Subgroups — #12004512

Order 1280.

842 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×C₅×#405	C₂	1	1	yes	maximal, characteristic
2	C₂×#65390	C₂	1	1	yes	maximal, characteristic
3	C₂×#65390	C₂	1	1	yes	maximal, characteristic
4	C₂×#64779	C₂	1	1	yes	maximal, characteristic
5	#10602780	C₂	1	1	yes	maximal, characteristic
6	#10602386	C₂	1	1	yes	maximal, characteristic
7	C₂×#64753	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	C₂×#4072	C₂²	1	1	yes	characteristic
13	C₂²×#681	C₂²	1	1	yes	characteristic
14	C₂²×#681	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	1	no	—
20	#65390	—	2	1	no	—
21	#65390	—	2	1	no	—
22	#65390	—	2	1	no	—
23	#65390	—	2	2	no	—
24	#65390	C₄	1	4	yes	complemented
25	C₂×#3947	—	2	1	no	—
26	C₂×#3947	C₄	1	2	yes	complemented
27	C₂×C₈×Dic₅	—	2	1	no	—
28	C₂×C₈×Dic₅	C₄	1	2	yes	complemented
29	#64779	C₄	1	4	yes	complemented
30	#64774	C₄	1	4	yes	complemented
31	#64753	C₄	1	4	yes	complemented
32	#64747	C₄	1	4	yes	—
33	#10711	—	5	1	no	maximal, Sylow
34	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
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	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
45	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
46	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
47	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
48	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
49	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
50	C₂²×C₅×C₈	D₄	1	2	yes	—
51	C₂²×C₅×C₈	Q₈	1	2	yes	—
52	C₅×#117	—	2	1	no	—
53	C₅×#117	—	2	1	no	—
54	C₅×#117	C₂×C₄	1	2	yes	—
55	C₅×#117	C₂×C₄	1	2	yes	—
56	C₂×C₅×C₄⋊C₄	—	2	1	no	—
57	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₅	—	2	1	no	—
59	C₂×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
60	C₂×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
61	#4072	—	2	1	no	—
62	#4072	—	2	1	no	—
63	#4072	—	2	1	no	—
64	#4072	—	2	1	no	—
65	#4072	—	2	1	no	—
66	#4072	—	2	1	no	—
67	#4072	C₂×C₄	1	2	yes	—
68	#4072	C₂×C₄	1	2	yes	—
69	C₂×C₄⋊Dic₅	—	2	1	no	—
70	C₂×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
71	C₂×C₄×Dic₅	—	2	1	no	—
72	C₂×C₄×Dic₅	C₂×C₄	1	2	yes	—
73	C₂×#681	—	2	1	no	—
74	C₂×#681	—	2	1	no	—
75	C₂×#681	—	2	1	no	—
76	C₂×#681	—	2	1	no	—
77	C₂×#681	—	2	1	no	—
78	C₂×#681	—	2	1	no	—
79	C₂×#681	—	2	1	no	—
80	C₂×#681	C₂×C₄	1	2	yes	—
81	C₂×#681	C₂×C₄	1	2	yes	—
82	C₂×#681	C₂×C₄	1	2	yes	—
83	C₂×#681	C₂×C₄	1	2	yes	—
84	C₂×#681	C₂×C₄	1	2	yes	—
85	C₂²×#168	—	2	1	no	—
86	C₂²×#168	C₂×C₄	1	2	yes	—
87	C₅×#97	—	2	4	no	—
88	C₄×C₅×C₈	—	2	4	no	—
89	#3947	—	2	4	no	—
90	#3947	—	2	2	no	—
91	#3947	—	2	2	no	—
92	C₈×Dic₅	—	2	4	no	—
93	C₈×Dic₅	—	2	2	no	—
94	C₈×Dic₅	—	2	2	no	—
95	C₂×#405	—	5	1	no	—
96	C₂×#405	—	5	1	no	—
97	C₂×#405	D₅	1	1	yes	characteristic
98	C₂×#344	—	5	1	no	—
99	C₂×#344	—	5	1	no	—
100	#1742	—	5	1	no	—
101	#1740	—	5	1	no	—
102	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₅	—	2	2	no	—
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	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
114	C₂²×C₄×C₅	#41	1	1	yes	characteristic
115	C₂²×C₄×C₅	#41	1	1	yes	characteristic
116	C₂²×C₄×C₅	#41	1	1	yes	characteristic
