Subgroups — #61515

Order 256.

908 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3517	C₂	1	1	yes	maximal, characteristic, complemented
2	#3516	C₂	1	1	yes	maximal, characteristic, complemented
3	#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	#3390	C₂	1	1	yes	maximal, characteristic, complemented
5	#3377	C₂	1	1	yes	maximal, characteristic, complemented
6	#3368	C₂	1	1	yes	maximal, characteristic, complemented
7	#3355	C₂	1	1	yes	maximal, characteristic, complemented
8	#3346	C₂	1	1	yes	maximal, characteristic, complemented
9	#3343	C₂	1	1	yes	maximal, characteristic, complemented
10	#3333	C₂	1	1	yes	maximal, characteristic, complemented
11	#3326	C₂	1	1	yes	maximal, characteristic, complemented
12	#3320	C₂	1	1	yes	maximal, characteristic, complemented
13	#3317	C₂	1	1	yes	maximal, characteristic, complemented
14	#3309	C₂	1	1	yes	maximal, characteristic, complemented
15	#3308	C₂	1	1	yes	maximal, characteristic, complemented
16	#3278	C₂	1	1	yes	maximal, characteristic, complemented
17	#3271	C₂	1	1	yes	maximal, characteristic, complemented
18	#3271	C₂	1	1	yes	maximal, characteristic, complemented
19	#3179	C₂	1	1	yes	maximal, characteristic, complemented
20	#3174	C₂	1	1	yes	maximal, characteristic, complemented
21	#3171	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	#3120	C₂	1	1	yes	maximal, characteristic, complemented
25	#3119	C₂	1	1	yes	maximal, characteristic, complemented
26	#3112	C₂	1	1	yes	maximal, characteristic, complemented
27	#3111	C₂	1	1	yes	maximal, characteristic, complemented
28	#2967	C₂	1	1	yes	maximal, characteristic, complemented
29	#2951	C₂	1	1	yes	maximal, characteristic, complemented
30	#2947	C₂	1	1	yes	maximal, characteristic, complemented
31	C₄×#137	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#137	C₂²	1	1	yes	characteristic
33	C₂×#137	C₂²	1	1	yes	characteristic
34	C₂×#135	C₂²	1	1	yes	characteristic
35	#557	C₂²	1	1	yes	characteristic
36	#557	C₂²	1	1	yes	characteristic
37	#556	—	2	1	no	—
38	#556	C₂²	1	1	yes	characteristic
39	#554	—	2	1	no	—
40	#554	C₂²	1	1	yes	characteristic
41	#553	—	2	1	no	—
42	#553	—	2	1	no	—
43	#553	—	2	1	no	—
44	#553	C₂²	1	1	yes	characteristic
45	#553	C₂²	1	1	yes	characteristic
46	#553	C₂²	1	1	yes	characteristic
47	#552	—	2	1	no	—
48	#552	C₂²	1	1	yes	characteristic
49	#550	—	2	1	no	—
50	#550	C₂²	1	1	yes	characteristic
51	#550	C₂²	1	1	yes	characteristic
52	#550	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	#547	—	2	1	no	—
58	#547	C₂²	1	1	yes	characteristic
59	#542	—	2	1	no	—
60	#542	C₂²	1	1	yes	characteristic
61	#541	—	2	1	no	—
62	#541	C₂²	1	1	yes	characteristic
63	#540	—	2	1	no	—
64	#540	—	2	1	no	—
65	#540	C₂²	1	1	yes	characteristic
66	#540	C₂²	1	1	yes	characteristic
67	#532	—	2	1	no	—
68	#532	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	#520	C₂²	1	1	yes	characteristic
76	#520	C₂²	1	1	yes	characteristic
77	#519	C₂²	1	1	yes	characteristic
78	C₄×#41	C₂²	1	1	yes	characteristic
