Subgroups — C₂×#10603851 #13033547

Order 1280.

1102 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅⋊#108	C₂	1	1	yes	maximal, characteristic
2	C₂×#65721	C₂	1	1	yes	maximal, characteristic
3	C₂×#65718	C₂	1	2	yes	maximal
4	C₂×C₄×C₈×D₅	C₂	1	1	yes	maximal, characteristic
5	C₂×#64862	C₂	1	2	yes	maximal
6	#10603851	C₂	1	8	yes	maximal, direct product factor
7	C₂×#4130	C₂²	1	2	yes	—
8	C₂×D₅⋊M₁₆	C₂²	1	2	yes	—
9	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
10	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
11	C₂×C₄²×D₅	C₂²	1	1	yes	characteristic
12	D₅⋊#108	C₄	1	4	yes	complemented
13	D₅⋊#108	C₂²	1	4	yes	—
14	C₂×#3996	C₄	1	2	yes	complemented
15	C₂×#3995	C₄	1	2	yes	complemented
16	#65721	C₄	1	4	yes	complemented
17	#65721	C₂²	1	4	yes	—
18	C₂×#3994	C₄	1	2	yes	complemented
19	C₂×#3993	C₄	1	2	yes	complemented
20	#65718	—	2	4	no	—
21	#65718	C₂²	1	8	yes	—
22	C₂×#3992	—	2	2	no	—
23	C₂×C₈×AGL(1,𝔽₅)	—	2	2	no	—
24	C₂×C₄×C₅×C₈	C₄	1	1	yes	characteristic, complemented
25	C₂×C₈×Dic₅	C₄	1	1	yes	characteristic, complemented
26	C₂×C₈×Dic₅	C₄	1	1	yes	characteristic, complemented
27	C₂×C₄×#168	C₄	1	1	yes	characteristic, complemented
28	C₄×C₈×D₅	C₄	1	4	yes	complemented
29	C₄×C₈×D₅	C₂²	1	4	yes	—
30	#64862	C₂²	1	8	yes	—
31	C₂×#1772	—	5	1	no	maximal, Sylow
32	C₂²×C₄×D₅	—	2	1	no	—
33	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
34	C₂×C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
35	C₂×#704	—	2	2	no	—
36	#4130	—	2	2	no	—
37	#4130	—	2	2	no	—
38	#4130	C₂×C₄	1	4	yes	—
39	#4130	C₂³	1	4	yes	—
40	C₂×C₄⋊AGL(1,𝔽₅)	C₂×C₄	1	4	yes	—
41	C₂×C₄×AGL(1,𝔽₅)	—	2	2	no	—
42	D₅⋊M₁₆	—	2	2	no	—
43	D₅⋊M₁₆	—	2	2	no	—
44	D₅⋊M₁₆	C₂×C₄	1	4	yes	—
45	D₅⋊M₁₆	C₂³	1	4	yes	—
46	C₂×#700	C₂×C₄	1	4	yes	—
47	C₂×D₅⋊C₈	—	2	2	no	—
48	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄×Dic₅	—	2	1	no	—
52	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
53	C₂²×#168	C₂×C₄	1	1	yes	characteristic
54	C₂²×#168	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
56	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
59	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
62	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
63	C₂×C₈×D₅	D₄	1	1	yes	characteristic
64	C₂×C₈×D₅	D₄	1	1	yes	characteristic
65	C₂×C₈×D₅	D₄	1	2	yes	—
66	C₂×C₈×D₅	Q₈	1	2	yes	—
