Subgroups — #62044

Order 256.

915 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	#3546	C₂	1	1	yes	maximal, characteristic
2	#3523	C₂	1	1	yes	maximal, characteristic, complemented
3	#3398	C₂	1	1	yes	maximal, characteristic, complemented
4	#3392	C₂	1	1	yes	maximal, characteristic, complemented
5	#3368	C₂	1	1	yes	maximal, characteristic, complemented
6	#3364	C₂	1	1	yes	maximal, characteristic, complemented
7	#3324	C₂	1	1	yes	maximal, characteristic, complemented
8	#3323	C₂	1	2	yes	maximal, complemented
9	#3317	C₂	1	2	yes	maximal, complemented
10	#3302	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	#3278	C₂	1	2	yes	maximal, complemented
13	#3276	C₂	1	1	yes	maximal, characteristic, complemented
14	#3266	C₂	1	2	yes	maximal, complemented
15	#3258	C₂	1	2	yes	maximal, complemented
16	#3254	C₂	1	1	yes	maximal, characteristic, complemented
17	#3222	C₂	1	2	yes	maximal, complemented
18	#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	#3121	C₂	1	2	yes	maximal, complemented
20	#3103	C₂	1	1	yes	maximal, characteristic, complemented
21	#3043	C₂	1	2	yes	maximal, complemented
22	#3037	C₂	1	1	yes	maximal, characteristic, complemented
23	#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137	C₂²	1	2	yes	complemented
25	C₂×#137	C₂²	1	2	yes	complemented
26	C₂²×SD₁₆	C₂²	1	2	yes	—
27	#560	—	2	2	no	—
28	#557	—	2	1	no	—
29	#557	C₂²	1	1	yes	characteristic, complemented
30	#557	C₂²	1	1	yes	characteristic, complemented
31	#556	—	2	1	no	—
32	#556	C₂²	1	1	yes	characteristic
33	#556	C₂²	1	1	yes	characteristic
34	#553	—	2	1	no	—
35	#552	—	2	2	no	—
36	#552	C₂²	1	2	yes	complemented
37	#550	C₂²	1	2	yes	—
38	#550	C₂²	1	1	yes	characteristic
39	D₄×Q₈	C₂²	1	1	yes	characteristic
40	D₄×Q₈	C₂²	1	2	yes	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	C₂²	1	2	yes	—
46	#541	—	2	2	no	—
47	#541	C₂²	1	2	yes	complemented
48	#538	—	2	2	no	—
49	#537	—	2	1	no	—
50	#535	—	2	1	no	—
51	#535	C₂²	1	2	yes	—
52	#533	—	2	1	no	—
53	#533	C₂²	1	1	yes	characteristic, complemented
54	#532	C₂²	1	1	yes	characteristic
55	#532	C₂²	1	1	yes	characteristic
56	#529	—	2	1	no	—
57	#529	C₂²	1	1	yes	characteristic
58	#519	C₂²	1	2	yes	complemented
59	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
60	#497	C₂²	1	2	yes	—
61	#494	C₂²	1	1	yes	characteristic, complemented
62	#492	C₂²	1	1	yes	characteristic
63	#492	C₂²	1	2	yes	complemented
64	#490	C₂²	1	2	yes	complemented
65	#488	C₂²	1	2	yes	—
66	#487	C₂²	1	1	yes	characteristic, complemented
67	#486	C₂²	1	1	yes	characteristic
68	#485	C₂²	1	2	yes	complemented
69	#482	C₂²	1	2	yes	—
70	#481	C₂²	1	1	yes	characteristic
71	#481	C₂²	1	1	yes	characteristic, complemented
72	#479	C₂²	1	2	yes	complemented
73	#478	C₂²	1	2	yes	complemented
74	#477	C₂²	1	2	yes	complemented
75	#475	C₂²	1	1	yes	characteristic, complemented
76	#475	C₂²	1	1	yes	characteristic, complemented
77	#474	C₂²	1	1	yes	characteristic
78	#474	C₂²	1	1	yes	characteristic, complemented
79	#470	C₂²	1	2	yes	complemented
80	#468	C₂²	1	2	yes	—
