Subgroups — #61920

Order 256.

908 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3554	C₂	1	1	yes	maximal, characteristic, complemented
2	#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	#3403	C₂	1	2	yes	maximal, complemented
4	#3399	C₂	1	2	yes	maximal, complemented
5	#3399	C₂	1	1	yes	maximal, characteristic, complemented
6	#3399	C₂	1	1	yes	maximal, characteristic, complemented
7	#3396	C₂	1	1	yes	maximal, characteristic, complemented
8	#3391	C₂	1	1	yes	maximal, characteristic, complemented
9	#3373	C₂	1	1	yes	maximal, characteristic, complemented
10	#3370	C₂	1	2	yes	maximal, complemented
11	#3368	C₂	1	1	yes	maximal, characteristic, complemented
12	#3366	C₂	1	2	yes	maximal, complemented
13	#3365	C₂	1	1	yes	maximal, characteristic, complemented
14	#3358	C₂	1	1	yes	maximal, characteristic, complemented
15	#3224	C₂	1	2	yes	maximal, complemented
16	#3220	C₂	1	2	yes	maximal, complemented
17	#3217	C₂	1	1	yes	maximal, characteristic, complemented
18	#3205	C₂	1	1	yes	maximal, characteristic, complemented
19	#3122	C₂	1	2	yes	maximal, complemented
20	#3118	C₂	1	2	yes	maximal, complemented
21	#3115	C₂	1	1	yes	maximal, characteristic, complemented
22	#3102	C₂	1	1	yes	maximal, characteristic, complemented
23	#2985	C₂	1	1	yes	maximal, characteristic, complemented
24	#562	—	2	2	no	—
25	#559	C₂²	1	1	yes	characteristic
26	#559	C₂²	1	2	yes	—
27	#559	C₂²	1	1	yes	characteristic
28	#559	C₂²	1	1	yes	characteristic, complemented
29	#559	C₂²	1	2	yes	complemented
30	#557	C₂²	1	1	yes	characteristic, complemented
31	#554	C₂²	1	2	yes	complemented
32	#550	C₂²	1	1	yes	characteristic
33	#550	C₂²	1	2	yes	—
34	#550	C₂²	1	1	yes	characteristic
35	#550	C₂²	1	1	yes	characteristic, complemented
36	D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
37	#548	—	2	1	no	—
38	#547	—	2	1	no	—
39	#546	—	2	1	no	—
40	#546	—	2	1	no	—
41	#546	—	2	2	no	—
42	#542	—	2	1	no	—
43	#542	C₂²	1	2	yes	—
44	#540	—	2	2	no	—
45	#540	C₂²	1	2	yes	—
46	#539	—	2	2	no	—
47	#536	—	2	1	no	—
48	#535	C₂²	1	2	yes	—
49	#533	C₂²	1	1	yes	characteristic
50	#532	—	2	1	no	—
51	#532	—	2	1	no	—
52	#532	C₂²	1	1	yes	characteristic
53	C₂×#127	C₂²	1	1	yes	characteristic
54	#529	C₂²	1	1	yes	characteristic
55	#518	C₂²	1	2	yes	—
56	C₄×#41	C₂²	1	1	yes	characteristic
57	#496	C₂²	1	2	yes	—
58	#496	C₂²	1	2	yes	complemented
59	#496	C₂²	1	2	yes	complemented
60	#495	C₂²	1	2	yes	complemented
61	#493	C₂²	1	1	yes	characteristic
62	#493	C₂²	1	1	yes	characteristic
63	#493	C₂²	1	2	yes	complemented
64	#490	C₂²	1	2	yes	—
65	#490	C₂²	1	2	yes	complemented
66	#489	C₂²	1	2	yes	complemented
67	#488	C₂²	1	2	yes	complemented
68	#486	C₂²	1	1	yes	characteristic
69	#486	C₂²	1	1	yes	characteristic
70	#486	C₂²	1	2	yes	complemented
71	#485	C₂²	1	1	yes	characteristic
72	#482	C₂²	1	1	yes	characteristic
73	#482	C₂²	1	2	yes	—
