Subgroups — #497263

Order 512.

525 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#124	C₂	1	1	yes	maximal, characteristic
2	#13264	C₂	1	1	yes	maximal, characteristic, complemented
3	#13263	C₂	1	1	yes	maximal, characteristic, complemented
4	#13121	C₂	1	1	yes	maximal, characteristic, complemented
5	#13121	C₂	1	1	yes	maximal, characteristic, complemented
6	#13121	C₂	1	1	yes	maximal, characteristic, complemented
7	#13120	C₂	1	1	yes	maximal, characteristic, complemented
8	#12977	C₂	1	1	yes	maximal, characteristic
9	#12976	C₂	1	1	yes	maximal, characteristic
10	#12913	C₂	1	1	yes	maximal, characteristic, complemented
11	#12912	C₂	1	1	yes	maximal, characteristic, complemented
12	#12894	C₂	1	1	yes	maximal, characteristic, complemented
13	#12653	C₂	1	1	yes	maximal, characteristic, complemented
14	#12612	C₂	1	1	yes	maximal, characteristic, complemented
15	#12611	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×C₈×Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₈×D₄	C₂²	1	1	yes	characteristic
20	C₄×#124	C₄	1	1	yes	characteristic
21	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊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×#346	C₂²	1	1	yes	characteristic
32	C₂×#346	C₂²	1	1	yes	characteristic
33	C₂×#346	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
35	#1984	C₄	1	1	yes	characteristic
36	#1954	C₄	1	1	yes	characteristic
37	#1923	C₄	1	1	yes	characteristic
38	#1923	C₄	1	1	yes	characteristic
39	#1923	C₄	1	1	yes	characteristic
40	#1923	C₄	1	1	yes	characteristic
41	#1831	C₄	1	1	yes	characteristic
42	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
46	C₄²×C₈	C₂²	1	1	yes	characteristic
47	#1374	C₂²	1	1	yes	characteristic
48	#1374	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	C₂³×C₈	C₂³	1	1	yes	characteristic
60	C₂³×C₈	C₂³	1	1	yes	characteristic
61	C₂×#124	C₈	1	1	yes	characteristic
62	C₂×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×D₄	C₂×C₄	1	1	yes	characteristic
64	C₂×M₃₂	—	2	2	no	—
65	C₂×M₃₂	—	4	1	no	—
66	C₂×M₃₂	—	4	1	no	—
67	C₂²×C₁₆	—	2	2	no	—
68	C₂²×C₁₆	—	4	1	no	—
69	C₂²×C₁₆	—	4	1	no	—
70	C₂²×C₁₆	C₂³	1	1	yes	characteristic
71	C₂²×C₁₆	C₂³	1	1	yes	characteristic
72	C₂²×C₁₆	C₂³	1	1	yes	characteristic
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	C₈×Q₈	—	4	1	no	—
79	C₈×Q₈	—	4	1	no	—
80	C₈×D₄	—	4	1	no	—
81	C₈×D₄	—	4	1	no	—
82	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
86	C₂×C₂²⋊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	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
96	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
97	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
98	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
99	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
100	#391	C₈	1	1	yes	characteristic
101	#390	C₈	1	1	yes	characteristic
102	#388	C₈	1	1	yes	characteristic
103	#388	C₈	1	1	yes	characteristic
104	#388	C₈	1	1	yes	characteristic
105	#388	C₈	1	1	yes	characteristic
106	#382	C₈	1	1	yes	characteristic
107	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
108	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
109	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
110	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
111	C₄³	C₂×C₄	1	1	yes	characteristic
112	C₄⋊C₁₆	—	2	2	no	—
113	C₄⋊C₁₆	—	2	2	no	—
114	C₄⋊C₁₆	—	4	1	no	—
115	C₄⋊C₁₆	—	4	1	no	—
116	C₂²⋊C₁₆	—	2	2	no	—
117	C₂²⋊C₁₆	—	2	2	no	—
118	C₂²⋊C₁₆	—	4	1	no	—
119	C₂²⋊C₁₆	—	4	1	no	—
120	C₂²⋊C₁₆	—	4	1	no	—
121	C₂²⋊C₁₆	—	4	1	no	—
122	#346	—	4	1	no	—
123	#346	—	4	1	no	—
124	#346	—	4	1	no	—
125	C₄×C₁₆	—	4	1	no	—
126	#336	C₂×C₄	1	1	yes	characteristic
127	#336	C₂×C₄	1	1	yes	characteristic
128	#336	C₂×C₄	1	1	yes	characteristic
129	#336	C₂×C₄	1	1	yes	characteristic
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	C₂²×Q₈	C₂×C₈	1	1	yes	characteristic
135	C₂²×D₄	C₂×C₈	1	1	yes	characteristic
136	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
137	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₈	—	2	1	no	—
139	C₂²×C₈	—	2	1	no	—
