Subgroups — #7625048

Order 512.

1147 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#62490	C₂	1	2	yes	maximal, complemented
2	#33955	C₂	1	2	yes	maximal, complemented
3	#33950	C₂	1	1	yes	maximal, characteristic, complemented
4	#33947	C₂	1	1	yes	maximal, characteristic, complemented
5	#33918	C₂	1	2	yes	maximal, complemented
6	#33917	C₂	1	2	yes	maximal, complemented
7	#33915	C₂	1	2	yes	maximal, complemented
8	#33909	C₂	1	1	yes	maximal, characteristic, complemented
9	#33908	C₂	1	1	yes	maximal, characteristic, complemented
10	#33906	C₂	1	1	yes	maximal, characteristic, complemented
11	#33906	C₂	1	1	yes	maximal, characteristic, complemented
12	#33903	C₂	1	1	yes	maximal, characteristic, complemented
13	#33903	C₂	1	1	yes	maximal, characteristic, complemented
14	#33810	C₂	1	2	yes	maximal, complemented
15	#33810	C₂	1	2	yes	maximal, complemented
16	#33806	C₂	1	2	yes	maximal, complemented
17	#33739	C₂	1	1	yes	maximal, characteristic, complemented
18	#33739	C₂	1	1	yes	maximal, characteristic, complemented
19	#33735	C₂	1	1	yes	maximal, characteristic, complemented
20	#33729	C₂	1	1	yes	maximal, characteristic, complemented
21	#33729	C₂	1	1	yes	maximal, characteristic, complemented
22	#33726	C₂	1	1	yes	maximal, characteristic, complemented
23	#33480	C₂	1	1	yes	maximal, characteristic, complemented
24	#3565	—	2	2	no	—
25	#3388	—	2	2	no	—
26	#3383	C₂²	1	2	yes	—
27	#3380	C₂²	1	2	yes	—
28	#3351	—	2	2	no	—
29	#3350	—	2	2	no	—
30	#3348	—	2	2	no	—
31	#3342	C₂²	1	2	yes	—
32	#3341	C₂²	1	2	yes	—
33	#3339	C₂²	1	2	yes	—
34	#3339	C₂²	1	2	yes	—
35	#3336	C₂²	1	2	yes	—
36	#3336	C₂²	1	2	yes	—
37	#3244	—	2	2	no	—
38	#3244	—	2	2	no	—
39	#3240	—	2	2	no	—
40	#3175	C₂²	1	2	yes	—
41	#3175	C₂²	1	2	yes	—
42	#3168	C₂²	1	2	yes	—
43	#3164	C₂²	1	2	yes	—
44	#3164	C₂²	1	2	yes	—
45	#3160	C₂²	1	2	yes	—
46	#2966	C₂²	1	1	yes	characteristic
47	#2255	C₂²	1	2	yes	—
48	#2255	C₂²	1	2	yes	—
49	#2255	C₂²	1	2	yes	—
50	#2255	C₂²	1	2	yes	—
51	#2254	C₂²	1	2	yes	—
52	#2253	C₂²	1	1	yes	characteristic
53	#2253	C₂²	1	1	yes	characteristic
54	#2253	C₂²	1	1	yes	characteristic
55	#2253	C₂²	1	1	yes	characteristic
56	#2253	C₂²	1	2	yes	—
57	#2253	C₂²	1	1	yes	characteristic
58	#2252	C₂²	1	1	yes	characteristic
59	#2252	C₂²	1	1	yes	characteristic
60	#2252	C₂²	1	1	yes	characteristic
61	#2252	C₂²	1	1	yes	characteristic
62	#2249	C₂²	1	1	yes	characteristic
63	#2243	C₂²	1	2	yes	—
64	#2243	C₂²	1	2	yes	—
65	#2242	C₂²	1	2	yes	—
66	#2237	C₂²	1	2	yes	—
67	#2237	C₂²	1	2	yes	—
68	#2237	C₂²	1	2	yes	—
69	#2237	C₂²	1	2	yes	—
70	#2235	C₂²	1	2	yes	—
71	#2235	C₂²	1	2	yes	—
72	#2234	C₂²	1	2	yes	—
73	#2234	C₂²	1	2	yes	—
74	#2234	C₂²	1	2	yes	—
75	#2234	C₂²	1	2	yes	—
