Subgroups — C₂×#10611629 #12963611

Order 1280.

2674 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#66102	C₂	1	1	yes	maximal, characteristic
2	C₂×#66084	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×#444	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#65485	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#65433	C₂	1	2	yes	maximal, complemented
6	#10611629	C₂	1	16	yes	maximal, direct product factor
7	C₂×#65182	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#65184	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×D₅×#104	C₂	1	2	yes	maximal, complemented
10	C₂×#65112	C₂	1	2	yes	maximal, complemented
11	C₂×#65006	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#64996	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×D₅×#41	C₂²	1	2	yes	—
14	C₂×C₅×#135	C₂²	1	1	yes	characteristic
15	C₂×C₅×#131	C₂²	1	2	yes	complemented
16	C₂×#4096	C₂²	1	2	yes	—
17	C₂×#4094	C₂²	1	2	yes	complemented
18	#66102	C₄	1	8	yes	complemented
19	#66102	C₂²	1	8	yes	—
20	C₂×#4064	C₄	1	2	yes	complemented
21	C₂×#4061	C₄	1	2	yes	complemented
22	C₂×#4060	C₄	1	2	yes	complemented
23	C₂×#4057	C₄	1	2	yes	complemented
24	#66084	—	2	8	no	—
25	#66084	C₂²	1	16	yes	complemented
26	C₂×#4053	—	2	2	no	—
27	C₂×#4053	C₂²	1	2	yes	complemented
28	C₂×D₅×M₁₆	—	2	2	no	—
29	C₂×D₅×M₁₆	C₂²	1	2	yes	—
30	C₂×#4050	C₂²	1	1	yes	characteristic
31	C₂×#4047	—	2	2	no	—
32	C₂×#4047	C₂²	1	2	yes	complemented
33	C₂²×#676	—	2	2	no	—
34	C₂²×#676	C₂²	1	1	yes	characteristic
35	C₂²×#676	C₂²	1	1	yes	characteristic
36	C₂×C₄²×D₅	C₂²	1	1	yes	characteristic
37	C₅×#444	C₂²	1	8	yes	complemented
38	C₂×C₅×#108	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₅×#104	C₂²	1	2	yes	complemented
40	C₂×C₅×#97	C₂²	1	1	yes	characteristic, complemented
41	C₂×#3969	C₂²	1	2	yes	complemented
42	#65485	C₂²	1	8	yes	complemented
43	#65433	C₂²	1	16	yes	complemented
44	C₂×#3957	C₂²	1	2	yes	complemented
45	C₂×#3954	C₂²	1	2	yes	complemented
46	C₂×#3951	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
49	C₂×#3937	C₂²	1	2	yes	complemented
50	C₂×#3935	C₂²	1	1	yes	characteristic, complemented
51	#65184	C₂²	1	8	yes	complemented
52	#65182	C₂²	1	8	yes	complemented
53	#65112	C₂²	1	16	yes	complemented
54	D₅×#104	C₂²	1	16	yes	complemented
55	#65006	C₂²	1	8	yes	complemented
56	#64996	C₂²	1	8	yes	complemented
57	C₂×#2956	—	5	1	no	maximal, Sylow
58	C₂×C₅×#41	C₂³	1	2	yes	—
59	D₅×#41	—	2	4	no	—
60	D₅×#41	—	2	4	no	—
61	D₅×#41	C₂×C₄	1	8	yes	—
62	D₅×#41	C₂³	1	8	yes	—
63	C₂×#713	C₂×C₄	1	2	yes	—
64	C₂×Q₈×D₅	C₂×C₄	1	2	yes	—
65	C₂×#711	—	2	2	no	—
66	C₂×#711	C₂×C₄	1	2	yes	—
67	C₂×D₄×D₅	—	2	2	no	—
68	C₂×D₄×D₅	C₂×C₄	1	2	yes	—
69	C₂×#709	—	2	2	no	—
70	C₂×#709	C₂³	1	2	yes	—
71	C₂²×C₄×D₅	—	2	2	no	—
72	C₂²×C₄×D₅	—	2	1	no	—
73	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
74	C₅×#135	C₂×C₄	1	4	yes	complemented
