Subgroups — #38549

Order 256.

924 conjugacy classes of subgroups.

The subgroup lattice has 759 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2853	C₂	1	1	yes	maximal, characteristic, complemented
2	#2797	C₂	1	1	yes	maximal, characteristic, complemented
3	#2786	C₂	1	1	yes	maximal, characteristic, complemented
4	#2782	C₂	1	1	yes	maximal, characteristic, complemented
5	#2772	C₂	1	1	yes	maximal, characteristic, complemented
6	#2742	C₂	1	1	yes	maximal, characteristic, complemented
7	#2691	C₂	1	1	yes	maximal, characteristic, complemented
8	#2685	C₂	1	1	yes	maximal, characteristic, complemented
9	#2684	C₂	1	1	yes	maximal, characteristic, complemented
10	#2654	C₂	1	1	yes	maximal, characteristic, complemented
11	#2638	C₂	1	1	yes	maximal, characteristic, complemented
12	#2574	C₂	1	1	yes	maximal, characteristic, complemented
13	#2559	C₂	1	1	yes	maximal, characteristic, complemented
14	#2526	C₂	1	1	yes	maximal, characteristic, complemented
15	#2521	C₂	1	1	yes	maximal, characteristic, complemented
16	#2516	C₂	1	1	yes	maximal, characteristic, complemented
17	#2513	C₂	1	1	yes	maximal, characteristic, complemented
18	#2480	C₂	1	1	yes	maximal, characteristic, complemented
19	#2477	C₂	1	1	yes	maximal, characteristic, complemented
20	#2468	C₂	1	1	yes	maximal, characteristic, complemented
21	#2466	C₂	1	1	yes	maximal, characteristic, complemented
22	#2461	C₂	1	1	yes	maximal, characteristic, complemented
23	#2424	C₂	1	1	yes	maximal, characteristic
24	#2420	C₂	1	1	yes	maximal, characteristic, complemented
25	#2418	C₂	1	1	yes	maximal, characteristic, complemented
26	#2373	C₂	1	1	yes	maximal, characteristic, complemented
27	#2342	C₂	1	1	yes	maximal, characteristic, complemented
28	#2334	C₂	1	1	yes	maximal, characteristic, complemented
29	#2321	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×#121	C₂	1	1	yes	maximal, characteristic, complemented
31	#2290	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#126	C₂²	1	1	yes	characteristic
33	C₂×#126	C₂²	1	1	yes	characteristic
34	C₂×#126	C₂²	1	1	yes	characteristic, complemented
35	C₂×#124	C₂²	1	1	yes	characteristic
36	C₂×#123	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₂×#121	C₂²	1	1	yes	characteristic
39	C₂×#121	C₂²	1	1	yes	characteristic
40	C₂×#120	C₂²	1	1	yes	characteristic
41	C₂×#120	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, complemented
46	C₂×#117	C₂²	1	1	yes	characteristic
47	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
48	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
49	C₂²×C₄²	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	#399	C₂²	1	1	yes	characteristic
55	#399	C₂²	1	1	yes	characteristic
56	#398	C₂²	1	1	yes	characteristic, complemented
57	#398	C₂²	1	1	yes	characteristic, complemented
58	#398	C₂²	1	1	yes	characteristic, complemented
59	#397	C₂²	1	1	yes	characteristic
60	#397	C₂²	1	1	yes	characteristic
61	#397	C₂²	1	1	yes	characteristic
62	#397	C₂²	1	1	yes	characteristic
63	#397	C₂²	1	1	yes	characteristic
64	#397	C₂²	1	1	yes	characteristic
65	#397	C₂²	1	1	yes	characteristic, complemented
66	#397	C₂²	1	1	yes	characteristic, complemented
67	#397	C₂²	1	1	yes	characteristic, complemented
68	#397	C₂²	1	1	yes	characteristic, complemented
69	#397	C₂²	1	1	yes	characteristic, complemented
70	#396	C₂²	1	1	yes	characteristic
71	#396	C₂²	1	1	yes	characteristic
72	#396	C₂²	1	1	yes	characteristic
73	#396	C₂²	1	1	yes	characteristic, complemented
74	#395	C₂²	1	1	yes	characteristic, complemented
75	#395	C₂²	1	1	yes	characteristic, complemented
76	#394	C₂²	1	1	yes	characteristic
77	#394	C₂²	1	1	yes	characteristic
78	#394	C₂²	1	1	yes	characteristic
79	#394	C₂²	1	1	yes	characteristic
80	#394	C₂²	1	1	yes	characteristic
81	#394	C₂²	1	1	yes	characteristic
82	#394	C₂²	1	1	yes	characteristic
83	#394	C₂²	1	1	yes	characteristic
84	#394	C₂²	1	1	yes	characteristic
85	#394	C₂²	1	1	yes	characteristic
86	#394	C₂²	1	1	yes	characteristic, complemented
