Subgroups — #13043706

Order 1280.

626 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#65014	C₂	1	1	yes	maximal, characteristic
2	#10604872	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂²⋊#674	C₂	1	1	yes	maximal, characteristic, complemented
4	#10604710	C₂	1	1	yes	maximal, characteristic, complemented
5	#10604709	C₂	1	1	yes	maximal, characteristic, complemented
6	#10604706	C₂	1	1	yes	maximal, characteristic, complemented
7	D₅⋊(C₂²⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
8	#10603906	C₂	1	2	yes	maximal, complemented
9	#10603905	C₂	1	2	yes	maximal, complemented
10	#10603904	C₂	1	2	yes	maximal, complemented
11	#10603903	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×C₂²⋊D₅	C₄	1	1	yes	characteristic
13	C₂³×#168	C₂²	1	1	yes	characteristic
14	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
15	C₂×#3998	C₂²	1	2	yes	complemented
16	C₂²×#674	C₂²	1	2	yes	complemented
17	C₂×#3990	C₂²	1	2	yes	complemented
18	C₂×D₅⋊C₁₆	C₂²	1	2	yes	complemented
19	C₂×C₅×C₂²⋊C₈	C₄	1	1	yes	characteristic
20	C₂×#3952	C₄	1	1	yes	characteristic
21	C₂×#3946	C₄	1	1	yes	characteristic
22	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
23	#65014	C₄	1	1	yes	characteristic
24	#65014	C₄	1	1	yes	characteristic
25	#65014	C₄	1	1	yes	characteristic
26	#65014	C₄	1	1	yes	characteristic
27	#65014	C₂²	1	1	yes	characteristic
28	#65014	C₂²	1	1	yes	characteristic
29	#65014	C₂²	1	1	yes	characteristic
30	#65014	C₂²	1	1	yes	characteristic
31	C₂²⋊#674	C₂²	1	1	yes	characteristic
32	C₂²⋊#674	C₂²	1	1	yes	characteristic
33	C₂²⋊#674	C₂²	1	1	yes	characteristic
34	C₂²⋊#674	C₂²	1	1	yes	characteristic
35	C₂²⋊#674	C₂²	1	2	yes	complemented
36	C₂²⋊#674	C₂²	1	2	yes	complemented
37	#64888	C₂²	1	2	yes	complemented
38	#64888	C₂²	1	2	yes	complemented
39	#64887	C₂²	1	2	yes	complemented
40	#64887	C₂²	1	2	yes	complemented
41	#64886	C₂²	1	2	yes	complemented
42	#64885	C₂²	1	2	yes	complemented
43	#33488	—	5	1	no	maximal, Sylow
44	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₂²⋊D₅	C₈	1	1	yes	characteristic
46	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
49	C₂×C₂²⋊Dic₅	C₈	1	1	yes	characteristic
50	C₄×C₂²⋊D₅	C₈	1	1	yes	characteristic
51	C₄×C₂²⋊D₅	C₈	1	1	yes	characteristic
52	C₄×C₂²⋊D₅	C₈	1	1	yes	characteristic
53	C₄×C₂²⋊D₅	C₈	1	1	yes	characteristic
54	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
55	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
56	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
57	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
58	C₂×#685	C₈	1	1	yes	characteristic
59	C₂×#683	C₈	1	1	yes	characteristic
60	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
