Subgroups — C₅×#22232 #11944952

Order 1280.

838 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#490	C₂	1	1	yes	maximal, characteristic
2	C₅×#2330	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2328	C₂	1	1	yes	maximal, characteristic
4	C₅×#1991	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1957	C₂	1	1	yes	maximal, characteristic
6	C₅×#1926	C₂	1	2	yes	maximal, complemented
7	C₅×#1925	C₂	1	2	yes	maximal, complemented
8	C₅×#1864	C₂	1	2	yes	maximal, complemented
9	C₅×#1862	C₂	1	2	yes	maximal, complemented
10	C₅×#1847	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1746	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#127	C₂²	1	1	yes	characteristic
13	C₂×C₅×#125	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₅×#490	C₄	1	8	yes	complemented
17	C₂×C₅×#107	C₂²	1	2	yes	—
18	C₂×C₅×#106	C₂²	1	2	yes	—
19	C₂×C₅×#102	C₂²	1	2	yes	—
20	C₂×C₅×#102	C₂²	1	2	yes	—
21	C₂×C₅×#102	C₂²	1	2	yes	—
22	C₂×C₅×#102	C₂²	1	2	yes	—
23	C₂×C₅×#97	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
25	C₅×#390	C₂²	1	1	yes	characteristic
26	C₅×#390	C₂²	1	1	yes	characteristic
27	C₅×#389	—	2	2	no	—
28	C₅×#389	C₂²	1	2	yes	—
29	C₅×#387	—	2	2	no	—
30	C₅×#386	—	2	2	no	—
31	C₅×#386	—	2	2	no	—
32	C₅×#384	C₂²	1	1	yes	characteristic
33	C₅×#382	C₂²	1	1	yes	characteristic
34	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
35	C₅×#376	C₂²	1	1	yes	characteristic
36	C₅×#340	C₂²	1	2	yes	—
37	C₅×#340	C₂²	1	2	yes	—
38	C₅×#336	C₂²	1	2	yes	—
39	C₅×#336	C₂²	1	2	yes	—
40	#22232	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂²×C₅×D₄	—	2	2	no	—
42	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
43	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₅	—	2	1	no	—
45	C₂³×C₄×C₅	—	2	1	no	—
46	C₂²×C₅×C₈	C₂³	1	2	yes	—
47	C₂²×C₅×C₈	C₂³	1	2	yes	—
48	C₅×#127	—	2	2	no	—
49	C₅×#127	C₂×C₄	1	4	yes	—
50	C₅×#125	—	2	2	no	—
51	C₅×#125	C₂×C₄	1	4	yes	complemented
52	C₄×C₅×D₄	—	4	2	no	—
53	C₄×C₅×D₄	—	4	2	no	—
54	C₂×C₅×C₄⋊C₄	—	2	2	no	—
55	C₂×C₅×C₄⋊C₄	—	2	2	no	—
56	C₂×C₅×C₄⋊C₄	—	2	2	no	—
57	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
58	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
59	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
60	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
61	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
62	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
63	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
64	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
65	C₂×C₄²×C₅	—	2	2	no	—
66	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
69	C₅×#107	—	4	2	no	—
70	C₅×#106	—	4	2	no	—
71	C₅×#102	—	4	2	no	—
72	C₅×#102	—	4	2	no	—
73	C₅×#102	C₂×C₄	1	8	yes	complemented
74	C₅×#102	C₂×C₄	1	8	yes	complemented
75	C₅×#97	C₂×C₄	1	4	yes	complemented
76	C₄×C₅×C₈	—	2	2	no	—
77	C₅×#95	—	2	2	no	—
78	C₅×#95	—	2	2	no	—
79	C₅×#95	—	2	2	no	—
80	C₅×#95	D₄	1	2	yes	—
81	C₅×#95	D₄	1	2	yes	—
82	C₂×#490	C₂×C₅	1	1	yes	characteristic
83	#2330	C₂×C₅	1	1	yes	characteristic, complemented
84	#2328	C₂×C₅	1	1	yes	characteristic
85	#1991	C₂×C₅	1	1	yes	characteristic, complemented
86	#1957	C₂×C₅	1	1	yes	characteristic
87	#1926	C₂×C₅	1	2	yes	complemented
88	#1925	C₂×C₅	1	2	yes	complemented