76	#2233	C₂²	1	2	yes	—
77	#2233	C₂²	1	2	yes	—
78	#2229	C₂²	1	2	yes	—
79	#2229	C₂²	1	2	yes	—
80	#2229	C₂²	1	2	yes	—
81	#2229	C₂²	1	2	yes	—
82	#2228	C₂²	1	2	yes	—
83	#2228	C₂²	1	2	yes	—
84	#2228	C₂²	1	2	yes	—
85	#2228	C₂²	1	2	yes	—
86	#2226	C₂²	1	2	yes	—
87	#2226	C₂²	1	2	yes	—
88	#2225	C₂²	1	2	yes	—
89	#2225	C₂²	1	2	yes	—
90	#2220	C₂²	1	2	yes	—
91	#2220	C₂²	1	2	yes	—
92	#2217	C₂²	1	2	yes	—
93	#2216	C₂²	1	1	yes	characteristic
94	#2216	C₂²	1	1	yes	characteristic
95	#2216	C₂²	1	1	yes	characteristic
96	#2215	C₂²	1	1	yes	characteristic
97	#2215	C₂²	1	1	yes	characteristic
98	#2215	C₂²	1	1	yes	characteristic
99	#2183	C₂²	1	1	yes	characteristic
100	Q₈×C₁₆	C₂²	1	1	yes	characteristic
101	#2175	C₂²	1	2	yes	—
102	#2175	C₂²	1	2	yes	—
103	C₄×Q₃₂	C₂²	1	1	yes	characteristic
104	C₄×Q₃₂	C₂²	1	1	yes	characteristic
105	C₄×Q₃₂	C₂²	1	1	yes	characteristic
106	C₄×SD₃₂	C₂²	1	2	yes	—
107	C₄×D₁₆	C₂²	1	1	yes	characteristic
108	C₄×D₁₆	C₂²	1	1	yes	characteristic
109	C₄×D₁₆	C₂²	1	1	yes	characteristic
110	#2169	C₂²	1	1	yes	characteristic
111	#2168	C₂²	1	1	yes	characteristic
112	#2168	C₂²	1	1	yes	characteristic
113	D₄×C₁₆	C₂²	1	1	yes	characteristic
114	D₄×C₁₆	C₂²	1	1	yes	characteristic
115	D₄×C₁₆	C₂²	1	1	yes	characteristic
116	#2164	C₂²	1	1	yes	characteristic
117	#2164	C₂²	1	1	yes	characteristic
118	#2163	C₂²	1	1	yes	characteristic
119	#2159	C₂²	1	2	yes	—
120	#2159	C₂²	1	2	yes	—
121	#2158	C₂²	1	1	yes	characteristic
122	#2158	C₂²	1	1	yes	characteristic
123	#2158	C₂²	1	1	yes	characteristic
124	#2158	C₂²	1	1	yes	characteristic
125	#2158	C₂²	1	2	yes	—
126	C₂×#366	C₂²	1	1	yes	characteristic
127	C₂×#366	C₂²	1	1	yes	characteristic
128	#2108	C₂²	1	1	yes	characteristic
129	#2108	C₂²	1	1	yes	characteristic
130	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
131	#563	—	4	2	no	—
132	#562	—	4	2	no	—
133	#557	—	2	2	no	—
134	#556	—	2	2	no	—
135	#556	—	4	2	no	—
136	#555	—	2	2	no	—
137	#554	—	2	2	no	—
138	#553	—	2	2	no	—
139	#553	—	2	2	no	—
140	#552	—	2	2	no	—
141	#552	—	2	2	no	—
142	#552	—	4	2	no	—
143	#544	—	2	2	no	—
144	#544	—	2	2	no	—
145	#542	—	2	2	no	—
146	#542	—	2	2	no	—
147	#542	—	4	2	no	—
148	#542	—	4	2	no	—
149	#541	—	4	2	no	—
150	#539	—	4	2	no	—
151	#533	—	2	2	no	—
152	#529	—	2	2	no	—
153	#529	D₄	1	1	yes	characteristic
154	C₂×Q₃₂	C₂³	1	1	yes	characteristic
155	C₂×SD₃₂	C₂³	1	2	yes	—
156	C₂×D₁₆	C₂³	1	1	yes	characteristic
157	C₂×M₃₂	C₂³	1	1	yes	characteristic
158	C₂×M₃₂	C₂³	1	1	yes	characteristic
159	C₂²×C₁₆	C₂³	1	1	yes	characteristic
160	C₂²×C₁₆	C₂³	1	1	yes	characteristic
161	C₂²×C₁₆	C₂³	1	1	yes	characteristic
162	C₂²×C₁₆	C₂³	1	1	yes	characteristic
163	#501	—	2	2	no	—
164	#501	—	2	2	no	—
165	#501	—	2	2	no	—
166	#501	—	2	2	no	—
