Finite Group Databasebeta

← #14298391

Subgroups — #14298391

Order 1920.

632 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 128 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
1C2×C4⋊C4×D15C211yesmaximal, characteristic
2#11748351C212yesmaximal
3C5×#4530C211yesmaximal, characteristic, complemented
4C3×#64750C211yesmaximal, characteristic, complemented
5#11745987C212yesmaximal, complemented
6#10599783—31nomaximal, Hall
7C22×C4×D15C412yes—
8C22×C4×D15C2211yescharacteristic
9C2×C3×C5×C4⋊C4C2211yescharacteristic
10C2×C4⋊Dic15C2211yescharacteristic
11C2×#6712C412yes—
12C4⋊C4×D15—22no—
13C4⋊C4×D15—22no—
14C2×C5×#208C2212yes—
15C2×C3×#681C2212yes—
16#90957—22no—
17#90957—22no—
18#68990—51nomaximal, Hall
19C2×D5×C4⋊C4—31no—
20#65415—32no—
21C5×#343—31no—
22#64774—32no—
23#64750D311yescharacteristic, complemented
24C23×D15C2×C411yescharacteristic
25C22×C3×C4×C5C2×C412yes—
26C22×C3×C4×C5C2311yescharacteristic
27C22×Dic15C2×C411yescharacteristic
28C22×Dic15C2×C412yes—
29C2×C4×D15—22no—
30C2×C4×D15—21no—
31C2×C4×D15—21no—
32C2×C4×D15—22no—
33C2×C4×D15—22no—
34C2×C4×D15—44no—
35C2×C4×D15D412yes—
36C2×C4×D15D412yes—
37C3×C5×C4⋊C4—22no—
38C4⋊Dic15—22no—
39#6712—24no—
40C5×#208—22no—
41C5×#208—22no—
42C2×C5×C3⋊C8—22no—
43C3×#681—22no—
44C3×#681—22no—
45C2×C3×#168—22no—
46C2×D3×C4⋊C4—51no—
47#5126—52no—
48C3×#343—51no—
49#4554—52no—
50#4530D511yescharacteristic, complemented
51C22×C4×D5—31no—
52C22×C4×D5—32no—
53C2×C5×M16—32no—
54C2×C5×C4⋊C4C2×D311yescharacteristic
55C2×C4⋊Dic5—31no—
56C2×#683—32no—
57C2×#681C2×D312yes—
58D5×C4⋊C4—62no—
59D5×C4⋊C4—62no—
60#3952—62no—
61#3952—62no—
62#1821—151noSylow
63C23×C3×C5C22×C411yescharacteristic
64C22×D15—21no—
65C22×D15—21no—
66C22×D15—22no—
67C22×D15—22no—
68C22×D15C22⋊C411yescharacteristic
69C22×D15C22⋊C411yescharacteristic
70C2×C3×C4×C5—22no—
71C2×C3×C4×C5—42no—
72C2×C3×C4×C5C2×D412yes—
73C2×C3×C4×C5#4112yes—
74C2×C3×C4×C5#4111yescharacteristic
75C2×C3×C4×C5#4111yescharacteristic
76C2×Dic15—21no—
77C2×Dic15—21no—
78C2×Dic15—22no—
79C2×Dic15—42no—
80C2×Dic15C22⋊C412yes—
81C4×D15—22no—
82C4×D15—22no—
83C4×D15—22no—
84C4×D15—22no—
85C4×D15—44no—
86C4×D15—44no—
87C3×#168—42no—
88C5×C3⋊C8—42no—
89C22×C4×D3—51no—
90C22×C4×D3—52no—
91C2×C3×M16—52no—
92C2×C3×C4⋊C4C2×D511yescharacteristic
93C2×C4⋊Dic3—51no—
94C2×Dic3⋊C4—52no—
95C2×#208C2×D512yes—
96D3×C4⋊C4—102no—
97D3×C4⋊C4—102no—
98(C2×D3)⋊C8—102no—
99(C2×D3)⋊C8—102no—
100C23×D5—31no—
101C22×C4×C5C4×D312yes—
102C22×C4×C5C22×D311yescharacteristic
103C22×Dic5—31no—
104C22×Dic5—32no—
105C2×C4×D5—32no—
106C2×C4×D5—32no—
107C2×C4×D5—62no—
108C2×C4×D5—61no—
109C2×C4×D5—61no—
110C2×C4×D5—62no—
111C2×C4×D5—62no—
112C2×C4×D5—124no—
113C5×M16—62no—
