Subgroups — C₅×#17820 #11940540

Order 1280.

662 conjugacy classes of subgroups.

The subgroup lattice has 392 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	C₅×#2920	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#423	C₂	1	1	yes	maximal, characteristic
4	C₅×#1574	C₂	1	4	yes	maximal, complemented
5	C₅×#1571	C₂	1	2	yes	maximal, complemented
6	C₅×#1570	C₂	1	2	yes	maximal, complemented
7	C₅×#1569	C₂	1	4	yes	maximal, complemented
8	C₂²×C₅×M₁₆	—	2	1	no	—
9	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
10	C₅×#432	—	2	1	no	—
11	C₅×#432	C₄	1	2	yes	—
12	C₅×#432	C₄	1	2	yes	—
13	C₅×#432	C₂²	1	2	yes	—
14	C₅×#431	—	2	1	no	—
15	C₅×#431	C₂²	1	2	yes	—
16	C₅×#431	C₂²	1	2	yes	—
17	C₅×#431	C₂²	1	2	yes	—
18	C₅×#423	—	2	1	no	—
19	C₅×#423	—	2	1	no	—
20	C₅×#423	C₄	1	2	yes	—
21	C₅×#423	C₂²	1	2	yes	—
22	C₅×#423	C₂²	1	1	yes	characteristic
23	C₅×#423	C₂²	1	1	yes	characteristic
24	C₅×#423	C₂²	1	2	yes	—
25	C₂×C₅×C₄⋊C₈	—	2	1	no	—
26	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
27	C₅×#407	—	2	1	no	—
28	C₅×#407	C₄	1	2	yes	—
29	C₄×C₅×M₁₆	—	2	1	no	—
30	C₄×C₅×M₁₆	C₂²	1	2	yes	—
31	C₅×#335	C₂²	1	8	yes	complemented
32	C₅×#334	C₂²	1	8	yes	complemented
33	#17820	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
34	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₅	Q₈	1	1	yes	characteristic
37	C₂×C₅×M₁₆	—	2	1	no	—
38	C₂×C₅×M₁₆	—	2	1	no	—
39	C₂×C₅×M₁₆	—	2	2	no	—
40	C₂×C₅×M₁₆	—	2	2	no	—
41	C₂×C₅×M₁₆	—	4	4	no	—
42	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	—
43	C₂²×C₅×C₈	—	2	2	no	—
44	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₅	C₂×C₄	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	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₅	Q₈	1	1	yes	characteristic
51	C₂×C₄²×C₅	Q₈	1	1	yes	characteristic
52	C₂×C₄²×C₅	Q₈	1	1	yes	characteristic
53	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
54	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
55	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
56	C₅×C₄⋊C₈	—	2	2	no	—
57	C₅×C₄⋊C₈	—	2	2	no	—
58	C₅×C₄⋊C₈	—	2	2	no	—
59	C₅×C₄⋊C₈	—	2	1	no	—
60	C₅×C₄⋊C₈	—	2	1	no	—
61	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
62	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
63	C₅×C₄⋊C₈	C₂³	1	2	yes	—
64	C₅×C₄⋊C₈	C₂³	1	4	yes	—
65	C₅×C₄⋊C₈	C₂³	1	2	yes	—
66	C₅×C₂²⋊C₈	—	2	2	no	—
67	C₅×C₂²⋊C₈	—	2	2	no	—
68	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	—
69	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	—
70	C₅×#97	—	2	2	no	—
71	C₅×#97	C₂×C₄	1	4	yes	—
72	C₄×C₅×C₈	—	2	2	no	—
73	C₄×C₅×C₈	C₂³	1	4	yes	—
74	#2920	C₂×C₅	1	1	yes	characteristic
75	#2920	C₂×C₅	1	1	yes	characteristic
76	C₂×#423	C₂×C₅	1	1	yes	characteristic
77	#1574	C₂×C₅	1	4	yes	complemented
78	#1571	C₂×C₅	1	2	yes	complemented
79	#1570	C₂×C₅	1	2	yes	complemented
80	#1569	C₂×C₅	1	4	yes	complemented
81	C₂⁴×C₅	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₅	—	2	2	no	—
83	C₂²×C₄×C₅	—	2	2	no	—
84	C₂²×C₄×C₅	—	4	2	no	—
85	C₂²×C₄×C₅	—	4	2	no	—
86	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
102	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
103	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
104	C₅×M₁₆	—	4	4	no	—
105	C₅×M₁₆	—	4	4	no	—
106	C₅×M₁₆	—	4	4	no	—
107	C₅×M₁₆	—	4	2	no	—
108	C₅×M₁₆	—	4	2	no	—
109	C₂×C₅×C₈	—	2	4	no	—
110	C₂×C₅×C₈	—	2	2	no	—
111	C₂×C₅×C₈	—	2	2	no	—
112	C₂×C₅×C₈	—	4	4	no	—
113	C₂×C₅×C₈	C₂²×C₄	1	8	yes	—
114	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
115	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
116	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
117	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
118	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
119	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
120	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
127	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
128	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
129	C₄²×C₅	C₂⁴	1	1	yes	characteristic
130	C₂²×M₁₆	—	2	1	no	—
131	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
132	#432	—	2	1	no	—
133	#432	C₄×C₅	1	2	yes	—
134	#432	C₄×C₅	1	2	yes	—
