Subgroups — #61533

Order 256.

887 conjugacy classes of subgroups.

The subgroup lattice has 839 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3524	C₂	1	1	yes	maximal, characteristic, complemented
2	#3518	C₂	1	1	yes	maximal, characteristic, complemented
3	#3401	C₂	1	1	yes	maximal, characteristic, complemented
4	#3387	C₂	1	1	yes	maximal, characteristic, complemented
5	#3377	C₂	1	1	yes	maximal, characteristic, complemented
6	#3375	C₂	1	1	yes	maximal, characteristic, complemented
7	#3349	C₂	1	1	yes	maximal, characteristic, complemented
8	#3347	C₂	1	1	yes	maximal, characteristic, complemented
9	#3340	C₂	1	1	yes	maximal, characteristic, complemented
10	#3321	C₂	1	1	yes	maximal, characteristic, complemented
11	#3321	C₂	1	1	yes	maximal, characteristic, complemented
12	#3320	C₂	1	1	yes	maximal, characteristic, complemented
13	#3313	C₂	1	1	yes	maximal, characteristic, complemented
14	#3304	C₂	1	1	yes	maximal, characteristic, complemented
15	#3300	C₂	1	1	yes	maximal, characteristic, complemented
16	#3285	C₂	1	1	yes	maximal, characteristic, complemented
17	#3271	C₂	1	1	yes	maximal, characteristic, complemented
18	#3270	C₂	1	1	yes	maximal, characteristic, complemented
19	#3181	C₂	1	1	yes	maximal, characteristic, complemented
20	#3179	C₂	1	1	yes	maximal, characteristic, complemented
21	#3173	C₂	1	1	yes	maximal, characteristic, complemented
22	#3126	C₂	1	1	yes	maximal, characteristic, complemented
23	#3124	C₂	1	1	yes	maximal, characteristic, complemented
24	#3121	C₂	1	1	yes	maximal, characteristic, complemented
25	#3121	C₂	1	1	yes	maximal, characteristic, complemented
26	#3107	C₂	1	1	yes	maximal, characteristic, complemented
27	#3102	C₂	1	1	yes	maximal, characteristic, complemented
28	#2968	C₂	1	1	yes	maximal, characteristic, complemented
29	#2950	C₂	1	1	yes	maximal, characteristic, complemented
30	#2947	C₂	1	1	yes	maximal, characteristic, complemented
31	#2943	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#137	C₂²	1	1	yes	characteristic
33	C₂×#135	C₂²	1	1	yes	characteristic
34	C₂²×Q₁₆	C₂²	1	1	yes	characteristic
35	#559	—	2	1	no	—
36	#559	C₂²	1	1	yes	characteristic
37	Q₈²	C₂²	1	1	yes	characteristic
38	#557	C₂²	1	1	yes	characteristic
39	#556	—	2	1	no	—
40	#556	—	2	1	no	—
41	#556	—	2	1	no	—
42	#556	C₂²	1	1	yes	characteristic
43	#556	C₂²	1	1	yes	characteristic
44	#556	C₂²	1	1	yes	characteristic
45	#555	—	2	1	no	—
46	#555	—	2	1	no	—
47	#555	C₂²	1	1	yes	characteristic
48	#555	C₂²	1	1	yes	characteristic
49	#553	—	2	1	no	—
50	#553	C₂²	1	1	yes	characteristic
51	#552	—	2	1	no	—
52	#552	C₂²	1	1	yes	characteristic
53	#550	C₂²	1	1	yes	characteristic
54	D₄×Q₈	C₂²	1	1	yes	characteristic
55	#548	C₂²	1	1	yes	characteristic
56	#548	C₂²	1	1	yes	characteristic
57	#548	C₂²	1	1	yes	characteristic
58	#548	C₂²	1	1	yes	characteristic
59	#542	—	2	1	no	—
60	#542	—	2	1	no	—
61	#542	—	2	1	no	—
62	#542	C₂²	1	1	yes	characteristic
63	#542	C₂²	1	1	yes	characteristic
64	#542	C₂²	1	1	yes	characteristic
65	#540	—	2	1	no	—
66	#540	C₂²	1	1	yes	characteristic
67	#533	—	2	1	no	—
68	#533	C₂²	1	1	yes	characteristic
69	#529	—	2	1	no	—
70	#529	—	2	1	no	—
71	#529	—	2	1	no	—
72	#529	C₂²	1	1	yes	characteristic
73	#529	C₂²	1	1	yes	characteristic
74	#520	C₂²	1	1	yes	characteristic
