Subgroups — C₅×#17990 #11940710

Order 1280.

584 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3167	C₂	1	1	yes	maximal, characteristic
2	C₅×#2985	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2981	C₂	1	1	yes	maximal, characteristic
4	C₅×#1588	C₂	1	2	yes	maximal, complemented
5	C₅×#1585	C₂	1	2	yes	maximal, complemented
6	C₅×#1583	C₂	1	2	yes	maximal, complemented
7	C₅×#1582	C₂	1	2	yes	maximal, complemented
8	C₅×#1568	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1497	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1496	C₂	1	1	yes	maximal, characteristic
11	C₅×#1452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#533	C₂²	1	1	yes	characteristic
13	C₅×#532	C₂²	1	1	yes	characteristic
14	C₅×#498	C₄	1	1	yes	characteristic
15	C₅×#492	C₄	1	1	yes	characteristic
16	C₅×#487	C₄	1	1	yes	characteristic
17	C₅×#486	C₄	1	1	yes	characteristic
18	C₅×#465	C₄	1	2	yes	—
19	C₅×#465	C₄	1	2	yes	—
20	C₅×#446	—	2	2	no	—
21	C₅×#446	C₂²	1	2	yes	—
22	C₅×C₈×Q₈	C₂²	1	2	yes	—
23	C₄×C₅×SD₁₆	C₂²	1	2	yes	—
24	C₄×C₅×SD₁₆	C₂²	1	2	yes	—
25	C₅×#436	C₂²	1	2	yes	—
26	C₅×#435	—	2	2	no	—
27	C₅×C₈×D₄	C₂²	1	2	yes	—
28	C₅×#433	—	2	2	no	—
29	C₅×#432	C₂²	1	1	yes	characteristic
30	C₅×#432	C₂²	1	1	yes	characteristic
31	C₅×#431	C₂²	1	1	yes	characteristic
32	C₅×#431	C₂²	1	1	yes	characteristic
33	C₅×#408	—	2	2	no	—
34	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
35	C₅×#335	C₂²	1	2	yes	—
36	C₅×#334	C₂²	1	2	yes	—
37	C₅×Q₈⋊C₈	C₂²	1	2	yes	—
38	C₅×Q₈⋊C₈	C₂²	1	2	yes	—
39	C₅×D₄⋊C₈	C₂²	1	2	yes	—
40	C₅×D₄⋊C₈	C₂²	1	2	yes	—
41	C₅×#322	C₂²	1	1	yes	characteristic
42	C₅×#322	C₂²	1	1	yes	characteristic
43	C₅×#322	C₂²	1	1	yes	characteristic
44	C₅×#322	C₂²	1	1	yes	characteristic
45	#17990	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂×C₅×#41	—	2	1	no	—
47	C₂×C₅×SD₁₆	C₂×C₄	1	2	yes	—
48	C₂×C₅×SD₁₆	C₂×C₄	1	2	yes	—
49	C₂×C₅×M₁₆	—	2	2	no	—
50	C₂²×C₅×C₈	—	2	2	no	—
51	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
53	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
54	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
55	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
56	C₅×#127	C₂×C₄	1	1	yes	characteristic
57	C₅×#125	—	2	1	no	—
58	C₅×#124	—	2	1	no	—
59	C₅×C₂²⋊Q₈	—	2	1	no	—
60	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
61	C₅×#121	—	2	1	no	—
62	C₅×#121	C₂×C₄	1	2	yes	—
63	C₄×C₅×Q₈	—	2	1	no	—
64	C₄×C₅×Q₈	C₂³	1	2	yes	—
65	C₄×C₅×D₄	—	2	1	no	—
66	C₄×C₅×D₄	C₂³	1	2	yes	—
67	C₅×#117	—	2	1	no	—
68	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
69	C₅×#106	C₂×C₄	1	2	yes	—
70	C₅×#106	C₂×C₄	1	2	yes	—
71	C₅×C₄⋊C₈	—	2	2	no	—
72	C₅×C₄⋊C₈	—	2	2	no	—
73	C₅×C₄⋊C₈	—	2	1	no	—
74	C₅×C₄⋊C₈	D₄	1	2	yes	—
75	C₅×C₄⋊C₈	C₂³	1	2	yes	—
76	C₅×C₄⋊C₈	C₂³	1	2	yes	—
77	C₅×#103	C₂×C₄	1	2	yes	—
78	C₅×#103	C₂×C₄	1	2	yes	—
79	C₅×#102	C₂×C₄	1	2	yes	—
80	C₅×#102	C₂×C₄	1	2	yes	—
81	C₅×C₂²⋊C₈	—	2	1	no	—
82	C₅×C₂²⋊C₈	—	2	1	no	—
83	C₅×C₂²⋊C₈	—	2	1	no	—
84	C₅×C₂²⋊C₈	—	2	2	no	—
85	C₅×C₂²⋊C₈	—	2	2	no	—
86	C₅×C₂²⋊C₈	D₄	1	2	yes	—
87	C₅×#97	—	2	2	no	—
88	C₅×#97	—	2	1	no	—
89	C₅×#97	—	2	1	no	—
90	C₄×C₅×C₈	—	2	2	no	—
91	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
92	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
93	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
94	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
