Subgroups — #49568

Order 256.

979 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#563	C₂	1	1	yes	maximal, characteristic
2	C₂×#544	C₂	1	1	yes	maximal, characteristic, complemented
3	#2734	C₂	1	1	yes	maximal, characteristic, complemented
4	#2729	C₂	1	1	yes	maximal, characteristic, complemented
5	#2726	C₂	1	1	yes	maximal, characteristic, complemented
6	#2725	C₂	1	1	yes	maximal, characteristic, complemented
7	#2719	C₂	1	1	yes	maximal, characteristic, complemented
8	#2716	C₂	1	1	yes	maximal, characteristic, complemented
9	#2713	C₂	1	1	yes	maximal, characteristic, complemented
10	#2698	C₂	1	1	yes	maximal, characteristic, complemented
11	#2689	C₂	1	1	yes	maximal, characteristic, complemented
12	#2680	C₂	1	1	yes	maximal, characteristic
13	#2677	C₂	1	1	yes	maximal, characteristic, complemented
14	#2674	C₂	1	1	yes	maximal, characteristic
15	#2663	C₂	1	1	yes	maximal, characteristic
16	#2621	C₂	1	1	yes	maximal, characteristic, complemented
17	#2583	C₂	1	1	yes	maximal, characteristic, complemented
18	#2556	C₂	1	1	yes	maximal, characteristic, complemented
19	#2551	C₂	1	1	yes	maximal, characteristic, complemented
20	#2550	C₂	1	1	yes	maximal, characteristic, complemented
21	#2546	C₂	1	1	yes	maximal, characteristic, complemented
22	#2519	C₂	1	1	yes	maximal, characteristic, complemented
23	#2519	C₂	1	1	yes	maximal, characteristic, complemented
24	#2506	C₂	1	1	yes	maximal, characteristic, complemented
25	#2478	C₂	1	1	yes	maximal, characteristic, complemented
26	#2478	C₂	1	1	yes	maximal, characteristic, complemented
27	#2474	C₂	1	1	yes	maximal, characteristic
28	#2470	C₂	1	1	yes	maximal, characteristic
29	#2429	C₂	1	1	yes	maximal, characteristic, complemented
30	#2413	C₂	1	1	yes	maximal, characteristic
31	#2362	C₂	1	1	yes	maximal, characteristic, complemented
32	#563	—	2	8	no	—
33	#544	—	2	8	no	—
34	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic
42	C₂×#126	C₂²	1	1	yes	characteristic
43	C₂×#126	C₂²	1	1	yes	characteristic
44	C₂×#126	C₂²	1	1	yes	characteristic
45	C₂×#126	C₂²	1	1	yes	characteristic
46	C₂×#125	C₂²	1	1	yes	characteristic
47	C₂×#125	C₂²	1	1	yes	characteristic
48	C₂×#125	C₂²	1	1	yes	characteristic
49	C₂×#125	C₂²	1	1	yes	characteristic
50	C₂×#125	C₂²	1	1	yes	characteristic
51	C₂×#125	C₂²	1	1	yes	characteristic
52	C₂×#124	C₂²	1	1	yes	characteristic
53	C₂×#123	C₂²	1	1	yes	characteristic
54	C₂×#123	C₂²	1	1	yes	characteristic
55	C₂×#123	C₂²	1	1	yes	characteristic
56	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
57	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
58	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
59	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
60	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
61	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
