Subgroups — #497907

Order 512.

597 conjugacy classes of subgroups.

The subgroup lattice has 527 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×M₃₂	C₂	1	1	yes	maximal, characteristic
2	D₄×#108	C₂	1	1	yes	maximal, characteristic
3	#22654	C₂	1	1	yes	maximal, characteristic
4	#13185	C₂	1	1	yes	maximal, characteristic, complemented
5	#13184	C₂	1	1	yes	maximal, characteristic, complemented
6	#12930	C₂	1	1	yes	maximal, characteristic, complemented
7	#12929	C₂	1	1	yes	maximal, characteristic, complemented
8	#12928	C₂	1	1	yes	maximal, characteristic, complemented
9	#12928	C₂	1	1	yes	maximal, characteristic, complemented
10	#12887	C₂	1	1	yes	maximal, characteristic, complemented
11	#12831	C₂	1	1	yes	maximal, characteristic, complemented
12	#12831	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×#365	C₂	1	1	yes	maximal, characteristic, complemented
14	#12563	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#1383	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×M₃₂	C₂²	1	1	yes	characteristic
17	C₂²×M₃₂	C₂²	1	1	yes	characteristic
18	D₄×M₁₆	—	2	1	no	—
19	C₂×C₈×D₄	C₂²	1	1	yes	characteristic
20	C₂²×#108	C₂²	1	1	yes	characteristic
21	C₂²×#108	C₂²	1	1	yes	characteristic
22	C₂×#427	C₂²	1	1	yes	characteristic
23	C₂²×#106	C₂²	1	1	yes	characteristic
24	#2352	—	2	1	no	—
25	#2169	C₄	1	2	yes	complemented
26	#2168	C₄	1	2	yes	complemented
27	#2168	C₄	1	2	yes	complemented
28	D₄×C₁₆	C₄	1	2	yes	complemented
29	C₂×#365	C₂²	1	1	yes	characteristic
30	C₂×#365	C₂²	1	1	yes	characteristic
31	C₂×#365	C₂²	1	1	yes	characteristic
32	C₂×#365	C₂²	1	1	yes	characteristic
33	C₂×#365	C₂²	1	1	yes	characteristic
34	C₂×#365	C₂²	1	1	yes	characteristic
35	#2150	C₂²	1	1	yes	characteristic
36	#2112	C₂²	1	1	yes	characteristic
37	#2112	C₂²	1	1	yes	characteristic
38	C₄×M₃₂	C₂²	1	1	yes	characteristic
39	#1950	—	2	1	no	—
40	#1949	—	2	1	no	—
41	#1855	—	2	1	no	—
42	#1855	—	2	1	no	—
43	#1854	—	2	1	no	—
44	#1852	—	2	1	no	—
45	#1848	C₂²	1	1	yes	characteristic
46	#1846	C₂²	1	1	yes	characteristic
47	#1810	C₂²	1	1	yes	characteristic
48	#1810	C₂²	1	1	yes	characteristic
49	#1807	C₂²	1	1	yes	characteristic
50	#1807	C₂²	1	1	yes	characteristic
51	C₄×#108	C₂²	1	1	yes	characteristic
52	C₄×#106	C₂²	1	1	yes	characteristic
53	#1383	C₂²	1	1	yes	characteristic
54	#1383	C₂²	1	1	yes	characteristic
55	#1383	C₂²	1	1	yes	characteristic
56	#1383	C₂²	1	1	yes	characteristic
57	#1383	C₂²	1	1	yes	characteristic
58	#1383	C₂²	1	1	yes	characteristic
59	#1383	C₂²	1	1	yes	characteristic
60	#1383	C₂²	1	1	yes	characteristic
61	#1383	C₂²	1	1	yes	characteristic
