Subgroups — #12005268

Order 1280.

974 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×Dic₅	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊#168	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#336	C₂	1	1	yes	maximal, characteristic
4	C₂×#64770	C₂	1	1	yes	maximal, characteristic
5	C₂×#64770	C₂	1	1	yes	maximal, characteristic
6	C₂×#64770	C₂	1	1	yes	maximal, characteristic
7	C₄×#3963	C₂	1	1	yes	maximal, characteristic
8	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
9	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
10	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₅	C₂²	1	1	yes	characteristic
12	C₂²×C₄×Dic₅	C₂²	1	1	yes	characteristic
13	C₂³×#168	C₂²	1	1	yes	characteristic
14	C₂³×#168	C₂²	1	1	yes	characteristic
15	C₂×#3963	C₄	1	2	yes	—
16	C₂×#3963	C₄	1	2	yes	—
17	C₂×C₈×Dic₅	—	2	2	no	—
18	C₂×C₈×Dic₅	—	2	2	no	—
19	C₂×C₈×Dic₅	—	2	2	no	—
20	C₂×C₄⋊#168	—	2	2	no	—
21	C₂×C₄⋊#168	—	2	2	no	—
22	C₂×C₄⋊#168	C₄	1	4	yes	complemented
23	C₅×#336	C₄	1	4	yes	complemented
24	#64770	—	2	2	no	—
25	#64770	—	2	2	no	—
26	#64770	—	2	2	no	—
27	#10876	—	5	1	no	maximal, Sylow
28	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
31	C₂³×Dic₅	C₂×C₄	1	2	yes	—
32	C₂³×Dic₅	C₂×C₄	1	2	yes	—
33	C₂²×C₅×C₈	—	2	1	no	—
34	C₂²×C₅×C₈	—	2	1	no	—
35	C₂²×C₅×C₈	—	2	1	no	—
36	C₂²×C₅×C₈	—	2	1	no	—
37	C₂²×C₅×C₈	—	2	1	no	—
38	C₂²×C₅×C₈	—	2	1	no	—
39	C₂²×C₅×C₈	—	2	1	no	—
40	C₂²×C₅×C₈	—	2	1	no	—
41	C₂²×C₅×C₈	—	2	1	no	—
42	C₂²×C₅×C₈	—	2	1	no	—
43	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
44	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
45	C₂²×C₅×C₈	D₄	1	2	yes	—
46	C₂²×C₅×C₈	Q₈	1	2	yes	—
47	C₂×C₄²×C₅	—	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	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
53	C₂×C₄×Dic₅	—	2	1	no	—
54	C₂×C₄×Dic₅	—	2	1	no	—
55	C₂×C₄×Dic₅	—	2	1	no	—
56	C₂×C₄×Dic₅	—	2	1	no	—
57	C₂×C₄×Dic₅	—	2	1	no	—
58	C₂×C₄×Dic₅	—	2	1	no	—
59	C₂×C₄×Dic₅	—	2	1	no	—
60	C₂×C₄×Dic₅	—	2	1	no	—
61	C₂×C₄×Dic₅	—	2	1	no	—
62	C₂×C₄×Dic₅	—	2	1	no	—
63	C₂×C₄×Dic₅	D₄	1	2	yes	—
64	C₂×C₄×Dic₅	Q₈	1	2	yes	—
65	C₂²×#168	—	2	1	no	—
66	C₂²×#168	—	2	1	no	—
67	C₂²×#168	—	2	1	no	—
68	C₂²×#168	—	2	1	no	—
69	C₂²×#168	—	2	1	no	—
70	C₂²×#168	—	2	1	no	—
71	C₂²×#168	—	2	1	no	—
72	C₂²×#168	—	2	1	no	—
73	C₂²×#168	—	2	1	no	—
