Subgroups — #52321

Order 256.

910 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2841	C₂	1	1	yes	maximal, characteristic, complemented
2	#2841	C₂	1	1	yes	maximal, characteristic, complemented
3	#2832	C₂	1	1	yes	maximal, characteristic, complemented
4	#2831	C₂	1	1	yes	maximal, characteristic, complemented
5	#2831	C₂	1	1	yes	maximal, characteristic, complemented
6	#2830	C₂	1	1	yes	maximal, characteristic, complemented
7	#2820	C₂	1	1	yes	maximal, characteristic, complemented
8	#2814	C₂	1	1	yes	maximal, characteristic, complemented
9	#2806	C₂	1	1	yes	maximal, characteristic, complemented
10	#2788	C₂	1	1	yes	maximal, characteristic, complemented
11	#2755	C₂	1	1	yes	maximal, characteristic, complemented
12	#2704	C₂	1	1	yes	maximal, characteristic, complemented
13	#2700	C₂	1	1	yes	maximal, characteristic, complemented
14	#2692	C₂	1	1	yes	maximal, characteristic, complemented
15	#2686	C₂	1	1	yes	maximal, characteristic, complemented
16	#2672	C₂	1	1	yes	maximal, characteristic, complemented
17	#2623	C₂	1	1	yes	maximal, characteristic, complemented
18	#2618	C₂	1	1	yes	maximal, characteristic, complemented
19	#2488	C₂	1	1	yes	maximal, characteristic, complemented
20	#2473	C₂	1	1	yes	maximal, characteristic, complemented
21	#2450	C₂	1	1	yes	maximal, characteristic, complemented
22	#2444	C₂	1	1	yes	maximal, characteristic, complemented
23	#2443	C₂	1	1	yes	maximal, characteristic, complemented
24	#2436	C₂	1	1	yes	maximal, characteristic, complemented
25	#2425	C₂	1	1	yes	maximal, characteristic, complemented
26	#2425	C₂	1	1	yes	maximal, characteristic, complemented
27	#2419	C₂	1	1	yes	maximal, characteristic, complemented
28	#2417	C₂	1	1	yes	maximal, characteristic, complemented
29	#2416	C₂	1	1	yes	maximal, characteristic
30	#2409	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×#395	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂³×Q₈	C₂²	1	1	yes	characteristic
33	C₂×#125	C₂²	1	1	yes	characteristic
34	C₂×#124	C₂²	1	1	yes	characteristic
35	C₂×#124	C₂²	1	1	yes	characteristic
36	C₂×#123	C₂²	1	1	yes	characteristic
37	C₂×#123	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×#121	C₂²	1	1	yes	characteristic
45	C₂×#121	C₂²	1	1	yes	characteristic
46	C₂×#121	C₂²	1	1	yes	characteristic
47	C₂×#121	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	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic
52	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic
53	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic
54	#400	C₂²	1	1	yes	characteristic
55	#400	C₂²	1	1	yes	characteristic
56	#400	C₂²	1	1	yes	characteristic
57	#400	C₂²	1	1	yes	characteristic
58	#400	C₂²	1	1	yes	characteristic
59	#400	C₂²	1	1	yes	characteristic
60	#400	C₂²	1	1	yes	characteristic
61	#400	C₂²	1	1	yes	characteristic
62	#399	C₂²	1	1	yes	characteristic
63	#399	C₂²	1	1	yes	characteristic
64	#399	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	#398	C₂²	1	1	yes	characteristic
74	#398	C₂²	1	1	yes	characteristic
75	#398	C₂²	1	1	yes	characteristic
76	#398	C₂²	1	1	yes	characteristic
77	#398	C₂²	1	1	yes	characteristic
78	#398	C₂²	1	1	yes	characteristic
79	#397	C₂²	1	1	yes	characteristic
80	#397	C₂²	1	1	yes	characteristic
81	#397	C₂²	1	1	yes	characteristic
82	#397	C₂²	1	1	yes	characteristic
83	#397	C₂²	1	1	yes	characteristic
84	#397	C₂²	1	1	yes	characteristic
