Subgroups — #12252510

Order 1280.

734 conjugacy classes of subgroups.

The subgroup lattice has 582 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×#3930	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×D₄×D₅	C₂	1	1	yes	maximal, characteristic
4	C₅×#2168	C₂	1	1	yes	maximal, characteristic, complemented
5	#10602223	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₆×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601650	C₂	1	1	yes	maximal, characteristic, complemented
8	#10600077	C₂	1	1	yes	maximal, characteristic, complemented
9	#10600071	C₂	1	1	yes	maximal, characteristic, complemented
10	#10599899	C₂	1	1	yes	maximal, characteristic, complemented
11	#10599899	C₂	1	1	yes	maximal, characteristic, complemented
12	#10599897	C₂	1	1	yes	maximal, characteristic, complemented
13	#10599894	C₂	1	1	yes	maximal, characteristic, complemented
14	#10599868	C₂	1	1	yes	maximal, characteristic, complemented
15	#10599864	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
17	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
18	C₄×D₄×D₅	C₄	1	1	yes	characteristic
19	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
21	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
22	C₈×C₂²⋊D₅	C₂²	1	1	yes	characteristic
23	C₈×C₂²⋊D₅	C₂²	1	1	yes	characteristic
24	C₂×#3944	C₂²	1	1	yes	characteristic, complemented
25	C₂²×#672	C₂²	1	1	yes	characteristic, complemented
26	D₄×#168	C₄	1	1	yes	characteristic
27	D₅×M₃₂	—	2	4	no	—
28	C₂×#3930	—	2	4	no	—
29	C₂×#3930	C₂²	1	1	yes	characteristic
30	C₂×#3930	C₂²	1	1	yes	characteristic
31	C₂×#3930	C₂²	1	1	yes	characteristic
32	C₂×#3930	C₂²	1	1	yes	characteristic
33	C₂×#3930	C₂²	1	1	yes	characteristic, complemented
34	C₂×#3930	C₂²	1	1	yes	characteristic, complemented
35	C₂×D₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
36	C₂×D₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
37	#65123	C₄	1	1	yes	characteristic
38	D₅×C₄⋊C₈	C₄	1	1	yes	characteristic
39	#65014	C₄	1	1	yes	characteristic
40	#65014	C₄	1	1	yes	characteristic
41	D₅×C₂²⋊C₈	C₄	1	1	yes	characteristic
42	D₅×C₂²⋊C₈	C₄	1	1	yes	characteristic
43	C₈×D₂₀	C₂²	1	1	yes	characteristic
44	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
45	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
46	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
47	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
48	C₅×#346	C₂²	1	1	yes	characteristic, complemented
49	C₂²⋊#672	C₂²	1	1	yes	characteristic, complemented
50	C₂²⋊#672	C₂²	1	1	yes	characteristic, complemented
51	#64727	C₂²	1	1	yes	characteristic, complemented
52	#64727	C₂²	1	1	yes	characteristic, complemented
53	#64727	C₂²	1	1	yes	characteristic, complemented
54	#64727	C₂²	1	1	yes	characteristic, complemented
55	#64721	C₂²	1	1	yes	characteristic, complemented
56	#64721	C₂²	1	1	yes	characteristic, complemented
57	C₁₆×Dic₅	C₂²	1	1	yes	characteristic, complemented
