Subgroups — #43009

Order 256.

1215 conjugacy classes of subgroups.

The subgroup lattice has 815 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#539	C₂	1	1	yes	maximal, characteristic, complemented
3	#2718	C₂	1	1	yes	maximal, characteristic, complemented
4	#2706	C₂	1	1	yes	maximal, characteristic, complemented
5	#2701	C₂	1	1	yes	maximal, characteristic, complemented
6	#2694	C₂	1	1	yes	maximal, characteristic, complemented
7	#2687	C₂	1	1	yes	maximal, characteristic, complemented
8	#2677	C₂	1	1	yes	maximal, characteristic, complemented
9	#2672	C₂	1	1	yes	maximal, characteristic, complemented
10	#2671	C₂	1	1	yes	maximal, characteristic, complemented
11	#2583	C₂	1	1	yes	maximal, characteristic, complemented
12	#2556	C₂	1	1	yes	maximal, characteristic, complemented
13	#2553	C₂	1	1	yes	maximal, characteristic, complemented
14	#2550	C₂	1	1	yes	maximal, characteristic, complemented
15	#2473	C₂	1	1	yes	maximal, characteristic, complemented
16	#2468	C₂	1	1	yes	maximal, characteristic, complemented
17	#2466	C₂	1	1	yes	maximal, characteristic, complemented
18	#2464	C₂	1	1	yes	maximal, characteristic, complemented
19	#2461	C₂	1	1	yes	maximal, characteristic, complemented
20	#2455	C₂	1	1	yes	maximal, characteristic, complemented
21	#2455	C₂	1	1	yes	maximal, characteristic, complemented
22	#2449	C₂	1	1	yes	maximal, characteristic, complemented
23	#2440	C₂	1	1	yes	maximal, characteristic, complemented
24	#2432	C₂	1	1	yes	maximal, characteristic, complemented
25	#2407	C₂	1	1	yes	maximal, characteristic, complemented
26	#2406	C₂	1	1	yes	maximal, characteristic, complemented
27	#2388	C₂	1	1	yes	maximal, characteristic, complemented
28	#2374	C₂	1	1	yes	maximal, characteristic, complemented
29	#2361	C₂	1	1	yes	maximal, characteristic, complemented
30	D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
31	#2322	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×#41	C₂²	1	1	yes	characteristic
33	C₂²×#41	C₂²	1	1	yes	characteristic
34	#547	—	2	8	no	—
35	#539	—	2	8	no	—
36	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic
38	C₂×#126	C₂²	1	1	yes	characteristic
39	C₂×#126	C₂²	1	1	yes	characteristic
40	C₂×#125	C₂²	1	1	yes	characteristic
41	C₂×#125	C₂²	1	1	yes	characteristic
42	C₂×#124	C₂²	1	1	yes	characteristic
43	C₂×#123	C₂²	1	1	yes	characteristic
44	C₂×#123	C₂²	1	1	yes	characteristic
45	C₂×#123	C₂²	1	1	yes	characteristic
46	C₂×#123	C₂²	1	1	yes	characteristic
47	C₂×#123	C₂²	1	1	yes	characteristic
48	C₂×#123	C₂²	1	1	yes	characteristic
49	C₂×#123	C₂²	1	1	yes	characteristic
50	C₂×#123	C₂²	1	1	yes	characteristic