74	C₂²×#168	—	2	1	no	—
75	C₂²×#168	C₂×C₄	1	2	yes	—
76	C₂²×#168	C₂×C₄	1	2	yes	—
77	C₂²×#168	D₄	1	2	yes	—
78	C₂²×#168	D₄	1	2	yes	—
79	#3963	—	2	4	no	—
80	#3963	C₈	1	8	yes	complemented
81	C₈×Dic₅	—	2	8	no	—
82	C₄⋊#168	—	2	8	no	—
83	C₂²×C₄⋊C₈	—	5	1	no	—
84	C₂²×C₄×C₈	—	5	1	no	—
85	C₂×#336	—	5	1	no	—
86	C₂×#336	—	5	1	no	—
87	C₂×#336	—	5	1	no	—
88	C₂×#336	D₅	1	1	yes	characteristic
89	C₄×#95	—	5	1	no	—
90	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₅	—	2	1	no	—
92	C₂²×C₄×C₅	—	2	1	no	—
93	C₂²×C₄×C₅	—	2	2	no	—
94	C₂²×C₄×C₅	—	2	1	no	—
95	C₂²×C₄×C₅	—	2	1	no	—
96	C₂²×C₄×C₅	—	2	2	no	—
97	C₂²×C₄×C₅	—	2	2	no	—
98	C₂²×C₄×C₅	C₄²	1	2	yes	—
99	C₂²×C₄×C₅	C₄²	1	2	yes	—
100	C₂²×C₄×C₅	C₂×C₈	1	4	yes	—
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×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
108	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
109	C₂²×C₄×C₅	#41	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×C₄×C₅	#41	1	1	yes	characteristic
115	C₂²×Dic₅	—	2	2	no	—
116	C₂²×Dic₅	—	2	2	no	—
117	C₂²×Dic₅	—	2	2	no	—
118	C₂²×Dic₅	—	2	2	no	—
119	C₂²×Dic₅	—	2	2	no	—
120	C₂²×Dic₅	—	2	2	no	—
121	C₂²×Dic₅	—	2	2	no	—
122	C₂²×Dic₅	—	2	2	no	—
123	C₂²×Dic₅	—	2	2	no	—
124	C₂²×Dic₅	—	2	2	no	—
125	C₂²×Dic₅	C₄⋊C₄	1	4	yes	—
126	C₂²×Dic₅	C₂×C₈	1	4	yes	—
127	C₂²×Dic₅	C₂×C₈	1	4	yes	—
128	C₂²×Dic₅	M₁₆	1	4	yes	—
129	C₂×C₅×C₈	—	2	2	no	—
130	C₂×C₅×C₈	—	2	2	no	—
131	C₂×C₅×C₈	—	2	2	no	—
132	C₂×C₅×C₈	—	2	2	no	—
133	C₂×C₅×C₈	—	2	2	no	—
134	C₂×C₅×C₈	—	2	2	no	—
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	—	2	2	no	—
137	C₂×C₅×C₈	—	2	2	no	—
138	C₂×C₅×C₈	—	4	1	no	—
139	C₂×C₅×C₈	—	4	1	no	—
140	C₂×C₅×C₈	—	4	1	no	—
141	C₂×C₅×C₈	—	4	1	no	—
142	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
143	C₄²×C₅	—	2	2	no	—
144	C₄²×C₅	—	2	2	no	—
145	C₄²×C₅	—	2	2	no	—
146	C₄²×C₅	—	2	2	no	—
147	C₄×Dic₅	—	2	2	no	—
148	C₄×Dic₅	—	2	2	no	—
149	C₄×Dic₅	—	2	2	no	—
150	C₄×Dic₅	—	2	2	no	—
151	C₄×Dic₅	—	4	1	no	—
152	C₄×Dic₅	—	4	1	no	—
153	C₄×Dic₅	—	4	1	no	—
154	C₄×Dic₅	—	4	1	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	—	2	2	no	—
162	C₂×#168	—	2	2	no	—
163	C₂×#168	—	2	2	no	—
164	C₂×#168	—	4	1	no	—
165	C₂×#168	—	4	1	no	—
166	C₂×#168	—	4	1	no	—
167	C₂×#168	—	4	1	no	—
168	C₂×#168	C₂²⋊C₄	1	4	yes	—
169	C₂³×C₈	—	5	1	no	—
170	C₂³×C₈	—	5	1	no	—
