Subgroups — #62339

Order 256.

924 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	#3546	C₂	1	1	yes	maximal, characteristic, complemented
3	#3356	C₂	1	1	yes	maximal, characteristic, complemented
4	#3354	C₂	1	1	yes	maximal, characteristic, complemented
5	#3351	C₂	1	2	yes	maximal, complemented
6	#3305	C₂	1	1	yes	maximal, characteristic, complemented
7	#3302	C₂	1	1	yes	maximal, characteristic, complemented
8	#3301	C₂	1	2	yes	maximal, complemented
9	#3298	C₂	1	1	yes	maximal, characteristic, complemented
10	#3296	C₂	1	2	yes	maximal, complemented
11	#3295	C₂	1	1	yes	maximal, characteristic, complemented
12	#3278	C₂	1	1	yes	maximal, characteristic, complemented
13	#3275	C₂	1	2	yes	maximal, complemented
14	#3272	C₂	1	1	yes	maximal, characteristic, complemented
15	#3252	C₂	1	1	yes	maximal, characteristic, complemented
16	#3251	C₂	1	1	yes	maximal, characteristic, complemented
17	#3204	C₂	1	2	yes	maximal, complemented
18	#3200	C₂	1	2	yes	maximal, complemented
19	#3168	C₂	1	1	yes	maximal, characteristic, complemented
20	#3167	C₂	1	1	yes	maximal, characteristic, complemented
21	#3063	C₂	1	2	yes	maximal, complemented
22	#3062	C₂	1	2	yes	maximal, complemented
23	#2931	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137	C₂²	1	2	yes	complemented
25	C₂×AGL(1,ℤ/8)	C₂²	1	2	yes	—
26	C₂×#131	C₂²	1	2	yes	complemented
27	#562	—	2	2	no	—
28	#560	—	2	2	no	—
29	#556	C₂²	1	1	yes	characteristic
30	#555	—	2	1	no	—
31	#555	C₂²	1	1	yes	characteristic, complemented
32	#554	C₂²	1	1	yes	characteristic
33	#553	—	2	1	no	—
34	#553	C₂²	1	2	yes	—
35	#552	C₂²	1	2	yes	complemented
36	#550	—	2	1	no	—
37	#550	C₂²	1	1	yes	characteristic
38	D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
39	#548	C₂²	1	2	yes	complemented
40	#547	C₂²	1	1	yes	characteristic
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	#544	—	2	1	no	—
46	#542	—	2	1	no	—
47	#542	—	2	2	no	—
48	#540	—	2	1	no	—
49	#538	—	2	2	no	—
50	#537	C₂²	1	2	yes	—
51	#537	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	#532	C₂²	1	1	yes	characteristic
57	#532	C₂²	1	1	yes	characteristic
58	#529	C₂²	1	1	yes	characteristic
59	#529	C₂²	1	1	yes	characteristic, complemented
60	#499	C₂²	1	1	yes	characteristic, complemented
61	#498	C₂²	1	1	yes	characteristic, complemented
62	#495	C₂²	1	1	yes	characteristic
63	#492	C₂²	1	1	yes	characteristic
64	#488	C₂²	1	1	yes	characteristic
65	#488	C₂²	1	1	yes	characteristic, complemented
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	#483	C₂²	1	2	yes	complemented
71	#483	C₂²	1	2	yes	complemented
72	#482	C₂²	1	2	yes	—
73	#482	C₂²	1	2	yes	complemented
74	#481	C₂²	1	2	yes	—
75	#481	C₂²	1	2	yes	complemented
76	#479	C₂²	1	2	yes	complemented
77	#478	C₂²	1	2	yes	complemented
78	#477	C₂²	1	1	yes	characteristic, complemented
79	#476	C₂²	1	1	yes	characteristic
80	#475	C₂²	1	1	yes	characteristic, complemented
81	#474	C₂²	1	1	yes	characteristic, complemented
82	#470	C₂²	1	2	yes	complemented