167	#500	C₂³	1	2	yes	—
168	#500	C₂³	1	2	yes	—
169	#500	C₂³	1	2	yes	—
170	#500	C₂³	1	2	yes	—
171	#499	—	2	2	no	—
172	#499	C₂³	1	2	yes	—
173	#499	C₂³	1	2	yes	—
174	#499	C₂³	1	2	yes	—
175	#499	C₂³	1	2	yes	—
176	#499	C₂³	1	2	yes	—
177	#498	—	2	2	no	—
178	#495	C₂³	1	2	yes	—
179	#489	—	2	2	no	—
180	#489	—	2	2	no	—
181	#488	—	2	2	no	—
182	#485	—	2	2	no	—
183	#485	—	2	2	no	—
184	#485	—	2	2	no	—
185	#485	—	2	2	no	—
186	#483	—	2	2	no	—
187	#483	—	2	2	no	—
188	#482	—	2	2	no	—
189	#482	—	2	2	no	—
190	#482	—	2	2	no	—
191	#482	—	2	2	no	—
192	#481	—	2	2	no	—
193	#481	—	2	2	no	—
194	#479	—	2	2	no	—
195	#479	—	2	2	no	—
196	#479	—	2	2	no	—
197	#479	—	2	2	no	—
198	#478	—	2	2	no	—
199	#478	—	2	2	no	—
200	#478	—	2	2	no	—
201	#478	—	2	2	no	—
202	#476	—	2	2	no	—
203	#476	—	2	2	no	—
204	#475	—	2	2	no	—
205	#475	—	2	2	no	—
206	#468	—	2	2	no	—
207	#468	—	2	2	no	—
208	#467	C₂³	1	2	yes	—
209	#467	C₂³	1	2	yes	—
210	#467	C₂³	1	2	yes	—
211	#466	C₂³	1	2	yes	—
212	#466	C₂³	1	2	yes	—
213	#466	C₂³	1	2	yes	—
214	#465	—	2	2	no	—
215	#446	D₄	1	1	yes	characteristic
216	C₈×Q₈	C₂³	1	1	yes	characteristic
217	#440	—	2	2	no	—
218	#440	—	2	2	no	—
219	C₄×Q₁₆	C₂³	1	2	yes	—
220	C₄×Q₁₆	C₂³	1	2	yes	—
221	C₄×Q₁₆	C₂³	1	2	yes	—
222	C₄×SD₁₆	—	2	2	no	—
223	C₄×D₈	C₂³	1	2	yes	—
224	C₄×D₈	C₂³	1	2	yes	—
225	C₄×D₈	C₂³	1	2	yes	—
226	#436	D₄	1	1	yes	characteristic
227	#435	D₄	1	1	yes	characteristic
228	#435	D₄	1	1	yes	characteristic
229	C₈×D₄	C₂³	1	1	yes	characteristic
230	C₈×D₄	C₂³	1	1	yes	characteristic
231	C₈×D₄	C₂³	1	1	yes	characteristic
232	#433	D₄	1	1	yes	characteristic
233	#433	D₄	1	1	yes	characteristic
234	#432	D₄	1	1	yes	characteristic
235	#428	—	2	2	no	—
236	#428	—	2	2	no	—
237	#427	—	2	2	no	—
238	#427	C₂³	1	2	yes	—
239	#427	C₂³	1	2	yes	—
240	#427	C₂³	1	2	yes	—
241	#427	C₂³	1	2	yes	—
242	C₂×#107	C₂³	1	2	yes	—
243	C₂×#107	C₂³	1	2	yes	—
244	#405	C₂³	1	1	yes	characteristic
245	#405	C₂³	1	1	yes	characteristic
246	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
247	#367	C₂³	1	2	yes	—
248	#367	C₂³	1	2	yes	—
249	#367	C₂³	1	2	yes	—
250	#367	C₂³	1	2	yes	—
251	#367	C₂³	1	2	yes	—
252	#367	C₂³	1	2	yes	—
253	#367	C₂³	1	2	yes	—
254	#367	C₂³	1	2	yes	—
255	#367	C₂³	1	2	yes	—
256	#366	C₂³	1	1	yes	characteristic
257	#366	C₂³	1	1	yes	characteristic
258	#366	C₂³	1	1	yes	characteristic
259	#366	C₂³	1	1	yes	characteristic
260	#366	C₂³	1	2	yes	—
261	#366	C₂³	1	2	yes	—
262	#366	C₂³	1	1	yes	characteristic
263	#366	C₂³	1	1	yes	characteristic
264	#366	C₂³	1	2	yes	—
265	#366	C₂³	1	2	yes	—
266	#366	C₂³	1	2	yes	—
267	#366	C₂³	1	2	yes	—
268	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
269	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
