Subgroups — #62406

Order 256.

797 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3556	C₂	1	1	yes	maximal, characteristic, complemented
2	#3555	C₂	1	1	yes	maximal, characteristic
3	#3398	C₂	1	1	yes	maximal, characteristic, complemented
4	#3398	C₂	1	2	yes	maximal, complemented
5	#3395	C₂	1	1	yes	maximal, characteristic, complemented
6	#3390	C₂	1	2	yes	maximal, complemented
7	#3387	C₂	1	1	yes	maximal, characteristic, complemented
8	#3381	C₂	1	1	yes	maximal, characteristic, complemented
9	#3377	C₂	1	2	yes	maximal, complemented
10	#3374	C₂	1	1	yes	maximal, characteristic, complemented
11	#3374	C₂	1	2	yes	maximal, complemented
12	#3372	C₂	1	1	yes	maximal, characteristic, complemented
13	#3364	C₂	1	1	yes	maximal, characteristic, complemented
14	#3363	C₂	1	1	yes	maximal, characteristic, complemented
15	#3261	C₂	1	2	yes	maximal, complemented
16	#3258	C₂	1	2	yes	maximal
17	#3249	C₂	1	1	yes	maximal, characteristic, complemented
18	#3248	C₂	1	1	yes	maximal, characteristic
19	#3185	C₂	1	1	yes	maximal, characteristic, complemented
20	#3178	C₂	1	2	yes	maximal
21	#3177	C₂	1	2	yes	maximal, complemented
22	#3172	C₂	1	1	yes	maximal, characteristic
23	#2962	C₂	1	1	yes	maximal, characteristic, complemented
24	#564	—	2	2	no	—
25	#563	—	2	2	no	—
26	Q₈²	C₂²	1	1	yes	characteristic
27	#557	—	2	1	no	—
28	#557	—	2	1	no	—
29	#557	C₂²	1	1	yes	characteristic
30	#557	C₂²	1	1	yes	characteristic
31	#557	C₂²	1	1	yes	characteristic
32	#557	C₂²	1	2	yes	—
33	#557	C₂²	1	1	yes	characteristic
34	#557	C₂²	1	1	yes	characteristic
35	#557	C₂²	1	2	yes	—
36	#557	C₂²	1	2	yes	—
37	#556	—	2	1	no	—
38	#556	C₂²	1	1	yes	characteristic
39	#556	C₂²	1	2	yes	—
40	#554	C₂²	1	1	yes	characteristic
41	#552	—	2	1	no	—
42	#544	—	2	1	no	—
43	#542	C₂²	1	2	yes	—
44	#541	—	2	1	no	—
45	#541	—	2	2	no	—
46	#541	—	2	1	no	—
47	#541	—	2	1	no	—
48	#541	—	2	2	no	—
49	#541	C₂²	1	2	yes	—
50	#541	C₂²	1	2	yes	—
51	#541	C₂²	1	2	yes	—
52	#533	C₂²	1	1	yes	characteristic
53	#533	C₂²	1	1	yes	characteristic
54	#533	C₂²	1	1	yes	characteristic
55	#533	C₂²	1	1	yes	characteristic
56	#529	C₂²	1	1	yes	characteristic
57	#501	C₂²	1	2	yes	—
58	#501	C₂²	1	1	yes	characteristic
59	#499	C₂²	1	2	yes	—
60	#498	C₂²	1	1	yes	characteristic
61	#497	C₂²	1	1	yes	characteristic
62	#497	C₂²	1	2	yes	—
