Subgroups — #497836

Order 512.

633 conjugacy classes of subgroups.

The subgroup lattice has 533 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	C₂×#2155	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#365	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×#108	C₂	1	1	yes	maximal, characteristic
5	#22654	C₂	1	1	yes	maximal, characteristic
6	#13185	C₂	1	1	yes	maximal, characteristic, complemented
7	#13184	C₂	1	1	yes	maximal, characteristic, complemented
8	#12930	C₂	1	1	yes	maximal, characteristic, complemented
9	#12929	C₂	1	1	yes	maximal, characteristic, complemented
10	#12928	C₂	1	1	yes	maximal, characteristic, complemented
11	#12928	C₂	1	1	yes	maximal, characteristic, complemented
12	#12904	C₂	1	1	yes	maximal, characteristic, complemented
13	#12831	C₂	1	1	yes	maximal, characteristic, complemented
14	#12831	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#365	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	#2155	—	2	4	no	—
30	C₂×#365	—	2	4	no	—
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	C₂×#365	C₂²	1	1	yes	characteristic
36	C₂×#365	C₂²	1	1	yes	characteristic
37	C₂×#365	C₂²	1	1	yes	characteristic
38	C₂×#365	C₂²	1	1	yes	characteristic
39	C₂×#365	C₂²	1	1	yes	characteristic
40	C₂×#365	C₂²	1	1	yes	characteristic
41	#2150	C₂²	1	1	yes	characteristic
42	#2112	C₂²	1	1	yes	characteristic
43	#2112	C₂²	1	1	yes	characteristic
44	C₄×M₃₂	C₂²	1	1	yes	characteristic
45	#1950	—	2	1	no	—
46	#1949	—	2	1	no	—
47	#1855	—	2	1	no	—
48	#1855	—	2	1	no	—
49	#1854	—	2	1	no	—
50	#1852	—	2	1	no	—
51	#1848	C₂²	1	1	yes	characteristic
52	#1846	C₂²	1	1	yes	characteristic
53	#1810	C₂²	1	1	yes	characteristic
54	#1810	C₂²	1	1	yes	characteristic
55	#1807	C₂²	1	1	yes	characteristic
56	#1807	C₂²	1	1	yes	characteristic
57	C₄×#108	C₂²	1	1	yes	characteristic
58	C₄×#106	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	#1383	C₂²	1	1	yes	characteristic
64	#1383	C₂²	1	1	yes	characteristic
65	C₂²×M₁₆	—	2	1	no	—
66	C₂²×M₁₆	—	2	1	no	—
67	C₂³×C₈	C₂³	1	1	yes	characteristic
68	C₂³×C₈	C₂³	1	1	yes	characteristic
69	C₂×C₄×D₄	D₄	1	1	yes	characteristic
70	C₂×#117	—	2	1	no	—
71	C₂²×C₄⋊C₄	—	2	1	no	—
72	C₂×M₃₂	—	2	2	no	—
73	C₂×M₃₂	—	2	2	no	—
74	C₂×M₃₂	—	2	2	no	—
75	C₂×M₃₂	—	2	2	no	—
76	C₂×M₃₂	C₂×C₄	1	2	yes	—
77	C₂×M₃₂	C₂×C₄	1	2	yes	complemented
78	C₂×M₃₂	C₂³	1	1	yes	characteristic
79	C₂×M₃₂	C₂³	1	1	yes	characteristic
80	C₂×M₃₂	C₂³	1	1	yes	characteristic
81	C₂×M₃₂	C₂³	1	1	yes	characteristic
82	C₂²×C₁₆	C₂×C₄	1	2	yes	—
