Subgroups — C₂×C₅×#1303 #11930811

Order 1280.

810 conjugacy classes of subgroups.

The subgroup lattice has 424 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	C₂×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₅×#1303	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₅×M₁₆	—	2	1	no	—
6	C₂²×C₅×C₄⋊C₄	—	2	1	no	—
7	C₂²×C₄²×C₅	—	2	1	no	—
8	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
9	C₅×#431	—	2	1	no	—
10	C₅×#431	—	2	1	no	—
11	C₅×#431	C₄	1	2	yes	complemented
12	C₅×#431	C₂²	1	2	yes	—
13	C₅×#423	—	2	1	no	—
14	C₅×#423	—	2	1	no	—
15	C₅×#423	C₄	1	2	yes	complemented
16	C₅×#423	C₂²	1	2	yes	—
17	C₂×C₅×C₄⋊C₈	—	2	1	no	—
18	C₂×C₅×C₄⋊C₈	C₄	1	2	yes	complemented
19	C₂×C₅×C₄⋊C₈	C₄	1	2	yes	complemented
20	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
21	C₂×C₄×C₅×C₈	—	2	1	no	—
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	—
25	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
26	C₂×C₅×#95	C₄	1	2	yes	—
27	C₂×#1303	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂³×C₄×C₅	—	2	2	no	—
29	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
32	C₂×C₅×M₁₆	—	2	2	no	—
33	C₂×C₅×M₁₆	—	2	2	no	—
34	C₂×C₅×M₁₆	—	4	2	no	—
35	C₂×C₅×M₁₆	—	4	2	no	—
36	C₂²×C₅×C₈	—	2	2	no	—
37	C₂²×C₅×C₈	—	2	2	no	—
38	C₂×C₅×C₄⋊C₄	—	2	8	no	—
39	C₂×C₅×C₄⋊C₄	—	2	2	no	—
40	C₂×C₅×C₄⋊C₄	—	2	2	no	—
41	C₂×C₄²×C₅	—	2	2	no	—
42	C₂×C₄²×C₅	—	2	2	no	—
43	C₂×C₄²×C₅	—	4	2	no	—
44	C₂×C₄²×C₅	—	4	2	no	—
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	C₂×C₄	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	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₅	Q₈	1	1	yes	characteristic
55	C₂×C₄²×C₅	Q₈	1	1	yes	characteristic
56	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
61	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
62	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
63	C₅×C₂²⋊C₈	—	2	2	no	—
64	C₅×C₂²⋊C₈	—	2	2	no	—
65	C₄×C₅×C₈	—	2	2	no	—
66	C₄×C₅×C₈	—	2	2	no	—
67	C₅×#95	—	2	2	no	—
68	C₅×#95	C₂×C₄	1	4	yes	—
69	C₂×#431	C₂×C₅	1	1	yes	characteristic
70	C₂×#423	C₂×C₅	1	1	yes	characteristic
71	C₂×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
72	#1303	C₂×C₅	1	4	yes	direct product factor
73	C₂⁴×C₅	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₅	—	2	4	no	—
75	C₂²×C₄×C₅	—	2	8	no	—
76	C₂²×C₄×C₅	—	2	4	no	—
77	C₂²×C₄×C₅	—	4	2	no	—
78	C₂²×C₄×C₅	—	4	4	no	—
79	C₂²×C₄×C₅	—	4	4	no	—
80	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
81	C₂²×C₄×C₅	C₄²	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	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₅	C₂²⋊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	D₈	1	2	yes	—
96	C₂²×C₄×C₅	SD₁₆	1	2	yes	—
97	C₂²×C₄×C₅	SD₁₆	1	2	yes	—
98	C₂²×C₄×C₅	Q₁₆	1	2	yes	—
99	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₅×M₁₆	—	4	4	no	—
103	C₅×M₁₆	—	4	2	no	—
104	C₅×M₁₆	—	4	2	no	—
105	C₂×C₅×C₈	—	2	4	no	—
106	C₂×C₅×C₈	—	2	4	no	—
107	C₂×C₅×C₈	—	4	4	no	—
108	C₂×C₅×C₈	—	4	4	no	—
109	C₅×C₄⋊C₄	—	2	8	no	—
110	C₅×C₄⋊C₄	—	2	8	no	—
111	C₄²×C₅	—	4	4	no	—
112	C₄²×C₅	—	4	2	no	—
113	C₄²×C₅	—	4	2	no	—
114	C₄²×C₅	C₄²	1	1	yes	characteristic
115	C₄²×C₅	C₄²	1	1	yes	characteristic
116	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
117	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
118	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
119	C₄²×C₅	C₂²⋊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	C₄⋊C₄	1	1	yes	characteristic
124	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
125	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
