Subgroups — C₅×#21148 #11943868

Order 1280.

1002 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#424	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#424	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#423	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#405	C₂	1	1	yes	maximal, characteristic
5	C₅×#2296	C₂	1	1	yes	maximal, characteristic
6	C₅×#1940	C₂	1	4	yes	maximal, complemented
7	C₅×#1939	C₂	1	4	yes	maximal, complemented
8	C₅×#1729	C₂	1	1	yes	maximal, characteristic
9	C₂×C₅×#336	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₂³×C₅×C₈	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	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₅×#424	—	2	4	no	—
18	C₅×#424	—	2	4	no	—
19	C₅×#423	—	2	4	no	—
20	C₂×C₅×C₄⋊C₈	C₂²	1	4	yes	—
21	C₂×C₅×C₄⋊C₈	C₂²	1	4	yes	—
22	C₂×C₅×C₄⋊C₈	C₂²	1	4	yes	—
23	C₅×#405	—	2	4	no	—
24	C₂×C₅×#97	C₂²	1	2	yes	—
25	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
26	C₅×#389	C₄	1	2	yes	—
27	C₅×#389	C₄	1	2	yes	—
28	C₅×#385	C₄	1	4	yes	—
29	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	—
30	C₅×#336	C₂²	1	2	yes	—
31	C₅×#336	C₂²	1	2	yes	—
32	C₅×#336	C₂²	1	2	yes	—
33	C₅×#336	C₂²	1	2	yes	—
34	#21148	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₂³×C₄×C₅	C₂×C₄	1	2	yes	—
36	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂×C₅×M₁₆	—	2	2	no	—
38	C₂×C₅×M₁₆	—	2	2	no	—
39	C₂×C₅×M₁₆	—	2	2	no	—
40	C₂×C₅×M₁₆	—	2	2	no	—
41	C₂×C₅×M₁₆	—	2	2	no	—
42	C₂×C₅×M₁₆	D₄	1	4	yes	—
43	C₂²×C₅×C₈	—	2	2	no	—
44	C₂²×C₅×C₈	—	2	2	no	—
45	C₂²×C₅×C₈	—	2	2	no	—
46	C₂²×C₅×C₈	—	2	2	no	—
47	C₂²×C₅×C₈	—	2	2	no	—
48	C₂²×C₅×C₈	Q₈	1	4	yes	—
49	C₂²×C₅×C₈	C₂³	1	2	yes	—
50	C₂²×C₅×C₈	C₂³	1	2	yes	—
51	C₂²×C₅×C₈	C₂³	1	2	yes	—
52	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
54	C₅×#117	—	2	2	no	—
55	C₅×#117	—	2	2	no	—
56	C₅×#117	D₄	1	4	yes	—
57	C₅×#117	Q₈	1	4	yes	—
58	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
59	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
60	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
61	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
62	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
63	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₅	—	2	2	no	—
65	C₂×C₄²×C₅	—	2	2	no	—
66	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₅	C₂³	1	2	yes	—
69	C₂×C₄²×C₅	C₂³	1	2	yes	—
70	C₂×C₄²×C₅	C₂³	1	2	yes	—
71	C₅×C₄⋊C₈	—	2	8	no	—
72	C₅×C₄⋊C₈	—	2	8	no	—
73	C₅×C₄⋊C₈	—	2	8	no	—
74	C₅×#97	—	2	4	no	—
75	C₄×C₅×C₈	—	2	4	no	—
76	C₅×#95	C₂×C₄	1	4	yes	—
77	C₅×#95	C₂×C₄	1	4	yes	—
78	C₂×#424	C₂×C₅	1	1	yes	characteristic
79	C₂×#424	C₂×C₅	1	1	yes	characteristic
80	C₂×#423	C₂×C₅	1	1	yes	characteristic
81	C₂×#405	C₂×C₅	1	1	yes	characteristic
82	#2296	C₂×C₅	1	1	yes	characteristic
83	#1940	C₂×C₅	1	4	yes	complemented
84	#1939	C₂×C₅	1	4	yes	complemented
85	#1729	C₂×C₅	1	1	yes	characteristic
86	C₂×#336	C₂×C₅	1	1	yes	characteristic
87	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₅	—	2	4	no	—
89	C₂²×C₄×C₅	—	2	4	no	—
90	C₂²×C₄×C₅	—	4	2	no	—
91	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
93	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