62	#1383	C₂²	1	1	yes	characteristic
63	C₂²×M₁₆	—	2	1	no	—
64	C₂²×M₁₆	—	2	1	no	—
65	C₂³×C₈	C₂³	1	1	yes	characteristic
66	C₂³×C₈	C₂³	1	1	yes	characteristic
67	C₂×C₄×D₄	D₄	1	1	yes	characteristic
68	C₂×#117	—	2	1	no	—
69	C₂²×C₄⋊C₄	—	2	1	no	—
70	C₂×M₃₂	—	4	1	no	—
71	C₂×M₃₂	—	4	1	no	—
72	C₂×M₃₂	—	4	1	no	—
73	C₂×M₃₂	—	4	1	no	—
74	C₂×M₃₂	C₂×C₄	1	2	yes	—
75	C₂×M₃₂	C₂×C₄	1	2	yes	complemented
76	C₂×M₃₂	C₂³	1	1	yes	characteristic
77	C₂×M₃₂	C₂³	1	1	yes	characteristic
78	C₂×M₃₂	C₂³	1	1	yes	characteristic
79	C₂×M₃₂	C₂³	1	1	yes	characteristic
80	C₂²×C₁₆	C₂×C₄	1	2	yes	—
81	C₂²×C₁₆	C₂×C₄	1	2	yes	complemented
82	#436	—	4	1	no	—
83	#435	—	4	1	no	—
84	#435	—	4	1	no	—
85	C₈×D₄	—	4	1	no	—
86	C₈×D₄	C₂×C₄	1	1	yes	characteristic
87	C₈×D₄	C₂×C₄	1	1	yes	characteristic
88	C₈×D₄	C₂×C₄	1	1	yes	characteristic
89	C₈×D₄	C₂×C₄	1	1	yes	characteristic
90	C₈×D₄	Q₈	1	1	yes	characteristic
91	C₈×D₄	Q₈	1	1	yes	characteristic
92	C₈×D₄	Q₈	1	1	yes	characteristic
93	C₈×D₄	Q₈	1	1	yes	characteristic
94	C₂×#108	—	2	2	no	—
95	C₂×#108	—	2	2	no	—
96	C₂×#108	—	2	1	no	—
97	C₂×#108	—	2	1	no	—
98	C₂×#108	—	2	1	no	—
99	C₂×#108	—	4	1	no	—
100	C₂×#108	—	4	1	no	—
101	C₂×#108	C₂³	1	1	yes	characteristic
102	C₂×#108	C₂³	1	1	yes	characteristic
103	C₂×#108	C₂³	1	1	yes	characteristic
104	C₂×#108	C₂³	1	1	yes	characteristic
105	#427	—	2	2	no	—
106	#427	—	4	1	no	—
107	C₂×#107	—	2	1	no	—
108	C₂×#107	—	2	1	no	—
109	C₂×#106	—	2	2	no	—
110	C₂×#106	—	2	1	no	—
111	C₂×#106	—	4	1	no	—
112	C₂×#106	C₂³	1	1	yes	characteristic
113	C₂×#106	C₂³	1	1	yes	characteristic
114	C₂×#106	C₂³	1	1	yes	characteristic
115	C₂×#106	C₂³	1	1	yes	characteristic
116	#423	—	2	1	no	—
117	C₂×C₄⋊C₈	D₄	1	1	yes	characteristic
118	#407	—	2	1	no	—
119	#407	—	2	1	no	—
120	C₂×C₂²⋊C₈	D₄	1	1	yes	characteristic
121	C₂×C₂²⋊C₈	D₄	1	1	yes	characteristic
122	C₄×M₁₆	—	2	1	no	—
123	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
124	#388	—	4	1	no	—
125	#387	—	4	1	no	—
126	#386	—	4	1	no	—
127	#382	—	2	1	no	—
128	#380	—	2	1	no	—
129	#380	—	2	1	no	—
130	C₄×C₄⋊C₄	—	2	1	no	—
131	C₄×C₂²⋊C₄	—	4	1	no	—
132	#365	—	2	2	no	—
133	#365	—	2	2	no	—
134	#365	—	4	1	no	—
135	#365	—	4	1	no	—
136	#365	—	4	1	no	—
137	#365	—	4	1	no	—
138	C₄⋊C₁₆	C₂×C₄	1	2	yes	complemented
139	C₄⋊C₁₆	C₂×C₄	1	2	yes	complemented
140	C₂²⋊C₁₆	C₂×C₄	1	2	yes	—
141	C₂²⋊C₁₆	C₂×C₄	1	2	yes	—
142	C₂²⋊C₁₆	C₂×C₄	1	2	yes	complemented
143	C₂²⋊C₁₆	C₂×C₄	1	2	yes	complemented
144	#346	C₂×C₄	1	2	yes	complemented
145	C₄×C₁₆	C₂×C₄	1	2	yes	complemented
146	#341	—	2	1	no	—
147	#341	—	2	1	no	—
148	#341	—	2	1	no	—
149	#340	—	2	1	no	—
150	#340	—	2	1	no	—
151	#340	—	2	1	no	—
