Subgroups — C₂×C₅×#1378 #11935272

Order 1280.

586 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×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×M₃₂	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#405	C₂	1	1	yes	maximal, characteristic
4	C₅×#1378	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₅×M₁₆	C₄	1	1	yes	characteristic
6	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
7	C₂×C₅×#117	C₄	1	1	yes	characteristic
8	C₂×C₅×M₃₂	—	2	1	no	—
9	C₂×C₅×M₃₂	—	2	1	no	—
10	C₂×C₅×M₃₂	—	2	1	no	—
11	C₂×C₅×M₃₂	—	2	1	no	—
12	C₂×C₅×M₃₂	—	2	1	no	—
13	C₂×C₅×M₃₂	—	2	1	no	—
14	C₂×C₅×M₃₂	—	2	1	no	—
15	C₂×C₅×M₃₂	C₄	1	2	yes	complemented
16	C₂×C₅×M₃₂	C₄	1	2	yes	complemented
17	C₂×C₅×M₃₂	C₄	1	2	yes	complemented
18	C₂×C₅×M₃₂	C₂²	1	2	yes	—
19	C₂×C₅×M₃₂	C₂²	1	2	yes	—
20	C₂²×C₅×C₁₆	—	2	1	no	—
21	C₂²×C₅×C₁₆	C₄	1	2	yes	complemented
22	C₅×#405	—	2	1	no	—
23	C₅×#405	—	2	1	no	—
24	C₅×#405	C₄	1	2	yes	—
25	C₅×#405	C₂²	1	2	yes	—
26	C₂×C₅×#97	—	2	1	no	—
27	C₂×C₄×C₅×C₈	—	2	1	no	—
28	C₂×#1378	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
29	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
30	C₂×C₅×M₁₆	—	2	1	no	—
31	C₂×C₅×M₁₆	—	2	1	no	—
32	C₂×C₅×M₁₆	—	2	1	no	—
33	C₂×C₅×M₁₆	C₈	1	2	yes	—
34	C₂×C₅×M₁₆	C₈	1	2	yes	—
35	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
36	C₂²×C₅×C₈	—	2	1	no	—
37	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
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	1	yes	characteristic
42	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
43	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
44	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
45	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
46	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
47	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
48	C₂²×C₅×C₈	Q₈	1	1	yes	characteristic
49	C₂²×C₅×C₈	Q₈	1	1	yes	characteristic
50	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
51	C₅×#117	—	2	1	no	—
52	C₅×#117	—	2	1	no	—
53	C₅×#117	C₈	1	2	yes	—
54	C₅×#117	C₂×C₄	1	2	yes	—
55	C₂×C₅×C₄⋊C₄	—	2	1	no	—
56	C₂×C₅×C₂²⋊C₄	C₈	1	2	yes	—
57	C₂×C₄²×C₅	—	2	1	no	—
58	C₅×M₃₂	—	2	2	no	—
59	C₅×M₃₂	—	2	2	no	—
60	C₅×M₃₂	—	2	2	no	—
61	C₅×M₃₂	—	2	2	no	—
62	C₅×M₃₂	—	2	2	no	—
63	C₅×M₃₂	—	2	2	no	—
64	C₅×M₃₂	—	2	2	no	—
65	C₅×M₃₂	C₂×C₄	1	4	yes	complemented
66	C₂×C₅×C₁₆	—	2	2	no	—
67	C₂×C₅×C₁₆	—	2	2	no	—
68	C₂×C₅×C₁₆	—	2	2	no	—
69	C₂×C₅×C₁₆	—	2	2	no	—
70	C₂×C₅×C₁₆	—	2	2	no	—
71	C₂×C₅×C₁₆	C₂×C₄	1	4	yes	complemented
72	C₅×#97	—	2	2	no	—
73	C₅×#97	—	2	2	no	—
74	C₄×C₅×C₈	—	2	2	no	—
75	C₄×C₅×C₈	—	2	2	no	—
76	C₂²×M₃₂	C₂×C₅	1	1	yes	characteristic
77	C₂²×M₃₂	C₂×C₅	1	1	yes	characteristic
78	C₂×#405	C₂×C₅	1	1	yes	characteristic
79	#1378	C₂×C₅	1	4	yes	direct product factor
80	C₂⁴×C₅	C₂×C₈	1	1	yes	characteristic
81	C₂²×C₄×C₅	—	2	2	no	—
82	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
83	C₂²×C₄×C₅	C₄²	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	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
89	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
90	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
91	C₂²×C₄×C₅	M₁₆	1	1	yes	characteristic
92	C₂²×C₄×C₅	M₁₆	1	1	yes	characteristic
93	C₂²×C₄×C₅	M₁₆	1	1	yes	characteristic
94	C₂²×C₄×C₅	M₁₆	1	1	yes	characteristic
95	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
96	C₅×M₁₆	—	2	2	no	—
