Subgroups — #61784

Order 256.

905 conjugacy classes of subgroups.

The subgroup lattice has 589 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3546	C₂	1	1	yes	maximal, characteristic, complemented
2	#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	#3355	C₂	1	2	yes	maximal, complemented
4	#3354	C₂	1	1	yes	maximal, characteristic, complemented
5	#3353	C₂	1	1	yes	maximal, characteristic, complemented
6	#3340	C₂	1	1	yes	maximal, characteristic, complemented
7	#3339	C₂	1	2	yes	maximal, complemented
8	#3334	C₂	1	1	yes	maximal, characteristic, complemented
9	#3332	C₂	1	1	yes	maximal, characteristic, complemented
10	#3325	C₂	1	1	yes	maximal, characteristic, complemented
11	#3322	C₂	1	2	yes	maximal, complemented
12	#3305	C₂	1	1	yes	maximal, characteristic, complemented
13	#3297	C₂	1	2	yes	maximal, complemented
14	#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	#3233	C₂	1	1	yes	maximal, characteristic, complemented
16	#3228	C₂	1	1	yes	maximal, characteristic, complemented
17	#3199	C₂	1	2	yes	maximal, complemented
18	#3198	C₂	1	2	yes	maximal, complemented
19	#3105	C₂	1	1	yes	maximal, characteristic, complemented
20	#3100	C₂	1	1	yes	maximal, characteristic, complemented
21	#3098	C₂	1	2	yes	maximal, complemented
22	#3096	C₂	1	2	yes	maximal, complemented
23	#2979	C₂	1	1	yes	maximal, characteristic, complemented
24	#560	—	2	2	no	—
25	#559	—	2	2	no	—
26	#556	—	2	1	no	—
27	#556	C₂²	1	1	yes	characteristic, complemented
28	#555	C₂²	1	1	yes	characteristic
29	#555	C₂²	1	1	yes	characteristic, complemented
30	#553	C₂²	1	2	yes	complemented
31	#553	C₂²	1	2	yes	complemented
32	#553	C₂²	1	2	yes	complemented
33	#550	—	2	1	no	—
34	#550	—	2	1	no	—
35	#550	C₂²	1	1	yes	characteristic, complemented
36	#547	C₂²	1	1	yes	characteristic
37	#547	C₂²	1	1	yes	characteristic, complemented
38	#547	C₂²	1	1	yes	characteristic, complemented
39	#546	—	2	1	no	—
40	#546	C₂²	1	2	yes	complemented
41	D₄²	C₂²	1	1	yes	characteristic, complemented
42	#542	—	2	1	no	—
43	#538	—	2	2	no	—
44	#538	—	2	2	no	—
45	#537	C₂²	1	2	yes	—
46	#535	—	2	1	no	—
47	#535	C₂²	1	2	yes	—
48	#535	C₂²	1	2	yes	complemented
49	#533	C₂²	1	1	yes	characteristic, complemented
50	#532	C₂²	1	1	yes	characteristic
51	#532	C₂²	1	1	yes	characteristic
52	#529	C₂²	1	1	yes	characteristic
53	#525	—	2	1	no	—
54	#525	—	2	1	no	—
55	#520	C₂²	1	2	yes	complemented
56	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
57	#500	C₂²	1	1	yes	characteristic, complemented
58	#499	C₂²	1	2	yes	complemented
59	#498	C₂²	1	1	yes	characteristic, complemented
60	#488	C₂²	1	2	yes	complemented
61	#486	C₂²	1	1	yes	characteristic, complemented
62	#486	C₂²	1	1	yes	characteristic, complemented
63	#485	C₂²	1	2	yes	complemented
64	#485	C₂²	1	2	yes	complemented
