Subgroups — C₅×#11328 #11934048

Order 1280.

958 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#107	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#389	C₂	1	2	yes	maximal
3	C₂×C₅×#340	C₂	1	2	yes	maximal
4	C₂×C₅×#340	C₂	1	1	yes	maximal, characteristic
5	C₂×C₅×#336	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
7	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
8	C₂²×C₅×C₄⋊C₄	—	2	2	no	—
9	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
10	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
11	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₂×C₅×#107	—	2	2	no	—
13	C₂×C₅×#107	—	2	4	no	—
14	C₅×#389	—	2	4	no	—
15	C₅×#389	—	2	4	no	—
16	C₂×C₅×#95	—	2	2	no	—
17	C₅×#340	—	2	4	no	—
18	C₅×#340	C₄	1	4	yes	complemented
19	C₅×#336	—	2	2	no	—
20	#11328	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂³×C₄×C₅	—	2	2	no	—
22	C₂³×C₄×C₅	—	2	2	no	—
23	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
24	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
25	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
26	C₂²×C₅×C₈	—	2	2	no	—
27	C₂²×C₅×C₈	—	2	2	no	—
28	C₂²×C₅×C₈	—	2	1	no	—
29	C₂²×C₅×C₈	—	2	2	no	—
30	C₂²×C₅×C₈	—	2	2	no	—
31	C₂²×C₅×C₈	—	2	1	no	—
32	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
33	C₂²×C₅×C₈	D₄	1	2	yes	—
34	C₂²×C₅×C₈	Q₈	1	2	yes	—
35	C₂²×C₅×C₈	Q₈	1	2	yes	—
36	C₂×C₅×C₄⋊C₄	—	2	2	no	—
37	C₂×C₅×C₄⋊C₄	—	2	2	no	—
38	C₂×C₅×C₄⋊C₄	—	2	2	no	—
39	C₂×C₅×C₄⋊C₄	—	2	2	no	—
40	C₂×C₅×C₄⋊C₄	—	2	2	no	—
41	C₂×C₅×C₄⋊C₄	—	2	2	no	—
42	C₂×C₅×C₄⋊C₄	—	2	2	no	—
43	C₂×C₅×C₄⋊C₄	—	2	8	no	—
44	C₂×C₅×C₄⋊C₄	—	2	2	no	—
45	C₂×C₅×C₄⋊C₄	—	4	4	no	—
46	C₂×C₅×C₄⋊C₄	—	4	4	no	—
47	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
48	C₂×C₅×C₄⋊C₄	D₄	1	4	yes	—
49	C₂×C₅×C₄⋊C₄	D₄	1	4	yes	—
50	C₂×C₅×C₄⋊C₄	Q₈	1	4	yes	—
51	C₂×C₄²×C₅	—	2	2	no	—
52	C₂×C₄²×C₅	—	2	2	no	—
53	C₂×C₄²×C₅	—	2	1	no	—
54	C₂×C₄²×C₅	—	2	1	no	—
55	C₅×#107	—	2	8	no	—
56	C₅×#95	—	2	8	no	—
57	C₂²×#107	C₂×C₅	1	1	yes	characteristic
58	C₂×#389	C₂×C₅	1	2	yes	—
59	C₂×#340	C₂×C₅	1	2	yes	—
60	C₂×#340	C₂×C₅	1	1	yes	characteristic
61	C₂×#336	C₂×C₅	1	1	yes	characteristic
62	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₅	—	2	4	no	—
64	C₂²×C₄×C₅	—	2	2	no	—
65	C₂²×C₄×C₅	—	2	2	no	—
66	C₂²×C₄×C₅	—	2	4	no	—
67	C₂²×C₄×C₅	—	2	1	no	—
68	C₂²×C₄×C₅	—	2	1	no	—
69	C₂²×C₄×C₅	—	2	4	no	—
70	C₂²×C₄×C₅	—	2	1	no	—
71	C₂²×C₄×C₅	—	2	1	no	—
72	C₂²×C₄×C₅	—	2	2	no	—
73	C₂²×C₄×C₅	—	2	2	no	—
74	C₂²×C₄×C₅	—	2	4	no	—
75	C₂²×C₄×C₅	—	4	2	no	—
76	C₂²×C₄×C₅	—	4	2	no	—
77	C₂²×C₄×C₅	—	4	2	no	—
78	C₂²×C₄×C₅	—	4	2	no	—
79	C₂²×C₄×C₅	—	4	2	no	—
80	C₂²×C₄×C₅	—	4	2	no	—
81	C₂²×C₄×C₅	—	4	2	no	—
82	C₂²×C₄×C₅	—	4	2	no	—
83	C₂²×C₄×C₅	—	4	2	no	—
