Subgroups — #45365

Order 256.

966 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2757	C₂	1	2	yes	maximal, complemented
2	#2737	C₂	1	2	yes	maximal, complemented
3	#2736	C₂	1	2	yes	maximal, complemented
4	#2735	C₂	1	2	yes	maximal, complemented
5	#2597	C₂	1	2	yes	maximal, complemented
6	#2592	C₂	1	1	yes	maximal, characteristic, complemented
7	#2580	C₂	1	1	yes	maximal, characteristic, complemented
8	#2513	C₂	1	1	yes	maximal, characteristic, complemented
9	#2512	C₂	1	1	yes	maximal, characteristic, complemented
10	#2499	C₂	1	1	yes	maximal, characteristic, complemented
11	#2482	C₂	1	2	yes	maximal, complemented
12	#2480	C₂	1	2	yes	maximal, complemented
13	#2479	C₂	1	2	yes	maximal, complemented
14	#2448	C₂	1	1	yes	maximal, characteristic, complemented
15	#2447	C₂	1	1	yes	maximal, characteristic, complemented
16	#2435	C₂	1	1	yes	maximal, characteristic
17	#2396	C₂	1	1	yes	maximal, characteristic, complemented
18	#2367	C₂	1	1	yes	maximal, characteristic, complemented
19	#2354	C₂	1	1	yes	maximal, characteristic, complemented
20	#2347	C₂	1	1	yes	maximal, characteristic, complemented
21	D₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
22	#2323	C₂	1	1	yes	maximal, characteristic, complemented
23	#2309	C₂	1	1	yes	maximal, characteristic
24	C₂³×D₄	C₂²	1	1	yes	characteristic
25	C₂×#126	C₂²	1	2	yes	complemented
26	C₂×#124	C₂²	1	1	yes	characteristic
27	C₂×#124	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
33	C₂×#117	C₂²	1	1	yes	characteristic
34	C₂×#117	C₂²	1	1	yes	characteristic
35	C₂×#117	C₂²	1	2	yes	complemented
36	C₂²×C₂²⋊C₄	C₂²	1	2	yes	—
37	#400	C₂²	1	1	yes	characteristic, complemented
38	#399	C₂²	1	1	yes	characteristic
39	#399	C₂²	1	2	yes	complemented
40	#399	C₂²	1	2	yes	complemented
41	#398	C₂²	1	1	yes	characteristic, complemented
42	#398	C₂²	1	1	yes	characteristic, complemented
43	#397	C₂²	1	2	yes	—
44	#397	C₂²	1	2	yes	—
45	#397	C₂²	1	2	yes	complemented
46	#397	C₂²	1	2	yes	complemented
47	#397	C₂²	1	2	yes	complemented
48	#397	C₂²	1	2	yes	complemented
49	#397	C₂²	1	2	yes	complemented
50	#397	C₂²	1	2	yes	complemented
51	#397	C₂²	1	2	yes	complemented
52	#396	C₂²	1	1	yes	characteristic
53	#396	C₂²	1	1	yes	characteristic
54	#396	C₂²	1	2	yes	complemented
55	#395	C₂²	1	1	yes	characteristic, complemented
56	#394	C₂²	1	2	yes	—
57	#394	C₂²	1	2	yes	—
58	#393	C₂²	1	1	yes	characteristic
59	#393	C₂²	1	2	yes	complemented
60	#393	C₂²	1	2	yes	complemented
61	#391	C₂²	1	1	yes	characteristic, complemented
62	#391	C₂²	1	1	yes	characteristic, complemented
63	#391	C₂²	1	1	yes	characteristic, complemented
64	#390	C₂²	1	1	yes	characteristic
65	#390	C₂²	1	1	yes	characteristic
66	#390	C₂²	1	2	yes	—
67	#390	C₂²	1	1	yes	characteristic
68	#390	C₂²	1	1	yes	characteristic
69	#390	C₂²	1	2	yes	—
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	1	yes	characteristic
74	#389	C₂²	1	1	yes	characteristic, complemented
75	#389	C₂²	1	2	yes	complemented
76	#389	C₂²	1	1	yes	characteristic, complemented
77	#389	C₂²	1	1	yes	characteristic, complemented
78	#388	C₂²	1	2	yes	—
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	#388	C₂²	1	2	yes	complemented
93	#387	C₂²	1	2	yes	complemented
94	#387	C₂²	1	2	yes	complemented
