Finite Group Databasebeta

← #14289498

Subgroups — #14289498

Order 1920.

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

normal subgroups only

This group has 428 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#11756338C211yesmaximal, characteristic
2#11751122C211yesmaximal, characteristic, complemented
3#11750943C211yesmaximal, characteristic
4#11750800C211yesmaximal, characteristic, complemented
5C3×C5×Q8⋊C8C211yesmaximal, characteristic, complemented
6#11746302C211yesmaximal, characteristic, complemented
7#11746280C211yesmaximal, characteristic
8#10599039—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10#91835—21no—
11C2×Dic60—22no—
12#91785—22no—
13C4⋊C4×D15—21no—
14C4×D60—21no—
15C4×D60C2211yescharacteristic
16#91759—21no—
17#91758C2211yescharacteristic
18#91758C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×C4×C5×C8C2211yescharacteristic
21#91119—21no—
22#91105—21no—
23#91101—21no—
24#91091—21no—
25C4⋊(C3⋊#168)C2211yescharacteristic
26#68246—51nomaximal, Hall
27#65913—31no—
28#65310—31no—
29#65131—31no—
30#64988—31no—
31C5×Q8⋊C8D311yescharacteristic, complemented
32#64701—31no—
33#64679—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×D60D411yescharacteristic
36C2×C4×D15—21no—
37C2×C4×D15—22no—
38C2×Dic30—21no—
39C2×Dic30D412yes—
40C2×C3×C5×C8—21no—
41C2×C3×C5×C8—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4D411yescharacteristic
44C3×C42×C5—21no—
45C3×C42×C5C2311yescharacteristic
46#6714—22no—
47#6714—21no—
48C4⋊Dic15—21no—
49C4⋊Dic15—21no—
50C4⋊Dic15—21no—
51C4⋊Dic15—21no—
52C4⋊Dic15D411yescharacteristic
53#6712—22no—
54#6712—22no—
55C2×C3⋊#168—21no—
56Dic60—44no—
57#5579—51no—
58#5021—51no—
59#4842—51no—
60#4699—51no—
61C3×Q8⋊C8D511yescharacteristic, complemented
62#4481—51no—
63#4459—51no—
64C4×C5×Q8C2×D311yescharacteristic
65#4092—61no—
66C2×Dic20—62no—
67#4042—62no—
68D5×C4⋊C4—61no—
69C4×D20—31no—
70C4×D20—61no—
71#4016—61no—
72#4015—31no—
73#4015—31no—
74C5×C4⋊C8C2×D311yescharacteristic
75C4×C5×C8C2×D311yescharacteristic
76#3967—61no—
77#3953—61no—
78#3949—61no—
79#3939—61no—
80C4⋊#168—31no—
81#1632—151noSylow
82C22×D15—21no—
83C3×C5×Q8—21no—
84C3×C5×Q8—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×Dic15—21no—
91C2×Dic15—22no—
92C2×Dic15—41no—
93D60—21no—
94D60Q1612yescomplemented
95C4×D15—41no—
96C4×D15—41no—
97C4×D15—82no—
98Dic30—42no—
99Dic30—42no—
100C3×C5×C8—22no—
101C3×C5×C8—41no—
102C3⋊#168—41no—
103C3×C4×Q8C2×D511yescharacteristic
104#946—101no—
105C2×Dic12—102no—
106#896—102no—
107D3×C4⋊C4—101no—
108C4×D12—51no—
109C4×D12—101no—
110#870—101no—
111#869—51no—
112#869—51no—
113C3×C4⋊C8C2×D511yescharacteristic
114C3×C4×C8C2×D511yescharacteristic
115#835—101no—
116#821—101no—
117#817—101no—
118#807—101no—