95	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
96	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
97	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
98	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
99	#3167	C₂×C₅	1	1	yes	characteristic
100	#2985	C₂×C₅	1	1	yes	characteristic, complemented
101	#2981	C₂×C₅	1	1	yes	characteristic
102	#1588	C₂×C₅	1	2	yes	complemented
103	#1585	C₂×C₅	1	2	yes	complemented
104	#1583	C₂×C₅	1	2	yes	complemented
105	#1582	C₂×C₅	1	2	yes	complemented
106	#1568	C₂×C₅	1	1	yes	characteristic, complemented
107	#1497	C₂×C₅	1	1	yes	characteristic, complemented
108	#1496	C₂×C₅	1	1	yes	characteristic
109	#1452	C₂×C₅	1	1	yes	characteristic, complemented
110	C₅×#41	—	8	2	no	—
111	C₂×C₅×Q₈	—	2	1	no	—
112	C₂×C₅×Q₈	—	2	1	no	—
113	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
114	C₂×C₅×D₄	—	2	2	no	—
115	C₂×C₅×D₄	—	2	1	no	—
116	C₂×C₅×D₄	—	2	1	no	—
117	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₅	—	2	2	no	—
119	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₅	#41	1	1	yes	characteristic
122	C₅×SD₁₆	—	4	2	no	—
123	C₅×SD₁₆	—	4	2	no	—
124	C₅×M₁₆	—	8	2	no	—
125	C₂×C₅×C₈	—	2	2	no	—
126	C₂×C₅×C₈	—	2	2	no	—
127	C₂×C₅×C₈	—	2	1	no	—
128	C₂×C₅×C₈	—	2	1	no	—
129	C₂×C₅×C₈	—	4	1	no	—
130	C₂×C₅×C₈	—	4	1	no	—
131	C₂×C₅×C₈	—	8	2	no	—
132	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
137	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
138	C₅×C₄⋊C₄	—	2	1	no	—
139	C₅×C₄⋊C₄	—	2	1	no	—
140	C₅×C₄⋊C₄	—	2	1	no	—
141	C₅×C₄⋊C₄	—	2	1	no	—
142	C₅×C₄⋊C₄	—	2	2	no	—
143	C₅×C₄⋊C₄	—	2	2	no	—
144	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
145	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
146	C₅×C₂²⋊C₄	—	2	2	no	—
147	C₅×C₂²⋊C₄	—	2	2	no	—
148	C₅×C₂²⋊C₄	—	2	2	no	—
149	C₄²×C₅	—	2	2	no	—
150	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
151	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₅	#41	1	1	yes	characteristic
153	C₄²×C₅	C₂⁴	1	1	yes	characteristic
154	#533	C₂²×C₅	1	1	yes	characteristic
155	#532	C₂²×C₅	1	1	yes	characteristic
156	#498	C₄×C₅	1	1	yes	characteristic
157	#492	C₄×C₅	1	1	yes	characteristic
158	#487	C₄×C₅	1	1	yes	characteristic
159	#486	C₄×C₅	1	1	yes	characteristic
160	#465	C₄×C₅	1	2	yes	—
161	#465	C₄×C₅	1	2	yes	—
162	#446	—	2	2	no	—
163	#446	C₂²×C₅	1	2	yes	—
164	C₈×Q₈	C₂²×C₅	1	2	yes	—
165	C₄×SD₁₆	C₂²×C₅	1	2	yes	—
166	C₄×SD₁₆	C₂²×C₅	1	2	yes	—
167	#436	C₂²×C₅	1	2	yes	—
168	#435	—	2	2	no	—
169	C₈×D₄	C₂²×C₅	1	2	yes	—
170	#433	—	2	2	no	—
171	#432	C₂²×C₅	1	1	yes	characteristic
172	#432	C₂²×C₅	1	1	yes	characteristic
173	#431	C₂²×C₅	1	1	yes	characteristic
174	#431	C₂²×C₅	1	1	yes	characteristic
175	#408	—	2	2	no	—
176	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
177	#335	C₂²×C₅	1	2	yes	—
178	#334	C₂²×C₅	1	2	yes	—
179	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
180	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
181	D₄⋊C₈	C₂²×C₅	1	2	yes	—
182	D₄⋊C₈	C₂²×C₅	1	2	yes	—
183	#322	C₂²×C₅	1	1	yes	characteristic
184	#322	C₂²×C₅	1	1	yes	characteristic
185	#322	C₂²×C₅	1	1	yes	characteristic
186	#322	C₂²×C₅	1	1	yes	characteristic
187	C₂³×C₅	—	2	2	no	—
188	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
189	C₅×Q₈	—	2	2	no	—
190	C₅×Q₈	—	2	2	no	—
191	C₅×Q₈	—	8	1	no	—
