Subgroups — C₂×#10601457 #12098939

Order 1280.

1346 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#4047	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#427	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#65395	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#65295	C₂	1	2	yes	maximal
5	C₂×#64751	C₂	1	2	yes	maximal, complemented
6	#10601457	C₂	1	8	yes	maximal, direct product factor
7	C₂²×#709	C₂²	1	1	yes	characteristic
8	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
9	C₂×C₅×#117	C₂²	1	2	yes	—
10	C₂×#4072	C₂²	1	2	yes	—
11	C₂²×#681	C₂²	1	1	yes	characteristic
12	C₂×#4047	—	2	1	no	—
13	C₂×#4047	—	2	1	no	—
14	C₂×#4047	—	2	2	no	—
15	C₂×#4047	—	2	1	no	—
16	C₂×#4047	—	2	1	no	—
17	C₂×#4047	—	2	2	no	—
18	C₂×#4047	C₄	1	4	yes	complemented
19	C₂×#4047	C₂²	1	4	yes	—
20	C₂²×#676	C₄	1	2	yes	complemented
21	C₂²×C₈×D₅	C₄	1	2	yes	complemented
22	C₅×#427	—	2	2	no	—
23	C₅×#427	C₂²	1	4	yes	complemented
24	C₂×C₅×#107	—	2	1	no	—
25	C₂×C₅×#106	—	2	1	no	—
26	#65395	—	2	2	no	—
27	#65395	C₂²	1	4	yes	complemented
28	C₂×#3950	—	2	1	no	—
29	C₂×#3949	—	2	1	no	—
30	#65295	—	2	4	no	—
31	#65295	C₂²	1	8	yes	—
32	C₂×#3938	—	2	4	no	—
33	#64751	C₂²	1	8	yes	complemented
34	C₂×#1812	—	5	1	no	maximal, Sylow
35	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
36	C₂²×C₂²⋊D₅	D₄	1	2	yes	—
37	C₂×#709	—	2	1	no	—
38	C₂×#709	—	2	1	no	—
39	C₂×#709	—	2	1	no	—
40	C₂×#709	—	2	1	no	—
41	C₂×#709	—	2	1	no	—
42	C₂×#709	—	2	1	no	—
43	C₂×#709	—	2	1	no	—
44	C₂×#709	—	2	1	no	—
45	C₂×#709	C₂×C₄	1	2	yes	—
46	C₂×#709	D₄	1	2	yes	—
47	C₂×#709	Q₈	1	2	yes	—
48	C₂×#709	C₂³	1	2	yes	—
49	C₂²×D₂₀	Q₈	1	1	yes	characteristic
50	C₂²×C₄×D₅	C₂×C₄	1	2	yes	—
51	C₂²×Dic₁₀	Q₈	1	1	yes	characteristic
52	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
55	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
56	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
57	C₂²×C₅×C₈	D₄	1	2	yes	—
58	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
59	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
60	C₂²×C₅×C₈	D₄	1	2	yes	—
61	C₂²×C₅×C₈	C₂³	1	2	yes	—
62	C₅×#117	—	2	2	no	—
63	C₅×#117	—	2	2	no	—
64	C₅×#117	—	2	2	no	—
65	C₅×#117	C₂³	1	4	yes	—
66	C₂×C₅×C₄⋊C₄	—	2	2	no	—
67	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₄²×C₅	—	2	2	no	—
69	C₂×C₂²⋊Dic₅	—	2	2	no	—
70	#4072	—	2	2	no	—
71	#4072	—	2	2	no	—
72	#4072	—	2	2	no	—
73	#4072	C₂³	1	4	yes	—
74	C₂×C₄⋊Dic₅	—	2	2	no	—
75	C₂×C₄×Dic₅	—	2	2	no	—
76	C₂×#681	—	2	1	no	—
77	C₂×#681	—	2	1	no	—
78	C₂×#681	—	2	1	no	—
79	C₂×#681	—	2	1	no	—
80	C₂×#681	C₂×C₄	1	2	yes	—
81	C₂×#681	C₂³	1	2	yes	—
82	C₂²×#168	C₂×C₄	1	2	yes	—
83	#4047	—	2	4	no	—
84	#4047	—	2	4	no	—
85	#4047	—	2	4	no	—
86	#4047	—	2	4	no	—
87	#4047	—	2	4	no	—
88	#4047	—	2	4	no	—
89	#4047	—	2	4	no	—
