Subgroups — C₅×#8610 #11931330

Order 1280.

524 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#435	C₂	1	1	yes	maximal, characteristic
2	C₅×#1808	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#1807	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1799	C₂	1	2	yes	maximal
5	C₅×#1289	C₂	1	2	yes	maximal, complemented
6	C₂²×C₅×M₁₆	C₄	1	1	yes	characteristic, complemented
7	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
9	C₅×#435	—	2	1	no	—
10	C₅×#435	—	2	1	no	—
11	C₅×#435	—	2	1	no	—
12	C₅×#435	—	2	1	no	—
13	C₂×C₅×#107	—	2	1	no	—
14	C₂×C₅×#106	—	2	1	no	—
15	C₂×C₅×C₄⋊C₈	C₄	1	1	yes	characteristic, complemented
16	C₂×C₅×#99	—	2	2	no	—
17	C₂×C₅×C₂²⋊C₈	C₄	1	1	yes	characteristic, complemented
18	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×#97	C₄	1	1	yes	characteristic, complemented
20	C₅×#380	C₂²	1	2	yes	—
21	C₅×#380	C₂²	1	2	yes	—
22	C₅×#342	—	2	2	no	—
23	C₅×#340	—	2	1	no	—
24	C₅×#340	—	2	1	no	—
25	#8610	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
26	C₂²×C₅×D₄	D₄	1	1	yes	characteristic
27	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
29	C₂×C₅×M₁₆	—	2	1	no	—
30	C₂×C₅×M₁₆	—	2	1	no	—
31	C₂×C₅×M₁₆	—	4	2	no	—
32	C₂²×C₅×C₈	—	4	2	no	—
33	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
38	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
39	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
40	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
41	C₄×C₅×D₄	—	2	1	no	—
42	C₄×C₅×D₄	—	2	1	no	—
43	C₄×C₅×D₄	—	2	1	no	—
44	C₄×C₅×D₄	—	2	1	no	—
45	C₂×C₅×C₄⋊C₄	—	2	2	no	—
46	C₂×C₅×C₄⋊C₄	—	2	2	no	—
47	C₂×C₅×C₄⋊C₄	Q₈	1	1	yes	characteristic
48	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
49	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
50	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
51	C₂×C₅×C₂²⋊C₄	Q₈	1	1	yes	characteristic
52	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
53	C₅×#107	—	4	2	no	—
54	C₅×#106	—	4	2	no	—
55	C₅×C₄⋊C₈	—	2	1	no	—
56	C₅×C₄⋊C₈	—	2	1	no	—
57	C₅×#99	—	4	4	no	—
58	C₅×C₂²⋊C₈	—	2	1	no	—
59	C₅×C₂²⋊C₈	—	2	1	no	—
60	C₅×C₂²⋊C₈	—	2	1	no	—
61	C₅×C₂²⋊C₈	—	2	1	no	—
62	C₅×#97	—	2	1	no	—
63	C₅×#97	—	2	1	no	—
64	C₅×#95	—	2	2	no	—
65	C₅×#95	—	2	2	no	—
66	C₂×#435	C₂×C₅	1	1	yes	characteristic
67	#1808	C₂×C₅	1	1	yes	characteristic, complemented
68	#1807	C₂×C₅	1	1	yes	characteristic, complemented
69	#1799	C₂×C₅	1	2	yes	—
70	#1289	C₂×C₅	1	2	yes	complemented
71	C₂⁴×C₅	C₄⋊C₄	1	1	yes	characteristic
72	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
73	C₂×C₅×D₄	—	2	1	no	—
74	C₂×C₅×D₄	—	2	1	no	—
75	C₂×C₅×D₄	—	2	2	no	—
76	C₂×C₅×D₄	—	2	2	no	—
77	C₂²×C₄×C₅	—	2	1	no	—
78	C₂²×C₄×C₅	—	2	1	no	—
79	C₂²×C₄×C₅	—	4	1	no	—
80	C₂²×C₄×C₅	—	4	1	no	—
81	C₂²×C₄×C₅	—	4	1	no	—
82	C₂²×C₄×C₅	—	4	1	no	—
83	C₂²×C₄×C₅	—	4	2	no	—
84	C₂²×C₄×C₅	—	4	2	no	—
85	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
92	C₂²×C₄×C₅	#41	1	1	yes	characteristic
93	C₂²×C₄×C₅	#41	1	1	yes	characteristic
94	C₅×M₁₆	—	4	2	no	—
95	C₅×M₁₆	—	4	2	no	—
96	C₂×C₅×C₈	—	2	2	no	—
97	C₂×C₅×C₈	—	2	2	no	—
98	C₂×C₅×C₈	—	2	2	no	—
99	C₂×C₅×C₈	—	2	1	no	—
100	C₂×C₅×C₈	—	2	1	no	—