84	C₂²×C₄×C₅	—	4	2	no	—
85	C₂²×C₄×C₅	D₈	1	2	yes	—
86	C₂²×C₄×C₅	Q₁₆	1	2	yes	—
87	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
92	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
93	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
94	C₂²×C₄×C₅	#41	1	2	yes	—
95	C₂²×C₄×C₅	#41	1	1	yes	characteristic
96	C₂²×C₄×C₅	#41	1	1	yes	characteristic
97	C₂×C₅×C₈	—	2	4	no	—
98	C₂×C₅×C₈	—	2	2	no	—
99	C₂×C₅×C₈	—	2	4	no	—
100	C₂×C₅×C₈	—	2	2	no	—
101	C₂×C₅×C₈	—	2	4	no	—
102	C₂×C₅×C₈	—	2	2	no	—
103	C₂×C₅×C₈	—	4	1	no	—
104	C₂×C₅×C₈	—	4	2	no	—
105	C₂×C₅×C₈	—	4	1	no	—
106	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	complemented
107	C₅×C₄⋊C₄	—	2	4	no	—
108	C₅×C₄⋊C₄	—	2	4	no	—
109	C₅×C₄⋊C₄	—	2	4	no	—
110	C₅×C₄⋊C₄	—	2	4	no	—
111	C₅×C₄⋊C₄	—	2	4	no	—
112	C₅×C₄⋊C₄	—	4	16	no	—
113	C₅×C₄⋊C₄	—	4	2	no	—
114	C₅×C₄⋊C₄	—	4	2	no	—
115	C₅×C₄⋊C₄	C₄⋊C₄	1	8	yes	complemented
116	C₄²×C₅	—	4	1	no	—
117	C₄²×C₅	—	4	2	no	—
118	C₄²×C₅	—	4	1	no	—
119	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
120	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
121	C₂²×C₄⋊C₄	—	2	2	no	—
122	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
123	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
124	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
125	C₂×#107	—	2	2	no	—
126	C₂×#107	—	2	4	no	—
127	#389	—	2	4	no	—
128	#389	—	2	4	no	—
129	C₂×#95	—	2	2	no	—
130	#340	—	2	4	no	—
131	#340	C₄×C₅	1	4	yes	complemented
132	#336	—	2	2	no	—
133	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
134	C₂³×C₅	#120	1	2	yes	—
135	C₂³×C₅	#121	1	1	yes	characteristic
136	C₂³×C₅	C₂²⋊Q₈	1	2	yes	—
137	C₂³×C₅	C₄⋊Q₈	1	1	yes	characteristic
138	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
139	C₂³×C₅	C₂×Q₁₆	1	1	yes	characteristic
140	C₂³×C₅	#135	1	1	yes	characteristic
141	C₂³×C₅	#135	1	1	yes	characteristic
142	C₂³×C₅	AGL(1,ℤ/8)	1	2	yes	—
143	C₂³×C₅	#137	1	2	yes	—
144	C₂×C₄×C₅	—	2	8	no	—
145	C₂×C₄×C₅	—	2	4	no	—
146	C₂×C₄×C₅	—	2	4	no	—
147	C₂×C₄×C₅	—	2	2	no	—
148	C₂×C₄×C₅	—	2	2	no	—
149	C₂×C₄×C₅	—	4	1	no	—
150	C₂×C₄×C₅	—	4	1	no	—
151	C₂×C₄×C₅	—	4	4	no	—
152	C₂×C₄×C₅	—	4	4	no	—
153	C₂×C₄×C₅	—	4	4	no	—
154	C₂×C₄×C₅	—	4	2	no	—
155	C₂×C₄×C₅	—	4	2	no	—
156	C₂×C₄×C₅	—	4	4	no	—
157	C₂×C₄×C₅	—	4	1	no	—
158	C₂×C₄×C₅	—	4	1	no	—
159	C₂×C₄×C₅	—	4	4	no	—
160	C₂×C₄×C₅	—	4	4	no	—
161	C₂×C₄×C₅	—	4	4	no	—
162	C₂×C₄×C₅	—	4	4	no	—
163	C₂×C₄×C₅	—	4	4	no	—
164	C₂×C₄×C₅	—	8	2	no	—
165	C₂×C₄×C₅	—	8	2	no	—
166	C₂×C₄×C₅	—	8	2	no	—
167	C₂×C₄×C₅	—	8	2	no	—
168	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
170	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
171	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
