Subgroups — C₅×#79282 #14413900

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₅×D₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4925	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4837	C₂	1	2	yes	maximal, complemented
5	C₅×#4835	C₂	1	2	yes	maximal, complemented
6	C₅×#4726	C₂	1	2	yes	maximal
7	C₅×#4719	C₂	1	2	yes	maximal, complemented
8	C₄×C₅×ΓL(1,𝔽₂₅)	C₂	1	2	yes	maximal, complemented
9	C₅×#4685	C₂	1	2	yes	maximal, complemented
10	C₅×#2920	—	3	1	no	maximal, Hall
11	C₂²×C₄×C₅×D₃	C₄	1	1	yes	characteristic
12	C₂²×C₄×C₅×D₃	C₄	1	1	yes	characteristic
13	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₅×Dic₃	C₄	1	1	yes	characteristic
16	C₂×C₄×C₅×Dic₃	C₄	1	1	yes	characteristic
17	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
18	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	4	yes	—
19	C₄²×C₅×D₃	C₄	1	1	yes	characteristic
20	C₄²×C₅×D₃	C₄	1	1	yes	characteristic
21	C₄²×C₅×D₃	C₄	1	1	yes	characteristic
22	C₄²×C₅×D₃	C₄	1	1	yes	characteristic
23	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
24	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
25	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
26	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
27	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
28	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₃×C₄×C₅×C₈	C₂²	1	2	yes	complemented
30	C₅×#830	C₂²	1	2	yes	—
31	C₅×(C₂×D₃)⋊C₈	C₂²	1	4	yes	—
32	C₅×#815	C₂²	1	4	yes	complemented
33	C₅×Dic₃⋊C₈	C₂²	1	4	yes	complemented
34	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	complemented
35	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	complemented
36	#79282	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
37	C₂²×C₄²×C₅	—	3	1	no	—
38	C₅×#432	—	3	2	no	—
39	C₅×#432	—	3	2	no	—
40	C₅×#431	—	3	2	no	—
41	C₅×#431	—	3	1	no	—
42	C₅×#431	D₃	1	1	yes	characteristic, complemented
43	C₅×#423	—	3	2	no	—
44	C₅×#407	—	3	2	no	—
45	C₄×C₅×M₁₆	—	3	2	no	—
46	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×C₅×D₃	—	2	4	no	—
54	C₂×C₄×C₅×D₃	—	2	4	no	—
55	C₂×C₄×C₅×D₃	—	2	4	no	—
56	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
67	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
68	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
69	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
70	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
71	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
72	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
74	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
75	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
76	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
77	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
78	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
79	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
80	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
81	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
82	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