58	C₁₆×Dic₅	C₂²	1	1	yes	characteristic, complemented
59	C₄⋊#672	C₂²	1	1	yes	characteristic, complemented
60	#64681	C₂²	1	1	yes	characteristic, complemented
61	D₄×M₃₂	—	5	1	no	maximal, Sylow
62	C₂×D₄×D₅	C₈	1	1	yes	characteristic
63	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
68	D₄×Dic₅	C₈	1	1	yes	characteristic
69	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
70	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
71	C₂²×#168	C₂×C₄	1	1	yes	characteristic
72	C₂²×#168	C₂×C₄	1	1	yes	characteristic
73	C₂×C₈×D₅	—	2	2	no	—
74	C₂×C₈×D₅	—	2	2	no	—
75	C₂×C₈×D₅	—	2	2	no	—
76	C₂×C₈×D₅	—	2	2	no	—
77	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
78	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
79	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
80	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
81	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
82	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
83	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
84	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
85	#4039	C₈	1	1	yes	characteristic
86	D₅×C₄⋊C₄	C₈	1	1	yes	characteristic
87	#4027	C₈	1	1	yes	characteristic
88	#4027	C₈	1	1	yes	characteristic
89	D₅×C₂²⋊C₄	C₈	1	1	yes	characteristic
90	D₅×C₂²⋊C₄	C₈	1	1	yes	characteristic
91	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
92	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
93	C₅×M₃₂	—	2	2	no	—
94	C₂×C₅×C₁₆	—	2	2	no	—
95	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
96	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
97	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
98	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
99	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
100	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
101	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
102	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
103	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
104	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
105	#3952	C₂×C₄	1	1	yes	characteristic
106	#3952	C₂×C₄	1	1	yes	characteristic
107	#3952	C₂×C₄	1	1	yes	characteristic
108	#3952	C₂×C₄	1	1	yes	characteristic
109	#3946	C₂×C₄	1	1	yes	characteristic
110	#3946	C₂×C₄	1	1	yes	characteristic
111	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
112	C₈×Dic₅	C₂³	1	1	yes	characteristic
113	#3944	—	2	2	no	—
114	C₂×#672	—	2	2	no	—
115	C₂×#672	C₂³	1	1	yes	characteristic
116	C₂×#672	C₂³	1	1	yes	characteristic
117	C₂×#672	C₂³	1	1	yes	characteristic
118	C₂×#672	C₂³	1	1	yes	characteristic
119	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
120	C₄×#168	C₂×C₄	1	1	yes	characteristic
121	#3930	—	2	2	no	—
122	#3930	—	2	2	no	—
123	#3930	—	2	2	no	—
124	#3930	—	2	2	no	—
125	#3930	—	2	2	no	—
126	#3930	D₄	1	4	yes	complemented
127	D₅×C₁₆	—	2	2	no	—
128	D₅×C₁₆	—	2	2	no	—
129	C₂²×M₃₂	—	5	1	no	—
