Subgroups — #203680

Order 512.

672 conjugacy classes of subgroups.

The subgroup lattice has 529 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21349	C₂	1	1	yes	maximal, characteristic
2	#20815	C₂	1	1	yes	maximal, characteristic
3	#20470	C₂	1	1	yes	maximal, characteristic
4	C₂×#1572	C₂	1	1	yes	maximal, characteristic
5	C₂×#1564	C₂	1	1	yes	maximal, characteristic
6	#9606	C₂	1	1	yes	maximal, characteristic, complemented
7	#9606	C₂	1	1	yes	maximal, characteristic, complemented
8	#9605	C₂	1	1	yes	maximal, characteristic, complemented
9	#9604	C₂	1	1	yes	maximal, characteristic, complemented
10	#9603	C₂	1	1	yes	maximal, characteristic, complemented
11	#9603	C₂	1	1	yes	maximal, characteristic, complemented
12	#9602	C₂	1	1	yes	maximal, characteristic, complemented
13	#9601	C₂	1	1	yes	maximal, characteristic, complemented
14	#7878	C₂	1	1	yes	maximal, characteristic
15	#7875	C₂	1	1	yes	maximal, characteristic
16	C₂×#432	C₂²	1	1	yes	characteristic
17	C₂×#432	C₂²	1	1	yes	characteristic
18	C₂×#431	C₂²	1	1	yes	characteristic
19	C₂×#431	C₂²	1	1	yes	characteristic
20	C₂×#431	C₂²	1	1	yes	characteristic
21	C₂²×C₄×C₈	C₂²	1	1	yes	characteristic
22	C₄×#117	C₂²	1	1	yes	characteristic
23	#1939	C₄	1	1	yes	characteristic
24	#1939	C₄	1	1	yes	characteristic
25	#1939	C₄	1	1	yes	characteristic
26	#1939	C₄	1	1	yes	characteristic
27	#1850	C₄	1	1	yes	characteristic
28	#1850	C₄	1	1	yes	characteristic
29	#1850	C₄	1	1	yes	characteristic
30	#1850	C₄	1	1	yes	characteristic
31	#1842	C₂²	1	1	yes	characteristic
32	#1842	C₂²	1	1	yes	characteristic
33	#1831	C₂²	1	1	yes	characteristic
34	#1831	C₂²	1	1	yes	characteristic
35	#1798	—	2	1	no	—
36	#1798	—	2	1	no	—
37	#1768	—	2	1	no	—
38	#1768	—	2	1	no	—
39	#1767	C₂²	1	1	yes	characteristic
40	#1767	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
44	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
45	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
47	#1750	—	2	1	no	—
48	#1750	—	2	1	no	—
49	#1746	—	2	1	no	—
50	#1726	—	2	1	no	—
51	#1572	—	2	4	no	—
52	#1564	—	2	4	no	—
53	C₂×#335	C₂²	1	1	yes	characteristic
54	C₂×#335	C₂²	1	1	yes	characteristic
55	C₂×#335	C₂²	1	1	yes	characteristic
56	C₂×#335	C₂²	1	1	yes	characteristic
57	C₂×#334	C₂²	1	1	yes	characteristic
58	C₂×#334	C₂²	1	1	yes	characteristic
59	C₂×#334	C₂²	1	1	yes	characteristic
60	C₂×#334	C₂²	1	1	yes	characteristic
61	#1277	C₂²	1	1	yes	characteristic
62	#1277	C₂²	1	1	yes	characteristic
63	#1277	C₂²	1	1	yes	characteristic
64	#1277	C₂²	1	1	yes	characteristic
65	#1277	C₂²	1	1	yes	characteristic
66	#1277	C₂²	1	1	yes	characteristic
67	#1277	C₂²	1	1	yes	characteristic
68	#1277	C₂²	1	1	yes	characteristic
69	C₂³×C₈	C₂×C₄	1	1	yes	characteristic
70	C₂³×C₈	C₂×C₄	1	1	yes	characteristic
71	C₂×#117	D₄	1	1	yes	characteristic
72	C₂×#117	D₄	1	1	yes	characteristic
73	C₂²×C₄²	C₂³	1	1	yes	characteristic
74	#432	—	2	2	no	—
75	#432	—	2	2	no	—
76	#432	—	2	2	no	—
77	#432	Q₈	1	4	yes	—
78	#431	—	2	2	no	—
79	#431	—	2	2	no	—
