Subgroups — #217556

Order 512.

626 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21430	C₂	1	1	yes	maximal, characteristic
2	#20812	C₂	1	1	yes	maximal, characteristic
3	#20793	C₂	1	1	yes	maximal, characteristic
4	#9605	C₂	1	1	yes	maximal, characteristic, complemented
5	#9605	C₂	1	1	yes	maximal, characteristic, complemented
6	#9602	C₂	1	1	yes	maximal, characteristic, complemented
7	#9602	C₂	1	1	yes	maximal, characteristic, complemented
8	#8833	C₂	1	1	yes	maximal, characteristic
9	#8833	C₂	1	1	yes	maximal, characteristic
10	#8830	C₂	1	1	yes	maximal, characteristic
11	#8830	C₂	1	1	yes	maximal, characteristic
12	#8809	C₂	1	1	yes	maximal, characteristic, complemented
13	#8805	C₂	1	1	yes	maximal, characteristic, complemented
14	#8787	C₂	1	1	yes	maximal, characteristic, complemented
15	#8784	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#433	—	2	1	no	—
17	C₂×#424	—	2	1	no	—
18	C₂×#424	—	2	1	no	—
19	C₂×#423	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₄×#117	C₂²	1	1	yes	characteristic
22	#1923	C₄	1	1	yes	characteristic
23	#1923	C₄	1	1	yes	characteristic
24	#1923	C₄	1	1	yes	characteristic
25	#1923	C₄	1	1	yes	characteristic
26	#1916	C₄	1	1	yes	characteristic
27	#1916	C₄	1	1	yes	characteristic
28	#1916	C₄	1	1	yes	characteristic
29	#1916	C₄	1	1	yes	characteristic
30	#1843	—	2	1	no	—
31	#1843	—	2	1	no	—
32	#1842	C₂²	1	1	yes	characteristic
33	#1842	C₂²	1	1	yes	characteristic
34	#1842	C₂²	1	1	yes	characteristic
35	#1842	C₂²	1	1	yes	characteristic
36	#1842	C₂²	1	1	yes	characteristic
37	#1842	C₂²	1	1	yes	characteristic
38	#1832	—	2	1	no	—
39	#1798	—	2	1	no	—
40	#1797	C₂²	1	1	yes	characteristic
41	#1797	C₂²	1	1	yes	characteristic
42	#1768	—	2	1	no	—
43	#1767	C₂²	1	1	yes	characteristic
44	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
45	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
47	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
49	#1744	C₂²	1	1	yes	characteristic
50	C₄²×C₈	C₂²	1	1	yes	characteristic
51	C₂×#334	C₂²	1	1	yes	characteristic
52	C₂×#334	C₂²	1	1	yes	characteristic
53	C₂×#334	C₂²	1	1	yes	characteristic
54	C₂×#334	C₂²	1	1	yes	characteristic
55	C₂×#334	C₂²	1	1	yes	characteristic
56	C₂×#334	C₂²	1	1	yes	characteristic
57	C₂×#334	C₂²	1	1	yes	characteristic
58	C₂×#334	C₂²	1	1	yes	characteristic
59	#1277	C₂²	1	1	yes	characteristic
60	#1277	C₂²	1	1	yes	characteristic
61	#1277	C₂²	1	1	yes	characteristic
62	#1277	C₂²	1	1	yes	characteristic
63	#1277	C₂²	1	1	yes	characteristic
64	#1277	C₂²	1	1	yes	characteristic
65	#1277	C₂²	1	1	yes	characteristic
66	#1277	C₂²	1	1	yes	characteristic
67	C₂²×M₁₆	—	2	1	no	—
68	C₂³×C₈	—	2	1	no	—
69	C₂×#117	D₄	1	1	yes	characteristic
70	C₂×#117	D₄	1	1	yes	characteristic
71	C₂²×C₄²	C₂³	1	1	yes	characteristic
72	#433	—	4	4	no	—
73	#424	—	4	4	no	—
74	#424	—	4	4	no	—
75	#423	—	4	1	no	—
76	#423	—	4	1	no	—
77	C₂×C₄⋊C₈	—	2	1	no	—
78	C₂×C₄⋊C₈	—	2	1	no	—
79	C₂×C₄⋊C₈	—	2	1	no	—
80	C₂×C₄⋊C₈	—	2	1	no	—
81	C₂×C₄⋊C₈	—	2	1	no	—