83	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
84	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
85	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
86	C₅×ΓL(1,𝔽₂₅)	—	2	8	no	—
87	C₂×C₄²×D₃	C₂×C₅	1	1	yes	characteristic
88	C₃×#431	C₂×C₅	1	1	yes	characteristic, complemented
89	#4925	C₂×C₅	1	1	yes	characteristic, complemented
90	#4837	C₂×C₅	1	2	yes	complemented
91	#4835	C₂×C₅	1	2	yes	complemented
92	#4726	C₂×C₅	1	2	yes	—
93	#4719	C₂×C₅	1	2	yes	complemented
94	C₄×ΓL(1,𝔽₂₅)	C₂×C₅	1	2	yes	complemented
95	#4685	C₂×C₅	1	2	yes	complemented
96	C₂³×C₄×C₅	—	3	1	no	—
97	C₂³×C₄×C₅	—	3	1	no	—
98	C₂³×C₄×C₅	—	3	1	no	—
99	C₂×C₅×M₁₆	—	3	4	no	—
100	C₂×C₄²×C₅	—	3	1	no	—
101	C₂×C₄²×C₅	—	3	1	no	—
102	C₂×C₄²×C₅	—	3	1	no	—
103	C₂×C₄²×C₅	—	3	1	no	—
104	C₂×C₄²×C₅	—	3	1	no	—
105	C₂×C₄²×C₅	—	3	1	no	—
106	C₂×C₄²×C₅	—	3	1	no	—
107	C₂×C₄²×C₅	—	3	1	no	—
108	C₂×C₄²×C₅	—	3	1	no	—
109	C₂×C₄²×C₅	—	3	1	no	—
110	C₂×C₄²×C₅	—	3	1	no	—
111	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
112	C₅×C₄⋊C₈	—	3	4	no	—
113	C₅×C₄⋊C₈	—	3	2	no	—
114	C₅×C₄⋊C₈	C₂×D₃	1	2	yes	complemented
115	C₅×C₂²⋊C₈	—	3	2	no	—
116	C₅×C₂²⋊C₈	—	3	4	no	—
117	C₅×C₂²⋊C₈	C₂×D₃	1	2	yes	—
118	C₅×#97	—	3	4	no	—
119	C₄×C₅×C₈	—	3	2	no	—
120	C₄×C₅×C₈	C₂×D₃	1	2	yes	complemented
121	#2920	—	3	1	no	Sylow
122	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₅×D₃	—	2	2	no	—
124	C₂²×C₅×D₃	—	2	2	no	—
125	C₂²×C₅×D₃	—	2	2	no	—
126	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₃×C₄×C₅	—	2	2	no	—
129	C₂×C₃×C₄×C₅	—	2	2	no	—
130	C₂×C₃×C₄×C₅	M₁₆	1	4	yes	complemented
131	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
137	C₂×C₅×Dic₃	—	2	2	no	—
138	C₂×C₅×Dic₃	—	2	2	no	—
139	C₂×C₅×Dic₃	—	2	2	no	—
140	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
146	C₄×C₅×D₃	—	2	2	no	—
147	C₄×C₅×D₃	—	2	2	no	—
148	C₄×C₅×D₃	—	2	2	no	—
149	C₄×C₅×D₃	—	2	2	no	—
150	C₄×C₅×D₃	—	2	2	no	—
151	C₄×C₅×D₃	—	2	2	no	—
152	C₄×C₅×D₃	—	2	2	no	—
153	C₄×C₅×D₃	—	2	2	no	—
154	C₄×C₅×D₃	—	2	2	no	—
155	C₄×C₅×D₃	—	2	2	no	—
156	C₄×C₅×D₃	M₁₆	1	4	yes	complemented
157	C₄×C₅×D₃	#41	1	4	yes	—
158	C₃×C₅×C₈	—	2	4	no	—
159	C₅×C₃⋊C₈	—	2	4	no	—
160	C₂²×C₄×D₃	C₄×C₅	1	1	yes	characteristic
161	C₂²×C₄×D₃	C₄×C₅	1	1	yes	characteristic
162	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
163	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
164	C₂×C₄×Dic₃	C₄×C₅	1	1	yes	characteristic
165	C₂×C₄×Dic₃	C₄×C₅	1	1	yes	characteristic
166	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
167	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	4	yes	—
168	C₄²×D₃	C₄×C₅	1	1	yes	characteristic
169	C₄²×D₃	C₄×C₅	1	1	yes	characteristic
170	C₄²×D₃	C₄×C₅	1	1	yes	characteristic
171	C₄²×D₃	C₄×C₅	1	1	yes	characteristic
172	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
173	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
174	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
175	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
176	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	complemented
