Subgroups — #498174

Order 512.

654 conjugacy classes of subgroups.

The subgroup lattice has 481 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#2162	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×#123	C₂	1	1	yes	maximal, characteristic
4	#13159	C₂	1	1	yes	maximal, characteristic, complemented
5	#13120	C₂	1	1	yes	maximal, characteristic, complemented
6	#13120	C₂	1	1	yes	maximal, characteristic, complemented
7	#13104	C₂	1	1	yes	maximal, characteristic, complemented
8	#13104	C₂	1	1	yes	maximal, characteristic, complemented
9	#12976	C₂	1	1	yes	maximal, characteristic
10	#12912	C₂	1	1	yes	maximal, characteristic, complemented
11	#12912	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₆×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₆×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₆×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#1374	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×C₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₁₆	C₂²	1	1	yes	characteristic
18	C₂³×C₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₈×D₄	C₂²	1	1	yes	characteristic
20	C₂²×C₄×C₈	C₂²	1	1	yes	characteristic
21	C₄×#123	C₄	1	1	yes	characteristic
22	D₄×C₁₆	—	2	4	no	—
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×C₄⋊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×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	#1923	C₄	1	1	yes	characteristic
40	#1923	C₄	1	1	yes	characteristic
41	#1916	C₄	1	1	yes	characteristic
42	#1916	C₄	1	1	yes	characteristic
43	#1869	C₄	1	1	yes	characteristic
44	#1850	C₄	1	1	yes	characteristic
45	#1817	C₄	1	1	yes	characteristic
46	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₈×C₄⋊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	#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	C₂³×C₈	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₈	C₂³	1	1	yes	characteristic
63	C₂³×C₈	C₂³	1	1	yes	characteristic
64	C₂×#123	C₈	1	1	yes	characteristic
65	C₂×C₄×D₄	C₂×C₄	1	1	yes	characteristic
66	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₁₆	—	2	2	no	—
68	C₂²×C₁₆	—	2	2	no	—
69	C₂²×C₁₆	—	2	2	no	—
70	C₂²×C₁₆	—	2	2	no	—
71	C₂²×C₁₆	—	2	2	no	—
72	C₂²×C₁₆	—	2	2	no	—
73	C₂²×C₁₆	—	4	1	no	—
74	C₂²×C₁₆	—	4	1	no	—
75	C₂²×C₁₆	—	4	1	no	—
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	C₂²×C₁₆	C₂³	1	1	yes	characteristic
83	C₂²×C₁₆	C₂³	1	1	yes	characteristic
84	C₈×D₄	—	2	2	no	—
85	C₈×D₄	—	2	2	no	—
86	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄⋊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	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×C₄×C₈	—	2	2	no	—
95	C₂×C₄×C₈	—	2	2	no	—
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	#388	C₈	1	1	yes	characteristic
104	#388	C₈	1	1	yes	characteristic
105	#387	C₈	1	1	yes	characteristic
106	#387	C₈	1	1	yes	characteristic
107	#386	C₈	1	1	yes	characteristic
108	#385	C₈	1	1	yes	characteristic
109	#381	C₈	1	1	yes	characteristic
