Subgroups — #13043539

Order 1280.

734 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅⋊M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#3990	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×D₄×D₅	C₂	1	1	yes	maximal, characteristic
4	#10604706	C₂	1	1	yes	maximal, characteristic, complemented
5	#10604706	C₂	1	1	yes	maximal, characteristic, complemented
6	#10604413	C₂	1	2	yes	maximal, complemented
7	#10604022	C₂	1	2	yes	maximal, complemented
8	#10603906	C₂	1	2	yes	maximal, complemented
9	#10603903	C₂	1	2	yes	maximal, complemented
10	#10603827	C₂	1	1	yes	maximal, characteristic, complemented
11	#10603825	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
13	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
14	C₄×D₄×D₅	C₄	1	1	yes	characteristic
15	C₂×#3998	C₂²	1	2	yes	complemented
16	C₂²×#674	C₂²	1	2	yes	complemented
17	D₅⋊M₃₂	—	2	4	no	—
18	C₂×#3990	—	2	4	no	—
19	C₂×#3990	C₂²	1	1	yes	characteristic
20	C₂×#3990	C₂²	1	1	yes	characteristic
21	C₂×#3990	C₂²	1	1	yes	characteristic
22	C₂×#3990	C₂²	1	1	yes	characteristic
23	C₂×#3990	C₂²	1	2	yes	complemented
24	C₂×D₅⋊C₁₆	C₂²	1	2	yes	complemented
25	C₅×C₈×D₄	C₄	1	1	yes	characteristic
26	C₈×C₂²⋊D₅	C₄	1	1	yes	characteristic
27	C₈×C₂²⋊D₅	C₄	1	1	yes	characteristic
28	D₄×#168	C₂²	1	1	yes	characteristic
29	#65123	C₂²	1	1	yes	characteristic
30	D₅×C₄⋊C₈	C₄	1	1	yes	characteristic
31	#65014	C₂²	1	1	yes	characteristic
32	#65014	C₂²	1	1	yes	characteristic
33	D₅×C₂²⋊C₈	C₄	1	1	yes	characteristic
34	D₅×C₂²⋊C₈	C₄	1	1	yes	characteristic
35	C₈×D₂₀	C₄	1	1	yes	characteristic
36	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
37	C₂²⋊#674	C₂²	1	2	yes	complemented
38	C₂²⋊#674	C₂²	1	2	yes	complemented
39	#64888	C₂²	1	2	yes	complemented
40	#64887	C₂²	1	2	yes	complemented
41	#64887	C₂²	1	2	yes	complemented
42	#64885	C₂²	1	2	yes	complemented
43	#64859	C₂²	1	2	yes	complemented
44	C₄⋊#674	C₂²	1	2	yes	complemented
45	D₄×M₃₂	—	5	1	no	maximal, Sylow
46	C₂×D₄×D₅	C₈	1	1	yes	characteristic
47	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
51	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
52	D₄×Dic₅	C₈	1	1	yes	characteristic
53	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
54	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
55	C₂²×#168	C₂³	1	1	yes	characteristic
56	C₂²×#168	C₂³	1	1	yes	characteristic
57	C₂×C₈×D₅	—	2	2	no	—
58	C₂×C₈×D₅	—	2	2	no	—
59	C₂×C₈×D₅	—	2	2	no	—
60	C₂×C₈×D₅	—	2	2	no	—
61	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
64	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
67	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
68	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
69	#4039	C₈	1	1	yes	characteristic
70	D₅×C₄⋊C₄	C₈	1	1	yes	characteristic
71	#4027	C₈	1	1	yes	characteristic
72	#4027	C₈	1	1	yes	characteristic
73	D₅×C₂²⋊C₄	C₈	1	1	yes	characteristic