177	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
178	C₃×C₄×C₈	C₂²×C₅	1	2	yes	complemented
179	#830	C₂²×C₅	1	2	yes	—
180	(C₂×D₃)⋊C₈	C₂²×C₅	1	4	yes	—
181	#815	C₂²×C₅	1	4	yes	complemented
182	Dic₃⋊C₈	C₂²×C₅	1	4	yes	complemented
183	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	complemented
184	C₄×C₃⋊C₈	C₂²×C₅	1	2	yes	complemented
185	C₂⁴×C₅	—	3	1	no	—
186	C₂²×C₄×C₅	—	3	1	no	—
187	C₂²×C₄×C₅	—	3	1	no	—
188	C₂²×C₄×C₅	—	3	1	no	—
189	C₂²×C₄×C₅	—	3	1	no	—
190	C₂²×C₄×C₅	—	3	1	no	—
191	C₂²×C₄×C₅	—	3	1	no	—
192	C₂²×C₄×C₅	—	3	1	no	—
193	C₂²×C₄×C₅	—	3	1	no	—
194	C₂²×C₄×C₅	—	3	1	no	—
195	C₂²×C₄×C₅	—	3	1	no	—
196	C₂²×C₄×C₅	—	3	1	no	—
197	C₂²×C₄×C₅	—	3	1	no	—
198	C₂²×C₄×C₅	—	3	1	no	—
199	C₂²×C₄×C₅	—	3	1	no	—
200	C₂²×C₄×C₅	—	3	1	no	—
201	C₂²×C₄×C₅	—	6	4	no	—
202	C₂²×C₄×C₅	—	6	4	no	—
203	C₂²×C₄×C₅	—	6	4	no	—
204	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
205	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
206	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
207	C₅×M₁₆	—	6	8	no	—
208	C₂×C₅×C₈	—	3	4	no	—
209	C₂×C₅×C₈	C₂²×D₃	1	4	yes	—
210	C₄²×C₅	—	3	1	no	—
211	C₄²×C₅	—	3	1	no	—
212	C₄²×C₅	—	3	1	no	—
213	C₄²×C₅	—	3	1	no	—
214	C₄²×C₅	—	3	1	no	—
215	C₄²×C₅	—	3	1	no	—
216	C₄²×C₅	—	3	1	no	—
217	C₄²×C₅	—	3	1	no	—
218	C₄²×C₅	—	3	1	no	—
219	C₄²×C₅	—	3	1	no	—
220	C₄²×C₅	—	3	1	no	—
221	C₄²×C₅	—	3	1	no	—
222	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
223	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
224	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
225	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
226	C₂²×C₄²	—	3	1	no	—
227	#432	—	3	2	no	—
228	#432	—	3	2	no	—
229	#431	—	3	1	no	—
230	#431	—	3	2	no	—
231	#431	C₅×D₃	1	1	yes	characteristic, complemented
232	#423	—	3	2	no	—
233	#407	—	3	2	no	—
234	C₄×M₁₆	—	3	2	no	—
235	C₂²×C₃×C₅	—	2	1	no	—
236	C₂²×C₃×C₅	—	2	1	no	—
237	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
238	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
239	C₂×C₅×D₃	—	2	8	no	—
240	C₂×C₅×D₃	—	2	1	no	—
241	C₂×C₅×D₃	—	2	1	no	—
242	C₂×C₅×D₃	—	2	1	no	—
243	C₂×C₅×D₃	—	2	1	no	—
244	C₂×C₅×D₃	#117	1	2	yes	—
245	C₂×C₅×D₃	C₂×M₁₆	1	2	yes	—
246	C₃×C₄×C₅	—	2	1	no	—
247	C₃×C₄×C₅	—	2	1	no	—
248	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	—
249	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	—
250	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	—
251	C₃×C₄×C₅	C₂×#41	1	2	yes	—
252	C₅×Dic₃	—	2	1	no	—
253	C₅×Dic₃	—	2	1	no	—
254	C₅×Dic₃	—	2	1	no	—
255	C₅×Dic₃	—	2	1	no	—
256	C₅×Dic₃	#117	1	2	yes	—
257	C₅×Dic₃	C₂×M₁₆	1	2	yes	—
258	C₂³×D₃	C₂×C₄×C₅	1	1	yes	characteristic
259	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
260	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
261	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
262	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
263	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
264	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
