Subgroups — #61473

Order 256.

885 conjugacy classes of subgroups.

The subgroup lattice has 531 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3516	C₂	1	2	yes	maximal, complemented
2	#3393	C₂	1	1	yes	maximal, characteristic, complemented
3	#3383	C₂	1	1	yes	maximal, characteristic, complemented
4	#3377	C₂	1	2	yes	maximal, complemented
5	#3339	C₂	1	1	yes	maximal, characteristic, complemented
6	#3338	C₂	1	1	yes	maximal, characteristic, complemented
7	#3336	C₂	1	1	yes	maximal, characteristic, complemented
8	#3327	C₂	1	2	yes	maximal, complemented
9	#3320	C₂	1	2	yes	maximal, complemented
10	#3316	C₂	1	2	yes	maximal, complemented
11	D₄×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	#3285	C₂	1	1	yes	maximal, characteristic, complemented
13	#3285	C₂	1	1	yes	maximal, characteristic, complemented
14	#3177	C₂	1	1	yes	maximal, characteristic, complemented
15	#3175	C₂	1	1	yes	maximal, characteristic, complemented
16	#3168	C₂	1	1	yes	maximal, characteristic, complemented
17	#3121	C₂	1	2	yes	maximal, complemented
18	#3120	C₂	1	2	yes	maximal, complemented
19	#3117	C₂	1	2	yes	maximal, complemented
20	#2966	C₂	1	1	yes	maximal, characteristic, complemented
21	#2951	C₂	1	1	yes	maximal, characteristic, complemented
22	#2950	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#135	C₂²	1	1	yes	characteristic
25	C₂²×Q₁₆	C₂²	1	1	yes	characteristic
26	C₂²×Q₁₆	C₂²	1	1	yes	characteristic
27	#557	C₂²	1	2	yes	—
28	#556	—	2	2	no	—
29	#556	C₂²	1	2	yes	—
30	#554	—	2	2	no	—
31	#554	C₂²	1	2	yes	—
32	#553	—	2	2	no	—
33	#553	C₂²	1	2	yes	—
34	#552	—	2	2	no	—
35	#552	C₂²	1	2	yes	—
36	D₄×Q₈	C₂²	1	2	yes	—
37	#548	C₂²	1	2	yes	—
38	#548	C₂²	1	2	yes	—
39	#542	—	2	2	no	—
40	#542	C₂²	1	2	yes	—
41	#541	—	2	2	no	—
42	#541	C₂²	1	2	yes	—
43	#529	—	2	2	no	—
44	#529	—	2	2	no	—
45	#529	C₂²	1	2	yes	—
46	#529	C₂²	1	1	yes	characteristic
47	#520	C₂²	1	2	yes	—
48	#519	C₂²	1	2	yes	—
49	C₂×C₄×Q₈	C₂²	1	2	yes	—
50	#500	C₂²	1	1	yes	characteristic
51	#499	C₂²	1	1	yes	characteristic
52	#499	C₂²	1	1	yes	characteristic
53	#495	C₂²	1	1	yes	characteristic
54	#495	C₂²	1	1	yes	characteristic
55	#494	C₂²	1	1	yes	characteristic
56	#491	C₂²	1	2	yes	—
57	#489	C₂²	1	2	yes	—
58	#488	C₂²	1	2	yes	—
59	#485	C₂²	1	2	yes	—
60	#484	C₂²	1	2	yes	—
61	#484	C₂²	1	2	yes	—
62	#483	C₂²	1	2	yes	—
63	#482	C₂²	1	2	yes	—
64	#481	C₂²	1	2	yes	—
65	#479	C₂²	1	2	yes	—
66	#479	C₂²	1	2	yes	—
67	#479	C₂²	1	2	yes	—
68	#478	C₂²	1	2	yes	—
69	#477	C₂²	1	2	yes	—
70	#475	C₂²	1	2	yes	—
71	#470	C₂²	1	2	yes	—
72	#468	C₂²	1	2	yes	—