171	C₂³×C₈	C₂×D₅	1	1	yes	characteristic
172	C₂³×C₈	C₂×D₅	1	1	yes	characteristic
173	C₂²×C₄²	—	5	1	no	—
174	C₂²×C₄²	—	5	1	no	—
175	C₂²×C₄²	C₂×D₅	1	1	yes	characteristic
176	C₂×C₄⋊C₈	—	5	4	no	—
177	C₂×C₄⋊C₈	—	10	2	no	—
178	C₂×C₄⋊C₈	—	10	2	no	—
179	C₂×C₄×C₈	—	10	2	no	—
180	C₂×C₄×C₈	—	10	2	no	—
181	C₂×C₄×C₈	—	10	2	no	—
182	C₂×#95	—	5	2	no	—
183	C₂×#95	—	5	2	no	—
184	#336	—	10	2	no	—
185	#336	—	10	2	no	—
186	#336	—	10	2	no	—
187	#336	Dic₅	1	4	yes	complemented
188	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
189	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂³×C₅	#117	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×Q₈	1	1	yes	characteristic
195	C₂³×C₅	C₂²×C₈	1	2	yes	—
196	C₂³×C₅	C₂×M₁₆	1	2	yes	—
197	C₂³×C₅	#131	1	2	yes	—
198	C₂³×C₅	#131	1	2	yes	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	—	2	4	no	—
202	C₂×C₄×C₅	—	2	4	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	2	2	no	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	—	4	2	no	—
207	C₂×C₄×C₅	—	4	2	no	—
208	C₂×C₄×C₅	C₄×C₈	1	4	yes	complemented
209	C₂×C₄×C₅	C₂×C₂²⋊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	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×Q₈	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	#120	1	1	yes	characteristic
222	C₂×C₄×C₅	#121	1	1	yes	characteristic
223	C₂×C₄×C₅	#121	1	1	yes	characteristic
224	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
225	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
226	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
227	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
228	C₂×C₄×C₅	#123	1	1	yes	characteristic
229	C₂×C₄×C₅	#123	1	1	yes	characteristic
230	C₂×C₄×C₅	#123	1	1	yes	characteristic
231	C₂×C₄×C₅	#124	1	1	yes	characteristic
232	C₂×C₄×C₅	#125	1	1	yes	characteristic
233	C₂×C₄×C₅	#125	1	1	yes	characteristic
234	C₂×C₄×C₅	#126	1	1	yes	characteristic
235	C₂×C₄×C₅	#126	1	1	yes	characteristic
236	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
237	C₂×Dic₅	—	2	4	no	—
238	C₂×Dic₅	—	2	4	no	—
239	C₂×Dic₅	—	2	4	no	—
240	C₂×Dic₅	—	2	4	no	—
241	C₂×Dic₅	—	2	4	no	—
242	C₂×Dic₅	—	2	4	no	—
243	C₂×Dic₅	—	2	4	no	—
244	C₂×Dic₅	—	2	4	no	—
245	C₂×Dic₅	—	2	4	no	—
246	C₂×Dic₅	—	4	2	no	—
247	C₂×Dic₅	—	4	2	no	—
248	C₂×Dic₅	—	4	2	no	—
249	C₂×Dic₅	—	4	2	no	—
