Subgroups — #62584

Order 256.

896 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3514	C₂	1	1	yes	maximal, characteristic, complemented
2	#3511	C₂	1	1	yes	maximal, characteristic, complemented
3	#3376	C₂	1	2	yes	maximal, complemented
4	#3370	C₂	1	2	yes	maximal, complemented
5	#3321	C₂	1	2	yes	maximal, complemented
6	#3320	C₂	1	2	yes	maximal, complemented
7	#3319	C₂	1	2	yes	maximal, complemented
8	#3318	C₂	1	2	yes	maximal, complemented
9	#3301	C₂	1	2	yes	maximal, complemented
10	#3297	C₂	1	2	yes	maximal, complemented
11	#3240	C₂	1	1	yes	maximal, characteristic, complemented
12	#3240	C₂	1	1	yes	maximal, characteristic, complemented
13	#3239	C₂	1	1	yes	maximal, characteristic, complemented
14	#3214	C₂	1	1	yes	maximal, characteristic, complemented
15	#3213	C₂	1	1	yes	maximal, characteristic, complemented
16	#3213	C₂	1	1	yes	maximal, characteristic, complemented
17	#3180	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	#3140	C₂	1	1	yes	maximal, characteristic, complemented
21	#3135	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#489	C₂	1	1	yes	maximal, characteristic, complemented
23	#2970	C₂	1	1	yes	maximal, characteristic, complemented
24	#559	C₂²	1	1	yes	characteristic
25	#556	—	2	1	no	—
26	#556	C₂²	1	1	yes	characteristic
27	#555	—	2	1	no	—
28	#555	C₂²	1	2	yes	complemented
29	#554	C₂²	1	2	yes	complemented
30	#553	C₂²	1	2	yes	—
31	#553	C₂²	1	2	yes	complemented
32	#551	—	2	1	no	—
33	#551	—	2	1	no	—
34	D₄×Q₈	C₂²	1	1	yes	characteristic
35	#548	—	2	1	no	—
36	#548	—	2	1	no	—
37	#548	C₂²	1	1	yes	characteristic
38	#548	C₂²	1	1	yes	characteristic
39	#547	—	2	1	no	—
40	#546	—	2	1	no	—
41	#546	C₂²	1	1	yes	characteristic
42	#546	C₂²	1	1	yes	characteristic
43	D₄²	C₂²	1	1	yes	characteristic
44	#542	—	2	1	no	—
45	#542	—	2	1	no	—
46	#542	—	2	1	no	—
47	#538	—	2	1	no	—
48	#538	—	2	1	no	—
49	#537	—	2	1	no	—
50	#533	C₂²	1	1	yes	characteristic, complemented
51	#533	C₂²	1	1	yes	characteristic, complemented
52	#532	C₂²	1	1	yes	characteristic
53	#532	C₂²	1	1	yes	characteristic, complemented
54	#532	C₂²	1	1	yes	characteristic, complemented
55	#532	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
57	#529	C₂²	1	1	yes	characteristic
58	#529	C₂²	1	1	yes	characteristic
59	#529	C₂²	1	1	yes	characteristic
60	C₂×#124	C₂²	1	1	yes	characteristic
61	C₂×#124	C₂²	1	1	yes	characteristic
62	#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	#496	C₂²	1	1	yes	characteristic
69	#496	C₂²	1	1	yes	characteristic, complemented
70	#496	C₂²	1	1	yes	characteristic, complemented
71	#491	C₂²	1	2	yes	complemented
72	#490	C₂²	1	2	yes	—
73	#490	C₂²	1	1	yes	characteristic, complemented
74	#489	C₂²	1	2	yes	—
75	#489	C₂²	1	1	yes	characteristic
76	#489	C₂²	1	1	yes	characteristic
77	#489	C₂²	1	1	yes	characteristic
78	#489	C₂²	1	2	yes	complemented
79	#489	C₂²	1	1	yes	characteristic, complemented
