Subgroups — #53166

Order 256.

888 conjugacy classes of subgroups.

The subgroup lattice has 737 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2849	C₂	1	1	yes	maximal, characteristic
2	#2848	C₂	1	1	yes	maximal, characteristic, complemented
3	#2848	C₂	1	1	yes	maximal, characteristic, complemented
4	#2807	C₂	1	1	yes	maximal, characteristic, complemented
5	#2796	C₂	1	1	yes	maximal, characteristic, complemented
6	#2788	C₂	1	1	yes	maximal, characteristic, complemented
7	#2787	C₂	1	1	yes	maximal, characteristic, complemented
8	#2781	C₂	1	1	yes	maximal, characteristic, complemented
9	#2763	C₂	1	1	yes	maximal, characteristic, complemented
10	#2750	C₂	1	1	yes	maximal, characteristic, complemented
11	#2747	C₂	1	1	yes	maximal, characteristic, complemented
12	#2746	C₂	1	1	yes	maximal, characteristic, complemented
13	#2745	C₂	1	1	yes	maximal, characteristic, complemented
14	#2744	C₂	1	1	yes	maximal, characteristic, complemented
15	#2736	C₂	1	1	yes	maximal, characteristic, complemented
16	#2735	C₂	1	1	yes	maximal, characteristic, complemented
17	#2729	C₂	1	1	yes	maximal, characteristic, complemented
18	#2729	C₂	1	1	yes	maximal, characteristic, complemented
19	#2723	C₂	1	1	yes	maximal, characteristic, complemented
20	#2702	C₂	1	1	yes	maximal, characteristic, complemented
21	#2698	C₂	1	1	yes	maximal, characteristic, complemented
22	#2695	C₂	1	1	yes	maximal, characteristic, complemented
23	#2692	C₂	1	1	yes	maximal, characteristic, complemented
24	#2692	C₂	1	1	yes	maximal, characteristic, complemented
25	#2689	C₂	1	1	yes	maximal, characteristic, complemented
26	#2687	C₂	1	1	yes	maximal, characteristic, complemented
27	#2685	C₂	1	1	yes	maximal, characteristic
28	#2684	C₂	1	1	yes	maximal, characteristic
29	#2677	C₂	1	1	yes	maximal, characteristic, complemented
30	#2674	C₂	1	1	yes	maximal, characteristic, complemented
31	#2674	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂⁴×C₄	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₂×#126	C₂²	1	1	yes	characteristic
36	C₂×#126	C₂²	1	1	yes	characteristic, complemented
37	C₂×#124	C₂²	1	1	yes	characteristic
38	C₂×#123	C₂²	1	1	yes	characteristic
39	C₂×#123	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
42	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
43	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
44	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
47	C₂×#120	C₂²	1	1	yes	characteristic
48	#401	C₂²	1	1	yes	characteristic, complemented
49	#400	C₂²	1	1	yes	characteristic, complemented
50	#400	C₂²	1	1	yes	characteristic, complemented
51	#400	C₂²	1	1	yes	characteristic, complemented
52	#400	C₂²	1	1	yes	characteristic, complemented
53	#400	C₂²	1	1	yes	characteristic, complemented
54	#400	C₂²	1	1	yes	characteristic, complemented
55	#400	C₂²	1	1	yes	characteristic, complemented
56	#400	C₂²	1	1	yes	characteristic, complemented
57	#400	C₂²	1	1	yes	characteristic, complemented
58	#399	C₂²	1	1	yes	characteristic
59	#399	C₂²	1	1	yes	characteristic
60	#399	C₂²	1	1	yes	characteristic, complemented
61	#399	C₂²	1	1	yes	characteristic, complemented
62	#398	C₂²	1	1	yes	characteristic, complemented
