Subgroups — C₂×D₃×D₅×AGL(1,𝔽₅) #72229891

Order 2400.

976 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×D₅²	C₂	1	1	yes	maximal, characteristic
2	C₂×ΓL(1,𝔽₁₆)⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×AGL(1,𝔽₅)×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₅×ΓL(1,𝔽₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₃×#1042	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×D₃×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×D₅×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic, complemented
8	D₃×D₅×AGL(1,𝔽₅)	C₂	1	8	yes	maximal, direct product factor
9	C₂²×D₅×AGL(1,𝔽₅)	—	3	1	no	maximal, Hall
10	C₂×D₁₅⋊D₅	C₄	1	1	yes	characteristic, complemented
11	C₂×D₅×D₁₅	C₄	1	1	yes	characteristic, complemented
12	C₂×D₅×D₁₅	C₂²	1	1	yes	characteristic
13	C₂×D₃×C₅⋊D₅	C₄	1	1	yes	characteristic, complemented
14	C₂×C₅×D₃×D₅	C₄	1	1	yes	characteristic, complemented
15	C₂×C₅×D₃×D₅	C₂²	1	1	yes	characteristic
16	C₂×C₃×D₅²	C₂²	1	1	yes	characteristic
17	C₂×C₃⋊#1042	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₅×ΓL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₃×#1042	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₃×C₅×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic, complemented
21	D₃×D₅²	C₄	1	4	yes	complemented
22	D₃×D₅²	C₂²	1	4	yes	—
23	D₃×#1042	C₂²	1	4	yes	complemented
24	ΓL(1,𝔽₁₆)⋊D₅	C₂²	1	4	yes	complemented
25	D₅×ΓL(1,𝔽₁₆)	C₂²	1	4	yes	complemented
26	AGL(1,𝔽₅)×D₁₅	C₂²	1	4	yes	complemented
27	C₅×D₃×AGL(1,𝔽₅)	C₂²	1	4	yes	complemented
28	C₃×D₅×AGL(1,𝔽₅)	C₂²	1	4	yes	complemented
29	C₂²×D₃×AGL(1,𝔽₅)	—	5	1	no	maximal
30	C₂×C₄×D₃×D₅	—	5	1	no	maximal
31	C₂²×D₅²	—	3	1	no	—
32	C₂²×#1042	—	3	1	no	—
33	C₂²×C₅×AGL(1,𝔽₅)	—	3	1	no	—
34	C₂×D₅×AGL(1,𝔽₅)	—	3	1	no	—
35	C₂×D₅×AGL(1,𝔽₅)	—	3	1	no	—
36	C₂×D₅×AGL(1,𝔽₅)	—	3	1	no	—
37	C₂×D₅×AGL(1,𝔽₅)	—	3	8	no	—
38	C₂×D₅×AGL(1,𝔽₅)	D₃	1	1	yes	characteristic, direct product factor
39	C₂×C₃⋊(C₅⋊D₅)	C₂×C₄	1	1	yes	characteristic, complemented
40	C₂×C₅×D₁₅	C₂×C₄	1	1	yes	characteristic, complemented
41	C₂×C₅×D₁₅	C₂×C₄	1	1	yes	characteristic, complemented
42	C₂×C₅²×D₃	C₂×C₄	1	1	yes	characteristic, complemented
43	C₂×C₃×C₅⋊D₅	C₂×C₄	1	1	yes	characteristic, complemented
44	C₂×C₃×C₅×D₅	C₂×C₄	1	1	yes	characteristic, complemented
45	C₂×C₃×C₅×D₅	C₂³	1	1	yes	characteristic
46	D₁₅⋊D₅	C₂×C₄	1	4	yes	complemented