80	#489	C₂²	1	1	yes	characteristic, complemented
81	#489	C₂²	1	1	yes	characteristic, complemented
82	#489	C₂²	1	1	yes	characteristic, complemented
83	#489	C₂²	1	1	yes	characteristic, complemented
84	#489	C₂²	1	1	yes	characteristic, complemented
85	#488	C₂²	1	2	yes	—
86	#488	C₂²	1	2	yes	complemented
87	#485	C₂²	1	2	yes	complemented
88	#485	C₂²	1	2	yes	complemented
89	#484	C₂²	1	2	yes	complemented
90	#482	C₂²	1	2	yes	—
91	#482	C₂²	1	2	yes	—
92	#481	C₂²	1	2	yes	—
93	#479	C₂²	1	2	yes	complemented
94	#479	C₂²	1	2	yes	complemented
95	#478	C₂²	1	2	yes	—
96	#478	C₂²	1	2	yes	complemented
97	#475	C₂²	1	2	yes	complemented
98	#474	C₂²	1	2	yes	complemented
99	#469	C₂²	1	2	yes	—
100	#468	C₂²	1	2	yes	complemented
101	#466	C₂²	1	2	yes	—
102	#466	C₂²	1	2	yes	—
103	#465	C₂²	1	2	yes	complemented
104	#465	C₂²	1	2	yes	complemented
105	#463	C₂²	1	2	yes	—
106	#463	C₂²	1	2	yes	—
107	#463	C₂²	1	2	yes	complemented
108	#463	C₂²	1	2	yes	complemented
109	#461	C₂²	1	2	yes	complemented
110	#459	C₂²	1	2	yes	—
111	#449	C₂²	1	2	yes	complemented
112	#449	C₂²	1	2	yes	complemented
113	#448	C₂²	1	2	yes	complemented
114	#448	C₂²	1	2	yes	complemented
115	#447	C₂²	1	2	yes	—
116	#447	C₂²	1	2	yes	—
117	#446	C₂²	1	2	yes	complemented
118	#442	C₂²	1	2	yes	—
119	#442	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	complemented
127	#432	C₂²	1	1	yes	characteristic, complemented
128	#432	C₂²	1	1	yes	characteristic, complemented
129	#432	C₂²	1	1	yes	characteristic, complemented
130	#419	C₂²	1	2	yes	complemented
131	#418	C₂²	1	2	yes	—
132	#416	C₂²	1	2	yes	complemented
133	#416	C₂²	1	2	yes	complemented
134	C₂×#103	C₂²	1	2	yes	complemented
135	C₂×#102	C₂²	1	2	yes	—
136	C₄×M₁₆	C₂²	1	1	yes	characteristic, complemented
137	C₂×#97	C₂²	1	1	yes	characteristic, complemented
138	C₂×#97	C₂²	1	1	yes	characteristic, complemented
139	C₂×#41	—	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	1	yes	characteristic
144	C₂×#41	C₂³	1	1	yes	characteristic
145	C₂²×Q₈	—	2	1	no	—
146	C₂²×Q₈	C₂³	1	1	yes	characteristic
147	C₂²×Q₈	C₂³	1	1	yes	characteristic
148	C₂²×D₄	—	2	1	no	—
149	C₂²×D₄	C₂³	1	1	yes	characteristic
150	C₂²×D₄	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆	C₂³	1	2	yes	—
152	C₂×SD₁₆	C₂³	1	2	yes	—
153	C₂×SD₁₆	C₂³	1	2	yes	—
154	C₂×D₈	C₂³	1	2	yes	—
155	C₂×D₈	C₂³	1	2	yes	—
156	C₂×D₈	C₂³	1	2	yes	—
157	C₂×M₁₆	C₂³	1	2	yes	—
158	C₂²×C₈	C₂³	1	2	yes	—
159	C₂²×C₈	C₂³	1	2	yes	—
160	C₄⋊Q₈	—	2	1	no	—
161	C₄⋊Q₈	—	2	1	no	—
162	C₄⋊Q₈	—	2	1	no	—
163	C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₄⋊Q₈	C₂³	1	2	yes	—
167	C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	#127	C₂³	1	1	yes	characteristic
169	#127	C₂³	1	1	yes	characteristic
170	#126	—	2	1	no	—
171	#126	—	2	1	no	—
172	#126	—	2	2	no	—
173	#126	—	2	2	no	—
174	#126	—	2	1	no	—
175	#126	—	2	1	no	—
176	#126	—	2	1	no	—