63	#398	C₂²	1	1	yes	characteristic, complemented
64	#398	C₂²	1	1	yes	characteristic, complemented
65	#398	C₂²	1	1	yes	characteristic, complemented
66	#398	C₂²	1	1	yes	characteristic, complemented
67	#398	C₂²	1	1	yes	characteristic, complemented
68	#398	C₂²	1	1	yes	characteristic, complemented
69	#398	C₂²	1	1	yes	characteristic, complemented
70	#398	C₂²	1	1	yes	characteristic, complemented
71	#397	C₂²	1	1	yes	characteristic
72	#397	C₂²	1	1	yes	characteristic
73	#397	C₂²	1	1	yes	characteristic
74	#397	C₂²	1	1	yes	characteristic
75	#397	C₂²	1	1	yes	characteristic
76	#397	C₂²	1	1	yes	characteristic
77	#397	C₂²	1	1	yes	characteristic
78	#397	C₂²	1	1	yes	characteristic
79	#397	C₂²	1	1	yes	characteristic, complemented
80	#397	C₂²	1	1	yes	characteristic, complemented
81	#396	C₂²	1	1	yes	characteristic
82	#396	C₂²	1	1	yes	characteristic
83	#396	C₂²	1	1	yes	characteristic
84	#396	C₂²	1	1	yes	characteristic, complemented
85	#396	C₂²	1	1	yes	characteristic, complemented
86	#395	C₂²	1	1	yes	characteristic, complemented
87	#395	C₂²	1	1	yes	characteristic, complemented
88	#395	C₂²	1	1	yes	characteristic, complemented
89	#395	C₂²	1	1	yes	characteristic, complemented
90	#395	C₂²	1	1	yes	characteristic, complemented
91	#394	C₂²	1	1	yes	characteristic
92	#394	C₂²	1	1	yes	characteristic
93	#394	C₂²	1	1	yes	characteristic
94	#394	C₂²	1	1	yes	characteristic
95	#394	C₂²	1	1	yes	characteristic
96	#394	C₂²	1	1	yes	characteristic
97	#393	C₂²	1	1	yes	characteristic
98	#393	C₂²	1	1	yes	characteristic
99	#393	C₂²	1	1	yes	characteristic
100	#393	C₂²	1	1	yes	characteristic
101	#393	C₂²	1	1	yes	characteristic
102	#393	C₂²	1	1	yes	characteristic, complemented
103	#393	C₂²	1	1	yes	characteristic, complemented
104	#391	C₂²	1	1	yes	characteristic, complemented
105	#391	C₂²	1	1	yes	characteristic, complemented
106	#391	C₂²	1	1	yes	characteristic, complemented
107	#391	C₂²	1	1	yes	characteristic, complemented
108	#390	C₂²	1	1	yes	characteristic
109	#390	C₂²	1	1	yes	characteristic
110	#389	C₂²	1	1	yes	characteristic, complemented
111	#389	C₂²	1	1	yes	characteristic, complemented
112	#389	C₂²	1	1	yes	characteristic, complemented
113	#389	C₂²	1	1	yes	characteristic, complemented
114	#389	C₂²	1	1	yes	characteristic, complemented
115	#389	C₂²	1	1	yes	characteristic, complemented
116	#388	C₂²	1	1	yes	characteristic
117	#388	C₂²	1	1	yes	characteristic
118	#388	C₂²	1	1	yes	characteristic
119	#388	C₂²	1	1	yes	characteristic
120	#388	C₂²	1	1	yes	characteristic
121	#388	C₂²	1	1	yes	characteristic
122	#388	C₂²	1	1	yes	characteristic
123	#388	C₂²	1	1	yes	characteristic
124	#388	C₂²	1	1	yes	characteristic
125	#388	C₂²	1	1	yes	characteristic
126	#388	C₂²	1	1	yes	characteristic
127	#388	C₂²	1	1	yes	characteristic
128	#388	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, complemented
134	#388	C₂²	1	1	yes	characteristic, complemented
135	#388	C₂²	1	1	yes	characteristic, complemented
136	#387	C₂²	1	1	yes	characteristic, complemented
137	#387	C₂²	1	1	yes	characteristic, complemented
138	#387	C₂²	1	1	yes	characteristic, complemented
139	#387	C₂²	1	1	yes	characteristic, complemented
