Subgroups — #34325

Order 256.

1186 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#553	C₂	1	1	yes	maximal, characteristic
2	#2374	C₂	1	1	yes	maximal, characteristic, complemented
3	#2373	C₂	1	1	yes	maximal, characteristic, complemented
4	#2373	C₂	1	1	yes	maximal, characteristic, complemented
5	#2371	C₂	1	1	yes	maximal, characteristic, complemented
6	#2364	C₂	1	1	yes	maximal, characteristic, complemented
7	#2364	C₂	1	1	yes	maximal, characteristic, complemented
8	#2364	C₂	1	1	yes	maximal, characteristic, complemented
9	#2361	C₂	1	1	yes	maximal, characteristic, complemented
10	#2359	C₂	1	1	yes	maximal, characteristic, complemented
11	#2353	C₂	1	1	yes	maximal, characteristic, complemented
12	#2353	C₂	1	1	yes	maximal, characteristic, complemented
13	#2353	C₂	1	1	yes	maximal, characteristic, complemented
14	#2352	C₂	1	1	yes	maximal, characteristic, complemented
15	#2345	C₂	1	1	yes	maximal, characteristic, complemented
16	#2343	C₂	1	1	yes	maximal, characteristic, complemented
17	#2336	C₂	1	1	yes	maximal, characteristic, complemented
18	#2335	C₂	1	1	yes	maximal, characteristic, complemented
19	#2334	C₂	1	1	yes	maximal, characteristic, complemented
20	#2333	C₂	1	1	yes	maximal, characteristic, complemented
21	#2325	C₂	1	1	yes	maximal, characteristic, complemented
22	#2325	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#126	C₂	1	1	yes	maximal, characteristic, complemented
24	C₄×#123	C₂	1	1	yes	maximal, characteristic, complemented
25	C₄×#121	C₂	1	1	yes	maximal, characteristic, complemented
26	#2298	C₂	1	1	yes	maximal, characteristic, complemented
27	#2290	C₂	1	1	yes	maximal, characteristic, complemented
28	C₂×#387	C₂	1	1	yes	maximal, characteristic, complemented
29	#2275	C₂	1	1	yes	maximal, characteristic, complemented
30	#2275	C₂	1	1	yes	maximal, characteristic, complemented
31	C₄²×D₄	C₂	1	1	yes	maximal, characteristic, complemented
32	#553	C₄	1	16	yes	complemented
33	C₂×#126	C₂²	1	1	yes	characteristic
34	C₂×#126	C₂²	1	1	yes	characteristic
35	C₂×#125	C₂²	1	1	yes	characteristic
36	C₂×#123	C₂²	1	1	yes	characteristic
37	C₂×#123	C₂²	1	1	yes	characteristic
38	C₂×#121	C₂²	1	1	yes	characteristic
39	C₂×#121	C₂²	1	1	yes	characteristic
40	C₂×#121	C₂²	1	1	yes	characteristic
41	C₂×#121	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
52	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
53	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
54	C₂×#117	C₂²	1	1	yes	characteristic
55	C₂×#117	C₂²	1	1	yes	characteristic
56	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic
57	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic
58	C₂²×C₄²	C₂²	1	1	yes	characteristic
59	C₂²×C₄²	C₂²	1	1	yes	characteristic
60	#390	C₂²	1	1	yes	characteristic
61	#390	C₂²	1	1	yes	characteristic
62	#389	C₂²	1	1	yes	characteristic
63	#389	C₂²	1	1	yes	characteristic
64	#389	C₂²	1	1	yes	characteristic
65	#389	C₂²	1	1	yes	characteristic
