Subgroups — #12004497

Order 1280.

886 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#405	C₂	1	1	yes	maximal, characteristic
2	C₂×#65390	C₂	1	1	yes	maximal, characteristic
3	C₂²×#3947	C₂	1	1	yes	maximal, characteristic
4	C₂×#64778	C₂	1	1	yes	maximal, characteristic
5	C₂×#64775	C₂	1	1	yes	maximal, characteristic
6	#10602373	C₂	1	1	yes	maximal, characteristic
7	C₂×#64752	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
9	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
10	C₂×C₅×#117	C₂²	1	1	yes	characteristic
11	C₂×#4072	C₂²	1	1	yes	characteristic
12	C₂²×C₄×Dic₅	C₂²	1	1	yes	characteristic
13	C₂²×#681	C₂²	1	1	yes	characteristic
14	C₂³×#168	C₂²	1	1	yes	characteristic
15	C₅×#405	—	2	2	no	—
16	C₅×#405	C₄	1	4	yes	complemented
17	C₂×C₅×#97	—	2	1	no	—
18	C₂×C₄×C₅×C₈	—	2	1	no	—
19	#65390	—	2	2	no	—
20	#65390	C₄	1	4	yes	complemented
21	C₂×#3947	—	2	2	no	—
22	C₂×#3947	—	2	2	no	—
23	C₂×#3947	—	2	1	no	—
24	C₂×#3947	C₄	1	4	yes	complemented
25	C₂×C₈×Dic₅	—	2	1	no	—
26	#64778	C₄	1	4	yes	complemented
27	#64775	C₄	1	4	yes	complemented
28	#64752	C₄	1	4	yes	complemented
29	#64749	C₄	1	4	yes	complemented
30	#10707	—	5	1	no	maximal, Sylow
31	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
32	C₂³×Dic₅	—	2	1	no	—
33	C₂×C₅×M₁₆	—	2	1	no	—
34	C₂×C₅×M₁₆	—	2	1	no	—
35	C₂×C₅×M₁₆	—	2	1	no	—
36	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
37	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
38	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
39	C₂²×C₅×C₈	—	2	1	no	—
40	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
41	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
42	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
43	C₂²×C₅×C₈	D₄	1	2	yes	—
44	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
45	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
46	C₂²×C₅×C₈	D₄	1	2	yes	—
47	C₂²×C₅×C₈	Q₈	1	2	yes	—
48	C₅×#117	—	2	1	no	—
49	C₅×#117	—	2	1	no	—
50	C₅×#117	C₂×C₄	1	2	yes	—
51	C₅×#117	C₂×C₄	1	2	yes	—
52	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
54	C₂×C₄²×C₅	—	2	1	no	—
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	C₂×C₄	1	2	yes	—
66	C₂×C₄×Dic₅	C₂×C₄	1	2	yes	—
67	C₂×C₄×Dic₅	C₂×C₄	1	2	yes	—
68	C₂×#681	—	2	1	no	—
69	C₂×#681	—	2	1	no	—
70	C₂×#681	—	2	1	no	—
71	C₂×#681	C₂×C₄	1	2	yes	—
72	C₂×#681	C₂×C₄	1	2	yes	—
73	C₂×#681	C₂×C₄	1	2	yes	—
74	C₂²×#168	—	2	1	no	—
75	C₂²×#168	—	2	1	no	—
76	C₂²×#168	—	2	1	no	—
77	C₂²×#168	—	2	1	no	—
78	C₂²×#168	—	2	1	no	—
79	C₂²×#168	C₂×C₄	1	2	yes	—
80	C₂²×#168	C₂×C₄	1	2	yes	—
81	C₂²×#168	C₂×C₄	1	2	yes	—
82	C₅×#97	—	2	4	no	—
83	C₄×C₅×C₈	—	2	4	no	—
84	#3947	—	2	8	no	—
85	#3947	—	2	4	no	—
86	C₈×Dic₅	—	2	4	no	—
87	C₂×#405	—	5	1	no	—
88	C₂×#405	D₅	1	1	yes	characteristic
89	C₂²×#97	—	5	1	no	—
90	C₂×#341	—	5	1	no	—
91	#1735	—	5	1	no	—
92	C₂×#339	—	5	1	no	—
93	C₂×#339	—	5	1	no	—
94	C₂⁴×C₅	#41	1	1	yes	characteristic
95	C₂²×C₄×C₅	—	2	2	no	—
96	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
107	C₂²×C₄×C₅	#41	1	1	yes	characteristic
108	C₂²×C₄×C₅	#41	1	1	yes	characteristic
109	C₂²×C₄×C₅	#41	1	1	yes	characteristic
