Subgroups — #52237

Order 256.

856 conjugacy classes of subgroups.

The subgroup lattice has 681 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2792	C₂	1	1	yes	maximal, characteristic, complemented
2	#2791	C₂	1	1	yes	maximal, characteristic, complemented
3	#2790	C₂	1	1	yes	maximal, characteristic, complemented
4	#2788	C₂	1	1	yes	maximal, characteristic, complemented
5	#2784	C₂	1	1	yes	maximal, characteristic
6	#2780	C₂	1	1	yes	maximal, characteristic
7	#2774	C₂	1	1	yes	maximal, characteristic, complemented
8	#2768	C₂	1	1	yes	maximal, characteristic, complemented
9	#2768	C₂	1	1	yes	maximal, characteristic, complemented
10	#2763	C₂	1	1	yes	maximal, characteristic, complemented
11	#2755	C₂	1	1	yes	maximal, characteristic, complemented
12	#2748	C₂	1	1	yes	maximal, characteristic
13	#2742	C₂	1	1	yes	maximal, characteristic, complemented
14	#2720	C₂	1	1	yes	maximal, characteristic, complemented
15	#2704	C₂	1	1	yes	maximal, characteristic, complemented
16	#2692	C₂	1	1	yes	maximal, characteristic
17	#2402	C₂	1	1	yes	maximal, characteristic, complemented
18	#2399	C₂	1	1	yes	maximal, characteristic, complemented
19	#2396	C₂	1	1	yes	maximal, characteristic, complemented
20	#2396	C₂	1	1	yes	maximal, characteristic, complemented
21	#2396	C₂	1	1	yes	maximal, characteristic, complemented
22	#2396	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#125	C₂	1	1	yes	maximal, characteristic, complemented
24	C₄×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
25	C₄×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
26	#2296	C₂	1	1	yes	maximal, characteristic, complemented
27	#2295	C₂	1	1	yes	maximal, characteristic, complemented
28	#2293	C₂	1	1	yes	maximal, characteristic
29	#2290	C₂	1	1	yes	maximal, characteristic
30	#2290	C₂	1	1	yes	maximal, characteristic
31	#2285	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#125	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊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×D₄	C₂²	1	1	yes	characteristic
39	C₂×#117	C₂²	1	1	yes	characteristic
40	C₂×#117	C₂²	1	1	yes	characteristic
41	C₂×#117	C₂²	1	1	yes	characteristic
42	C₂×#117	C₂²	1	1	yes	characteristic
43	C₂²×C₄²	C₂²	1	1	yes	characteristic
44	C₂²×C₄²	C₂²	1	1	yes	characteristic
45	#400	C₂²	1	1	yes	characteristic
46	#400	C₂²	1	1	yes	characteristic
47	#400	C₂²	1	1	yes	characteristic
48	#400	C₂²	1	1	yes	characteristic
49	#400	C₂²	1	1	yes	characteristic
50	#400	C₂²	1	1	yes	characteristic
51	#400	C₂²	1	1	yes	characteristic
52	#400	C₂²	1	1	yes	characteristic
53	#399	C₂²	1	1	yes	characteristic
54	#399	C₂²	1	1	yes	characteristic
55	#399	C₂²	1	1	yes	characteristic
56	#399	C₂²	1	1	yes	characteristic
57	#398	C₂²	1	1	yes	characteristic
58	#398	C₂²	1	1	yes	characteristic
59	#398	C₂²	1	1	yes	characteristic
60	#398	C₂²	1	1	yes	characteristic
61	#398	C₂²	1	1	yes	characteristic
62	#398	C₂²	1	1	yes	characteristic
63	#398	C₂²	1	1	yes	characteristic
64	#398	C₂²	1	1	yes	characteristic
65	#398	C₂²	1	1	yes	characteristic
66	#398	C₂²	1	1	yes	characteristic
67	#398	C₂²	1	1	yes	characteristic
68	#398	C₂²	1	1	yes	characteristic
69	#398	C₂²	1	1	yes	characteristic
