Subgroups — C₂×D₅×#508 #13005783

Order 1280.

2118 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅×#135	C₂	1	2	yes	maximal, complemented
2	C₂×C₅×#508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#65483	C₂	1	2	yes	maximal, complemented
4	D₅×#508	C₂	1	16	yes	maximal, direct product factor
5	C₂×#65208	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₅×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#65205	C₂	1	2	yes	maximal, complemented
8	C₂×D₅×SD₃₂	C₂	1	2	yes	maximal, complemented
9	C₂×#65201	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×D₅×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#65193	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₅×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×D₅×#41	—	2	2	no	—
14	C₂×C₅×#135	C₂²	1	2	yes	complemented
15	C₂×#4096	—	2	2	no	—
16	D₅×#135	—	2	8	no	—
17	D₅×#135	C₂²	1	16	yes	complemented
18	C₂×#4065	C₂²	1	2	yes	complemented
19	C₂×D₅×Q₁₆	C₂²	1	2	yes	—
20	C₂×#4062	—	2	2	no	—
21	C₂×D₅×SD₁₆	—	2	2	no	—
22	C₂×#4058	C₂²	1	2	yes	complemented
23	C₂×D₅×D₈	C₂²	1	2	yes	—
24	C₂×#4050	C₂²	1	2	yes	complemented
25	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
26	C₅×#508	C₂²	1	8	yes	complemented
27	C₂×C₅×Q₃₂	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₅×SD₃₂	C₂²	1	2	yes	complemented
29	C₂×C₅×D₁₆	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
31	#65483	C₂²	1	16	yes	complemented
32	C₂×#3961	C₂²	1	2	yes	complemented
33	C₂×#3960	C₂²	1	2	yes	complemented
34	C₂×#3959	C₂²	1	2	yes	complemented
35	C₂×#3958	C₂²	1	2	yes	complemented
36	C₂²×#672	C₂²	1	1	yes	characteristic, complemented
37	#65208	C₂²	1	8	yes	complemented
38	D₅×Q₃₂	C₂²	1	8	yes	complemented
39	#65205	C₂²	1	16	yes	complemented
40	D₅×SD₃₂	C₂²	1	16	yes	complemented
41	#65201	C₂²	1	8	yes	complemented
42	D₅×D₁₆	C₂²	1	8	yes	complemented
43	C₂×Dic₄₀	C₂²	1	1	yes	characteristic, complemented
44	#65193	C₂²	1	8	yes	complemented
45	C₂×#3932	C₂²	1	2	yes	complemented
46	C₂×D₈₀	C₂²	1	1	yes	characteristic, complemented
47	C₂×D₅×C₁₆	C₂²	1	1	yes	characteristic
48	C₂×D₅×C₁₆	C₂²	1	1	yes	characteristic
49	C₂×D₅×C₁₆	C₂²	1	8	yes	complemented
50	C₂×D₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
