Subgroups — C₂×C₅×#1279 #11930609

Order 1280.

974 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₅×#1279	C₂	1	4	yes	maximal, direct product factor
5	C₂³×C₅×C₈	—	2	1	no	—
6	C₂³×C₅×C₈	—	2	1	no	—
7	C₂²×C₅×C₄⋊C₄	C₄	1	2	yes	—
8	C₂²×C₄²×C₅	—	2	1	no	—
9	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
10	C₂×C₅×C₄⋊C₈	—	2	1	no	—
11	C₂×C₅×C₄⋊C₈	—	2	2	no	—
12	C₂×C₅×C₄⋊C₈	C₄	1	4	yes	complemented
13	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₄×C₅×C₈	—	2	1	no	—
15	C₂×C₄×C₅×C₈	—	2	2	no	—
16	C₂×C₄×C₅×C₈	C₄	1	4	yes	complemented
17	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
18	C₄×C₅×C₄⋊C₄	—	2	1	no	—
19	C₄×C₅×C₄⋊C₄	—	2	1	no	—
20	C₄×C₅×C₄⋊C₄	C₄	1	2	yes	—
21	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂×C₅×#95	—	2	1	no	—
23	C₂×#1279	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₂³×C₄×C₅	—	2	2	no	—
25	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
27	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
28	C₂²×C₅×C₈	—	2	8	no	—
29	C₂²×C₅×C₈	—	2	4	no	—
30	C₂²×C₅×C₈	—	2	2	no	—
31	C₂²×C₅×C₈	—	2	4	no	—
32	C₂²×C₅×C₈	—	2	2	no	—
33	C₂²×C₅×C₈	—	4	2	no	—
34	C₂²×C₅×C₈	—	4	2	no	—
35	C₂×C₅×C₄⋊C₄	—	2	2	no	—
36	C₂×C₅×C₄⋊C₄	—	2	4	no	—
37	C₂×C₅×C₄⋊C₄	C₈	1	8	yes	complemented
38	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
39	C₂×C₄²×C₅	—	2	2	no	—
40	C₂×C₄²×C₅	—	2	2	no	—
41	C₂×C₄²×C₅	—	4	2	no	—
42	C₂×C₄²×C₅	—	4	2	no	—
43	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
46	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₅	D₄	1	2	yes	—
49	C₂×C₄²×C₅	Q₈	1	2	yes	—
50	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
51	C₅×C₄⋊C₈	—	2	4	no	—
52	C₅×C₄⋊C₈	—	2	2	no	—
53	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
54	C₄×C₅×C₈	—	2	4	no	—
55	C₄×C₅×C₈	—	2	2	no	—
56	C₄×C₅×C₈	C₂×C₄	1	4	yes	complemented
57	C₅×#95	—	2	2	no	—
58	C₅×#95	—	2	2	no	—
59	C₂²×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic
60	C₂²×C₄×C₈	C₂×C₅	1	1	yes	characteristic
61	C₂×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
62	#1279	C₂×C₅	1	4	yes	direct product factor
63	C₂⁴×C₅	C₂²⋊C₄	1	1	yes	characteristic
64	C₂²×C₄×C₅	—	2	4	no	—
65	C₂²×C₄×C₅	—	2	8	no	—
66	C₂²×C₄×C₅	—	2	4	no	—
67	C₂²×C₄×C₅	—	4	4	no	—
68	C₂²×C₄×C₅	—	4	4	no	—
69	C₂²×C₄×C₅	C₄²	1	2	yes	—
70	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₅	C₂²⋊C₄	1	2	yes	—
72	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₅	C₂²⋊C₄	1	2	yes	—
75	C₂²×C₄×C₅	C₄⋊C₄	1	2	yes	—
76	C₂²×C₄×C₅	C₄⋊C₄	1	2	yes	—
77	C₂²×C₄×C₅	C₄⋊C₄	1	2	yes	—
