Subgroups — #61471

Order 256.

955 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3513	C₂	1	2	yes	maximal, complemented
2	#3396	C₂	1	1	yes	maximal, characteristic, complemented
3	#3380	C₂	1	1	yes	maximal, characteristic, complemented
4	#3370	C₂	1	2	yes	maximal, complemented
5	#3339	C₂	1	1	yes	maximal, characteristic, complemented
6	#3336	C₂	1	1	yes	maximal, characteristic, complemented
7	#3334	C₂	1	1	yes	maximal, characteristic, complemented
8	#3322	C₂	1	2	yes	maximal, complemented
9	#3310	C₂	1	2	yes	maximal, complemented
10	#3306	C₂	1	2	yes	maximal, complemented
11	#3280	C₂	1	1	yes	maximal, characteristic, complemented
12	#3280	C₂	1	1	yes	maximal, characteristic, complemented
13	D₄×D₈	C₂	1	1	yes	maximal, characteristic, complemented
14	#3176	C₂	1	1	yes	maximal, characteristic, complemented
15	#3175	C₂	1	1	yes	maximal, characteristic, complemented
16	#3168	C₂	1	1	yes	maximal, characteristic, complemented
17	#3119	C₂	1	2	yes	maximal, complemented
18	#3118	C₂	1	2	yes	maximal, complemented
19	#3114	C₂	1	2	yes	maximal, complemented
20	#2966	C₂	1	1	yes	maximal, characteristic, complemented
21	#2951	C₂	1	1	yes	maximal, characteristic, complemented
22	#2948	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×D₈	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#135	C₂²	1	1	yes	characteristic
25	C₂²×D₈	C₂²	1	1	yes	characteristic
26	C₂²×D₈	C₂²	1	1	yes	characteristic
27	#559	C₂²	1	2	yes	complemented
28	#554	C₂²	1	2	yes	complemented
29	#553	—	2	2	no	—
30	#553	C₂²	1	2	yes	complemented
31	#552	C₂²	1	2	yes	—
32	#551	—	2	2	no	—
33	#551	—	2	2	no	—
34	#547	C₂²	1	2	yes	complemented
35	#546	—	2	2	no	—
36	#546	C₂²	1	2	yes	complemented
37	#546	C₂²	1	2	yes	complemented
38	D₄²	C₂²	1	2	yes	—
39	#542	C₂²	1	2	yes	complemented
40	#540	C₂²	1	2	yes	complemented
41	#539	—	2	2	no	—
42	#538	—	2	2	no	—
43	#529	C₂²	1	1	yes	characteristic
44	#529	C₂²	1	2	yes	complemented
45	#525	—	2	2	no	—
46	C₂×#123	—	2	2	no	—
47	#520	C₂²	1	2	yes	complemented
48	#518	C₂²	1	2	yes	complemented
49	C₂×C₄×D₄	C₂²	1	2	yes	complemented
50	#500	C₂²	1	1	yes	characteristic, complemented
51	#499	C₂²	1	1	yes	characteristic, complemented
52	#499	C₂²	1	1	yes	characteristic, complemented
53	#495	C₂²	1	1	yes	characteristic, complemented
54	#495	C₂²	1	1	yes	characteristic, complemented
55	#493	C₂²	1	1	yes	characteristic
56	#490	C₂²	1	2	yes	complemented
57	#489	C₂²	1	2	yes	complemented
58	#488	C₂²	1	2	yes	complemented
59	#485	C₂²	1	2	yes	complemented
60	#483	C₂²	1	2	yes	complemented
61	#482	C₂²	1	2	yes	complemented
62	#481	C₂²	1	2	yes	complemented
63	#480	C₂²	1	2	yes	complemented
