Subgroups — #61539

Order 256.

975 conjugacy classes of subgroups.

The subgroup lattice has 601 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3519	C₂	1	1	yes	maximal, characteristic, complemented
2	#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	#3361	C₂	1	1	yes	maximal, characteristic, complemented
6	#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	#3347	C₂	1	2	yes	maximal, complemented
8	#3340	C₂	1	1	yes	maximal, characteristic, complemented
9	#3325	C₂	1	1	yes	maximal, characteristic, complemented
10	#3325	C₂	1	2	yes	maximal, complemented
11	#3324	C₂	1	1	yes	maximal, characteristic, complemented
12	#3322	C₂	1	2	yes	maximal, complemented
13	D₄×D₈	C₂	1	1	yes	maximal, characteristic, complemented
14	#3264	C₂	1	2	yes	maximal, complemented
15	#3184	C₂	1	1	yes	maximal, characteristic, complemented
16	#3179	C₂	1	2	yes	maximal, complemented
17	#3122	C₂	1	2	yes	maximal, complemented
18	#3118	C₂	1	2	yes	maximal, complemented
19	#3106	C₂	1	1	yes	maximal, characteristic, complemented
20	#3100	C₂	1	1	yes	maximal, characteristic, complemented
21	#2969	C₂	1	1	yes	maximal, characteristic, complemented
22	#2948	C₂	1	2	yes	maximal, complemented
23	C₄×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
25	C₂²×D₈	C₂²	1	2	yes	—
26	#559	C₂²	1	1	yes	characteristic, complemented
27	#556	C₂²	1	1	yes	characteristic, complemented
28	#555	C₂²	1	1	yes	characteristic
29	#555	C₂²	1	2	yes	complemented
30	#554	C₂²	1	1	yes	characteristic, complemented
31	#553	—	2	1	no	—
32	#553	C₂²	1	2	yes	complemented
33	#551	—	2	2	no	—
34	#550	C₂²	1	1	yes	characteristic, complemented
35	D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
36	#548	—	2	1	no	—
37	#546	—	2	1	no	—
38	#546	—	2	2	no	—
39	#546	—	2	1	no	—
40	#546	C₂²	1	2	yes	complemented
41	D₄²	C₂²	1	1	yes	characteristic
42	D₄²	C₂²	1	1	yes	characteristic, complemented
43	D₄²	C₂²	1	2	yes	complemented
44	#542	C₂²	1	2	yes	complemented
45	#540	C₂²	1	2	yes	complemented
46	#538	—	2	2	no	—
47	#538	—	2	2	no	—
48	#532	C₂²	1	1	yes	characteristic, complemented
49	#532	C₂²	1	1	yes	characteristic, complemented
50	#529	—	2	1	no	—
51	#529	C₂²	1	1	yes	characteristic
52	C₂×#124	—	2	1	no	—
53	#525	—	2	1	no	—
54	C₂×#121	—	2	1	no	—
55	#518	C₂²	1	2	yes	complemented
56	#518	C₂²	1	2	yes	complemented
57	C₄×#41	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
59	#501	C₂²	1	2	yes	complemented
60	#498	C₂²	1	1	yes	characteristic, complemented
61	#496	C₂²	1	2	yes	complemented
62	#493	C₂²	1	1	yes	characteristic, complemented