66	#388	C₂²	1	1	yes	characteristic
67	#388	C₂²	1	1	yes	characteristic
68	#388	C₂²	1	1	yes	characteristic
69	#388	C₂²	1	1	yes	characteristic
70	#388	C₂²	1	1	yes	characteristic
71	#388	C₂²	1	1	yes	characteristic
72	#388	C₂²	1	1	yes	characteristic
73	#388	C₂²	1	1	yes	characteristic
74	#388	C₂²	1	1	yes	characteristic
75	#388	C₂²	1	1	yes	characteristic
76	#388	C₂²	1	1	yes	characteristic
77	#388	C₂²	1	1	yes	characteristic
78	#388	C₂²	1	1	yes	characteristic
79	#388	C₂²	1	1	yes	characteristic
80	#388	C₂²	1	1	yes	characteristic
81	#388	C₂²	1	1	yes	characteristic
82	#388	C₂²	1	1	yes	characteristic
83	#388	C₂²	1	1	yes	characteristic
84	#387	C₂²	1	1	yes	characteristic
85	#387	C₂²	1	1	yes	characteristic
86	#387	C₂²	1	1	yes	characteristic
87	#387	C₂²	1	1	yes	characteristic
88	#387	C₂²	1	1	yes	characteristic
89	#387	C₂²	1	1	yes	characteristic
90	#387	C₂²	1	1	yes	characteristic
91	#387	C₂²	1	1	yes	characteristic
92	#387	C₂²	1	1	yes	characteristic
93	#387	C₂²	1	1	yes	characteristic
94	#387	C₂²	1	1	yes	characteristic
95	#387	C₂²	1	1	yes	characteristic
96	#387	C₂²	1	1	yes	characteristic
97	#387	C₂²	1	1	yes	characteristic
98	#387	C₂²	1	1	yes	characteristic
99	#387	C₂²	1	1	yes	characteristic
100	#387	C₂²	1	1	yes	characteristic
101	#387	C₂²	1	1	yes	characteristic
102	#387	C₂²	1	1	yes	characteristic
103	#387	C₂²	1	1	yes	characteristic
104	#387	C₂²	1	1	yes	characteristic
105	#387	C₂²	1	1	yes	characteristic
106	#387	C₂²	1	1	yes	characteristic
107	#387	C₂²	1	1	yes	characteristic
108	#387	C₂²	1	1	yes	characteristic
109	#387	C₂²	1	1	yes	characteristic
110	#386	C₂²	1	1	yes	characteristic
111	#386	C₂²	1	1	yes	characteristic
112	#386	C₂²	1	1	yes	characteristic
113	#386	C₂²	1	1	yes	characteristic
114	#386	C₂²	1	1	yes	characteristic
115	#386	C₂²	1	1	yes	characteristic
116	#386	C₂²	1	1	yes	characteristic
117	#386	C₂²	1	1	yes	characteristic
118	#386	C₂²	1	1	yes	characteristic
119	#386	C₂²	1	1	yes	characteristic
120	#386	C₂²	1	1	yes	characteristic
121	#386	C₂²	1	1	yes	characteristic
122	#386	C₂²	1	1	yes	characteristic
123	#386	C₂²	1	1	yes	characteristic
124	#385	C₂²	1	1	yes	characteristic
125	#385	C₂²	1	1	yes	characteristic
126	#385	C₂²	1	1	yes	characteristic
127	#385	C₂²	1	1	yes	characteristic
128	#385	C₂²	1	1	yes	characteristic
129	#385	C₂²	1	1	yes	characteristic
130	#383	C₂²	1	1	yes	characteristic
131	#383	C₂²	1	1	yes	characteristic
132	#382	C₂²	1	1	yes	characteristic
133	#381	C₂²	1	1	yes	characteristic
134	#381	C₂²	1	1	yes	characteristic
135	#380	C₂²	1	1	yes	characteristic
136	#380	C₂²	1	1	yes	characteristic
137	#380	C₂²	1	1	yes	characteristic
138	#380	C₂²	1	1	yes	characteristic
139	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
140	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
141	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
142	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
143	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
