Subgroups — #498732

Order 512.

541 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21491	C₂	1	1	yes	maximal, characteristic
2	#13190	C₂	1	1	yes	maximal, characteristic, complemented
3	#13189	C₂	1	1	yes	maximal, characteristic, complemented
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, complemented
9	#12977	C₂	1	1	yes	maximal, characteristic, complemented
10	#12977	C₂	1	1	yes	maximal, characteristic, complemented
11	#12977	C₂	1	1	yes	maximal, characteristic, complemented
12	#12913	C₂	1	1	yes	maximal, characteristic, complemented
13	#12913	C₂	1	1	yes	maximal, characteristic, complemented
14	#12845	C₂	1	1	yes	maximal, characteristic, complemented
15	#12784	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×M₃₂	C₂²	1	1	yes	characteristic
17	C₂²×M₃₂	C₂²	1	1	yes	characteristic
18	C₂×C₈×D₄	C₂²	1	1	yes	characteristic
19	C₂×C₈×D₄	C₂²	1	1	yes	characteristic
20	C₂×C₈×D₄	C₂²	1	1	yes	characteristic
21	C₂×#405	C₂²	1	1	yes	characteristic
22	#2392	C₄	1	1	yes	characteristic
23	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
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×C₂²⋊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	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	#1955	C₄	1	1	yes	characteristic
40	#1940	C₄	1	1	yes	characteristic
41	#1924	C₄	1	1	yes	characteristic
42	#1924	C₄	1	1	yes	characteristic
43	#1870	C₄	1	1	yes	characteristic
44	#1870	C₄	1	1	yes	characteristic
45	#1798	C₄	1	1	yes	characteristic
46	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
48	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
49	#1374	C₂²	1	1	yes	characteristic
50	#1374	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	C₂²×M₁₆	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₈	C₂³	1	1	yes	characteristic
61	C₂³×C₈	C₂³	1	1	yes	characteristic
62	C₂³×C₈	C₂³	1	1	yes	characteristic
63	C₂×C₄×D₄	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄×D₄	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄×D₄	C₂×C₄	1	1	yes	characteristic
66	C₂×#117	C₂×C₄	1	1	yes	characteristic
67	C₂×M₃₂	—	4	1	no	—
68	C₂×M₃₂	—	4	1	no	—
69	C₂×M₃₂	—	4	1	no	—
70	C₂×M₃₂	—	4	1	no	—
71	C₂×M₃₂	—	4	1	no	—
72	C₂×M₃₂	—	4	1	no	—
73	C₂²×C₁₆	C₂³	1	1	yes	characteristic
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	C₈×D₄	—	4	1	no	—
82	C₈×D₄	—	4	1	no	—
83	C₈×D₄	—	4	1	no	—
84	C₈×D₄	—	4	1	no	—
85	C₈×D₄	—	4	1	no	—
86	C₈×D₄	—	4	1	no	—
87	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
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×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
92	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
93	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
94	C₂×C₂²⋊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	—	4	1	no	—
100	#405	—	4	1	no	—
101	C₂×#97	C₂×C₄	1	1	yes	characteristic
102	C₂×#97	C₂×C₄	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	#398	C₈	1	1	yes	characteristic
108	#397	C₈	1	1	yes	characteristic
109	#396	C₈	1	1	yes	characteristic
110	#396	C₈	1	1	yes	characteristic
111	#394	C₈	1	1	yes	characteristic
112	#394	C₈	1	1	yes	characteristic
113	#394	C₈	1	1	yes	characteristic
114	#392	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	C₄⋊C₁₆	—	4	1	no	—
119	C₄⋊C₁₆	—	4	1	no	—
120	C₄⋊C₁₆	—	4	1	no	—
121	C₄⋊C₁₆	—	4	1	no	—
122	C₂²⋊C₁₆	—	4	1	no	—
123	C₂²⋊C₁₆	—	4	1	no	—