90	#4047	—	2	4	no	—
91	C₂×#676	—	2	2	no	—
92	C₂×#676	—	2	2	no	—
93	C₂×#676	—	2	4	no	—
94	C₂×#676	C₂×C₄	1	8	yes	complemented
95	C₂×C₈×D₅	—	2	2	no	—
96	C₂×C₈×D₅	—	2	2	no	—
97	C₂×C₈×D₅	—	2	4	no	—
98	C₂×C₈×D₅	C₂×C₄	1	8	yes	complemented
99	C₅×#107	—	2	4	no	—
100	C₅×#106	—	2	4	no	—
101	#3950	—	2	4	no	—
102	#3949	—	2	4	no	—
103	#3938	—	2	16	no	—
104	C₂²×#131	—	5	1	no	—
105	C₂×#427	—	5	1	no	—
106	C₂×#427	D₅	1	1	yes	characteristic, complemented
107	C₂×#410	—	5	2	no	—
108	#1812	—	5	8	no	—
109	C₂×H(3,ℤ/4)	—	5	2	no	—
110	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
111	C₂³×D₅	C₄⋊C₄	1	2	yes	—
112	C₂²×C₄×C₅	—	4	2	no	—
113	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
122	C₂²×C₄×C₅	#41	1	1	yes	characteristic
123	C₂²×C₄×C₅	#41	1	1	yes	characteristic
124	C₂²×C₄×C₅	#41	1	1	yes	characteristic
125	C₂²×C₄×C₅	#41	1	1	yes	characteristic
126	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
127	C₂×C₂²⋊D₅	—	2	2	no	—
128	C₂×C₂²⋊D₅	—	2	2	no	—
129	C₂×C₂²⋊D₅	—	2	2	no	—
130	C₂×C₂²⋊D₅	—	2	2	no	—
131	C₂×C₂²⋊D₅	C₄⋊C₄	1	4	yes	—
132	C₂×C₂²⋊D₅	C₂×D₄	1	4	yes	—
133	C₂²×Dic₅	—	4	2	no	—
134	C₂²×Dic₅	C₄⋊C₄	1	2	yes	—
135	#709	—	2	2	no	—
136	#709	—	2	2	no	—
137	#709	—	2	2	no	—
138	#709	—	2	2	no	—
139	#709	—	2	2	no	—
140	#709	—	2	2	no	—
141	#709	—	2	2	no	—
142	#709	—	2	2	no	—
143	#709	—	2	2	no	—
144	#709	—	2	2	no	—
145	#709	—	2	2	no	—
146	#709	—	2	2	no	—
147	#709	—	2	2	no	—
148	#709	—	2	2	no	—
149	#709	—	2	2	no	—
150	#709	—	2	2	no	—
151	C₂×D₂₀	—	2	1	no	—
152	C₂×D₂₀	—	2	1	no	—
153	C₂×D₂₀	—	2	1	no	—
154	C₂×D₂₀	—	2	1	no	—
155	C₂×D₂₀	C₄⋊C₄	1	2	yes	—
156	C₂×D₂₀	C₂×Q₈	1	2	yes	—
157	C₂×C₄×D₅	—	2	2	no	—
158	C₂×C₄×D₅	—	2	2	no	—
159	C₂×C₄×D₅	—	2	2	no	—
160	C₂×C₄×D₅	—	2	2	no	—
161	C₂×C₄×D₅	C₄⋊C₄	1	4	yes	—
162	C₂×C₄×D₅	C₂²×C₄	1	4	yes	—
163	C₂×Dic₁₀	—	2	1	no	—
164	C₂×Dic₁₀	—	2	1	no	—
165	C₂×Dic₁₀	—	2	1	no	—
166	C₂×Dic₁₀	—	2	1	no	—
167	C₂×Dic₁₀	C₄⋊C₄	1	2	yes	—
168	C₂×Dic₁₀	C₂×Q₈	1	2	yes	—
169	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
170	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
171	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
172	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
173	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
174	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
175	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
176	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
177	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
178	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
179	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
180	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
181	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
182	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
