Subgroups — #62345

Order 256.

917 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	#3546	C₂	1	1	yes	maximal, characteristic
3	#3353	C₂	1	1	yes	maximal, characteristic, complemented
4	#3350	C₂	1	2	yes	maximal, complemented
5	#3342	C₂	1	1	yes	maximal, characteristic, complemented
6	#3328	C₂	1	1	yes	maximal, characteristic, complemented
7	#3324	C₂	1	1	yes	maximal, characteristic, complemented
8	#3320	C₂	1	2	yes	maximal, complemented
9	#3311	C₂	1	2	yes	maximal, complemented
10	#3304	C₂	1	1	yes	maximal, characteristic, complemented
11	#3298	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
13	#3278	C₂	1	1	yes	maximal, characteristic, complemented
14	#3266	C₂	1	2	yes	maximal, complemented
15	#3248	C₂	1	1	yes	maximal, characteristic, complemented
16	#3246	C₂	1	1	yes	maximal, characteristic, complemented
17	#3201	C₂	1	2	yes	maximal, complemented
18	#3200	C₂	1	2	yes	maximal, complemented
19	#3182	C₂	1	1	yes	maximal, characteristic, complemented
20	#3172	C₂	1	1	yes	maximal, characteristic, complemented
21	#3063	C₂	1	2	yes	maximal, complemented
22	#3057	C₂	1	2	yes	maximal, complemented
23	#2935	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137	C₂²	1	2	yes	complemented
25	C₂²×SD₁₆	C₂²	1	2	yes	—
26	C₂×#131	C₂²	1	2	yes	complemented
27	#563	—	2	2	no	—
28	#560	—	2	2	no	—
29	#559	—	2	1	no	—
30	Q₈²	—	2	1	no	—
31	#556	C₂²	1	1	yes	characteristic
32	#556	C₂²	1	1	yes	characteristic
33	#556	C₂²	1	2	yes	complemented
34	#556	C₂²	1	1	yes	characteristic, complemented
35	#553	C₂²	1	2	yes	—
36	#550	—	2	1	no	—
37	#550	C₂²	1	1	yes	characteristic
38	D₄×Q₈	C₂²	1	1	yes	characteristic
39	D₄×Q₈	C₂²	1	2	yes	complemented
40	D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
41	#547	C₂²	1	1	yes	characteristic
42	#546	—	2	1	no	—
43	#546	C₂²	1	2	yes	—
44	D₄²	C₂²	1	1	yes	characteristic
45	#542	—	2	1	no	—
46	#542	—	2	1	no	—
47	#542	—	2	1	no	—
48	#542	—	2	2	no	—
49	#538	—	2	2	no	—
50	#537	C₂²	1	2	yes	—
51	#536	C₂²	1	2	yes	complemented
52	#536	C₂²	1	2	yes	complemented
53	#535	—	2	1	no	—
54	#535	C₂²	1	2	yes	—
55	#533	C₂²	1	1	yes	characteristic, complemented
56	#533	C₂²	1	1	yes	characteristic, complemented
57	#532	C₂²	1	1	yes	characteristic
58	#532	C₂²	1	1	yes	characteristic
59	#529	C₂²	1	1	yes	characteristic
60	#501	C₂²	1	1	yes	characteristic, complemented
61	#500	C₂²	1	1	yes	characteristic, complemented
62	#497	C₂²	1	1	yes	characteristic
63	#492	C₂²	1	1	yes	characteristic