51	C₂×D₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
52	C₂²×#508	—	5	1	no	maximal, Sylow
53	C₂×C₅×#41	—	2	2	no	—
54	D₅×#41	—	2	16	no	—
55	D₅×#41	—	4	8	no	—
56	C₂×#713	—	2	2	no	—
57	C₂×Q₈×D₅	—	2	2	no	—
58	C₂×#711	—	2	2	no	—
59	C₂×#711	—	4	2	no	—
60	C₂×D₄×D₅	—	2	2	no	—
61	C₂×D₄×D₅	—	4	2	no	—
62	C₂×#709	—	2	2	no	—
63	C₂×#709	—	4	2	no	—
64	C₂²×C₄×D₅	—	4	2	no	—
65	C₂²×C₄×D₅	D₄	1	1	yes	characteristic
66	C₅×#135	—	2	4	no	—
67	C₅×#135	C₂³	1	8	yes	complemented
68	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
69	C₂×C₅×SD₁₆	—	2	2	no	—
70	C₂×C₅×D₈	C₂³	1	2	yes	—
71	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
72	#4096	—	2	16	no	—
73	C₂×#689	—	2	2	no	—
74	C₂×#688	—	2	2	no	—
75	C₂×#687	—	2	2	no	—
76	C₂×#686	—	2	2	no	—
77	C₂²×#168	D₄	1	1	yes	characteristic
78	#4065	—	2	4	no	—
79	#4065	C₂³	1	8	yes	complemented
80	D₅×Q₁₆	—	2	4	no	—
81	D₅×Q₁₆	C₂³	1	8	yes	—
82	#4062	—	2	16	no	—
83	D₅×SD₁₆	—	2	16	no	—
84	#4058	—	2	4	no	—
85	#4058	C₂³	1	8	yes	complemented
86	D₅×D₈	—	2	4	no	—
87	D₅×D₈	C₂³	1	8	yes	—
88	C₂×Dic₂₀	C₂³	1	2	yes	—
89	#4050	—	2	4	no	—
90	#4050	C₂³	1	8	yes	complemented
91	C₂×D₄₀	C₂³	1	2	yes	—
92	C₂×#677	—	2	2	no	—
93	C₂×C₈×D₅	D₄	1	1	yes	characteristic
94	C₂×C₈×D₅	D₄	1	1	yes	characteristic
95	C₂×C₈×D₅	D₄	1	4	yes	—
96	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
97	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
98	C₂×C₈×D₅	C₂³	1	4	yes	—
99	C₅×Q₃₂	C₂³	1	4	yes	complemented
100	C₅×SD₃₂	C₂³	1	8	yes	complemented
101	C₅×D₁₆	C₂³	1	4	yes	complemented
102	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
103	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
104	C₂×C₅×C₁₆	C₂³	1	4	yes	complemented
105	#3961	C₂³	1	8	yes	complemented
106	#3960	C₂³	1	8	yes	complemented
107	#3959	C₂³	1	8	yes	complemented
108	#3958	C₂³	1	8	yes	complemented
109	C₂×#672	C₂³	1	1	yes	characteristic
110	C₂×#672	C₂³	1	1	yes	characteristic
111	C₂×#672	C₂³	1	4	yes	complemented
112	Dic₄₀	C₂³	1	4	yes	complemented
113	#3932	C₂³	1	8	yes	complemented
114	D₈₀	C₂³	1	4	yes	complemented
115	D₅×C₁₆	C₂³	1	4	yes	—
116	D₅×C₁₆	C₂³	1	4	yes	—
117	D₅×C₁₆	C₂³	1	4	yes	complemented
118	D₅×C₁₆	C₂³	1	4	yes	complemented
119	C₂²×#135	—	5	2	no	—
120	C₂×#508	—	5	16	no	—
121	C₂×#508	—	5	1	no	—
