Subgroups — #497902

Order 512.

674 conjugacy classes of subgroups.

The subgroup lattice has 495 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#2168	C₂	1	1	yes	maximal, characteristic
2	C₂×D₄×C₁₆	C₂	1	1	yes	maximal, characteristic
3	#20484	C₂	1	1	yes	maximal, characteristic
4	#13160	C₂	1	1	yes	maximal, characteristic, complemented
5	#13159	C₂	1	1	yes	maximal, characteristic, complemented
6	#12913	C₂	1	1	yes	maximal, characteristic, complemented
7	#12912	C₂	1	1	yes	maximal, characteristic, complemented
8	#12912	C₂	1	1	yes	maximal, characteristic, complemented
9	#12912	C₂	1	1	yes	maximal, characteristic, complemented
10	#12880	C₂	1	1	yes	maximal, characteristic, complemented
11	#12784	C₂	1	1	yes	maximal, characteristic, complemented
12	#12783	C₂	1	1	yes	maximal, characteristic, complemented
13	#12654	C₂	1	1	yes	maximal, characteristic, complemented
14	#12545	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#1374	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×M₃₂	C₂²	1	1	yes	characteristic
17	C₂³×C₁₆	C₂²	1	1	yes	characteristic
18	C₂³×C₁₆	C₂²	1	1	yes	characteristic
19	C₂³×C₁₆	C₂²	1	1	yes	characteristic
20	C₂×#435	C₄	1	1	yes	characteristic
21	C₂×C₈×D₄	C₂²	1	1	yes	characteristic
22	C₂×#405	C₂²	1	1	yes	characteristic
23	C₂²×C₄×C₈	C₂²	1	1	yes	characteristic
24	#2290	C₄	1	1	yes	characteristic
25	#2168	—	2	4	no	—
26	D₄×C₁₆	—	2	4	no	—
27	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
39	C₂×#346	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
41	#1771	C₄	1	1	yes	characteristic
42	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	#1768	C₄	1	1	yes	characteristic
44	#1753	C₄	1	1	yes	characteristic
45	#1752	C₄	1	1	yes	characteristic
46	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
47	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
48	#1750	C₄	1	1	yes	characteristic
49	#1749	C₄	1	1	yes	characteristic
50	#1726	C₂²	1	1	yes	characteristic
51	#1374	C₂²	1	1	yes	characteristic
52	#1374	C₂²	1	1	yes	characteristic
53	#1374	C₂²	1	1	yes	characteristic
54	#1374	C₂²	1	1	yes	characteristic
55	#1374	C₂²	1	1	yes	characteristic
56	#1374	C₂²	1	1	yes	characteristic
57	#1374	C₂²	1	1	yes	characteristic
58	#1374	C₂²	1	1	yes	characteristic
59	#1374	C₂²	1	1	yes	characteristic
60	#1374	C₂²	1	1	yes	characteristic
61	C₂²×M₁₆	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₈	C₂×C₄	1	1	yes	characteristic
63	C₂³×C₈	C₂³	1	1	yes	characteristic
64	C₂³×C₈	C₂³	1	1	yes	characteristic
65	C₂×C₄×D₄	C₂×C₄	1	1	yes	characteristic
66	C₂×#117	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
68	C₂×M₃₂	—	2	2	no	—
69	C₂×M₃₂	—	2	2	no	—
70	C₂×M₃₂	—	4	1	no	—
71	C₂²×C₁₆	—	2	2	no	—
72	C₂²×C₁₆	—	2	2	no	—
73	C₂²×C₁₆	—	2	2	no	—
74	C₂²×C₁₆	—	2	2	no	—
75	C₂²×C₁₆	—	2	2	no	—
76	C₂²×C₁₆	—	2	2	no	—
77	C₂²×C₁₆	—	4	1	no	—