64	#491	C₂²	1	1	yes	characteristic, complemented
65	#489	C₂²	1	1	yes	characteristic
66	#487	C₂²	1	1	yes	characteristic, complemented
67	#486	C₂²	1	1	yes	characteristic
68	#485	C₂²	1	2	yes	complemented
69	#485	C₂²	1	2	yes	complemented
70	#485	C₂²	1	2	yes	complemented
71	#484	C₂²	1	2	yes	complemented
72	#483	C₂²	1	2	yes	complemented
73	#482	C₂²	1	2	yes	—
74	#482	C₂²	1	2	yes	—
75	#482	C₂²	1	2	yes	complemented
76	#479	C₂²	1	2	yes	complemented
77	#476	C₂²	1	2	yes	complemented
78	#475	C₂²	1	1	yes	characteristic, complemented
79	#475	C₂²	1	1	yes	characteristic, complemented
80	#475	C₂²	1	1	yes	characteristic, complemented
81	#474	C₂²	1	1	yes	characteristic
82	#470	C₂²	1	2	yes	complemented
83	#470	C₂²	1	1	yes	characteristic, complemented
84	#470	C₂²	1	1	yes	characteristic, complemented
85	#468	C₂²	1	2	yes	—
86	#468	C₂²	1	1	yes	characteristic
87	#468	C₂²	1	1	yes	characteristic
88	#468	C₂²	1	2	yes	—
89	#468	C₂²	1	2	yes	complemented
90	#468	C₂²	1	2	yes	complemented
91	#468	C₂²	1	2	yes	complemented
92	#467	C₂²	1	2	yes	complemented
93	#467	C₂²	1	2	yes	complemented
94	#465	C₂²	1	2	yes	—
95	#465	C₂²	1	2	yes	—
96	#465	C₂²	1	2	yes	—
97	#465	C₂²	1	2	yes	complemented
98	#465	C₂²	1	2	yes	complemented
99	#465	C₂²	1	2	yes	complemented
100	#464	C₂²	1	2	yes	—
101	#462	C₂²	1	1	yes	characteristic, complemented
102	#461	C₂²	1	1	yes	characteristic
103	#461	C₂²	1	2	yes	complemented
104	#460	C₂²	1	1	yes	characteristic
105	#460	C₂²	1	1	yes	characteristic
106	#452	C₂²	1	2	yes	complemented
107	#452	C₂²	1	2	yes	complemented
108	#451	C₂²	1	2	yes	complemented
109	#450	C₂²	1	2	yes	—
110	#450	C₂²	1	2	yes	—
111	#448	C₂²	1	2	yes	—
112	#448	C₂²	1	2	yes	—
113	#448	C₂²	1	2	yes	complemented
114	#440	C₂²	1	2	yes	complemented
115	#440	C₂²	1	2	yes	complemented
116	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
117	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
118	C₄×SD₁₆	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆	C₂²	1	1	yes	characteristic
120	#436	C₂²	1	1	yes	characteristic
121	#436	C₂²	1	1	yes	characteristic, complemented
122	#435	C₂²	1	2	yes	complemented
123	#435	C₂²	1	2	yes	complemented
124	C₈×D₄	C₂²	1	1	yes	characteristic
125	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
126	#428	C₂²	1	2	yes	complemented
127	#427	C₂²	1	2	yes	complemented
128	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
129	#419	C₂²	1	2	yes	complemented
130	#418	C₂²	1	2	yes	—
131	#416	C₂²	1	2	yes	complemented