122	C₂×#508	—	5	2	no	—
123	C₂×#508	—	5	1	no	—
124	C₂×#508	—	5	1	no	—
125	C₂×#508	—	5	2	no	—
126	C₂×#508	D₅	1	1	yes	characteristic, direct product factor
127	C₂²×Q₃₂	—	5	1	no	—
128	C₂²×SD₃₂	—	5	2	no	—
129	C₂²×D₁₆	—	5	1	no	—
130	C₂³×C₁₆	—	5	1	no	—
131	C₂³×D₅	—	4	2	no	—
132	C₂³×D₅	D₈	1	1	yes	characteristic
133	C₅×#41	—	2	8	no	—
134	C₅×#41	—	4	4	no	—
135	C₂×C₅×Q₈	—	2	2	no	—
136	C₂×C₅×D₄	—	2	2	no	—
137	C₂×C₅×D₄	—	4	2	no	—
138	C₂²×C₄×C₅	—	4	2	no	—
139	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
140	C₂×C₂²⋊D₅	—	4	2	no	—
141	C₂×C₂²⋊D₅	—	4	2	no	—
142	C₂×C₂²⋊D₅	—	4	2	no	—
143	C₂²×Dic₅	—	4	2	no	—
144	C₂²×Dic₅	D₈	1	1	yes	characteristic
145	#713	—	2	8	no	—
146	#713	—	4	4	no	—
147	Q₈×D₅	—	2	8	no	—
148	Q₈×D₅	—	4	4	no	—
149	#711	—	2	8	no	—
150	#711	—	4	16	no	—
151	#711	—	4	4	no	—
152	D₄×D₅	—	2	8	no	—
153	D₄×D₅	—	4	16	no	—
154	D₄×D₅	—	4	4	no	—
155	#709	—	2	8	no	—
156	#709	—	4	4	no	—
157	#709	—	4	16	no	—
158	C₂×D₂₀	—	2	2	no	—
159	C₂×D₂₀	—	4	2	no	—
160	C₂×C₄×D₅	—	4	2	no	—
161	C₂×C₄×D₅	—	4	2	no	—
162	C₂×C₄×D₅	—	4	2	no	—
163	C₂×C₄×D₅	—	4	16	no	—
164	C₂×C₄×D₅	D₈	1	1	yes	characteristic
165	C₂×C₄×D₅	D₈	1	1	yes	characteristic
166	C₂×C₄×D₅	D₈	1	4	yes	—
167	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
168	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
169	C₂×C₄×D₅	C₂×D₄	1	4	yes	—
170	C₂×Dic₁₀	—	2	2	no	—
171	C₂×Dic₁₀	—	4	2	no	—
172	C₅×Q₁₆	—	2	2	no	—
173	C₅×Q₁₆	C₂⁴	1	4	yes	—
174	C₅×SD₁₆	—	2	8	no	—
175	C₅×D₈	—	2	2	no	—
176	C₅×D₈	C₂⁴	1	4	yes	—
177	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
178	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
179	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
180	C₂×C₅×C₈	C₂⁴	1	2	yes	—
181	#689	—	2	8	no	—
182	#688	—	2	8	no	—
183	#687	—	2	8	no	—
184	#686	—	2	8	no	—
185	C₂×#168	C₂×D₄	1	4	yes	—
186	C₂×#168	C₂×D₄	1	1	yes	characteristic
187	C₂×#168	C₂×D₄	1	1	yes	characteristic
188	Dic₂₀	—	2	2	no	—
189	Dic₂₀	C₂⁴	1	4	yes	—
190	D₄₀	—	2	2	no	—
191	D₄₀	C₂⁴	1	4	yes	—
192	#677	—	2	8	no	—
193	C₈×D₅	C₂×D₄	1	2	yes	—
194	C₈×D₅	C₂×D₄	1	2	yes	—
195	C₈×D₅	C₂×D₄	1	4	yes	—
196	C₈×D₅	C₂×D₄	1	4	yes	—
197	C₈×D₅	C₂⁴	1	2	yes	—
198	C₈×D₅	C₂⁴	1	2	yes	—
199	C₅×C₁₆	C₂⁴	1	2	yes	—
200	C₅×C₁₆	C₂⁴	1	2	yes	—
201	#672	C₂⁴	1	2	yes	—