250	C₂×Dic₅	C₄⋊C₈	1	8	yes	complemented
251	C₅×C₈	—	2	4	no	—
252	C₅×C₈	—	4	2	no	—
253	#168	—	2	4	no	—
254	#168	—	4	2	no	—
255	C₂³×C₄	—	5	2	no	—
256	C₂³×C₄	—	5	2	no	—
257	C₂³×C₄	C₄×D₅	1	1	yes	characteristic
258	C₂³×C₄	C₄×D₅	1	1	yes	characteristic
259	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
260	C₂²×C₈	—	2	1	no	—
261	C₂²×C₈	—	2	1	no	—
262	C₂²×C₈	—	2	1	no	—
263	C₂²×C₈	—	2	1	no	—
264	C₂²×C₈	—	2	1	no	—
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	—	2	1	no	—
267	C₂²×C₈	—	2	1	no	—
268	C₂²×C₈	—	2	1	no	—
269	C₂²×C₈	—	2	1	no	—
270	C₂²×C₈	—	5	2	no	—
271	C₂²×C₈	—	5	2	no	—
272	C₂²×C₈	—	5	2	no	—
273	C₂²×C₈	—	5	2	no	—
274	C₂²×C₈	—	10	1	no	—
275	C₂²×C₈	—	10	1	no	—
276	C₂²×C₈	—	10	1	no	—
277	C₂²×C₈	—	10	1	no	—
278	C₂²×C₈	—	10	1	no	—
279	C₂²×C₈	—	10	1	no	—
280	C₂²×C₈	—	10	1	no	—
281	C₂²×C₈	—	10	1	no	—
282	C₂²×C₈	—	10	1	no	—
283	C₂²×C₈	—	10	1	no	—
284	C₂²×C₈	Dic₁₀	1	2	yes	—
285	C₂²×C₈	D₂₀	1	2	yes	—
286	C₂²×C₈	C₂×Dic₅	1	2	yes	—
287	C₂²×C₈	C₂×Dic₅	1	2	yes	—
288	C₂×C₄²	—	2	1	no	—
289	C₂×C₄²	—	2	1	no	—
290	C₂×C₄²	—	2	1	no	—
291	C₂×C₄²	—	2	1	no	—
292	C₂×C₄²	—	5	2	no	—
293	C₂×C₄²	—	5	2	no	—
294	C₂×C₄²	—	10	1	no	—
295	C₂×C₄²	—	10	1	no	—
296	C₂×C₄²	—	10	1	no	—
297	C₂×C₄²	—	10	1	no	—
298	C₂×C₄²	—	10	1	no	—
299	C₂×C₄²	—	10	1	no	—
300	C₂×C₄²	—	10	1	no	—
301	C₂×C₄²	—	10	1	no	—
302	C₂×C₄²	—	10	1	no	—
303	C₂×C₄²	—	10	1	no	—
304	C₂×C₄²	C₄×D₅	1	2	yes	—
305	C₂×C₄²	C₂×Dic₅	1	2	yes	—
306	C₄⋊C₈	—	10	8	no	—
307	C₄×C₈	—	10	8	no	—
308	#95	—	5	8	no	—
309	#95	—	10	4	no	—
310	C₂²×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
311	C₂²×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
312	C₂²×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
313	C₂²×C₅	#385	1	1	yes	characteristic
314	C₂²×C₅	#387	1	1	yes	characteristic
315	C₂²×C₅	#388	1	1	yes	characteristic
316	C₂²×C₅	#389	1	1	yes	characteristic
317	C₂²×C₅	C₂×C₄×C₈	1	1	yes	characteristic
318	C₂²×C₅	C₄×M₁₆	1	1	yes	characteristic
319	C₂²×C₅	#405	1	1	yes	characteristic
320	C₂²×C₅	#405	1	1	yes	characteristic
321	C₂²×C₅	C₂×C₄⋊C₈	1	2	yes	—
322	C₂²×C₅	#424	1	2	yes	—
323	C₂²×C₅	#431	1	2	yes	—
324	C₂²×C₅	#433	1	2	yes	—
325	C₂²×C₅	C₈×D₄	1	2	yes	—
326	C₂²×C₅	C₈×D₄	1	2	yes	—
327	C₂²×C₅	C₈×D₄	1	2	yes	—
328	C₂²×C₅	#435	1	2	yes	—
329	C₂²×C₅	#435	1	2	yes	—
330	C₂²×C₅	#436	1	2	yes	—
