Subgroups — #59310

Order 256.

1125 conjugacy classes of subgroups.

The subgroup lattice has 769 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#551	C₂	1	1	yes	maximal, characteristic
3	#2721	C₂	1	1	yes	maximal, characteristic, complemented
4	#2720	C₂	1	1	yes	maximal, characteristic, complemented
5	#2718	C₂	1	1	yes	maximal, characteristic, complemented
6	#2680	C₂	1	1	yes	maximal, characteristic, complemented
7	#2553	C₂	1	1	yes	maximal, characteristic, complemented
8	#2549	C₂	1	1	yes	maximal, characteristic, complemented
9	#2534	C₂	1	1	yes	maximal, characteristic
10	#2521	C₂	1	1	yes	maximal, characteristic, complemented
11	#2519	C₂	1	1	yes	maximal, characteristic, complemented
12	#2519	C₂	1	1	yes	maximal, characteristic, complemented
13	#2489	C₂	1	1	yes	maximal, characteristic, complemented
14	#2488	C₂	1	1	yes	maximal, characteristic, complemented
15	#2484	C₂	1	1	yes	maximal, characteristic, complemented
16	#2482	C₂	1	1	yes	maximal, characteristic, complemented
17	#2475	C₂	1	1	yes	maximal, characteristic, complemented
18	#2474	C₂	1	1	yes	maximal, characteristic, complemented
19	#2469	C₂	1	1	yes	maximal, characteristic, complemented
20	#2468	C₂	1	1	yes	maximal, characteristic, complemented
21	#2438	C₂	1	1	yes	maximal, characteristic, complemented
22	#2437	C₂	1	1	yes	maximal, characteristic, complemented
23	#2419	C₂	1	1	yes	maximal, characteristic, complemented
24	#2418	C₂	1	1	yes	maximal, characteristic
25	#2362	C₂	1	1	yes	maximal, characteristic, complemented
26	#2359	C₂	1	1	yes	maximal, characteristic, complemented
27	#2349	C₂	1	1	yes	maximal, characteristic, complemented
28	#2342	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×#123	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#388	C₂	1	1	yes	maximal, characteristic, complemented
31	#2285	C₂	1	1	yes	maximal, characteristic, complemented
32	#552	—	2	8	no	—
33	#551	—	2	8	no	—
34	C₂×#126	C₂²	1	1	yes	characteristic
35	C₂×#126	C₂²	1	1	yes	characteristic
36	C₂×#126	C₂²	1	1	yes	characteristic, complemented
37	C₂×#126	C₂²	1	1	yes	characteristic, complemented
38	C₂×#125	C₂²	1	1	yes	characteristic, complemented
39	C₂×#125	C₂²	1	1	yes	characteristic, complemented
40	C₂×#125	C₂²	1	1	yes	characteristic, complemented
41	C₂×#124	C₂²	1	1	yes	characteristic
42	C₂×#123	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×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
49	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
50	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
52	C₂×#120	C₂²	1	1	yes	characteristic
53	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
56	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
57	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
58	C₂×#117	C₂²	1	1	yes	characteristic
59	C₂×#117	C₂²	1	1	yes	characteristic
60	C₂×#117	C₂²	1	1	yes	characteristic
61	C₂×#117	C₂²	1	1	yes	characteristic