183	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
184	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
185	C₅×C₄⋊C₄	—	2	4	no	—
186	C₅×C₄⋊C₄	—	4	2	no	—
187	C₅×C₂²⋊C₄	—	2	4	no	—
188	C₅×C₂²⋊C₄	—	4	2	no	—
189	C₄²×C₅	—	2	4	no	—
190	C₄²×C₅	—	4	2	no	—
191	C₂²⋊Dic₅	—	2	4	no	—
192	C₂²⋊Dic₅	—	4	2	no	—
193	C₄⋊Dic₅	—	2	4	no	—
194	C₄⋊Dic₅	—	4	2	no	—
195	C₄×Dic₅	—	2	4	no	—
196	C₄×Dic₅	—	4	2	no	—
197	#681	—	2	2	no	—
198	#681	—	2	2	no	—
199	#681	—	2	2	no	—
200	#681	—	2	2	no	—
201	C₂×#168	—	2	2	no	—
202	C₂×#168	—	2	2	no	—
203	C₂×#168	C₂²×C₄	1	4	yes	—
204	#676	—	2	8	no	—
205	#676	—	2	8	no	—
206	C₈×D₅	—	2	8	no	—
207	C₈×D₅	—	2	8	no	—
208	C₂²×#41	—	5	1	no	—
209	C₂×#131	—	5	4	no	—
210	C₂×#131	—	5	4	no	—
211	C₂×#131	—	10	1	no	—
212	C₂×#131	—	10	1	no	—
213	C₂×#131	—	10	2	no	—
214	C₂×#131	—	10	1	no	—
215	C₂×#131	—	10	1	no	—
216	C₂×#131	—	10	2	no	—
217	C₂²×M₁₆	—	5	1	no	—
218	C₂²×M₁₆	—	5	2	no	—
219	C₂³×C₈	—	5	2	no	—
220	C₂³×C₈	C₂×D₅	1	1	yes	characteristic
221	C₂×#117	—	5	2	no	—
222	C₂×#117	C₂×D₅	1	2	yes	—
223	#427	—	2	2	no	—
224	#427	—	5	4	no	—
225	#427	—	10	2	no	—
226	#427	C₂×D₅	1	4	yes	complemented
227	C₂×#107	—	2	1	no	—
228	C₂×#107	—	10	1	no	—
229	C₂×#106	—	2	1	no	—
230	C₂×#106	—	10	1	no	—
231	#410	—	5	8	no	—
232	#410	—	10	4	no	—
233	C₂×#99	—	10	4	no	—
234	H(3,ℤ/4)	—	5	8	no	—
235	C₂³×C₅	—	4	2	no	—
236	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
237	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
238	C₂³×C₅	#121	1	1	yes	characteristic
239	C₂³×C₅	#121	1	1	yes	characteristic
240	C₂³×C₅	#121	1	1	yes	characteristic
241	C₂³×C₅	#121	1	1	yes	characteristic
242	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
243	C₂²×D₅	—	2	2	no	—
244	C₂²×D₅	—	2	2	no	—
245	C₂²×D₅	—	4	4	no	—
246	C₂²×D₅	C₂×C₄⋊C₄	1	4	yes	—
247	C₂×C₄×C₅	—	4	4	no	—
248	C₂×C₄×C₅	—	8	4	no	—
249	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
251	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
252	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
253	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
254	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
255	C₂×C₄×C₅	#117	1	1	yes	characteristic
256	C₂×C₄×C₅	#117	1	1	yes	characteristic
257	C₂×C₄×C₅	#117	1	1	yes	characteristic
258	C₂×C₄×C₅	#117	1	1	yes	characteristic
259	C₂×C₄×C₅	#121	1	1	yes	characteristic
260	C₂×C₄×C₅	#121	1	1	yes	characteristic
261	C₂×C₄×C₅	#121	1	1	yes	characteristic
262	C₂×C₄×C₅	#121	1	1	yes	characteristic
263	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
264	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
265	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
266	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
267	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
