Subgroups — #62585

Order 256.

868 conjugacy classes of subgroups.

The subgroup lattice has 632 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
2	#3509	C₂	1	1	yes	maximal, characteristic, complemented
3	#3377	C₂	1	2	yes	maximal, complemented
4	#3371	C₂	1	2	yes	maximal, complemented
5	#3313	C₂	1	2	yes	maximal, complemented
6	#3312	C₂	1	2	yes	maximal, complemented
7	#3311	C₂	1	2	yes	maximal, complemented
8	#3310	C₂	1	2	yes	maximal, complemented
9	#3300	C₂	1	2	yes	maximal, complemented
10	#3296	C₂	1	2	yes	maximal, complemented
11	#3240	C₂	1	1	yes	maximal, characteristic, complemented
12	#3240	C₂	1	1	yes	maximal, characteristic, complemented
13	#3238	C₂	1	1	yes	maximal, characteristic, complemented
14	#3216	C₂	1	1	yes	maximal, characteristic, complemented
15	#3215	C₂	1	1	yes	maximal, characteristic, complemented
16	#3215	C₂	1	1	yes	maximal, characteristic, complemented
17	#3181	C₂	1	1	yes	maximal, characteristic, complemented
18	#3181	C₂	1	1	yes	maximal, characteristic, complemented
19	#3172	C₂	1	1	yes	maximal, characteristic, complemented
20	#3140	C₂	1	1	yes	maximal, characteristic, complemented
21	#3135	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#489	C₂	1	1	yes	maximal, characteristic, complemented
23	#2970	C₂	1	1	yes	maximal, characteristic, complemented
24	#559	C₂²	1	1	yes	characteristic
25	#557	—	2	1	no	—
26	#557	C₂²	1	2	yes	complemented
27	#556	—	2	1	no	—
28	#556	C₂²	1	1	yes	characteristic
29	#556	C₂²	1	2	yes	complemented
30	#555	—	2	1	no	—
31	#552	—	2	1	no	—
32	#552	—	2	1	no	—
33	#552	C₂²	1	2	yes	—
34	#552	C₂²	1	2	yes	complemented
35	#551	—	2	1	no	—
36	#551	—	2	1	no	—
37	D₄×Q₈	C₂²	1	1	yes	characteristic
38	#548	C₂²	1	1	yes	characteristic
39	#548	C₂²	1	1	yes	characteristic
40	#546	—	2	1	no	—
41	#546	C₂²	1	1	yes	characteristic
42	#546	C₂²	1	1	yes	characteristic
43	D₄²	C₂²	1	1	yes	characteristic
44	#542	—	2	1	no	—
45	#541	—	2	1	no	—
46	#541	—	2	1	no	—
47	#538	—	2	1	no	—
48	#538	—	2	1	no	—
49	#536	—	2	1	no	—
50	#533	C₂²	1	1	yes	characteristic, complemented
51	#533	C₂²	1	1	yes	characteristic, complemented
52	#533	C₂²	1	1	yes	characteristic, complemented
53	#533	C₂²	1	1	yes	characteristic, complemented
54	#533	C₂²	1	1	yes	characteristic, complemented
55	#532	C₂²	1	1	yes	characteristic
56	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
57	#529	C₂²	1	1	yes	characteristic
58	#529	C₂²	1	1	yes	characteristic
59	#529	C₂²	1	1	yes	characteristic
60	C₂×#124	C₂²	1	1	yes	characteristic
61	C₂×#124	C₂²	1	1	yes	characteristic
62	#519	—	2	1	no	—
63	#518	—	2	1	no	—
64	C₄×#41	C₂²	1	1	yes	characteristic
65	#501	C₂²	1	1	yes	characteristic, complemented
66	#501	C₂²	1	1	yes	characteristic, complemented
