Subgroups — #497831

Order 512.

726 conjugacy classes of subgroups.

The subgroup lattice has 501 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#2168	C₂	1	1	yes	maximal, characteristic
2	C₂×D₄×C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂×#2151	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	#20484	C₂	1	1	yes	maximal, characteristic
6	#13160	C₂	1	1	yes	maximal, characteristic, complemented
7	#13159	C₂	1	1	yes	maximal, characteristic, complemented
8	#12913	C₂	1	1	yes	maximal, characteristic, complemented
9	#12912	C₂	1	1	yes	maximal, characteristic, complemented
10	#12912	C₂	1	1	yes	maximal, characteristic, complemented
11	#12912	C₂	1	1	yes	maximal, characteristic, complemented
12	#12899	C₂	1	1	yes	maximal, characteristic, complemented
13	#12784	C₂	1	1	yes	maximal, characteristic, complemented
14	#12783	C₂	1	1	yes	maximal, characteristic, complemented
15	#12654	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×M₃₂	C₂²	1	1	yes	characteristic
17	C₂³×C₁₆	C₂²	1	1	yes	characteristic
18	C₂³×C₁₆	C₂²	1	1	yes	characteristic
19	C₂³×C₁₆	C₂²	1	1	yes	characteristic
20	C₂×#435	C₄	1	1	yes	characteristic
21	C₂×C₈×D₄	C₂²	1	1	yes	characteristic
22	C₂×#405	C₂²	1	1	yes	characteristic
23	C₂²×C₄×C₈	C₂²	1	1	yes	characteristic
24	#2290	C₄	1	1	yes	characteristic
25	#2168	—	2	4	no	—
26	D₄×C₁₆	—	2	4	no	—
27	#2151	—	2	4	no	—
28	C₂×C₄⋊C₁₆	—	2	4	no	—
29	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₁₆	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	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
42	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
43	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
44	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
45	C₂×#346	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
47	#1771	C₄	1	1	yes	characteristic
48	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	#1768	C₄	1	1	yes	characteristic
50	#1753	C₄	1	1	yes	characteristic
51	#1752	C₄	1	1	yes	characteristic
52	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
53	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
54	#1750	C₄	1	1	yes	characteristic
55	#1749	C₄	1	1	yes	characteristic
56	#1726	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	#1374	C₂²	1	1	yes	characteristic
62	#1374	C₂²	1	1	yes	characteristic
63	C₂²×M₁₆	C₂×C₄	1	1	yes	characteristic
64	C₂³×C₈	C₂×C₄	1	1	yes	characteristic
65	C₂³×C₈	C₂³	1	1	yes	characteristic
66	C₂³×C₈	C₂³	1	1	yes	characteristic
67	C₂×C₄×D₄	C₂×C₄	1	1	yes	characteristic
68	C₂×#117	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
70	C₂×M₃₂	—	2	2	no	—
71	C₂×M₃₂	—	2	2	no	—
72	C₂×M₃₂	—	4	1	no	—
73	C₂²×C₁₆	—	2	2	no	—
74	C₂²×C₁₆	—	2	2	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	—	4	1	no	—
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	C₂²×C₁₆	C₂³	1	1	yes	characteristic
90	#435	—	2	4	no	—
91	C₈×D₄	D₄	1	4	yes	—
92	C₈×D₄	Q₈	1	4	yes	—
93	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
95	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
