Subgroups — #12004475

Order 1280.

998 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×Dic₅	C₂	1	1	yes	maximal, characteristic
2	Dic₅×#117	C₂	1	1	yes	maximal, characteristic
3	C₂×#65221	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#339	C₂	1	1	yes	maximal, characteristic
5	C₂×#64775	C₂	1	1	yes	maximal, characteristic
6	C₂×#64752	C₂	1	1	yes	maximal, characteristic
7	C₂×#64743	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
9	C₂×C₅×#117	C₂²	1	1	yes	characteristic
10	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
11	C₂×#4072	C₂²	1	1	yes	characteristic
12	C₂²×C₄×Dic₅	C₂²	1	1	yes	characteristic
13	C₂²×C₄×Dic₅	C₂²	1	1	yes	characteristic
14	C₂²×#681	C₂²	1	1	yes	characteristic
15	C₂×#3963	—	2	2	no	—
16	M₁₆×Dic₅	—	2	2	no	—
17	M₁₆×Dic₅	C₄	1	4	yes	complemented
18	C₂×#3947	—	2	1	no	—
19	C₂×C₈×Dic₅	—	2	1	no	—
20	C₄⋊C₄×Dic₅	C₄	1	4	yes	complemented
21	C₂²⋊C₄×Dic₅	—	2	2	no	—
22	#65221	—	2	2	no	—
23	#65221	—	2	1	no	—
24	#65221	C₄	1	4	yes	complemented
25	C₄²×Dic₅	—	2	1	no	—
26	C₅×#339	C₄	1	4	yes	complemented
27	#64775	C₄	1	4	yes	complemented
28	#64752	C₄	1	4	yes	complemented
29	#64743	C₄	1	4	yes	complemented
30	#10701	—	5	1	no	maximal, Sylow
31	C₂³×C₄×C₅	—	2	1	no	—
32	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
33	C₂³×Dic₅	—	2	1	no	—
34	C₂³×Dic₅	D₄	1	2	yes	—
35	C₂×C₅×M₁₆	—	2	1	no	—
36	C₂×C₅×M₁₆	—	2	1	no	—
37	C₂×C₅×M₁₆	—	2	1	no	—
38	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
39	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
40	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
41	C₂²×C₅×C₈	—	2	1	no	—
42	C₅×#117	—	2	1	no	—
43	C₅×#117	—	2	1	no	—
44	C₅×#117	C₂×C₄	1	2	yes	—
45	C₅×#117	C₂×C₄	1	2	yes	—
46	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
47	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
48	C₂×C₄²×C₅	—	2	1	no	—
49	C₂×C₄²×C₅	—	2	1	no	—
50	C₂×C₄²×C₅	—	2	1	no	—
51	C₂×C₄²×C₅	—	2	1	no	—
52	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
53	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
55	C₂×C₂²⋊Dic₅	—	2	1	no	—
56	#4072	—	2	1	no	—
57	#4072	—	2	1	no	—
58	#4072	C₂×C₄	1	2	yes	—
59	#4072	C₂×C₄	1	2	yes	—
60	C₂×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
61	C₂×C₄×Dic₅	—	2	1	no	—
62	C₂×C₄×Dic₅	—	2	1	no	—
63	C₂×C₄×Dic₅	—	2	1	no	—
64	C₂×C₄×Dic₅	—	2	1	no	—
65	C₂×C₄×Dic₅	—	2	4	no	—
66	C₂×C₄×Dic₅	C₂×C₄	1	2	yes	—
67	C₂×C₄×Dic₅	C₂×C₄	1	2	yes	—
68	C₂×C₄×Dic₅	C₂×C₄	1	2	yes	—
69	C₂×C₄×Dic₅	C₂×C₄	1	2	yes	—
70	C₂×C₄×Dic₅	C₂×C₄	1	2	yes	—
71	C₂×C₄×Dic₅	C₂×C₄	1	2	yes	—
72	C₂×C₄×Dic₅	D₄	1	1	yes	characteristic
73	C₂×C₄×Dic₅	D₄	1	1	yes	characteristic
74	C₂×C₄×Dic₅	D₄	1	2	yes	—
75	C₂×C₄×Dic₅	Q₈	1	2	yes	—
76	C₂×#681	—	2	1	no	—