130	C₂²×M₃₂	—	5	1	no	—
131	C₂×C₈×D₄	—	5	1	no	—
132	#2169	—	5	1	no	—
133	#2169	—	5	1	no	—
134	#2168	—	5	1	no	—
135	#2168	—	5	1	no	—
136	#2168	—	5	1	no	—
137	#2168	D₅	1	1	yes	characteristic, complemented
138	D₄×C₁₆	—	5	1	no	—
139	D₄×C₁₆	—	5	1	no	—
140	#2150	—	5	1	no	—
141	#2112	—	5	1	no	—
142	#2112	—	5	1	no	—
143	C₄×M₃₂	—	5	1	no	—
144	C₂³×D₅	C₂×C₈	1	1	yes	characteristic
145	C₂³×D₅	C₂×C₈	1	1	yes	characteristic
146	C₂×C₅×D₄	C₂×C₈	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₂²⋊D₅	C₂×C₈	1	1	yes	characteristic
150	C₂×C₂²⋊D₅	C₂×C₈	1	1	yes	characteristic
151	C₂²×Dic₅	C₂×C₈	1	1	yes	characteristic
152	C₂²×Dic₅	C₂×C₈	1	1	yes	characteristic
153	D₄×D₅	—	2	4	no	—
154	C₂×D₂₀	C₂×C₈	1	1	yes	characteristic
155	C₂×C₄×D₅	—	2	2	no	—
156	C₂×C₄×D₅	—	2	2	no	—
157	C₂×C₄×D₅	—	2	2	no	—
158	C₂×C₄×D₅	—	2	2	no	—
159	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
160	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
161	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
162	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
163	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
164	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
165	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₅×C₈	—	2	1	no	—
169	C₂×C₅×C₈	—	2	1	no	—
170	C₂×C₅×C₈	—	2	1	no	—
171	C₂×C₅×C₈	—	2	1	no	—
172	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
176	C₅×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
177	C₅×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
178	C₅×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
179	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
180	C₂²⋊Dic₅	C₂×C₈	1	1	yes	characteristic
181	C₂²⋊Dic₅	C₂×C₈	1	1	yes	characteristic
182	#685	C₂×C₈	1	1	yes	characteristic
183	#685	C₂×C₈	1	1	yes	characteristic
184	#685	C₂×C₈	1	1	yes	characteristic
185	#685	C₂×C₈	1	1	yes	characteristic
186	C₄⋊Dic₅	C₂×C₈	1	1	yes	characteristic
187	#683	C₂×C₈	1	1	yes	characteristic
188	#683	C₂×C₈	1	1	yes	characteristic
189	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
190	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
191	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
192	C₂×#168	—	2	2	no	—
193	C₂×#168	—	2	2	no	—
194	C₂×#168	C₂²×C₄	1	1	yes	characteristic
195	C₂×#168	C₂²×C₄	1	1	yes	characteristic
196	C₂×#168	C₂²×C₄	1	1	yes	characteristic
197	C₂×#168	C₂²×C₄	1	1	yes	characteristic
198	C₈×D₅	—	2	2	no	—
199	C₈×D₅	—	2	2	no	—
200	C₈×D₅	—	2	2	no	—
201	C₈×D₅	—	2	1	no	—
202	C₈×D₅	—	2	1	no	—
203	C₈×D₅	—	2	1	no	—
204	C₈×D₅	—	2	1	no	—
205	C₈×D₅	—	2	2	no	—
206	C₈×D₅	—	2	2	no	—
207	C₈×D₅	C₂×D₄	1	2	yes	—
208	C₈×D₅	#41	1	2	yes	—
209	C₅×C₁₆	—	2	1	no	—
210	C₅×C₁₆	—	2	1	no	—
211	C₅×C₁₆	—	2	1	no	—
212	C₅×C₁₆	C₂×D₄	1	2	yes	complemented
213	#672	—	2	1	no	—
214	#672	—	2	1	no	—
215	#672	—	2	1	no	—
216	#672	C₂×D₄	1	2	yes	complemented
217	C₂³×C₈	—	5	1	no	—
218	C₂³×C₈	—	5	1	no	—
219	C₂×C₄×D₄	—	5	1	no	—
220	C₂×M₃₂	—	5	1	no	—
