Subgroups — C₅×#21371 #11944091

Order 1280.

760 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2920	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#432	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic
4	C₅×#1950	C₂	1	4	yes	maximal, complemented
5	C₅×#1855	C₂	1	4	yes	maximal
6	C₅×#1778	C₂	1	4	yes	maximal, complemented
7	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
8	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
9	C₅×#432	—	2	1	no	—
10	C₅×#432	—	2	1	no	—
11	C₅×#432	C₄	1	2	yes	—
12	C₅×#432	C₄	1	2	yes	—
13	C₅×#432	C₄	1	2	yes	—
14	C₅×#432	C₄	1	2	yes	—
15	C₅×#431	—	2	1	no	—
16	C₅×#431	—	2	1	no	—
17	C₂×C₅×#108	C₂²	1	8	yes	—
18	C₅×#423	C₂²	1	2	yes	—
19	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
20	C₅×#407	C₂²	1	2	yes	—
21	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₄×C₅×M₁₆	—	2	1	no	—
23	C₄×C₅×M₁₆	—	2	1	no	—
24	C₄×C₅×M₁₆	C₂²	1	2	yes	—
25	C₄×C₅×M₁₆	C₂²	1	2	yes	—
26	C₄×C₅×M₁₆	C₂²	1	2	yes	—
27	C₂×C₅×#97	—	2	1	no	—
28	C₂×C₅×#97	C₂²	1	2	yes	—
29	C₂×C₄×C₅×C₈	—	2	1	no	—
30	C₅×#341	C₂²	1	8	yes	—
31	#21371	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₂³×C₄×C₅	Q₈	1	1	yes	characteristic
33	C₂³×C₄×C₅	Q₈	1	1	yes	characteristic
34	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
35	C₂×C₅×M₁₆	—	2	2	no	—
36	C₂×C₅×M₁₆	—	2	8	no	—
37	C₂×C₅×M₁₆	C₂³	1	4	yes	—
38	C₂×C₅×M₁₆	C₂³	1	4	yes	—
39	C₂²×C₅×C₈	—	2	2	no	—
40	C₂²×C₅×C₈	C₂³	1	4	yes	—
41	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₅	Q₈	1	1	yes	characteristic
50	C₂×C₄²×C₅	Q₈	1	1	yes	characteristic
51	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
52	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
53	C₅×#108	—	2	16	no	—
54	C₅×C₄⋊C₈	—	2	2	no	—
55	C₅×C₄⋊C₈	—	2	2	no	—
56	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
57	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
58	C₅×C₂²⋊C₈	—	2	2	no	—
59	C₅×C₂²⋊C₈	—	2	2	no	—
60	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	—
61	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	—
62	C₅×#97	—	2	2	no	—
63	C₅×#97	—	2	2	no	—
64	C₅×#97	—	2	2	no	—
65	C₅×#97	C₂×C₄	1	4	yes	—
66	C₅×#97	C₂×C₄	1	4	yes	—
67	C₄×C₅×C₈	—	2	2	no	—
68	C₄×C₅×C₈	—	2	2	no	—
69	C₄×C₅×C₈	—	2	2	no	—
70	#2920	C₂×C₅	1	1	yes	characteristic
71	C₂×#432	C₂×C₅	1	1	yes	characteristic
72	C₂×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic
73	#1950	C₂×C₅	1	4	yes	complemented
74	#1855	C₂×C₅	1	4	yes	—
75	#1778	C₂×C₅	1	4	yes	complemented
76	C₂⁴×C₅	C₂×Q₈	1	1	yes	characteristic
77	C₂²×C₄×C₅	—	2	4	no	—
78	C₂²×C₄×C₅	—	4	2	no	—
79	C₂²×C₄×C₅	—	4	2	no	—
80	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
93	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
94	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
95	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
96	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
97	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
98	C₅×M₁₆	—	2	8	no	—
99	C₅×M₁₆	—	2	4	no	—
100	C₅×M₁₆	—	2	8	no	—
101	C₅×M₁₆	#41	1	8	yes	—
102	C₂×C₅×C₈	—	2	8	no	—
103	C₂×C₅×C₈	—	2	4	no	—
104	C₂×C₅×C₈	—	2	8	no	—
105	C₂×C₅×C₈	—	2	4	no	—
106	C₂×C₅×C₈	C₂²×C₄	1	8	yes	—
107	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
110	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
111	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
112	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
113	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
114	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
115	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
123	C₂²×M₁₆	C₂²×C₅	1	2	yes	—
124	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
125	#432	—	2	1	no	—
126	#432	—	2	1	no	—
127	#432	C₄×C₅	1	2	yes	—
128	#432	C₄×C₅	1	2	yes	—
129	#432	C₄×C₅	1	2	yes	—
130	#432	C₄×C₅	1	2	yes	—
131	#431	—	2	1	no	—
132	#431	—	2	1	no	—
133	C₂×#108	C₂²×C₅	1	8	yes	—
134	#423	C₂²×C₅	1	2	yes	—
135	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