202	#672	C₂⁴	1	2	yes	—
203	C₂²×#41	—	10	2	no	—
204	C₂×#135	—	5	16	no	—
205	C₂×#135	—	5	2	no	—
206	C₂×#135	—	5	2	no	—
207	C₂×#135	—	5	2	no	—
208	C₂×#135	—	10	2	no	—
209	C₂×#135	—	10	8	no	—
210	C₂×#135	—	10	2	no	—
211	C₂×#135	C₂×D₅	1	2	yes	complemented
212	C₂²×Q₁₆	—	5	2	no	—
213	C₂²×SD₁₆	—	10	2	no	—
214	C₂²×D₈	—	5	2	no	—
215	C₂³×C₈	—	5	1	no	—
216	#508	—	5	16	no	—
217	#508	—	5	8	no	—
218	#508	—	5	16	no	—
219	#508	—	5	8	no	—
220	#508	—	5	8	no	—
221	#508	C₂×D₅	1	8	yes	direct product factor
222	C₂×Q₃₂	—	5	2	no	—
223	C₂×Q₃₂	—	5	8	no	—
224	C₂×Q₃₂	—	5	1	no	—
225	C₂×Q₃₂	C₂×D₅	1	1	yes	characteristic, complemented
226	C₂×SD₃₂	—	5	2	no	—
227	C₂×SD₃₂	—	5	2	no	—
228	C₂×SD₃₂	—	5	16	no	—
229	C₂×SD₃₂	—	5	2	no	—
230	C₂×SD₃₂	C₂×D₅	1	2	yes	complemented
231	C₂×D₁₆	—	5	2	no	—
232	C₂×D₁₆	—	5	8	no	—
233	C₂×D₁₆	—	5	1	no	—
234	C₂×D₁₆	C₂×D₅	1	1	yes	characteristic, complemented
235	C₂²×C₁₆	—	5	1	no	—
236	C₂²×C₁₆	—	5	1	no	—
237	C₂²×C₁₆	—	5	1	no	—
238	C₂²×C₁₆	—	5	1	no	—
239	C₂²×C₁₆	—	5	1	no	—
240	C₂²×C₁₆	—	5	8	no	—
241	C₂²×C₁₆	C₂×D₅	1	1	yes	characteristic, complemented
242	C₂³×C₅	—	4	2	no	—
243	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
244	C₂²×D₅	—	2	4	no	—
245	C₂²×D₅	—	4	2	no	—
246	C₂²×D₅	—	4	8	no	—
247	C₂²×D₅	—	8	8	no	—
248	C₂²×D₅	C₂×D₈	1	1	yes	characteristic
249	C₂²×D₅	C₂×D₈	1	4	yes	—
250	C₂²×D₅	C₂×D₈	1	1	yes	characteristic
251	C₅×Q₈	—	2	4	no	—
252	C₅×Q₈	—	4	2	no	—
253	C₅×D₄	—	2	4	no	—
254	C₅×D₄	—	4	8	no	—
255	C₅×D₄	—	4	2	no	—
256	C₂×C₄×C₅	—	4	2	no	—
257	C₂×C₄×C₅	—	4	8	no	—
258	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
259	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
260	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
262	C₂²⋊D₅	—	4	8	no	—
263	C₂²⋊D₅	—	4	8	no	—
264	C₂²⋊D₅	—	4	8	no	—
265	C₂×Dic₅	—	4	2	no	—
266	C₂×Dic₅	—	4	8	no	—
267	C₂×Dic₅	C₂×D₈	1	1	yes	characteristic
268	C₂×Dic₅	C₂×D₈	1	1	yes	characteristic
269	C₂×Dic₅	C₂×D₈	1	4	yes	—
270	D₂₀	—	2	4	no	—
271	D₂₀	—	4	8	no	—
272	D₂₀	—	4	2	no	—
273	C₄×D₅	—	4	8	no	—
274	C₄×D₅	—	4	8	no	—
275	C₄×D₅	—	4	8	no	—
276	C₄×D₅	C₂×D₈	1	4	yes	—
277	C₄×D₅	C₂×D₈	1	4	yes	—
278	C₄×D₅	C₂×D₈	1	2	yes	—
279	C₄×D₅	C₂×D₈	1	2	yes	—
280	C₄×D₅	C₂²×D₄	1	2	yes	—
281	C₄×D₅	C₂²×D₄	1	2	yes	—
282	Dic₁₀	—	2	4	no	—