65	#484	C₂²	1	2	yes	complemented
66	#484	C₂²	1	1	yes	characteristic, complemented
67	#482	C₂²	1	2	yes	—
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	#482	C₂²	1	2	yes	complemented
73	#482	C₂²	1	2	yes	complemented
74	#482	C₂²	1	2	yes	complemented
75	#481	C₂²	1	1	yes	characteristic
76	#481	C₂²	1	2	yes	complemented
77	#481	C₂²	1	2	yes	complemented
78	#480	C₂²	1	2	yes	complemented
79	#480	C₂²	1	2	yes	complemented
80	#480	C₂²	1	2	yes	complemented
81	#480	C₂²	1	2	yes	complemented
82	#478	C₂²	1	1	yes	characteristic, complemented
83	#478	C₂²	1	2	yes	complemented
84	#478	C₂²	1	1	yes	characteristic, complemented
85	#478	C₂²	1	2	yes	complemented
86	#477	C₂²	1	1	yes	characteristic, complemented
87	#476	C₂²	1	1	yes	characteristic, complemented
88	#475	C₂²	1	1	yes	characteristic, complemented
89	#474	C₂²	1	1	yes	characteristic, complemented
90	#474	C₂²	1	1	yes	characteristic, complemented
91	#474	C₂²	1	1	yes	characteristic, complemented
92	#469	C₂²	1	2	yes	—
93	#469	C₂²	1	2	yes	—
94	#469	C₂²	1	2	yes	complemented
95	#468	C₂²	1	2	yes	complemented
96	#466	C₂²	1	2	yes	—
97	#466	C₂²	1	2	yes	—
98	#466	C₂²	1	2	yes	complemented
99	#465	C₂²	1	2	yes	complemented
100	#463	C₂²	1	1	yes	characteristic
101	#463	C₂²	1	1	yes	characteristic
102	#459	C₂²	1	1	yes	characteristic
103	#459	C₂²	1	1	yes	characteristic
104	#450	C₂²	1	1	yes	characteristic, complemented
105	#449	C₂²	1	2	yes	complemented
106	#449	C₂²	1	2	yes	complemented
107	#447	C₂²	1	1	yes	characteristic
108	#447	C₂²	1	2	yes	—
109	#447	C₂²	1	2	yes	—
110	#447	C₂²	1	2	yes	complemented
111	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
112	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
113	C₄×D₈	C₂²	1	1	yes	characteristic
114	C₄×D₈	C₂²	1	1	yes	characteristic
115	C₄×D₈	C₂²	1	2	yes	complemented
116	C₄×D₈	C₂²	1	2	yes	complemented
117	#436	C₂²	1	1	yes	characteristic, complemented
118	#436	C₂²	1	1	yes	characteristic, complemented
119	#436	C₂²	1	2	yes	complemented
120	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
121	C₈×D₄	C₂²	1	2	yes	complemented
122	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
123	#431	C₂²	1	1	yes	characteristic, complemented
124	#431	C₂²	1	1	yes	characteristic, complemented
125	#428	C₂²	1	2	yes	complemented
126	#428	C₂²	1	2	yes	complemented
127	#427	C₂²	1	2	yes	complemented
128	C₂×#107	C₂²	1	2	yes	complemented
129	#418	C₂²	1	2	yes	complemented
130	#417	C₂²	1	2	yes	complemented
131	#416	C₂²	1	2	yes	complemented
132	C₂×#102	C₂²	1	2	yes	complemented
133	#408	C₂²	1	2	yes	complemented
134	#408	C₂²	1	2	yes	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	2	yes	—
140	C₂×#41	C₂³	1	2	yes	—
141	C₂²×D₄	—	2	1	no	—
142	C₂²×D₄	C₂³	1	1	yes	characteristic
143	C₂²×D₄	C₂³	1	2	yes	—