67	#501	C₂²	1	1	yes	characteristic, complemented
68	#497	C₂²	1	1	yes	characteristic
69	#497	C₂²	1	1	yes	characteristic, complemented
70	#497	C₂²	1	1	yes	characteristic, complemented
71	#491	C₂²	1	2	yes	complemented
72	#491	C₂²	1	1	yes	characteristic, complemented
73	#490	C₂²	1	2	yes	—
74	#489	C₂²	1	2	yes	—
75	#489	C₂²	1	1	yes	characteristic
76	#489	C₂²	1	1	yes	characteristic
77	#489	C₂²	1	1	yes	characteristic
78	#489	C₂²	1	2	yes	complemented
79	#489	C₂²	1	1	yes	characteristic, complemented
80	#489	C₂²	1	1	yes	characteristic, complemented
81	#489	C₂²	1	1	yes	characteristic, complemented
82	#489	C₂²	1	1	yes	characteristic, complemented
83	#489	C₂²	1	1	yes	characteristic, complemented
84	#489	C₂²	1	1	yes	characteristic, complemented
85	#488	C₂²	1	2	yes	—
86	#488	C₂²	1	2	yes	complemented
87	#485	C₂²	1	2	yes	complemented
88	#485	C₂²	1	2	yes	complemented
89	#483	C₂²	1	2	yes	complemented
90	#482	C₂²	1	2	yes	—
91	#482	C₂²	1	2	yes	—
92	#480	C₂²	1	2	yes	—
93	#479	C₂²	1	2	yes	complemented
94	#479	C₂²	1	2	yes	complemented
95	#478	C₂²	1	2	yes	—
96	#478	C₂²	1	2	yes	complemented
97	#477	C₂²	1	2	yes	complemented
98	#476	C₂²	1	2	yes	complemented
99	#470	C₂²	1	2	yes	complemented
100	#468	C₂²	1	2	yes	—
101	#467	C₂²	1	2	yes	complemented
102	#467	C₂²	1	2	yes	complemented
103	#465	C₂²	1	2	yes	—
104	#465	C₂²	1	2	yes	—
105	#464	C₂²	1	2	yes	—
106	#464	C₂²	1	2	yes	—
107	#464	C₂²	1	2	yes	complemented
108	#464	C₂²	1	2	yes	complemented
109	#462	C₂²	1	2	yes	complemented
110	#460	C₂²	1	2	yes	—
111	#452	C₂²	1	2	yes	complemented
112	#452	C₂²	1	2	yes	complemented
113	#451	C₂²	1	2	yes	complemented
114	#451	C₂²	1	2	yes	complemented
115	#450	C₂²	1	2	yes	—
116	#450	C₂²	1	2	yes	—
117	#446	C₂²	1	2	yes	complemented
118	#441	C₂²	1	2	yes	complemented
119	#441	C₂²	1	2	yes	complemented
120	#440	C₂²	1	2	yes	—
121	#440	C₂²	1	2	yes	complemented
122	C₄×Q₁₆	C₂²	1	2	yes	complemented
123	C₄×SD₁₆	C₂²	1	2	yes	complemented
124	#435	C₂²	1	2	yes	—
125	#435	C₂²	1	2	yes	complemented
126	C₈×D₄	C₂²	1	2	yes	complemented
127	#432	C₂²	1	1	yes	characteristic, complemented
128	#432	C₂²	1	1	yes	characteristic, complemented
129	#432	C₂²	1	1	yes	characteristic, complemented
130	#419	C₂²	1	2	yes	complemented
131	#418	C₂²	1	2	yes	—
132	#416	C₂²	1	2	yes	complemented
133	#416	C₂²	1	2	yes	complemented
134	C₂×#103	C₂²	1	2	yes	complemented
135	C₂×#102	C₂²	1	2	yes	—
136	C₄×M₁₆	C₂²	1	1	yes	characteristic, complemented
137	C₂×#97	C₂²	1	1	yes	characteristic, complemented
138	C₂×#97	C₂²	1	1	yes	characteristic, complemented
139	C₂×#41	D₄	1	1	yes	characteristic
140	C₂×#41	C₂³	1	1	yes	characteristic
141	C₂×#41	C₂³	1	1	yes	characteristic
142	C₂²×Q₈	—	2	1	no	—