114C5×M16—62no—
115C2×C5×C8—62no—
116C5×C4⋊C4—22no—
117C4⋊Dic5—62no—
118#683—64no—
119#681—22no—
120#681—22no—
121C2×#168—22no—
122C22×C4⋊C4—151no—
123#407—152no—
124#343—31no—
125#343—51no—
126#343—152no—
127C22×C3×C5—21no—
128C22×C3×C5—21no—
129C22×C3×C5C2×C22⋊C411yescharacteristic
130C22×C3×C5#11711yescharacteristic
131C22×C3×C5#11711yescharacteristic
132C2×D15—24no—
133C2×D15—24no—
134C2×D15—21no—
135C2×D15—21no—
136C2×D15—21no—
137C2×D15—21no—
138C2×D15#10012yes—
139C2×D15#10112yes—
140C3×C4×C5—42no—
141C3×C4×C5#12312yes—
142C3×C4×C5#12312yes—
143Dic15—22no—
144Dic15—42no—
145C23×D3—51no—
146C22×C3×C4C4×D512yes—
147C22×C3×C4C22×D511yescharacteristic
148C22×Dic3—51no—
149C22×Dic3—52no—
150C2×C4×D3—52no—
151C2×C4×D3—52no—
152C2×C4×D3—102no—
153C2×C4×D3—101no—
154C2×C4×D3—101no—
155C2×C4×D3—102no—
156C2×C4×D3—102no—
157C2×C4×D3—204no—
158C3×M16—102no—
159C3×M16—102no—
160C2×C3×C8—102no—
161C3×C4⋊C4—22no—
162C4⋊Dic3—102no—
163Dic3⋊C4—104no—
164#208—22no—
165#208—22no—
166C2×C3⋊C8—22no—
167C23×C5C2×C4×D311yescharacteristic
168C22×D5—31no—
169C22×D5—31no—
170C22×D5—62no—
171C22×D5—62no—
172C22×D5—61no—
173C22×D5—61no—
174C2×C4×C5—22no—
175C2×C4×C5—42no—
176C2×C4×C5#23512yes—
177C2×C4×C5D3×D412yes—
178C2×C4×C5#23711yescharacteristic
179C2×C4×C5#23911yescharacteristic
180C2×Dic5—32no—
181C2×Dic5—61no—
182C2×Dic5—61no—
183C2×Dic5—62no—
184C2×Dic5—122no—
185C4×D5—62no—
186C4×D5—62no—
187C4×D5—62no—
188C4×D5—62no—
189C4×D5—124no—
190C4×D5—124no—
191C5×C8—122no—
192#168—42no—
193C23×C4—151no—
194C23×C4—152no—
195C2×M16—32no—
196C2×M16—52no—
197C2×C4⋊C4—152no—
198C2×C4⋊C4—151no—
199C2×C4⋊C4—302no—
200C2×C4⋊C4—302no—
201C2×C4⋊C4D3×D511yescharacteristic
202C22⋊C8—302no—
203C22⋊C8—302no—
204C2×C3×C5—21no—
205C2×C3×C5—21no—
206C2×C3×C5#38111yescharacteristic
207C2×C3×C5C2×#10011yescharacteristic
208C2×C3×C5C2×#10111yescharacteristic
209D15—22no—
210D15—22no—
211C23×C3C2×C4×D511yescharacteristic
212C22×D3—51no—
213C22×D3—51no—
214C22×D3—102no—
215C22×D3—102no—
216C22×D3—101no—
217C22×D3—101no—
218C2×C3×C4—22no—
219C2×C3×C4—42no—
220C2×C3×C4#70912yes—
221C2×C3×C4D4×D512yes—
222C2×C3×C4#71111yescharacteristic
223C2×C3×C4#71311yescharacteristic
224C2×Dic3—52no—
225C2×Dic3—101no—
226C2×Dic3—101no—
227C2×Dic3—102no—
228C2×Dic3—202no—
229C4×D3—102no—
230C4×D3—102no—
231C4×D3—102no—
232C4×D3—102no—
233C4×D3—204no—
234C4×D3—204no—
235C3×C8—202no—
236C3⋊C8—42no—
237C22×C5—21no—
238C22×C5—21no—
239C22×C5#87211yescharacteristic
240C22×C5D3×C22⋊C411yescharacteristic
241C22×C5#89211yescharacteristic
242C2×D5—32no—
243C2×D5—32no—
244C2×D5—64no—
245C2×D5—64no—
246C2×D5—61no—
247C2×D5—61no—
248C2×D5—61no—
249C2×D5—61no—
250C4×C5—42no—
251C4×C5#88312yes—
