Subgroups — C₅×#8095 #11930815

Order 1280.

674 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#431	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#423	C₂	1	1	yes	maximal, characteristic
3	C₅×#2285	C₂	1	1	yes	maximal, characteristic
4	C₅×#1303	C₂	1	4	yes	maximal, complemented
5	C₂²×C₅×M₁₆	—	2	1	no	—
6	C₂×C₅×#117	—	2	1	no	—
7	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
8	C₅×#431	—	2	1	no	—
9	C₅×#431	—	2	1	no	—
10	C₅×#431	C₄	1	2	yes	complemented
11	C₅×#431	C₂²	1	2	yes	—
12	C₅×#423	—	2	1	no	—
13	C₅×#423	—	2	1	no	—
14	C₅×#423	C₄	1	2	yes	complemented
15	C₅×#423	C₂²	1	2	yes	—
16	C₂×C₅×C₄⋊C₈	—	2	1	no	—
17	C₂×C₅×C₄⋊C₈	C₄	1	2	yes	complemented
18	C₂×C₅×C₄⋊C₈	C₄	1	2	yes	complemented
19	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
20	C₂×C₄×C₅×C₈	—	2	1	no	—
21	C₅×#384	—	2	1	no	—
22	C₅×#382	C₄	1	2	yes	—
23	C₅×#380	—	2	1	no	—
24	C₅×#380	C₄	1	2	yes	—
25	C₄×C₅×C₄⋊C₄	—	2	1	no	—
26	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
27	#8095	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
31	C₂×C₅×M₁₆	—	2	2	no	—
32	C₂×C₅×M₁₆	—	2	2	no	—
33	C₂×C₅×M₁₆	—	4	2	no	—
34	C₂×C₅×M₁₆	—	4	2	no	—
35	C₂²×C₅×C₈	—	2	2	no	—
36	C₂²×C₅×C₈	—	2	2	no	—
37	C₅×#117	—	4	2	no	—
38	C₅×#117	—	4	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×C₂²⋊C₄	—	2	2	no	—
43	C₂×C₄²×C₅	—	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	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₅	C₂×C₄	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	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₅	Q₈	1	1	yes	characteristic
54	C₂×C₄²×C₅	Q₈	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	2	no	—
60	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
61	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
62	C₅×C₂²⋊C₈	—	2	2	no	—
63	C₅×C₂²⋊C₈	—	2	2	no	—
64	C₄×C₅×C₈	—	2	2	no	—
65	C₄×C₅×C₈	—	2	2	no	—
66	C₅×#95	—	2	2	no	—
67	C₅×#95	C₂×C₄	1	4	yes	—
68	C₂×#431	C₂×C₅	1	1	yes	characteristic
69	C₂×#423	C₂×C₅	1	1	yes	characteristic
70	#2285	C₂×C₅	1	1	yes	characteristic
71	#1303	C₂×C₅	1	4	yes	complemented
72	C₂⁴×C₅	C₂²⋊C₄	1	1	yes	characteristic
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	C₄²	1	1	yes	characteristic
77	C₂²×C₄×C₅	C₄²	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	C₂²⋊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	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	D₈	1	2	yes	—
92	C₂²×C₄×C₅	SD₁₆	1	2	yes	—
93	C₂²×C₄×C₅	SD₁₆	1	2	yes	—
94	C₂²×C₄×C₅	Q₁₆	1	2	yes	—
95	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
98	C₅×M₁₆	—	4	4	no	—
99	C₅×M₁₆	—	4	2	no	—
100	C₅×M₁₆	—	4	2	no	—
101	C₂×C₅×C₈	—	2	4	no	—
102	C₂×C₅×C₈	—	2	4	no	—
103	C₂×C₅×C₈	—	4	4	no	—
104	C₂×C₅×C₈	—	4	4	no	—
105	C₅×C₄⋊C₄	—	4	4	no	—
106	C₅×C₄⋊C₄	—	4	4	no	—
107	C₅×C₄⋊C₄	—	4	4	no	—
108	C₅×C₂²⋊C₄	—	4	4	no	—
109	C₄²×C₅	—	4	2	no	—
110	C₄²×C₅	—	4	2	no	—
111	C₄²×C₅	C₄²	1	1	yes	characteristic
112	C₄²×C₅	C₄²	1	1	yes	characteristic
113	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
114	C₄²×C₅	C₂²⋊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	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	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
122	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
123	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