143	C₂²×Q₈	C₂³	1	1	yes	characteristic
144	C₂²×Q₈	C₂³	1	1	yes	characteristic
145	C₂²×D₄	—	2	1	no	—
146	C₂²×D₄	C₂³	1	1	yes	characteristic
147	C₂²×D₄	C₂³	1	1	yes	characteristic
148	C₂×Q₁₆	C₂³	1	2	yes	—
149	C₂×Q₁₆	C₂³	1	2	yes	—
150	C₂×Q₁₆	C₂³	1	2	yes	—
151	C₂×SD₁₆	C₂³	1	2	yes	—
152	C₂×SD₁₆	C₂³	1	2	yes	—
153	C₂×SD₁₆	C₂³	1	2	yes	—
154	C₂×M₁₆	C₂³	1	2	yes	—
155	C₂²×C₈	C₂³	1	2	yes	—
156	C₂²×C₈	C₂³	1	2	yes	—
157	C₄⋊Q₈	—	2	2	no	—
158	C₄⋊Q₈	—	2	1	no	—
159	C₄⋊Q₈	—	2	1	no	—
160	C₄⋊Q₈	—	2	1	no	—
161	C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈	C₂³	1	2	yes	—
166	C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	#127	C₂³	1	1	yes	characteristic
168	#126	—	2	1	no	—
169	#126	—	2	1	no	—
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	1	no	—
176	#126	—	2	1	no	—
177	#125	—	2	2	no	—
178	#125	—	2	2	no	—
179	#125	—	2	2	no	—
180	#125	—	2	2	no	—
181	#125	—	2	1	no	—
182	#125	—	2	1	no	—
183	#125	—	2	1	no	—
184	#125	C₂³	1	1	yes	characteristic
185	#125	C₂³	1	2	yes	—
186	#125	C₂³	1	2	yes	—
187	#124	—	2	1	no	—
188	#124	—	2	2	no	—
189	#124	—	2	1	no	—
190	#124	—	2	1	no	—
191	#124	—	2	1	no	—
192	#124	—	2	1	no	—
193	#124	—	2	1	no	—
194	#124	—	2	1	no	—
195	#124	C₂³	1	1	yes	characteristic
196	#124	C₂³	1	1	yes	characteristic
197	#124	C₂³	1	1	yes	characteristic
198	#124	C₂³	1	1	yes	characteristic
199	#124	C₂³	1	1	yes	characteristic
200	#124	C₂³	1	1	yes	characteristic
201	#124	C₂³	1	1	yes	characteristic
202	#123	—	2	2	no	—
203	#123	—	2	2	no	—
204	#123	—	2	1	no	—
205	#123	—	2	1	no	—
206	#123	—	2	1	no	—
207	#123	—	2	1	no	—
208	#123	—	2	1	no	—
209	#123	—	2	1	no	—
210	#123	—	2	1	no	—
211	C₂²⋊Q₈	—	2	1	no	—
212	C₂²⋊Q₈	—	2	1	no	—
213	C₂²⋊Q₈	—	2	1	no	—
214	C₂²⋊Q₈	—	2	1	no	—
215	C₂²⋊Q₈	—	2	1	no	—
216	C₂²⋊Q₈	—	2	1	no	—
217	C₂²⋊Q₈	—	2	1	no	—
218	C₂²⋊Q₈	—	2	1	no	—
219	C₂²⋊Q₈	—	2	1	no	—
220	C₂²⋊Q₈	—	2	1	no	—
221	C₂²⋊Q₈	—	2	1	no	—
222	C₂²⋊Q₈	—	2	1	no	—
223	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
224	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
225	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
226	C₂²⋊Q₈	C₂³	1	2	yes	—
227	C₂²⋊Q₈	C₂³	1	2	yes	—
228	C₂²⋊Q₈	C₂³	1	2	yes	—
229	#121	—	2	1	no	—
230	#121	—	2	1	no	—
231	#121	—	2	1	no	—
232	#121	—	2	1	no	—
233	#121	—	2	1	no	—
234	#121	—	2	1	no	—
235	#121	—	2	1	no	—
236	#121	C₂³	1	1	yes	characteristic
237	#121	C₂³	1	1	yes	characteristic
238	#121	C₂³	1	1	yes	characteristic
239	#120	—	2	1	no	—
240	#120	—	2	1	no	—
241	#120	—	2	1	no	—
242	#120	—	2	1	no	—
243	C₄×Q₈	—	2	2	no	—
244	C₄×Q₈	—	2	2	no	—
245	C₄×Q₈	—	2	1	no	—
246	C₄×Q₈	—	2	1	no	—
247	C₄×Q₈	—	2	1	no	—
248	C₄×Q₈	—	2	1	no	—
249	C₄×Q₈	—	2	1	no	—
250	C₄×Q₈	—	2	1	no	—
251	C₄×Q₈	—	2	1	no	—
252	C₄×Q₈	D₄	1	1	yes	characteristic