83	#470	C₂²	1	2	yes	complemented
84	#469	C₂²	1	2	yes	—
85	#469	C₂²	1	2	yes	complemented
86	#468	C₂²	1	2	yes	—
87	#468	C₂²	1	2	yes	—
88	#468	C₂²	1	2	yes	complemented
89	#468	C₂²	1	2	yes	complemented
90	#467	C₂²	1	1	yes	characteristic, complemented
91	#467	C₂²	1	2	yes	complemented
92	#466	C₂²	1	1	yes	characteristic
93	#466	C₂²	1	2	yes	complemented
94	#465	C₂²	1	1	yes	characteristic
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	1	yes	characteristic, complemented
100	#464	C₂²	1	2	yes	—
101	#463	C₂²	1	2	yes	complemented
102	#462	C₂²	1	1	yes	characteristic, complemented
103	#461	C₂²	1	1	yes	characteristic
104	#460	C₂²	1	1	yes	characteristic
105	#459	C₂²	1	1	yes	characteristic
106	#452	C₂²	1	2	yes	complemented
107	#452	C₂²	1	2	yes	complemented
108	#450	C₂²	1	2	yes	—
109	#450	C₂²	1	2	yes	—
110	#449	C₂²	1	2	yes	—
111	#449	C₂²	1	2	yes	complemented
112	#448	C₂²	1	2	yes	—
113	#448	C₂²	1	2	yes	complemented
114	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
115	C₄×SD₁₆	C₂²	1	1	yes	characteristic
116	C₄×SD₁₆	C₂²	1	2	yes	complemented
117	C₄×SD₁₆	C₂²	1	2	yes	complemented
118	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₈	C₂²	1	1	yes	characteristic
120	#436	C₂²	1	1	yes	characteristic
121	#436	C₂²	1	2	yes	complemented
122	#436	C₂²	1	1	yes	characteristic, complemented
123	C₈×D₄	C₂²	1	1	yes	characteristic
124	C₈×D₄	C₂²	1	2	yes	complemented
125	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
126	#428	C₂²	1	2	yes	complemented
127	#428	C₂²	1	2	yes	complemented
128	#423	C₂²	1	1	yes	characteristic, complemented
129	#416	C₂²	1	2	yes	complemented
130	#416	C₂²	1	2	yes	complemented
131	C₂×#103	C₂²	1	2	yes	complemented
132	C₂×#102	C₂²	1	2	yes	—
133	#408	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	C₂³	1	2	yes	—
138	C₂×#41	C₂³	1	2	yes	—
139	C₂×#41	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	AGL(1,ℤ/8)	—	4	4	no	—
145	C₂×Q₁₆	C₂³	1	1	yes	characteristic
146	C₂×Q₁₆	C₂³	1	2	yes	—
147	C₂×SD₁₆	C₂³	1	2	yes	—
148	C₂×SD₁₆	C₂³	1	2	yes	—
149	C₂×SD₁₆	C₂³	1	2	yes	—
150	C₂×SD₁₆	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆	C₂³	1	2	yes	—
152	C₂×SD₁₆	C₂³	1	1	yes	characteristic
153	C₂×D₈	C₂³	1	1	yes	characteristic
154	C₂×D₈	C₂³	1	2	yes	—
155	#131	—	4	4	no	—
156	C₂×M₁₆	C₂³	1	2	yes	—
157	C₂×M₁₆	C₂³	1	2	yes	—
158	C₂×M₁₆	C₂³	1	2	yes	—
159	C₂²×C₈	C₂³	1	1	yes	characteristic
160	C₂²×C₈	C₂³	1	2	yes	—
161	C₂²×C₈	C₂³	1	2	yes	—
162	C₂²×C₈	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈	—	2	2	no	—
164	C₄⋊Q₈	—	2	1	no	—
165	C₄⋊Q₈	D₄	1	1	yes	characteristic
166	C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₄⋊Q₈	C₂³	1	1	yes	characteristic
169	#127	—	2	1	no	—
170	#127	—	2	2	no	—
171	#127	D₄	1	1	yes	characteristic
172	#127	C₂³	1	1	yes	characteristic
173	#126	—	2	2	no	—
174	#126	—	2	2	no	—
175	#126	—	2	2	no	—
176	#126	—	2	1	no	—
177	#126	—	2	1	no	—
178	#125	—	2	2	no	—
179	#125	—	2	1	no	—
180	#125	—	2	1	no	—
181	#125	C₂³	1	1	yes	characteristic