82	C₂×C₄⋊C₈	—	2	1	no	—
83	C₂×C₄⋊C₈	—	2	1	no	—
84	C₂×C₄⋊C₈	—	2	1	no	—
85	C₂×C₄⋊C₈	—	2	1	no	—
86	C₂×C₄⋊C₈	—	2	1	no	—
87	C₂×C₄⋊C₈	—	2	1	no	—
88	C₂×C₄⋊C₈	—	2	1	no	—
89	C₂×C₄⋊C₈	—	2	1	no	—
90	C₂×C₄⋊C₈	—	2	1	no	—
91	C₂×C₄⋊C₈	—	4	1	no	—
92	C₂×C₄⋊C₈	—	4	1	no	—
93	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
105	C₂×C₂²⋊C₈	—	2	1	no	—
106	C₂×C₂²⋊C₈	—	2	1	no	—
107	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
108	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
109	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
110	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
111	C₂×#97	—	2	1	no	—
112	C₂×C₄×C₈	—	2	1	no	—
113	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
114	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
115	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
116	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
117	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
118	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
119	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
120	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
121	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
122	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
123	C₄×C₄⋊C₄	Q₈	1	1	yes	characteristic
124	C₄×C₄⋊C₄	Q₈	1	1	yes	characteristic
125	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
126	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
127	C₄×C₂²⋊C₄	Q₈	1	1	yes	characteristic
128	C₄×C₂²⋊C₄	Q₈	1	1	yes	characteristic
129	#376	D₄	1	1	yes	characteristic
130	#376	D₄	1	1	yes	characteristic
131	C₄³	C₂³	1	1	yes	characteristic
132	C₄³	C₂³	1	1	yes	characteristic
133	#336	—	2	1	no	—
134	#336	—	2	1	no	—
135	#336	—	2	1	no	—
136	#336	—	2	1	no	—
137	#336	C₂×C₄	1	1	yes	characteristic
138	#336	C₂×C₄	1	1	yes	characteristic
139	#336	C₂×C₄	1	1	yes	characteristic
140	#336	C₂×C₄	1	1	yes	characteristic
141	#336	C₂×C₄	1	1	yes	characteristic
142	#336	C₂×C₄	1	1	yes	characteristic
143	#336	C₂×C₄	1	1	yes	characteristic
144	#336	C₂×C₄	1	1	yes	characteristic
145	#336	C₂×C₄	1	1	yes	characteristic
146	#336	C₂×C₄	1	1	yes	characteristic
147	#336	C₂×C₄	1	1	yes	characteristic
148	#336	C₂×C₄	1	1	yes	characteristic
149	#334	—	4	1	no	—
150	#334	—	4	1	no	—
151	#334	—	4	1	no	—
152	#334	—	4	1	no	—
153	#334	—	4	1	no	—
154	#334	—	4	1	no	—
155	#334	—	4	1	no	—
156	#334	—	4	1	no	—
157	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
158	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
159	C₂³×C₄	C₂×Q₈	1	1	yes	characteristic
160	C₂×M₁₆	—	4	2	no	—
161	C₂×M₁₆	—	4	2	no	—
162	C₂×M₁₆	—	4	2	no	—
163	C₂²×C₈	—	2	1	no	—
164	C₂²×C₈	—	2	1	no	—
165	C₂²×C₈	—	2	1	no	—
166	C₂²×C₈	—	2	1	no	—
167	C₂²×C₈	—	2	1	no	—
168	C₂²×C₈	—	2	1	no	—
169	C₂²×C₈	—	2	1	no	—
170	C₂²×C₈	—	2	1	no	—
171	C₂²×C₈	—	4	2	no	—
172	C₂²×C₈	—	4	2	no	—
173	C₂²×C₈	—	4	2	no	—
174	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
181	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
182	#117	—	2	2	no	—