101	C₂×C₅×C₈	—	4	1	no	—
102	C₂×C₅×C₈	—	4	1	no	—
103	C₂×C₅×C₈	—	4	1	no	—
104	C₂×C₅×C₈	—	4	1	no	—
105	C₂×C₅×C₈	—	4	1	no	—
106	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
107	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
108	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
109	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
110	C₅×C₄⋊C₄	—	2	1	no	—
111	C₅×C₄⋊C₄	—	2	1	no	—
112	C₅×C₄⋊C₄	—	4	2	no	—
113	C₅×C₄⋊C₄	—	4	2	no	—
114	C₅×C₄⋊C₄	—	4	2	no	—
115	C₅×C₄⋊C₄	—	4	2	no	—
116	C₅×C₂²⋊C₄	—	2	1	no	—
117	C₅×C₂²⋊C₄	—	2	1	no	—
118	C₅×C₂²⋊C₄	—	2	1	no	—
119	C₅×C₂²⋊C₄	—	2	1	no	—
120	C₅×C₂²⋊C₄	—	4	2	no	—
121	C₅×C₂²⋊C₄	—	4	2	no	—
122	C₅×C₂²⋊C₄	—	4	2	no	—
123	C₅×C₂²⋊C₄	—	4	2	no	—
124	C₄²×C₅	—	2	1	no	—
125	C₄²×C₅	—	2	1	no	—
126	C₂²×M₁₆	C₄×C₅	1	1	yes	characteristic, complemented
127	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
128	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
129	#435	—	2	1	no	—
130	#435	—	2	1	no	—
131	#435	—	2	1	no	—
132	#435	—	2	1	no	—
133	C₂×#107	—	2	1	no	—
134	C₂×#106	—	2	1	no	—
135	C₂×C₄⋊C₈	C₄×C₅	1	1	yes	characteristic, complemented
136	C₂×#99	—	2	2	no	—
137	C₂×C₂²⋊C₈	C₄×C₅	1	1	yes	characteristic, complemented
138	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
139	C₂×#97	C₄×C₅	1	1	yes	characteristic, complemented
140	#380	C₂²×C₅	1	2	yes	—
141	#380	C₂²×C₅	1	2	yes	—
142	#342	—	2	2	no	—
143	#340	—	2	1	no	—
144	#340	—	2	1	no	—
145	C₂³×C₅	—	2	1	no	—
146	C₂³×C₅	—	2	2	no	—
147	C₂³×C₅	—	4	1	no	—
148	C₂³×C₅	—	4	1	no	—
149	C₂³×C₅	—	4	1	no	—
150	C₂³×C₅	—	4	1	no	—
151	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂³×C₅	#121	1	1	yes	characteristic
153	C₂³×C₅	#121	1	1	yes	characteristic
154	C₂³×C₅	AGL(1,ℤ/8)	1	2	yes	—
155	C₂³×C₅	#137	1	2	yes	—
156	C₅×D₄	—	4	2	no	—
157	C₅×D₄	—	4	1	no	—
158	C₅×D₄	—	4	1	no	—
159	C₂×C₄×C₅	—	2	1	no	—
160	C₂×C₄×C₅	—	2	1	no	—
161	C₂×C₄×C₅	—	2	1	no	—
162	C₂×C₄×C₅	—	2	1	no	—
163	C₂×C₄×C₅	—	2	1	no	—
164	C₂×C₄×C₅	—	2	1	no	—
165	C₂×C₄×C₅	—	2	1	no	—
166	C₂×C₄×C₅	—	2	1	no	—
167	C₂×C₄×C₅	—	2	1	no	—
168	C₂×C₄×C₅	—	2	2	no	—
169	C₂×C₄×C₅	—	4	1	no	—
170	C₂×C₄×C₅	—	4	1	no	—
171	C₂×C₄×C₅	—	4	1	no	—
172	C₂×C₄×C₅	—	4	2	no	—
173	C₂×C₄×C₅	—	4	1	no	—
174	C₂×C₄×C₅	—	4	1	no	—
175	C₂×C₄×C₅	—	4	1	no	—
176	C₂×C₄×C₅	—	4	1	no	—
177	C₂×C₄×C₅	—	8	2	no	—
178	C₂×C₄×C₅	—	8	2	no	—
179	C₂×C₄×C₅	—	8	2	no	—
180	C₂×C₄×C₅	—	8	2	no	—
181	C₂×C₄×C₅	—	8	2	no	—
182	C₂×C₄×C₅	—	8	2	no	—
183	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₅	#117	1	1	yes	characteristic
185	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
186	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
187	C₅×C₈	—	2	1	no	—
188	C₅×C₈	—	2	1	no	—
189	C₅×C₈	—	2	1	no	—
190	C₅×C₈	—	4	1	no	—
191	C₅×C₈	—	4	1	no	—
192	C₅×C₈	#99	1	2	yes	complemented
193	C₂²×D₄	C₅×D₄	1	1	yes	characteristic
194	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
195	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
196	C₂×M₁₆	—	2	1	no	—
197	C₂×M₁₆	—	2	1	no	—
198	C₂×M₁₆	—	4	2	no	—
199	C₂²×C₈	—	4	2	no	—
200	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
201	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