265	C₂×C₄×D₃	—	2	4	no	—
266	C₂×C₄×D₃	—	2	4	no	—
267	C₂×C₄×D₃	—	2	4	no	—
268	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
269	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
270	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
271	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
272	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
273	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
274	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
275	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
276	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
277	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
278	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
279	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
280	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
281	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
282	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
283	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
284	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
285	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
286	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
287	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
288	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
289	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
290	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
291	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
292	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
293	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
294	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
295	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
296	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
297	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	—
298	ΓL(1,𝔽₂₅)	—	2	8	no	—
299	C₂³×C₅	—	3	1	no	—
300	C₂³×C₅	—	3	1	no	—
301	C₂³×C₅	—	6	2	no	—
302	C₂³×C₅	—	6	2	no	—
303	C₂³×C₅	—	6	2	no	—
304	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
305	C₂×C₄×C₅	—	2	2	no	—
306	C₂×C₄×C₅	—	2	2	no	—
307	C₂×C₄×C₅	—	3	1	no	—
308	C₂×C₄×C₅	—	3	1	no	—
309	C₂×C₄×C₅	—	3	4	no	—
310	C₂×C₄×C₅	—	3	4	no	—
311	C₂×C₄×C₅	—	3	1	no	—
312	C₂×C₄×C₅	—	3	1	no	—
313	C₂×C₄×C₅	—	3	1	no	—
314	C₂×C₄×C₅	—	3	1	no	—
315	C₂×C₄×C₅	—	6	2	no	—
316	C₂×C₄×C₅	—	6	2	no	—
317	C₂×C₄×C₅	—	6	2	no	—
318	C₂×C₄×C₅	—	6	2	no	—
319	C₂×C₄×C₅	—	6	2	no	—
320	C₂×C₄×C₅	—	6	2	no	—
321	C₂×C₄×C₅	—	6	2	no	—
322	C₂×C₄×C₅	—	6	2	no	—
323	C₂×C₄×C₅	—	6	2	no	—
324	C₂×C₄×C₅	—	6	2	no	—
325	C₂×C₄×C₅	—	6	2	no	—
326	C₂×C₄×C₅	—	6	2	no	—
327	C₂×C₄×C₅	—	6	2	no	—
328	C₂×C₄×C₅	ΓL(1,𝔽₂₅)	1	4	yes	complemented
329	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
330	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
331	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
332	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
333	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
334	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
