Subgroups — C₅×D₄×C₄⋊C₈ #11945366

Order 1280.

1200 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₈×D₄	C₂	1	2	yes	maximal
2	C₂²×C₅×C₄⋊C₈	C₂	1	2	yes	maximal, complemented
3	C₄²×C₅×D₄	C₂	1	1	yes	maximal, characteristic
4	C₅×#1939	C₂	1	2	yes	maximal, complemented
5	C₅×#1850	C₂	1	4	yes	maximal, complemented
6	C₅×#1842	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1797	C₂	1	2	yes	maximal, complemented
8	C₄×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×C₅×C₈	C₂²	1	4	yes	—
10	C₂×C₄×C₅×D₄	C₄	1	1	yes	characteristic
11	C₂×C₄×C₅×D₄	C₄	1	1	yes	characteristic
12	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
13	C₂²×C₄²×C₅	C₂²	1	2	yes	—
14	C₅×C₈×D₄	—	2	8	no	—
15	C₂×C₅×C₄⋊C₈	—	2	8	no	—
16	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₅×C₄⋊C₈	C₂²	1	4	yes	—
20	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₅×C₂²⋊C₈	C₂²	1	4	yes	—
23	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
24	C₄×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
25	C₄×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
26	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₄×C₅×C₂²⋊C₄	C₄	1	2	yes	—
28	C₄×C₅×C₂²⋊C₄	C₄	1	2	yes	—
29	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₄³×C₅	C₂²	1	1	yes	characteristic
31	C₅×#336	C₂²	1	2	yes	—
32	C₅×#336	C₂²	1	4	yes	—
33	D₄×C₄⋊C₈	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
34	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₅	C₂×C₄	1	2	yes	—
36	C₂³×C₄×C₅	C₂×C₄	1	2	yes	—
37	C₂³×C₄×C₅	C₂³	1	2	yes	—
38	C₂²×C₅×C₈	—	2	8	no	—
39	C₂²×C₅×C₈	—	2	8	no	—
40	C₂²×C₅×C₈	—	4	4	no	—
41	C₂²×C₅×C₈	C₂³	1	2	yes	—
42	C₂²×C₅×C₈	C₂³	1	4	yes	—
43	C₂²×C₅×C₈	C₂³	1	2	yes	—
44	C₄×C₅×D₄	—	2	4	no	—
45	C₄×C₅×D₄	C₈	1	8	yes	complemented
46	C₄×C₅×D₄	D₄	1	4	yes	—
47	C₄×C₅×D₄	Q₈	1	4	yes	—
48	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
49	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
50	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
51	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
52	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₅	—	2	4	no	—
55	C₂×C₄²×C₅	—	2	4	no	—
56	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
59	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
60	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₅	C₂³	1	2	yes	—
64	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₅×C₄⋊C₈	—	2	8	no	—
67	C₅×C₄⋊C₈	—	2	4	no	—
68	C₅×C₄⋊C₈	—	2	4	no	—
69	C₅×C₄⋊C₈	—	2	2	no	—
70	C₅×C₄⋊C₈	—	4	2	no	—
71	C₅×C₄⋊C₈	D₄	1	4	yes	direct product factor
72	C₅×C₂²⋊C₈	—	2	8	no	—
73	C₄×C₅×C₈	—	2	4	no	—
74	C₅×#95	C₂×C₄	1	2	yes	—
75	C₅×#95	C₂×C₄	1	2	yes	—
76	C₅×#95	C₂×C₄	1	2	yes	—
77	C₂×C₈×D₄	C₂×C₅	1	2	yes	—
78	C₂²×C₄⋊C₈	C₂×C₅	1	2	yes	complemented
79	C₄²×D₄	C₂×C₅	1	1	yes	characteristic
80	#1939	C₂×C₅	1	2	yes	complemented
81	#1850	C₂×C₅	1	4	yes	complemented
82	#1842	C₂×C₅	1	1	yes	characteristic, complemented
83	#1797	C₂×C₅	1	2	yes	complemented
84	C₄×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
85	C₂⁴×C₅	C₂²×C₄	1	2	yes	—
86	C₂×C₅×D₄	C₄⋊C₄	1	4	yes	—
87	C₂×C₅×D₄	C₂×C₈	1	4	yes	—