81	#468	C₂²	1	2	yes	—
82	#468	C₂²	1	2	yes	complemented
83	#467	C₂²	1	2	yes	complemented
84	#465	C₂²	1	2	yes	—
85	#464	C₂²	1	2	yes	—
86	#464	C₂²	1	2	yes	—
87	#464	C₂²	1	2	yes	complemented
88	#464	C₂²	1	2	yes	complemented
89	#464	C₂²	1	2	yes	complemented
90	#464	C₂²	1	2	yes	complemented
91	#462	C₂²	1	1	yes	characteristic, complemented
92	#462	C₂²	1	2	yes	complemented
93	#462	C₂²	1	1	yes	characteristic, complemented
94	#461	C₂²	1	1	yes	characteristic
95	#461	C₂²	1	1	yes	characteristic, complemented
96	#461	C₂²	1	2	yes	complemented
97	#460	C₂²	1	1	yes	characteristic
98	#460	C₂²	1	1	yes	characteristic
99	#460	C₂²	1	1	yes	characteristic
100	#460	C₂²	1	1	yes	characteristic
101	#460	C₂²	1	2	yes	—
102	#460	C₂²	1	2	yes	complemented
103	#460	C₂²	1	2	yes	complemented
104	#452	C₂²	1	2	yes	complemented
105	#452	C₂²	1	2	yes	complemented
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	1	yes	characteristic
112	#448	C₂²	1	2	yes	—
113	#448	C₂²	1	1	yes	characteristic, complemented
114	#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
116	#441	C₂²	1	2	yes	complemented
117	#440	C₂²	1	2	yes	complemented
118	C₄×Q₁₆	C₂²	1	2	yes	complemented
119	C₄×SD₁₆	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆	C₂²	1	1	yes	characteristic
121	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
122	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
123	C₄×SD₁₆	C₂²	1	2	yes	complemented
124	#436	C₂²	1	1	yes	characteristic
125	#436	C₂²	1	2	yes	complemented
126	#435	C₂²	1	2	yes	complemented
127	C₈×D₄	C₂²	1	1	yes	characteristic
128	#433	C₂²	1	2	yes	complemented
129	#431	C₂²	1	1	yes	characteristic, complemented
130	#424	C₂²	1	2	yes	complemented
131	#423	C₂²	1	1	yes	characteristic, complemented
132	#418	C₂²	1	2	yes	—
133	#417	C₂²	1	2	yes	complemented
134	#416	C₂²	1	2	yes	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	1	yes	characteristic
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	#137	—	4	4	no	—
145	C₂×Q₁₆	C₂³	1	2	yes	—
146	C₂×Q₁₆	C₂³	1	2	yes	—
147	C₂×Q₁₆	C₂³	1	2	yes	—
148	C₂×Q₁₆	C₂³	1	2	yes	—
149	C₂×SD₁₆	—	4	4	no	—
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×SD₁₆	C₂³	1	2	yes	—
154	C₂×SD₁₆	C₂³	1	2	yes	—
155	C₂×SD₁₆	C₂³	1	2	yes	—
156	C₂×SD₁₆	C₂³	1	2	yes	—
157	C₂×SD₁₆	C₂³	1	1	yes	characteristic
158	C₂×SD₁₆	C₂³	1	2	yes	—
159	C₂×SD₁₆	C₂³	1	1	yes	characteristic
160	C₂×M₁₆	C₂³	1	2	yes	—
161	C₂×M₁₆	C₂³	1	2	yes	—
162	C₂²×C₈	C₂³	1	2	yes	—
163	C₄⋊Q₈	—	2	1	no	—
164	C₄⋊Q₈	—	2	1	no	—
165	C₄⋊Q₈	—	2	2	no	—
166	C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₄⋊Q₈	C₂³	1	2	yes	—
169	C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	#127	—	2	2	no	—
172	#127	C₂³	1	1	yes	characteristic
173	#127	C₂³	1	1	yes	characteristic
174	#127	C₂³	1	2	yes	—
175	#126	—	2	2	no	—
176	#126	—	2	2	no	—
177	#126	—	2	2	no	—
178	#126	—	2	2	no	—
179	#126	—	2	2	no	—
180	#126	—	2	2	no	—
181	#126	D₄	1	2	yes	—
182	#125	—	2	1	no	—
183	#125	—	2	2	no	—
184	#125	—	2	2	no	—
185	#125	—	2	2	no	—
186	#125	—	2	2	no	—