270	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
271	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
272	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
273	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
274	#358	C₂³	1	2	yes	—
275	#358	C₂³	1	2	yes	—
276	#358	C₂³	1	2	yes	—
277	#358	C₂³	1	2	yes	—
278	#358	C₂³	1	2	yes	—
279	#358	C₂³	1	2	yes	—
280	#357	C₂³	1	2	yes	—
281	#357	C₂³	1	2	yes	—
282	#357	C₂³	1	2	yes	—
283	#357	C₂³	1	2	yes	—
284	#357	C₂³	1	2	yes	—
285	#357	C₂³	1	2	yes	—
286	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
287	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
288	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
289	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
290	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
291	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
292	#346	C₂³	1	1	yes	characteristic
293	#346	C₂³	1	1	yes	characteristic
294	#346	C₂³	1	1	yes	characteristic
295	#346	C₂³	1	1	yes	characteristic
296	C₄×C₁₆	C₂³	1	1	yes	characteristic
297	C₄×C₁₆	C₂³	1	1	yes	characteristic
298	C₄×C₁₆	C₂³	1	1	yes	characteristic
299	C₄×C₁₆	C₂³	1	1	yes	characteristic
300	C₄×C₁₆	C₂³	1	1	yes	characteristic
301	C₄×C₁₆	C₂³	1	1	yes	characteristic
302	C₂×Q₁₆	C₂⁴	1	2	yes	—
303	C₂×SD₁₆	—	2	2	no	—
304	C₂×D₈	C₂⁴	1	2	yes	—
305	C₂×M₁₆	C₂×D₄	1	1	yes	characteristic
306	C₂×M₁₆	C₂×D₄	1	1	yes	characteristic
307	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
308	C₂²×C₈	C₂⁴	1	1	yes	characteristic
309	C₂²×C₈	C₂⁴	1	1	yes	characteristic
310	C₂²×C₈	C₂⁴	1	1	yes	characteristic
311	C₄⋊Q₈	—	2	2	no	—
312	C₄⋊Q₈	—	2	2	no	—
313	C₄⋊Q₈	—	2	2	no	—
314	C₄⋊Q₈	—	2	2	no	—
315	C₄⋊Q₈	—	4	2	no	—
316	C₄⋊Q₈	—	4	2	no	—
317	C₄⋊Q₈	—	4	2	no	—
318	#126	—	4	2	no	—
319	#126	—	4	2	no	—
320	#126	—	4	2	no	—
321	#126	—	4	2	no	—
322	#126	—	4	2	no	—
323	#126	—	4	2	no	—
324	#126	—	4	2	no	—
325	#126	—	4	2	no	—
326	#126	—	4	2	no	—
327	#126	D₈	1	1	yes	characteristic
328	#126	D₈	1	1	yes	characteristic
329	#125	—	2	2	no	—
330	#125	—	2	2	no	—
331	#125	—	2	2	no	—
332	#125	—	2	2	no	—
333	#125	—	2	2	no	—
334	#125	—	4	2	no	—
335	#125	—	4	2	no	—
336	#125	—	4	2	no	—
337	#125	—	4	2	no	—
338	#125	—	4	2	no	—
339	#125	—	4	2	no	—
340	#125	D₈	1	1	yes	characteristic
341	#124	—	2	2	no	—
342	#124	—	4	2	no	—
343	#124	—	4	2	no	—
344	#124	—	4	2	no	—
345	#124	—	4	2	no	—
346	#124	—	4	2	no	—
347	#124	D₈	1	1	yes	characteristic
348	#123	—	4	2	no	—
349	#123	—	4	2	no	—
350	#123	—	4	2	no	—
351	#123	—	4	2	no	—
352	#123	—	4	2	no	—
353	#123	—	4	2	no	—
354	#123	—	4	2	no	—
355	#123	D₈	1	1	yes	characteristic
356	#123	D₈	1	1	yes	characteristic
357	C₂²⋊Q₈	—	2	2	no	—
358	C₂²⋊Q₈	—	2	2	no	—
359	C₂²⋊Q₈	—	2	2	no	—
360	C₂²⋊Q₈	—	4	2	no	—