64	#480	C₂²	1	2	yes	complemented
65	#479	C₂²	1	2	yes	complemented
66	#478	C₂²	1	2	yes	complemented
67	#478	C₂²	1	2	yes	complemented
68	#478	C₂²	1	2	yes	complemented
69	#476	C₂²	1	2	yes	complemented
70	#474	C₂²	1	2	yes	complemented
71	#469	C₂²	1	2	yes	complemented
72	#468	C₂²	1	2	yes	complemented
73	#467	C₂²	1	1	yes	characteristic, complemented
74	#467	C₂²	1	1	yes	characteristic, complemented
75	#466	C₂²	1	1	yes	characteristic
76	#466	C₂²	1	1	yes	characteristic
77	#466	C₂²	1	1	yes	characteristic, complemented
78	#466	C₂²	1	1	yes	characteristic, complemented
79	#465	C₂²	1	2	yes	complemented
80	#463	C₂²	1	2	yes	complemented
81	#463	C₂²	1	2	yes	complemented
82	#463	C₂²	1	2	yes	complemented
83	#463	C₂²	1	2	yes	complemented
84	#460	C₂²	1	2	yes	complemented
85	#459	C₂²	1	2	yes	—
86	#450	C₂²	1	2	yes	complemented
87	#450	C₂²	1	2	yes	complemented
88	#449	C₂²	1	2	yes	complemented
89	#449	C₂²	1	2	yes	complemented
90	#447	C₂²	1	2	yes	—
91	#447	C₂²	1	2	yes	—
92	#446	C₂²	1	1	yes	characteristic, complemented
93	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
94	#442	C₂²	1	2	yes	complemented
95	#442	C₂²	1	2	yes	complemented
96	#442	C₂²	1	2	yes	complemented
97	#440	C₂²	1	2	yes	complemented
98	#440	C₂²	1	2	yes	complemented
99	#440	C₂²	1	2	yes	complemented
100	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
101	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
102	C₄×SD₁₆	C₂²	1	2	yes	complemented
103	C₄×D₈	C₂²	1	1	yes	characteristic
104	C₄×D₈	C₂²	1	1	yes	characteristic
105	C₄×D₈	C₂²	1	1	yes	characteristic
106	C₄×D₈	C₂²	1	1	yes	characteristic
107	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
108	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
109	C₄×D₈	C₂²	1	2	yes	complemented
110	C₄×D₈	C₂²	1	2	yes	complemented
111	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
112	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
113	#436	C₂²	1	1	yes	characteristic, complemented
114	#435	C₂²	1	1	yes	characteristic
115	#435	C₂²	1	1	yes	characteristic, complemented
116	C₈×D₄	C₂²	1	1	yes	characteristic
117	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
118	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
119	#433	C₂²	1	1	yes	characteristic, complemented
120	#433	C₂²	1	1	yes	characteristic, complemented
121	#432	C₂²	1	1	yes	characteristic, complemented
122	#427	C₂²	1	1	yes	characteristic, complemented
123	C₂×#107	C₂²	1	1	yes	characteristic, complemented
124	C₂×#107	C₂²	1	1	yes	characteristic, complemented
125	#418	C₂²	1	2	yes	complemented
126	#417	C₂²	1	2	yes	complemented
127	C₂×#102	C₂²	1	2	yes	complemented
