Subgroups — C₅×#21175 #11943895

Order 1280.

990 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#428	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#427	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#424	C₂	1	1	yes	maximal, characteristic
4	C₅×#2317	C₂	1	1	yes	maximal, characteristic
5	C₅×#2274	C₂	1	1	yes	maximal, characteristic
6	C₅×#1949	C₂	1	2	yes	maximal, complemented
7	C₅×#1949	C₂	1	2	yes	maximal, complemented
8	C₅×#1948	C₂	1	2	yes	maximal, complemented
9	C₅×#1947	C₂	1	2	yes	maximal, complemented
10	C₅×#1736	C₂	1	1	yes	maximal, characteristic
11	C₂×C₅×#340	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₅×#117	C₂²	1	1	yes	characteristic
15	C₂×C₅×#117	C₂²	1	1	yes	characteristic
16	C₂×C₅×#117	C₂²	1	1	yes	characteristic
17	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₅×#428	—	2	4	no	—
20	C₅×#427	—	2	4	no	—
21	C₂×C₅×#107	C₂²	1	1	yes	characteristic
22	C₂×C₅×#107	C₂²	1	1	yes	characteristic
23	C₂×C₅×#107	C₂²	1	2	yes	—
24	C₂×C₅×#106	C₂²	1	1	yes	characteristic
25	C₂×C₅×#106	C₂²	1	1	yes	characteristic
26	C₂×C₅×#106	C₂²	1	2	yes	—
27	C₅×#424	C₄	1	8	yes	complemented
28	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
29	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
30	C₅×#389	—	2	1	no	—
31	C₅×#389	—	2	1	no	—
32	C₅×#385	—	2	2	no	—
33	C₅×#384	C₂²	1	2	yes	—
34	C₅×#382	C₂²	1	2	yes	—
35	C₄×C₅×C₄⋊C₄	—	2	1	no	—
36	C₄×C₅×C₄⋊C₄	—	2	1	no	—
37	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
38	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
39	C₄×C₅×C₂²⋊C₄	—	2	2	no	—
40	C₅×#340	C₂²	1	2	yes	—
41	C₅×#340	C₂²	1	2	yes	—
42	C₅×#340	C₂²	1	2	yes	—
43	C₅×#340	C₂²	1	2	yes	—
44	#21175	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂³×C₄×C₅	—	2	1	no	—
46	C₂³×C₄×C₅	—	2	1	no	—
47	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₂×C₅×M₁₆	—	2	2	no	—
49	C₂×C₅×M₁₆	—	2	2	no	—
50	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	—
51	C₂²×C₅×C₈	—	2	2	no	—
52	C₂²×C₅×C₈	—	2	2	no	—
53	C₂²×C₅×C₈	C₂×C₄	1	4	yes	—
54	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
55	C₂²×C₅×C₈	C₂³	1	2	yes	—
56	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
57	C₅×#117	—	2	2	no	—
58	C₅×#117	—	2	2	no	—
59	C₅×#117	—	2	2	no	—
60	C₅×#117	C₂×C₄	1	4	yes	—
61	C₅×#117	D₄	1	4	yes	—
62	C₅×#117	Q₈	1	4	yes	—
63	C₂×C₅×C₄⋊C₄	—	2	1	no	—
64	C₂×C₅×C₄⋊C₄	—	2	2	no	—
65	C₂×C₅×C₄⋊C₄	—	2	2	no	—
66	C₂×C₅×C₄⋊C₄	—	2	2	no	—
67	C₂×C₅×C₄⋊C₄	—	2	1	no	—
68	C₂×C₅×C₄⋊C₄	—	2	2	no	—
69	C₂×C₅×C₄⋊C₄	—	2	2	no	—
70	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
71	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
72	C₂×C₅×C₄⋊C₄	Q₈	1	4	yes	—
73	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
74	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
75	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
76	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
79	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
80	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
81	C₂×C₅×C₂²⋊C₄	D₄	1	2	yes	—
82	C₂×C₄²×C₅	—	2	1	no	—
83	C₂×C₄²×C₅	—	2	1	no	—