62	C₂×#117	C₂²	1	1	yes	characteristic, complemented
63	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic
64	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
65	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
66	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
67	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
68	C₂²×C₄²	C₂²	1	1	yes	characteristic
69	#400	C₂²	1	1	yes	characteristic, complemented
70	#400	C₂²	1	1	yes	characteristic, complemented
71	#400	C₂²	1	1	yes	characteristic, complemented
72	#400	C₂²	1	1	yes	characteristic, complemented
73	#399	C₂²	1	1	yes	characteristic
74	#399	C₂²	1	1	yes	characteristic
75	#399	C₂²	1	1	yes	characteristic
76	#399	C₂²	1	1	yes	characteristic
77	#398	C₂²	1	1	yes	characteristic, complemented
78	#398	C₂²	1	1	yes	characteristic, complemented
79	#398	C₂²	1	1	yes	characteristic, complemented
80	#398	C₂²	1	1	yes	characteristic, complemented
81	#398	C₂²	1	1	yes	characteristic, complemented
82	#398	C₂²	1	1	yes	characteristic, complemented
83	#398	C₂²	1	1	yes	characteristic, complemented
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, complemented
88	#397	C₂²	1	1	yes	characteristic, complemented
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	#395	C₂²	1	1	yes	characteristic, complemented
94	#395	C₂²	1	1	yes	characteristic, complemented
95	#395	C₂²	1	1	yes	characteristic, complemented
96	#394	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	#393	C₂²	1	1	yes	characteristic
101	#391	C₂²	1	1	yes	characteristic, complemented
102	#391	C₂²	1	1	yes	characteristic, complemented
103	#391	C₂²	1	1	yes	characteristic, complemented
104	#389	C₂²	1	1	yes	characteristic, complemented
105	#389	C₂²	1	1	yes	characteristic, complemented
106	#389	C₂²	1	1	yes	characteristic, complemented
107	#389	C₂²	1	1	yes	characteristic, complemented
108	#389	C₂²	1	1	yes	characteristic, complemented
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
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, complemented
130	#388	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	#387	C₂²	1	1	yes	characteristic, complemented
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	#385	C₂²	1	1	yes	characteristic
146	#385	C₂²	1	1	yes	characteristic
147	#385	C₂²	1	1	yes	characteristic
148	#385	C₂²	1	1	yes	characteristic
149	#385	C₂²	1	1	yes	characteristic
150	#385	C₂²	1	1	yes	characteristic
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, complemented
155	#385	C₂²	1	1	yes	characteristic, complemented
156	#385	C₂²	1	1	yes	characteristic, complemented
157	#384	C₂²	1	1	yes	characteristic, complemented
158	#384	C₂²	1	1	yes	characteristic, complemented
159	#382	C₂²	1	1	yes	characteristic, complemented
160	#382	C₂²	1	1	yes	characteristic, complemented
161	#382	C₂²	1	1	yes	characteristic, complemented
162	#381	C₂²	1	1	yes	characteristic