127	C₂²×M₁₆	—	2	1	no	—
128	C₂×#117	—	2	1	no	—
129	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
130	#431	—	2	1	no	—
131	#431	—	2	1	no	—
132	#431	C₄×C₅	1	2	yes	complemented
133	#431	C₂²×C₅	1	2	yes	—
134	#423	—	2	1	no	—
135	#423	—	2	1	no	—
136	#423	C₄×C₅	1	2	yes	complemented
137	#423	C₂²×C₅	1	2	yes	—
138	C₂×C₄⋊C₈	—	2	1	no	—
139	C₂×C₄⋊C₈	C₄×C₅	1	2	yes	complemented
140	C₂×C₄⋊C₈	C₄×C₅	1	2	yes	complemented
141	C₂×C₂²⋊C₈	—	2	1	no	—
142	C₂×C₄×C₈	—	2	1	no	—
143	#384	—	2	1	no	—
144	#382	C₄×C₅	1	2	yes	—
145	#380	—	2	1	no	—
146	#380	C₄×C₅	1	2	yes	—
147	C₄×C₄⋊C₄	—	2	1	no	—
148	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
149	C₂³×C₅	—	4	1	no	—
150	C₂³×C₅	—	4	1	no	—
151	C₂³×C₅	#95	1	1	yes	characteristic
152	C₂³×C₅	#95	1	1	yes	characteristic
153	C₂³×C₅	#102	1	2	yes	—
154	C₂³×C₅	#103	1	2	yes	—
155	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
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	—	4	1	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	4	no	—
169	C₂×C₄×C₅	—	4	4	no	—
170	C₂×C₄×C₅	—	4	4	no	—
171	C₂×C₄×C₅	#95	1	1	yes	characteristic
172	C₂×C₄×C₅	#95	1	1	yes	characteristic
173	C₂×C₄×C₅	#95	1	1	yes	characteristic
174	C₂×C₄×C₅	#95	1	1	yes	characteristic
175	C₂×C₄×C₅	#95	1	1	yes	characteristic
176	C₂×C₄×C₅	#95	1	1	yes	characteristic
177	C₂×C₄×C₅	#102	1	2	yes	—
178	C₂×C₄×C₅	#102	1	2	yes	—
179	C₂×C₄×C₅	#102	1	2	yes	—
180	C₂×C₄×C₅	#103	1	2	yes	—
181	C₂×C₄×C₅	#103	1	2	yes	—
182	C₂×C₄×C₅	#103	1	2	yes	—
183	C₂×C₄×C₅	#106	1	2	yes	—
184	C₂×C₄×C₅	#106	1	2	yes	—
185	C₂×C₄×C₅	#107	1	2	yes	—
186	C₂×C₄×C₅	#107	1	2	yes	—
187	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
188	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
192	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
193	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
194	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
195	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
196	C₂×C₄×C₅	C₂×Q₁₆	1	1	yes	characteristic
197	C₅×C₈	—	4	4	no	—
198	C₅×C₈	—	4	4	no	—
199	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
200	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
201	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
202	C₂×M₁₆	—	2	2	no	—
203	C₂×M₁₆	—	2	2	no	—
204	C₂×M₁₆	—	4	2	no	—
205	C₂×M₁₆	—	4	2	no	—
206	C₂²×C₈	—	2	2	no	—
207	C₂²×C₈	—	2	2	no	—
208	#117	—	4	2	no	—
209	#117	—	4	2	no	—
210	C₂×C₄⋊C₄	—	2	2	no	—
211	C₂×C₄⋊C₄	—	2	2	no	—
212	C₂×C₄⋊C₄	—	2	2	no	—
213	C₂×C₂²⋊C₄	—	2	2	no	—
214	C₂×C₄²	—	2	2	no	—
215	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
216	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
217	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
218	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
219	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
220	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
221	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
222	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
223	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
224	C₂×C₄²	C₅×Q₈	1	1	yes	characteristic
225	C₂×C₄²	C₅×Q₈	1	1	yes	characteristic
226	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
227	C₄⋊C₈	—	2	2	no	—
228	C₄⋊C₈	—	2	2	no	—
229	C₄⋊C₈	—	2	2	no	—