80	#431	—	2	2	no	—
81	#431	—	2	2	no	—
82	#431	—	2	2	no	—
83	#431	D₄	1	4	yes	—
84	C₂×C₄⋊C₈	—	2	1	no	—
85	C₂×C₄⋊C₈	—	2	1	no	—
86	C₂×C₄⋊C₈	—	2	1	no	—
87	C₂×C₄⋊C₈	—	2	1	no	—
88	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
106	C₂×C₂²⋊C₈	—	2	1	no	—
107	C₂×C₂²⋊C₈	—	2	1	no	—
108	C₂×C₂²⋊C₈	—	2	1	no	—
109	C₂×C₂²⋊C₈	—	2	1	no	—
110	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
111	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
112	C₂×#97	—	2	1	no	—
113	C₂×#97	—	2	1	no	—
114	C₂×#97	—	2	1	no	—
115	C₂×#97	—	2	1	no	—
116	C₂×C₄×C₈	—	2	2	no	—
117	C₂×C₄×C₈	—	2	1	no	—
118	C₂×C₄×C₈	—	2	2	no	—
119	C₂×C₄×C₈	—	2	1	no	—
120	C₂×C₄×C₈	—	2	1	no	—
121	C₂×C₄×C₈	—	2	1	no	—
122	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
123	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
124	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
125	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
126	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
127	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
128	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
129	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
130	C₄×C₄⋊C₄	Q₈	1	1	yes	characteristic
131	C₄×C₄⋊C₄	Q₈	1	1	yes	characteristic
132	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
133	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
134	C₄×C₂²⋊C₄	Q₈	1	1	yes	characteristic
135	C₄×C₂²⋊C₄	Q₈	1	1	yes	characteristic
136	#376	D₄	1	1	yes	characteristic
137	#376	D₄	1	1	yes	characteristic
138	C₄³	C₂³	1	1	yes	characteristic
139	C₄³	C₂³	1	1	yes	characteristic
140	#336	—	2	1	no	—
141	#336	—	2	1	no	—
142	#336	—	2	1	no	—
143	#336	—	2	1	no	—
144	#336	—	2	1	no	—
145	#336	—	2	1	no	—
146	#336	—	2	1	no	—
147	#336	—	2	1	no	—
148	#336	C₂×C₄	1	1	yes	characteristic
149	#336	C₂×C₄	1	1	yes	characteristic
150	#336	C₂×C₄	1	1	yes	characteristic
151	#336	C₂×C₄	1	1	yes	characteristic
152	#336	C₂×C₄	1	1	yes	characteristic
153	#336	C₂×C₄	1	1	yes	characteristic
154	#336	C₂×C₄	1	1	yes	characteristic
155	#336	C₂×C₄	1	1	yes	characteristic
156	#335	—	2	2	no	—
157	#335	—	2	2	no	—
158	#335	—	2	2	no	—
159	#335	—	2	2	no	—
160	#334	—	2	2	no	—
161	#334	—	2	2	no	—
162	#334	—	2	2	no	—
163	#334	—	2	2	no	—
164	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
165	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
166	C₂³×C₄	C₂×Q₈	1	1	yes	characteristic
167	C₂²×C₈	—	2	2	no	—
168	C₂²×C₈	—	2	2	no	—
169	C₂²×C₈	—	2	2	no	—
170	C₂²×C₈	—	2	2	no	—
171	C₂²×C₈	—	2	1	no	—
172	C₂²×C₈	—	2	1	no	—
173	C₂²×C₈	—	2	1	no	—
174	C₂²×C₈	—	2	1	no	—
175	C₂²×C₈	—	2	1	no	—
176	C₂²×C₈	—	2	1	no	—
177	C₂²×C₈	—	2	1	no	—
178	C₂²×C₈	—	2	1	no	—
179	C₂²×C₈	—	4	1	no	—
180	C₂²×C₈	—	4	1	no	—
181	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
183	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
184	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
186	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
188	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
