Subgroups — C₅×#10852 #11933572

Order 1280.

986 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#423	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#339	C₂	1	4	yes	maximal
5	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
6	C₂×C₅×#117	C₂²	1	2	yes	—
7	C₂²×C₅×C₄⋊C₄	—	2	1	no	—
8	C₂²×C₄²×C₅	C₂²	1	2	yes	—
9	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
10	C₅×#423	—	2	2	no	—
11	C₅×#423	C₄	1	4	yes	complemented
12	C₂×C₅×C₄⋊C₈	—	2	1	no	—
13	C₂×C₅×C₄⋊C₈	—	2	1	no	—
14	C₄×C₅×C₄⋊C₄	—	2	2	no	—
15	C₄×C₅×C₄⋊C₄	C₄	1	2	yes	complemented
16	C₄×C₅×C₄⋊C₄	C₄	1	2	yes	complemented
17	C₄×C₅×C₄⋊C₄	C₄	1	4	yes	complemented
18	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
19	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
20	C₅×#376	—	2	1	no	—
21	C₂×C₅×#95	—	2	1	no	—
22	C₄³×C₅	—	2	1	no	—
23	C₅×#339	—	2	8	no	—
24	#10852	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂³×C₄×C₅	—	2	2	no	—
26	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
27	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
28	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
29	C₂×C₅×M₁₆	—	2	2	no	—
30	C₂×C₅×M₁₆	—	2	4	no	—
31	C₂×C₅×M₁₆	—	2	4	no	—
32	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	—
33	C₂²×C₅×C₈	—	2	2	no	—
34	C₅×#117	—	2	2	no	—
35	C₅×#117	—	2	2	no	—
36	C₅×#117	D₄	1	4	yes	—
37	C₅×#117	Q₈	1	4	yes	—
38	C₂×C₅×C₄⋊C₄	—	2	8	no	—
39	C₂×C₅×C₄⋊C₄	—	2	4	no	—
40	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
41	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
42	C₂×C₄²×C₅	—	2	2	no	—
43	C₂×C₄²×C₅	—	2	4	no	—
44	C₂×C₄²×C₅	—	2	4	no	—
45	C₂×C₄²×C₅	—	2	2	no	—
46	C₂×C₄²×C₅	—	2	2	no	—
47	C₂×C₄²×C₅	—	2	2	no	—
48	C₂×C₄²×C₅	C₂×C₄	1	4	yes	—
49	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
50	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₅	D₄	1	2	yes	—
54	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₅	Q₈	1	2	yes	—
57	C₅×C₄⋊C₈	—	2	4	no	—
58	C₅×C₄⋊C₈	—	2	4	no	—
59	C₅×#95	—	2	4	no	—
60	C₅×#95	—	2	2	no	—
61	C₅×#95	—	2	2	no	—
62	C₂×#423	C₂×C₅	1	1	yes	characteristic
63	C₄×#117	C₂×C₅	1	1	yes	characteristic
64	C₂×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
65	C₂×#339	C₂×C₅	1	4	yes	—
66	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₅	—	2	4	no	—
68	C₂²×C₄×C₅	—	2	8	no	—
69	C₂²×C₄×C₅	—	2	4	no	—
70	C₂²×C₄×C₅	—	2	4	no	—
71	C₂²×C₄×C₅	—	4	2	no	—
72	C₂²×C₄×C₅	—	4	4	no	—
73	C₂²×C₄×C₅	—	4	4	no	—
74	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₅	C₂²⋊C₄	1	2	yes	—
76	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₅	C₂²⋊C₄	1	2	yes	—
79	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₅	C₄⋊C₄	1	2	yes	—
81	C₂²×C₄×C₅	C₄⋊C₄	1	2	yes	—
82	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
89	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
90	C₂²×C₄×C₅	#41	1	2	yes	—
91	C₂²×C₄×C₅	#41	1	2	yes	—
92	C₅×M₁₆	—	2	8	no	—
93	C₅×M₁₆	—	4	2	no	—
94	C₅×M₁₆	—	4	2	no	—
95	C₂×C₅×C₈	—	2	4	no	—
96	C₂×C₅×C₈	—	4	4	no	—
97	C₅×C₄⋊C₄	—	2	16	no	—
98	C₅×C₄⋊C₄	—	2	4	no	—
99	C₅×C₄⋊C₄	C₄⋊C₄	1	8	yes	complemented
100	C₅×C₂²⋊C₄	—	2	4	no	—
101	C₅×C₂²⋊C₄	—	2	4	no	—
102	C₄²×C₅	—	2	4	no	—