140	C₂²×C₈	—	2	1	no	—
141	C₂²×C₈	—	2	1	no	—
142	C₂²×C₈	—	2	1	no	—
143	C₂²×C₈	—	2	1	no	—
144	C₂²×C₈	—	2	1	no	—
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	1	no	—
150	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₈	C₂⁴	1	1	yes	characteristic
158	#124	—	2	4	no	—
159	C₄×Q₈	—	4	1	no	—
160	C₄×Q₈	—	4	1	no	—
161	C₄×D₄	—	4	1	no	—
162	C₄×D₄	—	4	1	no	—
163	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
164	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
165	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
166	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
167	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
168	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
169	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
170	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
171	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
172	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
173	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
174	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
175	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
176	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
177	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
178	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
179	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
180	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
181	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
182	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
183	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
186	M₃₂	—	4	4	no	—
187	C₂×C₁₆	—	2	1	no	—
188	C₂×C₁₆	—	2	1	no	—
189	C₂×C₁₆	—	2	1	no	—
190	C₂×C₁₆	—	2	1	no	—
191	C₂×C₁₆	—	2	1	no	—
192	C₂×C₁₆	—	2	1	no	—
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	—	4	4	no	—
210	C₂×C₁₆	#41	1	2	yes	—
211	C₂×C₁₆	#41	1	2	yes	—
212	C₄⋊C₈	—	4	1	no	—
213	C₄⋊C₈	—	4	1	no	—
214	C₄⋊C₈	—	4	1	no	—
215	C₄⋊C₈	—	4	1	no	—
216	C₂²⋊C₈	—	2	2	no	—
217	C₂²⋊C₈	—	2	2	no	—
218	C₂²⋊C₈	—	4	1	no	—
219	C₂²⋊C₈	—	4	1	no	—
220	C₂²⋊C₈	—	4	1	no	—
221	C₂²⋊C₈	—	4	1	no	—
222	C₄×C₈	—	2	2	no	—
223	C₄×C₈	—	2	1	no	—
224	C₄×C₈	—	2	1	no	—
225	C₄×C₈	—	2	1	no	—
226	C₄×C₈	—	2	1	no	—
227	C₄×C₈	—	2	1	no	—
228	C₄×C₈	—	2	1	no	—
229	C₄×C₈	—	2	1	no	—
230	C₄×C₈	—	2	1	no	—
231	C₄×C₈	—	2	1	no	—
232	C₄×C₈	—	2	1	no	—
233	C₄×C₈	—	4	1	no	—
234	C₄×C₈	—	4	1	no	—
235	#95	C₂×C₈	1	1	yes	characteristic
236	#95	C₂×C₈	1	1	yes	characteristic
237	#95	C₂×C₈	1	1	yes	characteristic
238	#95	C₂×C₈	1	1	yes	characteristic
239	#95	C₂×C₈	1	1	yes	characteristic
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	C₂⁴	C₂²×C₈	1	1	yes	characteristic
244	C₂⁴	C₂²×C₈	1	1	yes	characteristic
245	C₂×Q₈	—	2	2	no	—
246	C₂×Q₈	—	2	2	no	—
247	C₂×Q₈	—	4	1	no	—
248	C₂×D₄	—	2	2	no	—
249	C₂×D₄	—	2	2	no	—
250	C₂×D₄	—	4	1	no	—
251	C₂²×C₄	—	2	1	no	—
252	C₂²×C₄	—	2	1	no	—
253	C₂²×C₄	—	2	1	no	—
254	C₂²×C₄	—	2	1	no	—
255	C₂²×C₄	—	2	1	no	—
256	C₂²×C₄	—	2	1	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	1	no	—
262	C₂²×C₄	—	2	1	no	—
263	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
264	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
265	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
266	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
267	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
268	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
269	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
270	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
271	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
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	C₂³×C₄	1	1	yes	characteristic
276	C₂×C₈	—	2	1	no	—
277	C₂×C₈	—	2	1	no	—
278	C₂×C₈	—	2	1	no	—
279	C₂×C₈	—	2	1	no	—
280	C₂×C₈	—	2	1	no	—
281	C₂×C₈	—	2	1	no	—
282	C₂×C₈	—	2	1	no	—
283	C₂×C₈	—	2	1	no	—
284	C₂×C₈	—	2	1	no	—
285	C₂×C₈	—	2	1	no	—
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	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	—	4	1	no	—
297	C₂×C₈	—	4	1	no	—
298	C₂×C₈	—	4	1	no	—
299	C₂×C₈	—	4	1	no	—