51	C₂×#123	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
54	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
55	C₂×C₂²⋊Q₈	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×#121	C₂²	1	1	yes	characteristic
59	C₂×#121	C₂²	1	1	yes	characteristic
60	C₂×#121	C₂²	1	1	yes	characteristic
61	C₂×#121	C₂²	1	1	yes	characteristic
62	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
63	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
64	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
65	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
66	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
67	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
68	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
69	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
70	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic
71	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic
72	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic
73	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic
74	#400	C₂²	1	1	yes	characteristic
75	#399	C₂²	1	1	yes	characteristic
76	#399	C₂²	1	1	yes	characteristic
77	#399	C₂²	1	1	yes	characteristic
78	#399	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	#397	C₂²	1	1	yes	characteristic
88	#397	C₂²	1	1	yes	characteristic
89	#396	C₂²	1	1	yes	characteristic
90	#396	C₂²	1	1	yes	characteristic
91	#396	C₂²	1	1	yes	characteristic
92	#395	C₂²	1	1	yes	characteristic
93	#395	C₂²	1	1	yes	characteristic
94	#395	C₂²	1	1	yes	characteristic
95	#395	C₂²	1	1	yes	characteristic
96	#395	C₂²	1	1	yes	characteristic
97	#394	C₂²	1	1	yes	characteristic
98	#394	C₂²	1	1	yes	characteristic
99	#394	C₂²	1	1	yes	characteristic
100	#394	C₂²	1	1	yes	characteristic
101	#394	C₂²	1	1	yes	characteristic
102	#394	C₂²	1	1	yes	characteristic
103	#394	C₂²	1	1	yes	characteristic
104	#394	C₂²	1	1	yes	characteristic
105	#394	C₂²	1	1	yes	characteristic
106	#394	C₂²	1	1	yes	characteristic
107	#394	C₂²	1	1	yes	characteristic
108	#394	C₂²	1	1	yes	characteristic
109	#393	C₂²	1	1	yes	characteristic
110	#392	C₂²	1	1	yes	characteristic
111	#392	C₂²	1	1	yes	characteristic
112	#392	C₂²	1	1	yes	characteristic
113	#392	C₂²	1	1	yes	characteristic
114	#391	C₂²	1	1	yes	characteristic
115	#391	C₂²	1	1	yes	characteristic
116	#390	C₂²	1	1	yes	characteristic
117	#390	C₂²	1	1	yes	characteristic
118	#390	C₂²	1	1	yes	characteristic
119	#389	C₂²	1	1	yes	characteristic
120	#389	C₂²	1	1	yes	characteristic
121	#389	C₂²	1	1	yes	characteristic
122	#389	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	#388	C₂²	1	1	yes	characteristic
