Subgroups — #494945

Order 512.

662 conjugacy classes of subgroups.

The subgroup lattice has 489 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#2162	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#2108	C₂	1	1	yes	maximal, characteristic, complemented
3	#20484	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	#13105	C₂	1	1	yes	maximal, characteristic, complemented
7	#13104	C₂	1	1	yes	maximal, characteristic, complemented
8	#12977	C₂	1	1	yes	maximal, characteristic
9	#12976	C₂	1	1	yes	maximal, characteristic
10	#12913	C₂	1	1	yes	maximal, characteristic, complemented
11	#12912	C₂	1	1	yes	maximal, characteristic, complemented
12	#12654	C₂	1	1	yes	maximal, characteristic, complemented
13	#12600	C₂	1	1	yes	maximal, characteristic, complemented
14	#12599	C₂	1	1	yes	maximal, characteristic, complemented
15	#12592	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×M₃₂	C₂²	1	1	yes	characteristic
17	C₂³×C₁₆	C₂²	1	1	yes	characteristic
18	C₂×#435	C₄	1	1	yes	characteristic
19	C₂×C₈×D₄	C₂²	1	1	yes	characteristic
20	C₂×#405	C₂²	1	1	yes	characteristic
21	C₂²×C₄×C₈	C₂²	1	1	yes	characteristic
22	#2290	C₄	1	1	yes	characteristic
23	#2162	—	2	4	no	—
24	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊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	#2108	—	2	4	no	—
35	C₂×#346	C₂²	1	1	yes	characteristic
36	C₂×#346	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	#1771	C₄	1	1	yes	characteristic
42	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	#1768	C₄	1	1	yes	characteristic
44	#1753	C₄	1	1	yes	characteristic
45	#1752	C₄	1	1	yes	characteristic
46	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
47	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
48	#1750	C₄	1	1	yes	characteristic
49	#1749	C₄	1	1	yes	characteristic
50	#1726	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	C₂×C₄	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×#117	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
68	C₂×M₃₂	—	2	2	no	—
69	C₂×M₃₂	—	2	2	no	—
70	C₂×M₃₂	—	2	2	no	—
71	C₂²×C₁₆	—	2	2	no	—
72	C₂²×C₁₆	—	2	2	no	—
73	C₂²×C₁₆	—	2	2	no	—
74	C₂²×C₁₆	C₂³	1	1	yes	characteristic
75	C₂²×C₁₆	C₂³	1	1	yes	characteristic
76	C₂²×C₁₆	C₂³	1	1	yes	characteristic
77	C₂²×C₁₆	C₂³	1	1	yes	characteristic
78	C₂²×C₁₆	C₂³	1	1	yes	characteristic
79	C₂²×C₁₆	C₂³	1	1	yes	characteristic
80	C₂²×C₁₆	C₂³	1	1	yes	characteristic
81	C₂²×C₁₆	C₂³	1	1	yes	characteristic
82	#435	—	2	4	no	—
83	C₈×D₄	—	2	2	no	—
84	C₈×D₄	—	2	2	no	—
85	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
87	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
88	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
89	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
90	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
91	#405	—	2	2	no	—
92	#405	—	2	2	no	—
93	C₂×#97	C₂×C₄	1	1	yes	characteristic
94	C₂×#97	C₂×C₄	1	1	yes	characteristic
95	C₂×#97	C₂×C₄	1	1	yes	characteristic
96	C₂×#97	C₂×C₄	1	1	yes	characteristic
97	C₂×#97	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄×C₈	—	2	2	no	—
99	C₂×C₄×C₈	—	2	2	no	—
100	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
101	C₂×C₄×C₈	C₂×C₄	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×C₄×C₈	C₂³	1	1	yes	characteristic
107	#388	C₈	1	1	yes	characteristic