126	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
127	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
130	C₂²×M₁₆	—	2	1	no	—
131	C₂²×C₄⋊C₄	—	2	1	no	—
132	C₂²×C₄²	—	2	1	no	—
133	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
134	#431	—	2	1	no	—
135	#431	—	2	1	no	—
136	#431	C₄×C₅	1	2	yes	complemented
137	#431	C₂²×C₅	1	2	yes	—
138	#423	—	2	1	no	—
139	#423	—	2	1	no	—
140	#423	C₄×C₅	1	2	yes	complemented
141	#423	C₂²×C₅	1	2	yes	—
142	C₂×C₄⋊C₈	—	2	1	no	—
143	C₂×C₄⋊C₈	C₄×C₅	1	2	yes	complemented
144	C₂×C₄⋊C₈	C₄×C₅	1	2	yes	complemented
145	C₂×C₂²⋊C₈	—	2	1	no	—
146	C₂×C₄×C₈	—	2	1	no	—
147	C₄×C₄⋊C₄	—	2	1	no	—
148	C₄×C₄⋊C₄	—	2	1	no	—
149	C₄×C₄⋊C₄	C₄×C₅	1	2	yes	—
150	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
151	C₂×#95	C₄×C₅	1	2	yes	—
152	C₂³×C₅	—	2	2	no	—
153	C₂³×C₅	—	2	2	no	—
154	C₂³×C₅	#95	1	1	yes	characteristic
155	C₂³×C₅	#95	1	1	yes	characteristic
156	C₂³×C₅	#102	1	2	yes	—
157	C₂³×C₅	#103	1	2	yes	—
158	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
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	—	2	2	no	—
165	C₂×C₄×C₅	—	2	2	no	—
166	C₂×C₄×C₅	—	2	8	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	1	no	—
171	C₂×C₄×C₅	—	4	16	no	—
172	C₂×C₄×C₅	—	4	4	no	—
173	C₂×C₄×C₅	—	4	4	no	—
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	#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	#102	1	2	yes	—
181	C₂×C₄×C₅	#102	1	2	yes	—
182	C₂×C₄×C₅	#102	1	2	yes	—
183	C₂×C₄×C₅	#103	1	2	yes	—
184	C₂×C₄×C₅	#103	1	2	yes	—
185	C₂×C₄×C₅	#103	1	2	yes	—
186	C₂×C₄×C₅	#104	1	4	yes	—
187	C₂×C₄×C₅	#106	1	2	yes	—
188	C₂×C₄×C₅	#106	1	2	yes	—
189	C₂×C₄×C₅	#107	1	2	yes	—
190	C₂×C₄×C₅	#107	1	2	yes	—
191	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
192	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
193	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
194	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
196	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
197	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
198	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
199	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
200	C₂×C₄×C₅	C₂×Q₁₆	1	1	yes	characteristic
201	C₅×C₈	—	4	4	no	—
202	C₅×C₈	—	4	4	no	—
203	C₂³×C₄	—	2	2	no	—
204	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
205	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
206	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
207	C₂×M₁₆	—	2	2	no	—
208	C₂×M₁₆	—	2	2	no	—
209	C₂×M₁₆	—	4	2	no	—
210	C₂×M₁₆	—	4	2	no	—
211	C₂²×C₈	—	2	2	no	—
212	C₂²×C₈	—	2	2	no	—
213	C₂×C₄⋊C₄	—	2	8	no	—
214	C₂×C₄⋊C₄	—	2	2	no	—
215	C₂×C₄⋊C₄	—	2	2	no	—
216	C₂×C₄²	—	2	2	no	—
217	C₂×C₄²	—	2	2	no	—
218	C₂×C₄²	—	4	2	no	—
219	C₂×C₄²	—	4	2	no	—
220	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
221	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
222	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
223	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
224	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
225	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
226	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
227	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
228	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
229	C₂×C₄²	C₅×Q₈	1	1	yes	characteristic
230	C₂×C₄²	C₅×Q₈	1	1	yes	characteristic
231	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
232	C₄⋊C₈	—	2	2	no	—
233	C₄⋊C₈	—	2	2	no	—
234	C₄⋊C₈	—	2	2	no	—
235	C₄⋊C₈	—	2	2	no	—
236	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	complemented