268	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
270	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
271	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
272	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
275	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
276	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
277	C₂²⋊D₅	—	2	4	no	—
278	C₂²⋊D₅	—	2	4	no	—
279	C₂²⋊D₅	—	2	4	no	—
280	C₂²⋊D₅	—	2	4	no	—
281	C₂×Dic₅	—	2	2	no	—
282	C₂×Dic₅	—	2	2	no	—
283	C₂×Dic₅	—	4	4	no	—
284	C₂×Dic₅	—	8	4	no	—
285	C₂×Dic₅	C₂×C₄⋊C₄	1	4	yes	—
286	D₂₀	—	2	2	no	—
287	D₂₀	—	2	2	no	—
288	D₂₀	—	2	2	no	—
289	D₂₀	—	2	2	no	—
290	C₄×D₅	—	2	4	no	—
291	C₄×D₅	—	2	4	no	—
292	C₄×D₅	—	2	4	no	—
293	C₄×D₅	—	2	4	no	—
294	Dic₁₀	—	2	2	no	—
295	Dic₁₀	—	2	2	no	—
296	Dic₁₀	—	2	2	no	—
297	Dic₁₀	—	2	2	no	—
298	C₅×C₈	C₂×C₂²⋊C₄	1	2	yes	—
299	C₅×C₈	C₂×C₂²⋊C₄	1	2	yes	—
300	C₅×C₈	C₂×C₂²⋊C₄	1	2	yes	—
301	C₅×C₈	C₂×C₂²⋊C₄	1	2	yes	—
302	#168	—	2	4	no	—
303	C₂×#41	—	5	2	no	—
304	C₂×#41	—	5	2	no	—
305	C₂×#41	—	5	2	no	—
306	C₂×#41	—	5	2	no	—
307	C₂×#41	—	10	1	no	—
308	C₂×#41	—	10	1	no	—
309	C₂×#41	—	10	1	no	—
310	C₂×#41	—	10	1	no	—
311	C₂×#41	—	10	1	no	—
312	C₂×#41	—	10	1	no	—
313	C₂×#41	—	10	1	no	—
314	C₂×#41	—	10	1	no	—
315	C₂²×Q₈	—	5	1	no	—
316	C₂²×D₄	—	5	2	no	—
317	C₂²×D₄	—	5	1	no	—
318	C₂³×C₄	—	5	2	no	—
319	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
320	#131	—	10	4	no	—
321	#131	—	10	4	no	—
322	#131	—	10	4	no	—
323	#131	—	10	4	no	—
324	#131	—	10	4	no	—
325	#131	—	10	4	no	—
326	#131	—	10	4	no	—
327	#131	—	10	4	no	—
328	C₂×M₁₆	—	5	2	no	—
329	C₂×M₁₆	—	5	2	no	—
330	C₂×M₁₆	—	5	8	no	—
331	C₂×M₁₆	—	10	1	no	—
332	C₂×M₁₆	—	10	1	no	—
333	C₂×M₁₆	—	10	1	no	—
334	C₂×M₁₆	—	10	1	no	—
335	C₂×M₁₆	—	10	2	no	—
336	C₂×M₁₆	—	10	2	no	—
337	C₂×M₁₆	—	10	4	no	—
338	C₂²×C₈	—	5	2	no	—
339	C₂²×C₈	—	5	8	no	—
340	C₂²×C₈	—	10	2	no	—
341	C₂²×C₈	—	10	2	no	—
342	C₂²×C₈	—	10	4	no	—
343	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
344	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
345	C₂²×C₈	C₄×D₅	1	2	yes	—
346	C₂²×C₈	D₂₀	1	1	yes	characteristic
347	C₂²×C₈	D₂₀	1	1	yes	characteristic
348	C₂²×C₈	D₂₀	1	2	yes	—
349	C₂²×C₈	C₂²⋊D₅	1	1	yes	characteristic
350	C₂²×C₈	C₂²⋊D₅	1	1	yes	characteristic
351	C₂²×C₈	C₂²⋊D₅	1	2	yes	—
352	C₂²×C₈	C₂²×D₅	1	2	yes	—
353	#117	—	2	2	no	—
354	#117	—	2	2	no	—
355	#117	—	2	2	no	—
356	#117	—	5	4	no	—
357	#117	—	10	2	no	—
358	#117	—	10	2	no	—
359	#117	—	10	2	no	—
360	#117	C₂²×D₅	1	4	yes	—
361	C₂×C₄⋊C₄	—	2	2	no	—
362	C₂×C₄⋊C₄	—	10	2	no	—
363	C₂×C₂²⋊C₄	—	2	2	no	—
364	C₂×C₂²⋊C₄	—	10	2	no	—
365	C₂×C₄²	—	2	2	no	—
366	C₂×C₄²	—	10	2	no	—
367	#107	—	2	4	no	—
368	#107	—	10	4	no	—
369	#106	—	2	4	no	—
370	#106	—	10	4	no	—
371	#99	—	10	16	no	—
372	C₂²×C₅	—	2	2	no	—
373	C₂²×C₅	—	2	2	no	—