177	#125	C₂³	1	1	yes	characteristic
178	#125	C₂³	1	2	yes	—
179	#125	C₂³	1	2	yes	—
180	#124	—	2	1	no	—
181	#124	—	2	1	no	—
182	#124	—	2	1	no	—
183	#124	—	2	2	no	—
184	#124	—	2	2	no	—
185	#124	—	2	1	no	—
186	#124	—	2	1	no	—
187	#124	—	2	1	no	—
188	#124	—	2	1	no	—
189	#124	—	2	1	no	—
190	#124	—	2	1	no	—
191	#124	—	2	1	no	—
192	#124	C₂³	1	1	yes	characteristic
193	#124	C₂³	1	1	yes	characteristic
194	#124	C₂³	1	1	yes	characteristic
195	#124	C₂³	1	1	yes	characteristic
196	#124	C₂³	1	1	yes	characteristic
197	#124	C₂³	1	1	yes	characteristic
198	#124	C₂³	1	1	yes	characteristic
199	#123	—	2	1	no	—
200	#123	—	2	1	no	—
201	#123	—	2	1	no	—
202	#123	—	2	1	no	—
203	#123	—	2	1	no	—
204	#123	—	2	1	no	—
205	#123	—	2	1	no	—
206	#123	—	2	2	no	—
207	#123	—	2	2	no	—
208	C₂²⋊Q₈	—	2	2	no	—
209	C₂²⋊Q₈	—	2	1	no	—
210	C₂²⋊Q₈	—	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	2	no	—
215	C₂²⋊Q₈	—	2	2	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	#121	—	2	2	no	—
224	#121	—	2	2	no	—
225	#121	—	2	2	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	1	no	—
233	#121	—	2	1	no	—
234	#121	—	2	1	no	—
235	#121	—	2	1	no	—
236	#121	C₂³	1	1	yes	characteristic
237	#121	C₂³	1	1	yes	characteristic
238	#121	C₂³	1	1	yes	characteristic
239	#121	C₂³	1	2	yes	—
240	#121	C₂³	1	2	yes	—
241	#121	C₂³	1	2	yes	—
242	#120	—	2	1	no	—
243	#120	—	2	1	no	—
244	#120	—	2	1	no	—
245	#120	—	2	1	no	—
246	C₄×Q₈	—	2	1	no	—
247	C₄×Q₈	—	2	1	no	—
248	C₄×Q₈	—	2	1	no	—
249	C₄×Q₈	—	2	1	no	—
250	C₄×Q₈	D₄	1	1	yes	characteristic
251	C₄×Q₈	C₂³	1	1	yes	characteristic
252	C₄×Q₈	C₂³	1	1	yes	characteristic
253	C₄×Q₈	C₂³	1	1	yes	characteristic
254	C₄×Q₈	C₂³	1	1	yes	characteristic
255	C₄×D₄	—	2	1	no	—
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	—	2	1	no	—
258	C₄×D₄	—	2	1	no	—
259	C₄×D₄	—	2	1	no	—
260	C₄×D₄	—	2	1	no	—
261	C₄×D₄	—	2	1	no	—
262	C₄×D₄	—	2	2	no	—
263	C₄×D₄	—	2	2	no	—
264	C₄×D₄	—	2	1	no	—
265	C₄×D₄	—	2	1	no	—
266	C₄×D₄	—	2	1	no	—
267	C₄×D₄	—	2	1	no	—
268	C₄×D₄	—	2	1	no	—
269	C₄×D₄	D₄	1	1	yes	characteristic
270	C₄×D₄	D₄	1	1	yes	characteristic
271	C₄×D₄	D₄	1	1	yes	characteristic
272	C₄×D₄	C₂³	1	1	yes	characteristic
273	C₄×D₄	C₂³	1	1	yes	characteristic
274	C₄×D₄	C₂³	1	1	yes	characteristic
275	C₄×D₄	C₂³	1	2	yes	—
276	C₄×D₄	C₂³	1	2	yes	—
277	C₄×D₄	C₂³	1	2	yes	—
278	C₄×D₄	C₂³	1	1	yes	characteristic
279	C₄×D₄	C₂³	1	1	yes	characteristic
280	C₄×D₄	C₂³	1	1	yes	characteristic
281	#117	—	2	1	no	—
282	#117	—	2	2	no	—
283	#117	—	2	1	no	—
284	#117	—	2	1	no	—
285	#117	—	2	1	no	—
286	#117	D₄	1	1	yes	characteristic
287	#117	D₄	1	1	yes	characteristic
288	#117	D₄	1	1	yes	characteristic
289	#117	C₂³	1	2	yes	—
290	#117	C₂³	1	2	yes	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	2	no	—
293	C₂×C₄⋊C₄	C₂³	1	2	yes	—
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₂²⋊C₄	—	2	1	no	—
298	C₂×C₂²⋊C₄	—	2	1	no	—