108	#388	C₈	1	1	yes	characteristic
109	#387	C₈	1	1	yes	characteristic
110	#387	C₈	1	1	yes	characteristic
111	#386	C₈	1	1	yes	characteristic
112	#386	C₈	1	1	yes	characteristic
113	#385	C₈	1	1	yes	characteristic
114	#385	C₈	1	1	yes	characteristic
115	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
116	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
117	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
118	#376	C₂×C₄	1	1	yes	characteristic
119	C₄⋊C₁₆	—	2	2	no	—
120	C₄⋊C₁₆	—	2	2	no	—
121	C₄⋊C₁₆	—	2	2	no	—
122	C₄⋊C₁₆	—	2	2	no	—
123	C₂²⋊C₁₆	—	2	2	no	—
124	C₂²⋊C₁₆	—	2	2	no	—
125	C₂²⋊C₁₆	—	2	2	no	—
126	C₂²⋊C₁₆	—	2	2	no	—
127	C₂²⋊C₁₆	—	2	2	no	—
128	C₂²⋊C₁₆	—	2	2	no	—
129	#346	—	2	2	no	—
130	#346	—	2	2	no	—
131	#346	—	2	2	no	—
132	C₄×C₁₆	—	2	2	no	—
133	C₄×C₁₆	—	2	2	no	—
134	C₄×C₁₆	D₄	1	4	yes	complemented
135	#336	C₂×C₄	1	1	yes	characteristic
136	#336	C₂×C₄	1	1	yes	characteristic
137	#336	C₂×C₄	1	1	yes	characteristic
138	#336	C₂×C₄	1	1	yes	characteristic
139	#336	C₂×C₄	1	1	yes	characteristic
140	#336	C₂×C₄	1	1	yes	characteristic
141	C₂²×D₄	C₂×C₈	1	1	yes	characteristic
142	C₂³×C₄	C₂×C₈	1	1	yes	characteristic
143	C₂³×C₄	C₂×C₈	1	1	yes	characteristic
144	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
145	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
146	C₂×M₁₆	—	2	2	no	—
147	C₂×M₁₆	—	2	2	no	—
148	C₂×M₁₆	M₁₆	1	4	yes	—
149	C₂²×C₈	—	2	1	no	—
150	C₂²×C₈	—	2	1	no	—
151	C₂²×C₈	—	2	1	no	—
152	C₂²×C₈	—	2	1	no	—
153	C₂²×C₈	—	2	2	no	—
154	C₂²×C₈	—	2	2	no	—
155	C₂²×C₈	—	2	2	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	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₈	#41	1	2	yes	—
170	C₂²×C₈	#41	1	2	yes	—
171	C₂²×C₈	C₂⁴	1	1	yes	characteristic
172	C₄×D₄	—	2	2	no	—
173	C₄×D₄	—	2	2	no	—
174	#117	—	2	2	no	—
175	#117	—	2	2	no	—
176	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
177	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
178	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
179	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
180	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
181	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
182	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
183	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
184	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
185	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
186	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
187	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
188	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
189	C₂×C₄²	—	2	2	no	—
190	C₂×C₄²	—	2	2	no	—
191	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
192	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
193	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
194	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
195	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
196	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
197	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
198	M₃₂	—	2	8	no	—
199	C₂×C₁₆	—	2	8	no	—
200	C₂×C₁₆	—	2	1	no	—
201	C₂×C₁₆	—	2	1	no	—
202	C₂×C₁₆	—	2	1	no	—
203	C₂×C₁₆	—	2	1	no	—
204	C₂×C₁₆	—	2	1	no	—
205	C₂×C₁₆	—	2	1	no	—
206	C₂×C₁₆	—	2	1	no	—
207	C₂×C₁₆	—	2	1	no	—
208	C₂×C₁₆	—	2	1	no	—