132	C₂×#103	C₂²	1	2	yes	complemented
133	#408	C₂²	1	2	yes	complemented
134	C₄×M₁₆	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41	—	2	1	no	—
136	C₂×#41	—	2	1	no	—
137	C₂×#41	C₂³	1	2	yes	—
138	C₂×#41	C₂³	1	2	yes	—
139	C₂²×Q₈	C₂³	1	2	yes	—
140	C₂²×Q₈	C₂³	1	2	yes	—
141	C₂²×D₄	—	2	1	no	—
142	C₂²×D₄	C₂³	1	2	yes	—
143	#137	—	4	4	no	—
144	C₂×Q₁₆	C₂³	1	1	yes	characteristic
145	C₂×Q₁₆	C₂³	1	2	yes	—
146	C₂×Q₁₆	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆	—	4	4	no	—
148	C₂×SD₁₆	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆	C₂³	1	2	yes	—
150	C₂×SD₁₆	C₂³	1	2	yes	—
151	C₂×SD₁₆	C₂³	1	2	yes	—
152	C₂×SD₁₆	C₂³	1	2	yes	—
153	C₂×SD₁₆	C₂³	1	1	yes	characteristic
154	C₂×SD₁₆	C₂³	1	2	yes	—
155	#131	—	4	4	no	—
156	C₂×M₁₆	C₂³	1	1	yes	characteristic
157	C₂×M₁₆	C₂³	1	2	yes	—
158	C₂×M₁₆	C₂³	1	2	yes	—
159	C₂×M₁₆	C₂³	1	1	yes	characteristic
160	C₂²×C₈	C₂³	1	2	yes	—
161	C₂²×C₈	C₂³	1	2	yes	—
162	C₂²×C₈	C₂³	1	2	yes	—
163	C₄⋊Q₈	—	2	2	no	—
164	C₄⋊Q₈	—	2	2	no	—
165	C₄⋊Q₈	—	2	1	no	—
166	C₄⋊Q₈	—	2	1	no	—
167	C₄⋊Q₈	—	2	2	no	—
168	C₄⋊Q₈	D₄	1	1	yes	characteristic
169	C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	C₄⋊Q₈	C₂³	1	1	yes	characteristic
172	C₄⋊Q₈	C₂³	1	1	yes	characteristic
173	C₄⋊Q₈	C₂³	1	1	yes	characteristic
174	#127	—	2	1	no	—
175	#127	—	2	2	no	—
176	#127	D₄	1	1	yes	characteristic
177	#127	C₂³	1	1	yes	characteristic
178	#126	—	2	2	no	—
179	#126	—	2	2	no	—
180	#126	—	2	2	no	—
181	#126	—	2	2	no	—
182	#126	—	2	2	no	—
183	#126	—	2	2	no	—
184	#126	—	2	1	no	—
185	#125	—	2	1	no	—
186	#125	—	2	1	no	—
187	#125	C₂³	1	1	yes	characteristic
188	#124	—	2	2	no	—
189	#124	—	2	1	no	—
190	#124	—	2	2	no	—
191	#124	—	2	2	no	—
192	#124	—	2	1	no	—
193	#124	—	2	1	no	—
194	#124	—	2	2	no	—
195	#124	—	2	1	no	—
196	#124	D₄	1	2	yes	—
197	#124	C₂³	1	1	yes	characteristic
198	#123	—	2	2	no	—
199	#123	—	2	2	no	—
200	#123	—	2	2	no	—
201	#123	—	2	2	no	—
202	#123	—	2	1	no	—
203	#123	—	2	2	no	—
204	#123	—	2	2	no	—
205	#123	—	2	2	no	—
206	C₂²⋊Q₈	—	2	2	no	—
207	C₂²⋊Q₈	—	2	1	no	—
208	C₂²⋊Q₈	—	2	1	no	—
209	C₂²⋊Q₈	—	2	1	no	—
210	C₂²⋊Q₈	—	2	2	no	—
211	C₂²⋊Q₈	—	2	2	no	—
212	C₂²⋊Q₈	—	2	2	no	—
213	C₂²⋊Q₈	—	2	2	no	—
214	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
215	C₂²⋊Q₈	C₂³	1	2	yes	—
216	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
217	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
218	C₂²⋊Q₈	C₂³	1	2	yes	—
219	C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₂²⋊Q₈	C₂³	1	2	yes	—