130	#388	C₂²	1	1	yes	characteristic
131	#388	C₂²	1	1	yes	characteristic
132	#388	C₂²	1	1	yes	characteristic
133	#388	C₂²	1	1	yes	characteristic
134	#388	C₂²	1	1	yes	characteristic
135	#388	C₂²	1	1	yes	characteristic
136	#388	C₂²	1	1	yes	characteristic
137	#388	C₂²	1	1	yes	characteristic
138	#388	C₂²	1	1	yes	characteristic
139	#388	C₂²	1	1	yes	characteristic
140	#388	C₂²	1	1	yes	characteristic
141	#387	C₂²	1	1	yes	characteristic
142	#387	C₂²	1	1	yes	characteristic
143	#387	C₂²	1	1	yes	characteristic
144	#387	C₂²	1	1	yes	characteristic
145	#387	C₂²	1	1	yes	characteristic
146	#386	C₂²	1	1	yes	characteristic
147	#386	C₂²	1	1	yes	characteristic
148	#386	C₂²	1	1	yes	characteristic
149	#386	C₂²	1	1	yes	characteristic
150	#386	C₂²	1	1	yes	characteristic
151	#386	C₂²	1	1	yes	characteristic
152	#386	C₂²	1	1	yes	characteristic
153	#385	C₂²	1	1	yes	characteristic
154	#385	C₂²	1	1	yes	characteristic
155	#385	C₂²	1	1	yes	characteristic
156	#385	C₂²	1	1	yes	characteristic
157	#385	C₂²	1	1	yes	characteristic
158	#385	C₂²	1	1	yes	characteristic
159	#385	C₂²	1	1	yes	characteristic
160	#385	C₂²	1	1	yes	characteristic
161	#385	C₂²	1	1	yes	characteristic
162	#385	C₂²	1	1	yes	characteristic
163	#385	C₂²	1	1	yes	characteristic
164	#385	C₂²	1	1	yes	characteristic
165	#385	C₂²	1	1	yes	characteristic
166	#385	C₂²	1	1	yes	characteristic
167	#385	C₂²	1	1	yes	characteristic
168	#385	C₂²	1	1	yes	characteristic
169	#385	C₂²	1	1	yes	characteristic
170	#385	C₂²	1	1	yes	characteristic
171	#385	C₂²	1	1	yes	characteristic
172	#384	C₂²	1	1	yes	characteristic
173	#382	C₂²	1	1	yes	characteristic
174	#381	C₂²	1	1	yes	characteristic
175	#381	C₂²	1	1	yes	characteristic
176	#380	C₂²	1	1	yes	characteristic
177	#380	C₂²	1	1	yes	characteristic
178	#380	C₂²	1	1	yes	characteristic
179	#380	C₂²	1	1	yes	characteristic
180	C₄×C₄⋊C₄	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×C₂²⋊C₄	C₂²	1	1	yes	characteristic
184	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
185	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
186	C₄×C₂²⋊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	C₂×#41	—	2	4	no	—
190	C₂×#41	—	2	4	no	—
191	C₂×#41	—	4	2	no	—
192	C₂×#41	—	4	2	no	—
193	C₂×#41	—	4	2	no	—
194	C₂×#41	—	4	2	no	—
195	C₂²×Q₈	C₂³	1	1	yes	characteristic
196	C₂²×Q₈	C₂³	1	1	yes	characteristic
197	C₂²×Q₈	C₂³	1	1	yes	characteristic
198	C₂²×D₄	C₂³	1	1	yes	characteristic
199	C₂²×D₄	C₂³	1	1	yes	characteristic
200	C₂²×D₄	C₂³	1	1	yes	characteristic
201	C₂²×D₄	C₂³	1	1	yes	characteristic
202	C₂²×D₄	C₂³	1	1	yes	characteristic