63	#494	C₂²	1	2	yes	—
64	#494	C₂²	1	1	yes	characteristic
65	#491	C₂²	1	2	yes	—
66	#491	C₂²	1	1	yes	characteristic
67	#491	C₂²	1	2	yes	—
68	#489	C₂²	1	1	yes	characteristic
69	#488	C₂²	1	2	yes	—
70	#487	C₂²	1	1	yes	characteristic
71	#487	C₂²	1	2	yes	—
72	#487	C₂²	1	1	yes	characteristic
73	#479	C₂²	1	2	yes	—
74	#479	C₂²	1	2	yes	—
75	#479	C₂²	1	2	yes	—
76	#479	C₂²	1	2	yes	—
77	#479	C₂²	1	2	yes	—
78	#479	C₂²	1	2	yes	—
79	#478	C₂²	1	2	yes	—
80	#477	C₂²	1	1	yes	characteristic
81	#477	C₂²	1	2	yes	—
82	#477	C₂²	1	1	yes	characteristic
83	#477	C₂²	1	2	yes	—
84	#475	C₂²	1	1	yes	characteristic
85	#475	C₂²	1	2	yes	—
86	#474	C₂²	1	1	yes	characteristic
87	#470	C₂²	1	1	yes	characteristic
88	#470	C₂²	1	1	yes	characteristic
89	#470	C₂²	1	2	yes	—
90	#470	C₂²	1	2	yes	—
91	#468	C₂²	1	1	yes	characteristic
92	#468	C₂²	1	1	yes	characteristic
93	#467	C₂²	1	2	yes	—
94	#467	C₂²	1	2	yes	—
95	#467	C₂²	1	2	yes	—
96	#465	C₂²	1	2	yes	—
97	#464	C₂²	1	2	yes	—
98	#464	C₂²	1	2	yes	—
99	#464	C₂²	1	2	yes	—
100	#462	C₂²	1	1	yes	characteristic
101	#462	C₂²	1	2	yes	—
102	#462	C₂²	1	1	yes	characteristic
103	#462	C₂²	1	2	yes	—
104	#462	C₂²	1	2	yes	—
105	#462	C₂²	1	1	yes	characteristic
106	#462	C₂²	1	2	yes	—
107	#462	C₂²	1	2	yes	—
108	#462	C₂²	1	2	yes	—
109	#461	C₂²	1	1	yes	characteristic
110	#461	C₂²	1	2	yes	—
111	#446	C₂²	1	1	yes	characteristic
112	#446	C₂²	1	2	yes	—
113	#446	C₂²	1	1	yes	characteristic
114	#446	C₂²	1	2	yes	—
115	C₈×Q₈	C₂²	1	1	yes	characteristic
116	C₈×Q₈	C₂²	1	1	yes	characteristic
117	#441	C₂²	1	2	yes	—
118	#441	C₂²	1	2	yes	—
119	#441	C₂²	1	2	yes	—
120	#441	C₂²	1	2	yes	—
121	#441	C₂²	1	2	yes	—
122	#440	C₂²	1	2	yes	—
123	C₄×Q₁₆	C₂²	1	1	yes	characteristic
124	C₄×Q₁₆	C₂²	1	2	yes	—
125	C₄×Q₁₆	C₂²	1	2	yes	—
126	C₄×Q₁₆	C₂²	1	1	yes	characteristic
127	C₄×Q₁₆	C₂²	1	2	yes	—
128	C₄×SD₁₆	C₂²	1	1	yes	characteristic
129	C₄×SD₁₆	C₂²	1	1	yes	characteristic
130	C₄×SD₁₆	C₂²	1	2	yes	—
131	#424	C₂²	1	2	yes	—
132	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic
133	#405	C₂²	1	2	yes	—
134	C₄×M₁₆	C₂²	1	1	yes	characteristic
135	C₂×Q₁₆	C₂³	1	1	yes	characteristic
136	C₂×Q₁₆	C₂³	1	2	yes	—
137	C₂×Q₁₆	C₂³	1	1	yes	characteristic
138	C₂×Q₁₆	C₂³	1	2	yes	—
139	C₂×Q₁₆	C₂³	1	2	yes	—
140	C₂×Q₁₆	C₂³	1	2	yes	—
141	C₂×Q₁₆	C₂³	1	2	yes	—