75	C₅×#135	C₂³	1	4	yes	—
76	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
77	C₂×C₅×SD₁₆	C₂×C₄	1	2	yes	complemented
78	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic, complemented
79	C₅×#131	—	2	4	no	—
80	C₅×#131	C₂³	1	8	yes	complemented
81	C₂×C₅×M₁₆	—	2	2	no	—
82	C₂×C₅×M₁₆	C₂³	1	2	yes	—
83	C₂²×C₅×C₈	—	2	2	no	—
84	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
85	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
87	#4096	C₂×C₄	1	8	yes	complemented
88	#4096	C₂³	1	8	yes	—
89	#4094	—	2	4	no	—
90	#4094	C₂³	1	8	yes	complemented
91	C₂×#689	C₂×C₄	1	2	yes	complemented
92	C₂×#688	C₂×C₄	1	2	yes	complemented
93	C₂×#687	C₂×C₄	1	2	yes	complemented
94	C₂×#686	C₂×C₄	1	2	yes	complemented
95	C₂×C₄×Dic₅	—	2	1	no	—
96	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
97	C₂×#681	—	2	2	no	—
98	C₂×#681	C₂³	1	2	yes	—
99	C₂²×#168	—	2	2	no	—
100	C₂²×#168	C₂³	1	1	yes	characteristic
101	C₂²×#168	C₂³	1	1	yes	characteristic
102	#4064	C₂×C₄	1	16	yes	complemented
103	#4061	C₂×C₄	1	16	yes	complemented
104	#4060	C₂×C₄	1	16	yes	complemented
105	#4057	C₂×C₄	1	16	yes	complemented
106	#4053	—	2	4	no	—
107	#4053	—	2	16	no	—
108	#4053	C₂³	1	8	yes	complemented
109	D₅×M₁₆	—	2	4	no	—
110	D₅×M₁₆	—	2	16	no	—
111	D₅×M₁₆	C₂³	1	8	yes	—
112	C₂×Dic₂₀	C₂×C₄	1	1	yes	characteristic, complemented
113	#4050	C₂×C₄	1	4	yes	complemented
114	#4050	C₂³	1	4	yes	—
115	C₂×D₄₀	C₂×C₄	1	1	yes	characteristic, complemented
116	C₂×#677	C₂×C₄	1	2	yes	complemented
117	#4047	—	2	4	no	—
118	#4047	—	2	16	no	—
119	#4047	C₂³	1	8	yes	complemented
120	C₂×#676	—	2	2	no	—
121	C₂×#676	—	2	2	no	—
122	C₂×#676	—	2	2	no	—
123	C₂×#676	—	2	16	no	—
124	C₂×#676	C₂×C₄	1	2	yes	—
125	C₂×#676	C₂×C₄	1	2	yes	—
126	C₂×#676	C₂×C₄	1	4	yes	—
127	C₂×#676	D₄	1	2	yes	—
128	C₂×#676	D₄	1	2	yes	—
129	C₂×#676	D₄	1	4	yes	—
130	C₂×#676	C₂³	1	4	yes	—
131	C₂×#676	C₂³	1	4	yes	—
132	C₂×C₈×D₅	—	2	2	no	—
133	C₂×C₈×D₅	—	2	2	no	—
134	C₂×C₈×D₅	—	2	2	no	—
135	C₄²×D₅	—	2	2	no	—
136	C₄²×D₅	C₂³	1	4	yes	—
137	C₅×#108	C₂³	1	4	yes	complemented
138	C₅×#104	C₂³	1	8	yes	complemented
139	C₅×#97	C₂³	1	4	yes	complemented
140	#3969	C₂³	1	8	yes	complemented
141	#3957	C₂³	1	8	yes	complemented
142	#3954	C₂³	1	8	yes	complemented
143	#3951	C₂³	1	4	yes	complemented
144	C₈×Dic₅	C₂³	1	4	yes	complemented
145	C₈×Dic₅	C₂³	1	4	yes	complemented
146	#3937	C₂³	1	8	yes	complemented
147	#3935	C₂³	1	4	yes	complemented
148	C₂×#575	—	5	1	no	—
149	C₂×#568	—	5	2	no	—
150	#2956	—	5	16	no	—
151	C₂×#444	—	5	2	no	—
152	C₂×#444	—	5	1	no	—
153	C₂×#444	D₅	1	1	yes	characteristic, complemented
154	C₂×#443	—	5	1	no	—
155	C₂×#443	—	5	1	no	—
156	C₂×#443	—	5	2	no	—
157	C₂×#430	—	5	1	no	—
158	C₂²×#104	—	5	2	no	—
159	C₂×C₄×M₁₆	—	5	1	no	—
160	C₂³×D₅	—	2	2	no	—
161	C₂³×D₅	#41	1	1	yes	characteristic
162	C₅×#41	—	2	2	no	—
163	C₅×#41	—	2	2	no	—
164	C₅×#41	C₂²×C₄	1	4	yes	—
165	C₅×#41	C₂⁴	1	4	yes	—