128	#405	C₂²	1	1	yes	characteristic, complemented
129	#405	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
131	C₂×#41	—	2	2	no	—
132	C₂×#41	C₂³	1	2	yes	—
133	C₂²×D₄	—	2	2	no	—
134	C₂²×D₄	C₂³	1	2	yes	—
135	C₂²×D₄	C₂³	1	2	yes	—
136	C₂³×C₄	—	2	2	no	—
137	#135	—	2	4	no	—
138	C₂×Q₁₆	C₂³	1	1	yes	characteristic
139	C₂×SD₁₆	C₂³	1	2	yes	—
140	C₂×SD₁₆	C₂³	1	2	yes	—
141	C₂×SD₁₆	C₂³	1	2	yes	—
142	C₂×D₈	—	2	4	no	—
143	C₂×D₈	—	2	4	no	—
144	C₂×D₈	C₂³	1	2	yes	—
145	C₂×D₈	C₂³	1	1	yes	characteristic
146	C₂×D₈	C₂³	1	1	yes	characteristic
147	C₂×D₈	C₂³	1	2	yes	—
148	C₂×D₈	C₂³	1	2	yes	—
149	C₂×D₈	C₂³	1	1	yes	characteristic
150	C₂×M₁₆	C₂³	1	1	yes	characteristic
151	C₂×M₁₆	C₂³	1	1	yes	characteristic
152	C₂²×C₈	C₂³	1	1	yes	characteristic
153	C₂²×C₈	C₂³	1	1	yes	characteristic
154	C₂²×C₈	C₂³	1	1	yes	characteristic
155	C₂²×C₈	C₂³	1	1	yes	characteristic
156	C₄⋊Q₈	C₂³	1	2	yes	—
157	#127	C₂³	1	2	yes	—
158	#126	—	2	2	no	—
159	#126	—	2	2	no	—
160	#126	—	2	2	no	—
161	#126	—	2	2	no	—
162	#126	D₄	1	1	yes	characteristic
163	#126	D₄	1	1	yes	characteristic
164	#125	—	2	2	no	—
165	#125	D₄	1	1	yes	characteristic
166	#125	C₂³	1	2	yes	—
167	#125	C₂³	1	2	yes	—
168	#124	—	2	2	no	—
169	#124	—	2	2	no	—
170	#124	D₄	1	1	yes	characteristic
171	#124	C₂³	1	2	yes	—
172	#124	C₂³	1	2	yes	—
173	#123	—	2	2	no	—
174	#123	—	2	2	no	—
175	#123	—	2	2	no	—
176	#123	—	2	2	no	—
177	#123	—	2	2	no	—
178	#123	—	2	2	no	—
179	#123	—	2	2	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	D₄	1	1	yes	characteristic
186	#123	D₄	1	1	yes	characteristic
187	C₂²⋊Q₈	—	2	2	no	—
188	C₂²⋊Q₈	—	2	2	no	—
189	C₂²⋊Q₈	—	2	2	no	—
190	C₂²⋊Q₈	—	2	2	no	—
191	C₂²⋊Q₈	—	2	2	no	—
192	C₂²⋊Q₈	D₄	1	1	yes	characteristic
193	C₂²⋊Q₈	C₂³	1	2	yes	—
194	C₂²⋊Q₈	C₂³	1	2	yes	—
195	#121	—	2	2	no	—
196	#121	—	2	2	no	—
197	#121	—	2	2	no	—
198	#121	—	2	2	no	—
199	#121	—	2	2	no	—
200	#121	—	2	2	no	—
201	#121	D₄	1	1	yes	characteristic
202	#121	C₂³	1	2	yes	—
203	#121	C₂³	1	2	yes	—
204	#121	C₂³	1	2	yes	—
205	#121	C₂³	1	2	yes	—
206	#120	—	2	2	no	—
207	#120	—	2	2	no	—
208	#120	—	2	2	no	—
209	#120	—	2	2	no	—
210	C₄×Q₈	C₂³	1	2	yes	—
211	C₄×Q₈	C₂³	1	2	yes	—
212	C₄×Q₈	C₂³	1	1	yes	characteristic
213	C₄×D₄	—	2	2	no	—
214	C₄×D₄	—	2	2	no	—
215	C₄×D₄	—	2	2	no	—
216	C₄×D₄	—	2	2	no	—
217	C₄×D₄	—	2	2	no	—
218	C₄×D₄	—	2	2	no	—
219	C₄×D₄	—	2	2	no	—
220	C₄×D₄	—	2	2	no	—
221	C₄×D₄	—	2	2	no	—
222	C₄×D₄	C₂³	1	2	yes	—
223	C₄×D₄	C₂³	1	2	yes	—
224	C₄×D₄	C₂³	1	2	yes	—
225	C₄×D₄	C₂³	1	2	yes	—
226	C₄×D₄	C₂³	1	2	yes	—
227	C₄×D₄	C₂³	1	2	yes	—
228	C₄×D₄	C₂³	1	2	yes	—
229	C₄×D₄	C₂³	1	2	yes	—
230	C₄×D₄	C₂³	1	1	yes	characteristic
231	C₄×D₄	C₂³	1	1	yes	characteristic