87	#393	C₂²	1	1	yes	characteristic
88	#393	C₂²	1	1	yes	characteristic
89	#392	C₂²	1	1	yes	characteristic
90	#391	C₂²	1	1	yes	characteristic, complemented
91	#390	C₂²	1	1	yes	characteristic
92	#390	C₂²	1	1	yes	characteristic
93	#390	C₂²	1	1	yes	characteristic
94	#390	C₂²	1	1	yes	characteristic
95	#390	C₂²	1	1	yes	characteristic
96	#390	C₂²	1	1	yes	characteristic, complemented
97	#389	C₂²	1	1	yes	characteristic, complemented
98	#389	C₂²	1	1	yes	characteristic, complemented
99	#389	C₂²	1	1	yes	characteristic, complemented
100	#389	C₂²	1	1	yes	characteristic, complemented
101	#389	C₂²	1	1	yes	characteristic, complemented
102	#388	C₂²	1	1	yes	characteristic
103	#388	C₂²	1	1	yes	characteristic
104	#388	C₂²	1	1	yes	characteristic
105	#388	C₂²	1	1	yes	characteristic
106	#388	C₂²	1	1	yes	characteristic
107	#388	C₂²	1	1	yes	characteristic
108	#388	C₂²	1	1	yes	characteristic
109	#388	C₂²	1	1	yes	characteristic
110	#388	C₂²	1	1	yes	characteristic
111	#388	C₂²	1	1	yes	characteristic
112	#388	C₂²	1	1	yes	characteristic
113	#388	C₂²	1	1	yes	characteristic
114	#388	C₂²	1	1	yes	characteristic
115	#388	C₂²	1	1	yes	characteristic
116	#388	C₂²	1	1	yes	characteristic
117	#388	C₂²	1	1	yes	characteristic
118	#388	C₂²	1	1	yes	characteristic
119	#388	C₂²	1	1	yes	characteristic
120	#388	C₂²	1	1	yes	characteristic
121	#388	C₂²	1	1	yes	characteristic, complemented
122	#388	C₂²	1	1	yes	characteristic, complemented
123	#388	C₂²	1	1	yes	characteristic, complemented
124	#388	C₂²	1	1	yes	characteristic, complemented
125	#388	C₂²	1	1	yes	characteristic, complemented
126	#388	C₂²	1	1	yes	characteristic, complemented
127	#387	C₂²	1	1	yes	characteristic, complemented
128	#387	C₂²	1	1	yes	characteristic, complemented
129	#387	C₂²	1	1	yes	characteristic, complemented
130	#387	C₂²	1	1	yes	characteristic, complemented
131	#387	C₂²	1	1	yes	characteristic, complemented
132	#387	C₂²	1	1	yes	characteristic, complemented
133	#387	C₂²	1	1	yes	characteristic, complemented
134	#387	C₂²	1	1	yes	characteristic, complemented
135	#387	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	#386	C₂²	1	1	yes	characteristic
141	#386	C₂²	1	1	yes	characteristic
142	#386	C₂²	1	1	yes	characteristic
143	#386	C₂²	1	1	yes	characteristic
144	#386	C₂²	1	1	yes	characteristic
145	#386	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, complemented
151	#385	C₂²	1	1	yes	characteristic
152	#385	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, complemented
159	#385	C₂²	1	1	yes	characteristic, complemented
160	#385	C₂²	1	1	yes	characteristic, complemented
161	#385	C₂²	1	1	yes	characteristic, complemented
162	#382	C₂²	1	1	yes	characteristic, complemented
163	#382	C₂²	1	1	yes	characteristic, complemented
164	#381	C₂²	1	1	yes	characteristic
165	#381	C₂²	1	1	yes	characteristic, complemented
166	#381	C₂²	1	1	yes	characteristic, complemented
167	#380	C₂²	1	1	yes	characteristic
168	#380	C₂²	1	1	yes	characteristic
169	#380	C₂²	1	1	yes	characteristic
170	#380	C₂²	1	1	yes	characteristic, complemented
171	#379	C₂²	1	1	yes	characteristic
172	#379	C₂²	1	1	yes	characteristic
173	#379	C₂²	1	1	yes	characteristic
174	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
175	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
176	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
177	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
178	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
179	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
180	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
181	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
182	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
183	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
184	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
185	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
186	#376	C₂²	1	1	yes	characteristic, complemented
187	C₂⁵	C₂³	1	1	yes	characteristic
