Subgroups — #497970

Order 512.

625 conjugacy classes of subgroups.

The subgroup lattice has 487 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	C₂×#2151	C₂	1	1	yes	maximal, characteristic, complemented
3	#20485	C₂	1	1	yes	maximal, characteristic
4	#13120	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	#12879	C₂	1	1	yes	maximal, characteristic, complemented
11	#12784	C₂	1	1	yes	maximal, characteristic, complemented
12	#12784	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
14	#12612	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₆×C₂²⋊C₄	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×#436	C₄	1	1	yes	characteristic
19	C₂×C₈×D₄	C₂²	1	1	yes	characteristic
20	C₂×#405	C₂²	1	1	yes	characteristic
21	C₂×#405	C₂²	1	1	yes	characteristic
22	#2293	C₄	1	1	yes	characteristic
23	#2164	—	2	4	no	—
24	#2151	—	2	4	no	—
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×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊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	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
41	#1770	C₄	1	1	yes	characteristic
42	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	#1767	C₄	1	1	yes	characteristic
44	#1753	C₄	1	1	yes	characteristic
45	#1753	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	#1750	C₄	1	1	yes	characteristic
50	C₄²×C₈	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	C₂²×M₁₆	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	C₂×#117	C₂×C₄	1	1	yes	characteristic
68	C₂×M₃₂	—	2	2	no	—
69	C₂×M₃₂	—	2	2	no	—
70	C₂×M₃₂	—	4	1	no	—
71	C₂²×C₁₆	—	2	2	no	—
72	C₂²×C₁₆	—	2	2	no	—
73	C₂²×C₁₆	—	4	1	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	#436	—	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	#405	—	2	2	no	—
94	#405	—	2	2	no	—
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×#97	C₂×C₄	1	1	yes	characteristic
99	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
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	#390	C₈	1	1	yes	characteristic
108	#390	C₈	1	1	yes	characteristic
109	#389	C₈	1	1	yes	characteristic
110	#389	C₈	1	1	yes	characteristic
111	#388	C₈	1	1	yes	characteristic
112	#388	C₈	1	1	yes	characteristic
113	#388	C₈	1	1	yes	characteristic
114	#388	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	C₄³	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	C₄⋊C₁₆	—	2	2	no	—
124	C₄⋊C₁₆	D₄	1	4	yes	complemented
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	—	4	1	no	—
130	C₂²⋊C₁₆	—	4	1	no	—
131	#346	—	2	2	no	—
132	C₄×C₁₆	—	2	2	no	—
133	C₄×C₁₆	—	4	1	no	—
134	C₄×C₁₆	—	4	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
143	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
144	C₂×M₁₆	—	2	2	no	—
145	C₂×M₁₆	—	2	2	no	—
146	C₂×M₁₆	—	2	2	no	—
147	C₂×M₁₆	—	2	2	no	—
148	C₂×M₁₆	—	4	1	no	—
149	C₂×M₁₆	—	4	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	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	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₈	#41	1	2	yes	—
168	C₂²×C₈	#41	1	2	yes	—
169	C₂²×C₈	C₂⁴	1	1	yes	characteristic
170	C₄×D₄	—	2	2	no	—
171	C₄×D₄	—	2	2	no	—
172	#117	—	2	2	no	—
173	#117	—	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×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
182	C₂×C₄⋊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×C₂²⋊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×C₄²	C₂×C₈	1	1	yes	characteristic
194	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
195	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
196	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
197	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
198	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
200	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
201	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
202	M₃₂	—	4	4	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	—	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	—	4	4	no	—
226	C₂×C₁₆	C₂×D₄	1	2	yes	—
227	C₂×C₁₆	C₂×D₄	1	2	yes	—
228	C₄⋊C₈	—	2	2	no	—
229	C₄⋊C₈	—	2	2	no	—
230	C₂²⋊C₈	—	2	2	no	—
231	C₂²⋊C₈	—	2	2	no	—
232	C₂²⋊C₈	—	2	2	no	—
233	C₂²⋊C₈	M₁₆	1	4	yes	—
234	#97	—	2	2	no	—
235	#97	—	2	2	no	—