335	C₅×C₈	—	2	4	no	—
336	C₅×C₈	—	6	4	no	—
337	C₂³×C₄	—	3	1	no	—
338	C₂³×C₄	—	3	1	no	—
339	C₂³×C₄	—	3	1	no	—
340	C₂×M₁₆	—	3	4	no	—
341	C₂×C₄²	—	3	1	no	—
342	C₂×C₄²	—	3	1	no	—
343	C₂×C₄²	—	3	1	no	—
344	C₂×C₄²	—	3	1	no	—
345	C₂×C₄²	—	3	1	no	—
346	C₂×C₄²	—	3	1	no	—
347	C₂×C₄²	—	3	1	no	—
348	C₂×C₄²	—	3	1	no	—
349	C₂×C₄²	—	3	1	no	—
350	C₂×C₄²	—	3	1	no	—
351	C₂×C₄²	—	3	1	no	—
352	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
353	C₄⋊C₈	—	3	4	no	—
354	C₄⋊C₈	—	3	2	no	—
355	C₄⋊C₈	C₂×C₅×D₃	1	2	yes	complemented
356	C₂²⋊C₈	—	3	2	no	—
357	C₂²⋊C₈	—	3	4	no	—
358	C₂²⋊C₈	C₂×C₅×D₃	1	2	yes	—
359	#97	—	3	4	no	—
360	C₄×C₈	—	3	2	no	—
361	C₄×C₈	C₂×C₅×D₃	1	2	yes	complemented
362	C₂×C₃×C₅	—	2	2	no	—
363	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
364	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
365	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
366	C₅×D₃	—	2	2	no	—
367	C₅×D₃	—	2	2	no	—
368	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
369	C₂²×D₃	—	2	2	no	—
370	C₂²×D₃	—	2	2	no	—
371	C₂²×D₃	—	2	2	no	—
372	C₂²×D₃	C₂²×C₄×C₅	1	1	yes	characteristic
373	C₂²×D₃	C₂²×C₄×C₅	1	1	yes	characteristic
374	C₂×C₃×C₄	—	2	2	no	—
375	C₂×C₃×C₄	—	2	2	no	—
376	C₂×C₃×C₄	C₅×M₁₆	1	4	yes	complemented
377	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
378	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
379	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
380	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
381	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
382	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
383	C₂×Dic₃	—	2	2	no	—
384	C₂×Dic₃	—	2	2	no	—
385	C₂×Dic₃	—	2	2	no	—
386	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
387	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
388	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
389	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
390	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
391	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
392	C₄×D₃	—	2	2	no	—
393	C₄×D₃	—	2	2	no	—
394	C₄×D₃	—	2	2	no	—
395	C₄×D₃	—	2	2	no	—
396	C₄×D₃	—	2	2	no	—
397	C₄×D₃	—	2	2	no	—
398	C₄×D₃	—	2	2	no	—
399	C₄×D₃	—	2	2	no	—
400	C₄×D₃	—	2	2	no	—
401	C₄×D₃	—	2	2	no	—
402	C₄×D₃	C₅×M₁₆	1	4	yes	complemented
403	C₄×D₃	C₅×#41	1	4	yes	—
404	C₃×C₈	—	2	4	no	—
405	C₃⋊C₈	—	2	4	no	—
406	C₂²×C₅	—	2	1	no	—
407	C₂²×C₅	—	2	1	no	—
408	C₂²×C₅	—	3	2	no	—
409	C₂²×C₅	—	3	2	no	—
410	C₂²×C₅	—	6	8	no	—
411	C₂²×C₅	—	6	1	no	—
412	C₂²×C₅	—	6	1	no	—
413	C₂²×C₅	—	6	1	no	—
414	C₂²×C₅	—	6	1	no	—
415	C₂²×C₅	C₂×ΓL(1,𝔽₂₅)	1	2	yes	—
416	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
417	C₄×C₅	—	2	1	no	—
418	C₄×C₅	—	2	1	no	—
419	C₄×C₅	—	3	2	no	—
420	C₄×C₅	—	3	2	no	—
421	C₄×C₅	—	6	1	no	—
422	C₄×C₅	—	6	1	no	—
423	C₄×C₅	—	6	1	no	—
424	C₄×C₅	—	6	1	no	—
425	C₄×C₅	C₂×ΓL(1,𝔽₂₅)	1	2	yes	—
426	C₄×C₅	C₂×ΓL(1,𝔽₂₅)	1	2	yes	—
427	C₄×C₅	D₃×M₁₆	1	2	yes	—
428	C₄×C₅	D₃×#41	1	2	yes	—
429	C₂⁴	—	3	1	no	—
430	C₂²×C₄	—	3	1	no	—
431	C₂²×C₄	—	3	1	no	—