70	#398	C₂²	1	1	yes	characteristic
71	#398	C₂²	1	1	yes	characteristic
72	#398	C₂²	1	1	yes	characteristic
73	#396	C₂²	1	1	yes	characteristic
74	#396	C₂²	1	1	yes	characteristic
75	#396	C₂²	1	1	yes	characteristic
76	#396	C₂²	1	1	yes	characteristic
77	#396	C₂²	1	1	yes	characteristic
78	#396	C₂²	1	1	yes	characteristic
79	#396	C₂²	1	1	yes	characteristic
80	#396	C₂²	1	1	yes	characteristic
81	#395	C₂²	1	1	yes	characteristic
82	#395	C₂²	1	1	yes	characteristic
83	#395	C₂²	1	1	yes	characteristic
84	#395	C₂²	1	1	yes	characteristic
85	#395	C₂²	1	1	yes	characteristic
86	#395	C₂²	1	1	yes	characteristic
87	#395	C₂²	1	1	yes	characteristic
88	#395	C₂²	1	1	yes	characteristic
89	#393	C₂²	1	1	yes	characteristic
90	#393	C₂²	1	1	yes	characteristic
91	#393	C₂²	1	1	yes	characteristic
92	#393	C₂²	1	1	yes	characteristic
93	#391	C₂²	1	1	yes	characteristic
94	#391	C₂²	1	1	yes	characteristic
95	#391	C₂²	1	1	yes	characteristic
96	#391	C₂²	1	1	yes	characteristic
97	#390	C₂²	1	1	yes	characteristic
98	#390	C₂²	1	1	yes	characteristic
99	#389	C₂²	1	1	yes	characteristic
100	#389	C₂²	1	1	yes	characteristic
101	#389	C₂²	1	1	yes	characteristic
102	#389	C₂²	1	1	yes	characteristic
103	#389	C₂²	1	1	yes	characteristic
104	#389	C₂²	1	1	yes	characteristic
105	#389	C₂²	1	1	yes	characteristic
106	#389	C₂²	1	1	yes	characteristic
107	#389	C₂²	1	1	yes	characteristic
108	#389	C₂²	1	1	yes	characteristic
109	#389	C₂²	1	1	yes	characteristic
110	#389	C₂²	1	1	yes	characteristic
111	#388	C₂²	1	1	yes	characteristic
112	#388	C₂²	1	1	yes	characteristic
113	#388	C₂²	1	1	yes	characteristic
114	#388	C₂²	1	1	yes	characteristic
115	#388	C₂²	1	1	yes	characteristic
116	#388	C₂²	1	1	yes	characteristic
117	#388	C₂²	1	1	yes	characteristic
118	#388	C₂²	1	1	yes	characteristic
119	#387	C₂²	1	1	yes	characteristic
120	#387	C₂²	1	1	yes	characteristic
121	#387	C₂²	1	1	yes	characteristic
122	#387	C₂²	1	1	yes	characteristic
123	#387	C₂²	1	1	yes	characteristic
124	#387	C₂²	1	1	yes	characteristic
125	#387	C₂²	1	1	yes	characteristic
126	#387	C₂²	1	1	yes	characteristic
127	#387	C₂²	1	1	yes	characteristic
128	#387	C₂²	1	1	yes	characteristic
129	#387	C₂²	1	1	yes	characteristic
130	#387	C₂²	1	1	yes	characteristic
131	#387	C₂²	1	1	yes	characteristic
132	#387	C₂²	1	1	yes	characteristic
133	#387	C₂²	1	1	yes	characteristic
134	#387	C₂²	1	1	yes	characteristic
135	#386	C₂²	1	1	yes	characteristic
136	#386	C₂²	1	1	yes	characteristic
137	#386	C₂²	1	1	yes	characteristic
138	#386	C₂²	1	1	yes	characteristic
139	#385	C₂²	1	1	yes	characteristic
140	#385	C₂²	1	1	yes	characteristic
141	#385	C₂²	1	1	yes	characteristic
142	#385	C₂²	1	1	yes	characteristic
143	#385	C₂²	1	1	yes	characteristic
144	#385	C₂²	1	1	yes	characteristic
145	#385	C₂²	1	1	yes	characteristic
146	#385	C₂²	1	1	yes	characteristic
147	#385	C₂²	1	1	yes	characteristic
148	#385	C₂²	1	1	yes	characteristic
149	#385	C₂²	1	1	yes	characteristic
150	#385	C₂²	1	1	yes	characteristic
151	#384	C₂²	1	1	yes	characteristic
152	#384	C₂²	1	1	yes	characteristic
153	#382	C₂²	1	1	yes	characteristic
154	#382	C₂²	1	1	yes	characteristic
155	#382	C₂²	1	1	yes	characteristic
156	#380	C₂²	1	1	yes	characteristic