361	C₂²⋊Q₈	—	4	2	no	—
362	C₂²⋊Q₈	—	4	2	no	—
363	C₂²⋊Q₈	—	4	2	no	—
364	C₂²⋊Q₈	—	4	2	no	—
365	C₂²⋊Q₈	—	4	2	no	—
366	C₂²⋊Q₈	—	4	2	no	—
367	C₂²⋊Q₈	—	4	2	no	—
368	C₂²⋊Q₈	—	4	2	no	—
369	C₂²⋊Q₈	—	4	2	no	—
370	C₂²⋊Q₈	—	4	2	no	—
371	C₂²⋊Q₈	D₈	1	1	yes	characteristic
372	#121	—	2	2	no	—
373	#121	—	2	2	no	—
374	#121	—	2	2	no	—
375	#121	—	4	2	no	—
376	#121	—	4	2	no	—
377	#121	—	4	2	no	—
378	#121	D₈	1	1	yes	characteristic
379	C₄×Q₈	—	2	2	no	—
380	C₄×Q₈	—	2	2	no	—
381	C₄×Q₈	—	2	2	no	—
382	C₄×Q₈	—	4	2	no	—
383	C₄×Q₈	—	4	2	no	—
384	C₄×Q₈	—	4	2	no	—
385	C₄×Q₈	—	4	2	no	—
386	C₄×Q₈	C₂×D₄	1	1	yes	characteristic
387	C₄×D₄	—	2	2	no	—
388	C₄×D₄	—	2	2	no	—
389	C₄×D₄	—	2	2	no	—
390	C₄×D₄	—	4	2	no	—
391	C₄×D₄	—	4	2	no	—
392	C₄×D₄	—	4	2	no	—
393	C₄×D₄	C₂×D₄	1	1	yes	characteristic
394	C₄×D₄	C₂×D₄	1	1	yes	characteristic
395	C₄×D₄	C₂×D₄	1	1	yes	characteristic
396	#117	—	2	2	no	—
397	#117	—	2	2	no	—
398	#117	—	2	2	no	—
399	#117	—	2	2	no	—
400	#117	—	4	2	no	—
401	#117	—	4	2	no	—
402	#117	—	4	2	no	—
403	#117	—	4	2	no	—
404	#117	C₂×D₄	1	1	yes	characteristic
405	#117	C₂×D₄	1	1	yes	characteristic
406	C₂×C₄⋊C₄	—	2	2	no	—
407	C₂×C₄⋊C₄	—	2	2	no	—
408	C₂×C₄⋊C₄	—	4	2	no	—
409	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
410	Q₃₂	—	2	2	no	—
411	SD₃₂	—	2	4	no	—
412	D₁₆	—	2	2	no	—
413	M₃₂	—	2	2	no	—
414	M₃₂	—	2	2	no	—
415	C₂×C₁₆	—	2	2	no	—
416	C₂×C₁₆	—	2	2	no	—
417	C₂×C₁₆	—	2	2	no	—
418	C₂×C₁₆	—	2	2	no	—
419	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
420	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
421	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
422	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
423	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
424	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
425	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
426	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
427	#107	—	2	2	no	—
428	#107	—	2	2	no	—
429	#107	—	2	2	no	—
430	#107	—	2	2	no	—
431	#107	—	2	2	no	—
432	#107	—	2	2	no	—
433	#107	C₂⁴	1	2	yes	—
434	#107	C₂⁴	1	2	yes	—
435	#107	C₂⁴	1	2	yes	—
436	#107	C₂⁴	1	2	yes	—
437	#107	C₂⁴	1	2	yes	—
438	#107	C₂⁴	1	2	yes	—
439	#106	—	2	2	no	—
440	#106	—	2	2	no	—
441	#106	—	2	2	no	—
442	#106	—	2	2	no	—
443	#106	—	2	2	no	—
444	#106	—	2	2	no	—
445	#106	—	2	2	no	—
446	#106	—	2	2	no	—
447	#106	—	2	2	no	—
448	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
449	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
450	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
451	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
452	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
453	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