187	#125	—	2	2	no	—
188	#125	—	2	1	no	—
189	#125	D₄	1	1	yes	characteristic
190	#125	C₂³	1	2	yes	—
191	#124	—	2	1	no	—
192	#124	—	2	2	no	—
193	#124	—	2	1	no	—
194	#124	D₄	1	1	yes	characteristic
195	#124	C₂³	1	2	yes	—
196	#124	C₂³	1	2	yes	—
197	#123	—	2	2	no	—
198	#123	—	2	2	no	—
199	#123	—	2	2	no	—
200	#123	—	2	2	no	—
201	#123	D₄	1	2	yes	—
202	C₂²⋊Q₈	—	2	1	no	—
203	C₂²⋊Q₈	—	2	1	no	—
204	C₂²⋊Q₈	—	2	2	no	—
205	C₂²⋊Q₈	—	2	2	no	—
206	C₂²⋊Q₈	—	2	2	no	—
207	C₂²⋊Q₈	—	2	2	no	—
208	C₂²⋊Q₈	D₄	1	1	yes	characteristic
209	C₂²⋊Q₈	C₂³	1	2	yes	—
210	C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₂²⋊Q₈	C₂³	1	2	yes	—
213	#121	—	2	1	no	—
214	#121	—	2	1	no	—
215	#121	—	2	1	no	—
216	#121	—	2	1	no	—
217	#121	—	2	1	no	—
218	#121	—	2	2	no	—
219	#121	—	2	2	no	—
220	#121	—	2	1	no	—
221	#121	—	2	2	no	—
222	#121	—	2	2	no	—
223	#121	—	2	2	no	—
224	#121	—	2	2	no	—
225	#121	D₄	1	1	yes	characteristic
226	#121	C₂³	1	1	yes	characteristic
227	#121	C₂³	1	1	yes	characteristic
228	#121	C₂³	1	2	yes	—
229	#120	—	2	2	no	—
230	#120	—	2	2	no	—
231	#120	—	2	2	no	—
232	#120	—	2	2	no	—
233	C₄×Q₈	—	2	1	no	—
234	C₄×Q₈	—	2	2	no	—
235	C₄×Q₈	—	2	2	no	—
236	C₄×Q₈	—	2	1	no	—
237	C₄×Q₈	—	2	1	no	—
238	C₄×Q₈	—	2	1	no	—
239	C₄×Q₈	—	2	1	no	—
240	C₄×Q₈	—	2	1	no	—
241	C₄×Q₈	C₂³	1	1	yes	characteristic
242	C₄×Q₈	C₂³	1	1	yes	characteristic
243	C₄×Q₈	C₂³	1	1	yes	characteristic
244	C₄×Q₈	C₂³	1	1	yes	characteristic
245	C₄×Q₈	C₂³	1	2	yes	—
246	C₄×Q₈	C₂³	1	2	yes	—
247	C₄×Q₈	C₂³	1	2	yes	—
248	C₄×Q₈	C₂³	1	2	yes	—
249	C₄×Q₈	C₂³	1	1	yes	characteristic
250	C₄×D₄	—	2	1	no	—
251	C₄×D₄	—	2	2	no	—
252	C₄×D₄	—	2	2	no	—
253	C₄×D₄	—	2	1	no	—
254	C₄×D₄	—	2	1	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	#117	—	2	1	no	—
262	#117	—	2	1	no	—
263	#117	—	2	2	no	—
264	#117	—	2	2	no	—
265	#117	—	2	2	no	—
266	#117	C₂³	1	2	yes	—
267	#117	C₂³	1	2	yes	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₄²	—	2	1	no	—
273	C₂×C₄²	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
279	#106	C₂³	1	1	yes	characteristic
280	C₄⋊C₈	C₂³	1	2	yes	—
281	C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₄⋊C₈	C₂³	1	2	yes	—
285	C₄⋊C₈	C₂³	1	2	yes	—
286	C₄⋊C₈	C₂³	1	1	yes	characteristic
287	#103	C₂³	1	2	yes	—
288	#103	C₂³	1	2	yes	—
289	#103	C₂³	1	2	yes	—
290	#103	C₂³	1	1	yes	characteristic
291	#103	C₂³	1	1	yes	characteristic
292	#103	C₂³	1	1	yes	characteristic
293	#103	C₂³	1	1	yes	characteristic
294	#103	C₂³	1	2	yes	—
295	#103	C₂³	1	2	yes	—
296	#103	C₂³	1	2	yes	—
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	1	yes	characteristic
308	C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈	C₂³	1	2	yes	—
310	C₂²⋊C₈	C₂³	1	2	yes	—
311	#97	C₂³	1	2	yes	—
312	C₄×C₈	C₂³	1	1	yes	characteristic
313	C₄×C₈	C₂³	1	1	yes	characteristic
314	C₄×C₈	C₂³	1	2	yes	—
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	2	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	2	4	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	4	2	no	—
329	C₂×Q₈	—	4	1	no	—