85	#397	C₂²	1	1	yes	characteristic
86	#397	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	#396	C₂²	1	1	yes	characteristic
93	#396	C₂²	1	1	yes	characteristic
94	#396	C₂²	1	1	yes	characteristic
95	#396	C₂²	1	1	yes	characteristic
96	#396	C₂²	1	1	yes	characteristic
97	#396	C₂²	1	1	yes	characteristic
98	#396	C₂²	1	1	yes	characteristic
99	#396	C₂²	1	1	yes	characteristic
100	#395	C₂²	1	1	yes	characteristic
101	#395	C₂²	1	1	yes	characteristic
102	#395	C₂²	1	1	yes	characteristic
103	#395	C₂²	1	1	yes	characteristic
104	#395	C₂²	1	1	yes	characteristic
105	#395	C₂²	1	1	yes	characteristic
106	#395	C₂²	1	1	yes	characteristic
107	#395	C₂²	1	1	yes	characteristic
108	#395	C₂²	1	1	yes	characteristic
109	#395	C₂²	1	1	yes	characteristic
110	#394	C₂²	1	1	yes	characteristic
111	#394	C₂²	1	1	yes	characteristic
112	#394	C₂²	1	1	yes	characteristic
113	#394	C₂²	1	1	yes	characteristic
114	#394	C₂²	1	1	yes	characteristic
115	#394	C₂²	1	1	yes	characteristic
116	#394	C₂²	1	1	yes	characteristic
117	#394	C₂²	1	1	yes	characteristic
118	#393	C₂²	1	1	yes	characteristic
119	#393	C₂²	1	1	yes	characteristic
120	#393	C₂²	1	1	yes	characteristic
121	#393	C₂²	1	1	yes	characteristic
122	#393	C₂²	1	1	yes	characteristic
123	#393	C₂²	1	1	yes	characteristic
124	#393	C₂²	1	1	yes	characteristic
125	#393	C₂²	1	1	yes	characteristic
126	#391	C₂²	1	1	yes	characteristic
127	#391	C₂²	1	1	yes	characteristic
128	#391	C₂²	1	1	yes	characteristic
129	#391	C₂²	1	1	yes	characteristic
130	#391	C₂²	1	1	yes	characteristic
131	#391	C₂²	1	1	yes	characteristic
132	#391	C₂²	1	1	yes	characteristic
133	#390	C₂²	1	1	yes	characteristic
134	#389	C₂²	1	1	yes	characteristic
135	#389	C₂²	1	1	yes	characteristic
136	#389	C₂²	1	1	yes	characteristic
137	#389	C₂²	1	1	yes	characteristic
138	#389	C₂²	1	1	yes	characteristic
139	#388	C₂²	1	1	yes	characteristic
140	#388	C₂²	1	1	yes	characteristic
141	#388	C₂²	1	1	yes	characteristic
142	#388	C₂²	1	1	yes	characteristic
143	#388	C₂²	1	1	yes	characteristic
144	#388	C₂²	1	1	yes	characteristic
145	#387	C₂²	1	1	yes	characteristic
146	#387	C₂²	1	1	yes	characteristic
147	#387	C₂²	1	1	yes	characteristic
148	#387	C₂²	1	1	yes	characteristic
149	#387	C₂²	1	1	yes	characteristic
150	#387	C₂²	1	1	yes	characteristic
151	#387	C₂²	1	1	yes	characteristic
152	#386	C₂²	1	1	yes	characteristic
153	#386	C₂²	1	1	yes	characteristic
154	#386	C₂²	1	1	yes	characteristic
155	#386	C₂²	1	1	yes	characteristic
156	#386	C₂²	1	1	yes	characteristic
157	#386	C₂²	1	1	yes	characteristic
158	#386	C₂²	1	1	yes	characteristic
159	#386	C₂²	1	1	yes	characteristic
160	#386	C₂²	1	1	yes	characteristic
161	#386	C₂²	1	1	yes	characteristic
162	#386	C₂²	1	1	yes	characteristic
163	#386	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	#382	C₂²	1	1	yes	characteristic
173	#381	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	#380	C₂²	1	1	yes	characteristic
181	#380	C₂²	1	1	yes	characteristic
182	#380	C₂²	1	1	yes	characteristic
183	C₄×C₂²⋊C₄	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	C₂²×Q₈	—	4	2	no	—
188	C₂²×Q₈	—	4	2	no	—
189	C₂²×Q₈	—	4	2	no	—
190	C₂²×Q₈	C₂³	1	1	yes	characteristic
191	C₂²×Q₈	C₂³	1	1	yes	characteristic
192	C₂²×Q₈	C₂³	1	1	yes	characteristic
193	C₂²×Q₈	C₂³	1	1	yes	characteristic
194	C₂²×Q₈	C₂³	1	1	yes	characteristic
195	C₂²×D₄	C₂³	1	1	yes	characteristic
196	C₂²×D₄	C₂³	1	1	yes	characteristic