75	#519	C₂²	1	1	yes	characteristic
76	#519	C₂²	1	1	yes	characteristic
77	#519	C₂²	1	1	yes	characteristic
78	C₄×#41	C₂²	1	1	yes	characteristic
79	C₄×#41	C₂²	1	1	yes	characteristic
80	#501	C₂²	1	1	yes	characteristic
81	#501	C₂²	1	1	yes	characteristic
82	#498	C₂²	1	1	yes	characteristic
83	#497	C₂²	1	1	yes	characteristic
84	#496	C₂²	1	1	yes	characteristic
85	#495	C₂²	1	1	yes	characteristic
86	#491	C₂²	1	1	yes	characteristic
87	#489	C₂²	1	1	yes	characteristic
88	#489	C₂²	1	1	yes	characteristic
89	#489	C₂²	1	1	yes	characteristic
90	#488	C₂²	1	1	yes	characteristic
91	#486	C₂²	1	1	yes	characteristic
92	#485	C₂²	1	1	yes	characteristic
93	#485	C₂²	1	1	yes	characteristic
94	#485	C₂²	1	1	yes	characteristic
95	#485	C₂²	1	1	yes	characteristic
96	#485	C₂²	1	1	yes	characteristic
97	#484	C₂²	1	1	yes	characteristic
98	#482	C₂²	1	1	yes	characteristic
99	#482	C₂²	1	1	yes	characteristic
100	#482	C₂²	1	1	yes	characteristic
101	#482	C₂²	1	1	yes	characteristic
102	#482	C₂²	1	1	yes	characteristic
103	#480	C₂²	1	1	yes	characteristic
104	#479	C₂²	1	1	yes	characteristic
105	#479	C₂²	1	1	yes	characteristic
106	#479	C₂²	1	1	yes	characteristic
107	#478	C₂²	1	1	yes	characteristic
108	#477	C₂²	1	1	yes	characteristic
109	#477	C₂²	1	1	yes	characteristic
110	#477	C₂²	1	1	yes	characteristic
111	#475	C₂²	1	1	yes	characteristic
112	#475	C₂²	1	1	yes	characteristic
113	#475	C₂²	1	1	yes	characteristic
114	#474	C₂²	1	1	yes	characteristic
115	#474	C₂²	1	1	yes	characteristic
116	#470	C₂²	1	1	yes	characteristic
117	#469	C₂²	1	1	yes	characteristic
118	#469	C₂²	1	1	yes	characteristic
119	#468	C₂²	1	1	yes	characteristic
120	#467	C₂²	1	1	yes	characteristic
121	#467	C₂²	1	1	yes	characteristic
122	#466	C₂²	1	1	yes	characteristic
123	#465	C₂²	1	1	yes	characteristic
124	#465	C₂²	1	1	yes	characteristic
125	#465	C₂²	1	1	yes	characteristic
126	#465	C₂²	1	1	yes	characteristic
127	#465	C₂²	1	1	yes	characteristic
128	#464	C₂²	1	1	yes	characteristic
129	#464	C₂²	1	1	yes	characteristic
130	#464	C₂²	1	1	yes	characteristic
131	#464	C₂²	1	1	yes	characteristic
132	#464	C₂²	1	1	yes	characteristic
133	#464	C₂²	1	1	yes	characteristic
134	#463	C₂²	1	1	yes	characteristic
135	#463	C₂²	1	1	yes	characteristic
136	#462	C₂²	1	1	yes	characteristic
137	#461	C₂²	1	1	yes	characteristic
138	#460	C₂²	1	1	yes	characteristic
139	#460	C₂²	1	1	yes	characteristic
140	#452	C₂²	1	1	yes	characteristic
141	#452	C₂²	1	1	yes	characteristic
142	#452	C₂²	1	1	yes	characteristic
143	#452	C₂²	1	1	yes	characteristic
144	#451	C₂²	1	1	yes	characteristic
145	#451	C₂²	1	1	yes	characteristic
146	#449	C₂²	1	1	yes	characteristic
147	#449	C₂²	1	1	yes	characteristic
148	#448	C₂²	1	1	yes	characteristic
149	#448	C₂²	1	1	yes	characteristic
150	#448	C₂²	1	1	yes	characteristic
151	#448	C₂²	1	1	yes	characteristic
152	#446	C₂²	1	1	yes	characteristic
153	#446	C₂²	1	1	yes	characteristic
154	#442	C₂²	1	1	yes	characteristic
155	#442	C₂²	1	1	yes	characteristic
156	#441	C₂²	1	1	yes	characteristic
157	#441	C₂²	1	1	yes	characteristic
158	#441	C₂²	1	1	yes	characteristic
159	#441	C₂²	1	1	yes	characteristic
160	#441	C₂²	1	1	yes	characteristic
161	#441	C₂²	1	1	yes	characteristic
162	#441	C₂²	1	1	yes	characteristic
163	#440	C₂²	1	1	yes	characteristic