331	C₂²×C₅	C₈×Q₈	1	2	yes	—
332	C₂²×C₅	#446	1	2	yes	—
333	C₄×C₅	—	2	4	no	—
334	C₄×C₅	—	4	2	no	—
335	C₄×C₅	#385	1	1	yes	characteristic
336	C₄×C₅	#386	1	1	yes	characteristic
337	C₄×C₅	#387	1	1	yes	characteristic
338	C₄×C₅	#387	1	1	yes	characteristic
339	C₄×C₅	#387	1	1	yes	characteristic
340	C₄×C₅	#388	1	1	yes	characteristic
341	C₄×C₅	#389	1	1	yes	characteristic
342	C₄×C₅	#391	1	1	yes	characteristic
343	Dic₅	—	2	8	no	—
344	Dic₅	—	4	4	no	—
345	C₂⁴	C₂×C₄×D₅	1	1	yes	characteristic
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	5	4	no	—
354	C₂²×C₄	—	5	4	no	—
355	C₂²×C₄	—	5	4	no	—
356	C₂²×C₄	—	5	4	no	—
357	C₂²×C₄	—	10	2	no	—
358	C₂²×C₄	—	10	2	no	—
359	C₂²×C₄	—	10	2	no	—
360	C₂²×C₄	—	10	2	no	—
361	C₂²×C₄	—	10	2	no	—
362	C₂²×C₄	—	10	2	no	—
363	C₂²×C₄	—	10	2	no	—
364	C₂²×C₄	—	10	2	no	—
365	C₂²×C₄	—	10	2	no	—
366	C₂²×C₄	—	10	2	no	—
367	C₂²×C₄	C₈×D₅	1	4	yes	—
368	C₂²×C₄	C₄×Dic₅	1	2	yes	—
369	C₂²×C₄	C₄×Dic₅	1	2	yes	—
370	C₂²×C₄	C₂×Dic₁₀	1	1	yes	characteristic
371	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
373	C₂²×C₄	#709	1	1	yes	characteristic
374	C₂²×C₄	#709	1	1	yes	characteristic
375	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
376	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
377	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
378	C₂²×C₄	#711	1	1	yes	characteristic
379	C₂²×C₄	#711	1	1	yes	characteristic
380	C₂²×C₄	#711	1	1	yes	characteristic
381	C₂²×C₄	Q₈×D₅	1	1	yes	characteristic
382	C₂²×C₄	#713	1	1	yes	characteristic
383	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	4	1	no	—
394	C₂×C₈	—	4	1	no	—
395	C₂×C₈	—	4	1	no	—
396	C₂×C₈	—	4	1	no	—
397	C₂×C₈	—	5	4	no	—
398	C₂×C₈	—	10	2	no	—
399	C₂×C₈	—	10	2	no	—
400	C₂×C₈	—	10	2	no	—
401	C₂×C₈	—	10	2	no	—
402	C₂×C₈	—	10	2	no	—
403	C₂×C₈	—	10	2	no	—
404	C₂×C₈	—	10	2	no	—
405	C₂×C₈	—	10	2	no	—
406	C₂×C₈	—	10	2	no	—
407	C₂×C₈	—	20	1	no	—
408	C₂×C₈	—	20	1	no	—
409	C₂×C₈	—	20	1	no	—
410	C₂×C₈	—	20	1	no	—
411	C₂×C₈	C₄⋊Dic₅	1	4	yes	—
412	C₄²	—	2	2	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	2	2	no	—
415	C₄²	—	2	2	no	—
416	C₄²	—	10	2	no	—
417	C₄²	—	10	2	no	—
418	C₄²	—	10	2	no	—
419	C₄²	—	10	2	no	—
420	C₄²	—	20	1	no	—
421	C₄²	—	20	1	no	—
422	C₄²	—	20	1	no	—
423	C₄²	—	20	1	no	—
424	C₂×C₅	#1436	1	1	yes	characteristic
425	C₂×C₅	C₈×C₂²⋊C₄	1	1	yes	characteristic