110	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
111	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
112	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
113	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
114	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
115	C₄⋊C₁₆	—	2	2	no	—
116	C₄⋊C₁₆	—	2	2	no	—
117	C₄⋊C₁₆	—	2	2	no	—
118	C₄⋊C₁₆	—	2	2	no	—
119	C₄⋊C₁₆	—	4	1	no	—
120	C₂²⋊C₁₆	—	2	2	no	—
121	C₂²⋊C₁₆	—	2	2	no	—
122	C₂²⋊C₁₆	—	2	2	no	—
123	C₂²⋊C₁₆	—	4	1	no	—
124	C₂²⋊C₁₆	D₄	1	4	yes	—
125	C₄×C₁₆	—	2	2	no	—
126	C₄×C₁₆	—	2	2	no	—
127	C₄×C₁₆	—	2	2	no	—
128	C₄×C₁₆	—	2	2	no	—
129	C₄×C₁₆	—	4	1	no	—
130	#336	C₂×C₄	1	1	yes	characteristic
131	#336	C₂×C₄	1	1	yes	characteristic
132	#336	C₂×C₄	1	1	yes	characteristic
133	#336	C₂×C₄	1	1	yes	characteristic
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	C₂³×C₄	C₂×C₈	1	1	yes	characteristic
142	C₂³×C₄	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	C₂²×C₈	—	2	1	no	—
146	C₂²×C₈	—	2	1	no	—
147	C₂²×C₈	—	2	1	no	—
148	C₂²×C₈	—	2	1	no	—
149	C₂²×C₈	—	2	2	no	—
150	C₂²×C₈	—	2	2	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	—	4	1	no	—
158	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
166	C₂²×C₈	#41	1	2	yes	—
167	C₂²×C₈	C₂⁴	1	1	yes	characteristic
168	#123	C₁₆	1	8	yes	complemented
169	C₄×D₄	—	2	2	no	—
170	C₄×D₄	—	2	2	no	—
171	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
172	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
173	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
174	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
175	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
176	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
177	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
178	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
179	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
180	C₂×C₂²⋊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×C₄²	—	2	2	no	—
185	C₂×C₄²	—	2	2	no	—
186	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
187	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
188	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₁₆	—	2	1	no	—
194	C₂×C₁₆	—	2	1	no	—
195	C₂×C₁₆	—	2	1	no	—
196	C₂×C₁₆	—	2	1	no	—
197	C₂×C₁₆	—	2	1	no	—
198	C₂×C₁₆	—	2	1	no	—
199	C₂×C₁₆	—	2	1	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	—	4	4	no	—
214	C₂×C₁₆	—	4	4	no	—
215	C₂×C₁₆	—	4	4	no	—
216	C₂×C₁₆	C₂×D₄	1	2	yes	—
217	C₂×C₁₆	C₂×D₄	1	2	yes	—
218	C₂×C₁₆	#41	1	2	yes	—
219	C₂×C₁₆	#41	1	2	yes	—
220	C₄⋊C₈	—	2	2	no	—
221	C₄⋊C₈	—	2	2	no	—
222	C₄⋊C₈	—	4	1	no	—
223	C₂²⋊C₈	—	2	2	no	—
224	C₂²⋊C₈	—	2	2	no	—
225	C₂²⋊C₈	—	2	2	no	—
226	C₂²⋊C₈	—	2	2	no	—
227	C₂²⋊C₈	—	4	1	no	—
228	C₄×C₈	—	2	2	no	—
229	C₄×C₈	—	2	2	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	—	2	1	no	—
240	#95	C₂×C₈	1	1	yes	characteristic
241	#95	C₂×C₈	1	1	yes	characteristic
242	#95	C₂×C₈	1	1	yes	characteristic
243	#95	C₂×C₈	1	1	yes	characteristic