61	C₂²×#168	—	4	2	no	—
62	C₂²×#168	C₂×C₄	1	1	yes	characteristic
63	C₂²×#168	C₂×C₄	1	1	yes	characteristic
64	C₂²×#168	C₂×C₄	1	1	yes	characteristic
65	C₂²×#168	C₂³	1	1	yes	characteristic
66	C₂²×#168	C₂³	1	1	yes	characteristic
67	C₂²×#168	C₂³	1	1	yes	characteristic
68	C₂×C₈×D₅	—	4	2	no	—
69	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
70	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
71	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
72	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
73	#3998	—	4	2	no	—
74	C₂×#674	—	4	2	no	—
75	C₂×#674	C₂³	1	2	yes	—
76	C₂×#674	C₂³	1	2	yes	—
77	C₂×#674	C₂³	1	2	yes	—
78	C₂×#674	C₂³	1	2	yes	—
79	#3990	—	4	2	no	—
80	D₅⋊C₁₆	—	4	2	no	—
81	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
82	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
83	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
84	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
85	#3952	C₂×C₄	1	1	yes	characteristic
86	#3952	C₂×C₄	1	1	yes	characteristic
87	#3952	C₂×C₄	1	1	yes	characteristic
88	#3952	C₂×C₄	1	1	yes	characteristic
89	#3946	C₂×C₄	1	1	yes	characteristic
90	#3946	C₂×C₄	1	1	yes	characteristic
91	#3946	C₂×C₄	1	1	yes	characteristic
92	#3946	C₂×C₄	1	1	yes	characteristic
93	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
94	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
95	C₈×Dic₅	C₂³	1	1	yes	characteristic
96	C₈×Dic₅	C₂³	1	1	yes	characteristic
97	C₂×C₈×D₄	—	5	1	no	—
98	#2169	—	5	2	no	—
99	#2168	—	5	2	no	—
100	#2168	—	5	2	no	—
101	D₄×C₁₆	—	5	2	no	—
102	#2163	—	5	1	no	—
103	#2162	—	5	1	no	—
104	#2112	—	5	1	no	—
105	#2112	—	5	1	no	—
106	C₂×C₂²⋊C₁₆	—	5	1	no	—
107	C₂×C₂²⋊C₁₆	—	5	1	no	—
108	C₂⁴×C₅	C₂×C₈	1	1	yes	characteristic
109	C₂³×D₅	C₂×C₈	1	1	yes	characteristic
110	C₂²×C₄×C₅	—	4	1	no	—
111	C₂²×C₄×C₅	—	4	1	no	—
112	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
113	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
114	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
115	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₂²⋊D₅	—	2	4	no	—
119	C₂×C₂²⋊D₅	C₂×C₈	1	1	yes	characteristic
120	C₂×C₂²⋊D₅	C₂×C₈	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	C₂²×Dic₅	C₂×C₈	1	1	yes	characteristic
126	C₂×C₄×D₅	—	4	1	no	—
127	C₂×C₄×D₅	—	4	1	no	—
128	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
129	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
130	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₅×C₈	—	4	1	no	—
133	C₂×C₅×C₈	—	4	1	no	—
134	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
138	C₂²⋊Dic₅	C₂×C₈	1	1	yes	characteristic
139	C₂²⋊Dic₅	C₂×C₈	1	1	yes	characteristic
140	C₂²⋊Dic₅	C₂×C₈	1	1	yes	characteristic