283	Dic₁₀	—	4	2	no	—
284	Dic₁₀	—	4	8	no	—
285	C₅×C₈	C₂²×D₄	1	2	yes	—
286	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
287	C₅×C₈	C₂⁵	1	1	yes	characteristic
288	#168	C₂²×D₄	1	2	yes	—
289	#168	C₂²×D₄	1	2	yes	—
290	C₂×#41	—	2	2	no	—
291	C₂×#41	—	10	2	no	—
292	C₂×#41	—	10	2	no	—
293	C₂×#41	—	10	16	no	—
294	C₂×#41	—	10	2	no	—
295	C₂×#41	—	20	2	no	—
296	C₂×#41	—	20	2	no	—
297	C₂×#41	—	20	8	no	—
298	C₂²×Q₈	—	10	2	no	—
299	C₂²×D₄	—	10	2	no	—
300	C₂²×D₄	—	20	2	no	—
301	C₂³×C₄	—	5	1	no	—
302	C₂³×C₄	—	20	2	no	—
303	#135	—	2	4	no	—
304	#135	—	5	8	no	—
305	#135	—	5	8	no	—
306	#135	—	5	8	no	—
307	#135	—	10	4	no	—
308	#135	—	10	16	no	—
309	#135	—	10	4	no	—
310	#135	—	10	16	no	—
311	#135	—	10	4	no	—
312	#135	C₂²×D₅	1	8	yes	complemented
313	C₂×Q₁₆	—	5	8	no	—
314	C₂×Q₁₆	—	5	2	no	—
315	C₂×Q₁₆	—	10	4	no	—
316	C₂×Q₁₆	—	10	2	no	—
317	C₂×Q₁₆	C₂²×D₅	1	2	yes	—
318	C₂×SD₁₆	—	2	2	no	—
319	C₂×SD₁₆	—	10	16	no	—
320	C₂×SD₁₆	—	10	2	no	—
321	C₂×SD₁₆	—	10	2	no	—
322	C₂×SD₁₆	—	10	2	no	—
323	C₂×D₈	—	5	8	no	—
324	C₂×D₈	—	5	2	no	—
325	C₂×D₈	—	10	4	no	—
326	C₂×D₈	—	10	2	no	—
327	C₂×D₈	C₂²×D₅	1	2	yes	—
328	C₂²×C₈	—	5	1	no	—
329	C₂²×C₈	—	5	1	no	—
330	C₂²×C₈	—	5	1	no	—
331	C₂²×C₈	—	5	4	no	—
332	C₂²×C₈	—	5	1	no	—
333	C₂²×C₈	—	5	1	no	—
334	C₂²×C₈	—	5	4	no	—
335	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
336	Q₃₂	—	5	8	no	—
337	Q₃₂	—	5	4	no	—
338	Q₃₂	C₂²×D₅	1	4	yes	complemented
339	SD₃₂	—	5	8	no	—
340	SD₃₂	—	5	8	no	—
341	SD₃₂	—	5	8	no	—
342	SD₃₂	C₂²×D₅	1	8	yes	complemented
343	D₁₆	—	5	8	no	—
344	D₁₆	—	5	4	no	—
345	D₁₆	C₂²×D₅	1	4	yes	complemented
346	C₂×C₁₆	—	5	1	no	—
347	C₂×C₁₆	—	5	1	no	—
348	C₂×C₁₆	—	5	4	no	—
349	C₂×C₁₆	—	5	4	no	—
350	C₂×C₁₆	—	5	4	no	—
351	C₂×C₁₆	—	5	4	no	—
352	C₂×C₁₆	—	5	4	no	—
353	C₂×C₁₆	C₂²×D₅	1	1	yes	characteristic
354	C₂×C₁₆	C₂²×D₅	1	1	yes	characteristic
355	C₂×C₁₆	C₂²×D₅	1	4	yes	complemented
356	C₂²×C₅	—	2	2	no	—
357	C₂²×C₅	—	4	4	no	—
358	C₂²×C₅	—	8	4	no	—
359	C₂²×C₅	C₂²×D₈	1	2	yes	—
360	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
361	C₂×D₅	—	2	2	no	—
362	C₂×D₅	—	2	8	no	—
363	C₂×D₅	—	4	4	no	—
364	C₂×D₅	—	8	4	no	—
365	C₂×D₅	—	8	16	no	—
366	C₂×D₅	#508	1	4	yes	direct product factor
367	C₂×D₅	C₂²×D₈	1	2	yes	—
368	C₂×D₅	C₂²×D₈	1	2	yes	—
369	C₄×C₅	—	4	4	no	—