144	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
145	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
146	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
147	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
148	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
149	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
150	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
151	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
152	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
153	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
154	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
155	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
156	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
157	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
158	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
159	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
160	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
161	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
162	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
163	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
164	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
165	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
166	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
167	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
168	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
169	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
170	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
171	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
172	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
173	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
174	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
175	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
176	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
177	#376	C₂²	1	1	yes	characteristic
178	#376	C₂²	1	1	yes	characteristic
179	#376	C₂²	1	1	yes	characteristic
180	#376	C₂²	1	1	yes	characteristic
181	C₂×#95	C₂²	1	1	yes	characteristic
182	C₂×#95	C₂²	1	1	yes	characteristic
183	C₂×#95	C₂²	1	1	yes	characteristic
184	C₂×#95	C₂²	1	1	yes	characteristic
185	C₂×#95	C₂²	1	1	yes	characteristic
186	C₂×#95	C₂²	1	1	yes	characteristic
187	C₄³	C₂²	1	1	yes	characteristic
188	C₂²×D₄	C₂³	1	1	yes	characteristic
189	C₂²×D₄	C₂³	1	1	yes	characteristic
190	C₂²×D₄	C₂³	1	1	yes	characteristic
191	C₂²×D₄	C₂³	1	1	yes	characteristic
192	C₂²×D₄	C₂³	1	1	yes	characteristic
193	C₂²×D₄	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	C₂³×C₄	C₂³	1	1	yes	characteristic
198	C₂³×C₄	C₂³	1	1	yes	characteristic
199	C₂³×C₄	C₂³	1	1	yes	characteristic
200	C₂³×C₄	C₂³	1	1	yes	characteristic
201	C₂³×C₄	C₂³	1	1	yes	characteristic
202	C₂³×C₄	C₂³	1	1	yes	characteristic
203	C₂³×C₄	C₂³	1	1	yes	characteristic
204	C₂³×C₄	C₂³	1	1	yes	characteristic