203	C₂²×D₄	C₂³	1	1	yes	characteristic
204	C₂²×D₄	C₂³	1	1	yes	characteristic
205	C₂²×D₄	C₂³	1	1	yes	characteristic
206	C₂²×D₄	C₂³	1	1	yes	characteristic
207	C₂²×D₄	C₂³	1	1	yes	characteristic
208	C₂³×C₄	C₂³	1	1	yes	characteristic
209	C₂³×C₄	C₂³	1	1	yes	characteristic
210	C₂³×C₄	C₂³	1	1	yes	characteristic
211	C₂³×C₄	C₂³	1	1	yes	characteristic
212	C₂³×C₄	C₂³	1	1	yes	characteristic
213	C₂³×C₄	C₂³	1	1	yes	characteristic
214	C₂³×C₄	C₂³	1	1	yes	characteristic
215	C₂³×C₄	C₂³	1	1	yes	characteristic
216	C₂³×C₄	C₂³	1	1	yes	characteristic
217	C₂³×C₄	C₂³	1	1	yes	characteristic
218	C₂³×C₄	C₂³	1	1	yes	characteristic
219	C₂³×C₄	C₂³	1	1	yes	characteristic
220	C₂³×C₄	C₂³	1	1	yes	characteristic
221	C₄⋊Q₈	—	2	4	no	—
222	C₄⋊Q₈	—	4	2	no	—
223	#126	—	2	4	no	—
224	#126	—	2	4	no	—
225	#125	—	2	4	no	—
226	#125	—	2	4	no	—
227	#124	—	4	2	no	—
228	#123	—	2	4	no	—
229	#123	—	2	4	no	—
230	#123	—	2	4	no	—
231	#123	—	2	4	no	—
232	#123	—	2	4	no	—
233	#123	—	2	4	no	—
234	#123	—	2	4	no	—
235	#123	—	4	2	no	—
236	#123	D₄	1	8	yes	complemented
237	C₂²⋊Q₈	—	2	4	no	—
238	C₂²⋊Q₈	—	2	4	no	—
239	C₂²⋊Q₈	—	2	4	no	—
240	C₂²⋊Q₈	—	2	4	no	—
241	C₂²⋊Q₈	—	2	4	no	—
242	C₂²⋊Q₈	—	4	2	no	—
243	#121	—	2	4	no	—
244	#121	—	2	4	no	—
245	#121	—	2	4	no	—
246	#121	—	2	4	no	—
247	C₄×D₄	—	2	4	no	—
248	C₄×D₄	—	2	4	no	—
249	C₄×D₄	—	2	4	no	—
250	C₄×D₄	—	2	4	no	—
251	C₄×D₄	—	2	4	no	—
252	C₄×D₄	—	4	2	no	—
253	C₄×D₄	—	4	2	no	—
254	C₄×D₄	—	4	2	no	—
255	C₂×C₄⋊C₄	—	2	4	no	—
256	C₂×C₄⋊C₄	—	2	4	no	—
257	C₂×C₄⋊C₄	—	2	4	no	—
258	C₂×C₄⋊C₄	—	4	2	no	—
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×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×C₄⋊C₄	C₂³	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
300	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
301	C₂×C₄⋊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×C₂²⋊C₄	C₂³	1	1	yes	characteristic
319	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
320	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
321	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
322	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
323	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
324	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
325	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
326	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
327	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
328	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
329	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
330	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