221	C₂²⋊Q₈	C₂³	1	2	yes	—
222	C₂²⋊Q₈	C₂³	1	2	yes	—
223	#121	—	2	2	no	—
224	#121	—	2	2	no	—
225	#121	—	2	2	no	—
226	#121	—	2	2	no	—
227	#121	—	2	1	no	—
228	#121	—	2	1	no	—
229	#121	—	2	2	no	—
230	#121	—	2	2	no	—
231	#121	D₄	1	1	yes	characteristic
232	#121	D₄	1	1	yes	characteristic
233	#121	D₄	1	2	yes	—
234	#121	C₂³	1	1	yes	characteristic
235	#121	C₂³	1	2	yes	—
236	#121	C₂³	1	2	yes	—
237	#121	C₂³	1	2	yes	—
238	#121	C₂³	1	2	yes	—
239	#120	—	2	2	no	—
240	#120	—	2	2	no	—
241	#120	—	2	2	no	—
242	#120	—	2	2	no	—
243	C₄×Q₈	—	2	1	no	—
244	C₄×Q₈	—	2	1	no	—
245	C₄×Q₈	—	2	1	no	—
246	C₄×Q₈	—	2	2	no	—
247	C₄×Q₈	—	2	1	no	—
248	C₄×Q₈	—	2	1	no	—
249	C₄×Q₈	C₂³	1	1	yes	characteristic
250	C₄×Q₈	C₂³	1	1	yes	characteristic
251	C₄×Q₈	C₂³	1	1	yes	characteristic
252	C₄×Q₈	C₂³	1	2	yes	—
253	C₄×D₄	—	2	1	no	—
254	C₄×D₄	—	2	1	no	—
255	C₄×D₄	—	2	2	no	—
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	—	2	1	no	—
258	C₄×D₄	—	2	2	no	—
259	C₄×D₄	—	2	1	no	—
260	C₄×D₄	C₂³	1	1	yes	characteristic
261	C₄×D₄	C₂³	1	2	yes	—
262	C₄×D₄	C₂³	1	1	yes	characteristic
263	C₄×D₄	C₂³	1	2	yes	—
264	C₄×D₄	C₂³	1	1	yes	characteristic
265	#117	—	2	1	no	—
266	#117	—	2	1	no	—
267	#117	—	2	1	no	—
268	#117	C₂³	1	2	yes	—
269	#117	C₂³	1	2	yes	—
270	#117	C₂³	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³	1	2	yes	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₄²	C₂³	1	1	yes	characteristic
274	#107	C₂³	1	1	yes	characteristic
275	#107	C₂³	1	2	yes	—
276	#107	C₂³	1	2	yes	—
277	#107	C₂³	1	1	yes	characteristic
278	#107	C₂³	1	2	yes	—
279	#106	C₂³	1	2	yes	—
280	#106	C₂³	1	2	yes	—
281	#106	C₂³	1	1	yes	characteristic
282	#106	C₂³	1	2	yes	—
283	#106	C₂³	1	1	yes	characteristic
284	C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₄⋊C₈	C₂³	1	2	yes	—
286	C₄⋊C₈	C₂³	1	1	yes	characteristic
287	#103	C₂³	1	1	yes	characteristic
288	#103	C₂³	1	2	yes	—
289	#103	C₂³	1	2	yes	—
290	#103	C₂³	1	2	yes	—
291	#103	C₂³	1	1	yes	characteristic
292	#103	C₂³	1	2	yes	—
293	#103	C₂³	1	1	yes	characteristic
294	#103	C₂³	1	2	yes	—
295	#103	C₂³	1	2	yes	—
296	#103	C₂³	1	1	yes	characteristic
297	#103	C₂³	1	1	yes	characteristic
298	#103	C₂³	1	1	yes	characteristic
299	#103	C₂³	1	2	yes	—
300	#102	C₂³	1	2	yes	—
301	#102	C₂³	1	2	yes	—
302	#102	C₂³	1	1	yes	characteristic
303	#102	C₂³	1	2	yes	—
304	#102	C₂³	1	2	yes	—
305	#102	C₂³	1	1	yes	characteristic
306	#102	C₂³	1	2	yes	—
307	C₂²⋊C₈	C₂³	1	2	yes	—
308	C₂²⋊C₈	C₂³	1	2	yes	—
309	C₂²⋊C₈	C₂³	1	2	yes	—