74	#479	C₂²	1	1	yes	characteristic, complemented
75	#478	C₂²	1	1	yes	characteristic, complemented
76	#478	C₂²	1	2	yes	complemented
77	#478	C₂²	1	2	yes	complemented
78	#476	C₂²	1	2	yes	complemented
79	#475	C₂²	1	1	yes	characteristic, complemented
80	#474	C₂²	1	1	yes	characteristic, complemented
81	#474	C₂²	1	2	yes	complemented
82	#464	C₂²	1	1	yes	characteristic, complemented
83	#464	C₂²	1	2	yes	complemented
84	#463	C₂²	1	1	yes	characteristic, complemented
85	#463	C₂²	1	2	yes	complemented
86	#463	C₂²	1	2	yes	complemented
87	#463	C₂²	1	2	yes	complemented
88	#463	C₂²	1	2	yes	complemented
89	#463	C₂²	1	2	yes	complemented
90	#460	C₂²	1	1	yes	characteristic
91	#460	C₂²	1	1	yes	characteristic
92	#460	C₂²	1	2	yes	complemented
93	#460	C₂²	1	1	yes	characteristic, complemented
94	#459	C₂²	1	1	yes	characteristic
95	#459	C₂²	1	2	yes	—
96	#459	C₂²	1	2	yes	—
97	#459	C₂²	1	1	yes	characteristic
98	#459	C₂²	1	2	yes	complemented
99	#459	C₂²	1	2	yes	complemented
100	#459	C₂²	1	2	yes	complemented
101	#459	C₂²	1	1	yes	characteristic, complemented
102	#459	C₂²	1	2	yes	complemented
103	#459	C₂²	1	2	yes	complemented
104	#452	C₂²	1	1	yes	characteristic
105	#450	C₂²	1	2	yes	—
106	#449	C₂²	1	1	yes	characteristic
107	#449	C₂²	1	2	yes	—
108	#447	C₂²	1	2	yes	—
109	#447	C₂²	1	2	yes	—
110	#447	C₂²	1	2	yes	—
111	#446	C₂²	1	2	yes	complemented
112	#446	C₂²	1	1	yes	characteristic, complemented
113	#446	C₂²	1	2	yes	complemented
114	#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
116	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
117	#442	C₂²	1	2	yes	complemented
118	#442	C₂²	1	2	yes	complemented
119	#442	C₂²	1	2	yes	complemented
120	#442	C₂²	1	2	yes	complemented
121	#440	C₂²	1	2	yes	complemented
122	#440	C₂²	1	2	yes	complemented
123	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
124	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
125	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
126	C₄×SD₁₆	C₂²	1	2	yes	complemented
127	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
128	C₄×D₈	C₂²	1	2	yes	complemented
129	C₄×D₈	C₂²	1	2	yes	complemented
130	C₄×D₈	C₂²	1	2	yes	complemented
131	#433	C₂²	1	2	yes	—
132	#433	C₂²	1	2	yes	—
133	#432	C₂²	1	1	yes	characteristic
134	#431	C₂²	1	1	yes	characteristic
135	C₂×#41	—	2	1	no	—
136	C₂×#41	—	2	1	no	—
137	C₂×#41	—	2	2	no	—
138	C₂×#41	—	2	1	no	—
139	C₂×#41	—	2	1	no	—
140	C₂×#41	C₂³	1	1	yes	characteristic
141	C₂²×Q₈	—	2	1	no	—
142	C₂²×D₄	—	2	1	no	—
143	C₂²×D₄	—	2	1	no	—
144	C₂²×D₄	C₂³	1	2	yes	—
145	C₂×Q₁₆	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆	C₂³	1	2	yes	—
148	C₂×SD₁₆	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆	C₂³	1	2	yes	—
150	C₂×SD₁₆	C₂³	1	2	yes	—
151	C₂×D₈	C₂³	1	2	yes	—
152	C₂×D₈	C₂³	1	2	yes	—
153	C₂×D₈	C₂³	1	2	yes	—
154	C₂×D₈	C₂³	1	1	yes	characteristic