135	#432	C₂²×C₅	1	2	yes	—
136	#431	—	2	1	no	—
137	#431	C₂²×C₅	1	2	yes	—
138	#431	C₂²×C₅	1	2	yes	—
139	#431	C₂²×C₅	1	2	yes	—
140	#423	—	2	1	no	—
141	#423	—	2	1	no	—
142	#423	C₄×C₅	1	2	yes	—
143	#423	C₂²×C₅	1	2	yes	—
144	#423	C₂²×C₅	1	1	yes	characteristic
145	#423	C₂²×C₅	1	1	yes	characteristic
146	#423	C₂²×C₅	1	2	yes	—
147	C₂×C₄⋊C₈	—	2	1	no	—
148	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
149	#407	—	2	1	no	—
150	#407	C₄×C₅	1	2	yes	—
151	C₄×M₁₆	—	2	1	no	—
152	C₄×M₁₆	C₂²×C₅	1	2	yes	—
153	#335	C₂²×C₅	1	8	yes	complemented
154	#334	C₂²×C₅	1	8	yes	complemented
155	C₂³×C₅	—	2	2	no	—
156	C₂³×C₅	—	4	1	no	—
157	C₂³×C₅	—	4	1	no	—
158	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₅	—	2	2	no	—
162	C₂×C₄×C₅	—	2	2	no	—
163	C₂×C₄×C₅	—	2	2	no	—
164	C₂×C₄×C₅	—	2	2	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	1	no	—
169	C₂×C₄×C₅	—	2	2	no	—
170	C₂×C₄×C₅	—	2	2	no	—
171	C₂×C₄×C₅	—	2	2	no	—
172	C₂×C₄×C₅	—	2	2	no	—
173	C₂×C₄×C₅	—	2	2	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	—	4	1	no	—
178	C₂×C₄×C₅	—	4	1	no	—
179	C₂×C₄×C₅	—	4	1	no	—
180	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
190	C₂×C₄×C₅	#137	1	2	yes	—
191	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
192	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
194	C₅×C₈	—	2	8	no	—
195	C₅×C₈	—	4	4	no	—
196	C₅×C₈	—	4	2	no	—
197	C₅×C₈	—	4	2	no	—
198	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
199	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
200	C₂³×C₄	C₅×Q₈	1	1	yes	characteristic
201	C₂×M₁₆	—	2	2	no	—
202	C₂×M₁₆	—	2	2	no	—
203	C₂×M₁₆	—	2	1	no	—
204	C₂×M₁₆	—	2	1	no	—
205	C₂×M₁₆	—	4	4	no	—
206	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	—
207	C₂²×C₈	—	2	2	no	—
208	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
209	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
210	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
211	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
212	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
213	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
214	C₂×C₄²	C₅×Q₈	1	1	yes	characteristic
215	C₂×C₄²	C₅×Q₈	1	1	yes	characteristic
216	C₂×C₄²	C₅×Q₈	1	1	yes	characteristic
217	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
218	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
219	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
220	C₄⋊C₈	—	2	2	no	—
221	C₄⋊C₈	—	2	2	no	—
222	C₄⋊C₈	—	2	2	no	—
223	C₄⋊C₈	—	2	1	no	—
224	C₄⋊C₈	—	2	1	no	—
225	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
226	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
227	C₄⋊C₈	C₂³×C₅	1	2	yes	—
228	C₄⋊C₈	C₂³×C₅	1	4	yes	—
229	C₄⋊C₈	C₂³×C₅	1	2	yes	—
230	C₂²⋊C₈	—	2	2	no	—
231	C₂²⋊C₈	—	2	2	no	—
232	C₂²⋊C₈	C₂×C₄×C₅	1	4	yes	—
233	C₂²⋊C₈	C₂×C₄×C₅	1	4	yes	—
234	#97	—	2	2	no	—
235	#97	C₂×C₄×C₅	1	4	yes	—
236	C₄×C₈	—	2	2	no	—
237	C₄×C₈	C₂³×C₅	1	4	yes	—
238	C₂²×C₅	—	2	1	no	—
239	C₂²×C₅	—	2	1	no	—
240	C₂²×C₅	—	2	1	no	—
241	C₂²×C₅	—	2	1	no	—
242	C₂²×C₅	—	2	1	no	—
243	C₂²×C₅	—	2	1	no	—
244	C₂²×C₅	—	2	1	no	—
245	C₂²×C₅	—	2	1	no	—
246	C₂²×C₅	—	4	4	no	—
247	C₂²×C₅	#428	1	2	yes	—
248	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
249	C₄×C₅	—	2	1	no	—
250	C₄×C₅	—	2	1	no	—
251	C₄×C₅	—	2	1	no	—
252	C₄×C₅	—	2	1	no	—
253	C₄×C₅	—	2	1	no	—
254	C₄×C₅	—	2	1	no	—
255	C₄×C₅	—	2	1	no	—
256	C₄×C₅	—	2	1	no	—
257	C₄×C₅	#428	1	2	yes	—
258	C₄×C₅	#430	1	2	yes	—
259	C₄×C₅	#568	1	2	yes	—
260	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
261	C₄×C₅	C₂×#137	1	1	yes	characteristic
262	C₂⁴	C₅×C₄⋊C₄	1	1	yes	characteristic
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	4	2	no	—
266	C₂²×C₄	—	4	2	no	—
267	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
268	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
269	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
270	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
271	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
272	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
273	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
274	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