209	C₂×C₁₆	—	2	1	no	—
210	C₂×C₁₆	—	2	1	no	—
211	C₂×C₁₆	—	2	1	no	—
212	C₂×C₁₆	—	2	1	no	—
213	C₂×C₁₆	—	2	1	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	C₂×D₄	1	2	yes	—
221	C₂×C₁₆	C₂×D₄	1	2	yes	—
222	C₂×C₁₆	#41	1	2	yes	—
223	C₂×C₁₆	#41	1	2	yes	—
224	C₄⋊C₈	—	2	2	no	—
225	C₄⋊C₈	—	2	2	no	—
226	C₂²⋊C₈	—	2	2	no	—
227	C₂²⋊C₈	—	2	2	no	—
228	C₂²⋊C₈	—	2	2	no	—
229	C₂²⋊C₈	—	2	2	no	—
230	#97	—	2	2	no	—
231	#97	—	2	2	no	—
232	#97	—	2	2	no	—
233	#97	—	2	2	no	—
234	#97	—	2	2	no	—
235	C₄×C₈	—	2	2	no	—
236	C₄×C₈	—	2	1	no	—
237	C₄×C₈	—	2	1	no	—
238	C₄×C₈	—	2	1	no	—
239	C₄×C₈	—	2	1	no	—
240	C₄×C₈	—	2	1	no	—
241	C₄×C₈	—	2	1	no	—
242	C₄×C₈	—	2	1	no	—
243	C₄×C₈	—	2	1	no	—
244	C₄×C₈	—	2	2	no	—
245	C₄×C₈	C₂×D₄	1	2	yes	—
246	C₄×C₈	#41	1	2	yes	—
247	#95	C₂×C₈	1	1	yes	characteristic
248	#95	C₂×C₈	1	1	yes	characteristic
249	#95	C₂×C₈	1	1	yes	characteristic
250	#95	C₂×C₈	1	1	yes	characteristic
251	#95	C₂×C₈	1	1	yes	characteristic
252	#95	C₂×C₈	1	1	yes	characteristic
253	#95	C₂×C₈	1	1	yes	characteristic
254	#95	C₂×C₈	1	1	yes	characteristic
255	#95	C₂×C₈	1	1	yes	characteristic
256	#95	C₂×C₈	1	1	yes	characteristic
257	C₂⁴	C₂²×C₈	1	1	yes	characteristic
258	C₂⁴	C₂²×C₈	1	1	yes	characteristic
259	C₂×D₄	—	2	2	no	—
260	C₂×D₄	—	2	2	no	—
261	C₂×D₄	—	4	1	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	2	1	no	—
265	C₂²×C₄	—	2	1	no	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	1	no	—
270	C₂²×C₄	—	2	1	no	—
271	C₂²×C₄	—	2	1	no	—
272	C₂²×C₄	—	2	1	no	—
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	4	1	no	—
277	C₂²×C₄	—	4	1	no	—
278	C₂²×C₄	#117	1	2	yes	—
279	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
280	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
281	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
282	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
283	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
284	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
285	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
286	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
287	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
288	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
289	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
290	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
291	C₂²×C₄	C₂×M₁₆	1	2	yes	—
292	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
293	M₁₆	—	2	8	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	4	1	no	—
315	C₂×C₈	—	4	1	no	—
316	C₂×C₈	—	4	1	no	—
317	C₂×C₈	—	4	1	no	—
318	C₂×C₈	—	4	4	no	—
319	C₂×C₈	#117	1	2	yes	—
320	C₂×C₈	C₄×D₄	1	2	yes	—
321	C₂×C₈	C₂×M₁₆	1	2	yes	—
322	C₂×C₈	C₂×M₁₆	1	2	yes	—
323	C₂×C₈	#131	1	2	yes	—
324	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₈	C₂×#41	1	1	yes	characteristic
326	C₂×C₈	C₂×#41	1	1	yes	characteristic
327	C₂×C₈	C₂×#41	1	1	yes	characteristic
328	C₂×C₈	C₂×#41	1	1	yes	characteristic
329	C₂×C₈	C₂×#41	1	1	yes	characteristic
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	4	1	no	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	—	2	2	no	—
337	C₂²⋊C₄	—	2	2	no	—
338	C₂²⋊C₄	—	2	2	no	—
339	C₂²⋊C₄	—	2	2	no	—
340	C₂²⋊C₄	—	2	2	no	—
341	C₂²⋊C₄	—	4	1	no	—
342	C₂²⋊C₄	—	4	1	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	2	1	no	—
347	C₄²	—	2	1	no	—
348	C₄²	—	2	1	no	—