164	#440	C₂²	1	1	yes	characteristic
165	#440	C₂²	1	1	yes	characteristic
166	#440	C₂²	1	1	yes	characteristic
167	#440	C₂²	1	1	yes	characteristic
168	#440	C₂²	1	1	yes	characteristic
169	#440	C₂²	1	1	yes	characteristic
170	C₄×Q₁₆	C₂²	1	1	yes	characteristic
171	C₄×Q₁₆	C₂²	1	1	yes	characteristic
172	C₄×Q₁₆	C₂²	1	1	yes	characteristic
173	C₄×Q₁₆	C₂²	1	1	yes	characteristic
174	C₄×Q₁₆	C₂²	1	1	yes	characteristic
175	C₄×Q₁₆	C₂²	1	1	yes	characteristic
176	C₄×SD₁₆	C₂²	1	1	yes	characteristic
177	C₄×SD₁₆	C₂²	1	1	yes	characteristic
178	C₄×SD₁₆	C₂²	1	1	yes	characteristic
179	C₄×SD₁₆	C₂²	1	1	yes	characteristic
180	C₄×SD₁₆	C₂²	1	1	yes	characteristic
181	C₄×D₈	C₂²	1	1	yes	characteristic
182	#435	C₂²	1	1	yes	characteristic
183	#435	C₂²	1	1	yes	characteristic
184	#435	C₂²	1	1	yes	characteristic
185	#435	C₂²	1	1	yes	characteristic
186	C₈×D₄	C₂²	1	1	yes	characteristic
187	C₈×D₄	C₂²	1	1	yes	characteristic
188	#433	C₂²	1	1	yes	characteristic
189	#433	C₂²	1	1	yes	characteristic
190	#431	C₂²	1	1	yes	characteristic
191	#428	C₂²	1	1	yes	characteristic
192	#427	C₂²	1	1	yes	characteristic
193	#427	C₂²	1	1	yes	characteristic
194	#419	C₂²	1	1	yes	characteristic
195	#419	C₂²	1	1	yes	characteristic
196	#416	C₂²	1	1	yes	characteristic
197	#416	C₂²	1	1	yes	characteristic
198	#416	C₂²	1	1	yes	characteristic
199	C₂×#103	C₂²	1	1	yes	characteristic
200	#405	C₂²	1	1	yes	characteristic
201	#405	C₂²	1	1	yes	characteristic
202	C₂×#97	C₂²	1	1	yes	characteristic
203	C₂×#41	C₂³	1	1	yes	characteristic
204	C₂×#41	C₂³	1	1	yes	characteristic
205	C₂×#41	C₂³	1	1	yes	characteristic
206	C₂²×Q₈	C₂³	1	1	yes	characteristic
207	C₂²×Q₈	C₂³	1	1	yes	characteristic
208	C₂²×Q₈	C₂³	1	1	yes	characteristic
209	#137	—	2	4	no	—
210	#135	—	2	4	no	—
211	C₂×Q₁₆	—	2	4	no	—
212	C₂×Q₁₆	C₂³	1	1	yes	characteristic
213	C₂×Q₁₆	C₂³	1	1	yes	characteristic
214	C₂×Q₁₆	C₂³	1	1	yes	characteristic
215	C₂×Q₁₆	C₂³	1	1	yes	characteristic
216	C₂×Q₁₆	C₂³	1	1	yes	characteristic
217	C₂×Q₁₆	C₂³	1	1	yes	characteristic
218	C₂×SD₁₆	C₂³	1	1	yes	characteristic
219	C₂×SD₁₆	C₂³	1	1	yes	characteristic
220	C₂×SD₁₆	C₂³	1	1	yes	characteristic
221	C₂×SD₁₆	C₂³	1	1	yes	characteristic
222	C₂×SD₁₆	C₂³	1	1	yes	characteristic
223	C₂×SD₁₆	C₂³	1	1	yes	characteristic
224	C₂×SD₁₆	C₂³	1	1	yes	characteristic
225	C₂×SD₁₆	C₂³	1	1	yes	characteristic
226	C₂×D₈	C₂³	1	1	yes	characteristic
227	C₂×D₈	C₂³	1	1	yes	characteristic
228	C₂×M₁₆	C₂³	1	1	yes	characteristic
229	C₂×M₁₆	C₂³	1	1	yes	characteristic
230	C₂²×C₈	C₂³	1	1	yes	characteristic
231	C₂²×C₈	C₂³	1	1	yes	characteristic
232	C₂²×C₈	C₂³	1	1	yes	characteristic
233	C₂²×C₈	C₂³	1	1	yes	characteristic
234	C₄⋊Q₈	—	2	1	no	—
235	C₄⋊Q₈	—	2	1	no	—
236	C₄⋊Q₈	—	2	1	no	—
237	C₄⋊Q₈	—	2	1	no	—
238	C₄⋊Q₈	—	2	1	no	—
239	C₄⋊Q₈	C₂³	1	1	yes	characteristic
240	C₄⋊Q₈	C₂³	1	1	yes	characteristic
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	#127	—	2	1	no	—
245	#127	C₂³	1	1	yes	characteristic
246	#126	—	2	1	no	—
247	#126	—	2	1	no	—
248	#126	—	2	1	no	—
249	#126	—	2	1	no	—
250	#126	—	2	1	no	—
251	#126	—	2	1	no	—
252	#126	—	2	1	no	—
253	#126	—	2	1	no	—
254	#126	—	2	1	no	—
255	#126	—	2	1	no	—
256	#126	—	2	1	no	—
257	#126	—	2	1	no	—
258	#126	D₄	1	1	yes	characteristic
259	#126	D₄	1	1	yes	characteristic