89	#1864	C₂×C₅	1	2	yes	complemented
90	#1862	C₂×C₅	1	2	yes	complemented
91	#1847	C₂×C₅	1	1	yes	characteristic, complemented
92	#1746	C₂×C₅	1	1	yes	characteristic, complemented
93	C₂⁴×C₅	—	2	1	no	—
94	C₂⁴×C₅	—	2	1	no	—
95	C₂×C₅×D₄	—	2	8	no	—
96	C₂×C₅×D₄	—	2	1	no	—
97	C₂×C₅×D₄	—	2	1	no	—
98	C₂×C₅×D₄	—	2	2	no	—
99	C₂×C₅×D₄	—	2	2	no	—
100	C₂×C₅×D₄	—	2	2	no	—
101	C₂×C₅×D₄	—	2	2	no	—
102	C₂×C₅×D₄	—	8	2	no	—
103	C₂×C₅×D₄	—	8	2	no	—
104	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
105	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₅	—	2	2	no	—
107	C₂²×C₄×C₅	—	2	2	no	—
108	C₂²×C₄×C₅	—	2	1	no	—
109	C₂²×C₄×C₅	—	2	1	no	—
110	C₂²×C₄×C₅	—	4	2	no	—
111	C₂²×C₄×C₅	—	4	2	no	—
112	C₂²×C₄×C₅	—	8	2	no	—
113	C₂²×C₄×C₅	—	8	2	no	—
114	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
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	2	yes	—
118	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
119	C₂×C₅×C₈	—	2	2	no	—
120	C₂×C₅×C₈	—	2	2	no	—
121	C₂×C₅×C₈	—	2	2	no	—
122	C₂×C₅×C₈	—	2	2	no	—
123	C₂×C₅×C₈	—	2	2	no	—
124	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
125	C₅×C₄⋊C₄	—	2	8	no	—
126	C₅×C₄⋊C₄	—	2	2	no	—
127	C₅×C₄⋊C₄	—	2	2	no	—
128	C₅×C₄⋊C₄	—	2	2	no	—
129	C₅×C₄⋊C₄	—	2	2	no	—
130	C₅×C₄⋊C₄	—	2	2	no	—
131	C₅×C₄⋊C₄	—	8	2	no	—
132	C₅×C₄⋊C₄	—	8	2	no	—
133	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
134	C₅×C₂²⋊C₄	—	4	2	no	—
135	C₅×C₂²⋊C₄	—	4	2	no	—
136	C₅×C₂²⋊C₄	—	8	2	no	—
137	C₅×C₂²⋊C₄	—	8	2	no	—
138	C₄²×C₅	—	2	2	no	—
139	C₄²×C₅	—	2	2	no	—
140	C₄²×C₅	—	8	2	no	—
141	C₄²×C₅	C₂²×C₄	1	2	yes	—
142	C₄²×C₅	#41	1	2	yes	—
143	C₂×#127	C₂²×C₅	1	1	yes	characteristic
144	C₂×#125	C₂²×C₅	1	1	yes	characteristic
145	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
146	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
147	#490	C₄×C₅	1	8	yes	complemented
148	C₂×#107	C₂²×C₅	1	2	yes	—
149	C₂×#106	C₂²×C₅	1	2	yes	—
150	C₂×#102	C₂²×C₅	1	2	yes	—
151	C₂×#102	C₂²×C₅	1	2	yes	—
152	C₂×#102	C₂²×C₅	1	2	yes	—
153	C₂×#102	C₂²×C₅	1	2	yes	—
154	C₂×#97	C₂²×C₅	1	1	yes	characteristic
155	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
156	#390	C₂²×C₅	1	1	yes	characteristic
157	#390	C₂²×C₅	1	1	yes	characteristic
158	#389	—	2	2	no	—
159	#389	C₂²×C₅	1	2	yes	—
160	#387	—	2	2	no	—
161	#386	—	2	2	no	—
162	#386	—	2	2	no	—
163	#384	C₂²×C₅	1	1	yes	characteristic
164	#382	C₂²×C₅	1	1	yes	characteristic
165	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
166	#376	C₂²×C₅	1	1	yes	characteristic
167	#340	C₂²×C₅	1	2	yes	—
168	#340	C₂²×C₅	1	2	yes	—
169	#336	C₂²×C₅	1	2	yes	—
170	#336	C₂²×C₅	1	2	yes	—
171	C₂³×C₅	—	2	2	no	—
172	C₂³×C₅	—	2	2	no	—
173	C₂³×C₅	—	4	1	no	—
174	C₂³×C₅	—	4	1	no	—
175	C₂³×C₅	—	4	1	no	—
176	C₂³×C₅	—	4	1	no	—
177	C₂³×C₅	—	4	2	no	—
178	C₂³×C₅	—	4	2	no	—
179	C₂³×C₅	—	4	2	no	—
180	C₂³×C₅	—	4	2	no	—
181	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
182	C₅×D₄	—	2	4	no	—
183	C₅×D₄	—	2	4	no	—
184	C₅×D₄	—	4	2	no	—
185	C₅×D₄	—	4	2	no	—
186	C₅×D₄	—	8	8	no	—
187	C₂×C₄×C₅	—	2	2	no	—
188	C₂×C₄×C₅	—	2	2	no	—
189	C₂×C₄×C₅	—	2	4	no	—
190	C₂×C₄×C₅	—	2	1	no	—
191	C₂×C₄×C₅	—	2	1	no	—
192	C₂×C₄×C₅	—	2	2	no	—
193	C₂×C₄×C₅	—	2	2	no	—
194	C₂×C₄×C₅	—	2	2	no	—
195	C₂×C₄×C₅	—	2	2	no	—
196	C₂×C₄×C₅	—	2	2	no	—