221	C₂×M₃₂	—	5	1	no	—
222	C₂×M₃₂	—	5	1	no	—
223	C₂×M₃₂	—	5	1	no	—
224	C₂×M₃₂	—	5	1	no	—
225	C₂×M₃₂	—	5	1	no	—
226	C₂×M₃₂	—	5	1	no	—
227	C₂×M₃₂	—	10	4	no	—
228	C₂×M₃₂	—	10	4	no	—
229	C₂×M₃₂	C₂×D₅	1	1	yes	characteristic, complemented
230	C₂²×C₁₆	—	5	1	no	—
231	C₂²×C₁₆	—	5	1	no	—
232	C₂²×C₁₆	—	5	1	no	—
233	C₂²×C₁₆	C₂×D₅	1	1	yes	characteristic, complemented
234	C₈×D₄	—	5	1	no	—
235	C₈×D₄	—	5	1	no	—
236	C₈×D₄	—	5	1	no	—
237	C₈×D₄	—	5	1	no	—
238	C₈×D₄	—	5	1	no	—
239	C₈×D₄	—	5	1	no	—
240	C₈×D₄	—	5	1	no	—
241	C₈×D₄	C₂×D₅	1	1	yes	characteristic
242	C₂×C₄⋊C₈	—	5	1	no	—
243	C₂×C₂²⋊C₈	—	5	1	no	—
244	C₂×C₂²⋊C₈	—	5	1	no	—
245	C₂×C₄×C₈	—	5	1	no	—
246	C₄⋊C₁₆	—	5	1	no	—
247	C₄⋊C₁₆	—	5	1	no	—
248	C₄⋊C₁₆	—	5	1	no	—
249	C₄⋊C₁₆	C₂×D₅	1	1	yes	characteristic, complemented
250	C₂²⋊C₁₆	—	5	1	no	—
251	C₂²⋊C₁₆	—	5	1	no	—
252	C₂²⋊C₁₆	—	5	1	no	—
253	C₂²⋊C₁₆	—	5	1	no	—
254	C₂²⋊C₁₆	—	5	1	no	—
255	C₂²⋊C₁₆	—	5	1	no	—
256	C₂²⋊C₁₆	C₂×D₅	1	1	yes	characteristic, complemented
257	C₂²⋊C₁₆	C₂×D₅	1	1	yes	characteristic, complemented
258	#346	—	5	1	no	—
259	#346	C₂×D₅	1	1	yes	characteristic, complemented
260	C₄×C₁₆	—	5	1	no	—
261	C₄×C₁₆	—	5	1	no	—
262	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
263	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
264	C₂²×D₅	—	2	2	no	—
265	C₂²×D₅	—	2	2	no	—
266	C₂²×D₅	—	2	2	no	—
267	C₂²×D₅	—	2	2	no	—
268	C₂²×D₅	—	4	1	no	—
269	C₂²×D₅	—	4	1	no	—
270	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
271	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
272	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
273	C₅×D₄	—	2	2	no	—
274	C₂×C₄×C₅	—	2	1	no	—
275	C₂×C₄×C₅	—	2	1	no	—
276	C₂×C₄×C₅	—	2	1	no	—
277	C₂×C₄×C₅	—	2	1	no	—
278	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
279	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
280	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
281	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
282	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
283	C₂²⋊D₅	—	2	2	no	—
284	C₂²⋊D₅	M₃₂	1	4	yes	complemented
285	C₂×Dic₅	—	2	2	no	—
286	C₂×Dic₅	—	2	2	no	—
287	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
288	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
289	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
290	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
291	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
292	D₂₀	—	2	2	no	—
293	C₄×D₅	—	2	2	no	—
294	C₄×D₅	—	2	2	no	—
295	C₄×D₅	—	2	1	no	—
296	C₄×D₅	—	2	1	no	—
297	C₄×D₅	—	2	1	no	—
298	C₄×D₅	—	2	1	no	—
299	C₄×D₅	—	2	2	no	—
300	C₄×D₅	—	2	2	no	—
301	C₄×D₅	—	2	2	no	—
302	C₄×D₅	—	4	1	no	—
303	C₄×D₅	C₄×D₄	1	2	yes	—
304	C₄×D₅	#131	1	2	yes	—
305	C₅×C₈	—	2	1	no	—
306	C₅×C₈	—	2	1	no	—
307	C₅×C₈	—	2	1	no	—
308	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
309	C₅×C₈	C₂×#41	1	1	yes	characteristic
310	#168	—	2	1	no	—
311	#168	—	2	1	no	—
312	#168	—	2	1	no	—