432	C₂²×C₄	—	3	1	no	—
433	C₂²×C₄	—	3	1	no	—
434	C₂²×C₄	—	3	1	no	—
435	C₂²×C₄	—	3	1	no	—
436	C₂²×C₄	—	3	1	no	—
437	C₂²×C₄	—	3	1	no	—
438	C₂²×C₄	—	3	1	no	—
439	C₂²×C₄	—	3	1	no	—
440	C₂²×C₄	—	3	1	no	—
441	C₂²×C₄	—	3	1	no	—
442	C₂²×C₄	—	3	1	no	—
443	C₂²×C₄	—	3	1	no	—
444	C₂²×C₄	—	3	1	no	—
445	C₂²×C₄	—	6	4	no	—
446	C₂²×C₄	—	6	4	no	—
447	C₂²×C₄	—	6	4	no	—
448	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
449	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
450	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
451	M₁₆	—	6	8	no	—
452	C₂×C₈	—	3	4	no	—
453	C₂×C₈	C₂²×C₅×D₃	1	4	yes	—
454	C₄²	—	3	1	no	—
455	C₄²	—	3	1	no	—
456	C₄²	—	3	1	no	—
457	C₄²	—	3	1	no	—
458	C₄²	—	3	1	no	—
459	C₄²	—	3	1	no	—
460	C₄²	—	3	1	no	—
461	C₄²	—	3	1	no	—
462	C₄²	—	3	1	no	—
463	C₄²	—	3	1	no	—
464	C₄²	—	3	1	no	—
465	C₄²	—	3	1	no	—
466	C₄²	C₄×C₅×D₃	1	1	yes	characteristic
467	C₄²	C₄×C₅×D₃	1	1	yes	characteristic
468	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
469	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
470	C₃×C₅	#2920	1	1	yes	characteristic, complemented, Hall
471	C₂²×C₃	—	2	1	no	—
472	C₂²×C₃	—	2	1	no	—
473	C₂²×C₃	C₂×C₅×M₁₆	1	2	yes	—
474	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
475	C₂×D₃	—	2	8	no	—
476	C₂×D₃	—	2	1	no	—
477	C₂×D₃	—	2	1	no	—
478	C₂×D₃	—	2	1	no	—
479	C₂×D₃	—	2	1	no	—
480	C₂×D₃	C₅×#117	1	2	yes	—
481	C₂×D₃	C₂×C₅×M₁₆	1	2	yes	—
482	C₃×C₄	—	2	1	no	—
483	C₃×C₄	—	2	1	no	—
484	C₃×C₄	C₂×C₅×M₁₆	1	2	yes	—
485	C₃×C₄	C₂×C₅×M₁₆	1	2	yes	—
486	C₃×C₄	C₂×C₅×M₁₆	1	2	yes	—
487	C₃×C₄	C₂×C₅×#41	1	2	yes	—
488	Dic₃	—	2	1	no	—
489	Dic₃	—	2	1	no	—
490	Dic₃	—	2	1	no	—
491	Dic₃	—	2	1	no	—
492	Dic₃	C₅×#117	1	2	yes	—
493	Dic₃	C₂×C₅×M₁₆	1	2	yes	—
494	C₂×C₅	—	2	2	no	—
495	C₂×C₅	—	6	2	no	—
496	C₂×C₅	—	6	2	no	—
497	C₂×C₅	D₃×#117	1	1	yes	characteristic
498	C₂×C₅	C₂²×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
499	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
500	C₂³	—	3	1	no	—
501	C₂³	—	3	1	no	—
502	C₂³	—	6	2	no	—
503	C₂³	—	6	2	no	—
504	C₂³	—	6	2	no	—
505	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	3	1	no	—
509	C₂×C₄	—	3	1	no	—
510	C₂×C₄	—	3	4	no	—
511	C₂×C₄	—	3	4	no	—
512	C₂×C₄	—	3	1	no	—
513	C₂×C₄	—	3	1	no	—
514	C₂×C₄	—	3	1	no	—
515	C₂×C₄	—	3	1	no	—
516	C₂×C₄	—	6	2	no	—
517	C₂×C₄	—	6	2	no	—
518	C₂×C₄	—	6	2	no	—
519	C₂×C₄	—	6	2	no	—
520	C₂×C₄	—	6	2	no	—
521	C₂×C₄	—	6	2	no	—
522	C₂×C₄	—	6	2	no	—
523	C₂×C₄	—	6	2	no	—
524	C₂×C₄	—	6	2	no	—
525	C₂×C₄	—	6	2	no	—
526	C₂×C₄	—	6	2	no	—
527	C₂×C₄	—	6	2	no	—
528	C₂×C₄	—	6	2	no	—
529	C₂×C₄	C₅×ΓL(1,𝔽₂₅)	1	4	yes	complemented
530	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
531	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
532	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
533	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
534	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
535	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
536	C₈	—	2	4	no	—
537	C₈	—	6	4	no	—
538	C₂×C₃	—	2	2	no	—