141	C₂²⋊Dic₅	C₂×C₈	1	1	yes	characteristic
142	#685	C₂×C₈	1	1	yes	characteristic
143	#685	C₂×C₈	1	1	yes	characteristic
144	#685	C₂×C₈	1	1	yes	characteristic
145	#685	C₂×C₈	1	1	yes	characteristic
146	#683	C₂×C₈	1	1	yes	characteristic
147	#683	C₂×C₈	1	1	yes	characteristic
148	#683	C₂×C₈	1	1	yes	characteristic
149	#683	C₂×C₈	1	1	yes	characteristic
150	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
151	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
152	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
153	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
154	C₂×#168	—	2	2	no	—
155	C₂×#168	—	2	2	no	—
156	C₂×#168	—	2	2	no	—
157	C₂×#168	—	4	1	no	—
158	C₂×#168	—	4	1	no	—
159	C₂×#168	—	4	1	no	—
160	C₂×#168	C₂²×C₄	1	1	yes	characteristic
161	C₂×#168	C₂²×C₄	1	1	yes	characteristic
162	C₂×#168	C₂²×C₄	1	1	yes	characteristic
163	C₂×#168	C₂⁴	1	1	yes	characteristic
164	C₈×D₅	—	2	2	no	—
165	C₈×D₅	—	2	2	no	—
166	C₈×D₅	—	4	1	no	—
167	C₈×D₅	—	4	1	no	—
168	#674	—	2	2	no	—
169	#674	—	2	2	no	—
170	#674	—	2	2	no	—
171	#674	—	2	2	no	—
172	C₂³×C₈	—	5	1	no	—
173	C₂³×C₈	—	5	1	no	—
174	C₂×C₄×D₄	—	5	1	no	—
175	C₂×M₃₂	—	5	2	no	—
176	C₂×M₃₂	—	5	2	no	—
177	C₂²×C₁₆	—	5	2	no	—
178	C₂²×C₁₆	—	5	2	no	—
179	C₈×D₄	—	5	1	no	—
180	C₈×D₄	—	5	1	no	—
181	C₈×D₄	—	5	1	no	—
182	C₈×D₄	—	5	1	no	—
183	C₈×D₄	—	5	1	no	—
184	C₈×D₄	—	5	1	no	—
185	C₈×D₄	—	5	1	no	—
186	C₈×D₄	—	5	1	no	—
187	C₂×C₄⋊C₈	—	5	1	no	—
188	C₂×C₂²⋊C₈	—	5	1	no	—
189	C₂×C₂²⋊C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
190	C₂×C₄×C₈	—	5	1	no	—
191	C₄⋊C₁₆	—	5	2	no	—
192	C₄⋊C₁₆	—	5	2	no	—
193	C₂²⋊C₁₆	—	5	1	no	—
194	C₂²⋊C₁₆	—	5	1	no	—
195	C₂²⋊C₁₆	—	5	1	no	—
196	C₂²⋊C₁₆	—	5	2	no	—
197	C₂²⋊C₁₆	—	5	2	no	—
198	C₂²⋊C₁₆	—	5	1	no	—
199	C₂²⋊C₁₆	—	5	2	no	—
200	C₂²⋊C₁₆	—	5	2	no	—
201	#346	—	5	2	no	—
202	C₄×C₁₆	—	5	2	no	—
203	C₂³×C₅	—	2	2	no	—
204	C₂³×C₅	—	2	2	no	—
205	C₂³×C₅	—	4	1	no	—
206	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
207	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
208	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
209	C₂²×D₅	—	2	2	no	—
210	C₂²×D₅	—	2	2	no	—
211	C₂²×D₅	—	4	1	no	—
212	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
213	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
214	C₂×C₄×C₅	—	2	1	no	—
215	C₂×C₄×C₅	—	2	1	no	—
216	C₂×C₄×C₅	—	2	1	no	—
217	C₂×C₄×C₅	—	2	1	no	—
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	2	1	no	—
220	C₂×C₄×C₅	—	4	1	no	—
221	C₂×C₄×C₅	—	4	1	no	—
222	C₂×C₄×C₅	—	4	1	no	—
223	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
224	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
225	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
