Subgroups — #12098069

Order 1280.

906 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#65129	C₂	1	1	yes	maximal, characteristic
2	C₂×#64998	C₂	1	1	yes	maximal, characteristic
3	#10605486	C₂	1	1	yes	maximal, characteristic
4	C₅×#1771	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601258	C₂	1	1	yes	maximal, characteristic, complemented
6	#10600623	C₂	1	1	yes	maximal, characteristic
7	#10600604	C₂	1	1	yes	maximal, characteristic, complemented
8	#10600603	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×#683	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#3952	C₂	1	1	yes	maximal, characteristic
11	C₄⋊C₄×#168	C₂	1	1	yes	maximal, characteristic, complemented
12	#10599446	C₂	1	1	yes	maximal, characteristic, complemented
13	#10599444	C₂	1	1	yes	maximal, characteristic, complemented
14	#10599394	C₂	1	1	yes	maximal, characteristic
15	#10599392	C₂	1	1	yes	maximal, characteristic
16	C₂×#4018	C₂²	1	1	yes	characteristic
17	C₂×#4018	C₂²	1	1	yes	characteristic
18	C₂×C₄²×D₅	C₂²	1	1	yes	characteristic
19	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×#97	C₂²	1	1	yes	characteristic
21	C₂×C₅×#97	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
23	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×#3952	C₂²	1	1	yes	characteristic
25	C₂×#3952	C₂²	1	1	yes	characteristic
26	C₂×#3952	C₂²	1	1	yes	characteristic
27	C₂×#3952	C₂²	1	1	yes	characteristic
28	C₂×#3947	C₂²	1	1	yes	characteristic
29	C₂×#3947	C₂²	1	1	yes	characteristic
30	C₂×#3946	C₂²	1	1	yes	characteristic
31	C₂×#3946	C₂²	1	1	yes	characteristic
32	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
35	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
36	#65278	C₄	1	2	yes	—
37	#65261	C₄	1	2	yes	—
38	C₄×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
39	C₄×#683	C₂²	1	1	yes	characteristic
40	C₄×#683	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
42	C₂×C₄×#168	C₂²	1	1	yes	characteristic
43	C₂×C₄×#168	C₂²	1	1	yes	characteristic
44	C₂×C₄×#168	C₂²	1	1	yes	characteristic
45	#65129	C₄	1	8	yes	complemented
46	#64998	C₄	1	8	yes	complemented
47	#64957	C₄	1	2	yes	—
48	#64936	C₄	1	2	yes	—
49	C₅×#336	C₂²	1	1	yes	characteristic
50	C₅×#336	C₂²	1	1	yes	characteristic
51	#64770	C₂²	1	1	yes	characteristic
52	#64770	C₂²	1	1	yes	characteristic
53	#64770	C₂²	1	1	yes	characteristic
54	#64770	C₂²	1	1	yes	characteristic
55	#64744	C₂²	1	1	yes	characteristic
56	#64744	C₂²	1	1	yes	characteristic
57	#20540	—	5	1	no	maximal, Sylow
58	C₂²×C₄×D₅	C₂×C₄	1	2	yes	—
59	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
60	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
62	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