244	#95	C₂×C₈	1	1	yes	characteristic
245	#95	C₂×C₈	1	1	yes	characteristic
246	#95	C₂×C₈	1	1	yes	characteristic
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	C₂⁴	C₂²×C₈	1	1	yes	characteristic
251	C₂⁴	C₂²×C₈	1	1	yes	characteristic
252	C₂×D₄	—	2	2	no	—
253	C₂×D₄	—	2	2	no	—
254	C₂×D₄	C₂×C₁₆	1	4	yes	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	1	no	—
258	C₂²×C₄	—	2	1	no	—
259	C₂²×C₄	—	2	1	no	—
260	C₂²×C₄	—	2	1	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	1	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	1	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	4	1	no	—
270	C₂²×C₄	C₂×C₁₆	1	4	yes	complemented
271	C₂²×C₄	C₄×D₄	1	2	yes	—
272	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
273	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
274	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
275	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
276	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
277	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
278	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
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	#131	1	2	yes	—
285	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
286	C₂×C₈	—	2	1	no	—
287	C₂×C₈	—	2	1	no	—
288	C₂×C₈	—	2	1	no	—
289	C₂×C₈	—	2	1	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	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	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	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	—	4	4	no	—
310	C₂×C₈	—	4	1	no	—
311	C₂×C₈	—	4	1	no	—
312	C₂×C₈	—	4	1	no	—
313	C₂×C₈	—	4	1	no	—
314	C₂×C₈	C₄×D₄	1	2	yes	—
315	C₂×C₈	#131	1	2	yes	—
316	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
317	C₂×C₈	C₂×#41	1	1	yes	characteristic
318	C₂×C₈	C₂×#41	1	1	yes	characteristic
319	C₂×C₈	C₂×#41	1	1	yes	characteristic
320	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
321	C₂×C₈	2₋¹⁺⁴	1	1	yes	characteristic
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	C₂×C₁₆	1	4	yes	complemented
326	C₄⋊C₄	C₂×C₁₆	1	4	yes	complemented
327	C₂²⋊C₄	—	2	2	no	—
328	C₂²⋊C₄	—	2	2	no	—
329	C₂²⋊C₄	—	2	2	no	—
330	C₂²⋊C₄	—	2	2	no	—
331	C₂²⋊C₄	—	4	1	no	—
332	C₂²⋊C₄	C₂×C₁₆	1	4	yes	complemented
333	C₂²⋊C₄	C₂×C₁₆	1	4	yes	complemented
334	C₂²⋊C₄	C₂×C₁₆	1	4	yes	complemented
335	C₄²	—	2	1	no	—
336	C₄²	—	2	1	no	—
337	C₄²	—	2	1	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	2	1	no	—
342	C₄²	—	2	1	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	2	no	—
346	C₄²	—	2	2	no	—
347	C₁₆	—	2	2	no	—
348	C₁₆	—	2	2	no	—
349	C₁₆	—	2	2	no	—
350	C₁₆	—	2	2	no	—
351	C₁₆	—	4	1	no	—
352	C₁₆	—	4	1	no	—
353	C₁₆	—	4	1	no	—
354	C₁₆	—	4	1	no	—
355	C₂³	—	2	1	no	—
356	C₂³	—	2	1	no	—
357	C₂³	—	2	1	no	—
358	C₂³	—	2	1	no	—
359	C₂³	—	2	1	no	—
360	C₂³	—	2	1	no	—
361	C₂³	—	2	1	no	—
362	C₂³	—	2	1	no	—
363	C₂³	—	2	1	no	—
364	C₂³	—	2	1	no	—
365	C₂³	C₈×D₄	1	2	yes	—
366	C₂³	C₂²×C₁₆	1	2	yes	—
367	C₂³	C₂²×C₁₆	1	2	yes	—
368	C₂³	#504	1	2	yes	—