74	D₅×C₂²⋊C₄	C₈	1	1	yes	characteristic
75	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
76	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
77	#3998	—	2	4	no	—
78	C₂×#674	—	2	4	no	—
79	C₂×#674	C₂³	1	2	yes	—
80	C₂×#674	C₂³	1	2	yes	—
81	C₂×#674	C₂³	1	2	yes	—
82	C₂×#674	C₂³	1	2	yes	—
83	#3990	—	2	2	no	—
84	#3990	—	2	2	no	—
85	#3990	—	2	2	no	—
86	#3990	—	2	4	no	—
87	#3990	D₄	1	4	yes	complemented
88	D₅⋊C₁₆	—	2	4	no	—
89	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
90	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
91	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
92	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
93	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
94	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
95	#3952	C₂×C₄	1	1	yes	characteristic
96	#3952	C₂×C₄	1	1	yes	characteristic
97	#3952	C₂×C₄	1	1	yes	characteristic
98	#3952	C₂×C₄	1	1	yes	characteristic
99	#3946	C₂×C₄	1	1	yes	characteristic
100	#3946	C₂×C₄	1	1	yes	characteristic
101	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
102	C₈×Dic₅	C₂³	1	1	yes	characteristic
103	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
104	C₄×#168	C₂³	1	1	yes	characteristic
105	C₂²×M₃₂	—	5	1	no	—
106	C₂²×M₃₂	—	5	1	no	—
107	C₂×C₈×D₄	—	5	1	no	—
108	#2169	—	5	2	no	—
109	#2168	—	5	2	no	—
110	#2168	—	5	2	no	—
111	D₄×C₁₆	—	5	2	no	—
112	#2150	—	5	1	no	—
113	#2112	—	5	1	no	—
114	#2112	—	5	1	no	—
115	C₄×M₃₂	—	5	1	no	—
116	C₂³×D₅	C₂×C₈	1	1	yes	characteristic
117	C₂³×D₅	C₂×C₈	1	1	yes	characteristic
118	C₂×C₅×D₄	C₂×C₈	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₂²⋊D₅	C₂×C₈	1	1	yes	characteristic
122	C₂×C₂²⋊D₅	C₂×C₈	1	1	yes	characteristic
123	C₂²×Dic₅	C₂×C₈	1	1	yes	characteristic
124	C₂²×Dic₅	C₂×C₈	1	1	yes	characteristic
125	D₄×D₅	—	2	4	no	—
126	C₂×D₂₀	C₂×C₈	1	1	yes	characteristic
127	C₂×C₄×D₅	—	2	2	no	—
128	C₂×C₄×D₅	—	2	2	no	—
129	C₂×C₄×D₅	—	2	2	no	—
130	C₂×C₄×D₅	—	2	2	no	—
131	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
132	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
133	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
134	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
135	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
136	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
137	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₅×C₈	—	2	2	no	—
141	C₂×C₅×C₈	—	2	2	no	—
142	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
146	C₅×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
147	C₅×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
148	C₅×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
149	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
150	C₂²⋊Dic₅	C₂×C₈	1	1	yes	characteristic
151	C₂²⋊Dic₅	C₂×C₈	1	1	yes	characteristic
152	#685	C₂×C₈	1	1	yes	characteristic