94	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
99	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
100	C₂²×C₄×C₅	#41	1	2	yes	—
101	C₂²×C₄×C₅	#41	1	2	yes	—
102	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
103	C₅×M₁₆	—	2	8	no	—
104	C₅×M₁₆	—	4	4	no	—
105	C₂×C₅×C₈	—	2	8	no	—
106	C₂×C₅×C₈	—	2	1	no	—
107	C₂×C₅×C₈	—	2	1	no	—
108	C₂×C₅×C₈	—	2	2	no	—
109	C₂×C₅×C₈	—	2	1	no	—
110	C₂×C₅×C₈	—	2	1	no	—
111	C₂×C₅×C₈	—	2	2	no	—
112	C₂×C₅×C₈	—	2	2	no	—
113	C₂×C₅×C₈	—	2	2	no	—
114	C₂×C₅×C₈	—	2	2	no	—
115	C₂×C₅×C₈	—	2	2	no	—
116	C₂×C₅×C₈	—	2	2	no	—
117	C₂×C₅×C₈	—	2	2	no	—
118	C₂×C₅×C₈	—	4	4	no	—
119	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
120	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
121	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
122	C₅×C₄⋊C₄	—	2	4	no	—
123	C₅×C₄⋊C₄	—	2	8	no	—
124	C₅×C₄⋊C₄	—	4	4	no	—
125	C₅×C₄⋊C₄	C₄⋊C₄	1	8	yes	—
126	C₅×C₂²⋊C₄	—	2	4	no	—
127	C₅×C₂²⋊C₄	C₄⋊C₄	1	8	yes	—
128	C₄²×C₅	—	2	2	no	—
129	C₄²×C₅	—	2	2	no	—
130	C₄²×C₅	—	2	2	no	—
131	C₄²×C₅	—	2	2	no	—
132	C₄²×C₅	—	2	2	no	—
133	C₄²×C₅	—	2	2	no	—
134	C₄²×C₅	C₂×D₄	1	4	yes	—
135	C₄²×C₅	C₂×Q₈	1	4	yes	—
136	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
137	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
138	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
139	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
140	C₂×#117	C₂²×C₅	1	1	yes	characteristic
141	C₂×#117	C₂²×C₅	1	1	yes	characteristic
142	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
143	#424	—	2	4	no	—
144	#424	—	2	4	no	—
145	#423	—	2	4	no	—
146	C₂×C₄⋊C₈	C₂²×C₅	1	4	yes	—
147	C₂×C₄⋊C₈	C₂²×C₅	1	4	yes	—
148	C₂×C₄⋊C₈	C₂²×C₅	1	4	yes	—
149	#405	—	2	4	no	—
150	C₂×#97	C₂²×C₅	1	2	yes	—
151	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
152	#389	C₄×C₅	1	2	yes	—
153	#389	C₄×C₅	1	2	yes	—
154	#385	C₄×C₅	1	4	yes	—
155	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	—
156	#336	C₂²×C₅	1	2	yes	—
157	#336	C₂²×C₅	1	2	yes	—
158	#336	C₂²×C₅	1	2	yes	—
159	#336	C₂²×C₅	1	2	yes	—
160	C₂³×C₅	—	2	2	no	—
161	C₂³×C₅	—	2	2	no	—
162	C₂³×C₅	C₂×C₄⋊C₄	1	2	yes	—
163	C₂³×C₅	C₄×D₄	1	2	yes	—
164	C₂³×C₅	C₄×Q₈	1	2	yes	—
165	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₅	—	2	2	no	—
167	C₂×C₄×C₅	—	2	4	no	—
168	C₂×C₄×C₅	—	2	4	no	—
169	C₂×C₄×C₅	—	2	2	no	—
170	C₂×C₄×C₅	—	2	2	no	—
171	C₂×C₄×C₅	—	2	4	no	—
172	C₂×C₄×C₅	—	2	4	no	—
173	C₂×C₄×C₅	—	2	2	no	—
174	C₂×C₄×C₅	—	2	2	no	—
175	C₂×C₄×C₅	—	2	4	no	—
176	C₂×C₄×C₅	—	4	8	no	—
177	C₂×C₄×C₅	C₂×C₄⋊C₄	1	8	yes	—
178	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
179	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
180	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
181	C₂×C₄×C₅	#121	1	4	yes	—
182	C₂×C₄×C₅	C₂²⋊Q₈	1	4	yes	—
183	C₂×C₄×C₅	#125	1	4	yes	—
184	C₂×C₄×C₅	C₄⋊Q₈	1	4	yes	—
185	C₂×C₄×C₅	#131	1	4	yes	—
186	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
189	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
190	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
191	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