78	C₂²×C₄×C₅	C₂×C₈	1	4	yes	—
79	C₂²×C₄×C₅	M₁₆	1	4	yes	—
80	C₂²×C₄×C₅	D₈	1	2	yes	—
81	C₂²×C₄×C₅	SD₁₆	1	2	yes	—
82	C₂²×C₄×C₅	SD₁₆	1	2	yes	—
83	C₂²×C₄×C₅	Q₁₆	1	2	yes	—
84	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
87	C₂×C₅×C₈	—	2	16	no	—
88	C₂×C₅×C₈	—	2	8	no	—
89	C₂×C₅×C₈	—	2	4	no	—
90	C₂×C₅×C₈	—	2	4	no	—
91	C₂×C₅×C₈	—	4	8	no	—
92	C₂×C₅×C₈	—	4	2	no	—
93	C₂×C₅×C₈	—	4	2	no	—
94	C₅×C₄⋊C₄	—	2	8	no	—
95	C₅×C₄⋊C₄	—	2	4	no	—
96	C₅×C₄⋊C₄	C₂×C₈	1	8	yes	complemented
97	C₄²×C₅	—	4	4	no	—
98	C₄²×C₅	—	4	2	no	—
99	C₄²×C₅	—	4	2	no	—
100	C₄²×C₅	C₄²	1	2	yes	—
101	C₄²×C₅	C₂²⋊C₄	1	2	yes	—
102	C₄²×C₅	C₂²⋊C₄	1	2	yes	—
103	C₄²×C₅	C₄⋊C₄	1	2	yes	—
104	C₄²×C₅	C₄⋊C₄	1	2	yes	—
105	C₄²×C₅	C₄⋊C₄	1	2	yes	—
106	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
108	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
109	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
110	C₂³×C₈	—	2	1	no	—
111	C₂³×C₈	—	2	1	no	—
112	C₂²×C₄⋊C₄	C₄×C₅	1	2	yes	—
113	C₂²×C₄²	—	2	1	no	—
114	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
115	C₂×C₄⋊C₈	—	2	1	no	—
116	C₂×C₄⋊C₈	—	2	2	no	—
117	C₂×C₄⋊C₈	C₄×C₅	1	4	yes	complemented
118	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
119	C₂×C₄×C₈	—	2	1	no	—
120	C₂×C₄×C₈	—	2	2	no	—
121	C₂×C₄×C₈	C₄×C₅	1	4	yes	complemented
122	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
123	C₄×C₄⋊C₄	—	2	1	no	—
124	C₄×C₄⋊C₄	—	2	1	no	—
125	C₄×C₄⋊C₄	C₄×C₅	1	2	yes	—
126	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
127	C₂×#95	—	2	1	no	—
128	C₂³×C₅	#95	1	2	yes	—
129	C₂³×C₅	C₂²⋊C₈	1	4	yes	—
130	C₂³×C₅	#102	1	2	yes	—
131	C₂³×C₅	#103	1	2	yes	—
132	C₂³×C₅	#104	1	4	yes	—
133	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₅	—	2	4	no	—
135	C₂×C₄×C₅	—	2	4	no	—
136	C₂×C₄×C₅	—	2	2	no	—
137	C₂×C₄×C₅	—	2	2	no	—
138	C₂×C₄×C₅	—	2	8	no	—
139	C₂×C₄×C₅	—	4	16	no	—
140	C₂×C₄×C₅	—	4	4	no	—
141	C₂×C₄×C₅	—	4	4	no	—
142	C₂×C₄×C₅	#95	1	2	yes	—
143	C₂×C₄×C₅	#95	1	2	yes	—
144	C₂×C₄×C₅	#95	1	2	yes	—
145	C₂×C₄×C₅	C₄×C₈	1	4	yes	—
146	C₂×C₄×C₅	#97	1	4	yes	—
147	C₂×C₄×C₅	C₂²⋊C₈	1	4	yes	—
148	C₂×C₄×C₅	#102	1	2	yes	—
149	C₂×C₄×C₅	#102	1	4	yes	—
150	C₂×C₄×C₅	#103	1	2	yes	—
151	C₂×C₄×C₅	#103	1	4	yes	—
152	C₂×C₄×C₅	C₄⋊C₈	1	8	yes	—
153	C₂×C₄×C₅	#106	1	4	yes	—
154	C₂×C₄×C₅	#107	1	4	yes	—
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×C₄⋊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	C₂²×C₈	1	2	yes	—
162	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
163	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