166	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
167	C₂×C₅×D₄	—	2	2	no	—
168	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
169	C₂²×C₄×C₅	—	2	2	no	—
170	C₂²×C₄×C₅	—	2	1	no	—
171	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
172	C₂×C₂²⋊D₅	—	2	2	no	—
173	C₂×C₂²⋊D₅	—	2	2	no	—
174	C₂×C₂²⋊D₅	—	2	2	no	—
175	C₂²×Dic₅	—	2	1	no	—
176	C₂²×Dic₅	—	2	2	no	—
177	C₂²×Dic₅	#41	1	1	yes	characteristic
178	#713	—	2	4	no	—
179	#713	C₂²×C₄	1	8	yes	—
180	Q₈×D₅	—	2	4	no	—
181	Q₈×D₅	C₂²×C₄	1	8	yes	—
182	#711	—	2	8	no	—
183	#711	—	2	8	no	—
184	#711	—	2	4	no	—
185	#711	C₂²×C₄	1	8	yes	—
186	D₄×D₅	—	2	8	no	—
187	D₄×D₅	—	2	8	no	—
188	D₄×D₅	—	2	4	no	—
189	D₄×D₅	C₂²×C₄	1	8	yes	—
190	#709	—	2	2	no	—
191	#709	—	2	2	no	—
192	#709	—	2	8	no	—
193	#709	—	2	8	no	—
194	#709	C₂²×C₄	1	4	yes	—
195	#709	C₂⁴	1	4	yes	—
196	C₂×D₂₀	—	2	2	no	—
197	C₂×D₂₀	C₂²×C₄	1	2	yes	—
198	C₂×C₄×D₅	—	2	2	no	—
199	C₂×C₄×D₅	—	2	2	no	—
200	C₂×C₄×D₅	—	2	2	no	—
201	C₂×C₄×D₅	—	2	8	no	—
202	C₂×C₄×D₅	—	2	8	no	—
203	C₂×C₄×D₅	—	2	4	no	—
204	C₂×C₄×D₅	—	4	4	no	—
205	C₂×C₄×D₅	C₂²×C₄	1	2	yes	—
206	C₂×C₄×D₅	C₂²×C₄	1	2	yes	—
207	C₂×C₄×D₅	C₂×D₄	1	2	yes	—
208	C₂×C₄×D₅	C₂×D₄	1	2	yes	—
209	C₂×C₄×D₅	#41	1	2	yes	—
210	C₂×C₄×D₅	C₂⁴	1	2	yes	—
211	C₂×Dic₁₀	—	2	2	no	—
212	C₂×Dic₁₀	C₂²×C₄	1	2	yes	—
213	C₅×Q₁₆	C₂²×C₄	1	4	yes	complemented
214	C₅×SD₁₆	C₂²×C₄	1	8	yes	complemented
215	C₅×D₈	C₂²×C₄	1	4	yes	complemented
216	C₅×M₁₆	—	2	2	no	—
217	C₅×M₁₆	—	2	8	no	—
218	C₅×M₁₆	C₂⁴	1	4	yes	—
219	C₂×C₅×C₈	—	2	2	no	—
220	C₂×C₅×C₈	—	2	8	no	—
221	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
222	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
223	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
224	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
225	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
226	C₂×C₅×C₈	C₂⁴	1	2	yes	—
227	C₂×C₅×C₈	C₂⁴	1	2	yes	—
228	C₄²×C₅	—	2	1	no	—
229	C₄²×C₅	C₂⁴	1	2	yes	—
230	#689	C₂²×C₄	1	8	yes	complemented
231	#688	C₂²×C₄	1	8	yes	complemented
232	#687	C₂²×C₄	1	8	yes	complemented
233	#686	C₂²×C₄	1	8	yes	complemented
234	C₄×Dic₅	—	2	1	no	—
235	C₄×Dic₅	—	2	4	no	—
236	C₄×Dic₅	C₂⁴	1	2	yes	—
237	#681	—	2	2	no	—
238	#681	—	2	8	no	—
239	#681	C₂⁴	1	4	yes	—
240	C₂×#168	—	2	2	no	—
241	C₂×#168	—	2	8	no	—
242	C₂×#168	C₂²×C₄	1	2	yes	—
243	C₂×#168	C₂²×C₄	1	2	yes	—
244	C₂×#168	C₂×D₄	1	1	yes	characteristic
245	C₂×#168	C₂×D₄	1	1	yes	characteristic
246	C₂×#168	C₂×D₄	1	2	yes	—
247	C₂×#168	C₂⁴	1	2	yes	—
248	C₂×#168	C₂⁴	1	2	yes	—
249	Dic₂₀	C₂²×C₄	1	4	yes	complemented
250	D₄₀	C₂²×C₄	1	4	yes	complemented
251	#677	C₂²×C₄	1	8	yes	complemented
252	#676	—	2	8	no	—
253	#676	—	2	8	no	—
254	#676	—	2	8	no	—
255	#676	C₂²×C₄	1	8	yes	—
256	#676	C₂²×C₄	1	8	yes	—
257	#676	C₂×D₄	1	8	yes	—
258	#676	C₂×D₄	1	8	yes	—
259	C₈×D₅	—	2	8	no	—
260	C₈×D₅	—	2	8	no	—
261	C₈×D₅	—	2	8	no	—
262	C₂²×#41	—	5	2	no	—