155	C₂×D₈	C₂³	1	2	yes	—
156	C₂×D₈	C₂³	1	2	yes	—
157	C₂×D₈	C₂³	1	2	yes	—
158	C₂×D₈	C₂³	1	2	yes	—
159	C₄⋊Q₈	—	2	1	no	—
160	C₄⋊Q₈	D₄	1	1	yes	characteristic
161	C₄⋊Q₈	D₄	1	1	yes	characteristic
162	C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈	C₂³	1	2	yes	—
164	#127	—	2	1	no	—
165	#127	—	2	1	no	—
166	#127	C₂³	1	2	yes	—
167	#127	C₂³	1	1	yes	characteristic
168	#127	C₂³	1	1	yes	characteristic
169	#127	C₂³	1	1	yes	characteristic
170	#127	C₂³	1	2	yes	—
171	#127	C₂³	1	2	yes	—
172	#127	C₂³	1	2	yes	—
173	#126	—	2	2	no	—
174	#126	—	2	1	no	—
175	#125	—	2	2	no	—
176	#125	D₄	1	2	yes	—
177	#125	C₂³	1	1	yes	characteristic
178	#125	C₂³	1	2	yes	—
179	#124	—	2	1	no	—
180	#124	—	2	1	no	—
181	#124	—	2	2	no	—
182	#124	—	2	1	no	—
183	#124	—	2	2	no	—
184	#124	—	2	2	no	—
185	#124	—	2	1	no	—
186	#124	C₂³	1	1	yes	characteristic
187	#124	C₂³	1	2	yes	—
188	#124	C₂³	1	2	yes	—
189	#124	C₂³	1	2	yes	—
190	#123	—	2	1	no	—
191	#123	—	2	2	no	—
192	#123	—	2	2	no	—
193	#123	—	2	2	no	—
194	#123	—	2	2	no	—
195	#123	—	2	2	no	—
196	#123	—	2	2	no	—
197	#123	—	2	2	no	—
198	#123	—	2	2	no	—
199	#123	—	2	2	no	—
200	#123	—	2	2	no	—
201	C₂²⋊Q₈	—	2	2	no	—
202	C₂²⋊Q₈	—	2	2	no	—
203	C₂²⋊Q₈	—	2	2	no	—
204	C₂²⋊Q₈	—	2	2	no	—
205	C₂²⋊Q₈	—	2	2	no	—
206	C₂²⋊Q₈	—	2	1	no	—
207	C₂²⋊Q₈	D₄	1	1	yes	characteristic
208	C₂²⋊Q₈	D₄	1	1	yes	characteristic
209	C₂²⋊Q₈	D₄	1	2	yes	—
210	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
211	#121	—	2	1	no	—
212	#121	—	2	2	no	—
213	#121	—	2	2	no	—
214	#121	—	2	1	no	—
215	#121	—	2	1	no	—
216	#121	—	2	2	no	—
217	#121	—	2	2	no	—
218	#121	—	2	2	no	—
219	#121	—	2	2	no	—
220	#121	—	2	2	no	—
221	#121	—	2	2	no	—
222	#121	—	2	1	no	—
223	#121	—	2	2	no	—
224	#121	—	2	2	no	—
225	#121	C₂³	1	1	yes	characteristic
226	#121	C₂³	1	2	yes	—
227	#120	—	2	2	no	—
228	#120	—	2	2	no	—
229	C₄×Q₈	—	2	1	no	—
230	C₄×Q₈	C₂³	1	1	yes	characteristic
231	C₄×Q₈	C₂³	1	1	yes	characteristic
232	C₄×Q₈	C₂³	1	1	yes	characteristic
233	C₄×Q₈	C₂³	1	2	yes	—
234	C₄×Q₈	C₂³	1	1	yes	characteristic
235	C₄×Q₈	C₂³	1	1	yes	characteristic
236	C₄×Q₈	C₂³	1	2	yes	—
237	C₄×D₄	—	2	1	no	—
238	C₄×D₄	—	2	1	no	—
239	C₄×D₄	—	2	1	no	—
240	C₄×D₄	—	2	2	no	—
241	C₄×D₄	—	2	2	no	—
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	—	2	1	no	—
244	C₄×D₄	—	2	2	no	—
245	C₄×D₄	—	2	2	no	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	—	2	1	no	—
248	C₄×D₄	C₂³	1	1	yes	characteristic
249	C₄×D₄	C₂³	1	1	yes	characteristic
250	C₄×D₄	C₂³	1	2	yes	—
251	C₄×D₄	C₂³	1	2	yes	—
252	C₄×D₄	C₂³	1	2	yes	—
253	C₄×D₄	C₂³	1	2	yes	—
254	C₄×D₄	C₂³	1	1	yes	characteristic
255	C₄×D₄	C₂³	1	2	yes	—
256	C₄×D₄	C₂³	1	2	yes	—
257	C₄×D₄	C₂³	1	2	yes	—
258	C₄×D₄	C₂³	1	2	yes	—
259	#117	—	2	1	no	—
260	#117	—	2	1	no	—
261	#117	C₂³	1	1	yes	characteristic
262	#117	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₄²	—	2	1	no	—