226	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
227	C₂²⋊D₅	—	2	2	no	—
228	C₂²⋊D₅	—	2	2	no	—
229	C₂²⋊D₅	—	2	2	no	—
230	C₂²⋊D₅	M₃₂	1	4	yes	complemented
231	C₂×Dic₅	—	2	2	no	—
232	C₂×Dic₅	—	2	2	no	—
233	C₂×Dic₅	—	4	1	no	—
234	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
235	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
236	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
237	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
238	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
239	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
240	C₄×D₅	—	2	1	no	—
241	C₄×D₅	—	2	1	no	—
242	C₄×D₅	—	2	1	no	—
243	C₄×D₅	—	2	1	no	—
244	C₄×D₅	—	4	1	no	—
245	C₄×D₅	—	4	1	no	—
246	C₅×C₈	—	2	1	no	—
247	C₅×C₈	—	2	1	no	—
248	C₅×C₈	—	2	1	no	—
249	C₅×C₈	—	2	1	no	—
250	#168	—	2	1	no	—
251	#168	—	2	1	no	—
252	#168	—	2	1	no	—
253	#168	H(5,𝔽₂)	1	2	yes	—
254	C₂²×D₄	—	5	1	no	—
255	C₂³×C₄	—	5	1	no	—
256	C₂³×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
257	C₂²×C₈	—	5	1	no	—
258	C₂²×C₈	—	5	1	no	—
259	C₂²×C₈	—	5	1	no	—
260	C₂²×C₈	—	5	1	no	—
261	C₂²×C₈	—	5	1	no	—
262	C₂²×C₈	—	5	1	no	—
263	C₂²×C₈	—	5	1	no	—
264	C₂²×C₈	—	5	1	no	—
265	C₂²×C₈	—	5	1	no	—
266	C₂²×C₈	—	5	1	no	—
267	C₂²×C₈	—	20	2	no	—
268	C₂²×C₈	—	20	2	no	—
269	C₂²×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
270	C₂²×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
271	C₄×D₄	—	5	1	no	—
272	C₄×D₄	—	5	1	no	—
273	C₄×D₄	—	5	1	no	—
274	C₄×D₄	—	5	1	no	—
275	C₄×D₄	—	5	1	no	—
276	C₄×D₄	—	5	1	no	—
277	C₄×D₄	—	5	1	no	—
278	C₄×D₄	—	5	1	no	—
279	C₂×C₄⋊C₄	—	5	1	no	—
280	C₂×C₂²⋊C₄	—	5	1	no	—
281	C₂×C₂²⋊C₄	—	5	1	no	—
282	C₂×C₄²	—	5	1	no	—
283	M₃₂	—	20	2	no	—
284	M₃₂	—	20	2	no	—
285	C₂×C₁₆	—	5	2	no	—
286	C₂×C₁₆	—	5	2	no	—
287	C₂×C₁₆	—	5	2	no	—
288	C₂×C₁₆	—	5	2	no	—
289	C₂×C₁₆	—	20	2	no	—
290	C₂×C₁₆	—	20	2	no	—
291	C₄⋊C₈	—	5	1	no	—
292	C₄⋊C₈	—	5	1	no	—
293	C₄⋊C₈	—	5	1	no	—
294	C₄⋊C₈	—	5	1	no	—
295	C₂²⋊C₈	—	5	1	no	—
296	C₂²⋊C₈	—	5	1	no	—
297	C₂²⋊C₈	—	5	1	no	—
298	C₂²⋊C₈	—	5	1	no	—
299	C₂²⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
300	C₂²⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
301	C₂²⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
302	C₂²⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
303	C₄×C₈	—	5	1	no	—
304	C₄×C₈	—	5	1	no	—
305	C₄×C₈	—	5	1	no	—
306	C₄×C₈	—	5	1	no	—
307	C₂²×C₅	—	2	1	no	—
308	C₂²×C₅	—	2	1	no	—
309	C₂²×C₅	—	2	1	no	—
310	C₂²×C₅	—	2	1	no	—
311	C₂²×C₅	—	2	1	no	—
312	C₂²×C₅	—	2	1	no	—
313	C₂²×C₅	—	2	1	no	—
314	C₂²×C₅	—	4	4	no	—
315	C₂²×C₅	C₂×M₃₂	1	2	yes	—
316	C₂²×C₅	#504	1	2	yes	—
317	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
318	C₂×D₅	—	2	1	no	—
319	C₂×D₅	—	2	1	no	—
320	C₂×D₅	—	2	1	no	—