192	C₅×C₈	—	2	4	no	—
193	C₅×C₈	—	2	2	no	—
194	C₅×C₈	—	2	2	no	—
195	C₅×C₈	—	4	2	no	—
196	C₅×C₈	—	4	2	no	—
197	C₂³×C₄	C₂×C₄×C₅	1	2	yes	—
198	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
199	C₂×M₁₆	—	2	2	no	—
200	C₂×M₁₆	—	2	2	no	—
201	C₂×M₁₆	—	2	2	no	—
202	C₂×M₁₆	—	2	2	no	—
203	C₂×M₁₆	—	2	2	no	—
204	C₂×M₁₆	C₅×D₄	1	4	yes	—
205	C₂²×C₈	—	2	2	no	—
206	C₂²×C₈	—	2	2	no	—
207	C₂²×C₈	—	2	2	no	—
208	C₂²×C₈	—	2	2	no	—
209	C₂²×C₈	—	2	2	no	—
210	C₂²×C₈	C₅×Q₈	1	4	yes	—
211	C₂²×C₈	C₂³×C₅	1	2	yes	—
212	C₂²×C₈	C₂³×C₅	1	2	yes	—
213	C₂²×C₈	C₂³×C₅	1	2	yes	—
214	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
215	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
216	#117	—	2	2	no	—
217	#117	—	2	2	no	—
218	#117	C₅×D₄	1	4	yes	—
219	#117	C₅×Q₈	1	4	yes	—
220	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
221	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
222	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
223	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
224	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
225	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
226	C₂×C₄²	—	2	2	no	—
227	C₂×C₄²	—	2	2	no	—
228	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
229	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
230	C₂×C₄²	C₂³×C₅	1	2	yes	—
231	C₂×C₄²	C₂³×C₅	1	2	yes	—
232	C₂×C₄²	C₂³×C₅	1	2	yes	—
233	C₄⋊C₈	—	2	8	no	—
234	C₄⋊C₈	—	2	8	no	—
235	C₄⋊C₈	—	2	8	no	—
236	#97	—	2	4	no	—
237	C₄×C₈	—	2	4	no	—
238	#95	C₂×C₄×C₅	1	4	yes	—
239	#95	C₂×C₄×C₅	1	4	yes	—
240	C₂²×C₅	—	2	4	no	—
241	C₂²×C₅	—	2	4	no	—
242	C₂²×C₅	—	2	2	no	—
243	C₂²×C₅	—	2	2	no	—
244	C₂²×C₅	#389	1	4	yes	—
245	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
246	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
247	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
248	C₂²×C₅	C₂×#131	1	2	yes	—
249	C₂²×C₅	#568	1	2	yes	—
250	C₄×C₅	—	2	8	no	—
251	C₄×C₅	—	2	4	no	—
252	C₄×C₅	—	4	4	no	—
253	C₄×C₅	—	4	2	no	—
254	C₄×C₅	#389	1	4	yes	—
255	C₄×C₅	C₂×#121	1	1	yes	characteristic
256	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
257	C₄×C₅	C₂×#125	1	1	yes	characteristic
258	C₄×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
259	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	4	2	no	—
263	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
264	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
265	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
266	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
267	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
268	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
269	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
270	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
271	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
272	C₂²×C₄	C₅×#41	1	2	yes	—
273	C₂²×C₄	C₅×#41	1	2	yes	—
274	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
275	M₁₆	—	2	8	no	—
276	M₁₆	—	4	4	no	—
277	C₂×C₈	—	2	8	no	—
278	C₂×C₈	—	2	1	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	1	no	—
281	C₂×C₈	—	2	1	no	—