253	C₄×Q₈	C₂³	1	1	yes	characteristic
254	C₄×Q₈	C₂³	1	1	yes	characteristic
255	C₄×Q₈	C₂³	1	1	yes	characteristic
256	C₄×Q₈	C₂³	1	2	yes	—
257	C₄×Q₈	C₂³	1	2	yes	—
258	C₄×Q₈	C₂³	1	2	yes	—
259	C₄×Q₈	C₂³	1	1	yes	characteristic
260	C₄×D₄	—	2	1	no	—
261	C₄×D₄	—	2	1	no	—
262	C₄×D₄	—	2	1	no	—
263	C₄×D₄	—	2	1	no	—
264	C₄×D₄	—	2	1	no	—
265	C₄×D₄	—	2	1	no	—
266	C₄×D₄	—	2	1	no	—
267	C₄×D₄	—	2	1	no	—
268	C₄×D₄	—	2	1	no	—
269	C₄×D₄	D₄	1	1	yes	characteristic
270	C₄×D₄	D₄	1	1	yes	characteristic
271	C₄×D₄	D₄	1	1	yes	characteristic
272	C₄×D₄	C₂³	1	1	yes	characteristic
273	C₄×D₄	C₂³	1	1	yes	characteristic
274	C₄×D₄	C₂³	1	1	yes	characteristic
275	C₄×D₄	C₂³	1	1	yes	characteristic
276	C₄×D₄	C₂³	1	1	yes	characteristic
277	C₄×D₄	C₂³	1	1	yes	characteristic
278	#117	—	2	1	no	—
279	#117	—	2	1	no	—
280	#117	—	2	1	no	—
281	#117	—	2	1	no	—
282	#117	—	2	2	no	—
283	#117	—	2	2	no	—
284	#117	—	2	1	no	—
285	#117	—	2	1	no	—
286	#117	—	2	1	no	—
287	#117	D₄	1	1	yes	characteristic
288	#117	D₄	1	1	yes	characteristic
289	#117	D₄	1	1	yes	characteristic
290	#117	C₂³	1	2	yes	—
291	#117	C₂³	1	2	yes	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	C₂³	1	2	yes	—
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₂²⋊C₄	—	2	1	no	—
298	C₂×C₂²⋊C₄	—	2	1	no	—
299	C₂×C₂²⋊C₄	—	2	1	no	—
300	C₂×C₄²	C₂³	1	1	yes	characteristic
301	C₂×C₄²	C₂³	1	1	yes	characteristic
302	C₂×C₄²	C₂³	1	1	yes	characteristic
303	#107	C₂³	1	2	yes	—
304	#107	C₂³	1	2	yes	—
305	#107	C₂³	1	2	yes	—
306	#106	C₂³	1	2	yes	—
307	#106	C₂³	1	2	yes	—
308	#106	C₂³	1	2	yes	—
309	C₄⋊C₈	C₂³	1	2	yes	—
310	C₄⋊C₈	C₂³	1	2	yes	—
311	C₄⋊C₈	C₂³	1	2	yes	—
312	#103	C₂³	1	2	yes	—
313	#103	C₂³	1	2	yes	—
314	#103	C₂³	1	2	yes	—
315	#103	C₂³	1	2	yes	—
316	#103	C₂³	1	2	yes	—
317	#103	C₂³	1	2	yes	—
318	#103	C₂³	1	2	yes	—
319	#103	C₂³	1	2	yes	—
320	#103	C₂³	1	2	yes	—
321	#103	C₂³	1	2	yes	—
322	#103	C₂³	1	2	yes	—
323	#102	C₂³	1	2	yes	—
324	#102	C₂³	1	2	yes	—
325	#102	C₂³	1	2	yes	—
326	#102	C₂³	1	2	yes	—
327	#102	C₂³	1	2	yes	—
328	#102	C₂³	1	2	yes	—
329	#102	C₂³	1	2	yes	—
330	#102	C₂³	1	2	yes	—
331	#102	C₂³	1	2	yes	—
332	C₂²⋊C₈	C₂³	1	2	yes	—
333	C₂²⋊C₈	C₂³	1	2	yes	—
334	C₂²⋊C₈	C₂³	1	2	yes	—
335	#97	C₂³	1	1	yes	characteristic
336	#97	C₂³	1	1	yes	characteristic
337	#97	C₂³	1	1	yes	characteristic
338	#97	C₂³	1	2	yes	—
339	#97	C₂³	1	2	yes	—
340	#97	C₂³	1	1	yes	characteristic
341	C₄×C₈	C₂³	1	2	yes	—
342	C₂⁴	—	2	1	no	—
343	C₂⁴	—	2	1	no	—
344	#41	—	4	2	no	—
345	#41	—	4	2	no	—
346	#41	—	4	2	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	4	4	no	—
354	C₂×Q₈	—	4	2	no	—
355	C₂×Q₈	—	4	2	no	—
356	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
357	C₂×Q₈	C₂⁴	1	1	yes	characteristic
358	C₂×Q₈	C₂⁴	1	1	yes	characteristic