163	#381	C₂²	1	1	yes	characteristic
164	#381	C₂²	1	1	yes	characteristic
165	#381	C₂²	1	1	yes	characteristic, complemented
166	#380	C₂²	1	1	yes	characteristic
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
171	#380	C₂²	1	1	yes	characteristic, complemented
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×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
180	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
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	C₂×#95	C₂²	1	1	yes	characteristic
187	C₂×#95	C₂²	1	1	yes	characteristic
188	C₂×#95	C₂²	1	1	yes	characteristic, complemented
189	C₂⁵	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	C₂³	1	1	yes	characteristic
196	C₂³×C₄	C₂³	1	1	yes	characteristic
197	C₂³×C₄	C₂³	1	1	yes	characteristic
198	C₂³×C₄	C₂³	1	1	yes	characteristic
199	C₂³×C₄	C₂³	1	1	yes	characteristic
200	C₂³×C₄	C₂³	1	1	yes	characteristic
201	C₂³×C₄	C₂³	1	1	yes	characteristic
202	C₂³×C₄	C₂³	1	1	yes	characteristic
203	C₂³×C₄	C₂³	1	1	yes	characteristic
204	C₂³×C₄	C₂³	1	1	yes	characteristic
205	C₂³×C₄	C₂³	1	1	yes	characteristic
206	#126	—	2	4	no	—
207	#126	—	2	4	no	—
208	#126	—	2	4	no	—
209	#126	—	2	4	no	—
210	#125	—	2	4	no	—
211	#125	—	2	4	no	—
212	#125	—	2	4	no	—
213	#124	—	2	4	no	—
214	#123	—	2	4	no	—
215	#123	—	2	4	no	—
216	#123	—	2	4	no	—
217	#123	—	2	4	no	—
218	#123	D₄	1	8	yes	—
219	C₂²⋊Q₈	—	2	4	no	—
220	C₂²⋊Q₈	—	2	4	no	—
221	C₂²⋊Q₈	—	2	4	no	—
222	C₂²⋊Q₈	—	2	4	no	—
223	C₂²⋊Q₈	—	2	4	no	—
224	#120	—	2	4	no	—
225	C₄×Q₈	—	2	4	no	—
226	C₄×D₄	—	2	4	no	—
227	C₄×D₄	—	2	4	no	—
228	C₄×D₄	—	2	4	no	—
229	C₄×D₄	—	2	4	no	—
230	#117	—	2	4	no	—
231	#117	—	2	4	no	—
232	#117	—	2	4	no	—
233	#117	—	2	4	no	—
234	#117	—	2	4	no	—
235	C₂×C₄⋊C₄	—	2	4	no	—
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×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×C₂²⋊C₄	—	2	4	no	—
278	C₂×C₂²⋊C₄	—	2	4	no	—
279	C₂×C₂²⋊C₄	—	2	4	no	—
280	C₂×C₂²⋊C₄	—	2	4	no	—
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×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×C₄²	—	2	4	no	—
322	C₂×C₄²	C₂³	1	1	yes	characteristic
323	C₂×C₄²	C₂³	1	1	yes	characteristic
324	C₂×C₄²	C₂³	1	1	yes	characteristic
325	C₂×C₄²	C₂³	1	1	yes	characteristic
326	C₂×C₄²	C₂³	1	1	yes	characteristic
327	C₂×C₄²	C₂³	1	1	yes	characteristic
328	C₂×C₄²	C₂³	1	1	yes	characteristic
329	C₂×C₄²	C₂³	1	1	yes	characteristic
330	C₂×C₄²	C₂³	1	1	yes	characteristic
331	C₂×C₄²	C₂³	1	1	yes	characteristic
332	C₂×C₄²	C₂³	1	1	yes	characteristic
333	C₂×C₄²	C₂³	1	1	yes	characteristic
334	C₂×C₄²	C₂³	1	1	yes	characteristic
335	C₂×C₄²	C₂³	1	1	yes	characteristic
336	C₂×C₄²	C₂³	1	1	yes	characteristic
337	#95	C₂³	1	1	yes	characteristic
338	#95	C₂³	1	1	yes	characteristic
339	#95	C₂³	1	1	yes	characteristic
340	#95	C₂³	1	1	yes	characteristic
341	#95	C₂³	1	1	yes	characteristic
342	#95	C₂³	1	1	yes	characteristic
343	#95	C₂³	1	1	yes	characteristic
344	#95	C₂³	1	1	yes	characteristic