96	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
97	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
98	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
99	#405	—	2	2	no	—
100	#405	—	2	2	no	—
101	C₂×#97	C₂×C₄	1	1	yes	characteristic
102	C₂×#97	C₂×C₄	1	1	yes	characteristic
103	C₂×#97	C₂×C₄	1	1	yes	characteristic
104	C₂×#97	C₂×C₄	1	1	yes	characteristic
105	C₂×#97	C₂×C₄	1	1	yes	characteristic
106	C₂×C₄×C₈	—	2	2	no	—
107	C₂×C₄×C₈	—	2	2	no	—
108	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
109	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
110	C₂×C₄×C₈	C₂³	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	#388	C₈	1	1	yes	characteristic
116	#388	C₈	1	1	yes	characteristic
117	#387	C₈	1	1	yes	characteristic
118	#387	C₈	1	1	yes	characteristic
119	#386	C₈	1	1	yes	characteristic
120	#386	C₈	1	1	yes	characteristic
121	#385	C₈	1	1	yes	characteristic
122	#385	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	#376	C₂×C₄	1	1	yes	characteristic
127	C₄⋊C₁₆	—	2	2	no	—
128	C₄⋊C₁₆	—	2	2	no	—
129	C₄⋊C₁₆	—	2	2	no	—
130	C₄⋊C₁₆	—	2	2	no	—
131	C₄⋊C₁₆	—	2	2	no	—
132	C₄⋊C₁₆	—	2	2	no	—
133	C₄⋊C₁₆	—	2	2	no	—
134	C₄⋊C₁₆	—	2	2	no	—
135	C₄⋊C₁₆	—	2	2	no	—
136	C₄⋊C₁₆	—	4	1	no	—
137	C₄⋊C₁₆	—	4	1	no	—
138	C₄⋊C₁₆	D₄	1	4	yes	complemented
139	C₂²⋊C₁₆	—	2	2	no	—
140	C₂²⋊C₁₆	—	2	2	no	—
141	C₂²⋊C₁₆	—	2	2	no	—
142	C₂²⋊C₁₆	—	2	2	no	—
143	#346	—	2	2	no	—
144	C₄×C₁₆	—	2	2	no	—
145	#336	C₂×C₄	1	1	yes	characteristic
146	#336	C₂×C₄	1	1	yes	characteristic
147	#336	C₂×C₄	1	1	yes	characteristic
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	C₂²×D₄	C₂×C₈	1	1	yes	characteristic
152	C₂³×C₄	C₂×C₈	1	1	yes	characteristic
153	C₂³×C₄	C₂×C₈	1	1	yes	characteristic
154	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
155	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
156	C₂×M₁₆	—	2	2	no	—
157	C₂×M₁₆	—	2	2	no	—
158	C₂×M₁₆	—	4	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	2	no	—
168	C₂²×C₈	—	2	2	no	—
169	C₂²×C₈	—	4	1	no	—
170	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
178	C₂²×C₈	C₂×D₄	1	2	yes	—
179	C₂²×C₈	C₂×Q₈	1	2	yes	—
180	C₂²×C₈	C₂×Q₈	1	2	yes	—
181	C₂²×C₈	C₂⁴	1	1	yes	characteristic
182	C₄×D₄	C₄⋊C₄	1	4	yes	—
183	C₄×D₄	M₁₆	1	4	yes	—
184	#117	—	2	2	no	—
185	#117	—	2	2	no	—
186	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
187	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
188	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
189	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
190	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
191	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
192	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
193	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
194	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
195	C₂×C₂²⋊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×C₄²	—	2	2	no	—
200	C₂×C₄²	—	2	2	no	—
201	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
202	C₂×C₄²	C₂×C₈	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	C₂²×C₄	1	1	yes	characteristic