84	C₂×C₄²×C₅	—	2	2	no	—
85	C₂×C₄²×C₅	—	2	2	no	—
86	C₂×C₄²×C₅	C₂³	1	2	yes	—
87	C₅×#107	—	2	2	no	—
88	C₅×#107	—	2	2	no	—
89	C₅×#107	—	2	4	no	—
90	C₅×#106	—	2	2	no	—
91	C₅×#106	—	2	2	no	—
92	C₅×#106	—	2	4	no	—
93	C₅×C₄⋊C₈	C₂×C₄	1	8	yes	complemented
94	C₅×C₄⋊C₈	C₂×C₄	1	8	yes	complemented
95	C₅×#95	—	2	2	no	—
96	C₅×#95	—	2	2	no	—
97	C₅×#95	—	2	2	no	—
98	C₅×#95	—	2	2	no	—
99	C₂×#428	C₂×C₅	1	1	yes	characteristic
100	C₂×#427	C₂×C₅	1	1	yes	characteristic
101	C₂×#424	C₂×C₅	1	1	yes	characteristic
102	#2317	C₂×C₅	1	1	yes	characteristic
103	#2274	C₂×C₅	1	1	yes	characteristic
104	#1949	C₂×C₅	1	2	yes	complemented
105	#1949	C₂×C₅	1	2	yes	complemented
106	#1948	C₂×C₅	1	2	yes	complemented
107	#1947	C₂×C₅	1	2	yes	complemented
108	#1736	C₂×C₅	1	1	yes	characteristic
109	C₂×#340	C₂×C₅	1	1	yes	characteristic
110	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₅	—	2	1	no	—
112	C₂²×C₄×C₅	—	2	1	no	—
113	C₂²×C₄×C₅	—	2	2	no	—
114	C₂²×C₄×C₅	—	2	4	no	—
115	C₂²×C₄×C₅	—	2	1	no	—
116	C₂²×C₄×C₅	—	2	1	no	—
117	C₂²×C₄×C₅	—	2	2	no	—
118	C₂²×C₄×C₅	—	4	2	no	—
119	C₂²×C₄×C₅	—	8	1	no	—
120	C₂²×C₄×C₅	—	8	1	no	—
121	C₂²×C₄×C₅	—	8	1	no	—
122	C₂²×C₄×C₅	—	8	1	no	—
123	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
124	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
129	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
130	C₂²×C₄×C₅	#41	1	2	yes	—
131	C₂²×C₄×C₅	#41	1	2	yes	—
132	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
133	C₅×M₁₆	—	2	8	no	—
134	C₂×C₅×C₈	—	2	8	no	—
135	C₂×C₅×C₈	—	2	1	no	—
136	C₂×C₅×C₈	—	2	1	no	—
137	C₂×C₅×C₈	—	2	2	no	—
138	C₂×C₅×C₈	—	2	1	no	—
139	C₂×C₅×C₈	—	2	1	no	—
140	C₂×C₅×C₈	—	2	2	no	—
141	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
142	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
143	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
144	C₅×C₄⋊C₄	—	2	4	no	—
145	C₅×C₄⋊C₄	—	2	2	no	—
146	C₅×C₄⋊C₄	—	2	1	no	—
147	C₅×C₄⋊C₄	—	2	1	no	—
148	C₅×C₄⋊C₄	—	2	2	no	—
149	C₅×C₄⋊C₄	—	2	1	no	—
150	C₅×C₄⋊C₄	—	2	1	no	—
151	C₅×C₄⋊C₄	—	2	2	no	—
152	C₅×C₄⋊C₄	—	2	1	no	—
153	C₅×C₄⋊C₄	—	2	1	no	—
154	C₅×C₄⋊C₄	—	4	2	no	—
155	C₅×C₄⋊C₄	—	8	2	no	—
156	C₅×C₄⋊C₄	—	8	2	no	—
157	C₅×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
158	C₅×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
159	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
160	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
161	C₅×C₄⋊C₄	C₂×Q₈	1	4	yes	—
162	C₅×C₂²⋊C₄	—	2	4	no	—
163	C₅×C₂²⋊C₄	—	4	2	no	—
164	C₅×C₂²⋊C₄	C₄⋊C₄	1	8	yes	—
165	C₄²×C₅	—	2	4	no	—
166	C₄²×C₅	—	4	2	no	—
167	C₄²×C₅	—	8	2	no	—
168	C₄²×C₅	—	8	2	no	—
169	C₄²×C₅	C₂²×C₄	1	4	yes	—
170	C₄²×C₅	C₂×Q₈	1	4	yes	—
171	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
172	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
173	C₂×#117	C₂²×C₅	1	1	yes	characteristic
174	C₂×#117	C₂²×C₅	1	1	yes	characteristic
175	C₂×#117	C₂²×C₅	1	1	yes	characteristic
176	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
177	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
178	#428	—	2	4	no	—
179	#427	—	2	4	no	—