83	C₂²×C₁₆	C₂×C₄	1	2	yes	complemented
84	#436	—	4	1	no	—
85	#435	—	4	1	no	—
86	#435	—	4	1	no	—
87	C₈×D₄	—	4	1	no	—
88	C₈×D₄	C₂×C₄	1	1	yes	characteristic
89	C₈×D₄	C₂×C₄	1	1	yes	characteristic
90	C₈×D₄	C₂×C₄	1	1	yes	characteristic
91	C₈×D₄	C₂×C₄	1	1	yes	characteristic
92	C₈×D₄	Q₈	1	1	yes	characteristic
93	C₈×D₄	Q₈	1	1	yes	characteristic
94	C₈×D₄	Q₈	1	1	yes	characteristic
95	C₈×D₄	Q₈	1	1	yes	characteristic
96	C₂×#108	—	2	2	no	—
97	C₂×#108	—	2	2	no	—
98	C₂×#108	—	2	1	no	—
99	C₂×#108	—	2	1	no	—
100	C₂×#108	—	2	1	no	—
101	C₂×#108	—	4	1	no	—
102	C₂×#108	—	4	1	no	—
103	C₂×#108	C₂³	1	1	yes	characteristic
104	C₂×#108	C₂³	1	1	yes	characteristic
105	C₂×#108	C₂³	1	1	yes	characteristic
106	C₂×#108	C₂³	1	1	yes	characteristic
107	#427	—	2	2	no	—
108	#427	—	4	1	no	—
109	C₂×#107	—	2	1	no	—
110	C₂×#107	—	2	1	no	—
111	C₂×#106	—	2	2	no	—
112	C₂×#106	—	2	1	no	—
113	C₂×#106	—	4	1	no	—
114	C₂×#106	C₂³	1	1	yes	characteristic
115	C₂×#106	C₂³	1	1	yes	characteristic
116	C₂×#106	C₂³	1	1	yes	characteristic
117	C₂×#106	C₂³	1	1	yes	characteristic
118	#423	—	2	1	no	—
119	C₂×C₄⋊C₈	D₄	1	1	yes	characteristic
120	#407	—	2	1	no	—
121	#407	—	2	1	no	—
122	C₂×C₂²⋊C₈	D₄	1	1	yes	characteristic
123	C₂×C₂²⋊C₈	D₄	1	1	yes	characteristic
124	C₄×M₁₆	—	2	1	no	—
125	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
126	#388	—	4	1	no	—
127	#387	—	4	1	no	—
128	#386	—	4	1	no	—
129	#382	—	2	1	no	—
130	#380	—	2	1	no	—
131	#380	—	2	1	no	—
132	C₄×C₄⋊C₄	—	2	1	no	—
133	C₄×C₂²⋊C₄	—	4	1	no	—
134	#365	—	2	2	no	—
135	#365	—	2	2	no	—
136	#365	—	2	2	no	—
137	#365	—	2	2	no	—
138	#365	—	2	2	no	—
139	#365	—	2	2	no	—
140	#365	—	2	2	no	—
141	#365	—	4	1	no	—
142	#365	—	4	1	no	—
143	#365	D₄	1	4	yes	complemented
144	C₄⋊C₁₆	C₂×C₄	1	2	yes	complemented
145	C₄⋊C₁₆	C₂×C₄	1	2	yes	complemented
146	C₂²⋊C₁₆	C₂×C₄	1	2	yes	—
147	C₂²⋊C₁₆	C₂×C₄	1	2	yes	—
148	C₂²⋊C₁₆	C₂×C₄	1	2	yes	complemented
149	C₂²⋊C₁₆	C₂×C₄	1	2	yes	complemented
150	#346	C₂×C₄	1	2	yes	complemented
151	C₄×C₁₆	C₂×C₄	1	2	yes	complemented
152	#341	—	2	1	no	—
153	#341	—	2	1	no	—
154	#341	—	2	1	no	—
155	#340	—	2	1	no	—
156	#340	—	2	1	no	—
157	#340	—	2	1	no	—
158	C₂²×D₄	SD₁₆	1	1	yes	characteristic
159	C₂³×C₄	—	4	1	no	—
160	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
161	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
162	C₂×M₁₆	—	2	1	no	—
163	C₂×M₁₆	—	2	1	no	—
164	C₂×M₁₆	—	2	1	no	—
165	C₂×M₁₆	—	2	1	no	—
166	C₂×M₁₆	—	4	1	no	—
167	C₂×M₁₆	—	4	1	no	—
168	C₂×M₁₆	—	4	2	no	—
169	C₂×M₁₆	—	4	2	no	—
170	C₂×M₁₆	—	8	1	no	—