164	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
165	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
166	C₂×C₄×C₅	C₂×Q₁₆	1	1	yes	characteristic
167	C₅×C₈	—	2	8	no	—
168	C₅×C₈	—	4	4	no	—
169	C₂³×C₄	—	2	2	no	—
170	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
171	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
172	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
173	C₂²×C₈	—	2	8	no	—
174	C₂²×C₈	—	2	4	no	—
175	C₂²×C₈	—	2	2	no	—
176	C₂²×C₈	—	2	4	no	—
177	C₂²×C₈	—	2	2	no	—
178	C₂²×C₈	—	4	2	no	—
179	C₂²×C₈	—	4	2	no	—
180	C₂×C₄⋊C₄	—	2	2	no	—
181	C₂×C₄⋊C₄	—	2	4	no	—
182	C₂×C₄⋊C₄	C₅×C₈	1	8	yes	complemented
183	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
184	C₂×C₄²	—	2	2	no	—
185	C₂×C₄²	—	2	2	no	—
186	C₂×C₄²	—	4	2	no	—
187	C₂×C₄²	—	4	2	no	—
188	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
189	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
190	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
191	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
192	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
193	C₂×C₄²	C₅×D₄	1	2	yes	—
194	C₂×C₄²	C₅×Q₈	1	2	yes	—
195	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
196	C₄⋊C₈	—	2	4	no	—
197	C₄⋊C₈	—	2	2	no	—
198	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	complemented
199	C₄×C₈	—	2	4	no	—
200	C₄×C₈	—	2	2	no	—
201	C₄×C₈	C₂×C₄×C₅	1	4	yes	complemented
202	#95	—	2	2	no	—
203	#95	—	2	2	no	—
204	C₂²×C₅	D₄⋊C₈	1	8	yes	—
205	C₂²×C₅	Q₈⋊C₈	1	8	yes	—
206	C₂²×C₅	#336	1	4	yes	—
207	C₂²×C₅	#339	1	4	yes	—
208	C₂²×C₅	#340	1	4	yes	—
209	C₂²×C₅	C₂×#95	1	1	yes	characteristic
210	C₂²×C₅	C₂×C₂²⋊C₈	1	2	yes	—
211	C₂²×C₅	C₂×#102	1	1	yes	characteristic
212	C₂²×C₅	C₂×#103	1	1	yes	characteristic
213	C₂²×C₅	C₂×#104	1	2	yes	—
214	C₄×C₅	—	2	1	no	—
215	C₄×C₅	—	2	2	no	—
216	C₄×C₅	—	2	1	no	—
217	C₄×C₅	—	4	8	no	—
218	C₄×C₅	#336	1	4	yes	—
219	C₄×C₅	#340	1	4	yes	—
220	C₄×C₅	C₂×C₄×C₈	1	1	yes	characteristic
221	C₄×C₅	C₂×#97	1	1	yes	characteristic
222	C₄×C₅	C₂×#102	1	1	yes	characteristic
223	C₄×C₅	C₂×#103	1	1	yes	characteristic
224	C₄×C₅	C₂×C₄⋊C₈	1	2	yes	—
225	C₄×C₅	C₂×#106	1	1	yes	characteristic
226	C₄×C₅	C₂×#107	1	1	yes	characteristic
227	C₂⁴	C₅×C₂²⋊C₄	1	1	yes	characteristic
228	C₂²×C₄	—	2	4	no	—
229	C₂²×C₄	—	2	4	no	—
230	C₂²×C₄	—	2	8	no	—
231	C₂²×C₄	—	4	4	no	—
232	C₂²×C₄	—	4	4	no	—
233	C₂²×C₄	C₄²×C₅	1	2	yes	—
234	C₂²×C₄	C₅×C₂²⋊C₄	1	2	yes	—
235	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