237	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	complemented
238	C₂²⋊C₈	—	2	2	no	—
239	C₂²⋊C₈	—	2	2	no	—
240	C₄×C₈	—	2	2	no	—
241	C₄×C₈	—	2	2	no	—
242	#95	—	2	2	no	—
243	#95	C₂×C₄×C₅	1	4	yes	—
244	C₂²×C₅	—	2	4	no	—
245	C₂²×C₅	—	2	4	no	—
246	C₂²×C₅	—	2	1	no	—
247	C₂²×C₅	—	2	1	no	—
248	C₂²×C₅	—	2	1	no	—
249	C₂²×C₅	—	2	1	no	—
250	C₂²×C₅	#339	1	2	yes	—
251	C₂²×C₅	#340	1	2	yes	—
252	C₂²×C₅	#340	1	2	yes	—
253	C₂²×C₅	#344	1	2	yes	—
254	C₂²×C₅	C₂×#95	1	1	yes	characteristic
255	C₂²×C₅	C₂×#102	1	1	yes	characteristic
256	C₂²×C₅	C₂×#103	1	1	yes	characteristic
257	C₄×C₅	—	2	1	no	—
258	C₄×C₅	—	2	1	no	—
259	C₄×C₅	—	2	1	no	—
260	C₄×C₅	—	2	1	no	—
261	C₄×C₅	—	2	1	no	—
262	C₄×C₅	—	2	1	no	—
263	C₄×C₅	—	4	8	no	—
264	C₄×C₅	#339	1	2	yes	—
265	C₄×C₅	#340	1	2	yes	—
266	C₄×C₅	#340	1	2	yes	—
267	C₄×C₅	C₂×#102	1	1	yes	characteristic
268	C₄×C₅	C₂×#103	1	1	yes	characteristic
269	C₄×C₅	C₂×#104	1	2	yes	—
270	C₄×C₅	C₂×#106	1	1	yes	characteristic
271	C₄×C₅	C₂×#107	1	1	yes	characteristic
272	C₂⁴	C₅×C₂²⋊C₄	1	1	yes	characteristic
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	8	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	4	4	no	—
278	C₂²×C₄	—	4	4	no	—
279	C₂²×C₄	C₄²×C₅	1	1	yes	characteristic
280	C₂²×C₄	C₄²×C₅	1	1	yes	characteristic
281	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
282	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
283	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
284	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
285	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
286	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
287	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
288	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
289	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
290	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
291	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
292	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
293	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
294	C₂²×C₄	C₅×D₈	1	2	yes	—
295	C₂²×C₄	C₅×SD₁₆	1	2	yes	—
296	C₂²×C₄	C₅×SD₁₆	1	2	yes	—
297	C₂²×C₄	C₅×Q₁₆	1	2	yes	—
298	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
300	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
301	M₁₆	—	4	2	no	—
302	M₁₆	—	4	2	no	—
303	M₁₆	—	4	4	no	—
304	C₂×C₈	—	2	4	no	—
305	C₂×C₈	—	2	4	no	—
306	C₂×C₈	—	4	4	no	—
307	C₂×C₈	—	4	4	no	—
308	C₄⋊C₄	—	2	8	no	—
309	C₄⋊C₄	—	2	8	no	—
310	C₄²	—	4	2	no	—
311	C₄²	—	4	2	no	—
312	C₄²	—	4	4	no	—
313	C₄²	C₄²×C₅	1	1	yes	characteristic
314	C₄²	C₄²×C₅	1	1	yes	characteristic
315	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
316	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
317	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
318	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
319	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
320	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
321	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
322	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
323	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
324	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
325	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
326	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
327	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
328	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
329	C₂×C₅	—	2	1	no	—
330	C₂×C₅	—	2	2	no	—
331	C₂×C₅	—	2	1	no	—
332	C₂×C₅	#1303	1	4	yes	direct product factor
333	C₂×C₅	C₂×#339	1	1	yes	characteristic