171	C₂×M₁₆	—	8	1	no	—
172	C₂²×C₈	—	2	1	no	—
173	C₂²×C₈	—	2	1	no	—
174	C₂²×C₈	—	2	1	no	—
175	C₂²×C₈	—	2	1	no	—
176	C₂²×C₈	—	2	1	no	—
177	C₂²×C₈	—	2	1	no	—
178	C₂²×C₈	—	2	1	no	—
179	C₂²×C₈	—	2	1	no	—
180	C₂²×C₈	—	4	1	no	—
181	C₂²×C₈	—	4	1	no	—
182	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
183	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
184	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
186	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₈	C₂×Q₈	1	1	yes	characteristic
190	C₂²×C₈	C₂×Q₈	1	1	yes	characteristic
191	C₂²×C₈	C₂×Q₈	1	1	yes	characteristic
192	C₂²×C₈	C₂×Q₈	1	1	yes	characteristic
193	C₂²×C₈	C₂⁴	1	1	yes	characteristic
194	C₄×D₄	C₄⋊C₄	1	1	yes	characteristic
195	C₄×D₄	C₄⋊C₄	1	1	yes	characteristic
196	C₄×D₄	C₄⋊C₄	1	1	yes	characteristic
197	C₄×D₄	C₄⋊C₄	1	1	yes	characteristic
198	C₄×D₄	SD₁₆	1	1	yes	characteristic
199	C₄×D₄	SD₁₆	1	1	yes	characteristic
200	C₄×D₄	SD₁₆	1	1	yes	characteristic
201	C₄×D₄	SD₁₆	1	1	yes	characteristic
202	#117	—	4	2	no	—
203	#117	—	8	1	no	—
204	C₂×C₄⋊C₄	—	2	1	no	—
205	C₂×C₄⋊C₄	—	2	1	no	—
206	C₂×C₄⋊C₄	—	2	1	no	—
207	C₂×C₄⋊C₄	—	2	1	no	—
208	C₂×C₄⋊C₄	—	4	2	no	—
209	C₂×C₄⋊C₄	—	4	1	no	—
210	C₂×C₄⋊C₄	—	8	1	no	—
211	C₂×C₄⋊C₄	SD₁₆	1	1	yes	characteristic
212	C₂×C₂²⋊C₄	—	4	1	no	—
213	C₂×C₂²⋊C₄	—	4	1	no	—
214	C₂×C₂²⋊C₄	—	4	1	no	—
215	C₂×C₂²⋊C₄	SD₁₆	1	1	yes	characteristic
216	C₂×C₂²⋊C₄	SD₁₆	1	1	yes	characteristic
217	C₂×C₄²	—	4	1	no	—
218	C₂×C₄²	—	4	1	no	—
219	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
220	M₃₂	—	2	1	no	—
221	M₃₂	—	2	1	no	—
222	M₃₂	—	2	1	no	—
223	M₃₂	—	2	1	no	—
224	M₃₂	—	2	1	no	—
225	M₃₂	—	2	1	no	—
226	M₃₂	—	2	4	no	—
227	M₃₂	—	2	4	no	—
228	M₃₂	C₂×D₄	1	2	yes	—
229	M₃₂	#41	1	2	yes	—
230	C₂×C₁₆	—	2	4	no	—
231	C₂×C₁₆	—	2	4	no	—
232	C₂×C₁₆	C₂²×C₄	1	2	yes	—
233	C₂×C₁₆	C₂²×C₄	1	2	yes	—
234	C₂×C₁₆	C₂²×C₄	1	2	yes	—
235	C₂×C₁₆	C₂²×C₄	1	2	yes	—
236	#108	—	2	1	no	—
237	#108	—	2	1	no	—
238	#108	—	2	1	no	—
239	#108	—	2	1	no	—
240	#108	—	2	1	no	—
241	#108	—	2	1	no	—
242	#108	—	2	1	no	—
243	#108	—	4	2	no	—
244	#108	—	4	2	no	—
245	#108	—	8	1	no	—
246	#108	C₂×D₄	1	2	yes	—
247	#107	—	4	2	no	—
248	#107	—	8	1	no	—
249	#106	—	2	1	no	—
250	#106	—	2	1	no	—
251	#106	—	2	1	no	—
252	#106	—	2	1	no	—
253	#106	—	2	1	no	—
254	#106	—	2	1	no	—
255	#106	—	2	1	no	—
256	#106	—	4	2	no	—
257	#106	C₂×D₄	1	2	yes	—
258	C₄⋊C₈	—	4	1	no	—
259	C₄⋊C₈	—	4	1	no	—
260	C₄⋊C₈	C₄⋊C₄	1	1	yes	characteristic
261	C₄⋊C₈	C₄⋊C₄	1	1	yes	characteristic
262	C₄⋊C₈	C₄⋊C₄	1	1	yes	characteristic