345	#95	C₂³	1	1	yes	characteristic
346	#95	C₂³	1	1	yes	characteristic
347	#95	C₂³	1	1	yes	characteristic
348	#95	C₂³	1	1	yes	characteristic
349	#95	C₂³	1	1	yes	characteristic
350	#95	C₂³	1	1	yes	characteristic
351	#95	C₂³	1	1	yes	characteristic
352	#95	C₂³	1	1	yes	characteristic
353	#95	C₂³	1	1	yes	characteristic
354	#95	C₂³	1	1	yes	characteristic
355	#95	C₂³	1	1	yes	characteristic
356	#95	C₂³	1	1	yes	characteristic
357	#95	C₂³	1	1	yes	characteristic
358	#95	C₂³	1	1	yes	characteristic
359	#95	C₂³	1	1	yes	characteristic
360	#95	C₂³	1	1	yes	characteristic
361	#95	C₂³	1	1	yes	characteristic
362	#95	C₂³	1	1	yes	characteristic
363	#95	C₂³	1	1	yes	characteristic
364	#95	C₂³	1	1	yes	characteristic
365	#95	C₂³	1	1	yes	characteristic
366	#95	C₂³	1	1	yes	characteristic
367	#95	C₂³	1	1	yes	characteristic
368	#95	C₂³	1	1	yes	characteristic
369	#95	C₂³	1	1	yes	characteristic
370	#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	C₂⁴	—	2	2	no	—
380	C₂⁴	—	2	2	no	—
381	C₂⁴	—	2	2	no	—
382	C₂⁴	—	2	2	no	—
383	C₂⁴	—	4	1	no	—
384	C₂⁴	—	4	1	no	—
385	C₂⁴	—	4	1	no	—
386	C₂⁴	C₂⁴	1	1	yes	characteristic
387	C₂⁴	C₂⁴	1	1	yes	characteristic
388	C₂⁴	C₂⁴	1	1	yes	characteristic
389	C₂⁴	C₂⁴	1	1	yes	characteristic
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	2	no	—
392	C₂×Q₈	—	2	2	no	—
393	C₂×Q₈	—	4	1	no	—
394	C₂×Q₈	—	4	1	no	—
395	C₂×Q₈	—	4	1	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	4	1	no	—
402	C₂×D₄	—	4	1	no	—
403	C₂×D₄	—	4	1	no	—
404	C₂×D₄	C₂×D₄	1	4	yes	—
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	—	2	2	no	—
421	C₂²×C₄	—	2	2	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	—	4	1	no	—
435	C₂²×C₄	—	4	1	no	—
436	C₂²×C₄	C₂×D₄	1	4	yes	—
437	C₂²×C₄	#41	1	4	yes	—
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	C₂²×C₄	C₂⁴	1	1	yes	characteristic
462	C₂²×C₄	C₂⁴	1	1	yes	characteristic
463	C₂²×C₄	C₂⁴	1	1	yes	characteristic
464	C₂²×C₄	C₂⁴	1	1	yes	characteristic
465	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	—	2	2	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	—	2	2	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	2	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	C₄⋊C₄	—	4	1	no	—
503	C₄⋊C₄	—	4	1	no	—
504	C₄⋊C₄	C₂×D₄	1	4	yes	—
505	C₄⋊C₄	C₂×D₄	1	4	yes	—
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	—	2	2	no	—
513	C₂²⋊C₄	—	2	2	no	—
514	C₂²⋊C₄	—	2	2	no	—
515	C₂²⋊C₄	—	2	2	no	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₂²⋊C₄	—	2	2	no	—
521	C₂²⋊C₄	—	2	2	no	—
522	C₂²⋊C₄	—	2	2	no	—
523	C₂²⋊C₄	—	2	2	no	—
524	C₂²⋊C₄	—	2	2	no	—
525	C₂²⋊C₄	—	2	2	no	—
526	C₂²⋊C₄	—	2	2	no	—
527	C₂²⋊C₄	—	2	2	no	—
528	C₂²⋊C₄	—	2	2	no	—
529	C₂²⋊C₄	—	2	2	no	—
530	C₂²⋊C₄	—	2	2	no	—
531	C₂²⋊C₄	—	2	2	no	—
532	C₂²⋊C₄	—	2	2	no	—
533	C₂²⋊C₄	—	2	2	no	—
534	C₂²⋊C₄	—	2	2	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	C₂²⋊C₄	—	4	1	no	—
541	C₂²⋊C₄	—	4	1	no	—