230	C₄⋊C₈	—	2	2	no	—
231	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
232	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
233	C₂²⋊C₈	—	2	2	no	—
234	C₂²⋊C₈	—	2	2	no	—
235	C₄×C₈	—	2	2	no	—
236	C₄×C₈	—	2	2	no	—
237	#95	—	2	2	no	—
238	#95	C₂×C₄×C₅	1	4	yes	—
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	—	4	2	no	—
246	C₂²×C₅	—	4	2	no	—
247	C₂²×C₅	#340	1	2	yes	—
248	C₂²×C₅	#340	1	2	yes	—
249	C₂²×C₅	C₂×#95	1	1	yes	characteristic
250	C₂²×C₅	C₂×#102	1	1	yes	characteristic
251	C₂²×C₅	C₂×#103	1	1	yes	characteristic
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	—	2	1	no	—
258	C₄×C₅	—	8	4	no	—
259	C₄×C₅	#340	1	2	yes	—
260	C₄×C₅	#340	1	2	yes	—
261	C₄×C₅	#344	1	2	yes	—
262	C₄×C₅	C₂×#102	1	1	yes	characteristic
263	C₄×C₅	C₂×#103	1	1	yes	characteristic
264	C₄×C₅	#421	1	2	yes	—
265	C₄×C₅	C₂×#106	1	1	yes	characteristic
266	C₄×C₅	C₂×#107	1	1	yes	characteristic
267	C₂⁴	C₅×C₂²⋊C₄	1	1	yes	characteristic
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	4	2	no	—
270	C₂²×C₄	—	4	2	no	—
271	C₂²×C₄	C₄²×C₅	1	1	yes	characteristic
272	C₂²×C₄	C₄²×C₅	1	1	yes	characteristic
273	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
274	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
275	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
276	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
277	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
278	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
279	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
280	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
281	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
282	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
283	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
284	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
285	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
286	C₂²×C₄	C₅×D₈	1	2	yes	—
287	C₂²×C₄	C₅×SD₁₆	1	2	yes	—
288	C₂²×C₄	C₅×SD₁₆	1	2	yes	—
289	C₂²×C₄	C₅×Q₁₆	1	2	yes	—
290	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
291	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
292	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
293	M₁₆	—	4	2	no	—
294	M₁₆	—	4	2	no	—
295	M₁₆	—	4	4	no	—
296	C₂×C₈	—	2	4	no	—
297	C₂×C₈	—	2	4	no	—
298	C₂×C₈	—	4	4	no	—
299	C₂×C₈	—	4	4	no	—
300	C₄⋊C₄	—	4	4	no	—
301	C₄⋊C₄	—	4	4	no	—
302	C₄⋊C₄	—	4	4	no	—
303	C₂²⋊C₄	—	4	4	no	—
304	C₄²	—	4	2	no	—
305	C₄²	—	4	2	no	—
306	C₄²	C₄²×C₅	1	1	yes	characteristic
307	C₄²	C₄²×C₅	1	1	yes	characteristic
308	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
309	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
310	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
311	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
312	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
313	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
314	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
315	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
316	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
317	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
318	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
319	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
320	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