153	#685	C₂×C₈	1	1	yes	characteristic
154	#685	C₂×C₈	1	1	yes	characteristic
155	#685	C₂×C₈	1	1	yes	characteristic
156	C₄⋊Dic₅	C₂×C₈	1	1	yes	characteristic
157	#683	C₂×C₈	1	1	yes	characteristic
158	#683	C₂×C₈	1	1	yes	characteristic
159	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
160	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
161	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
162	C₂×#168	—	2	1	no	—
163	C₂×#168	—	2	1	no	—
164	C₂×#168	—	2	1	no	—
165	C₂×#168	—	2	1	no	—
166	C₂×#168	C₂²×C₄	1	1	yes	characteristic
167	C₂×#168	C₂²×C₄	1	1	yes	characteristic
168	C₂×#168	C₂²×C₄	1	1	yes	characteristic
169	C₂×#168	C₂⁴	1	1	yes	characteristic
170	C₈×D₅	—	2	2	no	—
171	C₈×D₅	—	2	2	no	—
172	C₈×D₅	—	2	2	no	—
173	C₈×D₅	—	2	2	no	—
174	C₈×D₅	—	2	2	no	—
175	C₈×D₅	—	2	1	no	—
176	C₈×D₅	—	2	1	no	—
177	C₈×D₅	—	2	1	no	—
178	C₈×D₅	—	2	1	no	—
179	C₈×D₅	C₂×D₄	1	2	yes	—
180	C₈×D₅	#41	1	2	yes	—
181	#674	—	2	2	no	—
182	#674	—	2	2	no	—
183	#674	—	2	2	no	—
184	#674	C₂×D₄	1	4	yes	complemented
185	C₂³×C₈	—	5	1	no	—
186	C₂³×C₈	—	5	1	no	—
187	C₂×C₄×D₄	—	5	1	no	—
188	C₂×M₃₂	—	5	1	no	—
189	C₂×M₃₂	—	5	1	no	—
190	C₂×M₃₂	—	5	1	no	—
191	C₂×M₃₂	—	5	1	no	—
192	C₂×M₃₂	—	5	2	no	—
193	C₂×M₃₂	—	5	2	no	—
194	C₂×M₃₂	—	10	4	no	—
195	C₂×M₃₂	—	10	4	no	—
196	C₂²×C₁₆	—	5	2	no	—
197	C₂²×C₁₆	—	5	2	no	—
198	C₈×D₄	—	5	1	no	—
199	C₈×D₄	—	5	1	no	—
200	C₈×D₄	—	5	1	no	—
201	C₈×D₄	—	5	1	no	—
202	C₈×D₄	—	5	1	no	—
203	C₈×D₄	—	5	1	no	—
204	C₈×D₄	—	5	1	no	—
205	C₈×D₄	AGL(1,𝔽₅)	1	1	yes	characteristic
206	C₂×C₄⋊C₈	—	5	1	no	—
207	C₂×C₂²⋊C₈	—	5	1	no	—
208	C₂×C₂²⋊C₈	—	5	1	no	—
209	C₂×C₄×C₈	—	5	1	no	—
210	C₄⋊C₁₆	—	5	2	no	—
211	C₄⋊C₁₆	—	5	2	no	—
212	C₂²⋊C₁₆	—	5	2	no	—
213	C₂²⋊C₁₆	—	5	2	no	—
214	C₂²⋊C₁₆	—	5	2	no	—
215	C₂²⋊C₁₆	—	5	2	no	—
216	#346	—	5	2	no	—
217	C₄×C₁₆	—	5	2	no	—
218	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
219	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
220	C₂²×D₅	—	2	2	no	—
221	C₂²×D₅	—	2	2	no	—
222	C₂²×D₅	—	2	2	no	—
223	C₂²×D₅	—	2	2	no	—
224	C₂²×D₅	—	4	1	no	—
225	C₂²×D₅	—	4	1	no	—
226	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
227	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
228	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
229	C₅×D₄	—	2	2	no	—
230	C₂×C₄×C₅	—	2	1	no	—
231	C₂×C₄×C₅	—	2	1	no	—
232	C₂×C₄×C₅	—	2	1	no	—
233	C₂×C₄×C₅	—	2	1	no	—
234	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
235	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
236	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
237	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
238	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
239	C₂²⋊D₅	—	2	2	no	—
240	C₂²⋊D₅	M₃₂	1	4	yes	complemented
241	C₂×Dic₅	—	2	2	no	—
242	C₂×Dic₅	—	2	2	no	—
243	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
244	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