144	C₂³×C₄	—	2	1	no	—
145	C₂×SD₁₆	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆	C₂³	1	1	yes	characteristic
147	C₂×D₈	C₂³	1	1	yes	characteristic
148	C₂×D₈	C₂³	1	1	yes	characteristic
149	C₂×D₈	C₂³	1	2	yes	—
150	C₂×D₈	C₂³	1	2	yes	—
151	C₂×M₁₆	C₂³	1	2	yes	—
152	C₂×M₁₆	C₂³	1	2	yes	—
153	C₂²×C₈	C₂³	1	2	yes	—
154	C₂²×C₈	C₂³	1	2	yes	—
155	C₄⋊Q₈	D₄	1	1	yes	characteristic
156	C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	#127	—	2	1	no	—
160	#127	—	2	2	no	—
161	#127	—	2	2	no	—
162	#127	D₄	1	1	yes	characteristic
163	#127	C₂³	1	1	yes	characteristic
164	#126	—	2	2	no	—
165	#126	—	2	2	no	—
166	#126	—	2	2	no	—
167	#126	—	2	2	no	—
168	#126	—	2	1	no	—
169	#125	C₂³	1	1	yes	characteristic
170	#125	C₂³	1	2	yes	—
171	#124	—	2	2	no	—
172	#124	—	2	2	no	—
173	#124	—	2	1	no	—
174	#124	—	2	2	no	—
175	#124	—	2	2	no	—
176	#124	—	2	1	no	—
177	#124	D₄	1	2	yes	—
178	#124	C₂³	1	1	yes	characteristic
179	#123	—	2	1	no	—
180	#123	—	2	2	no	—
181	#123	—	2	2	no	—
182	#123	—	2	2	no	—
183	#123	—	2	2	no	—
184	#123	—	2	2	no	—
185	#123	—	2	2	no	—
186	#123	—	2	2	no	—
187	C₂²⋊Q₈	—	2	2	no	—
188	C₂²⋊Q₈	—	2	1	no	—
189	C₂²⋊Q₈	—	2	1	no	—
190	C₂²⋊Q₈	—	2	1	no	—
191	C₂²⋊Q₈	—	2	1	no	—
192	C₂²⋊Q₈	—	2	1	no	—
193	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
194	C₂²⋊Q₈	C₂³	1	2	yes	—
195	#121	—	2	1	no	—
196	#121	—	2	1	no	—
197	#121	—	2	2	no	—
198	#121	—	2	2	no	—
199	#121	—	2	2	no	—
200	#121	—	2	2	no	—
201	#121	—	2	2	no	—
202	#121	—	2	2	no	—
203	#121	—	2	1	no	—
204	#121	—	2	1	no	—
205	#121	—	2	2	no	—
206	#121	—	2	2	no	—
207	#121	D₄	1	1	yes	characteristic
208	#121	D₄	1	1	yes	characteristic
209	#121	D₄	1	2	yes	—
210	#121	C₂³	1	1	yes	characteristic
211	#121	C₂³	1	2	yes	—
212	#121	C₂³	1	2	yes	—
213	#121	C₂³	1	2	yes	—
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	#120	—	2	2	no	—
222	#120	—	2	2	no	—
223	#120	—	2	2	no	—
224	#120	—	2	2	no	—
225	C₄×Q₈	—	2	2	no	—
226	C₄×Q₈	—	2	1	no	—
227	C₄×Q₈	—	2	1	no	—
228	C₄×Q₈	—	2	1	no	—
229	C₄×Q₈	C₂³	1	1	yes	characteristic
230	C₄×D₄	—	2	2	no	—
231	C₄×D₄	—	2	2	no	—
232	C₄×D₄	—	2	2	no	—
233	C₄×D₄	—	2	1	no	—
234	C₄×D₄	—	2	1	no	—
235	C₄×D₄	—	2	2	no	—
236	C₄×D₄	—	2	2	no	—
237	C₄×D₄	—	2	2	no	—
238	C₄×D₄	—	2	1	no	—
239	C₄×D₄	—	2	1	no	—
240	C₄×D₄	—	2	1	no	—
241	C₄×D₄	C₂³	1	1	yes	characteristic
242	C₄×D₄	C₂³	1	1	yes	characteristic
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	2	yes	—
247	C₄×D₄	C₂³	1	1	yes	characteristic
248	C₄×D₄	C₂³	1	2	yes	—
249	C₄×D₄	C₂³	1	1	yes	characteristic
250	#117	—	2	1	no	—
251	#117	—	2	1	no	—
252	#117	—	2	1	no	—
253	#117	C₂³	1	2	yes	—
254	#117	C₂³	1	2	yes	—
255	#117	C₂³	1	2	yes	—
256	#117	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄	C₂³	1	2	yes	—
261	C₂×C₂²⋊C₄	—	2	1	no	—
262	C₂×C₂²⋊C₄	—	2	2	no	—