192	C₅×Q₈	—	8	1	no	—
193	C₅×D₄	—	2	2	no	—
194	C₅×D₄	—	2	2	no	—
195	C₅×D₄	—	8	1	no	—
196	C₅×D₄	—	8	1	no	—
197	C₅×D₄	—	8	2	no	—
198	C₂×C₄×C₅	—	2	1	no	—
199	C₂×C₄×C₅	—	2	1	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	—	2	2	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	4	1	no	—
205	C₂×C₄×C₅	—	4	2	no	—
206	C₂×C₄×C₅	—	4	2	no	—
207	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
208	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
209	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
210	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
213	C₅×C₈	—	2	1	no	—
214	C₅×C₈	—	2	1	no	—
215	C₅×C₈	—	2	1	no	—
216	C₅×C₈	—	2	1	no	—
217	C₅×C₈	—	2	2	no	—
218	C₅×C₈	—	2	2	no	—
219	C₅×C₈	—	4	1	no	—
220	C₅×C₈	—	4	1	no	—
221	C₅×C₈	—	4	2	no	—
222	C₅×C₈	—	4	2	no	—
223	C₂×#41	—	2	1	no	—
224	C₂×SD₁₆	C₂×C₄×C₅	1	2	yes	—
225	C₂×SD₁₆	C₂×C₄×C₅	1	2	yes	—
226	C₂×M₁₆	—	2	2	no	—
227	C₂²×C₈	—	2	2	no	—
228	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
229	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
230	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
231	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
232	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
233	#127	C₂×C₄×C₅	1	1	yes	characteristic
234	#125	—	2	1	no	—
235	#124	—	2	1	no	—
236	C₂²⋊Q₈	—	2	1	no	—
237	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
238	#121	—	2	1	no	—
239	#121	C₂×C₄×C₅	1	2	yes	—
240	C₄×Q₈	—	2	1	no	—
241	C₄×Q₈	C₂³×C₅	1	2	yes	—
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	C₂³×C₅	1	2	yes	—
244	#117	—	2	1	no	—
245	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
246	#106	C₂×C₄×C₅	1	2	yes	—
247	#106	C₂×C₄×C₅	1	2	yes	—
248	C₄⋊C₈	—	2	2	no	—
249	C₄⋊C₈	—	2	2	no	—
250	C₄⋊C₈	—	2	1	no	—
251	C₄⋊C₈	C₅×D₄	1	2	yes	—
252	C₄⋊C₈	C₂³×C₅	1	2	yes	—
253	C₄⋊C₈	C₂³×C₅	1	2	yes	—
254	#103	C₂×C₄×C₅	1	2	yes	—
255	#103	C₂×C₄×C₅	1	2	yes	—
256	#102	C₂×C₄×C₅	1	2	yes	—
257	#102	C₂×C₄×C₅	1	2	yes	—
258	C₂²⋊C₈	—	2	1	no	—
259	C₂²⋊C₈	—	2	1	no	—
260	C₂²⋊C₈	—	2	1	no	—
261	C₂²⋊C₈	—	2	2	no	—
262	C₂²⋊C₈	—	2	2	no	—
263	C₂²⋊C₈	C₅×D₄	1	2	yes	—
264	#97	—	2	2	no	—
265	#97	—	2	1	no	—
266	#97	—	2	1	no	—
267	C₄×C₈	—	2	2	no	—
268	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
269	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
270	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
271	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
272	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
273	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
274	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
275	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
276	C₂²×C₅	—	2	1	no	—
277	C₂²×C₅	—	2	1	no	—
278	C₂²×C₅	—	2	1	no	—
279	C₂²×C₅	—	4	2	no	—
280	C₂²×C₅	—	4	2	no	—
281	C₂²×C₅	—	4	2	no	—
282	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
283	C₄×C₅	—	2	1	no	—
284	C₄×C₅	—	2	1	no	—
285	C₄×C₅	—	2	1	no	—
286	C₄×C₅	—	2	1	no	—
287	C₄×C₅	—	4	2	no	—
288	C₄×C₅	—	4	2	no	—
289	C₄×C₅	—	4	2	no	—
290	C₄×C₅	#568	1	1	yes	characteristic
291	C₄×C₅	#568	1	1	yes	characteristic
292	C₄×C₅	#577	1	2	yes	—
293	#41	—	8	2	no	—
294	C₂×Q₈	—	2	1	no	—
295	C₂×Q₈	—	2	1	no	—
296	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
303	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
