Subgroups — #44903

Order 256.

1026 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2752	C₂	1	2	yes	maximal, complemented
2	#2735	C₂	1	2	yes	maximal, complemented
3	#2730	C₂	1	2	yes	maximal, complemented
4	#2685	C₂	1	2	yes	maximal, complemented
5	#2561	C₂	1	2	yes	maximal, complemented
6	#2560	C₂	1	2	yes	maximal, complemented
7	#2542	C₂	1	1	yes	maximal, characteristic, complemented
8	#2516	C₂	1	2	yes	maximal, complemented
9	#2513	C₂	1	1	yes	maximal, characteristic, complemented
10	#2512	C₂	1	1	yes	maximal, characteristic, complemented
11	#2500	C₂	1	1	yes	maximal, characteristic, complemented
12	#2491	C₂	1	1	yes	maximal, characteristic, complemented
13	#2472	C₂	1	2	yes	maximal, complemented
14	#2439	C₂	1	1	yes	maximal, characteristic, complemented
15	#2420	C₂	1	1	yes	maximal, characteristic, complemented
16	#2408	C₂	1	1	yes	maximal, characteristic
17	#2395	C₂	1	1	yes	maximal, characteristic, complemented
18	#2363	C₂	1	1	yes	maximal, characteristic, complemented
19	#2357	C₂	1	1	yes	maximal, characteristic, complemented
20	#2354	C₂	1	1	yes	maximal, characteristic, complemented
21	D₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
22	#2314	C₂	1	1	yes	maximal, characteristic, complemented
23	#2309	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×D₄	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₂×#126	C₂²	1	2	yes	complemented
27	C₂×#124	C₂²	1	2	yes	complemented
28	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
29	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
30	C₂×#121	C₂²	1	1	yes	characteristic
31	C₂×#121	C₂²	1	1	yes	characteristic
32	C₂×#120	C₂²	1	2	yes	—
33	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
36	C₂×#117	C₂²	1	1	yes	characteristic
37	C₂×#117	C₂²	1	1	yes	characteristic
38	C₂×#117	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₂²⋊C₄	C₂²	1	2	yes	—
40	#400	C₂²	1	1	yes	characteristic, complemented
41	#399	C₂²	1	1	yes	characteristic, complemented
42	#399	C₂²	1	2	yes	complemented
43	#399	C₂²	1	2	yes	complemented
44	#398	C₂²	1	1	yes	characteristic, complemented
45	#397	C₂²	1	1	yes	characteristic
46	#397	C₂²	1	1	yes	characteristic
47	#397	C₂²	1	2	yes	complemented
48	#397	C₂²	1	2	yes	complemented
49	#397	C₂²	1	1	yes	characteristic, complemented
50	#397	C₂²	1	2	yes	complemented
51	#397	C₂²	1	2	yes	complemented
52	#396	C₂²	1	2	yes	—
53	#396	C₂²	1	2	yes	complemented
54	#394	C₂²	1	2	yes	—
55	#394	C₂²	1	1	yes	characteristic
56	#394	C₂²	1	1	yes	characteristic
57	#394	C₂²	1	2	yes	complemented
58	#394	C₂²	1	2	yes	complemented
59	#394	C₂²	1	2	yes	complemented
60	#394	C₂²	1	2	yes	complemented
61	#393	C₂²	1	2	yes	—
62	#393	C₂²	1	2	yes	complemented
63	#392	C₂²	1	2	yes	—
64	#391	C₂²	1	2	yes	complemented
65	#390	C₂²	1	2	yes	—
66	#390	C₂²	1	1	yes	characteristic
67	#390	C₂²	1	1	yes	characteristic
68	#390	C₂²	1	2	yes	—
69	#390	C₂²	1	1	yes	characteristic