110	C₂²×Dic₅	—	2	2	no	—
111	C₂²×Dic₅	—	2	2	no	—
112	C₂²×Dic₅	—	2	2	no	—
113	C₂²×Dic₅	—	2	2	no	—
114	C₂²×Dic₅	—	4	4	no	—
115	C₅×M₁₆	—	2	2	no	—
116	C₅×M₁₆	—	2	2	no	—
117	C₅×M₁₆	—	2	2	no	—
118	C₅×M₁₆	C₄²	1	4	yes	—
119	C₂×C₅×C₈	—	2	2	no	—
120	C₂×C₅×C₈	—	2	2	no	—
121	C₂×C₅×C₈	—	2	2	no	—
122	C₂×C₅×C₈	C₄²	1	4	yes	—
123	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
124	C₂×C₅×C₈	C₂²⋊C₄	1	4	yes	—
125	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
126	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
127	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
128	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
129	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
130	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
131	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
132	C₅×C₄⋊C₄	—	2	2	no	—
133	C₅×C₄⋊C₄	C₄²	1	4	yes	—
134	C₅×C₂²⋊C₄	—	2	2	no	—
135	C₅×C₂²⋊C₄	—	2	2	no	—
136	C₄²×C₅	—	2	2	no	—
137	C₄²×C₅	—	2	2	no	—
138	C₂²⋊Dic₅	—	2	2	no	—
139	C₂²⋊Dic₅	—	2	2	no	—
140	C₄⋊Dic₅	—	2	2	no	—
141	C₄⋊Dic₅	C₄²	1	4	yes	—
142	C₄×Dic₅	—	2	2	no	—
143	C₄×Dic₅	—	2	2	no	—
144	C₄×Dic₅	—	2	2	no	—
145	C₄×Dic₅	—	2	2	no	—
146	C₄×Dic₅	—	2	2	no	—
147	C₄×Dic₅	C₄²	1	4	yes	—
148	#681	—	2	2	no	—
149	#681	—	2	2	no	—
150	#681	—	2	2	no	—
151	#681	C₄²	1	4	yes	—
152	C₂×#168	—	2	2	no	—
153	C₂×#168	—	2	2	no	—
154	C₂×#168	—	2	2	no	—
155	C₂×#168	—	2	2	no	—
156	C₂×#168	—	2	2	no	—
157	C₂×#168	—	2	2	no	—
158	C₂×#168	—	2	2	no	—
159	C₂×#168	—	2	2	no	—
160	C₂×#168	—	2	2	no	—
161	C₂×#168	C₄²	1	4	yes	—
162	C₂²×M₁₆	—	5	1	no	—
163	C₂²×M₁₆	C₂×D₅	1	1	yes	characteristic
164	C₂³×C₈	—	5	1	no	—
165	C₂³×C₈	C₂×D₅	1	1	yes	characteristic
166	C₂×#117	—	5	1	no	—
167	C₂×#117	C₂×D₅	1	1	yes	characteristic
168	C₂²×C₄²	—	5	1	no	—
169	#405	—	2	2	no	—
170	#405	—	5	4	no	—
171	#405	—	10	2	no	—
172	#405	Dic₅	1	4	yes	complemented
173	C₂×#97	—	2	1	no	—
174	C₂×#97	—	5	4	no	—
175	C₂×#97	—	10	2	no	—
176	C₂×#97	—	10	2	no	—
177	C₂×#97	—	10	1	no	—
178	C₂×C₄×C₈	—	2	1	no	—
179	C₂×C₄×C₈	—	10	1	no	—
180	#341	—	5	4	no	—
181	#340	—	5	4	no	—
182	#339	—	5	4	no	—
183	#339	—	5	4	no	—
184	C₂³×C₅	—	2	4	no	—
185	C₂³×C₅	#117	1	1	yes	characteristic
186	C₂³×C₅	#117	1	1	yes	characteristic
187	C₂³×C₅	#117	1	1	yes	characteristic
188	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
189	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
190	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
191	C₂³×C₅	C₄×Q₈	1	1	yes	characteristic
192	C₂×C₄×C₅	—	2	4	no	—
193	C₂×C₄×C₅	—	4	4	no	—
194	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
195	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
196	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
197	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
198	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
199	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
200	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
201	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
202	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