197	C₂×C₄×C₅	—	4	2	no	—
198	C₂×C₄×C₅	—	4	2	no	—
199	C₂×C₄×C₅	—	4	1	no	—
200	C₂×C₄×C₅	—	4	1	no	—
201	C₂×C₄×C₅	—	4	2	no	—
202	C₂×C₄×C₅	—	4	2	no	—
203	C₂×C₄×C₅	—	4	2	no	—
204	C₂×C₄×C₅	—	4	2	no	—
205	C₂×C₄×C₅	—	4	2	no	—
206	C₂×C₄×C₅	—	8	4	no	—
207	C₂×C₄×C₅	—	8	4	no	—
208	C₂×C₄×C₅	C₄×D₄	1	4	yes	—
209	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
210	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
212	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
213	C₅×C₈	—	2	4	no	—
214	C₅×C₈	—	4	2	no	—
215	C₂²×D₄	—	2	2	no	—
216	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
217	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
218	C₂³×C₄	—	2	1	no	—
219	C₂³×C₄	—	2	1	no	—
220	C₂²×C₈	C₂³×C₅	1	2	yes	—
221	C₂²×C₈	C₂³×C₅	1	2	yes	—
222	#127	—	2	2	no	—
223	#127	C₂×C₄×C₅	1	4	yes	—
224	#125	—	2	2	no	—
225	#125	C₂×C₄×C₅	1	4	yes	complemented
226	C₄×D₄	—	4	2	no	—
227	C₄×D₄	—	4	2	no	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	—	2	2	no	—
231	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
232	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
233	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
234	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
235	C₂×C₂²⋊C₄	—	2	1	no	—
236	C₂×C₂²⋊C₄	—	2	1	no	—
237	C₂×C₂²⋊C₄	—	2	2	no	—
238	C₂×C₂²⋊C₄	—	2	2	no	—
239	C₂×C₄²	—	2	2	no	—
240	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
241	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
242	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
243	#107	—	4	2	no	—
244	#106	—	4	2	no	—
245	#102	—	4	2	no	—
246	#102	—	4	2	no	—
247	#102	C₂×C₄×C₅	1	8	yes	complemented
248	#102	C₂×C₄×C₅	1	8	yes	complemented
249	#97	C₂×C₄×C₅	1	4	yes	complemented
250	C₄×C₈	—	2	2	no	—
251	#95	—	2	2	no	—
252	#95	—	2	2	no	—
253	#95	—	2	2	no	—
254	#95	C₅×D₄	1	2	yes	—
255	#95	C₅×D₄	1	2	yes	—
256	C₂²×C₅	—	4	2	no	—
257	C₂²×C₅	—	4	2	no	—
258	C₂²×C₅	—	4	4	no	—
259	C₂²×C₅	—	4	4	no	—
260	C₂²×C₅	—	8	1	no	—
261	C₂²×C₅	—	8	1	no	—
262	C₂²×C₅	—	8	1	no	—
263	C₂²×C₅	—	8	1	no	—
264	C₂²×C₅	—	8	2	no	—
265	C₂²×C₅	—	8	2	no	—
266	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
267	C₂²×C₅	#535	1	1	yes	characteristic
268	C₂²×C₅	#536	1	1	yes	characteristic
269	C₂²×C₅	#576	1	2	yes	—
270	C₂²×C₅	#577	1	2	yes	—
271	C₄×C₅	—	2	4	no	—
272	C₄×C₅	—	4	4	no	—
273	C₄×C₅	—	4	1	no	—
274	C₄×C₅	—	4	1	no	—
275	C₄×C₅	—	4	2	no	—
276	C₄×C₅	—	8	2	no	—
277	C₄×C₅	—	8	1	no	—
278	C₄×C₅	—	8	1	no	—
279	C₄×C₅	#520	1	2	yes	—
280	C₄×C₅	#542	1	2	yes	—
281	C₂⁴	—	2	1	no	—
282	C₂⁴	—	2	1	no	—
283	C₂×D₄	—	2	8	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	—	2	1	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	8	2	no	—
291	C₂×D₄	—	8	2	no	—
292	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
293	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	—	4	2	no	—
300	C₂²×C₄	—	8	2	no	—
301	C₂²×C₄	—	8	2	no	—
302	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
303	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
304	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
305	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
306	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
313	C₄⋊C₄	—	2	8	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	8	2	no	—