70	#390	C₂²	1	1	yes	characteristic
71	#390	C₂²	1	1	yes	characteristic
72	#390	C₂²	1	1	yes	characteristic
73	#390	C₂²	1	2	yes	—
74	#390	C₂²	1	1	yes	characteristic
75	#390	C₂²	1	1	yes	characteristic
76	#390	C₂²	1	2	yes	complemented
77	#389	C₂²	1	1	yes	characteristic, complemented
78	#389	C₂²	1	1	yes	characteristic, complemented
79	#388	C₂²	1	2	yes	—
80	#388	C₂²	1	2	yes	—
81	#388	C₂²	1	2	yes	—
82	#388	C₂²	1	2	yes	complemented
83	#388	C₂²	1	2	yes	complemented
84	#388	C₂²	1	2	yes	complemented
85	#388	C₂²	1	2	yes	complemented
86	#388	C₂²	1	2	yes	complemented
87	#388	C₂²	1	2	yes	complemented
88	#388	C₂²	1	2	yes	complemented
89	#388	C₂²	1	2	yes	complemented
90	#388	C₂²	1	2	yes	complemented
91	#388	C₂²	1	2	yes	complemented
92	#387	C₂²	1	2	yes	complemented
93	#387	C₂²	1	2	yes	complemented
94	#387	C₂²	1	2	yes	complemented
95	#386	C₂²	1	2	yes	—
96	#386	C₂²	1	2	yes	—
97	#386	C₂²	1	2	yes	complemented
98	#386	C₂²	1	2	yes	complemented
99	#384	C₂²	1	1	yes	characteristic, complemented
100	#384	C₂²	1	1	yes	characteristic, complemented
101	#382	C₂²	1	1	yes	characteristic, complemented
102	#382	C₂²	1	1	yes	characteristic, complemented
103	#381	C₂²	1	2	yes	complemented
104	#381	C₂²	1	2	yes	complemented
105	#380	C₂²	1	1	yes	characteristic
106	#380	C₂²	1	1	yes	characteristic
107	#380	C₂²	1	1	yes	characteristic, complemented
108	#379	C₂²	1	2	yes	—
109	#379	C₂²	1	2	yes	—
110	#379	C₂²	1	2	yes	—
111	#379	C₂²	1	2	yes	—
112	C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
113	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
114	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
115	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
116	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
117	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
118	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
120	C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
121	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
122	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
123	C₂⁵	C₂³	1	2	yes	—
124	C₂²×Q₈	C₂³	1	2	yes	—
125	C₂²×D₄	—	2	4	no	—
126	C₂²×D₄	—	2	4	no	—
127	C₂²×D₄	—	4	2	no	—
128	C₂²×D₄	C₂³	1	1	yes	characteristic
129	C₂²×D₄	C₂³	1	1	yes	characteristic
130	C₂²×D₄	C₂³	1	2	yes	—
131	C₂²×D₄	C₂³	1	1	yes	characteristic
132	C₂²×D₄	C₂³	1	2	yes	—
133	C₂²×D₄	C₂³	1	2	yes	—
134	C₂³×C₄	C₂³	1	1	yes	characteristic
135	C₂³×C₄	C₂³	1	1	yes	characteristic
136	C₂³×C₄	C₂³	1	2	yes	—
137	C₂³×C₄	C₂³	1	2	yes	—
138	C₄⋊Q₈	—	4	2	no	—
139	#126	—	4	4	no	—
140	#124	—	4	4	no	—
141	C₂²⋊Q₈	—	4	4	no	—
142	C₂²⋊Q₈	—	4	4	no	—
143	#121	—	2	4	no	—
144	#121	—	4	2	no	—
145	#120	—	4	4	no	—
146	C₄×D₄	—	2	4	no	—
147	C₄×D₄	—	2	4	no	—
148	C₄×D₄	—	4	2	no	—
149	#117	—	2	4	no	—
150	#117	—	4	2	no	—
151	#117	—	4	2	no	—
152	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄	—	4	4	no	—
173	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