157	#380	C₂²	1	1	yes	characteristic
158	#380	C₂²	1	1	yes	characteristic
159	#380	C₂²	1	1	yes	characteristic
160	#380	C₂²	1	1	yes	characteristic
161	#380	C₂²	1	1	yes	characteristic
162	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
163	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
164	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
165	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
166	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
167	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
168	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
169	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
170	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
171	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
172	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
173	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
174	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
175	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
176	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
177	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
178	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
179	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
180	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
181	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
182	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
183	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
184	#376	C₂²	1	1	yes	characteristic
185	#376	C₂²	1	1	yes	characteristic
186	C₄³	C₂²	1	1	yes	characteristic
187	C₂²×Q₈	C₂³	1	1	yes	characteristic
188	C₂²×Q₈	C₂³	1	1	yes	characteristic
189	C₂²×Q₈	C₂³	1	1	yes	characteristic
190	C₂²×D₄	C₂³	1	1	yes	characteristic
191	C₂³×C₄	C₂³	1	1	yes	characteristic
192	C₂³×C₄	C₂³	1	1	yes	characteristic
193	C₂³×C₄	C₂³	1	1	yes	characteristic
194	C₂³×C₄	C₂³	1	1	yes	characteristic
195	C₂³×C₄	C₂³	1	1	yes	characteristic
196	C₂³×C₄	C₂³	1	1	yes	characteristic
197	#125	—	2	4	no	—
198	C₂²⋊Q₈	—	2	4	no	—
199	C₂²⋊Q₈	—	2	4	no	—
200	C₄×Q₈	—	2	4	no	—
201	C₄×Q₈	—	4	2	no	—
202	C₄×Q₈	—	4	2	no	—
203	C₄×D₄	Q₈	1	8	yes	complemented
204	#117	—	2	4	no	—
205	#117	—	4	2	no	—
206	#117	—	4	2	no	—
207	#117	—	4	2	no	—
208	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
209	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
210	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
211	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
212	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
213	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
214	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
215	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
216	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
218	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
219	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
260	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
261	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
265	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
267	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