73	#467	C₂²	1	1	yes	characteristic
74	#467	C₂²	1	1	yes	characteristic
75	#467	C₂²	1	1	yes	characteristic
76	#467	C₂²	1	1	yes	characteristic
77	#466	C₂²	1	1	yes	characteristic
78	#466	C₂²	1	1	yes	characteristic
79	#465	C₂²	1	2	yes	—
80	#464	C₂²	1	2	yes	—
81	#464	C₂²	1	2	yes	—
82	#464	C₂²	1	2	yes	—
83	#464	C₂²	1	2	yes	—
84	#462	C₂²	1	2	yes	—
85	#461	C₂²	1	2	yes	—
86	#452	C₂²	1	2	yes	—
87	#452	C₂²	1	2	yes	—
88	#451	C₂²	1	2	yes	—
89	#451	C₂²	1	2	yes	—
90	#448	C₂²	1	2	yes	—
91	#448	C₂²	1	2	yes	—
92	#446	C₂²	1	1	yes	characteristic
93	C₈×Q₈	C₂²	1	1	yes	characteristic
94	#441	C₂²	1	2	yes	—
95	#441	C₂²	1	2	yes	—
96	#441	C₂²	1	2	yes	—
97	#440	C₂²	1	2	yes	—
98	#440	C₂²	1	2	yes	—
99	#440	C₂²	1	2	yes	—
100	C₄×Q₁₆	C₂²	1	1	yes	characteristic
101	C₄×Q₁₆	C₂²	1	1	yes	characteristic
102	C₄×Q₁₆	C₂²	1	2	yes	—
103	C₄×Q₁₆	C₂²	1	2	yes	—
104	C₄×Q₁₆	C₂²	1	1	yes	characteristic
105	C₄×Q₁₆	C₂²	1	1	yes	characteristic
106	C₄×Q₁₆	C₂²	1	1	yes	characteristic
107	C₄×Q₁₆	C₂²	1	1	yes	characteristic
108	C₄×Q₁₆	C₂²	1	1	yes	characteristic
109	C₄×Q₁₆	C₂²	1	1	yes	characteristic
110	C₄×SD₁₆	C₂²	1	2	yes	—
111	C₄×D₈	C₂²	1	1	yes	characteristic
112	C₄×D₈	C₂²	1	1	yes	characteristic
113	#436	C₂²	1	1	yes	characteristic
114	#435	C₂²	1	1	yes	characteristic
115	#435	C₂²	1	1	yes	characteristic
116	C₈×D₄	C₂²	1	1	yes	characteristic
117	C₈×D₄	C₂²	1	1	yes	characteristic
118	C₈×D₄	C₂²	1	1	yes	characteristic
119	#433	C₂²	1	1	yes	characteristic
120	#433	C₂²	1	1	yes	characteristic
121	#432	C₂²	1	1	yes	characteristic
122	#427	C₂²	1	1	yes	characteristic
123	C₂×#107	C₂²	1	1	yes	characteristic
124	C₂×#107	C₂²	1	1	yes	characteristic
125	#419	C₂²	1	2	yes	—
126	#417	C₂²	1	2	yes	—
127	C₂×#103	C₂²	1	2	yes	—
128	#405	C₂²	1	1	yes	characteristic
129	#405	C₂²	1	1	yes	characteristic
130	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
131	C₂×#41	C₂³	1	2	yes	—
132	C₂²×Q₈	C₂³	1	2	yes	—
133	C₂²×Q₈	C₂³	1	2	yes	—
134	#135	—	2	4	no	—
135	C₂×Q₁₆	—	2	4	no	—
136	C₂×Q₁₆	—	2	4	no	—
137	C₂×Q₁₆	C₂³	1	2	yes	—
138	C₂×Q₁₆	C₂³	1	1	yes	characteristic
139	C₂×Q₁₆	C₂³	1	1	yes	characteristic
140	C₂×Q₁₆	C₂³	1	2	yes	—
141	C₂×Q₁₆	C₂³	1	2	yes	—
142	C₂×Q₁₆	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆	C₂³	1	2	yes	—
144	C₂×SD₁₆	C₂³	1	2	yes	—
145	C₂×SD₁₆	C₂³	1	2	yes	—
146	C₂×D₈	C₂³	1	1	yes	characteristic
147	C₂×M₁₆	C₂³	1	1	yes	characteristic
148	C₂×M₁₆	C₂³	1	1	yes	characteristic
149	C₂²×C₈	C₂³	1	1	yes	characteristic
150	C₂²×C₈	C₂³	1	1	yes	characteristic
151	C₂²×C₈	C₂³	1	1	yes	characteristic
152	C₂²×C₈	C₂³	1	1	yes	characteristic