184	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₂×C₄²	C₂³	1	1	yes	characteristic
209	C₂×C₄²	C₂³	1	1	yes	characteristic
210	C₂×C₄²	C₂³	1	1	yes	characteristic
211	C₂×C₄²	C₂³	1	1	yes	characteristic
212	C₂×C₄²	C₂³	1	1	yes	characteristic
213	C₂×C₄²	C₂³	1	2	yes	—
214	C₂×C₄²	C₂³	1	2	yes	—
215	C₂×C₄²	C₂³	1	2	yes	—
216	C₂×C₄²	C₂³	1	2	yes	—
217	C₂×C₄²	C₂³	1	2	yes	—
218	#95	C₂³	1	1	yes	characteristic
219	#95	C₂³	1	1	yes	characteristic
220	#95	C₂³	1	1	yes	characteristic
221	#95	C₂³	1	1	yes	characteristic
222	#95	C₂³	1	1	yes	characteristic
223	#95	C₂³	1	2	yes	—
224	#95	C₂³	1	2	yes	—
225	#95	C₂³	1	1	yes	characteristic
226	#95	C₂³	1	1	yes	characteristic
227	#95	C₂³	1	2	yes	—
228	#95	C₂³	1	2	yes	—
229	#95	C₂³	1	1	yes	characteristic
230	#95	C₂³	1	2	yes	—
231	#95	C₂³	1	2	yes	—
232	#95	C₂³	1	2	yes	—
233	#95	C₂³	1	1	yes	characteristic
234	#95	C₂³	1	1	yes	characteristic
235	#95	C₂³	1	2	yes	—
236	#95	C₂³	1	2	yes	—
237	#95	C₂³	1	2	yes	—
238	#95	C₂³	1	2	yes	—
239	#95	C₂³	1	2	yes	—
240	C₂⁴	—	2	4	no	—
241	C₂⁴	—	2	4	no	—
242	C₂⁴	—	4	2	no	—
243	C₂⁴	—	4	2	no	—
244	C₂⁴	—	4	2	no	—
245	C₂⁴	—	4	2	no	—
246	C₂⁴	—	4	2	no	—
247	C₂⁴	C₂⁴	1	2	yes	—
248	C₂⁴	C₂⁴	1	1	yes	characteristic
249	C₂⁴	C₂⁴	1	1	yes	characteristic
250	C₂⁴	C₂⁴	1	2	yes	—
251	C₂×Q₈	—	2	4	no	—
252	C₂×Q₈	—	4	2	no	—
253	C₂×Q₈	—	4	2	no	—
254	C₂×D₄	—	2	2	no	—
255	C₂×D₄	—	2	4	no	—
256	C₂×D₄	—	2	4	no	—
257	C₂×D₄	—	2	2	no	—
258	C₂×D₄	—	2	4	no	—
259	C₂×D₄	—	2	2	no	—
260	C₂×D₄	—	2	2	no	—
261	C₂×D₄	—	2	2	no	—
262	C₂×D₄	—	2	2	no	—
263	C₂×D₄	—	2	2	no	—
264	C₂×D₄	—	4	16	no	—
265	C₂×D₄	—	4	2	no	—
266	C₂×D₄	—	4	1	no	—
267	C₂×D₄	—	4	2	no	—
268	C₂×D₄	—	4	2	no	—
269	C₂×D₄	—	4	2	no	—
270	C₂×D₄	—	4	2	no	—
271	C₂×D₄	—	4	2	no	—
272	C₂×D₄	#41	1	4	yes	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	4	2	no	—
281	C₂²×C₄	—	4	2	no	—
282	C₂²×C₄	—	4	2	no	—
283	C₂²×C₄	—	4	2	no	—
284	C₂²×C₄	#41	1	4	yes	—
285	C₂²×C₄	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄	C₂⁴	1	2	yes	—
288	C₂²×C₄	C₂⁴	1	2	yes	—
289	C₂²×C₄	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄	C₂⁴	1	2	yes	—
292	C₂²×C₄	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄	C₂⁴	1	2	yes	—
298	C₂²×C₄	C₂⁴	1	2	yes	—
299	C₂²×C₄	C₂⁴	1	2	yes	—
300	C₂²×C₄	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄	C₂⁴	1	1	yes	characteristic
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	—	4	2	no	—
319	C₄⋊C₄	—	4	2	no	—
320	C₄⋊C₄	—	4	2	no	—
321	C₄⋊C₄	—	4	2	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₂²⋊C₄	—	2	2	no	—
325	C₂²⋊C₄	—	2	2	no	—
326	C₂²⋊C₄	—	2	2	no	—
327	C₂²⋊C₄	—	2	4	no	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₂²⋊C₄	—	2	2	no	—
330	C₂²⋊C₄	—	2	2	no	—
331	C₂²⋊C₄	—	2	4	no	—
332	C₂²⋊C₄	—	2	4	no	—
333	C₂²⋊C₄	—	2	4	no	—
334	C₂²⋊C₄	—	2	2	no	—
335	C₂²⋊C₄	—	4	2	no	—
336	C₂²⋊C₄	—	4	2	no	—
337	C₂²⋊C₄	—	4	2	no	—
338	C₂²⋊C₄	—	4	2	no	—
339	C₂²⋊C₄	—	4	2	no	—
340	C₂²⋊C₄	—	4	1	no	—
341	C₂²⋊C₄	—	4	2	no	—
342	C₂²⋊C₄	—	4	1	no	—
