Subgroups — C₅×#10860 #11933580

Order 1280.

782 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	C₂²×C₅×#108	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#427	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₅×#97	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#339	C₂	1	2	yes	maximal
5	C₅×#1729	C₂	1	2	yes	maximal
6	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
7	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
8	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
9	C₂×C₅×#117	C₂²	1	2	yes	—
10	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
11	C₂×C₅×#108	—	2	2	no	—
12	C₂×C₅×#108	—	2	2	no	—
13	C₂×C₅×#108	C₄	1	4	yes	complemented
14	C₅×#427	—	2	2	no	—
15	C₅×#427	—	2	2	no	—
16	C₂×C₅×#107	C₄	1	2	yes	complemented
17	C₂×C₅×#106	C₄	1	2	yes	complemented
18	C₂×C₅×#97	—	2	2	no	—
19	C₂×C₅×#97	—	2	2	no	—
20	C₂×C₅×#97	C₄	1	4	yes	complemented
21	C₅×#339	—	2	4	no	—
22	C₅×#336	—	2	4	no	—
23	#10860	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₂³×C₄×C₅	—	2	1	no	—
25	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
26	C₂×C₅×M₁₆	—	2	2	no	—
27	C₂×C₅×M₁₆	—	2	2	no	—
28	C₂×C₅×M₁₆	—	2	2	no	—
29	C₂×C₅×M₁₆	—	2	2	no	—
30	C₂×C₅×M₁₆	—	2	2	no	—
31	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	—
32	C₂²×C₅×C₈	—	2	1	no	—
33	C₂²×C₅×C₈	—	2	1	no	—
34	C₂²×C₅×C₈	—	2	1	no	—
35	C₂²×C₅×C₈	—	2	1	no	—
36	C₂²×C₅×C₈	—	2	2	no	—
37	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
38	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
39	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
42	C₂²×C₅×C₈	D₄	1	2	yes	—
43	C₂²×C₅×C₈	D₄	1	2	yes	—
44	C₂²×C₅×C₈	D₄	1	2	yes	—
45	C₂²×C₅×C₈	D₄	1	2	yes	—
46	C₂²×C₅×C₈	Q₈	1	2	yes	—
47	C₂²×C₅×C₈	Q₈	1	2	yes	—
48	C₅×#117	—	2	2	no	—
49	C₅×#117	—	2	2	no	—
50	C₅×#117	—	2	2	no	—
51	C₅×#117	—	2	2	no	—
52	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
53	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
54	C₂×C₄²×C₅	—	2	1	no	—
55	C₂×C₄²×C₅	—	2	1	no	—
56	C₂×C₄²×C₅	—	2	1	no	—
57	C₂×C₄²×C₅	—	2	2	no	—
58	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
59	C₂×C₄²×C₅	D₄	1	2	yes	—
60	C₂×C₄²×C₅	Q₈	1	2	yes	—
61	C₅×#108	—	2	8	no	—
62	C₅×#107	—	2	4	no	—
63	C₅×#106	—	2	4	no	—
64	C₅×#97	—	2	8	no	—
65	C₂²×#108	C₂×C₅	1	1	yes	characteristic
66	C₂×#427	C₂×C₅	1	1	yes	characteristic
67	C₂²×#97	C₂×C₅	1	1	yes	characteristic
68	C₂×#339	C₂×C₅	1	2	yes	—
69	#1729	C₂×C₅	1	2	yes	—
70	C₂⁴×C₅	#41	1	1	yes	characteristic
71	C₂²×C₄×C₅	—	2	2	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	4	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	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
85	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
86	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
87	C₂²×C₄×C₅	#41	1	1	yes	characteristic
88	C₂²×C₄×C₅	#41	1	1	yes	characteristic
89	C₂²×C₄×C₅	#41	1	1	yes	characteristic
90	C₅×M₁₆	—	2	4	no	—
91	C₅×M₁₆	—	2	4	no	—
92	C₅×M₁₆	—	4	2	no	—
93	C₅×M₁₆	—	4	2	no	—
94	C₂×C₅×C₈	—	2	2	no	—
95	C₂×C₅×C₈	—	2	2	no	—
96	C₂×C₅×C₈	—	2	2	no	—
97	C₂×C₅×C₈	—	2	2	no	—
98	C₂×C₅×C₈	—	2	2	no	—
99	C₂×C₅×C₈	—	2	2	no	—
100	C₂×C₅×C₈	—	2	4	no	—
101	C₂×C₅×C₈	—	4	2	no	—
102	C₂×C₅×C₈	—	4	2	no	—
103	C₂×C₅×C₈	C₄²	1	2	yes	—
104	C₂×C₅×C₈	C₄²	1	2	yes	—
105	C₂×C₅×C₈	C₂²⋊C₄	1	4	yes	—
106	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
107	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