331	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
332	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
333	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
334	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
335	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
336	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
337	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
338	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
339	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
340	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
341	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
342	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
343	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
344	C₂×C₄²	C₂³	1	1	yes	characteristic
345	C₂×C₄²	C₂³	1	1	yes	characteristic
346	C₂×C₄²	C₂³	1	1	yes	characteristic
347	C₂×C₄²	C₂³	1	1	yes	characteristic
348	C₂×C₄²	C₂³	1	1	yes	characteristic
349	C₂×C₄²	C₂³	1	1	yes	characteristic
350	C₂×C₄²	C₂³	1	1	yes	characteristic
351	C₂×C₄²	C₂³	1	1	yes	characteristic
352	C₂×C₄²	C₂³	1	1	yes	characteristic
353	C₂×C₄²	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	#95	C₂³	1	1	yes	characteristic
380	#95	C₂³	1	1	yes	characteristic
381	#95	C₂³	1	1	yes	characteristic
382	#95	C₂³	1	1	yes	characteristic
383	#95	C₂³	1	1	yes	characteristic
384	#95	C₂³	1	1	yes	characteristic
385	#95	C₂³	1	1	yes	characteristic
386	#95	C₂³	1	1	yes	characteristic
387	#95	C₂³	1	1	yes	characteristic
388	C₂⁴	C₂⁴	1	1	yes	characteristic
389	C₂⁴	C₂⁴	1	1	yes	characteristic
390	C₂⁴	C₂⁴	1	1	yes	characteristic
391	C₂⁴	C₂⁴	1	1	yes	characteristic
392	C₂⁴	C₂⁴	1	1	yes	characteristic
393	#41	—	4	16	no	—
394	#41	—	4	16	no	—
395	C₂×Q₈	—	2	2	no	—
396	C₂×Q₈	—	2	2	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	—	2	2	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	4	1	no	—
401	C₂×Q₈	—	4	1	no	—
402	C₂×Q₈	—	4	1	no	—
403	C₂×Q₈	—	4	1	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	4	1	no	—
424	C₂×D₄	—	4	1	no	—
425	C₂×D₄	—	4	1	no	—
426	C₂×D₄	—	4	1	no	—
427	C₂×D₄	—	4	1	no	—
428	C₂×D₄	—	4	1	no	—
429	C₂×D₄	—	4	1	no	—
430	C₂×D₄	—	4	1	no	—
431	C₂×D₄	—	4	1	no	—
432	C₂×D₄	—	4	1	no	—
433	C₂×D₄	C₂×D₄	1	4	yes	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	4	1	no	—
455	C₂²×C₄	—	4	1	no	—
456	C₂²×C₄	—	4	1	no	—
457	C₂²×C₄	—	4	1	no	—
458	C₂²×C₄	—	4	1	no	—
459	C₂²×C₄	—	4	1	no	—
460	C₂²×C₄	—	4	1	no	—
461	C₂²×C₄	—	4	1	no	—
462	C₂²×C₄	—	4	1	no	—
463	C₂²×C₄	—	4	1	no	—
464	C₂²×C₄	—	4	1	no	—
465	C₂²×C₄	—	4	1	no	—
466	C₂²×C₄	—	4	1	no	—
467	C₂²×C₄	—	4	1	no	—
468	C₂²×C₄	—	4	1	no	—