426	C₂×C₅	#1753	1	1	yes	characteristic
427	C₂×C₅	C₄×C₄⋊C₈	1	1	yes	characteristic
428	C₂×C₅	#1768	1	1	yes	characteristic
429	C₂×C₅	C₈×C₄⋊C₄	1	1	yes	characteristic
430	C₂×C₅	#1771	1	1	yes	characteristic
431	C₂×C₅	#1850	1	2	yes	—
432	C₂×C₅	#1916	1	2	yes	—
433	C₂×C₅	#1923	1	2	yes	—
434	C₂×C₅	#1939	1	2	yes	—
435	C₂³	C₄×Dic₁₀	1	1	yes	characteristic
436	C₂³	C₄×D₂₀	1	1	yes	characteristic
437	C₂³	#4027	1	1	yes	characteristic
438	C₂³	#4027	1	1	yes	characteristic
439	C₂³	D₅×C₄⋊C₄	1	1	yes	characteristic
440	C₂³	#4038	1	1	yes	characteristic
441	C₂³	C₂×C₈×D₅	1	2	yes	—
442	C₂³	#4047	1	2	yes	—
443	C₂³	D₅×M₁₆	1	2	yes	—
444	C₂³	#4053	1	2	yes	—
445	C₂³	C₂×C₄×Dic₅	1	1	yes	characteristic
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	5	8	no	—
456	C₂×C₄	—	10	4	no	—
457	C₂×C₄	—	10	4	no	—
458	C₂×C₄	—	10	4	no	—
459	C₂×C₄	—	10	4	no	—
460	C₂×C₄	—	10	4	no	—
461	C₂×C₄	—	10	4	no	—
462	C₂×C₄	—	10	4	no	—
463	C₂×C₄	—	10	4	no	—
464	C₂×C₄	—	10	4	no	—
465	C₂×C₄	—	20	2	no	—
466	C₂×C₄	—	20	2	no	—
467	C₂×C₄	—	20	2	no	—
468	C₂×C₄	—	20	2	no	—
469	C₂×C₄	C₈×Dic₅	1	4	yes	complemented
470	C₂×C₄	C₄×Dic₁₀	1	1	yes	characteristic
471	C₂×C₄	C₄×D₂₀	1	1	yes	characteristic
472	C₂×C₄	#4023	1	1	yes	characteristic
473	C₂×C₄	#4024	1	1	yes	characteristic
474	C₂×C₄	#4024	1	1	yes	characteristic
475	C₂×C₄	#4025	1	1	yes	characteristic
476	C₂×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
477	C₂×C₄	#4028	1	1	yes	characteristic
478	C₂×C₄	#4029	1	1	yes	characteristic
479	C₂×C₄	#4030	1	1	yes	characteristic
480	C₂×C₄	#4031	1	1	yes	characteristic
481	C₂×C₄	#4032	1	1	yes	characteristic
482	C₂×C₄	#4033	1	1	yes	characteristic
483	C₂×C₄	#4034	1	1	yes	characteristic
484	C₂×C₄	#4035	1	1	yes	characteristic
485	C₂×C₄	#4036	1	1	yes	characteristic
486	C₂×C₄	#4039	1	1	yes	characteristic
487	C₂×C₄	#4040	1	1	yes	characteristic
488	C₂×C₄	#4041	1	1	yes	characteristic
489	C₂×C₄	#4042	1	1	yes	characteristic
490	C₂×C₄	#4043	1	1	yes	characteristic
491	C₂×C₄	#4044	1	1	yes	characteristic
492	C₂×C₄	C₂×C₄⋊Dic₅	1	1	yes	characteristic
493	C₂×C₄	#4072	1	1	yes	characteristic
494	C₂×C₄	D₄×Dic₅	1	1	yes	characteristic
495	C₂×C₄	D₄×Dic₅	1	1	yes	characteristic
496	C₂×C₄	D₄×Dic₅	1	1	yes	characteristic
497	C₂×C₄	Q₈×Dic₅	1	1	yes	characteristic
498	C₈	—	2	4	no	—
499	C₈	—	4	2	no	—
500	C₈	—	10	4	no	—