62	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
63	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
64	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic
65	C₂×#117	C₂²	1	1	yes	characteristic
66	C₂×#117	C₂²	1	1	yes	characteristic
67	C₂×#117	C₂²	1	1	yes	characteristic
68	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic
69	#400	C₂²	1	1	yes	characteristic
70	#400	C₂²	1	1	yes	characteristic
71	#400	C₂²	1	1	yes	characteristic
72	#400	C₂²	1	1	yes	characteristic
73	#400	C₂²	1	1	yes	characteristic
74	#399	C₂²	1	1	yes	characteristic
75	#399	C₂²	1	1	yes	characteristic
76	#398	C₂²	1	1	yes	characteristic
77	#398	C₂²	1	1	yes	characteristic
78	#398	C₂²	1	1	yes	characteristic
79	#398	C₂²	1	1	yes	characteristic
80	#398	C₂²	1	1	yes	characteristic
81	#398	C₂²	1	1	yes	characteristic
82	#398	C₂²	1	1	yes	characteristic
83	#398	C₂²	1	1	yes	characteristic
84	#398	C₂²	1	1	yes	characteristic
85	#398	C₂²	1	1	yes	characteristic
86	#398	C₂²	1	1	yes	characteristic
87	#398	C₂²	1	1	yes	characteristic
88	#398	C₂²	1	1	yes	characteristic
89	#398	C₂²	1	1	yes	characteristic
90	#398	C₂²	1	1	yes	characteristic
91	#398	C₂²	1	1	yes	characteristic
92	#398	C₂²	1	1	yes	characteristic
93	#397	C₂²	1	1	yes	characteristic
94	#397	C₂²	1	1	yes	characteristic
95	#397	C₂²	1	1	yes	characteristic
96	#397	C₂²	1	1	yes	characteristic
97	#397	C₂²	1	1	yes	characteristic
98	#397	C₂²	1	1	yes	characteristic
99	#397	C₂²	1	1	yes	characteristic
100	#396	C₂²	1	1	yes	characteristic
101	#396	C₂²	1	1	yes	characteristic
102	#396	C₂²	1	1	yes	characteristic
103	#396	C₂²	1	1	yes	characteristic
104	#396	C₂²	1	1	yes	characteristic
105	#395	C₂²	1	1	yes	characteristic
106	#395	C₂²	1	1	yes	characteristic
107	#395	C₂²	1	1	yes	characteristic
108	#395	C₂²	1	1	yes	characteristic
109	#395	C₂²	1	1	yes	characteristic
110	#395	C₂²	1	1	yes	characteristic
111	#395	C₂²	1	1	yes	characteristic
112	#395	C₂²	1	1	yes	characteristic
113	#394	C₂²	1	1	yes	characteristic
114	#394	C₂²	1	1	yes	characteristic
115	#393	C₂²	1	1	yes	characteristic
116	#393	C₂²	1	1	yes	characteristic
117	#391	C₂²	1	1	yes	characteristic
118	#391	C₂²	1	1	yes	characteristic
119	#391	C₂²	1	1	yes	characteristic
120	#391	C₂²	1	1	yes	characteristic
121	#391	C₂²	1	1	yes	characteristic
122	#391	C₂²	1	1	yes	characteristic
123	#389	C₂²	1	1	yes	characteristic
124	#389	C₂²	1	1	yes	characteristic
125	#389	C₂²	1	1	yes	characteristic
126	#389	C₂²	1	1	yes	characteristic
127	#389	C₂²	1	1	yes	characteristic
128	#389	C₂²	1	1	yes	characteristic
129	#389	C₂²	1	1	yes	characteristic
130	#389	C₂²	1	1	yes	characteristic
131	#389	C₂²	1	1	yes	characteristic
132	#389	C₂²	1	1	yes	characteristic
133	#389	C₂²	1	1	yes	characteristic
134	#389	C₂²	1	1	yes	characteristic
135	#389	C₂²	1	1	yes	characteristic
136	#389	C₂²	1	1	yes	characteristic