47	D₅×D₁₅	C₂×C₄	1	2	yes	complemented
48	D₅×D₁₅	C₂×C₄	1	4	yes	complemented
49	D₅×D₁₅	C₂³	1	2	yes	—
50	D₃×C₅⋊D₅	C₂×C₄	1	4	yes	complemented
51	C₅×D₃×D₅	C₂×C₄	1	2	yes	complemented
52	C₅×D₃×D₅	C₂×C₄	1	4	yes	complemented
53	C₅×D₃×D₅	C₂³	1	2	yes	—
54	C₃×D₅²	C₂×C₄	1	2	yes	complemented
55	C₃×D₅²	C₂³	1	2	yes	—
56	C₃⋊#1042	C₂³	1	2	yes	complemented
57	C₅×ΓL(1,𝔽₁₆)	C₂³	1	2	yes	complemented
58	C₃×#1042	C₂³	1	2	yes	complemented
59	C₃×C₅×AGL(1,𝔽₅)	C₂³	1	2	yes	complemented
60	C₂²×D₃×D₅	—	5	1	no	—
61	C₂²×D₃×D₅	—	5	1	no	—
62	C₂²×ΓL(1,𝔽₁₆)	—	5	1	no	—
63	C₂²×C₃×AGL(1,𝔽₅)	—	5	1	no	—
64	C₂×D₃×AGL(1,𝔽₅)	—	5	1	no	—
65	C₂×D₃×AGL(1,𝔽₅)	—	5	1	no	—
66	C₂×D₃×AGL(1,𝔽₅)	—	5	1	no	—
67	C₂×D₃×AGL(1,𝔽₅)	—	5	8	no	—
68	C₂×D₃×AGL(1,𝔽₅)	D₅	1	1	yes	characteristic, direct product factor
69	C₂×C₄×D₁₅	—	5	1	no	—
70	C₂×C₄×C₅×D₃	—	5	1	no	—
71	C₂×C₃×C₄×D₅	—	5	1	no	—
72	C₂×#1200	—	5	1	no	—
73	C₂×D₃×Dic₅	—	5	1	no	—
74	C₂×D₅×Dic₃	—	5	1	no	—
75	C₄×D₃×D₅	—	5	8	no	—
76	C₂²×C₅⋊D₅	—	3	1	no	—
77	C₂²×C₅×D₅	—	3	1	no	—
78	C₂²×C₅×D₅	—	3	1	no	—
79	C₂×D₅²	—	3	1	no	—
80	C₂×D₅²	—	3	1	no	—
81	C₂×D₅²	—	3	1	no	—
82	C₂×D₅²	—	3	4	no	—
83	C₂×D₅²	—	3	4	no	—
84	C₂×D₅²	C₂×D₃	1	1	yes	characteristic
85	C₂×#1042	—	3	1	no	—
86	C₂×#1042	—	3	4	no	—
87	C₂×#1042	C₂×D₃	1	1	yes	characteristic, complemented
88	C₂×C₅×AGL(1,𝔽₅)	—	3	1	no	—
89	C₂×C₅×AGL(1,𝔽₅)	—	3	4	no	—
90	C₂×C₅×AGL(1,𝔽₅)	C₂×D₃	1	1	yes	characteristic, complemented
91	D₅×AGL(1,𝔽₅)	—	3	4	no	—
92	D₅×AGL(1,𝔽₅)	—	3	4	no	—
93	D₅×AGL(1,𝔽₅)	—	3	4	no	—
94	D₅×AGL(1,𝔽₅)	C₂×D₃	1	4	yes	direct product factor
95	C₂³×AGL(1,𝔽₅)	—	15	1	no	—
96	C₂²×C₄×D₅	—	15	1	no	—
97	C₂×C₃×C₅²	C₂²×C₄	1	1	yes	characteristic, complemented
98	C₃⋊(C₅⋊D₅)	C₂²×C₄	1	2	yes	complemented
99	C₅×D₁₅	C₂²×C₄	1	2	yes	complemented
100	C₅×D₁₅	C₂²×C₄	1	2	yes	complemented
101	C₅²×D₃	C₂²×C₄	1	2	yes	complemented
102	C₃×C₅⋊D₅	C₂²×C₄	1	2	yes	complemented
103	C₃×C₅×D₅	C₂²×C₄	1	1	yes	characteristic, complemented
104	C₃×C₅×D₅	C₂²×C₄	1	2	yes	complemented
105	C₃×C₅×D₅	C₂⁴	1	1	yes	characteristic
106	C₂²×D₁₅	—	5	1	no	—
107	C₂²×D₁₅	—	5	1	no	—
108	C₂²×C₅×D₃	—	5	1	no	—
109	C₂²×C₅×D₃	—	5	1	no	—
110	C₂²×C₃×D₅	—	5	1	no	—
111	C₂²×C₃×D₅	—	5	1	no	—
112	C₂×D₃×D₅	—	5	1	no	—
113	C₂×D₃×D₅	—	5	1	no	—
114	C₂×D₃×D₅	—	5	1	no	—
115	C₂×D₃×D₅	—	5	1	no	—
116	C₂×D₃×D₅	—	5	1	no	—
117	C₂×D₃×D₅	—	5	1	no	—
118	C₂×D₃×D₅	—	5	4	no	—
119	C₂×D₃×D₅	—	5	4	no	—
120	C₂×D₃×D₅	—	5	4	no	—
121	C₂×D₃×D₅	—	5	4	no	—