374	C₂²×C₅	—	2	2	no	—
375	C₂²×C₅	—	4	1	no	—
376	C₂²×C₅	—	4	1	no	—
377	C₂²×C₅	—	4	1	no	—
378	C₂²×C₅	—	4	1	no	—
379	C₂²×C₅	#380	1	1	yes	characteristic
380	C₂²×C₅	#380	1	1	yes	characteristic
381	C₂²×C₅	#380	1	1	yes	characteristic
382	C₂²×C₅	#380	1	1	yes	characteristic
383	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
384	C₂²×C₅	C₂×#121	1	1	yes	characteristic
385	C₂²×C₅	C₂×#121	1	1	yes	characteristic
386	C₂×D₅	—	2	4	no	—
387	C₂×D₅	—	4	4	no	—
388	C₂×D₅	—	4	4	no	—
389	C₂×D₅	—	4	4	no	—
390	C₄×C₅	—	8	4	no	—
391	C₄×C₅	#380	1	1	yes	characteristic
392	C₄×C₅	#380	1	1	yes	characteristic
393	C₄×C₅	#380	1	1	yes	characteristic
394	C₄×C₅	#380	1	1	yes	characteristic
395	C₄×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
396	C₄×C₅	C₂×#117	1	1	yes	characteristic
397	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
398	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
399	Dic₅	—	2	4	no	—
400	Dic₅	—	8	4	no	—
401	C₂⁴	—	5	2	no	—
402	C₂⁴	D₄×D₅	1	1	yes	characteristic
403	#41	—	10	2	no	—
404	#41	—	10	2	no	—
405	#41	—	10	2	no	—
406	#41	—	10	2	no	—
407	#41	—	10	2	no	—
408	#41	—	10	2	no	—
409	#41	—	10	2	no	—
410	#41	—	10	2	no	—
411	#41	—	10	2	no	—
412	#41	—	10	2	no	—
413	#41	—	10	2	no	—
414	#41	—	10	2	no	—
415	#41	—	10	2	no	—
416	#41	—	10	2	no	—
417	#41	—	10	2	no	—
418	#41	—	10	2	no	—
419	C₂×Q₈	—	5	2	no	—
420	C₂×Q₈	—	5	2	no	—
421	C₂×Q₈	—	10	1	no	—
422	C₂×Q₈	—	10	1	no	—
423	C₂×Q₈	—	10	1	no	—
424	C₂×Q₈	—	10	1	no	—
425	C₂×D₄	—	5	4	no	—
426	C₂×D₄	—	5	4	no	—
427	C₂×D₄	—	5	2	no	—
428	C₂×D₄	—	5	2	no	—
429	C₂×D₄	—	10	2	no	—
430	C₂×D₄	—	10	2	no	—
431	C₂×D₄	—	10	2	no	—
432	C₂×D₄	—	10	2	no	—
433	C₂×D₄	—	10	1	no	—
434	C₂×D₄	—	10	1	no	—
435	C₂×D₄	—	10	1	no	—
436	C₂×D₄	—	10	1	no	—
437	C₂²×C₄	—	4	2	no	—
438	C₂²×C₄	—	5	2	no	—
439	C₂²×C₄	—	5	4	no	—
440	C₂²×C₄	—	5	4	no	—
441	C₂²×C₄	—	10	2	no	—
442	C₂²×C₄	—	10	2	no	—
443	C₂²×C₄	—	10	2	no	—
444	C₂²×C₄	—	10	2	no	—
445	C₂²×C₄	—	20	2	no	—
446	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
447	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
448	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
449	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
450	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
451	C₂²×C₄	#711	1	1	yes	characteristic
452	C₂²×C₄	#711	1	1	yes	characteristic
453	C₂²×C₄	Q₈×D₅	1	1	yes	characteristic
454	C₂²×C₄	Q₈×D₅	1	1	yes	characteristic
455	C₂²×C₄	#713	1	1	yes	characteristic
456	C₂²×C₄	#713	1	1	yes	characteristic
457	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
458	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
459	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
460	M₁₆	—	10	2	no	—
461	M₁₆	—	10	2	no	—
462	M₁₆	—	10	2	no	—
463	M₁₆	—	10	2	no	—
464	M₁₆	—	10	8	no	—
