Subgroups — #62006

Order 256.

934 conjugacy classes of subgroups.

The subgroup lattice has 583 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3514	C₂	1	1	yes	maximal, characteristic, complemented
2	#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	#3396	C₂	1	1	yes	maximal, characteristic, complemented
4	#3394	C₂	1	1	yes	maximal, characteristic, complemented
5	#3365	C₂	1	1	yes	maximal, characteristic, complemented
6	#3364	C₂	1	1	yes	maximal, characteristic, complemented
7	#3328	C₂	1	1	yes	maximal, characteristic, complemented
8	#3326	C₂	1	2	yes	maximal, complemented
9	#3324	C₂	1	1	yes	maximal, characteristic, complemented
10	#3322	C₂	1	2	yes	maximal, complemented
11	#3278	C₂	1	1	yes	maximal, characteristic, complemented
12	#3277	C₂	1	2	yes	maximal, complemented
13	#3275	C₂	1	2	yes	maximal, complemented
14	#3274	C₂	1	1	yes	maximal, characteristic, complemented
15	#3256	C₂	1	2	yes	maximal, complemented
16	#3251	C₂	1	1	yes	maximal, characteristic, complemented
17	#3211	C₂	1	2	yes	maximal, complemented
18	#3207	C₂	1	1	yes	maximal, characteristic, complemented
19	#3108	C₂	1	1	yes	maximal, characteristic, complemented
20	#3102	C₂	1	2	yes	maximal, complemented
21	#3040	C₂	1	2	yes	maximal, complemented
22	#3037	C₂	1	1	yes	maximal, characteristic, complemented
23	#2991	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137	C₂²	1	2	yes	complemented
25	C₂×#137	C₂²	1	2	yes	complemented
26	C₂×AGL(1,ℤ/8)	C₂²	1	2	yes	—
27	#559	—	2	1	no	—
28	#559	C₂²	1	1	yes	characteristic
29	#559	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	#555	—	2	1	no	—
35	#553	—	2	2	no	—
36	#553	C₂²	1	2	yes	complemented
37	#551	—	2	2	no	—
38	#550	C₂²	1	1	yes	characteristic
39	D₄×Q₈	C₂²	1	1	yes	characteristic
40	#548	C₂²	1	2	yes	—
41	#548	C₂²	1	2	yes	complemented
42	#546	—	2	1	no	—
43	#546	C₂²	1	2	yes	—
44	D₄²	C₂²	1	1	yes	characteristic
45	#542	—	2	1	no	—
46	#538	—	2	2	no	—
47	#532	—	2	1	no	—
48	#532	C₂²	1	1	yes	characteristic
49	#532	C₂²	1	1	yes	characteristic, complemented
50	#529	—	2	2	no	—
51	#529	C₂²	1	2	yes	—
52	#529	C₂²	1	1	yes	characteristic
53	#529	C₂²	1	2	yes	complemented
54	C₂×#124	C₂²	1	2	yes	—
55	#518	—	2	1	no	—
56	C₄×#41	—	2	1	no	—
57	C₄×#41	C₂²	1	1	yes	characteristic
58	C₄×#41	C₂²	1	2	yes	complemented
59	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
60	#495	C₂²	1	2	yes	—
61	#495	C₂²	1	2	yes	complemented
62	#493	C₂²	1	1	yes	characteristic
63	#492	C₂²	1	1	yes	characteristic, complemented
64	#488	C₂²	1	2	yes	—
65	#488	C₂²	1	2	yes	complemented
66	#487	C₂²	1	1	yes	characteristic, complemented
67	#486	C₂²	1	1	yes	characteristic
68	#485	C₂²	1	2	yes	complemented
69	#483	C₂²	1	1	yes	characteristic, complemented
70	#482	C₂²	1	2	yes	—
71	#480	C₂²	1	1	yes	characteristic
72	#479	C₂²	1	1	yes	characteristic, complemented
73	#479	C₂²	1	1	yes	characteristic, complemented
74	#479	C₂²	1	2	yes	complemented
75	#478	C₂²	1	2	yes	complemented
76	#478	C₂²	1	2	yes	complemented
77	#475	C₂²	1	1	yes	characteristic, complemented
78	#474	C₂²	1	1	yes	characteristic
79	#470	C₂²	1	2	yes	complemented
80	#469	C₂²	1	2	yes	—
81	#469	C₂²	1	2	yes	—
82	#468	C₂²	1	2	yes	—
83	#468	C₂²	1	2	yes	complemented