79	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic
80	#501	C₂²	1	1	yes	characteristic
81	#501	C₂²	1	1	yes	characteristic
82	#499	C₂²	1	1	yes	characteristic
83	#496	C₂²	1	1	yes	characteristic
84	#496	C₂²	1	1	yes	characteristic
85	#492	C₂²	1	1	yes	characteristic
86	#491	C₂²	1	1	yes	characteristic
87	#490	C₂²	1	1	yes	characteristic
88	#490	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	#484	C₂²	1	1	yes	characteristic
94	#484	C₂²	1	1	yes	characteristic
95	#483	C₂²	1	1	yes	characteristic
96	#482	C₂²	1	1	yes	characteristic
97	#482	C₂²	1	1	yes	characteristic
98	#482	C₂²	1	1	yes	characteristic
99	#481	C₂²	1	1	yes	characteristic
100	#480	C₂²	1	1	yes	characteristic
101	#480	C₂²	1	1	yes	characteristic
102	#480	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	#479	C₂²	1	1	yes	characteristic
108	#479	C₂²	1	1	yes	characteristic
109	#478	C₂²	1	1	yes	characteristic
110	#478	C₂²	1	1	yes	characteristic
111	#478	C₂²	1	1	yes	characteristic
112	#477	C₂²	1	1	yes	characteristic
113	#477	C₂²	1	1	yes	characteristic
114	#477	C₂²	1	1	yes	characteristic
115	#474	C₂²	1	1	yes	characteristic
116	#469	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	#468	C₂²	1	1	yes	characteristic
121	#468	C₂²	1	1	yes	characteristic
122	#468	C₂²	1	1	yes	characteristic
123	#468	C₂²	1	1	yes	characteristic
124	#466	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	#463	C₂²	1	1	yes	characteristic
131	#463	C₂²	1	1	yes	characteristic
132	#462	C₂²	1	1	yes	characteristic
133	#461	C₂²	1	1	yes	characteristic
134	#460	C₂²	1	1	yes	characteristic
135	#460	C₂²	1	1	yes	characteristic
136	#460	C₂²	1	1	yes	characteristic
137	#460	C₂²	1	1	yes	characteristic
138	#460	C₂²	1	1	yes	characteristic
139	#459	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	#449	C₂²	1	1	yes	characteristic
145	#449	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	#441	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	#440	C₂²	1	1	yes	characteristic
160	#440	C₂²	1	1	yes	characteristic
161	#440	C₂²	1	1	yes	characteristic
162	#440	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×SD₁₆	C₂²	1	1	yes	characteristic
175	C₄×SD₁₆	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×D₈	C₂²	1	1	yes	characteristic
180	C₄×D₈	C₂²	1	1	yes	characteristic
181	C₄×D₈	C₂²	1	1	yes	characteristic
182	#436	C₂²	1	1	yes	characteristic
183	#436	C₂²	1	1	yes	characteristic
184	#435	C₂²	1	1	yes	characteristic
185	#435	C₂²	1	1	yes	characteristic
186	#435	C₂²	1	1	yes	characteristic
187	#435	C₂²	1	1	yes	characteristic
188	#433	C₂²	1	1	yes	characteristic
189	#433	C₂²	1	1	yes	characteristic
190	#432	C₂²	1	1	yes	characteristic
191	#428	C₂²	1	1	yes	characteristic
192	#428	C₂²	1	1	yes	characteristic
193	C₂×#107	C₂²	1	1	yes	characteristic
194	#419	C₂²	1	1	yes	characteristic
195	#417	C₂²	1	1	yes	characteristic
196	#417	C₂²	1	1	yes	characteristic
197	#417	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	C₄×M₁₆	C₂²	1	1	yes	characteristic
203	C₂×#41	—	2	1	no	—
204	C₂×#41	—	2	1	no	—