267	C₂×C₄²	C₂³	1	1	yes	characteristic
268	#107	C₂³	1	1	yes	characteristic
269	#107	C₂³	1	1	yes	characteristic
270	#107	C₂³	1	2	yes	—
271	#106	C₂³	1	2	yes	—
272	#106	C₂³	1	1	yes	characteristic
273	#106	C₂³	1	1	yes	characteristic
274	C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₄⋊C₈	C₂³	1	1	yes	characteristic
277	C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₄⋊C₈	C₂³	1	2	yes	—
279	C₄⋊C₈	C₂³	1	2	yes	—
280	C₄⋊C₈	C₂³	1	2	yes	—
281	C₄⋊C₈	C₂³	1	2	yes	—
282	#103	C₂³	1	1	yes	characteristic
283	#103	C₂³	1	1	yes	characteristic
284	#103	C₂³	1	1	yes	characteristic
285	#103	C₂³	1	1	yes	characteristic
286	#103	C₂³	1	2	yes	—
287	#102	C₂³	1	1	yes	characteristic
288	#102	C₂³	1	2	yes	—
289	#102	C₂³	1	2	yes	—
290	#102	C₂³	1	2	yes	—
291	#102	C₂³	1	2	yes	—
292	#102	C₂³	1	2	yes	—
293	#102	C₂³	1	1	yes	characteristic
294	#102	C₂³	1	1	yes	characteristic
295	#102	C₂³	1	2	yes	—
296	#102	C₂³	1	1	yes	characteristic
297	#102	C₂³	1	2	yes	—
298	#102	C₂³	1	2	yes	—
299	#102	C₂³	1	2	yes	—
300	#102	C₂³	1	2	yes	—
301	#102	C₂³	1	2	yes	—
302	C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₂²⋊C₈	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈	C₂³	1	2	yes	—
305	#97	C₂³	1	2	yes	—
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	C₂⁴	—	2	2	no	—
313	#41	—	4	1	no	—
314	#41	—	4	1	no	—
315	#41	—	8	2	no	—
316	#41	—	8	2	no	—
317	#41	—	8	2	no	—
318	#41	—	8	2	no	—
319	#41	—	8	4	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	8	2	no	—
323	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈	C₂×D₄	1	2	yes	—
326	C₂×Q₈	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈	C₂⁴	1	1	yes	characteristic
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	1	no	—
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	2	no	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	4	2	no	—
347	C₂×D₄	—	4	2	no	—
348	C₂×D₄	—	8	2	no	—
349	C₂×D₄	—	8	2	no	—
350	C₂×D₄	C₂⁴	1	2	yes	—
351	C₂×D₄	C₂⁴	1	2	yes	—
352	C₂×D₄	C₂⁴	1	1	yes	characteristic
353	C₂×D₄	C₂⁴	1	1	yes	characteristic
354	C₂×D₄	C₂⁴	1	2	yes	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
369	C₂²×C₄	C₂⁴	1	1	yes	characteristic
370	Q₁₆	—	4	1	no	—
371	SD₁₆	—	4	1	no	—
372	SD₁₆	—	4	2	no	—
373	SD₁₆	—	4	1	no	—
374	SD₁₆	—	4	2	no	—
375	SD₁₆	—	4	2	no	—
376	D₈	—	4	1	no	—
377	D₈	—	4	2	no	—
378	D₈	—	4	2	no	—
379	D₈	—	4	2	no	—
380	D₈	—	4	2	no	—
381	D₈	—	4	2	no	—
382	D₈	—	4	2	no	—
383	D₈	—	4	2	no	—
384	C₂×C₈	C₂⁴	1	1	yes	characteristic
385	C₂×C₈	C₂⁴	1	1	yes	characteristic
386	C₂×C₈	C₂⁴	1	2	yes	—
387	C₂×C₈	C₂⁴	1	1	yes	characteristic
388	C₂×C₈	C₂⁴	1	1	yes	characteristic
389	C₂×C₈	C₂⁴	1	2	yes	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	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	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	C₂×D₄	1	2	yes	—
402	C₄⋊C₄	C₂×D₄	1	2	yes	—
403	C₄⋊C₄	C₂×D₄	1	2	yes	—
