Subgroups — C₅×#7984 #11930704

Order 1280.

650 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#432	C₂	1	1	yes	maximal, characteristic
2	C₅×#2285	C₂	1	1	yes	maximal, characteristic
3	C₅×#2283	C₂	1	1	yes	maximal, characteristic
4	C₅×#1289	C₂	1	4	yes	maximal
5	C₂×C₅×#117	—	2	1	no	—
6	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
7	C₅×#432	—	2	1	no	—
8	C₅×#432	—	2	1	no	—
9	C₅×#432	—	2	1	no	—
10	C₅×#432	—	2	1	no	—
11	C₂×C₅×C₄⋊C₈	C₄	1	2	yes	complemented
12	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
13	C₂×C₅×#97	C₄	1	2	yes	complemented
14	C₅×#384	—	2	1	no	—
15	C₅×#383	C₄	1	2	yes	complemented
16	C₅×#382	—	2	1	no	—
17	C₅×#382	C₄	1	2	yes	complemented
18	C₅×#381	—	2	1	no	—
19	C₅×#380	—	2	1	no	—
20	C₅×#380	C₂²	1	2	yes	—
21	C₅×#380	C₂²	1	2	yes	—
22	C₄×C₅×C₄⋊C₄	—	2	1	no	—
23	C₄×C₅×C₄⋊C₄	—	2	1	no	—
24	C₄×C₅×C₄⋊C₄	C₄	1	2	yes	complemented
25	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
26	C₅×#376	C₄	1	2	yes	complemented
27	#7984	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
31	C₂²×C₅×C₈	C₂×C₄	1	4	yes	—
32	C₅×#117	—	4	4	no	—
33	C₂×C₅×C₄⋊C₄	—	2	2	no	—
34	C₂×C₅×C₄⋊C₄	—	2	2	no	—
35	C₂×C₅×C₄⋊C₄	—	2	2	no	—
36	C₂×C₅×C₄⋊C₄	—	2	2	no	—
37	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
38	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
39	C₂×C₄²×C₅	—	2	2	no	—
40	C₂×C₄²×C₅	—	2	2	no	—
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	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	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₅	Q₈	1	1	yes	characteristic
52	C₂×C₄²×C₅	Q₈	1	1	yes	characteristic
53	C₅×C₄⋊C₈	—	2	2	no	—
54	C₅×C₄⋊C₈	—	2	2	no	—
55	C₅×C₂²⋊C₈	—	2	2	no	—
56	C₅×C₂²⋊C₈	—	2	2	no	—
57	C₅×#97	—	2	2	no	—
58	C₅×#97	—	2	2	no	—
59	C₅×#95	—	2	2	no	—
60	C₅×#95	—	2	2	no	—
61	C₅×#95	—	2	2	no	—
62	C₅×#95	—	2	2	no	—
63	C₅×#95	C₂×C₄	1	4	yes	—
64	C₅×#95	C₂×C₄	1	4	yes	—
65	C₂×#432	C₂×C₅	1	1	yes	characteristic
66	#2285	C₂×C₅	1	1	yes	characteristic
67	#2283	C₂×C₅	1	1	yes	characteristic
68	#1289	C₂×C₅	1	4	yes	—
69	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₅	—	2	2	no	—
71	C₂²×C₄×C₅	—	2	2	no	—
72	C₂²×C₄×C₅	—	2	4	no	—
73	C₂²×C₄×C₅	—	2	4	no	—
74	C₂²×C₄×C₅	—	4	2	no	—
75	C₂²×C₄×C₅	—	4	2	no	—
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	1	yes	characteristic
79	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₅	C₂²⋊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	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
94	C₂×C₅×C₈	—	2	4	no	—
95	C₂×C₅×C₈	—	4	4	no	—
96	C₅×C₄⋊C₄	—	4	4	no	—
97	C₅×C₄⋊C₄	—	4	4	no	—
98	C₅×C₄⋊C₄	—	4	4	no	—
99	C₅×C₄⋊C₄	—	4	4	no	—
100	C₅×C₂²⋊C₄	—	4	2	no	—
101	C₅×C₂²⋊C₄	—	4	4	no	—
102	C₅×C₂²⋊C₄	—	4	2	no	—
103	C₄²×C₅	—	4	4	no	—
104	C₄²×C₅	—	4	4	no	—
105	C₄²×C₅	C₄²	1	1	yes	characteristic
106	C₄²×C₅	C₄²	1	1	yes	characteristic
107	C₄²×C₅	C₄²	1	1	yes	characteristic
108	C₄²×C₅	C₄²	1	1	yes	characteristic
109	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
110	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
111	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
112	C₄²×C₅	C₂²⋊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	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	C₄⋊C₄	1	1	yes	characteristic
121	C₂×#117	—	2	1	no	—
122	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
123	#432	—	2	1	no	—
124	#432	—	2	1	no	—
125	#432	—	2	1	no	—
126	#432	—	2	1	no	—
127	C₂×C₄⋊C₈	C₄×C₅	1	2	yes	complemented
128	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
129	C₂×#97	C₄×C₅	1	2	yes	complemented
130	#384	—	2	1	no	—
131	#383	C₄×C₅	1	2	yes	complemented
132	#382	—	2	1	no	—
133	#382	C₄×C₅	1	2	yes	complemented
134	#381	—	2	1	no	—
135	#380	—	2	1	no	—
136	#380	C₂²×C₅	1	2	yes	—
137	#380	C₂²×C₅	1	2	yes	—