140	#387	C₂²	1	1	yes	characteristic, complemented
141	#387	C₂²	1	1	yes	characteristic, complemented
142	#387	C₂²	1	1	yes	characteristic, complemented
143	#387	C₂²	1	1	yes	characteristic, complemented
144	#387	C₂²	1	1	yes	characteristic, complemented
145	#387	C₂²	1	1	yes	characteristic, complemented
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, complemented
170	#382	C₂²	1	1	yes	characteristic, complemented
171	#382	C₂²	1	1	yes	characteristic, complemented
172	#381	C₂²	1	1	yes	characteristic
173	#381	C₂²	1	1	yes	characteristic
174	#381	C₂²	1	1	yes	characteristic, complemented
175	#380	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	#380	C₂²	1	1	yes	characteristic
181	#380	C₂²	1	1	yes	characteristic, complemented
182	#379	C₂²	1	1	yes	characteristic
183	#379	C₂²	1	1	yes	characteristic
184	#379	C₂²	1	1	yes	characteristic
185	#379	C₂²	1	1	yes	characteristic
186	#379	C₂²	1	1	yes	characteristic
187	C₂⁵	C₂³	1	1	yes	characteristic
188	C₂²×Q₈	C₂³	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×D₄	C₂³	1	1	yes	characteristic
193	C₂²×D₄	C₂³	1	1	yes	characteristic
194	C₂²×D₄	C₂³	1	1	yes	characteristic
195	C₂³×C₄	—	4	2	no	—
196	C₂³×C₄	—	4	2	no	—
197	C₂³×C₄	—	4	2	no	—
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	C₄⋊Q₈	—	4	2	no	—
206	C₄⋊Q₈	—	4	2	no	—
207	#126	—	4	2	no	—
208	#126	—	4	2	no	—
209	#124	—	4	2	no	—
210	#123	—	4	2	no	—
211	#123	—	4	2	no	—
212	C₂²⋊Q₈	—	4	2	no	—
213	C₂²⋊Q₈	—	4	2	no	—
214	C₂²⋊Q₈	—	4	2	no	—
215	C₂²⋊Q₈	—	4	2	no	—
216	C₂²⋊Q₈	—	4	2	no	—
217	C₂²⋊Q₈	—	4	2	no	—
218	C₂²⋊Q₈	—	4	2	no	—
219	#120	—	4	2	no	—
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×C₄⋊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×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×C₂²⋊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×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	#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	#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	C₂⁴	—	2	2	no	—
361	C₂⁴	—	2	2	no	—
362	C₂⁴	—	2	2	no	—
363	C₂⁴	—	4	1	no	—
364	C₂⁴	—	4	1	no	—
365	C₂⁴	—	4	1	no	—
366	C₂⁴	—	4	1	no	—
367	C₂⁴	C₂⁴	1	1	yes	characteristic
368	C₂⁴	C₂⁴	1	1	yes	characteristic
369	C₂⁴	C₂⁴	1	1	yes	characteristic
370	C₂⁴	C₂⁴	1	1	yes	characteristic
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	4	1	no	—
374	C₂×Q₈	—	4	1	no	—
375	C₂×Q₈	—	4	1	no	—
376	C₂×Q₈	—	4	1	no	—
377	C₂×Q₈	—	4	1	no	—
378	C₂×Q₈	—	4	1	no	—
379	C₂×Q₈	—	4	1	no	—
380	C₂×Q₈	—	4	1	no	—
381	C₂×Q₈	—	4	1	no	—
382	C₂×Q₈	—	4	1	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	4	1	no	—
387	C₂×D₄	—	4	1	no	—
388	C₂×D₄	—	4	1	no	—
389	C₂×D₄	—	4	1	no	—
390	C₂×D₄	—	4	1	no	—
391	C₂×D₄	—	4	1	no	—
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	—	4	1	no	—
401	C₂²×C₄	—	4	1	no	—
402	C₂²×C₄	—	4	1	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	16	no	—
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	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	2	no	—
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	—	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	—	4	1	no	—
465	C₄⋊C₄	—	4	1	no	—
466	C₄⋊C₄	—	4	1	no	—
467	C₄⋊C₄	—	4	1	no	—
468	C₄⋊C₄	—	4	1	no	—
