Subgroups — #498479

Order 512.

655 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×#2169	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#21491	C₂	1	1	yes	maximal, characteristic
4	#13121	C₂	1	1	yes	maximal, characteristic, complemented
5	#13120	C₂	1	1	yes	maximal, characteristic, complemented
6	#13104	C₂	1	1	yes	maximal, characteristic, complemented
7	#13104	C₂	1	1	yes	maximal, characteristic, complemented
8	#12977	C₂	1	1	yes	maximal, characteristic, complemented
9	#12977	C₂	1	1	yes	maximal, characteristic, complemented
10	#12976	C₂	1	1	yes	maximal, characteristic, complemented
11	#12976	C₂	1	1	yes	maximal, characteristic, complemented
12	#12612	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₆×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	#12600	C₂	1	1	yes	maximal, characteristic, complemented
15	#12545	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×M₃₂	C₂²	1	1	yes	characteristic
17	C₂²×M₃₂	C₂²	1	1	yes	characteristic
18	C₂³×C₁₆	C₂²	1	1	yes	characteristic
19	C₂³×C₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₈×D₄	C₂²	1	1	yes	characteristic
21	C₂×C₈×D₄	C₂²	1	1	yes	characteristic
22	C₂×C₈×D₄	C₂²	1	1	yes	characteristic
23	C₂×#405	C₂²	1	1	yes	characteristic
24	#2392	C₄	1	1	yes	characteristic
25	#2169	—	2	4	no	—
26	D₄×C₁₆	—	2	4	no	—
27	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
37	C₂×#346	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
41	#1955	C₄	1	1	yes	characteristic
42	#1940	C₄	1	1	yes	characteristic
43	#1924	C₄	1	1	yes	characteristic
44	#1924	C₄	1	1	yes	characteristic
45	#1870	C₄	1	1	yes	characteristic
46	#1870	C₄	1	1	yes	characteristic
47	#1798	C₄	1	1	yes	characteristic
48	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
50	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
51	#1374	C₂²	1	1	yes	characteristic
52	#1374	C₂²	1	1	yes	characteristic
53	#1374	C₂²	1	1	yes	characteristic
54	#1374	C₂²	1	1	yes	characteristic
55	#1374	C₂²	1	1	yes	characteristic
56	#1374	C₂²	1	1	yes	characteristic
57	#1374	C₂²	1	1	yes	characteristic
58	#1374	C₂²	1	1	yes	characteristic
59	#1374	C₂²	1	1	yes	characteristic
60	#1374	C₂²	1	1	yes	characteristic
61	C₂²×M₁₆	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₈	C₂³	1	1	yes	characteristic
63	C₂³×C₈	C₂³	1	1	yes	characteristic
64	C₂³×C₈	C₂³	1	1	yes	characteristic
65	C₂×C₄×D₄	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄×D₄	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄×D₄	C₂×C₄	1	1	yes	characteristic
68	C₂×#117	C₂×C₄	1	1	yes	characteristic
69	C₂×M₃₂	—	2	2	no	—
70	C₂×M₃₂	—	2	2	no	—
71	C₂×M₃₂	—	2	2	no	—
72	C₂×M₃₂	—	2	2	no	—
73	C₂×M₃₂	—	4	1	no	—
74	C₂×M₃₂	—	4	1	no	—
75	C₂²×C₁₆	—	2	2	no	—
76	C₂²×C₁₆	—	2	2	no	—
77	C₂²×C₁₆	—	2	2	no	—
78	C₂²×C₁₆	—	2	2	no	—
79	C₂²×C₁₆	—	4	1	no	—
80	C₂²×C₁₆	—	4	1	no	—
81	C₂²×C₁₆	C₂³	1	1	yes	characteristic
82	C₂²×C₁₆	C₂³	1	1	yes	characteristic
83	C₂²×C₁₆	C₂³	1	1	yes	characteristic
84	C₂²×C₁₆	C₂³	1	1	yes	characteristic
85	C₂²×C₁₆	C₂³	1	1	yes	characteristic
86	C₂²×C₁₆	C₂³	1	1	yes	characteristic
87	C₂²×C₁₆	C₂³	1	1	yes	characteristic
88	C₂²×C₁₆	C₂³	1	1	yes	characteristic
89	C₈×D₄	—	2	2	no	—
90	C₈×D₄	—	2	2	no	—
91	C₈×D₄	—	2	2	no	—
92	C₈×D₄	—	2	2	no	—
93	C₈×D₄	—	4	1	no	—
94	C₈×D₄	—	4	1	no	—
95	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
99	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
100	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
101	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
102	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
103	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