263	C₂×C₄²	C₂³	1	1	yes	characteristic
264	#107	C₂³	1	1	yes	characteristic
265	#107	C₂³	1	2	yes	—
266	#107	C₂³	1	2	yes	—
267	#107	C₂³	1	2	yes	—
268	#107	C₂³	1	2	yes	—
269	#107	C₂³	1	1	yes	characteristic
270	#107	C₂³	1	2	yes	—
271	#107	C₂³	1	2	yes	—
272	#106	C₂³	1	1	yes	characteristic
273	#106	C₂³	1	2	yes	—
274	#106	C₂³	1	1	yes	characteristic
275	#106	C₂³	1	2	yes	—
276	#106	C₂³	1	2	yes	—
277	#106	C₂³	1	2	yes	—
278	C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₄⋊C₈	C₂³	1	1	yes	characteristic
282	#103	C₂³	1	1	yes	characteristic
283	#103	C₂³	1	2	yes	—
284	#103	C₂³	1	1	yes	characteristic
285	#103	C₂³	1	2	yes	—
286	#102	C₂³	1	1	yes	characteristic
287	#102	C₂³	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
301	#102	C₂³	1	1	yes	characteristic
302	C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₂²⋊C₈	C₂³	1	2	yes	—
304	C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₂²⋊C₈	C₂³	1	2	yes	—
306	C₂²⋊C₈	C₂³	1	2	yes	—
307	C₂²⋊C₈	C₂³	1	2	yes	—
308	C₂²⋊C₈	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	2	yes	—
312	C₂⁴	—	2	1	no	—
313	C₂⁴	—	2	2	no	—
314	#41	—	4	2	no	—
315	#41	—	4	2	no	—
316	#41	—	4	2	no	—
317	#41	—	4	2	no	—
318	#41	—	8	2	no	—
319	#41	—	8	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	C₂×D₄	1	2	yes	—
326	C₂×Q₈	C₂⁴	1	1	yes	characteristic
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	4	1	no	—
342	C₂×D₄	—	4	1	no	—
343	C₂×D₄	—	4	2	no	—
344	C₂×D₄	—	4	2	no	—
345	C₂×D₄	—	8	2	no	—
346	C₂×D₄	C₂×D₄	1	1	yes	characteristic
347	C₂×D₄	C₂×D₄	1	1	yes	characteristic
348	C₂×D₄	C₂×D₄	1	2	yes	—
349	C₂×D₄	C₂×D₄	1	2	yes	—
350	C₂×D₄	C₂×D₄	1	2	yes	—
351	C₂×D₄	C₂×D₄	1	2	yes	—
352	C₂×D₄	C₂⁴	1	1	yes	characteristic
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	1	no	—
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	1	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	8	2	no	—
368	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
370	C₂²×C₄	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄	C₂⁴	1	2	yes	—
372	C₂²×C₄	C₂⁴	1	2	yes	—
373	SD₁₆	—	4	1	no	—
374	SD₁₆	—	4	1	no	—
375	D₈	—	4	2	no	—
376	D₈	—	4	1	no	—
377	D₈	—	4	2	no	—
378	D₈	—	4	1	no	—
379	M₁₆	—	4	2	no	—
380	M₁₆	—	4	2	no	—
381	C₂×C₈	—	4	2	no	—
382	C₂×C₈	—	4	2	no	—
383	C₂×C₈	C₂⁴	1	1	yes	characteristic
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	2	yes	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	2	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	2	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
404	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄	C₂×D₄	1	2	yes	—
406	C₄⋊C₄	C₂⁴	1	2	yes	—
407	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄	C₂⁴	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	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₂²⋊C₄	—	2	2	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₂²⋊C₄	—	2	1	no	—