330	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈	C₂⁴	1	2	yes	—
332	C₂×Q₈	C₂⁴	1	2	yes	—
333	C₂×Q₈	C₂⁴	1	1	yes	characteristic
334	C₂×Q₈	C₂⁴	1	1	yes	characteristic
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	1	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	4	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	1	yes	characteristic
353	C₂×D₄	C₂⁴	1	2	yes	—
354	C₂×D₄	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
365	C₂²×C₄	C₂⁴	1	1	yes	characteristic
366	C₂²×C₄	C₂⁴	1	2	yes	—
367	Q₁₆	—	2	4	no	—
368	Q₁₆	—	4	2	no	—
369	Q₁₆	—	4	2	no	—
370	Q₁₆	—	4	2	no	—
371	SD₁₆	—	2	2	no	—
372	SD₁₆	—	2	4	no	—
373	SD₁₆	—	2	2	no	—
374	SD₁₆	—	4	2	no	—
375	SD₁₆	—	4	2	no	—
376	SD₁₆	—	4	2	no	—
377	SD₁₆	—	4	1	no	—
378	SD₁₆	—	4	1	no	—
379	SD₁₆	—	4	2	no	—
380	SD₁₆	—	4	2	no	—
381	M₁₆	—	4	2	no	—
382	M₁₆	—	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	1	yes	characteristic
389	C₂×C₈	C₂⁴	1	2	yes	—
390	C₄⋊C₄	—	2	1	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	2	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	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	C₂×D₄	1	2	yes	—
417	C₄⋊C₄	C₂×D₄	1	2	yes	—
418	C₄⋊C₄	C₂×D₄	1	2	yes	—
419	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄	C₂⁴	1	2	yes	—
422	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	2	2	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	1	no	—
433	C₂²⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	2	1	no	—
437	C₂²⋊C₄	—	2	2	no	—
438	C₂²⋊C₄	—	2	1	no	—
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	C₂²⋊C₄	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄	C₂×D₄	1	2	yes	—
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	—	2	2	no	—
451	C₄²	—	2	2	no	—
452	C₄²	—	2	2	no	—
453	C₄²	C₂×D₄	1	1	yes	characteristic
454	C₄²	C₂×D₄	1	1	yes	characteristic
455	C₄²	C₂⁴	1	1	yes	characteristic
456	C₄²	C₂⁴	1	2	yes	—
457	C₄²	C₂⁴	1	1	yes	characteristic
458	C₂³	—	2	1	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	1	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	Q₈	—	2	2	no	—
467	Q₈	—	2	1	no	—
468	Q₈	—	2	2	no	—
469	Q₈	—	2	1	no	—
470	Q₈	—	2	2	no	—
471	Q₈	—	2	1	no	—
472	Q₈	—	2	2	no	—
473	Q₈	—	2	2	no	—
474	Q₈	—	4	2	no	—
475	Q₈	—	4	4	no	—
476	Q₈	—	4	2	no	—
477	Q₈	—	8	1	no	—
478	Q₈	H(5,𝔽₂)	1	2	yes	—
479	D₄	—	2	2	no	—
480	D₄	—	2	1	no	—
481	D₄	—	2	2	no	—
482	D₄	—	2	1	no	—
483	D₄	—	2	1	no	—
484	D₄	—	2	2	no	—
485	D₄	—	2	1	no	—
486	D₄	—	4	2	no	—
487	D₄	—	4	2	no	—
488	D₄	—	8	1	no	—
489	D₄	—	8	1	no	—
490	D₄	—	8	2	no	—
491	D₄	—	8	2	no	—
492	D₄	—	8	1	no	—
493	D₄	—	8	2	no	—
494	D₄	—	8	2	no	—
495	D₄	—	8	2	no	—
496	D₄	—	8	2	no	—
497	D₄	—	8	1	no	—
498	D₄	—	8	1	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	2	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	4	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	8	2	no	—
520	C₂×C₄	—	8	2	no	—
521	C₂×C₄	—	8	2	no	—
522	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
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	2	yes	—
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	2	no	—
