Subgroups — #62578

Order 256.

896 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3515	C₂	1	1	yes	maximal, characteristic, complemented
2	#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	#3371	C₂	1	2	yes	maximal, complemented
4	#3370	C₂	1	2	yes	maximal, complemented
5	#3317	C₂	1	2	yes	maximal, complemented
6	#3314	C₂	1	2	yes	maximal, complemented
7	#3309	C₂	1	2	yes	maximal, complemented
8	#3306	C₂	1	2	yes	maximal, complemented
9	#3297	C₂	1	2	yes	maximal, complemented
10	#3296	C₂	1	2	yes	maximal, complemented
11	#3236	C₂	1	1	yes	maximal, characteristic, complemented
12	#3235	C₂	1	1	yes	maximal, characteristic, complemented
13	#3234	C₂	1	1	yes	maximal, characteristic, complemented
14	#3219	C₂	1	1	yes	maximal, characteristic, complemented
15	#3219	C₂	1	1	yes	maximal, characteristic, complemented
16	#3217	C₂	1	1	yes	maximal, characteristic, complemented
17	#3181	C₂	1	1	yes	maximal, characteristic, complemented
18	#3180	C₂	1	1	yes	maximal, characteristic, complemented
19	#3171	C₂	1	1	yes	maximal, characteristic, complemented
20	#3142	C₂	1	1	yes	maximal, characteristic, complemented
21	#3135	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#490	C₂	1	1	yes	maximal, characteristic, complemented
23	#2970	C₂	1	1	yes	maximal, characteristic, complemented
24	#559	—	2	1	no	—
25	#559	C₂²	1	2	yes	—
26	#557	C₂²	1	1	yes	characteristic, complemented
27	#554	C₂²	1	1	yes	characteristic
28	#554	C₂²	1	1	yes	characteristic, complemented
29	#553	C₂²	1	1	yes	characteristic
30	#553	C₂²	1	1	yes	characteristic, complemented
31	#552	—	2	1	no	—
32	#552	—	2	1	no	—
33	#552	—	2	1	no	—
34	#552	C₂²	1	1	yes	characteristic
35	#552	C₂²	1	1	yes	characteristic, complemented
36	#550	—	2	1	no	—
37	#550	C₂²	1	2	yes	—
38	#547	—	2	1	no	—
39	#547	C₂²	1	1	yes	characteristic
40	#546	—	2	1	no	—
41	#546	—	2	1	no	—
42	#546	C₂²	1	2	yes	—
43	#546	C₂²	1	2	yes	—
44	#541	—	2	1	no	—
45	#540	—	2	1	no	—
46	#540	—	2	1	no	—
47	#539	—	2	1	no	—
48	#539	—	2	1	no	—
49	#535	—	2	1	no	—
50	#533	C₂²	1	1	yes	characteristic
51	#533	C₂²	1	1	yes	characteristic, complemented
52	#532	C₂²	1	1	yes	characteristic
53	#532	C₂²	1	1	yes	characteristic
54	#532	C₂²	1	1	yes	characteristic
55	#532	C₂²	1	1	yes	characteristic
56	C₂×#127	C₂²	1	1	yes	characteristic
57	#529	C₂²	1	1	yes	characteristic
58	#529	C₂²	1	1	yes	characteristic, complemented
59	#529	C₂²	1	1	yes	characteristic, complemented
60	C₂×#125	C₂²	1	1	yes	characteristic
61	C₂×#125	C₂²	1	1	yes	characteristic, complemented
62	#520	—	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, complemented
69	#496	C₂²	1	1	yes	characteristic
70	#496	C₂²	1	1	yes	characteristic
71	#491	C₂²	1	1	yes	characteristic, complemented
72	#491	C₂²	1	1	yes	characteristic, complemented
73	#491	C₂²	1	1	yes	characteristic, complemented
74	#490	C₂²	1	2	yes	—
75	#490	C₂²	1	2	yes	—
76	#490	C₂²	1	1	yes	characteristic
77	#490	C₂²	1	1	yes	characteristic
78	#490	C₂²	1	1	yes	characteristic
79	#490	C₂²	1	1	yes	characteristic
80	#490	C₂²	1	1	yes	characteristic
81	#490	C₂²	1	1	yes	characteristic
82	#489	C₂²	1	2	yes	complemented
83	#489	C₂²	1	2	yes	complemented
84	#489	C₂²	1	1	yes	characteristic, complemented
85	#488	C₂²	1	2	yes	complemented
86	#488	C₂²	1	2	yes	complemented