321	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
322	C₂×C₅	—	2	1	no	—
323	C₂×C₅	—	2	2	no	—
324	C₂×C₅	—	2	2	no	—
325	C₂×C₅	—	2	1	no	—
326	C₂×C₅	#1733	1	1	yes	characteristic
327	C₂×C₅	C₂×#340	1	1	yes	characteristic
328	C₂×C₅	C₂×#344	1	1	yes	characteristic
329	C₂³	—	4	1	no	—
330	C₂³	—	4	1	no	—
331	C₂³	C₅×#95	1	1	yes	characteristic
332	C₂³	C₅×#95	1	1	yes	characteristic
333	C₂³	C₅×#102	1	2	yes	—
334	C₂³	C₅×#103	1	2	yes	—
335	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	C₅×#95	1	1	yes	characteristic
352	C₂×C₄	C₅×#95	1	1	yes	characteristic
353	C₂×C₄	C₅×#95	1	1	yes	characteristic
354	C₂×C₄	C₅×#95	1	1	yes	characteristic
355	C₂×C₄	C₅×#95	1	1	yes	characteristic
356	C₂×C₄	C₅×#95	1	1	yes	characteristic
357	C₂×C₄	C₅×#102	1	2	yes	—
358	C₂×C₄	C₅×#102	1	2	yes	—
359	C₂×C₄	C₅×#102	1	2	yes	—
360	C₂×C₄	C₅×#103	1	2	yes	—
361	C₂×C₄	C₅×#103	1	2	yes	—
362	C₂×C₄	C₅×#103	1	2	yes	—
363	C₂×C₄	C₅×#106	1	2	yes	—
364	C₂×C₄	C₅×#106	1	2	yes	—
365	C₂×C₄	C₅×#107	1	2	yes	—
366	C₂×C₄	C₅×#107	1	2	yes	—
367	C₂×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
368	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
369	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
370	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
371	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
372	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
373	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
374	C₂×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
375	C₂×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
376	C₂×C₄	C₂×C₅×Q₁₆	1	1	yes	characteristic
377	C₈	—	4	4	no	—
378	C₈	—	4	4	no	—
379	C₅	#8095	1	1	yes	characteristic, direct product factor, Sylow
380	C₂²	—	2	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	C₅×#340	1	2	yes	—
389	C₂²	C₅×#340	1	2	yes	—
390	C₂²	C₂×C₅×#95	1	1	yes	characteristic
391	C₂²	C₂×C₅×#102	1	1	yes	characteristic
392	C₂²	C₂×C₅×#103	1	1	yes	characteristic
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	8	4	no	—
400	C₄	C₅×#340	1	2	yes	—
401	C₄	C₅×#340	1	2	yes	—
402	C₄	C₅×#344	1	2	yes	—
403	C₄	C₂×C₅×#102	1	1	yes	characteristic
404	C₄	C₂×C₅×#103	1	1	yes	characteristic
405	C₄	C₅×#421	1	2	yes	—
406	C₄	C₂×C₅×#106	1	1	yes	characteristic
407	C₄	C₂×C₅×#107	1	1	yes	characteristic
408	C₂	—	2	1	no	—
409	C₂	—	2	2	no	—
410	C₂	—	2	2	no	—
411	C₂	—	2	1	no	—
412	C₂	C₅×#1733	1	1	yes	characteristic
413	C₂	C₂×C₅×#340	1	1	yes	characteristic
414	C₂	C₂×C₅×#344	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂×C₄²×C₅
Frattini, cosocle	C₂×C₄²	C₂³×C₅
socle	C₂²×C₅	C₂×#95
prime radical	C₂⁴×C₅	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ 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×#1303	C₂	semidirect
10. C₅×#431	C₄	semidirect
14. C₅×#423	C₄	semidirect
17. C₂×C₅×C₄⋊C₈	C₄	semidirect
18. C₂×C₅×C₄⋊C₈	C₄	semidirect
27. #8095	C₅	direct (N × H)
71. #1303	C₂×C₅	semidirect
132. #431	C₄×C₅	semidirect
136. #423	C₄×C₅	semidirect
139. C₂×C₄⋊C₈	C₄×C₅	semidirect
140. C₂×C₄⋊C₈	C₄×C₅	semidirect
379. C₅	#8095	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×#431	2
C₂×C₅×#423	2
C₅×#2285	2
C₅×#1303	2
#8095	5

Subgroups — C5×#8095 #11930815

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#8095 #11930815