119C4⋊(C3⋊C8)—51no—
120C2×C5×Q8D1211yescharacteristic
121C2×D20—31no—
122C2×C4×D5—61no—
123C2×C4×D5—62no—
124C2×Dic10—32no—
125C2×Dic10—61no—
126C2×C5×C8—21no—
127C2×C5×C8—21no—
128C5×C4⋊C4—21no—
129C5×C4⋊C4D1211yescharacteristic
130C42×C5—21no—
131C42×C5C22×D311yescharacteristic
132#685—62no—
133#685—61no—
134C4⋊Dic5—31no—
135C4⋊Dic5—61no—
136C4⋊Dic5—61no—
137C4⋊Dic5—61no—
138C4⋊Dic5—61no—
139#683—62no—
140#683—62no—
141C2×#168—61no—
142Dic20—124no—
143#554—151no—
144#494—151no—
145#477—151no—
146#476—151no—
147#333—151no—
148Q8⋊C8D1511yescharacteristic, complemented
149D4⋊C8—151no—
150C22×C3×C5#12011yescharacteristic
151C2×D15—22no—
152C2×D15—41no—
153C2×D15—41no—
154C3×C4×C5—21no—
155C3×C4×C5—41no—
156C3×C4×C5—41no—
157C3×C4×C5C2×Q1611yescharacteristic
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5#13711yescharacteristic
160C3×C4×C5#13711yescharacteristic
161Dic15—41no—
162Dic15—42no—
163Dic15—81no—
164C2×C3×Q8D2011yescharacteristic
165C2×D12—51no—
166C2×C4×D3—101no—
167C2×C4×D3—102no—
168C2×Dic6—52no—
169C2×Dic6—101no—
170C2×C3×C8—21no—
171C2×C3×C8—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4D2011yescharacteristic
174C3×C42—21no—
175C3×C42C22×D511yescharacteristic
176(C2×D3)⋊C4—102no—
177(C2×D3)⋊C4—101no—
178C4⋊Dic3—51no—
179C4⋊Dic3—101no—
180C4⋊Dic3—101no—
181C4⋊Dic3—101no—
182C4⋊Dic3—101no—
183Dic3⋊C4—102no—
184Dic3⋊C4—102no—
185C2×C3⋊C8—101no—
186Dic12—204no—
187C22×D5—61no—
188C5×Q8—21no—
189C5×Q8—21no—
190C2×C4×C5—21no—
191C2×C4×C5—21no—
192C2×C4×C5C2×D1211yescharacteristic
193C2×C4×C5D3×D411yescharacteristic
194C2×C4×C5D3×D411yescharacteristic
195C2×Dic5—61no—
196C2×Dic5—62no—
197C2×Dic5—121no—
198D20—32no—
199D20—61no—
200C4×D5—121no—
201C4×D5—121no—
202C4×D5—242no—
203Dic10—122no—
204Dic10—122no—
205C5×C8—22no—
206C5×C8—41no—
207#168—121no—
208C2×Q16—302no—
209C4⋊Q8—151no—
210C4⋊Q8—151no—
211#125—301no—
212C22⋊Q8—302no—
213C22⋊Q8—301no—
214C4×Q8C2×D1511yescharacteristic
215C4×D4—151no—
216C4×D4—301no—
217C2×C4⋊C4—301no—
218#107—301no—
219#106—301no—
220C4⋊C8—151no—
221C4⋊C8C2×D1511yescharacteristic
222#103—301no—
223#102—301no—
224C4×C8C2×D1511yescharacteristic
225C2×C3×C5#45111yescharacteristic
226C2×C3×C5#45211yescharacteristic
227C2×C3×C5#45311yescharacteristic
228D15—42no—
229C22×D3—101no—
230C3×Q8—21no—
231C3×Q8—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4C2×D2011yescharacteristic
235C2×C3×C4D4×D511yescharacteristic
236C2×C3×C4D4×D511yescharacteristic
237C2×Dic3—101no—
238C2×Dic3—102no—
239C2×Dic3—201no—
240D12—52no—
241D12—101no—
242C4×D3—201no—
243C4×D3—201no—
244C4×D3—402no—
245Dic6—202no—
246Dic6—202no—
247C3×C8—22no—
248C3×C8—41no—
249C3⋊C8—201no—
250C22×C5#88211yescharacteristic
251C2×D5—62no—
252C2×D5—121no—
253C2×D5—121no—