343	C₂²⋊C₄	—	4	1	no	—
344	C₂²⋊C₄	—	4	2	no	—
345	C₂²⋊C₄	—	4	1	no	—
346	C₂²⋊C₄	—	4	2	no	—
347	C₂²⋊C₄	—	4	2	no	—
348	C₂²⋊C₄	—	4	2	no	—
349	C₂²⋊C₄	—	4	2	no	—
350	C₂²⋊C₄	—	4	2	no	—
351	C₂²⋊C₄	—	4	2	no	—
352	C₂²⋊C₄	—	4	2	no	—
353	C₂²⋊C₄	—	4	2	no	—
354	C₂²⋊C₄	—	4	2	no	—
355	C₂²⋊C₄	—	4	2	no	—
356	C₂²⋊C₄	—	4	2	no	—
357	C₂²⋊C₄	—	4	2	no	—
358	C₂²⋊C₄	—	4	2	no	—
359	C₄²	—	2	2	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	4	2	no	—
365	C₄²	—	4	2	no	—
366	C₄²	—	4	2	no	—
367	C₄²	—	4	2	no	—
368	C₄²	—	4	2	no	—
369	C₂³	—	2	1	no	—
370	C₂³	—	2	2	no	—
371	C₂³	—	2	1	no	—
372	C₂³	—	2	2	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	1	no	—
375	C₂³	—	2	1	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	2	2	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	2	1	no	—
380	C₂³	—	2	1	no	—
381	C₂³	—	2	1	no	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	1	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	1	no	—
391	C₂³	—	2	1	no	—
392	C₂³	—	2	2	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	2	1	no	—
395	C₂³	—	4	8	no	—
396	C₂³	—	4	8	no	—
397	C₂³	—	8	4	no	—
398	C₂³	—	8	4	no	—
399	C₂³	—	8	4	no	—
400	C₂³	—	8	4	no	—
401	C₂³	—	8	4	no	—
402	C₂³	C₂×#41	1	2	yes	—
403	C₂³	C₂×#41	1	4	yes	—
404	C₂³	C₂⁵	1	1	yes	characteristic
405	Q₈	—	8	4	no	—
406	D₄	—	2	8	no	—
407	D₄	—	4	4	no	—
408	D₄	—	4	8	no	—
409	D₄	—	4	4	no	—
410	D₄	—	8	4	no	—
411	D₄	—	8	4	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	8	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	8	4	no	—
466	C₂×C₄	—	8	4	no	—
467	C₂×C₄	C₂×#41	1	2	yes	—
468	C₂×C₄	C₂×#41	1	2	yes	—
469	C₂×C₄	C₂×#41	1	2	yes	—
470	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
471	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
472	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	4	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	4	no	—
478	C₂²	—	2	4	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	4	1	no	—
482	C₂²	—	4	1	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	1	no	—
487	C₂²	—	4	1	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	1	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	1	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	4	1	no	—
494	C₂²	—	4	1	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	4	2	no	—
497	C₂²	—	4	1	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	4	1	no	—
500	C₂²	—	4	2	no	—
501	C₂²	—	8	16	no	—
502	C₂²	C₂²×#41	1	1	yes	characteristic
503	C₂²	C₂²×#41	1	1	yes	characteristic
504	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
505	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
506	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
507	C₂²	#585	1	1	yes	characteristic
508	C₂²	#585	1	1	yes	characteristic
509	C₄	—	2	2	no	—
510	C₄	—	2	2	no	—
511	C₄	—	2	2	no	—
512	C₄	—	4	1	no	—
513	C₄	—	4	1	no	—
514	C₄	—	4	1	no	—
515	C₄	—	4	1	no	—
516	C₄	—	4	1	no	—
517	C₄	—	4	1	no	—