97	C₅×M₁₆	—	2	2	no	—
98	C₅×M₁₆	—	2	2	no	—
99	C₅×M₁₆	C₂×C₈	1	4	yes	—
100	C₂×C₅×C₈	—	2	2	no	—
101	C₂×C₅×C₈	—	2	2	no	—
102	C₂×C₅×C₈	—	2	2	no	—
103	C₂×C₅×C₈	C₄²	1	1	yes	characteristic
104	C₂×C₅×C₈	C₄²	1	1	yes	characteristic
105	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
106	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
107	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
108	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
109	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
110	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
111	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
112	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
113	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
114	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
115	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
116	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
117	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
118	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
119	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
120	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
121	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
122	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
123	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
124	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
125	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
128	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
129	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
130	C₂×C₅×C₈	C₂×Q₈	1	1	yes	characteristic
131	C₅×C₄⋊C₄	—	2	2	no	—
132	C₅×C₄⋊C₄	—	2	2	no	—
133	C₅×C₂²⋊C₄	—	2	2	no	—
134	C₅×C₂²⋊C₄	C₂×C₈	1	4	yes	—
135	C₄²×C₅	—	2	2	no	—
136	C₄²×C₅	—	2	2	no	—
137	C₅×C₁₆	—	2	4	no	—
138	C₅×C₁₆	—	2	4	no	—
139	C₂²×M₁₆	C₄×C₅	1	1	yes	characteristic
140	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
141	C₂×#117	C₄×C₅	1	1	yes	characteristic
142	C₂×M₃₂	—	2	1	no	—
143	C₂×M₃₂	—	2	1	no	—
144	C₂×M₃₂	—	2	1	no	—
145	C₂×M₃₂	—	2	1	no	—
146	C₂×M₃₂	—	2	1	no	—
147	C₂×M₃₂	—	2	1	no	—
148	C₂×M₃₂	—	2	1	no	—
149	C₂×M₃₂	C₄×C₅	1	2	yes	complemented
150	C₂×M₃₂	C₄×C₅	1	2	yes	complemented
151	C₂×M₃₂	C₄×C₅	1	2	yes	complemented
152	C₂×M₃₂	C₂²×C₅	1	2	yes	—
153	C₂×M₃₂	C₂²×C₅	1	2	yes	—
154	C₂²×C₁₆	—	2	1	no	—
155	C₂²×C₁₆	C₄×C₅	1	2	yes	complemented
156	#405	—	2	1	no	—
157	#405	—	2	1	no	—
158	#405	C₄×C₅	1	2	yes	—
159	#405	C₂²×C₅	1	2	yes	—
160	C₂×#97	—	2	1	no	—
161	C₂×C₄×C₈	—	2	1	no	—
162	C₂³×C₅	—	4	2	no	—
163	C₂³×C₅	C₄×C₈	1	1	yes	characteristic
164	C₂³×C₅	C₄×C₈	1	1	yes	characteristic
165	C₂³×C₅	C₂²⋊C₈	1	1	yes	characteristic
166	C₂³×C₅	C₂²⋊C₈	1	1	yes	characteristic
167	C₂³×C₅	C₄⋊C₈	1	1	yes	characteristic
168	C₂³×C₅	C₄⋊C₈	1	1	yes	characteristic
169	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
170	C₂×C₄×C₅	—	2	4	no	—
171	C₂×C₄×C₅	—	4	4	no	—
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	C₄×C₈	1	1	yes	characteristic
177	C₂×C₄×C₅	C₄×C₈	1	1	yes	characteristic
178	C₂×C₄×C₅	#97	1	1	yes	characteristic
179	C₂×C₄×C₅	#97	1	1	yes	characteristic
180	C₂×C₄×C₅	#97	1	1	yes	characteristic
181	C₂×C₄×C₅	#97	1	1	yes	characteristic
182	C₂×C₄×C₅	C₂²⋊C₈	1	1	yes	characteristic
183	C₂×C₄×C₅	C₂²⋊C₈	1	1	yes	characteristic
184	C₂×C₄×C₅	C₂²⋊C₈	1	1	yes	characteristic
185	C₂×C₄×C₅	C₂²⋊C₈	1	1	yes	characteristic