205	C₂³×C₄	C₂³	1	1	yes	characteristic
206	C₂³×C₄	C₂³	1	1	yes	characteristic
207	C₂³×C₄	C₂³	1	1	yes	characteristic
208	C₂³×C₄	C₂³	1	1	yes	characteristic
209	C₂³×C₄	C₂³	1	1	yes	characteristic
210	#126	C₂×C₄	1	8	yes	complemented
211	#126	C₂×C₄	1	8	yes	complemented
212	#125	C₂×C₄	1	8	yes	complemented
213	#123	C₂×C₄	1	8	yes	complemented
214	#123	C₂×C₄	1	8	yes	complemented
215	#121	C₂×C₄	1	8	yes	complemented
216	#121	C₂×C₄	1	8	yes	complemented
217	#121	C₂×C₄	1	8	yes	complemented
218	#121	C₂×C₄	1	8	yes	complemented
219	C₄×D₄	—	2	4	no	—
220	C₄×D₄	—	2	4	no	—
221	C₄×D₄	—	2	4	no	—
222	C₄×D₄	—	2	4	no	—
223	C₄×D₄	—	2	4	no	—
224	C₄×D₄	—	2	4	no	—
225	C₄×D₄	—	4	2	no	—
226	C₄×D₄	—	4	2	no	—
227	C₄×D₄	C₂×C₄	1	8	yes	complemented
228	C₄×D₄	C₂×C₄	1	8	yes	complemented
229	C₄×D₄	C₂×C₄	1	8	yes	complemented
230	C₄×D₄	C₂×C₄	1	8	yes	complemented
231	#117	—	4	2	no	—
232	#117	C₂×C₄	1	8	yes	complemented
233	C₂×C₄⋊C₄	—	4	2	no	—
234	C₂×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
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×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×C₂²⋊C₄	C₂³	1	1	yes	characteristic
281	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
282	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
283	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
285	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
286	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
287	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
288	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
289	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
290	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
291	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
292	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
293	C₂×C₄²	—	4	2	no	—
294	C₂×C₄²	—	4	2	no	—
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	C₂×C₄²	C₂³	1	1	yes	characteristic
304	C₂×C₄²	C₂³	1	1	yes	characteristic
305	C₂×C₄²	C₂³	1	1	yes	characteristic
306	C₂×C₄²	C₂³	1	1	yes	characteristic
307	C₂×C₄²	C₂³	1	1	yes	characteristic
308	C₂×C₄²	C₂³	1	1	yes	characteristic
309	C₂×C₄²	C₂³	1	1	yes	characteristic
310	C₂×C₄²	C₂³	1	1	yes	characteristic
311	C₂×C₄²	C₂³	1	1	yes	characteristic
312	C₂×C₄²	C₂³	1	1	yes	characteristic
313	C₂×C₄²	C₂³	1	1	yes	characteristic
314	C₂×C₄²	C₂³	1	1	yes	characteristic
315	C₂×C₄²	C₂³	1	1	yes	characteristic
316	C₂×C₄²	C₂³	1	1	yes	characteristic
317	C₂×C₄²	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	#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	#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	C₂⁴	C₂⁴	1	1	yes	characteristic
371	C₂⁴	C₂⁴	1	1	yes	characteristic
372	C₂⁴	C₂⁴	1	1	yes	characteristic
373	C₂⁴	C₂⁴	1	1	yes	characteristic
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	4	1	no	—
381	C₂×D₄	—	4	1	no	—
382	C₂×D₄	—	4	1	no	—
383	C₂×D₄	—	4	1	no	—
384	C₂×D₄	—	4	1	no	—
385	C₂×D₄	—	4	1	no	—
386	C₂×D₄	C₂²×C₄	1	4	yes	—
387	C₂×D₄	C₂²×C₄	1	4	yes	—