183	#117	—	2	2	no	—
184	#117	SD₁₆	1	4	yes	—
185	#117	SD₁₆	1	4	yes	—
186	C₂×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
187	C₂×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
188	C₂×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
189	C₂×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
190	C₂×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
191	C₂×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
192	C₂×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
193	C₂×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
194	C₂×C₄²	—	2	1	no	—
195	C₂×C₄²	—	2	1	no	—
196	C₂×C₄²	—	2	1	no	—
197	C₂×C₄²	—	2	1	no	—
198	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
200	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
201	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
202	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
203	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
204	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
205	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
206	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
207	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
208	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
209	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
210	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
211	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
212	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
213	C₂×C₄²	C₂⁴	1	1	yes	characteristic
214	C₄⋊C₈	—	2	2	no	—
215	C₄⋊C₈	—	2	2	no	—
216	C₄⋊C₈	—	2	1	no	—
217	C₄⋊C₈	—	2	1	no	—
218	C₄⋊C₈	—	2	1	no	—
219	C₄⋊C₈	—	2	1	no	—
220	C₄⋊C₈	—	2	1	no	—
221	C₄⋊C₈	—	2	1	no	—
222	C₄⋊C₈	—	2	1	no	—
223	C₄⋊C₈	—	2	1	no	—
224	C₄⋊C₈	—	2	1	no	—
225	C₄⋊C₈	—	2	1	no	—
226	C₄⋊C₈	—	2	1	no	—
227	C₄⋊C₈	—	2	1	no	—
228	C₄⋊C₈	—	2	1	no	—
229	C₄⋊C₈	—	2	1	no	—
230	C₄⋊C₈	—	2	1	no	—
231	C₄⋊C₈	—	2	1	no	—
232	C₄⋊C₈	—	4	1	no	—
233	C₄⋊C₈	—	4	1	no	—
234	C₄⋊C₈	—	4	2	no	—
235	C₄⋊C₈	—	4	2	no	—
236	C₄⋊C₈	—	4	2	no	—
237	C₄⋊C₈	—	4	2	no	—
238	C₄⋊C₈	—	4	2	no	—
239	C₄⋊C₈	—	4	2	no	—
240	C₄⋊C₈	—	4	2	no	—
241	C₄⋊C₈	—	4	2	no	—
242	C₄⋊C₈	—	4	2	no	—
243	C₄⋊C₈	—	4	2	no	—
244	C₄⋊C₈	—	4	2	no	—
245	C₄⋊C₈	—	4	2	no	—
246	C₄⋊C₈	—	4	2	no	—
247	C₄⋊C₈	—	4	2	no	—
248	C₂²⋊C₈	—	2	2	no	—
249	C₂²⋊C₈	—	2	2	no	—
250	C₂²⋊C₈	—	4	1	no	—
251	C₂²⋊C₈	—	4	1	no	—
252	C₂²⋊C₈	—	4	2	no	—
253	C₂²⋊C₈	—	4	2	no	—
254	#97	—	4	2	no	—
255	C₄×C₈	—	2	2	no	—
256	C₄×C₈	—	2	2	no	—
257	C₄×C₈	—	2	1	no	—
258	C₄×C₈	—	2	1	no	—
259	C₄×C₈	—	2	1	no	—
260	C₄×C₈	—	2	1	no	—
261	C₄×C₈	—	2	1	no	—
262	C₄×C₈	—	2	1	no	—
263	C₄×C₈	—	2	1	no	—
264	C₄×C₈	—	2	1	no	—
265	C₄×C₈	—	4	1	no	—
266	C₄×C₈	—	4	1	no	—
267	C₄×C₈	—	4	2	no	—
268	#95	C₄⋊C₄	1	1	yes	characteristic
269	#95	C₄⋊C₄	1	1	yes	characteristic
270	#95	C₄⋊C₄	1	1	yes	characteristic
271	#95	C₄⋊C₄	1	1	yes	characteristic
272	#95	C₄⋊C₄	1	1	yes	characteristic
273	#95	C₄⋊C₄	1	1	yes	characteristic
274	#95	C₄⋊C₄	1	1	yes	characteristic
275	#95	C₄⋊C₄	1	1	yes	characteristic