64	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
68	C₂×#685	C₂×C₄	1	2	yes	—
69	C₂×#685	C₂×C₄	1	1	yes	characteristic
70	C₂×#685	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
72	C₂×#683	C₂×C₄	1	2	yes	—
73	C₂×#683	C₂×C₄	1	2	yes	—
74	C₂×#683	C₂×C₄	1	2	yes	—
75	C₂×#683	C₂×C₄	1	1	yes	characteristic
76	C₂×#683	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×Dic₅	C₂×C₄	1	2	yes	—
78	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
79	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
80	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
81	C₂²×#168	C₂³	1	1	yes	characteristic
82	C₂²×#168	C₂³	1	1	yes	characteristic
83	C₂²×#168	C₂³	1	1	yes	characteristic
84	C₂²×#168	C₂³	1	1	yes	characteristic
85	#4018	—	4	1	no	—
86	#4018	—	4	1	no	—
87	#4018	C₂×C₄	1	4	yes	—
88	#4018	C₂×C₄	1	4	yes	—
89	C₄²×D₅	—	4	1	no	—
90	C₄²×D₅	—	4	1	no	—
91	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
92	C₅×#97	—	4	1	no	—
93	C₅×#97	C₂×C₄	1	4	yes	complemented
94	C₄×C₅×C₈	—	4	1	no	—
95	C₅×#95	C₂×C₄	1	2	yes	—
96	#3963	C₂×C₄	1	2	yes	—
97	#3963	C₂×C₄	1	2	yes	—
98	#3963	C₂×C₄	1	2	yes	—
99	#3952	C₂×C₄	1	4	yes	—
100	#3952	C₂×C₄	1	4	yes	—
101	#3952	C₂×C₄	1	4	yes	—
102	#3952	C₂×C₄	1	4	yes	—
103	#3947	—	4	1	no	—
104	#3947	C₂×C₄	1	4	yes	complemented
105	#3946	C₂×C₄	1	4	yes	complemented
106	#3946	C₂×C₄	1	4	yes	complemented
107	C₈×Dic₅	—	4	1	no	—
108	C₈×Dic₅	—	4	1	no	—
109	C₈×Dic₅	—	4	1	no	—
110	C₈×Dic₅	C₂×C₄	1	4	yes	complemented
111	C₄⋊#168	C₂×C₄	1	4	yes	complemented
112	C₄×#168	—	4	1	no	—
113	C₄×#168	—	4	1	no	—
114	C₄×#168	C₂×C₄	1	4	yes	complemented
115	C₂×#433	—	5	1	no	—
116	C₂×#433	—	5	1	no	—
117	#2296	—	5	1	no	—
118	#1771	—	5	1	no	—
119	#1771	—	5	1	no	—
120	#1771	—	5	1	no	—
121	#1771	D₅	1	1	yes	characteristic, complemented
122	C₈×C₄⋊C₄	—	5	1	no	—
123	C₈×C₄⋊C₄	—	5	1	no	—
124	C₈×C₄⋊C₄	—	5	1	no	—
125	C₈×C₄⋊C₄	—	5	1	no	—
126	#1750	—	5	1	no	—
127	#1750	—	5	1	no	—
128	C₄×C₂²⋊C₈	—	5	1	no	—
129	C₄×C₂²⋊C₈	—	5	1	no	—
130	C₂³×D₅	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
132	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
135	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
136	C₂²×Dic₅	C₂²×C₄	1	2	yes	—
137	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
138	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
139	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
140	C₂²×Dic₅	C₂²×C₄	1	2	yes	—
141	C₂×C₄×D₅	—	2	1	no	—
142	C₂×C₄×D₅	—	2	1	no	—
143	C₂×C₄×D₅	—	2	1	no	—
144	C₂×C₄×D₅	—	2	1	no	—
145	C₂×C₄×D₅	—	2	4	no	—
146	C₂×C₄×D₅	—	2	4	no	—
147	C₂×C₄×D₅	—	4	2	no	—
148	C₂×C₄×D₅	C₂²×C₄	1	2	yes	—
149	C₂×C₄×D₅	C₂²×C₄	1	2	yes	—
150	C₂×C₅×C₈	—	2	1	no	—
151	C₂×C₅×C₈	—	2	1	no	—
152	C₂×C₅×C₈	—	2	1	no	—
153	C₂×C₅×C₈	—	2	1	no	—
154	C₂×C₅×C₈	—	2	1	no	—
