Subgroups — #61494

Order 256.

945 conjugacy classes of subgroups.

The subgroup lattice has 587 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3517	C₂	1	1	yes	maximal, characteristic, complemented
2	#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	#3386	C₂	1	1	yes	maximal, characteristic, complemented
5	#3365	C₂	1	1	yes	maximal, characteristic, complemented
6	#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	#3353	C₂	1	1	yes	maximal, characteristic, complemented
8	#3347	C₂	1	2	yes	maximal, complemented
9	#3305	C₂	1	2	yes	maximal, complemented
10	#3304	C₂	1	1	yes	maximal, characteristic, complemented
11	#3297	C₂	1	2	yes	maximal, complemented
12	#3294	C₂	1	1	yes	maximal, characteristic, complemented
13	#3274	C₂	1	1	yes	maximal, characteristic, complemented
14	#3268	C₂	1	2	yes	maximal, complemented
15	#3179	C₂	1	2	yes	maximal, complemented
16	#3169	C₂	1	1	yes	maximal, characteristic, complemented
17	#3124	C₂	1	2	yes	maximal, complemented
18	#3122	C₂	1	2	yes	maximal, complemented
19	#3115	C₂	1	1	yes	maximal, characteristic, complemented
20	#3115	C₂	1	1	yes	maximal, characteristic, complemented
21	#2966	C₂	1	1	yes	maximal, characteristic, complemented
22	#2946	C₂	1	2	yes	maximal, complemented
23	C₄×#135	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)	C₂²	1	2	yes	—
25	C₂×#135	C₂²	1	1	yes	characteristic
26	#559	C₂²	1	1	yes	characteristic
27	#557	C₂²	1	1	yes	characteristic, complemented
28	#556	C₂²	1	1	yes	characteristic
29	#555	C₂²	1	2	yes	—
30	#553	—	2	2	no	—
31	#553	C₂²	1	2	yes	complemented
32	#551	—	2	2	no	—
33	#550	—	2	1	no	—
34	#550	C₂²	1	1	yes	characteristic
35	#550	C₂²	1	2	yes	complemented
36	#550	C₂²	1	1	yes	characteristic, complemented
37	D₄×Q₈	C₂²	1	1	yes	characteristic
38	#548	—	2	1	no	—
39	#547	—	2	1	no	—
40	#547	C₂²	1	1	yes	characteristic
41	#546	—	2	1	no	—
42	#546	C₂²	1	2	yes	—
43	D₄²	C₂²	1	1	yes	characteristic
44	#542	C₂²	1	2	yes	—
45	#540	—	2	2	no	—
46	#540	C₂²	1	2	yes	complemented
47	#538	—	2	2	no	—
48	#532	—	2	1	no	—
49	#532	C₂²	1	1	yes	characteristic
50	#532	C₂²	1	1	yes	characteristic, complemented
51	#529	—	2	1	no	—
52	#529	—	2	1	no	—
53	#529	C₂²	1	1	yes	characteristic
54	C₂×#124	—	2	1	no	—
55	#520	C₂²	1	2	yes	complemented
56	#518	C₂²	1	2	yes	—
57	C₄×#41	C₂²	1	1	yes	characteristic
58	C₄×#41	C₂²	1	1	yes	characteristic, complemented
59	#501	C₂²	1	2	yes	complemented
60	#500	C₂²	1	1	yes	characteristic, complemented
61	#496	C₂²	1	2	yes	complemented
62	#493	C₂²	1	1	yes	characteristic
63	#488	C₂²	1	2	yes	complemented
64	#486	C₂²	1	1	yes	characteristic
65	#486	C₂²	1	1	yes	characteristic, complemented
66	#486	C₂²	1	2	yes	complemented
67	#484	C₂²	1	2	yes	complemented
68	#482	C₂²	1	2	yes	complemented
69	#482	C₂²	1	2	yes	complemented
70	#482	C₂²	1	2	yes	complemented
