Finite Group Databasebeta

← #14285449

Subgroups — #14285449

Order 1920.

420 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 105 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#11756487C211yesmaximal, characteristic
2#11750938C211yesmaximal, characteristic
3#11750938C211yesmaximal, characteristic
4C3×C5×#332C211yesmaximal, characteristic, complemented
5#11746368C211yesmaximal, characteristic, complemented
6#11746307C211yesmaximal, characteristic, complemented
7#11746303C211yesmaximal, characteristic, complemented
8#10599224—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91835—21no—
11Q8×Dic15—21no—
12C2×#6705—21no—
13C2×#6705—21no—
14#91786—21no—
15#91781C412yes—
16#91779C412yes—
17#91776—21no—
18C42×D15C2211yescharacteristic
19#91758C2211yescharacteristic
20C3×C5×C4⋊C8C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic
22#91098—21no—
23#91098—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4⋊(C3⋊#168)C2211yescharacteristic
26#68431—51nomaximal, Hall
27#66062—31no—
28#65126—31no—
29#65126—31no—
30C5×#332D311yescharacteristic, complemented
31#64767—31no—
32#64706—31no—
33#64702—31no—
34C2×C3×C5×Q8—21no—
35C2×C4×D15C2×C411yescharacteristic
36C2×C4×D15D411yescharacteristic
37C2×C4×D15D411yescharacteristic
38C2×Dic30—21no—
39C2×C3×C5×C8—21no—
40C2×C3×C5×C8—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4C2×C412yes—
43C3×C42×C5C2311yescharacteristic
44#6714—22no—
45C4⋊Dic15—21no—
46C4⋊Dic15—22no—
47C4⋊Dic15C2×C412yes—
48#6712—22no—
49C4×Dic15—22no—
50C4×Dic15C2×C411yescharacteristic
51C4×Dic15D411yescharacteristic
52C4×Dic15D411yescharacteristic
53C2×C3⋊#168—21no—
54C2×C3⋊#168—21no—
55#6705—42no—
56#6705—42no—
57#5728—51no—
58#4837—51no—
59#4837—51no—
60C3×#332D511yescharacteristic, complemented
61#4547—51no—
62#4486—51no—
63#4482—51no—
64C5×C4⋊Q8C2×D311yescharacteristic
65#4092—61no—
66Q8×Dic5—61no—
67C2×#676—61no—
68C2×#676—61no—
69#4043—61no—
70#4038—32no—
71#4036—32no—
72#4033—61no—
73C42×D5—31no—
74#4015—31no—
75C5×C4⋊C8C2×D311yescharacteristic
76C5×C4⋊C8C2×D311yescharacteristic
77#3946—61no—
78#3946—61no—
79C4⋊#168—31no—
80C4⋊#168—31no—
81#1561—151noSylow
82C22×D15C22⋊C411yescharacteristic
83C3×C5×Q8—41no—
84C3×C5×Q8—41no—
85C2×C3×C4×C5—22no—
86C2×C3×C4×C5C22×C411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×Dic15—22no—
90C2×Dic15C22⋊C411yescharacteristic
91C2×Dic15C22⋊C411yescharacteristic
92C2×Dic15C22⋊C411yescharacteristic
93C4×D15—21no—
94C4×D15—21no—
95C4×D15—21no—
96C4×D15—21no—
97C4×D15—22no—
98Dic30—41no—
99Dic30—41no—
100C3×C5×C8—41no—
101C3×C5×C8—41no—
102C3⋊#168—41no—
103C3⋊#168—41no—
104C3×C4⋊Q8C2×D511yescharacteristic
105#946—101no—
106Q8×Dic3—101no—
107C2×ΓL(1,𝔽25)—101no—
108C2×ΓL(1,𝔽25)—101no—
109#897—101no—
110#892—52no—
111#890—52no—
112#887—101no—
113C42×D3—51no—
114#869—51no—