276	C₂⁴	C₂×C₄⋊C₄	1	1	yes	characteristic
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	—	4	1	no	—
291	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
292	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
293	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
294	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
295	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
296	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
297	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
298	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
300	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
302	C₂²×C₄	C₂×SD₁₆	1	2	yes	—
303	C₂²×C₄	C₂×SD₁₆	1	2	yes	—
304	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
305	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
306	C₂²×C₄	C₂²×Q₈	1	1	yes	characteristic
307	M₁₆	—	8	4	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	4	1	no	—
331	C₂×C₈	—	4	1	no	—
332	C₂×C₈	—	4	1	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	4	1	no	—
336	C₂×C₈	—	4	1	no	—
337	C₂×C₈	—	4	1	no	—
338	C₂×C₈	—	4	1	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	4	1	no	—
342	C₂×C₈	—	4	1	no	—
343	C₂×C₈	—	4	1	no	—
344	C₂×C₈	—	4	1	no	—
345	C₂×C₈	—	4	1	no	—
346	C₂×C₈	—	4	1	no	—
347	C₂×C₈	—	4	1	no	—
348	C₂×C₈	—	4	1	no	—
349	C₂×C₈	—	4	1	no	—
350	C₂×C₈	—	4	1	no	—
351	C₂×C₈	—	4	1	no	—
352	C₂×C₈	—	4	1	no	—
353	C₂×C₈	—	4	1	no	—
354	C₂×C₈	—	8	4	no	—
355	C₂×C₈	#131	1	2	yes	—
356	C₂×C₈	#131	1	2	yes	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	#106	1	4	yes	—
360	C₄⋊C₄	#106	1	4	yes	—
361	C₂²⋊C₄	—	2	2	no	—
362	C₂²⋊C₄	—	2	2	no	—
363	C₂²⋊C₄	#106	1	4	yes	—
364	C₂²⋊C₄	#106	1	4	yes	—
365	C₄²	—	2	1	no	—
366	C₄²	—	2	1	no	—
367	C₄²	—	2	1	no	—
368	C₄²	—	2	1	no	—
369	C₄²	—	2	1	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₄²	—	2	1	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	1	no	—
377	C₄²	—	2	1	no	—
378	C₄²	—	2	1	no	—
379	C₄²	—	2	1	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	4	1	no	—
382	C₄²	—	4	1	no	—
383	C₄²	—	4	1	no	—
384	C₄²	—	4	1	no	—
385	C₄²	C₂×SD₁₆	1	2	yes	—
386	C₄²	C₂×SD₁₆	1	2	yes	—
387	C₄²	C₂×SD₁₆	1	2	yes	—
388	C₄²	C₂×SD₁₆	1	2	yes	—
389	C₄²	AGL(1,ℤ/8)	1	2	yes	—
390	C₄²	#137	1	2	yes	—
391	C₄²	H(5,𝔽₂)	1	1	yes	characteristic
392	C₄²	H(5,𝔽₂)	1	1	yes	characteristic
393	C₄²	2₋¹⁺⁴	1	1	yes	characteristic
394	C₄²	2₋¹⁺⁴	1	1	yes	characteristic
395	C₂³	—	2	1	no	—
396	C₂³	—	2	1	no	—
397	C₂³	—	2	1	no	—
398	C₂³	—	2	1	no	—
399	C₂³	—	2	1	no	—
400	C₂³	—	2	1	no	—
401	C₂³	C₂×#106	1	2	yes	—
402	C₂³	C₂²×C₄⋊C₄	1	1	yes	characteristic
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	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	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	1	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	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	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	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	8	1	no	—