103	C₄²×C₅	—	2	4	no	—
104	C₄²×C₅	—	2	8	no	—
105	C₄²×C₅	—	4	4	no	—
106	C₄²×C₅	—	4	4	no	—
107	C₄²×C₅	—	4	2	no	—
108	C₄²×C₅	—	4	2	no	—
109	C₄²×C₅	C₄²	1	2	yes	—
110	C₄²×C₅	C₄²	1	2	yes	—
111	C₄²×C₅	C₂²⋊C₄	1	2	yes	—
112	C₄²×C₅	C₂²⋊C₄	1	2	yes	—
113	C₄²×C₅	C₄⋊C₄	1	2	yes	—
114	C₄²×C₅	C₄⋊C₄	1	2	yes	—
115	C₄²×C₅	C₄⋊C₄	1	2	yes	—
116	C₄²×C₅	C₄⋊C₄	1	2	yes	—
117	C₂²×M₁₆	C₂²×C₅	1	2	yes	—
118	C₂×#117	C₂²×C₅	1	2	yes	—
119	C₂²×C₄⋊C₄	—	2	1	no	—
120	C₂²×C₄²	C₂²×C₅	1	2	yes	—
121	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
122	#423	—	2	2	no	—
123	#423	C₄×C₅	1	4	yes	complemented
124	C₂×C₄⋊C₈	—	2	1	no	—
125	C₂×C₄⋊C₈	—	2	1	no	—
126	C₄×C₄⋊C₄	—	2	2	no	—
127	C₄×C₄⋊C₄	C₄×C₅	1	2	yes	complemented
128	C₄×C₄⋊C₄	C₄×C₅	1	2	yes	complemented
129	C₄×C₄⋊C₄	C₄×C₅	1	4	yes	complemented
130	C₄×C₂²⋊C₄	—	2	1	no	—
131	C₄×C₂²⋊C₄	—	2	1	no	—
132	#376	—	2	1	no	—
133	C₂×#95	—	2	1	no	—
134	C₄³	—	2	1	no	—
135	#339	—	2	8	no	—
136	C₂³×C₅	—	2	2	no	—
137	C₂³×C₅	—	2	2	no	—
138	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂³×C₅	#121	1	2	yes	—
142	C₂³×C₅	C₂²⋊Q₈	1	2	yes	—
143	C₂×C₄×C₅	—	2	2	no	—
144	C₂×C₄×C₅	—	2	2	no	—
145	C₂×C₄×C₅	—	2	2	no	—
146	C₂×C₄×C₅	—	2	4	no	—
147	C₂×C₄×C₅	—	2	4	no	—
148	C₂×C₄×C₅	—	2	8	no	—
149	C₂×C₄×C₅	—	2	8	no	—
150	C₂×C₄×C₅	—	4	2	no	—
151	C₂×C₄×C₅	—	4	2	no	—
152	C₂×C₄×C₅	—	4	16	no	—
153	C₂×C₄×C₅	—	4	4	no	—
154	C₂×C₄×C₅	—	4	4	no	—
155	C₂×C₄×C₅	—	4	4	no	—
156	C₂×C₄×C₅	—	4	4	no	—
157	C₂×C₄×C₅	#95	1	2	yes	—
158	C₂×C₄×C₅	#95	1	2	yes	—
159	C₂×C₄×C₅	#95	1	2	yes	—
160	C₂×C₄×C₅	#95	1	2	yes	—
161	C₂×C₄×C₅	#104	1	4	yes	—
162	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
163	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
165	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₅	#117	1	2	yes	—
168	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
169	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
170	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
171	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
172	C₂×C₄×C₅	#121	1	2	yes	—
173	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
174	C₂×C₄×C₅	#124	1	1	yes	characteristic
175	C₂×C₄×C₅	#124	1	1	yes	characteristic
176	C₂×C₄×C₅	#125	1	2	yes	—
177	C₂×C₄×C₅	#127	1	1	yes	characteristic
178	C₂×C₄×C₅	C₄⋊Q₈	1	2	yes	—
179	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
180	C₅×C₈	—	4	4	no	—
181	C₂³×C₄	—	2	2	no	—
182	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
183	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
184	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
185	C₂×M₁₆	—	2	2	no	—
186	C₂×M₁₆	—	2	4	no	—
187	C₂×M₁₆	—	2	4	no	—
188	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	—
189	C₂²×C₈	—	2	2	no	—
190	#117	—	2	2	no	—
191	#117	—	2	2	no	—
192	#117	C₅×D₄	1	4	yes	—
193	#117	C₅×Q₈	1	4	yes	—
194	C₂×C₄⋊C₄	—	2	8	no	—
195	C₂×C₄⋊C₄	—	2	4	no	—
196	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
197	C₂×C₂²⋊C₄	—	2	2	no	—
198	C₂×C₄²	—	2	2	no	—
199	C₂×C₄²	—	2	4	no	—
200	C₂×C₄²	—	2	4	no	—
201	C₂×C₄²	—	2	2	no	—
202	C₂×C₄²	—	2	2	no	—
203	C₂×C₄²	—	2	2	no	—
204	C₂×C₄²	C₂×C₄×C₅	1	4	yes	—
205	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