115C3×C4⋊C8C2×D511yescharacteristic
116C3×C4⋊C8C2×D511yescharacteristic
117Dic3⋊C8—101no—
118Dic3⋊C8—101no—
119C4⋊(C3⋊C8)—51no—
120C4⋊(C3⋊C8)—51no—
121C2×C5×Q8—21no—
122C2×C4×D5—31no—
123C2×C4×D5—31no—
124C2×C4×D5—31no—
125C2×Dic10—61no—
126C2×C5×C8—21no—
127C2×C5×C8—21no—
128C5×C4⋊C4—21no—
129C5×C4⋊C4C4×D312yes—
130C42×C5C22×D311yescharacteristic
131#685—62no—
132C4⋊Dic5—32no—
133C4⋊Dic5—62no—
134C4⋊Dic5—61no—
135#683—62no—
136C4×Dic5—31no—
137C4×Dic5—31no—
138C4×Dic5—31no—
139C4×Dic5—62no—
140C2×#168—61no—
141C2×#168—61no—
142#676—122no—
143#676—122no—
144#533—151no—
145#423—151no—
146#423—151no—
147#332—151no—
148#332—151no—
149#332—151no—
150#332D1511yescharacteristic, complemented
151C22×C3×C5C2×C22⋊C411yescharacteristic
152C2×D15—21no—
153C2×D15—21no—
154C2×D15—21no—
155C3×C4×C5—21no—
156C3×C4×C5—42no—
157C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
158C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
159C3×C4×C5#13711yescharacteristic
160C3×C4×C5#13711yescharacteristic
161Dic15—21no—
162Dic15—21no—
163Dic15—42no—
164Dic15#10112yes—
165C2×C3×Q8—21no—
166C2×C4×D3—51no—
167C2×C4×D3—51no—
168C2×C4×D3—51no—
169C2×Dic6—101no—
170C2×C3×C8—21no—
171C2×C3×C8—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4C4×D512yes—
174C3×C42C22×D511yescharacteristic
175(C2×D3)⋊C4—102no—
176C4⋊Dic3—52no—
177C4⋊Dic3—102no—
178C4⋊Dic3—101no—
179Dic3⋊C4—102no—
180C4×Dic3—51no—
181C4×Dic3—51no—
182C4×Dic3—51no—
183C4×Dic3—102no—
184C2×C3⋊C8—101no—
185C2×C3⋊C8—101no—
186ΓL(1,𝔽25)—202no—
187ΓL(1,𝔽25)—202no—
188C22×D5—31no—
189C5×Q8—41no—
190C5×Q8—41no—
191C2×C4×C5—22no—
192C2×C4×C5C2×C4×D311yescharacteristic
193C2×C4×C5D3×D411yescharacteristic
194C2×C4×C5D3×D411yescharacteristic
195C2×Dic5—31no—
196C2×Dic5—31no—
197C2×Dic5—31no—
198C2×Dic5—62no—
199C4×D5—62no—
200C4×D5—61no—
201C4×D5—61no—
202C4×D5—61no—
203C4×D5—61no—
204Dic10—121no—
205Dic10—121no—
206C5×C8—41no—
207C5×C8—41no—
208#168—121no—
209#168—121no—
210C2×M16—301no—
211C2×M16—301no—
212C4⋊Q8—151no—
213C4⋊Q8C2×D1511yescharacteristic
214#125—152no—
215C22⋊Q8—301no—
216C22⋊Q8—301no—
217C4×Q8—301no—
218C4×Q8—301no—
219#117—152no—
220C2×C42—151no—
221C4⋊C8—151no—
222C4⋊C8—151no—
223C4⋊C8—301no—
224C4⋊C8—301no—
225C4⋊C8C2×D1511yescharacteristic
226C4⋊C8C2×D1511yescharacteristic
227C2×C3×C5C2×#10111yescharacteristic
228C2×C3×C5#41711yescharacteristic
229C2×C3×C5#41711yescharacteristic
230D15—41no—
231C22×D3—51no—
232C3×Q8—41no—
233C3×Q8—41no—
234C2×C3×C4—22no—
235C2×C3×C4C2×C4×D511yescharacteristic
236C2×C3×C4D4×D511yescharacteristic
237C2×C3×C4D4×D511yescharacteristic
238C2×Dic3—51no—
239C2×Dic3—51no—
240C2×Dic3—51no—
241C2×Dic3—102no—
242C4×D3—102no—
243C4×D3—101no—
244C4×D3—101no—
245C4×D3—101no—
246C4×D3—101no—
247Dic6—201no—
248Dic6—201no—
249C3×C8—41no—
250C3×C8—41no—
251C3⋊C8—201no—
252C3⋊C8—201no—