142	C₂×SD₁₆	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆	C₂³	1	2	yes	—
145	C₂×M₁₆	C₂³	1	1	yes	characteristic
146	C₂×M₁₆	C₂³	1	1	yes	characteristic
147	C₂²×C₈	C₂³	1	2	yes	—
148	C₄⋊Q₈	—	2	1	no	—
149	C₄⋊Q₈	—	2	1	no	—
150	C₄⋊Q₈	—	2	2	no	—
151	C₄⋊Q₈	—	2	2	no	—
152	C₄⋊Q₈	—	2	2	no	—
153	C₄⋊Q₈	—	2	1	no	—
154	C₄⋊Q₈	D₄	1	1	yes	characteristic
155	C₄⋊Q₈	D₄	1	1	yes	characteristic
156	C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈	C₂³	1	2	yes	—
160	C₄⋊Q₈	C₂³	1	2	yes	—
161	C₄⋊Q₈	C₂³	1	2	yes	—
162	C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈	C₂³	1	2	yes	—
166	#126	—	2	2	no	—
167	#126	—	2	2	no	—
168	#126	—	2	2	no	—
169	#126	—	2	2	no	—
170	#126	—	2	2	no	—
171	#126	—	2	2	no	—
172	#126	—	2	2	no	—
173	#126	—	2	2	no	—
174	#126	—	2	2	no	—
175	#126	—	2	2	no	—
176	#126	—	2	1	no	—
177	#125	—	2	2	no	—
178	#125	—	2	2	no	—
179	#125	—	2	2	no	—
180	#125	—	2	1	no	—
181	#125	—	2	1	no	—
182	#125	—	2	2	no	—
183	#125	—	2	2	no	—
184	#125	—	2	2	no	—
185	#125	—	2	2	no	—
186	#125	—	2	2	no	—
187	#125	—	2	2	no	—
188	#125	—	2	2	no	—
189	#125	—	2	2	no	—
190	#125	—	2	2	no	—
191	#125	—	2	2	no	—
192	#125	—	2	2	no	—
193	#125	—	2	2	no	—
194	#125	—	2	2	no	—
195	#125	—	2	2	no	—
196	#125	—	2	2	no	—
197	#125	—	2	1	no	—
198	#125	—	2	1	no	—
199	#125	—	2	1	no	—
200	#125	—	2	1	no	—
201	#125	D₄	1	2	yes	—
202	#125	C₂³	1	1	yes	characteristic
203	#125	C₂³	1	2	yes	—
204	#125	C₂³	1	2	yes	—
205	#125	C₂³	1	2	yes	—
206	#124	—	2	2	no	—
207	#124	C₂³	1	1	yes	characteristic
208	#124	C₂³	1	2	yes	—
209	#123	—	2	1	no	—
210	#123	—	2	2	no	—
211	C₂²⋊Q₈	—	2	1	no	—
212	C₂²⋊Q₈	—	2	1	no	—
213	C₂²⋊Q₈	—	2	2	no	—
214	C₂²⋊Q₈	—	2	1	no	—
215	C₂²⋊Q₈	—	2	1	no	—
216	C₂²⋊Q₈	—	2	1	no	—
217	C₂²⋊Q₈	—	2	2	no	—
218	C₂²⋊Q₈	—	2	2	no	—
219	C₂²⋊Q₈	D₄	1	1	yes	characteristic
220	C₂²⋊Q₈	D₄	1	1	yes	characteristic
221	C₂²⋊Q₈	D₄	1	2	yes	—
222	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
223	C₂²⋊Q₈	C₂³	1	2	yes	—
224	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
225	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
226	C₂²⋊Q₈	C₂³	1	2	yes	—
227	#121	C₂³	1	1	yes	characteristic
228	C₄×Q₈	—	2	1	no	—
229	C₄×Q₈	—	2	1	no	—
230	C₄×Q₈	—	2	1	no	—
231	C₄×Q₈	—	2	1	no	—
232	C₄×Q₈	—	2	2	no	—
233	C₄×Q₈	—	2	2	no	—
234	C₄×Q₈	—	2	1	no	—
235	C₄×Q₈	—	2	1	no	—
236	C₄×Q₈	—	2	2	no	—