304	C₂²×C₄	C₅×#41	1	1	yes	characteristic
305	SD₁₆	—	4	2	no	—
306	SD₁₆	—	4	2	no	—
307	M₁₆	—	8	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	4	1	no	—
313	C₂×C₈	—	4	1	no	—
314	C₂×C₈	—	8	2	no	—
315	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
316	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
317	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
318	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
319	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
320	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
328	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
329	C₂²⋊C₄	—	2	2	no	—
330	C₂²⋊C₄	—	2	2	no	—
331	C₂²⋊C₄	—	2	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
334	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
335	C₄²	C₅×#41	1	1	yes	characteristic
336	C₄²	C₂⁴×C₅	1	1	yes	characteristic
337	C₂×C₅	—	4	1	no	—
338	C₂×C₅	—	8	2	no	—
339	C₂×C₅	#2932	1	1	yes	characteristic
340	C₂×C₅	#2949	1	1	yes	characteristic
341	C₂×C₅	#2957	1	1	yes	characteristic
342	C₂³	—	2	2	no	—
343	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
344	Q₈	—	2	2	no	—
345	Q₈	—	2	2	no	—
346	Q₈	—	8	1	no	—
347	Q₈	—	8	1	no	—
348	D₄	—	2	2	no	—
349	D₄	—	2	2	no	—
350	D₄	—	8	1	no	—
351	D₄	—	8	1	no	—
352	D₄	—	8	2	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
363	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
364	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
365	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
366	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
367	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
368	C₈	—	2	1	no	—
369	C₈	—	2	1	no	—
370	C₈	—	2	1	no	—
371	C₈	—	2	1	no	—
372	C₈	—	2	2	no	—
373	C₈	—	2	2	no	—
374	C₈	—	4	1	no	—
375	C₈	—	4	1	no	—
376	C₈	—	4	2	no	—
377	C₈	—	4	2	no	—
378	C₅	#17990	1	1	yes	characteristic, direct product factor, Sylow
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	4	2	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	4	2	no	—
385	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	4	2	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	2	no	—
393	C₄	C₅×#568	1	1	yes	characteristic
394	C₄	C₅×#568	1	1	yes	characteristic
395	C₄	C₅×#577	1	2	yes	—
396	C₂	—	4	1	no	—
397	C₂	—	8	2	no	—
398	C₂	C₅×#2932	1	1	yes	characteristic
399	C₂	C₅×#2949	1	1	yes	characteristic
400	C₂	C₅×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₄²	C₂⁴×C₅
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₅×#532	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2985	C₂	semidirect
4. C₅×#1588	C₂	semidirect
5. C₅×#1585	C₂	semidirect
6. C₅×#1583	C₂	semidirect
7. C₅×#1582	C₂	semidirect
8. C₅×#1568	C₂	semidirect
9. C₅×#1497	C₂	semidirect
11. C₅×#1452	C₂	semidirect
45. #17990	C₅	direct (N × H)
100. #2985	C₂×C₅	semidirect
102. #1588	C₂×C₅	semidirect
103. #1585	C₂×C₅	semidirect
104. #1583	C₂×C₅	semidirect
105. #1582	C₂×C₅	semidirect
106. #1568	C₂×C₅	semidirect
107. #1497	C₂×C₅	semidirect
109. #1452	C₂×C₅	semidirect
378. C₅	#17990	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×#3167	2
C₅×#2985	2
C₅×#2981	2
C₅×#1588	2
C₅×#1585	2
C₅×#1583	2
C₅×#1582	2
C₅×#1568	2
C₅×#1497	2
C₅×#1496	2
C₅×#1452	2
#17990	5

Subgroups — C5×#17990 #11940710

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17990 #11940710