469	C₄⋊C₄	—	4	1	no	—
470	C₄⋊C₄	—	4	1	no	—
471	C₄⋊C₄	—	4	1	no	—
472	C₄⋊C₄	—	4	1	no	—
473	C₄⋊C₄	—	4	1	no	—
474	C₄⋊C₄	—	4	1	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	C₂²⋊C₄	—	2	2	no	—
481	C₂²⋊C₄	—	2	2	no	—
482	C₂²⋊C₄	—	2	2	no	—
483	C₂²⋊C₄	—	2	2	no	—
484	C₂²⋊C₄	—	2	2	no	—
485	C₂²⋊C₄	—	2	2	no	—
486	C₂²⋊C₄	—	2	2	no	—
487	C₂²⋊C₄	—	2	2	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	4	1	no	—
494	C₂²⋊C₄	—	4	1	no	—
495	C₂²⋊C₄	—	4	1	no	—
496	C₂²⋊C₄	—	4	1	no	—
497	C₂²⋊C₄	—	4	1	no	—
498	C₂²⋊C₄	—	4	1	no	—
499	C₂²⋊C₄	—	4	1	no	—
500	C₂²⋊C₄	—	4	1	no	—
501	C₂²⋊C₄	—	4	1	no	—
502	C₂²⋊C₄	—	4	1	no	—
503	C₂²⋊C₄	—	4	1	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	—	4	1	no	—
515	C₂²⋊C₄	—	4	1	no	—
516	C₂²⋊C₄	—	4	1	no	—
517	C₂²⋊C₄	—	4	1	no	—
518	C₂²⋊C₄	—	4	1	no	—
519	C₂²⋊C₄	—	4	1	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	C₄²	—	4	1	no	—
525	C₄²	—	4	1	no	—
526	C₄²	—	4	1	no	—
527	C₄²	—	4	1	no	—
528	C₄²	—	4	1	no	—
529	C₄²	—	4	1	no	—
530	C₄²	—	4	1	no	—
531	C₂³	—	2	1	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	2	1	no	—
534	C₂³	—	2	1	no	—
535	C₂³	—	2	1	no	—
536	C₂³	—	2	1	no	—
537	C₂³	—	2	1	no	—
538	C₂³	—	2	1	no	—
539	C₂³	—	2	1	no	—
540	C₂³	—	2	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	—	2	1	no	—
555	C₂³	—	2	1	no	—
556	C₂³	—	4	4	no	—
557	C₂³	—	4	4	no	—
558	C₂³	—	4	4	no	—
559	C₂³	—	4	4	no	—
560	C₂³	—	4	4	no	—
561	C₂³	—	4	4	no	—
562	C₂³	—	4	4	no	—
563	C₂³	H(5,𝔽₂)	1	2	yes	—
564	C₂³	2₋¹⁺⁴	1	2	yes	—
565	C₂³	2₋¹⁺⁴	1	2	yes	—
566	C₂³	C₂⁵	1	1	yes	characteristic
567	Q₈	—	8	2	no	—
568	Q₈	—	8	2	no	—
569	Q₈	—	8	2	no	—
570	Q₈	—	8	2	no	—
571	D₄	—	8	2	no	—
572	D₄	—	8	2	no	—
573	D₄	—	8	2	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	—	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	—	2	1	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	—	8	2	no	—
660	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
661	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	2	no	—
666	C₂²	—	2	2	no	—
667	C₂²	—	2	2	no	—
668	C₂²	—	2	2	no	—
669	C₂²	—	2	2	no	—
670	C₂²	—	2	2	no	—
671	C₂²	—	4	16	no	—
672	C₂²	—	4	1	no	—
673	C₂²	—	4	1	no	—
674	C₂²	—	4	1	no	—
675	C₂²	—	4	1	no	—
676	C₂²	—	4	1	no	—
677	C₂²	—	4	1	no	—
678	C₂²	—	4	1	no	—
679	C₂²	—	4	1	no	—
680	C₂²	—	4	1	no	—
681	C₂²	—	4	1	no	—
682	C₂²	—	4	1	no	—
683	C₂²	—	4	1	no	—
684	C₂²	—	4	1	no	—
685	C₂²	—	4	1	no	—
686	C₂²	—	4	1	no	—
687	C₂²	—	4	1	no	—
688	C₂²	—	4	1	no	—
689	C₂²	—	4	1	no	—
690	C₂²	—	4	1	no	—
691	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
692	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
693	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
694	C₂²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
695	C₂²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
696	C₂²	#585	1	1	yes	characteristic
697	C₂²	#585	1	1	yes	characteristic
698	C₄	—	2	2	no	—
699	C₄	—	2	2	no	—
700	C₄	—	4	1	no	—
701	C₄	—	4	1	no	—
702	C₄	—	4	1	no	—
703	C₄	—	4	1	no	—
704	C₄	—	4	1	no	—
705	C₄	—	4	1	no	—
706	C₄	—	4	1	no	—
707	C₄	—	4	1	no	—
708	C₄	—	4	1	no	—
709	C₄	—	4	1	no	—
710	C₄	—	4	1	no	—
711	C₄	—	4	1	no	—
712	C₄	—	4	1	no	—
713	C₄	—	4	1	no	—
714	C₄	—	4	1	no	—
715	C₄	—	4	1	no	—
