Finite Group Databasebeta

← #14289819

Subgroups — #14289819

Order 1920.

388 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 103 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
1C3×C5×#556C211yesmaximal, characteristic
2#11751194C211yesmaximal, characteristic, complemented
3#11751122C211yesmaximal, characteristic, complemented
4#11751109C211yesmaximal, characteristic
5#11746368C211yesmaximal, characteristic, complemented
6#11746356C211yesmaximal, characteristic, complemented
7D4⋊(C3⋊#168)C211yesmaximal, characteristic
8#10602725—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×#126—22no—
11C3×C5×#124—21no—
12C3×C5×C22⋊Q8—21no—
13C3×C4×C5×Q8—21no—
14C3×C4×C5×Q8C2211yescharacteristic
15C3×C4×C5×D4C2211yescharacteristic
16C3×C5×#117—21no—
17#91758C2211yescharacteristic
18#91119—21no—
19#91116—21no—
20#91094—22no—
21#91092—21no—
22#91091—21no—
23C4⋊(C3⋊#168)C2211yescharacteristic
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4×C3⋊#168C2211yescharacteristic
26#71932—51nomaximal, Hall
27C5×#556D311yescharacteristic
28#65382—31no—
29#65310—31no—
30#65297—31no—
31#64767—31no—
32Q8⋊#168—31no—
33D4⋊#168—31no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8D411yescharacteristic
36C2×C3×C5×D4D411yescharacteristic
37C22×C3×C4×C5—21no—
38C2×Dic30—21no—
39C3×C5×C4⋊C4—22no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4D411yescharacteristic
43C3×C5×C4⋊C4D411yescharacteristic
44C3×C5×C4⋊C4D412yes—
45C3×C5×C22⋊C4—22no—
46C3×C5×C22⋊C4—22no—
47C3×C5×C22⋊C4—21no—
48C3×C42×C5—22no—
49C3×C42×C5—21no—
50C3×C42×C5C2311yescharacteristic
51C4⋊Dic15—21no—
52C4⋊Dic15—21no—
53C2×C3⋊#168—21no—
54C2×C3⋊#168—21no—
55C2×C3⋊#168—21no—
56C3×#556D511yescharacteristic
57#5093—51no—
58#5021—51no—
59#5008—51no—
60#4547—51no—
61#4535—51no—
62D4⋊(C3⋊C8)—51no—
63C5×C4⋊Q8C2×D311yescharacteristic
64C5×#126—22no—
65C5×#124—21no—
66C5×C22⋊Q8—21no—
67C4×C5×Q8—21no—
68C4×C5×Q8C2×D311yescharacteristic
69C4×C5×D4C2×D311yescharacteristic
70C5×#117—21no—
71#4015—31no—
72#3967—61no—
73#3964—61no—
74#3942—62no—
75#3940—61no—
76#3939—61no—
77C4⋊#168—31no—
78C4⋊#168—31no—
79C4×#168—31no—
80#1638—151noSylow
81C23×C3×C5—21no—
82C3×C5×Q8—21no—
83C3×C5×Q8—21no—
84C3×C5×Q8—41no—
85C3×C5×Q8—41no—
86C3×C5×D4—21no—
87C3×C5×D4—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—21no—
91C2×C3×C4×C5—22no—
92C2×C3×C4×C5—41no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×Dic15—41no—
98Dic30—42no—
99C3⋊#168—41no—
100C3⋊#168—41no—
101C3⋊#168—41no—
102C3×C4⋊Q8C2×D511yescharacteristic
103C3×#126—22no—
104C3×#124—21no—
105C3×C22⋊Q8—21no—
106C3×C4×Q8—21no—
107C3×C4×Q8C2×D511yescharacteristic
108C3×C4×D4C2×D511yescharacteristic
109C3×#117—21no—
110#869—51no—
111#835—101no—
112#832—101no—
113#810—102no—
114#808—101no—
115#807—101no—