88	C₂×C₅×D₄	M₁₆	1	4	yes	—
89	C₂²×C₄×C₅	—	2	4	no	—
90	C₂²×C₄×C₅	—	2	4	no	—
91	C₂²×C₄×C₅	—	2	2	no	—
92	C₂²×C₄×C₅	—	2	2	no	—
93	C₂²×C₄×C₅	—	2	2	no	—
94	C₂²×C₄×C₅	—	2	2	no	—
95	C₂²×C₄×C₅	—	2	4	no	—
96	C₂²×C₄×C₅	—	2	4	no	—
97	C₂²×C₄×C₅	—	4	2	no	—
98	C₂²×C₄×C₅	C₂×C₈	1	8	yes	complemented
99	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
109	C₂²×C₄×C₅	C₂×Q₈	1	4	yes	—
110	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
111	C₂×C₅×C₈	—	2	2	no	—
112	C₂×C₅×C₈	—	2	2	no	—
113	C₂×C₅×C₈	—	2	4	no	—
114	C₂×C₅×C₈	—	2	4	no	—
115	C₂×C₅×C₈	—	2	2	no	—
116	C₂×C₅×C₈	—	2	2	no	—
117	C₂×C₅×C₈	—	2	4	no	—
118	C₂×C₅×C₈	—	2	2	no	—
119	C₂×C₅×C₈	—	4	16	no	—
120	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
121	C₅×C₄⋊C₄	—	2	2	no	—
122	C₅×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
123	C₅×C₄⋊C₄	C₂×C₈	1	4	yes	complemented
124	C₅×C₂²⋊C₄	—	2	4	no	—
125	C₅×C₂²⋊C₄	C₄⋊C₄	1	8	yes	—
126	C₅×C₂²⋊C₄	C₂×C₈	1	8	yes	complemented
127	C₄²×C₅	—	2	4	no	—
128	C₄²×C₅	—	2	4	no	—
129	C₄²×C₅	—	2	2	no	—
130	C₄²×C₅	—	2	2	no	—
131	C₄²×C₅	—	2	2	no	—
132	C₄²×C₅	—	2	2	no	—
133	C₄²×C₅	—	2	1	no	—
134	C₄²×C₅	—	2	1	no	—
135	C₄²×C₅	—	4	1	no	—
136	C₄²×C₅	C₂×C₈	1	4	yes	complemented
137	C₄²×C₅	C₂×D₄	1	2	yes	—
138	C₄²×C₅	C₂×D₄	1	2	yes	—
139	C₄²×C₅	C₂×Q₈	1	2	yes	—
140	C₄²×C₅	#41	1	2	yes	—
141	C₂³×C₈	C₂²×C₅	1	4	yes	—
142	C₂×C₄×D₄	C₄×C₅	1	1	yes	characteristic
143	C₂×C₄×D₄	C₄×C₅	1	1	yes	characteristic
144	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
145	C₂²×C₄²	C₂²×C₅	1	2	yes	—
146	C₈×D₄	—	2	8	no	—
147	C₂×C₄⋊C₈	—	2	8	no	—
148	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
149	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
150	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
151	C₂×C₄⋊C₈	C₂²×C₅	1	4	yes	—
152	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
153	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
154	C₂×C₂²⋊C₈	C₂²×C₅	1	4	yes	—
155	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
156	C₄×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
157	C₄×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
158	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
159	C₄×C₂²⋊C₄	C₄×C₅	1	2	yes	—
160	C₄×C₂²⋊C₄	C₄×C₅	1	2	yes	—
161	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
162	C₄³	C₂²×C₅	1	1	yes	characteristic
163	#336	C₂²×C₅	1	4	yes	—
164	#336	C₂²×C₅	1	2	yes	—
165	C₂³×C₅	—	2	2	no	—
166	C₂³×C₅	—	2	2	no	—
167	C₂³×C₅	—	2	2	no	—
168	C₂³×C₅	—	2	2	no	—
169	C₂³×C₅	C₂×C₄⋊C₄	1	4	yes	—
170	C₂³×C₅	C₂²×C₈	1	4	yes	—
171	C₂³×C₅	C₂×M₁₆	1	4	yes	—
172	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
173	C₅×D₄	C₄⋊C₈	1	16	yes	direct product factor
174	C₂×C₄×C₅	—	2	2	no	—
175	C₂×C₄×C₅	—	2	2	no	—
176	C₂×C₄×C₅	—	2	1	no	—
177	C₂×C₄×C₅	—	2	2	no	—
178	C₂×C₄×C₅	—	2	1	no	—
179	C₂×C₄×C₅	—	2	1	no	—
180	C₂×C₄×C₅	—	2	2	no	—
181	C₂×C₄×C₅	—	2	1	no	—
182	C₂×C₄×C₅	—	2	1	no	—
183	C₂×C₄×C₅	—	2	1	no	—
184	C₂×C₄×C₅	—	2	4	no	—
185	C₂×C₄×C₅	—	2	4	no	—
186	C₂×C₄×C₅	—	2	4	no	—
187	C₂×C₄×C₅	—	2	4	no	—
188	C₂×C₄×C₅	—	2	16	no	—
189	C₂×C₄×C₅	—	2	2	no	—
190	C₂×C₄×C₅	—	2	1	no	—
191	C₂×C₄×C₅	—	2	1	no	—