206	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
207	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
208	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
209	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
210	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
211	C₂×C₄²	C₅×D₄	1	2	yes	—
212	C₂×C₄²	C₅×Q₈	1	2	yes	—
213	C₄⋊C₈	—	2	4	no	—
214	C₄⋊C₈	—	2	4	no	—
215	#95	—	2	4	no	—
216	#95	—	2	2	no	—
217	#95	—	2	2	no	—
218	C₂²×C₅	—	2	4	no	—
219	C₂²×C₅	—	2	4	no	—
220	C₂²×C₅	—	2	1	no	—
221	C₂²×C₅	—	2	1	no	—
222	C₂²×C₅	—	2	1	no	—
223	C₂²×C₅	—	2	1	no	—
224	C₂²×C₅	C₂×#95	1	1	yes	characteristic
225	C₂²×C₅	#380	1	2	yes	—
226	C₂²×C₅	#389	1	2	yes	—
227	C₂²×C₅	#390	1	1	yes	characteristic
228	C₂²×C₅	#391	1	1	yes	characteristic
229	C₂²×C₅	C₂×#104	1	2	yes	—
230	C₂²×C₅	#421	1	2	yes	—
231	C₄×C₅	—	2	2	no	—
232	C₄×C₅	—	2	2	no	—
233	C₄×C₅	—	2	2	no	—
234	C₄×C₅	—	4	8	no	—
235	C₄×C₅	—	4	8	no	—
236	C₄×C₅	#339	1	4	yes	complemented
237	C₄×C₅	C₄×C₄⋊C₄	1	2	yes	—
238	C₄×C₅	#382	1	1	yes	characteristic
239	C₄×C₅	#384	1	1	yes	characteristic
240	C₄×C₅	#389	1	2	yes	—
241	C₄×C₅	#390	1	1	yes	characteristic
242	C₄×C₅	#391	1	1	yes	characteristic
243	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
244	C₂²×C₄	—	2	4	no	—
245	C₂²×C₄	—	2	8	no	—
246	C₂²×C₄	—	2	4	no	—
247	C₂²×C₄	—	2	4	no	—
248	C₂²×C₄	—	4	2	no	—
249	C₂²×C₄	—	4	4	no	—
250	C₂²×C₄	—	4	4	no	—
251	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
252	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
253	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
254	C₂²×C₄	C₅×C₂²⋊C₄	1	2	yes	—
255	C₂²×C₄	C₅×C₂²⋊C₄	1	2	yes	—
256	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
257	C₂²×C₄	C₅×C₄⋊C₄	1	2	yes	—
258	C₂²×C₄	C₅×C₄⋊C₄	1	2	yes	—
259	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
260	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
261	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
262	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
263	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
264	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
265	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
266	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
267	C₂²×C₄	C₅×#41	1	2	yes	—
268	C₂²×C₄	C₅×#41	1	2	yes	—
269	M₁₆	—	2	8	no	—
270	M₁₆	—	4	2	no	—
271	M₁₆	—	4	2	no	—
272	C₂×C₈	—	2	4	no	—
273	C₂×C₈	—	4	4	no	—
274	C₄⋊C₄	—	2	16	no	—
275	C₄⋊C₄	—	2	4	no	—
276	C₄⋊C₄	C₅×C₄⋊C₄	1	8	yes	complemented
277	C₂²⋊C₄	—	2	4	no	—
278	C₂²⋊C₄	—	2	4	no	—
279	C₄²	—	2	4	no	—
280	C₄²	—	2	4	no	—
281	C₄²	—	2	8	no	—
282	C₄²	—	4	4	no	—
283	C₄²	—	4	2	no	—
284	C₄²	—	4	2	no	—
285	C₄²	—	4	4	no	—
286	C₄²	C₄²×C₅	1	2	yes	—
287	C₄²	C₄²×C₅	1	2	yes	—
288	C₄²	C₅×C₂²⋊C₄	1	2	yes	—
289	C₄²	C₅×C₂²⋊C₄	1	2	yes	—
290	C₄²	C₅×C₄⋊C₄	1	2	yes	—
291	C₄²	C₅×C₄⋊C₄	1	2	yes	—
292	C₄²	C₅×C₄⋊C₄	1	2	yes	—
293	C₄²	C₅×C₄⋊C₄	1	2	yes	—
294	C₂×C₅	—	2	1	no	—
295	C₂×C₅	—	2	2	no	—
296	C₂×C₅	—	2	1	no	—
297	C₂×C₅	C₄⋊#95	1	1	yes	characteristic
298	C₂×C₅	C₂×#339	1	1	yes	characteristic
299	C₂×C₅	#1733	1	1	yes	characteristic
300	C₂×C₅	#1806	1	4	yes	—
301	C₂³	—	2	2	no	—
302	C₂³	—	2	2	no	—