155	C₂×C₅×C₈	—	2	1	no	—
156	C₂×C₅×C₈	—	2	1	no	—
157	C₂×C₅×C₈	—	2	1	no	—
158	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
159	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
160	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
161	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
162	C₅×C₄⋊C₄	—	2	4	no	—
163	C₄²×C₅	—	2	1	no	—
164	C₄²×C₅	—	2	1	no	—
165	C₄²×C₅	—	2	1	no	—
166	C₄²×C₅	—	2	1	no	—
167	C₄²×C₅	C₂²×C₄	1	2	yes	—
168	C₄²×C₅	C₂²×C₄	1	2	yes	—
169	#685	—	4	2	no	—
170	#685	C₄²	1	4	yes	—
171	#685	C₄²	1	4	yes	—
172	C₄⋊Dic₅	—	2	4	no	—
173	#683	—	2	4	no	—
174	#683	—	2	4	no	—
175	#683	—	4	2	no	—
176	#683	C₄²	1	4	yes	—
177	#683	C₄²	1	4	yes	—
178	C₄×Dic₅	—	2	1	no	—
179	C₄×Dic₅	—	2	1	no	—
180	C₄×Dic₅	—	2	1	no	—
181	C₄×Dic₅	—	2	1	no	—
182	C₄×Dic₅	—	4	2	no	—
183	C₄×Dic₅	C₂²×C₄	1	2	yes	—
184	C₄×Dic₅	C₂²×C₄	1	2	yes	—
185	C₂×#168	—	2	1	no	—
186	C₂×#168	—	2	1	no	—
187	C₂×#168	—	2	1	no	—
188	C₂×#168	—	2	1	no	—
189	C₂×#168	—	2	1	no	—
190	C₂×#168	—	2	1	no	—
191	C₂×#168	—	2	1	no	—
192	C₂×#168	—	2	1	no	—
193	C₂×#168	C₂²×C₄	1	2	yes	—
194	C₂×#168	C₂²×C₄	1	2	yes	—
195	C₂×#168	C₂²×C₄	1	2	yes	—
196	C₂×#168	C₂²×C₄	1	2	yes	—
197	C₂×#117	—	5	1	no	—
198	C₂×#117	—	5	1	no	—
199	C₂²×C₄²	—	5	1	no	—
200	#433	—	5	8	no	—
201	#433	—	5	8	no	—
202	C₂×C₄⋊C₈	—	5	1	no	—
203	C₂×C₄⋊C₈	—	5	1	no	—
204	C₂×C₄⋊C₈	—	5	1	no	—
205	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
206	C₂×C₂²⋊C₈	—	5	1	no	—
207	C₂×C₂²⋊C₈	—	5	1	no	—
208	C₂×C₂²⋊C₈	—	5	1	no	—
209	C₂×C₂²⋊C₈	—	5	1	no	—
210	C₂×#97	—	5	1	no	—
211	C₂×#97	—	5	1	no	—
212	C₂×#97	C₂×D₅	1	1	yes	characteristic
213	C₂×#97	C₂×D₅	1	1	yes	characteristic
214	C₂×C₄×C₈	—	5	1	no	—
215	C₂×C₄×C₈	—	5	1	no	—
216	C₂×C₄×C₈	—	5	1	no	—
217	C₂×C₄×C₈	—	5	1	no	—
218	C₂×C₄×C₈	—	5	1	no	—
219	C₂×C₄×C₈	—	5	1	no	—
220	C₂×C₄×C₈	—	5	1	no	—
221	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
222	#389	—	5	2	no	—
223	#389	—	5	2	no	—
224	#385	—	5	2	no	—
225	#385	—	5	2	no	—
226	C₄×C₄⋊C₄	—	5	1	no	—
227	C₄×C₄⋊C₄	—	5	1	no	—
228	C₄×C₄⋊C₄	—	5	1	no	—
229	C₄×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
230	#336	—	5	1	no	—
231	#336	—	5	1	no	—
232	#336	—	5	1	no	—
233	#336	—	5	1	no	—
234	#336	—	5	1	no	—
235	#336	—	5	1	no	—
236	#336	C₂×D₅	1	1	yes	characteristic
237	#336	C₂×D₅	1	1	yes	characteristic
238	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
239	C₂²×D₅	—	2	1	no	—
240	C₂²×D₅	—	2	1	no	—
241	C₂²×D₅	—	2	2	no	—
242	C₂²×D₅	—	2	2	no	—
243	C₂²×D₅	C₂×C₄²	1	2	yes	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	2	2	no	—
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	—	2	2	no	—
251	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
252	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