535	C₈	—	2	1	no	—
536	C₈	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	1	no	—
540	C₂²	—	2	2	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	4	1	no	—
546	C₂²	—	4	1	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	—	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	2	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	2	no	—
562	C₄	—	4	1	no	—
563	C₄	—	4	1	no	—
564	C₄	—	4	2	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	2	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	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	—	8	1	no	—
576	C₂	—	8	2	no	—
577	C₂	—	8	1	no	—
578	C₂	#3488	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 ◁ #529 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #3523	C₂	semidirect
3. #3398	C₂	semidirect
4. #3392	C₂	semidirect
5. #3368	C₂	semidirect
6. #3364	C₂	semidirect
7. #3324	C₂	semidirect
8. #3323	C₂	semidirect
9. #3317	C₂	semidirect
10. #3302	C₂	semidirect
11. D₄×SD₁₆	C₂	semidirect
12. #3278	C₂	semidirect
13. #3276	C₂	semidirect
14. #3266	C₂	semidirect
15. #3258	C₂	semidirect
16. #3254	C₂	semidirect
17. #3222	C₂	semidirect
18. #3210	C₂	semidirect
19. #3121	C₂	semidirect
20. #3103	C₂	semidirect
21. #3043	C₂	semidirect
22. #3037	C₂	semidirect
23. #2993	C₂	semidirect
24. C₂×#137	C₂²	semidirect
25. C₂×#137	C₂²	semidirect
29. #557	C₂²	semidirect
30. #557	C₂²	semidirect
36. #552	C₂²	semidirect
40. D₄×Q₈	C₂²	semidirect
47. #541	C₂²	semidirect
53. #533	C₂²	semidirect
58. #519	C₂²	semidirect
59. C₂×C₄×Q₈	C₂²	semidirect
61. #494	C₂²	semidirect
63. #492	C₂²	semidirect
64. #490	C₂²	semidirect
66. #487	C₂²	semidirect
68. #485	C₂²	semidirect
71. #481	C₂²	semidirect
72. #479	C₂²	semidirect
73. #478	C₂²	semidirect
74. #477	C₂²	semidirect
75. #475	C₂²	semidirect
76. #475	C₂²	semidirect
78. #474	C₂²	semidirect
79. #470	C₂²	semidirect
82. #468	C₂²	semidirect
83. #467	C₂²	semidirect
87. #464	C₂²	semidirect
88. #464	C₂²	semidirect
89. #464	C₂²	semidirect
90. #464	C₂²	semidirect
91. #462	C₂²	semidirect
92. #462	C₂²	semidirect
93. #462	C₂²	semidirect
95. #461	C₂²	semidirect
96. #461	C₂²	semidirect
102. #460	C₂²	semidirect
103. #460	C₂²	semidirect
104. #452	C₂²	semidirect
105. #452	C₂²	semidirect
106. #452	C₂²	semidirect
107. #452	C₂²	semidirect
108. #451	C₂²	semidirect
113. #448	C₂²	semidirect
114. #446	C₂²	semidirect
115. C₈×Q₈	C₂²	semidirect
116. #441	C₂²	semidirect
117. #440	C₂²	semidirect
118. C₄×Q₁₆	C₂²	semidirect
121. C₄×SD₁₆	C₂²	semidirect
122. C₄×SD₁₆	C₂²	semidirect
123. C₄×SD₁₆	C₂²	semidirect
125. #436	C₂²	semidirect
126. #435	C₂²	semidirect
128. #433	C₂²	semidirect
129. #431	C₂²	semidirect
130. #424	C₂²	semidirect
131. #423	C₂²	semidirect
133. #417	C₂²	semidirect
134. #416	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
#3523	2
#3398	2
#3392	2
#3368	2
#3364	2
#3324	2
#3323	2
#3317	2
#3302	2
D₄×SD₁₆	2
#3278	2
#3276	2
#3266	2
#3258	2
#3254	2
#3222	2
#3210	2
#3121	2
#3103	2
#3043	2
#3037	2
#2993	2