186	C₂×C₄×C₅	C₂²⋊C₈	1	1	yes	characteristic
187	C₂×C₄×C₅	C₂²⋊C₈	1	1	yes	characteristic
188	C₂×C₄×C₅	C₄⋊C₈	1	1	yes	characteristic
189	C₂×C₄×C₅	C₄⋊C₈	1	1	yes	characteristic
190	C₂×C₄×C₅	C₄⋊C₈	1	1	yes	characteristic
191	C₂×C₄×C₅	C₄⋊C₈	1	1	yes	characteristic
192	C₂×C₄×C₅	C₄⋊C₈	1	1	yes	characteristic
193	C₂×C₄×C₅	C₄⋊C₈	1	1	yes	characteristic
194	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
195	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
197	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
198	C₂×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
199	C₂×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
200	C₅×C₈	—	2	4	no	—
201	C₅×C₈	#95	1	1	yes	characteristic
202	C₅×C₈	#95	1	1	yes	characteristic
203	C₅×C₈	#95	1	1	yes	characteristic
204	C₅×C₈	#95	1	1	yes	characteristic
205	C₅×C₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₅×C₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	C₅×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
208	C₅×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
209	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
210	C₂×M₁₆	—	2	1	no	—
211	C₂×M₁₆	—	2	1	no	—
212	C₂×M₁₆	—	2	1	no	—
213	C₂×M₁₆	C₅×C₈	1	2	yes	—
214	C₂×M₁₆	C₅×C₈	1	2	yes	—
215	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
216	C₂²×C₈	—	2	1	no	—
217	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
218	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
219	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
220	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
221	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
222	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
223	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
224	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
225	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
226	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
227	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
228	C₂²×C₈	C₅×Q₈	1	1	yes	characteristic
229	C₂²×C₈	C₅×Q₈	1	1	yes	characteristic
230	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
231	#117	—	2	1	no	—
232	#117	—	2	1	no	—
233	#117	C₅×C₈	1	2	yes	—
234	#117	C₂×C₄×C₅	1	2	yes	—
235	C₂×C₄⋊C₄	—	2	1	no	—
236	C₂×C₂²⋊C₄	C₅×C₈	1	2	yes	—
237	C₂×C₄²	—	2	1	no	—
238	M₃₂	—	2	2	no	—
239	M₃₂	—	2	2	no	—
240	M₃₂	—	2	2	no	—
241	M₃₂	—	2	2	no	—
242	M₃₂	—	2	2	no	—
243	M₃₂	—	2	2	no	—
244	M₃₂	—	2	2	no	—
245	M₃₂	C₂×C₄×C₅	1	4	yes	complemented
246	C₂×C₁₆	—	2	2	no	—
247	C₂×C₁₆	—	2	2	no	—
248	C₂×C₁₆	—	2	2	no	—
249	C₂×C₁₆	—	2	2	no	—
250	C₂×C₁₆	—	2	2	no	—
251	C₂×C₁₆	C₂×C₄×C₅	1	4	yes	complemented
252	#97	—	2	2	no	—
253	#97	—	2	2	no	—
254	C₄×C₈	—	2	2	no	—
255	C₄×C₈	—	2	2	no	—
256	C₂²×C₅	—	2	2	no	—
257	C₂²×C₅	—	2	2	no	—
258	C₂²×C₅	—	2	2	no	—
259	C₂²×C₅	—	4	1	no	—
260	C₂²×C₅	—	4	1	no	—
261	C₂²×C₅	—	4	1	no	—
262	C₂²×C₅	—	4	1	no	—
263	C₂²×C₅	#336	1	1	yes	characteristic
264	C₂²×C₅	#336	1	1	yes	characteristic
265	C₂²×C₅	#336	1	1	yes	characteristic
266	C₂²×C₅	#336	1	1	yes	characteristic
267	C₂²×C₅	C₂×C₄×C₈	1	1	yes	characteristic
268	C₂²×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
269	C₂²×C₅	C₂×C₄⋊C₈	1	1	yes	characteristic
270	C₄×C₅	—	4	4	no	—
271	C₄×C₅	#336	1	1	yes	characteristic
272	C₄×C₅	#336	1	1	yes	characteristic
273	C₄×C₅	#336	1	1	yes	characteristic
274	C₄×C₅	#336	1	1	yes	characteristic
275	C₄×C₅	C₂×#95	1	1	yes	characteristic