207	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
208	M₃₂	—	4	4	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	—	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	—	4	4	no	—
232	C₂×C₁₆	—	4	4	no	—
233	C₂×C₁₆	—	4	4	no	—
234	C₂×C₁₆	C₂×D₄	1	2	yes	—
235	C₂×C₁₆	C₂×D₄	1	2	yes	—
236	C₄⋊C₈	—	2	2	no	—
237	C₄⋊C₈	C₄⋊C₄	1	4	yes	—
238	C₂²⋊C₈	—	2	2	no	—
239	C₂²⋊C₈	—	2	2	no	—
240	C₂²⋊C₈	C₄⋊C₄	1	4	yes	—
241	C₂²⋊C₈	C₄⋊C₄	1	4	yes	—
242	#97	—	2	2	no	—
243	#97	—	2	2	no	—
244	#97	—	2	2	no	—
245	#97	—	2	2	no	—
246	#97	—	4	1	no	—
247	C₄×C₈	—	2	2	no	—
248	C₄×C₈	—	2	1	no	—
249	C₄×C₈	—	2	1	no	—
250	C₄×C₈	—	2	1	no	—
251	C₄×C₈	—	2	1	no	—
252	C₄×C₈	—	2	1	no	—
253	C₄×C₈	—	2	1	no	—
254	C₄×C₈	—	2	2	no	—
255	C₄×C₈	C₂×D₄	1	2	yes	—
256	C₄×C₈	C₂×D₄	1	2	yes	—
257	C₄×C₈	C₂×Q₈	1	2	yes	—
258	C₄×C₈	#41	1	2	yes	—
259	#95	C₂×C₈	1	1	yes	characteristic
260	#95	C₂×C₈	1	1	yes	characteristic
261	#95	C₂×C₈	1	1	yes	characteristic
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	#95	C₂×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	C₄⋊C₈	1	4	yes	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	4	1	no	—
288	C₂²×C₄	C₂×C₄⋊C₄	1	2	yes	—
289	C₂²×C₄	C₂×C₄⋊C₄	1	2	yes	—
290	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
291	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
292	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
293	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
294	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
295	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
296	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
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	C₂×M₁₆	1	2	yes	—
303	C₂²×C₄	C₂×M₁₆	1	2	yes	—
304	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
305	M₁₆	—	4	4	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	—	2	2	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	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	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	—	4	4	no	—
332	C₂×C₈	C₂×C₄⋊C₄	1	2	yes	—
333	C₂×C₈	C₂×C₄⋊C₄	1	2	yes	—
334	C₂×C₈	C₂×C₄⋊C₄	1	2	yes	—
335	C₂×C₈	C₄×D₄	1	2	yes	—
336	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₈	C₂²×Q₈	1	1	yes	characteristic
339	C₂×C₈	C₂×#41	1	1	yes	characteristic
340	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
341	C₂×C₈	2₋¹⁺⁴	1	1	yes	characteristic
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	4	1	no	—
346	C₄⋊C₄	C₄⋊C₈	1	4	yes	—
347	C₂²⋊C₄	—	2	2	no	—
348	C₂²⋊C₄	—	2	2	no	—
349	C₂²⋊C₄	—	2	2	no	—
350	C₂²⋊C₄	—	2	2	no	—
351	C₂²⋊C₄	—	2	2	no	—
352	C₂²⋊C₄	—	4	1	no	—
353	C₂²⋊C₄	C₄⋊C₈	1	4	yes	—
354	C₂²⋊C₄	C₄⋊C₈	1	4	yes	—
355	C₄²	—	2	1	no	—
356	C₄²	—	2	1	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	C₂×C₄⋊C₄	1	2	yes	—
364	C₄²	C₄×D₄	1	2	yes	—
365	C₄²	C₂×M₁₆	1	2	yes	—
366	C₄²	#131	1	2	yes	—
367	C₁₆	—	2	2	no	—
368	C₁₆	—	2	2	no	—
369	C₁₆	—	4	1	no	—
370	C₁₆	—	4	1	no	—
371	C₁₆	—	4	1	no	—
372	C₁₆	—	4	1	no	—
373	C₁₆	—	4	1	no	—
374	C₁₆	—	4	1	no	—
375	C₂³	—	2	1	no	—
376	C₂³	—	2	1	no	—
377	C₂³	—	2	1	no	—
378	C₂³	—	2	1	no	—