77	C₂×#681	—	2	1	no	—
78	C₂×#681	—	2	1	no	—
79	C₂×#681	C₂×C₄	1	2	yes	—
80	C₂×#681	C₂×C₄	1	2	yes	—
81	C₂×#681	C₂×C₄	1	2	yes	—
82	C₂²×#168	—	2	1	no	—
83	#3963	—	2	8	no	—
84	#3963	—	2	4	no	—
85	#3947	—	2	4	no	—
86	C₈×Dic₅	—	2	4	no	—
87	C₂×C₄×M₁₆	—	5	1	no	—
88	C₄×#117	—	5	1	no	—
89	C₂×#376	—	5	1	no	—
90	C₂×#339	—	5	1	no	—
91	C₂×#339	—	5	1	no	—
92	C₂×#339	—	5	1	no	—
93	C₂×#339	D₅	1	1	yes	characteristic
94	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₅	—	2	2	no	—
96	C₂²×C₄×C₅	—	2	2	no	—
97	C₂²×C₄×C₅	—	2	2	no	—
98	C₂²×C₄×C₅	—	2	2	no	—
99	C₂²×C₄×C₅	—	4	4	no	—
100	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
110	C₂²×C₄×C₅	#41	1	1	yes	characteristic
111	C₂²×C₄×C₅	#41	1	1	yes	characteristic
112	C₂²×C₄×C₅	#41	1	1	yes	characteristic
113	C₂²×C₄×C₅	#41	1	1	yes	characteristic
114	C₂²×Dic₅	—	2	2	no	—
115	C₂²×Dic₅	—	2	2	no	—
116	C₂²×Dic₅	—	2	2	no	—
117	C₂²×Dic₅	—	2	2	no	—
118	C₂²×Dic₅	—	4	4	no	—
119	C₂²×Dic₅	—	4	4	no	—
120	C₂²×Dic₅	C₂²⋊C₄	1	2	yes	—
121	C₂²×Dic₅	C₂²⋊C₄	1	2	yes	—
122	C₂²×Dic₅	C₂²⋊C₄	1	4	yes	—
123	C₂²×Dic₅	C₄⋊C₄	1	4	yes	—
124	C₅×M₁₆	—	2	2	no	—
125	C₅×M₁₆	—	2	2	no	—
126	C₅×M₁₆	—	2	2	no	—
127	C₅×M₁₆	C₄²	1	4	yes	complemented
128	C₂×C₅×C₈	—	2	2	no	—
129	C₂×C₅×C₈	—	2	2	no	—
130	C₂×C₅×C₈	—	2	2	no	—
131	C₅×C₄⋊C₄	—	2	2	no	—
132	C₅×C₄⋊C₄	C₄²	1	4	yes	—
133	C₅×C₂²⋊C₄	—	2	2	no	—
134	C₅×C₂²⋊C₄	—	2	2	no	—
135	C₄²×C₅	—	2	2	no	—
136	C₄²×C₅	—	2	2	no	—
137	C₄²×C₅	—	2	2	no	—
138	C₄²×C₅	—	2	2	no	—
139	C₄²×C₅	—	2	2	no	—
140	C₄²×C₅	C₄²	1	4	yes	complemented
141	C₂²⋊Dic₅	—	2	2	no	—
142	C₂²⋊Dic₅	—	2	2	no	—
143	C₄⋊Dic₅	—	2	2	no	—
144	C₄⋊Dic₅	C₄²	1	4	yes	—
145	C₄×Dic₅	—	2	2	no	—
146	C₄×Dic₅	—	2	2	no	—
147	C₄×Dic₅	—	2	2	no	—
148	C₄×Dic₅	—	2	2	no	—
149	C₄×Dic₅	—	2	2	no	—
150	C₄×Dic₅	—	4	8	no	—
151	C₄×Dic₅	C₄²	1	4	yes	—
152	C₄×Dic₅	C₄²	1	4	yes	complemented
153	C₄×Dic₅	C₂²⋊C₄	1	2	yes	—
154	C₄×Dic₅	C₂²⋊C₄	1	2	yes	—
155	C₄×Dic₅	C₄⋊C₄	1	2	yes	—
156	C₄×Dic₅	C₄⋊C₄	1	2	yes	—
157	C₄×Dic₅	C₄⋊C₄	1	4	yes	—
158	#681	—	2	2	no	—
159	#681	—	2	2	no	—
160	#681	—	2	2	no	—
161	#681	C₄²	1	4	yes	complemented
162	C₂×#168	—	2	2	no	—
163	C₂×#168	—	2	2	no	—
164	C₂×#168	—	2	2	no	—
165	C₂²×M₁₆	—	5	1	no	—
166	C₂²×M₁₆	C₂×D₅	1	1	yes	characteristic
167	C₂×#117	—	5	1	no	—
168	C₂×#117	C₂×D₅	1	1	yes	characteristic
169	C₂²×C₄²	—	5	1	no	—
170	C₂²×C₄²	—	5	1	no	—
171	C₂²×C₄²	C₂×D₅	1	1	yes	characteristic
172	C₄×M₁₆	—	5	4	no	—
173	C₄×M₁₆	—	10	2	no	—
174	C₂×#97	—	10	1	no	—
175	C₂×C₄×C₈	—	10	1	no	—
176	C₄×C₄⋊C₄	—	5	4	no	—
177	C₄×C₂²⋊C₄	—	10	2	no	—
178	#376	—	5	4	no	—
179	#376	—	10	2	no	—
180	#376	—	10	1	no	—
181	C₂×#95	—	10	2	no	—
182	C₄³	—	10	1	no	—
183	#339	—	5	4	no	—
184	#339	—	5	4	no	—
185	#339	—	5	4	no	—
186	#339	Dic₅	1	4	yes	complemented