205	C₂×#41	—	2	1	no	—
206	C₂×#41	C₂³	1	1	yes	characteristic
207	C₂×#41	C₂³	1	1	yes	characteristic
208	C₂×#41	C₂³	1	1	yes	characteristic
209	C₂×#41	C₂³	1	1	yes	characteristic
210	C₂²×Q₈	C₂³	1	1	yes	characteristic
211	C₂²×Q₈	C₂³	1	1	yes	characteristic
212	#137	—	2	4	no	—
213	#137	—	2	4	no	—
214	#135	—	2	4	no	—
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×SD₁₆	C₂³	1	1	yes	characteristic
227	C₂×SD₁₆	C₂³	1	1	yes	characteristic
228	C₂×D₈	C₂³	1	1	yes	characteristic
229	C₂×D₈	C₂³	1	1	yes	characteristic
230	C₂×D₈	C₂³	1	1	yes	characteristic
231	C₂×M₁₆	C₂³	1	1	yes	characteristic
232	C₂×M₁₆	C₂³	1	1	yes	characteristic
233	C₂×M₁₆	C₂³	1	1	yes	characteristic
234	C₂×M₁₆	C₂³	1	1	yes	characteristic
235	C₂²×C₈	C₂³	1	1	yes	characteristic
236	C₂²×C₈	C₂³	1	1	yes	characteristic
237	C₄⋊Q₈	—	2	1	no	—
238	C₄⋊Q₈	—	2	1	no	—
239	C₄⋊Q₈	—	2	1	no	—
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	#127	—	2	1	no	—
244	#127	—	2	1	no	—
245	#127	—	2	1	no	—
246	#127	C₂³	1	1	yes	characteristic
247	#127	C₂³	1	1	yes	characteristic
248	#127	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
259	#126	D₄	1	1	yes	characteristic
260	#126	D₄	1	1	yes	characteristic
261	#125	—	2	1	no	—
262	#125	—	2	1	no	—
263	#125	—	2	1	no	—
264	#125	—	2	1	no	—
265	#125	—	2	1	no	—
266	#125	—	2	1	no	—
267	#125	—	2	1	no	—
268	#125	—	2	1	no	—
269	#125	D₄	1	1	yes	characteristic
270	#125	C₂³	1	1	yes	characteristic
271	#125	C₂³	1	1	yes	characteristic
272	#125	C₂³	1	1	yes	characteristic
273	#125	C₂³	1	1	yes	characteristic
274	#124	—	2	1	no	—
275	#124	—	2	1	no	—
276	#124	—	2	1	no	—
277	#124	—	2	1	no	—
278	#124	D₄	1	1	yes	characteristic
279	#124	C₂³	1	1	yes	characteristic
280	#124	C₂³	1	1	yes	characteristic
281	#123	—	2	1	no	—
282	#123	—	2	1	no	—
283	#123	—	2	1	no	—
284	#123	—	2	1	no	—
285	#123	—	2	1	no	—
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	D₄	1	1	yes	characteristic
294	#123	D₄	1	1	yes	characteristic
295	C₂²⋊Q₈	—	2	1	no	—
296	C₂²⋊Q₈	—	2	1	no	—
297	C₂²⋊Q₈	—	2	1	no	—
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	D₄	1	1	yes	characteristic
305	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
306	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
307	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
308	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
309	#121	—	2	1	no	—
310	#121	—	2	1	no	—
311	#121	—	2	1	no	—
312	#121	—	2	1	no	—
313	#121	—	2	1	no	—
314	#121	—	2	1	no	—
315	#121	—	2	1	no	—
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	—	2	1	no	—
328	#121	D₄	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	#121	C₂³	1	1	yes	characteristic
335	#121	C₂³	1	1	yes	characteristic
336	#121	C₂³	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
344	C₄×Q₈	C₂³	1	1	yes	characteristic
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×D₄	—	2	1	no	—
357	C₄×D₄	—	2	1	no	—
358	C₄×D₄	—	2	1	no	—
359	C₄×D₄	—	2	1	no	—
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	—	2	1	no	—