518	C₄	—	4	1	no	—
519	C₄	—	4	2	no	—
520	C₄	—	4	1	no	—
521	C₄	—	4	2	no	—
522	C₄	—	4	2	no	—
523	C₄	—	4	2	no	—
524	C₄	—	4	2	no	—
525	C₄	—	4	1	no	—
526	C₄	—	4	2	no	—
527	C₄	#551	1	4	yes	—
528	C₂	—	4	4	no	—
529	C₂	—	4	2	no	—
530	C₂	—	8	1	no	—
531	C₂	—	8	2	no	—
532	C₂	C₂×#551	1	1	yes	characteristic
533	C₂	#3494	1	1	yes	characteristic
534	C₂	#3506	1	1	yes	characteristic
535	C₂	#3514	1	1	yes	characteristic
536	C₂	#3514	1	1	yes	characteristic
537	C₂	#3543	1	1	yes	characteristic
538	C₂	#3562	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂³	C₂⁵
prime radical	#2408	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. #2752	C₂	semidirect
2. #2735	C₂	semidirect
3. #2730	C₂	semidirect
4. #2685	C₂	semidirect
5. #2561	C₂	semidirect
6. #2560	C₂	semidirect
7. #2542	C₂	semidirect
8. #2516	C₂	semidirect
9. #2513	C₂	semidirect
10. #2512	C₂	semidirect
11. #2500	C₂	semidirect
12. #2491	C₂	semidirect
13. #2472	C₂	semidirect
14. #2439	C₂	semidirect
15. #2420	C₂	semidirect
17. #2395	C₂	semidirect
18. #2363	C₂	semidirect
19. #2357	C₂	semidirect
20. #2354	C₂	semidirect
21. D₄×C₂²⋊C₄	C₂	semidirect
22. #2314	C₂	semidirect
23. #2309	C₂	semidirect
25. C₂×C₄⋊Q₈	C₂²	semidirect
26. C₂×#126	C₂²	semidirect
27. C₂×#124	C₂²	semidirect
28. C₂×C₂²⋊Q₈	C₂²	semidirect
29. C₂×C₂²⋊Q₈	C₂²	semidirect
38. C₂×#117	C₂²	semidirect
40. #400	C₂²	semidirect
41. #399	C₂²	semidirect
42. #399	C₂²	semidirect
43. #399	C₂²	semidirect
44. #398	C₂²	semidirect
47. #397	C₂²	semidirect
48. #397	C₂²	semidirect
49. #397	C₂²	semidirect
50. #397	C₂²	semidirect
51. #397	C₂²	semidirect
53. #396	C₂²	semidirect
57. #394	C₂²	semidirect
58. #394	C₂²	semidirect
59. #394	C₂²	semidirect
60. #394	C₂²	semidirect
62. #393	C₂²	semidirect
64. #391	C₂²	semidirect
76. #390	C₂²	semidirect
77. #389	C₂²	semidirect
78. #389	C₂²	semidirect
82. #388	C₂²	semidirect
83. #388	C₂²	semidirect
84. #388	C₂²	semidirect
85. #388	C₂²	semidirect
86. #388	C₂²	semidirect
87. #388	C₂²	semidirect
88. #388	C₂²	semidirect
89. #388	C₂²	semidirect
90. #388	C₂²	semidirect
91. #388	C₂²	semidirect
92. #387	C₂²	semidirect
93. #387	C₂²	semidirect
94. #387	C₂²	semidirect
97. #386	C₂²	semidirect
98. #386	C₂²	semidirect
99. #384	C₂²	semidirect
100. #384	C₂²	semidirect
101. #382	C₂²	semidirect
102. #382	C₂²	semidirect
103. #381	C₂²	semidirect
104. #381	C₂²	semidirect
107. #380	C₂²	semidirect
112. C₄×C₄⋊C₄	C₂²	semidirect
113. C₄×C₄⋊C₄	C₂²	semidirect
114. C₄×C₄⋊C₄	C₂²	semidirect
115. C₄×C₄⋊C₄	C₂²	semidirect
116. C₄×C₄⋊C₄	C₂²	semidirect
117. C₄×C₄⋊C₄	C₂²	semidirect
119. C₄×C₂²⋊C₄	C₂²	semidirect
120. C₄×C₂²⋊C₄	C₂²	semidirect
121. C₄×C₂²⋊C₄	C₂²	semidirect
122. C₄×C₂²⋊C₄	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#2752	2
#2735	2
#2730	2
#2685	2
#2561	2
#2560	2
#2542	2
#2516	2
#2513	2
#2512	2
#2500	2
#2491	2
#2472	2
#2439	2
#2420	2
#2408	2
#2395	2
#2363	2
#2357	2
#2354	2
D₄×C₂²⋊C₄	2
#2314	2
#2309	2