152	C₂²×D₄	SD₁₆	1	1	yes	characteristic
153	C₂³×C₄	—	4	1	no	—
154	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
155	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
156	C₂×M₁₆	—	2	1	no	—
157	C₂×M₁₆	—	2	1	no	—
158	C₂×M₁₆	—	2	1	no	—
159	C₂×M₁₆	—	2	1	no	—
160	C₂×M₁₆	—	4	1	no	—
161	C₂×M₁₆	—	4	1	no	—
162	C₂×M₁₆	—	4	2	no	—
163	C₂×M₁₆	—	4	2	no	—
164	C₂×M₁₆	—	8	1	no	—
165	C₂×M₁₆	—	8	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	—	4	1	no	—
175	C₂²×C₈	—	4	1	no	—
176	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₈	C₂×Q₈	1	1	yes	characteristic
184	C₂²×C₈	C₂×Q₈	1	1	yes	characteristic
185	C₂²×C₈	C₂×Q₈	1	1	yes	characteristic
186	C₂²×C₈	C₂×Q₈	1	1	yes	characteristic
187	C₂²×C₈	C₂⁴	1	1	yes	characteristic
188	C₄×D₄	C₄⋊C₄	1	1	yes	characteristic
189	C₄×D₄	C₄⋊C₄	1	1	yes	characteristic
190	C₄×D₄	C₄⋊C₄	1	1	yes	characteristic
191	C₄×D₄	C₄⋊C₄	1	1	yes	characteristic
192	C₄×D₄	SD₁₆	1	1	yes	characteristic
193	C₄×D₄	SD₁₆	1	1	yes	characteristic
194	C₄×D₄	SD₁₆	1	1	yes	characteristic
195	C₄×D₄	SD₁₆	1	1	yes	characteristic
196	#117	—	4	2	no	—
197	#117	—	8	1	no	—
198	C₂×C₄⋊C₄	—	2	1	no	—
199	C₂×C₄⋊C₄	—	2	1	no	—
200	C₂×C₄⋊C₄	—	2	1	no	—
201	C₂×C₄⋊C₄	—	2	1	no	—
202	C₂×C₄⋊C₄	—	4	2	no	—
203	C₂×C₄⋊C₄	—	4	1	no	—
204	C₂×C₄⋊C₄	—	8	1	no	—
205	C₂×C₄⋊C₄	SD₁₆	1	1	yes	characteristic
206	C₂×C₂²⋊C₄	—	4	1	no	—
207	C₂×C₂²⋊C₄	—	4	1	no	—
208	C₂×C₂²⋊C₄	—	4	1	no	—
209	C₂×C₂²⋊C₄	SD₁₆	1	1	yes	characteristic
210	C₂×C₂²⋊C₄	SD₁₆	1	1	yes	characteristic
211	C₂×C₄²	—	4	1	no	—
212	C₂×C₄²	—	4	1	no	—
213	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
214	M₃₂	—	2	1	no	—
215	M₃₂	—	2	1	no	—
216	M₃₂	—	2	1	no	—
217	M₃₂	—	2	1	no	—
218	M₃₂	—	2	1	no	—
219	M₃₂	—	2	1	no	—
220	M₃₂	—	2	1	no	—
221	M₃₂	—	2	1	no	—
222	M₃₂	—	4	2	no	—
223	M₃₂	—	4	2	no	—
224	C₂×C₁₆	—	4	2	no	—
225	C₂×C₁₆	—	4	2	no	—
226	C₂×C₁₆	C₂²×C₄	1	2	yes	—
227	C₂×C₁₆	C₂²×C₄	1	2	yes	—
228	C₂×C₁₆	C₂²×C₄	1	2	yes	—
229	C₂×C₁₆	C₂²×C₄	1	2	yes	—
230	#108	—	2	1	no	—
231	#108	—	2	1	no	—
232	#108	—	2	1	no	—
233	#108	—	2	1	no	—
234	#108	—	2	1	no	—
235	#108	—	2	1	no	—
236	#108	—	2	1	no	—
237	#108	—	4	2	no	—
238	#108	—	4	2	no	—
239	#108	—	8	1	no	—
240	#108	#41	1	2	yes	—
241	#107	—	4	2	no	—
242	#107	—	8	1	no	—
243	#106	—	2	1	no	—
244	#106	—	2	1	no	—
245	#106	—	2	1	no	—
246	#106	—	2	1	no	—
247	#106	—	2	1	no	—
248	#106	—	2	1	no	—
249	#106	—	2	1	no	—
250	#106	—	4	2	no	—
251	#106	#41	1	2	yes	—
252	C₄⋊C₈	—	4	1	no	—
253	C₄⋊C₈	—	4	1	no	—
254	C₄⋊C₈	C₄⋊C₄	1	1	yes	characteristic
255	C₄⋊C₈	C₄⋊C₄	1	1	yes	characteristic
256	C₄⋊C₈	C₄⋊C₄	1	1	yes	characteristic
257	C₄⋊C₈	C₄⋊C₄	1	1	yes	characteristic