260	#125	—	2	1	no	—
261	#125	—	2	1	no	—
262	#125	—	2	1	no	—
263	#125	—	2	1	no	—
264	#125	D₄	1	1	yes	characteristic
265	#125	C₂³	1	1	yes	characteristic
266	#125	C₂³	1	1	yes	characteristic
267	#124	—	2	1	no	—
268	#124	—	2	1	no	—
269	#124	—	2	1	no	—
270	#124	—	2	1	no	—
271	#124	—	2	1	no	—
272	#124	—	2	1	no	—
273	#124	—	2	1	no	—
274	#124	—	2	1	no	—
275	#124	—	2	1	no	—
276	#124	—	2	1	no	—
277	#124	—	2	1	no	—
278	#124	—	2	1	no	—
279	#124	—	2	1	no	—
280	#124	—	2	1	no	—
281	#124	D₄	1	1	yes	characteristic
282	#124	C₂³	1	1	yes	characteristic
283	#124	C₂³	1	1	yes	characteristic
284	#124	C₂³	1	1	yes	characteristic
285	#124	C₂³	1	1	yes	characteristic
286	#123	—	2	1	no	—
287	#123	—	2	1	no	—
288	#123	—	2	1	no	—
289	#123	—	2	1	no	—
290	#123	—	2	1	no	—
291	#123	—	2	1	no	—
292	#123	—	2	1	no	—
293	#123	—	2	1	no	—
294	#123	—	2	1	no	—
295	#123	—	2	1	no	—
296	#123	D₄	1	1	yes	characteristic
297	#123	D₄	1	1	yes	characteristic
298	C₂²⋊Q₈	—	2	1	no	—
299	C₂²⋊Q₈	—	2	1	no	—
300	C₂²⋊Q₈	—	2	1	no	—
301	C₂²⋊Q₈	—	2	1	no	—
302	C₂²⋊Q₈	—	2	1	no	—
303	C₂²⋊Q₈	—	2	1	no	—
304	C₂²⋊Q₈	—	2	1	no	—
305	C₂²⋊Q₈	—	2	1	no	—
306	C₂²⋊Q₈	—	2	1	no	—
307	C₂²⋊Q₈	—	2	1	no	—
308	C₂²⋊Q₈	—	2	1	no	—
309	C₂²⋊Q₈	D₄	1	1	yes	characteristic
310	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
311	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
312	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
313	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
314	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
315	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
316	#121	—	2	1	no	—
317	#121	—	2	1	no	—
318	#121	—	2	1	no	—
319	#121	—	2	1	no	—
320	#121	—	2	1	no	—
321	#121	—	2	1	no	—
322	#121	—	2	1	no	—
323	#121	—	2	1	no	—
324	#121	—	2	1	no	—
325	#121	—	2	1	no	—
326	#121	—	2	1	no	—
327	#121	D₄	1	1	yes	characteristic
328	#121	C₂³	1	1	yes	characteristic
329	#121	C₂³	1	1	yes	characteristic
330	#121	C₂³	1	1	yes	characteristic
331	#121	C₂³	1	1	yes	characteristic
332	#121	C₂³	1	1	yes	characteristic
333	#121	C₂³	1	1	yes	characteristic
334	C₄×Q₈	—	2	1	no	—
335	C₄×Q₈	—	2	1	no	—
336	C₄×Q₈	—	2	1	no	—
337	C₄×Q₈	—	2	1	no	—
338	C₄×Q₈	—	2	1	no	—
339	C₄×Q₈	—	2	1	no	—
340	C₄×Q₈	—	2	1	no	—
341	C₄×Q₈	—	2	1	no	—
342	C₄×Q₈	—	2	1	no	—
343	C₄×Q₈	—	2	1	no	—
344	C₄×Q₈	—	2	1	no	—
345	C₄×Q₈	C₂³	1	1	yes	characteristic
346	C₄×Q₈	C₂³	1	1	yes	characteristic
347	C₄×Q₈	C₂³	1	1	yes	characteristic
348	C₄×Q₈	C₂³	1	1	yes	characteristic
349	C₄×Q₈	C₂³	1	1	yes	characteristic
350	C₄×Q₈	C₂³	1	1	yes	characteristic
351	C₄×Q₈	C₂³	1	1	yes	characteristic
352	C₄×Q₈	C₂³	1	1	yes	characteristic
353	C₄×Q₈	C₂³	1	1	yes	characteristic
354	C₄×Q₈	C₂³	1	1	yes	characteristic
355	C₄×Q₈	C₂³	1	1	yes	characteristic
356	C₄×Q₈	C₂³	1	1	yes	characteristic
357	C₄×Q₈	C₂³	1	1	yes	characteristic
358	C₄×Q₈	C₂³	1	1	yes	characteristic
359	C₄×Q₈	C₂³	1	1	yes	characteristic
360	C₄×D₄	—	2	1	no	—
361	C₄×D₄	—	2	1	no	—
362	C₄×D₄	—	2	1	no	—
363	C₄×D₄	—	2	1	no	—
364	C₄×D₄	—	2	1	no	—
365	C₄×D₄	—	2	1	no	—
366	C₄×D₄	—	2	1	no	—
367	C₄×D₄	—	2	1	no	—
368	C₄×D₄	—	2	1	no	—
369	C₄×D₄	—	2	1	no	—
370	C₄×D₄	—	2	1	no	—
371	C₄×D₄	—	2	1	no	—
372	C₄×D₄	—	2	1	no	—
373	C₄×D₄	—	2	1	no	—
374	C₄×D₄	—	2	1	no	—
375	C₄×D₄	C₂³	1	1	yes	characteristic
376	C₄×D₄	C₂³	1	1	yes	characteristic