71	#482	C₂²	1	2	yes	complemented
72	#480	C₂²	1	2	yes	—
73	#478	C₂²	1	2	yes	—
74	#478	C₂²	1	2	yes	complemented
75	#477	C₂²	1	2	yes	complemented
76	#475	C₂²	1	1	yes	characteristic, complemented
77	#475	C₂²	1	1	yes	characteristic, complemented
78	#474	C₂²	1	1	yes	characteristic
79	#474	C₂²	1	2	yes	complemented
80	#474	C₂²	1	1	yes	characteristic, complemented
81	#469	C₂²	1	2	yes	—
82	#468	C₂²	1	2	yes	complemented
83	#466	C₂²	1	2	yes	—
84	#466	C₂²	1	2	yes	complemented
85	#466	C₂²	1	2	yes	complemented
86	#465	C₂²	1	2	yes	complemented
87	#464	C₂²	1	2	yes	complemented
88	#463	C₂²	1	2	yes	complemented
89	#460	C₂²	1	1	yes	characteristic
90	#460	C₂²	1	1	yes	characteristic, complemented
91	#459	C₂²	1	1	yes	characteristic
92	#459	C₂²	1	2	yes	—
93	#459	C₂²	1	1	yes	characteristic
94	#459	C₂²	1	2	yes	complemented
95	#452	C₂²	1	2	yes	complemented
96	#449	C₂²	1	2	yes	—
97	#449	C₂²	1	2	yes	—
98	#449	C₂²	1	2	yes	complemented
99	#447	C₂²	1	2	yes	—
100	#447	C₂²	1	2	yes	—
101	#446	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
103	#442	C₂²	1	2	yes	—
104	#442	C₂²	1	2	yes	complemented
105	#442	C₂²	1	2	yes	complemented
106	#440	C₂²	1	2	yes	—
107	#440	C₂²	1	2	yes	complemented
108	#440	C₂²	1	2	yes	complemented
109	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
110	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
111	C₄×SD₁₆	C₂²	1	1	yes	characteristic
112	C₄×SD₁₆	C₂²	1	1	yes	characteristic
113	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
114	C₄×SD₁₆	C₂²	1	2	yes	complemented
115	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₈	C₂²	1	1	yes	characteristic
117	C₄×D₈	C₂²	1	2	yes	—
118	C₄×D₈	C₂²	1	1	yes	characteristic
119	C₄×D₈	C₂²	1	2	yes	complemented
120	C₄×D₈	C₂²	1	2	yes	complemented
121	#436	C₂²	1	1	yes	characteristic
122	#435	C₂²	1	2	yes	complemented
123	C₈×D₄	C₂²	1	1	yes	characteristic
124	C₈×D₄	C₂²	1	2	yes	complemented
125	#433	C₂²	1	2	yes	complemented
126	#432	C₂²	1	1	yes	characteristic, complemented
127	#428	C₂²	1	2	yes	complemented
128	#427	C₂²	1	1	yes	characteristic, complemented
129	#416	C₂²	1	1	yes	characteristic
130	#416	C₂²	1	1	yes	characteristic, complemented
131	#416	C₂²	1	2	yes	complemented
132	C₂×#102	C₂²	1	2	yes	—
133	#405	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41	—	2	1	no	—
136	C₂×#41	—	2	1	no	—
137	C₂×#41	—	2	1	no	—
138	C₂×#41	—	2	1	no	—
139	C₂×#41	C₂³	1	1	yes	characteristic
140	C₂×#41	C₂³	1	1	yes	characteristic
141	C₂×#41	C₂³	1	2	yes	—
142	C₂²×Q₈	—	2	1	no	—
143	C₂²×D₄	—	2	1	no	—
144	C₂²×D₄	C₂³	1	2	yes	—
145	AGL(1,ℤ/8)	—	2	8	no	—
146	#135	—	2	4	no	—
147	C₂×Q₁₆	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
152	C₂×D₈	C₂³	1	1	yes	characteristic
153	C₂×D₈	C₂³	1	2	yes	—
154	C₂×D₈	C₂³	1	2	yes	—
155	C₂×D₈	C₂³	1	2	yes	—
156	C₂×D₈	C₂³	1	2	yes	—
157	C₂×M₁₆	C₂³	1	2	yes	—