237	C₄×Q₈	—	2	1	no	—
238	C₄×Q₈	—	2	1	no	—
239	C₄×Q₈	—	2	1	no	—
240	C₄×Q₈	C₂³	1	1	yes	characteristic
241	C₄×Q₈	C₂³	1	2	yes	—
242	C₄×Q₈	C₂³	1	1	yes	characteristic
243	C₄×Q₈	C₂³	1	1	yes	characteristic
244	C₄×Q₈	C₂³	1	2	yes	—
245	C₄×Q₈	C₂³	1	2	yes	—
246	C₄×Q₈	C₂³	1	2	yes	—
247	C₄×Q₈	C₂³	1	2	yes	—
248	C₄×Q₈	C₂³	1	2	yes	—
249	C₄×Q₈	C₂³	1	2	yes	—
250	C₄×Q₈	C₂³	1	2	yes	—
251	C₄×Q₈	C₂³	1	2	yes	—
252	C₄×Q₈	C₂³	1	1	yes	characteristic
253	C₄×Q₈	C₂³	1	2	yes	—
254	C₄×Q₈	C₂³	1	1	yes	characteristic
255	C₄×D₄	—	2	1	no	—
256	C₄×D₄	C₂³	1	1	yes	characteristic
257	C₄×D₄	C₂³	1	2	yes	—
258	#117	—	2	1	no	—
259	#117	—	2	1	no	—
260	#117	—	2	1	no	—
261	#117	—	2	2	no	—
262	#117	—	2	1	no	—
263	#117	—	2	1	no	—
264	#117	C₂³	1	2	yes	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄²	C₂³	1	1	yes	characteristic
267	#107	C₂³	1	1	yes	characteristic
268	#107	C₂³	1	2	yes	—
269	#107	C₂³	1	2	yes	—
270	#107	C₂³	1	1	yes	characteristic
271	#107	C₂³	1	2	yes	—
272	#106	C₂³	1	2	yes	—
273	#106	C₂³	1	1	yes	characteristic
274	#106	C₂³	1	1	yes	characteristic
275	#106	C₂³	1	2	yes	—
276	#106	C₂³	1	2	yes	—
277	C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₄⋊C₈	C₂³	1	2	yes	—
280	C₄⋊C₈	C₂³	1	2	yes	—
281	C₄⋊C₈	C₂³	1	2	yes	—
282	C₄⋊C₈	C₂³	1	2	yes	—
283	C₄⋊C₈	C₂³	1	2	yes	—
284	#103	C₂³	1	1	yes	characteristic
285	#103	C₂³	1	2	yes	—
286	#103	C₂³	1	1	yes	characteristic
287	#103	C₂³	1	1	yes	characteristic
288	#103	C₂³	1	2	yes	—
289	#103	C₂³	1	1	yes	characteristic
290	#103	C₂³	1	2	yes	—
291	#103	C₂³	1	2	yes	—
292	#103	C₂³	1	2	yes	—
293	#103	C₂³	1	1	yes	characteristic
294	#103	C₂³	1	1	yes	characteristic
295	#103	C₂³	1	2	yes	—
296	#103	C₂³	1	2	yes	—
297	#103	C₂³	1	2	yes	—
298	#103	C₂³	1	2	yes	—
299	#103	C₂³	1	2	yes	—
300	#103	C₂³	1	2	yes	—
301	#102	C₂³	1	1	yes	characteristic
302	#102	C₂³	1	2	yes	—
303	#102	C₂³	1	1	yes	characteristic
304	#97	C₂³	1	1	yes	characteristic
305	#97	C₂³	1	1	yes	characteristic
306	#97	C₂³	1	2	yes	—
307	#97	C₂³	1	2	yes	—
308	C₄×C₈	C₂³	1	1	yes	characteristic
309	C₄×C₈	C₂³	1	1	yes	characteristic
310	C₄×C₈	C₂³	1	2	yes	—
311	C₄×C₈	C₂³	1	2	yes	—
312	C₂×Q₈	—	2	1	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
317	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
318	C₂×Q₈	C₂×D₄	1	2	yes	—
319	C₂×Q₈	C₂⁴	1	1	yes	characteristic