182	#125	C₂³	1	1	yes	characteristic
183	#124	—	2	2	no	—
184	#124	—	2	1	no	—
185	#124	—	2	2	no	—
186	#124	—	2	2	no	—
187	#124	—	2	2	no	—
188	#124	—	2	1	no	—
189	#124	D₄	1	2	yes	—
190	#124	C₂³	1	1	yes	characteristic
191	#124	C₂³	1	1	yes	characteristic
192	#123	—	2	2	no	—
193	#123	—	2	2	no	—
194	#123	—	2	2	no	—
195	#123	—	2	1	no	—
196	#123	—	2	1	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	1	no	—
204	C₂²⋊Q₈	—	2	1	no	—
205	C₂²⋊Q₈	—	2	2	no	—
206	C₂²⋊Q₈	—	2	2	no	—
207	C₂²⋊Q₈	—	2	2	no	—
208	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
209	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
210	C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₂²⋊Q₈	C₂³	1	2	yes	—
215	#121	—	2	2	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	1	no	—
225	#121	—	2	1	no	—
226	#121	—	2	1	no	—
227	#121	—	2	2	no	—
228	#121	—	2	2	no	—
229	#121	D₄	1	1	yes	characteristic
230	#121	D₄	1	1	yes	characteristic
231	#121	D₄	1	2	yes	—
232	#121	C₂³	1	1	yes	characteristic
233	#121	C₂³	1	1	yes	characteristic
234	#121	C₂³	1	2	yes	—
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	C₂³	1	1	yes	characteristic
246	C₄×Q₈	C₂³	1	1	yes	characteristic
247	C₄×Q₈	C₂³	1	2	yes	—
248	C₄×D₄	—	2	1	no	—
249	C₄×D₄	—	2	1	no	—
250	C₄×D₄	—	2	1	no	—
251	C₄×D₄	—	2	1	no	—
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	—	2	2	no	—
254	C₄×D₄	—	2	2	no	—
255	C₄×D₄	—	2	1	no	—
256	C₄×D₄	C₂³	1	1	yes	characteristic
257	C₄×D₄	C₂³	1	1	yes	characteristic
258	C₄×D₄	C₂³	1	2	yes	—
259	C₄×D₄	C₂³	1	1	yes	characteristic
260	C₄×D₄	C₂³	1	2	yes	—
261	C₄×D₄	C₂³	1	1	yes	characteristic
262	#117	—	2	1	no	—
263	#117	—	2	1	no	—
264	#117	—	2	2	no	—
265	#117	—	2	1	no	—
266	#117	—	2	1	no	—
267	#117	C₂³	1	2	yes	—
268	#117	C₂³	1	2	yes	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	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	1	yes	characteristic
276	#107	C₂³	1	2	yes	—
277	#107	C₂³	1	2	yes	—
278	#106	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	1	yes	characteristic
283	#106	C₂³	1	2	yes	—
284	C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₄⋊C₈	C₂³	1	2	yes	—
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	2	yes	—
294	#103	C₂³	1	2	yes	—
295	#103	C₂³	1	1	yes	characteristic
296	#103	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	1	yes	characteristic
302	#102	C₂³	1	2	yes	—
303	#102	C₂³	1	2	yes	—
304	#102	C₂³	1	1	yes	characteristic
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	C₄×C₈	C₂³	1	1	yes	characteristic
312	C₄×C₈	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	—	4	2	no	—
321	#41	—	4	2	no	—
322	#41	—	8	2	no	—
323	#41	—	8	2	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	4	2	no	—
328	C₂×Q₈	—	4	2	no	—
329	C₂×Q₈	C₂×D₄	1	2	yes	—
330	C₂×Q₈	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈	C₂⁴	1	1	yes	characteristic
332	C₂×Q₈	C₂⁴	1	2	yes	—
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	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	1	yes	characteristic