299	C₂×C₂²⋊C₄	—	2	1	no	—
300	C₂×C₄²	C₂³	1	1	yes	characteristic
301	C₂×C₄²	C₂³	1	1	yes	characteristic
302	C₂×C₄²	C₂³	1	1	yes	characteristic
303	#107	C₂³	1	2	yes	—
304	#107	C₂³	1	2	yes	—
305	#107	C₂³	1	2	yes	—
306	#106	C₂³	1	2	yes	—
307	#106	C₂³	1	2	yes	—
308	#106	C₂³	1	2	yes	—
309	C₄⋊C₈	C₂³	1	2	yes	—
310	C₄⋊C₈	C₂³	1	2	yes	—
311	C₄⋊C₈	C₂³	1	2	yes	—
312	#103	C₂³	1	2	yes	—
313	#103	C₂³	1	2	yes	—
314	#103	C₂³	1	2	yes	—
315	#103	C₂³	1	2	yes	—
316	#103	C₂³	1	2	yes	—
317	#103	C₂³	1	2	yes	—
318	#103	C₂³	1	2	yes	—
319	#103	C₂³	1	2	yes	—
320	#103	C₂³	1	2	yes	—
321	#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	1	yes	characteristic
338	#97	C₂³	1	2	yes	—
339	#97	C₂³	1	2	yes	—
340	#97	C₂³	1	1	yes	characteristic
341	C₄×C₈	C₂³	1	2	yes	—
342	C₂⁴	—	2	1	no	—
343	C₂⁴	—	2	1	no	—
344	#41	—	4	2	no	—
345	#41	—	4	4	no	—
346	#41	—	4	2	no	—
347	#41	—	4	2	no	—
348	#41	—	8	2	no	—
349	#41	—	8	2	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	4	2	no	—
357	C₂×Q₈	—	4	2	no	—
358	C₂×Q₈	—	8	2	no	—
359	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
360	C₂×Q₈	C₂⁴	1	1	yes	characteristic
361	C₂×Q₈	C₂⁴	1	1	yes	characteristic
362	C₂×Q₈	C₂⁴	1	1	yes	characteristic
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	1	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	—	2	1	no	—
372	C₂×D₄	—	2	1	no	—
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	—	4	2	no	—
378	C₂×D₄	—	4	2	no	—
379	C₂×D₄	—	4	4	no	—
380	C₂×D₄	C₂×D₄	1	1	yes	characteristic
381	C₂×D₄	C₂×D₄	1	1	yes	characteristic
382	C₂×D₄	C₂×D₄	1	1	yes	characteristic
383	C₂×D₄	C₂⁴	1	1	yes	characteristic
384	C₂×D₄	C₂⁴	1	1	yes	characteristic
385	C₂×D₄	C₂⁴	1	1	yes	characteristic
386	C₂×D₄	C₂⁴	1	2	yes	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
401	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
404	C₂²×C₄	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄	C₂⁴	1	1	yes	characteristic
406	C₂²×C₄	C₂⁴	1	1	yes	characteristic
407	SD₁₆	—	4	2	no	—
408	SD₁₆	—	4	2	no	—
409	SD₁₆	—	4	2	no	—
410	D₈	—	4	2	no	—
411	D₈	—	4	2	no	—
412	D₈	—	4	2	no	—
413	M₁₆	—	4	2	no	—
414	C₂×C₈	—	4	2	no	—
415	C₂×C₈	—	4	2	no	—
416	C₂×C₈	C₂⁴	1	2	yes	—
417	C₂×C₈	C₂⁴	1	2	yes	—
418	C₂×C₈	C₂⁴	1	2	yes	—
419	C₂×C₈	C₂⁴	1	2	yes	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	2	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	2	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
440	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
441	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
442	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
443	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
444	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
445	C₄⋊C₄	C₂⁴	1	2	yes	—
446	C₄⋊C₄	C₂⁴	1	2	yes	—
447	C₄⋊C₄	C₂⁴	1	2	yes	—
448	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
449	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