187	C₂³×C₅	—	2	4	no	—
188	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
192	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
193	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
194	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₅	—	2	4	no	—
196	C₂×C₄×C₅	—	2	4	no	—
197	C₂×C₄×C₅	—	4	4	no	—
198	C₂×C₄×C₅	—	4	4	no	—
199	C₂×C₄×C₅	—	4	4	no	—
200	C₂×C₄×C₅	—	4	4	no	—
201	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
202	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
203	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
204	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
206	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
207	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
208	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
210	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
211	C₂×C₄×C₅	#117	1	1	yes	characteristic
212	C₂×C₄×C₅	#117	1	1	yes	characteristic
213	C₂×C₄×C₅	#117	1	1	yes	characteristic
214	C₂×C₄×C₅	#117	1	1	yes	characteristic
215	C₂×C₄×C₅	#117	1	1	yes	characteristic
216	C₂×C₄×C₅	#117	1	1	yes	characteristic
217	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
218	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
219	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
220	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
221	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
222	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
223	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
224	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
225	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
226	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
227	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
228	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
229	C₂×Dic₅	—	2	4	no	—
230	C₂×Dic₅	—	2	4	no	—
231	C₂×Dic₅	—	2	4	no	—
232	C₂×Dic₅	—	2	4	no	—
233	C₂×Dic₅	—	4	4	no	—
234	C₂×Dic₅	—	4	4	no	—
235	C₂×Dic₅	—	4	4	no	—
236	C₂×Dic₅	—	4	4	no	—
237	C₂×Dic₅	—	4	4	no	—
238	C₂×Dic₅	—	4	4	no	—
239	C₂×Dic₅	#95	1	4	yes	—
240	C₂×Dic₅	#95	1	4	yes	—
241	C₅×C₈	—	2	4	no	—
242	#168	—	2	4	no	—
243	C₂³×C₄	—	2	1	no	—
244	C₂³×C₄	—	5	2	no	—
245	C₂³×C₄	—	10	1	no	—
246	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
247	C₂×M₁₆	—	2	1	no	—
248	C₂×M₁₆	—	2	1	no	—
249	C₂×M₁₆	—	2	1	no	—
250	C₂×M₁₆	—	5	2	no	—
251	C₂×M₁₆	—	5	2	no	—
252	C₂×M₁₆	—	5	2	no	—
253	C₂×M₁₆	—	10	1	no	—
254	C₂×M₁₆	—	10	1	no	—
255	C₂×M₁₆	—	10	1	no	—
256	C₂×M₁₆	C₄×D₅	1	2	yes	—
257	C₂×M₁₆	C₄×D₅	1	2	yes	—
258	C₂×M₁₆	C₂×Dic₅	1	2	yes	—
259	C₂²×C₈	—	2	1	no	—
260	C₂²×C₈	—	10	1	no	—
261	#117	—	2	1	no	—
262	#117	—	2	1	no	—
263	#117	—	5	2	no	—
264	#117	—	5	2	no	—