189	#117	—	2	2	no	—
190	#117	—	2	2	no	—
191	#117	—	4	1	no	—
192	#117	—	4	1	no	—
193	C₂×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
194	C₂×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
195	C₂×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
196	C₂×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
197	C₂×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
198	C₂×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
199	C₂×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
200	C₂×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
201	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
202	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
203	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
204	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
205	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
206	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
207	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
208	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
209	C₂×C₄²	C₂×D₄	1	2	yes	—
210	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
211	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
212	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
213	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
214	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
215	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
216	C₂×C₄²	C₂×Q₈	1	2	yes	—
217	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
218	C₂×C₄²	#41	1	2	yes	—
219	C₂×C₄²	#41	1	2	yes	—
220	C₂×C₄²	C₂⁴	1	1	yes	characteristic
221	C₄⋊C₈	—	2	2	no	—
222	C₄⋊C₈	—	2	2	no	—
223	C₄⋊C₈	—	2	2	no	—
224	C₄⋊C₈	—	2	2	no	—
225	C₄⋊C₈	—	2	2	no	—
226	C₄⋊C₈	—	2	2	no	—
227	C₄⋊C₈	—	2	1	no	—
228	C₄⋊C₈	—	2	1	no	—
229	C₄⋊C₈	—	2	1	no	—
230	C₄⋊C₈	—	2	1	no	—
231	C₄⋊C₈	—	2	1	no	—
232	C₄⋊C₈	—	2	1	no	—
233	C₄⋊C₈	—	2	1	no	—
234	C₄⋊C₈	—	2	1	no	—
235	C₄⋊C₈	—	2	1	no	—
236	C₄⋊C₈	—	2	1	no	—
237	C₄⋊C₈	—	2	1	no	—
238	C₄⋊C₈	—	2	1	no	—
239	C₄⋊C₈	—	4	1	no	—
240	C₄⋊C₈	—	4	1	no	—
241	C₄⋊C₈	—	4	1	no	—
242	C₄⋊C₈	—	4	1	no	—
243	C₄⋊C₈	—	4	2	no	—
244	C₄⋊C₈	—	4	2	no	—
245	C₄⋊C₈	—	4	2	no	—
246	C₄⋊C₈	—	4	2	no	—
247	C₄⋊C₈	C₂×D₄	1	2	yes	—
248	C₄⋊C₈	C₂×D₄	1	2	yes	—
249	C₄⋊C₈	C₂×Q₈	1	2	yes	—
250	C₄⋊C₈	C₂×Q₈	1	2	yes	—
251	C₂²⋊C₈	—	2	2	no	—
252	C₂²⋊C₈	—	2	2	no	—
253	C₂²⋊C₈	—	2	4	no	—
254	C₂²⋊C₈	—	2	4	no	—
255	C₂²⋊C₈	—	4	2	no	—
256	C₂²⋊C₈	—	4	2	no	—
257	#97	—	2	4	no	—
258	#97	—	4	2	no	—
259	#97	—	4	2	no	—
260	#97	—	4	2	no	—
261	C₄×C₈	—	2	2	no	—
262	C₄×C₈	—	2	2	no	—
263	C₄×C₈	—	2	4	no	—
264	C₄×C₈	—	2	1	no	—
265	C₄×C₈	—	2	1	no	—
266	C₄×C₈	—	2	1	no	—
267	C₄×C₈	—	2	1	no	—
268	C₄×C₈	—	2	1	no	—
269	C₄×C₈	—	2	1	no	—
270	C₄×C₈	—	2	1	no	—
271	C₄×C₈	—	2	1	no	—
272	C₄×C₈	—	4	2	no	—
273	C₄×C₈	—	4	2	no	—
274	C₄×C₈	—	4	2	no	—
275	#95	C₄⋊C₄	1	1	yes	characteristic
276	#95	C₄⋊C₄	1	1	yes	characteristic
277	#95	C₄⋊C₄	1	1	yes	characteristic
278	#95	C₄⋊C₄	1	1	yes	characteristic
279	#95	C₄⋊C₄	1	1	yes	characteristic