203	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
207	C₂×C₄×C₅	#117	1	1	yes	characteristic
208	C₂×C₄×C₅	#117	1	1	yes	characteristic
209	C₂×C₄×C₅	#117	1	1	yes	characteristic
210	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
211	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
212	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
213	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
214	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
215	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
216	C₂×C₄×C₅	C₄×D₄	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×Q₈	1	1	yes	characteristic
220	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
221	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
222	C₂×Dic₅	—	2	4	no	—
223	C₂×Dic₅	—	2	4	no	—
224	C₂×Dic₅	—	4	4	no	—
225	C₂×Dic₅	—	4	4	no	—
226	C₂×Dic₅	—	4	4	no	—
227	C₂×Dic₅	—	4	4	no	—
228	C₅×C₈	—	2	4	no	—
229	C₅×C₈	#95	1	4	yes	—
230	C₅×C₈	#95	1	4	yes	—
231	#168	—	2	4	no	—
232	#168	—	2	4	no	—
233	C₂³×C₄	—	10	1	no	—
234	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
235	C₂×M₁₆	—	2	1	no	—
236	C₂×M₁₆	—	2	1	no	—
237	C₂×M₁₆	—	2	1	no	—
238	C₂×M₁₆	—	5	2	no	—
239	C₂×M₁₆	—	5	2	no	—
240	C₂×M₁₆	—	5	2	no	—
241	C₂×M₁₆	—	10	1	no	—
242	C₂×M₁₆	—	10	1	no	—
243	C₂×M₁₆	—	10	1	no	—
244	C₂×M₁₆	C₄×D₅	1	2	yes	—
245	C₂×M₁₆	C₄×D₅	1	2	yes	—
246	C₂×M₁₆	C₂×Dic₅	1	2	yes	—
247	C₂²×C₈	—	2	1	no	—
248	C₂²×C₈	—	5	2	no	—
249	C₂²×C₈	—	5	2	no	—
250	C₂²×C₈	—	5	2	no	—
251	C₂²×C₈	—	10	1	no	—
252	C₂²×C₈	—	10	1	no	—
253	C₂²×C₈	—	10	1	no	—
254	C₂²×C₈	—	10	1	no	—
255	C₂²×C₈	—	10	1	no	—
256	C₂²×C₈	Dic₁₀	1	2	yes	—
257	C₂²×C₈	C₄×D₅	1	2	yes	—
258	C₂²×C₈	C₄×D₅	1	2	yes	—
259	C₂²×C₈	D₂₀	1	2	yes	—
260	C₂²×C₈	C₂×Dic₅	1	2	yes	—
261	C₂²×C₈	C₂²⋊D₅	1	2	yes	—
262	C₂²×C₈	C₂²⋊D₅	1	1	yes	characteristic
263	C₂²×C₈	C₂²⋊D₅	1	1	yes	characteristic
264	#117	—	2	1	no	—
265	#117	—	2	1	no	—
266	#117	—	5	2	no	—
267	#117	—	5	2	no	—
268	#117	—	10	1	no	—
269	#117	—	10	1	no	—
270	#117	C₄×D₅	1	2	yes	—
271	#117	C₂×Dic₅	1	2	yes	—
272	C₂×C₄⋊C₄	—	5	2	no	—
273	C₂×C₄⋊C₄	C₄×D₅	1	2	yes	—
274	C₂×C₂²⋊C₄	—	2	1	no	—
275	C₂×C₂²⋊C₄	—	10	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	—	10	1	no	—
281	C₂×C₄²	—	10	1	no	—
282	C₂×C₄²	—	10	1	no	—
283	C₂×C₄²	—	10	1	no	—
284	#97	—	2	4	no	—
285	#97	—	10	8	no	—
286	#97	—	10	4	no	—
287	C₄×C₈	—	2	4	no	—
288	C₄×C₈	—	10	4	no	—
289	C₂²×C₅	—	2	2	no	—
290	C₂²×C₅	—	2	2	no	—
291	C₂²×C₅	—	2	2	no	—
292	C₂²×C₅	—	2	2	no	—
293	C₂²×C₅	—	2	2	no	—
294	C₂²×C₅	—	2	2	no	—
295	C₂²×C₅	#376	1	1	yes	characteristic
296	C₂²×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
297	C₂²×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
298	C₂²×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
299	C₂²×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
300	C₂²×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
301	C₂²×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
302	C₂²×C₅	#444	1	4	yes	—
303	C₄×C₅	—	4	4	no	—
304	C₄×C₅	C₄³	1	1	yes	characteristic
305	C₄×C₅	C₂×#95	1	1	yes	characteristic
306	C₄×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