313	#168	C₄×D₄	1	2	yes	—
314	C₂²×D₄	—	5	1	no	—
315	C₂³×C₄	—	5	1	no	—
316	C₂³×C₄	—	5	1	no	—
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	—	5	1	no	—
324	C₂²×C₈	—	5	1	no	—
325	C₂²×C₈	—	5	1	no	—
326	C₂²×C₈	—	5	1	no	—
327	C₂²×C₈	—	10	2	no	—
328	C₂²×C₈	—	10	2	no	—
329	C₂²×C₈	—	10	2	no	—
330	C₂²×C₈	—	10	2	no	—
331	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
332	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
333	C₄×D₄	—	5	1	no	—
334	C₄×D₄	—	5	1	no	—
335	C₄×D₄	—	5	1	no	—
336	C₄×D₄	—	5	1	no	—
337	C₄×D₄	—	5	1	no	—
338	C₄×D₄	—	5	1	no	—
339	C₄×D₄	—	5	1	no	—
340	C₄×D₄	C₄×D₅	1	1	yes	characteristic
341	C₂×C₄⋊C₄	—	5	1	no	—
342	C₂×C₂²⋊C₄	—	5	1	no	—
343	C₂×C₂²⋊C₄	—	5	1	no	—
344	C₂×C₄²	—	5	1	no	—
345	M₃₂	—	2	2	no	—
346	M₃₂	—	5	4	no	—
347	M₃₂	—	10	2	no	—
348	M₃₂	—	10	2	no	—
349	M₃₂	—	10	2	no	—
350	M₃₂	—	10	2	no	—
351	M₃₂	—	10	2	no	—
352	M₃₂	—	10	2	no	—
353	C₂×C₁₆	—	2	2	no	—
354	C₂×C₁₆	—	5	1	no	—
355	C₂×C₁₆	—	5	1	no	—
356	C₂×C₁₆	—	5	1	no	—
357	C₂×C₁₆	—	5	1	no	—
358	C₂×C₁₆	—	10	2	no	—
359	C₂×C₁₆	—	10	2	no	—
360	C₂×C₁₆	—	10	2	no	—
361	C₂×C₁₆	C₂²×D₅	1	1	yes	characteristic
362	C₂×C₁₆	C₂²×D₅	1	1	yes	characteristic
363	C₂×C₁₆	C₂²×D₅	1	1	yes	characteristic
364	C₂×C₁₆	C₂²×D₅	1	1	yes	characteristic
365	C₄⋊C₈	—	5	1	no	—
366	C₄⋊C₈	—	5	1	no	—
367	C₄⋊C₈	—	5	1	no	—
368	C₄⋊C₈	C₄×D₅	1	1	yes	characteristic
369	C₂²⋊C₈	—	5	1	no	—
370	C₂²⋊C₈	—	5	1	no	—
371	C₂²⋊C₈	—	5	1	no	—
372	C₂²⋊C₈	—	5	1	no	—
373	C₂²⋊C₈	—	5	1	no	—
374	C₂²⋊C₈	—	5	1	no	—
375	C₂²⋊C₈	C₄×D₅	1	1	yes	characteristic
376	C₂²⋊C₈	C₄×D₅	1	1	yes	characteristic
377	C₄×C₈	—	5	1	no	—
378	C₄×C₈	—	5	1	no	—
379	C₄×C₈	—	5	1	no	—
380	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
381	C₂²×C₅	—	2	1	no	—
382	C₂²×C₅	—	2	1	no	—
383	C₂²×C₅	—	2	1	no	—
384	C₂²×C₅	—	2	1	no	—
385	C₂²×C₅	—	2	1	no	—
386	C₂²×C₅	C₂×M₃₂	1	2	yes	complemented
387	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
388	C₂×D₅	—	2	1	no	—
389	C₂×D₅	—	2	1	no	—
390	C₂×D₅	—	2	1	no	—
391	C₂×D₅	—	2	1	no	—
392	C₂×D₅	—	2	1	no	—
393	C₂×D₅	—	2	1	no	—
394	C₂×D₅	—	2	1	no	—
395	C₂×D₅	—	4	4	no	—
396	C₂×D₅	—	4	4	no	—
397	C₂×D₅	C₈×D₄	1	2	yes	—
398	C₂×D₅	C₂×M₃₂	1	2	yes	complemented
399	C₄×C₅	—	2	1	no	—
400	C₄×C₅	—	2	1	no	—
401	C₄×C₅	—	2	1	no	—
402	C₄×C₅	—	2	1	no	—
403	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
404	C₄×C₅	C₂×#131	1	1	yes	characteristic
405	Dic₅	—	2	1	no	—
406	Dic₅	—	2	1	no	—
407	Dic₅	—	2	1	no	—
408	Dic₅	C₈×D₄	1	2	yes	—
409	Dic₅	C₂×M₃₂	1	2	yes	complemented
410	C₂⁴	—	5	1	no	—
411	C₂⁴	—	5	1	no	—
412	C₂×D₄	—	5	1	no	—
413	C₂×D₄	—	5	1	no	—
414	C₂×D₄	—	5	1	no	—
415	C₂×D₄	—	10	4	no	—
416	C₂×D₄	C₈×D₅	1	1	yes	characteristic
417	C₂²×C₄	—	5	1	no	—
418	C₂²×C₄	—	5	1	no	—
419	C₂²×C₄	—	5	1	no	—
420	C₂²×C₄	—	5	1	no	—
421	C₂²×C₄	—	5	1	no	—
422	C₂²×C₄	—	5	1	no	—
423	C₂²×C₄	—	5	1	no	—
424	C₂²×C₄	—	5	1	no	—
425	C₂²×C₄	—	5	1	no	—
426	C₂²×C₄	—	5	1	no	—
427	C₂²×C₄	—	5	1	no	—
428	C₂²×C₄	—	10	2	no	—
429	C₂²×C₄	—	10	2	no	—