465	M₁₆	—	10	8	no	—
466	C₂×C₈	—	5	4	no	—
467	C₂×C₈	—	10	2	no	—
468	C₂×C₈	—	10	2	no	—
469	C₂×C₈	—	10	8	no	—
470	C₂×C₈	—	10	8	no	—
471	C₂×C₈	#685	1	1	yes	characteristic
472	C₂×C₈	#685	1	1	yes	characteristic
473	C₂×C₈	#685	1	2	yes	—
474	C₂×C₈	#685	1	1	yes	characteristic
475	C₂×C₈	#685	1	1	yes	characteristic
476	C₂×C₈	#685	1	2	yes	—
477	C₂×C₈	#685	1	2	yes	—
478	C₂×C₈	#685	1	2	yes	—
479	C₂×C₈	#685	1	2	yes	—
480	C₂×C₈	#685	1	2	yes	—
481	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
482	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
483	C₂×C₈	C₂×D₂₀	1	2	yes	—
484	C₂×C₈	C₂×D₂₀	1	2	yes	—
485	C₂×C₈	C₂×C₂²⋊D₅	1	2	yes	—
486	C₂×C₈	C₂×C₂²⋊D₅	1	2	yes	—
487	C₄⋊C₄	—	2	4	no	—
488	C₄⋊C₄	—	4	2	no	—
489	C₄⋊C₄	—	10	4	no	—
490	C₄⋊C₄	—	20	2	no	—
491	C₂²⋊C₄	—	2	4	no	—
492	C₂²⋊C₄	—	4	2	no	—
493	C₂²⋊C₄	—	10	4	no	—
494	C₂²⋊C₄	—	20	2	no	—
495	C₄²	—	2	4	no	—
496	C₄²	—	4	2	no	—
497	C₄²	—	10	4	no	—
498	C₄²	—	20	2	no	—
499	C₂×C₅	—	2	1	no	—
500	C₂×C₅	—	2	1	no	—
501	C₂×C₅	—	2	1	no	—
502	C₂×C₅	—	2	1	no	—
503	C₂×C₅	—	2	1	no	—
504	C₂×C₅	—	2	1	no	—
505	C₂×C₅	#1812	1	2	yes	complemented
506	C₂×C₅	C₂×#380	1	1	yes	characteristic
507	D₅	—	4	4	no	—
508	C₂³	—	4	2	no	—
509	C₂³	—	5	4	no	—
510	C₂³	—	10	2	no	—
511	C₂³	—	10	2	no	—
512	C₂³	—	20	4	no	—
513	C₂³	D₅×C₄⋊C₄	1	1	yes	characteristic
514	C₂³	D₅×C₄⋊C₄	1	1	yes	characteristic
515	C₂³	#4041	1	1	yes	characteristic
516	C₂³	#4041	1	1	yes	characteristic
517	C₂³	#4084	1	1	yes	characteristic
518	C₂³	#4084	1	1	yes	characteristic
519	C₂³	C₂×D₄×D₅	1	1	yes	characteristic
520	Q₈	—	10	2	no	—
521	Q₈	—	10	2	no	—
522	Q₈	—	10	2	no	—
523	Q₈	—	10	2	no	—
524	D₄	—	10	4	no	—
525	D₄	—	10	4	no	—
526	D₄	—	10	4	no	—
527	D₄	—	10	4	no	—
528	D₄	—	10	2	no	—
529	D₄	—	10	2	no	—
530	D₄	—	10	2	no	—
531	D₄	—	10	2	no	—
532	C₂×C₄	—	4	4	no	—
533	C₂×C₄	—	5	4	no	—
534	C₂×C₄	—	8	4	no	—
535	C₂×C₄	—	10	2	no	—
536	C₂×C₄	—	10	2	no	—
537	C₂×C₄	—	10	4	no	—
538	C₂×C₄	—	10	4	no	—
539	C₂×C₄	—	10	4	no	—
540	C₂×C₄	—	10	4	no	—
541	C₂×C₄	—	20	4	no	—
542	C₂×C₄	—	40	4	no	—
543	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
544	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
545	C₂×C₄	#4038	1	1	yes	characteristic
546	C₂×C₄	#4038	1	1	yes	characteristic
547	C₂×C₄	#4038	1	1	yes	characteristic
548	C₂×C₄	#4038	1	1	yes	characteristic
549	C₂×C₄	#4041	1	1	yes	characteristic
550	C₂×C₄	#4041	1	1	yes	characteristic
551	C₂×C₄	#4043	1	1	yes	characteristic
552	C₂×C₄	#4043	1	1	yes	characteristic
553	C₂×C₄	#4043	1	1	yes	characteristic
554	C₂×C₄	#4043	1	1	yes	characteristic
555	C₂×C₄	C₂×#685	1	1	yes	characteristic
556	C₂×C₄	C₂×#685	1	1	yes	characteristic
557	C₂×C₄	C₂×#685	1	1	yes	characteristic
558	C₂×C₄	C₂×#685	1	1	yes	characteristic
559	C₂×C₄	#4084	1	1	yes	characteristic
560	C₂×C₄	#4084	1	1	yes	characteristic
