Subgroups — #497688

Order 512.

794 conjugacy classes of subgroups.

The subgroup lattice has 557 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#2164	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	#20385	C₂	1	1	yes	maximal, characteristic
4	#13121	C₂	1	1	yes	maximal, characteristic, complemented
5	#13121	C₂	1	1	yes	maximal, characteristic, complemented
6	#13120	C₂	1	1	yes	maximal, characteristic, complemented
7	#13120	C₂	1	1	yes	maximal, characteristic, complemented
8	#12912	C₂	1	1	yes	maximal, characteristic, complemented
9	#12912	C₂	1	1	yes	maximal, characteristic, complemented
10	#12845	C₂	1	1	yes	maximal, characteristic, complemented
11	#12784	C₂	1	1	yes	maximal, characteristic, complemented
12	#12679	C₂	1	1	yes	maximal, characteristic
13	#12611	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₆×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	#12600	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂⁴×C₈	C₂²	1	1	yes	characteristic
17	C₂³×C₁₆	C₂²	1	1	yes	characteristic
18	C₂³×C₁₆	C₂²	1	1	yes	characteristic
19	C₂×#407	C₄	1	1	yes	characteristic
20	C₂×#405	C₂²	1	1	yes	characteristic
21	C₂×#405	C₂²	1	1	yes	characteristic
22	#2280	C₄	1	1	yes	characteristic
23	#2164	—	2	4	no	—
24	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₂²⋊C₁₆	—	2	4	no	—
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×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
39	C₂×#346	C₂²	1	1	yes	characteristic, complemented
40	C₂×#346	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic, complemented
43	#1752	C₄	1	1	yes	characteristic
44	#1752	C₄	1	1	yes	characteristic
45	#1752	C₄	1	1	yes	characteristic
46	#1752	C₄	1	1	yes	characteristic
47	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
48	C₈×C₂²⋊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	#1729	C₄	1	1	yes	characteristic
52	#1729	C₄	1	1	yes	characteristic
53	#1374	C₂²	1	1	yes	characteristic, complemented
54	#1374	C₂²	1	1	yes	characteristic, complemented
55	#1374	C₂²	1	1	yes	characteristic, complemented
56	#1374	C₂²	1	1	yes	characteristic, complemented
57	#1374	C₂²	1	1	yes	characteristic, complemented
58	#1374	C₂²	1	1	yes	characteristic, complemented
59	#1374	C₂²	1	1	yes	characteristic, complemented
60	#1374	C₂²	1	1	yes	characteristic, complemented
61	C₂⁴×C₄	C₂×C₄	1	1	yes	characteristic
62	C₂²×M₁₆	C₂×C₄	1	1	yes	characteristic
63	C₂²×M₁₆	C₂×C₄	1	1	yes	characteristic
64	C₂³×C₈	—	2	2	no	—
65	C₂³×C₈	—	2	2	no	—
66	C₂³×C₈	—	2	2	no	—
67	C₂³×C₈	—	2	2	no	—
68	C₂³×C₈	—	4	1	no	—
69	C₂³×C₈	—	4	1	no	—
70	C₂³×C₈	C₂×C₄	1	1	yes	characteristic
71	C₂³×C₈	C₂×C₄	1	1	yes	characteristic
72	C₂³×C₈	C₂×C₄	1	1	yes	characteristic
73	C₂³×C₈	C₂³	1	1	yes	characteristic
74	C₂³×C₈	C₂³	1	1	yes	characteristic
75	C₂³×C₈	C₂³	1	1	yes	characteristic
76	C₂×#117	C₂×C₄	1	1	yes	characteristic
77	C₂×#117	C₂×C₄	1	1	yes	characteristic
78	C₂²×C₁₆	—	2	2	no	—
79	C₂²×C₁₆	—	2	2	no	—
80	C₂²×C₁₆	—	2	2	no	—
81	C₂²×C₁₆	—	2	2	no	—
82	C₂²×C₁₆	—	4	1	no	—
83	C₂²×C₁₆	—	4	1	no	—