282	C₂×C₈	—	2	1	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	4	4	no	—
291	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
292	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
293	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
294	C₄⋊C₄	—	2	4	no	—
295	C₄⋊C₄	—	2	8	no	—
296	C₄⋊C₄	—	4	4	no	—
297	C₄⋊C₄	C₅×C₄⋊C₄	1	8	yes	—
298	C₂²⋊C₄	—	2	4	no	—
299	C₂²⋊C₄	C₅×C₄⋊C₄	1	8	yes	—
300	C₄²	—	2	2	no	—
301	C₄²	—	2	2	no	—
302	C₄²	—	2	2	no	—
303	C₄²	—	2	2	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	2	2	no	—
306	C₄²	C₂×C₅×D₄	1	4	yes	—
307	C₄²	C₂×C₅×Q₈	1	4	yes	—
308	C₂×C₅	—	2	4	no	—
309	C₂×C₅	C₂×#389	1	1	yes	characteristic
310	C₂×C₅	#2906	1	2	yes	—
311	C₂×C₅	#2933	1	2	yes	—
312	C₂×C₅	#2960	1	1	yes	characteristic
313	C₂×C₅	#2961	1	1	yes	characteristic
314	C₂³	—	2	2	no	—
315	C₂³	—	2	2	no	—
316	C₂³	C₂×C₅×C₄⋊C₄	1	2	yes	—
317	C₂³	C₄×C₅×D₄	1	2	yes	—
318	C₂³	C₄×C₅×Q₈	1	2	yes	—
319	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	4	8	no	—
331	C₂×C₄	C₂×C₅×C₄⋊C₄	1	8	yes	—
332	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
333	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
334	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
335	C₂×C₄	C₅×#121	1	4	yes	—
336	C₂×C₄	C₅×C₂²⋊Q₈	1	4	yes	—
337	C₂×C₄	C₅×#125	1	4	yes	—
338	C₂×C₄	C₅×C₄⋊Q₈	1	4	yes	—
339	C₂×C₄	C₅×#131	1	4	yes	—
340	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
341	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
342	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
343	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
344	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
345	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
346	C₈	—	2	4	no	—
347	C₈	—	2	2	no	—
348	C₈	—	2	2	no	—
349	C₈	—	4	2	no	—
350	C₈	—	4	2	no	—
351	C₅	#21148	1	1	yes	characteristic, direct product factor, Sylow
352	C₂²	—	2	4	no	—
353	C₂²	—	2	4	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	2	no	—
356	C₂²	C₅×#389	1	4	yes	—
357	C₂²	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
358	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
359	C₂²	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
360	C₂²	C₂×C₅×#131	1	2	yes	—
361	C₂²	C₅×#568	1	2	yes	—
362	C₄	—	2	8	no	—
363	C₄	—	2	4	no	—
364	C₄	—	4	2	no	—
365	C₄	—	4	4	no	—
366	C₄	C₅×#389	1	4	yes	—
367	C₄	C₂×C₅×#121	1	1	yes	characteristic
368	C₄	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
369	C₄	C₂×C₅×#125	1	1	yes	characteristic
370	C₄	C₂×C₅×C₄⋊Q₈	1	1	yes	characteristic
371	C₂	—	2	4	no	—
372	C₂	C₂×C₅×#389	1	1	yes	characteristic
373	C₂	C₅×#2906	1	2	yes	—
374	C₂	C₅×#2933	1	2	yes	—
375	C₂	C₅×#2960	1	1	yes	characteristic
376	C₂	C₅×#2961	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
6. C₅×#1940	C₂	semidirect
7. C₅×#1939	C₂	semidirect
34. #21148	C₅	direct (N × H)
83. #1940	C₂×C₅	semidirect
84. #1939	C₂×C₅	semidirect
351. C₅	#21148	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×#424	2
C₂×C₅×#423	2
C₂×C₅×#405	2
C₅×#2296	2
C₅×#1940	2
C₅×#1939	2
C₅×#1729	2
C₂×C₅×#336	2
#21148	5

Subgroups — C5×#21148 #11943868

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21148 #11943868