320	C₄⋊C₄	—	8	2	no	—
321	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
322	C₂²⋊C₄	—	4	2	no	—
323	C₂²⋊C₄	—	4	2	no	—
324	C₂²⋊C₄	—	8	2	no	—
325	C₂²⋊C₄	—	8	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	8	2	no	—
329	C₄²	C₂²×C₄×C₅	1	2	yes	—
330	C₄²	C₅×#41	1	2	yes	—
331	C₂×C₅	—	8	2	no	—
332	C₂×C₅	—	8	2	no	—
333	C₂×C₅	#2326	1	1	yes	characteristic
334	C₂×C₅	#2946	1	2	yes	—
335	C₂×C₅	#3220	1	1	yes	characteristic
336	C₂×C₅	#3222	1	1	yes	characteristic
337	C₂×C₅	#3241	1	2	yes	—
338	C₂³	—	2	2	no	—
339	C₂³	—	2	2	no	—
340	C₂³	—	4	1	no	—
341	C₂³	—	4	1	no	—
342	C₂³	—	4	1	no	—
343	C₂³	—	4	1	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
349	D₄	—	2	4	no	—
350	D₄	—	2	4	no	—
351	D₄	—	4	2	no	—
352	D₄	—	4	2	no	—
353	D₄	—	8	8	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	8	4	no	—
374	C₂×C₄	—	8	4	no	—
375	C₂×C₄	C₄×C₅×D₄	1	4	yes	—
376	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
377	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
378	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
379	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
380	C₈	—	2	4	no	—
381	C₈	—	4	2	no	—
382	C₅	#22232	1	1	yes	characteristic, direct product factor, Sylow
383	C₂²	—	4	2	no	—
384	C₂²	—	4	2	no	—
385	C₂²	—	4	4	no	—
386	C₂²	—	4	4	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	8	1	no	—
390	C₂²	—	8	1	no	—
391	C₂²	—	8	1	no	—
392	C₂²	—	8	1	no	—
393	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
394	C₂²	C₅×#535	1	1	yes	characteristic
395	C₂²	C₅×#536	1	1	yes	characteristic
396	C₂²	C₅×#576	1	2	yes	—
397	C₂²	C₅×#577	1	2	yes	—
398	C₄	—	2	4	no	—
399	C₄	—	4	2	no	—
400	C₄	—	4	4	no	—
401	C₄	—	4	1	no	—
402	C₄	—	4	1	no	—
403	C₄	—	8	1	no	—
404	C₄	—	8	2	no	—
405	C₄	—	8	1	no	—
406	C₄	C₅×#520	1	2	yes	—
407	C₄	C₅×#542	1	2	yes	—
408	C₂	—	8	2	no	—
409	C₂	—	8	2	no	—
410	C₂	C₅×#2326	1	1	yes	characteristic
411	C₂	C₅×#2946	1	2	yes	—
412	C₂	C₅×#3220	1	1	yes	characteristic
413	C₂	C₅×#3222	1	1	yes	characteristic
414	C₂	C₅×#3241	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂×C₅×#127	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#376 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2330	C₂	semidirect
4. C₅×#1991	C₂	semidirect
6. C₅×#1926	C₂	semidirect
7. C₅×#1925	C₂	semidirect
8. C₅×#1864	C₂	semidirect
9. C₅×#1862	C₂	semidirect
10. C₅×#1847	C₂	semidirect
11. C₅×#1746	C₂	semidirect
16. C₅×#490	C₄	semidirect
40. #22232	C₅	direct (N × H)
51. C₅×#125	C₂×C₄	semidirect
73. C₅×#102	C₂×C₄	semidirect
74. C₅×#102	C₂×C₄	semidirect
75. C₅×#97	C₂×C₄	semidirect
83. #2330	C₂×C₅	semidirect
85. #1991	C₂×C₅	semidirect
87. #1926	C₂×C₅	semidirect
88. #1925	C₂×C₅	semidirect
89. #1864	C₂×C₅	semidirect
90. #1862	C₂×C₅	semidirect
91. #1847	C₂×C₅	semidirect
92. #1746	C₂×C₅	semidirect
147. #490	C₄×C₅	semidirect
225. #125	C₂×C₄×C₅	semidirect
247. #102	C₂×C₄×C₅	semidirect
248. #102	C₂×C₄×C₅	semidirect
249. #97	C₂×C₄×C₅	semidirect
382. C₅	#22232	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×#490	2
C₅×#2330	2
C₅×#2328	2
C₅×#1991	2
C₅×#1957	2
C₅×#1926	2
C₅×#1925	2
C₅×#1864	2
C₅×#1862	2
C₅×#1847	2
C₅×#1746	2
#22232	5

Subgroups — C5×#22232 #11944952

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22232 #11944952