153	C₄⋊Q₈	—	2	2	no	—
154	C₄⋊Q₈	—	2	2	no	—
155	C₄⋊Q₈	C₂³	1	2	yes	—
156	C₄⋊Q₈	C₂³	1	2	yes	—
157	#126	—	2	2	no	—
158	#126	—	2	2	no	—
159	#126	—	2	2	no	—
160	#126	—	2	2	no	—
161	#126	—	2	2	no	—
162	#126	—	2	2	no	—
163	#126	—	2	2	no	—
164	#126	—	2	2	no	—
165	#126	D₄	1	1	yes	characteristic
166	#126	D₄	1	1	yes	characteristic
167	#125	—	2	2	no	—
168	#125	—	2	2	no	—
169	#125	—	2	2	no	—
170	#125	—	2	2	no	—
171	#125	—	2	2	no	—
172	#125	—	2	2	no	—
173	#125	D₄	1	1	yes	characteristic
174	#125	C₂³	1	2	yes	—
175	#125	C₂³	1	2	yes	—
176	#124	—	2	2	no	—
177	#124	—	2	2	no	—
178	#124	—	2	2	no	—
179	#124	D₄	1	1	yes	characteristic
180	#124	C₂³	1	2	yes	—
181	#124	C₂³	1	2	yes	—
182	#123	—	2	2	no	—
183	#123	—	2	2	no	—
184	#123	—	2	2	no	—
185	#123	—	2	2	no	—
186	#123	D₄	1	1	yes	characteristic
187	#123	D₄	1	1	yes	characteristic
188	C₂²⋊Q₈	—	2	2	no	—
189	C₂²⋊Q₈	—	2	2	no	—
190	C₂²⋊Q₈	—	2	2	no	—
191	C₂²⋊Q₈	—	2	2	no	—
192	C₂²⋊Q₈	—	2	2	no	—
193	C₂²⋊Q₈	—	2	2	no	—
194	C₂²⋊Q₈	—	2	2	no	—
195	C₂²⋊Q₈	—	2	2	no	—
196	C₂²⋊Q₈	D₄	1	1	yes	characteristic
197	C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₂²⋊Q₈	C₂³	1	2	yes	—
201	#121	—	2	2	no	—
202	#121	—	2	2	no	—
203	#121	—	2	2	no	—
204	#121	D₄	1	1	yes	characteristic
205	#121	C₂³	1	2	yes	—
206	#121	C₂³	1	2	yes	—
207	C₄×Q₈	—	2	2	no	—
208	C₄×Q₈	—	2	2	no	—
209	C₄×Q₈	—	2	2	no	—
210	C₄×Q₈	—	2	2	no	—
211	C₄×Q₈	—	2	2	no	—
212	C₄×Q₈	C₂³	1	2	yes	—
213	C₄×Q₈	C₂³	1	2	yes	—
214	C₄×Q₈	C₂³	1	2	yes	—
215	C₄×Q₈	C₂³	1	2	yes	—
216	C₄×Q₈	C₂³	1	2	yes	—
217	C₄×Q₈	C₂³	1	2	yes	—
218	C₄×Q₈	C₂³	1	2	yes	—
219	C₄×Q₈	C₂³	1	2	yes	—
220	C₄×Q₈	C₂³	1	1	yes	characteristic
221	C₄×D₄	—	2	2	no	—
222	C₄×D₄	—	2	2	no	—
223	C₄×D₄	—	2	2	no	—
224	C₄×D₄	—	2	2	no	—
225	C₄×D₄	—	2	2	no	—
226	C₄×D₄	—	2	2	no	—
227	C₄×D₄	—	2	2	no	—
228	C₄×D₄	—	2	2	no	—
229	C₄×D₄	C₂³	1	2	yes	—
230	C₄×D₄	C₂³	1	2	yes	—
231	C₄×D₄	C₂³	1	1	yes	characteristic
232	C₄×D₄	C₂³	1	1	yes	characteristic
233	C₄×D₄	C₂³	1	1	yes	characteristic
234	#117	—	2	2	no	—
235	#117	—	2	2	no	—
236	#117	—	2	2	no	—
237	#117	—	2	2	no	—
238	#117	—	2	2	no	—
239	#117	—	2	2	no	—
240	#117	C₂³	1	2	yes	—
241	#117	C₂³	1	1	yes	characteristic
242	#117	C₂³	1	1	yes	characteristic
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	C₂³	1	2	yes	—
246	C₂×C₄⋊C₄	C₂³	1	2	yes	—
247	C₂×C₄²	—	2	2	no	—
248	C₂×C₄²	C₂³	1	1	yes	characteristic
249	#107	C₂³	1	1	yes	characteristic
250	#107	C₂³	1	1	yes	characteristic
251	#107	C₂³	1	1	yes	characteristic
252	#107	C₂³	1	2	yes	—
253	#107	C₂³	1	2	yes	—
254	#107	C₂³	1	1	yes	characteristic