377	C₄×D₄	C₂³	1	1	yes	characteristic
378	C₄×D₄	C₂³	1	1	yes	characteristic
379	C₄×D₄	C₂³	1	1	yes	characteristic
380	C₄×D₄	C₂³	1	1	yes	characteristic
381	C₄×D₄	C₂³	1	1	yes	characteristic
382	C₄×D₄	C₂³	1	1	yes	characteristic
383	C₄×D₄	C₂³	1	1	yes	characteristic
384	#117	—	2	1	no	—
385	#117	—	2	1	no	—
386	#117	—	2	1	no	—
387	#117	—	2	1	no	—
388	#117	—	2	1	no	—
389	#117	—	2	1	no	—
390	#117	—	2	1	no	—
391	#117	—	2	1	no	—
392	#117	—	2	1	no	—
393	#117	—	2	1	no	—
394	#117	—	2	1	no	—
395	#117	—	2	1	no	—
396	#117	—	2	1	no	—
397	#117	—	2	1	no	—
398	#117	—	2	1	no	—
399	#117	C₂³	1	1	yes	characteristic
400	#117	C₂³	1	1	yes	characteristic
401	#117	C₂³	1	1	yes	characteristic
402	#117	C₂³	1	1	yes	characteristic
403	#117	C₂³	1	1	yes	characteristic
404	#117	C₂³	1	1	yes	characteristic
405	#117	C₂³	1	1	yes	characteristic
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
408	C₂×C₄²	—	2	1	no	—
409	C₂×C₄²	—	2	1	no	—
410	C₂×C₄²	C₂³	1	1	yes	characteristic
411	#107	C₂³	1	1	yes	characteristic
412	#107	C₂³	1	1	yes	characteristic
413	#107	C₂³	1	1	yes	characteristic
414	#107	C₂³	1	1	yes	characteristic
415	#107	C₂³	1	1	yes	characteristic
416	#107	C₂³	1	1	yes	characteristic
417	#107	C₂³	1	1	yes	characteristic
418	#107	C₂³	1	1	yes	characteristic
419	#106	C₂³	1	1	yes	characteristic
420	#106	C₂³	1	1	yes	characteristic
421	#106	C₂³	1	1	yes	characteristic
422	#106	C₂³	1	1	yes	characteristic
423	#106	C₂³	1	1	yes	characteristic
424	#106	C₂³	1	1	yes	characteristic
425	#106	C₂³	1	1	yes	characteristic
426	#106	C₂³	1	1	yes	characteristic
427	C₄⋊C₈	C₂³	1	1	yes	characteristic
428	C₄⋊C₈	C₂³	1	1	yes	characteristic
429	C₄⋊C₈	C₂³	1	1	yes	characteristic
430	C₄⋊C₈	C₂³	1	1	yes	characteristic
431	C₄⋊C₈	C₂³	1	1	yes	characteristic
432	C₄⋊C₈	C₂³	1	1	yes	characteristic
433	#103	C₂³	1	1	yes	characteristic
434	#103	C₂³	1	1	yes	characteristic
435	#103	C₂³	1	1	yes	characteristic
436	#103	C₂³	1	1	yes	characteristic
437	#103	C₂³	1	1	yes	characteristic
438	#103	C₂³	1	1	yes	characteristic
439	#103	C₂³	1	1	yes	characteristic
440	#103	C₂³	1	1	yes	characteristic
441	#103	C₂³	1	1	yes	characteristic
442	#103	C₂³	1	1	yes	characteristic
443	#103	C₂³	1	1	yes	characteristic
444	#103	C₂³	1	1	yes	characteristic
445	#103	C₂³	1	1	yes	characteristic
446	#103	C₂³	1	1	yes	characteristic
447	#103	C₂³	1	1	yes	characteristic
448	#103	C₂³	1	1	yes	characteristic
449	#103	C₂³	1	1	yes	characteristic
450	#103	C₂³	1	1	yes	characteristic
451	#103	C₂³	1	1	yes	characteristic
452	#103	C₂³	1	1	yes	characteristic
453	#102	C₂³	1	1	yes	characteristic
454	#102	C₂³	1	1	yes	characteristic
455	#102	C₂³	1	1	yes	characteristic
456	#102	C₂³	1	1	yes	characteristic
457	#102	C₂³	1	1	yes	characteristic
458	#102	C₂³	1	1	yes	characteristic
459	#102	C₂³	1	1	yes	characteristic
460	#102	C₂³	1	1	yes	characteristic
461	#102	C₂³	1	1	yes	characteristic
462	#102	C₂³	1	1	yes	characteristic
463	#102	C₂³	1	1	yes	characteristic
464	#102	C₂³	1	1	yes	characteristic
465	C₂²⋊C₈	C₂³	1	1	yes	characteristic
466	C₂²⋊C₈	C₂³	1	1	yes	characteristic
467	C₂²⋊C₈	C₂³	1	1	yes	characteristic
468	C₂²⋊C₈	C₂³	1	1	yes	characteristic
469	C₂²⋊C₈	C₂³	1	1	yes	characteristic
470	C₂²⋊C₈	C₂³	1	1	yes	characteristic
471	#97	C₂³	1	1	yes	characteristic
