Subgroups — #12252379

Order 1280.

682 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₈×D₅	C₂	1	1	yes	maximal, characteristic
2	C₅×#2163	C₂	1	1	yes	maximal, characteristic, complemented
3	#10600538	C₂	1	1	yes	maximal, characteristic, complemented
4	#10600077	C₂	1	2	yes	maximal, complemented
5	#10600067	C₂	1	2	yes	maximal, complemented
6	#10599899	C₂	1	2	yes	maximal
7	#10599885	C₂	1	2	yes	maximal, complemented
8	#10599866	C₂	1	2	yes	maximal, complemented
9	#10599864	C₂	1	2	yes	maximal, complemented
10	C₂²×C₈×D₅	C₄	1	1	yes	characteristic
11	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
12	C₂×C₄²×D₅	C₄	1	1	yes	characteristic
13	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₈×Dic₅	C₄	1	1	yes	characteristic
15	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
16	C₂×C₄×#168	C₄	1	1	yes	characteristic
17	C₂×#3930	C₂²	1	4	yes	—
18	C₄×C₈×D₅	C₄	1	1	yes	characteristic
19	C₄×C₈×D₅	C₄	1	1	yes	characteristic
20	C₄×C₈×D₅	C₄	1	1	yes	characteristic
21	C₄×C₈×D₅	C₄	1	1	yes	characteristic
22	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
23	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
24	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
25	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
26	C₅×C₄⋊C₁₆	C₂²	1	2	yes	complemented
27	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	—
28	C₅×#346	C₂²	1	2	yes	complemented
29	C₂²⋊#672	C₂²	1	2	yes	—
30	#64727	C₂²	1	4	yes	—
31	#64721	C₂²	1	4	yes	complemented
32	C₁₆×Dic₅	C₂²	1	4	yes	complemented
33	C₄⋊#672	C₂²	1	2	yes	complemented
34	#64681	C₂²	1	2	yes	complemented
35	#33418	—	5	1	no	maximal, Sylow
36	C₂²×C₄×D₅	C₈	1	1	yes	characteristic
37	C₂²×C₄×D₅	C₈	1	1	yes	characteristic
38	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
41	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄×Dic₅	C₈	1	1	yes	characteristic
43	C₂×C₄×Dic₅	C₈	1	1	yes	characteristic
44	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
45	C₂²×#168	C₂×C₄	1	1	yes	characteristic
46	C₂²×#168	C₂×C₄	1	1	yes	characteristic
47	C₂×C₈×D₅	—	2	4	no	—
48	C₂×C₈×D₅	—	2	4	no	—
49	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
51	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
56	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
57	C₄²×D₅	C₈	1	1	yes	characteristic
58	C₄²×D₅	C₈	1	1	yes	characteristic
59	C₄²×D₅	C₈	1	1	yes	characteristic
60	C₄²×D₅	C₈	1	1	yes	characteristic
61	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
62	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
63	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
64	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
65	C₂×C₅×C₁₆	C₂³	1	4	yes	—
66	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
67	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
68	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
70	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
71	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
72	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