172	C₂×C₄×C₅	#120	1	1	yes	characteristic
173	C₂×C₄×C₅	#121	1	2	yes	—
174	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
175	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
176	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
177	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
178	C₂×C₄×C₅	#123	1	1	yes	characteristic
179	C₂×C₄×C₅	#123	1	2	yes	—
180	C₂×C₄×C₅	#125	1	2	yes	—
181	C₂×C₄×C₅	#125	1	1	yes	characteristic
182	C₂×C₄×C₅	#127	1	1	yes	characteristic
183	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
184	C₂×C₄×C₅	C₄⋊Q₈	1	2	yes	—
185	C₂×C₄×C₅	C₄⋊Q₈	1	2	yes	—
186	C₅×C₈	—	2	4	no	—
187	C₅×C₈	—	4	2	no	—
188	C₂³×C₄	—	2	2	no	—
189	C₂³×C₄	—	2	2	no	—
190	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
191	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
192	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
193	C₂²×C₈	—	2	2	no	—
194	C₂²×C₈	—	2	2	no	—
195	C₂²×C₈	—	2	1	no	—
196	C₂²×C₈	—	2	2	no	—
197	C₂²×C₈	—	2	2	no	—
198	C₂²×C₈	—	2	1	no	—
199	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
200	C₂²×C₈	C₅×D₄	1	2	yes	—
201	C₂²×C₈	C₅×Q₈	1	2	yes	—
202	C₂²×C₈	C₅×Q₈	1	2	yes	—
203	C₂×C₄⋊C₄	—	2	2	no	—
204	C₂×C₄⋊C₄	—	2	2	no	—
205	C₂×C₄⋊C₄	—	2	2	no	—
206	C₂×C₄⋊C₄	—	2	2	no	—
207	C₂×C₄⋊C₄	—	2	2	no	—
208	C₂×C₄⋊C₄	—	2	2	no	—
209	C₂×C₄⋊C₄	—	2	2	no	—
210	C₂×C₄⋊C₄	—	2	8	no	—
211	C₂×C₄⋊C₄	—	2	2	no	—
212	C₂×C₄⋊C₄	—	4	4	no	—
213	C₂×C₄⋊C₄	—	4	4	no	—
214	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
215	C₂×C₄⋊C₄	C₅×D₄	1	4	yes	—
216	C₂×C₄⋊C₄	C₅×D₄	1	4	yes	—
217	C₂×C₄⋊C₄	C₅×Q₈	1	4	yes	—
218	C₂×C₄²	—	2	1	no	—
219	C₂×C₄²	—	2	2	no	—
220	C₂×C₄²	—	2	2	no	—
221	C₂×C₄²	—	2	1	no	—
222	#107	—	2	8	no	—
223	#95	—	2	8	no	—
224	C₂²×C₅	#385	1	2	yes	—
225	C₂²×C₅	#389	1	1	yes	characteristic
226	C₂²×C₅	#392	1	1	yes	characteristic
227	C₂²×C₅	#395	1	2	yes	—
228	C₂²×C₅	#398	1	1	yes	characteristic
229	C₂²×C₅	C₄×D₈	1	1	yes	characteristic
230	C₂²×C₅	C₄×Q₁₆	1	1	yes	characteristic
231	C₂²×C₅	#440	1	2	yes	—
232	C₂²×C₅	#447	1	2	yes	—
233	C₂²×C₅	#449	1	2	yes	—
234	C₂²×C₅	#451	1	2	yes	—
235	C₂²×C₅	#452	1	2	yes	—
236	C₂²×C₅	#466	1	1	yes	characteristic
237	C₂²×C₅	#467	1	1	yes	characteristic
238	C₂²×C₅	#469	1	1	yes	characteristic
239	C₂²×C₅	#470	1	1	yes	characteristic
240	C₂²×C₅	#474	1	2	yes	—
241	C₂²×C₅	#477	1	2	yes	—
242	C₂²×C₅	#478	1	2	yes	—
243	C₂²×C₅	#479	1	2	yes	—
244	C₂²×C₅	#499	1	1	yes	characteristic
245	C₂²×C₅	#500	1	1	yes	characteristic
246	C₂²×C₅	#501	1	2	yes	—
247	C₄×C₅	—	4	8	no	—
248	C₄×C₅	—	4	2	no	—
249	C₄×C₅	—	4	2	no	—
250	C₄×C₅	—	8	4	no	—
251	C₄×C₅	#384	1	1	yes	characteristic
252	C₄×C₅	#385	1	1	yes	characteristic
253	C₄×C₅	#389	1	2	yes	—
254	C₄×C₅	#395	1	1	yes	characteristic