303	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
304	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
305	C₂³	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
306	C₂³	C₅×#121	1	2	yes	—
307	C₂³	C₅×C₂²⋊Q₈	1	2	yes	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	8	no	—
314	C₂×C₄	—	2	8	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	4	16	no	—
318	C₂×C₄	—	4	4	no	—
319	C₂×C₄	—	4	4	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	C₅×#95	1	2	yes	—
323	C₂×C₄	C₅×#95	1	2	yes	—
324	C₂×C₄	C₅×#95	1	2	yes	—
325	C₂×C₄	C₅×#95	1	2	yes	—
326	C₂×C₄	C₅×#104	1	4	yes	—
327	C₂×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
328	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
329	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
330	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
331	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
332	C₂×C₄	C₅×#117	1	2	yes	—
333	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
334	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
335	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
336	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
337	C₂×C₄	C₅×#121	1	2	yes	—
338	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
339	C₂×C₄	C₅×#124	1	1	yes	characteristic
340	C₂×C₄	C₅×#124	1	1	yes	characteristic
341	C₂×C₄	C₅×#125	1	2	yes	—
342	C₂×C₄	C₅×#127	1	1	yes	characteristic
343	C₂×C₄	C₅×C₄⋊Q₈	1	2	yes	—
344	C₂×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
345	C₈	—	4	4	no	—
346	C₅	#10852	1	1	yes	characteristic, direct product factor, Sylow
347	C₂²	—	2	4	no	—
348	C₂²	—	2	4	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	C₂×C₅×#95	1	1	yes	characteristic
354	C₂²	C₅×#380	1	2	yes	—
355	C₂²	C₅×#389	1	2	yes	—
356	C₂²	C₅×#390	1	1	yes	characteristic
357	C₂²	C₅×#391	1	1	yes	characteristic
358	C₂²	C₂×C₅×#104	1	2	yes	—
359	C₂²	C₅×#421	1	2	yes	—
360	C₄	—	2	2	no	—
361	C₄	—	2	2	no	—
362	C₄	—	2	2	no	—
363	C₄	—	4	8	no	—
364	C₄	—	4	8	no	—
365	C₄	C₅×#339	1	4	yes	complemented
366	C₄	C₄×C₅×C₄⋊C₄	1	2	yes	—
367	C₄	C₅×#382	1	1	yes	characteristic
368	C₄	C₅×#384	1	1	yes	characteristic
369	C₄	C₅×#389	1	2	yes	—
370	C₄	C₅×#390	1	1	yes	characteristic
371	C₄	C₅×#391	1	1	yes	characteristic
372	C₂	—	2	1	no	—
373	C₂	—	2	2	no	—
374	C₂	—	2	1	no	—
375	C₂	C₅×C₄⋊#95	1	1	yes	characteristic
376	C₂	C₂×C₅×#339	1	1	yes	characteristic
377	C₂	C₅×#1733	1	1	yes	characteristic
378	C₂	C₅×#1806	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
11. C₅×#423	C₄	semidirect
15. C₄×C₅×C₄⋊C₄	C₄	semidirect
16. C₄×C₅×C₄⋊C₄	C₄	semidirect
17. C₄×C₅×C₄⋊C₄	C₄	semidirect
24. #10852	C₅	direct (N × H)
99. C₅×C₄⋊C₄	C₄⋊C₄	semidirect
123. #423	C₄×C₅	semidirect
127. C₄×C₄⋊C₄	C₄×C₅	semidirect
128. C₄×C₄⋊C₄	C₄×C₅	semidirect
129. C₄×C₄⋊C₄	C₄×C₅	semidirect
236. C₄×C₅	#339	semidirect
276. C₄⋊C₄	C₅×C₄⋊C₄	semidirect
346. C₅	#10852	direct (N × H)
365. C₄	C₅×#339	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#423	2
C₄×C₅×#117	2
C₂×C₄×C₅×C₄⋊C₄	2
C₂×C₅×#339	2
#10852	5

Subgroups — C5×#10852 #11933572

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#10852 #11933572