307	C₄×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
308	C₄×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
309	C₄×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
310	C₄×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
311	C₄×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
312	Dic₅	—	4	4	no	—
313	Dic₅	—	4	4	no	—
314	C₂⁴	#709	1	1	yes	characteristic
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	10	2	no	—
317	C₂²×C₄	—	10	2	no	—
318	C₂²×C₄	—	10	2	no	—
319	C₂²×C₄	—	10	2	no	—
320	C₂²×C₄	—	20	4	no	—
321	C₂²×C₄	C₂×Dic₁₀	1	1	yes	characteristic
322	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
323	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
324	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
325	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
326	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
327	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
329	C₂²×C₄	#709	1	1	yes	characteristic
330	C₂²×C₄	#709	1	1	yes	characteristic
331	C₂²×C₄	#709	1	1	yes	characteristic
332	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
333	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
334	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
335	M₁₆	—	2	2	no	—
336	M₁₆	—	2	2	no	—
337	M₁₆	—	2	2	no	—
338	M₁₆	—	5	4	no	—
339	M₁₆	—	10	2	no	—
340	M₁₆	—	10	2	no	—
341	M₁₆	—	10	2	no	—
342	M₁₆	C₄×Dic₅	1	4	yes	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	5	4	no	—
347	C₂×C₈	—	10	2	no	—
348	C₂×C₈	—	10	2	no	—
349	C₂×C₈	—	10	2	no	—
350	C₂×C₈	—	10	2	no	—
351	C₂×C₈	—	10	2	no	—
352	C₂×C₈	—	10	2	no	—
353	C₂×C₈	—	10	2	no	—
354	C₂×C₈	—	10	2	no	—
355	C₂×C₈	—	10	2	no	—
356	C₂×C₈	C₄×Dic₅	1	4	yes	—
357	C₂×C₈	#683	1	4	yes	—
358	C₂×C₈	#683	1	2	yes	—
359	C₂×C₈	#683	1	2	yes	—
360	C₂×C₈	C₄⋊Dic₅	1	4	yes	—
361	C₂×C₈	#685	1	2	yes	—
362	C₂×C₈	#685	1	4	yes	—
363	C₂×C₈	#685	1	2	yes	—
364	C₂×C₈	C₂²⋊Dic₅	1	2	yes	—
365	C₂×C₈	C₂²⋊Dic₅	1	2	yes	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	5	4	no	—
368	C₄⋊C₄	—	10	2	no	—
369	C₄⋊C₄	C₄×Dic₅	1	4	yes	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	—	10	2	no	—
373	C₂²⋊C₄	—	10	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	5	4	no	—
377	C₄²	—	10	2	no	—
378	C₄²	—	10	2	no	—
379	C₄²	—	10	2	no	—
380	C₄²	—	10	2	no	—
381	C₄²	—	10	2	no	—
382	C₂×C₅	—	2	1	no	—
383	C₂×C₅	—	2	1	no	—
384	C₂×C₅	—	2	1	no	—
385	C₂×C₅	—	2	1	no	—
386	C₂×C₅	C₄×#95	1	1	yes	characteristic
387	C₂×C₅	#1765	1	2	yes	—
388	C₂×C₅	#1765	1	2	yes	—
389	C₂×C₅	#1773	1	2	yes	—
390	C₂³	—	2	4	no	—
391	C₂³	C₄×Dic₁₀	1	1	yes	characteristic
392	C₂³	#4018	1	1	yes	characteristic
393	C₂³	#4018	1	1	yes	characteristic
394	C₂³	C₄×D₂₀	1	1	yes	characteristic
395	C₂³	#4072	1	1	yes	characteristic
396	C₂³	C₄×C₂²⋊D₅	1	1	yes	characteristic
397	C₂³	C₄×C₂²⋊D₅	1	1	yes	characteristic
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	4	4	no	—
400	C₂×C₄	—	10	4	no	—
401	C₂×C₄	—	10	4	no	—
402	C₂×C₄	—	20	4	no	—
403	C₂×C₄	—	20	4	no	—
404	C₂×C₄	—	20	4	no	—
405	C₂×C₄	—	20	4	no	—
406	C₂×C₄	C₄×Dic₁₀	1	1	yes	characteristic
407	C₂×C₄	C₄×Dic₁₀	1	1	yes	characteristic