137	#389	C₂²	1	1	yes	characteristic
138	#389	C₂²	1	1	yes	characteristic
139	#389	C₂²	1	1	yes	characteristic
140	#389	C₂²	1	1	yes	characteristic
141	#389	C₂²	1	1	yes	characteristic
142	#388	C₂²	1	1	yes	characteristic
143	#388	C₂²	1	1	yes	characteristic
144	#388	C₂²	1	1	yes	characteristic
145	#388	C₂²	1	1	yes	characteristic
146	#388	C₂²	1	1	yes	characteristic
147	#388	C₂²	1	1	yes	characteristic
148	#388	C₂²	1	1	yes	characteristic
149	#388	C₂²	1	1	yes	characteristic
150	#388	C₂²	1	1	yes	characteristic
151	#388	C₂²	1	1	yes	characteristic
152	#388	C₂²	1	1	yes	characteristic
153	#388	C₂²	1	1	yes	characteristic
154	#388	C₂²	1	1	yes	characteristic
155	#388	C₂²	1	1	yes	characteristic
156	#387	C₂²	1	1	yes	characteristic
157	#387	C₂²	1	1	yes	characteristic
158	#387	C₂²	1	1	yes	characteristic
159	#387	C₂²	1	1	yes	characteristic
160	#387	C₂²	1	1	yes	characteristic
161	#387	C₂²	1	1	yes	characteristic
162	#387	C₂²	1	1	yes	characteristic
163	#387	C₂²	1	1	yes	characteristic
164	#387	C₂²	1	1	yes	characteristic
165	#387	C₂²	1	1	yes	characteristic
166	#387	C₂²	1	1	yes	characteristic
167	#387	C₂²	1	1	yes	characteristic
168	#387	C₂²	1	1	yes	characteristic
169	#386	C₂²	1	1	yes	characteristic
170	#385	C₂²	1	1	yes	characteristic
171	#385	C₂²	1	1	yes	characteristic
172	#385	C₂²	1	1	yes	characteristic
173	#385	C₂²	1	1	yes	characteristic
174	#385	C₂²	1	1	yes	characteristic
175	#385	C₂²	1	1	yes	characteristic
176	#385	C₂²	1	1	yes	characteristic
177	#384	C₂²	1	1	yes	characteristic
178	#382	C₂²	1	1	yes	characteristic
179	#382	C₂²	1	1	yes	characteristic
180	#381	C₂²	1	1	yes	characteristic
181	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
182	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
183	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
184	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
185	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
186	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
187	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
188	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
189	C₂²×Q₈	C₂³	1	1	yes	characteristic
190	C₂²×Q₈	C₂³	1	1	yes	characteristic
191	C₂²×Q₈	C₂³	1	1	yes	characteristic
192	C₂²×Q₈	C₂³	1	1	yes	characteristic
193	C₂²×Q₈	C₂³	1	1	yes	characteristic
194	C₂²×Q₈	C₂³	1	1	yes	characteristic
195	C₂²×D₄	C₂³	1	1	yes	characteristic
196	C₂³×C₄	C₂³	1	1	yes	characteristic
197	C₂³×C₄	C₂³	1	1	yes	characteristic
198	C₂³×C₄	C₂³	1	1	yes	characteristic
199	C₂³×C₄	C₂³	1	1	yes	characteristic
200	C₄⋊Q₈	—	2	4	no	—
201	C₄⋊Q₈	—	2	4	no	—
202	C₄⋊Q₈	—	2	4	no	—
203	C₄⋊Q₈	—	2	4	no	—
204	C₄⋊Q₈	—	2	4	no	—
205	C₄⋊Q₈	—	2	4	no	—
206	C₄⋊Q₈	—	4	2	no	—
207	C₄⋊Q₈	—	4	2	no	—
208	#126	—	2	4	no	—
209	#126	—	2	4	no	—
210	#126	—	2	4	no	—
211	#126	—	2	4	no	—
212	#125	—	2	4	no	—