180	C₂×#107	C₂²×C₅	1	1	yes	characteristic
181	C₂×#107	C₂²×C₅	1	1	yes	characteristic
182	C₂×#107	C₂²×C₅	1	2	yes	—
183	C₂×#106	C₂²×C₅	1	1	yes	characteristic
184	C₂×#106	C₂²×C₅	1	1	yes	characteristic
185	C₂×#106	C₂²×C₅	1	2	yes	—
186	#424	C₄×C₅	1	8	yes	complemented
187	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
188	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
189	#389	—	2	1	no	—
190	#389	—	2	1	no	—
191	#385	—	2	2	no	—
192	#384	C₂²×C₅	1	2	yes	—
193	#382	C₂²×C₅	1	2	yes	—
194	C₄×C₄⋊C₄	—	2	1	no	—
195	C₄×C₄⋊C₄	—	2	1	no	—
196	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
197	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
198	C₄×C₂²⋊C₄	—	2	2	no	—
199	#340	C₂²×C₅	1	2	yes	—
200	#340	C₂²×C₅	1	2	yes	—
201	#340	C₂²×C₅	1	2	yes	—
202	#340	C₂²×C₅	1	2	yes	—
203	C₂³×C₅	—	2	1	no	—
204	C₂³×C₅	—	2	1	no	—
205	C₂³×C₅	—	2	1	no	—
206	C₂³×C₅	—	2	1	no	—
207	C₂³×C₅	C₂×C₄⋊C₄	1	2	yes	—
208	C₂³×C₅	#121	1	2	yes	—
209	C₂³×C₅	C₂²⋊Q₈	1	2	yes	—
210	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	2	2	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	2	2	no	—
215	C₂×C₄×C₅	—	2	2	no	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	2	4	no	—
218	C₂×C₄×C₅	—	4	1	no	—
219	C₂×C₄×C₅	—	4	2	no	—
220	C₂×C₄×C₅	—	4	1	no	—
221	C₂×C₄×C₅	—	4	2	no	—
222	C₂×C₄×C₅	—	4	1	no	—
223	C₂×C₄×C₅	—	4	1	no	—
224	C₂×C₄×C₅	—	4	1	no	—
225	C₂×C₄×C₅	—	4	1	no	—
226	C₂×C₄×C₅	—	4	2	no	—
227	C₂×C₄×C₅	—	4	1	no	—
228	C₂×C₄×C₅	—	4	2	no	—
229	C₂×C₄×C₅	—	4	1	no	—
230	C₂×C₄×C₅	—	4	2	no	—
231	C₂×C₄×C₅	—	4	1	no	—
232	C₂×C₄×C₅	—	4	1	no	—
233	C₂×C₄×C₅	—	8	4	no	—
234	C₂×C₄×C₅	—	8	4	no	—
235	C₂×C₄×C₅	C₂×C₄⋊C₄	1	4	yes	—
236	C₂×C₄×C₅	C₂×C₄⋊C₄	1	4	yes	—
237	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
238	C₂×C₄×C₅	C₄×D₄	1	4	yes	—
239	C₂×C₄×C₅	C₄×Q₈	1	4	yes	—
240	C₂×C₄×C₅	#121	1	2	yes	—
241	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
242	C₂×C₄×C₅	#125	1	4	yes	—
243	C₂×C₄×C₅	C₄⋊Q₈	1	4	yes	—
244	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
245	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
248	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
249	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
250	C₅×C₈	—	2	2	no	—
251	C₅×C₈	—	2	2	no	—
252	C₅×C₈	—	2	4	no	—
253	C₂³×C₄	—	2	1	no	—
254	C₂³×C₄	—	2	1	no	—
255	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
256	C₂×M₁₆	—	2	2	no	—
257	C₂×M₁₆	—	2	2	no	—
258	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	—
259	C₂²×C₈	—	2	2	no	—
260	C₂²×C₈	—	2	2	no	—
261	C₂²×C₈	C₂×C₄×C₅	1	4	yes	—
262	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
263	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
264	C₂²×C₈	C₂³×C₅	1	2	yes	—
265	#117	—	2	2	no	—
266	#117	—	2	2	no	—
267	#117	—	2	2	no	—
268	#117	C₂×C₄×C₅	1	4	yes	—
269	#117	C₅×D₄	1	4	yes	—
270	#117	C₅×Q₈	1	4	yes	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₅×Q₈	1	4	yes	—
281	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
282	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
283	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