67	C₂×C₈×D₅	Q₈	1	1	yes	characteristic
68	C₂×C₈×D₅	Q₈	1	1	yes	characteristic
69	C₂×C₈×D₅	C₂³	1	2	yes	—
70	C₂×C₈×D₅	C₂³	1	2	yes	—
71	C₄²×D₅	—	2	1	no	—
72	C₄²×D₅	—	2	1	no	—
73	C₄²×D₅	C₂×C₄	1	2	yes	—
74	C₄²×D₅	C₂³	1	2	yes	—
75	#3996	C₂×C₄	1	8	yes	complemented
76	#3995	C₂×C₄	1	8	yes	complemented
77	#3994	C₂×C₄	1	8	yes	complemented
78	#3993	C₂×C₄	1	8	yes	complemented
79	#3992	—	2	8	no	—
80	C₈×AGL(1,𝔽₅)	—	2	8	no	—
81	C₄×C₅×C₈	C₂×C₄	1	4	yes	complemented
82	C₈×Dic₅	C₂×C₄	1	4	yes	complemented
83	C₈×Dic₅	C₂×C₄	1	4	yes	complemented
84	C₄×#168	C₂×C₄	1	4	yes	complemented
85	C₂²×#108	—	5	1	no	—
86	C₂×#427	—	5	1	no	—
87	C₂×#405	—	5	2	no	—
88	C₂²×C₄×C₈	—	5	1	no	—
89	#1772	—	5	8	no	—
90	C₂×#339	—	5	2	no	—
91	C₂³×D₅	#41	1	1	yes	characteristic
92	C₂²×AGL(1,𝔽₅)	—	2	4	no	—
93	C₂²×C₄×C₅	—	2	1	no	—
94	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
95	C₂²×Dic₅	—	2	1	no	—
96	C₂²×Dic₅	#41	1	1	yes	characteristic
97	C₂×C₄×D₅	—	2	8	no	—
98	C₂×C₄×D₅	—	2	2	no	—
99	C₂×C₄×D₅	—	2	2	no	—
100	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
106	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
107	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
108	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
109	C₂×C₄×D₅	#41	1	1	yes	characteristic
110	C₂×C₄×D₅	#41	1	1	yes	characteristic
111	C₂×C₄×D₅	C₂⁴	1	1	yes	characteristic
112	C₂²⋊AGL(1,𝔽₅)	—	2	4	no	—
113	C₂²⋊AGL(1,𝔽₅)	—	2	4	no	—
114	#704	—	2	4	no	—
115	#704	—	2	4	no	—
116	C₂×#170	—	2	4	no	—
117	C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
118	C₄⋊AGL(1,𝔽₅)	C₂²×C₄	1	8	yes	—
119	C₄×AGL(1,𝔽₅)	—	2	4	no	—
120	C₄×AGL(1,𝔽₅)	—	2	4	no	—
121	#700	—	2	4	no	—
122	#700	C₂²×C₄	1	8	yes	—
123	D₅⋊C₈	—	2	4	no	—
124	D₅⋊C₈	—	2	4	no	—
125	C₂×C₅×C₈	C₄²	1	1	yes	characteristic
126	C₂×C₅×C₈	C₄²	1	1	yes	characteristic
127	C₂×C₅×C₈	C₄²	1	2	yes	—
128	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
129	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
130	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
131	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
132	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
133	C₄²×C₅	—	2	1	no	—
134	C₄²×C₅	C₂²×C₄	1	2	yes	—
135	C₄×Dic₅	—	2	1	no	—
136	C₄×Dic₅	—	2	2	no	—
137	C₄×Dic₅	—	2	2	no	—
138	C₄×Dic₅	C₂²×C₄	1	2	yes	—
139	C₂×#168	C₄²	1	1	yes	characteristic