255	#107	C₂³	1	2	yes	—
256	#106	C₂³	1	2	yes	—
257	#106	C₂³	1	2	yes	—
258	#106	C₂³	1	2	yes	—
259	C₄⋊C₈	C₂³	1	1	yes	characteristic
260	C₄⋊C₈	C₂³	1	1	yes	characteristic
261	C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₄⋊C₈	C₂³	1	1	yes	characteristic
263	C₄⋊C₈	C₂³	1	1	yes	characteristic
264	C₄⋊C₈	C₂³	1	1	yes	characteristic
265	#103	C₂³	1	2	yes	—
266	#103	C₂³	1	2	yes	—
267	#103	C₂³	1	2	yes	—
268	#103	C₂³	1	2	yes	—
269	#103	C₂³	1	2	yes	—
270	#103	C₂³	1	2	yes	—
271	#103	C₂³	1	2	yes	—
272	#103	C₂³	1	2	yes	—
273	#103	C₂³	1	2	yes	—
274	#103	C₂³	1	2	yes	—
275	#103	C₂³	1	2	yes	—
276	#103	C₂³	1	2	yes	—
277	#102	C₂³	1	2	yes	—
278	#102	C₂³	1	2	yes	—
279	#102	C₂³	1	2	yes	—
280	#102	C₂³	1	2	yes	—
281	C₂²⋊C₈	C₂³	1	1	yes	characteristic
282	C₂²⋊C₈	C₂³	1	1	yes	characteristic
283	C₂²⋊C₈	C₂³	1	1	yes	characteristic
284	C₂²⋊C₈	C₂³	1	1	yes	characteristic
285	C₂²⋊C₈	C₂³	1	1	yes	characteristic
286	C₂²⋊C₈	C₂³	1	1	yes	characteristic
287	#97	C₂³	1	1	yes	characteristic
288	#97	C₂³	1	1	yes	characteristic
289	#97	C₂³	1	1	yes	characteristic
290	#97	C₂³	1	1	yes	characteristic
291	C₄×C₈	C₂³	1	1	yes	characteristic
292	C₄×C₈	C₂³	1	1	yes	characteristic
293	C₄×C₈	C₂³	1	1	yes	characteristic
294	C₄×C₈	C₂³	1	1	yes	characteristic
295	C₄×C₈	C₂³	1	1	yes	characteristic
296	C₄×C₈	C₂³	1	1	yes	characteristic
297	#41	—	2	4	no	—
298	#41	—	4	2	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	4	no	—
303	C₂×Q₈	—	2	4	no	—
304	C₂×Q₈	—	4	2	no	—
305	C₂×Q₈	—	4	2	no	—
306	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
307	C₂×Q₈	C₂⁴	1	2	yes	—
308	C₂×Q₈	C₂⁴	1	2	yes	—
309	C₂×Q₈	C₂⁴	1	2	yes	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	C₂×D₄	1	1	yes	characteristic
314	C₂×D₄	C₂×D₄	1	1	yes	characteristic
315	C₂×D₄	C₂×D₄	1	1	yes	characteristic
316	C₂×D₄	C₂⁴	1	2	yes	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
326	C₂²×C₄	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄	C₂⁴	1	1	yes	characteristic
329	Q₁₆	—	2	4	no	—
330	Q₁₆	—	2	4	no	—
331	Q₁₆	—	2	2	no	—
332	Q₁₆	—	2	2	no	—
333	Q₁₆	—	4	2	no	—
334	Q₁₆	#41	1	4	yes	—
335	SD₁₆	—	2	4	no	—
336	SD₁₆	—	4	2	no	—
337	SD₁₆	—	4	2	no	—
338	D₈	—	2	2	no	—
339	M₁₆	—	4	1	no	—
340	M₁₆	—	4	1	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	4	1	no	—
345	C₂×C₈	C₂⁴	1	1	yes	characteristic
346	C₂×C₈	C₂⁴	1	1	yes	characteristic
347	C₂×C₈	C₂⁴	1	1	yes	characteristic
348	C₂×C₈	C₂⁴	1	1	yes	characteristic
349	C₂×C₈	C₂⁴	1	1	yes	characteristic
350	C₂×C₈	C₂⁴	1	1	yes	characteristic
351	C₂×C₈	C₂⁴	1	1	yes	characteristic
352	C₂×C₈	C₂⁴	1	1	yes	characteristic