253	C₂×C₄×C₅	#131	1	4	yes	—
254	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
255	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
256	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
257	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
258	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
259	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
260	C₂×Dic₅	—	2	2	no	—
261	C₂×Dic₅	—	2	1	no	—
262	C₂×Dic₅	—	2	1	no	—
263	C₂×Dic₅	—	2	2	no	—
264	C₂×Dic₅	—	2	2	no	—
265	C₂×Dic₅	—	2	2	no	—
266	C₂×Dic₅	—	2	2	no	—
267	C₂×Dic₅	—	2	2	no	—
268	C₂×Dic₅	—	2	2	no	—
269	C₂×Dic₅	C₂×C₄²	1	2	yes	—
270	C₂×Dic₅	C₂×C₄²	1	2	yes	—
271	C₂×Dic₅	C₂×C₄²	1	2	yes	—
272	C₂×Dic₅	#131	1	4	yes	—
273	C₄×D₅	—	2	2	no	—
274	C₄×D₅	—	2	2	no	—
275	C₄×D₅	—	2	2	no	—
276	C₄×D₅	—	2	2	no	—
277	C₄×D₅	—	4	8	no	—
278	C₅×C₈	—	2	2	no	—
279	C₅×C₈	—	2	2	no	—
280	C₅×C₈	—	2	2	no	—
281	C₅×C₈	—	2	2	no	—
282	#168	—	2	2	no	—
283	#168	—	2	2	no	—
284	#168	—	2	2	no	—
285	#168	—	2	2	no	—
286	C₂³×C₄	—	5	1	no	—
287	C₂³×C₄	—	5	2	no	—
288	C₂²×C₈	—	5	1	no	—
289	C₂²×C₈	—	5	1	no	—
290	C₂²×C₈	—	5	1	no	—
291	C₂²×C₈	—	5	1	no	—
292	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
293	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
294	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
295	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
296	#117	—	5	4	no	—
297	#117	—	5	4	no	—
298	#117	—	20	1	no	—
299	#117	—	20	1	no	—
300	C₂×C₄⋊C₄	—	5	1	no	—
301	C₂×C₄⋊C₄	—	5	1	no	—
302	C₂×C₄⋊C₄	—	5	2	no	—
303	C₂×C₄⋊C₄	—	5	2	no	—
304	C₂×C₄⋊C₄	—	5	2	no	—
305	C₂×C₄⋊C₄	—	5	2	no	—
306	C₂×C₄⋊C₄	C₄×D₅	1	2	yes	—
307	C₂×C₂²⋊C₄	—	5	1	no	—
308	C₂×C₂²⋊C₄	—	5	1	no	—
309	C₂×C₂²⋊C₄	—	5	2	no	—
310	C₂×C₄²	—	5	1	no	—
311	C₂×C₄²	—	5	1	no	—
312	C₂×C₄²	—	5	1	no	—
313	C₂×C₄²	—	5	2	no	—
314	C₂×C₄²	—	20	1	no	—
315	C₂×C₄²	—	20	1	no	—
316	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
317	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
318	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
319	C₄⋊C₈	—	5	4	no	—
320	C₄⋊C₈	—	5	4	no	—
321	C₄⋊C₈	—	5	4	no	—
322	C₄⋊C₈	C₄×D₅	1	4	yes	complemented
323	C₂²⋊C₈	—	5	4	no	—
324	C₂²⋊C₈	—	5	4	no	—
325	C₂²⋊C₈	—	5	4	no	—
326	C₂²⋊C₈	—	5	4	no	—
327	#97	—	4	1	no	—
328	#97	—	5	4	no	—
329	#97	—	20	1	no	—
330	#97	C₄×D₅	1	4	yes	complemented
331	C₄×C₈	—	4	1	no	—
332	C₄×C₈	—	5	4	no	—
333	C₄×C₈	—	5	4	no	—
334	C₄×C₈	—	20	1	no	—
335	C₄×C₈	—	20	1	no	—
336	C₄×C₈	—	20	1	no	—
337	C₄×C₈	—	20	1	no	—
338	C₄×C₈	—	20	1	no	—
339	#95	—	5	2	no	—
340	#95	—	5	2	no	—
341	#95	—	5	2	no	—
342	#95	C₄×D₅	1	2	yes	—
343	C₂²×C₅	C₂²×C₄²	1	1	yes	characteristic
344	C₂²×C₅	#518	1	1	yes	characteristic
345	C₂²×C₅	#519	1	1	yes	characteristic
346	C₂²×C₅	C₂×#131	1	2	yes	—