73	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
74	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
75	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
76	C₈×Dic₅	C₂³	1	1	yes	characteristic
77	C₈×Dic₅	C₂³	1	1	yes	characteristic
78	C₂×#672	C₂³	1	4	yes	—
79	C₄×#168	C₂×C₄	1	1	yes	characteristic
80	C₄×#168	C₂×C₄	1	1	yes	characteristic
81	C₄×#168	C₂×C₄	1	1	yes	characteristic
82	C₄×#168	C₂×C₄	1	1	yes	characteristic
83	#3930	—	2	8	no	—
84	C₂²×C₄×C₈	—	5	1	no	—
85	#2163	—	5	1	no	—
86	#2163	—	5	2	no	—
87	#2163	D₅	1	1	yes	characteristic, complemented
88	#2162	—	5	2	no	—
89	#2162	—	5	2	no	—
90	#2150	—	5	2	no	—
91	#2112	—	5	2	no	—
92	C₄×M₃₂	—	5	2	no	—
93	C₂³×D₅	C₂×C₈	1	1	yes	characteristic
94	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
95	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
96	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂²×Dic₅	C₂×C₈	1	1	yes	characteristic
98	C₂²×Dic₅	C₂×C₈	1	1	yes	characteristic
99	C₂²×Dic₅	C₂×C₈	1	1	yes	characteristic
100	C₂×C₄×D₅	—	2	4	no	—
101	C₂×C₄×D₅	—	2	4	no	—
102	C₂×C₄×D₅	—	2	2	no	—
103	C₂×C₄×D₅	—	2	2	no	—
104	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
105	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
106	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
107	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
108	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
109	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
110	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
111	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
112	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
113	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
114	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₅×C₈	—	2	2	no	—
117	C₂×C₅×C₈	—	2	2	no	—
118	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
122	C₄²×C₅	C₂×C₈	1	1	yes	characteristic
123	C₄²×C₅	C₂×C₈	1	1	yes	characteristic
124	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
126	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
127	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
128	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
129	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
130	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
131	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
132	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
133	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
134	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
135	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
136	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
137	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
138	C₂×#168	—	2	2	no	—
139	C₂×#168	—	2	2	no	—
140	C₂×#168	C₂²×C₄	1	1	yes	characteristic
141	C₂×#168	C₂²×C₄	1	1	yes	characteristic
142	C₂×#168	C₂²×C₄	1	1	yes	characteristic
143	C₂×#168	C₂²×C₄	1	1	yes	characteristic
144	C₈×D₅	—	2	2	no	—
145	C₈×D₅	—	2	2	no	—
146	C₈×D₅	—	2	2	no	—
147	C₈×D₅	—	2	2	no	—
148	C₈×D₅	—	2	2	no	—