370	C₄×C₅	C₂²×D₈	1	1	yes	characteristic
371	C₄×C₅	C₂²×D₈	1	2	yes	—
372	C₄×C₅	C₂³×D₄	1	1	yes	characteristic
373	Dic₅	—	4	4	no	—
374	Dic₅	C₂²×D₈	1	2	yes	—
375	Dic₅	C₂²×D₈	1	2	yes	—
376	C₂⁴	—	5	1	no	—
377	C₂⁴	—	20	2	no	—
378	#41	—	2	8	no	—
379	#41	—	4	4	no	—
380	#41	—	10	8	no	—
381	#41	—	10	8	no	—
382	#41	—	10	8	no	—
383	#41	—	20	16	no	—
384	#41	—	20	16	no	—
385	#41	—	20	4	no	—
386	#41	—	20	4	no	—
387	#41	—	20	4	no	—
388	C₂×Q₈	—	2	2	no	—
389	C₂×Q₈	—	10	8	no	—
390	C₂×Q₈	—	10	2	no	—
391	C₂×Q₈	—	20	2	no	—
392	C₂×Q₈	—	20	4	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	4	2	no	—
395	C₂×D₄	—	10	8	no	—
396	C₂×D₄	—	10	2	no	—
397	C₂×D₄	—	20	2	no	—
398	C₂×D₄	—	20	4	no	—
399	C₂×D₄	—	20	2	no	—
400	C₂×D₄	—	20	16	no	—
401	C₂×D₄	—	20	2	no	—
402	C₂×D₄	—	20	2	no	—
403	C₂²×C₄	—	4	2	no	—
404	C₂²×C₄	—	5	1	no	—
405	C₂²×C₄	—	5	1	no	—
406	C₂²×C₄	—	5	1	no	—
407	C₂²×C₄	—	5	4	no	—
408	C₂²×C₄	—	5	4	no	—
409	C₂²×C₄	—	5	1	no	—
410	C₂²×C₄	—	5	1	no	—
411	C₂²×C₄	—	20	2	no	—
412	C₂²×C₄	—	20	16	no	—
413	C₂²×C₄	—	20	2	no	—
414	C₂²×C₄	—	20	2	no	—
415	C₂²×C₄	—	20	2	no	—
416	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
417	Q₁₆	—	2	2	no	—
418	Q₁₆	—	5	4	no	—
419	Q₁₆	—	10	8	no	—
420	Q₁₆	—	10	2	no	—
421	Q₁₆	C₂³×D₅	1	4	yes	—
422	SD₁₆	—	2	8	no	—
423	SD₁₆	—	10	8	no	—
424	SD₁₆	—	10	8	no	—
425	SD₁₆	—	10	8	no	—
426	D₈	—	2	2	no	—
427	D₈	—	5	4	no	—
428	D₈	—	10	8	no	—
429	D₈	—	10	2	no	—
430	D₈	C₂³×D₅	1	4	yes	—
431	C₂×C₈	—	5	1	no	—
432	C₂×C₈	—	5	1	no	—
433	C₂×C₈	—	5	4	no	—
434	C₂×C₈	—	5	2	no	—
435	C₂×C₈	—	5	4	no	—
436	C₂×C₈	—	5	4	no	—
437	C₂×C₈	—	5	2	no	—
438	C₂×C₈	—	5	2	no	—
439	C₂×C₈	—	5	2	no	—
440	C₂×C₈	D₄×D₅	1	1	yes	characteristic
441	C₂×C₈	D₄×D₅	1	2	yes	—
442	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
443	C₂×C₈	C₂³×D₅	1	2	yes	—
444	C₁₆	—	5	2	no	—
445	C₁₆	—	5	2	no	—
446	C₁₆	C₂³×D₅	1	2	yes	—
447	C₁₆	C₂³×D₅	1	2	yes	—
448	C₂×C₅	—	2	2	no	—
449	C₂×C₅	—	8	4	no	—
450	C₂×C₅	C₂×#508	1	2	yes	complemented
451	C₂×C₅	C₂³×D₈	1	1	yes	characteristic
452	D₅	—	2	2	no	—
453	D₅	—	8	4	no	—
454	D₅	C₂×#508	1	4	yes	direct product factor
455	C₂³	—	4	2	no	—
456	C₂³	—	5	1	no	—
457	C₂³	—	5	4	no	—
458	C₂³	—	5	1	no	—
459	C₂³	—	10	4	no	—
460	C₂³	—	20	8	no	—
461	C₂³	—	20	2	no	—
462	C₂³	—	40	8	no	—