454	#103	—	2	2	no	—
455	#103	—	2	2	no	—
456	#103	—	2	2	no	—
457	#103	—	2	2	no	—
458	#103	—	2	2	no	—
459	#103	—	2	2	no	—
460	#102	—	2	2	no	—
461	#102	—	2	2	no	—
462	#102	—	2	2	no	—
463	#102	—	2	2	no	—
464	#102	—	2	2	no	—
465	#102	—	2	2	no	—
466	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
467	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
468	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
469	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
470	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
471	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
472	#97	C₂×D₄	1	1	yes	characteristic
473	#97	C₂×D₄	1	1	yes	characteristic
474	#97	C₂×D₄	1	1	yes	characteristic
475	#97	C₂×D₄	1	1	yes	characteristic
476	C₄×C₈	C₂×D₄	1	1	yes	characteristic
477	C₄×C₈	C₂×D₄	1	1	yes	characteristic
478	C₄×C₈	C₂⁴	1	1	yes	characteristic
479	C₄×C₈	C₂⁴	1	1	yes	characteristic
480	C₄×C₈	C₂⁴	1	1	yes	characteristic
481	C₄×C₈	C₂⁴	1	1	yes	characteristic
482	C₂×Q₈	—	2	2	no	—
483	C₂×Q₈	—	4	2	no	—
484	C₂×Q₈	—	4	2	no	—
485	C₂×Q₈	—	4	2	no	—
486	C₂×Q₈	—	4	2	no	—
487	C₂×Q₈	C₂×D₈	1	1	yes	characteristic
488	C₂×D₄	—	2	2	no	—
489	C₂×D₄	—	4	2	no	—
490	C₂×D₄	—	4	2	no	—
491	C₂×D₄	—	4	2	no	—
492	C₂×D₄	C₂×D₈	1	1	yes	characteristic
493	C₂×D₄	C₂×D₈	1	1	yes	characteristic
494	C₂×D₄	C₂×D₈	1	1	yes	characteristic
495	C₂²×C₄	—	4	2	no	—
496	C₂²×C₄	—	4	2	no	—
497	C₂²×C₄	—	4	2	no	—
498	C₂²×C₄	—	4	2	no	—
499	C₂²×C₄	—	4	2	no	—
500	C₂²×C₄	C₂×D₈	1	1	yes	characteristic
501	C₂²×C₄	C₂×D₈	1	1	yes	characteristic
502	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
503	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
504	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
505	Q₁₆	—	2	2	no	—
506	Q₁₆	—	2	2	no	—
507	SD₁₆	—	4	4	no	—
508	D₈	—	2	2	no	—
509	D₈	—	2	2	no	—
510	M₁₆	—	2	2	no	—
511	M₁₆	—	2	2	no	—
512	C₂×C₈	—	2	2	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₈	C₂⁵	1	1	yes	characteristic
527	C₄⋊C₄	—	2	2	no	—
528	C₄⋊C₄	—	2	2	no	—
529	C₄⋊C₄	—	2	2	no	—
530	C₄⋊C₄	—	2	2	no	—
531	C₄⋊C₄	—	2	2	no	—
532	C₄⋊C₄	—	2	2	no	—
533	C₄⋊C₄	—	4	2	no	—
534	C₄⋊C₄	—	4	2	no	—
535	C₄⋊C₄	—	4	2	no	—
536	C₄⋊C₄	—	4	2	no	—
537	C₄⋊C₄	—	4	2	no	—
538	C₄⋊C₄	—	4	2	no	—
539	C₄⋊C₄	—	4	2	no	—
540	C₄⋊C₄	—	4	2	no	—
541	C₄⋊C₄	—	4	2	no	—
542	C₄⋊C₄	—	4	2	no	—
543	C₄⋊C₄	—	4	2	no	—
544	C₄⋊C₄	—	4	2	no	—
545	C₄⋊C₄	—	4	2	no	—
546	C₄⋊C₄	—	4	2	no	—
547	C₄⋊C₄	—	4	2	no	—
548	C₄⋊C₄	—	4	2	no	—
549	C₄⋊C₄	—	4	2	no	—
550	C₄⋊C₄	—	4	2	no	—
551	C₄⋊C₄	—	4	2	no	—
552	C₄⋊C₄	—	4	2	no	—
553	C₄⋊C₄	—	4	2	no	—
554	C₄⋊C₄	—	4	2	no	—
555	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
556	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