245	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
246	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
247	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
248	D₂₀	—	2	2	no	—
249	C₄×D₅	—	2	2	no	—
250	C₄×D₅	—	2	2	no	—
251	C₄×D₅	—	2	1	no	—
252	C₄×D₅	—	2	1	no	—
253	C₄×D₅	—	2	1	no	—
254	C₄×D₅	—	2	1	no	—
255	C₄×D₅	—	2	2	no	—
256	C₄×D₅	—	2	2	no	—
257	C₄×D₅	—	2	2	no	—
258	C₄×D₅	—	4	1	no	—
259	C₄×D₅	C₄×D₄	1	2	yes	—
260	C₄×D₅	#131	1	2	yes	—
261	C₅×C₈	—	2	1	no	—
262	C₅×C₈	—	2	1	no	—
263	C₅×C₈	—	2	1	no	—
264	C₅×C₈	C₄×D₄	1	2	yes	—
265	#168	—	2	1	no	—
266	#168	—	2	1	no	—
267	#168	—	2	1	no	—
268	#168	C₂²×D₄	1	1	yes	characteristic
269	#168	C₂×#41	1	1	yes	characteristic
270	C₂²×D₄	—	5	1	no	—
271	C₂³×C₄	—	5	1	no	—
272	C₂³×C₄	—	5	1	no	—
273	C₂²×C₈	—	5	1	no	—
274	C₂²×C₈	—	5	1	no	—
275	C₂²×C₈	—	5	1	no	—
276	C₂²×C₈	—	5	1	no	—
277	C₂²×C₈	—	5	1	no	—
278	C₂²×C₈	—	5	1	no	—
279	C₂²×C₈	—	5	1	no	—
280	C₂²×C₈	—	5	1	no	—
281	C₂²×C₈	—	5	1	no	—
282	C₂²×C₈	—	5	1	no	—
283	C₂²×C₈	—	10	2	no	—
284	C₂²×C₈	—	10	2	no	—
285	C₂²×C₈	—	10	2	no	—
286	C₂²×C₈	—	10	2	no	—
287	C₂²×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
288	C₂²×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
289	C₄×D₄	—	5	1	no	—
290	C₄×D₄	—	5	1	no	—
291	C₄×D₄	—	5	1	no	—
292	C₄×D₄	—	5	1	no	—
293	C₄×D₄	—	5	1	no	—
294	C₄×D₄	—	5	1	no	—
295	C₄×D₄	—	5	1	no	—
296	C₄×D₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
297	C₂×C₄⋊C₄	—	5	1	no	—
298	C₂×C₂²⋊C₄	—	5	1	no	—
299	C₂×C₂²⋊C₄	—	5	1	no	—
300	C₂×C₄²	—	5	1	no	—
301	M₃₂	—	5	4	no	—
302	M₃₂	—	10	4	no	—
303	M₃₂	—	10	4	no	—
304	M₃₂	—	10	2	no	—
305	M₃₂	—	10	2	no	—
306	M₃₂	—	10	2	no	—
307	C₂×C₁₆	—	5	2	no	—
308	C₂×C₁₆	—	5	2	no	—
309	C₂×C₁₆	—	5	2	no	—
310	C₂×C₁₆	—	5	2	no	—
311	C₂×C₁₆	—	10	4	no	—
312	C₂×C₁₆	—	10	4	no	—
313	C₄⋊C₈	—	5	1	no	—
314	C₄⋊C₈	—	5	1	no	—
315	C₄⋊C₈	—	5	1	no	—
316	C₄⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
317	C₂²⋊C₈	—	5	1	no	—
318	C₂²⋊C₈	—	5	1	no	—
319	C₂²⋊C₈	—	5	1	no	—
320	C₂²⋊C₈	—	5	1	no	—
321	C₂²⋊C₈	—	5	1	no	—
322	C₂²⋊C₈	—	5	1	no	—
323	C₂²⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
324	C₂²⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
325	C₄×C₈	—	5	1	no	—
326	C₄×C₈	—	5	1	no	—
327	C₄×C₈	—	5	1	no	—
328	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
329	C₂²×C₅	—	2	1	no	—
330	C₂²×C₅	—	2	1	no	—
331	C₂²×C₅	—	2	1	no	—
332	C₂²×C₅	—	2	1	no	—
333	C₂²×C₅	—	2	1	no	—
334	C₂²×C₅	C₂×M₃₂	1	2	yes	complemented
335	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
336	C₂×D₅	—	2	1	no	—
337	C₂×D₅	—	2	1	no	—
338	C₂×D₅	—	2	1	no	—
339	C₂×D₅	—	2	1	no	—
340	C₂×D₅	—	2	1	no	—
341	C₂×D₅	—	2	1	no	—
342	C₂×D₅	—	2	1	no	—
343	C₂×D₅	—	4	4	no	—
344	C₂×D₅	—	4	4	no	—
345	C₂×D₅	C₈×D₄	1	2	yes	—
346	C₂×D₅	C₂×M₃₂	1	2	yes	complemented
347	C₄×C₅	—	2	1	no	—
348	C₄×C₅	—	2	1	no	—
349	C₄×C₅	—	2	1	no	—