263	#575	—	5	8	no	—
264	#575	—	5	8	no	—
265	C₂×#137	—	5	2	no	—
266	C₂×#137	—	5	2	no	—
267	C₂×AGL(1,ℤ/8)	—	5	2	no	—
268	C₂×AGL(1,ℤ/8)	—	5	2	no	—
269	C₂×#135	—	5	2	no	—
270	C₂×#135	—	5	1	no	—
271	C₂×#135	C₂×D₅	1	1	yes	characteristic
272	#568	—	5	16	no	—
273	#568	—	10	8	no	—
274	C₂×#131	—	5	2	no	—
275	C₂×#131	—	5	2	no	—
276	C₂×#131	—	5	2	no	—
277	C₂×#131	—	10	2	no	—
278	C₂×#131	—	10	2	no	—
279	C₂×#131	C₂×D₅	1	2	yes	complemented
280	C₂²×M₁₆	—	5	1	no	—
281	C₂²×M₁₆	—	5	1	no	—
282	C₂²×M₁₆	—	5	2	no	—
283	C₂²×M₁₆	—	10	2	no	—
284	C₂²×M₁₆	—	10	2	no	—
285	C₂²×C₄²	—	5	1	no	—
286	#444	—	5	16	no	—
287	#444	—	5	8	no	—
288	#444	C₂×D₅	1	8	yes	complemented
289	#443	—	5	8	no	—
290	#443	—	5	16	no	—
291	#443	—	5	8	no	—
292	#430	—	5	8	no	—
293	C₂×#108	—	5	2	no	—
294	C₂×#108	—	5	1	no	—
295	C₂×#108	C₂×D₅	1	1	yes	characteristic, complemented
296	C₂×#104	—	5	2	no	—
297	C₂×#104	—	5	2	no	—
298	C₂×#104	—	5	2	no	—
299	C₂×#104	—	5	16	no	—
300	C₂×#104	C₂×D₅	1	2	yes	complemented
301	C₄×M₁₆	—	5	8	no	—
302	C₂×#97	—	5	1	no	—
303	C₂×#97	C₂×D₅	1	1	yes	characteristic, complemented
304	C₂×C₄×C₈	—	5	1	no	—
305	C₂×C₄×C₈	—	5	1	no	—
306	C₂³×C₅	—	2	2	no	—
307	C₂³×C₅	C₂×#41	1	1	yes	characteristic
308	C₂²×D₅	—	2	2	no	—
309	C₂²×D₅	—	2	8	no	—
310	C₂²×D₅	—	4	2	no	—
311	C₂²×D₅	—	8	4	no	—
312	C₂²×D₅	C₄×D₄	1	2	yes	—
313	C₂²×D₅	C₄×D₄	1	2	yes	—
314	C₂²×D₅	C₂×#41	1	2	yes	—
315	C₅×Q₈	—	2	2	no	—
316	C₅×Q₈	C₂³×C₄	1	4	yes	—
317	C₅×D₄	—	2	4	no	—
318	C₅×D₄	—	2	4	no	—
319	C₅×D₄	—	2	2	no	—
320	C₅×D₄	C₂³×C₄	1	4	yes	—
321	C₂×C₄×C₅	—	2	2	no	—
322	C₂×C₄×C₅	—	2	4	no	—
323	C₂×C₄×C₅	—	2	4	no	—
324	C₂×C₄×C₅	—	2	2	no	—
325	C₂×C₄×C₅	—	4	2	no	—
326	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
327	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
328	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
331	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
332	C₂²⋊D₅	—	2	4	no	—
333	C₂²⋊D₅	—	2	4	no	—
334	C₂²⋊D₅	—	2	8	no	—
335	C₂²⋊D₅	—	2	8	no	—
336	C₂×Dic₅	—	2	4	no	—
337	C₂×Dic₅	—	2	2	no	—
338	C₂×Dic₅	—	2	2	no	—
339	C₂×Dic₅	—	2	8	no	—
340	C₂×Dic₅	C₄×D₄	1	2	yes	—
341	C₂×Dic₅	C₄×D₄	1	2	yes	—
342	C₂×Dic₅	C₂×#41	1	2	yes	—
343	D₂₀	—	2	8	no	—
344	D₂₀	—	2	2	no	—
345	D₂₀	C₂³×C₄	1	4	yes	—
346	C₄×D₅	—	2	8	no	—
347	C₄×D₅	—	2	4	no	—
348	C₄×D₅	—	2	4	no	—
349	C₄×D₅	—	2	8	no	—
350	C₄×D₅	—	4	8	no	—
351	C₄×D₅	C₄×D₄	1	4	yes	—
352	C₄×D₅	C₄×D₄	1	4	yes	—
353	C₄×D₅	C₂³×C₄	1	4	yes	—
354	C₄×D₅	C₂²×D₄	1	4	yes	—
355	Dic₁₀	—	2	2	no	—
356	Dic₁₀	—	2	8	no	—
357	Dic₁₀	C₂³×C₄	1	4	yes	—
358	C₅×C₈	—	2	4	no	—
359	C₅×C₈	C₂³×C₄	1	2	yes	—
360	C₅×C₈	C₂³×C₄	1	2	yes	—
361	C₅×C₈	C₂²×D₄	1	4	yes	—
362	#168	—	2	4	no	—
363	#168	C₂³×C₄	1	4	yes	—
364	#168	C₂²×D₄	1	2	yes	—
365	#168	C₂²×D₄	1	2	yes	—
366	C₂×#41	—	5	8	no	—
367	C₂×#41	—	5	8	no	—
368	C₂×#41	—	5	2	no	—
369	C₂×#41	—	5	2	no	—
370	C₂×#41	—	5	2	no	—
371	C₂×#41	—	10	2	no	—
372	C₂×#41	—	10	2	no	—