232	C₄×D₄	C₂³	1	1	yes	characteristic
233	#117	—	2	2	no	—
234	#117	—	2	2	no	—
235	#117	—	2	2	no	—
236	#117	C₂³	1	2	yes	—
237	#117	C₂³	1	1	yes	characteristic
238	#117	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊C₄	—	2	2	no	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	C₂³	1	2	yes	—
242	C₂×C₄⋊C₄	C₂³	1	2	yes	—
243	C₂×C₂²⋊C₄	—	2	2	no	—
244	C₂×C₂²⋊C₄	—	2	2	no	—
245	C₂×C₂²⋊C₄	—	2	2	no	—
246	C₂×C₂²⋊C₄	—	2	2	no	—
247	C₂×C₂²⋊C₄	—	2	2	no	—
248	C₂×C₄²	C₂³	1	1	yes	characteristic
249	#107	C₂³	1	1	yes	characteristic
250	#107	C₂³	1	1	yes	characteristic
251	#107	C₂³	1	1	yes	characteristic
252	#107	C₂³	1	2	yes	—
253	#107	C₂³	1	2	yes	—
254	#107	C₂³	1	1	yes	characteristic
255	#107	C₂³	1	2	yes	—
256	#106	C₂³	1	2	yes	—
257	#106	C₂³	1	2	yes	—
258	#106	C₂³	1	2	yes	—
259	C₄⋊C₈	C₂³	1	1	yes	characteristic
260	C₄⋊C₈	C₂³	1	1	yes	characteristic
261	C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₄⋊C₈	C₂³	1	1	yes	characteristic
263	C₄⋊C₈	C₂³	1	1	yes	characteristic
264	C₄⋊C₈	C₂³	1	1	yes	characteristic
265	#103	C₂³	1	2	yes	—
266	#103	C₂³	1	2	yes	—
267	#103	C₂³	1	2	yes	—
268	#103	C₂³	1	2	yes	—
269	#102	C₂³	1	2	yes	—
270	#102	C₂³	1	2	yes	—
271	#102	C₂³	1	2	yes	—
272	#102	C₂³	1	2	yes	—
273	#102	C₂³	1	2	yes	—
274	#102	C₂³	1	2	yes	—
275	#102	C₂³	1	2	yes	—
276	#102	C₂³	1	2	yes	—
277	#102	C₂³	1	2	yes	—
278	#102	C₂³	1	2	yes	—
279	#102	C₂³	1	2	yes	—
280	#102	C₂³	1	2	yes	—
281	C₂²⋊C₈	C₂³	1	1	yes	characteristic
282	C₂²⋊C₈	C₂³	1	1	yes	characteristic
283	C₂²⋊C₈	C₂³	1	1	yes	characteristic
284	C₂²⋊C₈	C₂³	1	1	yes	characteristic
285	C₂²⋊C₈	C₂³	1	1	yes	characteristic
286	C₂²⋊C₈	C₂³	1	1	yes	characteristic
287	#97	C₂³	1	1	yes	characteristic
288	#97	C₂³	1	1	yes	characteristic
289	#97	C₂³	1	1	yes	characteristic
290	#97	C₂³	1	1	yes	characteristic
291	C₄×C₈	C₂³	1	1	yes	characteristic
292	C₄×C₈	C₂³	1	1	yes	characteristic
293	C₄×C₈	C₂³	1	1	yes	characteristic
294	C₄×C₈	C₂³	1	1	yes	characteristic
295	C₄×C₈	C₂³	1	1	yes	characteristic
296	C₄×C₈	C₂³	1	1	yes	characteristic
297	C₂⁴	—	2	2	no	—
298	C₂⁴	—	2	2	no	—
299	#41	—	2	4	no	—
300	#41	—	4	2	no	—
301	#41	—	8	4	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
304	C₂×Q₈	C₂⁴	1	2	yes	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	—	2	4	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	4	2	no	—
317	C₂×D₄	—	4	2	no	—
318	C₂×D₄	—	8	4	no	—
319	C₂×D₄	C₂×D₄	1	1	yes	characteristic
320	C₂×D₄	C₂×D₄	1	1	yes	characteristic
321	C₂×D₄	C₂×D₄	1	1	yes	characteristic
322	C₂×D₄	C₂⁴	1	2	yes	—
323	C₂×D₄	C₂⁴	1	2	yes	—
324	C₂×D₄	C₂⁴	1	2	yes	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	8	4	no	—