255	C₄×C₅	#398	1	2	yes	—
256	C₄×C₅	#399	1	1	yes	characteristic
257	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	1	no	—
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	2	1	no	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	4	2	no	—
271	C₂²×C₄	—	4	2	no	—
272	C₂²×C₄	—	4	2	no	—
273	C₂²×C₄	—	4	2	no	—
274	C₂²×C₄	—	4	2	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	—	4	2	no	—
280	C₂²×C₄	C₅×D₈	1	2	yes	—
281	C₂²×C₄	C₅×Q₁₆	1	2	yes	—
282	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
283	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
284	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
285	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
286	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
288	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
289	C₂²×C₄	C₅×#41	1	2	yes	—
290	C₂²×C₄	C₅×#41	1	1	yes	characteristic
291	C₂²×C₄	C₅×#41	1	1	yes	characteristic
292	C₂×C₈	—	2	4	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	4	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	4	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	4	1	no	—
299	C₂×C₈	—	4	2	no	—
300	C₂×C₈	—	4	1	no	—
301	C₂×C₈	C₅×C₄⋊C₄	1	4	yes	complemented
302	C₄⋊C₄	—	2	4	no	—
303	C₄⋊C₄	—	2	4	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	—	2	4	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	4	16	no	—
308	C₄⋊C₄	—	4	2	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₄⋊C₄	C₅×C₄⋊C₄	1	8	yes	complemented
311	C₄²	—	4	1	no	—
312	C₄²	—	4	2	no	—
313	C₄²	—	4	1	no	—
314	C₂×C₅	#1444	1	1	yes	characteristic
315	C₂×C₅	#1862	1	2	yes	—
316	C₂×C₅	#1863	1	2	yes	—
317	C₂×C₅	#1942	1	1	yes	characteristic
318	C₂×C₅	#1944	1	1	yes	characteristic
319	C₂×C₅	#1999	1	1	yes	characteristic
320	C₂×C₅	#2001	1	1	yes	characteristic
321	C₂×C₅	#2057	1	2	yes	—
322	C₂×C₅	#2059	1	2	yes	—
323	C₂×C₅	#2086	1	1	yes	characteristic
324	C₂×C₅	#2087	1	1	yes	characteristic
325	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
326	C₂³	C₅×#120	1	2	yes	—
327	C₂³	C₅×#121	1	1	yes	characteristic
328	C₂³	C₅×C₂²⋊Q₈	1	2	yes	—
329	C₂³	C₅×C₄⋊Q₈	1	1	yes	characteristic
330	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
331	C₂³	C₂×C₅×Q₁₆	1	1	yes	characteristic
332	C₂³	C₅×#135	1	1	yes	characteristic
333	C₂³	C₅×#135	1	1	yes	characteristic
334	C₂³	C₅×AGL(1,ℤ/8)	1	2	yes	—
335	C₂³	C₅×#137	1	2	yes	—
336	C₂×C₄	—	2	8	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	4	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	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
361	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
362	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