104	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
105	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
106	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
107	#405	—	4	1	no	—
108	#405	—	4	1	no	—
109	C₂×#97	C₂×C₄	1	1	yes	characteristic
110	C₂×#97	C₂×C₄	1	1	yes	characteristic
111	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
112	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
113	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
114	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
115	#398	C₈	1	1	yes	characteristic
116	#397	C₈	1	1	yes	characteristic
117	#396	C₈	1	1	yes	characteristic
118	#396	C₈	1	1	yes	characteristic
119	#394	C₈	1	1	yes	characteristic
120	#394	C₈	1	1	yes	characteristic
121	#394	C₈	1	1	yes	characteristic
122	#392	C₈	1	1	yes	characteristic
123	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
124	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
125	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
126	C₄⋊C₁₆	—	2	2	no	—
127	C₄⋊C₁₆	—	2	2	no	—
128	C₂²⋊C₁₆	—	2	2	no	—
129	C₂²⋊C₁₆	—	2	2	no	—
130	C₂²⋊C₁₆	—	2	2	no	—
131	C₂²⋊C₁₆	—	2	2	no	—
132	C₂²⋊C₁₆	—	2	2	no	—
133	C₂²⋊C₁₆	—	4	1	no	—
134	C₂²⋊C₁₆	—	4	1	no	—
135	C₂²⋊C₁₆	D₄	1	4	yes	complemented
136	#346	—	4	1	no	—
137	C₄×C₁₆	—	2	2	no	—
138	C₄×C₁₆	—	2	2	no	—
139	C₄×C₁₆	—	4	1	no	—
140	#336	C₂×C₄	1	1	yes	characteristic
141	#336	C₂×C₄	1	1	yes	characteristic
142	#336	C₂×C₄	1	1	yes	characteristic
143	#336	C₂×C₄	1	1	yes	characteristic
144	#336	C₂×C₄	1	1	yes	characteristic
145	#336	C₂×C₄	1	1	yes	characteristic
146	C₂²×D₄	C₂×C₈	1	1	yes	characteristic
147	C₂²×D₄	C₂×C₈	1	1	yes	characteristic
148	C₂²×D₄	C₂×C₈	1	1	yes	characteristic
149	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
150	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
151	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
152	C₂×M₁₆	—	2	2	no	—
153	C₂×M₁₆	—	2	2	no	—
154	C₂×M₁₆	—	4	1	no	—
155	C₂²×C₈	—	2	1	no	—
156	C₂²×C₈	—	2	1	no	—
157	C₂²×C₈	—	2	1	no	—
158	C₂²×C₈	—	2	1	no	—
159	C₂²×C₈	—	2	1	no	—
160	C₂²×C₈	—	2	1	no	—
161	C₂²×C₈	—	2	1	no	—
162	C₂²×C₈	—	2	1	no	—
163	C₂²×C₈	—	2	1	no	—
164	C₂²×C₈	—	2	1	no	—
165	C₂²×C₈	—	2	1	no	—
166	C₂²×C₈	—	2	1	no	—
167	C₂²×C₈	—	2	1	no	—
168	C₂²×C₈	—	2	1	no	—
169	C₂²×C₈	—	2	1	no	—
170	C₂²×C₈	—	2	1	no	—
171	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₈	C₂×D₄	1	2	yes	—
179	C₂²×C₈	#41	1	2	yes	—
180	C₂²×C₈	C₂⁴	1	1	yes	characteristic
181	C₄×D₄	—	2	2	no	—
182	C₄×D₄	—	2	2	no	—
183	C₄×D₄	—	2	2	no	—
184	C₄×D₄	—	2	2	no	—
185	C₄×D₄	—	4	1	no	—
186	C₄×D₄	—	4	1	no	—
187	#117	—	4	1	no	—
188	#117	—	4	1	no	—
189	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
190	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
191	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
192	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
193	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
194	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
195	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
196	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
197	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
198	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
199	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
200	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
201	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
202	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
203	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
204	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
205	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
206	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