84	#468	C₂²	1	2	yes	complemented
85	#464	C₂²	1	1	yes	characteristic
86	#464	C₂²	1	1	yes	characteristic
87	#464	C₂²	1	2	yes	—
88	#464	C₂²	1	2	yes	complemented
89	#464	C₂²	1	2	yes	complemented
90	#464	C₂²	1	2	yes	complemented
91	#464	C₂²	1	2	yes	complemented
92	#463	C₂²	1	2	yes	—
93	#463	C₂²	1	2	yes	—
94	#463	C₂²	1	2	yes	complemented
95	#463	C₂²	1	2	yes	complemented
96	#463	C₂²	1	2	yes	complemented
97	#463	C₂²	1	2	yes	complemented
98	#462	C₂²	1	1	yes	characteristic, complemented
99	#462	C₂²	1	1	yes	characteristic, complemented
100	#460	C₂²	1	1	yes	characteristic
101	#460	C₂²	1	1	yes	characteristic
102	#460	C₂²	1	1	yes	characteristic, complemented
103	#459	C₂²	1	1	yes	characteristic
104	#452	C₂²	1	2	yes	complemented
105	#451	C₂²	1	2	yes	complemented
106	#451	C₂²	1	1	yes	characteristic, complemented
107	#450	C₂²	1	2	yes	—
108	#449	C₂²	1	2	yes	—
109	#449	C₂²	1	2	yes	complemented
110	#449	C₂²	1	2	yes	complemented
111	#448	C₂²	1	1	yes	characteristic
112	#448	C₂²	1	2	yes	complemented
113	#447	C₂²	1	2	yes	—
114	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
116	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
117	C₄×Q₁₆	C₂²	1	2	yes	complemented
118	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆	C₂²	1	1	yes	characteristic
121	C₄×SD₁₆	C₂²	1	2	yes	complemented
122	C₄×SD₁₆	C₂²	1	2	yes	complemented
123	C₄×D₈	C₂²	1	2	yes	complemented
124	#436	C₂²	1	1	yes	characteristic
125	#436	C₂²	1	1	yes	characteristic
126	#436	C₂²	1	2	yes	complemented
127	#436	C₂²	1	2	yes	complemented
128	#431	C₂²	1	2	yes	complemented
129	#431	C₂²	1	1	yes	characteristic, complemented
130	#423	C₂²	1	1	yes	characteristic, complemented
131	#423	C₂²	1	2	yes	complemented
132	#419	C₂²	1	2	yes	complemented
133	#418	C₂²	1	2	yes	—
134	#417	C₂²	1	2	yes	complemented
135	C₂×#41	—	2	1	no	—
136	C₂×#41	D₄	1	1	yes	characteristic
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	AGL(1,ℤ/8)	—	4	4	no	—
146	C₂×Q₁₆	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆	C₂³	1	2	yes	—
148	C₂×Q₁₆	C₂³	1	2	yes	—
149	C₂×Q₁₆	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆	C₂³	1	2	yes	—
152	C₂×SD₁₆	C₂³	1	2	yes	—
153	C₂×SD₁₆	C₂³	1	2	yes	—
154	C₂×SD₁₆	C₂³	1	2	yes	—
155	C₂×SD₁₆	C₂³	1	1	yes	characteristic
156	C₂×SD₁₆	C₂³	1	2	yes	—
157	C₂×D₈	C₂³	1	2	yes	—
158	C₂×D₈	C₂³	1	2	yes	—
159	C₂×D₈	C₂³	1	2	yes	—
160	C₂×M₁₆	C₂³	1	2	yes	—
161	C₂×M₁₆	C₂³	1	2	yes	—
162	C₂×M₁₆	C₂³	1	2	yes	—
163	C₄⋊Q₈	—	2	1	no	—
164	C₄⋊Q₈	—	2	1	no	—
165	C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	#127	—	2	1	no	—
168	#127	C₂³	1	1	yes	characteristic
169	#127	C₂³	1	1	yes	characteristic
170	#126	—	2	2	no	—
171	#126	—	2	2	no	—
172	#126	—	2	2	no	—
173	#126	—	2	2	no	—
174	#126	—	2	1	no	—
175	#126	—	2	2	no	—
176	#125	—	2	2	no	—
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	1	no	—
182	#124	—	2	2	no	—
183	#124	—	2	2	no	—
184	#124	—	2	2	no	—
185	#124	—	2	2	no	—
186	#124	—	2	1	no	—
187	#124	C₂³	1	1	yes	characteristic
188	#124	C₂³	1	2	yes	—
189	#124	C₂³	1	2	yes	—
190	#124	C₂³	1	2	yes	—
191	#124	C₂³	1	2	yes	—
192	#123	—	2	1	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	C₂²⋊Q₈	—	2	1	no	—
200	C₂²⋊Q₈	—	2	2	no	—
201	C₂²⋊Q₈	—	2	2	no	—
202	C₂²⋊Q₈	—	2	2	no	—