350	C₄×C₅	—	2	1	no	—
351	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
352	C₄×C₅	C₂×#131	1	1	yes	characteristic
353	Dic₅	—	2	1	no	—
354	Dic₅	—	2	1	no	—
355	Dic₅	—	2	1	no	—
356	Dic₅	C₈×D₄	1	2	yes	—
357	Dic₅	C₂×M₃₂	1	2	yes	complemented
358	C₂⁴	—	5	1	no	—
359	C₂⁴	—	5	1	no	—
360	C₂×D₄	—	5	1	no	—
361	C₂×D₄	—	5	1	no	—
362	C₂×D₄	—	5	1	no	—
363	C₂×D₄	—	10	4	no	—
364	C₂×D₄	D₅⋊C₈	1	1	yes	characteristic
365	C₂²×C₄	—	5	1	no	—
366	C₂²×C₄	—	5	1	no	—
367	C₂²×C₄	—	5	1	no	—
368	C₂²×C₄	—	5	1	no	—
369	C₂²×C₄	—	5	1	no	—
370	C₂²×C₄	—	5	1	no	—
371	C₂²×C₄	—	5	1	no	—
372	C₂²×C₄	—	5	1	no	—
373	C₂²×C₄	—	5	1	no	—
374	C₂²×C₄	—	5	1	no	—
375	C₂²×C₄	—	5	1	no	—
376	C₂²×C₄	—	10	2	no	—
377	C₂²×C₄	—	10	2	no	—
378	C₂²×C₄	—	10	2	no	—
379	C₂²×C₄	—	10	2	no	—
380	C₂²×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
381	C₂²×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	5	1	no	—
385	C₂×C₈	—	5	2	no	—
386	C₂×C₈	—	5	2	no	—
387	C₂×C₈	—	5	1	no	—
388	C₂×C₈	—	5	1	no	—
389	C₂×C₈	—	5	1	no	—
390	C₂×C₈	—	10	1	no	—
391	C₂×C₈	—	10	1	no	—
392	C₂×C₈	—	10	1	no	—
393	C₂×C₈	—	10	1	no	—
394	C₂×C₈	—	10	2	no	—
395	C₂×C₈	—	10	2	no	—
396	C₂×C₈	—	10	2	no	—
397	C₂×C₈	—	10	1	no	—
398	C₂×C₈	—	10	1	no	—
399	C₂×C₈	—	10	1	no	—
400	C₂×C₈	—	10	1	no	—
401	C₂×C₈	—	10	2	no	—
402	C₂×C₈	—	10	2	no	—
403	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
404	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
405	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
406	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
407	C₄⋊C₄	—	5	1	no	—
408	C₄⋊C₄	—	5	1	no	—
409	C₄⋊C₄	—	5	1	no	—
410	C₄⋊C₄	D₅⋊C₈	1	1	yes	characteristic
411	C₂²⋊C₄	—	5	1	no	—
412	C₂²⋊C₄	—	5	1	no	—
413	C₂²⋊C₄	—	5	1	no	—
414	C₂²⋊C₄	—	5	1	no	—
415	C₂²⋊C₄	—	5	1	no	—
416	C₂²⋊C₄	—	5	1	no	—
417	C₂²⋊C₄	D₅⋊C₈	1	1	yes	characteristic
418	C₂²⋊C₄	D₅⋊C₈	1	1	yes	characteristic
419	C₄²	—	5	1	no	—
420	C₄²	—	5	1	no	—
421	C₄²	—	5	1	no	—
422	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
423	C₁₆	—	5	4	no	—
424	C₁₆	—	10	2	no	—
425	C₁₆	—	10	2	no	—
426	C₁₆	—	10	2	no	—
427	C₂×C₅	—	2	2	no	—
428	C₂×C₅	—	4	1	no	—
429	C₂×C₅	C₂×C₈×D₄	1	1	yes	characteristic
430	C₂×C₅	C₂²×M₃₂	1	1	yes	characteristic
431	C₂×C₅	#3407	1	1	yes	characteristic
432	D₅	—	2	2	no	—
433	D₅	—	2	2	no	—
434	D₅	—	4	1	no	—
435	C₂³	—	5	1	no	—
436	C₂³	—	5	1	no	—
437	C₂³	—	5	1	no	—
438	C₂³	—	10	2	no	—
439	C₂³	—	10	2	no	—
440	C₂³	—	10	2	no	—
441	C₂³	—	10	2	no	—
442	C₂³	—	20	1	no	—
443	C₂³	—	20	1	no	—
444	C₂³	C₂×D₅⋊C₈	1	1	yes	characteristic
445	C₂³	C₂×D₅⋊C₈	1	1	yes	characteristic
446	D₄	—	2	2	no	—
447	D₄	—	5	4	no	—
448	D₄	—	10	2	no	—
449	D₄	—	10	2	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	5	1	no	—
455	C₂×C₄	—	5	1	no	—
456	C₂×C₄	—	5	2	no	—
457	C₂×C₄	—	5	2	no	—
458	C₂×C₄	—	5	1	no	—
459	C₂×C₄	—	5	1	no	—
460	C₂×C₄	—	5	1	no	—
461	C₂×C₄	—	10	2	no	—
462	C₂×C₄	—	10	2	no	—