404	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
406	C₄⋊C₄	C₂×D₄	1	2	yes	—
407	C₄⋊C₄	C₂×D₄	1	2	yes	—
408	C₄⋊C₄	C₂×D₄	1	2	yes	—
409	C₄⋊C₄	C₂×D₄	1	2	yes	—
410	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄	C₂⁴	1	2	yes	—
413	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
415	C₂²⋊C₄	—	2	1	no	—
416	C₂²⋊C₄	—	2	1	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	1	no	—
422	C₂²⋊C₄	—	2	1	no	—
423	C₂²⋊C₄	—	2	1	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	2	no	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	—	2	2	no	—
433	C₂²⋊C₄	—	2	1	no	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	2	2	no	—
437	C₂²⋊C₄	—	2	2	no	—
438	C₂²⋊C₄	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄	C₂×D₄	1	2	yes	—
440	C₄²	—	2	1	no	—
441	C₄²	—	2	1	no	—
442	C₄²	—	2	1	no	—
443	C₄²	—	2	1	no	—
444	C₄²	—	2	2	no	—
445	C₄²	C₂×D₄	1	1	yes	characteristic
446	C₄²	C₂×D₄	1	1	yes	characteristic
447	C₄²	C₂⁴	1	1	yes	characteristic
448	C₄²	C₂⁴	1	2	yes	—
449	C₄²	C₂⁴	1	2	yes	—
450	C₄²	C₂⁴	1	1	yes	characteristic
451	C₂³	—	2	2	no	—
452	C₂³	—	2	1	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	2	2	no	—
455	C₂³	—	2	1	no	—
456	C₂³	—	4	4	no	—
457	C₂³	—	8	2	no	—
458	C₂³	—	8	2	no	—
459	C₂³	C₂²×D₄	1	1	yes	characteristic
460	Q₈	—	2	2	no	—
461	Q₈	—	2	2	no	—
462	Q₈	—	2	1	no	—
463	Q₈	—	2	1	no	—
464	Q₈	—	2	1	no	—
465	Q₈	—	2	1	no	—
466	Q₈	—	4	2	no	—
467	Q₈	—	4	2	no	—
468	Q₈	—	8	2	no	—
469	D₄	—	2	1	no	—
470	D₄	—	2	2	no	—
471	D₄	—	2	2	no	—
472	D₄	—	2	1	no	—
473	D₄	—	2	2	no	—
474	D₄	—	2	2	no	—
475	D₄	—	2	1	no	—
476	D₄	—	2	2	no	—
477	D₄	—	2	2	no	—
478	D₄	—	2	1	no	—
479	D₄	—	4	4	no	—
480	D₄	—	4	4	no	—
481	D₄	—	4	2	no	—
482	D₄	—	4	2	no	—
483	D₄	—	4	2	no	—
484	D₄	—	4	2	no	—
485	D₄	—	8	1	no	—
486	D₄	—	8	2	no	—
487	D₄	—	8	1	no	—
488	D₄	—	8	1	no	—
489	D₄	—	8	2	no	—
490	D₄	—	8	2	no	—
491	D₄	—	8	2	no	—
492	D₄	—	8	2	no	—
493	D₄	—	8	2	no	—
494	D₄	—	8	2	no	—
495	D₄	—	8	1	no	—
496	D₄	—	8	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	8	2	no	—
513	C₂×C₄	—	8	2	no	—
514	C₂×C₄	—	8	2	no	—
515	C₂×C₄	—	8	2	no	—
516	C₂×C₄	—	8	2	no	—
517	C₂×C₄	—	8	2	no	—
518	C₂×C₄	—	8	2	no	—
519	C₂×C₄	—	8	2	no	—
520	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄	C₂²×D₄	1	2	yes	—
523	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄	C₂²×D₄	1	2	yes	—
526	C₂×C₄	C₂²×D₄	1	2	yes	—
527	C₂×C₄	C₂²×D₄	1	2	yes	—
528	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄	C₂⁵	1	1	yes	characteristic
530	C₈	—	2	1	no	—
531	C₈	—	2	1	no	—
532	C₈	—	2	1	no	—
533	C₈	—	2	2	no	—
534	C₈	—	2	1	no	—
535	C₈	—	2	2	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	4	1	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	4	1	no	—
545	C₂²	—	4	2	no	—
546	C₂²	—	4	2	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	16	4	no	—
555	C₂²	C₂³×D₄	1	1	yes	characteristic
556	C₄	—	2	1	no	—