450	C₂²⋊C₄	—	2	1	no	—
451	C₂²⋊C₄	—	2	1	no	—
452	C₂²⋊C₄	—	2	2	no	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₂²⋊C₄	—	2	1	no	—
455	C₂²⋊C₄	—	2	1	no	—
456	C₂²⋊C₄	—	2	1	no	—
457	C₂²⋊C₄	—	2	1	no	—
458	C₂²⋊C₄	—	2	1	no	—
459	C₂²⋊C₄	—	2	1	no	—
460	C₂²⋊C₄	—	2	1	no	—
461	C₂²⋊C₄	—	2	1	no	—
462	C₂²⋊C₄	—	2	1	no	—
463	C₂²⋊C₄	—	2	1	no	—
464	C₂²⋊C₄	—	2	1	no	—
465	C₂²⋊C₄	—	2	1	no	—
466	C₂²⋊C₄	—	2	1	no	—
467	C₂²⋊C₄	—	2	1	no	—
468	C₂²⋊C₄	—	2	1	no	—
469	C₂²⋊C₄	—	2	1	no	—
470	C₂²⋊C₄	—	2	2	no	—
471	C₂²⋊C₄	—	2	2	no	—
472	C₂²⋊C₄	—	2	1	no	—
473	C₂²⋊C₄	—	2	1	no	—
474	C₂²⋊C₄	—	2	2	no	—
475	C₂²⋊C₄	—	2	1	no	—
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	2	1	no	—
478	C₂²⋊C₄	—	2	2	no	—
479	C₂²⋊C₄	—	2	2	no	—
480	C₂²⋊C₄	—	2	2	no	—
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	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	2	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	1	no	—
505	C₂³	—	2	1	no	—
506	C₂³	—	4	2	no	—
507	C₂³	—	4	2	no	—
508	C₂³	—	8	1	no	—
509	C₂³	—	8	1	no	—
510	C₂³	—	8	1	no	—
511	C₂³	—	8	1	no	—
512	C₂³	C₂²×D₄	1	1	yes	characteristic
513	C₂³	C₂²×D₄	1	1	yes	characteristic
514	C₂³	C₂²×D₄	1	1	yes	characteristic
515	Q₈	—	2	2	no	—
516	Q₈	—	2	2	no	—
517	Q₈	—	2	2	no	—
518	Q₈	—	4	1	no	—
519	Q₈	—	4	2	no	—
520	Q₈	—	4	2	no	—
521	Q₈	—	4	2	no	—
522	Q₈	—	8	1	no	—
523	Q₈	—	8	1	no	—
524	Q₈	—	8	2	no	—
525	D₄	—	2	2	no	—
526	D₄	—	2	2	no	—
527	D₄	—	2	2	no	—
528	D₄	—	2	2	no	—
529	D₄	—	2	2	no	—
530	D₄	—	2	2	no	—
531	D₄	—	2	2	no	—
532	D₄	—	4	1	no	—
533	D₄	—	4	2	no	—
534	D₄	—	4	2	no	—
535	D₄	—	4	2	no	—
536	D₄	—	4	2	no	—
537	D₄	—	4	2	no	—
538	D₄	—	4	4	no	—
539	D₄	—	8	1	no	—
540	D₄	—	8	1	no	—
541	D₄	—	8	1	no	—
542	D₄	—	8	1	no	—
543	D₄	—	8	1	no	—
544	D₄	—	8	1	no	—
545	D₄	—	8	2	no	—
546	D₄	—	8	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	—	4	4	no	—
566	C₂×C₄	—	8	1	no	—
567	C₂×C₄	—	8	1	no	—
568	C₂×C₄	—	8	1	no	—
569	C₂×C₄	—	8	1	no	—
570	C₂×C₄	—	8	2	no	—
571	C₂×C₄	—	8	2	no	—
572	C₂×C₄	—	8	1	no	—
573	C₂×C₄	—	8	1	no	—
574	C₂×C₄	—	8	2	no	—
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	C₂²×D₄	1	1	yes	characteristic
581	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
582	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
583	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
584	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
585	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
586	C₂×C₄	C₂⁵	1	1	yes	characteristic
587	C₈	—	2	2	no	—
588	C₈	—	2	2	no	—
589	C₈	—	2	2	no	—
590	C₈	—	2	2	no	—
591	C₂²	—	2	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	2	1	no	—
597	C₂²	—	2	1	no	—
598	C₂²	—	2	1	no	—
599	C₂²	—	4	2	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	4	1	no	—
611	C₂²	—	16	2	no	—
612	C₂²	—	16	2	no	—
613	C₂²	#575	1	2	yes	—
614	C₂²	C₂³×D₄	1	1	yes	characteristic
615	C₄	—	2	1	no	—