117	C₂²×C₄×C₅	#41	1	1	yes	characteristic
118	C₂²×Dic₅	—	2	2	no	—
119	C₂²×Dic₅	C₄²	1	4	yes	—
120	C₅×M₁₆	—	2	2	no	—
121	C₅×M₁₆	—	2	2	no	—
122	C₅×M₁₆	—	2	2	no	—
123	C₅×M₁₆	C₄²	1	4	yes	—
124	C₂×C₅×C₈	—	2	2	no	—
125	C₂×C₅×C₈	—	2	2	no	—
126	C₂×C₅×C₈	—	2	2	no	—
127	C₂×C₅×C₈	C₄²	1	2	yes	—
128	C₂×C₅×C₈	C₄²	1	2	yes	—
129	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
130	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
131	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
132	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
133	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
134	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
135	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
136	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
137	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
138	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
139	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
140	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
141	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
142	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
143	C₅×C₄⋊C₄	—	2	2	no	—
144	C₅×C₄⋊C₄	—	2	2	no	—
145	C₅×C₂²⋊C₄	—	2	2	no	—
146	C₅×C₂²⋊C₄	C₄²	1	4	yes	—
147	C₄²×C₅	—	2	2	no	—
148	C₄²×C₅	—	2	2	no	—
149	C₂²⋊Dic₅	—	2	2	no	—
150	C₂²⋊Dic₅	—	2	2	no	—
151	C₂²⋊Dic₅	—	2	2	no	—
152	C₂²⋊Dic₅	C₄²	1	4	yes	—
153	C₄⋊Dic₅	—	2	2	no	—
154	C₄⋊Dic₅	—	2	2	no	—
155	C₄⋊Dic₅	—	2	2	no	—
156	C₄⋊Dic₅	—	2	2	no	—
157	C₄×Dic₅	—	2	2	no	—
158	C₄×Dic₅	—	2	2	no	—
159	C₄×Dic₅	—	2	2	no	—
160	C₄×Dic₅	—	2	2	no	—
161	#681	—	2	2	no	—
162	#681	—	2	2	no	—
163	#681	—	2	2	no	—
164	#681	—	2	2	no	—
165	#681	—	2	2	no	—
166	#681	—	2	2	no	—
167	#681	—	2	2	no	—
168	#681	C₄²	1	4	yes	—
169	C₂×#168	—	2	2	no	—
170	C₂×#168	—	2	2	no	—
171	C₂×#168	—	2	2	no	—
172	C₂×#168	—	2	2	no	—
173	C₂×#168	—	2	2	no	—
174	C₂×#168	C₄²	1	4	yes	—
175	C₂²×M₁₆	—	5	1	no	—
176	C₂²×M₁₆	—	5	1	no	—
177	C₂²×M₁₆	C₂×D₅	1	1	yes	characteristic
178	C₂³×C₈	C₂×D₅	1	1	yes	characteristic
179	C₂×#117	—	5	1	no	—
180	C₂×#117	—	5	1	no	—
181	C₂×#117	C₂×D₅	1	1	yes	characteristic
182	#405	—	2	2	no	—
183	#405	—	5	4	no	—
184	#405	—	10	1	no	—
185	#405	—	10	1	no	—
186	#405	—	10	1	no	—
187	#405	—	10	2	no	—
188	#405	—	10	1	no	—
189	#405	Dic₅	1	4	yes	complemented
190	C₂×#97	—	2	1	no	—
191	C₂×#97	—	5	2	no	—
192	C₂×#97	—	10	1	no	—
193	C₂×C₄×C₈	—	2	1	no	—
194	C₂×C₄×C₈	—	5	2	no	—
195	C₂×C₄×C₈	—	10	1	no	—
196	#344	—	5	4	no	—
197	#344	—	5	4	no	—
198	#343	—	5	4	no	—
199	#342	—	5	4	no	—
200	C₂³×C₅	—	4	2	no	—
201	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
202	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
203	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
204	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
205	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
206	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
207	C₂³×C₅	C₄×Q₈	1	1	yes	characteristic
208	C₂×C₄×C₅	—	2	4	no	—
209	C₂×C₄×C₅	—	4	4	no	—
210	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
212	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
213	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