561	C₂×C₄	#4092	1	1	yes	characteristic
562	C₂×C₄	#4092	1	1	yes	characteristic
563	C₂×C₄	#4092	1	1	yes	characteristic
564	C₂×C₄	#4092	1	1	yes	characteristic
565	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
566	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
567	C₂×C₄	C₂×#711	1	1	yes	characteristic
568	C₂×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
569	C₂×C₄	C₂×#713	1	1	yes	characteristic
570	C₂×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
571	C₈	—	10	4	no	—
572	C₈	C₂×#685	1	2	yes	—
573	C₈	C₂×#685	1	2	yes	—
574	C₈	C₂×#685	1	2	yes	—
575	C₈	C₂×#685	1	2	yes	—
576	C₅	C₂×#1812	1	1	yes	characteristic, complemented, Sylow
577	C₂²	—	2	2	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	10	4	no	—
585	C₂²	—	20	4	no	—
586	C₂²	—	20	4	no	—
587	C₂²	—	20	4	no	—
588	C₂²	#65276	1	1	yes	characteristic
589	C₂²	#65276	1	1	yes	characteristic
590	C₂²	#65276	1	1	yes	characteristic
591	C₂²	#65276	1	1	yes	characteristic
592	C₂²	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
593	C₂²	C₂×#4041	1	1	yes	characteristic
594	C₂²	C₂×#4084	1	1	yes	characteristic
595	C₄	—	8	4	no	—
596	C₄	—	10	4	no	—
597	C₄	—	40	4	no	—
598	C₄	#65276	1	1	yes	characteristic
599	C₄	#65276	1	1	yes	characteristic
600	C₄	#65276	1	1	yes	characteristic
601	C₄	#65276	1	1	yes	characteristic
602	C₄	C₂×#4038	1	1	yes	characteristic
603	C₄	C₂×#4043	1	1	yes	characteristic
604	C₄	C₂²×#685	1	1	yes	characteristic
605	C₄	C₂×#4092	1	1	yes	characteristic
606	C₂	—	2	1	no	—
607	C₂	—	2	1	no	—
608	C₂	—	2	1	no	—
609	C₂	—	2	1	no	—
610	C₂	—	2	1	no	—
611	C₂	—	2	1	no	—
612	C₂	—	20	4	no	—
613	C₂	#10601457	1	2	yes	direct product factor
614	C₂	C₂×#65276	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#4038
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅
Fitting	C₂×C₅×#427	C₂
socle	C₂²×C₅	#380
prime radical	C₂²×#709	C₂²
cosocle	C₂²×C₄×C₅	C₂⁴
hypercenter	C₂×#427	D₅
hypocenter	C₅	C₂×#1812
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#427

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#427	C₂	semidirect
3. C₂×#65395	C₂	semidirect
5. C₂×#64751	C₂	semidirect
6. #10601457	C₂	direct (N × H)
18. C₂×#4047	C₄	semidirect
20. C₂²×#676	C₄	semidirect
21. C₂²×C₈×D₅	C₄	semidirect
23. C₅×#427	C₂²	semidirect
27. #65395	C₂²	semidirect
33. #64751	C₂²	semidirect
94. C₂×#676	C₂×C₄	semidirect
98. C₂×C₈×D₅	C₂×C₄	semidirect
106. C₂×#427	D₅	semidirect
226. #427	C₂×D₅	semidirect
505. C₂×C₅	#1812	semidirect
576. C₅	C₂×#1812	semidirect
613. C₂	#10601457	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#4047	2
C₂×C₅×#427	2
C₂×#65395	2
C₂×#65295	2
C₂×#64751	2
#10601457	2
C₂×#1812	5

Subgroups — C2×#10601457 #12098939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10601457 #12098939