207	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
208	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
209	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
210	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
211	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
212	M₃₂	—	4	4	no	—
213	M₃₂	—	4	4	no	—
214	C₂×C₁₆	—	2	1	no	—
215	C₂×C₁₆	—	2	1	no	—
216	C₂×C₁₆	—	2	1	no	—
217	C₂×C₁₆	—	2	1	no	—
218	C₂×C₁₆	—	2	1	no	—
219	C₂×C₁₆	—	2	1	no	—
220	C₂×C₁₆	—	2	1	no	—
221	C₂×C₁₆	—	2	1	no	—
222	C₂×C₁₆	—	2	1	no	—
223	C₂×C₁₆	—	2	1	no	—
224	C₂×C₁₆	—	2	1	no	—
225	C₂×C₁₆	—	2	1	no	—
226	C₂×C₁₆	—	2	1	no	—
227	C₂×C₁₆	—	2	1	no	—
228	C₂×C₁₆	—	2	1	no	—
229	C₂×C₁₆	—	2	1	no	—
230	C₂×C₁₆	—	2	1	no	—
231	C₂×C₁₆	—	2	1	no	—
232	C₂×C₁₆	—	2	1	no	—
233	C₂×C₁₆	—	2	1	no	—
234	C₂×C₁₆	—	4	4	no	—
235	C₂×C₁₆	—	4	4	no	—
236	C₂×C₁₆	C₂×D₄	1	2	yes	—
237	C₂×C₁₆	C₂×D₄	1	2	yes	—
238	C₂×C₁₆	#41	1	2	yes	—
239	C₂×C₁₆	#41	1	2	yes	—
240	C₄⋊C₈	—	2	2	no	—
241	C₄⋊C₈	—	2	2	no	—
242	C₄⋊C₈	—	4	1	no	—
243	C₄⋊C₈	—	4	1	no	—
244	C₂²⋊C₈	—	2	2	no	—
245	C₂²⋊C₈	—	2	2	no	—
246	C₂²⋊C₈	—	2	2	no	—
247	C₂²⋊C₈	—	2	2	no	—
248	C₂²⋊C₈	—	2	2	no	—
249	C₂²⋊C₈	—	2	2	no	—
250	C₂²⋊C₈	—	4	1	no	—
251	C₂²⋊C₈	—	4	1	no	—
252	#97	—	4	1	no	—
253	#97	—	4	1	no	—
254	C₄×C₈	—	2	1	no	—
255	C₄×C₈	—	2	1	no	—
256	C₄×C₈	—	2	1	no	—
257	C₄×C₈	—	2	1	no	—
258	C₄×C₈	—	2	1	no	—
259	C₄×C₈	—	2	1	no	—
260	C₄×C₈	—	2	1	no	—
261	C₄×C₈	—	2	1	no	—
262	#95	C₂×C₈	1	1	yes	characteristic
263	#95	C₂×C₈	1	1	yes	characteristic
264	#95	C₂×C₈	1	1	yes	characteristic
265	#95	C₂×C₈	1	1	yes	characteristic
266	#95	C₂×C₈	1	1	yes	characteristic
267	#95	C₂×C₈	1	1	yes	characteristic
268	C₂⁴	C₂²×C₈	1	1	yes	characteristic
269	C₂⁴	C₂²×C₈	1	1	yes	characteristic
270	C₂⁴	C₂²×C₈	1	1	yes	characteristic
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	2	2	no	—
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	—	4	1	no	—
278	C₂×D₄	—	4	1	no	—
279	C₂×D₄	—	4	1	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	C₄×D₄	1	2	yes	—
297	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
298	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
299	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
300	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
301	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
302	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
303	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
304	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
305	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
306	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
307	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
308	C₂²×C₄	#131	1	2	yes	—
309	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
310	M₁₆	—	4	4	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	4	1	no	—
336	C₂×C₈	—	4	1	no	—
337	C₂×C₈	—	4	1	no	—
338	C₂×C₈	—	4	1	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	4	1	no	—
342	C₂×C₈	C₄×D₄	1	2	yes	—
343	C₂×C₈	#131	1	2	yes	—
344	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₈	C₂×#41	1	1	yes	characteristic
346	C₂×C₈	C₂×#41	1	1	yes	characteristic
347	C₂×C₈	C₂×#41	1	1	yes	characteristic
348	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
349	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	4	1	no	—
355	C₄⋊C₄	—	4	1	no	—
356	C₄⋊C₄	—	4	1	no	—
357	C₂²⋊C₄	—	2	2	no	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₂²⋊C₄	—	2	2	no	—
361	C₂²⋊C₄	—	2	2	no	—
362	C₂²⋊C₄	—	2	2	no	—
363	C₂²⋊C₄	—	2	2	no	—
364	C₂²⋊C₄	—	4	1	no	—
365	C₂²⋊C₄	—	4	1	no	—
366	C₂²⋊C₄	—	4	1	no	—
367	C₂²⋊C₄	—	4	1	no	—
368	C₂²⋊C₄	—	4	1	no	—