276	C₄×C₅	C₂×#97	1	1	yes	characteristic
277	C₄×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
278	C₄×C₅	C₂×C₄⋊C₈	1	1	yes	characteristic
279	C₂⁴	C₂×C₅×C₈	1	1	yes	characteristic
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	C₄²×C₅	1	1	yes	characteristic
282	C₂²×C₄	C₄²×C₅	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×C₄⋊C₄	1	1	yes	characteristic
286	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
288	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
290	C₂²×C₄	C₅×M₁₆	1	1	yes	characteristic
291	C₂²×C₄	C₅×M₁₆	1	1	yes	characteristic
292	C₂²×C₄	C₅×M₁₆	1	1	yes	characteristic
293	C₂²×C₄	C₅×M₁₆	1	1	yes	characteristic
294	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
295	M₁₆	—	2	2	no	—
296	M₁₆	—	2	2	no	—
297	M₁₆	—	2	2	no	—
298	M₁₆	C₂×C₅×C₈	1	4	yes	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	C₄²×C₅	1	1	yes	characteristic
303	C₂×C₈	C₄²×C₅	1	1	yes	characteristic
304	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
305	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
306	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
307	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
308	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
309	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
310	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
311	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
312	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
313	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
314	C₂×C₈	C₅×C₄⋊C₄	1	1	yes	characteristic
315	C₂×C₈	C₅×C₄⋊C₄	1	1	yes	characteristic
316	C₂×C₈	C₅×C₄⋊C₄	1	1	yes	characteristic
317	C₂×C₈	C₅×C₄⋊C₄	1	1	yes	characteristic
318	C₂×C₈	C₅×C₄⋊C₄	1	1	yes	characteristic
319	C₂×C₈	C₅×C₄⋊C₄	1	1	yes	characteristic
320	C₂×C₈	C₅×C₄⋊C₄	1	1	yes	characteristic
321	C₂×C₈	C₅×C₄⋊C₄	1	1	yes	characteristic
322	C₂×C₈	C₅×C₄⋊C₄	1	1	yes	characteristic
323	C₂×C₈	C₅×C₄⋊C₄	1	1	yes	characteristic
324	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
325	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
326	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
327	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
328	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
329	C₂×C₈	C₂×C₅×Q₈	1	1	yes	characteristic
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₂²⋊C₄	—	2	2	no	—
333	C₂²⋊C₄	C₂×C₅×C₈	1	4	yes	—
334	C₄²	—	2	2	no	—
335	C₄²	—	2	2	no	—
336	C₁₆	—	2	4	no	—
337	C₁₆	—	2	4	no	—
338	C₂×C₅	—	2	1	no	—
339	C₂×C₅	—	2	1	no	—
340	C₂×C₅	—	2	1	no	—
341	C₂×C₅	—	2	1	no	—
342	C₂×C₅	—	2	1	no	—
343	C₂×C₅	—	2	1	no	—
344	C₂×C₅	#1378	1	2	yes	direct product factor
345	C₂×C₅	C₂×#336	1	1	yes	characteristic
346	C₂³	—	4	2	no	—
347	C₂³	C₄×C₅×C₈	1	1	yes	characteristic
348	C₂³	C₄×C₅×C₈	1	1	yes	characteristic
349	C₂³	C₅×C₂²⋊C₈	1	1	yes	characteristic
350	C₂³	C₅×C₂²⋊C₈	1	1	yes	characteristic
351	C₂³	C₅×C₄⋊C₈	1	1	yes	characteristic
352	C₂³	C₅×C₄⋊C₈	1	1	yes	characteristic
353	C₂³	C₂²×C₅×C₈	1	1	yes	characteristic
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	C₅×#95	1	1	yes	characteristic
357	C₂×C₄	C₅×#95	1	1	yes	characteristic
358	C₂×C₄	C₅×#95	1	1	yes	characteristic
359	C₂×C₄	C₅×#95	1	1	yes	characteristic
360	C₂×C₄	C₄×C₅×C₈	1	1	yes	characteristic
361	C₂×C₄	C₄×C₅×C₈	1	1	yes	characteristic
362	C₂×C₄	C₅×#97	1	1	yes	characteristic
363	C₂×C₄	C₅×#97	1	1	yes	characteristic