430	C₂²×C₄	—	10	2	no	—
431	C₂²×C₄	—	10	2	no	—
432	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
433	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	5	1	no	—
439	C₂×C₈	—	5	2	no	—
440	C₂×C₈	—	5	2	no	—
441	C₂×C₈	—	5	1	no	—
442	C₂×C₈	—	5	1	no	—
443	C₂×C₈	—	5	1	no	—
444	C₂×C₈	—	10	2	no	—
445	C₂×C₈	—	10	2	no	—
446	C₂×C₈	—	10	2	no	—
447	C₂×C₈	—	10	2	no	—
448	C₂×C₈	—	10	2	no	—
449	C₂×C₈	—	10	2	no	—
450	C₂×C₈	—	10	2	no	—
451	C₂×C₈	—	10	1	no	—
452	C₂×C₈	—	10	1	no	—
453	C₂×C₈	—	10	1	no	—
454	C₂×C₈	—	10	1	no	—
455	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
456	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
457	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
458	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
459	C₄⋊C₄	—	5	1	no	—
460	C₄⋊C₄	—	5	1	no	—
461	C₄⋊C₄	—	5	1	no	—
462	C₄⋊C₄	C₈×D₅	1	1	yes	characteristic
463	C₂²⋊C₄	—	5	1	no	—
464	C₂²⋊C₄	—	5	1	no	—
465	C₂²⋊C₄	—	5	1	no	—
466	C₂²⋊C₄	—	5	1	no	—
467	C₂²⋊C₄	—	5	1	no	—
468	C₂²⋊C₄	—	5	1	no	—
469	C₂²⋊C₄	C₈×D₅	1	1	yes	characteristic
470	C₂²⋊C₄	C₈×D₅	1	1	yes	characteristic
471	C₄²	—	5	1	no	—
472	C₄²	—	5	1	no	—
473	C₄²	—	5	1	no	—
474	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
475	C₁₆	—	2	1	no	—
476	C₁₆	—	2	1	no	—
477	C₁₆	—	2	1	no	—
478	C₁₆	—	5	2	no	—
479	C₁₆	—	10	1	no	—
480	C₁₆	—	10	1	no	—
481	C₁₆	—	10	1	no	—
482	C₁₆	D₄×D₅	1	2	yes	complemented
483	C₂×C₅	—	2	2	no	—
484	C₂×C₅	—	4	1	no	—
485	C₂×C₅	C₂×C₈×D₄	1	1	yes	characteristic
486	C₂×C₅	C₂²×M₃₂	1	1	yes	characteristic
487	C₂×C₅	#3407	1	1	yes	characteristic
488	D₅	—	2	2	no	—
489	D₅	—	2	2	no	—
490	D₅	—	4	1	no	—
491	C₂³	—	5	1	no	—
492	C₂³	—	5	1	no	—
493	C₂³	—	5	1	no	—
494	C₂³	—	10	2	no	—
495	C₂³	—	10	2	no	—
496	C₂³	—	10	2	no	—
497	C₂³	—	10	2	no	—
498	C₂³	—	20	1	no	—
499	C₂³	—	20	1	no	—
500	C₂³	C₂×C₈×D₅	1	1	yes	characteristic
501	C₂³	C₂×C₈×D₅	1	1	yes	characteristic
502	D₄	—	2	2	no	—
503	D₄	—	5	4	no	—
504	D₄	—	10	2	no	—
505	D₄	—	10	2	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	5	1	no	—
511	C₂×C₄	—	5	1	no	—
512	C₂×C₄	—	5	2	no	—
513	C₂×C₄	—	5	2	no	—
514	C₂×C₄	—	5	1	no	—
515	C₂×C₄	—	5	1	no	—
516	C₂×C₄	—	5	1	no	—
517	C₂×C₄	—	10	2	no	—
518	C₂×C₄	—	10	2	no	—
519	C₂×C₄	—	10	2	no	—
520	C₂×C₄	—	10	2	no	—
521	C₂×C₄	—	10	2	no	—
522	C₂×C₄	—	10	2	no	—
523	C₂×C₄	—	10	2	no	—
524	C₂×C₄	—	10	1	no	—
525	C₂×C₄	—	10	1	no	—
526	C₂×C₄	—	10	1	no	—
527	C₂×C₄	—	10	1	no	—
528	C₂×C₄	—	20	1	no	—
529	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
530	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
531	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
532	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
533	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
534	C₈	—	2	1	no	—
535	C₈	—	2	1	no	—
536	C₈	—	2	1	no	—
537	C₈	—	5	2	no	—
538	C₈	—	10	1	no	—
539	C₈	—	10	1	no	—
540	C₈	—	10	1	no	—
541	C₈	C₂×D₄×D₅	1	1	yes	characteristic
542	C₈	D₅×#41	1	1	yes	characteristic