122	C₂×D₃×D₅	—	20	1	no	—
123	C₂×D₃×D₅	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
124	C₂×D₃×D₅	C₂×D₅	1	1	yes	characteristic
125	C₂×ΓL(1,𝔽₁₆)	—	5	1	no	—
126	C₂×ΓL(1,𝔽₁₆)	—	5	4	no	—
127	C₂×ΓL(1,𝔽₁₆)	C₂×D₅	1	1	yes	characteristic, complemented
128	C₂×C₃×AGL(1,𝔽₅)	—	5	1	no	—
129	C₂×C₃×AGL(1,𝔽₅)	—	5	4	no	—
130	C₂×C₃×AGL(1,𝔽₅)	C₂×D₅	1	1	yes	characteristic, complemented
131	D₃×AGL(1,𝔽₅)	—	5	4	no	—
132	D₃×AGL(1,𝔽₅)	—	5	4	no	—
133	D₃×AGL(1,𝔽₅)	—	5	4	no	—
134	D₃×AGL(1,𝔽₅)	C₂×D₅	1	4	yes	direct product factor
135	C₂×C₃×C₄×C₅	—	5	1	no	—
136	C₂×Dic₁₅	—	5	1	no	—
137	C₄×D₁₅	—	5	4	no	—
138	C₂×C₅×Dic₃	—	5	1	no	—
139	C₄×C₅×D₃	—	5	4	no	—
140	C₂×C₃×Dic₅	—	5	1	no	—
141	C₃×C₄×D₅	—	5	4	no	—
142	#1200	—	5	4	no	—
143	D₃×Dic₅	—	5	4	no	—
144	D₅×Dic₃	—	5	4	no	—
145	C₂²×C₅²	—	3	1	no	—
146	C₂×C₅⋊D₅	—	3	1	no	—
147	C₂×C₅⋊D₅	—	3	4	no	—
148	C₂×C₅⋊D₅	C₄×D₃	1	1	yes	characteristic, complemented
149	C₂×C₅×D₅	—	3	2	no	—
150	C₂×C₅×D₅	—	3	4	no	—
151	C₂×C₅×D₅	—	3	2	no	—
152	C₂×C₅×D₅	—	3	1	no	—
153	C₂×C₅×D₅	—	3	1	no	—
154	C₂×C₅×D₅	C₄×D₃	1	1	yes	characteristic, complemented
155	C₂×C₅×D₅	C₂²×D₃	1	1	yes	characteristic
156	D₅²	—	3	2	no	—
157	D₅²	—	3	4	no	—
158	D₅²	—	3	2	no	—
159	D₅²	—	3	4	no	—
160	D₅²	C₄×D₃	1	2	yes	complemented
161	D₅²	C₂²×D₃	1	2	yes	—
162	#1042	—	3	2	no	—
163	#1042	C₂²×D₃	1	2	yes	complemented
164	C₅×AGL(1,𝔽₅)	—	3	2	no	—
165	C₅×AGL(1,𝔽₅)	C₂²×D₃	1	2	yes	complemented
166	C₂²×C₄×D₃	—	25	1	no	Hall
167	C₂³×D₅	—	15	1	no	—
168	C₂³×D₅	—	15	1	no	—
169	C₂²×AGL(1,𝔽₅)	—	3	1	no	—
170	C₂²×AGL(1,𝔽₅)	—	5	1	no	—
171	C₂²×AGL(1,𝔽₅)	—	15	1	no	—
172	C₂²×AGL(1,𝔽₅)	—	15	8	no	—
173	C₂²×AGL(1,𝔽₅)	—	15	1	no	—
174	C₂²×AGL(1,𝔽₅)	—	15	1	no	—
175	C₂²×AGL(1,𝔽₅)	—	15	1	no	—
176	C₂²×C₄×C₅	—	15	1	no	—
177	C₂²×Dic₅	—	15	1	no	—
178	C₂×C₄×D₅	—	5	1	no	—
179	C₂×C₄×D₅	—	15	8	no	—
180	C₂×C₄×D₅	—	15	1	no	—
181	C₂×C₄×D₅	—	15	1	no	—
182	C₂×C₄×D₅	—	15	1	no	—
183	C₃×C₅²	C₂³×C₄	1	1	yes	characteristic, complemented, Hall
184	C₂²×C₃×C₅	—	5	1	no	—
185	C₂²×C₃×C₅	—	5	1	no	—
186	C₂×D₁₅	—	5	1	no	—
187	C₂×D₁₅	—	5	1	no	—
188	C₂×D₁₅	—	5	4	no	—
189	C₂×D₁₅	—	5	2	no	—
190	C₂×D₁₅	—	5	2	no	—
191	C₂×D₁₅	—	20	1	no	—
192	C₂×D₁₅	C₄×D₅	1	1	yes	characteristic, complemented
193	C₂×D₁₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
194	C₂×C₅×D₃	—	4	1	no	—
195	C₂×C₅×D₃	—	5	1	no	—
196	C₂×C₅×D₃	—	5	1	no	—
197	C₂×C₅×D₃	—	5	4	no	—
198	C₂×C₅×D₃	—	5	2	no	—