138	C₄×C₄⋊C₄	—	2	1	no	—
139	C₄×C₄⋊C₄	—	2	1	no	—
140	C₄×C₄⋊C₄	C₄×C₅	1	2	yes	complemented
141	C₄×C₂²⋊C₄	—	2	1	no	—
142	#376	C₄×C₅	1	2	yes	complemented
143	C₂³×C₅	—	4	1	no	—
144	C₂³×C₅	—	4	1	no	—
145	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂³×C₅	AGL(1,ℤ/8)	1	2	yes	—
149	C₂³×C₅	#137	1	2	yes	—
150	C₂×C₄×C₅	—	2	2	no	—
151	C₂×C₄×C₅	—	2	2	no	—
152	C₂×C₄×C₅	—	2	1	no	—
153	C₂×C₄×C₅	—	2	1	no	—
154	C₂×C₄×C₅	—	2	1	no	—
155	C₂×C₄×C₅	—	2	1	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	—	2	2	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	—	4	4	no	—
171	C₂×C₄×C₅	—	4	4	no	—
172	C₂×C₄×C₅	—	4	4	no	—
173	C₂×C₄×C₅	—	4	4	no	—
174	C₂×C₄×C₅	—	4	4	no	—
175	C₂×C₄×C₅	—	4	4	no	—
176	C₂×C₄×C₅	#95	1	1	yes	characteristic
177	C₂×C₄×C₅	#95	1	1	yes	characteristic
178	C₂×C₄×C₅	#95	1	1	yes	characteristic
179	C₂×C₄×C₅	#95	1	1	yes	characteristic
180	C₂×C₄×C₅	#95	1	1	yes	characteristic
181	C₂×C₄×C₅	#95	1	1	yes	characteristic
182	C₂×C₄×C₅	#95	1	1	yes	characteristic
183	C₂×C₄×C₅	#95	1	1	yes	characteristic
184	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
185	C₂×C₄×C₅	C₂×C₂²⋊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	C₅×C₈	—	4	4	no	—
189	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
190	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
191	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
192	C₂²×C₈	C₂×C₄×C₅	1	4	yes	—
193	#117	—	4	4	no	—
194	C₂×C₄⋊C₄	—	2	2	no	—
195	C₂×C₄⋊C₄	—	2	2	no	—
196	C₂×C₄⋊C₄	—	2	2	no	—
197	C₂×C₄⋊C₄	—	2	2	no	—
198	C₂×C₂²⋊C₄	—	2	2	no	—
199	C₂×C₂²⋊C₄	—	2	2	no	—
200	C₂×C₄²	—	2	2	no	—
201	C₂×C₄²	—	2	2	no	—
202	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
203	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
204	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
205	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
206	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
207	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
208	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
209	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
210	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
211	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
212	C₂×C₄²	C₅×Q₈	1	1	yes	characteristic
213	C₂×C₄²	C₅×Q₈	1	1	yes	characteristic
214	C₄⋊C₈	—	2	2	no	—
215	C₄⋊C₈	—	2	2	no	—
216	C₂²⋊C₈	—	2	2	no	—
217	C₂²⋊C₈	—	2	2	no	—
218	#97	—	2	2	no	—
219	#97	—	2	2	no	—
220	#95	—	2	2	no	—
221	#95	—	2	2	no	—
222	#95	—	2	2	no	—
223	#95	—	2	2	no	—
224	#95	C₂×C₄×C₅	1	4	yes	—
225	#95	C₂×C₄×C₅	1	4	yes	—
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	—	2	1	no	—
232	C₂²×C₅	—	4	2	no	—
233	C₂²×C₅	—	4	2	no	—
234	C₂²×C₅	C₂×#95	1	1	yes	characteristic
235	C₂²×C₅	#417	1	2	yes	—
236	C₂²×C₅	#418	1	1	yes	characteristic
237	C₂²×C₅	#419	1	1	yes	characteristic
238	C₂²×C₅	#428	1	2	yes	—
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	—	2	1	no	—
245	C₄×C₅	—	2	1	no	—
246	C₄×C₅	—	2	1	no	—
247	C₄×C₅	—	2	1	no	—
248	C₄×C₅	—	2	1	no	—
249	C₄×C₅	—	8	4	no	—
250	C₄×C₅	—	8	4	no	—
251	C₄×C₅	H(3,ℤ/4)	1	2	yes	—
252	C₄×C₅	#410	1	2	yes	—
253	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	4	2	no	—
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
261	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
262	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
263	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
264	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
265	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
266	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
267	C₂²×C₄	C₅×C₂²⋊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	C₂²×C₄×C₅	1	1	yes	characteristic
273	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