321	C₂×D₅	—	2	1	no	—
322	C₂×D₅	—	2	1	no	—
323	C₂×D₅	—	4	4	no	—
324	C₂×D₅	C₂×M₃₂	1	2	yes	—
325	C₄×C₅	—	2	1	no	—
326	C₄×C₅	—	2	1	no	—
327	C₄×C₅	—	2	1	no	—
328	C₄×C₅	#518	1	1	yes	characteristic
329	C₄×C₅	#568	1	1	yes	characteristic
330	Dic₅	—	2	1	no	—
331	Dic₅	—	2	1	no	—
332	Dic₅	—	2	1	no	—
333	Dic₅	—	2	1	no	—
334	Dic₅	—	2	1	no	—
335	Dic₅	C₂×M₃₂	1	2	yes	—
336	C₂⁴	—	5	1	no	—
337	C₂⁴	D₅⋊C₈	1	1	yes	characteristic
338	C₂×D₄	—	5	1	no	—
339	C₂×D₄	—	5	1	no	—
340	C₂×D₄	—	5	1	no	—
341	C₂×D₄	—	5	1	no	—
342	C₂×D₄	—	10	4	no	—
343	C₂²×C₄	—	4	1	no	—
344	C₂²×C₄	—	4	1	no	—
345	C₂²×C₄	—	5	1	no	—
346	C₂²×C₄	—	5	1	no	—
347	C₂²×C₄	—	5	1	no	—
348	C₂²×C₄	—	5	1	no	—
349	C₂²×C₄	—	5	1	no	—
350	C₂²×C₄	—	5	1	no	—
351	C₂²×C₄	—	5	1	no	—
352	C₂²×C₄	—	20	1	no	—
353	C₂²×C₄	—	20	1	no	—
354	C₂²×C₄	D₅⋊C₈	1	1	yes	characteristic
355	C₂²×C₄	D₅⋊C₈	1	1	yes	characteristic
356	C₂²×C₄	D₅⋊C₈	1	1	yes	characteristic
357	C₂²×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
358	C₂²×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
359	C₂²×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
360	C₂×C₈	—	4	1	no	—
361	C₂×C₈	—	4	1	no	—
362	C₂×C₈	—	5	1	no	—
363	C₂×C₈	—	5	1	no	—
364	C₂×C₈	—	5	1	no	—
365	C₂×C₈	—	5	1	no	—
366	C₂×C₈	—	10	2	no	—
367	C₂×C₈	—	10	2	no	—
368	C₂×C₈	—	10	2	no	—
369	C₂×C₈	—	10	2	no	—
370	C₂×C₈	—	10	2	no	—
371	C₂×C₈	—	20	1	no	—
372	C₂×C₈	—	20	1	no	—
373	C₂×C₈	—	20	1	no	—
374	C₂×C₈	—	20	1	no	—
375	C₂×C₈	—	20	1	no	—
376	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
377	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
378	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
379	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
380	C₄⋊C₄	—	5	1	no	—
381	C₄⋊C₄	—	5	1	no	—
382	C₄⋊C₄	—	5	1	no	—
383	C₄⋊C₄	—	5	1	no	—
384	C₂²⋊C₄	—	5	1	no	—
385	C₂²⋊C₄	—	5	1	no	—
386	C₂²⋊C₄	—	5	1	no	—
387	C₂²⋊C₄	—	5	1	no	—
388	C₂²⋊C₄	—	5	1	no	—
389	C₂²⋊C₄	—	5	1	no	—
390	C₂²⋊C₄	—	5	1	no	—
391	C₂²⋊C₄	—	5	1	no	—
392	C₄²	—	5	1	no	—
393	C₄²	—	5	1	no	—
394	C₄²	—	5	1	no	—
395	C₄²	—	5	1	no	—
396	C₁₆	—	10	2	no	—
397	C₁₆	—	10	2	no	—
398	C₁₆	—	10	2	no	—
399	C₁₆	—	10	2	no	—
400	C₂×C₅	—	2	2	no	—
401	C₂×C₅	—	2	2	no	—
402	C₂×C₅	—	4	1	no	—
403	C₂×C₅	#2972	1	1	yes	characteristic
404	C₂×C₅	C₂²×M₃₂	1	1	yes	characteristic
405	C₂×C₅	C₂×#504	1	1	yes	characteristic
406	D₅	—	2	2	no	—
407	D₅	—	4	1	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	4	1	no	—
411	C₂³	—	5	1	no	—
412	C₂³	—	5	1	no	—
413	C₂³	—	10	2	no	—
414	C₂³	—	10	2	no	—
415	C₂³	—	20	1	no	—
416	C₂³	C₂×D₅⋊C₈	1	1	yes	characteristic
417	C₂³	C₂×D₅⋊C₈	1	1	yes	characteristic
418	C₂³	C₂×D₅⋊C₈	1	1	yes	characteristic
419	D₄	—	5	4	no	—
420	D₄	—	10	2	no	—
421	D₄	—	10	2	no	—