199	C₂×C₅×D₃	—	5	2	no	—
200	C₂×C₅×D₃	C₄×D₅	1	1	yes	characteristic, complemented
201	C₂×C₅×D₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
202	C₂×C₃×D₅	—	5	1	no	—
203	C₂×C₃×D₅	—	5	1	no	—
204	C₂×C₃×D₅	—	5	2	no	—
205	C₂×C₃×D₅	—	5	2	no	—
206	C₂×C₃×D₅	—	5	2	no	—
207	C₂×C₃×D₅	—	5	2	no	—
208	C₂×C₃×D₅	—	20	1	no	—
209	C₂×C₃×D₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
210	C₂×C₃×D₅	C₂²×D₅	1	1	yes	characteristic
211	D₃×D₅	—	5	4	no	—
212	D₃×D₅	—	5	4	no	—
213	D₃×D₅	—	5	2	no	—
214	D₃×D₅	—	5	4	no	—
215	D₃×D₅	—	5	2	no	—
216	D₃×D₅	—	5	4	no	—
217	D₃×D₅	—	5	4	no	—
218	D₃×D₅	—	20	4	no	—
219	D₃×D₅	C₄×D₅	1	2	yes	complemented
220	D₃×D₅	C₂×AGL(1,𝔽₅)	1	4	yes	direct product factor
221	D₃×D₅	C₂²×D₅	1	2	yes	—
222	ΓL(1,𝔽₁₆)	—	5	2	no	—
223	ΓL(1,𝔽₁₆)	C₂²×D₅	1	2	yes	complemented
224	C₃×AGL(1,𝔽₅)	—	5	2	no	—
225	C₃×AGL(1,𝔽₅)	C₂²×D₅	1	2	yes	complemented
226	C₃×C₄×C₅	—	5	2	no	—
227	Dic₁₅	—	5	2	no	—
228	C₃×Dic₅	—	5	2	no	—
229	C₅×Dic₃	—	5	2	no	—
230	C₂×C₅²	—	3	2	no	—
231	C₂×C₅²	C₂×C₄×D₃	1	1	yes	characteristic, complemented
232	C₅⋊D₅	—	3	2	no	—
233	C₅⋊D₅	C₂×C₄×D₃	1	2	yes	complemented
234	C₅×D₅	—	3	2	no	—
235	C₅×D₅	—	3	2	no	—
236	C₅×D₅	C₂×C₄×D₃	1	1	yes	characteristic, complemented
237	C₅×D₅	C₂×C₄×D₃	1	2	yes	complemented
238	C₅×D₅	C₂³×D₃	1	1	yes	characteristic
239	C₂³×D₃	—	25	1	no	—
240	C₂²×C₃×C₄	—	25	1	no	—
241	C₂²×Dic₃	—	25	1	no	—
242	C₂×C₄×D₃	—	5	1	no	—
243	C₂×C₄×D₃	—	25	8	no	—
244	C₂×C₄×D₃	—	25	1	no	—
245	C₂×C₄×D₃	—	25	1	no	—
246	C₂×C₄×D₃	—	25	1	no	—
247	C₂³×C₅	—	15	1	no	—
248	C₂³×C₅	—	15	1	no	—
249	C₂²×D₅	—	3	1	no	—
250	C₂²×D₅	—	3	1	no	—
251	C₂²×D₅	—	5	1	no	—
252	C₂²×D₅	—	5	1	no	—
253	C₂²×D₅	—	15	4	no	—
254	C₂²×D₅	—	15	4	no	—
255	C₂²×D₅	—	15	1	no	—
256	C₂²×D₅	—	15	1	no	—
257	C₂²×D₅	—	15	4	no	—
258	C₂²×D₅	—	15	4	no	—
259	C₂²×D₅	—	15	1	no	—
260	C₂²×D₅	—	15	1	no	—
261	C₂²×D₅	—	15	1	no	—
262	C₂²×D₅	—	15	1	no	—
263	C₂²×D₅	—	15	1	no	—
264	C₂²×D₅	—	15	1	no	—
265	C₂²×D₅	—	60	1	no	—
266	C₂×AGL(1,𝔽₅)	—	3	1	no	—
267	C₂×AGL(1,𝔽₅)	—	3	4	no	—
268	C₂×AGL(1,𝔽₅)	—	5	1	no	—
269	C₂×AGL(1,𝔽₅)	—	5	4	no	—
270	C₂×AGL(1,𝔽₅)	—	15	4	no	—
271	C₂×AGL(1,𝔽₅)	—	15	4	no	—
272	C₂×AGL(1,𝔽₅)	—	15	4	no	—
273	C₂×AGL(1,𝔽₅)	—	15	1	no	—
274	C₂×AGL(1,𝔽₅)	—	15	4	no	—
275	C₂×AGL(1,𝔽₅)	D₃×D₅	1	1	yes	characteristic, direct product factor
276	C₂×C₄×C₅	—	5	1	no	—
277	C₂×C₄×C₅	—	15	4	no	—
278	C₂×C₄×C₅	—	15	1	no	—
279	C₂×Dic₅	—	5	1	no	—