116C4⋊(C3⋊C8)—51no—
117C4⋊(C3⋊C8)—51no—
118C4×C3⋊C8—51no—
119C2×C5×Q8—21no—
120C2×C5×Q8#6711yescharacteristic
121C2×C5×D4#6711yescharacteristic
122C22×C4×C5—21no—
123C2×Dic10—61no—
124C5×C4⋊C4—22no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4#6711yescharacteristic
128C5×C4⋊C4#6711yescharacteristic
129C5×C4⋊C4#6712yes—
130C5×C22⋊C4—22no—
131C5×C22⋊C4—22no—
132C5×C22⋊C4—21no—
133C42×C5—22no—
134C42×C5—21no—
135C42×C5C22×D311yescharacteristic
136C4⋊Dic5—61no—
137C4⋊Dic5—61no—
138C2×#168—61no—
139C2×#168—61no—
140C2×#168—61no—
141#556D1511yescharacteristic
142#487—151no—
143#477—151no—
144#476—151no—
145#332—151no—
146Q8⋊C8—151no—
147D4⋊C8—151no—
148C22×C3×C5—41no—
149C22×C3×C5—41no—
150C22×C3×C5—41no—
151C22×C3×C5#12011yescharacteristic
152C3×C4×C5—21no—
153C3×C4×C5—41no—
154C3×C4×C5—41no—
155C3×C4×C5—42no—
156C3×C4×C5—41no—
157C3×C4×C5#13511yescharacteristic
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5#13711yescharacteristic
160C3×C4×C5#13711yescharacteristic
161Dic15—81no—
162C2×C3×Q8—21no—
163C2×C3×Q8C22⋊D511yescharacteristic
164C2×C3×D4C22⋊D511yescharacteristic
165C22×C3×C4—21no—
166C2×Dic6—101no—
167C3×C4⋊C4—22no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4C22⋊D511yescharacteristic
171C3×C4⋊C4C22⋊D511yescharacteristic
172C3×C4⋊C4C22⋊D512yes—
173C3×C22⋊C4—22no—
174C3×C22⋊C4—22no—
175C3×C22⋊C4—21no—
176C3×C42—22no—
177C3×C42—21no—
178C3×C42C22×D511yescharacteristic
179C4⋊Dic3—101no—
180C4⋊Dic3—101no—
181C2×C3⋊C8—101no—
182C2×C3⋊C8—101no—
183C2×C3⋊C8—101no—
184C23×C5—21no—
185C5×Q8—21no—
186C5×Q8—21no—
187C5×Q8—41no—
188C5×Q8—41no—
189C5×D4—21no—
190C5×D4—21no—
191C2×C4×C5—21no—
192C2×C4×C5—21no—
193C2×C4×C5—21no—
194C2×C4×C5—22no—
195C2×C4×C5—41no—
196C2×C4×C5—41no—
197C2×C4×C5C2×#6711yescharacteristic
198C2×C4×C5C2×#6711yescharacteristic
199C2×C4×C5C2×#6711yescharacteristic
200C2×Dic5—121no—
201Dic10—122no—
202#168—121no—
203#168—121no—
204#168—121no—
205C4⋊Q8—151no—
206C4⋊Q8C2×D1511yescharacteristic
207#126—22no—
208#124—21no—
209C22⋊Q8—21no—
210C4×Q8—21no—
211C4×Q8C2×D1511yescharacteristic
212C4×D4C2×D1511yescharacteristic
213#117—21no—
214#107—301no—
215#106—301no—
216C4⋊C8—151no—
217C4⋊C8—151no—
218#103—301no—
219#103—302no—
220#102—301no—
221C4×C8—151no—
222C2×C3×C5—81no—
223C2×C3×C5#45211yescharacteristic
224C2×C3×C5#45211yescharacteristic
225C2×C3×C5#45411yescharacteristic
226C23×C3—21no—
227C3×Q8—21no—
228C3×Q8—21no—
229C3×Q8—41no—
230C3×Q8—41no—
231C3×D4—21no—
232C3×D4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—22no—
237C2×C3×C4—41no—
238C2×C3×C4—41no—
239C2×C3×C4C2×C22⋊D511yescharacteristic
240C2×C3×C4C2×C22⋊D511yescharacteristic
241C2×C3×C4C2×C22⋊D511yescharacteristic
242C2×Dic3—201no—
243Dic6—202no—
244C3⋊C8—201no—
245C3⋊C8—201no—
246C3⋊C8—201no—