616	C₄	—	2	1	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	1	no	—
623	C₄	—	2	1	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	1	no	—
626	C₄	—	4	1	no	—
627	C₄	—	4	2	no	—
628	C₄	—	4	2	no	—
629	C₄	—	4	1	no	—
630	C₄	—	4	1	no	—
631	C₄	—	4	1	no	—
632	C₄	—	4	1	no	—
633	C₄	—	4	2	no	—
634	C₄	#585	1	2	yes	—
635	C₂	—	2	2	no	—
636	C₂	—	4	1	no	—
637	C₂	—	4	1	no	—
638	C₂	—	8	2	no	—
639	C₂	—	8	1	no	—
640	C₂	—	8	1	no	—
641	C₂	—	8	1	no	—
642	C₂	#3500	1	1	yes	characteristic
643	C₂	C₂×#575	1	1	yes	characteristic
644	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. #3514	C₂	semidirect
2. #3511	C₂	semidirect
3. #3376	C₂	semidirect
4. #3370	C₂	semidirect
5. #3321	C₂	semidirect
6. #3320	C₂	semidirect
7. #3319	C₂	semidirect
8. #3318	C₂	semidirect
9. #3301	C₂	semidirect
10. #3297	C₂	semidirect
11. #3240	C₂	semidirect
12. #3240	C₂	semidirect
13. #3239	C₂	semidirect
14. #3214	C₂	semidirect
15. #3213	C₂	semidirect
16. #3213	C₂	semidirect
17. #3180	C₂	semidirect
18. #3180	C₂	semidirect
19. #3171	C₂	semidirect
20. #3140	C₂	semidirect
21. #3135	C₂	semidirect
22. C₂×#489	C₂	semidirect
23. #2970	C₂	semidirect
28. #555	C₂²	semidirect
29. #554	C₂²	semidirect
31. #553	C₂²	semidirect
50. #533	C₂²	semidirect
51. #533	C₂²	semidirect
53. #532	C₂²	semidirect
54. #532	C₂²	semidirect
55. #532	C₂²	semidirect
56. C₂×C₄⋊Q₈	C₂²	semidirect
65. #501	C₂²	semidirect
66. #501	C₂²	semidirect
67. #501	C₂²	semidirect
69. #496	C₂²	semidirect
70. #496	C₂²	semidirect
71. #491	C₂²	semidirect
73. #490	C₂²	semidirect
78. #489	C₂²	semidirect
79. #489	C₂²	semidirect
80. #489	C₂²	semidirect
81. #489	C₂²	semidirect
82. #489	C₂²	semidirect
83. #489	C₂²	semidirect
84. #489	C₂²	semidirect
86. #488	C₂²	semidirect
87. #485	C₂²	semidirect
88. #485	C₂²	semidirect
89. #484	C₂²	semidirect
93. #479	C₂²	semidirect
94. #479	C₂²	semidirect
96. #478	C₂²	semidirect
97. #475	C₂²	semidirect
98. #474	C₂²	semidirect
100. #468	C₂²	semidirect
103. #465	C₂²	semidirect
104. #465	C₂²	semidirect
107. #463	C₂²	semidirect
108. #463	C₂²	semidirect
109. #461	C₂²	semidirect
111. #449	C₂²	semidirect
112. #449	C₂²	semidirect
113. #448	C₂²	semidirect
114. #448	C₂²	semidirect
117. #446	C₂²	semidirect
119. #442	C₂²	semidirect
120. #440	C₂²	semidirect
121. #440	C₂²	semidirect
122. C₄×SD₁₆	C₂²	semidirect
123. C₄×D₈	C₂²	semidirect
125. #435	C₂²	semidirect
126. C₈×D₄	C₂²	semidirect
127. #432	C₂²	semidirect
128. #432	C₂²	semidirect
129. #432	C₂²	semidirect
130. #419	C₂²	semidirect
132. #416	C₂²	semidirect
133. #416	C₂²	semidirect
134. C₂×#103	C₂²	semidirect
136. C₄×M₁₆	C₂²	semidirect
137. C₂×#97	C₂²	semidirect
138. C₂×#97	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3514	2
#3511	2
#3376	2
#3370	2
#3321	2
#3320	2
#3319	2
#3318	2
#3301	2
#3297	2
#3240	2
#3239	2
#3214	2
#3213	2
#3180	2
#3171	2
#3140	2
#3135	2
C₂×#489	2
#2970	2