310	C₂²⋊C₈	C₂³	1	2	yes	—
311	#97	C₂³	1	1	yes	characteristic
312	#97	C₂³	1	1	yes	characteristic
313	C₄×C₈	C₂³	1	1	yes	characteristic
314	C₄×C₈	C₂³	1	1	yes	characteristic
315	C₂⁴	—	2	2	no	—
316	#41	—	4	2	no	—
317	#41	—	4	2	no	—
318	#41	—	4	2	no	—
319	#41	—	4	2	no	—
320	#41	—	8	2	no	—
321	#41	—	8	2	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	4	2	no	—
328	C₂×Q₈	—	4	2	no	—
329	C₂×Q₈	—	4	2	no	—
330	C₂×Q₈	—	4	2	no	—
331	C₂×Q₈	C₂×D₄	1	2	yes	—
332	C₂×Q₈	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈	C₂⁴	1	1	yes	characteristic
334	C₂×Q₈	C₂⁴	1	2	yes	—
335	C₂×Q₈	C₂⁴	1	1	yes	characteristic
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	4	2	no	—
346	C₂×D₄	—	4	2	no	—
347	C₂×D₄	—	8	2	no	—
348	C₂×D₄	C₂×D₄	1	1	yes	characteristic
349	C₂×D₄	C₂×D₄	1	1	yes	characteristic
350	C₂×D₄	C₂×D₄	1	2	yes	—
351	C₂×D₄	C₂×D₄	1	2	yes	—
352	C₂×D₄	C₂×D₄	1	2	yes	—
353	C₂×D₄	C₂×D₄	1	2	yes	—
354	C₂×D₄	C₂⁴	1	1	yes	characteristic
355	C₂×D₄	C₂⁴	1	2	yes	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄	C₂⁴	1	2	yes	—
365	C₂²×C₄	C₂⁴	1	2	yes	—
366	C₂²×C₄	C₂⁴	1	1	yes	characteristic
367	Q₁₆	—	2	2	no	—
368	Q₁₆	—	4	1	no	—
369	Q₁₆	—	4	2	no	—
370	SD₁₆	—	2	2	no	—
371	SD₁₆	—	2	4	no	—
372	SD₁₆	—	4	2	no	—
373	SD₁₆	—	4	2	no	—
374	SD₁₆	—	4	2	no	—
375	SD₁₆	—	4	1	no	—
376	SD₁₆	—	4	2	no	—
377	M₁₆	—	2	2	no	—
378	M₁₆	—	2	4	no	—
379	M₁₆	—	4	1	no	—
380	M₁₆	—	4	2	no	—
381	C₂×C₈	—	2	4	no	—
382	C₂×C₈	—	4	2	no	—
383	C₂×C₈	—	4	2	no	—
384	C₂×C₈	C₂⁴	1	1	yes	characteristic
385	C₂×C₈	C₂⁴	1	1	yes	characteristic
386	C₂×C₈	C₂⁴	1	1	yes	characteristic
387	C₂×C₈	C₂⁴	1	2	yes	—
388	C₂×C₈	C₂⁴	1	2	yes	—
389	C₂×C₈	C₂⁴	1	1	yes	characteristic
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
414	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
415	C₄⋊C₄	C₂×D₄	1	2	yes	—
416	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄	C₂⁴	1	2	yes	—
419	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄	C₂⁴	1	2	yes	—
421	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	2	1	no	—
425	C₂²⋊C₄	—	2	1	no	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	2	1	no	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	—	2	2	no	—
433	C₂²⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	—	2	1	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	2	1	no	—
437	C₂²⋊C₄	—	2	1	no	—
438	C₂²⋊C₄	—	2	2	no	—
439	C₂²⋊C₄	—	2	2	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	2	1	no	—
442	C₂²⋊C₄	—	2	2	no	—