373	C₂×#41	—	10	4	no	—
374	C₂×#41	—	10	4	no	—
375	C₂×#41	C₂²×D₅	1	2	yes	—
376	C₂²×Q₈	—	5	2	no	—
377	C₂²×D₄	—	5	2	no	—
378	C₂²×D₄	—	10	2	no	—
379	C₂³×C₄	—	5	1	no	—
380	C₂³×C₄	—	10	2	no	—
381	C₂³×C₄	—	10	1	no	—
382	#137	—	5	16	no	—
383	#137	—	5	16	no	—
384	AGL(1,ℤ/8)	—	5	16	no	—
385	AGL(1,ℤ/8)	—	5	16	no	—
386	#135	—	5	8	no	—
387	#135	—	5	8	no	—
388	#135	—	5	4	no	—
389	#135	—	5	4	no	—
390	#135	C₄×D₅	1	4	yes	complemented
391	#135	C₂²×D₅	1	4	yes	—
392	C₂×Q₁₆	—	5	2	no	—
393	C₂×Q₁₆	—	5	1	no	—
394	C₂×Q₁₆	C₄×D₅	1	1	yes	characteristic, complemented
395	C₂×SD₁₆	—	5	2	no	—
396	C₂×SD₁₆	—	5	2	no	—
397	C₂×SD₁₆	—	5	2	no	—
398	C₂×SD₁₆	C₄×D₅	1	2	yes	complemented
399	C₂×D₈	—	5	2	no	—
400	C₂×D₈	—	5	1	no	—
401	C₂×D₈	C₄×D₅	1	1	yes	characteristic, complemented
402	#131	—	2	4	no	—
403	#131	—	5	8	no	—
404	#131	—	5	8	no	—
405	#131	—	5	8	no	—
406	#131	—	10	16	no	—
407	#131	—	10	4	no	—
408	#131	—	10	4	no	—
409	#131	—	10	16	no	—
410	#131	—	10	4	no	—
411	#131	C₂²×D₅	1	8	yes	complemented
412	C₂×M₁₆	—	2	2	no	—
413	C₂×M₁₆	—	5	2	no	—
414	C₂×M₁₆	—	5	2	no	—
415	C₂×M₁₆	—	5	4	no	—
416	C₂×M₁₆	—	5	2	no	—
417	C₂×M₁₆	—	5	2	no	—
418	C₂×M₁₆	—	5	4	no	—
419	C₂×M₁₆	—	5	4	no	—
420	C₂×M₁₆	—	5	4	no	—
421	C₂×M₁₆	—	5	2	no	—
422	C₂×M₁₆	—	5	8	no	—
423	C₂×M₁₆	—	10	2	no	—
424	C₂×M₁₆	—	10	16	no	—
425	C₂×M₁₆	—	10	2	no	—
426	C₂×M₁₆	—	10	2	no	—
427	C₂×M₁₆	—	10	16	no	—
428	C₂×M₁₆	—	10	4	no	—
429	C₂×M₁₆	—	10	2	no	—
430	C₂×M₁₆	C₂²×D₅	1	2	yes	—
431	C₂²×C₈	—	2	2	no	—
432	C₂²×C₈	—	5	1	no	—
433	C₂²×C₈	—	5	1	no	—
434	C₂²×C₈	—	10	2	no	—
435	C₂²×C₈	—	10	2	no	—
436	C₂²×C₈	—	10	2	no	—
437	C₂²×C₈	—	10	2	no	—
438	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
439	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
440	C₂×C₄²	—	5	1	no	—
441	C₂×C₄²	—	5	4	no	—
442	C₂×C₄²	—	10	2	no	—
443	C₂×C₄²	—	10	1	no	—
444	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
445	#108	—	5	8	no	—
446	#108	—	5	4	no	—
447	#108	C₂²×D₅	1	4	yes	complemented
448	#104	—	5	8	no	—
449	#104	—	5	8	no	—
450	#104	—	5	8	no	—
451	#104	C₂²×D₅	1	8	yes	complemented
452	#97	—	5	4	no	—
453	#97	C₂²×D₅	1	4	yes	complemented
454	C₄×C₈	—	5	4	no	—
455	C₄×C₈	—	5	4	no	—
456	C₂²×C₅	—	2	2	no	—
457	C₂²×C₅	—	2	4	no	—
458	C₂²×C₅	—	4	4	no	—
459	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
460	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
461	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
462	C₂×D₅	—	2	4	no	—
463	C₂×D₅	—	2	4	no	—
464	C₂×D₅	—	4	2	no	—
465	C₂×D₅	—	4	2	no	—
466	C₂×D₅	—	4	4	no	—
467	C₂×D₅	—	8	8	no	—
468	C₂×D₅	C₂×C₄×D₄	1	4	yes	—
469	C₄×C₅	—	2	4	no	—
470	C₄×C₅	—	4	2	no	—
471	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
472	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
473	C₄×C₅	C₂⁴×C₄	1	1	yes	characteristic
474	C₄×C₅	C₂³×D₄	1	1	yes	characteristic
475	Dic₅	—	2	4	no	—
476	Dic₅	—	2	4	no	—