337	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
339	C₂²×C₄	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄	C₂⁴	1	1	yes	characteristic
342	Q₁₆	—	2	2	no	—
343	SD₁₆	—	2	4	no	—
344	SD₁₆	—	4	2	no	—
345	SD₁₆	—	4	2	no	—
346	D₈	—	2	4	no	—
347	D₈	—	2	4	no	—
348	D₈	—	2	2	no	—
349	D₈	—	2	2	no	—
350	D₈	—	4	2	no	—
351	D₈	#41	1	4	yes	complemented
352	M₁₆	—	4	1	no	—
353	M₁₆	—	4	1	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	4	1	no	—
358	C₂×C₈	C₂⁴	1	1	yes	characteristic
359	C₂×C₈	C₂⁴	1	1	yes	characteristic
360	C₂×C₈	C₂⁴	1	1	yes	characteristic
361	C₂×C₈	C₂⁴	1	1	yes	characteristic
362	C₂×C₈	C₂⁴	1	1	yes	characteristic
363	C₂×C₈	C₂⁴	1	1	yes	characteristic
364	C₂×C₈	C₂⁴	1	1	yes	characteristic
365	C₂×C₈	C₂⁴	1	1	yes	characteristic
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
378	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
379	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
380	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
381	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
382	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
383	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
384	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
385	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
386	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
387	C₄⋊C₄	C₂⁴	1	2	yes	—
388	C₄⋊C₄	C₂⁴	1	2	yes	—
389	C₄⋊C₄	C₂⁴	1	2	yes	—
390	C₄⋊C₄	C₂⁴	1	2	yes	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	2	2	no	—
393	C₂²⋊C₄	—	2	2	no	—
394	C₂²⋊C₄	—	2	2	no	—
395	C₂²⋊C₄	—	2	2	no	—
396	C₂²⋊C₄	—	2	2	no	—
397	C₂²⋊C₄	—	2	2	no	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₂²⋊C₄	—	2	2	no	—
400	C₂²⋊C₄	—	2	2	no	—
401	C₂²⋊C₄	—	2	2	no	—
402	C₂²⋊C₄	—	2	2	no	—
403	C₂²⋊C₄	—	2	2	no	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₂²⋊C₄	—	2	2	no	—
409	C₂²⋊C₄	—	2	2	no	—
410	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
411	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
412	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
413	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
414	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
415	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
416	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
417	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
418	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
419	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
420	C₄²	—	2	2	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	2	2	no	—
423	C₄²	C₂×D₄	1	1	yes	characteristic
424	C₄²	C₂×D₄	1	1	yes	characteristic
425	C₄²	C₂⁴	1	1	yes	characteristic