87	#484	C₂²	1	2	yes	—
88	#483	C₂²	1	2	yes	—
89	#482	C₂²	1	2	yes	complemented
90	#482	C₂²	1	2	yes	complemented
91	#481	C₂²	1	2	yes	complemented
92	#480	C₂²	1	2	yes	complemented
93	#479	C₂²	1	2	yes	complemented
94	#479	C₂²	1	2	yes	complemented
95	#478	C₂²	1	2	yes	complemented
96	#478	C₂²	1	2	yes	complemented
97	#476	C₂²	1	2	yes	complemented
98	#474	C₂²	1	2	yes	complemented
99	#469	C₂²	1	2	yes	complemented
100	#468	C₂²	1	2	yes	complemented
101	#467	C₂²	1	2	yes	—
102	#466	C₂²	1	2	yes	complemented
103	#465	C₂²	1	2	yes	—
104	#465	C₂²	1	2	yes	complemented
105	#464	C₂²	1	2	yes	complemented
106	#464	C₂²	1	2	yes	complemented
107	#463	C₂²	1	2	yes	complemented
108	#463	C₂²	1	2	yes	complemented
109	#460	C₂²	1	2	yes	—
110	#459	C₂²	1	2	yes	—
111	#452	C₂²	1	2	yes	complemented
112	#452	C₂²	1	2	yes	complemented
113	#450	C₂²	1	2	yes	—
114	#449	C₂²	1	2	yes	complemented
115	#449	C₂²	1	2	yes	complemented
116	#447	C₂²	1	2	yes	—
117	#446	C₂²	1	2	yes	complemented
118	#442	C₂²	1	2	yes	complemented
119	#441	C₂²	1	2	yes	complemented
120	#440	C₂²	1	2	yes	complemented
121	#440	C₂²	1	2	yes	complemented
122	C₄×SD₁₆	C₂²	1	2	yes	complemented
123	C₄×D₈	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	—
127	#432	C₂²	1	1	yes	characteristic
128	#432	C₂²	1	1	yes	characteristic, complemented
129	#432	C₂²	1	1	yes	characteristic, complemented
130	#417	C₂²	1	2	yes	complemented
131	#417	C₂²	1	2	yes	complemented
132	#416	C₂²	1	2	yes	complemented
133	#416	C₂²	1	2	yes	complemented
134	C₂×#102	C₂²	1	2	yes	—
135	C₂×#102	C₂²	1	2	yes	—
136	C₄×M₁₆	C₂²	1	1	yes	characteristic, complemented
137	C₂×#97	C₂²	1	1	yes	characteristic
138	C₂×#97	C₂²	1	1	yes	characteristic, complemented
139	C₂×#41	—	2	1	no	—
140	C₂×#41	—	2	1	no	—
141	C₂×#41	—	2	1	no	—
142	C₂×#41	D₄	1	1	yes	characteristic
143	C₂×#41	C₂³	1	2	yes	—
144	C₂×#41	C₂³	1	2	yes	—
145	C₂²×D₄	—	2	1	no	—
146	C₂²×D₄	—	2	1	no	—
147	C₂²×D₄	C₂³	1	2	yes	—
148	C₂×Q₁₆	C₂³	1	2	yes	—
149	C₂×SD₁₆	C₂³	1	2	yes	—
150	C₂×SD₁₆	C₂³	1	2	yes	—
151	C₂×SD₁₆	C₂³	1	2	yes	—
152	C₂×D₈	C₂³	1	2	yes	—
153	C₂×D₈	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	1	no	—
158	C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	#127	—	2	2	no	—
163	#127	—	2	1	no	—
164	#127	—	2	1	no	—
165	#127	C₂³	1	1	yes	characteristic
166	#127	C₂³	1	1	yes	characteristic
167	#127	C₂³	1	2	yes	—
168	#126	—	2	1	no	—
169	#126	—	2	1	no	—
170	#126	—	2	1	no	—
171	#126	—	2	1	no	—
172	#126	—	2	1	no	—
173	#126	—	2	1	no	—
174	#126	—	2	1	no	—
175	#125	—	2	1	no	—
176	#125	—	2	1	no	—
177	#125	—	2	1	no	—
178	#125	—	2	1	no	—
179	#125	—	2	1	no	—
180	#125	—	2	1	no	—
181	#125	—	2	1	no	—
182	#125	—	2	1	no	—
183	#125	—	2	1	no	—
184	#125	—	2	1	no	—
185	#125	C₂³	1	1	yes	characteristic
186	#125	C₂³	1	1	yes	characteristic
187	#125	C₂³	1	1	yes	characteristic
188	#125	C₂³	1	1	yes	characteristic
189	#125	C₂³	1	1	yes	characteristic
190	#125	C₂³	1	1	yes	characteristic
191	#125	C₂³	1	1	yes	characteristic
192	#124	—	2	2	no	—
193	#124	—	2	1	no	—
194	#124	—	2	1	no	—
195	#124	C₂³	1	1	yes	characteristic
196	#124	C₂³	1	2	yes	—
197	#124	C₂³	1	2	yes	—
198	#123	—	2	1	no	—
199	#123	—	2	1	no	—
200	#123	—	2	1	no	—
201	#123	—	2	1	no	—
202	#123	—	2	1	no	—
203	#123	—	2	2	no	—
204	#123	—	2	2	no	—
205	#123	—	2	2	no	—