501	C₈	—	20	2	no	—
502	C₅	#10876	1	1	yes	characteristic, complemented, Sylow
503	C₂²	#64936	1	1	yes	characteristic
504	C₂²	#64944	1	1	yes	characteristic
505	C₂²	#64957	1	1	yes	characteristic
506	C₂²	#64959	1	1	yes	characteristic
507	C₂²	C₈×Dic₁₀	1	2	yes	—
508	C₂²	C₈×D₂₀	1	2	yes	—
509	C₂²	#64990	1	2	yes	—
510	C₂²	#64995	1	2	yes	—
511	C₂²	#65014	1	2	yes	—
512	C₂²	#65014	1	2	yes	—
513	C₂²	#65017	1	2	yes	—
514	C₂²	#65018	1	2	yes	—
515	C₂²	D₅×C₄⋊C₈	1	2	yes	—
516	C₂²	#65122	1	2	yes	—
517	C₂²	#65128	1	2	yes	—
518	C₂²	#65129	1	2	yes	—
519	C₂²	C₄×C₄⋊Dic₅	1	1	yes	characteristic
520	C₂²	C₂²⋊C₄×Dic₅	1	1	yes	characteristic
521	C₂²	C₄⋊C₄×Dic₅	1	1	yes	characteristic
522	C₂²	C₂×C₈×Dic₅	1	1	yes	characteristic
523	C₂²	#65390	1	1	yes	characteristic
524	C₂²	M₁₆×Dic₅	1	1	yes	characteristic
525	C₂²	#65411	1	1	yes	characteristic
526	C₄	—	2	4	no	—
527	C₄	—	4	2	no	—
528	C₄	—	10	8	no	—
529	C₄	—	20	4	no	—
530	C₄	#64935	1	1	yes	characteristic
531	C₄	#64942	1	1	yes	characteristic
532	C₄	#64943	1	1	yes	characteristic
533	C₄	#64954	1	1	yes	characteristic
534	C₄	#65239	1	1	yes	characteristic
535	C₄	#65240	1	1	yes	characteristic
536	C₄	#65270	1	1	yes	characteristic
537	C₄	#65274	1	1	yes	characteristic
538	C₂	#10599404	1	2	yes	—
539	C₂	#10599408	1	2	yes	—
540	C₂	#10599410	1	2	yes	—
541	C₂	#10599459	1	2	yes	—
542	C₂	#10600200	1	1	yes	characteristic
543	C₂	C₈×C₄⋊Dic₅	1	1	yes	characteristic
544	C₂	#10600603	1	1	yes	characteristic
545	C₂	#10600740	1	1	yes	characteristic
546	C₂	#10600742	1	1	yes	characteristic
547	C₂	Dic₅×C₄⋊C₈	1	1	yes	characteristic
548	C₂	#10601235	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³×C₄	C₂²×D₅
commutator	C₂²×C₅	C₂×C₄×C₈
Fitting	C₂×C₅×#336	C₂
socle, prime radical	C₂⁴×C₅	C₂²×C₄
cosocle	C₂³×C₄×C₅	C₂³
hypercenter	C₂×#336	D₅
hypocenter	C₅	#10876
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×#336

Complements

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

N	H ≅ G/N	type
22. C₂×C₄⋊#168	C₄	semidirect
23. C₅×#336	C₄	semidirect
80. #3963	C₈	semidirect
187. #336	Dic₅	semidirect
208. C₂×C₄×C₅	C₄×C₈	semidirect
250. C₂×Dic₅	C₄⋊C₈	semidirect
469. C₂×C₄	C₈×Dic₅	semidirect
502. C₅	#10876	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₈×Dic₅	2
C₂²×C₄⋊#168	2
C₂×C₅×#336	2
C₂×#64770	2
C₄×#3963	2
#10876	5