426	C₄²	C₂⁴	1	1	yes	characteristic
427	C₄²	C₂⁴	1	1	yes	characteristic
428	C₄²	C₂⁴	1	1	yes	characteristic
429	C₂³	—	2	2	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	2	2	no	—
432	C₂³	—	4	4	no	—
433	C₂³	—	4	4	no	—
434	C₂³	—	4	4	no	—
435	C₂³	—	8	2	no	—
436	C₂³	—	8	2	no	—
437	C₂³	—	8	2	no	—
438	C₂³	C₂²×D₄	1	1	yes	characteristic
439	C₂³	C₂²×D₄	1	1	yes	characteristic
440	C₂³	C₂²×D₄	1	1	yes	characteristic
441	Q₈	—	2	2	no	—
442	Q₈	—	2	2	no	—
443	Q₈	—	4	1	no	—
444	Q₈	—	8	2	no	—
445	D₄	—	2	2	no	—
446	D₄	—	2	2	no	—
447	D₄	—	2	2	no	—
448	D₄	—	2	2	no	—
449	D₄	—	2	2	no	—
450	D₄	—	2	2	no	—
451	D₄	—	2	2	no	—
452	D₄	—	4	1	no	—
453	D₄	—	4	4	no	—
454	D₄	—	4	4	no	—
455	D₄	—	4	4	no	—
456	D₄	—	4	4	no	—
457	D₄	—	8	2	no	—
458	D₄	—	8	2	no	—
459	D₄	—	8	2	no	—
460	D₄	—	8	2	no	—
461	D₄	—	8	2	no	—
462	D₄	C₂×#41	1	4	yes	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	—	8	2	no	—
479	C₂×C₄	—	8	2	no	—
480	C₂×C₄	—	8	2	no	—
481	C₂×C₄	—	8	2	no	—
482	C₂×C₄	—	8	2	no	—
483	C₂×C₄	—	8	2	no	—
484	C₂×C₄	—	8	2	no	—
485	C₂×C₄	—	8	2	no	—
486	C₂×C₄	—	8	2	no	—
487	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
488	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄	C₂⁵	1	1	yes	characteristic
499	C₈	—	2	1	no	—
500	C₈	—	2	1	no	—
501	C₈	—	2	1	no	—
502	C₈	—	2	1	no	—
503	C₈	—	2	1	no	—
504	C₈	—	2	1	no	—
505	C₈	—	2	1	no	—
506	C₈	C₂×#41	1	2	yes	—
507	C₂²	—	2	1	no	—
508	C₂²	—	2	1	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	2	1	no	—
511	C₂²	—	2	1	no	—
512	C₂²	—	2	1	no	—
513	C₂²	—	2	4	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	4	2	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	4	2	no	—
524	C₂²	—	8	8	no	—
525	C₂²	—	16	4	no	—
526	C₂²	#576	1	2	yes	—
527	C₂²	C₂³×D₄	1	1	yes	characteristic
528	C₄	—	2	1	no	—
529	C₄	—	2	1	no	—
530	C₄	—	2	1	no	—
531	C₄	—	2	1	no	—
532	C₄	—	2	1	no	—
533	C₄	—	2	1	no	—
534	C₄	—	2	1	no	—
535	C₄	—	2	1	no	—
536	C₄	—	2	1	no	—
537	C₄	—	2	1	no	—
538	C₄	—	2	1	no	—
539	C₄	—	4	2	no	—
540	C₄	—	4	2	no	—
541	C₄	—	4	2	no	—
542	C₄	—	4	2	no	—
543	C₄	—	4	2	no	—
544	C₄	C₂²×#41	1	1	yes	characteristic
545	C₄	#585	1	1	yes	characteristic
546	C₂	—	2	2	no	—
547	C₂	—	4	1	no	—
548	C₂	—	4	1	no	—
549	C₂	—	4	4	no	—
550	C₂	—	8	2	no	—
551	C₂	—	8	2	no	—
552	C₂	D₄×#41	1	1	yes	characteristic
553	C₂	C₂×#576	1	1	yes	characteristic
554	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. #3513	C₂	semidirect
2. #3396	C₂	semidirect
3. #3380	C₂	semidirect
4. #3370	C₂	semidirect
5. #3339	C₂	semidirect
6. #3336	C₂	semidirect
7. #3334	C₂	semidirect
8. #3322	C₂	semidirect
9. #3310	C₂	semidirect
10. #3306	C₂	semidirect
11. #3280	C₂	semidirect
12. #3280	C₂	semidirect