214	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
218	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₅	#117	1	1	yes	characteristic
221	C₂×C₄×C₅	#117	1	1	yes	characteristic
222	C₂×C₄×C₅	#117	1	1	yes	characteristic
223	C₂×C₄×C₅	#117	1	1	yes	characteristic
224	C₂×C₄×C₅	#117	1	1	yes	characteristic
225	C₂×C₄×C₅	#117	1	1	yes	characteristic
226	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
227	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
233	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
234	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
235	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
236	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
237	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
238	C₂×Dic₅	—	2	4	no	—
239	C₂×Dic₅	—	2	4	no	—
240	C₂×Dic₅	—	4	4	no	—
241	C₂×Dic₅	—	4	4	no	—
242	C₅×C₈	—	2	4	no	—
243	C₅×C₈	#95	1	2	yes	—
244	C₅×C₈	#95	1	2	yes	—
245	C₅×C₈	#95	1	2	yes	—
246	C₅×C₈	#95	1	2	yes	—
247	#168	—	2	4	no	—
248	#168	—	2	4	no	—
249	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
250	C₂×M₁₆	—	2	1	no	—
251	C₂×M₁₆	—	2	1	no	—
252	C₂×M₁₆	—	2	1	no	—
253	C₂×M₁₆	—	5	2	no	—
254	C₂×M₁₆	—	5	2	no	—
255	C₂×M₁₆	—	5	2	no	—
256	C₂×M₁₆	—	5	2	no	—
257	C₂×M₁₆	—	5	2	no	—
258	C₂×M₁₆	—	10	1	no	—
259	C₂×M₁₆	—	10	1	no	—
260	C₂×M₁₆	—	10	1	no	—
261	C₂×M₁₆	—	10	1	no	—
262	C₂×M₁₆	—	10	1	no	—
263	C₂×M₁₆	—	10	1	no	—
264	C₂×M₁₆	—	10	1	no	—
265	C₂×M₁₆	C₄×D₅	1	2	yes	—
266	C₂×M₁₆	C₄×D₅	1	2	yes	—
267	C₂×M₁₆	C₂×Dic₅	1	2	yes	—
268	C₂²×C₈	—	2	1	no	—
269	C₂²×C₈	—	5	2	no	—
270	C₂²×C₈	—	10	1	no	—
271	C₂²×C₈	Dic₁₀	1	2	yes	—
272	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
273	C₂²×C₈	C₄×D₅	1	2	yes	—
274	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
275	C₂²×C₈	D₂₀	1	1	yes	characteristic
276	C₂²×C₈	D₂₀	1	1	yes	characteristic
277	C₂²×C₈	C₂×Dic₅	1	2	yes	—
278	C₂²×C₈	C₂²⋊D₅	1	1	yes	characteristic
279	C₂²×C₈	C₂²⋊D₅	1	2	yes	—
280	C₂²×C₈	C₂²⋊D₅	1	1	yes	characteristic
281	#117	—	2	1	no	—
282	#117	—	2	1	no	—
283	#117	—	5	2	no	—
284	#117	—	5	2	no	—
285	#117	—	10	1	no	—
286	#117	—	10	1	no	—
287	#117	—	10	1	no	—
288	#117	—	10	1	no	—
289	#117	—	10	1	no	—
290	#117	—	10	1	no	—
291	#117	C₄×D₅	1	2	yes	—
292	#117	C₂×Dic₅	1	2	yes	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	5	2	no	—
295	C₂×C₄⋊C₄	—	10	1	no	—
296	C₂×C₂²⋊C₄	—	5	2	no	—
297	C₂×C₂²⋊C₄	—	5	2	no	—
298	C₂×C₂²⋊C₄	C₄×D₅	1	2	yes	—
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	—	5	2	no	—
301	C₂×C₄²	—	10	1	no	—
302	#97	—	2	4	no	—
303	#97	—	10	2	no	—
304	#97	—	10	2	no	—
305	#97	—	10	4	no	—
306	C₄×C₈	—	2	4	no	—
307	C₄×C₈	—	10	2	no	—
308	C₄×C₈	—	10	4	no	—
309	C₄×C₈	—	10	2	no	—
310	C₂²×C₅	—	2	2	no	—
311	C₂²×C₅	—	2	2	no	—
312	C₂²×C₅	—	2	2	no	—
313	C₂²×C₅	—	4	1	no	—
314	C₂²×C₅	—	4	1	no	—
315	C₂²×C₅	—	4	1	no	—
316	C₂²×C₅	—	4	1	no	—
317	C₂²×C₅	C₄³	1	1	yes	characteristic
318	C₂²×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
319	C₂²×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
320	C₂²×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
321	C₂²×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
322	C₂²×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