63	#488	C₂²	1	2	yes	complemented
64	#486	C₂²	1	2	yes	complemented
65	#486	C₂²	1	1	yes	characteristic, complemented
66	#486	C₂²	1	1	yes	characteristic, complemented
67	#485	C₂²	1	2	yes	complemented
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	#480	C₂²	1	2	yes	complemented
73	#478	C₂²	1	2	yes	complemented
74	#478	C₂²	1	2	yes	complemented
75	#477	C₂²	1	1	yes	characteristic, complemented
76	#476	C₂²	1	1	yes	characteristic, complemented
77	#476	C₂²	1	2	yes	complemented
78	#474	C₂²	1	1	yes	characteristic, complemented
79	#474	C₂²	1	2	yes	complemented
80	#474	C₂²	1	1	yes	characteristic, complemented
81	#469	C₂²	1	2	yes	complemented
82	#469	C₂²	1	2	yes	complemented
83	#469	C₂²	1	2	yes	complemented
84	#468	C₂²	1	2	yes	complemented
85	#466	C₂²	1	2	yes	complemented
86	#465	C₂²	1	2	yes	complemented
87	#463	C₂²	1	2	yes	complemented
88	#463	C₂²	1	2	yes	complemented
89	#460	C₂²	1	1	yes	characteristic, complemented
90	#459	C₂²	1	1	yes	characteristic
91	#459	C₂²	1	1	yes	characteristic, complemented
92	#459	C₂²	1	1	yes	characteristic, complemented
93	#459	C₂²	1	2	yes	complemented
94	#459	C₂²	1	2	yes	complemented
95	#450	C₂²	1	2	yes	complemented
96	#449	C₂²	1	2	yes	complemented
97	#447	C₂²	1	2	yes	—
98	#447	C₂²	1	2	yes	complemented
99	#447	C₂²	1	2	yes	complemented
100	#447	C₂²	1	2	yes	complemented
101	#446	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
103	#442	C₂²	1	2	yes	—
104	#442	C₂²	1	1	yes	characteristic
105	#442	C₂²	1	2	yes	complemented
106	#442	C₂²	1	2	yes	complemented
107	#442	C₂²	1	1	yes	characteristic, complemented
108	#442	C₂²	1	2	yes	complemented
109	#440	C₂²	1	1	yes	characteristic, complemented
110	#440	C₂²	1	1	yes	characteristic, complemented
111	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
112	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
113	C₄×SD₁₆	C₂²	1	2	yes	complemented
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	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₈	C₂²	1	2	yes	complemented
119	C₄×D₈	C₂²	1	2	yes	complemented
120	C₄×D₈	C₂²	1	2	yes	complemented
121	#436	C₂²	1	2	yes	complemented
122	#436	C₂²	1	1	yes	characteristic, complemented
123	#435	C₂²	1	2	yes	complemented
124	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
125	#433	C₂²	1	2	yes	complemented
126	#431	C₂²	1	1	yes	characteristic, complemented
127	#428	C₂²	1	1	yes	characteristic, complemented
128	#427	C₂²	1	2	yes	complemented
129	#418	C₂²	1	1	yes	characteristic, complemented
130	#418	C₂²	1	2	yes	complemented
131	#418	C₂²	1	2	yes	complemented