108	C₂×C₅×C₈	C₂²⋊C₄	1	4	yes	—
109	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
110	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
111	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
112	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
113	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
114	C₅×C₄⋊C₄	—	2	4	no	—
115	C₅×C₄⋊C₄	—	2	4	no	—
116	C₅×C₂²⋊C₄	—	4	2	no	—
117	C₅×C₂²⋊C₄	—	4	2	no	—
118	C₄²×C₅	—	2	2	no	—
119	C₄²×C₅	—	2	2	no	—
120	C₄²×C₅	—	2	2	no	—
121	C₄²×C₅	—	4	2	no	—
122	C₄²×C₅	—	4	2	no	—
123	C₄²×C₅	C₄⋊C₄	1	4	yes	—
124	C₂²×M₁₆	C₂²×C₅	1	2	yes	—
125	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
126	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
127	C₂×#117	C₂²×C₅	1	2	yes	—
128	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
129	C₂×#108	—	2	2	no	—
130	C₂×#108	—	2	2	no	—
131	C₂×#108	C₄×C₅	1	4	yes	complemented
132	#427	—	2	2	no	—
133	#427	—	2	2	no	—
134	C₂×#107	C₄×C₅	1	2	yes	complemented
135	C₂×#106	C₄×C₅	1	2	yes	complemented
136	C₂×#97	—	2	2	no	—
137	C₂×#97	—	2	2	no	—
138	C₂×#97	C₄×C₅	1	4	yes	complemented
139	#339	—	2	4	no	—
140	#336	—	2	4	no	—
141	C₂³×C₅	—	2	4	no	—
142	C₂³×C₅	#117	1	1	yes	characteristic
143	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
144	C₂³×C₅	C₄×Q₈	1	1	yes	characteristic
145	C₂³×C₅	#121	1	1	yes	characteristic
146	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
147	C₂³×C₅	#124	1	1	yes	characteristic
148	C₂³×C₅	#125	1	1	yes	characteristic
149	C₂×C₄×C₅	—	2	4	no	—
150	C₂×C₄×C₅	—	4	4	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	8	no	—
155	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
156	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₅	#117	1	1	yes	characteristic
165	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
166	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
169	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
170	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
171	C₂×C₄×C₅	#121	1	1	yes	characteristic
172	C₂×C₄×C₅	#121	1	1	yes	characteristic
173	C₂×C₄×C₅	#121	1	1	yes	characteristic
174	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
175	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
176	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
177	C₂×C₄×C₅	#124	1	1	yes	characteristic
178	C₂×C₄×C₅	#125	1	1	yes	characteristic
179	C₂×C₄×C₅	#127	1	1	yes	characteristic
180	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
181	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
182	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
183	C₅×C₈	—	2	4	no	—
184	C₅×C₈	—	4	4	no	—
185	C₅×C₈	#95	1	4	yes	—
186	C₅×C₈	#95	1	4	yes	—
187	C₂³×C₄	—	2	1	no	—
188	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
189	C₂×M₁₆	—	2	2	no	—
190	C₂×M₁₆	—	2	2	no	—
191	C₂×M₁₆	—	2	2	no	—
192	C₂×M₁₆	—	2	2	no	—
193	C₂×M₁₆	—	2	2	no	—
194	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	—
195	C₂²×C₈	—	2	1	no	—
196	C₂²×C₈	—	2	1	no	—
197	C₂²×C₈	—	2	1	no	—
198	C₂²×C₈	—	2	1	no	—
199	C₂²×C₈	—	2	2	no	—
200	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
201	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
202	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
203	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
204	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