274	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
275	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
276	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
278	C₂×C₈	—	2	4	no	—
279	C₂×C₈	—	4	4	no	—
280	C₄⋊C₄	—	4	4	no	—
281	C₄⋊C₄	—	4	4	no	—
282	C₄⋊C₄	—	4	4	no	—
283	C₄⋊C₄	—	4	4	no	—
284	C₂²⋊C₄	—	4	4	no	—
285	C₂²⋊C₄	—	4	2	no	—
286	C₂²⋊C₄	—	4	2	no	—
287	C₄²	—	4	4	no	—
288	C₄²	—	4	4	no	—
289	C₄²	C₄²×C₅	1	1	yes	characteristic
290	C₄²	C₄²×C₅	1	1	yes	characteristic
291	C₄²	C₄²×C₅	1	1	yes	characteristic
292	C₄²	C₄²×C₅	1	1	yes	characteristic
293	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
294	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
295	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
296	C₄²	C₅×C₂²⋊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	C₅×C₄⋊C₄	1	1	yes	characteristic
302	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
303	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
304	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
305	C₂×C₅	—	2	1	no	—
306	C₂×C₅	—	2	2	no	—
307	C₂×C₅	—	2	1	no	—
308	C₂×C₅	—	2	2	no	—
309	C₂×C₅	C₂×H(3,ℤ/4)	1	1	yes	characteristic
310	C₂×C₅	#1736	1	1	yes	characteristic
311	C₂×C₅	#1740	1	1	yes	characteristic
312	C₂³	—	4	1	no	—
313	C₂³	—	4	1	no	—
314	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
315	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
316	C₂³	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
317	C₂³	C₅×AGL(1,ℤ/8)	1	2	yes	—
318	C₂³	C₅×#137	1	2	yes	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	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	2	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	C₅×#95	1	1	yes	characteristic
346	C₂×C₄	C₅×#95	1	1	yes	characteristic
347	C₂×C₄	C₅×#95	1	1	yes	characteristic
348	C₂×C₄	C₅×#95	1	1	yes	characteristic
349	C₂×C₄	C₅×#95	1	1	yes	characteristic
350	C₂×C₄	C₅×#95	1	1	yes	characteristic
351	C₂×C₄	C₅×#95	1	1	yes	characteristic
352	C₂×C₄	C₅×#95	1	1	yes	characteristic
353	C₂×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
354	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
355	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
356	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
357	C₈	—	4	4	no	—
358	C₅	#7984	1	1	yes	characteristic, direct product factor, Sylow
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	4	2	no	—
366	C₂²	—	4	2	no	—
367	C₂²	C₂×C₅×#95	1	1	yes	characteristic
368	C₂²	C₅×#417	1	2	yes	—
369	C₂²	C₅×#418	1	1	yes	characteristic
370	C₂²	C₅×#419	1	1	yes	characteristic
371	C₂²	C₅×#428	1	2	yes	—
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	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	8	4	no	—
383	C₄	—	8	4	no	—
384	C₄	C₅×H(3,ℤ/4)	1	2	yes	—
385	C₄	C₅×#410	1	2	yes	—
386	C₂	—	2	1	no	—
387	C₂	—	2	2	no	—
388	C₂	—	2	1	no	—
389	C₂	—	2	2	no	—
390	C₂	C₂×C₅×H(3,ℤ/4)	1	1	yes	characteristic
391	C₂	C₅×#1736	1	1	yes	characteristic
392	C₂	C₅×#1740	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#95
commutator	C₂×C₄	C₂×C₄²×C₅
Frattini, cosocle	C₂³×C₄	C₂³×C₅
prime radical	C₂⁴×C₅	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
11. C₂×C₅×C₄⋊C₈	C₄	semidirect
13. C₂×C₅×#97	C₄	semidirect
15. C₅×#383	C₄	semidirect
17. C₅×#382	C₄	semidirect
24. C₄×C₅×C₄⋊C₄	C₄	semidirect
26. C₅×#376	C₄	semidirect
27. #7984	C₅	direct (N × H)
127. C₂×C₄⋊C₈	C₄×C₅	semidirect
129. C₂×#97	C₄×C₅	semidirect
131. #383	C₄×C₅	semidirect
133. #382	C₄×C₅	semidirect
140. C₄×C₄⋊C₄	C₄×C₅	semidirect
142. #376	C₄×C₅	semidirect
358. C₅	#7984	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#432	2
C₅×#2285	2
C₅×#2283	2
C₅×#1289	2
#7984	5

Subgroups — C5×#7984 #11930704

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#7984 #11930704