132	#417	C₂²	1	1	yes	characteristic, complemented
133	#405	C₂²	1	2	yes	complemented
134	C₄×M₁₆	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41	—	2	1	no	—
136	C₂×#41	—	2	1	no	—
137	C₂×#41	—	2	1	no	—
138	C₂×#41	C₂³	1	1	yes	characteristic
139	C₂²×Q₈	—	2	1	no	—
140	C₂²×D₄	—	2	1	no	—
141	C₂²×D₄	—	2	2	no	—
142	C₂²×D₄	—	2	1	no	—
143	C₂²×D₄	C₂³	1	1	yes	characteristic
144	C₂²×D₄	C₂³	1	2	yes	—
145	C₂²×D₄	C₂³	1	2	yes	—
146	C₂³×C₄	—	2	1	no	—
147	AGL(1,ℤ/8)	—	2	4	no	—
148	C₂×SD₁₆	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆	C₂³	1	2	yes	—
151	C₂×D₈	—	2	8	no	—
152	C₂×D₈	C₂³	1	2	yes	—
153	C₂×D₈	C₂³	1	2	yes	—
154	C₂×D₈	C₂³	1	2	yes	—
155	C₂×D₈	C₂³	1	1	yes	characteristic
156	C₂×D₈	C₂³	1	2	yes	—
157	C₂×D₈	C₂³	1	2	yes	—
158	C₂×D₈	C₂³	1	1	yes	characteristic
159	C₂×M₁₆	C₂³	1	1	yes	characteristic
160	C₂×M₁₆	C₂³	1	1	yes	characteristic
161	C₂×M₁₆	C₂³	1	2	yes	—
162	C₂²×C₈	C₂³	1	2	yes	—
163	C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈	C₂³	1	2	yes	—
166	#127	C₂³	1	1	yes	characteristic
167	#127	C₂³	1	1	yes	characteristic
168	#127	C₂³	1	2	yes	—
169	#126	—	2	2	no	—
170	#126	—	2	2	no	—
171	#126	—	2	2	no	—
172	#126	D₄	1	2	yes	—
173	#125	D₄	1	1	yes	characteristic
174	#125	C₂³	1	2	yes	—
175	#124	—	2	1	no	—
176	#124	—	2	1	no	—
177	#124	—	2	2	no	—
178	#124	—	2	2	no	—
179	#124	—	2	2	no	—
180	#124	—	2	2	no	—
181	#124	—	2	1	no	—
182	#124	—	2	1	no	—
183	#124	D₄	1	1	yes	characteristic
184	#124	C₂³	1	2	yes	—
185	#123	—	2	2	no	—
186	#123	—	2	2	no	—
187	#123	—	2	2	no	—
188	#123	—	2	2	no	—
189	#123	—	2	2	no	—
190	#123	—	2	2	no	—
191	#123	D₄	1	2	yes	—
192	C₂²⋊Q₈	—	2	1	no	—
193	C₂²⋊Q₈	—	2	1	no	—
194	C₂²⋊Q₈	—	2	2	no	—
195	C₂²⋊Q₈	—	2	2	no	—
196	C₂²⋊Q₈	—	2	2	no	—
197	C₂²⋊Q₈	D₄	1	1	yes	characteristic
198	C₂²⋊Q₈	C₂³	1	2	yes	—
199	#121	—	2	2	no	—
200	#121	—	2	1	no	—
201	#121	—	2	2	no	—
202	#121	—	2	1	no	—
203	#121	—	2	1	no	—
204	#121	—	2	1	no	—
205	#121	—	2	1	no	—
206	#121	—	2	1	no	—
207	#121	—	2	2	no	—
208	#121	—	2	2	no	—
209	#121	—	2	2	no	—
210	#121	—	2	2	no	—
211	#121	—	2	2	no	—
212	#121	D₄	1	1	yes	characteristic
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	#120	—	2	2	no	—
219	#120	—	2	2	no	—
220	#120	—	2	2	no	—
221	#120	—	2	2	no	—
222	#120	—	2	2	no	—
223	C₄×Q₈	—	2	1	no	—
224	C₄×Q₈	C₂³	1	1	yes	characteristic
225	C₄×Q₈	C₂³	1	1	yes	characteristic
226	C₄×Q₈	C₂³	1	1	yes	characteristic
227	C₄×D₄	—	2	1	no	—
228	C₄×D₄	—	2	1	no	—
229	C₄×D₄	—	2	2	no	—
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	2	no	—
235	C₄×D₄	—	2	1	no	—
236	C₄×D₄	—	2	1	no	—