419	C₂²⋊C₄	—	2	1	no	—
420	C₂²⋊C₄	—	2	1	no	—
421	C₂²⋊C₄	—	2	1	no	—
422	C₂²⋊C₄	—	2	1	no	—
423	C₂²⋊C₄	—	2	1	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	2	1	no	—
426	C₂²⋊C₄	—	2	1	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	2	no	—
434	C₂²⋊C₄	—	2	1	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	C₂×D₄	1	2	yes	—
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	C₄²	—	2	2	no	—
441	C₄²	—	2	2	no	—
442	C₄²	—	2	1	no	—
443	C₄²	—	2	2	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	1	yes	characteristic
449	C₂³	—	2	1	no	—
450	C₂³	—	2	1	no	—
451	C₂³	—	2	1	no	—
452	C₂³	—	2	2	no	—
453	C₂³	—	4	2	no	—
454	C₂³	—	8	1	no	—
455	C₂³	—	8	1	no	—
456	C₂³	—	8	2	no	—
457	C₂³	—	8	2	no	—
458	C₂³	—	8	2	no	—
459	C₂³	C₂²×D₄	1	2	yes	—
460	C₂³	C₂²×D₄	1	1	yes	characteristic
461	C₂³	C₂²×D₄	1	2	yes	—
462	Q₈	—	2	1	no	—
463	Q₈	—	2	1	no	—
464	Q₈	—	4	2	no	—
465	Q₈	—	4	2	no	—
466	Q₈	—	4	2	no	—
467	Q₈	—	8	1	no	—
468	D₄	—	2	2	no	—
469	D₄	—	2	2	no	—
470	D₄	—	2	1	no	—
471	D₄	—	2	1	no	—
472	D₄	—	2	1	no	—
473	D₄	—	2	1	no	—
474	D₄	—	2	1	no	—
475	D₄	—	2	1	no	—
476	D₄	—	2	2	no	—
477	D₄	—	2	2	no	—
478	D₄	—	4	2	no	—
479	D₄	—	4	2	no	—
480	D₄	—	4	2	no	—
481	D₄	—	4	2	no	—
482	D₄	—	4	2	no	—
483	D₄	—	4	2	no	—
484	D₄	—	8	1	no	—
485	D₄	—	8	2	no	—
486	D₄	—	8	1	no	—
487	D₄	—	8	2	no	—
488	D₄	—	8	2	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	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	2	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	—	2	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	8	1	no	—
516	C₂×C₄	—	8	1	no	—
517	C₂×C₄	—	8	2	no	—
518	C₂×C₄	—	8	2	no	—
519	C₂×C₄	—	8	1	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	1	no	—
532	C₈	—	2	2	no	—
533	C₈	—	2	1	no	—
534	C₈	—	2	1	no	—
535	C₈	—	2	2	no	—
536	C₈	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	4	1	no	—
547	C₂²	—	4	1	no	—
548	C₂²	—	4	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	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	8	4	no	—
559	C₂²	—	16	4	no	—
560	C₂²	C₂³×D₄	1	1	yes	characteristic
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	2	2	no	—
564	C₄	—	2	1	no	—
565	C₄	—	2	2	no	—
566	C₄	—	2	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	2	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	1	no	—
571	C₄	—	4	1	no	—
572	C₄	—	4	1	no	—
573	C₄	—	4	2	no	—
574	C₄	—	4	2	no	—
575	C₄	#576	1	2	yes	—
576	C₄	#585	1	1	yes	characteristic
577	C₄	#585	1	1	yes	characteristic
578	C₂	—	4	2	no	—
579	C₂	—	4	1	no	—
580	C₂	—	4	2	no	—
581	C₂	—	8	1	no	—
582	C₂	—	8	1	no	—
583	C₂	—	8	2	no	—
584	C₂	—	8	1	no	—
585	C₂	#3485	1	1	yes	characteristic
586	C₂	C₂×#576	1	1	yes	characteristic