539	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
540	C₂×C₃	C₂²×C₅×M₁₆	1	1	yes	characteristic
541	C₂×C₃	C₂²×C₅×M₁₆	1	1	yes	characteristic
542	D₃	—	2	2	no	—
543	D₃	—	2	2	no	—
544	C₅	#79282	1	1	yes	characteristic, direct product factor, Sylow
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	3	2	no	—
548	C₂²	—	3	2	no	—
549	C₂²	—	6	8	no	—
550	C₂²	—	6	1	no	—
551	C₂²	—	6	1	no	—
552	C₂²	—	6	1	no	—
553	C₂²	—	6	1	no	—
554	C₂²	C₂×C₅×ΓL(1,𝔽₂₅)	1	2	yes	—
555	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
556	C₄	—	2	1	no	—
557	C₄	—	2	1	no	—
558	C₄	—	3	2	no	—
559	C₄	—	3	2	no	—
560	C₄	—	6	1	no	—
561	C₄	—	6	1	no	—
562	C₄	—	6	1	no	—
563	C₄	—	6	1	no	—
564	C₄	C₂×C₅×ΓL(1,𝔽₂₅)	1	2	yes	—
565	C₄	C₂×C₅×ΓL(1,𝔽₂₅)	1	2	yes	—
566	C₄	C₅×D₃×M₁₆	1	2	yes	—
567	C₄	C₅×D₃×#41	1	2	yes	—
568	C₃	C₅×#2920	1	1	yes	characteristic, complemented, Sylow
569	C₂	—	2	2	no	—
570	C₂	—	6	2	no	—
571	C₂	—	6	2	no	—
572	C₂	C₅×D₃×#117	1	1	yes	characteristic
573	C₂	C₂²×C₅×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
574	C₂	C₂×C₅×D₃×M₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₄²×C₅	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#431	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂³×C₅×D₃	C₂×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#431	D₃
hypocenter	C₃	C₅×#2920
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₄²×C₅ ◁ C₅×#431

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#431	C₂	semidirect
3. C₅×#4925	C₂	semidirect
4. C₅×#4837	C₂	semidirect
5. C₅×#4835	C₂	semidirect
7. C₅×#4719	C₂	semidirect
8. C₄×C₅×ΓL(1,𝔽₂₅)	C₂	semidirect
9. C₅×#4685	C₂	semidirect
27. C₃×C₅×C₄⋊C₈	C₂²	semidirect
29. C₃×C₄×C₅×C₈	C₂²	semidirect
32. C₅×#815	C₂²	semidirect
33. C₅×Dic₃⋊C₈	C₂²	semidirect
34. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
35. C₄×C₅×C₃⋊C₈	C₂²	semidirect
36. #79282	C₅	direct (N × H)
42. C₅×#431	D₃	semidirect
88. C₃×#431	C₂×C₅	semidirect
89. #4925	C₂×C₅	semidirect
90. #4837	C₂×C₅	semidirect
91. #4835	C₂×C₅	semidirect
93. #4719	C₂×C₅	semidirect
94. C₄×ΓL(1,𝔽₂₅)	C₂×C₅	semidirect
95. #4685	C₂×C₅	semidirect
114. C₅×C₄⋊C₈	C₂×D₃	semidirect
120. C₄×C₅×C₈	C₂×D₃	semidirect
130. C₂×C₃×C₄×C₅	M₁₆	semidirect
156. C₄×C₅×D₃	M₁₆	semidirect
176. C₃×C₄⋊C₈	C₂²×C₅	semidirect
178. C₃×C₄×C₈	C₂²×C₅	semidirect
181. #815	C₂²×C₅	semidirect
182. Dic₃⋊C₈	C₂²×C₅	semidirect
183. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
184. C₄×C₃⋊C₈	C₂²×C₅	semidirect
231. #431	C₅×D₃	semidirect
328. C₂×C₄×C₅	ΓL(1,𝔽₂₅)	semidirect
355. C₄⋊C₈	C₂×C₅×D₃	semidirect
361. C₄×C₈	C₂×C₅×D₃	semidirect
376. C₂×C₃×C₄	C₅×M₁₆	semidirect
402. C₄×D₃	C₅×M₁₆	semidirect
470. C₃×C₅	#2920	semidirect
529. C₂×C₄	C₅×ΓL(1,𝔽₂₅)	semidirect
544. C₅	#79282	direct (N × H)
568. C₃	C₅×#2920	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄²×C₅×D₃	2
C₃×C₅×#431	2
C₅×#4925	2
C₅×#4837	2
C₅×#4835	2
C₅×#4726	2
C₅×#4719	2
C₄×C₅×ΓL(1,𝔽₂₅)	2
C₅×#4685	2
C₅×#2920	3
#79282	5

Subgroups — C5×#79282 #14413900

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79282 #14413900