136	#407	C₂²×C₅	1	2	yes	—
137	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
138	C₄×M₁₆	—	2	1	no	—
139	C₄×M₁₆	—	2	1	no	—
140	C₄×M₁₆	C₂²×C₅	1	2	yes	—
141	C₄×M₁₆	C₂²×C₅	1	2	yes	—
142	C₄×M₁₆	C₂²×C₅	1	2	yes	—
143	C₂×#97	—	2	1	no	—
144	C₂×#97	C₂²×C₅	1	2	yes	—
145	C₂×C₄×C₈	—	2	1	no	—
146	#341	C₂²×C₅	1	8	yes	—
147	C₂³×C₅	—	2	2	no	—
148	C₂³×C₅	—	2	2	no	—
149	C₂³×C₅	—	4	1	no	—
150	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂³×C₅	C₂²×Q₈	1	1	yes	characteristic
153	C₂×C₄×C₅	—	2	2	no	—
154	C₂×C₄×C₅	—	2	2	no	—
155	C₂×C₄×C₅	—	2	2	no	—
156	C₂×C₄×C₅	—	2	2	no	—
157	C₂×C₄×C₅	—	2	2	no	—
158	C₂×C₄×C₅	—	2	2	no	—
159	C₂×C₄×C₅	—	2	2	no	—
160	C₂×C₄×C₅	—	2	2	no	—
161	C₂×C₄×C₅	—	2	2	no	—
162	C₂×C₄×C₅	—	2	2	no	—
163	C₂×C₄×C₅	—	4	1	no	—
164	C₂×C₄×C₅	—	4	1	no	—
165	C₂×C₄×C₅	—	4	1	no	—
166	C₂×C₄×C₅	—	4	1	no	—
167	C₂×C₄×C₅	—	4	1	no	—
168	C₂×C₄×C₅	—	4	1	no	—
169	C₂×C₄×C₅	—	4	1	no	—
170	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
181	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₅	C₂×#41	1	4	yes	—
183	C₅×C₈	—	2	8	no	—
184	C₅×C₈	—	2	8	no	—
185	C₅×C₈	—	4	4	no	—
186	C₂³×C₄	C₅×Q₈	1	1	yes	characteristic
187	C₂³×C₄	C₅×Q₈	1	1	yes	characteristic
188	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
189	C₂×M₁₆	—	2	2	no	—
190	C₂×M₁₆	—	2	8	no	—
191	C₂×M₁₆	C₂³×C₅	1	4	yes	—
192	C₂×M₁₆	C₂³×C₅	1	4	yes	—
193	C₂²×C₈	—	2	2	no	—
194	C₂²×C₈	C₂³×C₅	1	4	yes	—
195	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
196	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
197	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
198	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
199	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
200	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
201	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
202	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
203	C₂×C₄²	C₅×Q₈	1	1	yes	characteristic
204	C₂×C₄²	C₅×Q₈	1	1	yes	characteristic
205	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
206	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
207	#108	—	2	16	no	—
208	C₄⋊C₈	—	2	2	no	—
209	C₄⋊C₈	—	2	2	no	—
210	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
211	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
212	C₂²⋊C₈	—	2	2	no	—
213	C₂²⋊C₈	—	2	2	no	—
214	C₂²⋊C₈	C₂×C₄×C₅	1	4	yes	—
215	C₂²⋊C₈	C₂×C₄×C₅	1	4	yes	—
216	#97	—	2	2	no	—
217	#97	—	2	2	no	—
218	#97	—	2	2	no	—
219	#97	C₂×C₄×C₅	1	4	yes	—
220	#97	C₂×C₄×C₅	1	4	yes	—
221	C₄×C₈	—	2	2	no	—
222	C₄×C₈	—	2	2	no	—
223	C₄×C₈	—	2	2	no	—
224	C₂²×C₅	—	2	1	no	—
225	C₂²×C₅	—	2	1	no	—
226	C₂²×C₅	—	2	1	no	—
227	C₂²×C₅	—	2	1	no	—
228	C₂²×C₅	—	2	1	no	—
229	C₂²×C₅	—	2	1	no	—
230	C₂²×C₅	—	2	1	no	—
231	C₂²×C₅	—	4	4	no	—
232	C₂²×C₅	#430	1	2	yes	—
233	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
234	C₂²×C₅	#533	1	2	yes	—
235	C₄×C₅	—	2	1	no	—
236	C₄×C₅	—	2	1	no	—
237	C₄×C₅	—	2	1	no	—
238	C₄×C₅	—	2	1	no	—
239	C₄×C₅	—	2	1	no	—
240	C₄×C₅	—	2	1	no	—
241	C₄×C₅	—	2	1	no	—
242	C₄×C₅	—	2	1	no	—
243	C₄×C₅	—	2	1	no	—
244	C₄×C₅	#430	1	2	yes	—
245	C₄×C₅	C₄×#41	1	2	yes	—
246	C₄×C₅	#525	1	2	yes	—
247	C₂⁴	C₂×C₅×Q₈	1	1	yes	characteristic
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	—	4	2	no	—
250	C₂²×C₄	—	4	2	no	—
251	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
252	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
253	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
254	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
255	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
256	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
257	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
258	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
259	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
260	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
261	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