347	C₂²×C₅	C₂×#131	1	2	yes	—
348	C₂×D₅	—	2	2	no	—
349	C₂×D₅	—	2	2	no	—
350	C₂×D₅	—	2	2	no	—
351	C₂×D₅	—	4	2	no	—
352	C₂×D₅	—	4	2	no	—
353	C₄×C₅	—	2	2	no	—
354	C₄×C₅	—	2	2	no	—
355	C₄×C₅	—	2	4	no	—
356	C₄×C₅	—	4	2	no	—
357	C₄×C₅	#520	1	1	yes	characteristic
358	C₄×C₅	#520	1	1	yes	characteristic
359	C₄×C₅	#520	1	1	yes	characteristic
360	C₄×C₅	#520	1	1	yes	characteristic
361	Dic₅	—	2	2	no	—
362	Dic₅	—	2	2	no	—
363	Dic₅	—	2	4	no	—
364	Dic₅	—	2	2	no	—
365	Dic₅	—	4	2	no	—
366	C₂⁴	—	5	1	no	—
367	C₂²×C₄	—	5	2	no	—
368	C₂²×C₄	—	5	1	no	—
369	C₂²×C₄	—	5	1	no	—
370	C₂²×C₄	—	5	1	no	—
371	C₂²×C₄	—	5	2	no	—
372	C₂²×C₄	—	5	2	no	—
373	C₂²×C₄	—	5	2	no	—
374	C₂²×C₄	—	10	4	no	—
375	C₂²×C₄	—	10	1	no	—
376	C₂²×C₄	—	10	1	no	—
377	C₂²×C₄	—	10	1	no	—
378	C₂²×C₄	—	10	1	no	—
379	C₂²×C₄	—	10	4	no	—
380	C₂²×C₄	—	20	2	no	—
381	C₂²×C₄	C₂×C₄×D₅	1	2	yes	—
382	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
383	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
384	C₂²×C₄	C₂×C₄×D₅	1	2	yes	—
385	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	5	2	no	—
395	C₂×C₈	—	5	2	no	—
396	C₂×C₈	—	5	2	no	—
397	C₂×C₈	—	5	2	no	—
398	C₂×C₈	—	10	1	no	—
399	C₂×C₈	—	10	1	no	—
400	C₂×C₈	—	10	1	no	—
401	C₂×C₈	—	10	1	no	—
402	C₂×C₈	—	10	1	no	—
403	C₂×C₈	—	10	1	no	—
404	C₂×C₈	—	10	1	no	—
405	C₂×C₈	—	10	1	no	—
406	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
407	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
408	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
409	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
410	C₄⋊C₄	—	2	4	no	—
411	C₄⋊C₄	—	5	4	no	—
412	C₄⋊C₄	—	5	4	no	—
413	C₄⋊C₄	—	10	4	no	—
414	C₄⋊C₄	—	10	4	no	—
415	C₄⋊C₄	—	10	4	no	—
416	C₄⋊C₄	—	20	2	no	—
417	C₂²⋊C₄	—	5	4	no	—
418	C₂²⋊C₄	—	5	4	no	—
419	C₂²⋊C₄	—	20	2	no	—
420	C₄²	—	2	1	no	—
421	C₄²	—	2	1	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	5	2	no	—
425	C₄²	—	5	2	no	—
426	C₄²	—	10	1	no	—
427	C₄²	—	10	1	no	—
428	C₄²	—	10	1	no	—
429	C₄²	—	10	1	no	—
430	C₄²	—	20	2	no	—
431	C₄²	C₂×C₄×D₅	1	2	yes	—
432	C₄²	C₂×C₄×D₅	1	2	yes	—
433	C₂×C₅	#2274	1	1	yes	characteristic
434	C₂×C₅	C₄×#131	1	1	yes	characteristic
435	C₂×C₅	C₄×#131	1	1	yes	characteristic
436	C₂×C₅	#2977	1	2	yes	—
437	C₂×C₅	#2986	1	2	yes	—
438	D₅	—	4	2	no	—
439	C₂³	—	5	2	no	—
440	C₂³	—	10	2	no	—
441	C₂³	—	10	2	no	—
442	C₂³	—	10	1	no	—
443	C₂³	—	10	1	no	—
444	C₂³	C₂²×C₄×D₅	1	1	yes	characteristic
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	5	2	no	—
453	C₂×C₄	—	5	2	no	—
454	C₂×C₄	—	5	2	no	—
455	C₂×C₄	—	5	4	no	—
456	C₂×C₄	—	10	2	no	—
457	C₂×C₄	—	10	2	no	—
458	C₂×C₄	—	10	2	no	—
459	C₂×C₄	—	10	2	no	—
460	C₂×C₄	—	10	1	no	—
461	C₂×C₄	—	10	1	no	—
462	C₂×C₄	—	10	2	no	—
463	C₂×C₄	—	10	2	no	—
464	C₂×C₄	—	10	2	no	—
465	C₂×C₄	—	10	2	no	—