188	C₂²×Q₈	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	C₂²×D₄	C₂³	1	1	yes	characteristic
195	C₂²×D₄	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	#126	—	2	4	no	—
205	#126	—	2	4	no	—
206	#126	—	4	2	no	—
207	#124	—	4	2	no	—
208	#123	—	4	2	no	—
209	C₂²⋊Q₈	—	4	2	no	—
210	#121	—	2	4	no	—
211	#121	—	4	2	no	—
212	#120	—	2	4	no	—
213	#120	—	4	2	no	—
214	C₄×D₄	—	2	4	no	—
215	C₄×D₄	—	4	2	no	—
216	C₄×D₄	—	4	2	no	—
217	C₄×D₄	—	4	2	no	—
218	#117	—	4	2	no	—
219	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
241	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
242	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
243	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
245	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
249	C₂×C₂²⋊C₄	—	2	4	no	—
250	C₂×C₂²⋊C₄	—	4	2	no	—
251	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
252	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
253	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
254	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
255	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
257	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
258	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
260	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
261	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
265	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
267	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
268	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
270	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
271	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
272	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
273	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
274	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
275	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
277	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
278	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
279	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
280	C₂×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×C₄²	—	4	2	no	—
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	#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	—	4	1	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	C₂⁴	C₂⁴	1	1	yes	characteristic
372	C₂×Q₈	—	4	1	no	—
373	C₂×Q₈	—	4	1	no	—
374	C₂×Q₈	—	4	1	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	—	2	2	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	2	2	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	C₂×D₄	—	4	1	no	—
393	C₂×D₄	—	4	1	no	—
394	C₂×D₄	—	4	1	no	—
395	C₂×D₄	—	4	1	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	—	2	2	no	—
404	C₂²×C₄	—	2	2	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	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	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	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	2	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	C₂²⋊C₄	—	2	2	no	—
477	C₂²⋊C₄	—	2	2	no	—
478	C₂²⋊C₄	—	2	2	no	—
479	C₂²⋊C₄	—	2	2	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	C₂²⋊C₄	#41	1	4	yes	—
525	C₂²⋊C₄	#41	1	4	yes	—
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	—	4	1	no	—
532	C₄²	—	4	1	no	—
533	C₄²	—	4	1	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	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	—	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	—	4	4	no	—
573	C₂³	—	4	4	no	—
574	C₂³	—	8	2	no	—
575	C₂³	—	8	2	no	—
576	C₂³	—	8	2	no	—
577	C₂³	—	8	2	no	—
578	C₂³	—	8	2	no	—
579	C₂³	C₂×#41	1	2	yes	—
580	C₂³	C₂×#41	1	2	yes	—
581	C₂³	H(5,𝔽₂)	1	2	yes	—
582	C₂³	C₂⁵	1	1	yes	characteristic
583	Q₈	—	8	2	no	—
584	D₄	—	4	4	no	—
585	D₄	—	4	4	no	—
586	D₄	—	4	4	no	—
587	D₄	—	4	4	no	—
588	D₄	—	8	2	no	—
589	D₄	—	8	2	no	—
590	D₄	—	8	2	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	—	2	1	no	—