95	#387	C₂²	1	2	yes	complemented
96	#386	C₂²	1	2	yes	—
97	#386	C₂²	1	2	yes	—
98	#385	C₂²	1	2	yes	complemented
99	#385	C₂²	1	2	yes	complemented
100	#385	C₂²	1	2	yes	complemented
101	#385	C₂²	1	2	yes	complemented
102	#384	C₂²	1	1	yes	characteristic, complemented
103	#383	C₂²	1	2	yes	complemented
104	#382	C₂²	1	1	yes	characteristic, complemented
105	#381	C₂²	1	2	yes	complemented
106	#380	C₂²	1	1	yes	characteristic
107	#380	C₂²	1	2	yes	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	#379	C₂²	1	2	yes	—
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	2	yes	complemented
116	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
117	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
118	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
122	C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
123	C₂⁵	C₂³	1	2	yes	—
124	C₂²×Q₈	C₂³	1	1	yes	characteristic
125	C₂²×Q₈	C₂³	1	1	yes	characteristic
126	C₂²×D₄	—	2	4	no	—
127	C₂²×D₄	—	2	4	no	—
128	C₂²×D₄	—	4	2	no	—
129	C₂²×D₄	C₂³	1	1	yes	characteristic
130	C₂²×D₄	C₂³	1	2	yes	—
131	C₂²×D₄	C₂³	1	1	yes	characteristic
132	C₂³×C₄	C₂³	1	2	yes	—
133	C₂³×C₄	C₂³	1	1	yes	characteristic
134	C₂³×C₄	C₂³	1	2	yes	—
135	#126	—	4	4	no	—
136	#124	—	2	4	no	—
137	#124	—	4	2	no	—
138	C₂²⋊Q₈	—	2	4	no	—
139	C₄×Q₈	—	4	2	no	—
140	C₄×Q₈	—	4	2	no	—
141	C₄×D₄	—	2	4	no	—
142	C₄×D₄	—	4	2	no	—
143	#117	—	2	4	no	—
144	#117	—	4	2	no	—
145	#117	—	4	4	no	—
146	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
160	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄	—	4	4	no	—
170	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
189	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
199	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂×C₄²	C₂³	1	1	yes	characteristic
202	C₂×C₄²	C₂³	1	1	yes	characteristic
203	C₂×C₄²	C₂³	1	2	yes	—
204	C₂×C₄²	C₂³	1	1	yes	characteristic
205	C₂×C₄²	C₂³	1	1	yes	characteristic
206	C₂×C₄²	C₂³	1	1	yes	characteristic
207	C₂×C₄²	C₂³	1	1	yes	characteristic
208	C₂×C₄²	C₂³	1	2	yes	—
209	C₂×C₄²	C₂³	1	2	yes	—
210	C₂×C₄²	C₂³	1	2	yes	—
211	C₂×C₄²	C₂³	1	2	yes	—
212	#95	C₂³	1	1	yes	characteristic
213	#95	C₂³	1	1	yes	characteristic
214	#95	C₂³	1	1	yes	characteristic
215	#95	C₂³	1	1	yes	characteristic
216	#95	C₂³	1	1	yes	characteristic
217	#95	C₂³	1	2	yes	—
218	#95	C₂³	1	2	yes	—
219	#95	C₂³	1	2	yes	—
220	#95	C₂³	1	2	yes	—
221	#95	C₂³	1	1	yes	characteristic
222	#95	C₂³	1	2	yes	—
223	#95	C₂³	1	1	yes	characteristic
224	#95	C₂³	1	1	yes	characteristic
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	2	yes	—
230	#95	C₂³	1	2	yes	—
231	#95	C₂³	1	2	yes	—
232	#95	C₂³	1	2	yes	—
233	#95	C₂³	1	2	yes	—
234	#95	C₂³	1	2	yes	—
235	#95	C₂³	1	2	yes	—
236	#95	C₂³	1	2	yes	—
237	C₂⁴	—	2	4	no	—
238	C₂⁴	—	2	4	no	—
239	C₂⁴	—	4	2	no	—
240	C₂⁴	—	4	2	no	—
241	C₂⁴	—	4	2	no	—
242	C₂⁴	—	4	2	no	—
243	C₂⁴	—	4	2	no	—
244	C₂⁴	C₂⁴	1	2	yes	—
245	C₂⁴	C₂⁴	1	1	yes	characteristic
246	C₂⁴	C₂⁴	1	2	yes	—
247	C₂×Q₈	—	2	2	no	—
248	C₂×Q₈	—	2	2	no	—
249	C₂×Q₈	—	2	2	no	—
250	C₂×Q₈	—	4	1	no	—
251	C₂×Q₈	—	4	1	no	—
252	C₂×Q₈	—	4	1	no	—
253	C₂×D₄	—	2	4	no	—
254	C₂×D₄	—	2	2	no	—
255	C₂×D₄	—	2	4	no	—
256	C₂×D₄	—	2	2	no	—
257	C₂×D₄	—	2	2	no	—
258	C₂×D₄	—	2	2	no	—
259	C₂×D₄	—	2	2	no	—
260	C₂×D₄	—	4	16	no	—