280	C₂×Dic₅	—	15	4	no	—
281	C₂×Dic₅	—	15	1	no	—
282	C₄×D₅	—	5	4	no	—
283	C₄×D₅	—	15	4	no	—
284	C₄×D₅	—	15	4	no	—
285	C₄×D₅	—	15	4	no	—
286	C₂³×C₄	—	75	1	no	Sylow
287	C₂×C₃×C₅	—	4	1	no	—
288	C₂×C₃×C₅	—	5	2	no	—
289	C₂×C₃×C₅	—	5	1	no	—
290	C₂×C₃×C₅	—	5	1	no	—
291	C₂×C₃×C₅	C₂×C₄×D₅	1	1	yes	characteristic, complemented
292	C₂×C₃×C₅	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
293	D₁₅	—	5	2	no	—
294	D₁₅	—	5	2	no	—
295	D₁₅	—	20	2	no	—
296	D₁₅	C₂×C₄×D₅	1	2	yes	complemented
297	D₁₅	C₂²×AGL(1,𝔽₅)	1	2	yes	complemented
298	C₃×D₅	—	5	2	no	—
299	C₃×D₅	—	5	2	no	—
300	C₃×D₅	—	20	2	no	—
301	C₃×D₅	C₂×C₄×D₅	1	1	yes	characteristic, complemented
302	C₃×D₅	C₂²×AGL(1,𝔽₅)	1	2	yes	complemented
303	C₃×D₅	C₂³×D₅	1	1	yes	characteristic
304	C₅×D₃	—	4	2	no	—
305	C₅×D₃	—	5	2	no	—
306	C₅×D₃	—	5	2	no	—
307	C₅×D₃	C₂×C₄×D₅	1	2	yes	complemented
308	C₅×D₃	C₂²×AGL(1,𝔽₅)	1	2	yes	complemented
309	C₅²	C₂²×C₄×D₃	1	1	yes	characteristic, complemented, Sylow
310	C₂³×C₃	—	25	1	no	—
311	C₂²×D₃	—	5	1	no	—
312	C₂²×D₃	—	5	1	no	—
313	C₂²×D₃	—	25	4	no	—
314	C₂²×D₃	—	25	1	no	—
315	C₂²×D₃	—	25	4	no	—
316	C₂²×D₃	—	25	1	no	—
317	C₂²×D₃	—	25	1	no	—
318	C₂²×D₃	—	25	1	no	—
319	C₂×C₃×C₄	—	5	1	no	—
320	C₂×C₃×C₄	—	25	4	no	—
321	C₂×C₃×C₄	—	25	1	no	—
322	C₂×Dic₃	—	5	1	no	—
323	C₂×Dic₃	—	25	4	no	—
324	C₂×Dic₃	—	25	1	no	—
325	C₄×D₃	—	5	4	no	—
326	C₄×D₃	—	25	4	no	—
327	C₄×D₃	—	25	4	no	—
328	C₄×D₃	—	25	4	no	—
329	C₂²×C₅	—	3	1	no	—
330	C₂²×C₅	—	3	1	no	—
331	C₂²×C₅	—	5	1	no	—
332	C₂²×C₅	—	5	1	no	—
333	C₂²×C₅	—	12	1	no	—
334	C₂²×C₅	—	15	2	no	—
335	C₂²×C₅	—	15	4	no	—
336	C₂²×C₅	—	15	2	no	—
337	C₂²×C₅	—	15	1	no	—
338	C₂²×C₅	—	15	1	no	—
339	C₂×D₅	—	3	1	no	—
340	C₂×D₅	—	3	1	no	—
341	C₂×D₅	—	3	2	no	—
342	C₂×D₅	—	3	4	no	—
343	C₂×D₅	—	3	2	no	—
344	C₂×D₅	—	5	1	no	—
345	C₂×D₅	—	5	1	no	—
346	C₂×D₅	—	5	2	no	—
347	C₂×D₅	—	5	2	no	—
348	C₂×D₅	—	5	2	no	—
349	C₂×D₅	—	5	2	no	—
350	C₂×D₅	—	15	4	no	—
351	C₂×D₅	—	15	4	no	—
352	C₂×D₅	—	15	2	no	—
353	C₂×D₅	—	15	4	no	—
354	C₂×D₅	—	15	2	no	—
355	C₂×D₅	—	15	4	no	—
356	C₂×D₅	—	15	4	no	—
357	C₂×D₅	—	15	1	no	—
358	C₂×D₅	—	15	1	no	—
359	C₂×D₅	—	15	2	no	—
360	C₂×D₅	—	15	4	no	—
361	C₂×D₅	—	15	2	no	—
362	C₂×D₅	—	20	1	no	—
363	C₂×D₅	—	60	4	no	—
364	C₂×D₅	—	60	1	no	—
365	C₂×D₅	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
366	C₂×D₅	C₂×D₃×D₅	1	1	yes	characteristic
367	AGL(1,𝔽₅)	—	3	2	no	—
368	AGL(1,𝔽₅)	—	5	2	no	—