140	C₂×#168	C₄²	1	1	yes	characteristic
141	C₂×#168	C₄²	1	2	yes	—
142	C₂×#168	C₄⋊C₄	1	1	yes	characteristic
143	C₂×#168	C₄⋊C₄	1	1	yes	characteristic
144	C₂×#168	C₄⋊C₄	1	2	yes	—
145	C₂×#168	C₂²×C₄	1	2	yes	—
146	C₂×#168	C₂²×C₄	1	2	yes	—
147	C₈×D₅	C₄²	1	2	yes	—
148	C₈×D₅	C₄²	1	2	yes	—
149	C₈×D₅	C₄²	1	2	yes	—
150	C₈×D₅	C₄²	1	2	yes	—
151	C₈×D₅	C₄⋊C₄	1	2	yes	—
152	C₈×D₅	C₄⋊C₄	1	2	yes	—
153	C₈×D₅	C₄⋊C₄	1	2	yes	—
154	C₈×D₅	C₄⋊C₄	1	2	yes	—
155	C₈×D₅	C₂²×C₄	1	2	yes	—
156	C₈×D₅	C₂²×C₄	1	2	yes	—
157	C₈×D₅	C₂²×C₄	1	2	yes	—
158	C₈×D₅	C₂²×C₄	1	2	yes	—
159	C₈×D₅	C₂×D₄	1	2	yes	—
160	C₈×D₅	C₂×D₄	1	2	yes	—
161	C₈×D₅	C₂×Q₈	1	2	yes	—
162	C₈×D₅	C₂×Q₈	1	2	yes	—
163	C₂²×M₁₆	—	5	2	no	—
164	C₂³×C₈	—	5	1	no	—
165	C₂³×C₈	—	5	1	no	—
166	C₂×#117	—	5	2	no	—
167	C₂²×C₄²	—	5	1	no	—
168	C₂×#108	—	5	2	no	—
169	C₂×#108	—	5	2	no	—
170	C₂×#108	—	5	4	no	—
171	C₂×#108	—	5	4	no	—
172	#427	—	5	4	no	—
173	#427	—	5	4	no	—
174	C₂×#107	—	5	2	no	—
175	C₂×#106	—	5	2	no	—
176	#405	—	5	8	no	—
177	#405	—	10	4	no	—
178	C₂×#97	—	10	2	no	—
179	C₂×C₄×C₈	—	5	1	no	—
180	C₂×C₄×C₈	—	5	1	no	—
181	C₂×C₄×C₈	—	5	1	no	—
182	C₂×C₄×C₈	—	5	4	no	—
183	C₂×C₄×C₈	—	5	4	no	—
184	C₂×C₄×C₈	—	10	2	no	—
185	C₂×C₄×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
186	#339	—	5	8	no	—
187	C₂³×C₅	#117	1	1	yes	characteristic
188	C₂²×D₅	—	2	4	no	—
189	C₂²×D₅	#117	1	1	yes	characteristic
190	C₂²×D₅	C₄×D₄	1	1	yes	characteristic
191	C₂²×D₅	C₄×D₄	1	1	yes	characteristic
192	C₂²×D₅	C₄×Q₈	1	1	yes	characteristic
193	C₂²×D₅	C₄×Q₈	1	1	yes	characteristic
194	C₂²×D₅	C₂×#41	1	1	yes	characteristic
195	C₂×AGL(1,𝔽₅)	—	2	8	no	—
196	C₂×AGL(1,𝔽₅)	—	4	8	no	—
197	C₂×C₄×C₅	—	2	4	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
200	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
201	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
202	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
203	C₂×C₄×C₅	#117	1	1	yes	characteristic
204	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
205	C₂×Dic₅	—	2	4	no	—
206	C₂×Dic₅	—	2	2	no	—
207	C₂×Dic₅	#117	1	1	yes	characteristic
208	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
209	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
210	C₂×Dic₅	C₄×Q₈	1	1	yes	characteristic
211	C₂×Dic₅	C₄×Q₈	1	1	yes	characteristic
212	C₂×Dic₅	C₂×#41	1	1	yes	characteristic
213	C₄×D₅	—	2	8	no	—