203	C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
205	C₂²⋊Q₈	C₂³	1	2	yes	—
206	#121	—	2	2	no	—
207	#121	—	2	2	no	—
208	#121	—	2	2	no	—
209	#121	—	2	1	no	—
210	#121	—	2	1	no	—
211	#121	—	2	1	no	—
212	#121	—	2	1	no	—
213	#121	—	2	2	no	—
214	#121	—	2	2	no	—
215	#121	C₂³	1	2	yes	—
216	#121	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
224	C₄×Q₈	—	2	1	no	—
225	C₄×Q₈	D₄	1	1	yes	characteristic
226	C₄×Q₈	C₂³	1	1	yes	characteristic
227	C₄×Q₈	C₂³	1	1	yes	characteristic
228	C₄×Q₈	C₂³	1	1	yes	characteristic
229	C₄×Q₈	C₂³	1	1	yes	characteristic
230	C₄×Q₈	C₂³	1	2	yes	—
231	C₄×Q₈	C₂³	1	2	yes	—
232	C₄×Q₈	C₂³	1	1	yes	characteristic
233	C₄×Q₈	C₂³	1	1	yes	characteristic
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	2	no	—
239	C₄×D₄	—	2	1	no	—
240	C₄×D₄	—	2	1	no	—
241	C₄×D₄	—	2	1	no	—
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	—	2	2	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	—	2	1	no	—
249	C₄×D₄	D₄	1	1	yes	characteristic
250	C₄×D₄	D₄	1	2	yes	—
251	C₄×D₄	C₂³	1	2	yes	—
252	C₄×D₄	C₂³	1	2	yes	—
253	C₄×D₄	C₂³	1	1	yes	characteristic
254	C₄×D₄	C₂³	1	2	yes	—
255	C₄×D₄	C₂³	1	1	yes	characteristic
256	C₄×D₄	C₂³	1	2	yes	—
257	#117	—	2	1	no	—
258	#117	—	2	2	no	—
259	#117	—	2	2	no	—
260	#117	—	2	1	no	—
261	#117	—	2	2	no	—
262	#117	D₄	1	1	yes	characteristic
263	#117	D₄	1	2	yes	—
264	#117	C₂³	1	2	yes	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₄²	—	2	1	no	—
271	C₂×C₄²	—	2	2	no	—
272	C₂×C₄²	C₂³	1	1	yes	characteristic
273	C₂×C₄²	C₂³	1	2	yes	—
274	#107	C₂³	1	1	yes	characteristic
275	#107	C₂³	1	2	yes	—
276	#107	C₂³	1	1	yes	characteristic
277	#106	C₂³	1	1	yes	characteristic
278	#106	C₂³	1	1	yes	characteristic
279	#106	C₂³	1	2	yes	—
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	1	yes	characteristic
290	#103	C₂³	1	2	yes	—
291	#103	C₂³	1	2	yes	—
292	#103	C₂³	1	1	yes	characteristic
293	#103	C₂³	1	1	yes	characteristic
294	#103	C₂³	1	1	yes	characteristic
295	#103	C₂³	1	1	yes	characteristic
296	#103	C₂³	1	1	yes	characteristic
297	#103	C₂³	1	2	yes	—
298	#102	C₂³	1	2	yes	—
299	#102	C₂³	1	2	yes	—
300	#102	C₂³	1	1	yes	characteristic
301	#102	C₂³	1	2	yes	—
302	#102	C₂³	1	2	yes	—
303	#102	C₂³	1	2	yes	—
304	#102	C₂³	1	1	yes	characteristic
305	#102	C₂³	1	2	yes	—
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	1	yes	characteristic
310	C₂²⋊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	C₄×C₈	C₂³	1	2	yes	—
315	C₂⁴	—	2	2	no	—
316	#41	—	2	4	no	—
317	#41	—	4	2	no	—
318	#41	—	4	2	no	—
319	#41	—	4	4	no	—
320	#41	—	4	2	no	—
321	#41	—	4	2	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	4	1	no	—
327	C₂×Q₈	—	4	2	no	—
328	C₂×Q₈	—	4	2	no	—
329	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
330	C₂×Q₈	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈	C₂⁴	1	2	yes	—
332	C₂×Q₈	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈	C₂⁴	1	1	yes	characteristic
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	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	1	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	—	4	4	no	—
348	C₂×D₄	C₂×D₄	1	1	yes	characteristic
349	C₂×D₄	C₂×D₄	1	2	yes	—
350	C₂×D₄	C₂⁴	1	1	yes	characteristic
351	C₂×D₄	C₂⁴	1	2	yes	—