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	C₂²×C₁₆	C₂³	1	1	yes	characteristic
91	C₂²×C₁₆	C₂³	1	1	yes	characteristic
92	#407	—	2	4	no	—
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	#405	—	2	2	no	—
98	#405	—	2	2	no	—
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×#97	C₂×C₄	1	1	yes	characteristic
104	C₂×#97	C₂×C₄	1	1	yes	characteristic
105	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
106	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
107	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
108	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
109	#381	C₈	1	1	yes	characteristic
110	#381	C₈	1	1	yes	characteristic
111	#380	C₈	1	1	yes	characteristic
112	#380	C₈	1	1	yes	characteristic
113	#380	C₈	1	1	yes	characteristic
114	#380	C₈	1	1	yes	characteristic
115	#379	C₈	1	1	yes	characteristic
116	#379	C₈	1	1	yes	characteristic
117	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
118	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
119	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
120	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
121	C₄⋊C₁₆	—	2	2	no	—
122	C₄⋊C₁₆	—	2	2	no	—
123	C₄⋊C₁₆	—	4	1	no	—
124	C₄⋊C₁₆	—	4	1	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	C₂²⋊C₁₆	—	2	2	no	—
130	C₂²⋊C₁₆	—	2	2	no	—
131	C₂²⋊C₁₆	—	2	2	no	—
132	C₂²⋊C₁₆	—	4	1	no	—
133	C₂²⋊C₁₆	—	4	1	no	—
134	C₂²⋊C₁₆	D₄	1	4	yes	—
135	#346	—	2	2	no	—
136	#346	—	4	1	no	—
137	C₄×C₁₆	—	2	2	no	—
138	C₄×C₁₆	—	4	1	no	—
139	#336	C₂×C₄	1	1	yes	characteristic
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	#336	C₂×C₄	1	1	yes	characteristic
147	C₂⁵	C₂×C₈	1	1	yes	characteristic
148	C₂³×C₄	—	2	2	no	—
149	C₂³×C₄	—	2	2	no	—
150	C₂³×C₄	—	2	2	no	—
151	C₂³×C₄	—	2	2	no	—
152	C₂³×C₄	—	4	1	no	—
153	C₂³×C₄	—	4	1	no	—
154	C₂³×C₄	C₂×C₈	1	1	yes	characteristic
155	C₂³×C₄	C₂×C₈	1	1	yes	characteristic
156	C₂³×C₄	C₂×C₈	1	1	yes	characteristic
157	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
158	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
159	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
160	C₂×M₁₆	—	2	2	no	—
161	C₂×M₁₆	—	2	2	no	—
162	C₂×M₁₆	—	2	2	no	—
163	C₂×M₁₆	—	2	2	no	—
164	C₂×M₁₆	—	4	1	no	—
165	C₂×M₁₆	—	4	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	—	2	1	no	—
172	C₂²×C₈	—	2	1	no	—
173	C₂²×C₈	—	2	1	no	—
174	C₂²×C₈	—	2	2	no	—
175	C₂²×C₈	—	2	2	no	—
176	C₂²×C₈	—	2	2	no	—
177	C₂²×C₈	—	2	2	no	—
178	C₂²×C₈	—	2	2	no	—
179	C₂²×C₈	—	2	2	no	—
180	C₂²×C₈	—	2	1	no	—
181	C₂²×C₈	—	2	1	no	—
182	C₂²×C₈	—	2	1	no	—
183	C₂²×C₈	—	2	1	no	—
184	C₂²×C₈	—	2	1	no	—
185	C₂²×C₈	—	2	1	no	—
186	C₂²×C₈	—	4	1	no	—
187	C₂²×C₈	—	4	1	no	—
188	C₂²×C₈	—	4	1	no	—
189	C₂²×C₈	—	4	4	no	—
190	C₂²×C₈	—	4	4	no	—
191	C₂²×C₈	—	4	4	no	—
192	C₂²×C₈	—	4	4	no	—
193	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
194	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
195	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
198	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