356	C₂×D₄	C₂⁴	1	2	yes	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄	C₂⁴	1	2	yes	—
368	C₂²×C₄	C₂⁴	1	2	yes	—
369	C₂²×C₄	C₂⁴	1	1	yes	characteristic
370	Q₁₆	—	2	2	no	—
371	Q₁₆	—	4	2	no	—
372	SD₁₆	—	2	4	no	—
373	SD₁₆	—	4	1	no	—
374	SD₁₆	—	4	2	no	—
375	SD₁₆	—	4	1	no	—
376	SD₁₆	—	4	2	no	—
377	SD₁₆	—	4	2	no	—
378	D₈	—	2	2	no	—
379	D₈	—	4	2	no	—
380	M₁₆	—	2	4	no	—
381	M₁₆	—	2	4	no	—
382	M₁₆	—	4	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	4	1	no	—
385	C₂×C₈	—	4	2	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	2	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	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	1	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	2	yes	—
418	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	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	2	no	—
430	C₂²⋊C₄	—	2	1	no	—
431	C₂²⋊C₄	—	2	1	no	—
432	C₂²⋊C₄	—	2	2	no	—
433	C₂²⋊C₄	—	2	1	no	—
434	C₂²⋊C₄	—	2	1	no	—
435	C₂²⋊C₄	—	2	1	no	—
436	C₂²⋊C₄	—	2	1	no	—
437	C₂²⋊C₄	—	2	2	no	—
438	C₂²⋊C₄	—	2	1	no	—
439	C₂²⋊C₄	—	2	2	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	2	1	no	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₂²⋊C₄	—	2	1	no	—
445	C₂²⋊C₄	C₂×D₄	1	2	yes	—
446	C₂²⋊C₄	C₂×D₄	1	2	yes	—
447	C₂²⋊C₄	C₂×D₄	1	2	yes	—
448	C₂²⋊C₄	C₂×D₄	1	2	yes	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	2	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	2	1	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	1	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	8	2	no	—
462	C₂³	—	8	2	no	—
463	C₂³	—	8	2	no	—
464	C₂³	C₂²×D₄	1	2	yes	—
465	C₂³	C₂²×D₄	1	1	yes	characteristic
466	C₂³	C₂²×D₄	1	2	yes	—
467	Q₈	—	2	2	no	—
468	Q₈	—	2	1	no	—
469	Q₈	—	2	1	no	—
470	Q₈	—	2	1	no	—
471	Q₈	—	2	2	no	—
472	Q₈	—	2	1	no	—
473	Q₈	—	4	2	no	—
474	Q₈	—	4	2	no	—
475	Q₈	—	8	1	no	—
476	Q₈	—	8	2	no	—
477	D₄	—	2	2	no	—
478	D₄	—	2	2	no	—
479	D₄	—	2	1	no	—
480	D₄	—	2	1	no	—
481	D₄	—	2	2	no	—
482	D₄	—	2	1	no	—
483	D₄	—	2	2	no	—
484	D₄	—	2	1	no	—
485	D₄	—	4	2	no	—
486	D₄	—	4	2	no	—
487	D₄	—	4	2	no	—
488	D₄	—	4	2	no	—
489	D₄	—	4	2	no	—
490	D₄	—	8	1	no	—
491	D₄	—	8	2	no	—
492	D₄	—	8	1	no	—
493	D₄	—	8	2	no	—
494	D₄	—	8	1	no	—
495	D₄	—	8	2	no	—
496	D₄	—	8	2	no	—
497	D₄	—	8	2	no	—
498	D₄	—	8	2	no	—
499	D₄	—	8	2	no	—
500	D₄	—	8	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	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	—	8	2	no	—
525	C₂×C₄	—	8	2	no	—
526	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄	C₂²×D₄	1	2	yes	—
528	C₂×C₄	C₂²×D₄	1	2	yes	—
529	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄	C₂⁵	1	1	yes	characteristic
534	C₈	—	2	1	no	—
535	C₈	—	2	2	no	—
536	C₈	—	2	2	no	—
537	C₈	—	2	1	no	—
538	C₈	—	2	1	no	—
539	C₈	H(5,𝔽₂)	1	2	yes	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	2	2	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	16	4	no	—
559	C₂²	C₂³×D₄	1	1	yes	characteristic