124	C₂²⋊C₁₆	—	4	1	no	—
125	C₂²⋊C₁₆	—	4	1	no	—
126	C₂²⋊C₁₆	—	4	1	no	—
127	C₂²⋊C₁₆	—	4	1	no	—
128	C₂²⋊C₁₆	—	4	1	no	—
129	C₂²⋊C₁₆	—	4	1	no	—
130	C₂²⋊C₁₆	—	4	1	no	—
131	C₂²⋊C₁₆	—	4	1	no	—
132	#346	—	4	1	no	—
133	C₄×C₁₆	—	4	1	no	—
134	#336	C₂×C₄	1	1	yes	characteristic
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	C₂²×D₄	C₂×C₈	1	1	yes	characteristic
141	C₂²×D₄	C₂×C₈	1	1	yes	characteristic
142	C₂²×D₄	C₂×C₈	1	1	yes	characteristic
143	C₂³×C₄	C₂²×C₄	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	—	4	1	no	—
147	C₂×M₁₆	—	4	1	no	—
148	C₂×M₁₆	—	4	1	no	—
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	1	no	—
154	C₂²×C₈	—	2	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	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
175	C₄×D₄	—	4	1	no	—
176	C₄×D₄	—	4	1	no	—
177	C₄×D₄	—	4	1	no	—
178	C₄×D₄	—	4	1	no	—
179	C₄×D₄	—	4	1	no	—
180	C₄×D₄	—	4	1	no	—
181	#117	—	4	1	no	—
182	#117	—	4	1	no	—
183	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
184	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
185	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
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×C₂²⋊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×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×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	M₃₂	—	4	4	no	—
207	M₃₂	—	4	4	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	—	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	C₄⋊C₈	—	4	1	no	—
233	C₄⋊C₈	—	4	1	no	—
234	C₄⋊C₈	—	4	1	no	—
235	C₄⋊C₈	—	4	1	no	—
236	C₂²⋊C₈	—	4	1	no	—
237	C₂²⋊C₈	—	4	1	no	—
238	C₂²⋊C₈	—	4	1	no	—
239	C₂²⋊C₈	—	4	1	no	—
240	C₂²⋊C₈	—	4	1	no	—
241	C₂²⋊C₈	—	4	1	no	—
242	C₂²⋊C₈	—	4	1	no	—
243	C₂²⋊C₈	—	4	1	no	—
244	#97	—	4	1	no	—
245	#97	—	4	1	no	—
246	C₄×C₈	—	2	1	no	—
247	C₄×C₈	—	2	1	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	#95	C₂×C₈	1	1	yes	characteristic
255	#95	C₂×C₈	1	1	yes	characteristic
256	#95	C₂×C₈	1	1	yes	characteristic
257	#95	C₂×C₈	1	1	yes	characteristic
258	#95	C₂×C₈	1	1	yes	characteristic
259	#95	C₂×C₈	1	1	yes	characteristic
260	C₂⁴	C₂²×C₈	1	1	yes	characteristic
261	C₂⁴	C₂²×C₈	1	1	yes	characteristic
262	C₂⁴	C₂²×C₈	1	1	yes	characteristic
263	C₂×D₄	—	2	2	no	—
264	C₂×D₄	—	4	1	no	—
265	C₂×D₄	—	4	1	no	—
266	C₂×D₄	—	4	1	no	—
267	C₂×D₄	—	4	1	no	—
268	C₂×D₄	—	4	1	no	—
269	C₂×D₄	—	4	1	no	—
270	C₂×D₄	—	4	1	no	—
271	C₂×D₄	—	4	1	no	—
272	C₂²×C₄	—	2	1	no	—
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	2	1	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	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	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	C₂³×C₄	1	1	yes	characteristic
302	M₁₆	—	4	4	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	—	2	1	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	—	4	1	no	—
325	C₂×C₈	—	4	1	no	—
326	C₂×C₈	—	4	1	no	—
327	C₂×C₈	—	4	1	no	—
328	C₂×C₈	—	4	1	no	—
329	C₂×C₈	—	4	1	no	—
330	C₂×C₈	—	4	1	no	—
331	C₂×C₈	—	4	1	no	—
332	C₂×C₈	—	4	1	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	4	1	no	—
336	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
337	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
338	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
339	C₂×C₈	H(5,𝔽₂)	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	—	4	1	no	—
344	C₄⋊C₄	—	4	1	no	—