543	C₅	D₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	2	1	no	—
549	C₂²	—	5	2	no	—
550	C₂²	—	5	2	no	—
551	C₂²	—	10	1	no	—
552	C₂²	—	10	1	no	—
553	C₂²	—	10	1	no	—
554	C₂²	—	10	1	no	—
555	C₂²	—	10	1	no	—
556	C₂²	—	10	1	no	—
557	C₂²	—	10	1	no	—
558	C₂²	—	20	4	no	—
559	C₂²	—	20	4	no	—
560	C₂²	D₅×M₃₂	1	2	yes	complemented
561	C₂²	C₂²×C₈×D₅	1	1	yes	characteristic
562	C₄	—	2	1	no	—
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	2	1	no	—
566	C₄	—	5	2	no	—
567	C₄	—	5	2	no	—
568	C₄	—	10	1	no	—
569	C₄	—	10	1	no	—
570	C₄	—	10	1	no	—
571	C₄	C₄×D₄×D₅	1	1	yes	characteristic
572	C₄	D₅×#131	1	1	yes	characteristic
573	C₂	—	2	2	no	—
574	C₂	—	4	1	no	—
575	C₂	—	10	2	no	—
576	C₂	—	10	2	no	—
577	C₂	—	20	1	no	—
578	C₂	C₈×D₄×D₅	1	1	yes	characteristic
579	C₂	C₂×D₅×M₃₂	1	1	yes	characteristic
580	C₂	#10613743	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₅
commutator, socle	C₂²×C₅	C₂³×C₈
Fitting	C₅×#2168	C₂
prime radical	C₂×D₄×D₅	C₈
cosocle	C₂×C₅×C₈	C₂⁴
hypercenter	#2168	D₅
hypocenter	C₅	D₄×M₃₂
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₈ ◁ #2168

Complements

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

N	H ≅ G/N	type
1. C₂×D₅×M₃₂	C₂	semidirect
2. C₂²×#3930	C₂	semidirect
4. C₅×#2168	C₂	semidirect
5. #10602223	C₂	semidirect
6. C₁₆×C₂²⋊D₅	C₂	semidirect
7. #10601650	C₂	semidirect
8. #10600077	C₂	semidirect
9. #10600071	C₂	semidirect
10. #10599899	C₂	semidirect
11. #10599899	C₂	semidirect
12. #10599897	C₂	semidirect
13. #10599894	C₂	semidirect
14. #10599868	C₂	semidirect
15. #10599864	C₂	semidirect
19. C₂×C₅×M₃₂	C₂²	semidirect
20. C₂²×C₅×C₁₆	C₂²	semidirect
24. C₂×#3944	C₂²	semidirect
25. C₂²×#672	C₂²	semidirect
33. C₂×#3930	C₂²	semidirect
34. C₂×#3930	C₂²	semidirect
35. C₂×D₅×C₁₆	C₂²	semidirect
36. C₂×D₅×C₁₆	C₂²	semidirect
45. C₅×C₄⋊C₁₆	C₂²	semidirect
46. C₅×C₂²⋊C₁₆	C₂²	semidirect
47. C₅×C₂²⋊C₁₆	C₂²	semidirect
48. C₅×#346	C₂²	semidirect
49. C₂²⋊#672	C₂²	semidirect
50. C₂²⋊#672	C₂²	semidirect
51. #64727	C₂²	semidirect
52. #64727	C₂²	semidirect
53. #64727	C₂²	semidirect
54. #64727	C₂²	semidirect
55. #64721	C₂²	semidirect
56. #64721	C₂²	semidirect
57. C₁₆×Dic₅	C₂²	semidirect
58. C₁₆×Dic₅	C₂²	semidirect
59. C₄⋊#672	C₂²	semidirect
60. #64681	C₂²	semidirect
126. #3930	D₄	semidirect
137. #2168	D₅	semidirect
212. C₅×C₁₆	C₂×D₄	semidirect
216. #672	C₂×D₄	semidirect
229. C₂×M₃₂	C₂×D₅	semidirect
233. C₂²×C₁₆	C₂×D₅	semidirect
249. C₄⋊C₁₆	C₂×D₅	semidirect
256. C₂²⋊C₁₆	C₂×D₅	semidirect
257. C₂²⋊C₁₆	C₂×D₅	semidirect
259. #346	C₂×D₅	semidirect
284. C₂²⋊D₅	M₃₂	semidirect
386. C₂²×C₅	C₂×M₃₂	semidirect
398. C₂×D₅	C₂×M₃₂	semidirect
409. Dic₅	C₂×M₃₂	semidirect
482. C₁₆	D₄×D₅	semidirect
543. C₅	D₄×M₃₂	semidirect
560. 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×#3930	2
C₈×D₄×D₅	2
C₅×#2168	2
#10602223	2
C₁₆×C₂²⋊D₅	2
#10601650	2
#10600077	2
#10600071	2
#10599899	2
#10599897	2
#10599894	2
#10599868	2
#10599864	2
D₄×M₃₂	5