78	C₂²×C₁₆	—	4	1	no	—
79	C₂²×C₁₆	—	4	1	no	—
80	C₂²×C₁₆	C₂³	1	1	yes	characteristic
81	C₂²×C₁₆	C₂³	1	1	yes	characteristic
82	C₂²×C₁₆	C₂³	1	1	yes	characteristic
83	C₂²×C₁₆	C₂³	1	1	yes	characteristic
84	C₂²×C₁₆	C₂³	1	1	yes	characteristic
85	C₂²×C₁₆	C₂³	1	1	yes	characteristic
86	C₂²×C₁₆	C₂³	1	1	yes	characteristic
87	C₂²×C₁₆	C₂³	1	1	yes	characteristic
88	#435	—	2	4	no	—
89	C₈×D₄	D₄	1	4	yes	—
90	C₈×D₄	Q₈	1	4	yes	—
91	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
93	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
94	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
95	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
96	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
97	#405	—	4	1	no	—
98	#405	—	4	1	no	—
99	C₂×#97	C₂×C₄	1	1	yes	characteristic
100	C₂×#97	C₂×C₄	1	1	yes	characteristic
101	C₂×#97	C₂×C₄	1	1	yes	characteristic
102	C₂×#97	C₂×C₄	1	1	yes	characteristic
103	C₂×#97	C₂×C₄	1	1	yes	characteristic
104	C₂×C₄×C₈	—	4	1	no	—
105	C₂×C₄×C₈	—	4	1	no	—
106	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
109	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
110	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
111	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
112	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
113	#388	C₈	1	1	yes	characteristic
114	#388	C₈	1	1	yes	characteristic
115	#387	C₈	1	1	yes	characteristic
116	#387	C₈	1	1	yes	characteristic
117	#386	C₈	1	1	yes	characteristic
118	#386	C₈	1	1	yes	characteristic
119	#385	C₈	1	1	yes	characteristic
120	#385	C₈	1	1	yes	characteristic
121	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
122	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
123	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
124	#376	C₂×C₄	1	1	yes	characteristic
125	C₄⋊C₁₆	—	2	2	no	—
126	C₄⋊C₁₆	—	2	2	no	—
127	C₄⋊C₁₆	—	2	2	no	—
128	C₄⋊C₁₆	—	2	2	no	—
129	C₄⋊C₁₆	—	4	1	no	—
130	C₄⋊C₁₆	—	4	1	no	—
131	C₄⋊C₁₆	—	4	1	no	—
132	C₄⋊C₁₆	—	4	1	no	—
133	C₂²⋊C₁₆	—	2	2	no	—
134	C₂²⋊C₁₆	—	2	2	no	—
135	C₂²⋊C₁₆	—	2	2	no	—
136	C₂²⋊C₁₆	—	2	2	no	—
137	#346	—	2	2	no	—
138	C₄×C₁₆	—	2	2	no	—
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	C₂²×D₄	C₂×C₈	1	1	yes	characteristic
146	C₂³×C₄	C₂×C₈	1	1	yes	characteristic
147	C₂³×C₄	C₂×C₈	1	1	yes	characteristic
148	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
149	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
150	C₂×M₁₆	—	2	2	no	—
151	C₂×M₁₆	—	2	2	no	—
152	C₂×M₁₆	—	4	1	no	—
153	C₂²×C₈	—	2	1	no	—
154	C₂²×C₈	—	2	1	no	—
155	C₂²×C₈	—	2	1	no	—
156	C₂²×C₈	—	2	1	no	—
157	C₂²×C₈	—	2	1	no	—
158	C₂²×C₈	—	2	1	no	—
159	C₂²×C₈	—	2	1	no	—
160	C₂²×C₈	—	2	1	no	—
161	C₂²×C₈	—	2	2	no	—
162	C₂²×C₈	—	2	2	no	—
163	C₂²×C₈	—	4	1	no	—
164	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₈	C₂×D₄	1	2	yes	—