149	C₈×D₅	—	2	2	no	—
150	C₈×D₅	M₁₆	1	4	yes	—
151	C₈×D₅	#41	1	4	yes	—
152	C₅×C₁₆	—	2	4	no	—
153	#672	—	2	4	no	—
154	C₂³×C₈	—	5	1	no	—
155	C₂³×C₈	—	5	1	no	—
156	C₂²×C₄²	—	5	1	no	—
157	C₂×M₃₂	—	5	4	no	—
158	C₂×C₄×C₈	—	5	1	no	—
159	C₂×C₄×C₈	—	5	1	no	—
160	C₂×C₄×C₈	—	5	1	no	—
161	C₂×C₄×C₈	—	5	1	no	—
162	C₂×C₄×C₈	—	5	1	no	—
163	C₂×C₄×C₈	—	5	1	no	—
164	C₂×C₄×C₈	—	5	1	no	—
165	C₂×C₄×C₈	—	5	1	no	—
166	C₂×C₄×C₈	—	5	1	no	—
167	C₂×C₄×C₈	—	5	1	no	—
168	C₂×C₄×C₈	—	5	1	no	—
169	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
170	C₄⋊C₁₆	—	5	4	no	—
171	C₄⋊C₁₆	—	5	2	no	—
172	C₄⋊C₁₆	C₂×D₅	1	2	yes	complemented
173	C₂²⋊C₁₆	—	5	2	no	—
174	C₂²⋊C₁₆	—	5	4	no	—
175	C₂²⋊C₁₆	C₂×D₅	1	2	yes	—
176	#346	—	5	2	no	—
177	#346	C₂×D₅	1	2	yes	complemented
178	C₄×C₁₆	—	5	4	no	—
179	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
180	C₂²×D₅	—	2	2	no	—
181	C₂²×D₅	—	2	2	no	—
182	C₂²×D₅	—	2	2	no	—
183	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
184	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
185	C₂×C₄×C₅	—	2	2	no	—
186	C₂×C₄×C₅	—	2	1	no	—
187	C₂×C₄×C₅	—	2	1	no	—
188	C₂×C₄×C₅	—	2	2	no	—
189	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
190	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
191	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
192	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
193	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
194	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
195	C₂×Dic₅	—	2	2	no	—
196	C₂×Dic₅	—	2	2	no	—
197	C₂×Dic₅	M₃₂	1	4	yes	complemented
198	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
199	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
200	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
201	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
202	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
203	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
204	C₄×D₅	—	2	2	no	—
205	C₄×D₅	—	2	2	no	—
206	C₄×D₅	—	2	1	no	—
207	C₄×D₅	—	2	1	no	—
208	C₄×D₅	—	2	2	no	—
209	C₄×D₅	—	2	2	no	—
210	C₄×D₅	—	2	2	no	—
211	C₄×D₅	—	2	2	no	—
212	C₄×D₅	—	2	2	no	—
213	C₄×D₅	—	2	2	no	—
214	C₄×D₅	—	2	2	no	—
215	C₄×D₅	M₃₂	1	4	yes	complemented
216	C₄×D₅	#117	1	2	yes	—
217	C₄×D₅	C₂×M₁₆	1	2	yes	—
218	C₅×C₈	—	2	1	no	—
219	C₅×C₈	—	2	1	no	—
220	C₅×C₈	C₂×M₁₆	1	2	yes	—
221	C₅×C₈	C₂×#41	1	2	yes	—
222	#168	—	2	1	no	—
223	#168	—	2	1	no	—
224	#168	#117	1	2	yes	—
225	#168	C₂×M₁₆	1	2	yes	—
226	C₂³×C₄	—	5	1	no	—
227	C₂³×C₄	—	5	1	no	—
228	C₂³×C₄	—	5	1	no	—
229	C₂²×C₈	—	5	1	no	—
230	C₂²×C₈	—	5	1	no	—
231	C₂²×C₈	—	5	1	no	—
232	C₂²×C₈	—	5	1	no	—
233	C₂²×C₈	—	5	1	no	—
234	C₂²×C₈	—	5	1	no	—
235	C₂²×C₈	—	5	1	no	—
236	C₂²×C₈	—	5	1	no	—
237	C₂²×C₈	—	5	1	no	—
238	C₂²×C₈	—	5	1	no	—
239	C₂²×C₈	—	10	4	no	—
240	C₂²×C₈	—	10	4	no	—
241	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
242	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
243	C₂×C₄²	—	5	1	no	—
244	C₂×C₄²	—	5	1	no	—
245	C₂×C₄²	—	5	1	no	—
246	C₂×C₄²	—	5	1	no	—
247	C₂×C₄²	—	5	1	no	—
248	C₂×C₄²	—	5	1	no	—