262	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
263	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
264	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
265	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
266	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
267	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
268	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
269	M₁₆	—	2	8	no	—
270	M₁₆	—	2	4	no	—
271	M₁₆	—	2	8	no	—
272	M₁₆	C₅×#41	1	8	yes	—
273	C₂×C₈	—	2	8	no	—
274	C₂×C₈	—	2	4	no	—
275	C₂×C₈	—	2	8	no	—
276	C₂×C₈	—	2	4	no	—
277	C₂×C₈	C₂²×C₄×C₅	1	8	yes	—
278	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
279	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
280	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
281	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
282	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
283	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
284	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
285	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
286	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
287	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
288	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
289	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
290	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
291	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
292	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
293	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
294	C₂×C₅	—	2	2	no	—
295	C₂×C₅	—	2	2	no	—
296	C₂×C₅	—	4	1	no	—
297	C₂×C₅	#2296	1	1	yes	characteristic
298	C₂×C₅	C₂×#430	1	1	yes	characteristic
299	C₂×C₅	C₂×#430	1	1	yes	characteristic
300	C₂³	—	2	2	no	—
301	C₂³	—	2	2	no	—
302	C₂³	—	4	1	no	—
303	C₂³	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
304	C₂³	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
305	C₂³	C₂²×C₅×Q₈	1	1	yes	characteristic
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	4	1	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	1	no	—
319	C₂×C₄	—	4	1	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
324	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
325	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
326	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
327	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
328	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
329	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
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	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
333	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
334	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
335	C₂×C₄	C₂×C₅×#41	1	4	yes	—
336	C₈	—	2	8	no	—
337	C₈	—	2	8	no	—
338	C₈	—	4	4	no	—
339	C₅	#21371	1	1	yes	characteristic, direct product factor, Sylow
340	C₂²	—	2	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	4	4	no	—
348	C₂²	C₅×#430	1	2	yes	—
349	C₂²	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
350	C₂²	C₅×#533	1	2	yes	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	C₅×#430	1	2	yes	—
361	C₄	C₄×C₅×#41	1	2	yes	—
362	C₄	C₅×#525	1	2	yes	—
363	C₂	—	2	2	no	—
364	C₂	—	2	2	no	—
365	C₂	—	4	1	no	—
366	C₂	C₅×#2296	1	1	yes	characteristic
367	C₂	C₂×C₅×#430	1	1	yes	characteristic
368	C₂	C₂×C₅×#430	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂²×C₅	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₅	C₂×Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1950	C₂	semidirect
6. C₅×#1778	C₂	semidirect
31. #21371	C₅	direct (N × H)
73. #1950	C₂×C₅	semidirect
75. #1778	C₂×C₅	semidirect
339. C₅	#21371	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×#2920	2
C₂×C₅×#432	2
C₂×C₄×C₅×M₁₆	2
C₅×#1950	2
C₅×#1855	2
C₅×#1778	2
#21371	5

Subgroups — C5×#21371 #11944091

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21371 #11944091