214	C₄×D₅	—	2	8	no	—
215	C₄×D₅	C₂×C₄²	1	1	yes	characteristic
216	C₄×D₅	C₂×C₄²	1	1	yes	characteristic
217	C₄×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
218	C₄×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
219	C₄×D₅	C₄×D₄	1	1	yes	characteristic
220	C₄×D₅	C₄×D₄	1	1	yes	characteristic
221	C₄×D₅	C₄×D₄	1	1	yes	characteristic
222	C₄×D₅	C₄×D₄	1	1	yes	characteristic
223	C₄×D₅	C₄×Q₈	1	1	yes	characteristic
224	C₄×D₅	C₄×Q₈	1	1	yes	characteristic
225	C₄×D₅	C₄×Q₈	1	1	yes	characteristic
226	C₄×D₅	C₄×Q₈	1	1	yes	characteristic
227	C₄×D₅	C₂³×C₄	1	1	yes	characteristic
228	C₄×D₅	C₂³×C₄	1	1	yes	characteristic
229	C₄×D₅	C₂²×D₄	1	1	yes	characteristic
230	C₄×D₅	C₂²×Q₈	1	1	yes	characteristic
231	#170	—	2	8	no	—
232	C₅×C₈	C₂×C₄²	1	2	yes	—
233	C₅×C₈	C₂×C₄²	1	2	yes	—
234	C₅×C₈	C₂×C₄⋊C₄	1	2	yes	—
235	C₅×C₈	C₂×C₄⋊C₄	1	2	yes	—
236	#168	C₂×C₄²	1	2	yes	—
237	#168	C₂×C₄²	1	2	yes	—
238	#168	C₂×C₄⋊C₄	1	2	yes	—
239	#168	C₂×C₄⋊C₄	1	2	yes	—
240	C₂³×C₄	—	5	1	no	—
241	C₂³×C₄	—	10	1	no	—
242	C₂×M₁₆	—	5	4	no	—
243	C₂×M₁₆	—	5	4	no	—
244	C₂×M₁₆	—	5	4	no	—
245	C₂×M₁₆	—	10	2	no	—
246	C₂×M₁₆	—	10	2	no	—
247	C₂×M₁₆	—	10	2	no	—
248	C₂²×C₈	—	5	1	no	—
249	C₂²×C₈	—	5	1	no	—
250	C₂²×C₈	—	5	1	no	—
251	C₂²×C₈	—	5	1	no	—
252	C₂²×C₈	—	5	2	no	—
253	C₂²×C₈	—	5	1	no	—
254	C₂²×C₈	—	5	1	no	—
255	C₂²×C₈	—	5	2	no	—
256	C₂²×C₈	—	5	1	no	—
257	C₂²×C₈	—	5	2	no	—
258	C₂²×C₈	—	5	2	no	—
259	C₂²×C₈	—	5	1	no	—
260	C₂²×C₈	—	5	1	no	—
261	C₂²×C₈	—	5	1	no	—
262	C₂²×C₈	—	5	2	no	—
263	C₂²×C₈	—	5	2	no	—
264	C₂²×C₈	—	5	2	no	—
265	C₂²×C₈	—	5	2	no	—
266	C₂²×C₈	—	10	2	no	—
267	C₂²×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
268	C₂²×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
269	#117	—	5	4	no	—
270	#117	—	5	4	no	—
271	#117	—	10	2	no	—
272	#117	—	10	2	no	—
273	C₂×C₄⋊C₄	—	5	4	no	—
274	C₂×C₂²⋊C₄	—	10	2	no	—
275	C₂×C₄²	—	5	1	no	—
276	C₂×C₄²	—	5	2	no	—
277	C₂×C₄²	—	5	2	no	—
278	C₂×C₄²	—	10	1	no	—
279	C₂×C₄²	—	10	1	no	—
280	C₂×C₄²	—	10	1	no	—
281	C₂×C₄²	—	10	2	no	—
282	C₂×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
283	#108	—	5	8	no	—
284	#108	—	5	8	no	—
285	#107	—	5	8	no	—
286	#106	—	5	8	no	—
287	#97	—	10	8	no	—
288	C₄×C₈	—	5	4	no	—
289	C₄×C₈	—	5	4	no	—
290	C₄×C₈	—	5	4	no	—
291	C₄×C₈	—	10	8	no	—
292	C₄×C₈	C₂×AGL(1,𝔽₅)	1	4	yes	complemented
293	C₂²×C₅	—	2	2	no	—