172	C₂²×C₈	C₂×D₄	1	2	yes	—
173	C₂²×C₈	C₂×Q₈	1	2	yes	—
174	C₂²×C₈	C₂×Q₈	1	2	yes	—
175	C₂²×C₈	C₂⁴	1	1	yes	characteristic
176	C₄×D₄	C₄⋊C₄	1	4	yes	—
177	C₄×D₄	M₁₆	1	4	yes	—
178	#117	—	4	1	no	—
179	#117	—	4	1	no	—
180	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
181	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
182	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
183	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
184	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
185	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
186	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
187	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
188	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
189	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
190	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
191	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
192	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
193	C₂×C₄²	—	4	1	no	—
194	C₂×C₄²	—	4	1	no	—
195	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
196	C₂×C₄²	C₂×C₈	1	1	yes	characteristic
197	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
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	M₃₂	—	4	4	no	—
203	C₂×C₁₆	—	2	1	no	—
204	C₂×C₁₆	—	2	1	no	—
205	C₂×C₁₆	—	2	1	no	—
206	C₂×C₁₆	—	2	1	no	—
207	C₂×C₁₆	—	2	1	no	—
208	C₂×C₁₆	—	2	1	no	—
209	C₂×C₁₆	—	2	1	no	—
210	C₂×C₁₆	—	2	1	no	—
211	C₂×C₁₆	—	2	1	no	—
212	C₂×C₁₆	—	2	1	no	—
213	C₂×C₁₆	—	2	1	no	—
214	C₂×C₁₆	—	2	1	no	—
215	C₂×C₁₆	—	2	1	no	—
216	C₂×C₁₆	—	2	1	no	—
217	C₂×C₁₆	—	2	1	no	—
218	C₂×C₁₆	—	2	1	no	—
219	C₂×C₁₆	—	2	1	no	—
220	C₂×C₁₆	—	2	1	no	—
221	C₂×C₁₆	—	2	1	no	—
222	C₂×C₁₆	—	2	1	no	—
223	C₂×C₁₆	—	2	1	no	—
224	C₂×C₁₆	—	2	1	no	—
225	C₂×C₁₆	—	4	4	no	—
226	C₂×C₁₆	—	4	4	no	—
227	C₂×C₁₆	—	4	4	no	—
228	C₂×C₁₆	#41	1	2	yes	—
229	C₂×C₁₆	#41	1	2	yes	—
230	C₄⋊C₈	—	2	2	no	—
231	C₄⋊C₈	C₄⋊C₄	1	4	yes	—
232	C₂²⋊C₈	—	2	2	no	—
233	C₂²⋊C₈	—	2	2	no	—
234	C₂²⋊C₈	C₄⋊C₄	1	4	yes	—
235	C₂²⋊C₈	C₄⋊C₄	1	4	yes	—
236	#97	—	2	2	no	—
237	#97	—	2	2	no	—
238	#97	—	4	1	no	—
239	#97	—	4	1	no	—
240	#97	—	4	1	no	—
241	C₄×C₈	—	2	1	no	—
242	C₄×C₈	—	2	1	no	—
243	C₄×C₈	—	2	1	no	—
244	C₄×C₈	—	2	1	no	—
245	C₄×C₈	—	2	1	no	—
246	C₄×C₈	—	2	1	no	—
247	C₄×C₈	—	2	1	no	—
248	C₄×C₈	—	2	1	no	—
249	C₄×C₈	—	4	1	no	—
250	C₄×C₈	—	4	1	no	—
251	C₄×C₈	C₂×D₄	1	2	yes	—
252	C₄×C₈	C₂×Q₈	1	2	yes	—
253	#95	C₂×C₈	1	1	yes	characteristic
254	#95	C₂×C₈	1	1	yes	characteristic
255	#95	C₂×C₈	1	1	yes	characteristic
256	#95	C₂×C₈	1	1	yes	characteristic
257	#95	C₂×C₈	1	1	yes	characteristic
258	#95	C₂×C₈	1	1	yes	characteristic
259	#95	C₂×C₈	1	1	yes	characteristic
260	#95	C₂×C₈	1	1	yes	characteristic
261	#95	C₂×C₈	1	1	yes	characteristic
262	#95	C₂×C₈	1	1	yes	characteristic
263	C₂⁴	C₂²×C₈	1	1	yes	characteristic