265	#117	—	10	1	no	—
266	#117	—	10	1	no	—
267	#117	C₄×D₅	1	2	yes	—
268	#117	C₂×Dic₅	1	2	yes	—
269	C₂×C₄⋊C₄	—	5	2	no	—
270	C₂×C₄⋊C₄	C₄×D₅	1	2	yes	—
271	C₂×C₂²⋊C₄	—	2	1	no	—
272	C₂×C₂²⋊C₄	—	10	1	no	—
273	C₂×C₄²	—	2	1	no	—
274	C₂×C₄²	—	2	1	no	—
275	C₂×C₄²	—	2	1	no	—
276	C₂×C₄²	—	2	1	no	—
277	C₂×C₄²	—	5	2	no	—
278	C₂×C₄²	—	5	2	no	—
279	C₂×C₄²	—	5	2	no	—
280	C₂×C₄²	—	5	2	no	—
281	C₂×C₄²	—	5	1	no	—
282	C₂×C₄²	—	5	1	no	—
283	C₂×C₄²	—	5	2	no	—
284	C₂×C₄²	—	5	2	no	—
285	C₂×C₄²	—	5	2	no	—
286	C₂×C₄²	—	5	2	no	—
287	C₂×C₄²	—	10	1	no	—
288	C₂×C₄²	—	10	1	no	—
289	C₂×C₄²	—	10	1	no	—
290	C₂×C₄²	—	10	1	no	—
291	C₂×C₄²	—	10	4	no	—
292	C₂×C₄²	C₄×D₅	1	2	yes	—
293	C₂×C₄²	C₄×D₅	1	2	yes	—
294	C₂×C₄²	C₂×Dic₅	1	2	yes	—
295	#97	—	10	4	no	—
296	C₄×C₈	—	10	4	no	—
297	#95	—	10	8	no	—
298	#95	—	10	4	no	—
299	C₂²×C₅	—	2	2	no	—
300	C₂²×C₅	—	2	2	no	—
301	C₂²×C₅	—	2	2	no	—
302	C₂²×C₅	—	2	2	no	—
303	C₂²×C₅	—	2	2	no	—
304	C₂²×C₅	—	2	2	no	—
305	C₂²×C₅	C₂×#95	1	1	yes	characteristic
306	C₂²×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
307	C₂²×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
308	C₂²×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
309	C₂²×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
310	C₂²×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
311	C₂²×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
312	C₂²×C₅	#421	1	4	yes	—
313	C₄×C₅	—	4	4	no	—
314	C₄×C₅	—	4	4	no	—
315	C₄×C₅	C₄³	1	1	yes	characteristic
316	C₄×C₅	#376	1	1	yes	characteristic
317	C₄×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
318	C₄×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
319	C₄×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
320	C₄×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
321	C₄×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
322	C₄×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
323	Dic₅	—	2	4	no	—
324	Dic₅	—	2	4	no	—
325	Dic₅	—	4	4	no	—
326	Dic₅	—	4	4	no	—
327	C₂⁴	D₄×D₅	1	1	yes	characteristic
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	4	4	no	—
333	C₂²×C₄	—	5	2	no	—
334	C₂²×C₄	—	5	2	no	—
335	C₂²×C₄	—	5	4	no	—
336	C₂²×C₄	—	5	4	no	—
337	C₂²×C₄	—	10	2	no	—
338	C₂²×C₄	—	10	2	no	—
339	C₂²×C₄	—	10	2	no	—
340	C₂²×C₄	—	10	2	no	—
341	C₂²×C₄	—	20	4	no	—
342	C₂²×C₄	—	20	4	no	—
343	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
344	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
345	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
346	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
347	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
348	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
349	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