249	C₂×C₄²	—	5	1	no	—
250	C₂×C₄²	—	5	1	no	—
251	C₂×C₄²	—	5	1	no	—
252	C₂×C₄²	—	5	1	no	—
253	C₂×C₄²	—	5	1	no	—
254	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
255	M₃₂	—	10	8	no	—
256	C₂×C₁₆	—	5	4	no	—
257	C₂×C₁₆	C₂²×D₅	1	4	yes	—
258	C₄×C₈	—	5	1	no	—
259	C₄×C₈	—	5	1	no	—
260	C₄×C₈	—	5	1	no	—
261	C₄×C₈	—	5	1	no	—
262	C₄×C₈	—	5	1	no	—
263	C₄×C₈	—	5	1	no	—
264	C₄×C₈	—	5	1	no	—
265	C₄×C₈	—	5	1	no	—
266	C₄×C₈	—	5	1	no	—
267	C₄×C₈	—	5	1	no	—
268	C₄×C₈	—	5	1	no	—
269	C₄×C₈	—	5	1	no	—
270	C₄×C₈	C₄×D₅	1	1	yes	characteristic
271	C₄×C₈	C₄×D₅	1	1	yes	characteristic
272	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
273	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
274	C₂²×C₅	—	2	1	no	—
275	C₂²×C₅	—	2	1	no	—
276	C₂²×C₅	C₂×M₃₂	1	2	yes	—
277	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
278	C₂×D₅	—	2	8	no	—
279	C₂×D₅	—	2	1	no	—
280	C₂×D₅	—	2	1	no	—
281	C₂×D₅	—	2	1	no	—
282	C₂×D₅	—	2	1	no	—
283	C₂×D₅	#431	1	2	yes	—
284	C₂×D₅	C₂×M₃₂	1	2	yes	—
285	C₄×C₅	—	2	1	no	—
286	C₄×C₅	—	2	1	no	—
287	C₄×C₅	—	2	1	no	—
288	C₄×C₅	—	2	1	no	—
289	C₄×C₅	C₂×M₃₂	1	2	yes	—
290	C₄×C₅	C₂×#117	1	1	yes	characteristic
291	C₄×C₅	C₂²×M₁₆	1	1	yes	characteristic
292	Dic₅	—	2	1	no	—
293	Dic₅	—	2	1	no	—
294	Dic₅	#431	1	2	yes	—
295	Dic₅	C₂×M₃₂	1	2	yes	—
296	Dic₅	C₂×M₃₂	1	2	yes	—
297	Dic₅	C₂×M₃₂	1	2	yes	—
298	C₂⁴	—	5	1	no	—
299	C₂²×C₄	—	5	1	no	—
300	C₂²×C₄	—	5	1	no	—
301	C₂²×C₄	—	5	1	no	—
302	C₂²×C₄	—	5	1	no	—
303	C₂²×C₄	—	5	1	no	—
304	C₂²×C₄	—	5	1	no	—
305	C₂²×C₄	—	5	1	no	—
306	C₂²×C₄	—	5	1	no	—
307	C₂²×C₄	—	5	1	no	—
308	C₂²×C₄	—	5	1	no	—
309	C₂²×C₄	—	5	1	no	—
310	C₂²×C₄	—	5	1	no	—
311	C₂²×C₄	—	5	1	no	—
312	C₂²×C₄	—	5	1	no	—
313	C₂²×C₄	—	5	1	no	—
314	C₂²×C₄	—	10	2	no	—
315	C₂²×C₄	—	10	2	no	—
316	C₂²×C₄	—	10	4	no	—
317	C₂²×C₄	—	10	4	no	—
318	C₂²×C₄	C₈×D₅	1	1	yes	characteristic
319	C₂²×C₄	C₈×D₅	1	1	yes	characteristic
320	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	5	1	no	—
324	C₂×C₈	—	5	1	no	—
325	C₂×C₈	—	5	4	no	—
326	C₂×C₈	—	5	4	no	—
327	C₂×C₈	—	5	1	no	—
328	C₂×C₈	—	5	1	no	—
329	C₂×C₈	—	10	2	no	—
330	C₂×C₈	—	10	2	no	—
331	C₂×C₈	—	10	2	no	—
332	C₂×C₈	—	10	2	no	—
333	C₂×C₈	—	10	2	no	—
334	C₂×C₈	—	10	2	no	—
335	C₂×C₈	—	10	2	no	—
336	C₂×C₈	—	10	2	no	—
337	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
338	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
339	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
340	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
341	C₄²	—	5	1	no	—
342	C₄²	—	5	1	no	—
343	C₄²	—	5	1	no	—
344	C₄²	—	5	1	no	—
345	C₄²	—	5	1	no	—
346	C₄²	—	5	1	no	—
347	C₄²	—	5	1	no	—
348	C₄²	—	5	1	no	—
349	C₄²	—	5	1	no	—
350	C₄²	—	5	1	no	—
351	C₄²	—	5	1	no	—
352	C₄²	—	5	1	no	—
353	C₄²	C₈×D₅	1	1	yes	characteristic
354	C₄²	C₈×D₅	1	1	yes	characteristic
355	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
356	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
357	C₁₆	—	2	4	no	—
358	C₁₆	—	10	4	no	—
359	C₂×C₅	—	2	2	no	—
360	C₂×C₅	C₂×#431	1	1	yes	characteristic
361	C₂×C₅	C₂²×M₃₂	1	1	yes	characteristic