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	2	no	—
563	C₄	—	2	2	no	—
564	C₄	—	2	1	no	—
565	C₄	—	2	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	2	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	2	no	—
571	C₄	—	4	1	no	—
572	C₄	—	4	1	no	—
573	C₄	—	4	1	no	—
574	C₄	—	4	2	no	—
575	C₄	#577	1	2	yes	—
576	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
577	C₄	#585	1	1	yes	characteristic
578	C₂	—	4	1	no	—
579	C₂	—	4	2	no	—
580	C₂	—	4	2	no	—
581	C₂	—	8	1	no	—
582	C₂	—	8	2	no	—
583	C₂	—	8	1	no	—
584	C₂	#3496	1	1	yes	characteristic
585	C₂	C₂×#577	1	1	yes	characteristic
586	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 ◁ #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. #3547	C₂	semidirect
2. #3546	C₂	semidirect
3. #3356	C₂	semidirect
4. #3354	C₂	semidirect
5. #3351	C₂	semidirect
6. #3305	C₂	semidirect
7. #3302	C₂	semidirect
8. #3301	C₂	semidirect
9. #3298	C₂	semidirect
10. #3296	C₂	semidirect
11. #3295	C₂	semidirect
12. #3278	C₂	semidirect
13. #3275	C₂	semidirect
14. #3272	C₂	semidirect
15. #3252	C₂	semidirect
16. #3251	C₂	semidirect
17. #3204	C₂	semidirect
18. #3200	C₂	semidirect
19. #3168	C₂	semidirect
20. #3167	C₂	semidirect
21. #3063	C₂	semidirect
22. #3062	C₂	semidirect
23. #2931	C₂	semidirect
24. C₂×#137	C₂²	semidirect
26. C₂×#131	C₂²	semidirect
31. #555	C₂²	semidirect
35. #552	C₂²	semidirect
38. D₄×Q₈	C₂²	semidirect
39. #548	C₂²	semidirect
51. #537	C₂²	semidirect
52. #536	C₂²	semidirect
55. #533	C₂²	semidirect
59. #529	C₂²	semidirect
60. #499	C₂²	semidirect
61. #498	C₂²	semidirect
65. #488	C₂²	semidirect
66. #487	C₂²	semidirect
68. #485	C₂²	semidirect
69. #485	C₂²	semidirect
70. #483	C₂²	semidirect
71. #483	C₂²	semidirect
73. #482	C₂²	semidirect
75. #481	C₂²	semidirect
76. #479	C₂²	semidirect
77. #478	C₂²	semidirect
78. #477	C₂²	semidirect
80. #475	C₂²	semidirect
81. #474	C₂²	semidirect
82. #470	C₂²	semidirect
83. #470	C₂²	semidirect
85. #469	C₂²	semidirect
88. #468	C₂²	semidirect
89. #468	C₂²	semidirect
90. #467	C₂²	semidirect
91. #467	C₂²	semidirect
93. #466	C₂²	semidirect
97. #465	C₂²	semidirect
98. #465	C₂²	semidirect
99. #465	C₂²	semidirect
101. #463	C₂²	semidirect
102. #462	C₂²	semidirect
106. #452	C₂²	semidirect
107. #452	C₂²	semidirect
111. #449	C₂²	semidirect
113. #448	C₂²	semidirect
114. C₄×Q₁₆	C₂²	semidirect
116. C₄×SD₁₆	C₂²	semidirect
117. C₄×SD₁₆	C₂²	semidirect
118. C₄×SD₁₆	C₂²	semidirect
121. #436	C₂²	semidirect
122. #436	C₂²	semidirect
124. C₈×D₄	C₂²	semidirect
125. C₈×D₄	C₂²	semidirect
126. #428	C₂²	semidirect
127. #428	C₂²	semidirect
128. #423	C₂²	semidirect
129. #416	C₂²	semidirect
130. #416	C₂²	semidirect
131. C₂×#103	C₂²	semidirect
133. #408	C₂²	semidirect
134. C₂×C₄×C₈	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3547	2
#3546	2
#3356	2
#3354	2
#3351	2
#3305	2
#3302	2
#3301	2
#3298	2
#3296	2
#3295	2
#3278	2
#3275	2
#3272	2
#3252	2
#3251	2
#3204	2
#3200	2
#3168	2
#3167	2
#3063	2
#3062	2
#2931	2