345	C₄⋊C₄	—	4	1	no	—
346	C₄⋊C₄	—	4	1	no	—
347	C₄⋊C₄	—	4	1	no	—
348	C₄⋊C₄	—	4	1	no	—
349	C₂²⋊C₄	—	2	2	no	—
350	C₂²⋊C₄	—	4	1	no	—
351	C₂²⋊C₄	—	4	1	no	—
352	C₂²⋊C₄	—	4	1	no	—
353	C₂²⋊C₄	—	4	1	no	—
354	C₂²⋊C₄	—	4	1	no	—
355	C₂²⋊C₄	—	4	1	no	—
356	C₂²⋊C₄	—	4	1	no	—
357	C₂²⋊C₄	—	4	1	no	—
358	C₂²⋊C₄	—	4	1	no	—
359	C₂²⋊C₄	—	4	1	no	—
360	C₂²⋊C₄	—	4	1	no	—
361	C₄²	—	2	1	no	—
362	C₄²	—	2	1	no	—
363	C₄²	—	2	1	no	—
364	C₄²	—	2	1	no	—
365	C₄²	—	2	1	no	—
366	C₄²	—	2	1	no	—
367	C₄²	—	2	1	no	—
368	C₄²	—	2	1	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	C₁₆	—	4	1	no	—
376	C₁₆	—	4	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	—	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	C₂³×C₈	1	1	yes	characteristic
399	D₄	—	4	4	no	—
400	D₄	—	4	4	no	—
401	D₄	—	4	4	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	—	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	—	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	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	#504	1	2	yes	—
447	C₂×C₄	#518	1	1	yes	characteristic
448	C₂×C₄	#518	1	1	yes	characteristic
449	C₂×C₄	#520	1	1	yes	characteristic
450	C₂×C₄	#568	1	1	yes	characteristic
451	C₂×C₄	#568	1	1	yes	characteristic
452	C₂×C₄	#568	1	1	yes	characteristic
453	C₈	—	4	1	no	—
454	C₈	—	4	1	no	—
455	C₈	—	4	1	no	—
456	C₈	—	4	1	no	—
457	C₈	—	4	1	no	—
458	C₈	—	4	1	no	—
459	C₈	—	4	1	no	—
460	C₈	#560	1	1	yes	characteristic
461	C₈	#560	1	1	yes	characteristic
462	C₈	#562	1	1	yes	characteristic
463	C₈	#562	1	1	yes	characteristic
464	C₂²	—	4	1	no	—
465	C₂²	—	4	1	no	—
466	C₂²	—	4	1	no	—
467	C₂²	—	4	1	no	—
468	C₂²	—	4	1	no	—
469	C₂²	—	4	1	no	—
470	C₂²	—	4	1	no	—
471	C₂²	—	4	1	no	—
472	C₂²	—	4	1	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	4	1	no	—
476	C₂²	—	4	1	no	—
477	C₂²	—	4	1	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	#2972	1	1	yes	characteristic
486	C₂²	#2972	1	1	yes	characteristic
487	C₂²	#2988	1	1	yes	characteristic
488	C₂²	C₂×#504	1	1	yes	characteristic
489	C₂²	#3407	1	1	yes	characteristic
490	C₂²	#3407	1	1	yes	characteristic
491	C₂²	#3407	1	1	yes	characteristic
492	C₄	—	2	2	no	—
493	C₄	—	4	1	no	—
494	C₄	—	4	1	no	—
495	C₄	—	4	1	no	—
496	C₄	—	4	1	no	—
497	C₄	—	4	1	no	—
498	C₄	—	4	1	no	—
499	C₄	—	4	1	no	—
500	C₄	—	4	1	no	—
501	C₄	—	4	1	no	—
502	C₄	—	4	1	no	—
503	C₄	#2377	1	1	yes	characteristic
504	C₄	#2978	1	1	yes	characteristic
505	C₄	#2980	1	1	yes	characteristic
506	C₄	#2995	1	1	yes	characteristic
507	C₂	—	8	1	no	—
508	C₂	—	8	1	no	—
509	C₂	—	8	1	no	—
510	C₂	#23326	1	1	yes	characteristic
511	C₂	#33490	1	1	yes	characteristic
512	C₂	#33492	1	1	yes	characteristic
513	C₂	#33492	1	1	yes	characteristic
514	C₂	#33495	1	1	yes	characteristic
515	C₂	#33507	1	1	yes	characteristic
516	C₂	#33509	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
2. #13190	C₂	semidirect
3. #13189	C₂	semidirect
4. #13121	C₂	semidirect
5. #13120	C₂	semidirect
6. #13105	C₂	semidirect
7. #13104	C₂	semidirect
8. #12977	C₂	semidirect
9. #12977	C₂	semidirect
10. #12977	C₂	semidirect
11. #12977	C₂	semidirect
12. #12913	C₂	semidirect
13. #12913	C₂	semidirect
14. #12845	C₂	semidirect
15. #12784	C₂	semidirect

Maximal subgroups

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

subgroup	index
#21491	2
#13190	2
#13189	2
#13121	2
#13120	2
#13105	2
#13104	2
#12977	2
#12913	2
#12845	2
#12784	2