369	AGL(1,𝔽₅)	—	15	2	no	—
370	AGL(1,𝔽₅)	C₂×D₃×D₅	1	2	yes	direct product factor
371	C₄×C₅	—	5	2	no	—
372	C₄×C₅	—	15	2	no	—
373	Dic₅	—	5	2	no	—
374	Dic₅	—	15	2	no	—
375	C₂⁴	—	75	1	no	—
376	C₂²×C₄	—	15	1	no	—
377	C₂²×C₄	—	25	1	no	—
378	C₂²×C₄	—	75	1	no	—
379	C₂²×C₄	—	75	8	no	—
380	C₂²×C₄	—	75	1	no	—
381	C₂²×C₄	—	75	1	no	—
382	C₂²×C₄	—	75	1	no	—
383	C₃×C₅	—	4	1	no	—
384	C₃×C₅	C₂²×C₄×D₅	1	1	yes	characteristic, complemented
385	C₃×C₅	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
386	C₂²×C₃	—	5	1	no	—
387	C₂²×C₃	—	5	1	no	—
388	C₂²×C₃	—	25	2	no	—
389	C₂²×C₃	—	25	2	no	—
390	C₂²×C₃	—	25	1	no	—
391	C₂×D₃	—	5	1	no	—
392	C₂×D₃	—	5	1	no	—
393	C₂×D₃	—	5	2	no	—
394	C₂×D₃	—	5	4	no	—
395	C₂×D₃	—	5	2	no	—
396	C₂×D₃	—	25	4	no	—
397	C₂×D₃	—	25	2	no	—
398	C₂×D₃	—	25	4	no	—
399	C₂×D₃	—	25	2	no	—
400	C₂×D₃	—	25	1	no	—
401	C₂×D₃	—	25	4	no	—
402	C₂×D₃	D₅×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
403	C₃×C₄	—	5	2	no	—
404	C₃×C₄	—	25	2	no	—
405	Dic₃	—	5	2	no	—
406	Dic₃	—	25	2	no	—
407	C₂×C₅	—	3	2	no	—
408	C₂×C₅	—	3	2	no	—
409	C₂×C₅	—	4	1	no	—
410	C₂×C₅	—	5	2	no	—
411	C₂×C₅	—	5	1	no	—
412	C₂×C₅	—	5	1	no	—
413	C₂×C₅	—	12	2	no	—
414	C₂×C₅	—	15	2	no	—
415	C₂×C₅	—	15	2	no	—
416	C₂×C₅	C₄×D₃×D₅	1	1	yes	characteristic, complemented
417	C₂×C₅	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
418	D₅	—	3	2	no	—
419	D₅	—	3	2	no	—
420	D₅	—	5	2	no	—
421	D₅	—	5	2	no	—
422	D₅	—	15	2	no	—
423	D₅	—	15	2	no	—
424	D₅	—	20	2	no	—
425	D₅	—	60	2	no	—
426	D₅	C₄×D₃×D₅	1	1	yes	characteristic, complemented
427	D₅	C₂×D₃×AGL(1,𝔽₅)	1	2	yes	direct product factor
428	D₅	C₂²×D₃×D₅	1	1	yes	characteristic
429	C₂³	—	15	1	no	—
430	C₂³	—	15	1	no	—
431	C₂³	—	25	1	no	—
432	C₂³	—	75	1	no	—
433	C₂³	—	75	1	no	—
434	C₂³	—	75	1	no	—
435	C₂³	—	75	4	no	—
436	C₂³	—	75	4	no	—
437	C₂³	—	75	1	no	—
438	C₂×C₄	—	5	1	no	—
439	C₂×C₄	—	15	4	no	—
440	C₂×C₄	—	15	1	no	—
441	C₂×C₄	—	25	4	no	—
442	C₂×C₄	—	25	1	no	—
443	C₂×C₄	—	75	4	no	—
444	C₂×C₄	—	75	4	no	—
445	C₂×C₄	—	75	4	no	—
446	C₂×C₄	—	75	4	no	—
447	C₂×C₄	—	75	1	no	—
448	C₂×C₃	—	5	1	no	—
449	C₂×C₃	—	5	1	no	—
450	C₂×C₃	—	5	2	no	—
451	C₂×C₃	—	25	2	no	—
452	C₂×C₃	C₂×D₅×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
453	D₃	—	5	2	no	—
454	D₃	—	5	2	no	—
455	D₃	—	25	2	no	—
456	D₃	C₂×D₅×AGL(1,𝔽₅)	1	2	yes	direct product factor
457	C₅	—	4	1	no	—
458	C₅	C₂×C₄×D₃×D₅	1	1	yes	characteristic, complemented