254C4×C5—21no—
255C4×C5—41no—
256C4×C5—41no—
257C4×C5#90411yescharacteristic
258C4×C5#90911yescharacteristic
259C4×C5#91511yescharacteristic
260C4×C5D3×Q1611yescharacteristic
261Dic5—121no—
262Dic5—122no—
263Dic5—241no—
264C2×Q8—152no—
265C2×Q8—301no—
266C2×Q8D6011yescharacteristic
267C2×D4—151no—
268C22×C4—302no—
269C22×C4—301no—
270Q16—604no—
271C2×C8—21no—
272C2×C8—21no—
273C2×C8—301no—
274C4⋊C4—21no—
275C4⋊C4—151no—
276C4⋊C4—302no—
277C4⋊C4—302no—
278C4⋊C4—301no—
279C4⋊C4—301no—
280C4⋊C4—301no—
281C4⋊C4—301no—
282C4⋊C4D6011yescharacteristic
283C22⋊C4—302no—
284C22⋊C4—301no—
285C42—21no—
286C42C22×D1511yescharacteristic
287C3×C5#163211yescharacteristic, complemented, Hall
288C22×C3#402811yescharacteristic
289C2×D3—102no—
290C2×D3—201no—
291C2×D3—201no—
292C3×C4—21no—
293C3×C4—41no—
294C3×C4—41no—
295C3×C4#405011yescharacteristic
296C3×C4#405511yescharacteristic
297C3×C4#406111yescharacteristic
298C3×C4D5×Q1611yescharacteristic
299Dic3—202no—
300Dic3—201no—
301Dic3—401no—
302C2×C5#473311yescharacteristic
303C2×C5#480911yescharacteristic
304C2×C5#482211yescharacteristic
305D5—122no—
306C23—301no—
307Q8—21no—
308Q8—21no—
309Q8—602no—
310Q8—602no—
311D4—152no—
312D4—301no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—301no—
316C2×C4—302no—
317C2×C4—601no—
318C2×C4—601no—
319C2×C4—601no—
320C2×C4—1202no—
321C2×C4C2×D6011yescharacteristic
322C2×C4D4×D1511yescharacteristic
323C2×C4D4×D1511yescharacteristic
324C8—22no—
325C8—41no—
326C8—601no—
327C2×C3#6502211yescharacteristic
328C2×C3#6509711yescharacteristic
329C2×C3#6511111yescharacteristic
330D3—202no—
331C5#6824611yescharacteristic, complemented, Sylow
332C22—302no—
333C22—601no—
334C22—601no—
335C22#9177111yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—602no—
340C4—601no—
341C4—1201no—
342C4#9179311yescharacteristic
343C4#9179811yescharacteristic
344C4#9180411yescharacteristic
345C4Q16×D1511yescharacteristic
346C3#1059903911yescharacteristic, complemented, Sylow
347C2—602no—
348C2#1175083411yescharacteristic
349C2#1175091011yescharacteristic
350C2#1175092311yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×Q8⋊C8C2
socleC22×C3×C5#120
prime radicalC2×D60D4
hypercenterQ8⋊C8D15
hypocenterC3×C5#1632
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #11751122C2semidirect
4. #11750800C2semidirect
5. C3×C5×Q8⋊C8C2semidirect
6. #11746302C2semidirect
31. C5×Q8⋊C8D3semidirect
61. C3×Q8⋊C8D5semidirect
94. D60Q16semidirect
148. Q8⋊C8D15semidirect
287. C3×C5#1632semidirect
331. C5#68246semidirect
346. C3#10599039semidirect

Maximal subgroups

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

subgroupindex
#117563382
#117511222
#117509432
#117508002
C3×C5×Q8⋊C82
#117463022
#117462802
#105990393
#682465