263	C₄⋊C₈	C₄⋊C₄	1	1	yes	characteristic
264	C₂²⋊C₈	—	4	1	no	—
265	C₂²⋊C₈	—	4	1	no	—
266	C₂²⋊C₈	—	4	1	no	—
267	C₂²⋊C₈	—	4	1	no	—
268	C₂²⋊C₈	C₄⋊C₄	1	1	yes	characteristic
269	C₂²⋊C₈	C₄⋊C₄	1	1	yes	characteristic
270	C₂²⋊C₈	C₄⋊C₄	1	1	yes	characteristic
271	C₂²⋊C₈	C₄⋊C₄	1	1	yes	characteristic
272	C₂²⋊C₈	C₄⋊C₄	1	1	yes	characteristic
273	C₂²⋊C₈	C₄⋊C₄	1	1	yes	characteristic
274	C₂²⋊C₈	C₄⋊C₄	1	1	yes	characteristic
275	C₂²⋊C₈	C₄⋊C₄	1	1	yes	characteristic
276	#97	—	4	1	no	—
277	C₄×C₈	—	4	1	no	—
278	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
279	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
280	C₄×C₈	C₂×Q₈	1	1	yes	characteristic
281	C₄×C₈	C₂×Q₈	1	1	yes	characteristic
282	#95	—	4	1	no	—
283	#95	—	4	1	no	—
284	#95	—	4	1	no	—
285	#95	—	4	1	no	—
286	#95	—	4	1	no	—
287	C₂⁴	C₂×SD₁₆	1	1	yes	characteristic
288	C₂⁴	C₂×SD₁₆	1	1	yes	characteristic
289	C₂×D₄	—	4	2	no	—
290	C₂×D₄	#106	1	1	yes	characteristic
291	C₂×D₄	#106	1	1	yes	characteristic
292	C₂×D₄	#106	1	1	yes	characteristic
293	C₂×D₄	#106	1	1	yes	characteristic
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	4	1	no	—
303	C₂²×C₄	—	4	1	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	—	8	2	no	—
307	C₂²×C₄	—	8	2	no	—
308	C₂²×C₄	—	16	1	no	—
309	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
310	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₄⋊C₄	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	C₂×SD₁₆	1	1	yes	characteristic
316	C₂²×C₄	C₂×SD₁₆	1	1	yes	characteristic
317	C₂²×C₄	C₂×SD₁₆	1	1	yes	characteristic
318	C₂²×C₄	C₂×SD₁₆	1	1	yes	characteristic
319	C₂²×C₄	C₂×SD₁₆	1	1	yes	characteristic
320	C₂²×C₄	C₂×SD₁₆	1	1	yes	characteristic
321	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
322	M₁₆	—	2	2	no	—
323	M₁₆	—	4	1	no	—
324	M₁₆	—	4	1	no	—
325	M₁₆	—	4	1	no	—
326	M₁₆	—	4	1	no	—
327	M₁₆	—	4	1	no	—
328	M₁₆	—	4	1	no	—
329	M₁₆	—	4	1	no	—
330	M₁₆	—	8	2	no	—
331	M₁₆	—	8	2	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	—	2	1	no	—
349	C₂×C₈	—	2	1	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	—	4	1	no	—
355	C₂×C₈	—	4	1	no	—
356	C₂×C₈	—	4	1	no	—
357	C₂×C₈	—	4	1	no	—
358	C₂×C₈	—	8	2	no	—
359	C₂×C₈	—	8	2	no	—
360	C₂×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
361	C₂×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
362	C₂×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
363	C₂×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
364	C₂×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
365	C₂×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