253C22×C5D3×C22⋊C411yescharacteristic
254C2×D5—61no—
255C2×D5—61no—
256C2×D5—61no—
257C4×C5—21no—
258C4×C5—42no—
259C4×C5#91111yescharacteristic
260C4×C5#91411yescharacteristic
261C4×C5#91511yescharacteristic
262C4×C5#91811yescharacteristic
263Dic5—32no—
264Dic5—61no—
265Dic5—61no—
266Dic5—122no—
267C2×Q8—21no—
268C2×Q8—301no—
269C22×C4—151no—
270C22×C4—151no—
271C22×C4—151no—
272M16—602no—
273M16—602no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—301no—
277C2×C8—301no—
278C4⋊C4—21no—
279C4⋊C4—152no—
280C4⋊C4—302no—
281C4⋊C4—302no—
282C4⋊C4—301no—
283C4⋊C4C4×D1512yes—
284C22⋊C4—302no—
285C42—151no—
286C42—151no—
287C42—151no—
288C42—302no—
289C42C22×D1511yescharacteristic
290C3×C5#156111yescharacteristic, complemented, Hall
291C22×C3D5×C22⋊C411yescharacteristic
292C2×D3—101no—
293C2×D3—101no—
294C2×D3—101no—
295C3×C4—21no—
296C3×C4—42no—
297C3×C4#405711yescharacteristic
298C3×C4#406011yescharacteristic
299C3×C4#406111yescharacteristic
300C3×C4#406411yescharacteristic
301Dic3—52no—
302Dic3—101no—
303Dic3—101no—
304Dic3—202no—
305C2×C5D3×#10111yescharacteristic
306C2×C5#477111yescharacteristic
307C2×C5#480311yescharacteristic
308D5—121no—
309C23—151no—
310Q8—41no—
311Q8—41no—
312Q8—601no—
313Q8—601no—
314C2×C4—22no—
315C2×C4—151no—
316C2×C4—151no—
317C2×C4—151no—
318C2×C4—302no—
319C2×C4—301no—
320C2×C4—301no—
321C2×C4—301no—
322C2×C4—301no—
323C2×C4—302no—
324C2×C4C2×C4×D1511yescharacteristic
325C2×C4D4×D1511yescharacteristic
326C2×C4D4×D1511yescharacteristic
327C8—41no—
328C8—41no—
329C8—601no—
330C8—601no—
331C2×C3D5×#10111yescharacteristic
332C2×C3#6506011yescharacteristic
333C2×C3#6509211yescharacteristic
334D3—201no—
335C5#6843111yescharacteristic, complemented, Sylow
336C22—301no—
337C22—301no—
338C22—301no—
339C22C22⋊C4×D1511yescharacteristic
340C4—21no—
341C4—42no—
342C4—152no—
343C4—301no—
344C4—301no—
345C4—602no—
346C4#9180011yescharacteristic
347C4#9180311yescharacteristic
348C4#9180411yescharacteristic
349C4#9180711yescharacteristic
350C3#1059922411yescharacteristic, complemented, Sylow
351C2—601no—
352C2D15×#10111yescharacteristic
353C2#1175087211yescharacteristic
354C2#1175090411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C22×D15
FittingC3×C5×#332C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×D15C22⋊C4
cosocleC3×C42×C5C23
hypercenter#332D15
hypocenterC3×C5#1561
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
4. C3×C5×#332C2semidirect
5. #11746368C2semidirect
6. #11746307C2semidirect
7. #11746303C2semidirect
30. C5×#332D3semidirect
60. C3×#332D5semidirect
150. #332D15semidirect
290. C3×C5#1561semidirect
335. C5#68431semidirect
350. C3#10599224semidirect

Maximal subgroups

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

subgroupindex
#117564872
#117509382
C3×C5×#3322
#117463682
#117463072
#117463032
#105992243
#684315