459	C₅	C₂²×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
460	C₂²	—	3	1	no	—
461	C₂²	—	5	1	no	—
462	C₂²	—	5	1	no	—
463	C₂²	—	15	2	no	—
464	C₂²	—	15	2	no	—
465	C₂²	—	15	4	no	—
466	C₂²	—	15	1	no	—
467	C₂²	—	15	1	no	—
468	C₂²	—	25	2	no	—
469	C₂²	—	25	2	no	—
470	C₂²	—	25	1	no	—
471	C₂²	—	75	4	no	—
472	C₂²	—	75	2	no	—
473	C₂²	—	75	2	no	—
474	C₂²	—	75	4	no	—
475	C₂²	—	75	4	no	—
476	C₂²	—	75	1	no	—
477	C₄	—	5	2	no	—
478	C₄	—	15	2	no	—
479	C₄	—	25	2	no	—
480	C₄	—	75	2	no	—
481	C₃	C₂²×D₅×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
482	C₂	—	3	2	no	—
483	C₂	—	5	1	no	—
484	C₂	—	5	1	no	—
485	C₂	—	5	2	no	—
486	C₂	—	15	2	no	—
487	C₂	—	15	2	no	—
488	C₂	—	25	2	no	—
489	C₂	—	75	2	no	—
490	C₂	D₃×D₅×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₃×D₅×AGL(1,𝔽₅)
commutator, hypocenter	C₃×C₅²	C₂³×C₄
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²	C₂²×C₄
prime radical	C₂×D₃×D₅²	C₂
cosocle	C₃×C₅×D₅	C₂⁴
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. C₂×ΓL(1,𝔽₁₆)⋊D₅	C₂	semidirect
3. C₂×AGL(1,𝔽₅)×D₁₅	C₂	semidirect
4. C₂×D₅×ΓL(1,𝔽₁₆)	C₂	semidirect
5. C₂×D₃×#1042	C₂	semidirect
6. C₂×C₅×D₃×AGL(1,𝔽₅)	C₂	semidirect
7. C₂×C₃×D₅×AGL(1,𝔽₅)	C₂	semidirect
8. D₃×D₅×AGL(1,𝔽₅)	C₂	direct (N × H)
10. C₂×D₁₅⋊D₅	C₄	semidirect
11. C₂×D₅×D₁₅	C₄	semidirect
13. C₂×D₃×C₅⋊D₅	C₄	semidirect
14. C₂×C₅×D₃×D₅	C₄	semidirect
17. C₂×C₃⋊#1042	C₂²	semidirect
18. C₂×C₅×ΓL(1,𝔽₁₆)	C₂²	semidirect
19. C₂×C₃×#1042	C₂²	semidirect
20. C₂×C₃×C₅×AGL(1,𝔽₅)	C₂²	semidirect
21. D₃×D₅²	C₄	semidirect
23. D₃×#1042	C₂²	semidirect
24. ΓL(1,𝔽₁₆)⋊D₅	C₂²	semidirect
25. D₅×ΓL(1,𝔽₁₆)	C₂²	semidirect
26. AGL(1,𝔽₅)×D₁₅	C₂²	semidirect
27. C₅×D₃×AGL(1,𝔽₅)	C₂²	semidirect
28. C₃×D₅×AGL(1,𝔽₅)	C₂²	semidirect
38. C₂×D₅×AGL(1,𝔽₅)	D₃	direct (N × H)
39. C₂×C₃⋊(C₅⋊D₅)	C₂×C₄	semidirect
40. C₂×C₅×D₁₅	C₂×C₄	semidirect
41. C₂×C₅×D₁₅	C₂×C₄	semidirect
42. C₂×C₅²×D₃	C₂×C₄	semidirect
43. C₂×C₃×C₅⋊D₅	C₂×C₄	semidirect
44. C₂×C₃×C₅×D₅	C₂×C₄	semidirect
46. D₁₅⋊D₅	C₂×C₄	semidirect
47. D₅×D₁₅	C₂×C₄	semidirect
48. D₅×D₁₅	C₂×C₄	semidirect
50. D₃×C₅⋊D₅	C₂×C₄	semidirect
51. C₅×D₃×D₅	C₂×C₄	semidirect
52. C₅×D₃×D₅	C₂×C₄	semidirect
54. C₃×D₅²	C₂×C₄	semidirect
56. C₃⋊#1042	C₂³	semidirect
57. C₅×ΓL(1,𝔽₁₆)	C₂³	semidirect
58. C₃×#1042	C₂³	semidirect
59. C₃×C₅×AGL(1,𝔽₅)	C₂³	semidirect
68. C₂×D₃×AGL(1,𝔽₅)	D₅	direct (N × H)
87. C₂×#1042	C₂×D₃	semidirect