352	C₂×D₄	C₂⁴	1	2	yes	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	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	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄	1	2	yes	—
364	C₂²×C₄	C₂×D₄	1	2	yes	—
365	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄	C₂⁴	1	2	yes	—
368	Q₁₆	—	2	2	no	—
369	Q₁₆	—	2	4	no	—
370	Q₁₆	—	4	1	no	—
371	Q₁₆	—	4	2	no	—
372	SD₁₆	—	2	2	no	—
373	SD₁₆	—	2	4	no	—
374	SD₁₆	—	4	2	no	—
375	SD₁₆	—	4	1	no	—
376	SD₁₆	—	4	2	no	—
377	SD₁₆	—	4	2	no	—
378	SD₁₆	—	4	2	no	—
379	D₈	—	4	2	no	—
380	D₈	—	4	2	no	—
381	D₈	—	4	2	no	—
382	M₁₆	—	4	2	no	—
383	M₁₆	—	4	2	no	—
384	M₁₆	—	4	2	no	—
385	C₂×C₈	C₂⁴	1	1	yes	characteristic
386	C₂×C₈	C₂⁴	1	1	yes	characteristic
387	C₂×C₈	C₂⁴	1	1	yes	characteristic
388	C₂×C₈	C₂⁴	1	2	yes	—
389	C₂×C₈	C₂⁴	1	2	yes	—
390	C₂×C₈	C₂⁴	1	1	yes	characteristic
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	1	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	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	1	no	—
409	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
410	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
411	C₄⋊C₄	C₂×D₄	1	2	yes	—
412	C₄⋊C₄	C₂×D₄	1	2	yes	—
413	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄	C₂⁴	1	2	yes	—
416	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	2	1	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	2	2	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	2	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	—	2	1	no	—
439	C₂²⋊C₄	—	2	2	no	—
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	C₄²	—	2	1	no	—
444	C₄²	—	2	1	no	—
445	C₄²	—	2	2	no	—
446	C₄²	—	2	2	no	—
447	C₄²	—	2	1	no	—
448	C₄²	—	2	1	no	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	1	no	—
451	C₄²	C₂×D₄	1	2	yes	—
452	C₄²	C₂×D₄	1	1	yes	characteristic
453	C₄²	C₂×D₄	1	2	yes	—
454	C₄²	C₂×D₄	1	1	yes	characteristic
455	C₄²	C₂⁴	1	2	yes	—
456	C₄²	C₂⁴	1	1	yes	characteristic
457	C₄²	C₂⁴	1	1	yes	characteristic
458	C₂³	—	2	1	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	4	4	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	1	no	—
469	Q₈	—	2	1	no	—
470	Q₈	—	2	2	no	—
471	Q₈	—	2	1	no	—
472	Q₈	—	2	2	no	—
473	Q₈	—	2	1	no	—
474	Q₈	—	4	2	no	—
475	Q₈	—	4	2	no	—
476	Q₈	—	8	2	no	—
477	Q₈	H(5,𝔽₂)	1	2	yes	—
478	D₄	—	2	2	no	—
479	D₄	—	2	1	no	—
480	D₄	—	2	2	no	—
481	D₄	—	2	2	no	—
482	D₄	—	2	2	no	—
483	D₄	—	2	2	no	—
484	D₄	—	2	1	no	—
485	D₄	—	4	2	no	—
486	D₄	—	4	4	no	—
487	D₄	—	4	4	no	—
488	D₄	—	4	4	no	—
489	D₄	—	4	2	no	—
490	D₄	—	4	2	no	—
491	D₄	—	8	1	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	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	1	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	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	—	4	2	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	4	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	4	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	8	2	no	—
519	C₂×C₄	—	8	2	no	—
520	C₂×C₄	—	8	2	no	—
521	C₂×C₄	—	8	1	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	2	yes	—
529	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄	C₂⁵	1	1	yes	characteristic
532	C₈	—	2	1	no	—
533	C₈	—	2	2	no	—
534	C₈	—	2	1	no	—
535	C₈	—	2	2	no	—