300	C₂×C₈	—	4	1	no	—
301	C₂×C₈	—	4	1	no	—
302	C₂×C₈	—	4	1	no	—
303	C₂×C₈	—	4	1	no	—
304	C₂×C₈	#131	1	2	yes	—
305	C₂×C₈	C₂×#41	1	1	yes	characteristic
306	C₂×C₈	C₂×#41	1	1	yes	characteristic
307	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
308	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
309	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
310	C₂×C₈	2₋¹⁺⁴	1	1	yes	characteristic
311	C₄⋊C₄	—	4	1	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₄⋊C₄	—	4	1	no	—
314	C₄⋊C₄	—	4	1	no	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₂²⋊C₄	—	2	2	no	—
317	C₂²⋊C₄	—	2	2	no	—
318	C₂²⋊C₄	—	4	1	no	—
319	C₂²⋊C₄	—	4	1	no	—
320	C₂²⋊C₄	—	4	1	no	—
321	C₂²⋊C₄	—	4	1	no	—
322	C₂²⋊C₄	—	4	1	no	—
323	C₂²⋊C₄	—	4	1	no	—
324	C₂²⋊C₄	M₃₂	1	4	yes	complemented
325	C₄²	—	2	1	no	—
326	C₄²	—	2	1	no	—
327	C₄²	—	2	1	no	—
328	C₄²	—	2	1	no	—
329	C₄²	—	2	1	no	—
330	C₄²	—	2	1	no	—
331	C₄²	—	2	1	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	2	1	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	4	1	no	—
338	C₄²	—	4	1	no	—
339	C₁₆	—	2	2	no	—
340	C₁₆	—	2	2	no	—
341	C₁₆	—	4	1	no	—
342	C₁₆	—	4	1	no	—
343	C₁₆	—	4	1	no	—
344	C₁₆	—	4	1	no	—
345	C₁₆	—	4	1	no	—
346	C₁₆	—	4	1	no	—
347	C₂³	—	2	1	no	—
348	C₂³	—	2	1	no	—
349	C₂³	—	2	1	no	—
350	C₂³	—	2	1	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	2	1	no	—
353	C₂³	—	2	1	no	—
354	C₂³	—	2	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	C₂×M₃₂	1	2	yes	—
361	C₂³	C₂³×C₈	1	1	yes	characteristic
362	Q₈	—	4	4	no	—
363	D₄	—	4	4	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	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	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	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	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	C₂×M₃₂	1	2	yes	—
406	C₂×C₄	C₂×M₃₂	1	2	yes	—
407	C₂×C₄	#504	1	2	yes	—
408	C₂×C₄	C₄×#41	1	1	yes	characteristic
409	C₂×C₄	#518	1	1	yes	characteristic
410	C₂×C₄	#520	1	1	yes	characteristic
411	C₂×C₄	C₂×#131	1	1	yes	characteristic
412	C₂×C₄	#568	1	1	yes	characteristic
413	C₂×C₄	#568	1	1	yes	characteristic
414	C₈	—	2	2	no	—
415	C₈	—	4	1	no	—
416	C₈	—	4	1	no	—
417	C₈	—	4	1	no	—
418	C₈	—	4	1	no	—
419	C₈	—	4	1	no	—
420	C₈	—	4	1	no	—
421	C₈	#538	1	1	yes	characteristic
422	C₈	#538	1	1	yes	characteristic
423	C₈	#542	1	1	yes	characteristic
424	C₈	#542	1	1	yes	characteristic
425	C₂²	—	2	2	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	4	1	no	—
429	C₂²	—	4	1	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	4	1	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	1	no	—
439	C₂²	C₈×#41	1	1	yes	characteristic
440	C₂²	#2972	1	1	yes	characteristic
441	C₂²	#2988	1	1	yes	characteristic
442	C₂²	C₂²×M₃₂	1	1	yes	characteristic
443	C₂²	C₂×#504	1	1	yes	characteristic
444	C₂²	#3407	1	1	yes	characteristic
445	C₂²	#3407	1	1	yes	characteristic
446	C₄	—	2	2	no	—
447	C₄	—	2	2	no	—
448	C₄	—	2	2	no	—
449	C₄	—	4	1	no	—
450	C₄	—	4	1	no	—
451	C₄	—	4	1	no	—
452	C₄	—	4	1	no	—
453	C₄	—	4	1	no	—
454	C₄	—	4	1	no	—
455	C₄	—	4	1	no	—
456	C₄	—	4	1	no	—
457	C₄	—	4	1	no	—
458	C₄	#2337	1	1	yes	characteristic
459	C₄	#2967	1	1	yes	characteristic
460	C₄	#2981	1	1	yes	characteristic
461	C₄	#2992	1	1	yes	characteristic
462	C₂	—	4	2	no	—
463	C₂	—	8	1	no	—
464	C₂	#22385	1	1	yes	characteristic
465	C₂	#33483	1	1	yes	characteristic
466	C₂	#33484	1	1	yes	characteristic
467	C₂	#33488	1	1	yes	characteristic
468	C₂	#33494	1	1	yes	characteristic
469	C₂	#33503	1	1	yes	characteristic
470	C₂	#33507	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
2. #13264	C₂	semidirect
3. #13263	C₂	semidirect
4. #13121	C₂	semidirect
5. #13121	C₂	semidirect
6. #13121	C₂	semidirect
7. #13120	C₂	semidirect
10. #12913	C₂	semidirect
11. #12912	C₂	semidirect
12. #12894	C₂	semidirect
13. #12653	C₂	semidirect
14. #12612	C₂	semidirect
15. #12611	C₂	semidirect
324. C₂²⋊C₄	M₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₈×#124	2
#13264	2
#13263	2
#13121	2
#13120	2
#12977	2
#12976	2
#12913	2
#12912	2
#12894	2
#12653	2
#12612	2
#12611	2