472	#97	C₂³	1	1	yes	characteristic
473	#97	C₂³	1	1	yes	characteristic
474	#97	C₂³	1	1	yes	characteristic
475	#97	C₂³	1	1	yes	characteristic
476	#97	C₂³	1	1	yes	characteristic
477	C₄×C₈	C₂³	1	1	yes	characteristic
478	C₄×C₈	C₂³	1	1	yes	characteristic
479	C₄×C₈	C₂³	1	1	yes	characteristic
480	C₄×C₈	C₂³	1	1	yes	characteristic
481	#41	—	2	2	no	—
482	#41	—	2	2	no	—
483	#41	—	2	2	no	—
484	#41	—	4	1	no	—
485	#41	—	4	1	no	—
486	#41	—	4	1	no	—
487	C₂×Q₈	—	2	1	no	—
488	C₂×Q₈	—	2	1	no	—
489	C₂×Q₈	—	2	1	no	—
490	C₂×Q₈	—	2	1	no	—
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	—	2	1	no	—
494	C₂×Q₈	—	2	2	no	—
495	C₂×Q₈	—	2	2	no	—
496	C₂×Q₈	—	2	2	no	—
497	C₂×Q₈	—	4	1	no	—
498	C₂×Q₈	—	4	1	no	—
499	C₂×Q₈	—	4	1	no	—
500	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
501	C₂×Q₈	C₂⁴	1	1	yes	characteristic
502	C₂×Q₈	C₂⁴	1	1	yes	characteristic
503	C₂×Q₈	C₂⁴	1	1	yes	characteristic
504	C₂×Q₈	C₂⁴	1	1	yes	characteristic
505	C₂×Q₈	C₂⁴	1	1	yes	characteristic
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	—	2	1	no	—
517	C₂×D₄	C₂×D₄	1	1	yes	characteristic
518	C₂×D₄	C₂×D₄	1	1	yes	characteristic
519	C₂×D₄	C₂×D₄	1	1	yes	characteristic
520	C₂×D₄	C₂⁴	1	1	yes	characteristic
521	C₂×D₄	C₂⁴	1	1	yes	characteristic
522	C₂×D₄	C₂⁴	1	1	yes	characteristic
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
537	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
538	C₂²×C₄	C₂⁴	1	1	yes	characteristic
539	C₂²×C₄	C₂⁴	1	1	yes	characteristic
540	C₂²×C₄	C₂⁴	1	1	yes	characteristic
541	Q₁₆	—	2	2	no	—
542	Q₁₆	—	2	2	no	—
543	Q₁₆	—	2	2	no	—
544	Q₁₆	—	2	2	no	—
545	Q₁₆	—	4	1	no	—
546	Q₁₆	#41	1	4	yes	—
547	SD₁₆	—	2	2	no	—
548	SD₁₆	—	2	2	no	—
549	SD₁₆	—	2	2	no	—
550	SD₁₆	—	2	2	no	—
551	SD₁₆	—	4	1	no	—
552	SD₁₆	—	4	1	no	—
553	SD₁₆	—	4	1	no	—
554	SD₁₆	—	4	1	no	—
555	D₈	—	2	2	no	—
556	D₈	—	4	1	no	—
557	M₁₆	—	2	2	no	—
558	M₁₆	—	4	1	no	—
559	C₂×C₈	—	2	2	no	—
560	C₂×C₈	—	2	2	no	—
561	C₂×C₈	—	4	1	no	—
562	C₂×C₈	—	4	1	no	—
563	C₂×C₈	C₂⁴	1	1	yes	characteristic
564	C₂×C₈	C₂⁴	1	1	yes	characteristic
565	C₂×C₈	C₂⁴	1	1	yes	characteristic
566	C₂×C₈	C₂⁴	1	1	yes	characteristic
567	C₂×C₈	C₂⁴	1	1	yes	characteristic
568	C₂×C₈	C₂⁴	1	1	yes	characteristic
569	C₂×C₈	C₂⁴	1	1	yes	characteristic
570	C₂×C₈	C₂⁴	1	1	yes	characteristic
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	2	1	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	2	1	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	2	1	no	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	1	no	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
603	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
604	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
605	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
606	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
607	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
608	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
609	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
610	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
611	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
612	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
613	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
614	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