237	C₄×D₄	—	2	1	no	—
238	C₄×D₄	—	2	1	no	—
239	C₄×D₄	C₂³	1	1	yes	characteristic
240	C₄×D₄	C₂³	1	1	yes	characteristic
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	2	yes	—
246	C₄×D₄	C₂³	1	2	yes	—
247	C₄×D₄	C₂³	1	2	yes	—
248	C₄×D₄	C₂³	1	2	yes	—
249	C₄×D₄	C₂³	1	2	yes	—
250	C₄×D₄	C₂³	1	2	yes	—
251	C₄×D₄	C₂³	1	1	yes	characteristic
252	C₄×D₄	C₂³	1	2	yes	—
253	#117	—	2	1	no	—
254	#117	—	2	2	no	—
255	#117	—	2	1	no	—
256	#117	C₂³	1	1	yes	characteristic
257	#117	C₂³	1	2	yes	—
258	#117	C₂³	1	2	yes	—
259	#117	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊C₄	—	2	1	no	—
263	C₂×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₄²	—	2	1	no	—
269	C₂×C₄²	C₂³	1	1	yes	characteristic
270	#107	C₂³	1	2	yes	—
271	#107	C₂³	1	2	yes	—
272	#107	C₂³	1	1	yes	characteristic
273	#107	C₂³	1	1	yes	characteristic
274	#107	C₂³	1	2	yes	—
275	#106	C₂³	1	1	yes	characteristic
276	#106	C₂³	1	2	yes	—
277	#106	C₂³	1	1	yes	characteristic
278	#106	C₂³	1	2	yes	—
279	#106	C₂³	1	2	yes	—
280	C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₄⋊C₈	C₂³	1	2	yes	—
283	C₄⋊C₈	C₂³	1	2	yes	—
284	#103	C₂³	1	1	yes	characteristic
285	#103	C₂³	1	1	yes	characteristic
286	#103	C₂³	1	2	yes	—
287	#102	C₂³	1	1	yes	characteristic
288	#102	C₂³	1	1	yes	characteristic
289	#102	C₂³	1	1	yes	characteristic
290	#102	C₂³	1	1	yes	characteristic
291	#102	C₂³	1	1	yes	characteristic
292	#102	C₂³	1	2	yes	—
293	#102	C₂³	1	2	yes	—
294	#102	C₂³	1	2	yes	—
295	#102	C₂³	1	2	yes	—
296	#102	C₂³	1	2	yes	—
297	#102	C₂³	1	2	yes	—
298	#102	C₂³	1	1	yes	characteristic
299	#102	C₂³	1	2	yes	—
300	#102	C₂³	1	2	yes	—
301	#102	C₂³	1	2	yes	—
302	#102	C₂³	1	2	yes	—
303	#102	C₂³	1	2	yes	—
304	C₂²⋊C₈	C₂³	1	2	yes	—
305	C₂²⋊C₈	C₂³	1	2	yes	—
306	C₂²⋊C₈	C₂³	1	2	yes	—
307	#97	C₂³	1	1	yes	characteristic
308	#97	C₂³	1	1	yes	characteristic
309	#97	C₂³	1	2	yes	—
310	C₄×C₈	C₂³	1	1	yes	characteristic
311	C₄×C₈	C₂³	1	1	yes	characteristic
312	C₄×C₈	C₂³	1	2	yes	—
313	C₄×C₈	C₂³	1	2	yes	—
314	C₂⁴	—	2	1	no	—
315	C₂⁴	—	2	2	no	—
316	C₂⁴	—	2	2	no	—
317	#41	—	2	2	no	—
318	#41	—	4	1	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	2	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	8	2	no	—
326	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈	C₂⁴	1	1	yes	characteristic
328	C₂×D₄	—	2	4	no	—
329	C₂×D₄	—	2	4	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	1	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	2	no	—
338	C₂×D₄	—	2	1	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	2	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	4	2	no	—