236	C₂²×C₄	C₅×C₂²⋊C₄	1	2	yes	—
237	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
238	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
239	C₂²×C₄	C₅×C₄⋊C₄	1	2	yes	—
240	C₂²×C₄	C₅×C₄⋊C₄	1	2	yes	—
241	C₂²×C₄	C₅×C₄⋊C₄	1	2	yes	—
242	C₂²×C₄	C₂×C₅×C₈	1	4	yes	—
243	C₂²×C₄	C₅×M₁₆	1	4	yes	—
244	C₂²×C₄	C₅×D₈	1	2	yes	—
245	C₂²×C₄	C₅×SD₁₆	1	2	yes	—
246	C₂²×C₄	C₅×SD₁₆	1	2	yes	—
247	C₂²×C₄	C₅×Q₁₆	1	2	yes	—
248	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
249	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
250	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
251	C₂×C₈	—	2	16	no	—
252	C₂×C₈	—	2	8	no	—
253	C₂×C₈	—	2	4	no	—
254	C₂×C₈	—	2	4	no	—
255	C₂×C₈	—	4	2	no	—
256	C₂×C₈	—	4	2	no	—
257	C₂×C₈	—	4	8	no	—
258	C₄⋊C₄	—	2	4	no	—
259	C₄⋊C₄	—	2	8	no	—
260	C₄⋊C₄	C₂×C₅×C₈	1	8	yes	complemented
261	C₄²	—	4	2	no	—
262	C₄²	—	4	2	no	—
263	C₄²	—	4	4	no	—
264	C₄²	C₄²×C₅	1	2	yes	—
265	C₄²	C₅×C₂²⋊C₄	1	2	yes	—
266	C₄²	C₅×C₂²⋊C₄	1	2	yes	—
267	C₄²	C₅×C₄⋊C₄	1	2	yes	—
268	C₄²	C₅×C₄⋊C₄	1	2	yes	—
269	C₄²	C₅×C₄⋊C₄	1	2	yes	—
270	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
271	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
272	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
273	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
274	C₂×C₅	#1279	1	8	yes	direct product factor
275	C₂×C₅	C₂×D₄⋊C₈	1	2	yes	—
276	C₂×C₅	C₂×Q₈⋊C₈	1	2	yes	—
277	C₂×C₅	C₂×#336	1	1	yes	characteristic
278	C₂×C₅	C₂×#339	1	1	yes	characteristic
279	C₂×C₅	C₂×#340	1	1	yes	characteristic
280	C₂³	C₅×#95	1	2	yes	—
281	C₂³	C₅×C₂²⋊C₈	1	4	yes	—
282	C₂³	C₅×#102	1	2	yes	—
283	C₂³	C₅×#103	1	2	yes	—
284	C₂³	C₅×#104	1	4	yes	—
285	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
286	C₂×C₄	—	2	4	no	—
287	C₂×C₄	—	2	4	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	8	no	—
291	C₂×C₄	—	4	16	no	—
292	C₂×C₄	—	4	4	no	—
293	C₂×C₄	—	4	4	no	—
294	C₂×C₄	C₅×#95	1	2	yes	—
295	C₂×C₄	C₅×#95	1	2	yes	—
296	C₂×C₄	C₅×#95	1	2	yes	—
297	C₂×C₄	C₄×C₅×C₈	1	4	yes	—
298	C₂×C₄	C₅×#97	1	4	yes	—
299	C₂×C₄	C₅×C₂²⋊C₈	1	4	yes	—
300	C₂×C₄	C₅×#102	1	2	yes	—
301	C₂×C₄	C₅×#102	1	4	yes	—
302	C₂×C₄	C₅×#103	1	2	yes	—
303	C₂×C₄	C₅×#103	1	4	yes	—
304	C₂×C₄	C₅×C₄⋊C₈	1	8	yes	—
305	C₂×C₄	C₅×#106	1	4	yes	—
306	C₂×C₄	C₅×#107	1	4	yes	—
307	C₂×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
308	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
309	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
310	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