275	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
276	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
277	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
278	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
279	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
280	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
283	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
284	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
285	M₁₆	—	4	4	no	—
286	M₁₆	—	4	4	no	—
287	M₁₆	—	4	4	no	—
288	M₁₆	—	4	2	no	—
289	M₁₆	—	4	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	4	no	—
293	C₂×C₈	—	4	4	no	—
294	C₂×C₈	C₂²×C₄×C₅	1	8	yes	—
295	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
296	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
297	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
298	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
299	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
300	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
301	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
302	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
303	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
304	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
305	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
306	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
307	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
308	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
309	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
310	C₄²	C₂⁴×C₅	1	1	yes	characteristic
311	C₂×C₅	—	2	2	no	—
312	C₂×C₅	—	4	1	no	—
313	C₂×C₅	—	4	1	no	—
314	C₂×C₅	#2905	1	1	yes	characteristic
315	C₂×C₅	C₂×#428	1	1	yes	characteristic
316	C₂×C₅	C₂×#430	1	1	yes	characteristic
317	C₂³	—	2	2	no	—
318	C₂³	—	4	1	no	—
319	C₂³	—	4	1	no	—
320	C₂³	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
321	C₂³	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
322	C₂³	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
343	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
344	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
345	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
346	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
347	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
348	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
349	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
350	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
351	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
352	C₂×C₄	C₅×#137	1	2	yes	—
353	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
354	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
355	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
356	C₈	—	2	8	no	—
357	C₈	—	4	4	no	—
358	C₈	—	4	2	no	—
359	C₈	—	4	2	no	—
360	C₅	#17820	1	1	yes	characteristic, direct product factor, Sylow
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	4	4	no	—
370	C₂²	C₅×#428	1	2	yes	—
371	C₂²	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	C₅×#428	1	2	yes	—
381	C₄	C₅×#430	1	2	yes	—
382	C₄	C₅×#568	1	2	yes	—
383	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
384	C₄	C₂×C₅×#137	1	1	yes	characteristic
385	C₂	—	2	2	no	—
386	C₂	—	4	1	no	—
387	C₂	—	4	1	no	—
388	C₂	C₅×#2905	1	1	yes	characteristic
389	C₂	C₂×C₅×#428	1	1	yes	characteristic
390	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	C₄²	C₂⁴×C₅
socle	C₂²×C₅	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₅	C₄⋊C₄
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×#1574	C₂	semidirect
5. C₅×#1571	C₂	semidirect
6. C₅×#1570	C₂	semidirect
7. C₅×#1569	C₂	semidirect
31. C₅×#335	C₂²	semidirect
32. C₅×#334	C₂²	semidirect
33. #17820	C₅	direct (N × H)
77. #1574	C₂×C₅	semidirect
78. #1571	C₂×C₅	semidirect
79. #1570	C₂×C₅	semidirect
80. #1569	C₂×C₅	semidirect
153. #335	C₂²×C₅	semidirect
154. #334	C₂²×C₅	semidirect
360. C₅	#17820	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×#423	2
C₅×#1574	2
C₅×#1571	2
C₅×#1570	2
C₅×#1569	2
#17820	5

Subgroups — C5×#17820 #11940540

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17820 #11940540