199	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₈	C₂×D₄	1	2	yes	—
201	C₂²×C₈	#41	1	2	yes	—
202	C₂²×C₈	#41	1	2	yes	—
203	C₂²×C₈	#41	1	2	yes	—
204	C₂²×C₈	C₂⁴	1	1	yes	characteristic
205	#117	—	2	2	no	—
206	#117	—	2	2	no	—
207	#117	—	4	1	no	—
208	#117	—	4	1	no	—
209	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
210	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
211	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
212	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
213	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
214	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
215	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
216	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
217	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
218	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
219	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
220	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
221	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
222	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
223	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
224	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
225	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
226	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
227	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
228	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
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	—	2	1	no	—
235	C₂×C₁₆	—	2	1	no	—
236	C₂×C₁₆	—	2	1	no	—
237	C₂×C₁₆	—	2	1	no	—
238	C₂×C₁₆	—	2	1	no	—
239	C₂×C₁₆	—	2	1	no	—
240	C₂×C₁₆	—	2	1	no	—
241	C₂×C₁₆	—	2	1	no	—
242	C₂×C₁₆	—	2	1	no	—
243	C₂×C₁₆	—	2	1	no	—
244	C₂×C₁₆	—	2	1	no	—
245	C₂×C₁₆	—	2	1	no	—
246	C₂×C₁₆	—	2	1	no	—
247	C₂×C₁₆	—	2	1	no	—
248	C₂×C₁₆	—	2	1	no	—
249	C₂×C₁₆	—	2	1	no	—
250	C₂×C₁₆	—	2	1	no	—
251	C₂×C₁₆	—	4	4	no	—
252	C₂×C₁₆	—	4	4	no	—
253	C₂×C₁₆	C₂×D₄	1	2	yes	—
254	C₂×C₁₆	C₂×D₄	1	2	yes	—
255	C₂²⋊C₈	—	2	2	no	—
256	C₂²⋊C₈	—	2	2	no	—
257	C₂²⋊C₈	—	2	2	no	—
258	C₂²⋊C₈	M₁₆	1	4	yes	—
259	#97	—	2	2	no	—
260	#97	—	2	2	no	—
261	#97	—	4	1	no	—
262	#97	—	4	1	no	—
263	C₄×C₈	—	2	1	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	#95	C₂×C₈	1	1	yes	characteristic
272	#95	C₂×C₈	1	1	yes	characteristic
273	#95	C₂×C₈	1	1	yes	characteristic
274	#95	C₂×C₈	1	1	yes	characteristic
275	#95	C₂×C₈	1	1	yes	characteristic
276	#95	C₂×C₈	1	1	yes	characteristic
277	#95	C₂×C₈	1	1	yes	characteristic
278	#95	C₂×C₈	1	1	yes	characteristic
279	C₂⁴	—	2	2	no	—
280	C₂⁴	—	2	2	no	—
281	C₂⁴	—	2	2	no	—
282	C₂⁴	—	2	2	no	—
283	C₂⁴	—	2	2	no	—
284	C₂⁴	—	4	1	no	—
285	C₂⁴	—	4	1	no	—
286	C₂⁴	C₂²×C₈	1	1	yes	characteristic
287	C₂⁴	C₂²×C₈	1	1	yes	characteristic
288	C₂⁴	C₂²×C₈	1	1	yes	characteristic
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	—	2	1	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	4	1	no	—
310	C₂²×C₄	—	4	1	no	—
311	C₂²×C₄	—	4	1	no	—
312	C₂²×C₄	—	4	4	no	—
313	C₂²×C₄	—	4	4	no	—
314	C₂²×C₄	—	4	4	no	—
315	C₂²×C₄	—	4	4	no	—