716	C₄	—	4	1	no	—
717	C₄	—	4	1	no	—
718	C₄	—	4	1	no	—
719	C₄	—	4	1	no	—
720	C₄	—	4	1	no	—
721	C₄	—	4	1	no	—
722	C₄	—	4	1	no	—
723	C₄	—	4	1	no	—
724	C₄	—	4	1	no	—
725	C₂	—	4	2	no	—
726	C₂	—	4	2	no	—
727	C₂	—	4	2	no	—
728	C₂	—	8	1	no	—
729	C₂	#3532	1	1	yes	characteristic
730	C₂	#3535	1	1	yes	characteristic
731	C₂	#3535	1	1	yes	characteristic
732	C₂	#3538	1	1	yes	characteristic
733	C₂	#3540	1	1	yes	characteristic
734	C₂	#3541	1	1	yes	characteristic
735	C₂	#3541	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂³	C₂⁵
prime radical	C₂×#120	C₂²
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. #2848	C₂	semidirect
3. #2848	C₂	semidirect
4. #2807	C₂	semidirect
5. #2796	C₂	semidirect
6. #2788	C₂	semidirect
7. #2787	C₂	semidirect
8. #2781	C₂	semidirect
9. #2763	C₂	semidirect
10. #2750	C₂	semidirect
11. #2747	C₂	semidirect
12. #2746	C₂	semidirect
13. #2745	C₂	semidirect
14. #2744	C₂	semidirect
15. #2736	C₂	semidirect
16. #2735	C₂	semidirect
17. #2729	C₂	semidirect
18. #2729	C₂	semidirect
19. #2723	C₂	semidirect
20. #2702	C₂	semidirect
21. #2698	C₂	semidirect
22. #2695	C₂	semidirect
23. #2692	C₂	semidirect
24. #2692	C₂	semidirect
25. #2689	C₂	semidirect
26. #2687	C₂	semidirect
29. #2677	C₂	semidirect
30. #2674	C₂	semidirect
31. #2674	C₂	semidirect
33. C₂×C₄⋊Q₈	C₂²	semidirect
34. C₂×C₄⋊Q₈	C₂²	semidirect
36. C₂×#126	C₂²	semidirect
46. C₂×C₂²⋊Q₈	C₂²	semidirect
48. #401	C₂²	semidirect
49. #400	C₂²	semidirect
50. #400	C₂²	semidirect
51. #400	C₂²	semidirect
52. #400	C₂²	semidirect
53. #400	C₂²	semidirect
54. #400	C₂²	semidirect
55. #400	C₂²	semidirect
56. #400	C₂²	semidirect
57. #400	C₂²	semidirect
60. #399	C₂²	semidirect
61. #399	C₂²	semidirect
62. #398	C₂²	semidirect
63. #398	C₂²	semidirect
64. #398	C₂²	semidirect
65. #398	C₂²	semidirect
66. #398	C₂²	semidirect
67. #398	C₂²	semidirect
68. #398	C₂²	semidirect
69. #398	C₂²	semidirect
70. #398	C₂²	semidirect
79. #397	C₂²	semidirect
80. #397	C₂²	semidirect
84. #396	C₂²	semidirect
85. #396	C₂²	semidirect
86. #395	C₂²	semidirect
87. #395	C₂²	semidirect
88. #395	C₂²	semidirect
89. #395	C₂²	semidirect
90. #395	C₂²	semidirect
102. #393	C₂²	semidirect
103. #393	C₂²	semidirect
104. #391	C₂²	semidirect
105. #391	C₂²	semidirect
106. #391	C₂²	semidirect
107. #391	C₂²	semidirect
110. #389	C₂²	semidirect
111. #389	C₂²	semidirect
112. #389	C₂²	semidirect
113. #389	C₂²	semidirect
114. #389	C₂²	semidirect
115. #389	C₂²	semidirect
133. #388	C₂²	semidirect
134. #388	C₂²	semidirect
135. #388	C₂²	semidirect
136. #387	C₂²	semidirect
137. #387	C₂²	semidirect
138. #387	C₂²	semidirect
139. #387	C₂²	semidirect
140. #387	C₂²	semidirect
141. #387	C₂²	semidirect
142. #387	C₂²	semidirect
143. #387	C₂²	semidirect
144. #387	C₂²	semidirect
145. #387	C₂²	semidirect
169. #385	C₂²	semidirect
170. #382	C₂²	semidirect
171. #382	C₂²	semidirect
174. #381	C₂²	semidirect
181. #380	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#2849	2
#2848	2
#2807	2
#2796	2
#2788	2
#2787	2
#2781	2
#2763	2
#2750	2
#2747	2
#2746	2
#2745	2
#2744	2
#2736	2
#2735	2
#2729	2
#2723	2
#2702	2
#2698	2
#2695	2
#2692	2
#2689	2
#2687	2
#2685	2
#2684	2
#2677	2
#2674	2