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	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	C₂×D₄	1	1	yes	characteristic
375	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
376	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
377	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
378	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
379	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
380	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
381	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
382	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
383	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
384	C₄⋊C₄	C₂⁴	1	2	yes	—
385	C₄⋊C₄	C₂⁴	1	2	yes	—
386	C₄⋊C₄	C₂⁴	1	2	yes	—
387	C₄⋊C₄	C₂⁴	1	2	yes	—
388	C₂²⋊C₄	—	2	2	no	—
389	C₂²⋊C₄	—	2	2	no	—
390	C₂²⋊C₄	—	2	2	no	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	2	2	no	—
393	C₂²⋊C₄	—	2	2	no	—
394	C₂²⋊C₄	—	2	2	no	—
395	C₂²⋊C₄	—	2	2	no	—
396	C₂²⋊C₄	—	2	2	no	—
397	C₂²⋊C₄	—	2	2	no	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₂²⋊C₄	—	2	2	no	—
400	C₂²⋊C₄	—	2	2	no	—
401	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
402	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
403	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
404	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
405	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
406	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
407	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
408	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
409	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
410	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
411	C₄²	—	2	2	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	2	2	no	—
415	C₄²	—	2	2	no	—
416	C₄²	—	2	2	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	2	2	no	—
419	C₄²	—	2	2	no	—
420	C₄²	C₂×D₄	1	1	yes	characteristic
421	C₄²	C₂×D₄	1	1	yes	characteristic
422	C₄²	C₂⁴	1	1	yes	characteristic
423	C₄²	C₂⁴	1	1	yes	characteristic
424	C₄²	C₂⁴	1	1	yes	characteristic
425	C₄²	C₂⁴	1	1	yes	characteristic
426	C₂³	—	2	2	no	—
427	C₂³	C₂²×D₄	1	1	yes	characteristic
428	C₂³	C₂²×D₄	1	1	yes	characteristic
429	C₂³	C₂²×D₄	1	1	yes	characteristic
430	Q₈	—	2	2	no	—
431	Q₈	—	2	2	no	—
432	Q₈	—	2	2	no	—
433	Q₈	—	2	2	no	—
434	Q₈	—	2	2	no	—
435	Q₈	—	4	1	no	—
436	Q₈	—	4	4	no	—
437	Q₈	—	4	4	no	—
438	Q₈	—	8	2	no	—
439	Q₈	C₂×#41	1	4	yes	—
440	D₄	—	2	2	no	—
441	D₄	—	2	2	no	—
442	D₄	—	2	2	no	—
443	D₄	—	2	2	no	—
444	D₄	—	4	1	no	—
