D4—601no—
384D4—601no—
385D4—601no—
386D4—1202no—
387C2×C4—301no—
388C2×C4—301no—
389C2×C4—301no—
390C2×C4—604no—
391C2×C4—601no—
392C2×C4—601no—
393C2×C4C2×D6011yescharacteristic
394C2×C4D4×D1511yescharacteristic
395C2×C4D4×D1511yescharacteristic
396C8—41no—
397C8—41no—
398C8—302no—
399C2×C3—82no—
400C2×C3#6503611yescharacteristic
401C2×C3#6506211yescharacteristic
402C2×C3#6507011yescharacteristic
403D3—401no—
404D3—801no—
405C5#6840311yescharacteristic, complemented, Sylow
406C22—42no—
407C22—42no—
408C22—42no—
409C22—601no—
410C22—601no—
411C22—601no—
412C22—1201no—
413C22—1201no—
414C22—1201no—
415C22#9177111yescharacteristic
416C4—21no—
417C4—302no—
418C4—601no—
419C4—601no—
420C4D8×D1511yescharacteristic
421C4#9180011yescharacteristic
422C4#9180311yescharacteristic
423C4#9180511yescharacteristic
424C3#1059919611yescharacteristic, complemented, Sylow
425C2—82no—
426C2—1201no—
427C2—2401no—
428C2#1175084811yescharacteristic
429C2#1175087411yescharacteristic
430C2#1175088211yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#331C2
socleC22×C3×C5#120
hypercenter#331D15
hypocenterC3×C5#1621
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
1. #11756477C2semidirect
2. #11751174C2semidirect
3. #11750949C2semidirect
4. #11750944C2semidirect
5. C3×C5×#331C2semidirect
6. #11746305C2semidirect
7. #11746304C2semidirect
31. C5×#331D3semidirect
65. C3×#331D5semidirect
113. Dic30D8semidirect
165. #331D15semidirect
343. C3×C5#1621semidirect
405. C5#68403semidirect
424. C3#10599196semidirect

Maximal subgroups

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

subgroupindex
#117564772
#117511742
#117509492
#117509442
C3×C5×#3312
#117463052
#117463042
#105991963
#684035