463	C₂×C₄	—	10	2	no	—
464	C₂×C₄	—	10	2	no	—
465	C₂×C₄	—	10	2	no	—
466	C₂×C₄	—	10	2	no	—
467	C₂×C₄	—	10	2	no	—
468	C₂×C₄	—	10	1	no	—
469	C₂×C₄	—	10	1	no	—
470	C₂×C₄	—	10	1	no	—
471	C₂×C₄	—	10	1	no	—
472	C₂×C₄	—	20	1	no	—
473	C₂×C₄	C₂×D₅⋊C₈	1	1	yes	characteristic
474	C₂×C₄	C₂×D₅⋊C₈	1	1	yes	characteristic
475	C₂×C₄	C₂×D₅⋊C₈	1	1	yes	characteristic
476	C₂×C₄	C₂×D₅⋊C₈	1	1	yes	characteristic
477	C₂×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
478	C₈	—	2	1	no	—
479	C₈	—	2	1	no	—
480	C₈	—	2	1	no	—
481	C₈	—	5	1	no	—
482	C₈	—	5	1	no	—
483	C₈	—	10	1	no	—
484	C₈	—	10	1	no	—
485	C₈	—	10	1	no	—
486	C₈	D₄×AGL(1,𝔽₅)	1	2	yes	—
487	C₅	D₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
488	C₂²	—	2	1	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	5	2	no	—
494	C₂²	—	5	2	no	—
495	C₂²	—	10	1	no	—
496	C₂²	—	10	1	no	—
497	C₂²	—	10	1	no	—
498	C₂²	—	10	1	no	—
499	C₂²	—	10	1	no	—
500	C₂²	—	10	1	no	—
501	C₂²	—	10	1	no	—
502	C₂²	—	20	4	no	—
503	C₂²	—	20	4	no	—
504	C₂²	D₅⋊M₃₂	1	2	yes	complemented
505	C₂²	C₂²×D₅⋊C₈	1	1	yes	characteristic
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	2	1	no	—
510	C₄	—	5	2	no	—
511	C₄	—	5	2	no	—
512	C₄	—	10	1	no	—
513	C₄	—	10	1	no	—
514	C₄	—	10	1	no	—
515	C₄	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
516	C₄	D₅⋊#131	1	1	yes	characteristic
517	C₂	—	2	2	no	—
518	C₂	—	4	1	no	—
519	C₂	—	10	2	no	—
520	C₂	—	10	2	no	—
521	C₂	—	20	1	no	—
522	C₂	D₄×D₅⋊C₈	1	1	yes	characteristic
523	C₂	C₂×D₅⋊M₃₂	1	1	yes	characteristic
524	C₂	#10617413	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×AGL(1,𝔽₅)
commutator, socle	C₂²×C₅	C₂³×C₈
Fitting	C₅×C₈×D₄	C₄
prime radical	C₂×D₄×D₅	C₈
cosocle	C₂×#168	C₂⁴
hypercenter	C₈×D₄	AGL(1,𝔽₅)
hypocenter	C₅	D₄×M₃₂
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₈×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×D₅⋊M₃₂	C₂	semidirect
2. C₂²×#3990	C₂	semidirect
4. #10604706	C₂	semidirect
5. #10604706	C₂	semidirect
6. #10604413	C₂	semidirect
7. #10604022	C₂	semidirect
8. #10603906	C₂	semidirect
9. #10603903	C₂	semidirect
10. #10603827	C₂	semidirect
11. #10603825	C₂	semidirect
15. C₂×#3998	C₂²	semidirect
16. C₂²×#674	C₂²	semidirect
23. C₂×#3990	C₂²	semidirect
24. C₂×D₅⋊C₁₆	C₂²	semidirect
37. C₂²⋊#674	C₂²	semidirect
38. C₂²⋊#674	C₂²	semidirect
39. #64888	C₂²	semidirect
40. #64887	C₂²	semidirect
41. #64887	C₂²	semidirect
42. #64885	C₂²	semidirect
43. #64859	C₂²	semidirect
44. C₄⋊#674	C₂²	semidirect
87. #3990	D₄	semidirect
184. #674	C₂×D₄	semidirect
240. C₂²⋊D₅	M₃₂	semidirect
334. C₂²×C₅	C₂×M₃₂	semidirect
346. C₂×D₅	C₂×M₃₂	semidirect
357. Dic₅	C₂×M₃₂	semidirect
487. C₅	D₄×M₃₂	semidirect
504. C₂²	D₅⋊M₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₅⋊M₃₂	2
C₂²×#3990	2
C₈×D₄×D₅	2
#10604706	2
#10604413	2
#10604022	2
#10603906	2
#10603903	2
#10603827	2
#10603825	2
D₄×M₃₂	5