294	C₂²×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
295	C₂²×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
296	C₂²×C₅	C₂×#117	1	1	yes	characteristic
297	C₂×D₅	—	2	2	no	—
298	C₂×D₅	—	2	2	no	—
299	C₂×D₅	—	2	2	no	—
300	C₂×D₅	—	2	2	no	—
301	C₂×D₅	—	2	2	no	—
302	C₂×D₅	C₄×C₄⋊C₄	1	1	yes	characteristic
303	C₂×D₅	C₄×C₄⋊C₄	1	1	yes	characteristic
304	C₂×D₅	#443	1	4	yes	—
305	C₂×D₅	C₂×C₄×D₄	1	1	yes	characteristic
306	C₂×D₅	C₂×C₄×Q₈	1	1	yes	characteristic
307	AGL(1,𝔽₅)	—	4	8	no	—
308	C₄×C₅	—	2	4	no	—
309	C₄×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
310	C₄×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
311	C₄×C₅	C₂²×C₄²	1	1	yes	characteristic
312	C₄×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
313	Dic₅	—	2	4	no	—
314	Dic₅	C₄×C₄⋊C₄	1	1	yes	characteristic
315	Dic₅	C₄×C₄⋊C₄	1	1	yes	characteristic
316	Dic₅	C₂×C₄×D₄	1	1	yes	characteristic
317	Dic₅	C₂×C₄×Q₈	1	1	yes	characteristic
318	C₂⁴	—	5	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	5	1	no	—
321	C₂²×C₄	—	5	1	no	—
322	C₂²×C₄	—	5	1	no	—
323	C₂²×C₄	—	5	1	no	—
324	C₂²×C₄	—	5	1	no	—
325	C₂²×C₄	—	5	1	no	—
326	C₂²×C₄	—	5	1	no	—
327	C₂²×C₄	—	5	1	no	—
328	C₂²×C₄	—	5	1	no	—
329	C₂²×C₄	—	5	1	no	—
330	C₂²×C₄	—	5	1	no	—
331	C₂²×C₄	—	5	1	no	—
332	C₂²×C₄	—	5	1	no	—
333	C₂²×C₄	—	10	2	no	—
334	C₂²×C₄	—	10	2	no	—
335	C₂²×C₄	—	10	8	no	—
336	C₂²×C₄	—	10	1	no	—
337	C₂²×C₄	—	10	4	no	—
338	C₂²×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
339	M₁₆	—	5	8	no	—
340	M₁₆	—	10	4	no	—
341	M₁₆	—	10	4	no	—
342	M₁₆	—	10	4	no	—
343	C₂×C₈	—	5	1	no	—
344	C₂×C₈	—	5	1	no	—
345	C₂×C₈	—	5	2	no	—
346	C₂×C₈	—	5	2	no	—
347	C₂×C₈	—	5	1	no	—
348	C₂×C₈	—	5	1	no	—
349	C₂×C₈	—	5	2	no	—
350	C₂×C₈	—	5	2	no	—
351	C₂×C₈	—	5	2	no	—
352	C₂×C₈	—	5	2	no	—
353	C₂×C₈	—	5	2	no	—
354	C₂×C₈	—	5	2	no	—
355	C₂×C₈	—	5	2	no	—
356	C₂×C₈	—	5	2	no	—
357	C₂×C₈	—	5	2	no	—
358	C₂×C₈	—	5	2	no	—
359	C₂×C₈	—	5	2	no	—
360	C₂×C₈	—	5	2	no	—
361	C₂×C₈	—	5	2	no	—
362	C₂×C₈	—	5	2	no	—
363	C₂×C₈	—	5	2	no	—
364	C₂×C₈	—	5	2	no	—
365	C₂×C₈	—	5	2	no	—
366	C₂×C₈	—	5	2	no	—
367	C₂×C₈	—	10	4	no	—
368	C₂×C₈	—	10	4	no	—
369	C₂×C₈	—	10	4	no	—
370	C₂×C₈	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
371	C₂×C₈	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
372	C₂×C₈	C₄×AGL(1,𝔽₅)	1	2	yes	—
373	C₂×C₈	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