388	C₂×D₄	C₂²×C₄	1	4	yes	—
389	C₂×D₄	C₂²×C₄	1	4	yes	—
390	C₂×D₄	C₂²×C₄	1	4	yes	—
391	C₂×D₄	C₂²×C₄	1	4	yes	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	4	1	no	—
404	C₂²×C₄	—	4	1	no	—
405	C₂²×C₄	—	4	1	no	—
406	C₂²×C₄	—	4	1	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	—	4	1	no	—
414	C₂²×C₄	—	4	1	no	—
415	C₂²×C₄	—	4	1	no	—
416	C₂²×C₄	—	4	1	no	—
417	C₂²×C₄	—	4	1	no	—
418	C₂²×C₄	—	4	1	no	—
419	C₂²×C₄	—	4	1	no	—
420	C₂²×C₄	—	4	1	no	—
421	C₂²×C₄	—	4	1	no	—
422	C₂²×C₄	—	4	1	no	—
423	C₂²×C₄	—	4	1	no	—
424	C₂²×C₄	—	4	1	no	—
425	C₂²×C₄	—	4	1	no	—
426	C₂²×C₄	—	4	1	no	—
427	C₂²×C₄	—	4	1	no	—
428	C₂²×C₄	—	4	1	no	—
429	C₂²×C₄	—	4	1	no	—
430	C₂²×C₄	—	4	1	no	—
431	C₂²×C₄	—	4	1	no	—
432	C₂²×C₄	—	4	1	no	—
433	C₂²×C₄	C₂²×C₄	1	4	yes	—
434	C₂²×C₄	C₂²×C₄	1	4	yes	—
435	C₂²×C₄	C₂²×C₄	1	4	yes	—
436	C₂²×C₄	C₂²×C₄	1	4	yes	—
437	C₂²×C₄	C₂²×C₄	1	4	yes	—
438	C₂²×C₄	C₂²×C₄	1	4	yes	—
439	C₂²×C₄	#41	1	4	yes	—
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	C₂²×C₄	C₂⁴	1	1	yes	characteristic
444	C₂²×C₄	C₂⁴	1	1	yes	characteristic
445	C₂²×C₄	C₂⁴	1	1	yes	characteristic
446	C₂²×C₄	C₂⁴	1	1	yes	characteristic
447	C₂²×C₄	C₂⁴	1	1	yes	characteristic
448	C₂²×C₄	C₂⁴	1	1	yes	characteristic
449	C₂²×C₄	C₂⁴	1	1	yes	characteristic
450	C₂²×C₄	C₂⁴	1	1	yes	characteristic
451	C₂²×C₄	C₂⁴	1	1	yes	characteristic
452	C₂²×C₄	C₂⁴	1	1	yes	characteristic
453	C₂²×C₄	C₂⁴	1	1	yes	characteristic
454	C₂²×C₄	C₂⁴	1	1	yes	characteristic
455	C₂²×C₄	C₂⁴	1	1	yes	characteristic
456	C₂²×C₄	C₂⁴	1	1	yes	characteristic
457	C₂²×C₄	C₂⁴	1	1	yes	characteristic
458	C₂²×C₄	C₂⁴	1	1	yes	characteristic
459	C₂²×C₄	C₂⁴	1	1	yes	characteristic
460	C₂²×C₄	C₂⁴	1	1	yes	characteristic
461	C₂²×C₄	C₂⁴	1	1	yes	characteristic
462	C₂²×C₄	C₂⁴	1	1	yes	characteristic
463	C₂²×C₄	C₂⁴	1	1	yes	characteristic
464	C₂²×C₄	C₂⁴	1	1	yes	characteristic
465	C₂²×C₄	C₂⁴	1	1	yes	characteristic
466	C₂²×C₄	C₂⁴	1	1	yes	characteristic
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	—	4	1	no	—
476	C₄⋊C₄	—	4	1	no	—
477	C₄⋊C₄	—	4	1	no	—
478	C₄⋊C₄	—	4	1	no	—
479	C₄⋊C₄	—	4	1	no	—
480	C₄⋊C₄	—	4	1	no	—
481	C₄⋊C₄	—	4	1	no	—
482	C₄⋊C₄	—	4	1	no	—
483	C₄⋊C₄	C₂²×C₄	1	4	yes	—
484	C₄⋊C₄	C₂²×C₄	1	4	yes	—
485	C₄⋊C₄	C₂²×C₄	1	4	yes	—
486	C₄⋊C₄	C₂²×C₄	1	4	yes	—
487	C₄⋊C₄	C₂²×C₄	1	4	yes	—
488	C₄⋊C₄	C₂²×C₄	1	4	yes	—
489	C₄⋊C₄	C₂²×C₄	1	4	yes	—
490	C₄⋊C₄	C₂²×C₄	1	4	yes	—
491	C₄⋊C₄	C₂²×C₄	1	4	yes	—
492	C₄⋊C₄	C₂²×C₄	1	4	yes	—
493	C₂²⋊C₄	—	2	2	no	—
494	C₂²⋊C₄	—	2	2	no	—
495	C₂²⋊C₄	—	2	2	no	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	—	2	2	no	—
501	C₂²⋊C₄	—	2	2	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	4	1	no	—
505	C₂²⋊C₄	—	4	1	no	—
506	C₂²⋊C₄	—	4	1	no	—
507	C₂²⋊C₄	—	4	1	no	—
508	C₂²⋊C₄	—	4	1	no	—
509	C₂²⋊C₄	—	4	1	no	—
510	C₂²⋊C₄	—	4	1	no	—
511	C₂²⋊C₄	—	4	1	no	—
512	C₂²⋊C₄	—	4	1	no	—
513	C₂²⋊C₄	—	4	1	no	—
514	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
515	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