320	C₂×Q₈	C₂⁴	1	2	yes	—
321	C₂×Q₈	C₂⁴	1	1	yes	characteristic
322	C₂×Q₈	C₂⁴	1	1	yes	characteristic
323	C₂×Q₈	C₂⁴	1	2	yes	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
329	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
330	C₂²×C₄	C₂⁴	1	1	yes	characteristic
331	Q₁₆	—	2	2	no	—
332	Q₁₆	—	2	4	no	—
333	Q₁₆	—	4	2	no	—
334	Q₁₆	—	4	2	no	—
335	Q₁₆	—	4	2	no	—
336	Q₁₆	—	4	1	no	—
337	Q₁₆	—	4	2	no	—
338	SD₁₆	—	2	2	no	—
339	SD₁₆	—	4	2	no	—
340	SD₁₆	—	4	1	no	—
341	M₁₆	—	2	2	no	—
342	M₁₆	—	4	1	no	—
343	C₂×C₈	—	4	2	no	—
344	C₂×C₈	C₂⁴	1	1	yes	characteristic
345	C₂×C₈	C₂⁴	1	2	yes	—
346	C₂×C₈	C₂⁴	1	1	yes	characteristic
347	C₂×C₈	C₂⁴	1	1	yes	characteristic
348	C₂×C₈	C₂⁴	1	2	yes	—
349	C₂×C₈	C₂⁴	1	1	yes	characteristic
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
392	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
393	C₄⋊C₄	C₂×D₄	1	2	yes	—
394	C₄⋊C₄	C₂×D₄	1	2	yes	—
395	C₄⋊C₄	C₂×D₄	1	2	yes	—
396	C₄⋊C₄	C₂×D₄	1	2	yes	—
397	C₄⋊C₄	C₂×D₄	1	2	yes	—
398	C₄⋊C₄	C₂×D₄	1	2	yes	—
399	C₄⋊C₄	C₂×D₄	1	2	yes	—
400	C₄⋊C₄	C₂⁴	1	2	yes	—
401	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄	C₂⁴	1	2	yes	—
405	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
406	C₂²⋊C₄	—	2	2	no	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₂²⋊C₄	—	2	1	no	—
409	C₂²⋊C₄	—	2	1	no	—
410	C₂²⋊C₄	—	2	1	no	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	1	no	—
413	C₂²⋊C₄	—	2	1	no	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₂²⋊C₄	—	2	2	no	—
416	C₂²⋊C₄	—	2	1	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₂²⋊C₄	C₂×D₄	1	2	yes	—
419	C₂²⋊C₄	C₂×D₄	1	2	yes	—
420	C₄²	—	2	2	no	—
421	C₄²	—	2	1	no	—
422	C₄²	—	2	2	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	2	1	no	—
425	C₄²	—	2	2	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	2	no	—
428	C₄²	—	2	2	no	—
429	C₄²	—	2	2	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	2	2	no	—
432	C₄²	C₂×D₄	1	1	yes	characteristic
433	C₄²	C₂×D₄	1	1	yes	characteristic
434	C₄²	C₂⁴	1	1	yes	characteristic
435	C₄²	C₂⁴	1	2	yes	—
436	C₄²	C₂⁴	1	2	yes	—
437	C₄²	C₂⁴	1	1	yes	characteristic
438	C₂³	—	2	1	no	—
439	C₂³	C₂²×D₄	1	1	yes	characteristic
440	Q₈	—	2	2	no	—
441	Q₈	—	2	2	no	—
442	Q₈	—	2	1	no	—
443	Q₈	—	2	1	no	—
444	Q₈	—	2	2	no	—
445	Q₈	—	2	1	no	—
446	Q₈	—	2	2	no	—
447	Q₈	—	2	2	no	—