374	C₂×C₈	C₄⋊AGL(1,𝔽₅)	1	2	yes	—
375	C₂×C₈	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
376	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	2	yes	—
377	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	2	yes	—
378	C₄⋊C₄	—	5	8	no	—
379	C₄⋊C₄	—	10	4	no	—
380	C₂²⋊C₄	—	10	4	no	—
381	C₂²⋊C₄	—	10	4	no	—
382	C₄²	—	2	1	no	—
383	C₄²	—	5	2	no	—
384	C₄²	—	10	2	no	—
385	C₄²	—	10	2	no	—
386	C₄²	—	10	4	no	—
387	C₄²	—	10	4	no	—
388	C₄²	—	10	1	no	—
389	C₄²	C₂²×AGL(1,𝔽₅)	1	2	yes	—
390	C₂×C₅	—	2	1	no	—
391	C₂×C₅	—	2	1	no	—
392	C₂×C₅	#1772	1	2	yes	complemented
393	C₂×C₅	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
394	D₅	—	2	1	no	—
395	D₅	—	2	1	no	—
396	D₅	#1772	1	2	yes	complemented
397	D₅	C₂×#443	1	2	yes	—
398	C₂³	—	5	1	no	—
399	C₂³	—	5	1	no	—
400	C₂³	—	5	1	no	—
401	C₂³	—	5	1	no	—
402	C₂³	—	5	1	no	—
403	C₂³	—	5	1	no	—
404	C₂³	—	10	4	no	—
405	C₂³	#4130	1	1	yes	characteristic
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	5	1	no	—
409	C₂×C₄	—	5	1	no	—
410	C₂×C₄	—	5	1	no	—
411	C₂×C₄	—	5	1	no	—
412	C₂×C₄	—	5	1	no	—
413	C₂×C₄	—	5	1	no	—
414	C₂×C₄	—	5	1	no	—
415	C₂×C₄	—	5	1	no	—
416	C₂×C₄	—	5	1	no	—
417	C₂×C₄	—	5	1	no	—
418	C₂×C₄	—	5	1	no	—
419	C₂×C₄	—	5	1	no	—
420	C₂×C₄	—	5	1	no	—
421	C₂×C₄	—	5	1	no	—
422	C₂×C₄	—	5	1	no	—
423	C₂×C₄	—	5	1	no	—
424	C₂×C₄	—	5	1	no	—
425	C₂×C₄	—	5	1	no	—
426	C₂×C₄	—	5	1	no	—
427	C₂×C₄	—	5	1	no	—
428	C₂×C₄	—	5	1	no	—
429	C₂×C₄	—	5	1	no	—
430	C₂×C₄	—	10	8	no	—
431	C₂×C₄	—	10	8	no	—
432	C₂×C₄	—	10	4	no	—
433	C₂×C₄	—	10	2	no	—
434	C₂×C₄	—	10	8	no	—
435	C₂×C₄	—	20	8	no	—
436	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
437	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
438	C₂×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
439	C₂×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
440	C₂×C₄	#4130	1	1	yes	characteristic
441	C₂×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
442	C₈	—	5	2	no	—
443	C₈	—	5	2	no	—
444	C₈	—	5	2	no	—
445	C₈	—	5	2	no	—
446	C₈	—	10	8	no	—
447	C₈	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	—
448	C₈	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	—
449	C₈	C₂×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
450	C₈	C₂×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