280	#95	C₄⋊C₄	1	1	yes	characteristic
281	#95	C₄⋊C₄	1	1	yes	characteristic
282	#95	C₄⋊C₄	1	1	yes	characteristic
283	C₂⁴	C₂×C₄⋊C₄	1	1	yes	characteristic
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	—	4	1	no	—
293	C₂²×C₄	—	4	1	no	—
294	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
295	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
296	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
297	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
298	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
300	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
302	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
303	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
304	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
305	C₂²×C₄	C₄×D₄	1	2	yes	—
306	C₂²×C₄	C₄×Q₈	1	2	yes	—
307	C₂²×C₄	#121	1	2	yes	—
308	C₂²×C₄	C₂²⋊Q₈	1	2	yes	—
309	C₂²×C₄	#125	1	2	yes	—
310	C₂²×C₄	C₄⋊Q₈	1	2	yes	—
311	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
312	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
313	C₂²×C₄	C₂²×Q₈	1	1	yes	characteristic
314	C₂×C₈	—	2	8	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	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	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	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	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	4	4	no	—
342	C₂×C₈	—	4	1	no	—
343	C₂×C₈	—	4	1	no	—
344	C₂×C₈	—	4	1	no	—
345	C₂×C₈	—	4	1	no	—
346	C₂×C₈	—	4	1	no	—
347	C₂×C₈	—	4	1	no	—
348	C₂×C₈	—	4	1	no	—
349	C₂×C₈	—	4	1	no	—
350	C₂×C₈	—	4	1	no	—
351	C₂×C₈	—	4	1	no	—
352	C₂×C₈	—	4	1	no	—
353	C₂×C₈	—	4	1	no	—
354	C₂×C₈	—	4	1	no	—
355	C₂×C₈	—	4	1	no	—
356	C₂×C₈	—	4	1	no	—
357	C₂×C₈	—	4	1	no	—
358	C₂×C₈	—	4	1	no	—
359	C₂×C₈	—	4	1	no	—
360	C₂×C₈	—	4	1	no	—
361	C₂×C₈	—	4	1	no	—
362	C₂×C₈	#131	1	2	yes	—
363	C₂×C₈	#131	1	2	yes	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	4	1	no	—
367	C₄⋊C₄	—	4	1	no	—
368	C₂²⋊C₄	—	2	2	no	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	4	1	no	—
371	C₂²⋊C₄	—	4	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	C₄²	—	2	1	no	—
378	C₄²	—	2	1	no	—
379	C₄²	—	2	1	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	2	1	no	—
383	C₄²	—	2	1	no	—
384	C₄²	—	2	1	no	—
385	C₄²	—	2	1	no	—
386	C₄²	—	4	1	no	—
387	C₄²	—	4	1	no	—
388	C₄²	—	4	1	no	—
389	C₄²	—	4	1	no	—
390	C₄²	C₄×D₄	1	2	yes	—
391	C₄²	C₄×Q₈	1	2	yes	—
392	C₄²	#121	1	2	yes	—
393	C₄²	C₂²⋊Q₈	1	2	yes	—
394	C₄²	#125	1	2	yes	—
395	C₄²	C₄⋊Q₈	1	2	yes	—
396	C₄²	#135	1	2	yes	—
397	C₄²	#135	1	2	yes	—
398	C₄²	C₂²×D₄	1	1	yes	characteristic
399	C₄²	C₂²×Q₈	1	1	yes	characteristic
400	C₄²	C₂×#41	1	1	yes	characteristic
401	C₄²	C₂×#41	1	1	yes	characteristic
402	C₂³	—	2	1	no	—
403	C₂³	—	2	1	no	—
404	C₂³	—	2	1	no	—
405	C₂³	—	2	1	no	—
406	C₂³	—	2	1	no	—
407	C₂³	—	2	1	no	—
408	C₂³	#389	1	2	yes	—
409	C₂³	C₂²×C₄⋊C₄	1	1	yes	characteristic