463	C₂³	D₅×D₈	1	1	yes	characteristic
464	Q₈	—	2	4	no	—
465	Q₈	—	4	2	no	—
466	Q₈	—	10	4	no	—
467	Q₈	—	20	8	no	—
468	Q₈	—	20	2	no	—
469	D₄	—	2	4	no	—
470	D₄	—	4	8	no	—
471	D₄	—	4	2	no	—
472	D₄	—	10	4	no	—
473	D₄	—	20	8	no	—
474	D₄	—	20	8	no	—
475	D₄	—	20	8	no	—
476	D₄	—	20	8	no	—
477	D₄	—	20	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	8	no	—
480	C₂×C₄	—	5	1	no	—
481	C₂×C₄	—	5	1	no	—
482	C₂×C₄	—	5	4	no	—
483	C₂×C₄	—	5	4	no	—
484	C₂×C₄	—	5	2	no	—
485	C₂×C₄	—	5	2	no	—
486	C₂×C₄	—	5	4	no	—
487	C₂×C₄	—	5	2	no	—
488	C₂×C₄	—	5	2	no	—
489	C₂×C₄	—	20	8	no	—
490	C₂×C₄	—	20	8	no	—
491	C₂×C₄	—	20	8	no	—
492	C₂×C₄	—	20	2	no	—
493	C₂×C₄	—	20	8	no	—
494	C₂×C₄	D₅×D₈	1	2	yes	—
495	C₂×C₄	D₅×D₈	1	1	yes	characteristic
496	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
497	C₂×C₄	C₂×D₄×D₅	1	2	yes	—
498	C₈	—	5	2	no	—
499	C₈	—	5	2	no	—
500	C₈	C₂×D₄×D₅	1	1	yes	characteristic
501	C₈	C₂×D₄×D₅	1	2	yes	—
502	C₈	C₂⁴×D₅	1	1	yes	characteristic
503	C₅	C₂²×#508	1	1	yes	characteristic, complemented, Sylow
504	C₂²	—	2	2	no	—
505	C₂²	—	4	4	no	—
506	C₂²	—	5	4	no	—
507	C₂²	—	5	2	no	—
508	C₂²	—	5	2	no	—
509	C₂²	—	8	4	no	—
510	C₂²	—	10	8	no	—
511	C₂²	—	10	2	no	—
512	C₂²	—	20	4	no	—
513	C₂²	—	40	16	no	—
514	C₂²	—	40	4	no	—
515	C₂²	C₂×D₅×D₈	1	2	yes	—
516	C₂²	C₂×D₅×D₈	1	1	yes	characteristic
517	C₄	—	4	4	no	—
518	C₄	—	5	2	no	—
519	C₄	—	5	2	no	—
520	C₄	—	20	4	no	—
521	C₄	C₂×D₅×D₈	1	2	yes	—
522	C₄	C₂×D₅×D₈	1	1	yes	characteristic
523	C₄	C₂²×D₄×D₅	1	1	yes	characteristic
524	C₂	—	2	2	no	—
525	C₂	—	5	4	no	—
526	C₂	—	8	4	no	—
527	C₂	—	10	2	no	—
528	C₂	—	40	4	no	—
529	C₂	D₅×#508	1	2	yes	direct product factor
530	C₂	C₂²×D₅×D₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₅×D₈
commutator, cosocle	C₅×C₈	C₂⁵
Frattini	C₈	C₂⁴×D₅
Fitting	C₂×C₅×#508	C₂
socle	C₂²×C₅	C₂²×D₈
hypercenter	C₂×#508	D₅
hypocenter	C₅	C₂²×#508
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#508

Complements

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

N	H ≅ G/N	type
1. C₂×D₅×#135	C₂	semidirect
2. C₂×C₅×#508	C₂	semidirect
3. C₂×#65483	C₂	semidirect
4. D₅×#508	C₂	direct (N × H)
5. C₂×#65208	C₂	semidirect
6. C₂×D₅×Q₃₂	C₂	semidirect
7. C₂×#65205	C₂	semidirect
8. C₂×D₅×SD₃₂	C₂	semidirect