542	C₂²⋊C₄	C₂×D₄	1	4	yes	—
543	C₂²⋊C₄	C₂×D₄	1	4	yes	—
544	C₂²⋊C₄	C₂×D₄	1	4	yes	—
545	C₂²⋊C₄	#41	1	4	yes	—
546	C₄²	—	2	2	no	—
547	C₄²	—	2	2	no	—
548	C₄²	—	2	2	no	—
549	C₄²	—	2	2	no	—
550	C₄²	—	2	2	no	—
551	C₄²	—	2	2	no	—
552	C₄²	—	2	2	no	—
553	C₄²	—	2	2	no	—
554	C₄²	—	2	2	no	—
555	C₄²	—	2	2	no	—
556	C₄²	—	2	2	no	—
557	C₄²	—	2	2	no	—
558	C₄²	—	2	2	no	—
559	C₄²	—	4	1	no	—
560	C₄²	—	4	1	no	—
561	C₂³	—	2	1	no	—
562	C₂³	—	2	1	no	—
563	C₂³	—	2	1	no	—
564	C₂³	—	2	1	no	—
565	C₂³	—	2	1	no	—
566	C₂³	—	2	1	no	—
567	C₂³	—	2	1	no	—
568	C₂³	—	2	1	no	—
569	C₂³	—	2	1	no	—
570	C₂³	—	2	1	no	—
571	C₂³	—	2	1	no	—
572	C₂³	—	2	1	no	—
573	C₂³	—	2	1	no	—
574	C₂³	—	2	1	no	—
575	C₂³	—	2	1	no	—
576	C₂³	—	2	1	no	—
577	C₂³	—	2	1	no	—
578	C₂³	—	2	1	no	—
579	C₂³	—	2	1	no	—
580	C₂³	—	2	1	no	—
581	C₂³	—	2	1	no	—
582	C₂³	—	2	1	no	—
583	C₂³	—	2	1	no	—
584	C₂³	—	4	4	no	—
585	C₂³	—	4	4	no	—
586	C₂³	—	4	4	no	—
587	C₂³	—	4	4	no	—
588	C₂³	—	8	2	no	—
589	C₂³	—	8	2	no	—
590	C₂³	—	8	2	no	—
591	C₂³	C₂²×D₄	1	2	yes	—
592	C₂³	C₂²×D₄	1	2	yes	—
593	C₂³	C₂×#41	1	2	yes	—
594	C₂³	C₂×#41	1	2	yes	—
595	C₂³	2₋¹⁺⁴	1	2	yes	—
596	C₂³	C₂⁵	1	1	yes	characteristic
597	Q₈	—	4	4	no	—
598	Q₈	—	8	2	no	—
599	D₄	—	2	8	no	—
600	D₄	—	4	4	no	—
601	D₄	—	8	2	no	—
602	C₂×C₄	—	2	8	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	—	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	—	4	4	no	—
676	C₂×C₄	—	4	4	no	—
677	C₂×C₄	—	4	4	no	—
678	C₂×C₄	—	4	4	no	—
679	C₂×C₄	—	4	4	no	—
680	C₂×C₄	—	4	4	no	—
681	C₂×C₄	—	8	2	no	—
682	C₂×C₄	—	8	2	no	—
683	C₂×C₄	—	8	2	no	—
684	C₂×C₄	—	8	2	no	—
685	C₂×C₄	C₂²×D₄	1	2	yes	—
686	C₂×C₄	C₂²×D₄	1	2	yes	—
687	C₂×C₄	C₂²×D₄	1	2	yes	—
688	C₂×C₄	C₂²×D₄	1	2	yes	—
689	C₂×C₄	C₂²×D₄	1	2	yes	—
690	C₂×C₄	C₂×#41	1	2	yes	—
691	C₂×C₄	C₂×#41	1	2	yes	—
692	C₂×C₄	C₂×#41	1	2	yes	—
693	C₂×C₄	C₂×#41	1	2	yes	—
694	C₂²	—	2	2	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	2	2	no	—
697	C₂²	—	2	2	no	—
698	C₂²	—	2	2	no	—
699	C₂²	—	2	2	no	—
700	C₂²	—	2	2	no	—
701	C₂²	—	2	2	no	—
702	C₂²	—	2	2	no	—
703	C₂²	—	2	2	no	—
704	C₂²	—	2	2	no	—
705	C₂²	—	2	2	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	—	4	1	no	—
713	C₂²	—	4	1	no	—
714	C₂²	—	4	1	no	—
715	C₂²	—	4	1	no	—
716	C₂²	—	4	1	no	—
717	C₂²	—	4	1	no	—
718	C₂²	—	4	1	no	—
719	C₂²	—	4	1	no	—
720	C₂²	—	4	1	no	—
721	C₂²	—	8	8	no	—
722	C₂²	#547	1	4	yes	—
723	C₂²	C₂³×D₄	1	1	yes	characteristic
724	C₂²	C₂²×#41	1	1	yes	characteristic
725	C₂²	C₂²×#41	1	1	yes	characteristic
726	C₂²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
727	C₂²	#585	1	1	yes	characteristic
728	C₂²	#585	1	1	yes	characteristic
729	C₂²	#585	1	1	yes	characteristic
730	C₄	—	2	2	no	—
731	C₄	—	2	2	no	—
732	C₄	—	2	2	no	—
733	C₄	—	2	2	no	—
734	C₄	—	2	2	no	—
735	C₄	—	2	2	no	—
736	C₄	—	2	2	no	—
737	C₄	—	2	2	no	—
738	C₄	—	2	2	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	C₄	—	4	1	no	—
747	C₄	—	4	1	no	—
748	C₄	—	4	1	no	—
749	C₄	—	4	1	no	—