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	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	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	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	#389	1	2	yes	—
451	C₂×C₄	#389	1	2	yes	—
452	C₂×C₄	#389	1	2	yes	—
453	C₂×C₄	#427	1	2	yes	—
454	C₂×C₄	#427	1	2	yes	—
455	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
456	C₂×C₄	C₂×C₄×Q₈	1	1	yes	characteristic
457	C₂×C₄	C₂×#121	1	1	yes	characteristic
458	C₂×C₄	C₂×C₂²⋊Q₈	1	1	yes	characteristic
459	C₂×C₄	C₂×#125	1	1	yes	characteristic
460	C₂×C₄	C₂×C₄⋊Q₈	1	1	yes	characteristic
461	C₂×C₄	C₂×#131	1	1	yes	characteristic
462	C₂×C₄	C₂×#131	1	1	yes	characteristic
463	C₂×C₄	#568	1	1	yes	characteristic
464	C₂×C₄	#568	1	1	yes	characteristic
465	C₂×C₄	C₂×#135	1	1	yes	characteristic
466	C₂×C₄	C₂×#135	1	1	yes	characteristic
467	C₂×C₄	#575	1	1	yes	characteristic
468	C₂×C₄	#575	1	1	yes	characteristic
469	C₈	—	2	2	no	—
470	C₈	—	2	2	no	—
471	C₈	—	4	2	no	—
472	C₈	—	4	2	no	—
473	C₈	—	4	1	no	—
474	C₈	—	4	1	no	—
475	C₈	—	4	1	no	—
476	C₈	—	4	1	no	—
477	C₈	—	4	1	no	—
478	C₈	—	4	1	no	—
479	C₈	—	4	2	no	—
480	C₈	—	4	2	no	—
481	C₈	—	8	1	no	—
482	C₈	—	8	1	no	—
483	C₈	—	8	1	no	—
484	C₈	—	8	1	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	2	2	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	4	1	no	—
489	C₂²	—	4	1	no	—
490	C₂²	—	4	1	no	—
491	C₂²	—	4	1	no	—
492	C₂²	C₂×#389	1	1	yes	characteristic
493	C₂²	#2906	1	1	yes	characteristic
494	C₂²	#2906	1	1	yes	characteristic
495	C₂²	C₂×#427	1	1	yes	characteristic
496	C₂²	#2911	1	1	yes	characteristic
497	C₂²	#2916	1	1	yes	characteristic
498	C₂²	#2916	1	1	yes	characteristic
499	C₄	—	2	2	no	—
500	C₄	—	2	2	no	—
501	C₄	—	2	2	no	—
502	C₄	—	2	2	no	—
503	C₄	—	2	1	no	—
504	C₄	—	2	1	no	—
505	C₄	—	2	2	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	—	4	1	no	—
512	C₄	#2929	1	1	yes	characteristic
513	C₄	#2930	1	1	yes	characteristic
514	C₄	#2962	1	1	yes	characteristic
515	C₄	#2962	1	1	yes	characteristic
516	C₄	#3035	1	1	yes	characteristic
517	C₄	#3035	1	1	yes	characteristic
518	C₄	#3076	1	1	yes	characteristic
519	C₄	#3076	1	1	yes	characteristic
520	C₂	—	4	2	no	—
521	C₂	#17827	1	1	yes	characteristic
522	C₂	#17829	1	1	yes	characteristic
523	C₂	#17831	1	1	yes	characteristic
524	C₂	#17833	1	1	yes	characteristic
525	C₂	#21147	1	1	yes	characteristic
526	C₂	#21169	1	1	yes	characteristic
527	C₂	#21178	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₄
commutator	C₂²×C₄	C₂³×C₄
Frattini, cosocle	C₂×C₄²	C₂⁴
socle	C₂³	C₂²×C₄⋊C₄
prime radical	C₂⁴	C₂×C₄⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#117 ◁ G
LECS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
6. #9606	C₂	semidirect
7. #9606	C₂	semidirect
8. #9605	C₂	semidirect
9. #9604	C₂	semidirect
10. #9603	C₂	semidirect
11. #9603	C₂	semidirect
12. #9602	C₂	semidirect
13. #9601	C₂	semidirect

Maximal subgroups

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

subgroup	index
#21349	2
#20815	2
#20470	2
C₂×#1572	2
C₂×#1564	2
#9606	2
#9605	2
#9604	2
#9603	2
#9602	2
#9601	2
#7878	2
#7875	2