364	C₂×C₄	C₅×#97	1	1	yes	characteristic
365	C₂×C₄	C₅×#97	1	1	yes	characteristic
366	C₂×C₄	C₅×C₂²⋊C₈	1	1	yes	characteristic
367	C₂×C₄	C₅×C₂²⋊C₈	1	1	yes	characteristic
368	C₂×C₄	C₅×C₂²⋊C₈	1	1	yes	characteristic
369	C₂×C₄	C₅×C₂²⋊C₈	1	1	yes	characteristic
370	C₂×C₄	C₅×C₂²⋊C₈	1	1	yes	characteristic
371	C₂×C₄	C₅×C₂²⋊C₈	1	1	yes	characteristic
372	C₂×C₄	C₅×C₄⋊C₈	1	1	yes	characteristic
373	C₂×C₄	C₅×C₄⋊C₈	1	1	yes	characteristic
374	C₂×C₄	C₅×C₄⋊C₈	1	1	yes	characteristic
375	C₂×C₄	C₅×C₄⋊C₈	1	1	yes	characteristic
376	C₂×C₄	C₅×C₄⋊C₈	1	1	yes	characteristic
377	C₂×C₄	C₅×C₄⋊C₈	1	1	yes	characteristic
378	C₂×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
379	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
380	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
381	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
382	C₂×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
383	C₂×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
384	C₈	—	2	4	no	—
385	C₈	C₅×#95	1	1	yes	characteristic
386	C₈	C₅×#95	1	1	yes	characteristic
387	C₈	C₅×#95	1	1	yes	characteristic
388	C₈	C₅×#95	1	1	yes	characteristic
389	C₈	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
390	C₈	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
391	C₈	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
392	C₈	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
393	C₅	C₂×#1378	1	1	yes	characteristic, direct product factor, Sylow
394	C₂²	—	2	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	C₅×#336	1	1	yes	characteristic
402	C₂²	C₅×#336	1	1	yes	characteristic
403	C₂²	C₅×#336	1	1	yes	characteristic
404	C₂²	C₅×#336	1	1	yes	characteristic
405	C₂²	C₂×C₄×C₅×C₈	1	1	yes	characteristic
406	C₂²	C₂×C₅×C₂²⋊C₈	1	1	yes	characteristic
407	C₂²	C₂×C₅×C₄⋊C₈	1	1	yes	characteristic
408	C₄	—	4	4	no	—
409	C₄	C₅×#336	1	1	yes	characteristic
410	C₄	C₅×#336	1	1	yes	characteristic
411	C₄	C₅×#336	1	1	yes	characteristic
412	C₄	C₅×#336	1	1	yes	characteristic
413	C₄	C₂×C₅×#95	1	1	yes	characteristic
414	C₄	C₂×C₅×#97	1	1	yes	characteristic
415	C₄	C₂×C₅×C₂²⋊C₈	1	1	yes	characteristic
416	C₄	C₂×C₅×C₄⋊C₈	1	1	yes	characteristic
417	C₂	—	2	1	no	—
418	C₂	—	2	1	no	—
419	C₂	—	2	1	no	—
420	C₂	—	2	1	no	—
421	C₂	—	2	1	no	—
422	C₂	—	2	1	no	—
423	C₂	C₅×#1378	1	2	yes	direct product factor
424	C₂	C₂×C₅×#336	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅×C₈	C₂²⋊C₄
commutator	C₂²	C₂×C₄×C₅×C₈
Frattini, cosocle	C₂²×C₈	C₂³×C₅
socle	C₂²×C₅	#336
prime radical	C₂⁴×C₅	C₂×C₈
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅×C₈ ◁ C₂³×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1378	C₂	direct (N × H)
15. C₂×C₅×M₃₂	C₄	semidirect
16. C₂×C₅×M₃₂	C₄	semidirect
17. C₂×C₅×M₃₂	C₄	semidirect
21. C₂²×C₅×C₁₆	C₄	semidirect
28. C₂×#1378	C₅	direct (N × H)
65. C₅×M₃₂	C₂×C₄	semidirect
71. C₂×C₅×C₁₆	C₂×C₄	semidirect
79. #1378	C₂×C₅	direct (N × H)
149. C₂×M₃₂	C₄×C₅	semidirect
150. C₂×M₃₂	C₄×C₅	semidirect
151. C₂×M₃₂	C₄×C₅	semidirect
155. C₂²×C₁₆	C₄×C₅	semidirect
245. M₃₂	C₂×C₄×C₅	semidirect
251. C₂×C₁₆	C₂×C₄×C₅	semidirect
344. C₂×C₅	#1378	direct (N × H)
393. C₅	C₂×#1378	direct (N × H)
423. C₂	C₅×#1378	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×M₃₂	2
C₂×C₅×#405	2
C₅×#1378	2
C₂×#1378	5

Subgroups — C2×C5×#1378 #11935272

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#1378 #11935272