536	C₈	—	2	1	no	—
537	C₈	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	2	2	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	4	2	no	—
546	C₂²	—	4	1	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	16	4	no	—
554	C₂²	C₂³×D₄	1	1	yes	characteristic
555	C₄	—	2	1	no	—
556	C₄	—	2	2	no	—
557	C₄	—	2	1	no	—
558	C₄	—	2	2	no	—
559	C₄	—	2	1	no	—
560	C₄	—	2	2	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	2	no	—
563	C₄	—	4	1	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	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	#575	1	2	yes	—
572	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
573	C₄	#585	1	1	yes	characteristic
574	C₂	—	4	1	no	—
575	C₂	—	4	2	no	—
576	C₂	—	8	2	no	—
577	C₂	—	8	2	no	—
578	C₂	—	8	1	no	—
579	C₂	#3488	1	1	yes	characteristic
580	C₂	C₂×#575	1	1	yes	characteristic
581	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 ◁ C₄×#41 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3514	C₂	semidirect
2. #3480	C₂	semidirect
3. #3396	C₂	semidirect
4. #3394	C₂	semidirect
5. #3365	C₂	semidirect
6. #3364	C₂	semidirect
7. #3328	C₂	semidirect
8. #3326	C₂	semidirect
9. #3324	C₂	semidirect
10. #3322	C₂	semidirect
11. #3278	C₂	semidirect
12. #3277	C₂	semidirect
13. #3275	C₂	semidirect
14. #3274	C₂	semidirect
15. #3256	C₂	semidirect
16. #3251	C₂	semidirect
17. #3211	C₂	semidirect
18. #3207	C₂	semidirect
19. #3108	C₂	semidirect
20. #3102	C₂	semidirect
21. #3040	C₂	semidirect
22. #3037	C₂	semidirect
23. #2991	C₂	semidirect
24. C₂×#137	C₂²	semidirect
25. C₂×#137	C₂²	semidirect
29. #559	C₂²	semidirect
30. #557	C₂²	semidirect
36. #553	C₂²	semidirect
41. #548	C₂²	semidirect
49. #532	C₂²	semidirect
53. #529	C₂²	semidirect
58. C₄×#41	C₂²	semidirect
59. C₂×C₄×Q₈	C₂²	semidirect
61. #495	C₂²	semidirect
63. #492	C₂²	semidirect
65. #488	C₂²	semidirect
66. #487	C₂²	semidirect
68. #485	C₂²	semidirect
69. #483	C₂²	semidirect
72. #479	C₂²	semidirect
73. #479	C₂²	semidirect
74. #479	C₂²	semidirect
75. #478	C₂²	semidirect
76. #478	C₂²	semidirect
77. #475	C₂²	semidirect
79. #470	C₂²	semidirect
83. #468	C₂²	semidirect
84. #468	C₂²	semidirect
88. #464	C₂²	semidirect
89. #464	C₂²	semidirect
90. #464	C₂²	semidirect
91. #464	C₂²	semidirect
94. #463	C₂²	semidirect
95. #463	C₂²	semidirect
96. #463	C₂²	semidirect
97. #463	C₂²	semidirect
98. #462	C₂²	semidirect
99. #462	C₂²	semidirect
102. #460	C₂²	semidirect
104. #452	C₂²	semidirect
105. #451	C₂²	semidirect
106. #451	C₂²	semidirect
109. #449	C₂²	semidirect
110. #449	C₂²	semidirect
112. #448	C₂²	semidirect
114. C₈×Q₈	C₂²	semidirect
115. C₈×Q₈	C₂²	semidirect
116. C₄×Q₁₆	C₂²	semidirect
117. C₄×Q₁₆	C₂²	semidirect
118. C₄×Q₁₆	C₂²	semidirect
121. C₄×SD₁₆	C₂²	semidirect
122. C₄×SD₁₆	C₂²	semidirect
123. C₄×D₈	C₂²	semidirect
126. #436	C₂²	semidirect
127. #436	C₂²	semidirect
128. #431	C₂²	semidirect
129. #431	C₂²	semidirect
130. #423	C₂²	semidirect
131. #423	C₂²	semidirect
132. #419	C₂²	semidirect
134. #417	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3514	2
#3480	2
#3396	2
#3394	2
#3365	2
#3364	2
#3328	2
#3326	2
#3324	2
#3322	2
#3278	2
#3277	2
#3275	2
#3274	2
#3256	2
#3251	2
#3211	2
#3207	2
#3108	2
#3102	2
#3040	2
#3037	2
#2991	2