516	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
517	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
518	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
519	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
520	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
521	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
522	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
523	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
524	C₂²⋊C₄	#41	1	4	yes	—
525	C₄²	—	2	2	no	—
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	—	4	1	no	—
535	C₄²	—	4	1	no	—
536	C₄²	—	4	1	no	—
537	C₄²	—	4	1	no	—
538	C₄²	—	4	1	no	—
539	C₄²	—	4	1	no	—
540	C₄²	—	4	1	no	—
541	C₄²	—	4	1	no	—
542	C₄²	—	4	1	no	—
543	C₄²	—	4	1	no	—
544	C₄²	—	4	1	no	—
545	C₄²	—	4	1	no	—
546	C₄²	—	4	1	no	—
547	C₄²	—	4	1	no	—
548	C₄²	—	4	1	no	—
549	C₄²	C₂²×C₄	1	4	yes	—
550	C₄²	C₂²×C₄	1	4	yes	—
551	C₄²	C₂²×C₄	1	4	yes	—
552	C₂³	—	2	1	no	—
553	C₂³	—	2	1	no	—
554	C₂³	—	2	1	no	—
555	C₂³	—	2	1	no	—
556	C₂³	—	2	1	no	—
557	C₂³	—	2	1	no	—
558	C₂³	—	2	1	no	—
559	C₂³	—	2	1	no	—
560	C₂³	—	2	1	no	—
561	C₂³	—	2	1	no	—
562	C₂³	—	2	1	no	—
563	C₂³	—	2	1	no	—
564	C₂³	—	2	1	no	—
565	C₂³	—	2	1	no	—
566	C₂³	—	2	1	no	—
567	C₂³	—	2	1	no	—
568	C₂³	—	2	1	no	—
569	C₂³	—	2	1	no	—
570	C₂³	—	2	1	no	—
571	C₂³	—	2	1	no	—
572	C₂³	—	2	1	no	—
573	C₂³	—	2	1	no	—
574	C₂³	C₂³×C₄	1	2	yes	—
575	C₂³	C₂³×C₄	1	2	yes	—
576	C₂³	C₂³×C₄	1	2	yes	—
577	C₂³	C₂³×C₄	1	2	yes	—
578	C₂³	C₂×#41	1	2	yes	—
579	C₂³	C₂×#41	1	2	yes	—
580	C₂³	C₂⁵	1	1	yes	characteristic
581	D₄	—	2	8	no	—
582	D₄	—	2	8	no	—
583	D₄	—	2	8	no	—
584	D₄	—	4	4	no	—
585	D₄	—	4	4	no	—
586	D₄	—	4	4	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	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	4	4	no	—
653	C₂×C₄	—	4	4	no	—
654	C₂×C₄	—	4	4	no	—
655	C₂×C₄	—	4	4	no	—
656	C₂×C₄	—	4	4	no	—
657	C₂×C₄	—	4	4	no	—
658	C₂×C₄	—	4	4	no	—
659	C₂×C₄	—	4	4	no	—
660	C₂×C₄	—	4	4	no	—
661	C₂×C₄	—	4	4	no	—
662	C₂×C₄	—	8	2	no	—
663	C₂×C₄	—	8	2	no	—
664	C₂×C₄	—	8	2	no	—
665	C₂×C₄	—	8	2	no	—
666	C₂×C₄	—	8	2	no	—
667	C₂×C₄	—	8	2	no	—
668	C₂×C₄	C₂³×C₄	1	2	yes	—
669	C₂×C₄	C₂³×C₄	1	2	yes	—
670	C₂×C₄	C₂³×C₄	1	2	yes	—
671	C₂×C₄	C₂³×C₄	1	2	yes	—
672	C₂×C₄	C₂³×C₄	1	2	yes	—
673	C₂×C₄	C₂³×C₄	1	2	yes	—
674	C₂×C₄	C₂³×C₄	1	2	yes	—
675	C₂×C₄	C₂³×C₄	1	2	yes	—
676	C₂×C₄	C₂³×C₄	1	2	yes	—
677	C₂×C₄	C₂³×C₄	1	2	yes	—
678	C₂×C₄	C₂³×C₄	1	2	yes	—
679	C₂×C₄	C₂×#41	1	2	yes	—
680	C₂×C₄	C₂×#41	1	2	yes	—
681	C₂×C₄	C₂×#41	1	2	yes	—
682	C₂×C₄	C₂×#41	1	2	yes	—
683	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
684	C₂²	—	2	2	no	—
685	C₂²	—	2	2	no	—
686	C₂²	—	2	2	no	—
687	C₂²	—	2	2	no	—
688	C₂²	—	2	2	no	—
689	C₂²	—	2	2	no	—
690	C₂²	—	2	2	no	—
691	C₂²	—	2	2	no	—
692	C₂²	—	2	2	no	—
693	C₂²	—	2	2	no	—
694	C₂²	—	2	2	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	2	2	no	—
697	C₂²	—	2	2	no	—
698	C₂²	—	2	2	no	—
699	C₂²	—	4	1	no	—
700	C₂²	—	4	1	no	—
701	C₂²	—	4	1	no	—