90. C₂×C₅×AGL(1,𝔽₅)	C₂×D₃	semidirect
94. D₅×AGL(1,𝔽₅)	C₂×D₃	direct (N × H)
97. C₂×C₃×C₅²	C₂²×C₄	semidirect
98. C₃⋊(C₅⋊D₅)	C₂²×C₄	semidirect
99. C₅×D₁₅	C₂²×C₄	semidirect
100. C₅×D₁₅	C₂²×C₄	semidirect
101. C₅²×D₃	C₂²×C₄	semidirect
102. C₃×C₅⋊D₅	C₂²×C₄	semidirect
103. C₃×C₅×D₅	C₂²×C₄	semidirect
104. C₃×C₅×D₅	C₂²×C₄	semidirect
123. C₂×D₃×D₅	AGL(1,𝔽₅)	direct (N × H)
127. C₂×ΓL(1,𝔽₁₆)	C₂×D₅	semidirect
130. C₂×C₃×AGL(1,𝔽₅)	C₂×D₅	semidirect
134. D₃×AGL(1,𝔽₅)	C₂×D₅	direct (N × H)
148. C₂×C₅⋊D₅	C₄×D₃	semidirect
154. C₂×C₅×D₅	C₄×D₃	semidirect
160. D₅²	C₄×D₃	semidirect
163. #1042	C₂²×D₃	semidirect
165. C₅×AGL(1,𝔽₅)	C₂²×D₃	semidirect
183. C₃×C₅²	C₂³×C₄	semidirect
192. C₂×D₁₅	C₄×D₅	semidirect
193. C₂×D₁₅	C₂×AGL(1,𝔽₅)	semidirect
200. C₂×C₅×D₃	C₄×D₅	semidirect
201. C₂×C₅×D₃	C₂×AGL(1,𝔽₅)	semidirect
209. C₂×C₃×D₅	C₂×AGL(1,𝔽₅)	semidirect
219. D₃×D₅	C₄×D₅	semidirect
220. D₃×D₅	C₂×AGL(1,𝔽₅)	direct (N × H)
223. ΓL(1,𝔽₁₆)	C₂²×D₅	semidirect
225. C₃×AGL(1,𝔽₅)	C₂²×D₅	semidirect
231. C₂×C₅²	C₂×C₄×D₃	semidirect
233. C₅⋊D₅	C₂×C₄×D₃	semidirect
236. C₅×D₅	C₂×C₄×D₃	semidirect
237. C₅×D₅	C₂×C₄×D₃	semidirect
275. C₂×AGL(1,𝔽₅)	D₃×D₅	direct (N × H)
291. C₂×C₃×C₅	C₂×C₄×D₅	semidirect
292. C₂×C₃×C₅	C₂²×AGL(1,𝔽₅)	semidirect
296. D₁₅	C₂×C₄×D₅	semidirect
297. D₁₅	C₂²×AGL(1,𝔽₅)	semidirect
301. C₃×D₅	C₂×C₄×D₅	semidirect
302. C₃×D₅	C₂²×AGL(1,𝔽₅)	semidirect
307. C₅×D₃	C₂×C₄×D₅	semidirect
308. C₅×D₃	C₂²×AGL(1,𝔽₅)	semidirect
309. C₅²	C₂²×C₄×D₃	semidirect
365. C₂×D₅	D₃×AGL(1,𝔽₅)	direct (N × H)
370. AGL(1,𝔽₅)	C₂×D₃×D₅	direct (N × H)
384. C₃×C₅	C₂²×C₄×D₅	semidirect
385. C₃×C₅	C₂³×AGL(1,𝔽₅)	semidirect
402. C₂×D₃	D₅×AGL(1,𝔽₅)	direct (N × H)
416. C₂×C₅	C₄×D₃×D₅	semidirect
417. C₂×C₅	C₂×D₃×AGL(1,𝔽₅)	semidirect
426. D₅	C₄×D₃×D₅	semidirect
427. D₅	C₂×D₃×AGL(1,𝔽₅)	direct (N × H)
452. C₂×C₃	C₂×D₅×AGL(1,𝔽₅)	semidirect
456. D₃	C₂×D₅×AGL(1,𝔽₅)	direct (N × H)
458. C₅	C₂×C₄×D₃×D₅	semidirect
459. C₅	C₂²×D₃×AGL(1,𝔽₅)	semidirect
481. C₃	C₂²×D₅×AGL(1,𝔽₅)	semidirect
490. C₂	D₃×D₅×AGL(1,𝔽₅)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×D₃×D₅²	2
C₂×ΓL(1,𝔽₁₆)⋊D₅	2
C₂×AGL(1,𝔽₅)×D₁₅	2
C₂×D₅×ΓL(1,𝔽₁₆)	2
C₂×D₃×#1042	2
C₂×C₅×D₃×AGL(1,𝔽₅)	2
C₂×C₃×D₅×AGL(1,𝔽₅)	2
D₃×D₅×AGL(1,𝔽₅)	2
C₂²×D₅×AGL(1,𝔽₅)	3
C₂²×D₃×AGL(1,𝔽₅)	5
C₂×C₄×D₃×D₅	5

Subgroups — C2×D3×D5×AGL(1,𝔽5) #72229891

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×D₅×AGL(1,𝔽₅) #72229891