362	C₂×C₅	C₂²×M₃₂	1	1	yes	characteristic
363	D₅	—	2	2	no	—
364	D₅	—	2	2	no	—
365	C₂³	—	5	1	no	—
366	C₂³	—	5	1	no	—
367	C₂³	—	10	2	no	—
368	C₂³	—	10	2	no	—
369	C₂³	—	10	2	no	—
370	C₂³	C₂×C₈×D₅	1	1	yes	characteristic
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	5	1	no	—
376	C₂×C₄	—	5	1	no	—
377	C₂×C₄	—	5	1	no	—
378	C₂×C₄	—	5	1	no	—
379	C₂×C₄	—	5	4	no	—
380	C₂×C₄	—	5	2	no	—
381	C₂×C₄	—	5	2	no	—
382	C₂×C₄	—	5	4	no	—
383	C₂×C₄	—	5	1	no	—
384	C₂×C₄	—	5	1	no	—
385	C₂×C₄	—	10	2	no	—
386	C₂×C₄	—	10	2	no	—
387	C₂×C₄	—	10	2	no	—
388	C₂×C₄	—	10	2	no	—
389	C₂×C₄	—	10	2	no	—
390	C₂×C₄	—	10	2	no	—
391	C₂×C₄	—	10	2	no	—
392	C₂×C₄	—	10	2	no	—
393	C₂×C₄	—	10	2	no	—
394	C₂×C₄	—	10	2	no	—
395	C₂×C₄	—	10	1	no	—
396	C₂×C₄	—	10	1	no	—
397	C₂×C₄	—	10	2	no	—
398	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
399	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
400	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
401	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
402	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
403	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
404	C₈	—	2	1	no	—
405	C₈	—	2	1	no	—
406	C₈	—	5	2	no	—
407	C₈	—	5	2	no	—
408	C₈	—	10	1	no	—
409	C₈	—	10	1	no	—
410	C₈	D₅×M₁₆	1	2	yes	—
411	C₈	D₅×#41	1	2	yes	—
412	C₅	#33418	1	1	yes	characteristic, complemented, Sylow
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	5	2	no	—
416	C₂²	—	5	2	no	—
417	C₂²	—	10	8	no	—
418	C₂²	—	10	1	no	—
419	C₂²	—	10	1	no	—
420	C₂²	—	10	1	no	—
421	C₂²	—	10	1	no	—
422	C₂²	D₅×M₃₂	1	2	yes	—
423	C₂²	C₂²×C₈×D₅	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	5	2	no	—
429	C₄	—	5	2	no	—
430	C₄	—	5	2	no	—
431	C₄	—	5	2	no	—
432	C₄	—	10	1	no	—
433	C₄	—	10	1	no	—
434	C₄	D₅×M₃₂	1	2	yes	—
435	C₄	D₅×#117	1	1	yes	characteristic
436	C₄	C₂×D₅×M₁₆	1	1	yes	characteristic
437	C₂	—	2	2	no	—
438	C₂	—	10	2	no	—
439	C₂	—	10	2	no	—
440	C₂	D₅×#431	1	1	yes	characteristic
441	C₂	C₂×D₅×M₃₂	1	1	yes	characteristic
442	C₂	C₂×D₅×M₃₂	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₅
commutator, socle	C₂²×C₅	C₂³×C₈
Fitting	C₅×#2163	C₂
prime radical	C₂³×D₅	C₂×C₈
cosocle	C₂×C₅×C₈	C₂⁴
hypercenter	#2163	D₅
hypocenter	C₅	#33418
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₈ ◁ #2163

Complements

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

N	H ≅ G/N	type
2. C₅×#2163	C₂	semidirect
3. #10600538	C₂	semidirect
4. #10600077	C₂	semidirect
5. #10600067	C₂	semidirect
7. #10599885	C₂	semidirect
8. #10599866	C₂	semidirect
9. #10599864	C₂	semidirect
26. C₅×C₄⋊C₁₆	C₂²	semidirect
28. C₅×#346	C₂²	semidirect
31. #64721	C₂²	semidirect
32. C₁₆×Dic₅	C₂²	semidirect
33. C₄⋊#672	C₂²	semidirect
34. #64681	C₂²	semidirect
87. #2163	D₅	semidirect
172. C₄⋊C₁₆	C₂×D₅	semidirect
177. #346	C₂×D₅	semidirect
197. C₂×Dic₅	M₃₂	semidirect
215. C₄×D₅	M₃₂	semidirect
412. C₅	#33418	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₈×D₅	2
C₅×#2163	2
#10600538	2
#10600077	2
#10600067	2
#10599899	2
#10599885	2
#10599866	2
#10599864	2
#33418	5