366	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
367	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₈	C₂²×Q₈	1	1	yes	characteristic
369	C₂×C₈	C₂×#41	1	1	yes	characteristic
370	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
371	C₂×C₈	2₋¹⁺⁴	1	1	yes	characteristic
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	4	1	no	—
374	C₄⋊C₄	—	4	1	no	—
375	C₄⋊C₄	—	4	1	no	—
376	C₄⋊C₄	—	4	1	no	—
377	C₄⋊C₄	—	4	1	no	—
378	C₄⋊C₄	—	4	1	no	—
379	C₄⋊C₄	—	4	1	no	—
380	C₄⋊C₄	—	8	2	no	—
381	C₄⋊C₄	#106	1	1	yes	characteristic
382	C₄⋊C₄	#106	1	1	yes	characteristic
383	C₄⋊C₄	#106	1	1	yes	characteristic
384	C₄⋊C₄	#106	1	1	yes	characteristic
385	C₂²⋊C₄	—	8	2	no	—
386	C₂²⋊C₄	—	8	2	no	—
387	C₂²⋊C₄	—	16	1	no	—
388	C₂²⋊C₄	#106	1	1	yes	characteristic
389	C₂²⋊C₄	#106	1	1	yes	characteristic
390	C₂²⋊C₄	#106	1	1	yes	characteristic
391	C₂²⋊C₄	#106	1	1	yes	characteristic
392	C₂²⋊C₄	#106	1	1	yes	characteristic
393	C₂²⋊C₄	#106	1	1	yes	characteristic
394	C₂²⋊C₄	#106	1	1	yes	characteristic
395	C₂²⋊C₄	#106	1	1	yes	characteristic
396	C₄²	—	8	2	no	—
397	C₄²	—	16	1	no	—
398	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
399	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
400	C₄²	C₂×SD₁₆	1	1	yes	characteristic
401	C₄²	C₂×SD₁₆	1	1	yes	characteristic
402	C₁₆	—	2	2	no	—
403	C₁₆	—	2	2	no	—
404	C₁₆	—	2	2	no	—
405	C₁₆	C₄×D₄	1	4	yes	—
406	C₂³	—	2	1	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	1	no	—
410	C₂³	—	2	1	no	—
411	C₂³	—	4	1	no	—
412	C₂³	—	4	1	no	—
413	C₂³	—	4	1	no	—
414	C₂³	C₂×#106	1	1	yes	characteristic
415	C₂³	C₂×#106	1	1	yes	characteristic
416	C₂³	C₂×#106	1	1	yes	characteristic
417	C₂³	C₂×#106	1	1	yes	characteristic
418	C₂³	C₂²×SD₁₆	1	1	yes	characteristic
419	D₄	—	2	2	no	—
420	D₄	—	2	2	no	—
421	D₄	—	4	1	no	—
422	D₄	—	4	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	—	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	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	2	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	—	8	1	no	—
452	C₂×C₄	—	8	1	no	—
453	C₂×C₄	—	8	1	no	—
454	C₂×C₄	—	8	1	no	—
455	C₂×C₄	—	8	1	no	—
456	C₂×C₄	—	8	1	no	—
457	C₂×C₄	—	16	4	no	—
458	C₂×C₄	C₂×#106	1	1	yes	characteristic
459	C₂×C₄	C₂×#106	1	1	yes	characteristic
460	C₂×C₄	C₂×#106	1	1	yes	characteristic
461	C₂×C₄	C₂×#106	1	1	yes	characteristic
462	C₂×C₄	C₂×#106	1	1	yes	characteristic
463	C₂×C₄	C₂×#106	1	1	yes	characteristic
464	C₂×C₄	C₂×#106	1	1	yes	characteristic
465	C₂×C₄	C₂×#106	1	1	yes	characteristic