258	C₂²⋊C₈	—	4	1	no	—
259	C₂²⋊C₈	—	4	1	no	—
260	C₂²⋊C₈	—	4	1	no	—
261	C₂²⋊C₈	—	4	1	no	—
262	C₂²⋊C₈	C₄⋊C₄	1	1	yes	characteristic
263	C₂²⋊C₈	C₄⋊C₄	1	1	yes	characteristic
264	C₂²⋊C₈	C₄⋊C₄	1	1	yes	characteristic
265	C₂²⋊C₈	C₄⋊C₄	1	1	yes	characteristic
266	C₂²⋊C₈	C₄⋊C₄	1	1	yes	characteristic
267	C₂²⋊C₈	C₄⋊C₄	1	1	yes	characteristic
268	C₂²⋊C₈	C₄⋊C₄	1	1	yes	characteristic
269	C₂²⋊C₈	C₄⋊C₄	1	1	yes	characteristic
270	#97	—	4	1	no	—
271	C₄×C₈	—	4	1	no	—
272	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
273	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
274	C₄×C₈	C₂×Q₈	1	1	yes	characteristic
275	C₄×C₈	C₂×Q₈	1	1	yes	characteristic
276	#95	—	4	1	no	—
277	#95	—	4	1	no	—
278	#95	—	4	1	no	—
279	#95	—	4	1	no	—
280	#95	—	4	1	no	—
281	C₂⁴	C₂×SD₁₆	1	1	yes	characteristic
282	C₂⁴	C₂×SD₁₆	1	1	yes	characteristic
283	C₂×D₄	—	4	2	no	—
284	C₂×D₄	#106	1	1	yes	characteristic
285	C₂×D₄	#106	1	1	yes	characteristic
286	C₂×D₄	#106	1	1	yes	characteristic
287	C₂×D₄	#106	1	1	yes	characteristic
288	C₂²×C₄	—	2	1	no	—
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	—	4	1	no	—
297	C₂²×C₄	—	4	1	no	—
298	C₂²×C₄	—	4	1	no	—
299	C₂²×C₄	—	4	1	no	—
300	C₂²×C₄	—	8	2	no	—
301	C₂²×C₄	—	8	2	no	—
302	C₂²×C₄	—	16	1	no	—
303	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
304	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
305	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
306	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
307	C₂²×C₄	C₂×SD₁₆	1	1	yes	characteristic
308	C₂²×C₄	C₂×SD₁₆	1	1	yes	characteristic
309	C₂²×C₄	C₂×SD₁₆	1	1	yes	characteristic
310	C₂²×C₄	C₂×SD₁₆	1	1	yes	characteristic
311	C₂²×C₄	C₂×SD₁₆	1	1	yes	characteristic
312	C₂²×C₄	C₂×SD₁₆	1	1	yes	characteristic
313	C₂²×C₄	C₂×SD₁₆	1	1	yes	characteristic
314	C₂²×C₄	C₂×SD₁₆	1	1	yes	characteristic
315	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
316	M₁₆	—	2	2	no	—
317	M₁₆	—	4	1	no	—
318	M₁₆	—	4	1	no	—
319	M₁₆	—	4	1	no	—
320	M₁₆	—	4	1	no	—
321	M₁₆	—	4	1	no	—
322	M₁₆	—	4	1	no	—
323	M₁₆	—	4	1	no	—
324	M₁₆	—	8	2	no	—
325	M₁₆	—	8	2	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	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	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	4	1	no	—
349	C₂×C₈	—	4	1	no	—
350	C₂×C₈	—	4	1	no	—
351	C₂×C₈	—	4	1	no	—
352	C₂×C₈	—	8	2	no	—
353	C₂×C₈	—	8	2	no	—
354	C₂×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
355	C₂×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
356	C₂×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
357	C₂×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