192	C₂×C₄×C₅	—	2	2	no	—
193	C₂×C₄×C₅	—	2	1	no	—
194	C₂×C₄×C₅	—	2	2	no	—
195	C₂×C₄×C₅	—	4	8	no	—
196	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
197	C₂×C₄×C₅	C₂×C₄⋊C₄	1	4	yes	—
198	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
199	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
200	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
201	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
202	C₂×C₄×C₅	C₂²×C₈	1	4	yes	—
203	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
204	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
205	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
206	C₂×C₄×C₅	#131	1	2	yes	—
207	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
210	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
212	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
213	C₅×C₈	—	2	4	no	—
214	C₅×C₈	—	4	4	no	—
215	C₅×C₈	—	4	2	no	—
216	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
217	C₂³×C₄	C₂×C₄×C₅	1	2	yes	—
218	C₂³×C₄	C₂×C₄×C₅	1	2	yes	—
219	C₂³×C₄	C₂³×C₅	1	2	yes	—
220	C₂²×C₈	—	2	8	no	—
221	C₂²×C₈	—	2	8	no	—
222	C₂²×C₈	—	4	4	no	—
223	C₂²×C₈	C₂³×C₅	1	4	yes	—
224	C₂²×C₈	C₂³×C₅	1	2	yes	—
225	C₂²×C₈	C₂³×C₅	1	2	yes	—
226	C₄×D₄	—	2	4	no	—
227	C₄×D₄	C₅×C₈	1	8	yes	complemented
228	C₄×D₄	C₅×D₄	1	4	yes	—
229	C₄×D₄	C₅×Q₈	1	4	yes	—
230	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
231	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
232	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
233	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
234	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
235	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
236	C₂×C₄²	—	2	4	no	—
237	C₂×C₄²	—	2	4	no	—
238	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
239	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
240	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
241	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
242	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
243	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
244	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
245	C₂×C₄²	C₂³×C₅	1	2	yes	—
246	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
247	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
248	C₄⋊C₈	—	2	8	no	—
249	C₄⋊C₈	—	2	4	no	—
250	C₄⋊C₈	—	2	4	no	—
251	C₄⋊C₈	—	2	2	no	—
252	C₄⋊C₈	—	4	2	no	—
253	C₄⋊C₈	C₅×D₄	1	4	yes	direct product factor
254	C₂²⋊C₈	—	2	8	no	—
255	C₄×C₈	—	2	4	no	—
256	#95	C₂×C₄×C₅	1	2	yes	—
257	#95	C₂×C₄×C₅	1	2	yes	—
258	#95	C₂×C₄×C₅	1	2	yes	—
259	C₂²×C₅	—	2	4	no	—
260	C₂²×C₅	—	2	4	no	—
261	C₂²×C₅	—	2	4	no	—
262	C₂²×C₅	—	2	4	no	—
263	C₂²×C₅	—	2	4	no	—
264	C₂²×C₅	—	2	4	no	—
265	C₂²×C₅	C₂×C₄⋊C₈	1	8	yes	complemented
266	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
267	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
268	C₂²×C₅	#520	1	1	yes	characteristic
269	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
270	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
271	C₂²×C₅	C₂×#131	1	1	yes	characteristic