347	C₂×D₄	—	4	2	no	—
348	C₂×D₄	—	4	1	no	—
349	C₂×D₄	—	8	2	no	—
350	C₂×D₄	—	8	2	no	—
351	C₂×D₄	—	8	4	no	—
352	C₂×D₄	C₂×D₄	1	1	yes	characteristic
353	C₂×D₄	C₂×D₄	1	2	yes	—
354	C₂×D₄	C₂⁴	1	2	yes	—
355	C₂×D₄	C₂⁴	1	2	yes	—
356	C₂×D₄	C₂⁴	1	1	yes	characteristic
357	C₂×D₄	C₂⁴	1	1	yes	characteristic
358	C₂×D₄	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	8	2	no	—
374	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
376	C₂²×C₄	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄	C₂⁴	1	2	yes	—
378	SD₁₆	—	2	2	no	—
379	SD₁₆	—	2	2	no	—
380	SD₁₆	—	4	2	no	—
381	D₈	—	2	4	no	—
382	D₈	—	2	4	no	—
383	D₈	—	2	2	no	—
384	D₈	—	2	4	no	—
385	D₈	—	4	2	no	—
386	D₈	—	4	2	no	—
387	D₈	#41	1	4	yes	complemented
388	M₁₆	—	2	2	no	—
389	M₁₆	—	4	1	no	—
390	M₁₆	—	4	2	no	—
391	C₂×C₈	—	2	4	no	—
392	C₂×C₈	C₂⁴	1	1	yes	characteristic
393	C₂×C₈	C₂⁴	1	2	yes	—
394	C₂×C₈	C₂⁴	1	1	yes	characteristic
395	C₂×C₈	C₂⁴	1	2	yes	—
396	C₂×C₈	C₂⁴	1	1	yes	characteristic
397	C₂×C₈	C₂⁴	1	1	yes	characteristic
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
409	C₄⋊C₄	C₂×D₄	1	2	yes	—
410	C₄⋊C₄	C₂×D₄	1	2	yes	—
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	2	yes	—
415	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄	C₂⁴	1	2	yes	—
417	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	2	1	no	—
423	C₂²⋊C₄	—	2	1	no	—
424	C₂²⋊C₄	—	2	1	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	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	2	no	—
439	C₂²⋊C₄	—	2	2	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄	C₂×D₄	1	2	yes	—
446	C₂²⋊C₄	C₂×D₄	1	2	yes	—
447	C₄²	—	2	1	no	—
448	C₄²	—	2	1	no	—
449	C₄²	—	2	1	no	—
450	C₄²	—	2	2	no	—
451	C₄²	—	2	2	no	—
452	C₄²	C₂×D₄	1	1	yes	characteristic
453	C₄²	C₂×D₄	1	1	yes	characteristic
454	C₄²	C₂⁴	1	1	yes	characteristic
455	C₄²	C₂⁴	1	1	yes	characteristic
456	C₄²	C₂⁴	1	2	yes	—
457	C₂³	—	2	1	no	—
458	C₂³	—	2	1	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	1	no	—
462	C₂³	—	4	2	no	—
463	C₂³	—	4	4	no	—
464	C₂³	—	4	4	no	—
465	C₂³	—	4	2	no	—
466	C₂³	—	8	1	no	—
467	C₂³	—	8	2	no	—
468	C₂³	—	8	2	no	—
469	C₂³	—	8	2	no	—
470	C₂³	—	8	2	no	—
471	C₂³	C₂²×D₄	1	2	yes	—
472	C₂³	C₂²×D₄	1	1	yes	characteristic
473	Q₈	—	2	2	no	—
474	Q₈	—	2	1	no	—
475	Q₈	—	2	1	no	—
476	Q₈	—	4	2	no	—
477	Q₈	—	8	2	no	—
478	Q₈	—	8	1	no	—
479	D₄	—	2	2	no	—
480	D₄	—	2	2	no	—
481	D₄	—	2	2	no	—
482	D₄	—	2	1	no	—
483	D₄	—	2	1	no	—
484	D₄	—	2	1	no	—
485	D₄	—	2	2	no	—
486	D₄	—	2	1	no	—
487	D₄	—	2	2	no	—
488	D₄	—	4	2	no	—
489	D₄	—	4	2	no	—
490	D₄	—	4	4	no	—