9. C₂×#65201	C₂	semidirect
10. C₂×D₅×D₁₆	C₂	semidirect
11. C₂×#65193	C₂	semidirect
12. C₂²×D₅×C₁₆	C₂	semidirect
14. C₂×C₅×#135	C₂²	semidirect
17. D₅×#135	C₂²	semidirect
18. C₂×#4065	C₂²	semidirect
22. C₂×#4058	C₂²	semidirect
24. C₂×#4050	C₂²	semidirect
26. C₅×#508	C₂²	semidirect
27. C₂×C₅×Q₃₂	C₂²	semidirect
28. C₂×C₅×SD₃₂	C₂²	semidirect
29. C₂×C₅×D₁₆	C₂²	semidirect
30. C₂²×C₅×C₁₆	C₂²	semidirect
31. #65483	C₂²	semidirect
32. C₂×#3961	C₂²	semidirect
33. C₂×#3960	C₂²	semidirect
34. C₂×#3959	C₂²	semidirect
35. C₂×#3958	C₂²	semidirect
36. C₂²×#672	C₂²	semidirect
37. #65208	C₂²	semidirect
38. D₅×Q₃₂	C₂²	semidirect
39. #65205	C₂²	semidirect
40. D₅×SD₃₂	C₂²	semidirect
41. #65201	C₂²	semidirect
42. D₅×D₁₆	C₂²	semidirect
43. C₂×Dic₄₀	C₂²	semidirect
44. #65193	C₂²	semidirect
45. C₂×#3932	C₂²	semidirect
46. C₂×D₈₀	C₂²	semidirect
49. C₂×D₅×C₁₆	C₂²	semidirect
50. C₂×D₅×C₁₆	C₂²	semidirect
51. C₂×D₅×C₁₆	C₂²	semidirect
67. C₅×#135	C₂³	semidirect
79. #4065	C₂³	semidirect
85. #4058	C₂³	semidirect
90. #4050	C₂³	semidirect
99. C₅×Q₃₂	C₂³	semidirect
100. C₅×SD₃₂	C₂³	semidirect
101. C₅×D₁₆	C₂³	semidirect
104. C₂×C₅×C₁₆	C₂³	semidirect
105. #3961	C₂³	semidirect
106. #3960	C₂³	semidirect
107. #3959	C₂³	semidirect
108. #3958	C₂³	semidirect
111. C₂×#672	C₂³	semidirect
112. Dic₄₀	C₂³	semidirect
113. #3932	C₂³	semidirect
114. D₈₀	C₂³	semidirect
117. D₅×C₁₆	C₂³	semidirect
118. D₅×C₁₆	C₂³	semidirect
126. C₂×#508	D₅	direct (N × H)
211. C₂×#135	C₂×D₅	semidirect
221. #508	C₂×D₅	direct (N × H)
225. C₂×Q₃₂	C₂×D₅	semidirect
230. C₂×SD₃₂	C₂×D₅	semidirect
234. C₂×D₁₆	C₂×D₅	semidirect
241. C₂²×C₁₆	C₂×D₅	semidirect
312. #135	C₂²×D₅	semidirect
338. Q₃₂	C₂²×D₅	semidirect
342. SD₃₂	C₂²×D₅	semidirect
345. D₁₆	C₂²×D₅	semidirect
355. C₂×C₁₆	C₂²×D₅	semidirect
366. C₂×D₅	#508	direct (N × H)
450. C₂×C₅	C₂×#508	semidirect
454. D₅	C₂×#508	direct (N × H)
503. C₅	C₂²×#508	semidirect
529. C₂	D₅×#508	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×D₅×#135	2
C₂×C₅×#508	2
C₂×#65483	2
D₅×#508	2
C₂×#65208	2
C₂×D₅×Q₃₂	2
C₂×#65205	2
C₂×D₅×SD₃₂	2
C₂×#65201	2
C₂×D₅×D₁₆	2
C₂×#65193	2
C₂²×D₅×C₁₆	2
C₂²×#508	5

Subgroups — C2×D5×#508 #13005783

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅×#508 #13005783