359	C₂×Q₈	C₂⁴	1	1	yes	characteristic
360	C₂×Q₈	C₂⁴	1	2	yes	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	4	2	no	—
371	C₂×D₄	—	4	2	no	—
372	C₂×D₄	—	4	4	no	—
373	C₂×D₄	C₂×D₄	1	1	yes	characteristic
374	C₂×D₄	C₂×D₄	1	1	yes	characteristic
375	C₂×D₄	C₂×D₄	1	1	yes	characteristic
376	C₂×D₄	C₂⁴	1	1	yes	characteristic
377	C₂×D₄	C₂⁴	1	1	yes	characteristic
378	C₂×D₄	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
388	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
393	C₂²×C₄	C₂⁴	1	1	yes	characteristic
394	C₂²×C₄	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄	C₂⁴	1	1	yes	characteristic
396	Q₁₆	—	4	2	no	—
397	Q₁₆	—	4	2	no	—
398	Q₁₆	—	4	2	no	—
399	SD₁₆	—	4	2	no	—
400	SD₁₆	—	4	2	no	—
401	SD₁₆	—	4	2	no	—
402	M₁₆	—	4	2	no	—
403	C₂×C₈	—	4	2	no	—
404	C₂×C₈	—	4	2	no	—
405	C₂×C₈	C₂⁴	1	2	yes	—
406	C₂×C₈	C₂⁴	1	2	yes	—
407	C₂×C₈	C₂⁴	1	2	yes	—
408	C₂×C₈	C₂⁴	1	2	yes	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
437	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
438	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
439	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
440	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
441	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
442	C₄⋊C₄	C₂⁴	1	2	yes	—
443	C₄⋊C₄	C₂⁴	1	2	yes	—
444	C₄⋊C₄	C₂⁴	1	2	yes	—
445	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
446	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
447	C₂²⋊C₄	—	2	1	no	—
448	C₂²⋊C₄	—	2	1	no	—
449	C₂²⋊C₄	—	2	2	no	—
450	C₂²⋊C₄	—	2	2	no	—
451	C₂²⋊C₄	—	2	2	no	—
452	C₂²⋊C₄	—	2	2	no	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₂²⋊C₄	—	2	1	no	—
455	C₂²⋊C₄	—	2	1	no	—
456	C₂²⋊C₄	—	2	1	no	—
457	C₂²⋊C₄	—	2	1	no	—
458	C₂²⋊C₄	—	2	1	no	—
459	C₂²⋊C₄	—	2	1	no	—
460	C₂²⋊C₄	—	2	1	no	—
461	C₂²⋊C₄	—	2	1	no	—
462	C₂²⋊C₄	—	2	1	no	—
463	C₂²⋊C₄	—	2	1	no	—
464	C₂²⋊C₄	—	2	1	no	—
465	C₂²⋊C₄	—	2	1	no	—
466	C₂²⋊C₄	—	2	1	no	—
467	C₂²⋊C₄	—	2	1	no	—
468	C₂²⋊C₄	—	2	1	no	—
469	C₂²⋊C₄	—	2	1	no	—
470	C₂²⋊C₄	—	2	1	no	—
471	C₂²⋊C₄	—	2	1	no	—
472	C₂²⋊C₄	—	2	1	no	—
473	C₂²⋊C₄	—	2	1	no	—
474	C₂²⋊C₄	—	2	1	no	—
475	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
476	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
477	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
478	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
479	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
480	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
481	C₄²	—	2	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	2	2	no	—
484	C₄²	—	2	2	no	—
485	C₄²	—	2	2	no	—
486	C₄²	—	2	2	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	2	no	—
489	C₄²	C₂×D₄	1	1	yes	characteristic