466	C₂×C₄	—	10	2	no	—
467	C₂×C₄	—	10	2	no	—
468	C₂×C₄	—	10	2	no	—
469	C₂×C₄	—	20	8	no	—
470	C₂×C₄	C₄²×D₅	1	2	yes	—
471	C₂×C₄	C₄²×D₅	1	2	yes	—
472	C₂×C₄	#4053	1	4	yes	—
473	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
474	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
475	C₂×C₄	#4144	1	1	yes	characteristic
476	C₂×C₄	#4147	1	1	yes	characteristic
477	C₂×C₄	#4149	1	1	yes	characteristic
478	C₂×C₄	#4150	1	1	yes	characteristic
479	C₈	—	2	2	no	—
480	C₈	—	2	2	no	—
481	C₈	—	2	2	no	—
482	C₈	—	2	2	no	—
483	C₈	—	10	2	no	—
484	C₈	—	10	2	no	—
485	C₈	—	10	2	no	—
486	C₈	—	10	2	no	—
487	C₅	#20540	1	1	yes	characteristic, complemented, Sylow
488	C₂²	—	10	2	no	—
489	C₂²	—	10	2	no	—
490	C₂²	—	10	2	no	—
491	C₂²	—	20	2	no	—
492	C₂²	—	20	2	no	—
493	C₂²	C₂×C₄²×D₅	1	1	yes	characteristic
494	C₂²	#65879	1	1	yes	characteristic
495	C₂²	#65906	1	1	yes	characteristic
496	C₂²	C₂×#4053	1	2	yes	—
497	C₂²	D₅×#131	1	2	yes	—
498	C₄	—	2	4	no	—
499	C₄	—	2	2	no	—
500	C₄	—	2	2	no	—
501	C₄	—	4	2	no	—
502	C₄	—	10	4	no	—
503	C₄	—	10	2	no	—
504	C₄	—	10	2	no	—
505	C₄	—	10	2	no	—
506	C₄	—	20	2	no	—
507	C₄	#65838	1	1	yes	characteristic
508	C₄	#65857	1	1	yes	characteristic
509	C₄	#65880	1	1	yes	characteristic
510	C₄	#65908	1	1	yes	characteristic
511	C₂	—	20	2	no	—
512	C₂	#10605481	1	1	yes	characteristic
513	C₂	C₄×#4053	1	1	yes	characteristic
514	C₂	#10610280	1	1	yes	characteristic
515	C₂	#10611220	1	2	yes	—
516	C₂	#10611698	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₅
commutator	C₂²×C₅	C₂²×C₄²
Fitting	C₅×#1771	C₂
socle	C₂³×C₅	C₂³×C₄
prime radical	C₂³×D₅	C₂²×C₄
cosocle	C₂²×C₄×C₅	C₂⁴
hypercenter	#1771	D₅
hypocenter	C₅	#20540
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₄ ◁ #1771

Complements

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

N	H ≅ G/N	type
4. C₅×#1771	C₂	semidirect
5. #10601258	C₂	semidirect
7. #10600604	C₂	semidirect
8. #10600603	C₂	semidirect
9. C₈×#683	C₂	semidirect
11. C₄⋊C₄×#168	C₂	semidirect
12. #10599446	C₂	semidirect
13. #10599444	C₂	semidirect
45. #65129	C₄	semidirect
46. #64998	C₄	semidirect
91. C₅×C₄⋊C₈	C₂×C₄	semidirect
93. C₅×#97	C₂×C₄	semidirect
104. #3947	C₂×C₄	semidirect
105. #3946	C₂×C₄	semidirect
106. #3946	C₂×C₄	semidirect
110. C₈×Dic₅	C₂×C₄	semidirect
111. C₄⋊#168	C₂×C₄	semidirect
114. C₄×#168	C₂×C₄	semidirect
121. #1771	D₅	semidirect
322. C₄⋊C₈	C₄×D₅	semidirect
330. #97	C₄×D₅	semidirect
487. C₅	#20540	semidirect

Maximal subgroups

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

subgroup	index
C₂×#65129	2
C₂×#64998	2
#10605486	2
C₅×#1771	2
#10601258	2
#10600623	2
#10600604	2
#10600603	2
C₈×#683	2
C₄×#3952	2
C₄⋊C₄×#168	2
#10599446	2
#10599444	2
#10599394	2
#10599392	2
#20540	5