440	C₂×C₄	—	8	1	no	—
441	C₂×C₄	C₂×#106	1	2	yes	—
442	C₂×C₄	C₂×#106	1	2	yes	—
443	C₂×C₄	C₂×#106	1	2	yes	—
444	C₂×C₄	C₂×#106	1	2	yes	—
445	C₂×C₄	C₂×#106	1	2	yes	—
446	C₂×C₄	#428	1	2	yes	—
447	C₂×C₄	#428	1	2	yes	—
448	C₂×C₄	#520	1	1	yes	characteristic
449	C₂×C₄	#520	1	1	yes	characteristic
450	C₂×C₄	#535	1	1	yes	characteristic
451	C₂×C₄	#536	1	1	yes	characteristic
452	C₂×C₄	#544	1	1	yes	characteristic
453	C₂×C₄	#544	1	1	yes	characteristic
454	C₂×C₄	C₂×#131	1	1	yes	characteristic
455	C₂×C₄	C₂×#131	1	1	yes	characteristic
456	C₂×C₄	#568	1	1	yes	characteristic
457	C₂×C₄	#568	1	1	yes	characteristic
458	C₂×C₄	C₂²×SD₁₆	1	1	yes	characteristic
459	C₂×C₄	C₂²×SD₁₆	1	1	yes	characteristic
460	C₂×C₄	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
461	C₂×C₄	C₂×#137	1	1	yes	characteristic
462	C₈	—	2	2	no	—
463	C₈	—	2	2	no	—
464	C₈	—	4	1	no	—
465	C₈	—	4	1	no	—
466	C₈	—	4	1	no	—
467	C₈	—	4	1	no	—
468	C₈	—	4	1	no	—
469	C₈	—	4	1	no	—
470	C₈	—	8	1	no	—
471	C₈	—	8	1	no	—
472	C₈	—	8	1	no	—
473	C₈	—	8	1	no	—
474	C₈	—	8	1	no	—
475	C₈	—	8	1	no	—
476	C₈	—	8	1	no	—
477	C₈	—	8	1	no	—
478	C₂²	—	2	2	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	4	1	no	—
482	C₂²	—	4	1	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	4	1	no	—
485	C₂²	#2317	1	1	yes	characteristic
486	C₂²	#2906	1	1	yes	characteristic
487	C₂²	#2906	1	1	yes	characteristic
488	C₂²	C₂²×#106	1	1	yes	characteristic
489	C₂²	C₂×#428	1	1	yes	characteristic
490	C₂²	#2916	1	1	yes	characteristic
491	C₂²	#2916	1	1	yes	characteristic
492	C₄	—	2	2	no	—
493	C₄	—	2	2	no	—
494	C₄	—	2	2	no	—
495	C₄	—	2	2	no	—
496	C₄	—	2	2	no	—
497	C₄	—	2	2	no	—
498	C₄	—	2	2	no	—
499	C₄	—	2	1	no	—
500	C₄	—	2	1	no	—
501	C₄	—	4	1	no	—
502	C₄	—	4	1	no	—
503	C₄	—	4	1	no	—
504	C₄	—	4	1	no	—
505	C₄	#2992	1	1	yes	characteristic
506	C₄	#2993	1	1	yes	characteristic
507	C₄	#2994	1	1	yes	characteristic
508	C₄	#2995	1	1	yes	characteristic
509	C₄	#3206	1	1	yes	characteristic
510	C₄	#3208	1	1	yes	characteristic
511	C₄	#3227	1	1	yes	characteristic
512	C₄	#3229	1	1	yes	characteristic
513	C₂	—	4	2	no	—
514	C₂	#17826	1	1	yes	characteristic
515	C₂	#17826	1	1	yes	characteristic
516	C₂	#17830	1	1	yes	characteristic
517	C₂	#17832	1	1	yes	characteristic
518	C₂	#21980	1	1	yes	characteristic
519	C₂	#21981	1	1	yes	characteristic
520	C₂	#21995	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₄
commutator	C₂²×C₄	C₂³×C₄
Frattini, cosocle	C₂×C₄²	C₂⁴
socle	C₂³	C₂²×C₄⋊C₄
prime radical	C₂⁴	C₂×C₄⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#117 ◁ G
LECS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. #9605	C₂	semidirect
5. #9605	C₂	semidirect
6. #9602	C₂	semidirect
7. #9602	C₂	semidirect
12. #8809	C₂	semidirect
13. #8805	C₂	semidirect
14. #8787	C₂	semidirect
15. #8784	C₂	semidirect

Maximal subgroups

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

subgroup	index
#21430	2
#20812	2
#20793	2
#9605	2
#9602	2
#8833	2
#8830	2
#8809	2
#8805	2
#8787	2
#8784	2