202	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
203	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
204	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
205	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
206	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
207	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
208	C₄×D₄	—	2	1	no	—
209	C₄×D₄	—	2	1	no	—
210	C₄×D₄	—	2	1	no	—
211	C₄×D₄	—	2	1	no	—
212	C₂×C₄⋊C₄	—	2	2	no	—
213	C₂×C₄⋊C₄	—	2	2	no	—
214	C₂×C₄⋊C₄	C₅×Q₈	1	1	yes	characteristic
215	C₂×C₂²⋊C₄	—	2	2	no	—
216	C₂×C₂²⋊C₄	—	2	2	no	—
217	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
218	C₂×C₂²⋊C₄	C₅×Q₈	1	1	yes	characteristic
219	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
220	#107	—	4	2	no	—
221	#106	—	4	2	no	—
222	C₄⋊C₈	—	2	1	no	—
223	C₄⋊C₈	—	2	1	no	—
224	#99	—	4	4	no	—
225	C₂²⋊C₈	—	2	1	no	—
226	C₂²⋊C₈	—	2	1	no	—
227	C₂²⋊C₈	—	2	1	no	—
228	C₂²⋊C₈	—	2	1	no	—
229	#97	—	2	1	no	—
230	#97	—	2	1	no	—
231	#95	—	2	2	no	—
232	#95	—	2	2	no	—
233	C₂²×C₅	—	2	1	no	—
234	C₂²×C₅	—	2	1	no	—
235	C₂²×C₅	—	2	1	no	—
236	C₂²×C₅	—	2	1	no	—
237	C₂²×C₅	—	2	1	no	—
238	C₂²×C₅	—	2	1	no	—
239	C₂²×C₅	—	4	2	no	—
240	C₂²×C₅	—	4	2	no	—
241	C₂²×C₅	—	4	1	no	—
242	C₂²×C₅	—	4	1	no	—
243	C₂²×C₅	—	4	1	no	—
244	C₂²×C₅	—	8	2	no	—
245	C₂²×C₅	#380	1	1	yes	characteristic
246	C₂²×C₅	#428	1	2	yes	—
247	C₂²×C₅	#468	1	2	yes	—
248	C₂²×C₅	#469	1	1	yes	characteristic
249	C₂²×C₅	#470	1	1	yes	characteristic
250	C₄×C₅	—	2	1	no	—
251	C₄×C₅	—	2	1	no	—
252	C₄×C₅	—	2	1	no	—
253	C₄×C₅	—	4	1	no	—
254	C₄×C₅	—	4	1	no	—
255	C₄×C₅	—	4	1	no	—
256	C₄×C₅	—	16	2	no	—
257	C₄×C₅	—	16	2	no	—
258	C₄×C₅	C₂×#99	1	1	yes	characteristic
259	C₄×C₅	#410	1	1	yes	characteristic
260	C₂⁴	C₅×C₄⋊C₄	1	1	yes	characteristic
261	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
262	C₂×D₄	—	2	1	no	—
263	C₂×D₄	—	2	1	no	—
264	C₂×D₄	—	2	2	no	—
265	C₂×D₄	—	2	2	no	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	4	1	no	—
269	C₂²×C₄	—	4	1	no	—
270	C₂²×C₄	—	4	1	no	—
271	C₂²×C₄	—	4	1	no	—
272	C₂²×C₄	—	4	2	no	—
273	C₂²×C₄	—	4	2	no	—
274	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
275	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
276	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
277	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
278	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
279	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
280	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
281	C₂²×C₄	C₅×#41	1	1	yes	characteristic
282	C₂²×C₄	C₅×#41	1	1	yes	characteristic
283	M₁₆	—	4	2	no	—
284	M₁₆	—	4	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	1	no	—
289	C₂×C₈	—	2	1	no	—
290	C₂×C₈	—	4	1	no	—
291	C₂×C₈	—	4	1	no	—
292	C₂×C₈	—	4	1	no	—
293	C₂×C₈	—	4	1	no	—
294	C₂×C₈	—	4	1	no	—
295	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
296	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
297	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
298	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	4	2	no	—
302	C₄⋊C₄	—	4	2	no	—
303	C₄⋊C₄	—	4	2	no	—