206	#123	—	2	2	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	C₂³	1	1	yes	characteristic
221	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
222	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
223	C₂²⋊Q₈	C₂³	1	2	yes	—
224	#121	—	2	1	no	—
225	#121	—	2	1	no	—
226	#121	—	2	1	no	—
227	#121	—	2	1	no	—
228	#121	—	2	1	no	—
229	#121	—	2	1	no	—
230	#121	—	2	1	no	—
231	#121	—	2	1	no	—
232	#121	—	2	2	no	—
233	#121	—	2	2	no	—
234	#121	—	2	2	no	—
235	#121	—	2	2	no	—
236	#121	C₂³	1	1	yes	characteristic
237	#121	C₂³	1	1	yes	characteristic
238	#121	C₂³	1	1	yes	characteristic
239	#121	C₂³	1	2	yes	—
240	#121	C₂³	1	2	yes	—
241	#120	—	2	2	no	—
242	#120	—	2	2	no	—
243	C₄×Q₈	—	2	1	no	—
244	C₄×Q₈	—	2	1	no	—
245	C₄×Q₈	—	2	1	no	—
246	C₄×Q₈	—	2	1	no	—
247	C₄×Q₈	D₄	1	1	yes	characteristic
248	C₄×Q₈	C₂³	1	1	yes	characteristic
249	C₄×Q₈	C₂³	1	1	yes	characteristic
250	C₄×Q₈	C₂³	1	1	yes	characteristic
251	C₄×Q₈	C₂³	1	2	yes	—
252	C₄×Q₈	C₂³	1	1	yes	characteristic
253	C₄×D₄	—	2	1	no	—
254	C₄×D₄	—	2	1	no	—
255	C₄×D₄	—	2	1	no	—
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	—	2	2	no	—
258	C₄×D₄	—	2	2	no	—
259	C₄×D₄	—	2	1	no	—
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	D₄	1	1	yes	characteristic
268	C₄×D₄	D₄	1	1	yes	characteristic
269	C₄×D₄	D₄	1	1	yes	characteristic
270	C₄×D₄	C₂³	1	1	yes	characteristic
271	C₄×D₄	C₂³	1	1	yes	characteristic
272	C₄×D₄	C₂³	1	1	yes	characteristic
273	C₄×D₄	C₂³	1	2	yes	—
274	C₄×D₄	C₂³	1	2	yes	—
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	1	no	—
283	#117	—	2	1	no	—
284	#117	D₄	1	1	yes	characteristic
285	#117	D₄	1	1	yes	characteristic
286	#117	D₄	1	1	yes	characteristic
287	#117	C₂³	1	1	yes	characteristic
288	#117	C₂³	1	1	yes	characteristic
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
297	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₂²⋊C₄	—	2	2	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	#102	C₂³	1	2	yes	—
320	#102	C₂³	1	2	yes	—
321	#102	C₂³	1	2	yes	—
322	#102	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	2	yes	—
338	#97	C₂³	1	1	yes	characteristic
339	#97	C₂³	1	2	yes	—
340	#97	C₂³	1	1	yes	characteristic
341	C₄×C₈	C₂³	1	2	yes	—
342	C₂⁴	—	2	2	no	—
343	#41	—	4	2	no	—
344	#41	—	4	2	no	—
345	#41	—	4	2	no	—
346	#41	—	4	2	no	—
347	#41	—	4	2	no	—
348	#41	—	4	4	no	—
349	#41	—	8	2	no	—
350	#41	—	8	2	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
355	C₂×Q₈	C₂⁴	1	2	yes	—
356	C₂×Q₈	C₂⁴	1	1	yes	characteristic
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	4	2	no	—
372	C₂×D₄	—	4	2	no	—
373	C₂×D₄	—	4	4	no	—
374	C₂×D₄	—	8	2	no	—
375	C₂×D₄	C₂×D₄	1	1	yes	characteristic
376	C₂×D₄	C₂×D₄	1	1	yes	characteristic
377	C₂×D₄	C₂×D₄	1	1	yes	characteristic
378	C₂×D₄	C₂⁴	1	2	yes	—
379	C₂×D₄	C₂⁴	1	2	yes	—
380	C₂×D₄	C₂⁴	1	1	yes	characteristic
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	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
398	C₂²×C₄	C₂⁴	1	1	yes	characteristic
399	C₂²×C₄	C₂⁴	1	1	yes	characteristic
400	C₂²×C₄	C₂⁴	1	1	yes	characteristic
401	Q₁₆	—	4	2	no	—
402	SD₁₆	—	4	2	no	—
403	SD₁₆	—	4	2	no	—
404	SD₁₆	—	4	2	no	—
405	D₈	—	4	2	no	—
406	D₈	—	4	2	no	—
407	M₁₆	—	4	2	no	—
408	C₂×C₈	—	4	2	no	—
409	C₂×C₈	—	4	2	no	—
410	C₂×C₈	C₂⁴	1	2	yes	—
411	C₂×C₈	C₂⁴	1	2	yes	—
412	C₂×C₈	C₂⁴	1	2	yes	—