445	D₄	—	4	4	no	—
446	D₄	—	4	4	no	—
447	D₄	—	8	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	4	4	no	—
466	C₂×C₄	—	8	2	no	—
467	C₂×C₄	—	8	2	no	—
468	C₂×C₄	—	8	2	no	—
469	C₂×C₄	—	8	2	no	—
470	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
471	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
472	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
473	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
474	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
475	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
476	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
480	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
481	C₂×C₄	C₂⁵	1	1	yes	characteristic
482	C₈	—	2	1	no	—
483	C₈	—	2	1	no	—
484	C₈	—	2	1	no	—
485	C₈	—	2	1	no	—
486	C₈	—	2	1	no	—
487	C₈	—	2	1	no	—
488	C₈	—	2	1	no	—
489	C₈	C₂×#41	1	2	yes	—
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	—	4	2	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	2	no	—
501	C₂²	#578	1	2	yes	—
502	C₂²	C₂³×D₄	1	1	yes	characteristic
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	—	2	1	no	—
510	C₄	—	2	4	no	—
511	C₄	—	2	1	no	—
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	2	1	no	—
515	C₄	—	4	2	no	—
516	C₄	—	4	2	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	2	no	—
519	C₄	—	4	2	no	—
520	C₄	—	4	2	no	—
521	C₄	C₂²×#41	1	1	yes	characteristic
522	C₄	#585	1	1	yes	characteristic
523	C₂	—	2	2	no	—
524	C₂	—	4	1	no	—
525	C₂	—	4	1	no	—
526	C₂	—	8	2	no	—
527	C₂	D₄×#41	1	1	yes	characteristic
528	C₂	C₂×#578	1	1	yes	characteristic
529	C₂	#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ #529 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3516	C₂	semidirect
2. #3393	C₂	semidirect
3. #3383	C₂	semidirect
4. #3377	C₂	semidirect
5. #3339	C₂	semidirect
6. #3338	C₂	semidirect
7. #3336	C₂	semidirect
8. #3327	C₂	semidirect
9. #3320	C₂	semidirect
10. #3316	C₂	semidirect
11. D₄×Q₁₆	C₂	semidirect
12. #3285	C₂	semidirect
13. #3285	C₂	semidirect
14. #3177	C₂	semidirect
15. #3175	C₂	semidirect
16. #3168	C₂	semidirect
17. #3121	C₂	semidirect
18. #3120	C₂	semidirect
19. #3117	C₂	semidirect
20. #2966	C₂	semidirect
21. #2951	C₂	semidirect
22. #2950	C₂	semidirect
23. C₂×C₄×Q₁₆	C₂	semidirect

Maximal subgroups

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

subgroup	index
#3516	2
#3393	2
#3383	2
#3377	2
#3339	2
#3338	2
#3336	2
#3327	2
#3320	2
#3316	2
D₄×Q₁₆	2
#3285	2
#3177	2
#3175	2
#3168	2
#3121	2
#3120	2
#3117	2
#2966	2
#2951	2
#2950	2
C₂×C₄×Q₁₆	2