615	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
616	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
617	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
618	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
619	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
620	C₂²⋊C₄	—	2	1	no	—
621	C₂²⋊C₄	—	2	1	no	—
622	C₂²⋊C₄	—	2	1	no	—
623	C₂²⋊C₄	—	2	1	no	—
624	C₂²⋊C₄	—	2	1	no	—
625	C₂²⋊C₄	—	2	1	no	—
626	C₂²⋊C₄	—	2	1	no	—
627	C₂²⋊C₄	—	2	1	no	—
628	C₂²⋊C₄	—	2	1	no	—
629	C₂²⋊C₄	—	2	1	no	—
630	C₂²⋊C₄	—	2	1	no	—
631	C₂²⋊C₄	—	2	1	no	—
632	C₂²⋊C₄	—	2	1	no	—
633	C₂²⋊C₄	—	2	1	no	—
634	C₂²⋊C₄	—	2	1	no	—
635	C₂²⋊C₄	—	2	1	no	—
636	C₂²⋊C₄	—	2	1	no	—
637	C₂²⋊C₄	—	2	1	no	—
638	C₂²⋊C₄	—	2	1	no	—
639	C₂²⋊C₄	—	2	1	no	—
640	C₂²⋊C₄	—	2	1	no	—
641	C₂²⋊C₄	—	2	1	no	—
642	C₂²⋊C₄	—	2	1	no	—
643	C₂²⋊C₄	—	2	1	no	—
644	C₂²⋊C₄	—	2	1	no	—
645	C₂²⋊C₄	—	2	1	no	—
646	C₂²⋊C₄	—	2	1	no	—
647	C₂²⋊C₄	—	2	1	no	—
648	C₂²⋊C₄	—	2	1	no	—
649	C₂²⋊C₄	—	2	1	no	—
650	C₂²⋊C₄	—	2	1	no	—
651	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
652	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
653	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
654	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
655	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
656	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
657	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
658	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
659	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
660	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
661	C₄²	—	2	1	no	—
662	C₄²	—	2	1	no	—
663	C₄²	—	2	1	no	—
664	C₄²	—	2	1	no	—
665	C₄²	—	2	1	no	—
666	C₄²	—	2	1	no	—
667	C₄²	—	2	1	no	—
668	C₄²	—	2	1	no	—
669	C₄²	—	2	1	no	—
670	C₄²	—	2	1	no	—
671	C₄²	—	2	1	no	—
672	C₄²	—	2	1	no	—
673	C₄²	—	2	1	no	—
674	C₄²	—	2	1	no	—
675	C₄²	—	2	1	no	—
676	C₄²	—	2	1	no	—
677	C₄²	—	2	1	no	—
678	C₄²	—	2	1	no	—
679	C₄²	—	2	1	no	—
680	C₄²	C₂×D₄	1	1	yes	characteristic
681	C₄²	C₂×D₄	1	1	yes	characteristic
682	C₄²	C₂⁴	1	1	yes	characteristic
683	C₄²	C₂⁴	1	1	yes	characteristic
684	C₄²	C₂⁴	1	1	yes	characteristic
685	C₄²	C₂⁴	1	1	yes	characteristic
686	C₂³	—	2	1	no	—
687	C₂³	—	2	1	no	—
688	C₂³	—	2	1	no	—
689	C₂³	C₂²×D₄	1	1	yes	characteristic
690	C₂³	C₂²×D₄	1	1	yes	characteristic
691	C₂³	C₂²×D₄	1	1	yes	characteristic
692	Q₈	—	2	1	no	—
693	Q₈	—	2	1	no	—
694	Q₈	—	2	1	no	—
695	Q₈	—	2	1	no	—
696	Q₈	—	2	1	no	—
697	Q₈	—	2	1	no	—
698	Q₈	—	2	1	no	—
699	Q₈	—	2	1	no	—
700	Q₈	—	4	1	no	—
701	Q₈	—	4	2	no	—
702	Q₈	—	4	2	no	—
703	Q₈	—	4	2	no	—
704	Q₈	—	8	1	no	—
705	Q₈	—	8	1	no	—
706	Q₈	—	8	1	no	—
707	Q₈	—	8	1	no	—
708	Q₈	C₂×#41	1	2	yes	—
709	Q₈	C₂×#41	1	2	yes	—
710	D₄	—	2	1	no	—
711	D₄	—	2	1	no	—
712	D₄	—	2	1	no	—
713	D₄	—	2	1	no	—
714	D₄	—	2	1	no	—
715	D₄	—	2	1	no	—
716	D₄	—	4	1	no	—
717	D₄	—	4	1	no	—
718	D₄	—	4	1	no	—
719	D₄	—	4	2	no	—
720	D₄	—	4	2	no	—
721	D₄	—	4	2	no	—
722	D₄	—	8	1	no	—
723	D₄	—	8	1	no	—
724	D₄	—	8	1	no	—
725	D₄	—	8	1	no	—
726	D₄	—	8	1	no	—
727	D₄	—	8	1	no	—
728	D₄	—	8	1	no	—
729	D₄	—	8	1	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	4	1	no	—
750	C₂×C₄	—	4	1	no	—
751	C₂×C₄	—	4	2	no	—
752	C₂×C₄	—	4	2	no	—
753	C₂×C₄	—	4	2	no	—
754	C₂×C₄	—	4	2	no	—
755	C₂×C₄	—	4	2	no	—