287	C₂×C₂²⋊C₄	—	2	1	no	—
288	C₂×C₂²⋊C₄	—	2	1	no	—
289	C₂×C₂²⋊C₄	C₅×D₄	1	2	yes	—
290	C₂×C₄²	—	2	1	no	—
291	C₂×C₄²	—	2	1	no	—
292	C₂×C₄²	—	2	2	no	—
293	C₂×C₄²	—	2	2	no	—
294	C₂×C₄²	C₂³×C₅	1	2	yes	—
295	#107	—	2	2	no	—
296	#107	—	2	2	no	—
297	#107	—	2	4	no	—
298	#106	—	2	2	no	—
299	#106	—	2	2	no	—
300	#106	—	2	4	no	—
301	C₄⋊C₈	C₂×C₄×C₅	1	8	yes	complemented
302	C₄⋊C₈	C₂×C₄×C₅	1	8	yes	complemented
303	#95	—	2	2	no	—
304	#95	—	2	2	no	—
305	#95	—	2	2	no	—
306	#95	—	2	2	no	—
307	C₂²×C₅	—	2	2	no	—
308	C₂²×C₅	—	2	2	no	—
309	C₂²×C₅	—	2	2	no	—
310	C₂²×C₅	—	2	2	no	—
311	C₂²×C₅	—	2	2	no	—
312	C₂²×C₅	—	2	2	no	—
313	C₂²×C₅	#389	1	4	yes	—
314	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
315	C₂²×C₅	C₂×#121	1	1	yes	characteristic
316	C₂²×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
317	C₂²×C₅	#576	1	1	yes	characteristic
318	C₂²×C₅	#577	1	1	yes	characteristic
319	C₂²×C₅	#577	1	1	yes	characteristic
320	C₂²×C₅	#578	1	1	yes	characteristic
321	C₄×C₅	—	2	4	no	—
322	C₄×C₅	—	2	4	no	—
323	C₄×C₅	—	4	4	no	—
324	C₄×C₅	—	4	2	no	—
325	C₄×C₅	—	4	2	no	—
326	C₄×C₅	—	8	1	no	—
327	C₄×C₅	—	8	2	no	—
328	C₄×C₅	—	8	1	no	—
329	C₄×C₅	#389	1	4	yes	—
330	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
331	C₄×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
332	C₄×C₅	C₂×#125	1	1	yes	characteristic
333	C₄×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
334	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	4	2	no	—
343	C₂²×C₄	—	8	1	no	—
344	C₂²×C₄	—	8	1	no	—
345	C₂²×C₄	—	8	1	no	—
346	C₂²×C₄	—	8	1	no	—
347	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
348	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
349	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
350	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
351	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
352	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
353	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
354	C₂²×C₄	C₅×#41	1	2	yes	—
355	C₂²×C₄	C₅×#41	1	2	yes	—
356	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
357	M₁₆	—	2	8	no	—
358	C₂×C₈	—	2	8	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
366	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
367	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	4	2	no	—
379	C₄⋊C₄	—	8	2	no	—
380	C₄⋊C₄	—	8	2	no	—
381	C₄⋊C₄	C₅×C₄⋊C₄	1	4	yes	—
382	C₄⋊C₄	C₅×C₄⋊C₄	1	4	yes	—
383	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
384	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
385	C₄⋊C₄	C₂×C₅×Q₈	1	4	yes	—
386	C₂²⋊C₄	—	2	4	no	—
387	C₂²⋊C₄	—	4	2	no	—
388	C₂²⋊C₄	C₅×C₄⋊C₄	1	8	yes	—
389	C₄²	—	2	4	no	—
390	C₄²	—	4	2	no	—
391	C₄²	—	8	2	no	—
392	C₄²	—	8	2	no	—
393	C₄²	C₂²×C₄×C₅	1	4	yes	—
394	C₄²	C₂×C₅×Q₈	1	4	yes	—
395	C₂×C₅	—	2	4	no	—
396	C₂×C₅	C₂×#389	1	1	yes	characteristic
397	C₂×C₅	#2912	1	1	yes	characteristic
398	C₂×C₅	#2913	1	1	yes	characteristic
399	C₂×C₅	#3045	1	1	yes	characteristic
400	C₂×C₅	#3046	1	1	yes	characteristic
401	C₂×C₅	#3081	1	1	yes	characteristic
402	C₂×C₅	#3082	1	1	yes	characteristic
403	C₂³	—	2	1	no	—