252C4×C5#89412yes—
253Dic5—62no—
254Dic5—122no—
255C24—151no—
256C22×C4—151no—
257C22×C4—152no—
258C22×C4—152no—
259C22×C4—152no—
260C22×C4—302no—
261C22×C4—302no—
262C22×C4—301no—
263C22×C4—301no—
264C22×C4—302no—
265C22×C4—604no—
266C22×C4#120012yes—
267C22×C4C2×D3×D511yescharacteristic
268M16—62no—
269M16—62no—
270M16—102no—
271M16—102no—
272C2×C8—62no—
273C2×C8—102no—
274C4⋊C4—22no—
275C4⋊C4—304no—
276C4⋊C4—302no—
277C3×C5#182111yescharacteristic, complemented, Hall
278C22×C3—21no—
279C22×C3—21no—
280C22×C3#401811yescharacteristic
281C22×C3D5×C22⋊C411yescharacteristic
282C22×C3#403811yescharacteristic
283C2×D3—52no—
284C2×D3—52no—
285C2×D3—104no—
286C2×D3—104no—
287C2×D3—101no—
288C2×D3—101no—
289C2×D3—101no—
290C2×D3—101no—
291C3×C4—42no—
292C3×C4#402912yes—
293C3×C4#404012yes—
294Dic3—102no—
295Dic3—202no—
296C2×C5—21no—
297C2×C5—21no—
298C2×C5#466411yescharacteristic
299C2×C5D3×#10011yescharacteristic
300C2×C5D3×#10111yescharacteristic
301D5—62no—
302D5—62no—
303C23—151no—
304C23—151no—
305C23—302no—
306C23—302no—
307C23—301no—
308C23—301no—
309C23C2×#120011yescharacteristic
310C2×C4—22no—
311C2×C4—42no—
312C2×C4—152no—
313C2×C4—301no—
314C2×C4—301no—
315C2×C4—302no—
316C2×C4—302no—
317C2×C4—302no—
318C2×C4—302no—
319C2×C4—302no—
320C2×C4—604no—
321C2×C4—604no—
322C2×C4—602no—
323C2×C4#676611yescharacteristic
324C2×C4#676811yescharacteristic
325C2×C4#677112yes—
326C2×C4#679012yes—
327C8—122no—
328C8—202no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3#6495311yescharacteristic
332C2×C3D5×#10011yescharacteristic
333C2×C3D5×#10111yescharacteristic
334D3—102no—
335D3—102no—
336C5#6899011yescharacteristic, complemented, Sylow
337C22—21no—
338C22—21no—
339C22—152no—
340C22—152no—
341C22—304no—
342C22—304no—
343C22—301no—
344C22—301no—
345C22—301no—
346C22—301no—
347C22#9134711yescharacteristic
348C22#9138611yescharacteristic
349C22#9156111yescharacteristic
350C4—42no—
351C4—302no—
352C4—602no—
353C4#9135412yes—
354C4#9135512yes—
355C3#1059978311yescharacteristic, complemented, Sylow
356C2—21no—
357C2—21no—
358C2—302no—
359C2—302no—
360C2#1174860611yescharacteristic
361C2#1174912711yescharacteristic
362C2#1174937311yescharacteristic
subgroupG/H
centerC22#91561
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×D15C2×C4
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1821
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C5×#4530C2semidirect
4. C3×#64750C2semidirect
5. #11745987C2semidirect
23. #64750D3semidirect
50. #4530D5semidirect
277. C3×C5#1821semidirect
336. C5#68990semidirect
355. C3#10599783semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D152
#117483512
C5×#45302
C3×#647502
#117459872
#105997833
#689905