205	C₂²×C₈	C₅×D₄	1	2	yes	—
206	C₂²×C₈	C₅×D₄	1	2	yes	—
207	C₂²×C₈	C₅×D₄	1	2	yes	—
208	C₂²×C₈	C₅×D₄	1	2	yes	—
209	C₂²×C₈	C₅×Q₈	1	2	yes	—
210	C₂²×C₈	C₅×Q₈	1	2	yes	—
211	#117	—	2	2	no	—
212	#117	—	2	2	no	—
213	#117	—	2	2	no	—
214	#117	—	2	2	no	—
215	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
216	C₂×C₂²⋊C₄	—	2	2	no	—
217	C₂×C₄²	—	2	1	no	—
218	C₂×C₄²	—	2	1	no	—
219	C₂×C₄²	—	2	1	no	—
220	C₂×C₄²	—	2	2	no	—
221	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
222	C₂×C₄²	C₅×D₄	1	2	yes	—
223	C₂×C₄²	C₅×Q₈	1	2	yes	—
224	#108	—	2	8	no	—
225	#107	—	2	4	no	—
226	#106	—	2	4	no	—
227	#97	—	2	8	no	—
228	C₂²×C₅	—	2	2	no	—
229	C₂²×C₅	—	2	2	no	—
230	C₂²×C₅	—	2	2	no	—
231	C₂²×C₅	—	2	2	no	—
232	C₂²×C₅	—	2	2	no	—
233	C₂²×C₅	—	2	2	no	—
234	C₂²×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
235	C₂²×C₅	#380	1	1	yes	characteristic
236	C₂²×C₅	#382	1	1	yes	characteristic
237	C₂²×C₅	#389	1	1	yes	characteristic
238	C₂²×C₅	#389	1	1	yes	characteristic
239	C₂²×C₅	#390	1	1	yes	characteristic
240	C₂²×C₅	#391	1	1	yes	characteristic
241	C₂²×C₅	#444	1	4	yes	—
242	C₄×C₅	—	4	4	no	—
243	C₄×C₅	—	8	4	no	—
244	C₄×C₅	C₂×#95	1	1	yes	characteristic
245	C₄×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
246	C₄×C₅	#380	1	1	yes	characteristic
247	C₄×C₅	#384	1	1	yes	characteristic
248	C₄×C₅	#389	1	1	yes	characteristic
249	C₄×C₅	#389	1	1	yes	characteristic
250	C₄×C₅	#390	1	1	yes	characteristic
251	C₄×C₅	#391	1	1	yes	characteristic
252	C₂⁴	C₅×#41	1	1	yes	characteristic
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	4	4	no	—
258	C₂²×C₄	C₂²×C₄×C₅	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×D₄	1	1	yes	characteristic
264	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
265	C₂²×C₄	C₂×C₅×D₄	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	C₂×C₅×Q₈	1	1	yes	characteristic
269	C₂²×C₄	C₅×#41	1	1	yes	characteristic
270	C₂²×C₄	C₅×#41	1	1	yes	characteristic
271	C₂²×C₄	C₅×#41	1	1	yes	characteristic
272	M₁₆	—	2	4	no	—
273	M₁₆	—	2	4	no	—
274	M₁₆	—	4	2	no	—
275	M₁₆	—	4	2	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	4	no	—
283	C₂×C₈	—	4	2	no	—
284	C₂×C₈	—	4	2	no	—
285	C₂×C₈	C₄²×C₅	1	2	yes	—
286	C₂×C₈	C₄²×C₅	1	2	yes	—
287	C₂×C₈	C₅×C₂²⋊C₄	1	4	yes	—
288	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
289	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
290	C₂×C₈	C₅×C₂²⋊C₄	1	4	yes	—
291	C₂×C₈	C₅×C₄⋊C₄	1	4	yes	—
292	C₂×C₈	C₅×C₄⋊C₄	1	4	yes	—
293	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
294	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
295	C₂×C₈	C₅×C₄⋊C₄	1	4	yes	—
296	C₄⋊C₄	—	2	4	no	—
297	C₄⋊C₄	—	2	4	no	—
298	C₂²⋊C₄	—	4	2	no	—
299	C₂²⋊C₄	—	4	2	no	—
300	C₄²	—	2	2	no	—
301	C₄²	—	2	2	no	—
302	C₄²	—	2	2	no	—
303	C₄²	—	4	2	no	—
304	C₄²	—	4	2	no	—
305	C₄²	C₅×C₄⋊C₄	1	4	yes	—
306	C₂×C₅	—	2	1	no	—
307	C₂×C₅	—	2	1	no	—
308	C₂×C₅	—	2	1	no	—
309	C₂×C₅	—	2	1	no	—
310	C₂×C₅	C₄⋊#95	1	1	yes	characteristic
311	C₂×C₅	#1773	1	2	yes	—
312	C₂×C₅	#1946	1	2	yes	—
313	C₂×C₅	#1975	1	2	yes	—
314	C₂³	—	2	4	no	—
315	C₂³	C₅×#117	1	1	yes	characteristic
316	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
317	C₂³	C₄×C₅×Q₈	1	1	yes	characteristic
318	C₂³	C₅×#121	1	1	yes	characteristic
319	C₂³	C₅×C₂²⋊Q₈	1	1	yes	characteristic
320	C₂³	C₅×#124	1	1	yes	characteristic
321	C₂³	C₅×#125	1	1	yes	characteristic
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	—	4	8	no	—