213	#125	—	2	4	no	—
214	#125	—	2	4	no	—
215	#125	—	2	4	no	—
216	#125	—	2	4	no	—
217	#125	—	2	4	no	—
218	#124	—	2	4	no	—
219	#123	—	2	4	no	—
220	#123	—	2	4	no	—
221	#123	—	4	2	no	—
222	C₂²⋊Q₈	—	2	4	no	—
223	C₂²⋊Q₈	—	2	4	no	—
224	C₂²⋊Q₈	—	2	4	no	—
225	C₂²⋊Q₈	—	2	4	no	—
226	C₂²⋊Q₈	—	2	4	no	—
227	C₂²⋊Q₈	—	2	4	no	—
228	C₂²⋊Q₈	—	4	2	no	—
229	C₂²⋊Q₈	D₄	1	8	yes	—
230	C₄×Q₈	—	4	2	no	—
231	#117	—	2	4	no	—
232	#117	—	2	4	no	—
233	#117	—	4	2	no	—
234	C₂×C₄⋊C₄	—	2	4	no	—
235	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
241	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
242	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
243	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
245	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
249	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
267	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
275	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
276	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
283	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
294	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
295	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
296	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
297	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
298	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
299	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
300	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
301	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
302	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
303	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
305	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
306	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
307	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
308	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
310	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
311	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
312	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
313	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
314	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
315	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
316	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
317	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
318	C₂×C₄²	C₂³	1	1	yes	characteristic
319	C₂×C₄²	C₂³	1	1	yes	characteristic
320	C₂×C₄²	C₂³	1	1	yes	characteristic
321	C₂×C₄²	C₂³	1	1	yes	characteristic
322	C₂×C₄²	C₂³	1	1	yes	characteristic
323	C₂×C₄²	C₂³	1	1	yes	characteristic
324	C₂×C₄²	C₂³	1	1	yes	characteristic
325	C₂×C₄²	C₂³	1	1	yes	characteristic
326	C₂×C₄²	C₂³	1	1	yes	characteristic
327	C₂×C₄²	C₂³	1	1	yes	characteristic
328	C₂×C₄²	C₂³	1	1	yes	characteristic