477	Dic₅	C₂×C₄×D₄	1	4	yes	—
478	C₂⁴	—	5	1	no	—
479	C₂⁴	—	10	2	no	—
480	#41	—	2	2	no	—
481	#41	—	2	2	no	—
482	#41	—	5	8	no	—
483	#41	—	5	8	no	—
484	#41	—	5	4	no	—
485	#41	—	5	4	no	—
486	#41	—	10	8	no	—
487	#41	—	10	8	no	—
488	#41	—	10	8	no	—
489	#41	—	10	8	no	—
490	#41	—	10	4	no	—
491	#41	—	10	4	no	—
492	#41	—	10	2	no	—
493	#41	—	10	2	no	—
494	#41	C₂×C₄×D₅	1	4	yes	—
495	#41	C₂³×D₅	1	4	yes	—
496	C₂×Q₈	—	5	8	no	—
497	C₂×Q₈	—	5	2	no	—
498	C₂×Q₈	—	10	2	no	—
499	C₂×Q₈	—	10	4	no	—
500	C₂×Q₈	C₂×C₄×D₅	1	2	yes	—
501	C₂×D₄	—	2	2	no	—
502	C₂×D₄	—	5	8	no	—
503	C₂×D₄	—	5	2	no	—
504	C₂×D₄	—	10	2	no	—
505	C₂×D₄	—	10	4	no	—
506	C₂×D₄	—	10	2	no	—
507	C₂×D₄	—	10	8	no	—
508	C₂×D₄	—	10	8	no	—
509	C₂×D₄	—	10	2	no	—
510	C₂×D₄	—	10	2	no	—
511	C₂×D₄	C₂×C₄×D₅	1	2	yes	—
512	C₂²×C₄	—	2	2	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	5	1	no	—
515	C₂²×C₄	—	5	2	no	—
516	C₂²×C₄	—	5	2	no	—
517	C₂²×C₄	—	5	2	no	—
518	C₂²×C₄	—	5	2	no	—
519	C₂²×C₄	—	5	2	no	—
520	C₂²×C₄	—	5	2	no	—
521	C₂²×C₄	—	10	8	no	—
522	C₂²×C₄	—	10	2	no	—
523	C₂²×C₄	—	10	8	no	—
524	C₂²×C₄	—	10	2	no	—
525	C₂²×C₄	—	10	4	no	—
526	C₂²×C₄	—	10	2	no	—
527	C₂²×C₄	—	10	1	no	—
528	C₂²×C₄	—	10	2	no	—
529	C₂²×C₄	—	20	4	no	—
530	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
531	Q₁₆	—	5	8	no	—
532	Q₁₆	—	5	4	no	—
533	Q₁₆	C₂×C₄×D₅	1	4	yes	complemented
534	SD₁₆	—	5	8	no	—
535	SD₁₆	—	5	8	no	—
536	SD₁₆	—	5	8	no	—
537	SD₁₆	C₂×C₄×D₅	1	8	yes	complemented
538	D₈	—	5	8	no	—
539	D₈	—	5	4	no	—
540	D₈	C₂×C₄×D₅	1	4	yes	complemented
541	M₁₆	—	2	2	no	—
542	M₁₆	—	2	8	no	—
543	M₁₆	—	5	8	no	—
544	M₁₆	—	5	8	no	—
545	M₁₆	—	5	8	no	—
546	M₁₆	—	5	8	no	—
547	M₁₆	—	5	4	no	—
548	M₁₆	—	10	8	no	—
549	M₁₆	—	10	8	no	—
550	M₁₆	—	10	8	no	—
551	M₁₆	—	10	2	no	—
552	M₁₆	—	10	8	no	—
553	M₁₆	C₂³×D₅	1	4	yes	—
554	C₂×C₈	—	2	2	no	—
555	C₂×C₈	—	2	8	no	—
556	C₂×C₈	—	5	2	no	—
557	C₂×C₈	—	5	2	no	—
558	C₂×C₈	—	5	2	no	—
559	C₂×C₈	—	5	1	no	—
560	C₂×C₈	—	5	1	no	—
561	C₂×C₈	—	5	2	no	—
562	C₂×C₈	—	5	2	no	—
563	C₂×C₈	—	10	8	no	—
564	C₂×C₈	—	10	8	no	—
565	C₂×C₈	—	10	8	no	—
566	C₂×C₈	—	10	2	no	—
567	C₂×C₈	—	10	8	no	—
568	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
569	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
570	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
571	C₂×C₈	D₄×D₅	1	2	yes	—
572	C₂×C₈	D₄×D₅	1	2	yes	—
573	C₂×C₈	C₂³×D₅	1	2	yes	—
574	C₂×C₈	C₂³×D₅	1	2	yes	—
575	C₄²	—	2	1	no	—
576	C₄²	—	5	2	no	—
577	C₄²	—	10	4	no	—
578	C₄²	—	10	1	no	—
579	C₄²	C₂³×D₅	1	2	yes	—
580	C₂×C₅	—	2	1	no	—
581	C₂×C₅	—	2	1	no	—
582	C₂×C₅	—	4	4	no	—
583	C₂×C₅	#2956	1	2	yes	complemented
584	C₂×C₅	C₂²×C₄×D₄	1	1	yes	characteristic
585	D₅	—	2	4	no	—
586	D₅	—	4	4	no	—
587	C₂³	—	2	2	no	—
588	C₂³	—	5	2	no	—
589	C₂³	—	5	2	no	—
590	C₂³	—	5	2	no	—
591	C₂³	—	10	8	no	—
592	C₂³	—	10	2	no	—
593	C₂³	—	20	2	no	—
594	C₂³	—	40	4	no	—
595	C₂³	D₅×#41	1	1	yes	characteristic
596	Q₈	—	2	2	no	—