422	D₄	—	10	2	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	5	1	no	—
433	C₂×C₄	—	5	1	no	—
434	C₂×C₄	—	5	1	no	—
435	C₂×C₄	—	5	1	no	—
436	C₂×C₄	—	5	1	no	—
437	C₂×C₄	—	5	1	no	—
438	C₂×C₄	—	10	2	no	—
439	C₂×C₄	—	10	2	no	—
440	C₂×C₄	—	10	1	no	—
441	C₂×C₄	—	10	1	no	—
442	C₂×C₄	—	10	1	no	—
443	C₂×C₄	—	10	1	no	—
444	C₂×C₄	—	20	1	no	—
445	C₂×C₄	—	20	1	no	—
446	C₂×C₄	—	20	1	no	—
447	C₂×C₄	C₂×D₅⋊C₈	1	1	yes	characteristic
448	C₂×C₄	C₂×D₅⋊C₈	1	1	yes	characteristic
449	C₂×C₄	C₂×D₅⋊C₈	1	1	yes	characteristic
450	C₂×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
451	C₈	—	2	1	no	—
452	C₈	—	2	1	no	—
453	C₈	—	2	1	no	—
454	C₈	—	2	1	no	—
455	C₈	—	5	2	no	—
456	C₈	—	10	1	no	—
457	C₈	—	10	1	no	—
458	C₈	—	10	1	no	—
459	C₅	#33488	1	1	yes	characteristic, complemented, Sylow
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	4	4	no	—
468	C₂²	—	5	2	no	—
469	C₂²	—	10	1	no	—
470	C₂²	—	10	1	no	—
471	C₂²	—	10	1	no	—
472	C₂²	—	10	1	no	—
473	C₂²	—	10	1	no	—
474	C₂²	—	20	4	no	—
475	C₂²	D₅⋊M₃₂	1	2	yes	—
476	C₂²	#65725	1	2	yes	—
477	C₂²	C₂²×D₅⋊C₈	1	1	yes	characteristic
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	5	2	no	—
482	C₄	—	10	1	no	—
483	C₄	—	10	1	no	—
484	C₄	—	10	1	no	—
485	C₄	—	10	1	no	—
486	C₄	—	10	1	no	—
487	C₄	#66256	1	1	yes	characteristic
488	C₄	#66258	1	1	yes	characteristic
489	C₂	—	2	2	no	—
490	C₂	—	2	2	no	—
491	C₂	—	4	1	no	—
492	C₂	—	10	2	no	—
493	C₂	—	20	1	no	—
494	C₂	#10617061	1	1	yes	characteristic
495	C₂	C₂×D₅⋊M₃₂	1	1	yes	characteristic
496	C₂	C₂×#65725	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×AGL(1,𝔽₅)
commutator, socle	C₂²×C₅	C₂³×C₈
Fitting	C₂×C₅×C₂²⋊C₈	C₄
prime radical	C₂²×C₂²⋊D₅	C₈
cosocle	C₂×#168	C₂⁴
hypercenter	C₂×C₂²⋊C₈	AGL(1,𝔽₅)
hypocenter	C₅	#33488
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
2. #10604872	C₂	semidirect
3. C₂×C₂²⋊#674	C₂	semidirect
4. #10604710	C₂	semidirect
5. #10604709	C₂	semidirect
6. #10604706	C₂	semidirect
7. D₅⋊(C₂²⋊C₁₆)	C₂	semidirect
8. #10603906	C₂	semidirect
9. #10603905	C₂	semidirect
10. #10603904	C₂	semidirect
11. #10603903	C₂	semidirect
15. C₂×#3998	C₂²	semidirect
16. C₂²×#674	C₂²	semidirect
17. C₂×#3990	C₂²	semidirect
18. C₂×D₅⋊C₁₆	C₂²	semidirect
35. C₂²⋊#674	C₂²	semidirect
36. C₂²⋊#674	C₂²	semidirect
37. #64888	C₂²	semidirect
38. #64888	C₂²	semidirect
39. #64887	C₂²	semidirect
40. #64887	C₂²	semidirect
41. #64886	C₂²	semidirect
42. #64885	C₂²	semidirect
230. C₂²⋊D₅	M₃₂	semidirect
459. C₅	#33488	semidirect

Maximal subgroups

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

subgroup	index
C₂×#65014	2
#10604872	2
C₂×C₂²⋊#674	2
#10604710	2
#10604709	2
#10604706	2
D₅⋊(C₂²⋊C₁₆)	2
#10603906	2
#10603905	2
#10603904	2
#10603903	2
#33488	5