369	C₂³	C₂³×C₈	1	1	yes	characteristic
370	D₄	—	2	8	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	8	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	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	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	—	4	4	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	C₈×D₄	1	2	yes	—
411	C₂×C₄	C₂²×C₁₆	1	2	yes	—
412	C₂×C₄	C₂²×C₁₆	1	2	yes	—
413	C₂×C₄	C₂²×C₁₆	1	2	yes	—
414	C₂×C₄	C₂²×C₁₆	1	2	yes	—
415	C₂×C₄	C₂²×C₁₆	1	2	yes	—
416	C₂×C₄	#504	1	2	yes	—
417	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
418	C₂×C₄	C₄×#41	1	1	yes	characteristic
419	C₂×C₄	#520	1	1	yes	characteristic
420	C₂×C₄	C₂×#131	1	1	yes	characteristic
421	C₂×C₄	C₂×#131	1	1	yes	characteristic
422	C₂×C₄	#568	1	1	yes	characteristic
423	C₈	—	2	2	no	—
424	C₈	—	2	2	no	—
425	C₈	—	4	1	no	—
426	C₈	—	4	1	no	—
427	C₈	—	4	1	no	—
428	C₈	—	4	1	no	—
429	C₈	—	4	1	no	—
430	C₈	#546	1	1	yes	characteristic
431	C₈	#547	1	1	yes	characteristic
432	C₈	#551	1	1	yes	characteristic
433	C₈	#552	1	1	yes	characteristic
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	4	1	no	—
446	C₂²	—	4	1	no	—
447	C₂²	D₄×C₁₆	1	4	yes	—
448	C₂²	C₂×C₈×D₄	1	1	yes	characteristic
449	C₂²	C₈×#41	1	1	yes	characteristic
450	C₂²	#2988	1	1	yes	characteristic
451	C₂²	C₂³×C₁₆	1	1	yes	characteristic
452	C₂²	C₂×#504	1	1	yes	characteristic
453	C₂²	C₂×#504	1	1	yes	characteristic
454	C₂²	#3407	1	1	yes	characteristic
455	C₄	—	2	2	no	—
456	C₄	—	2	2	no	—
457	C₄	—	2	2	no	—
458	C₄	—	2	2	no	—
459	C₄	—	2	2	no	—
460	C₄	—	2	2	no	—
461	C₄	—	2	2	no	—
462	C₄	—	4	1	no	—
463	C₄	—	4	1	no	—
464	C₄	—	4	1	no	—
465	C₄	—	4	1	no	—
466	C₄	—	4	1	no	—
467	C₄	#2359	1	1	yes	characteristic
468	C₄	#2933	1	1	yes	characteristic
469	C₄	#2968	1	1	yes	characteristic
470	C₄	#2994	1	1	yes	characteristic
471	C₂	—	2	4	no	—
472	C₂	—	4	2	no	—
473	C₂	#22900	1	1	yes	characteristic
474	C₂	C₂×D₄×C₁₆	1	1	yes	characteristic
475	C₂	#33436	1	1	yes	characteristic
476	C₂	C₁₆×#41	1	1	yes	characteristic
477	C₂	#33482	1	1	yes	characteristic
478	C₂	#33502	1	1	yes	characteristic
479	C₂	#33508	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, cosocle	C₂²×C₈	C₂⁴
commutator	C₂²	C₂³×C₁₆
socle	C₂³	C₂³×C₈
prime radical	C₂²×D₄	C₂×C₈
LCS	G ▷ C₂² ▷ 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. C₂×#2162	C₂	semidirect
4. #13159	C₂	semidirect
5. #13120	C₂	semidirect
6. #13120	C₂	semidirect
7. #13104	C₂	semidirect
8. #13104	C₂	semidirect
10. #12912	C₂	semidirect
11. #12912	C₂	semidirect
12. C₁₆×C₄⋊C₄	C₂	semidirect
13. C₁₆×C₂²⋊C₄	C₂	semidirect
14. C₁₆×C₂²⋊C₄	C₂	semidirect
15. C₂×#1374	C₂	semidirect
168. #123	C₁₆	semidirect
270. C₂²×C₄	C₂×C₁₆	semidirect
325. C₄⋊C₄	C₂×C₁₆	semidirect
326. C₄⋊C₄	C₂×C₁₆	semidirect
332. C₂²⋊C₄	C₂×C₁₆	semidirect
333. C₂²⋊C₄	C₂×C₁₆	semidirect
334. C₂²⋊C₄	C₂×C₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×C₁₆	2
C₂×#2162	2
C₈×#123	2
#13159	2
#13120	2
#13104	2
#12976	2
#12912	2
C₁₆×C₄⋊C₄	2
C₁₆×C₂²⋊C₄	2
C₂×#1374	2