587	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. #3546	C₂	semidirect
2. #3506	C₂	semidirect
3. #3355	C₂	semidirect
4. #3354	C₂	semidirect
5. #3353	C₂	semidirect
6. #3340	C₂	semidirect
7. #3339	C₂	semidirect
8. #3334	C₂	semidirect
9. #3332	C₂	semidirect
10. #3325	C₂	semidirect
11. #3322	C₂	semidirect
12. #3305	C₂	semidirect
13. #3297	C₂	semidirect
14. #3294	C₂	semidirect
15. #3233	C₂	semidirect
16. #3228	C₂	semidirect
17. #3199	C₂	semidirect
18. #3198	C₂	semidirect
19. #3105	C₂	semidirect
20. #3100	C₂	semidirect
21. #3098	C₂	semidirect
22. #3096	C₂	semidirect
23. #2979	C₂	semidirect
27. #556	C₂²	semidirect
29. #555	C₂²	semidirect
30. #553	C₂²	semidirect
31. #553	C₂²	semidirect
32. #553	C₂²	semidirect
35. #550	C₂²	semidirect
37. #547	C₂²	semidirect
38. #547	C₂²	semidirect
40. #546	C₂²	semidirect
41. D₄²	C₂²	semidirect
48. #535	C₂²	semidirect
49. #533	C₂²	semidirect
55. #520	C₂²	semidirect
56. C₂×C₄×D₄	C₂²	semidirect
57. #500	C₂²	semidirect
58. #499	C₂²	semidirect
59. #498	C₂²	semidirect
60. #488	C₂²	semidirect
61. #486	C₂²	semidirect
62. #486	C₂²	semidirect
63. #485	C₂²	semidirect
64. #485	C₂²	semidirect
65. #484	C₂²	semidirect
66. #484	C₂²	semidirect
68. #482	C₂²	semidirect
69. #482	C₂²	semidirect
70. #482	C₂²	semidirect
71. #482	C₂²	semidirect
72. #482	C₂²	semidirect
73. #482	C₂²	semidirect
74. #482	C₂²	semidirect
76. #481	C₂²	semidirect
77. #481	C₂²	semidirect
78. #480	C₂²	semidirect
79. #480	C₂²	semidirect
80. #480	C₂²	semidirect
81. #480	C₂²	semidirect
82. #478	C₂²	semidirect
83. #478	C₂²	semidirect
84. #478	C₂²	semidirect
85. #478	C₂²	semidirect
86. #477	C₂²	semidirect
87. #476	C₂²	semidirect
88. #475	C₂²	semidirect
89. #474	C₂²	semidirect
90. #474	C₂²	semidirect
91. #474	C₂²	semidirect
94. #469	C₂²	semidirect
95. #468	C₂²	semidirect
98. #466	C₂²	semidirect
99. #465	C₂²	semidirect
104. #450	C₂²	semidirect
105. #449	C₂²	semidirect
106. #449	C₂²	semidirect
110. #447	C₂²	semidirect
111. C₄×SD₁₆	C₂²	semidirect
112. C₄×SD₁₆	C₂²	semidirect
115. C₄×D₈	C₂²	semidirect
116. C₄×D₈	C₂²	semidirect
117. #436	C₂²	semidirect
118. #436	C₂²	semidirect
119. #436	C₂²	semidirect
120. C₈×D₄	C₂²	semidirect
121. C₈×D₄	C₂²	semidirect
122. C₈×D₄	C₂²	semidirect
123. #431	C₂²	semidirect
124. #431	C₂²	semidirect
125. #428	C₂²	semidirect
126. #428	C₂²	semidirect
127. #427	C₂²	semidirect
128. C₂×#107	C₂²	semidirect
129. #418	C₂²	semidirect
130. #417	C₂²	semidirect
131. #416	C₂²	semidirect
132. C₂×#102	C₂²	semidirect
133. #408	C₂²	semidirect
134. #408	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3546	2
#3506	2
#3355	2
#3354	2
#3353	2
#3340	2
#3339	2
#3334	2
#3332	2
#3325	2
#3322	2
#3305	2
#3297	2
#3294	2
#3233	2
#3228	2
#3199	2
#3198	2
#3105	2
#3100	2
#3098	2
#3096	2
#2979	2