490	C₄²	C₂×D₄	1	1	yes	characteristic
491	C₄²	C₂×D₄	1	1	yes	characteristic
492	C₄²	C₂×D₄	1	1	yes	characteristic
493	C₄²	C₂×D₄	1	1	yes	characteristic
494	C₄²	C₂×D₄	1	1	yes	characteristic
495	C₄²	C₂⁴	1	1	yes	characteristic
496	C₄²	C₂⁴	1	1	yes	characteristic
497	C₄²	C₂⁴	1	1	yes	characteristic
498	C₄²	C₂⁴	1	1	yes	characteristic
499	C₂³	—	2	1	no	—
500	C₂³	—	2	1	no	—
501	C₂³	—	2	1	no	—
502	C₂³	—	4	2	no	—
503	C₂³	—	4	2	no	—
504	C₂³	—	8	1	no	—
505	C₂³	—	8	1	no	—
506	C₂³	—	8	1	no	—
507	C₂³	—	8	1	no	—
508	C₂³	C₂²×D₄	1	1	yes	characteristic
509	C₂³	C₂²×D₄	1	1	yes	characteristic
510	C₂³	C₂²×D₄	1	1	yes	characteristic
511	Q₈	—	2	2	no	—
512	Q₈	—	2	2	no	—
513	Q₈	—	2	2	no	—
514	Q₈	—	2	2	no	—
515	Q₈	—	2	2	no	—
516	Q₈	—	4	1	no	—
517	Q₈	—	4	2	no	—
518	Q₈	—	4	2	no	—
519	Q₈	—	4	2	no	—
520	Q₈	—	4	4	no	—
521	Q₈	—	8	1	no	—
522	Q₈	—	8	1	no	—
523	D₄	—	2	2	no	—
524	D₄	—	2	2	no	—
525	D₄	—	2	2	no	—
526	D₄	—	2	2	no	—
527	D₄	—	2	2	no	—
528	D₄	—	4	1	no	—
529	D₄	—	4	2	no	—
530	D₄	—	4	2	no	—
531	D₄	—	4	2	no	—
532	D₄	—	8	1	no	—
533	D₄	—	8	1	no	—
534	D₄	—	8	1	no	—
535	D₄	—	8	1	no	—
536	D₄	—	8	1	no	—
537	D₄	—	8	1	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	4	no	—
558	C₂×C₄	—	8	1	no	—
559	C₂×C₄	—	8	1	no	—
560	C₂×C₄	—	8	1	no	—
561	C₂×C₄	—	8	1	no	—
562	C₂×C₄	—	8	1	no	—
563	C₂×C₄	—	8	1	no	—
564	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
565	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
566	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
567	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
568	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
569	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
570	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
571	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
572	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
573	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
574	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
575	C₂×C₄	C₂⁵	1	1	yes	characteristic
576	C₈	—	2	2	no	—
577	C₈	—	2	2	no	—
578	C₈	—	2	2	no	—
579	C₈	—	2	2	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	2	1	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	2	1	no	—
585	C₂²	—	2	1	no	—
586	C₂²	—	2	1	no	—
587	C₂²	—	2	1	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	16	2	no	—
598	C₂²	—	16	2	no	—
599	C₂²	#575	1	2	yes	—
600	C₂²	C₂³×D₄	1	1	yes	characteristic
601	C₄	—	2	1	no	—
602	C₄	—	2	1	no	—
603	C₄	—	2	1	no	—
604	C₄	—	2	1	no	—
605	C₄	—	2	1	no	—
606	C₄	—	2	1	no	—
607	C₄	—	2	1	no	—
608	C₄	—	2	1	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	1	no	—
611	C₄	—	2	1	no	—
612	C₄	—	4	1	no	—
613	C₄	—	4	2	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	1	no	—