349	C₄²	—	2	1	no	—
350	C₄²	—	2	1	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	2	2	no	—
353	C₄²	C₄×D₄	1	2	yes	—
354	C₄²	#131	1	2	yes	—
355	C₁₆	—	2	2	no	—
356	C₁₆	—	2	2	no	—
357	C₁₆	—	2	2	no	—
358	C₁₆	—	2	2	no	—
359	C₁₆	—	4	1	no	—
360	C₁₆	—	4	1	no	—
361	C₁₆	—	4	1	no	—
362	C₁₆	—	4	1	no	—
363	C₂³	—	2	1	no	—
364	C₂³	—	2	1	no	—
365	C₂³	—	2	1	no	—
366	C₂³	—	2	1	no	—
367	C₂³	—	2	1	no	—
368	C₂³	—	2	1	no	—
369	C₂³	—	2	1	no	—
370	C₂³	—	2	1	no	—
371	C₂³	—	2	1	no	—
372	C₂³	—	2	1	no	—
373	C₂³	—	2	1	no	—
374	C₂³	—	2	1	no	—
375	C₂³	#431	1	2	yes	—
376	C₂³	#504	1	2	yes	—
377	C₂³	C₂³×C₈	1	1	yes	characteristic
378	D₄	—	4	4	no	—
379	C₂×C₄	—	2	8	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	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	—	4	4	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	#431	1	2	yes	—
422	C₂×C₄	C₈×D₄	1	2	yes	—
423	C₂×C₄	C₈×D₄	1	2	yes	—
424	C₂×C₄	#504	1	2	yes	—
425	C₂×C₄	C₂×#117	1	1	yes	characteristic
426	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
427	C₂×C₄	C₄×#41	1	1	yes	characteristic
428	C₂×C₄	C₂²×M₁₆	1	1	yes	characteristic
429	C₂×C₄	C₂×#131	1	1	yes	characteristic
430	C₂×C₄	C₂×#131	1	1	yes	characteristic
431	C₈	—	2	2	no	—
432	C₈	—	2	2	no	—
433	C₈	—	4	1	no	—
434	C₈	—	4	1	no	—
435	C₈	—	4	1	no	—
436	C₈	—	4	1	no	—
437	C₈	#435	1	4	yes	—
438	C₈	#525	1	1	yes	characteristic
439	C₈	#525	1	1	yes	characteristic
440	C₈	#529	1	1	yes	characteristic
441	C₈	#529	1	1	yes	characteristic
442	C₂²	—	2	2	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	4	1	no	—
449	C₂²	—	4	1	no	—
450	C₂²	—	4	1	no	—
451	C₂²	—	4	1	no	—
452	C₂²	—	4	1	no	—
453	C₂²	—	4	1	no	—
454	C₂²	—	4	1	no	—
455	C₂²	—	4	1	no	—
456	C₂²	C₂×#431	1	1	yes	characteristic
457	C₂²	C₂×C₈×D₄	1	1	yes	characteristic
458	C₂²	C₈×#41	1	1	yes	characteristic
459	C₂²	C₂×#504	1	1	yes	characteristic
460	C₂²	C₂×#504	1	1	yes	characteristic
461	C₂²	#3407	1	1	yes	characteristic
462	C₂²	#3407	1	1	yes	characteristic
463	C₄	—	2	2	no	—
464	C₄	—	2	2	no	—
465	C₄	—	2	2	no	—
466	C₄	—	2	2	no	—
467	C₄	—	4	1	no	—
468	C₄	—	4	1	no	—
469	C₄	—	4	1	no	—
470	C₄	—	4	1	no	—
471	C₄	—	4	1	no	—
472	C₄	—	4	1	no	—
473	C₄	—	4	1	no	—
474	C₄	—	4	1	no	—
475	C₄	#2290	1	1	yes	characteristic
476	C₄	#2922	1	1	yes	characteristic
477	C₄	C₂×#435	1	1	yes	characteristic
478	C₄	#2965	1	1	yes	characteristic
479	C₂	—	4	2	no	—
480	C₂	—	4	2	no	—
481	C₂	#21101	1	1	yes	characteristic
482	C₂	#33422	1	1	yes	characteristic
483	C₂	#33423	1	1	yes	characteristic
484	C₂	#33432	1	1	yes	characteristic
485	C₂	#33433	1	1	yes	characteristic
486	C₂	#33482	1	1	yes	characteristic
487	C₂	#33483	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, cosocle	C₂²×C₈	C₂⁴
commutator, socle	C₂³	C₂³×C₈
prime radical	C₂²×D₄	C₂×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×#2162	C₂	semidirect
2. C₂×#2108	C₂	semidirect
4. #13121	C₂	semidirect
5. #13120	C₂	semidirect
6. #13105	C₂	semidirect
7. #13104	C₂	semidirect
10. #12913	C₂	semidirect
11. #12912	C₂	semidirect
12. #12654	C₂	semidirect
13. #12600	C₂	semidirect
14. #12599	C₂	semidirect
15. #12592	C₂	semidirect
134. C₄×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×#2162	2
C₂×#2108	2
#20484	2
#13121	2
#13120	2
#13105	2
#13104	2
#12977	2
#12976	2
#12913	2
#12912	2
#12654	2
#12600	2
#12599	2
#12592	2