466	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
467	C₂×C₄	D₄²	1	1	yes	characteristic
468	C₂×C₄	#547	1	1	yes	characteristic
469	C₂×C₄	C₂²×SD₁₆	1	1	yes	characteristic
470	C₂×C₄	#577	1	1	yes	characteristic
471	C₂×C₄	#577	1	1	yes	characteristic
472	C₈	—	2	1	no	—
473	C₈	—	2	1	no	—
474	C₈	—	2	1	no	—
475	C₈	—	2	1	no	—
476	C₈	—	2	1	no	—
477	C₈	—	2	1	no	—
478	C₈	—	4	2	no	—
479	C₈	—	8	1	no	—
480	C₈	—	8	1	no	—
481	C₈	—	8	1	no	—
482	C₈	C₂×C₄×D₄	1	1	yes	characteristic
483	C₈	#520	1	1	yes	characteristic
484	C₈	D₄×Q₈	1	1	yes	characteristic
485	C₈	#554	1	1	yes	characteristic
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	—	2	1	no	—
494	C₂²	—	2	1	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	2	1	no	—
498	C₂²	—	2	1	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	2	no	—
501	C₂²	—	8	1	no	—
502	C₂²	—	8	1	no	—
503	C₂²	#2155	1	2	yes	complemented
504	C₂²	C₂²×#106	1	1	yes	characteristic
505	C₂²	D₄×SD₁₆	1	1	yes	characteristic
506	C₂²	#3335	1	1	yes	characteristic
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	2	1	no	—
510	C₄	—	2	1	no	—
511	C₄	—	2	1	no	—
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	2	1	no	—
515	C₄	—	8	2	no	—
516	C₄	—	16	1	no	—
517	C₄	—	16	1	no	—
518	C₄	—	16	1	no	—
519	C₄	D₄×C₄⋊C₄	1	1	yes	characteristic
520	C₄	#2912	1	1	yes	characteristic
521	C₄	D₄×SD₁₆	1	1	yes	characteristic
522	C₄	#3335	1	1	yes	characteristic
523	C₂	—	2	1	no	—
524	C₂	—	2	1	no	—
525	C₂	—	2	2	no	—
526	C₂	—	4	1	no	—
527	C₂	—	4	1	no	—
528	C₂	—	4	1	no	—
529	C₂	D₄×#106	1	1	yes	characteristic
530	C₂	C₂×#2155	1	1	yes	characteristic
531	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
2. C₂×#2155	C₂	semidirect
3. C₂²×#365	C₂	semidirect
6. #13185	C₂	semidirect
7. #13184	C₂	semidirect
8. #12930	C₂	semidirect
9. #12929	C₂	semidirect
10. #12928	C₂	semidirect
11. #12928	C₂	semidirect
12. #12904	C₂	semidirect
13. #12831	C₂	semidirect
14. #12831	C₂	semidirect
15. C₄×#365	C₂	semidirect
25. #2169	C₄	semidirect
26. #2168	C₄	semidirect
27. #2168	C₄	semidirect
28. D₄×C₁₆	C₄	semidirect
77. C₂×M₃₂	C₂×C₄	semidirect
83. C₂²×C₁₆	C₂×C₄	semidirect
143. #365	D₄	semidirect
144. C₄⋊C₁₆	C₂×C₄	semidirect
145. C₄⋊C₁₆	C₂×C₄	semidirect
148. C₂²⋊C₁₆	C₂×C₄	semidirect
149. C₂²⋊C₁₆	C₂×C₄	semidirect
150. #346	C₂×C₄	semidirect
151. C₄×C₁₆	C₂×C₄	semidirect
503. C₂²	#2155	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
C₂×#2155	2
C₂²×#365	2
D₄×#108	2
#22654	2
#13185	2
#13184	2
#12930	2
#12929	2
#12928	2
#12904	2
#12831	2
C₄×#365	2