13. D₄×D₈	C₂	semidirect
14. #3176	C₂	semidirect
15. #3175	C₂	semidirect
16. #3168	C₂	semidirect
17. #3119	C₂	semidirect
18. #3118	C₂	semidirect
19. #3114	C₂	semidirect
20. #2966	C₂	semidirect
21. #2951	C₂	semidirect
22. #2948	C₂	semidirect
23. C₂×C₄×D₈	C₂	semidirect
27. #559	C₂²	semidirect
28. #554	C₂²	semidirect
30. #553	C₂²	semidirect
34. #547	C₂²	semidirect
36. #546	C₂²	semidirect
37. #546	C₂²	semidirect
39. #542	C₂²	semidirect
40. #540	C₂²	semidirect
44. #529	C₂²	semidirect
47. #520	C₂²	semidirect
48. #518	C₂²	semidirect
49. C₂×C₄×D₄	C₂²	semidirect
50. #500	C₂²	semidirect
51. #499	C₂²	semidirect
52. #499	C₂²	semidirect
53. #495	C₂²	semidirect
54. #495	C₂²	semidirect
56. #490	C₂²	semidirect
57. #489	C₂²	semidirect
58. #488	C₂²	semidirect
59. #485	C₂²	semidirect
60. #483	C₂²	semidirect
61. #482	C₂²	semidirect
62. #481	C₂²	semidirect
63. #480	C₂²	semidirect
64. #480	C₂²	semidirect
65. #479	C₂²	semidirect
66. #478	C₂²	semidirect
67. #478	C₂²	semidirect
68. #478	C₂²	semidirect
69. #476	C₂²	semidirect
70. #474	C₂²	semidirect
71. #469	C₂²	semidirect
72. #468	C₂²	semidirect
73. #467	C₂²	semidirect
74. #467	C₂²	semidirect
77. #466	C₂²	semidirect
78. #466	C₂²	semidirect
79. #465	C₂²	semidirect
80. #463	C₂²	semidirect
81. #463	C₂²	semidirect
82. #463	C₂²	semidirect
83. #463	C₂²	semidirect
84. #460	C₂²	semidirect
86. #450	C₂²	semidirect
87. #450	C₂²	semidirect
88. #449	C₂²	semidirect
89. #449	C₂²	semidirect
92. #446	C₂²	semidirect
93. C₈×Q₈	C₂²	semidirect
94. #442	C₂²	semidirect
95. #442	C₂²	semidirect
96. #442	C₂²	semidirect
97. #440	C₂²	semidirect
98. #440	C₂²	semidirect
99. #440	C₂²	semidirect
100. C₄×Q₁₆	C₂²	semidirect
101. C₄×Q₁₆	C₂²	semidirect
102. C₄×SD₁₆	C₂²	semidirect
107. C₄×D₈	C₂²	semidirect
108. C₄×D₈	C₂²	semidirect
109. C₄×D₈	C₂²	semidirect
110. C₄×D₈	C₂²	semidirect
111. C₄×D₈	C₂²	semidirect
112. C₄×D₈	C₂²	semidirect
113. #436	C₂²	semidirect
115. #435	C₂²	semidirect
117. C₈×D₄	C₂²	semidirect
118. C₈×D₄	C₂²	semidirect
119. #433	C₂²	semidirect
120. #433	C₂²	semidirect
121. #432	C₂²	semidirect
122. #427	C₂²	semidirect
123. C₂×#107	C₂²	semidirect
124. C₂×#107	C₂²	semidirect
125. #418	C₂²	semidirect
126. #417	C₂²	semidirect
127. C₂×#102	C₂²	semidirect
128. #405	C₂²	semidirect
129. #405	C₂²	semidirect
130. C₂×C₄×C₈	C₂²	semidirect
351. D₈	#41	semidirect

Maximal subgroups

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

subgroup	index
#3513	2
#3396	2
#3380	2
#3370	2
#3339	2
#3336	2
#3334	2
#3322	2
#3310	2
#3306	2
#3280	2
D₄×D₈	2
#3176	2
#3175	2
#3168	2
#3119	2
#3118	2
#3114	2
#2966	2
#2951	2
#2948	2
C₂×C₄×D₈	2