469	C₂²×C₄	—	4	1	no	—
470	C₂²×C₄	—	4	1	no	—
471	C₂²×C₄	—	4	1	no	—
472	C₂²×C₄	C₂×D₄	1	4	yes	—
473	C₂²×C₄	C₂⁴	1	1	yes	characteristic
474	C₂²×C₄	C₂⁴	1	1	yes	characteristic
475	C₂²×C₄	C₂⁴	1	1	yes	characteristic
476	C₂²×C₄	C₂⁴	1	1	yes	characteristic
477	C₂²×C₄	C₂⁴	1	1	yes	characteristic
478	C₂²×C₄	C₂⁴	1	1	yes	characteristic
479	C₂²×C₄	C₂⁴	1	1	yes	characteristic
480	C₂²×C₄	C₂⁴	1	1	yes	characteristic
481	C₂²×C₄	C₂⁴	1	1	yes	characteristic
482	C₂²×C₄	C₂⁴	1	1	yes	characteristic
483	C₂²×C₄	C₂⁴	1	1	yes	characteristic
484	C₂²×C₄	C₂⁴	1	1	yes	characteristic
485	C₂²×C₄	C₂⁴	1	1	yes	characteristic
486	C₂²×C₄	C₂⁴	1	1	yes	characteristic
487	C₂²×C₄	C₂⁴	1	1	yes	characteristic
488	C₂²×C₄	C₂⁴	1	1	yes	characteristic
489	C₂²×C₄	C₂⁴	1	1	yes	characteristic
490	C₂²×C₄	C₂⁴	1	1	yes	characteristic
491	C₂²×C₄	C₂⁴	1	1	yes	characteristic
492	C₂²×C₄	C₂⁴	1	1	yes	characteristic
493	C₂²×C₄	C₂⁴	1	1	yes	characteristic
494	C₂²×C₄	C₂⁴	1	1	yes	characteristic
495	C₂²×C₄	C₂⁴	1	1	yes	characteristic
496	C₂²×C₄	C₂⁴	1	1	yes	characteristic
497	C₂²×C₄	C₂⁴	1	1	yes	characteristic
498	C₂²×C₄	C₂⁴	1	1	yes	characteristic
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	2	2	no	—
514	C₄⋊C₄	—	2	2	no	—
515	C₄⋊C₄	—	2	2	no	—
516	C₄⋊C₄	—	2	2	no	—
517	C₄⋊C₄	—	2	2	no	—
518	C₄⋊C₄	—	2	2	no	—
519	C₄⋊C₄	—	2	2	no	—
520	C₄⋊C₄	—	2	2	no	—
521	C₄⋊C₄	—	2	2	no	—
522	C₄⋊C₄	—	2	2	no	—
523	C₄⋊C₄	—	2	2	no	—
524	C₄⋊C₄	—	2	2	no	—
525	C₄⋊C₄	—	2	2	no	—
526	C₄⋊C₄	—	2	2	no	—
527	C₄⋊C₄	—	4	1	no	—
528	C₄⋊C₄	—	4	1	no	—
529	C₄⋊C₄	—	4	1	no	—
530	C₄⋊C₄	—	4	1	no	—
531	C₄⋊C₄	—	4	1	no	—
532	C₄⋊C₄	—	4	1	no	—
533	C₄⋊C₄	—	4	1	no	—
534	C₄⋊C₄	—	4	1	no	—
535	C₄⋊C₄	—	4	1	no	—
536	C₄⋊C₄	—	4	1	no	—
537	C₄⋊C₄	—	4	1	no	—
538	C₄⋊C₄	—	4	1	no	—
539	C₄⋊C₄	—	4	1	no	—
540	C₄⋊C₄	C₂×D₄	1	4	yes	—
541	C₄⋊C₄	C₂×D₄	1	4	yes	—
542	C₂²⋊C₄	—	2	2	no	—
543	C₂²⋊C₄	—	2	2	no	—
544	C₂²⋊C₄	—	2	2	no	—
545	C₂²⋊C₄	—	2	2	no	—
546	C₂²⋊C₄	—	2	2	no	—
547	C₂²⋊C₄	—	2	2	no	—
548	C₂²⋊C₄	—	2	2	no	—
549	C₂²⋊C₄	—	2	2	no	—
550	C₂²⋊C₄	—	2	2	no	—
551	C₂²⋊C₄	—	2	2	no	—
552	C₂²⋊C₄	—	2	2	no	—
553	C₂²⋊C₄	—	2	2	no	—
554	C₂²⋊C₄	—	2	2	no	—
555	C₂²⋊C₄	—	2	2	no	—
556	C₂²⋊C₄	—	2	2	no	—
557	C₂²⋊C₄	—	2	2	no	—
558	C₂²⋊C₄	—	2	2	no	—
559	C₂²⋊C₄	—	2	2	no	—
560	C₂²⋊C₄	—	2	2	no	—
561	C₂²⋊C₄	—	2	2	no	—
562	C₂²⋊C₄	—	2	2	no	—
563	C₂²⋊C₄	—	2	2	no	—
564	C₂²⋊C₄	—	2	2	no	—
565	C₂²⋊C₄	—	2	2	no	—
566	C₂²⋊C₄	—	2	2	no	—
567	C₂²⋊C₄	—	4	1	no	—
568	C₂²⋊C₄	—	4	1	no	—
569	C₂²⋊C₄	—	4	1	no	—
570	C₂²⋊C₄	—	4	1	no	—
571	C₂²⋊C₄	—	4	1	no	—
572	C₂²⋊C₄	—	4	1	no	—
573	C₂²⋊C₄	—	4	1	no	—
574	C₂²⋊C₄	—	4	1	no	—
575	C₂²⋊C₄	—	4	1	no	—
576	C₂²⋊C₄	—	4	1	no	—
577	C₂²⋊C₄	—	4	1	no	—
578	C₂²⋊C₄	—	4	1	no	—