350	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
351	C₂²×C₄	#711	1	1	yes	characteristic
352	C₂²×C₄	#711	1	1	yes	characteristic
353	C₂²×C₄	#711	1	1	yes	characteristic
354	C₂²×C₄	Q₈×D₅	1	1	yes	characteristic
355	C₂²×C₄	#713	1	1	yes	characteristic
356	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
357	M₁₆	—	2	2	no	—
358	M₁₆	—	2	2	no	—
359	M₁₆	—	2	2	no	—
360	M₁₆	—	5	4	no	—
361	M₁₆	—	10	2	no	—
362	M₁₆	—	10	2	no	—
363	M₁₆	—	10	2	no	—
364	M₁₆	C₄×Dic₅	1	4	yes	complemented
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	10	2	no	—
369	C₂×C₈	—	10	2	no	—
370	C₂×C₈	—	10	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	5	4	no	—
373	C₄⋊C₄	—	10	2	no	—
374	C₄⋊C₄	C₄×Dic₅	1	4	yes	—
375	C₂²⋊C₄	—	2	2	no	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	10	2	no	—
378	C₂²⋊C₄	—	10	2	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	5	4	no	—
385	C₄²	—	5	2	no	—
386	C₄²	—	5	2	no	—
387	C₄²	—	5	4	no	—
388	C₄²	—	5	2	no	—
389	C₄²	—	5	2	no	—
390	C₄²	—	5	4	no	—
391	C₄²	—	10	2	no	—
392	C₄²	—	10	2	no	—
393	C₄²	—	10	2	no	—
394	C₄²	—	10	2	no	—
395	C₄²	—	10	2	no	—
396	C₄²	—	20	8	no	—
397	C₄²	C₄×Dic₅	1	4	yes	complemented
398	C₂×C₅	—	2	1	no	—
399	C₂×C₅	—	2	1	no	—
400	C₂×C₅	—	2	1	no	—
401	C₂×C₅	—	2	1	no	—
402	C₂×C₅	C₄×#95	1	1	yes	characteristic
403	C₂×C₅	#1733	1	2	yes	—
404	C₂×C₅	#1759	1	2	yes	—
405	C₂×C₅	#1759	1	2	yes	—
406	C₂³	—	2	4	no	—
407	C₂³	D₅×C₂²⋊C₄	1	1	yes	characteristic
408	C₂³	D₅×C₂²⋊C₄	1	1	yes	characteristic
409	C₂³	#4027	1	1	yes	characteristic
410	C₂³	#4027	1	1	yes	characteristic
411	C₂³	D₅×C₄⋊C₄	1	1	yes	characteristic
412	C₂³	#4039	1	1	yes	characteristic
413	C₂³	D₄×Dic₅	1	1	yes	characteristic
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	4	no	—
420	C₂×C₄	—	5	4	no	—
421	C₂×C₄	—	5	4	no	—
422	C₂×C₄	—	10	4	no	—
423	C₂×C₄	—	10	4	no	—
424	C₂×C₄	—	10	4	no	—
425	C₂×C₄	—	10	4	no	—
426	C₂×C₄	—	20	4	no	—
427	C₂×C₄	—	20	4	no	—
428	C₂×C₄	—	20	4	no	—
429	C₂×C₄	—	20	4	no	—
430	C₂×C₄	—	20	4	no	—
431	C₂×C₄	—	20	4	no	—
432	C₂×C₄	C₄²×D₅	1	1	yes	characteristic
433	C₂×C₄	C₄²×D₅	1	1	yes	characteristic
434	C₂×C₄	C₄²×D₅	1	1	yes	characteristic
435	C₂×C₄	C₄²×D₅	1	1	yes	characteristic
436	C₂×C₄	#4023	1	1	yes	characteristic
437	C₂×C₄	#4023	1	1	yes	characteristic
438	C₂×C₄	#4023	1	1	yes	characteristic
439	C₂×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
440	C₂×C₄	#4027	1	1	yes	characteristic
441	C₂×C₄	#4027	1	1	yes	characteristic
442	C₂×C₄	#4027	1	1	yes	characteristic
443	C₂×C₄	#4027	1	1	yes	characteristic
444	C₂×C₄	#4033	1	1	yes	characteristic
445	C₂×C₄	#4033	1	1	yes	characteristic
446	C₂×C₄	#4033	1	1	yes	characteristic
447	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