443	C₂²⋊C₄	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄	C₂×D₄	1	2	yes	—
446	C₂²⋊C₄	C₂×D₄	1	2	yes	—
447	C₄²	—	2	1	no	—
448	C₄²	—	2	2	no	—
449	C₄²	—	2	1	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	2	2	no	—
452	C₄²	—	2	2	no	—
453	C₄²	—	2	2	no	—
454	C₄²	C₂×D₄	1	1	yes	characteristic
455	C₄²	C₂×D₄	1	1	yes	characteristic
456	C₄²	C₂⁴	1	1	yes	characteristic
457	C₄²	C₂⁴	1	1	yes	characteristic
458	C₂³	—	2	1	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	8	2	no	—
461	C₂³	—	8	2	no	—
462	C₂³	—	8	2	no	—
463	C₂³	C₂²×D₄	1	2	yes	—
464	C₂³	C₂²×D₄	1	1	yes	characteristic
465	C₂³	C₂²×D₄	1	2	yes	—
466	Q₈	—	2	1	no	—
467	Q₈	—	2	2	no	—
468	Q₈	—	2	1	no	—
469	Q₈	—	2	1	no	—
470	Q₈	—	2	2	no	—
471	Q₈	—	2	1	no	—
472	Q₈	—	2	1	no	—
473	Q₈	—	2	1	no	—
474	Q₈	—	4	2	no	—
475	Q₈	—	4	2	no	—
476	Q₈	—	4	2	no	—
477	Q₈	—	4	2	no	—
478	Q₈	—	8	2	no	—
479	Q₈	—	8	2	no	—
480	D₄	—	2	2	no	—
481	D₄	—	2	2	no	—
482	D₄	—	2	1	no	—
483	D₄	—	2	2	no	—
484	D₄	—	2	1	no	—
485	D₄	—	2	2	no	—
486	D₄	—	4	2	no	—
487	D₄	—	4	2	no	—
488	D₄	—	4	2	no	—
489	D₄	—	4	2	no	—
490	D₄	—	4	2	no	—
491	D₄	—	8	1	no	—
492	D₄	—	8	2	no	—
493	D₄	—	8	1	no	—
494	D₄	—	8	2	no	—
495	D₄	—	8	2	no	—
496	D₄	—	8	2	no	—
497	D₄	—	8	2	no	—
498	D₄	—	8	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	8	2	no	—
519	C₂×C₄	—	8	2	no	—
520	C₂×C₄	—	8	2	no	—
521	C₂×C₄	—	8	2	no	—
522	C₂×C₄	—	8	2	no	—
523	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄	C₂²×D₄	1	2	yes	—
525	C₂×C₄	C₂²×D₄	1	2	yes	—
526	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄	C₂⁵	1	1	yes	characteristic
531	C₈	—	2	2	no	—
532	C₈	—	2	1	no	—
533	C₈	—	2	2	no	—
534	C₈	—	2	1	no	—
535	C₈	—	2	1	no	—
536	C₈	H(5,𝔽₂)	1	2	yes	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	2	2	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	4	2	no	—
547	C₂²	—	4	1	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	16	4	no	—
553	C₂²	C₂³×D₄	1	1	yes	characteristic
554	C₄	—	2	1	no	—
555	C₄	—	2	1	no	—
556	C₄	—	2	2	no	—
557	C₄	—	2	1	no	—
558	C₄	—	2	2	no	—
559	C₄	—	2	1	no	—
560	C₄	—	4	1	no	—
561	C₄	—	4	1	no	—
562	C₄	—	4	1	no	—
563	C₄	—	4	1	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	2	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	2	no	—
569	C₄	—	4	2	no	—
570	C₄	#577	1	2	yes	—
571	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
572	C₄	#585	1	1	yes	characteristic
573	C₂	—	4	1	no	—
574	C₂	—	4	2	no	—
575	C₂	—	4	2	no	—
576	C₂	—	8	2	no	—
577	C₂	—	8	1	no	—
578	C₂	#3496	1	1	yes	characteristic