451	C₅	C₂×#1772	1	1	yes	characteristic, complemented, Sylow
452	C₂²	—	2	2	no	—
453	C₂²	—	5	4	no	—
454	C₂²	—	5	1	no	—
455	C₂²	—	5	1	no	—
456	C₂²	—	5	1	no	—
457	C₂²	—	5	1	no	—
458	C₂²	—	10	2	no	—
459	C₂²	—	10	2	no	—
460	C₂²	—	10	2	no	—
461	C₂²	—	10	2	no	—
462	C₂²	—	10	2	no	—
463	C₂²	C₄×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
464	C₂²	C₄×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
465	C₂²	C₂×#4130	1	1	yes	characteristic
466	C₄	—	2	4	no	—
467	C₄	—	5	1	no	—
468	C₄	—	5	1	no	—
469	C₄	—	5	1	no	—
470	C₄	—	5	1	no	—
471	C₄	—	10	4	no	—
472	C₄	—	20	8	no	—
473	C₄	C₄×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
474	C₄	C₄×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
475	C₄	C₂²×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
476	C₄	C₂²×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
477	C₂	—	2	1	no	—
478	C₂	—	2	1	no	—
479	C₂	—	5	2	no	—
480	C₂	—	5	2	no	—
481	C₂	—	10	1	no	—
482	C₂	—	10	1	no	—
483	C₂	#10603851	1	2	yes	direct product factor
484	C₂	C₂×C₄×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₄⋊AGL(1,𝔽₅)
commutator	C₄×C₅	C₂²×C₄²
Frattini	C₂×C₄	C₂³×AGL(1,𝔽₅)
Fitting	C₂×C₄×C₅×C₈	C₄
socle	C₂²×C₅	C₄×C₄⋊C₄
prime radical	C₂³×D₅	#41
cosocle	C₂×C₄×D₅	C₂⁴
hypercenter	C₂×C₄×C₈	AGL(1,𝔽₅)
hypocenter	C₅	C₂×#1772
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
6. #10603851	C₂	direct (N × H)
12. D₅⋊#108	C₄	semidirect
14. C₂×#3996	C₄	semidirect
15. C₂×#3995	C₄	semidirect
16. #65721	C₄	semidirect
18. C₂×#3994	C₄	semidirect
19. C₂×#3993	C₄	semidirect
24. C₂×C₄×C₅×C₈	C₄	semidirect
25. C₂×C₈×Dic₅	C₄	semidirect
26. C₂×C₈×Dic₅	C₄	semidirect
27. C₂×C₄×#168	C₄	semidirect
28. C₄×C₈×D₅	C₄	semidirect
75. #3996	C₂×C₄	semidirect
76. #3995	C₂×C₄	semidirect
77. #3994	C₂×C₄	semidirect
78. #3993	C₂×C₄	semidirect
81. C₄×C₅×C₈	C₂×C₄	semidirect
82. C₈×Dic₅	C₂×C₄	semidirect
83. C₈×Dic₅	C₂×C₄	semidirect
84. C₄×#168	C₂×C₄	semidirect
185. C₂×C₄×C₈	AGL(1,𝔽₅)	semidirect
292. C₄×C₈	C₂×AGL(1,𝔽₅)	semidirect
392. C₂×C₅	#1772	semidirect
396. D₅	#1772	semidirect
451. C₅	C₂×#1772	semidirect
483. C₂	#10603851	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×D₅⋊#108	2
C₂×#65721	2
C₂×#65718	2
C₂×C₄×C₈×D₅	2
C₂×#64862	2
#10603851	2
C₂×#1772	5

Subgroups — C2×#10603851 #13033547

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10603851 #13033547