750	C₄	—	4	1	no	—
751	C₄	—	4	1	no	—
752	C₄	—	4	1	no	—
753	C₄	—	4	1	no	—
754	C₄	—	4	1	no	—
755	C₄	—	4	1	no	—
756	C₄	—	4	1	no	—
757	C₂	—	2	4	no	—
758	C₂	—	4	2	no	—
759	C₂	—	4	2	no	—
760	C₂	—	8	1	no	—
761	C₂	C₂×#547	1	1	yes	characteristic
762	C₂	D₄×#41	1	1	yes	characteristic
763	C₂	#3475	1	1	yes	characteristic
764	C₂	#3491	1	1	yes	characteristic
765	C₂	#3495	1	1	yes	characteristic
766	C₂	#3500	1	1	yes	characteristic
767	C₂	#3564	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
1. C₂×#552	C₂	semidirect
3. #2721	C₂	semidirect
4. #2720	C₂	semidirect
5. #2718	C₂	semidirect
6. #2680	C₂	semidirect
7. #2553	C₂	semidirect
8. #2549	C₂	semidirect
10. #2521	C₂	semidirect
11. #2519	C₂	semidirect
12. #2519	C₂	semidirect
13. #2489	C₂	semidirect
14. #2488	C₂	semidirect
15. #2484	C₂	semidirect
16. #2482	C₂	semidirect
17. #2475	C₂	semidirect
18. #2474	C₂	semidirect
19. #2469	C₂	semidirect
20. #2468	C₂	semidirect
21. #2438	C₂	semidirect
22. #2437	C₂	semidirect
23. #2419	C₂	semidirect
25. #2362	C₂	semidirect
26. #2359	C₂	semidirect
27. #2349	C₂	semidirect
28. #2342	C₂	semidirect
29. C₄×#123	C₂	semidirect
30. C₂×#388	C₂	semidirect
31. #2285	C₂	semidirect
36. C₂×#126	C₂²	semidirect
37. C₂×#126	C₂²	semidirect
38. C₂×#125	C₂²	semidirect
39. C₂×#125	C₂²	semidirect
40. C₂×#125	C₂²	semidirect
51. C₂×C₂²⋊Q₈	C₂²	semidirect
53. C₂×C₄×Q₈	C₂²	semidirect
62. C₂×#117	C₂²	semidirect
69. #400	C₂²	semidirect
70. #400	C₂²	semidirect
71. #400	C₂²	semidirect
72. #400	C₂²	semidirect
77. #398	C₂²	semidirect
78. #398	C₂²	semidirect
79. #398	C₂²	semidirect
80. #398	C₂²	semidirect
81. #398	C₂²	semidirect
82. #398	C₂²	semidirect
83. #398	C₂²	semidirect
87. #397	C₂²	semidirect
88. #397	C₂²	semidirect
93. #395	C₂²	semidirect
94. #395	C₂²	semidirect
95. #395	C₂²	semidirect
101. #391	C₂²	semidirect
102. #391	C₂²	semidirect
103. #391	C₂²	semidirect
104. #389	C₂²	semidirect
105. #389	C₂²	semidirect
106. #389	C₂²	semidirect
107. #389	C₂²	semidirect
108. #389	C₂²	semidirect
129. #388	C₂²	semidirect
130. #388	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
140. #387	C₂²	semidirect
154. #385	C₂²	semidirect
155. #385	C₂²	semidirect
156. #385	C₂²	semidirect
157. #384	C₂²	semidirect
158. #384	C₂²	semidirect
159. #382	C₂²	semidirect
160. #382	C₂²	semidirect
161. #382	C₂²	semidirect
165. #381	C₂²	semidirect
171. #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
179. C₄×C₄⋊C₄	C₂²	semidirect
180. C₄×C₄⋊C₄	C₂²	semidirect
184. C₄×C₂²⋊C₄	C₂²	semidirect
185. C₄×C₂²⋊C₄	C₂²	semidirect
188. C₂×#95	C₂²	semidirect

Maximal subgroups

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

subgroup	index
C₂×#552	2
C₂×#551	2
#2721	2
#2720	2
#2718	2
#2680	2
#2553	2
#2549	2
#2534	2
#2521	2
#2519	2
#2489	2
#2488	2
#2484	2
#2482	2
#2475	2
#2474	2
#2469	2
#2468	2
#2438	2
#2437	2
#2419	2
#2418	2
#2362	2
#2359	2
#2349	2
#2342	2
C₄×#123	2
C₂×#388	2
#2285	2