358	C₂×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
359	C₂×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
360	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
361	C₂×C₈	C₂²×Q₈	1	1	yes	characteristic
362	C₂×C₈	C₂×#41	1	1	yes	characteristic
363	C₂×C₈	C₂×#41	1	1	yes	characteristic
364	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
365	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	4	1	no	—
368	C₄⋊C₄	—	4	1	no	—
369	C₄⋊C₄	—	4	1	no	—
370	C₄⋊C₄	—	4	1	no	—
371	C₄⋊C₄	—	4	1	no	—
372	C₄⋊C₄	—	4	1	no	—
373	C₄⋊C₄	—	4	1	no	—
374	C₄⋊C₄	—	8	2	no	—
375	C₄⋊C₄	#106	1	1	yes	characteristic
376	C₄⋊C₄	#106	1	1	yes	characteristic
377	C₄⋊C₄	#106	1	1	yes	characteristic
378	C₄⋊C₄	#106	1	1	yes	characteristic
379	C₂²⋊C₄	—	8	2	no	—
380	C₂²⋊C₄	—	8	2	no	—
381	C₂²⋊C₄	—	16	1	no	—
382	C₂²⋊C₄	#106	1	1	yes	characteristic
383	C₂²⋊C₄	#106	1	1	yes	characteristic
384	C₂²⋊C₄	#106	1	1	yes	characteristic
385	C₂²⋊C₄	#106	1	1	yes	characteristic
386	C₂²⋊C₄	#106	1	1	yes	characteristic
387	C₂²⋊C₄	#106	1	1	yes	characteristic
388	C₂²⋊C₄	#106	1	1	yes	characteristic
389	C₂²⋊C₄	#106	1	1	yes	characteristic
390	C₄²	—	8	2	no	—
391	C₄²	—	16	1	no	—
392	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
393	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
394	C₄²	C₂×SD₁₆	1	1	yes	characteristic
395	C₄²	C₂×SD₁₆	1	1	yes	characteristic
396	C₁₆	—	2	2	no	—
397	C₁₆	—	2	2	no	—
398	C₁₆	—	2	2	no	—
399	C₁₆	—	2	2	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	2	1	no	—
402	C₂³	—	2	1	no	—
403	C₂³	—	2	1	no	—
404	C₂³	—	2	1	no	—
405	C₂³	—	4	1	no	—
406	C₂³	—	4	1	no	—
407	C₂³	—	4	1	no	—
408	C₂³	C₂×#106	1	1	yes	characteristic
409	C₂³	C₂×#106	1	1	yes	characteristic
410	C₂³	C₂×#106	1	1	yes	characteristic
411	C₂³	C₂×#106	1	1	yes	characteristic
412	C₂³	C₂²×SD₁₆	1	1	yes	characteristic
413	D₄	—	2	2	no	—
414	D₄	—	2	2	no	—
415	D₄	—	4	1	no	—
416	D₄	—	4	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	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	8	1	no	—
441	C₂×C₄	—	8	1	no	—
442	C₂×C₄	—	8	1	no	—
443	C₂×C₄	—	8	1	no	—
444	C₂×C₄	—	8	1	no	—
445	C₂×C₄	—	8	1	no	—
446	C₂×C₄	—	8	1	no	—
447	C₂×C₄	—	8	1	no	—
448	C₂×C₄	—	8	1	no	—
449	C₂×C₄	—	8	1	no	—
450	C₂×C₄	—	8	1	no	—
451	C₂×C₄	—	16	4	no	—
452	C₂×C₄	C₂×#106	1	1	yes	characteristic
453	C₂×C₄	C₂×#106	1	1	yes	characteristic
454	C₂×C₄	C₂×#106	1	1	yes	characteristic
455	C₂×C₄	C₂×#106	1	1	yes	characteristic
456	C₂×C₄	C₂×#106	1	1	yes	characteristic
457	C₂×C₄	C₂×#106	1	1	yes	characteristic
458	C₂×C₄	C₂×#106	1	1	yes	characteristic
459	C₂×C₄	C₂×#106	1	1	yes	characteristic