491	D₄	—	4	4	no	—
492	D₄	—	4	2	no	—
493	D₄	—	4	4	no	—
494	D₄	—	4	2	no	—
495	D₄	—	4	2	no	—
496	D₄	—	8	1	no	—
497	D₄	—	8	2	no	—
498	D₄	—	8	1	no	—
499	D₄	—	8	2	no	—
500	D₄	—	8	2	no	—
501	D₄	—	8	2	no	—
502	D₄	—	8	2	no	—
503	D₄	—	8	2	no	—
504	D₄	C₂×#41	1	2	yes	—
505	D₄	C₂×#41	1	2	yes	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	8	1	no	—
524	C₂×C₄	—	8	2	no	—
525	C₂×C₄	—	8	1	no	—
526	C₂×C₄	—	8	1	no	—
527	C₂×C₄	—	8	2	no	—
528	C₂×C₄	—	8	2	no	—
529	C₂×C₄	—	8	2	no	—
530	C₂×C₄	—	8	2	no	—
531	C₂×C₄	—	8	2	no	—
532	C₂×C₄	—	8	1	no	—
533	C₂×C₄	C₂²×D₄	1	2	yes	—
534	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
536	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄	C₂²×D₄	1	2	yes	—
539	C₂×C₄	C₂²×D₄	1	2	yes	—
540	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
541	C₂×C₄	C₂⁵	1	1	yes	characteristic
542	C₈	—	2	2	no	—
543	C₈	—	2	1	no	—
544	C₈	—	2	1	no	—
545	C₈	—	2	1	no	—
546	C₈	—	2	2	no	—
547	C₈	C₂×#41	1	2	yes	—
548	C₂²	—	2	1	no	—
549	C₂²	—	2	2	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	2	no	—
561	C₂²	—	4	2	no	—
562	C₂²	—	4	1	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	2	no	—
565	C₂²	—	4	2	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	4	2	no	—
568	C₂²	—	4	2	no	—
569	C₂²	—	8	4	no	—
570	C₂²	—	16	4	no	—
571	C₂²	—	16	4	no	—
572	C₂²	C₂³×D₄	1	1	yes	characteristic
573	C₄	—	2	1	no	—
574	C₄	—	2	1	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	1	no	—
577	C₄	—	2	2	no	—
578	C₄	—	2	1	no	—
579	C₄	—	2	2	no	—
580	C₄	—	4	1	no	—
581	C₄	—	4	2	no	—
582	C₄	—	4	1	no	—
583	C₄	—	4	1	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	2	no	—
587	C₄	#576	1	2	yes	—
588	C₄	C₂²×#41	1	1	yes	characteristic
589	C₄	#585	1	1	yes	characteristic
590	C₂	—	4	1	no	—
591	C₂	—	4	2	no	—
592	C₂	—	4	2	no	—
593	C₂	—	4	2	no	—
594	C₂	—	8	1	no	—
595	C₂	—	8	2	no	—
596	C₂	—	8	2	no	—
597	C₂	D₄×#41	1	1	yes	characteristic
598	C₂	C₂×#576	1	1	yes	characteristic
599	C₂	#3585	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. #3519	C₂	semidirect
2. #3514	C₂	semidirect
3. #3399	C₂	semidirect
4. #3384	C₂	semidirect
5. #3361	C₂	semidirect
6. #3358	C₂	semidirect
7. #3347	C₂	semidirect
8. #3340	C₂	semidirect
9. #3325	C₂	semidirect
10. #3325	C₂	semidirect
11. #3324	C₂	semidirect
12. #3322	C₂	semidirect
13. D₄×D₈	C₂	semidirect
14. #3264	C₂	semidirect
15. #3184	C₂	semidirect
16. #3179	C₂	semidirect
17. #3122	C₂	semidirect
18. #3118	C₂	semidirect
19. #3106	C₂	semidirect
20. #3100	C₂	semidirect
21. #2969	C₂	semidirect
22. #2948	C₂	semidirect
23. C₄×AGL(1,ℤ/8)	C₂	semidirect