404	C₂³	—	2	1	no	—
405	C₂³	—	2	1	no	—
406	C₂³	—	2	1	no	—
407	C₂³	C₂×C₅×C₄⋊C₄	1	2	yes	—
408	C₂³	C₅×#121	1	2	yes	—
409	C₂³	C₅×C₂²⋊Q₈	1	2	yes	—
410	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	8	4	no	—
434	C₂×C₄	—	8	4	no	—
435	C₂×C₄	C₂×C₅×C₄⋊C₄	1	4	yes	—
436	C₂×C₄	C₂×C₅×C₄⋊C₄	1	4	yes	—
437	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
438	C₂×C₄	C₄×C₅×D₄	1	4	yes	—
439	C₂×C₄	C₄×C₅×Q₈	1	4	yes	—
440	C₂×C₄	C₅×#121	1	2	yes	—
441	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
442	C₂×C₄	C₅×#125	1	4	yes	—
443	C₂×C₄	C₅×C₄⋊Q₈	1	4	yes	—
444	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
445	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
446	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
447	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
448	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
449	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
450	C₈	—	2	2	no	—
451	C₈	—	2	2	no	—
452	C₈	—	2	4	no	—
453	C₅	#21175	1	1	yes	characteristic, direct product factor, Sylow
454	C₂²	—	2	2	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	2	2	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	2	2	no	—
460	C₂²	C₅×#389	1	4	yes	—
461	C₂²	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
462	C₂²	C₂×C₅×#121	1	1	yes	characteristic
463	C₂²	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
464	C₂²	C₅×#576	1	1	yes	characteristic
465	C₂²	C₅×#577	1	1	yes	characteristic
466	C₂²	C₅×#577	1	1	yes	characteristic
467	C₂²	C₅×#578	1	1	yes	characteristic
468	C₄	—	2	4	no	—
469	C₄	—	2	4	no	—
470	C₄	—	4	2	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	4	no	—
473	C₄	—	8	2	no	—
474	C₄	—	8	1	no	—
475	C₄	—	8	1	no	—
476	C₄	C₅×#389	1	4	yes	—
477	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
478	C₄	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
479	C₄	C₂×C₅×#125	1	1	yes	characteristic
480	C₄	C₂×C₅×C₄⋊Q₈	1	1	yes	characteristic
481	C₂	—	2	4	no	—
482	C₂	C₂×C₅×#389	1	1	yes	characteristic
483	C₂	C₅×#2912	1	1	yes	characteristic
484	C₂	C₅×#2913	1	1	yes	characteristic
485	C₂	C₅×#3045	1	1	yes	characteristic
486	C₂	C₅×#3046	1	1	yes	characteristic
487	C₂	C₅×#3081	1	1	yes	characteristic
488	C₂	C₅×#3082	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂⁴×C₅	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
6. C₅×#1949	C₂	semidirect
7. C₅×#1949	C₂	semidirect
8. C₅×#1948	C₂	semidirect
9. C₅×#1947	C₂	semidirect
27. C₅×#424	C₄	semidirect
44. #21175	C₅	direct (N × H)
93. C₅×C₄⋊C₈	C₂×C₄	semidirect
94. C₅×C₄⋊C₈	C₂×C₄	semidirect
104. #1949	C₂×C₅	semidirect
105. #1949	C₂×C₅	semidirect
106. #1948	C₂×C₅	semidirect
107. #1947	C₂×C₅	semidirect
186. #424	C₄×C₅	semidirect
301. C₄⋊C₈	C₂×C₄×C₅	semidirect
302. C₄⋊C₈	C₂×C₄×C₅	semidirect
453. C₅	#21175	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×C₅×#428	2
C₂×C₅×#427	2
C₂×C₅×#424	2
C₅×#2317	2
C₅×#2274	2
C₅×#1949	2
C₅×#1948	2
C₅×#1947	2
C₅×#1736	2
C₂×C₅×#340	2
#21175	5

Subgroups — C5×#21175 #11943895

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21175 #11943895