272	C₂²×C₅	#568	1	1	yes	characteristic
273	C₄×C₅	—	2	4	no	—
274	C₄×C₅	—	2	2	no	—
275	C₄×C₅	—	2	4	no	—
276	C₄×C₅	—	2	2	no	—
277	C₄×C₅	—	2	2	no	—
278	C₄×C₅	—	4	2	no	—
279	C₄×C₅	—	4	1	no	—
280	C₄×C₅	C₂×C₄⋊C₈	1	4	yes	complemented
281	C₄×C₅	C₈×D₄	1	4	yes	complemented
282	C₄×C₅	D₄²	1	1	yes	characteristic
283	C₄×C₅	#547	1	1	yes	characteristic
284	C₄×C₅	D₄×Q₈	1	1	yes	characteristic
285	C₄×C₅	#554	1	1	yes	characteristic
286	C₂⁴	C₂²×C₄×C₅	1	2	yes	—
287	C₂×D₄	C₅×C₄⋊C₄	1	4	yes	—
288	C₂×D₄	C₂×C₅×C₈	1	4	yes	—
289	C₂×D₄	C₅×M₁₆	1	4	yes	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	C₂×C₅×C₈	1	8	yes	complemented
300	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
301	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
302	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
303	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
304	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
305	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
306	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
307	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
308	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
310	C₂²×C₄	C₂×C₅×Q₈	1	4	yes	—
311	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	4	no	—
316	C₂×C₈	—	2	4	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	4	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	4	16	no	—
321	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	C₅×C₄⋊C₄	1	4	yes	—
324	C₄⋊C₄	C₂×C₅×C₈	1	4	yes	complemented
325	C₂²⋊C₄	—	2	4	no	—
326	C₂²⋊C₄	C₅×C₄⋊C₄	1	8	yes	—
327	C₂²⋊C₄	C₂×C₅×C₈	1	8	yes	complemented
328	C₄²	—	2	4	no	—
329	C₄²	—	2	4	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	2	1	no	—
335	C₄²	—	2	1	no	—
336	C₄²	—	4	1	no	—
337	C₄²	C₂×C₅×C₈	1	4	yes	complemented
338	C₄²	C₂×C₅×D₄	1	2	yes	—
339	C₄²	C₂×C₅×D₄	1	2	yes	—
340	C₄²	C₂×C₅×Q₈	1	2	yes	—
341	C₄²	C₅×#41	1	2	yes	—
342	C₂×C₅	—	2	8	no	—
343	C₂×C₅	D₄×C₄⋊C₄	1	1	yes	characteristic
344	C₂×C₅	C₂²×C₄⋊C₈	1	1	yes	characteristic
345	C₂×C₅	#2906	1	1	yes	characteristic
346	C₂×C₅	C₂×C₈×D₄	1	1	yes	characteristic
347	C₂×C₅	D₄×M₁₆	1	1	yes	characteristic
348	C₂×C₅	#2988	1	1	yes	characteristic
349	C₂×C₅	#2990	1	1	yes	characteristic
350	C₂³	—	2	2	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	2	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	C₂×C₅×C₄⋊C₄	1	4	yes	—
355	C₂³	C₂²×C₅×C₈	1	4	yes	—
356	C₂³	C₂×C₅×M₁₆	1	4	yes	—
357	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
358	D₄	C₅×C₄⋊C₈	1	16	yes	direct product factor
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	16	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	8	no	—
381	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
382	C₂×C₄	C₂×C₅×C₄⋊C₄	1	4	yes	—
383	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
384	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
385	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
386	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
387	C₂×C₄	C₂²×C₅×C₈	1	4	yes	—
388	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
389	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