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	C₄×D₄	C₂³	1	1	yes	characteristic
385	C₄×D₄	C₂³	1	1	yes	characteristic
386	C₄×D₄	C₂³	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
397	#117	C₂³	1	1	yes	characteristic
398	#117	C₂³	1	1	yes	characteristic
399	#117	C₂³	1	1	yes	characteristic
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	#107	C₂³	1	1	yes	characteristic
420	#107	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	#102	C₂³	1	1	yes	characteristic
450	#102	C₂³	1	1	yes	characteristic
451	#102	C₂³	1	1	yes	characteristic
452	#102	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	—	2	2	no	—
485	#41	—	4	1	no	—
486	#41	—	4	1	no	—
487	#41	—	4	1	no	—
488	#41	—	4	1	no	—
489	#41	—	8	2	no	—
490	#41	—	8	2	no	—
491	#41	—	8	2	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	—	2	1	no	—
494	C₂×Q₈	—	2	1	no	—
495	C₂×Q₈	—	2	1	no	—
496	C₂×Q₈	—	2	2	no	—
497	C₂×Q₈	—	2	2	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×D₄	—	2	1	no	—
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	—	2	1	no	—
518	C₂×D₄	—	2	1	no	—
519	C₂×D₄	—	2	1	no	—
520	C₂×D₄	—	2	1	no	—
521	C₂×D₄	—	2	1	no	—
522	C₂×D₄	—	2	1	no	—
523	C₂×D₄	C₂×D₄	1	1	yes	characteristic
524	C₂×D₄	C₂×D₄	1	1	yes	characteristic
525	C₂×D₄	C₂×D₄	1	1	yes	characteristic
526	C₂×D₄	C₂⁴	1	1	yes	characteristic
527	C₂×D₄	C₂⁴	1	1	yes	characteristic
528	C₂×D₄	C₂⁴	1	1	yes	characteristic
529	C₂×D₄	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
549	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴	1	1	yes	characteristic
551	C₂²×C₄	C₂⁴	1	1	yes	characteristic
552	C₂²×C₄	C₂⁴	1	1	yes	characteristic
553	Q₁₆	—	2	2	no	—
554	Q₁₆	—	2	2	no	—
555	Q₁₆	#41	1	4	yes	complemented
556	SD₁₆	—	2	2	no	—
557	SD₁₆	—	2	2	no	—
558	SD₁₆	—	2	2	no	—
559	SD₁₆	—	2	2	no	—
560	SD₁₆	—	2	2	no	—
561	SD₁₆	—	2	2	no	—
562	SD₁₆	—	4	1	no	—
563	SD₁₆	—	4	1	no	—
564	SD₁₆	—	4	1	no	—
565	SD₁₆	—	4	1	no	—
566	D₈	—	2	2	no	—
567	D₈	—	4	1	no	—
568	D₈	—	4	1	no	—
569	M₁₆	—	2	2	no	—
570	M₁₆	—	2	2	no	—
571	M₁₆	—	4	1	no	—
572	M₁₆	—	4	1	no	—
573	C₂×C₈	—	2	2	no	—
574	C₂×C₈	—	4	1	no	—
575	C₂×C₈	C₂⁴	1	1	yes	characteristic
576	C₂×C₈	C₂⁴	1	1	yes	characteristic
577	C₂×C₈	C₂⁴	1	1	yes	characteristic
578	C₂×C₈	C₂⁴	1	1	yes	characteristic
579	C₂×C₈	C₂⁴	1	1	yes	characteristic
580	C₂×C₈	C₂⁴	1	1	yes	characteristic
581	C₂×C₈	C₂⁴	1	1	yes	characteristic
582	C₂×C₈	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
616	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
617	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
618	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
619	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
620	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
621	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
622	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
623	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
624	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
625	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