268	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
270	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
271	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
272	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
273	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
274	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
275	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
277	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
278	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
279	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
280	C₂×C₄²	—	2	4	no	—
281	C₂×C₄²	—	4	2	no	—
282	C₂×C₄²	C₂³	1	1	yes	characteristic
283	C₂×C₄²	C₂³	1	1	yes	characteristic
284	C₂×C₄²	C₂³	1	1	yes	characteristic
285	C₂×C₄²	C₂³	1	1	yes	characteristic
286	C₂×C₄²	C₂³	1	1	yes	characteristic
287	C₂×C₄²	C₂³	1	1	yes	characteristic
288	C₂×C₄²	C₂³	1	1	yes	characteristic
289	C₂×C₄²	C₂³	1	1	yes	characteristic
290	C₂×C₄²	C₂³	1	1	yes	characteristic
291	C₂×C₄²	C₂³	1	1	yes	characteristic
292	C₂×C₄²	C₂³	1	1	yes	characteristic
293	C₂×C₄²	C₂³	1	1	yes	characteristic
294	C₂×C₄²	C₂³	1	1	yes	characteristic
295	C₂×C₄²	C₂³	1	1	yes	characteristic
296	C₂×C₄²	C₂³	1	1	yes	characteristic
297	C₂×C₄²	C₂³	1	1	yes	characteristic
298	C₂×C₄²	C₂³	1	1	yes	characteristic
299	C₂×C₄²	C₂³	1	1	yes	characteristic
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	#95	C₂³	1	1	yes	characteristic
304	#95	C₂³	1	1	yes	characteristic
305	#95	C₂³	1	1	yes	characteristic
306	#95	C₂³	1	1	yes	characteristic
307	#95	C₂³	1	1	yes	characteristic
308	#95	C₂³	1	1	yes	characteristic
309	#95	C₂³	1	1	yes	characteristic
310	#95	C₂³	1	1	yes	characteristic
311	#95	C₂³	1	1	yes	characteristic
312	#95	C₂³	1	1	yes	characteristic
313	#95	C₂³	1	1	yes	characteristic
314	#95	C₂³	1	1	yes	characteristic
315	#95	C₂³	1	1	yes	characteristic
316	#95	C₂³	1	1	yes	characteristic
317	#95	C₂³	1	1	yes	characteristic
318	#95	C₂³	1	1	yes	characteristic
319	#95	C₂³	1	1	yes	characteristic
320	#95	C₂³	1	1	yes	characteristic
321	#95	C₂³	1	1	yes	characteristic
322	#95	C₂³	1	1	yes	characteristic
323	#95	C₂³	1	1	yes	characteristic
324	#95	C₂³	1	1	yes	characteristic
325	#95	C₂³	1	1	yes	characteristic
326	#95	C₂³	1	1	yes	characteristic
327	#95	C₂³	1	1	yes	characteristic
328	#95	C₂³	1	1	yes	characteristic
329	#95	C₂³	1	1	yes	characteristic
330	#95	C₂³	1	1	yes	characteristic
331	#95	C₂³	1	1	yes	characteristic
332	#95	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	C₂⁴	C₂⁴	1	1	yes	characteristic
356	C₂⁴	C₂⁴	1	1	yes	characteristic
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	4	1	no	—
361	C₂×Q₈	—	4	1	no	—
362	C₂×Q₈	—	4	1	no	—
363	C₂×Q₈	—	4	1	no	—
364	C₂×Q₈	—	4	1	no	—
365	C₂×Q₈	—	4	1	no	—
366	C₂×D₄	—	4	1	no	—
367	C₂×D₄	—	4	1	no	—
368	C₂×D₄	C₂×Q₈	1	4	yes	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	4	1	no	—
378	C₂²×C₄	—	4	1	no	—
379	C₂²×C₄	—	4	1	no	—
380	C₂²×C₄	—	4	1	no	—
381	C₂²×C₄	—	4	1	no	—
382	C₂²×C₄	—	4	1	no	—
383	C₂²×C₄	—	4	1	no	—
384	C₂²×C₄	—	4	1	no	—
385	C₂²×C₄	C₂×Q₈	1	4	yes	—
386	C₂²×C₄	C₂×Q₈	1	4	yes	—
387	C₂²×C₄	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄	C₂⁴	1	1	yes	characteristic