413	C₂×C₈	C₂⁴	1	2	yes	—
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	1	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
446	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
447	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
448	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
449	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
450	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
451	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
452	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
453	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
454	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
455	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
456	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
457	C₄⋊C₄	C₂⁴	1	2	yes	—
458	C₂²⋊C₄	—	2	2	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	2	no	—
465	C₂²⋊C₄	—	2	2	no	—
466	C₂²⋊C₄	—	2	2	no	—
467	C₂²⋊C₄	—	2	2	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	2	no	—
474	C₂²⋊C₄	—	2	2	no	—
475	C₂²⋊C₄	—	2	2	no	—
476	C₂²⋊C₄	—	2	2	no	—
477	C₂²⋊C₄	—	2	1	no	—
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	—	2	1	no	—
480	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
481	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
482	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
483	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
484	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
485	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
486	C₄²	—	2	1	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	2	2	no	—
491	C₄²	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
496	C₄²	C₂×D₄	1	1	yes	characteristic
497	C₄²	C₂×D₄	1	1	yes	characteristic
498	C₄²	C₂⁴	1	1	yes	characteristic
499	C₄²	C₂⁴	1	1	yes	characteristic
500	C₄²	C₂⁴	1	1	yes	characteristic
501	C₄²	C₂⁴	1	1	yes	characteristic
502	C₂³	—	2	1	no	—
503	C₂³	—	2	2	no	—
504	C₂³	—	2	2	no	—
505	C₂³	—	4	4	no	—
506	C₂³	—	8	2	no	—
507	C₂³	—	8	2	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	—	4	1	no	—
515	Q₈	—	4	2	no	—
516	Q₈	—	4	2	no	—
517	Q₈	—	8	1	no	—
518	D₄	—	2	2	no	—
519	D₄	—	2	2	no	—
520	D₄	—	2	2	no	—
521	D₄	—	2	2	no	—
522	D₄	—	2	2	no	—
523	D₄	—	2	2	no	—
524	D₄	—	2	2	no	—
525	D₄	—	4	1	no	—
526	D₄	—	4	2	no	—
527	D₄	—	4	2	no	—
528	D₄	—	4	4	no	—
529	D₄	—	4	2	no	—
530	D₄	—	4	2	no	—
531	D₄	—	4	2	no	—
532	D₄	—	4	2	no	—
533	D₄	—	8	2	no	—
534	D₄	—	8	2	no	—
535	D₄	—	8	1	no	—
536	D₄	—	8	2	no	—
537	D₄	—	8	2	no	—
538	D₄	—	8	2	no	—
539	D₄	—	8	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	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	8	1	no	—
562	C₂×C₄	—	8	1	no	—
563	C₂×C₄	—	8	2	no	—
564	C₂×C₄	—	8	2	no	—
565	C₂×C₄	—	8	2	no	—
566	C₂×C₄	—	8	2	no	—
567	C₂×C₄	—	8	1	no	—
568	C₂×C₄	—	8	1	no	—
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	C₂²×D₄	1	1	yes	characteristic
576	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
577	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
578	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
579	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
580	C₂×C₄	C₂⁵	1	1	yes	characteristic
581	C₈	—	2	2	no	—
582	C₈	—	2	2	no	—
583	C₈	—	2	2	no	—
584	C₈	—	2	2	no	—
585	C₂²	—	2	1	no	—