663	C₂×C₄	—	2	1	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	C₂×#41	1	2	yes	—
673	C₂×C₄	C₂×#41	1	2	yes	—
674	C₂×C₄	C₂×#41	1	2	yes	—
675	C₂×C₄	C₂×#41	1	2	yes	—
676	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
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	—	2	2	no	—
683	C₂²	—	2	2	no	—
684	C₂²	—	2	2	no	—
685	C₂²	—	2	2	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	—	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	—	4	1	no	—
712	C₂²	—	8	8	no	—
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	C₂×H(5,𝔽₂)	1	1	yes	characteristic
717	C₂²	#585	1	1	yes	characteristic
718	C₂²	#585	1	1	yes	characteristic
719	C₂²	#585	1	1	yes	characteristic
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	—	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	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	—	4	2	no	—
747	C₂	—	4	2	no	—
748	C₂	—	4	2	no	—
749	C₂	—	8	1	no	—
750	C₂	—	8	1	no	—
751	C₂	#3455	1	1	yes	characteristic
752	C₂	#3481	1	1	yes	characteristic
753	C₂	#3494	1	1	yes	characteristic
754	C₂	#3513	1	1	yes	characteristic
755	C₂	#3521	1	1	yes	characteristic
756	C₂	#3534	1	1	yes	characteristic
757	C₂	#3540	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂³	C₂⁵
prime radical	#2424	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. #2853	C₂	semidirect
2. #2797	C₂	semidirect
3. #2786	C₂	semidirect
4. #2782	C₂	semidirect
5. #2772	C₂	semidirect
6. #2742	C₂	semidirect
7. #2691	C₂	semidirect
8. #2685	C₂	semidirect
9. #2684	C₂	semidirect
10. #2654	C₂	semidirect
11. #2638	C₂	semidirect
12. #2574	C₂	semidirect
13. #2559	C₂	semidirect
14. #2526	C₂	semidirect
15. #2521	C₂	semidirect
16. #2516	C₂	semidirect
17. #2513	C₂	semidirect
18. #2480	C₂	semidirect
19. #2477	C₂	semidirect
20. #2468	C₂	semidirect
21. #2466	C₂	semidirect
22. #2461	C₂	semidirect
24. #2420	C₂	semidirect
25. #2418	C₂	semidirect
26. #2373	C₂	semidirect
27. #2342	C₂	semidirect
28. #2334	C₂	semidirect
29. #2321	C₂	semidirect
30. C₄×#121	C₂	semidirect
31. #2290	C₂	semidirect
34. C₂×#126	C₂²	semidirect
37. C₂×C₂²⋊Q₈	C₂²	semidirect
45. C₂×C₄×D₄	C₂²	semidirect
49. C₂²×C₄²	C₂²	semidirect
50. #400	C₂²	semidirect
51. #400	C₂²	semidirect
52. #400	C₂²	semidirect
53. #400	C₂²	semidirect
56. #398	C₂²	semidirect
57. #398	C₂²	semidirect
58. #398	C₂²	semidirect
65. #397	C₂²	semidirect
66. #397	C₂²	semidirect
67. #397	C₂²	semidirect
68. #397	C₂²	semidirect
69. #397	C₂²	semidirect
73. #396	C₂²	semidirect
74. #395	C₂²	semidirect
75. #395	C₂²	semidirect
86. #394	C₂²	semidirect
90. #391	C₂²	semidirect
96. #390	C₂²	semidirect
97. #389	C₂²	semidirect
98. #389	C₂²	semidirect
99. #389	C₂²	semidirect
100. #389	C₂²	semidirect
101. #389	C₂²	semidirect
121. #388	C₂²	semidirect
122. #388	C₂²	semidirect
123. #388	C₂²	semidirect
124. #388	C₂²	semidirect
125. #388	C₂²	semidirect
126. #388	C₂²	semidirect
127. #387	C₂²	semidirect
128. #387	C₂²	semidirect
129. #387	C₂²	semidirect
130. #387	C₂²	semidirect
131. #387	C₂²	semidirect
132. #387	C₂²	semidirect
133. #387	C₂²	semidirect
134. #387	C₂²	semidirect
135. #387	C₂²	semidirect
136. #387	C₂²	semidirect
137. #387	C₂²	semidirect
138. #387	C₂²	semidirect
139. #387	C₂²	semidirect
150. #386	C₂²	semidirect
158. #385	C₂²	semidirect
159. #385	C₂²	semidirect
160. #385	C₂²	semidirect
161. #385	C₂²	semidirect
162. #382	C₂²	semidirect
163. #382	C₂²	semidirect
165. #381	C₂²	semidirect
166. #381	C₂²	semidirect
170. #380	C₂²	semidirect
174. C₄×C₄⋊C₄	C₂²	semidirect
175. C₄×C₄⋊C₄	C₂²	semidirect
176. C₄×C₄⋊C₄	C₂²	semidirect
177. C₄×C₄⋊C₄	C₂²	semidirect
178. C₄×C₄⋊C₄	C₂²	semidirect
184. C₄×C₂²⋊C₄	C₂²	semidirect
185. C₄×C₂²⋊C₄	C₂²	semidirect
186. #376	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#2853	2
#2797	2
#2786	2
#2782	2
#2772	2
#2742	2
#2691	2
#2685	2
#2684	2
#2654	2
#2638	2
#2574	2
#2559	2
#2526	2
#2521	2
#2516	2
#2513	2
#2480	2
#2477	2
#2468	2
#2466	2
#2461	2
#2424	2
#2420	2
#2418	2
#2373	2
#2342	2
#2334	2
#2321	2
C₄×#121	2
#2290	2