702	C₂²	—	4	1	no	—
703	C₂²	—	4	1	no	—
704	C₂²	—	4	1	no	—
705	C₂²	—	4	1	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	4	1	no	—
708	C₂²	—	4	1	no	—
709	C₂²	—	4	1	no	—
710	C₂²	—	4	1	no	—
711	C₂²	C₄×#41	1	4	yes	—
712	C₂²	C₂⁴×C₄	1	1	yes	characteristic
713	C₂²	C₂²×#41	1	1	yes	characteristic
714	C₂²	C₂²×#41	1	1	yes	characteristic
715	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
716	C₂²	#585	1	1	yes	characteristic
717	C₂²	#585	1	1	yes	characteristic
718	C₂²	#585	1	1	yes	characteristic
719	C₄	—	2	2	no	—
720	C₄	—	2	2	no	—
721	C₄	—	2	2	no	—
722	C₄	—	2	2	no	—
723	C₄	—	2	2	no	—
724	C₄	—	2	2	no	—
725	C₄	—	2	2	no	—
726	C₄	—	2	2	no	—
727	C₄	—	2	2	no	—
728	C₄	—	2	2	no	—
729	C₄	—	2	2	no	—
730	C₄	—	2	2	no	—
731	C₄	—	2	2	no	—
732	C₄	—	2	2	no	—
733	C₄	—	2	2	no	—
734	C₄	—	2	2	no	—
735	C₄	—	4	1	no	—
736	C₄	—	4	1	no	—
737	C₄	—	4	1	no	—
738	C₄	—	4	1	no	—
739	C₄	—	4	1	no	—
740	C₄	—	4	1	no	—
741	C₄	—	4	1	no	—
742	C₄	—	4	1	no	—
743	C₄	—	4	1	no	—
744	C₄	—	4	1	no	—
745	C₄	—	4	1	no	—
746	C₂	—	2	4	no	—
747	C₂	—	4	2	no	—
748	C₂	—	4	2	no	—
749	C₂	—	4	2	no	—
750	C₂	C₂×C₄×#41	1	1	yes	characteristic
751	C₂	#3428	1	1	yes	characteristic
752	C₂	C₄×H(5,𝔽₂)	1	1	yes	characteristic
753	C₂	#3505	1	1	yes	characteristic
754	C₂	#3512	1	1	yes	characteristic
755	C₂	#3513	1	1	yes	characteristic
756	C₂	#3521	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, socle, cosocle	C₂³	C₂⁵
commutator	C₂²	C₂⁴×C₄
prime radical	C₂×#553	C₂
LCS	G ▷ C₂² ▷ 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. #2374	C₂	semidirect
3. #2373	C₂	semidirect
4. #2373	C₂	semidirect
5. #2371	C₂	semidirect
6. #2364	C₂	semidirect
7. #2364	C₂	semidirect
8. #2364	C₂	semidirect
9. #2361	C₂	semidirect
10. #2359	C₂	semidirect
11. #2353	C₂	semidirect
12. #2353	C₂	semidirect
13. #2353	C₂	semidirect
14. #2352	C₂	semidirect
15. #2345	C₂	semidirect
16. #2343	C₂	semidirect
17. #2336	C₂	semidirect
18. #2335	C₂	semidirect
19. #2334	C₂	semidirect
20. #2333	C₂	semidirect
21. #2325	C₂	semidirect
22. #2325	C₂	semidirect
23. C₄×#126	C₂	semidirect
24. C₄×#123	C₂	semidirect
25. C₄×#121	C₂	semidirect
26. #2298	C₂	semidirect
27. #2290	C₂	semidirect
28. C₂×#387	C₂	semidirect
29. #2275	C₂	semidirect
30. #2275	C₂	semidirect
31. C₄²×D₄	C₂	semidirect
32. #553	C₄	semidirect
210. #126	C₂×C₄	semidirect
211. #126	C₂×C₄	semidirect
212. #125	C₂×C₄	semidirect
213. #123	C₂×C₄	semidirect
214. #123	C₂×C₄	semidirect
215. #121	C₂×C₄	semidirect
216. #121	C₂×C₄	semidirect
217. #121	C₂×C₄	semidirect
218. #121	C₂×C₄	semidirect
227. C₄×D₄	C₂×C₄	semidirect
228. C₄×D₄	C₂×C₄	semidirect
229. C₄×D₄	C₂×C₄	semidirect
230. C₄×D₄	C₂×C₄	semidirect
232. #117	C₂×C₄	semidirect
234. C₂×C₄⋊C₄	C₂×C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#553	2
#2374	2
#2373	2
#2371	2
#2364	2
#2361	2
#2359	2
#2353	2
#2352	2
#2345	2
#2343	2
#2336	2
#2335	2
#2334	2
#2333	2
#2325	2
C₄×#126	2
C₄×#123	2
C₄×#121	2
#2298	2
#2290	2
C₂×#387	2
#2275	2
C₄²×D₄	2