597	Q₈	—	5	4	no	—
598	Q₈	—	10	8	no	—
599	Q₈	—	10	2	no	—
600	Q₈	C₂²×C₄×D₅	1	4	yes	—
601	D₄	—	2	4	no	—
602	D₄	—	2	4	no	—
603	D₄	—	2	2	no	—
604	D₄	—	5	4	no	—
605	D₄	—	10	8	no	—
606	D₄	—	10	8	no	—
607	D₄	—	10	8	no	—
608	D₄	—	10	4	no	—
609	D₄	—	10	4	no	—
610	D₄	—	10	2	no	—
611	D₄	C₂²×C₄×D₅	1	4	yes	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	4	2	no	—
617	C₂×C₄	—	5	2	no	—
618	C₂×C₄	—	5	2	no	—
619	C₂×C₄	—	5	2	no	—
620	C₂×C₄	—	5	4	no	—
621	C₂×C₄	—	5	4	no	—
622	C₂×C₄	—	5	4	no	—
623	C₂×C₄	—	5	4	no	—
624	C₂×C₄	—	10	8	no	—
625	C₂×C₄	—	10	8	no	—
626	C₂×C₄	—	10	8	no	—
627	C₂×C₄	—	10	4	no	—
628	C₂×C₄	—	10	2	no	—
629	C₂×C₄	—	10	2	no	—
630	C₂×C₄	—	10	4	no	—
631	C₂×C₄	—	10	4	no	—
632	C₂×C₄	—	20	8	no	—
633	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
634	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
635	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
636	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
637	C₂×C₄	D₅×#41	1	1	yes	characteristic
638	C₂×C₄	C₂⁴×D₅	1	1	yes	characteristic
639	C₈	—	2	4	no	—
640	C₈	—	5	4	no	—
641	C₈	—	5	2	no	—
642	C₈	—	5	2	no	—
643	C₈	—	10	4	no	—
644	C₈	C₂²×C₄×D₅	1	2	yes	—
645	C₈	C₂²×C₄×D₅	1	2	yes	—
646	C₈	C₂×D₄×D₅	1	4	yes	—
647	C₅	C₂×#2956	1	1	yes	characteristic, complemented, Sylow
648	C₂²	—	2	2	no	—
649	C₂²	—	2	4	no	—
650	C₂²	—	4	4	no	—
651	C₂²	—	5	4	no	—
652	C₂²	—	10	4	no	—
653	C₂²	—	10	4	no	—
654	C₂²	—	20	2	no	—
655	C₂²	—	20	2	no	—
656	C₂²	—	20	4	no	—
657	C₂²	—	40	8	no	—
658	C₂²	C₄×D₄×D₅	1	1	yes	characteristic
659	C₂²	C₄×D₄×D₅	1	1	yes	characteristic
660	C₂²	C₂×D₅×#41	1	1	yes	characteristic
661	C₄	—	2	4	no	—
662	C₄	—	4	2	no	—
663	C₄	—	5	4	no	—
664	C₄	—	10	4	no	—
665	C₄	—	10	4	no	—
666	C₄	C₄×D₄×D₅	1	1	yes	characteristic
667	C₄	C₄×D₄×D₅	1	1	yes	characteristic
668	C₄	C₂³×C₄×D₅	1	1	yes	characteristic
669	C₄	C₂²×D₄×D₅	1	1	yes	characteristic
670	C₂	—	2	1	no	—
671	C₂	—	2	1	no	—
672	C₂	—	4	4	no	—
673	C₂	—	10	4	no	—
674	C₂	—	20	4	no	—
675	C₂	#10611629	1	2	yes	direct product factor
676	C₂	C₂×C₄×D₄×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅
commutator	C₄×C₅	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₅
Fitting	C₂×C₅×#444	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂×#66102	C₂
cosocle	C₂×C₄×C₅	C₂⁵
hypercenter	C₂×#444	D₅
hypocenter	C₅	C₂×#2956
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×#444

Complements

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

N	H ≅ G/N	type
2. C₂×#66084	C₂	semidirect
3. C₂×C₅×#444	C₂	semidirect
4. C₂×#65485	C₂	semidirect
5. C₂×#65433	C₂	semidirect
6. #10611629	C₂	direct (N × H)
7. C₂×#65182	C₂	semidirect
8. C₂×#65184	C₂	semidirect
9. C₂×D₅×#104	C₂	semidirect
10. C₂×#65112	C₂	semidirect
11. C₂×#65006	C₂	semidirect
12. C₂×#64996	C₂	semidirect
15. C₂×C₅×#131	C₂²	semidirect
17. C₂×#4094	C₂²	semidirect
18. #66102	C₄	semidirect