756	C₂×C₄	—	4	2	no	—
757	C₂×C₄	—	4	2	no	—
758	C₂×C₄	—	8	1	no	—
759	C₂×C₄	—	8	1	no	—
760	C₂×C₄	—	8	1	no	—
761	C₂×C₄	—	8	1	no	—
762	C₂×C₄	—	8	1	no	—
763	C₂×C₄	—	8	1	no	—
764	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
765	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
766	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
767	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
768	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
769	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
770	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
771	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
772	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
773	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
774	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
775	C₂×C₄	C₂⁵	1	1	yes	characteristic
776	C₈	—	2	1	no	—
777	C₈	—	2	1	no	—
778	C₈	—	2	1	no	—
779	C₈	—	2	1	no	—
780	C₈	—	2	1	no	—
781	C₈	—	2	1	no	—
782	C₈	—	2	1	no	—
783	C₈	C₂×#41	1	2	yes	—
784	C₂²	—	2	1	no	—
785	C₂²	—	2	1	no	—
786	C₂²	—	2	1	no	—
787	C₂²	—	2	1	no	—
788	C₂²	—	2	1	no	—
789	C₂²	—	2	1	no	—
790	C₂²	—	2	1	no	—
791	C₂²	—	2	1	no	—
792	C₂²	—	2	1	no	—
793	C₂²	—	4	1	no	—
794	C₂²	—	4	1	no	—
795	C₂²	—	4	1	no	—
796	C₂²	—	4	1	no	—
797	C₂²	—	4	1	no	—
798	C₂²	—	4	1	no	—
799	C₂²	—	4	1	no	—
800	C₂²	—	4	1	no	—
801	C₂²	—	4	1	no	—
802	C₂²	C₂³×D₄	1	1	yes	characteristic
803	C₄	—	2	1	no	—
804	C₄	—	2	1	no	—
805	C₄	—	2	1	no	—
806	C₄	—	2	1	no	—
807	C₄	—	2	1	no	—
808	C₄	—	2	1	no	—
809	C₄	—	2	1	no	—
810	C₄	—	2	1	no	—
811	C₄	—	2	1	no	—
812	C₄	—	2	1	no	—
813	C₄	—	2	1	no	—
814	C₄	—	2	2	no	—
815	C₄	—	2	2	no	—
816	C₄	—	4	1	no	—
817	C₄	—	4	1	no	—
818	C₄	—	4	1	no	—
819	C₄	—	4	1	no	—
820	C₄	—	4	1	no	—
821	C₄	—	4	1	no	—
822	C₄	—	4	1	no	—
823	C₄	—	4	1	no	—
824	C₄	—	4	1	no	—
825	C₄	—	4	1	no	—
826	C₄	—	4	1	no	—
827	C₄	C₂²×#41	1	1	yes	characteristic
828	C₄	#585	1	1	yes	characteristic
829	C₂	—	4	1	no	—
830	C₂	—	4	1	no	—
831	C₂	—	4	1	no	—
832	C₂	—	8	1	no	—
833	C₂	—	8	1	no	—
834	C₂	—	8	1	no	—
835	C₂	D₄×#41	1	1	yes	characteristic
836	C₂	#3584	1	1	yes	characteristic
837	C₂	#3586	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. #3524	C₂	semidirect
2. #3518	C₂	semidirect
3. #3401	C₂	semidirect
4. #3387	C₂	semidirect
5. #3377	C₂	semidirect
6. #3375	C₂	semidirect
7. #3349	C₂	semidirect
8. #3347	C₂	semidirect
9. #3340	C₂	semidirect
10. #3321	C₂	semidirect
11. #3321	C₂	semidirect
12. #3320	C₂	semidirect
13. #3313	C₂	semidirect
14. #3304	C₂	semidirect
15. #3300	C₂	semidirect
16. #3285	C₂	semidirect
17. #3271	C₂	semidirect
18. #3270	C₂	semidirect
19. #3181	C₂	semidirect
20. #3179	C₂	semidirect
21. #3173	C₂	semidirect
22. #3126	C₂	semidirect
23. #3124	C₂	semidirect
24. #3121	C₂	semidirect
25. #3121	C₂	semidirect
26. #3107	C₂	semidirect
27. #3102	C₂	semidirect
28. #2968	C₂	semidirect
29. #2950	C₂	semidirect
30. #2947	C₂	semidirect
31. #2943	C₂	semidirect

Maximal subgroups

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

subgroup	index
#3524	2
#3518	2
#3401	2
#3387	2
#3377	2
#3375	2
#3349	2
#3347	2
#3340	2
#3321	2
#3320	2
#3313	2
#3304	2
#3300	2
#3285	2
#3271	2
#3270	2
#3181	2
#3179	2
#3173	2
#3126	2
#3124	2
#3121	2
#3107	2
#3102	2
#2968	2
#2950	2
#2947	2
#2943	2