579	C₂	C₂×#577	1	1	yes	characteristic
580	C₂	#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
prime radical	#3546	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ #532 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3550	C₂	semidirect
3. #3353	C₂	semidirect
4. #3350	C₂	semidirect
5. #3342	C₂	semidirect
6. #3328	C₂	semidirect
7. #3324	C₂	semidirect
8. #3320	C₂	semidirect
9. #3311	C₂	semidirect
10. #3304	C₂	semidirect
11. #3298	C₂	semidirect
12. D₄×SD₁₆	C₂	semidirect
13. #3278	C₂	semidirect
14. #3266	C₂	semidirect
15. #3248	C₂	semidirect
16. #3246	C₂	semidirect
17. #3201	C₂	semidirect
18. #3200	C₂	semidirect
19. #3182	C₂	semidirect
20. #3172	C₂	semidirect
21. #3063	C₂	semidirect
22. #3057	C₂	semidirect
23. #2935	C₂	semidirect
24. C₂×#137	C₂²	semidirect
26. C₂×#131	C₂²	semidirect
33. #556	C₂²	semidirect
34. #556	C₂²	semidirect
39. D₄×Q₈	C₂²	semidirect
40. D₄×Q₈	C₂²	semidirect
51. #536	C₂²	semidirect
52. #536	C₂²	semidirect
55. #533	C₂²	semidirect
56. #533	C₂²	semidirect
60. #501	C₂²	semidirect
61. #500	C₂²	semidirect
64. #491	C₂²	semidirect
66. #487	C₂²	semidirect
68. #485	C₂²	semidirect
69. #485	C₂²	semidirect
70. #485	C₂²	semidirect
71. #484	C₂²	semidirect
72. #483	C₂²	semidirect
75. #482	C₂²	semidirect
76. #479	C₂²	semidirect
77. #476	C₂²	semidirect
78. #475	C₂²	semidirect
79. #475	C₂²	semidirect
80. #475	C₂²	semidirect
82. #470	C₂²	semidirect
83. #470	C₂²	semidirect
84. #470	C₂²	semidirect
89. #468	C₂²	semidirect
90. #468	C₂²	semidirect
91. #468	C₂²	semidirect
92. #467	C₂²	semidirect
93. #467	C₂²	semidirect
97. #465	C₂²	semidirect
98. #465	C₂²	semidirect
99. #465	C₂²	semidirect
101. #462	C₂²	semidirect
103. #461	C₂²	semidirect
106. #452	C₂²	semidirect
107. #452	C₂²	semidirect
108. #451	C₂²	semidirect
113. #448	C₂²	semidirect
114. #440	C₂²	semidirect
115. #440	C₂²	semidirect
116. C₄×Q₁₆	C₂²	semidirect
117. C₄×Q₁₆	C₂²	semidirect
121. #436	C₂²	semidirect
122. #435	C₂²	semidirect
123. #435	C₂²	semidirect
125. C₈×D₄	C₂²	semidirect
126. #428	C₂²	semidirect
127. #427	C₂²	semidirect
128. C₂×C₄⋊C₈	C₂²	semidirect
129. #419	C₂²	semidirect
131. #416	C₂²	semidirect
132. C₂×#103	C₂²	semidirect
133. #408	C₂²	semidirect
134. C₄×M₁₆	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3550	2
#3546	2
#3353	2
#3350	2
#3342	2
#3328	2
#3324	2
#3320	2
#3311	2
#3304	2
#3298	2
D₄×SD₁₆	2
#3278	2
#3266	2
#3248	2
#3246	2
#3201	2
#3200	2
#3182	2
#3172	2
#3063	2
#3057	2
#2935	2