369	C₄²	—	2	1	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₄²	—	2	1	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	1	no	—
377	C₁₆	—	2	2	no	—
378	C₁₆	—	2	2	no	—
379	C₁₆	—	2	2	no	—
380	C₁₆	—	2	2	no	—
381	C₁₆	—	4	1	no	—
382	C₁₆	—	4	1	no	—
383	C₁₆	—	4	1	no	—
384	C₁₆	—	4	1	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	1	no	—
388	C₂³	—	2	1	no	—
389	C₂³	—	2	1	no	—
390	C₂³	—	2	1	no	—
391	C₂³	—	2	1	no	—
392	C₂³	—	2	1	no	—
393	C₂³	—	2	1	no	—
394	C₂³	—	2	1	no	—
395	C₂³	—	2	1	no	—
396	C₂³	—	2	1	no	—
397	C₂³	—	2	1	no	—
398	C₂³	—	2	1	no	—
399	C₂³	—	2	1	no	—
400	C₂³	—	2	1	no	—
401	C₂³	—	2	1	no	—
402	C₂³	—	2	1	no	—
403	C₂³	—	2	1	no	—
404	C₂³	C₈×D₄	1	2	yes	—
405	C₂³	#504	1	2	yes	—
406	C₂³	C₂³×C₈	1	1	yes	characteristic
407	D₄	—	2	8	no	—
408	D₄	—	4	4	no	—
409	D₄	—	4	4	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	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	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	C₈×D₄	1	2	yes	—
453	C₂×C₄	#504	1	2	yes	—
454	C₂×C₄	#504	1	2	yes	—
455	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
456	C₂×C₄	C₄×#41	1	1	yes	characteristic
457	C₂×C₄	#518	1	1	yes	characteristic
458	C₂×C₄	C₂×#131	1	1	yes	characteristic
459	C₂×C₄	C₂×#131	1	1	yes	characteristic
460	C₂×C₄	#568	1	1	yes	characteristic
461	C₈	—	2	2	no	—
462	C₈	—	2	2	no	—
463	C₈	—	4	1	no	—
464	C₈	—	4	1	no	—
465	C₈	—	4	1	no	—
466	C₈	—	4	1	no	—
467	C₈	—	4	1	no	—
468	C₈	#546	1	1	yes	characteristic
469	C₈	#546	1	1	yes	characteristic
470	C₈	#553	1	1	yes	characteristic
471	C₈	#553	1	1	yes	characteristic
472	C₂²	—	2	2	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	4	1	no	—
479	C₂²	—	4	1	no	—
480	C₂²	—	4	1	no	—
481	C₂²	—	4	1	no	—
482	C₂²	—	4	1	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	4	1	no	—
486	C₂²	—	4	1	no	—
487	C₂²	—	4	1	no	—
488	C₂²	—	4	1	no	—
489	C₂²	—	4	1	no	—
490	C₂²	—	4	1	no	—
491	C₂²	—	4	1	no	—
492	C₂²	—	4	1	no	—
493	C₂²	C₂×C₈×D₄	1	1	yes	characteristic
494	C₂²	C₈×#41	1	1	yes	characteristic
495	C₂²	#2972	1	1	yes	characteristic
496	C₂²	C₂×#504	1	1	yes	characteristic
497	C₂²	C₂×#504	1	1	yes	characteristic
498	C₂²	C₂×#504	1	1	yes	characteristic
499	C₂²	#3407	1	1	yes	characteristic
500	C₄	—	2	2	no	—
501	C₄	—	2	2	no	—
502	C₄	—	2	2	no	—
503	C₄	—	4	1	no	—
504	C₄	—	4	1	no	—
505	C₄	—	4	1	no	—
506	C₄	—	4	1	no	—
507	C₄	—	4	1	no	—
508	C₄	—	4	1	no	—
509	C₄	—	4	1	no	—
510	C₄	—	4	1	no	—
511	C₄	#2364	1	1	yes	characteristic
512	C₄	#2935	1	1	yes	characteristic
513	C₄	#2968	1	1	yes	characteristic
514	C₄	#2977	1	1	yes	characteristic
515	C₂	—	4	2	no	—
516	C₂	—	4	2	no	—
517	C₂	—	8	1	no	—
518	C₂	#23116	1	1	yes	characteristic
519	C₂	#33432	1	1	yes	characteristic
520	C₂	#33436	1	1	yes	characteristic
521	C₂	#33480	1	1	yes	characteristic
522	C₂	#33483	1	1	yes	characteristic
523	C₂	#33490	1	1	yes	characteristic
524	C₂	#33493	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, cosocle	C₂²×C₈	C₂⁴
commutator, socle	C₂³	C₂³×C₈
prime radical	#392	C₈
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₈ ◁ G
LECS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×#2169	C₂	semidirect
2. C₂×D₄×C₁₆	C₂	semidirect
4. #13121	C₂	semidirect
5. #13120	C₂	semidirect
6. #13104	C₂	semidirect
7. #13104	C₂	semidirect
8. #12977	C₂	semidirect
9. #12977	C₂	semidirect
10. #12976	C₂	semidirect
11. #12976	C₂	semidirect
12. #12612	C₂	semidirect
13. C₁₆×C₂²⋊C₄	C₂	semidirect
14. #12600	C₂	semidirect
15. #12545	C₂	semidirect
135. C₂²⋊C₁₆	D₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#2169	2
C₂×D₄×C₁₆	2
#21491	2
#13121	2
#13120	2
#13104	2
#12977	2
#12976	2
#12612	2
C₁₆×C₂²⋊C₄	2
#12600	2
#12545	2