158	C₂²×C₈	C₂³	1	1	yes	characteristic
159	C₂²×C₈	C₂³	1	1	yes	characteristic
160	C₂²×C₈	C₂³	1	2	yes	—
161	C₄⋊Q₈	—	2	1	no	—
162	C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈	C₂³	1	2	yes	—
165	#127	—	2	1	no	—
166	#127	—	2	2	no	—
167	#127	C₂³	1	1	yes	characteristic
168	#127	C₂³	1	1	yes	characteristic
169	#127	C₂³	1	2	yes	—
170	#126	—	2	2	no	—
171	#126	—	2	2	no	—
172	#126	—	2	2	no	—
173	#126	D₄	1	2	yes	—
174	#125	—	2	2	no	—
175	#125	D₄	1	1	yes	characteristic
176	#125	C₂³	1	2	yes	—
177	#124	—	2	1	no	—
178	#124	—	2	1	no	—
179	#124	—	2	2	no	—
180	#124	—	2	2	no	—
181	#124	—	2	2	no	—
182	#124	—	2	1	no	—
183	#124	—	2	1	no	—
184	#124	D₄	1	1	yes	characteristic
185	#124	C₂³	1	2	yes	—
186	#123	—	2	2	no	—
187	#123	—	2	2	no	—
188	#123	—	2	2	no	—
189	#123	—	2	2	no	—
190	#123	—	2	2	no	—
191	#123	—	2	2	no	—
192	#123	—	2	2	no	—
193	#123	D₄	1	2	yes	—
194	C₂²⋊Q₈	—	2	1	no	—
195	C₂²⋊Q₈	—	2	1	no	—
196	C₂²⋊Q₈	—	2	2	no	—
197	C₂²⋊Q₈	—	2	2	no	—
198	C₂²⋊Q₈	D₄	1	1	yes	characteristic
199	C₂²⋊Q₈	C₂³	1	2	yes	—
200	#121	—	2	2	no	—
201	#121	—	2	2	no	—
202	#121	—	2	1	no	—
203	#121	—	2	1	no	—
204	#121	—	2	1	no	—
205	#121	—	2	1	no	—
206	#121	—	2	2	no	—
207	#121	—	2	2	no	—
208	#121	—	2	2	no	—
209	#121	—	2	2	no	—
210	#121	—	2	2	no	—
211	#121	—	2	2	no	—
212	#121	—	2	2	no	—
213	#121	D₄	1	1	yes	characteristic
214	#121	C₂³	1	2	yes	—
215	#121	C₂³	1	2	yes	—
216	#121	C₂³	1	2	yes	—
217	#121	C₂³	1	2	yes	—
218	#121	C₂³	1	2	yes	—
219	#120	—	2	2	no	—
220	#120	—	2	2	no	—
221	C₄×Q₈	—	2	1	no	—
222	C₄×Q₈	—	2	1	no	—
223	C₄×Q₈	C₂³	1	1	yes	characteristic
224	C₄×Q₈	C₂³	1	1	yes	characteristic
225	C₄×Q₈	C₂³	1	1	yes	characteristic
226	C₄×Q₈	C₂³	1	1	yes	characteristic
227	C₄×Q₈	C₂³	1	2	yes	—
228	C₄×Q₈	C₂³	1	1	yes	characteristic
229	C₄×D₄	—	2	1	no	—
230	C₄×D₄	—	2	1	no	—
231	C₄×D₄	—	2	1	no	—
232	C₄×D₄	—	2	1	no	—
233	C₄×D₄	—	2	2	no	—
234	C₄×D₄	—	2	2	no	—
235	C₄×D₄	—	2	1	no	—
236	C₄×D₄	—	2	1	no	—
237	C₄×D₄	—	2	2	no	—
238	C₄×D₄	—	2	2	no	—
239	C₄×D₄	—	2	2	no	—
240	C₄×D₄	—	2	2	no	—
241	C₄×D₄	—	2	1	no	—
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	C₂³	1	1	yes	characteristic
244	C₄×D₄	C₂³	1	1	yes	characteristic
245	C₄×D₄	C₂³	1	1	yes	characteristic
246	C₄×D₄	C₂³	1	1	yes	characteristic
247	C₄×D₄	C₂³	1	2	yes	—
248	C₄×D₄	C₂³	1	2	yes	—
249	C₄×D₄	C₂³	1	2	yes	—
250	C₄×D₄	C₂³	1	2	yes	—
251	C₄×D₄	C₂³	1	2	yes	—
252	C₄×D₄	C₂³	1	1	yes	characteristic
253	C₄×D₄	C₂³	1	2	yes	—
254	#117	—	2	2	no	—
255	#117	—	2	2	no	—
256	#117	—	2	1	no	—
257	#117	—	2	1	no	—
258	#117	C₂³	1	1	yes	characteristic
259	#117	C₂³	1	1	yes	characteristic
260	#117	C₂³	1	2	yes	—
261	#117	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	C₂³	1	2	yes	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₄²	—	2	1	no	—
268	C₂×C₄²	—	2	1	no	—
269	C₂×C₄²	C₂³	1	1	yes	characteristic
270	#107	C₂³	1	1	yes	characteristic