261	C₂×D₄	—	4	2	no	—
262	C₂×D₄	#41	1	4	yes	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	4	2	no	—
268	C₂²×C₄	—	4	2	no	—
269	C₂²×C₄	—	4	2	no	—
270	C₂²×C₄	—	4	2	no	—
271	C₂²×C₄	#41	1	4	yes	—
272	C₂²×C₄	C₂⁴	1	2	yes	—
273	C₂²×C₄	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄	C₂⁴	1	2	yes	—
276	C₂²×C₄	C₂⁴	1	2	yes	—
277	C₂²×C₄	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄	C₂⁴	1	2	yes	—
283	C₂²×C₄	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄	C₂⁴	1	2	yes	—
285	C₂²×C₄	C₂⁴	1	2	yes	—
286	C₂²×C₄	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄	C₂⁴	1	1	yes	characteristic
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	4	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	4	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	4	1	no	—
302	C₄⋊C₄	—	4	1	no	—
303	C₄⋊C₄	—	4	2	no	—
304	C₄⋊C₄	—	4	1	no	—
305	C₄⋊C₄	—	4	2	no	—
306	C₄⋊C₄	—	4	2	no	—
307	C₄⋊C₄	—	4	1	no	—
308	C₄⋊C₄	—	4	1	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₄⋊C₄	—	4	1	no	—
311	C₄⋊C₄	—	4	1	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	—	4	2	no	—
315	C₂²⋊C₄	—	2	4	no	—
316	C₂²⋊C₄	—	2	4	no	—
317	C₂²⋊C₄	—	2	4	no	—
318	C₂²⋊C₄	—	2	4	no	—
319	C₂²⋊C₄	—	2	4	no	—
320	C₂²⋊C₄	—	2	2	no	—
321	C₂²⋊C₄	—	2	4	no	—
322	C₂²⋊C₄	—	4	2	no	—
323	C₂²⋊C₄	—	4	2	no	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₂²⋊C₄	—	4	2	no	—
326	C₂²⋊C₄	—	4	2	no	—
327	C₂²⋊C₄	—	4	2	no	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₂²⋊C₄	—	4	2	no	—
331	C₂²⋊C₄	—	4	2	no	—
332	C₂²⋊C₄	—	4	2	no	—
333	C₂²⋊C₄	—	4	2	no	—
334	C₂²⋊C₄	—	4	1	no	—
335	C₂²⋊C₄	—	4	1	no	—
336	C₂²⋊C₄	—	4	1	no	—
337	C₂²⋊C₄	—	4	1	no	—
338	C₂²⋊C₄	—	4	1	no	—
339	C₂²⋊C₄	—	4	2	no	—
340	C₂²⋊C₄	—	4	2	no	—
341	C₂²⋊C₄	—	4	2	no	—
342	C₂²⋊C₄	—	4	2	no	—
343	C₂²⋊C₄	—	4	2	no	—
344	C₂²⋊C₄	—	4	2	no	—
345	C₂²⋊C₄	—	4	2	no	—
346	C₄²	—	2	4	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	2	2	no	—
353	C₄²	—	4	2	no	—
354	C₄²	—	4	2	no	—
355	C₄²	—	4	2	no	—
356	C₄²	—	4	2	no	—
357	C₂³	—	2	1	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	1	no	—
360	C₂³	—	2	2	no	—
361	C₂³	—	2	1	no	—
362	C₂³	—	2	2	no	—
363	C₂³	—	2	2	no	—
364	C₂³	—	2	2	no	—
365	C₂³	—	2	2	no	—
366	C₂³	—	2	1	no	—
367	C₂³	—	2	1	no	—
368	C₂³	—	2	1	no	—
369	C₂³	—	2	2	no	—
370	C₂³	—	2	2	no	—
371	C₂³	—	2	2	no	—
372	C₂³	—	2	2	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	2	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	4	8	no	—
377	C₂³	—	4	8	no	—
378	C₂³	—	8	4	no	—
379	C₂³	—	8	4	no	—
380	C₂³	—	8	4	no	—
381	C₂³	—	8	4	no	—
382	C₂³	—	8	4	no	—
383	C₂³	C₂×#41	1	2	yes	—
384	C₂³	C₂×#41	1	4	yes	—
385	C₂³	C₂⁵	1	1	yes	characteristic
386	Q₈	—	4	4	no	—
387	Q₈	—	4	4	no	—
388	D₄	—	2	8	no	—
389	D₄	—	4	8	no	—
390	D₄	—	4	4	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	8	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	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	—	4	8	no	—
448	C₂×C₄	—	8	4	no	—
449	C₂×C₄	C₂×#41	1	2	yes	—
450	C₂×C₄	C₂×#41	1	2	yes	—
451	C₂×C₄	C₂×#41	1	2	yes	—
452	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
453	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
454	C₂²	—	2	2	no	—
455	C₂²	—	2	4	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	2	2	no	—
458	C₂²	—	2	4	no	—