408	C₂×C₄	C₄×Dic₁₀	1	1	yes	characteristic
409	C₂×C₄	C₄²×D₅	1	1	yes	characteristic
410	C₂×C₄	C₄²×D₅	1	1	yes	characteristic
411	C₂×C₄	C₄²×D₅	1	1	yes	characteristic
412	C₂×C₄	C₄²×D₅	1	1	yes	characteristic
413	C₂×C₄	#4018	1	1	yes	characteristic
414	C₂×C₄	#4018	1	1	yes	characteristic
415	C₂×C₄	C₄×D₂₀	1	1	yes	characteristic
416	C₂×C₄	C₄×D₂₀	1	1	yes	characteristic
417	C₂×C₄	C₄×D₂₀	1	1	yes	characteristic
418	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
419	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
420	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
421	C₂×C₄	C₂×#683	1	1	yes	characteristic
422	C₂×C₄	C₂×#683	1	1	yes	characteristic
423	C₂×C₄	C₂×C₄⋊Dic₅	1	1	yes	characteristic
424	C₂×C₄	#4072	1	1	yes	characteristic
425	C₂×C₄	C₂×#685	1	1	yes	characteristic
426	C₂×C₄	C₂×#685	1	1	yes	characteristic
427	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
428	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
429	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
430	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
431	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
432	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
433	C₂×C₄	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
434	C₈	—	2	4	no	—
435	C₈	—	10	4	no	—
436	C₈	—	10	4	no	—
437	C₈	#3963	1	4	yes	—
438	C₈	#3963	1	4	yes	—
439	C₅	#10707	1	1	yes	characteristic, complemented, Sylow
440	C₂²	—	2	2	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	C₄×#683	1	1	yes	characteristic
447	C₂²	C₄×#683	1	1	yes	characteristic
448	C₂²	#65221	1	1	yes	characteristic
449	C₂²	C₄×C₄⋊Dic₅	1	1	yes	characteristic
450	C₂²	C₄×#685	1	1	yes	characteristic
451	C₂²	C₄×#685	1	1	yes	characteristic
452	C₂²	#65434	1	4	yes	—
453	C₂²	C₄×C₂²⋊Dic₅	1	1	yes	characteristic
454	C₄	—	4	4	no	—
455	C₄	—	20	4	no	—
456	C₄	—	20	4	no	—
457	C₄	C₄²×Dic₅	1	1	yes	characteristic
458	C₄	C₄×#683	1	1	yes	characteristic
459	C₄	C₄×#683	1	1	yes	characteristic
460	C₄	C₄×C₄⋊Dic₅	1	1	yes	characteristic
461	C₄	C₄×#685	1	1	yes	characteristic
462	C₄	C₄×#685	1	1	yes	characteristic
463	C₄	C₂×#3963	1	1	yes	characteristic
464	C₄	C₄×C₂²⋊Dic₅	1	1	yes	characteristic
465	C₂	—	2	1	no	—
466	C₂	—	2	1	no	—
467	C₂	—	2	1	no	—
468	C₂	—	2	1	no	—
469	C₂	#10600681	1	2	yes	—
470	C₂	#10600683	1	2	yes	—
471	C₂	C₄×#3963	1	1	yes	characteristic
472	C₂	#10602802	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₅
commutator	C₄×C₅	C₄³
Frattini	C₂³×C₄	C₂²×D₅
Fitting	C₂×C₅×#405	C₂
socle	C₂³×C₅	C₄×D₄
prime radical	C₂⁴×C₅	#41
cosocle	C₂³×C₄×C₅	C₂³
hypercenter	C₂×#405	D₅
hypocenter	C₅	#10707
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₈ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
16. C₅×#405	C₄	semidirect
20. #65390	C₄	semidirect
24. C₂×#3947	C₄	semidirect
26. #64778	C₄	semidirect
27. #64775	C₄	semidirect
28. #64752	C₄	semidirect
29. #64749	C₄	semidirect
172. #405	Dic₅	semidirect
439. C₅	#10707	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#405	2
C₂×#65390	2
C₂²×#3947	2
C₂×#64778	2
C₂×#64775	2
#10602373	2
C₂×#64752	2
#10707	5