460	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
461	C₂×C₄	#546	1	1	yes	characteristic
462	C₂×C₄	#546	1	1	yes	characteristic
463	C₂×C₄	C₂²×SD₁₆	1	1	yes	characteristic
464	C₂×C₄	#576	1	1	yes	characteristic
465	C₂×C₄	#578	1	1	yes	characteristic
466	C₈	—	2	1	no	—
467	C₈	—	2	1	no	—
468	C₈	—	2	1	no	—
469	C₈	—	2	1	no	—
470	C₈	—	2	1	no	—
471	C₈	—	2	1	no	—
472	C₈	—	4	2	no	—
473	C₈	—	8	1	no	—
474	C₈	—	8	1	no	—
475	C₈	—	8	1	no	—
476	C₈	C₄×#41	1	1	yes	characteristic
477	C₈	#518	1	1	yes	characteristic
478	C₈	#554	1	1	yes	characteristic
479	C₈	#554	1	1	yes	characteristic
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	2	1	no	—
487	C₂²	—	2	1	no	—
488	C₂²	—	2	1	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	8	1	no	—
496	C₂²	—	8	1	no	—
497	C₂²	#2155	1	2	yes	—
498	C₂²	C₂²×#106	1	1	yes	characteristic
499	C₂²	#3295	1	1	yes	characteristic
500	C₂²	#3298	1	1	yes	characteristic
501	C₄	—	2	1	no	—
502	C₄	—	2	1	no	—
503	C₄	—	2	1	no	—
504	C₄	—	2	1	no	—
505	C₄	—	2	1	no	—
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	8	2	no	—
510	C₄	—	16	1	no	—
511	C₄	—	16	1	no	—
512	C₄	—	16	1	no	—
513	C₄	#2349	1	1	yes	characteristic
514	C₄	#2913	1	1	yes	characteristic
515	C₄	#3295	1	1	yes	characteristic
516	C₄	#3298	1	1	yes	characteristic
517	C₂	—	2	1	no	—
518	C₂	—	2	1	no	—
519	C₂	—	2	2	no	—
520	C₂	—	4	1	no	—
521	C₂	—	4	1	no	—
522	C₂	—	4	1	no	—
523	C₂	#22703	1	1	yes	characteristic
524	C₂	C₂×#2155	1	1	yes	characteristic
525	C₂	#33404	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂²×#106
commutator	C₂×C₈	C₂³×C₄
Frattini, cosocle	C₂²×C₈	C₂⁴
prime radical	C₂²×D₄	SD₁₆
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄×D₄ ◁ C₂×C₈×D₄ ◁ G
LECS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. #13185	C₂	semidirect
5. #13184	C₂	semidirect
6. #12930	C₂	semidirect
7. #12929	C₂	semidirect
8. #12928	C₂	semidirect
9. #12928	C₂	semidirect
10. #12887	C₂	semidirect
11. #12831	C₂	semidirect
12. #12831	C₂	semidirect
13. C₄×#365	C₂	semidirect
14. #12563	C₂	semidirect
15. C₂×#1383	C₂	semidirect
25. #2169	C₄	semidirect
26. #2168	C₄	semidirect
27. #2168	C₄	semidirect
28. D₄×C₁₆	C₄	semidirect
75. C₂×M₃₂	C₂×C₄	semidirect
81. C₂²×C₁₆	C₂×C₄	semidirect
138. C₄⋊C₁₆	C₂×C₄	semidirect
139. C₄⋊C₁₆	C₂×C₄	semidirect
142. C₂²⋊C₁₆	C₂×C₄	semidirect
143. C₂²⋊C₁₆	C₂×C₄	semidirect
144. #346	C₂×C₄	semidirect
145. C₄×C₁₆	C₂×C₄	semidirect

Maximal subgroups

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

subgroup	index
D₄×M₃₂	2
D₄×#108	2
#22654	2
#13185	2
#13184	2
#12930	2
#12929	2
#12928	2
#12887	2
#12831	2
C₄×#365	2
#12563	2
C₂×#1383	2