557	C₄	—	2	1	no	—
558	C₄	—	2	2	no	—
559	C₄	—	2	2	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	2	no	—
563	C₄	—	2	2	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	2	no	—
571	C₄	#576	1	2	yes	—
572	C₄	#585	1	1	yes	characteristic
573	C₄	#585	1	1	yes	characteristic
574	C₂	—	4	1	no	—
575	C₂	—	8	1	no	—
576	C₂	—	8	2	no	—
577	C₂	—	8	1	no	—
578	C₂	—	8	2	no	—
579	C₂	—	8	2	no	—
580	C₂	#3487	1	1	yes	characteristic
581	C₂	C₂×#576	1	1	yes	characteristic
582	C₂	#3585	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 ◁ #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. #3554	C₂	semidirect
2. #3508	C₂	semidirect
3. #3403	C₂	semidirect
4. #3399	C₂	semidirect
5. #3399	C₂	semidirect
6. #3399	C₂	semidirect
7. #3396	C₂	semidirect
8. #3391	C₂	semidirect
9. #3373	C₂	semidirect
10. #3370	C₂	semidirect
11. #3368	C₂	semidirect
12. #3366	C₂	semidirect
13. #3365	C₂	semidirect
14. #3358	C₂	semidirect
15. #3224	C₂	semidirect
16. #3220	C₂	semidirect
17. #3217	C₂	semidirect
18. #3205	C₂	semidirect
19. #3122	C₂	semidirect
20. #3118	C₂	semidirect
21. #3115	C₂	semidirect
22. #3102	C₂	semidirect
23. #2985	C₂	semidirect
28. #559	C₂²	semidirect
29. #559	C₂²	semidirect
30. #557	C₂²	semidirect
31. #554	C₂²	semidirect
35. #550	C₂²	semidirect
36. D₄×Q₈	C₂²	semidirect
58. #496	C₂²	semidirect
59. #496	C₂²	semidirect
60. #495	C₂²	semidirect
63. #493	C₂²	semidirect
65. #490	C₂²	semidirect
66. #489	C₂²	semidirect
67. #488	C₂²	semidirect
70. #486	C₂²	semidirect
74. #479	C₂²	semidirect
75. #478	C₂²	semidirect
76. #478	C₂²	semidirect
77. #478	C₂²	semidirect
78. #476	C₂²	semidirect
79. #475	C₂²	semidirect
80. #474	C₂²	semidirect
81. #474	C₂²	semidirect
82. #464	C₂²	semidirect
83. #464	C₂²	semidirect
84. #463	C₂²	semidirect
85. #463	C₂²	semidirect
86. #463	C₂²	semidirect
87. #463	C₂²	semidirect
88. #463	C₂²	semidirect
89. #463	C₂²	semidirect
92. #460	C₂²	semidirect
93. #460	C₂²	semidirect
98. #459	C₂²	semidirect
99. #459	C₂²	semidirect
100. #459	C₂²	semidirect
101. #459	C₂²	semidirect
102. #459	C₂²	semidirect
103. #459	C₂²	semidirect
111. #446	C₂²	semidirect
112. #446	C₂²	semidirect
113. #446	C₂²	semidirect
114. #446	C₂²	semidirect
115. C₈×Q₈	C₂²	semidirect
116. C₈×Q₈	C₂²	semidirect
117. #442	C₂²	semidirect
118. #442	C₂²	semidirect
119. #442	C₂²	semidirect
120. #442	C₂²	semidirect
121. #440	C₂²	semidirect
122. #440	C₂²	semidirect
123. C₄×Q₁₆	C₂²	semidirect
124. C₄×SD₁₆	C₂²	semidirect
125. C₄×SD₁₆	C₂²	semidirect
126. C₄×SD₁₆	C₂²	semidirect
127. C₄×D₈	C₂²	semidirect
128. C₄×D₈	C₂²	semidirect
129. C₄×D₈	C₂²	semidirect
130. C₄×D₈	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3554	2
#3508	2
#3403	2
#3399	2
#3396	2
#3391	2
#3373	2
#3370	2
#3368	2
#3366	2
#3365	2
#3358	2
#3224	2
#3220	2
#3217	2
#3205	2
#3122	2
#3118	2
#3115	2
#3102	2
#2985	2