247C22×C5—41no—
248C22×C5—41no—
249C22×C5—41no—
250C22×C5#95311yescharacteristic
251C4×C5—21no—
252C4×C5—41no—
253C4×C5—41no—
254C4×C5—42no—
255C4×C5—41no—
256C4×C5#95011yescharacteristic
257C4×C5#95011yescharacteristic
258C4×C5#95111yescharacteristic
259C4×C5#95111yescharacteristic
260Dic5—241no—
261C2×Q8—21no—
262C2×Q8—301no—
263C2×Q8#122011yescharacteristic
264C2×D4#122011yescharacteristic
265C22×C4—21no—
266C2×C8—301no—
267C2×C8—301no—
268C2×C8—301no—
269C4⋊C4—22no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—301no—
273C4⋊C4—301no—
274C4⋊C4#122012yes—
275C4⋊C4#122011yescharacteristic
276C4⋊C4#122011yescharacteristic
277C22⋊C4—22no—
278C22⋊C4—22no—
279C22⋊C4—21no—
280C42—22no—
281C42—21no—
282C42C22×D1511yescharacteristic
283C3×C5#163811yescharacteristic, complemented, Hall
284C22×C3—41no—
285C22×C3—41no—
286C22×C3—41no—
287C22×C3#409911yescharacteristic
288C3×C4—21no—
289C3×C4—41no—
290C3×C4—41no—
291C3×C4—42no—
292C3×C4—41no—
293C3×C4#409611yescharacteristic
294C3×C4#409611yescharacteristic
295C3×C4#409711yescharacteristic
296C3×C4#409711yescharacteristic
297Dic3—401no—
298C2×C5—81no—
299C2×C5#523911yescharacteristic
300C2×C5#523911yescharacteristic
301C2×C5#524511yescharacteristic
302C23—21no—
303Q8—21no—
304Q8—21no—
305Q8—41no—
306Q8—41no—
307Q8—602no—
308D4—21no—
309D4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—601no—
317C2×C4C2×#122011yescharacteristic
318C2×C4C2×#122011yescharacteristic
319C2×C4C2×#122011yescharacteristic
320C8—601no—
321C8—601no—
322C8—601no—
323C2×C3—81no—
324C2×C3#6552811yescharacteristic
325C2×C3#6552811yescharacteristic
326C2×C3#6553411yescharacteristic
327C5#7193211yescharacteristic, complemented, Sylow
328C22—41no—
329C22—41no—
330C22—41no—
331C22#9184211yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—42no—
336C4—41no—
337C4—1201no—
338C4#9183911yescharacteristic
339C4#9183911yescharacteristic
340C4#9184011yescharacteristic
341C4#9184011yescharacteristic
342C3#1060272511yescharacteristic, complemented, Sylow
343C2—81no—
344C2#1175134011yescharacteristic
345C2#1175134011yescharacteristic
346C2#1175134611yescharacteristic
subgroupG/H
centerC22#91842
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#556C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenter#556D15
hypocenterC3×C5#1638
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #556

Complements

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

NH ≅ G/Ntype
2. #11751194C2semidirect
3. #11751122C2semidirect
5. #11746368C2semidirect
6. #11746356C2semidirect
283. C3×C5#1638semidirect
327. C5#71932semidirect
342. C3#10602725semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5562
#117511942
#117511222
#117511092
#117463682
#117463562
D4⋊(C3⋊#168)2
#106027253
#719325