363	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
364	C₂×C₄	C₅×#120	1	1	yes	characteristic
365	C₂×C₄	C₅×#121	1	2	yes	—
366	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
367	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
368	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
369	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
370	C₂×C₄	C₅×#123	1	1	yes	characteristic
371	C₂×C₄	C₅×#123	1	2	yes	—
372	C₂×C₄	C₅×#125	1	2	yes	—
373	C₂×C₄	C₅×#125	1	1	yes	characteristic
374	C₂×C₄	C₅×#127	1	1	yes	characteristic
375	C₂×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
376	C₂×C₄	C₅×C₄⋊Q₈	1	2	yes	—
377	C₂×C₄	C₅×C₄⋊Q₈	1	2	yes	—
378	C₈	—	2	4	no	—
379	C₈	—	4	2	no	—
380	C₅	#11328	1	1	yes	characteristic, direct product factor, Sylow
381	C₂²	C₅×#385	1	2	yes	—
382	C₂²	C₅×#389	1	1	yes	characteristic
383	C₂²	C₅×#392	1	1	yes	characteristic
384	C₂²	C₅×#395	1	2	yes	—
385	C₂²	C₅×#398	1	1	yes	characteristic
386	C₂²	C₄×C₅×D₈	1	1	yes	characteristic
387	C₂²	C₄×C₅×Q₁₆	1	1	yes	characteristic
388	C₂²	C₅×#440	1	2	yes	—
389	C₂²	C₅×#447	1	2	yes	—
390	C₂²	C₅×#449	1	2	yes	—
391	C₂²	C₅×#451	1	2	yes	—
392	C₂²	C₅×#452	1	2	yes	—
393	C₂²	C₅×#466	1	1	yes	characteristic
394	C₂²	C₅×#467	1	1	yes	characteristic
395	C₂²	C₅×#469	1	1	yes	characteristic
396	C₂²	C₅×#470	1	1	yes	characteristic
397	C₂²	C₅×#474	1	2	yes	—
398	C₂²	C₅×#477	1	2	yes	—
399	C₂²	C₅×#478	1	2	yes	—
400	C₂²	C₅×#479	1	2	yes	—
401	C₂²	C₅×#499	1	1	yes	characteristic
402	C₂²	C₅×#500	1	1	yes	characteristic
403	C₂²	C₅×#501	1	2	yes	—
404	C₄	—	4	8	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	2	no	—
407	C₄	—	8	4	no	—
408	C₄	C₅×#384	1	1	yes	characteristic
409	C₄	C₅×#385	1	1	yes	characteristic
410	C₄	C₅×#389	1	2	yes	—
411	C₄	C₅×#395	1	1	yes	characteristic
412	C₄	C₅×#398	1	2	yes	—
413	C₄	C₅×#399	1	1	yes	characteristic
414	C₂	C₅×#1444	1	1	yes	characteristic
415	C₂	C₅×#1862	1	2	yes	—
416	C₂	C₅×#1863	1	2	yes	—
417	C₂	C₅×#1942	1	1	yes	characteristic
418	C₂	C₅×#1944	1	1	yes	characteristic
419	C₂	C₅×#1999	1	1	yes	characteristic
420	C₂	C₅×#2001	1	1	yes	characteristic
421	C₂	C₅×#2057	1	2	yes	—
422	C₂	C₅×#2059	1	2	yes	—
423	C₂	C₅×#2086	1	1	yes	characteristic
424	C₂	C₅×#2087	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
18. C₅×#340	C₄	semidirect
20. #11328	C₅	direct (N × H)
106. C₂×C₅×C₈	C₄⋊C₄	semidirect
115. C₅×C₄⋊C₄	C₄⋊C₄	semidirect
131. #340	C₄×C₅	semidirect
301. C₂×C₈	C₅×C₄⋊C₄	semidirect
310. C₄⋊C₄	C₅×C₄⋊C₄	semidirect
380. C₅	#11328	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×#107	2
C₂×C₅×#389	2
C₂×C₅×#340	2
C₂×C₅×#336	2
#11328	5

Subgroups — C5×#11328 #11934048

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#11328 #11934048