271	#107	C₂³	1	1	yes	characteristic
272	#107	C₂³	1	2	yes	—
273	#107	C₂³	1	2	yes	—
274	#107	C₂³	1	2	yes	—
275	#107	C₂³	1	2	yes	—
276	#106	C₂³	1	1	yes	characteristic
277	#106	C₂³	1	1	yes	characteristic
278	#106	C₂³	1	2	yes	—
279	#106	C₂³	1	2	yes	—
280	C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₄⋊C₈	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
286	#103	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	#102	C₂³	1	1	yes	characteristic
291	#102	C₂³	1	2	yes	—
292	#102	C₂³	1	2	yes	—
293	#102	C₂³	1	2	yes	—
294	#102	C₂³	1	1	yes	characteristic
295	#102	C₂³	1	2	yes	—
296	#102	C₂³	1	1	yes	characteristic
297	#102	C₂³	1	1	yes	characteristic
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	#102	C₂³	1	2	yes	—
303	#102	C₂³	1	2	yes	—
304	C₂²⋊C₈	C₂³	1	2	yes	—
305	C₂²⋊C₈	C₂³	1	2	yes	—
306	C₂²⋊C₈	C₂³	1	2	yes	—
307	#97	C₂³	1	2	yes	—
308	#97	C₂³	1	2	yes	—
309	C₄×C₈	C₂³	1	1	yes	characteristic
310	C₄×C₈	C₂³	1	1	yes	characteristic
311	C₄×C₈	C₂³	1	1	yes	characteristic
312	C₄×C₈	C₂³	1	1	yes	characteristic
313	C₄×C₈	C₂³	1	2	yes	—
314	C₂⁴	—	2	2	no	—
315	#41	—	2	2	no	—
316	#41	—	2	4	no	—
317	#41	—	2	2	no	—
318	#41	—	4	2	no	—
319	#41	—	4	1	no	—
320	#41	—	4	1	no	—
321	#41	—	8	2	no	—
322	#41	—	8	2	no	—
323	#41	—	8	2	no	—
324	#41	—	8	2	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	8	2	no	—
329	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
330	C₂×Q₈	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈	C₂⁴	1	1	yes	characteristic
332	C₂×D₄	—	2	4	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	2	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	1	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	4	2	no	—
349	C₂×D₄	—	8	2	no	—
350	C₂×D₄	C₂×D₄	1	1	yes	characteristic
351	C₂×D₄	C₂×D₄	1	2	yes	—
352	C₂×D₄	C₂⁴	1	2	yes	—
353	C₂×D₄	C₂⁴	1	2	yes	—
354	C₂×D₄	C₂⁴	1	1	yes	characteristic
355	C₂×D₄	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
371	C₂²×C₄	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄	C₂⁴	1	2	yes	—
373	Q₁₆	—	2	2	no	—
374	SD₁₆	—	2	4	no	—
375	SD₁₆	—	2	2	no	—
376	SD₁₆	—	4	2	no	—
377	SD₁₆	#41	1	4	yes	complemented
378	D₈	—	2	2	no	—
379	D₈	—	2	4	no	—
380	D₈	—	2	4	no	—
381	D₈	—	4	2	no	—
382	D₈	—	4	2	no	—
383	M₁₆	—	2	4	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	4	1	no	—
386	C₂×C₈	—	4	2	no	—
387	C₂×C₈	C₂⁴	1	1	yes	characteristic
388	C₂×C₈	C₂⁴	1	1	yes	characteristic
389	C₂×C₈	C₂⁴	1	1	yes	characteristic
390	C₂×C₈	C₂⁴	1	2	yes	—
391	C₂×C₈	C₂⁴	1	2	yes	—
392	C₂×C₈	C₂⁴	1	1	yes	characteristic
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	C₂×D₄	1	2	yes	—
406	C₄⋊C₄	C₂×D₄	1	2	yes	—
407	C₄⋊C₄	C₂×D₄	1	2	yes	—
408	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
409	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
410	C₄⋊C₄	C₂×D₄	1	2	yes	—