329	C₂×C₄²	C₂³	1	1	yes	characteristic
330	C₂×C₄²	C₂³	1	1	yes	characteristic
331	C₂×C₄²	C₂³	1	1	yes	characteristic
332	C₂×C₄²	C₂³	1	1	yes	characteristic
333	#95	C₂³	1	1	yes	characteristic
334	#95	C₂³	1	1	yes	characteristic
335	#95	C₂³	1	1	yes	characteristic
336	#95	C₂³	1	1	yes	characteristic
337	#95	C₂³	1	1	yes	characteristic
338	#95	C₂³	1	1	yes	characteristic
339	#95	C₂³	1	1	yes	characteristic
340	#95	C₂³	1	1	yes	characteristic
341	#95	C₂³	1	1	yes	characteristic
342	#95	C₂³	1	1	yes	characteristic
343	#95	C₂³	1	1	yes	characteristic
344	#95	C₂³	1	1	yes	characteristic
345	#95	C₂³	1	1	yes	characteristic
346	#95	C₂³	1	1	yes	characteristic
347	#95	C₂³	1	1	yes	characteristic
348	#95	C₂³	1	1	yes	characteristic
349	#95	C₂³	1	1	yes	characteristic
350	#95	C₂³	1	1	yes	characteristic
351	#95	C₂³	1	1	yes	characteristic
352	#95	C₂³	1	1	yes	characteristic
353	#95	C₂³	1	1	yes	characteristic
354	#95	C₂³	1	1	yes	characteristic
355	#95	C₂³	1	1	yes	characteristic
356	#95	C₂³	1	1	yes	characteristic
357	#95	C₂³	1	1	yes	characteristic
358	#95	C₂³	1	1	yes	characteristic
359	#95	C₂³	1	1	yes	characteristic
360	#95	C₂³	1	1	yes	characteristic
361	#95	C₂³	1	1	yes	characteristic
362	#95	C₂³	1	1	yes	characteristic
363	#95	C₂³	1	1	yes	characteristic
364	#95	C₂³	1	1	yes	characteristic
365	#95	C₂³	1	1	yes	characteristic
366	#95	C₂³	1	1	yes	characteristic
367	#95	C₂³	1	1	yes	characteristic
368	#95	C₂³	1	1	yes	characteristic
369	#95	C₂³	1	1	yes	characteristic
370	#95	C₂³	1	1	yes	characteristic
371	#95	C₂³	1	1	yes	characteristic
372	#95	C₂³	1	1	yes	characteristic
373	#95	C₂³	1	1	yes	characteristic
374	#95	C₂³	1	1	yes	characteristic
375	#95	C₂³	1	1	yes	characteristic
376	#95	C₂³	1	1	yes	characteristic
377	#95	C₂³	1	1	yes	characteristic
378	#95	C₂³	1	1	yes	characteristic
379	C₂⁴	C₂⁴	1	1	yes	characteristic
380	C₂⁴	C₂⁴	1	1	yes	characteristic
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	—	2	2	no	—
383	C₂×Q₈	—	2	2	no	—
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	—	4	1	no	—
387	C₂×Q₈	—	4	1	no	—
388	C₂×Q₈	—	4	1	no	—
389	C₂×Q₈	—	4	1	no	—
390	C₂×Q₈	—	4	1	no	—
391	C₂×Q₈	—	4	1	no	—
392	C₂×Q₈	—	4	1	no	—
393	C₂×Q₈	—	4	1	no	—
394	C₂×Q₈	—	4	1	no	—
395	C₂×Q₈	—	4	1	no	—
396	C₂×Q₈	—	4	1	no	—
397	C₂×Q₈	—	4	1	no	—
398	C₂×Q₈	C₂×D₄	1	4	yes	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	4	1	no	—
401	C₂×D₄	—	4	1	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	4	1	no	—
408	C₂²×C₄	—	4	1	no	—
409	C₂²×C₄	—	4	1	no	—
410	C₂²×C₄	—	4	1	no	—
411	C₂²×C₄	—	4	1	no	—
412	C₂²×C₄	—	4	1	no	—
413	C₂²×C₄	C₂×D₄	1	4	yes	—
414	C₂²×C₄	C₂⁴	1	1	yes	characteristic
415	C₂²×C₄	C₂⁴	1	1	yes	characteristic
416	C₂²×C₄	C₂⁴	1	1	yes	characteristic
417	C₂²×C₄	C₂⁴	1	1	yes	characteristic
418	C₂²×C₄	C₂⁴	1	1	yes	characteristic
419	C₂²×C₄	C₂⁴	1	1	yes	characteristic