197	C₂²×D₄	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	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	C₂³×C₄	C₂³	1	1	yes	characteristic
211	#125	—	4	2	no	—
212	#124	—	4	2	no	—
213	#124	—	4	2	no	—
214	#123	—	4	2	no	—
215	#123	—	4	2	no	—
216	#123	—	4	2	no	—
217	#123	—	4	2	no	—
218	C₂²⋊Q₈	—	4	2	no	—
219	C₂²⋊Q₈	—	4	2	no	—
220	C₂²⋊Q₈	—	4	2	no	—
221	C₂²⋊Q₈	—	4	2	no	—
222	#121	—	4	2	no	—
223	#121	—	4	2	no	—
224	#121	—	4	2	no	—
225	#121	—	4	2	no	—
226	C₄×D₄	—	4	2	no	—
227	C₄×D₄	—	4	2	no	—
228	C₄×D₄	—	4	2	no	—
229	C₂×C₄⋊C₄	—	4	2	no	—
230	C₂×C₄⋊C₄	—	4	2	no	—
231	C₂×C₄⋊C₄	—	4	2	no	—
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×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×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×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×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	#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	#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	C₂⁴	C₂⁴	1	1	yes	characteristic
367	C₂⁴	C₂⁴	1	1	yes	characteristic
368	C₂⁴	C₂⁴	1	1	yes	characteristic
369	C₂⁴	C₂⁴	1	1	yes	characteristic
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	2	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×Q₈	—	4	1	no	—
384	C₂×Q₈	—	4	1	no	—
385	C₂×Q₈	—	4	16	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	4	1	no	—
398	C₂×D₄	—	4	1	no	—
399	C₂×D₄	—	4	1	no	—
400	C₂×D₄	—	4	1	no	—
401	C₂×D₄	—	4	1	no	—
402	C₂×D₄	—	4	1	no	—
403	C₂×D₄	—	4	1	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	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	—	4	1	no	—
434	C₂²×C₄	C₂⁴	1	1	yes	characteristic
435	C₂²×C₄	C₂⁴	1	1	yes	characteristic
436	C₂²×C₄	C₂⁴	1	1	yes	characteristic
437	C₂²×C₄	C₂⁴	1	1	yes	characteristic
438	C₂²×C₄	C₂⁴	1	1	yes	characteristic
439	C₂²×C₄	C₂⁴	1	1	yes	characteristic
440	C₂²×C₄	C₂⁴	1	1	yes	characteristic
441	C₂²×C₄	C₂⁴	1	1	yes	characteristic
442	C₂²×C₄	C₂⁴	1	1	yes	characteristic
443	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	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	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	C₄⋊C₄	—	4	1	no	—
481	C₄⋊C₄	—	4	1	no	—
482	C₄⋊C₄	—	4	1	no	—
483	C₄⋊C₄	—	4	1	no	—
484	C₄⋊C₄	—	4	1	no	—
485	C₄⋊C₄	—	4	1	no	—
486	C₄⋊C₄	—	4	1	no	—
487	C₄⋊C₄	—	4	1	no	—
488	C₄⋊C₄	—	4	1	no	—
489	C₄⋊C₄	—	4	1	no	—
490	C₄⋊C₄	—	4	1	no	—
491	C₄⋊C₄	—	4	1	no	—
492	C₄⋊C₄	—	4	1	no	—
493	C₄⋊C₄	—	4	1	no	—
494	C₄⋊C₄	—	4	1	no	—
495	C₄⋊C₄	—	4	1	no	—
496	C₄⋊C₄	—	4	1	no	—
497	C₄⋊C₄	—	4	1	no	—
498	C₄⋊C₄	—	4	1	no	—
499	C₄⋊C₄	—	4	1	no	—
500	C₄⋊C₄	—	4	1	no	—
501	C₄⋊C₄	—	4	1	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	2	2	no	—
512	C₂²⋊C₄	—	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	C₂²⋊C₄	—	4	1	no	—
525	C₂²⋊C₄	—	4	1	no	—
526	C₂²⋊C₄	—	4	1	no	—
527	C₂²⋊C₄	—	4	1	no	—
528	C₂²⋊C₄	—	4	1	no	—
529	C₂²⋊C₄	—	4	1	no	—
530	C₂²⋊C₄	—	4	1	no	—
531	C₂²⋊C₄	—	4	1	no	—
532	C₂²⋊C₄	—	4	1	no	—
533	C₂²⋊C₄	—	4	1	no	—
534	C₂²⋊C₄	—	4	1	no	—
535	C₂²⋊C₄	—	4	1	no	—
536	C₂²⋊C₄	—	4	1	no	—
537	C₂²⋊C₄	—	4	1	no	—
538	C₂²⋊C₄	—	4	1	no	—
539	C₂²⋊C₄	—	4	1	no	—
540	C₄²	—	2	2	no	—
541	C₄²	—	4	1	no	—
542	C₄²	—	4	1	no	—
543	C₄²	—	4	1	no	—
544	C₄²	—	4	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	—	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	H(5,𝔽₂)	1	2	yes	—
571	C₂³	H(5,𝔽₂)	1	2	yes	—
572	C₂³	2₋¹⁺⁴	1	2	yes	—
573	C₂³	C₂⁵	1	1	yes	characteristic