390	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
391	C₂×C₄	C₅×#131	1	2	yes	—
392	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
393	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
394	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
395	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
396	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
397	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
398	C₈	—	2	4	no	—
399	C₈	—	4	4	no	—
400	C₈	—	4	2	no	—
401	C₅	D₄×C₄⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
402	C₂²	—	2	4	no	—
403	C₂²	—	2	4	no	—
404	C₂²	—	2	4	no	—
405	C₂²	—	2	4	no	—
406	C₂²	—	2	4	no	—
407	C₂²	—	2	4	no	—
408	C₂²	C₂×C₅×C₄⋊C₈	1	8	yes	complemented
409	C₂²	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
410	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
411	C₂²	C₅×#520	1	1	yes	characteristic
412	C₂²	C₂³×C₅×C₈	1	1	yes	characteristic
413	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
414	C₂²	C₂×C₅×#131	1	1	yes	characteristic
415	C₂²	C₅×#568	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	2	4	no	—
418	C₄	—	2	2	no	—
419	C₄	—	2	4	no	—
420	C₄	—	2	2	no	—
421	C₄	—	4	1	no	—
422	C₄	—	4	2	no	—
423	C₄	C₂×C₅×C₄⋊C₈	1	4	yes	complemented
424	C₄	C₅×C₈×D₄	1	4	yes	complemented
425	C₄	C₅×D₄²	1	1	yes	characteristic
426	C₄	C₅×#547	1	1	yes	characteristic
427	C₄	C₅×D₄×Q₈	1	1	yes	characteristic
428	C₄	C₅×#554	1	1	yes	characteristic
429	C₂	—	2	8	no	—
430	C₂	C₅×D₄×C₄⋊C₄	1	1	yes	characteristic
431	C₂	C₂²×C₅×C₄⋊C₈	1	1	yes	characteristic
432	C₂	C₅×#2906	1	1	yes	characteristic
433	C₂	C₂×C₅×C₈×D₄	1	1	yes	characteristic
434	C₂	C₅×D₄×M₁₆	1	1	yes	characteristic
435	C₂	C₅×#2988	1	1	yes	characteristic
436	C₂	C₅×#2990	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂²×C₅×C₄⋊C₈	C₂	semidirect
4. C₅×#1939	C₂	semidirect
5. C₅×#1850	C₂	semidirect
6. C₅×#1842	C₂	semidirect
7. C₅×#1797	C₂	semidirect
8. C₄×C₅×C₄⋊C₈	C₂	semidirect
33. D₄×C₄⋊C₈	C₅	direct (N × H)
45. C₄×C₅×D₄	C₈	semidirect
71. C₅×C₄⋊C₈	D₄	direct (N × H)
78. C₂²×C₄⋊C₈	C₂×C₅	semidirect
80. #1939	C₂×C₅	semidirect
81. #1850	C₂×C₅	semidirect
82. #1842	C₂×C₅	semidirect
83. #1797	C₂×C₅	semidirect
84. C₄×C₄⋊C₈	C₂×C₅	semidirect
98. C₂²×C₄×C₅	C₂×C₈	semidirect
123. C₅×C₄⋊C₄	C₂×C₈	semidirect
126. C₅×C₂²⋊C₄	C₂×C₈	semidirect
136. C₄²×C₅	C₂×C₈	semidirect
173. C₅×D₄	C₄⋊C₈	direct (N × H)
227. C₄×D₄	C₅×C₈	semidirect
253. C₄⋊C₈	C₅×D₄	direct (N × H)
265. C₂²×C₅	C₂×C₄⋊C₈	semidirect
280. C₄×C₅	C₂×C₄⋊C₈	semidirect
281. C₄×C₅	C₈×D₄	semidirect
299. C₂²×C₄	C₂×C₅×C₈	semidirect
324. C₄⋊C₄	C₂×C₅×C₈	semidirect
327. C₂²⋊C₄	C₂×C₅×C₈	semidirect
337. C₄²	C₂×C₅×C₈	semidirect
358. D₄	C₅×C₄⋊C₈	direct (N × H)
401. C₅	D₄×C₄⋊C₈	direct (N × H)
408. C₂²	C₂×C₅×C₄⋊C₈	semidirect
423. C₄	C₂×C₅×C₄⋊C₈	semidirect
424. C₄	C₅×C₈×D₄	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅×C₈×D₄	2
C₂²×C₅×C₄⋊C₈	2
C₄²×C₅×D₄	2
C₅×#1939	2
C₅×#1850	2
C₅×#1842	2
C₅×#1797	2
C₄×C₅×C₄⋊C₈	2
D₄×C₄⋊C₈	5

Subgroups — C5×D4×C4⋊C8 #11945366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₄×C₄⋊C₈ #11945366