323	C₂²×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
324	C₄×C₅	—	4	4	no	—
325	C₄×C₅	C₂×#95	1	1	yes	characteristic
326	C₄×C₅	#376	1	1	yes	characteristic
327	C₄×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
328	C₄×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
329	C₄×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
330	C₄×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
331	C₄×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
332	C₄×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
333	Dic₅	—	4	4	no	—
334	Dic₅	—	4	4	no	—
335	C₂⁴	C₂×C₄×D₅	1	1	yes	characteristic
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	5	4	no	—
338	C₂²×C₄	—	10	2	no	—
339	C₂²×C₄	C₂×Dic₁₀	1	1	yes	characteristic
340	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
341	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
342	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
343	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
344	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
346	C₂²×C₄	#709	1	1	yes	characteristic
347	C₂²×C₄	#709	1	1	yes	characteristic
348	C₂²×C₄	#709	1	1	yes	characteristic
349	C₂²×C₄	#709	1	1	yes	characteristic
350	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
351	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
353	M₁₆	—	2	2	no	—
354	M₁₆	—	2	2	no	—
355	M₁₆	—	2	2	no	—
356	M₁₆	—	5	4	no	—
357	M₁₆	—	10	2	no	—
358	M₁₆	—	10	2	no	—
359	M₁₆	—	10	2	no	—
360	M₁₆	—	10	2	no	—
361	M₁₆	—	10	2	no	—
362	M₁₆	—	10	2	no	—
363	M₁₆	—	10	2	no	—
364	M₁₆	C₄×Dic₅	1	4	yes	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	5	4	no	—
369	C₂×C₈	—	10	2	no	—
370	C₂×C₈	—	10	2	no	—
371	C₂×C₈	—	10	2	no	—
372	C₂×C₈	—	10	2	no	—
373	C₂×C₈	—	10	2	no	—
374	C₂×C₈	C₄×Dic₅	1	2	yes	—
375	C₂×C₈	C₄×Dic₅	1	2	yes	—
376	C₂×C₈	#683	1	2	yes	—
377	C₂×C₈	#683	1	2	yes	—
378	C₂×C₈	#683	1	2	yes	—
379	C₂×C₈	#683	1	2	yes	—
380	C₂×C₈	C₄⋊Dic₅	1	2	yes	—
381	C₂×C₈	C₄⋊Dic₅	1	2	yes	—
382	C₂×C₈	#685	1	1	yes	characteristic
383	C₂×C₈	#685	1	2	yes	—
384	C₂×C₈	#685	1	2	yes	—
385	C₂×C₈	#685	1	1	yes	characteristic
386	C₂×C₈	#685	1	1	yes	characteristic
387	C₂×C₈	#685	1	1	yes	characteristic
388	C₂×C₈	C₂²⋊Dic₅	1	2	yes	—
389	C₂×C₈	C₂²⋊Dic₅	1	2	yes	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	10	2	no	—
393	C₄⋊C₄	—	10	2	no	—
394	C₄⋊C₄	—	10	2	no	—
395	C₄⋊C₄	—	10	2	no	—
396	C₂²⋊C₄	—	2	2	no	—
397	C₂²⋊C₄	—	5	4	no	—
398	C₂²⋊C₄	—	10	2	no	—
399	C₂²⋊C₄	—	10	2	no	—
400	C₂²⋊C₄	—	10	2	no	—
401	C₂²⋊C₄	C₄×Dic₅	1	4	yes	—
402	C₄²	—	2	2	no	—
403	C₄²	—	2	2	no	—
404	C₄²	—	10	2	no	—
405	C₄²	—	10	2	no	—
406	C₄²	—	10	2	no	—
407	C₄²	—	10	2	no	—
408	C₂×C₅	—	2	1	no	—
409	C₂×C₅	—	2	1	no	—
410	C₂×C₅	—	2	1	no	—
411	C₂×C₅	—	2	1	no	—
412	C₂×C₅	—	2	1	no	—
413	C₂×C₅	—	2	1	no	—
414	C₂×C₅	C₄×#95	1	1	yes	characteristic
415	C₂×C₅	#1757	1	2	yes	—
416	C₂³	—	4	2	no	—
417	C₂³	C₄×Dic₁₀	1	1	yes	characteristic
418	C₂³	C₄²×D₅	1	1	yes	characteristic
419	C₂³	C₄²×D₅	1	1	yes	characteristic
420	C₂³	C₄×D₂₀	1	1	yes	characteristic
421	C₂³	C₂×C₄×Dic₅	1	1	yes	characteristic
422	C₂³	C₄×C₂²⋊D₅	1	1	yes	characteristic
423	C₂³	C₄×C₂²⋊D₅	1	1	yes	characteristic
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	4	4	no	—