411	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄	C₂⁴	1	2	yes	—
415	C₄⋊C₄	C₂⁴	1	2	yes	—
416	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
417	C₂²⋊C₄	—	2	2	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	1	no	—
420	C₂²⋊C₄	—	2	1	no	—
421	C₂²⋊C₄	—	2	1	no	—
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	2	1	no	—
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	2	1	no	—
430	C₂²⋊C₄	—	2	1	no	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	—	2	2	no	—
433	C₂²⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	2	2	no	—
437	C₂²⋊C₄	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄	C₂×D₄	1	2	yes	—
441	C₂²⋊C₄	C₂×D₄	1	2	yes	—
442	C₄²	—	2	1	no	—
443	C₄²	—	2	1	no	—
444	C₄²	—	2	1	no	—
445	C₄²	—	2	1	no	—
446	C₄²	—	2	1	no	—
447	C₄²	—	2	1	no	—
448	C₄²	—	2	2	no	—
449	C₄²	—	2	2	no	—
450	C₄²	C₂×D₄	1	1	yes	characteristic
451	C₄²	C₂×D₄	1	1	yes	characteristic
452	C₄²	C₂⁴	1	1	yes	characteristic
453	C₄²	C₂⁴	1	1	yes	characteristic
454	C₄²	C₂⁴	1	2	yes	—
455	C₂³	—	2	1	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	2	1	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	4	4	no	—
460	C₂³	—	8	2	no	—
461	C₂³	—	8	2	no	—
462	C₂³	C₂²×D₄	1	2	yes	—
463	C₂³	C₂²×D₄	1	1	yes	characteristic
464	Q₈	—	2	2	no	—
465	Q₈	—	2	1	no	—
466	Q₈	—	2	1	no	—
467	Q₈	—	2	1	no	—
468	Q₈	—	4	2	no	—
469	Q₈	—	4	2	no	—
470	Q₈	—	8	2	no	—
471	Q₈	C₂×#41	1	2	yes	—
472	D₄	—	2	2	no	—
473	D₄	—	2	2	no	—
474	D₄	—	2	2	no	—
475	D₄	—	2	1	no	—
476	D₄	—	2	1	no	—
477	D₄	—	2	2	no	—
478	D₄	—	2	1	no	—
479	D₄	—	2	2	no	—
480	D₄	—	4	2	no	—
481	D₄	—	4	4	no	—
482	D₄	—	4	2	no	—
483	D₄	—	4	4	no	—
484	D₄	—	4	2	no	—
485	D₄	—	4	2	no	—
486	D₄	—	4	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	2	no	—
496	D₄	C₂×#41	1	2	yes	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	4	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	8	1	no	—
517	C₂×C₄	—	8	1	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	—	8	2	no	—
524	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
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	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄	C₂²×D₄	1	2	yes	—
531	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄	C₂⁵	1	1	yes	characteristic
533	C₈	—	2	1	no	—
534	C₈	—	2	2	no	—
535	C₈	—	2	1	no	—
536	C₈	—	2	1	no	—
537	C₈	—	2	2	no	—
538	C₈	C₂×#41	1	2	yes	—
539	C₂²	—	2	1	no	—
540	C₂²	—	2	2	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	2	2	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	4	1	no	—
547	C₂²	—	4	1	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	4	2	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	4	2	no	—
557	C₂²	—	16	4	no	—
558	C₂²	C₂³×D₄	1	1	yes	characteristic
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	2	no	—
562	C₄	—	2	1	no	—
563	C₄	—	2	2	no	—
564	C₄	—	2	2	no	—