264	C₂⁴	C₂²×C₈	1	1	yes	characteristic
265	C₂×D₄	—	2	2	no	—
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	C₄⋊C₈	1	4	yes	—
268	C₂²×C₄	—	2	1	no	—
269	C₂²×C₄	—	2	1	no	—
270	C₂²×C₄	—	2	1	no	—
271	C₂²×C₄	—	2	1	no	—
272	C₂²×C₄	—	2	1	no	—
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	4	1	no	—
280	C₂²×C₄	—	4	1	no	—
281	C₂²×C₄	—	4	1	no	—
282	C₂²×C₄	C₂×C₄⋊C₄	1	2	yes	—
283	C₂²×C₄	C₂×C₄⋊C₄	1	2	yes	—
284	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
285	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
286	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
287	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
288	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
289	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
290	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
291	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
292	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
293	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
294	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
295	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
296	C₂²×C₄	C₂×M₁₆	1	2	yes	—
297	C₂²×C₄	C₂×M₁₆	1	2	yes	—
298	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
299	M₁₆	—	4	4	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	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	—	4	4	no	—
326	C₂×C₈	C₂×C₄⋊C₄	1	2	yes	—
327	C₂×C₈	C₂×C₄⋊C₄	1	2	yes	—
328	C₂×C₈	C₂×C₄⋊C₄	1	2	yes	—
329	C₂×C₈	#131	1	2	yes	—
330	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₈	C₂²×Q₈	1	1	yes	characteristic
332	C₂×C₈	C₂×#41	1	1	yes	characteristic
333	C₂×C₈	C₂×#41	1	1	yes	characteristic
334	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
335	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	1	no	—
339	C₄⋊C₄	—	4	1	no	—
340	C₄⋊C₄	C₄⋊C₈	1	4	yes	—
341	C₂²⋊C₄	—	2	2	no	—
342	C₂²⋊C₄	—	2	2	no	—
343	C₂²⋊C₄	—	2	2	no	—
344	C₂²⋊C₄	—	4	1	no	—
345	C₂²⋊C₄	—	4	1	no	—
346	C₂²⋊C₄	—	4	1	no	—
347	C₂²⋊C₄	C₄⋊C₈	1	4	yes	—
348	C₂²⋊C₄	C₄⋊C₈	1	4	yes	—
349	C₄²	—	2	1	no	—
350	C₄²	—	2	1	no	—
351	C₄²	—	2	1	no	—
352	C₄²	—	2	1	no	—
353	C₄²	—	2	1	no	—
354	C₄²	—	2	1	no	—
355	C₄²	—	2	1	no	—
356	C₄²	—	2	1	no	—
357	C₄²	—	4	1	no	—
358	C₄²	—	4	1	no	—
359	C₄²	C₂×C₄⋊C₄	1	2	yes	—
360	C₄²	C₂×M₁₆	1	2	yes	—
361	C₁₆	—	2	2	no	—
362	C₁₆	—	2	2	no	—
363	C₁₆	—	4	1	no	—
364	C₁₆	—	4	1	no	—
365	C₁₆	—	4	1	no	—
366	C₁₆	—	4	1	no	—
367	C₁₆	—	4	1	no	—
368	C₁₆	—	4	1	no	—
369	C₂³	—	2	1	no	—
370	C₂³	—	2	1	no	—
371	C₂³	—	2	1	no	—
372	C₂³	—	2	1	no	—
373	C₂³	—	2	1	no	—
374	C₂³	—	2	1	no	—
375	C₂³	—	2	1	no	—
376	C₂³	—	2	1	no	—
377	C₂³	—	2	1	no	—
378	C₂³	—	2	1	no	—
379	C₂³	C₂×C₄⋊C₈	1	2	yes	—
380	C₂³	C₂×C₄⋊C₈	1	2	yes	—
381	C₂³	#504	1	2	yes	—
382	C₂³	#504	1	2	yes	—
383	C₂³	C₂³×C₈	1	1	yes	characteristic