616	C₄	—	4	1	no	—
617	C₄	—	4	2	no	—
618	C₄	—	4	1	no	—
619	C₄	—	4	2	no	—
620	C₄	—	4	2	no	—
621	C₄	#585	1	2	yes	—
622	C₂	—	2	2	no	—
623	C₂	—	4	1	no	—
624	C₂	—	4	1	no	—
625	C₂	—	8	1	no	—
626	C₂	—	8	1	no	—
627	C₂	—	8	1	no	—
628	C₂	#3500	1	1	yes	characteristic
629	C₂	C₂×#575	1	1	yes	characteristic
630	C₂	#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
prime radical	#3514	C₂
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
2. #3509	C₂	semidirect
3. #3377	C₂	semidirect
4. #3371	C₂	semidirect
5. #3313	C₂	semidirect
6. #3312	C₂	semidirect
7. #3311	C₂	semidirect
8. #3310	C₂	semidirect
9. #3300	C₂	semidirect
10. #3296	C₂	semidirect
11. #3240	C₂	semidirect
12. #3240	C₂	semidirect
13. #3238	C₂	semidirect
14. #3216	C₂	semidirect
15. #3215	C₂	semidirect
16. #3215	C₂	semidirect
17. #3181	C₂	semidirect
18. #3181	C₂	semidirect
19. #3172	C₂	semidirect
20. #3140	C₂	semidirect
21. #3135	C₂	semidirect
22. C₂×#489	C₂	semidirect
23. #2970	C₂	semidirect
26. #557	C₂²	semidirect
29. #556	C₂²	semidirect
34. #552	C₂²	semidirect
50. #533	C₂²	semidirect
51. #533	C₂²	semidirect
52. #533	C₂²	semidirect
53. #533	C₂²	semidirect
54. #533	C₂²	semidirect
56. C₂×C₄⋊Q₈	C₂²	semidirect
65. #501	C₂²	semidirect
66. #501	C₂²	semidirect
67. #501	C₂²	semidirect
69. #497	C₂²	semidirect
70. #497	C₂²	semidirect
71. #491	C₂²	semidirect
72. #491	C₂²	semidirect
78. #489	C₂²	semidirect
79. #489	C₂²	semidirect
80. #489	C₂²	semidirect
81. #489	C₂²	semidirect
82. #489	C₂²	semidirect
83. #489	C₂²	semidirect
84. #489	C₂²	semidirect
86. #488	C₂²	semidirect
87. #485	C₂²	semidirect
88. #485	C₂²	semidirect
89. #483	C₂²	semidirect
93. #479	C₂²	semidirect
94. #479	C₂²	semidirect
96. #478	C₂²	semidirect
97. #477	C₂²	semidirect
98. #476	C₂²	semidirect
99. #470	C₂²	semidirect
101. #467	C₂²	semidirect
102. #467	C₂²	semidirect
107. #464	C₂²	semidirect
108. #464	C₂²	semidirect
109. #462	C₂²	semidirect
111. #452	C₂²	semidirect
112. #452	C₂²	semidirect
113. #451	C₂²	semidirect
114. #451	C₂²	semidirect
117. #446	C₂²	semidirect
118. #441	C₂²	semidirect
119. #441	C₂²	semidirect
121. #440	C₂²	semidirect
122. C₄×Q₁₆	C₂²	semidirect
123. C₄×SD₁₆	C₂²	semidirect
125. #435	C₂²	semidirect
126. C₈×D₄	C₂²	semidirect
127. #432	C₂²	semidirect
128. #432	C₂²	semidirect
129. #432	C₂²	semidirect
130. #419	C₂²	semidirect
132. #416	C₂²	semidirect
133. #416	C₂²	semidirect
134. C₂×#103	C₂²	semidirect
136. C₄×M₁₆	C₂²	semidirect
137. C₂×#97	C₂²	semidirect
138. C₂×#97	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
#3509	2
#3377	2
#3371	2
#3313	2
#3312	2
#3311	2
#3310	2
#3300	2
#3296	2
#3240	2
#3238	2
#3216	2
#3215	2
#3181	2
#3172	2
#3140	2
#3135	2
C₂×#489	2
#2970	2