557	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
558	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
559	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
560	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
561	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
562	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
563	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
564	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
565	C₂²⋊C₄	—	4	2	no	—
566	C₂²⋊C₄	—	4	2	no	—
567	C₂²⋊C₄	—	4	2	no	—
568	C₂²⋊C₄	—	4	2	no	—
569	C₂²⋊C₄	—	4	2	no	—
570	C₂²⋊C₄	—	4	2	no	—
571	C₂²⋊C₄	—	4	2	no	—
572	C₂²⋊C₄	—	4	2	no	—
573	C₂²⋊C₄	—	4	2	no	—
574	C₂²⋊C₄	—	4	2	no	—
575	C₂²⋊C₄	—	4	2	no	—
576	C₂²⋊C₄	—	4	2	no	—
577	C₂²⋊C₄	—	4	2	no	—
578	C₂²⋊C₄	—	4	2	no	—
579	C₂²⋊C₄	—	4	2	no	—
580	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
581	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
582	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
583	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
584	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
585	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
586	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
587	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
588	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
589	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
590	C₄²	—	4	2	no	—
591	C₄²	—	4	2	no	—
592	C₄²	—	4	2	no	—
593	C₄²	—	4	2	no	—
594	C₄²	—	4	2	no	—
595	C₄²	—	4	2	no	—
596	C₄²	—	4	2	no	—
597	C₄²	C₂×D₈	1	1	yes	characteristic
598	C₄²	C₂×D₈	1	1	yes	characteristic
599	C₄²	C₂²×D₄	1	1	yes	characteristic
600	C₄²	C₂²×D₄	1	1	yes	characteristic
601	C₄²	C₂²×D₄	1	1	yes	characteristic
602	C₄²	C₂²×D₄	1	1	yes	characteristic
603	C₁₆	—	2	1	no	—
604	C₁₆	—	2	1	no	—
605	C₁₆	—	2	1	no	—
606	C₁₆	—	2	1	no	—
607	C₁₆	—	2	1	no	—
608	C₁₆	—	2	1	no	—
609	C₁₆	2₋¹⁺⁴	1	2	yes	—
610	C₁₆	2₋¹⁺⁴	1	2	yes	—
611	C₂³	—	4	2	no	—
612	C₂³	C₂²×D₈	1	1	yes	characteristic
613	C₂³	C₂²×D₈	1	1	yes	characteristic
614	C₂³	C₂²×D₈	1	1	yes	characteristic
615	Q₈	—	4	1	no	—
616	Q₈	—	4	2	no	—
617	Q₈	—	4	2	no	—
618	Q₈	—	16	2	no	—
619	Q₈	—	16	2	no	—
620	Q₈	—	16	2	no	—
621	Q₈	—	16	2	no	—
622	D₄	—	4	1	no	—
623	D₄	—	4	1	no	—
624	D₄	—	4	1	no	—
625	D₄	—	4	2	no	—
626	D₄	—	4	2	no	—
627	D₄	—	16	2	no	—
628	D₄	—	16	2	no	—
629	D₄	—	16	2	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	2	no	—
639	C₂×C₄	—	4	2	no	—
640	C₂×C₄	—	4	2	no	—
641	C₂×C₄	—	4	2	no	—
642	C₂×C₄	—	4	2	no	—
643	C₂×C₄	—	4	2	no	—
644	C₂×C₄	—	4	2	no	—
645	C₂×C₄	—	16	2	no	—
646	C₂×C₄	—	16	2	no	—
647	C₂×C₄	—	16	2	no	—
648	C₂×C₄	—	16	2	no	—
649	C₂×C₄	—	16	2	no	—
650	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