448	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
449	C₂×C₄	#4038	1	1	yes	characteristic
450	C₂×C₄	#4038	1	1	yes	characteristic
451	C₂×C₄	#4038	1	1	yes	characteristic
452	C₂×C₄	#4039	1	1	yes	characteristic
453	C₂×C₄	#4039	1	1	yes	characteristic
454	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
455	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
456	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
457	C₂×C₄	D₄×Dic₅	1	1	yes	characteristic
458	C₂×C₄	D₄×Dic₅	1	1	yes	characteristic
459	C₂×C₄	Q₈×Dic₅	1	1	yes	characteristic
460	C₈	—	2	4	no	—
461	C₈	—	10	4	no	—
462	C₅	#10701	1	1	yes	characteristic, complemented, Sylow
463	C₂²	—	2	2	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	2	2	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	2	2	no	—
469	C₂²	#64938	1	1	yes	characteristic
470	C₂²	D₅×#95	1	1	yes	characteristic
471	C₂²	#64955	1	1	yes	characteristic
472	C₂²	#64955	1	1	yes	characteristic
473	C₂²	#65110	1	4	yes	—
474	C₂²	C₂²⋊C₄×Dic₅	1	1	yes	characteristic
475	C₂²	C₂²⋊C₄×Dic₅	1	1	yes	characteristic
476	C₂²	C₄⋊C₄×Dic₅	1	1	yes	characteristic
477	C₄	—	4	4	no	—
478	C₄	—	4	4	no	—
479	C₄	—	10	4	no	—
480	C₄	—	10	4	no	—
481	C₄	—	20	4	no	—
482	C₄	—	20	4	no	—
483	C₄	#64937	1	1	yes	characteristic
484	C₄	#64938	1	1	yes	characteristic
485	C₄	#64938	1	1	yes	characteristic
486	C₄	#64955	1	1	yes	characteristic
487	C₄	C₄²×Dic₅	1	1	yes	characteristic
488	C₄	C₂²⋊C₄×Dic₅	1	1	yes	characteristic
489	C₄	C₄⋊C₄×Dic₅	1	1	yes	characteristic
490	C₄	C₄⋊C₄×Dic₅	1	1	yes	characteristic
491	C₂	—	2	1	no	—
492	C₂	—	2	1	no	—
493	C₂	—	2	1	no	—
494	C₂	—	2	1	no	—
495	C₂	#10599522	1	2	yes	—
496	C₂	#10599546	1	2	yes	—
497	C₂	Dic₅×#95	1	1	yes	characteristic
498	C₂	#10601147	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₅
commutator	C₄×C₅	C₄³
Frattini	C₂³×C₄	C₂²×D₅
Fitting	C₂×C₅×#339	C₂
socle	C₂³×C₅	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₅	C₂×D₄
cosocle	C₂³×C₄×C₅	C₂³
hypercenter	C₂×#339	D₅
hypocenter	C₅	#10701
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂×#339

Complements

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

N	H ≅ G/N	type
17. M₁₆×Dic₅	C₄	semidirect
20. C₄⋊C₄×Dic₅	C₄	semidirect
24. #65221	C₄	semidirect
26. C₅×#339	C₄	semidirect
27. #64775	C₄	semidirect
28. #64752	C₄	semidirect
29. #64743	C₄	semidirect
127. C₅×M₁₆	C₄²	semidirect
140. C₄²×C₅	C₄²	semidirect
152. C₄×Dic₅	C₄²	semidirect
161. #681	C₄²	semidirect
186. #339	Dic₅	semidirect
364. M₁₆	C₄×Dic₅	semidirect
397. C₄²	C₄×Dic₅	semidirect
462. C₅	#10701	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₁₆×Dic₅	2
Dic₅×#117	2
C₂×#65221	2
C₂×C₅×#339	2
C₂×#64775	2
C₂×#64752	2
C₂×#64743	2
#10701	5