334	C₂×C₅	C₂×#340	1	1	yes	characteristic
335	C₂×C₅	C₂×#344	1	1	yes	characteristic
336	C₂³	—	2	2	no	—
337	C₂³	—	2	2	no	—
338	C₂³	C₅×#95	1	1	yes	characteristic
339	C₂³	C₅×#95	1	1	yes	characteristic
340	C₂³	C₅×#102	1	2	yes	—
341	C₂³	C₅×#103	1	2	yes	—
342	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	8	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	16	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	C₅×#95	1	1	yes	characteristic
359	C₂×C₄	C₅×#95	1	1	yes	characteristic
360	C₂×C₄	C₅×#95	1	1	yes	characteristic
361	C₂×C₄	C₅×#95	1	1	yes	characteristic
362	C₂×C₄	C₅×#95	1	1	yes	characteristic
363	C₂×C₄	C₅×#95	1	1	yes	characteristic
364	C₂×C₄	C₅×#102	1	2	yes	—
365	C₂×C₄	C₅×#102	1	2	yes	—
366	C₂×C₄	C₅×#102	1	2	yes	—
367	C₂×C₄	C₅×#103	1	2	yes	—
368	C₂×C₄	C₅×#103	1	2	yes	—
369	C₂×C₄	C₅×#103	1	2	yes	—
370	C₂×C₄	C₅×#104	1	4	yes	—
371	C₂×C₄	C₅×#106	1	2	yes	—
372	C₂×C₄	C₅×#106	1	2	yes	—
373	C₂×C₄	C₅×#107	1	2	yes	—
374	C₂×C₄	C₅×#107	1	2	yes	—
375	C₂×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
376	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
377	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
378	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
379	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
380	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
381	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
382	C₂×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
383	C₂×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
384	C₂×C₄	C₂×C₅×Q₁₆	1	1	yes	characteristic
385	C₈	—	4	4	no	—
386	C₈	—	4	4	no	—
387	C₅	C₂×#1303	1	1	yes	characteristic, direct product factor, Sylow
388	C₂²	—	2	4	no	—
389	C₂²	—	2	4	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	C₅×#339	1	2	yes	—
395	C₂²	C₅×#340	1	2	yes	—
396	C₂²	C₅×#340	1	2	yes	—
397	C₂²	C₅×#344	1	2	yes	—
398	C₂²	C₂×C₅×#95	1	1	yes	characteristic
399	C₂²	C₂×C₅×#102	1	1	yes	characteristic
400	C₂²	C₂×C₅×#103	1	1	yes	characteristic
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	2	1	no	—
407	C₄	—	4	8	no	—
408	C₄	C₅×#339	1	2	yes	—
409	C₄	C₅×#340	1	2	yes	—
410	C₄	C₅×#340	1	2	yes	—
411	C₄	C₂×C₅×#102	1	1	yes	characteristic
412	C₄	C₂×C₅×#103	1	1	yes	characteristic
413	C₄	C₂×C₅×#104	1	2	yes	—
414	C₄	C₂×C₅×#106	1	1	yes	characteristic
415	C₄	C₂×C₅×#107	1	1	yes	characteristic
416	C₂	—	2	1	no	—
417	C₂	—	2	2	no	—
418	C₂	—	2	1	no	—
419	C₂	C₅×#1303	1	4	yes	direct product factor
420	C₂	C₂×C₅×#339	1	1	yes	characteristic
421	C₂	C₂×C₅×#340	1	1	yes	characteristic
422	C₂	C₂×C₅×#344	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²⋊C₄
commutator	C₂×C₄	C₂×C₄²×C₅
Frattini, cosocle	C₂×C₄²	C₂³×C₅
socle	C₂³×C₅	#95
prime radical	C₂⁴×C₅	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×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	direct (N × H)
11. C₅×#431	C₄	semidirect
15. C₅×#423	C₄	semidirect
18. C₂×C₅×C₄⋊C₈	C₄	semidirect
19. C₂×C₅×C₄⋊C₈	C₄	semidirect
27. C₂×#1303	C₅	direct (N × H)
61. C₅×C₄⋊C₈	C₂×C₄	semidirect
62. C₅×C₄⋊C₈	C₂×C₄	semidirect
72. #1303	C₂×C₅	direct (N × H)
136. #431	C₄×C₅	semidirect
140. #423	C₄×C₅	semidirect
143. C₂×C₄⋊C₈	C₄×C₅	semidirect
144. C₂×C₄⋊C₈	C₄×C₅	semidirect
236. C₄⋊C₈	C₂×C₄×C₅	semidirect
237. C₄⋊C₈	C₂×C₄×C₅	semidirect
332. C₂×C₅	#1303	direct (N × H)
387. C₅	C₂×#1303	direct (N × H)
419. C₂	C₅×#1303	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
C₂×C₄×C₅×C₄⋊C₄	2
C₅×#1303	2
C₂×#1303	5

Subgroups — C2×C5×#1303 #11930811

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#1303 #11930811