389	C₂²×C₄	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄	C₂⁴	1	1	yes	characteristic
391	C₂²×C₄	C₂⁴	1	1	yes	characteristic
392	C₂²×C₄	C₂⁴	1	1	yes	characteristic
393	C₂²×C₄	C₂⁴	1	1	yes	characteristic
394	C₂²×C₄	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄	C₂⁴	1	1	yes	characteristic
397	C₂²×C₄	C₂⁴	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	C₂²×C₄	C₂⁴	1	1	yes	characteristic
402	C₂²×C₄	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄	C₂⁴	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	C₂²×C₄	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄	C₂⁴	1	1	yes	characteristic
409	C₂²×C₄	C₂⁴	1	1	yes	characteristic
410	C₂²×C₄	C₂⁴	1	1	yes	characteristic
411	C₂²×C₄	C₂⁴	1	1	yes	characteristic
412	C₂²×C₄	C₂⁴	1	1	yes	characteristic
413	C₂²×C₄	C₂⁴	1	1	yes	characteristic
414	C₂²×C₄	C₂⁴	1	1	yes	characteristic
415	C₂²×C₄	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	4	1	no	—
431	C₄⋊C₄	—	4	1	no	—
432	C₄⋊C₄	—	4	1	no	—
433	C₄⋊C₄	—	4	1	no	—
434	C₄⋊C₄	—	4	1	no	—
435	C₄⋊C₄	—	4	1	no	—
436	C₄⋊C₄	—	4	1	no	—
437	C₄⋊C₄	—	4	1	no	—
438	C₄⋊C₄	—	4	1	no	—
439	C₄⋊C₄	—	4	1	no	—
440	C₄⋊C₄	—	4	1	no	—
441	C₄⋊C₄	—	4	1	no	—
442	C₄⋊C₄	—	4	1	no	—
443	C₄⋊C₄	—	4	1	no	—
444	C₄⋊C₄	—	4	1	no	—
445	C₄⋊C₄	—	4	1	no	—
446	C₄⋊C₄	—	4	1	no	—
447	C₄⋊C₄	—	4	1	no	—
448	C₄⋊C₄	—	4	1	no	—
449	C₄⋊C₄	—	4	1	no	—
450	C₄⋊C₄	—	4	1	no	—
451	C₄⋊C₄	—	4	1	no	—
452	C₄⋊C₄	—	4	1	no	—
453	C₄⋊C₄	—	4	1	no	—
454	C₄⋊C₄	—	4	1	no	—
455	C₄⋊C₄	—	4	1	no	—
456	C₄⋊C₄	—	4	1	no	—
457	C₄⋊C₄	—	4	1	no	—
458	C₄⋊C₄	—	4	1	no	—
459	C₄⋊C₄	—	4	1	no	—
460	C₄⋊C₄	—	4	1	no	—
461	C₄⋊C₄	—	4	1	no	—
462	C₄⋊C₄	—	4	1	no	—
463	C₄⋊C₄	—	4	1	no	—
464	C₄⋊C₄	C₂×Q₈	1	4	yes	—
465	C₄⋊C₄	#41	1	4	yes	—
466	C₂²⋊C₄	—	2	2	no	—
467	C₂²⋊C₄	—	2	2	no	—
468	C₂²⋊C₄	—	2	2	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₂²⋊C₄	—	2	2	no	—
471	C₂²⋊C₄	—	2	2	no	—
472	C₂²⋊C₄	—	4	1	no	—
473	C₂²⋊C₄	—	4	1	no	—
474	C₂²⋊C₄	—	4	1	no	—
475	C₂²⋊C₄	—	4	1	no	—
476	C₂²⋊C₄	—	4	1	no	—
477	C₂²⋊C₄	—	4	1	no	—
478	C₂²⋊C₄	—	4	1	no	—
479	C₂²⋊C₄	—	4	1	no	—
480	C₂²⋊C₄	—	4	1	no	—
481	C₂²⋊C₄	—	4	1	no	—
482	C₂²⋊C₄	—	4	1	no	—
483	C₂²⋊C₄	—	4	1	no	—
484	C₂²⋊C₄	—	4	1	no	—
485	C₂²⋊C₄	—	4	1	no	—
486	C₂²⋊C₄	C₂×Q₈	1	4	yes	—
487	C₂²⋊C₄	C₂×Q₈	1	4	yes	—
488	C₄²	—	2	2	no	—
489	C₄²	—	2	2	no	—
490	C₄²	—	2	2	no	—
491	C₄²	—	2	2	no	—
492	C₄²	—	2	2	no	—
493	C₄²	—	2	2	no	—
494	C₄²	—	2	2	no	—
495	C₄²	—	2	2	no	—
496	C₄²	—	2	2	no	—
497	C₄²	—	2	2	no	—
498	C₄²	—	2	2	no	—
499	C₄²	—	2	2	no	—
500	C₄²	—	2	2	no	—
501	C₄²	—	2	2	no	—
502	C₄²	—	4	1	no	—
503	C₄²	—	4	1	no	—
504	C₄²	—	4	1	no	—
505	C₄²	—	4	1	no	—
506	C₄²	—	4	1	no	—
507	C₄²	C₂×Q₈	1	4	yes	—
508	C₄²	#41	1	4	yes	—
509	C₂³	—	2	1	no	—
510	C₂³	—	2	1	no	—
511	C₂³	—	2	1	no	—
512	C₂³	—	2	1	no	—
513	C₂³	—	2	1	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	2	1	no	—
516	C₂³	—	2	1	no	—
517	C₂³	—	2	1	no	—
518	C₂³	—	2	1	no	—
519	C₂³	—	2	1	no	—
520	C₂³	—	2	1	no	—
521	C₂³	C₂²×Q₈	1	2	yes	—
522	C₂³	C₂²×Q₈	1	2	yes	—
523	C₂³	C₂⁵	1	1	yes	characteristic
524	Q₈	—	4	4	no	—
525	Q₈	—	4	4	no	—
526	Q₈	—	4	4	no	—
527	D₄	—	4	4	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	8	no	—
547	C₂×C₄	—	2	8	no	—