26. #559	C₂²	semidirect
27. #556	C₂²	semidirect
29. #555	C₂²	semidirect
30. #554	C₂²	semidirect
32. #553	C₂²	semidirect
34. #550	C₂²	semidirect
35. D₄×Q₈	C₂²	semidirect
40. #546	C₂²	semidirect
42. D₄²	C₂²	semidirect
43. D₄²	C₂²	semidirect
44. #542	C₂²	semidirect
45. #540	C₂²	semidirect
48. #532	C₂²	semidirect
49. #532	C₂²	semidirect
55. #518	C₂²	semidirect
56. #518	C₂²	semidirect
57. C₄×#41	C₂²	semidirect
58. C₂×C₄×D₄	C₂²	semidirect
59. #501	C₂²	semidirect
60. #498	C₂²	semidirect
61. #496	C₂²	semidirect
62. #493	C₂²	semidirect
63. #488	C₂²	semidirect
64. #486	C₂²	semidirect
65. #486	C₂²	semidirect
66. #486	C₂²	semidirect
67. #485	C₂²	semidirect
68. #482	C₂²	semidirect
69. #482	C₂²	semidirect
70. #482	C₂²	semidirect
71. #482	C₂²	semidirect
72. #480	C₂²	semidirect
73. #478	C₂²	semidirect
74. #478	C₂²	semidirect
75. #477	C₂²	semidirect
76. #476	C₂²	semidirect
77. #476	C₂²	semidirect
78. #474	C₂²	semidirect
79. #474	C₂²	semidirect
80. #474	C₂²	semidirect
81. #469	C₂²	semidirect
82. #469	C₂²	semidirect
83. #469	C₂²	semidirect
84. #468	C₂²	semidirect
85. #466	C₂²	semidirect
86. #465	C₂²	semidirect
87. #463	C₂²	semidirect
88. #463	C₂²	semidirect
89. #460	C₂²	semidirect
91. #459	C₂²	semidirect
92. #459	C₂²	semidirect
93. #459	C₂²	semidirect
94. #459	C₂²	semidirect
95. #450	C₂²	semidirect
96. #449	C₂²	semidirect
98. #447	C₂²	semidirect
99. #447	C₂²	semidirect
100. #447	C₂²	semidirect
101. #446	C₂²	semidirect
102. C₈×Q₈	C₂²	semidirect
105. #442	C₂²	semidirect
106. #442	C₂²	semidirect
107. #442	C₂²	semidirect
108. #442	C₂²	semidirect
109. #440	C₂²	semidirect
110. #440	C₂²	semidirect
111. C₄×SD₁₆	C₂²	semidirect
112. C₄×SD₁₆	C₂²	semidirect
113. C₄×SD₁₆	C₂²	semidirect
115. C₄×D₈	C₂²	semidirect
116. C₄×D₈	C₂²	semidirect
117. C₄×D₈	C₂²	semidirect
118. C₄×D₈	C₂²	semidirect
119. C₄×D₈	C₂²	semidirect
120. C₄×D₈	C₂²	semidirect
121. #436	C₂²	semidirect
122. #436	C₂²	semidirect
123. #435	C₂²	semidirect
124. C₈×D₄	C₂²	semidirect
125. #433	C₂²	semidirect
126. #431	C₂²	semidirect
127. #428	C₂²	semidirect
128. #427	C₂²	semidirect
129. #418	C₂²	semidirect
130. #418	C₂²	semidirect
131. #418	C₂²	semidirect
132. #417	C₂²	semidirect
133. #405	C₂²	semidirect
134. C₄×M₁₆	C₂²	semidirect
387. D₈	#41	semidirect

Maximal subgroups

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

subgroup	index
#3519	2
#3514	2
#3399	2
#3384	2
#3361	2
#3358	2
#3347	2
#3340	2
#3325	2
#3324	2
#3322	2
D₄×D₈	2
#3264	2
#3184	2
#3179	2
#3122	2
#3118	2
#3106	2
#3100	2
#2969	2
#2948	2
C₄×AGL(1,ℤ/8)	2