20. C₂×#4064	C₄	semidirect
21. C₂×#4061	C₄	semidirect
22. C₂×#4060	C₄	semidirect
23. C₂×#4057	C₄	semidirect
25. #66084	C₂²	semidirect
27. C₂×#4053	C₂²	semidirect
32. C₂×#4047	C₂²	semidirect
37. C₅×#444	C₂²	semidirect
38. C₂×C₅×#108	C₂²	semidirect
39. C₂×C₅×#104	C₂²	semidirect
40. C₂×C₅×#97	C₂²	semidirect
41. C₂×#3969	C₂²	semidirect
42. #65485	C₂²	semidirect
43. #65433	C₂²	semidirect
44. C₂×#3957	C₂²	semidirect
45. C₂×#3954	C₂²	semidirect
46. C₂×#3951	C₂²	semidirect
47. C₂×C₈×Dic₅	C₂²	semidirect
48. C₂×C₈×Dic₅	C₂²	semidirect
49. C₂×#3937	C₂²	semidirect
50. C₂×#3935	C₂²	semidirect
51. #65184	C₂²	semidirect
52. #65182	C₂²	semidirect
53. #65112	C₂²	semidirect
54. D₅×#104	C₂²	semidirect
55. #65006	C₂²	semidirect
56. #64996	C₂²	semidirect
74. C₅×#135	C₂×C₄	semidirect
76. C₂×C₅×Q₁₆	C₂×C₄	semidirect
77. C₂×C₅×SD₁₆	C₂×C₄	semidirect
78. C₂×C₅×D₈	C₂×C₄	semidirect
80. C₅×#131	C₂³	semidirect
87. #4096	C₂×C₄	semidirect
90. #4094	C₂³	semidirect
91. C₂×#689	C₂×C₄	semidirect
92. C₂×#688	C₂×C₄	semidirect
93. C₂×#687	C₂×C₄	semidirect
94. C₂×#686	C₂×C₄	semidirect
102. #4064	C₂×C₄	semidirect
103. #4061	C₂×C₄	semidirect
104. #4060	C₂×C₄	semidirect
105. #4057	C₂×C₄	semidirect
108. #4053	C₂³	semidirect
112. C₂×Dic₂₀	C₂×C₄	semidirect
113. #4050	C₂×C₄	semidirect
115. C₂×D₄₀	C₂×C₄	semidirect
116. C₂×#677	C₂×C₄	semidirect
119. #4047	C₂³	semidirect
137. C₅×#108	C₂³	semidirect
138. C₅×#104	C₂³	semidirect
139. C₅×#97	C₂³	semidirect
140. #3969	C₂³	semidirect
141. #3957	C₂³	semidirect
142. #3954	C₂³	semidirect
143. #3951	C₂³	semidirect
144. C₈×Dic₅	C₂³	semidirect
145. C₈×Dic₅	C₂³	semidirect
146. #3937	C₂³	semidirect
147. #3935	C₂³	semidirect
153. C₂×#444	D₅	semidirect
213. C₅×Q₁₆	C₂²×C₄	semidirect
214. C₅×SD₁₆	C₂²×C₄	semidirect
215. C₅×D₈	C₂²×C₄	semidirect
230. #689	C₂²×C₄	semidirect
231. #688	C₂²×C₄	semidirect
232. #687	C₂²×C₄	semidirect
233. #686	C₂²×C₄	semidirect
249. Dic₂₀	C₂²×C₄	semidirect
250. D₄₀	C₂²×C₄	semidirect
251. #677	C₂²×C₄	semidirect
279. C₂×#131	C₂×D₅	semidirect
288. #444	C₂×D₅	semidirect
295. C₂×#108	C₂×D₅	semidirect
300. C₂×#104	C₂×D₅	semidirect
303. C₂×#97	C₂×D₅	semidirect
390. #135	C₄×D₅	semidirect
394. C₂×Q₁₆	C₄×D₅	semidirect
398. C₂×SD₁₆	C₄×D₅	semidirect
401. C₂×D₈	C₄×D₅	semidirect
411. #131	C₂²×D₅	semidirect
447. #108	C₂²×D₅	semidirect
451. #104	C₂²×D₅	semidirect
453. #97	C₂²×D₅	semidirect
533. Q₁₆	C₂×C₄×D₅	semidirect
537. SD₁₆	C₂×C₄×D₅	semidirect
540. D₈	C₂×C₄×D₅	semidirect
583. C₂×C₅	#2956	semidirect
647. C₅	C₂×#2956	semidirect
675. C₂	#10611629	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#66102	2
C₂×#66084	2
C₂×C₅×#444	2
C₂×#65485	2
C₂×#65433	2
#10611629	2
C₂×#65182	2
C₂×#65184	2
C₂×D₅×#104	2
C₂×#65112	2
C₂×#65006	2
C₂×#64996	2
C₂×#2956	5

Subgroups — C2×#10611629 #12963611

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10611629 #12963611