304	C₄⋊C₄	—	4	2	no	—
305	C₂²⋊C₄	—	2	1	no	—
306	C₂²⋊C₄	—	2	1	no	—
307	C₂²⋊C₄	—	2	1	no	—
308	C₂²⋊C₄	—	2	1	no	—
309	C₂²⋊C₄	—	4	2	no	—
310	C₂²⋊C₄	—	4	2	no	—
311	C₂²⋊C₄	—	4	2	no	—
312	C₂²⋊C₄	—	4	2	no	—
313	C₄²	—	2	1	no	—
314	C₄²	—	2	1	no	—
315	C₂×C₅	—	2	1	no	—
316	C₂×C₅	—	2	2	no	—
317	C₂×C₅	—	2	2	no	—
318	C₂×C₅	—	2	1	no	—
319	C₂×C₅	—	8	1	no	—
320	C₂×C₅	#1799	1	1	yes	characteristic
321	C₂×C₅	#1809	1	1	yes	characteristic
322	C₂×C₅	#1812	1	1	yes	characteristic
323	C₂³	—	2	1	no	—
324	C₂³	—	2	2	no	—
325	C₂³	—	4	1	no	—
326	C₂³	—	4	1	no	—
327	C₂³	—	4	1	no	—
328	C₂³	—	4	1	no	—
329	C₂³	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
330	C₂³	C₅×#121	1	1	yes	characteristic
331	C₂³	C₅×#121	1	1	yes	characteristic
332	C₂³	C₅×AGL(1,ℤ/8)	1	2	yes	—
333	C₂³	C₅×#137	1	2	yes	—
334	D₄	—	4	2	no	—
335	D₄	—	4	1	no	—
336	D₄	—	4	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	8	2	no	—
356	C₂×C₄	—	8	2	no	—
357	C₂×C₄	—	8	2	no	—
358	C₂×C₄	—	8	2	no	—
359	C₂×C₄	—	8	2	no	—
360	C₂×C₄	—	8	2	no	—
361	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
362	C₂×C₄	C₅×#117	1	1	yes	characteristic
363	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
364	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
365	C₈	—	2	1	no	—
366	C₈	—	2	1	no	—
367	C₈	—	2	1	no	—
368	C₈	—	4	1	no	—
369	C₈	—	4	1	no	—
370	C₈	C₅×#99	1	2	yes	complemented
371	C₅	#8610	1	1	yes	characteristic, direct product factor, Sylow
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	1	no	—
381	C₂²	—	4	1	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	8	2	no	—
384	C₂²	C₅×#380	1	1	yes	characteristic
385	C₂²	C₅×#428	1	2	yes	—
386	C₂²	C₅×#468	1	2	yes	—
387	C₂²	C₅×#469	1	1	yes	characteristic
388	C₂²	C₅×#470	1	1	yes	characteristic
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	4	1	no	—
393	C₄	—	4	1	no	—
394	C₄	—	4	1	no	—
395	C₄	—	16	2	no	—
396	C₄	—	16	2	no	—
397	C₄	C₂×C₅×#99	1	1	yes	characteristic
398	C₄	C₅×#410	1	1	yes	characteristic
399	C₂	—	2	1	no	—
400	C₂	—	2	2	no	—
401	C₂	—	2	2	no	—
402	C₂	—	2	1	no	—
403	C₂	—	8	1	no	—
404	C₂	C₅×#1799	1	1	yes	characteristic
405	C₂	C₅×#1809	1	1	yes	characteristic
406	C₂	C₅×#1812	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	#380
commutator	C₂²×C₄	C₂²×C₄×C₅
Frattini, cosocle	C₂³×C₄	C₂³×C₅
prime radical	C₂²×C₅×D₄	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂³×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#1808	C₂	semidirect
3. C₅×#1807	C₂	semidirect
5. C₅×#1289	C₂	semidirect
6. C₂²×C₅×M₁₆	C₄	semidirect
15. C₂×C₅×C₄⋊C₈	C₄	semidirect
17. C₂×C₅×C₂²⋊C₈	C₄	semidirect
19. C₂×C₅×#97	C₄	semidirect
25. #8610	C₅	direct (N × H)
67. #1808	C₂×C₅	semidirect
68. #1807	C₂×C₅	semidirect
70. #1289	C₂×C₅	semidirect
126. C₂²×M₁₆	C₄×C₅	semidirect
135. C₂×C₄⋊C₈	C₄×C₅	semidirect
137. C₂×C₂²⋊C₈	C₄×C₅	semidirect
139. C₂×#97	C₄×C₅	semidirect
192. C₅×C₈	#99	semidirect
370. C₈	C₅×#99	semidirect
371. C₅	#8610	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×#435	2
C₅×#1808	2
C₅×#1807	2
C₅×#1799	2
C₅×#1289	2
#8610	5

Subgroups — C5×#8610 #11931330

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#8610 #11931330