548	C₂×C₄	—	2	1	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	—	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	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	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	—	4	4	no	—
606	C₂×C₄	—	4	4	no	—
607	C₂×C₄	—	4	4	no	—
608	C₂×C₄	—	4	4	no	—
609	C₂×C₄	C₂²×Q₈	1	2	yes	—
610	C₂×C₄	C₂²×Q₈	1	2	yes	—
611	C₂×C₄	C₂²×Q₈	1	2	yes	—
612	C₂×C₄	C₂²×Q₈	1	2	yes	—
613	C₂×C₄	C₂²×Q₈	1	2	yes	—
614	C₂×C₄	C₂×#41	1	2	yes	—
615	C₂×C₄	C₂×#41	1	2	yes	—
616	C₂×C₄	C₂×#41	1	2	yes	—
617	C₂×C₄	C₂×#41	1	2	yes	—
618	C₂×C₄	C₂×#41	1	2	yes	—
619	C₂×C₄	C₂×#41	1	2	yes	—
620	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
621	C₂²	—	2	2	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	2	2	no	—
625	C₂²	—	2	2	no	—
626	C₂²	—	2	2	no	—
627	C₂²	—	4	1	no	—
628	C₂²	—	4	1	no	—
629	C₂²	—	4	1	no	—
630	C₂²	—	4	1	no	—
631	C₂²	—	4	1	no	—
632	C₂²	—	4	1	no	—
633	C₂²	—	4	1	no	—
634	C₂²	—	4	1	no	—
635	C₂²	C₂³×Q₈	1	1	yes	characteristic
636	C₂²	C₂²×#41	1	1	yes	characteristic
637	C₂²	C₂²×#41	1	1	yes	characteristic
638	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
639	C₂²	#585	1	1	yes	characteristic
640	C₂²	#585	1	1	yes	characteristic
641	C₂²	#585	1	1	yes	characteristic
642	C₄	—	2	2	no	—
643	C₄	—	2	2	no	—
644	C₄	—	2	2	no	—
645	C₄	—	2	2	no	—
646	C₄	—	2	2	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	2	no	—
651	C₄	—	4	1	no	—
652	C₄	—	4	1	no	—
653	C₄	—	4	1	no	—
654	C₄	—	4	1	no	—
655	C₄	—	4	1	no	—
656	C₄	—	4	1	no	—
657	C₄	—	4	1	no	—
658	C₄	—	4	1	no	—
659	C₄	—	4	1	no	—
660	C₄	—	4	1	no	—
661	C₄	—	4	1	no	—
662	C₄	—	4	1	no	—
663	C₄	—	4	1	no	—
664	C₄	—	4	1	no	—
665	C₄	—	4	1	no	—
666	C₄	—	4	1	no	—
667	C₄	—	4	1	no	—
668	C₄	—	4	1	no	—
669	C₄	—	4	1	no	—
670	C₄	#554	1	4	yes	—
671	C₂	—	4	2	no	—
672	C₂	—	4	2	no	—
673	C₂	#3455	1	1	yes	characteristic
674	C₂	#3458	1	1	yes	characteristic
675	C₂	#3460	1	1	yes	characteristic
676	C₂	C₂×#554	1	1	yes	characteristic
677	C₂	#3475	1	1	yes	characteristic
678	C₂	Q₈×#41	1	1	yes	characteristic
679	C₂	#3529	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂⁴
commutator, Frattini, socle, cosocle	C₂³	C₂⁵
prime radical	C₂²×D₄	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄ ◁ G
LECS	G ▷ C₂³ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #2792	C₂	semidirect
2. #2791	C₂	semidirect
3. #2790	C₂	semidirect
4. #2788	C₂	semidirect
7. #2774	C₂	semidirect
8. #2768	C₂	semidirect
9. #2768	C₂	semidirect
10. #2763	C₂	semidirect
11. #2755	C₂	semidirect
13. #2742	C₂	semidirect
14. #2720	C₂	semidirect
15. #2704	C₂	semidirect
17. #2402	C₂	semidirect
18. #2399	C₂	semidirect
19. #2396	C₂	semidirect
20. #2396	C₂	semidirect
21. #2396	C₂	semidirect
22. #2396	C₂	semidirect
23. C₄×#125	C₂	semidirect
24. C₄×C₂²⋊Q₈	C₂	semidirect
25. C₄×C₂²⋊Q₈	C₂	semidirect
26. #2296	C₂	semidirect
27. #2295	C₂	semidirect
31. #2285	C₂	semidirect
203. C₄×D₄	Q₈	semidirect

Maximal subgroups

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

subgroup	index
#2792	2
#2791	2
#2790	2
#2788	2
#2784	2
#2780	2
#2774	2
#2768	2
#2763	2
#2755	2
#2748	2
#2742	2
#2720	2
#2704	2
#2692	2
#2402	2
#2399	2
#2396	2
C₄×#125	2
C₄×C₂²⋊Q₈	2
#2296	2
#2295	2
#2293	2
#2290	2
#2285	2