328	C₂×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
329	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
330	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
331	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
332	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
333	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
334	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
335	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
336	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
337	C₂×C₄	C₅×#117	1	1	yes	characteristic
338	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
339	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
340	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
341	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
342	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
343	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
344	C₂×C₄	C₅×#121	1	1	yes	characteristic
345	C₂×C₄	C₅×#121	1	1	yes	characteristic
346	C₂×C₄	C₅×#121	1	1	yes	characteristic
347	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
348	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
349	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
350	C₂×C₄	C₅×#124	1	1	yes	characteristic
351	C₂×C₄	C₅×#125	1	1	yes	characteristic
352	C₂×C₄	C₅×#127	1	1	yes	characteristic
353	C₂×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
354	C₂×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
355	C₂×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
356	C₈	—	2	4	no	—
357	C₈	—	4	4	no	—
358	C₈	C₅×#95	1	4	yes	—
359	C₈	C₅×#95	1	4	yes	—
360	C₅	#10860	1	1	yes	characteristic, direct product factor, Sylow
361	C₂²	—	2	2	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	C₄×C₅×C₄⋊C₄	1	1	yes	characteristic
368	C₂²	C₅×#380	1	1	yes	characteristic
369	C₂²	C₅×#382	1	1	yes	characteristic
370	C₂²	C₅×#389	1	1	yes	characteristic
371	C₂²	C₅×#389	1	1	yes	characteristic
372	C₂²	C₅×#390	1	1	yes	characteristic
373	C₂²	C₅×#391	1	1	yes	characteristic
374	C₂²	C₅×#444	1	4	yes	—
375	C₄	—	4	4	no	—
376	C₄	—	8	4	no	—
377	C₄	C₂×C₅×#95	1	1	yes	characteristic
378	C₄	C₄×C₅×C₄⋊C₄	1	1	yes	characteristic
379	C₄	C₅×#380	1	1	yes	characteristic
380	C₄	C₅×#384	1	1	yes	characteristic
381	C₄	C₅×#389	1	1	yes	characteristic
382	C₄	C₅×#389	1	1	yes	characteristic
383	C₄	C₅×#390	1	1	yes	characteristic
384	C₄	C₅×#391	1	1	yes	characteristic
385	C₂	—	2	1	no	—
386	C₂	—	2	1	no	—
387	C₂	—	2	1	no	—
388	C₂	—	2	1	no	—
389	C₂	C₅×C₄⋊#95	1	1	yes	characteristic
390	C₂	C₅×#1773	1	2	yes	—
391	C₂	C₅×#1946	1	2	yes	—
392	C₂	C₅×#1975	1	2	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	C₄×D₄
prime radical	C₂⁴×C₅	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂³×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
13. C₂×C₅×#108	C₄	semidirect
16. C₂×C₅×#107	C₄	semidirect
17. C₂×C₅×#106	C₄	semidirect
20. C₂×C₅×#97	C₄	semidirect
23. #10860	C₅	direct (N × H)
131. C₂×#108	C₄×C₅	semidirect
134. C₂×#107	C₄×C₅	semidirect
135. C₂×#106	C₄×C₅	semidirect
138. C₂×#97	C₄×C₅	semidirect
360. C₅	#10860	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×#108	2
C₂×C₅×#427	2
C₂²×C₅×#97	2
C₂×C₅×#339	2
C₅×#1729	2
#10860	5

Subgroups — C5×#10860 #11933580

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#10860 #11933580