459	C₂²	—	2	4	no	—
460	C₂²	—	4	2	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	1	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	1	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	1	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	8	16	no	—
476	C₂²	C₂²×#41	1	1	yes	characteristic
477	C₂²	C₂²×#41	1	1	yes	characteristic
478	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
479	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
480	C₂²	#585	1	1	yes	characteristic
481	C₂²	#585	1	1	yes	characteristic
482	C₂²	#585	1	1	yes	characteristic
483	C₄	—	2	2	no	—
484	C₄	—	2	2	no	—
485	C₄	—	4	2	no	—
486	C₄	—	4	2	no	—
487	C₄	—	4	2	no	—
488	C₄	—	4	2	no	—
489	C₄	—	4	1	no	—
490	C₄	—	4	2	no	—
491	C₄	—	4	1	no	—
492	C₄	—	4	1	no	—
493	C₄	—	4	1	no	—
494	C₄	—	4	1	no	—
495	C₄	—	4	1	no	—
496	C₄	—	4	1	no	—
497	C₄	—	4	1	no	—
498	C₄	—	4	1	no	—
499	C₄	—	4	1	no	—
500	C₄	—	4	2	no	—
501	C₄	—	4	1	no	—
502	C₄	#551	1	4	yes	—
503	C₂	—	4	4	no	—
504	C₂	—	4	2	no	—
505	C₂	—	8	2	no	—
506	C₂	C₂×#551	1	1	yes	characteristic
507	C₂	#3506	1	1	yes	characteristic
508	C₂	#3510	1	1	yes	characteristic
509	C₂	#3513	1	1	yes	characteristic
510	C₂	#3521	1	1	yes	characteristic
511	C₂	#3540	1	1	yes	characteristic
512	C₂	#3546	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂³	C₂⁵
prime radical	C₂³×D₄	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. #2757	C₂	semidirect
2. #2737	C₂	semidirect
3. #2736	C₂	semidirect
4. #2735	C₂	semidirect
5. #2597	C₂	semidirect
6. #2592	C₂	semidirect
7. #2580	C₂	semidirect
8. #2513	C₂	semidirect
9. #2512	C₂	semidirect
10. #2499	C₂	semidirect
11. #2482	C₂	semidirect
12. #2480	C₂	semidirect
13. #2479	C₂	semidirect
14. #2448	C₂	semidirect
15. #2447	C₂	semidirect
17. #2396	C₂	semidirect
18. #2367	C₂	semidirect
19. #2354	C₂	semidirect
20. #2347	C₂	semidirect
22. #2323	C₂	semidirect
25. C₂×#126	C₂²	semidirect
29. C₂×C₄×Q₈	C₂²	semidirect
30. C₂×C₄×Q₈	C₂²	semidirect
35. C₂×#117	C₂²	semidirect
37. #400	C₂²	semidirect
39. #399	C₂²	semidirect
40. #399	C₂²	semidirect
41. #398	C₂²	semidirect
42. #398	C₂²	semidirect
45. #397	C₂²	semidirect
46. #397	C₂²	semidirect
47. #397	C₂²	semidirect
48. #397	C₂²	semidirect
49. #397	C₂²	semidirect
50. #397	C₂²	semidirect
51. #397	C₂²	semidirect
54. #396	C₂²	semidirect
55. #395	C₂²	semidirect
59. #393	C₂²	semidirect
60. #393	C₂²	semidirect
61. #391	C₂²	semidirect
62. #391	C₂²	semidirect
63. #391	C₂²	semidirect
74. #389	C₂²	semidirect
75. #389	C₂²	semidirect
76. #389	C₂²	semidirect
77. #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. #388	C₂²	semidirect
93. #387	C₂²	semidirect
94. #387	C₂²	semidirect
95. #387	C₂²	semidirect
98. #385	C₂²	semidirect
99. #385	C₂²	semidirect
100. #385	C₂²	semidirect
101. #385	C₂²	semidirect
102. #384	C₂²	semidirect
103. #383	C₂²	semidirect
104. #382	C₂²	semidirect
105. #381	C₂²	semidirect
107. #380	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
118. C₄×C₄⋊C₄	C₂²	semidirect
119. C₄×C₄⋊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
#2757	2
#2737	2
#2736	2
#2735	2
#2597	2
#2592	2
#2580	2
#2513	2
#2512	2
#2499	2
#2482	2
#2480	2
#2479	2
#2448	2
#2447	2
#2435	2
#2396	2
#2367	2
#2354	2
#2347	2
D₄×C₂²⋊C₄	2
#2323	2
#2309	2