311	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
312	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
313	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
314	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
315	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
316	C₂×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
317	C₂×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
318	C₂×C₄	C₂×C₅×Q₁₆	1	1	yes	characteristic
319	C₈	—	2	8	no	—
320	C₈	—	4	4	no	—
321	C₅	C₂×#1279	1	1	yes	characteristic, direct product factor, Sylow
322	C₂²	C₅×D₄⋊C₈	1	8	yes	—
323	C₂²	C₅×Q₈⋊C₈	1	8	yes	—
324	C₂²	C₅×#336	1	4	yes	—
325	C₂²	C₅×#339	1	4	yes	—
326	C₂²	C₅×#340	1	4	yes	—
327	C₂²	C₂×C₅×#95	1	1	yes	characteristic
328	C₂²	C₂×C₅×C₂²⋊C₈	1	2	yes	—
329	C₂²	C₂×C₅×#102	1	1	yes	characteristic
330	C₂²	C₂×C₅×#103	1	1	yes	characteristic
331	C₂²	C₂×C₅×#104	1	2	yes	—
332	C₄	—	2	1	no	—
333	C₄	—	2	1	no	—
334	C₄	—	2	2	no	—
335	C₄	—	4	8	no	—
336	C₄	C₅×#336	1	4	yes	—
337	C₄	C₅×#340	1	4	yes	—
338	C₄	C₂×C₄×C₅×C₈	1	1	yes	characteristic
339	C₄	C₂×C₅×#97	1	1	yes	characteristic
340	C₄	C₂×C₅×#102	1	1	yes	characteristic
341	C₄	C₂×C₅×#103	1	1	yes	characteristic
342	C₄	C₂×C₅×C₄⋊C₈	1	2	yes	—
343	C₄	C₂×C₅×#106	1	1	yes	characteristic
344	C₄	C₂×C₅×#107	1	1	yes	characteristic
345	C₂	C₅×#1279	1	8	yes	direct product factor
346	C₂	C₂×C₅×D₄⋊C₈	1	2	yes	—
347	C₂	C₂×C₅×Q₈⋊C₈	1	2	yes	—
348	C₂	C₂×C₅×#336	1	1	yes	characteristic
349	C₂	C₂×C₅×#339	1	1	yes	characteristic
350	C₂	C₂×C₅×#340	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄×C₅	D₄
commutator	C₄	C₂×C₄×C₅×C₈
Frattini, cosocle	C₂×C₄²	C₂³×C₅
socle, prime radical	C₂⁴×C₅	C₂²⋊C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1279	C₂	direct (N × H)
12. C₂×C₅×C₄⋊C₈	C₄	semidirect
16. C₂×C₄×C₅×C₈	C₄	semidirect
23. C₂×#1279	C₅	direct (N × H)
37. C₂×C₅×C₄⋊C₄	C₈	semidirect
53. C₅×C₄⋊C₈	C₂×C₄	semidirect
56. C₄×C₅×C₈	C₂×C₄	semidirect
62. #1279	C₂×C₅	direct (N × H)
96. C₅×C₄⋊C₄	C₂×C₈	semidirect
117. C₂×C₄⋊C₈	C₄×C₅	semidirect
121. C₂×C₄×C₈	C₄×C₅	semidirect
182. C₂×C₄⋊C₄	C₅×C₈	semidirect
198. C₄⋊C₈	C₂×C₄×C₅	semidirect
201. C₄×C₈	C₂×C₄×C₅	semidirect
260. C₄⋊C₄	C₂×C₅×C₈	semidirect
274. C₂×C₅	#1279	direct (N × H)
321. C₅	C₂×#1279	direct (N × H)
345. C₂	C₅×#1279	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×C₄⋊C₈	2
C₂²×C₄×C₅×C₈	2
C₂×C₄×C₅×C₄⋊C₄	2
C₅×#1279	2
C₂×#1279	5

Subgroups — C2×C5×#1279 #11930609

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#1279 #11930609