316	C₂²×C₄	#117	1	2	yes	—
317	C₂²×C₄	C₄×D₄	1	2	yes	—
318	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
319	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
320	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
321	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
322	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
323	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
324	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
325	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
326	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
327	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
328	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
329	C₂²×C₄	C₂×M₁₆	1	2	yes	—
330	C₂²×C₄	#131	1	2	yes	—
331	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
332	M₁₆	—	4	4	no	—
333	M₁₆	—	4	4	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	—	2	1	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	4	4	no	—
360	C₂×C₈	—	4	4	no	—
361	C₂×C₈	—	4	4	no	—
362	C₂×C₈	—	4	1	no	—
363	C₂×C₈	—	4	1	no	—
364	C₂×C₈	—	4	1	no	—
365	C₂×C₈	—	4	1	no	—
366	C₂×C₈	#117	1	2	yes	—
367	C₂×C₈	C₄×D₄	1	2	yes	—
368	C₂×C₈	C₂×M₁₆	1	2	yes	—
369	C₂×C₈	C₂×M₁₆	1	2	yes	—
370	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₈	C₂×#41	1	1	yes	characteristic
372	C₂×C₈	C₂×#41	1	1	yes	characteristic
373	C₂×C₈	C₂×#41	1	1	yes	characteristic
374	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
375	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	4	1	no	—
379	C₄⋊C₄	—	4	1	no	—
380	C₂²⋊C₄	—	2	2	no	—
381	C₂²⋊C₄	—	2	2	no	—
382	C₂²⋊C₄	—	2	2	no	—
383	C₂²⋊C₄	—	2	2	no	—
384	C₂²⋊C₄	—	2	2	no	—
385	C₂²⋊C₄	—	2	2	no	—
386	C₂²⋊C₄	—	2	2	no	—
387	C₂²⋊C₄	—	2	2	no	—
388	C₂²⋊C₄	—	4	1	no	—
389	C₂²⋊C₄	—	4	1	no	—
390	C₂²⋊C₄	—	4	1	no	—
391	C₂²⋊C₄	—	4	1	no	—
392	C₄²	—	2	1	no	—
393	C₄²	—	2	1	no	—
394	C₄²	—	2	1	no	—
395	C₄²	—	2	1	no	—
396	C₄²	—	2	1	no	—
397	C₄²	—	2	1	no	—
398	C₄²	—	2	1	no	—
399	C₄²	—	2	1	no	—
400	C₁₆	—	2	2	no	—
401	C₁₆	—	2	2	no	—
402	C₁₆	—	4	1	no	—
403	C₁₆	—	4	1	no	—
404	C₁₆	—	4	1	no	—
405	C₁₆	—	4	1	no	—
406	C₁₆	—	4	1	no	—
407	C₁₆	—	4	1	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	1	no	—
410	C₂³	—	2	1	no	—
411	C₂³	—	2	1	no	—
412	C₂³	—	2	8	no	—
413	C₂³	—	2	1	no	—
414	C₂³	—	2	1	no	—
415	C₂³	—	2	1	no	—
416	C₂³	—	2	1	no	—
417	C₂³	—	2	1	no	—
418	C₂³	—	2	1	no	—
419	C₂³	—	2	1	no	—
420	C₂³	—	2	1	no	—
421	C₂³	—	2	1	no	—
422	C₂³	—	2	1	no	—
423	C₂³	—	2	1	no	—
424	C₂³	—	2	1	no	—
425	C₂³	—	4	4	no	—
426	C₂³	—	4	4	no	—
427	C₂³	—	4	4	no	—
428	C₂³	—	4	4	no	—
429	C₂³	—	4	4	no	—
430	C₂³	—	4	4	no	—
431	C₂³	#431	1	2	yes	—
432	C₂³	C₈×D₄	1	2	yes	—
433	C₂³	#504	1	2	yes	—
434	C₂³	#504	1	2	yes	—
435	C₂³	#504	1	2	yes	—
436	C₂³	C₂³×C₈	1	1	yes	characteristic
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	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	—	4	4	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	#431	1	2	yes	—
484	C₂×C₄	C₈×D₄	1	2	yes	—
485	C₂×C₄	C₂×#117	1	1	yes	characteristic