379	C₂³	—	2	1	no	—
380	C₂³	—	2	1	no	—
381	C₂³	—	2	1	no	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	C₂×C₄⋊C₈	1	2	yes	—
386	C₂³	C₂×C₄⋊C₈	1	2	yes	—
387	C₂³	#504	1	2	yes	—
388	C₂³	#504	1	2	yes	—
389	C₂³	C₂³×C₈	1	1	yes	characteristic
390	D₄	—	2	8	no	—
391	C₂×C₄	—	2	8	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	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	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	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	—	4	4	no	—
430	C₂×C₄	C₂×C₄⋊C₈	1	2	yes	—
431	C₂×C₄	C₂×C₄⋊C₈	1	2	yes	—
432	C₂×C₄	C₂×C₄⋊C₈	1	2	yes	—
433	C₂×C₄	C₂×C₄⋊C₈	1	2	yes	—
434	C₂×C₄	C₈×D₄	1	2	yes	—
435	C₂×C₄	C₈×D₄	1	2	yes	—
436	C₂×C₄	#504	1	2	yes	—
437	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
438	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
439	C₂×C₄	#520	1	1	yes	characteristic
440	C₂×C₄	C₂²×M₁₆	1	1	yes	characteristic
441	C₂×C₄	C₂×#131	1	1	yes	characteristic
442	C₂×C₄	#568	1	1	yes	characteristic
443	C₈	—	2	2	no	—
444	C₈	—	2	2	no	—
445	C₈	—	2	2	no	—
446	C₈	—	2	2	no	—
447	C₈	—	4	1	no	—
448	C₈	—	4	1	no	—
449	C₈	—	4	1	no	—
450	C₈	D₄²	1	1	yes	characteristic
451	C₈	#547	1	1	yes	characteristic
452	C₈	D₄×Q₈	1	1	yes	characteristic
453	C₈	#554	1	1	yes	characteristic
454	C₂²	—	2	2	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	2	2	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	1	no	—
465	C₂²	—	4	1	no	—
466	C₂²	—	4	1	no	—
467	C₂²	#2151	1	4	yes	complemented
468	C₂²	C₂²×C₄⋊C₈	1	1	yes	characteristic
469	C₂²	C₂×C₈×D₄	1	1	yes	characteristic
470	C₂²	#2988	1	1	yes	characteristic
471	C₂²	C₂×#504	1	1	yes	characteristic
472	C₂²	C₂×#504	1	1	yes	characteristic
473	C₂²	C₂×#504	1	1	yes	characteristic
474	C₂²	#3407	1	1	yes	characteristic
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	2	2	no	—
478	C₄	—	2	2	no	—
479	C₄	—	2	2	no	—
480	C₄	—	2	2	no	—
481	C₄	—	2	2	no	—
482	C₄	—	4	1	no	—
483	C₄	—	4	1	no	—
484	C₄	—	4	1	no	—
485	C₄	—	4	1	no	—
486	C₄	—	4	1	no	—
487	C₄	D₄×C₄⋊C₄	1	1	yes	characteristic
488	C₄	#2906	1	1	yes	characteristic
489	C₄	D₄×M₁₆	1	1	yes	characteristic
490	C₄	#2990	1	1	yes	characteristic
491	C₂	—	2	4	no	—
492	C₂	—	4	2	no	—
493	C₂	D₄×C₄⋊C₈	1	1	yes	characteristic
494	C₂	C₂×#2151	1	1	yes	characteristic
495	C₂	#33398	1	1	yes	characteristic
496	C₂	#33432	1	1	yes	characteristic
497	C₂	#33436	1	1	yes	characteristic
498	C₂	#33506	1	1	yes	characteristic
499	C₂	#33508	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
3. C₂×#2151	C₂	semidirect
4. C₂²×C₄⋊C₁₆	C₂	semidirect
6. #13160	C₂	semidirect
7. #13159	C₂	semidirect
8. #12913	C₂	semidirect
9. #12912	C₂	semidirect
10. #12912	C₂	semidirect
11. #12912	C₂	semidirect
12. #12899	C₂	semidirect
13. #12784	C₂	semidirect
14. #12783	C₂	semidirect
15. #12654	C₂	semidirect
138. C₄⋊C₁₆	D₄	semidirect
467. C₂²	#2151	semidirect

Maximal subgroups

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

subgroup	index
C₂×#2168	2
C₂×D₄×C₁₆	2
C₂×#2151	2
C₂²×C₄⋊C₁₆	2
#20484	2
#13160	2
#13159	2
#12913	2
#12912	2
#12899	2
#12784	2
#12783	2
#12654	2