574	Q₈	—	4	4	no	—
575	Q₈	—	4	4	no	—
576	Q₈	—	4	4	no	—
577	Q₈	—	4	4	no	—
578	Q₈	—	8	2	no	—
579	D₄	—	4	4	no	—
580	D₄	—	4	4	no	—
581	D₄	—	4	4	no	—
582	D₄	—	8	2	no	—
583	D₄	—	8	2	no	—
584	D₄	—	8	2	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	—	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	—	4	4	no	—
663	C₂×C₄	—	4	4	no	—
664	C₂×C₄	—	4	4	no	—
665	C₂×C₄	—	4	4	no	—
666	C₂×C₄	—	4	4	no	—
667	C₂×C₄	—	4	4	no	—
668	C₂×C₄	—	8	2	no	—
669	C₂×C₄	—	8	2	no	—
670	C₂×C₄	—	8	2	no	—
671	C₂×C₄	—	8	2	no	—
672	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
673	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
674	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
675	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	2	2	no	—
680	C₂²	—	2	2	no	—
681	C₂²	—	2	2	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	—	4	1	no	—
692	C₂²	—	4	1	no	—
693	C₂²	—	4	1	no	—
694	C₂²	—	4	1	no	—
695	C₂²	—	4	1	no	—
696	C₂²	—	4	1	no	—
697	C₂²	—	4	1	no	—
698	C₂²	—	4	1	no	—
699	C₂²	—	4	1	no	—
700	C₂²	—	4	1	no	—
701	C₂²	—	4	1	no	—
702	C₂²	—	4	1	no	—
703	C₂²	#562	1	4	yes	—
704	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
705	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
706	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
707	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
708	C₂²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
709	C₂²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
710	C₂²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
711	C₄	—	2	2	no	—
712	C₄	—	2	2	no	—
713	C₄	—	2	2	no	—
714	C₄	—	2	2	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	C₄	—	4	1	no	—
726	C₄	—	4	1	no	—
727	C₄	—	4	1	no	—
728	C₄	—	4	1	no	—
729	C₄	—	4	1	no	—
730	C₄	—	4	1	no	—
731	C₄	—	4	1	no	—
732	C₄	—	4	1	no	—
733	C₄	—	4	1	no	—
734	C₄	—	4	1	no	—
735	C₄	—	4	1	no	—
736	C₄	—	4	1	no	—
737	C₄	—	4	1	no	—
738	C₂	—	2	4	no	—
739	C₂	—	8	1	no	—
740	C₂	—	8	1	no	—
741	C₂	—	8	1	no	—
742	C₂	C₂×#562	1	1	yes	characteristic
743	C₂	#3532	1	1	yes	characteristic
744	C₂	#3536	1	1	yes	characteristic
745	C₂	#3536	1	1	yes	characteristic
746	C₂	#3544	1	1	yes	characteristic
747	C₂	#3552	1	1	yes	characteristic
748	C₂	#3552	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂³	C₂⁵
prime radical	#2416	C₂
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. #2841	C₂	semidirect
2. #2841	C₂	semidirect
3. #2832	C₂	semidirect
4. #2831	C₂	semidirect
5. #2831	C₂	semidirect
6. #2830	C₂	semidirect
7. #2820	C₂	semidirect
8. #2814	C₂	semidirect
9. #2806	C₂	semidirect
10. #2788	C₂	semidirect
11. #2755	C₂	semidirect
12. #2704	C₂	semidirect
13. #2700	C₂	semidirect
14. #2692	C₂	semidirect
15. #2686	C₂	semidirect
16. #2672	C₂	semidirect
17. #2623	C₂	semidirect
18. #2618	C₂	semidirect
19. #2488	C₂	semidirect
20. #2473	C₂	semidirect
21. #2450	C₂	semidirect
22. #2444	C₂	semidirect
23. #2443	C₂	semidirect
24. #2436	C₂	semidirect
25. #2425	C₂	semidirect
26. #2425	C₂	semidirect
27. #2419	C₂	semidirect
28. #2417	C₂	semidirect
30. #2409	C₂	semidirect
31. C₂×#395	C₂	semidirect

Maximal subgroups

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

subgroup	index
#2841	2
#2832	2
#2831	2
#2830	2
#2820	2
#2814	2
#2806	2
#2788	2
#2755	2
#2704	2
#2700	2
#2692	2
#2686	2
#2672	2
#2623	2
#2618	2
#2488	2
#2473	2
#2450	2
#2444	2
#2443	2
#2436	2
#2425	2
#2419	2
#2417	2
#2416	2
#2409	2
C₂×#395	2