651	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
652	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
653	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
654	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
655	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
656	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
657	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
658	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
659	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
660	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
661	C₂×C₄	C₂³×D₄	1	1	yes	characteristic
662	C₈	—	2	1	no	—
663	C₈	—	2	1	no	—
664	C₈	—	2	1	no	—
665	C₈	—	2	1	no	—
666	C₈	—	2	1	no	—
667	C₈	—	2	1	no	—
668	C₈	#578	1	2	yes	—
669	C₈	C₂×2₋¹⁺⁴	1	1	yes	characteristic
670	C₈	C₂×2₋¹⁺⁴	1	1	yes	characteristic
671	C₂²	—	2	1	no	—
672	C₂²	—	2	1	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	1	no	—
677	C₂²	—	2	1	no	—
678	C₂²	—	2	1	no	—
679	C₂²	—	2	1	no	—
680	C₂²	—	8	2	no	—
681	C₂²	—	8	2	no	—
682	C₂²	—	8	2	no	—
683	C₂²	C₂³×D₈	1	1	yes	characteristic
684	C₄	—	2	1	no	—
685	C₄	—	2	1	no	—
686	C₄	—	2	1	no	—
687	C₄	—	2	1	no	—
688	C₄	—	2	1	no	—
689	C₄	—	2	1	no	—
690	C₄	—	2	1	no	—
691	C₄	—	2	1	no	—
692	C₄	—	2	1	no	—
693	C₄	—	2	1	no	—
694	C₄	—	2	1	no	—
695	C₄	—	8	2	no	—
696	C₄	—	8	2	no	—
697	C₄	—	8	2	no	—
698	C₄	—	8	2	no	—
699	C₄	—	8	2	no	—
700	C₄	—	8	2	no	—
701	C₄	—	8	2	no	—
702	C₄	#3499	1	1	yes	characteristic
703	C₄	C₂×#578	1	1	yes	characteristic
704	C₂	—	4	1	no	—
705	C₂	—	4	1	no	—
706	C₂	—	4	1	no	—
707	C₂	—	16	2	no	—
708	C₂	#62471	1	1	yes	characteristic
709	C₂	#62635	1	1	yes	characteristic
710	C₂	#62635	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁵
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ #529 ◁ #2966 ◁ G
LECS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #62490	C₂	semidirect
2. #33955	C₂	semidirect
3. #33950	C₂	semidirect
4. #33947	C₂	semidirect
5. #33918	C₂	semidirect
6. #33917	C₂	semidirect
7. #33915	C₂	semidirect
8. #33909	C₂	semidirect
9. #33908	C₂	semidirect
10. #33906	C₂	semidirect
11. #33906	C₂	semidirect
12. #33903	C₂	semidirect
13. #33903	C₂	semidirect
14. #33810	C₂	semidirect
15. #33810	C₂	semidirect
16. #33806	C₂	semidirect
17. #33739	C₂	semidirect
18. #33739	C₂	semidirect
19. #33735	C₂	semidirect
20. #33729	C₂	semidirect
21. #33729	C₂	semidirect
22. #33726	C₂	semidirect
23. #33480	C₂	semidirect

Maximal subgroups

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

subgroup	index
#62490	2
#33955	2
#33950	2
#33947	2
#33918	2
#33917	2
#33915	2
#33909	2
#33908	2
#33906	2
#33903	2
#33810	2
#33806	2
#33739	2
#33735	2
#33729	2
#33726	2
#33480	2