586	C₂²	—	2	1	no	—
587	C₂²	—	2	1	no	—
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	2	1	no	—
591	C₂²	—	2	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	2	no	—
595	C₂²	—	4	2	no	—
596	C₂²	—	4	2	no	—
597	C₂²	—	4	2	no	—
598	C₂²	—	4	1	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	4	2	no	—
601	C₂²	—	4	2	no	—
602	C₂²	—	16	4	no	—
603	C₂²	#575	1	2	yes	—
604	C₂²	C₂³×D₄	1	1	yes	characteristic
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	—	2	1	no	—
613	C₄	—	2	1	no	—
614	C₄	—	2	1	no	—
615	C₄	—	2	1	no	—
616	C₄	—	4	1	no	—
617	C₄	—	4	2	no	—
618	C₄	—	4	1	no	—
619	C₄	—	4	1	no	—
620	C₄	—	4	2	no	—
621	C₄	—	4	1	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	1	no	—
624	C₄	—	4	1	no	—
625	C₄	#585	1	2	yes	—
626	C₂	—	2	2	no	—
627	C₂	—	4	1	no	—
628	C₂	—	4	1	no	—
629	C₂	—	8	1	no	—
630	C₂	—	8	2	no	—
631	C₂	—	8	2	no	—
632	C₂	#3500	1	1	yes	characteristic
633	C₂	C₂×#575	1	1	yes	characteristic
634	C₂	#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ 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
1. #3515	C₂	semidirect
2. #3508	C₂	semidirect
3. #3371	C₂	semidirect
4. #3370	C₂	semidirect
5. #3317	C₂	semidirect
6. #3314	C₂	semidirect
7. #3309	C₂	semidirect
8. #3306	C₂	semidirect
9. #3297	C₂	semidirect
10. #3296	C₂	semidirect
11. #3236	C₂	semidirect
12. #3235	C₂	semidirect
13. #3234	C₂	semidirect
14. #3219	C₂	semidirect
15. #3219	C₂	semidirect
16. #3217	C₂	semidirect
17. #3181	C₂	semidirect
18. #3180	C₂	semidirect
19. #3171	C₂	semidirect
20. #3142	C₂	semidirect
21. #3135	C₂	semidirect
22. C₂×#490	C₂	semidirect
23. #2970	C₂	semidirect
26. #557	C₂²	semidirect
28. #554	C₂²	semidirect
30. #553	C₂²	semidirect
35. #552	C₂²	semidirect
51. #533	C₂²	semidirect
58. #529	C₂²	semidirect
59. #529	C₂²	semidirect
61. C₂×#125	C₂²	semidirect
65. #501	C₂²	semidirect
66. #501	C₂²	semidirect
67. #501	C₂²	semidirect
68. #497	C₂²	semidirect
71. #491	C₂²	semidirect
72. #491	C₂²	semidirect
73. #491	C₂²	semidirect
82. #489	C₂²	semidirect
83. #489	C₂²	semidirect
84. #489	C₂²	semidirect
85. #488	C₂²	semidirect
86. #488	C₂²	semidirect
89. #482	C₂²	semidirect
90. #482	C₂²	semidirect
91. #481	C₂²	semidirect
92. #480	C₂²	semidirect
93. #479	C₂²	semidirect
94. #479	C₂²	semidirect
95. #478	C₂²	semidirect
96. #478	C₂²	semidirect
97. #476	C₂²	semidirect
98. #474	C₂²	semidirect
99. #469	C₂²	semidirect
100. #468	C₂²	semidirect
102. #466	C₂²	semidirect
104. #465	C₂²	semidirect
105. #464	C₂²	semidirect
106. #464	C₂²	semidirect
107. #463	C₂²	semidirect
108. #463	C₂²	semidirect
111. #452	C₂²	semidirect
112. #452	C₂²	semidirect
114. #449	C₂²	semidirect
115. #449	C₂²	semidirect
117. #446	C₂²	semidirect
118. #442	C₂²	semidirect
119. #441	C₂²	semidirect
120. #440	C₂²	semidirect
121. #440	C₂²	semidirect
122. C₄×SD₁₆	C₂²	semidirect
123. C₄×D₈	C₂²	semidirect
125. #435	C₂²	semidirect
128. #432	C₂²	semidirect
129. #432	C₂²	semidirect
130. #417	C₂²	semidirect
131. #417	C₂²	semidirect
132. #416	C₂²	semidirect
133. #416	C₂²	semidirect
136. C₄×M₁₆	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
#3515	2
#3508	2
#3371	2
#3370	2
#3317	2
#3314	2
#3309	2
#3306	2
#3297	2
#3296	2
#3236	2
#3235	2
#3234	2
#3219	2
#3217	2
#3181	2
#3180	2
#3171	2
#3142	2
#3135	2
C₂×#490	2
#2970	2