486	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
487	C₂×C₄	#518	1	1	yes	characteristic
488	C₂×C₄	C₂²×M₁₆	1	1	yes	characteristic
489	C₂×C₄	C₂×#131	1	1	yes	characteristic
490	C₂×C₄	#568	1	1	yes	characteristic
491	C₈	—	2	2	no	—
492	C₈	—	2	2	no	—
493	C₈	—	2	2	no	—
494	C₈	—	2	2	no	—
495	C₈	—	4	1	no	—
496	C₈	—	4	1	no	—
497	C₈	—	4	1	no	—
498	C₈	#546	1	1	yes	characteristic
499	C₈	#546	1	1	yes	characteristic
500	C₈	#551	1	1	yes	characteristic
501	C₈	#551	1	1	yes	characteristic
502	C₂²	—	2	2	no	—
503	C₂²	—	2	2	no	—
504	C₂²	—	2	2	no	—
505	C₂²	—	2	2	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	2	2	no	—
509	C₂²	—	2	2	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	2	2	no	—
513	C₂²	—	2	2	no	—
514	C₂²	—	4	16	no	—
515	C₂²	—	4	1	no	—
516	C₂²	—	4	1	no	—
517	C₂²	—	4	1	no	—
518	C₂²	—	4	1	no	—
519	C₂²	—	4	1	no	—
520	C₂²	—	4	1	no	—
521	C₂²	—	4	1	no	—
522	C₂²	—	4	1	no	—
523	C₂²	#2164	1	4	yes	complemented
524	C₂²	C₂×#431	1	1	yes	characteristic
525	C₂²	C₂×C₈×D₄	1	1	yes	characteristic
526	C₂²	#2972	1	1	yes	characteristic
527	C₂²	C₂×#504	1	1	yes	characteristic
528	C₂²	C₂×#504	1	1	yes	characteristic
529	C₂²	C₂×#504	1	1	yes	characteristic
530	C₂²	#3407	1	1	yes	characteristic
531	C₄	—	2	2	no	—
532	C₄	—	2	2	no	—
533	C₄	—	4	1	no	—
534	C₄	—	4	1	no	—
535	C₄	—	4	1	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	1	no	—
538	C₄	—	4	1	no	—
539	C₄	—	4	1	no	—
540	C₄	—	4	1	no	—
541	C₄	—	4	1	no	—
542	C₄	#2342	1	1	yes	characteristic
543	C₄	#2924	1	1	yes	characteristic
544	C₄	D₄×M₁₆	1	1	yes	characteristic
545	C₄	#2974	1	1	yes	characteristic
546	C₂	—	2	4	no	—
547	C₂	—	4	2	no	—
548	C₂	—	4	2	no	—
549	C₂	#22552	1	1	yes	characteristic
550	C₂	C₂×#2164	1	1	yes	characteristic
551	C₂	#33422	1	1	yes	characteristic
552	C₂	#33432	1	1	yes	characteristic
553	C₂	#33436	1	1	yes	characteristic
554	C₂	#33490	1	1	yes	characteristic
555	C₂	#33491	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, cosocle	C₂²×C₈	C₂⁴
commutator, socle	C₂³	C₂³×C₈
prime radical	C₂⁵	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×#2164	C₂	semidirect
4. #13121	C₂	semidirect
5. #13121	C₂	semidirect
6. #13120	C₂	semidirect
7. #13120	C₂	semidirect
8. #12912	C₂	semidirect
9. #12912	C₂	semidirect
10. #12845	C₂	semidirect
11. #12784	C₂	semidirect
13. #12611	C₂	semidirect
14. C₁₆×C₂²⋊C₄	C₂	semidirect
15. #12600	C₂	semidirect
24. C₂×C₄⋊C₁₆	C₂²	semidirect
25. C₂×C₄⋊C₁₆	C₂²	semidirect
26. C₂×C₄⋊C₁₆	C₂²	semidirect
27. C₂×C₄⋊C₁₆	C₂²	semidirect
39. C₂×#346	C₂²	semidirect
40. C₂×#346	C₂²	semidirect
41. C₂×C₄×C₁₆	C₂²	semidirect
42. C₂×C₄×C₁₆	C₂²	semidirect
53. #1374	C₂²	semidirect
54. #1374	C₂²	semidirect
55. #1374	C₂²	semidirect
56. #1374	C₂²	semidirect
57. #1374	C₂²	semidirect
58. #1374	C₂²	semidirect
59. #1374	C₂²	semidirect
60. #1374	C₂²	semidirect
523. C₂²	#2164	semidirect

Maximal subgroups

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

subgroup	index
C₂×#2164	2
C₂²×C₂²⋊C₁₆	2
#20385	2
#13121	2
#13120	2
#12912	2
#12845	2
#12784	2
#12679	2
#12611	2
C₁₆×C₂²⋊C₄	2
#12600	2