236	#97	—	2	2	no	—
237	#97	—	2	2	no	—
238	C₄×C₈	—	2	2	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	1	no	—
245	C₄×C₈	—	2	1	no	—
246	C₄×C₈	—	2	1	no	—
247	C₄×C₈	—	2	2	no	—
248	C₄×C₈	—	4	1	no	—
249	C₄×C₈	C₂×D₄	1	2	yes	—
250	C₄×C₈	#41	1	2	yes	—
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	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	1	no	—
269	C₂²×C₄	—	2	1	no	—
270	C₂²×C₄	—	2	1	no	—
271	C₂²×C₄	—	2	1	no	—
272	C₂²×C₄	#117	1	2	yes	—
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	C₂²×C₈	1	1	yes	characteristic
285	C₂²×C₄	C₂×M₁₆	1	2	yes	—
286	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
287	M₁₆	—	4	4	no	—
288	M₁₆	—	4	4	no	—
289	C₂×C₈	—	2	1	no	—
290	C₂×C₈	—	2	1	no	—
291	C₂×C₈	—	2	1	no	—
292	C₂×C₈	—	2	1	no	—
293	C₂×C₈	—	2	1	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	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	—	2	1	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	#117	1	2	yes	—
315	C₂×C₈	C₄×D₄	1	2	yes	—
316	C₂×C₈	C₂×M₁₆	1	2	yes	—
317	C₂×C₈	C₂×M₁₆	1	2	yes	—
318	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₈	C₂×#41	1	1	yes	characteristic
320	C₂×C₈	C₂×#41	1	1	yes	characteristic
321	C₂×C₈	C₂×#41	1	1	yes	characteristic
322	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
323	C₂×C₈	2₋¹⁺⁴	1	1	yes	characteristic
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	4	1	no	—
331	C₂²⋊C₄	—	2	2	no	—
332	C₂²⋊C₄	—	2	2	no	—
333	C₂²⋊C₄	—	2	2	no	—
334	C₂²⋊C₄	—	2	2	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	C₄²	—	2	1	no	—
342	C₄²	—	2	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	2	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	4	1	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	—	4	1	no	—
358	C₁₆	—	4	1	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	—	2	1	no	—
376	C₂³	#431	1	2	yes	—
377	C₂³	C₂³×C₈	1	1	yes	characteristic
378	D₄	—	4	4	no	—
379	C₂×C₄	—	2	1	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	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	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	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	#431	1	2	yes	—
418	C₂×C₄	C₈×D₄	1	2	yes	—
419	C₂×C₄	C₈×D₄	1	2	yes	—
420	C₂×C₄	#504	1	2	yes	—
421	C₂×C₄	#504	1	2	yes	—
422	C₂×C₄	#504	1	2	yes	—
423	C₂×C₄	C₂×#117	1	1	yes	characteristic
424	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
425	C₂×C₄	#520	1	1	yes	characteristic
426	C₂×C₄	C₂²×M₁₆	1	1	yes	characteristic
427	C₂×C₄	C₂×#131	1	1	yes	characteristic
428	C₂×C₄	#568	1	1	yes	characteristic
429	C₈	—	2	2	no	—
430	C₈	—	2	2	no	—
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	#546	1	1	yes	characteristic
437	C₈	#548	1	1	yes	characteristic
438	C₈	#552	1	1	yes	characteristic
439	C₈	#553	1	1	yes	characteristic
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	—	4	1	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	C₂×#431	1	1	yes	characteristic
455	C₂²	C₂×C₈×D₄	1	1	yes	characteristic
456	C₂²	#2988	1	1	yes	characteristic
457	C₂²	C₂×#504	1	1	yes	characteristic
458	C₂²	C₂×#504	1	1	yes	characteristic
459	C₂²	C₂×#504	1	1	yes	characteristic
460	C₂²	#3407	1	1	yes	characteristic
461	C₄	—	2	2	no	—
462	C₄	—	2	2	no	—
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	#2352	1	1	yes	characteristic
474	C₄	#2925	1	1	yes	characteristic
475	C₄	D₄×M₁₆	1	1	yes	characteristic
476	C₄	#2990	1	1	yes	characteristic
477	C₂	—	4	2	no	—
478	C₂	—	8	1	no	—
479	C₂	#22748	1	1	yes	characteristic
480	C₂	#33420	1	1	yes	characteristic
481	C₂	#33422	1	1	yes	characteristic
482	C₂	#33434	1	1	yes	characteristic
483	C₂	#33438	1	1	yes	characteristic
484	C₂	#33506	1	1	yes	characteristic
485	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
1. C₂×#2164	C₂	semidirect
2. C₂×#2151	C₂	semidirect
4. #13120	C₂	semidirect
5. #13120	C₂	semidirect
6. #13105	C₂	semidirect
7. #13104	C₂	semidirect
10. #12879	C₂	semidirect
11. #12784	C₂	semidirect
12. #12784	C₂	semidirect
13. C₄×C₄⋊C₁₆	C₂	semidirect
14. #12612	C₂	semidirect
15. C₁₆×C₂²⋊C₄	C₂	semidirect
124. 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×#2164	2
C₂×#2151	2
#20485	2
#13120	2
#13105	2
#13104	2
#12977	2
#12976	2
#12879	2
#12784	2
C₄×C₄⋊C₁₆	2
#12612	2
C₁₆×C₂²⋊C₄	2