626	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
627	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
628	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
629	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
630	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
631	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
632	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
652	C₂²⋊C₄	—	2	1	no	—
653	C₂²⋊C₄	—	2	1	no	—
654	C₂²⋊C₄	—	2	1	no	—
655	C₂²⋊C₄	—	2	1	no	—
656	C₂²⋊C₄	—	2	1	no	—
657	C₂²⋊C₄	—	2	1	no	—
658	C₂²⋊C₄	—	2	1	no	—
659	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
660	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
661	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
662	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
663	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
664	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
665	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
666	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
667	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
668	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
681	C₄²	—	2	1	no	—
682	C₄²	—	2	1	no	—
683	C₄²	C₂×D₄	1	1	yes	characteristic
684	C₄²	C₂×D₄	1	1	yes	characteristic
685	C₄²	C₂⁴	1	1	yes	characteristic
686	C₄²	C₂⁴	1	1	yes	characteristic
687	C₄²	C₂⁴	1	1	yes	characteristic
688	C₄²	C₂⁴	1	1	yes	characteristic
689	C₂³	—	2	1	no	—
690	C₂³	—	2	1	no	—
691	C₂³	—	2	1	no	—
692	C₂³	—	2	1	no	—
693	C₂³	C₂²×D₄	1	1	yes	characteristic
694	C₂³	C₂²×D₄	1	1	yes	characteristic
695	C₂³	C₂²×D₄	1	1	yes	characteristic
696	Q₈	—	2	1	no	—
697	Q₈	—	2	1	no	—
698	Q₈	—	2	1	no	—
699	Q₈	—	2	1	no	—
700	Q₈	—	2	1	no	—
701	Q₈	—	2	1	no	—
702	Q₈	—	4	1	no	—
703	Q₈	—	4	2	no	—
704	Q₈	—	4	2	no	—
705	Q₈	—	4	2	no	—
706	Q₈	—	8	1	no	—
707	Q₈	C₂×#41	1	2	yes	—
708	Q₈	C₂×#41	1	2	yes	—
709	D₄	—	2	1	no	—
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	—	2	1	no	—
717	D₄	—	4	1	no	—
718	D₄	—	4	1	no	—
719	D₄	—	4	1	no	—
720	D₄	—	4	2	no	—
721	D₄	—	4	2	no	—
722	D₄	—	4	2	no	—
723	D₄	—	4	2	no	—
724	D₄	—	4	2	no	—
725	D₄	—	4	2	no	—
726	D₄	—	8	1	no	—
727	D₄	—	8	1	no	—
728	D₄	—	8	1	no	—
729	D₄	—	8	1	no	—
730	D₄	—	8	1	no	—
731	D₄	—	8	1	no	—
732	D₄	—	8	1	no	—
733	D₄	—	8	1	no	—
734	D₄	—	8	1	no	—
735	D₄	—	8	1	no	—
736	D₄	—	8	1	no	—
737	D₄	—	8	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	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	4	1	no	—
757	C₂×C₄	—	4	1	no	—
758	C₂×C₄	—	4	2	no	—
759	C₂×C₄	—	4	2	no	—
760	C₂×C₄	—	4	2	no	—
761	C₂×C₄	—	4	2	no	—
762	C₂×C₄	—	4	2	no	—
763	C₂×C₄	—	4	2	no	—
764	C₂×C₄	—	4	2	no	—
765	C₂×C₄	—	8	1	no	—
766	C₂×C₄	—	8	1	no	—
767	C₂×C₄	—	8	1	no	—
768	C₂×C₄	—	8	1	no	—
769	C₂×C₄	—	8	1	no	—
770	C₂×C₄	—	8	1	no	—
771	C₂×C₄	—	8	1	no	—
772	C₂×C₄	—	8	1	no	—
773	C₂×C₄	—	8	1	no	—
774	C₂×C₄	—	8	1	no	—
775	C₂×C₄	—	8	1	no	—
776	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
777	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
778	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