426	C₂×C₄	—	10	4	no	—
427	C₂×C₄	—	10	4	no	—
428	C₂×C₄	—	20	4	no	—
429	C₂×C₄	—	20	4	no	—
430	C₂×C₄	C₄×Dic₁₀	1	1	yes	characteristic
431	C₂×C₄	C₄×Dic₁₀	1	1	yes	characteristic
432	C₂×C₄	C₄×Dic₁₀	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	#4018	1	1	yes	characteristic
436	C₂×C₄	#4018	1	1	yes	characteristic
437	C₂×C₄	#4018	1	1	yes	characteristic
438	C₂×C₄	#4018	1	1	yes	characteristic
439	C₂×C₄	C₄×D₂₀	1	1	yes	characteristic
440	C₂×C₄	C₄×D₂₀	1	1	yes	characteristic
441	C₂×C₄	C₄×D₂₀	1	1	yes	characteristic
442	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
443	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
444	C₂×C₄	C₂×#683	1	1	yes	characteristic
445	C₂×C₄	C₂×#683	1	1	yes	characteristic
446	C₂×C₄	C₂×C₄⋊Dic₅	1	1	yes	characteristic
447	C₂×C₄	#4072	1	1	yes	characteristic
448	C₂×C₄	#4072	1	1	yes	characteristic
449	C₂×C₄	C₂×#685	1	1	yes	characteristic
450	C₂×C₄	C₂×#685	1	1	yes	characteristic
451	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
452	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
453	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
454	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
455	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
456	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
457	C₂×C₄	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
458	C₈	—	2	4	no	—
459	C₈	—	10	4	no	—
460	C₈	—	10	4	no	—
461	C₈	#3963	1	2	yes	—
462	C₈	#3963	1	2	yes	—
463	C₈	#3963	1	2	yes	—
464	C₈	#3963	1	2	yes	—
465	C₅	#10711	1	1	yes	characteristic, complemented, Sylow
466	C₂²	—	2	2	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	4	1	no	—
470	C₂²	—	4	1	no	—
471	C₂²	—	4	1	no	—
472	C₂²	—	4	1	no	—
473	C₂²	C₄²×Dic₅	1	1	yes	characteristic
474	C₂²	C₄×#683	1	1	yes	characteristic
475	C₂²	C₄×#683	1	1	yes	characteristic
476	C₂²	C₄×C₄⋊Dic₅	1	1	yes	characteristic
477	C₂²	C₄×#685	1	1	yes	characteristic
478	C₂²	C₄×#685	1	1	yes	characteristic
479	C₂²	C₄×C₂²⋊Dic₅	1	1	yes	characteristic
480	C₄	—	4	4	no	—
481	C₄	—	20	4	no	—
482	C₄	—	20	4	no	—
483	C₄	C₄×#683	1	1	yes	characteristic
484	C₄	C₄×#683	1	1	yes	characteristic
485	C₄	#65221	1	1	yes	characteristic
486	C₄	C₄×C₄⋊Dic₅	1	1	yes	characteristic
487	C₄	C₄×#685	1	1	yes	characteristic
488	C₄	C₄×#685	1	1	yes	characteristic
489	C₄	C₂×#3963	1	1	yes	characteristic
490	C₄	C₄×C₂²⋊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	—	2	1	no	—
496	C₂	—	2	1	no	—
497	C₂	#10600691	1	2	yes	—
498	C₂	C₄×#3963	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	#685
commutator	C₂²×C₅	C₄³
Frattini	C₂³×C₄	C₂²×D₅
Fitting	C₂×C₅×#405	C₂
socle	C₂²×C₅	C₄×C₂²⋊C₄
prime radical	C₂⁴×C₅	C₂²×C₄
cosocle	C₂³×C₄×C₅	C₂³
hypercenter	C₂×#405	D₅
hypocenter	C₅	#10711
LCS	G ▷ C₂²×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₈ ◁ 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
24. #65390	C₄	semidirect
26. C₂×#3947	C₄	semidirect
28. C₂×C₈×Dic₅	C₄	semidirect
29. #64779	C₄	semidirect
30. #64774	C₄	semidirect
31. #64753	C₄	semidirect
189. #405	Dic₅	semidirect
465. C₅	#10711	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
C₂×#64779	2
#10602780	2
#10602386	2
C₂×#64753	2
#10711	5