384	D₄	—	2	8	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	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	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	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	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	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	—	4	4	no	—
425	C₂×C₄	—	4	4	no	—
426	C₂×C₄	C₂×C₄⋊C₈	1	2	yes	—
427	C₂×C₄	C₂×C₄⋊C₈	1	2	yes	—
428	C₂×C₄	C₂×C₄⋊C₈	1	2	yes	—
429	C₂×C₄	C₂×C₄⋊C₈	1	2	yes	—
430	C₂×C₄	#504	1	2	yes	—
431	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
432	C₂×C₄	C₄×#41	1	1	yes	characteristic
433	C₂×C₄	#518	1	1	yes	characteristic
434	C₂×C₄	C₂²×M₁₆	1	1	yes	characteristic
435	C₂×C₄	C₂×#131	1	1	yes	characteristic
436	C₂×C₄	#568	1	1	yes	characteristic
437	C₈	—	2	2	no	—
438	C₈	—	2	2	no	—
439	C₈	—	2	2	no	—
440	C₈	—	2	2	no	—
441	C₈	—	4	1	no	—
442	C₈	—	4	1	no	—
443	C₈	—	4	1	no	—
444	C₈	#546	1	1	yes	characteristic
445	C₈	#546	1	1	yes	characteristic
446	C₈	#554	1	1	yes	characteristic
447	C₈	#554	1	1	yes	characteristic
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	4	1	no	—
458	C₂²	—	4	1	no	—
459	C₂²	—	4	1	no	—
460	C₂²	—	4	1	no	—
461	C₂²	#2151	1	4	yes	—
462	C₂²	C₂²×C₄⋊C₈	1	1	yes	characteristic
463	C₂²	C₈×#41	1	1	yes	characteristic
464	C₂²	#2972	1	1	yes	characteristic
465	C₂²	C₂×#504	1	1	yes	characteristic
466	C₂²	C₂×#504	1	1	yes	characteristic
467	C₂²	C₂×#504	1	1	yes	characteristic
468	C₂²	#3407	1	1	yes	characteristic
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	2	2	no	—
473	C₄	—	2	2	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	1	no	—
476	C₄	—	4	1	no	—
477	C₄	—	4	1	no	—
478	C₄	—	4	1	no	—
479	C₄	—	4	1	no	—
480	C₄	—	4	1	no	—
481	C₄	#2349	1	1	yes	characteristic
482	C₄	#2906	1	1	yes	characteristic
483	C₄	#2970	1	1	yes	characteristic
484	C₄	#2974	1	1	yes	characteristic
485	C₂	—	2	4	no	—
486	C₂	—	4	2	no	—
487	C₂	#22696	1	1	yes	characteristic
488	C₂	C₂×#2151	1	1	yes	characteristic
489	C₂	#33398	1	1	yes	characteristic
490	C₂	#33480	1	1	yes	characteristic
491	C₂	#33482	1	1	yes	characteristic
492	C₂	#33490	1	1	yes	characteristic
493	C₂	#33491	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, cosocle	C₂²×C₈	C₂⁴
commutator, socle	C₂³	C₂³×C₈
prime radical	C₂²×D₄	C₂×C₈
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₈ ◁ G
LECS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
4. #13160	C₂	semidirect
5. #13159	C₂	semidirect
6. #12913	C₂	semidirect
7. #12912	C₂	semidirect
8. #12912	C₂	semidirect
9. #12912	C₂	semidirect
10. #12880	C₂	semidirect
11. #12784	C₂	semidirect
12. #12783	C₂	semidirect
13. #12654	C₂	semidirect
14. #12545	C₂	semidirect
15. C₂×#1374	C₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×#2168	2
C₂×D₄×C₁₆	2
#20484	2
#13160	2
#13159	2
#12913	2
#12912	2
#12880	2
#12784	2
#12783	2
#12654	2
#12545	2
C₂×#1374	2