779	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
780	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
781	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
782	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
783	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
784	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
785	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
786	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
787	C₂×C₄	C₂⁵	1	1	yes	characteristic
788	C₈	—	2	1	no	—
789	C₈	—	2	1	no	—
790	C₈	—	2	1	no	—
791	C₈	—	2	1	no	—
792	C₈	—	2	1	no	—
793	C₈	—	2	1	no	—
794	C₈	—	2	1	no	—
795	C₈	C₂×#41	1	2	yes	—
796	C₂²	—	2	1	no	—
797	C₂²	—	2	1	no	—
798	C₂²	—	2	1	no	—
799	C₂²	—	2	1	no	—
800	C₂²	—	2	1	no	—
801	C₂²	—	2	1	no	—
802	C₂²	—	2	1	no	—
803	C₂²	—	2	1	no	—
804	C₂²	—	2	1	no	—
805	C₂²	—	4	1	no	—
806	C₂²	—	4	1	no	—
807	C₂²	—	4	1	no	—
808	C₂²	—	4	1	no	—
809	C₂²	—	4	1	no	—
810	C₂²	—	4	1	no	—
811	C₂²	—	4	1	no	—
812	C₂²	—	4	1	no	—
813	C₂²	—	4	1	no	—
814	C₂²	—	4	1	no	—
815	C₂²	—	4	1	no	—
816	C₂²	—	4	1	no	—
817	C₂²	C₂³×D₄	1	1	yes	characteristic
818	C₄	—	2	1	no	—
819	C₄	—	2	1	no	—
820	C₄	—	2	1	no	—
821	C₄	—	2	1	no	—
822	C₄	—	2	1	no	—
823	C₄	—	2	1	no	—
824	C₄	—	2	1	no	—
825	C₄	—	2	1	no	—
826	C₄	—	2	1	no	—
827	C₄	—	2	1	no	—
828	C₄	—	2	1	no	—
829	C₄	—	2	2	no	—
830	C₄	—	2	2	no	—
831	C₄	—	4	1	no	—
832	C₄	—	4	1	no	—
833	C₄	—	4	1	no	—
834	C₄	—	4	1	no	—
835	C₄	—	4	1	no	—
836	C₄	—	4	1	no	—
837	C₄	—	4	1	no	—
838	C₄	—	4	1	no	—
839	C₄	—	4	1	no	—
840	C₄	—	4	1	no	—
841	C₄	C₂²×#41	1	1	yes	characteristic
842	C₄	#585	1	1	yes	characteristic
843	C₂	—	4	1	no	—
844	C₂	—	4	1	no	—
845	C₂	—	4	1	no	—
846	C₂	—	8	1	no	—
847	C₂	—	8	1	no	—
848	C₂	—	8	1	no	—
849	C₂	—	8	1	no	—
850	C₂	D₄×#41	1	1	yes	characteristic
851	C₂	#3585	1	1	yes	characteristic
852	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. #3517	C₂	semidirect
2. #3516	C₂	semidirect
3. #3397	C₂	semidirect
4. #3390	C₂	semidirect
5. #3377	C₂	semidirect
6. #3368	C₂	semidirect
7. #3355	C₂	semidirect
8. #3346	C₂	semidirect
9. #3343	C₂	semidirect
10. #3333	C₂	semidirect
11. #3326	C₂	semidirect
12. #3320	C₂	semidirect
13. #3317	C₂	semidirect
14. #3309	C₂	semidirect
15. #3308	C₂	semidirect
16. #3278	C₂	semidirect
17. #3271	C₂	semidirect
18. #3271	C₂	semidirect
19. #3179	C₂	semidirect
20. #3174	C₂	semidirect
21. #3171	C₂	semidirect
22. #3126	C₂	semidirect
23. #3124	C₂	semidirect
24. #3120	C₂	semidirect
25. #3119	C₂	semidirect
26. #3112	C₂	semidirect
27. #3111	C₂	semidirect
28. #2967	C₂	semidirect
29. #2951	C₂	semidirect
30. #2947	C₂	semidirect
31. C₄×#137	C₂	semidirect
555. Q₁₆	#41	semidirect

Maximal subgroups

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

subgroup	index
#3517	2
#3516	2
#3397	2
#3390	2
#3377	2
#3368	2
#3355	2
#3346	2
#3343	2
#3333	2
#3326	2
#3320	2
#3317	2
#3309	2
#3308	2
#3278	2
#3271	2
#3179	2
#3174	2
#3171	2
#3126	2
#3124	2
#3120	2
#3119	2
#3112	2
#3111	2
#2967	2
#2951	2
#2947	2
C₄×#137	2