579	C₂²⋊C₄	—	4	1	no	—
580	C₂²⋊C₄	C₂×D₄	1	4	yes	—
581	C₂²⋊C₄	C₂×D₄	1	4	yes	—
582	C₂²⋊C₄	C₂×D₄	1	4	yes	—
583	C₂²⋊C₄	#41	1	4	yes	complemented
584	C₄²	—	2	2	no	—
585	C₄²	—	2	2	no	—
586	C₄²	—	2	2	no	—
587	C₄²	—	2	2	no	—
588	C₄²	—	2	2	no	—
589	C₄²	—	4	1	no	—
590	C₄²	—	4	1	no	—
591	C₄²	—	4	1	no	—
592	C₄²	—	4	1	no	—
593	C₄²	—	4	1	no	—
594	C₂³	—	2	1	no	—
595	C₂³	—	2	1	no	—
596	C₂³	—	2	1	no	—
597	C₂³	—	2	1	no	—
598	C₂³	—	2	1	no	—
599	C₂³	—	2	1	no	—
600	C₂³	—	2	1	no	—
601	C₂³	—	2	1	no	—
602	C₂³	—	2	1	no	—
603	C₂³	—	2	1	no	—
604	C₂³	—	2	1	no	—
605	C₂³	—	2	1	no	—
606	C₂³	—	2	1	no	—
607	C₂³	—	2	1	no	—
608	C₂³	—	2	1	no	—
609	C₂³	—	2	1	no	—
610	C₂³	—	2	1	no	—
611	C₂³	—	2	1	no	—
612	C₂³	—	2	1	no	—
613	C₂³	—	2	1	no	—
614	C₂³	—	2	1	no	—
615	C₂³	—	2	1	no	—
616	C₂³	—	2	1	no	—
617	C₂³	—	2	1	no	—
618	C₂³	—	2	1	no	—
619	C₂³	—	2	1	no	—
620	C₂³	—	2	1	no	—
621	C₂³	—	2	1	no	—
622	C₂³	—	2	1	no	—
623	C₂³	—	2	1	no	—
624	C₂³	—	2	1	no	—
625	C₂³	C₂²×D₄	1	2	yes	—
626	C₂³	C₂²×D₄	1	2	yes	—
627	C₂³	C₂×#41	1	2	yes	—
628	C₂³	H(5,𝔽₂)	1	2	yes	—
629	C₂³	C₂⁵	1	1	yes	characteristic
630	Q₈	—	4	4	no	—
631	Q₈	—	4	4	no	—
632	Q₈	—	8	2	no	—
633	D₄	—	2	8	no	—
634	D₄	—	2	8	no	—
635	D₄	—	4	4	no	—
636	D₄	—	4	4	no	—
637	D₄	—	4	4	no	—
638	D₄	—	4	4	no	—
639	D₄	—	4	4	no	—
640	D₄	—	4	4	no	—
641	D₄	—	4	4	no	—
642	D₄	—	4	4	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	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	4	4	no	—
712	C₂×C₄	—	4	4	no	—
713	C₂×C₄	—	4	4	no	—
714	C₂×C₄	—	4	4	no	—
715	C₂×C₄	—	4	4	no	—
716	C₂×C₄	—	4	4	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	4	4	no	—
719	C₂×C₄	—	4	4	no	—
720	C₂×C₄	—	4	4	no	—
721	C₂×C₄	—	8	2	no	—
722	C₂×C₄	—	8	2	no	—
723	C₂×C₄	—	8	2	no	—
724	C₂×C₄	C₂²×D₄	1	2	yes	—
725	C₂×C₄	C₂²×D₄	1	2	yes	—
726	C₂×C₄	C₂²×D₄	1	2	yes	—
727	C₂×C₄	C₂²×D₄	1	2	yes	—
728	C₂×C₄	C₂²×D₄	1	2	yes	—
729	C₂×C₄	C₂×#41	1	2	yes	—
730	C₂×C₄	C₂×#41	1	2	yes	—
731	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
732	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
733	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
734	C₂²	—	2	2	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	2	2	no	—
738	C₂²	—	2	2	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	2	2	no	—
741	C₂²	—	2	2	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	2	2	no	—
746	C₂²	—	4	1	no	—
747	C₂²	—	4	1	no	—
748	C₂²	—	4	1	no	—
749	C₂²	—	4	1	no	—
750	C₂²	—	4	1	no	—
751	C₂²	—	4	1	no	—
752	C₂²	—	4	1	no	—
753	C₂²	—	4	1	no	—
754	C₂²	—	4	1	no	—
755	C₂²	—	4	1	no	—
756	C₂²	—	4	1	no	—
757	C₂²	—	4	1	no	—
758	C₂²	—	4	1	no	—
759	C₂²	—	4	1	no	—
760	C₂²	—	4	1	no	—