565	C₄	—	2	1	no	—
566	C₄	—	2	2	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	1	no	—
571	C₄	—	4	1	no	—
572	C₄	—	4	2	no	—
573	C₄	—	4	2	no	—
574	C₄	#576	1	2	yes	—
575	C₄	C₂²×#41	1	1	yes	characteristic
576	C₄	#585	1	1	yes	characteristic
577	C₂	—	4	1	no	—
578	C₂	—	4	2	no	—
579	C₂	—	4	2	no	—
580	C₂	—	8	1	no	—
581	C₂	—	8	2	no	—
582	C₂	—	8	2	no	—
583	C₂	D₄×#41	1	1	yes	characteristic
584	C₂	C₂×#576	1	1	yes	characteristic
585	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. #3517	C₂	semidirect
2. #3514	C₂	semidirect
3. #3399	C₂	semidirect
4. #3386	C₂	semidirect
5. #3365	C₂	semidirect
6. #3358	C₂	semidirect
7. #3353	C₂	semidirect
8. #3347	C₂	semidirect
9. #3305	C₂	semidirect
10. #3304	C₂	semidirect
11. #3297	C₂	semidirect
12. #3294	C₂	semidirect
13. #3274	C₂	semidirect
14. #3268	C₂	semidirect
15. #3179	C₂	semidirect
16. #3169	C₂	semidirect
17. #3124	C₂	semidirect
18. #3122	C₂	semidirect
19. #3115	C₂	semidirect
20. #3115	C₂	semidirect
21. #2966	C₂	semidirect
22. #2946	C₂	semidirect
23. C₄×#135	C₂	semidirect
27. #557	C₂²	semidirect
31. #553	C₂²	semidirect
35. #550	C₂²	semidirect
36. #550	C₂²	semidirect
46. #540	C₂²	semidirect
50. #532	C₂²	semidirect
55. #520	C₂²	semidirect
58. C₄×#41	C₂²	semidirect
59. #501	C₂²	semidirect
60. #500	C₂²	semidirect
61. #496	C₂²	semidirect
63. #488	C₂²	semidirect
65. #486	C₂²	semidirect
66. #486	C₂²	semidirect
67. #484	C₂²	semidirect
68. #482	C₂²	semidirect
69. #482	C₂²	semidirect
70. #482	C₂²	semidirect
71. #482	C₂²	semidirect
74. #478	C₂²	semidirect
75. #477	C₂²	semidirect
76. #475	C₂²	semidirect
77. #475	C₂²	semidirect
79. #474	C₂²	semidirect
80. #474	C₂²	semidirect
82. #468	C₂²	semidirect
84. #466	C₂²	semidirect
85. #466	C₂²	semidirect
86. #465	C₂²	semidirect
87. #464	C₂²	semidirect
88. #463	C₂²	semidirect
90. #460	C₂²	semidirect
94. #459	C₂²	semidirect
95. #452	C₂²	semidirect
98. #449	C₂²	semidirect
101. #446	C₂²	semidirect
102. C₈×Q₈	C₂²	semidirect
104. #442	C₂²	semidirect
105. #442	C₂²	semidirect
107. #440	C₂²	semidirect
108. #440	C₂²	semidirect
109. C₄×Q₁₆	C₂²	semidirect
110. C₄×Q₁₆	C₂²	semidirect
113. C₄×SD₁₆	C₂²	semidirect
114. C₄×SD₁₆	C₂²	semidirect
115. C₄×SD₁₆	C₂²	semidirect
119. C₄×D₈	C₂²	semidirect
120. C₄×D₈	C₂²	semidirect
122. #435	C₂²	semidirect
124. C₈×D₄	C₂²	semidirect
125. #433	C₂²	semidirect
126. #432	C₂²	semidirect
127. #428	C₂²	semidirect
128. #427	C₂²	semidirect
130. #416	C₂²	semidirect
131. #416	C₂²	semidirect
133. #405	C₂²	semidirect
134. C₂×C₄×C₈	C₂²	semidirect
377. SD₁₆	#41	semidirect

Maximal subgroups

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

subgroup	index
#3517	2
#3514	2
#3399	2
#3386	2
#3365	2
#3358	2
#3353	2
#3347	2
#3305	2
#3304	2
#3297	2
#3294	2
#3274	2
#3268	2
#3179	2
#3169	2
#3124	2
#3122	2
#3115	2
#2966	2
#2946	2
C₄×#135	2