448	Q₈	—	2	1	no	—
449	Q₈	—	2	2	no	—
450	Q₈	—	2	1	no	—
451	Q₈	—	2	1	no	—
452	Q₈	—	4	2	no	—
453	Q₈	—	4	2	no	—
454	Q₈	—	4	2	no	—
455	Q₈	—	8	1	no	—
456	Q₈	—	8	2	no	—
457	D₄	—	2	1	no	—
458	D₄	—	2	1	no	—
459	D₄	—	8	1	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	8	2	no	—
477	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄	C₂²×D₄	1	2	yes	—
480	C₂×C₄	C₂²×D₄	1	2	yes	—
481	C₂×C₄	C₂²×D₄	1	2	yes	—
482	C₂×C₄	C₂²×D₄	1	2	yes	—
483	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄	C₂⁵	1	1	yes	characteristic
487	C₈	—	2	1	no	—
488	C₈	—	2	2	no	—
489	C₈	—	2	2	no	—
490	C₈	—	2	1	no	—
491	C₈	—	2	1	no	—
492	C₈	2₋¹⁺⁴	1	2	yes	—
493	C₂²	—	2	1	no	—
494	C₂²	—	2	1	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	4	1	no	—
497	C₂²	—	4	1	no	—
498	C₂²	—	4	1	no	—
499	C₂²	C₂³×D₄	1	1	yes	characteristic
500	C₄	—	2	1	no	—
501	C₄	—	2	1	no	—
502	C₄	—	2	2	no	—
503	C₄	—	2	2	no	—
504	C₄	—	2	1	no	—
505	C₄	—	2	1	no	—
506	C₄	—	2	2	no	—
507	C₄	—	2	2	no	—
508	C₄	—	4	2	no	—
509	C₄	—	4	1	no	—
510	C₄	—	4	1	no	—
511	C₄	—	4	1	no	—
512	C₄	—	4	2	no	—
513	C₄	—	4	1	no	—
514	C₄	—	4	1	no	—
515	C₄	—	4	2	no	—
516	C₄	—	4	1	no	—
517	C₄	—	4	1	no	—
518	C₄	—	4	2	no	—
519	C₄	#578	1	2	yes	—
520	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
521	C₄	#585	1	1	yes	characteristic
522	C₂	—	4	1	no	—
523	C₂	—	8	1	no	—
524	C₂	#3497	1	1	yes	characteristic
525	C₂	C₂×#578	1	1	yes	characteristic
526	C₂	#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
prime radical	#121	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ #533 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3556	C₂	semidirect
3. #3398	C₂	semidirect
4. #3398	C₂	semidirect
5. #3395	C₂	semidirect
6. #3390	C₂	semidirect
7. #3387	C₂	semidirect
8. #3381	C₂	semidirect
9. #3377	C₂	semidirect
10. #3374	C₂	semidirect
11. #3374	C₂	semidirect
12. #3372	C₂	semidirect
13. #3364	C₂	semidirect
14. #3363	C₂	semidirect
15. #3261	C₂	semidirect
17. #3249	C₂	semidirect
19. #3185	C₂	semidirect
21. #3177	C₂	semidirect
23. #2962	C₂	semidirect

Maximal subgroups

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

subgroup	index
#3556	2
#3555	2
#3398	2
#3395	2
#3390	2
#3387	2
#3381	2
#3377	2
#3374	2
#3372	2
#3364	2
#3363	2
#3261	2
#3258	2
#3249	2
#3248	2
#3185	2
#3178	2
#3177	2
#3172	2
#2962	2