420	C₂²×C₄	C₂⁴	1	1	yes	characteristic
421	C₂²×C₄	C₂⁴	1	1	yes	characteristic
422	C₂²×C₄	C₂⁴	1	1	yes	characteristic
423	C₂²×C₄	C₂⁴	1	1	yes	characteristic
424	C₂²×C₄	C₂⁴	1	1	yes	characteristic
425	C₂²×C₄	C₂⁴	1	1	yes	characteristic
426	C₂²×C₄	C₂⁴	1	1	yes	characteristic
427	C₂²×C₄	C₂⁴	1	1	yes	characteristic
428	C₂²×C₄	C₂⁴	1	1	yes	characteristic
429	C₂²×C₄	C₂⁴	1	1	yes	characteristic
430	C₂²×C₄	C₂⁴	1	1	yes	characteristic
431	C₂²×C₄	C₂⁴	1	1	yes	characteristic
432	C₂²×C₄	C₂⁴	1	1	yes	characteristic
433	C₂²×C₄	C₂⁴	1	1	yes	characteristic
434	C₂²×C₄	C₂⁴	1	1	yes	characteristic
435	C₂²×C₄	C₂⁴	1	1	yes	characteristic
436	C₂²×C₄	C₂⁴	1	1	yes	characteristic
437	C₂²×C₄	C₂⁴	1	1	yes	characteristic
438	C₂²×C₄	C₂⁴	1	1	yes	characteristic
439	C₂²×C₄	C₂⁴	1	1	yes	characteristic
440	C₂²×C₄	C₂⁴	1	1	yes	characteristic
441	C₂²×C₄	C₂⁴	1	1	yes	characteristic
442	C₂²×C₄	C₂⁴	1	1	yes	characteristic
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	—	2	2	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	4	1	no	—
489	C₄⋊C₄	—	4	1	no	—
490	C₄⋊C₄	—	4	1	no	—
491	C₄⋊C₄	—	4	1	no	—
492	C₄⋊C₄	—	4	1	no	—
493	C₄⋊C₄	—	4	1	no	—
494	C₄⋊C₄	—	4	1	no	—
495	C₄⋊C₄	—	4	1	no	—
496	C₄⋊C₄	—	4	1	no	—
497	C₄⋊C₄	—	4	1	no	—
498	C₄⋊C₄	—	4	1	no	—
499	C₄⋊C₄	C₂×D₄	1	4	yes	—
500	C₄⋊C₄	C₂×D₄	1	4	yes	—
501	C₄⋊C₄	C₂×D₄	1	4	yes	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	2	2	no	—
512	C₂²⋊C₄	—	2	2	no	—
513	C₂²⋊C₄	—	2	2	no	—
514	C₂²⋊C₄	—	2	2	no	—
515	C₂²⋊C₄	—	2	2	no	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₂²⋊C₄	—	4	1	no	—
521	C₂²⋊C₄	—	4	1	no	—
522	C₂²⋊C₄	—	4	1	no	—
523	C₂²⋊C₄	—	4	1	no	—
524	C₂²⋊C₄	C₂×D₄	1	4	yes	—
525	C₂²⋊C₄	C₂×D₄	1	4	yes	—
526	C₄²	—	2	2	no	—
527	C₄²	—	2	2	no	—
528	C₄²	—	2	2	no	—
529	C₄²	—	2	2	no	—
530	C₄²	—	2	2	no	—
531	C₄²	—	2	2	no	—
532	C₄²	—	2	2	no	—
533	C₄²	—	2	2	no	—
534	C₄²	—	2	2	no	—
535	C₄²	—	2	2	no	—
536	C₄²	—	2	2	no	—
537	C₄²	—	4	1	no	—
538	C₄²	—	4	1	no	—
539	C₄²	—	4	1	no	—
540	C₄²	—	4	1	no	—
541	C₂³	—	2	1	no	—
542	C₂³	—	2	1	no	—
543	C₂³	—	2	1	no	—
544	C₂³	—	2	1	no	—
545	C₂³	—	2	1	no	—
546	C₂³	—	2	1	no	—
547	C₂³	—	2	1	no	—
548	C₂³	—	2	1	no	—
549	C₂³	—	2	1	no	—
550	C₂³	—	2	1	no	—
551	C₂³	—	2	1	no	—
552	C₂³	—	2	1	no	—
553	C₂³	—	2	1	no	—
554	C₂³	C₂²×D₄	1	2	yes	—
555	C₂³	C₂⁵	1	1	yes	characteristic
556	Q₈	—	4	4	no	—
557	Q₈	—	8	2	no	—
558	Q₈	—	8	2	no	—
559	Q₈	—	8	2	no	—
560	Q₈	—	8	2	no	—
561	Q₈	—	8	2	no	—
562	D₄	—	8	2	no	—
563	C₂×C₄	—	2	8	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	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	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	4	4	no	—
641	C₂×C₄	—	8	2	no	—
642	C₂×C₄	—	8	2	no	—
643	C₂×C₄	C₂²×D₄	1	2	yes	—
644	C₂×C₄	C₂²×D₄	1	2	yes	—
645	C₂×C₄	C₂²×D₄	1	2	yes	—
646	C₂×C₄	C₂²×D₄	1	2	yes	—
647	C₂×C₄	C₂²×D₄	1	2	yes	—
648	C₂×C₄	C₂²×D₄	1	2	yes	—
649	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