761	C₂²	—	4	1	no	—
762	C₂²	—	4	1	no	—
763	C₂²	—	4	1	no	—
764	C₂²	—	4	1	no	—
765	C₂²	—	4	1	no	—
766	C₂²	—	4	1	no	—
767	C₂²	—	4	1	no	—
768	C₂²	—	4	1	no	—
769	C₂²	C₂³×D₄	1	1	yes	characteristic
770	C₂²	C₂²×#41	1	1	yes	characteristic
771	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
772	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
773	C₂²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
774	C₂²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
775	C₂²	#585	1	1	yes	characteristic
776	C₄	—	2	2	no	—
777	C₄	—	2	2	no	—
778	C₄	—	2	2	no	—
779	C₄	—	2	2	no	—
780	C₄	—	2	2	no	—
781	C₄	—	2	2	no	—
782	C₄	—	2	2	no	—
783	C₄	—	2	2	no	—
784	C₄	—	2	2	no	—
785	C₄	—	2	2	no	—
786	C₄	—	4	1	no	—
787	C₄	—	4	1	no	—
788	C₄	—	4	1	no	—
789	C₄	—	4	1	no	—
790	C₄	—	4	1	no	—
791	C₄	—	4	1	no	—
792	C₄	—	4	1	no	—
793	C₄	—	4	1	no	—
794	C₄	—	4	1	no	—
795	C₄	—	4	1	no	—
796	C₄	—	4	1	no	—
797	C₄	—	4	1	no	—
798	C₄	—	4	1	no	—
799	C₄	—	4	1	no	—
800	C₄	—	4	1	no	—
801	C₄	—	4	1	no	—
802	C₂	—	4	2	no	—
803	C₂	—	4	2	no	—
804	C₂	—	4	2	no	—
805	C₂	—	4	2	no	—
806	C₂	—	8	1	no	—
807	C₂	D₄×#41	1	1	yes	characteristic
808	C₂	#3484	1	1	yes	characteristic
809	C₂	#3492	1	1	yes	characteristic
810	C₂	#3499	1	1	yes	characteristic
811	C₂	#3520	1	1	yes	characteristic
812	C₂	#3554	1	1	yes	characteristic
813	C₂	#3559	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂³	C₂⁵
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
1. C₂×#547	C₂	semidirect
2. C₂×#539	C₂	semidirect
3. #2718	C₂	semidirect
4. #2706	C₂	semidirect
5. #2701	C₂	semidirect
6. #2694	C₂	semidirect
7. #2687	C₂	semidirect
8. #2677	C₂	semidirect
9. #2672	C₂	semidirect
10. #2671	C₂	semidirect
11. #2583	C₂	semidirect
12. #2556	C₂	semidirect
13. #2553	C₂	semidirect
14. #2550	C₂	semidirect
15. #2473	C₂	semidirect
16. #2468	C₂	semidirect
17. #2466	C₂	semidirect
18. #2464	C₂	semidirect
19. #2461	C₂	semidirect
20. #2455	C₂	semidirect
21. #2455	C₂	semidirect
22. #2449	C₂	semidirect
23. #2440	C₂	semidirect
24. #2432	C₂	semidirect
25. #2407	C₂	semidirect
26. #2406	C₂	semidirect
27. #2388	C₂	semidirect
28. #2374	C₂	semidirect
29. #2361	C₂	semidirect
30. D₄×C₄⋊C₄	C₂	semidirect
31. #2322	C₂	semidirect
236. #123	D₄	semidirect
583. C₂²⋊C₄	#41	semidirect

Maximal subgroups

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

subgroup	index
C₂×#547	2
C₂×#539	2
#2718	2
#2706	2
#2701	2
#2694	2
#2687	2
#2677	2
#2672	2
#2671	2
#2583	2
#2556	2
#2553	2
#2550	2
#2473	2
#2468	2
#2466	2
#2464	2
#2461	2
#2455	2
#2449	2
#2440	2
#2432	2
#2407	2
#2406	2
#2388	2
#2374	2
#2361	2
D₄×C₄⋊C₄	2
#2322	2