650	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
651	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
652	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
653	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
654	C₂²	—	2	2	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	4	1	no	—
658	C₂²	—	4	1	no	—
659	C₂²	—	4	1	no	—
660	C₂²	—	4	1	no	—
661	C₂²	—	4	1	no	—
662	C₂²	—	4	1	no	—
663	C₂²	—	4	1	no	—
664	C₂²	—	4	1	no	—
665	C₂²	—	4	1	no	—
666	C₂²	—	4	1	no	—
667	C₂²	—	4	1	no	—
668	C₂²	C₂³×D₄	1	1	yes	characteristic
669	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
670	C₂²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
671	C₂²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
672	C₂²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
673	C₂²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
674	C₂²	#585	1	1	yes	characteristic
675	C₄	—	2	2	no	—
676	C₄	—	2	2	no	—
677	C₄	—	2	2	no	—
678	C₄	—	2	2	no	—
679	C₄	—	2	2	no	—
680	C₄	—	2	2	no	—
681	C₄	—	2	2	no	—
682	C₄	—	2	2	no	—
683	C₄	—	2	2	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	2	no	—
686	C₄	—	4	1	no	—
687	C₄	—	4	1	no	—
688	C₄	—	4	1	no	—
689	C₄	—	4	1	no	—
690	C₄	—	4	1	no	—
691	C₄	—	4	1	no	—
692	C₄	—	4	1	no	—
693	C₄	—	4	1	no	—
694	C₄	—	4	1	no	—
695	C₄	—	4	1	no	—
696	C₄	—	4	1	no	—
697	C₄	—	4	1	no	—
698	C₄	—	4	1	no	—
699	C₄	—	4	1	no	—
700	C₄	—	4	1	no	—
701	C₄	—	4	1	no	—
702	C₄	—	4	1	no	—
703	C₄	—	4	1	no	—
704	C₂	—	4	2	no	—
705	C₂	—	8	1	no	—
706	C₂	#3486	1	1	yes	characteristic
707	C₂	#3496	1	1	yes	characteristic
708	C₂	#3499	1	1	yes	characteristic
709	C₂	#3544	1	1	yes	characteristic
710	C₂	#3552	1	1	yes	characteristic
711	C₂	#3555	1	1	yes	characteristic
712	C₂	#3563	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂³	C₂⁵
prime radical	C₂²×D₄	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ G
LECS	G ▷ C₂³ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. C₂×#544	C₂	semidirect
3. #2734	C₂	semidirect
4. #2729	C₂	semidirect
5. #2726	C₂	semidirect
6. #2725	C₂	semidirect
7. #2719	C₂	semidirect
8. #2716	C₂	semidirect
9. #2713	C₂	semidirect
10. #2698	C₂	semidirect
11. #2689	C₂	semidirect
13. #2677	C₂	semidirect
16. #2621	C₂	semidirect
17. #2583	C₂	semidirect
18. #2556	C₂	semidirect
19. #2551	C₂	semidirect
20. #2550	C₂	semidirect
21. #2546	C₂	semidirect
22. #2519	C₂	semidirect
23. #2519	C₂	semidirect
24. #2506	C₂	semidirect
25. #2478	C₂	semidirect
26. #2478	C₂	semidirect
29. #2429	C₂	semidirect
31. #2362	C₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×#563	2
C₂×#544	2
#2734	2
#2729	2
#2726	2
#2725	2
#2719	2
#2716	2
#2713	2
#2698	2
#2689	2
#2680	2
#2677	2
#2674	2
#2663	2
#2621	2
#2583	2
#2556	2
#2551	2
#2550	2
#2546	2
#2519	2
#2506	2
#2478	2
#2474	2
#2470	2
#2429	2
#2413	2
#2362	2