Subgroups — C₂×C₅×#5163 #14426010

Order 1920.

1168 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×Q₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×#215	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#940	C₂	1	1	yes	maximal, characteristic
5	C₂×C₅×#832	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5163	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₅×#821	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#460	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂²×C₅×#67	—	2	1	no	—
13	C₂²×C₅×#67	—	2	1	no	—
14	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×SD₁₆	—	2	4	no	—
16	C₂×C₃×C₅×SD₁₆	C₂²	1	4	yes	complemented
17	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
18	C₅×Q₈×Dic₃	—	2	2	no	—
19	C₅×Q₈×Dic₃	C₂²	1	4	yes	complemented
20	C₂×C₅×#215	—	2	4	no	—
21	C₂×C₅×#215	C₂²	1	4	yes	complemented
22	C₅×#940	—	2	2	no	—
23	C₅×#940	C₂²	1	4	yes	—
24	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
25	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₅×Dic₃	—	2	1	no	—
27	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
28	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
29	C₅×#832	C₂²	1	4	yes	complemented
30	C₅×#821	C₂²	1	4	yes	complemented
31	C₅×Dic₃⋊C₈	C₂²	1	4	yes	complemented
32	C₂×#5163	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₂²×C₅×SD₁₆	—	3	1	no	—
34	C₂²×C₅×SD₁₆	D₃	1	1	yes	characteristic, complemented
35	C₂×C₅×#127	—	3	1	no	—
36	C₂×C₄×C₅×Q₈	—	3	1	no	—
37	C₅×#460	—	3	8	no	—
38	C₂×C₅×C₄⋊C₈	—	3	1	no	—
39	C₂×C₅×#102	—	3	1	no	—
40	C₂×C₅×#102	—	3	1	no	—
41	C₂⁴×C₃×C₅	—	2	1	no	—
42	C₂³×C₅×D₃	—	2	1	no	—
43	C₂×C₃×C₅×Q₈	—	2	1	no	—
44	C₂×C₃×C₅×Q₈	—	2	2	no	—
45	C₂×C₃×C₅×Q₈	D₄	1	4	yes	complemented
46	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
47	C₂×C₃×C₅×D₄	—	2	2	no	—
48	C₂×C₃×C₅×D₄	—	2	1	no	—
49	C₂×C₃×C₅×D₄	—	2	2	no	—
50	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
51	C₂²×C₃×C₄×C₅	—	2	1	no	—
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂×C₅×#67	—	2	4	no	—
54	C₂×C₅×#67	—	2	4	no	—
55	C₂×C₅×#67	—	4	4	no	—
56	C₂×C₅×#67	—	4	4	no	—
57	C₂²×C₅×Dic₃	—	2	1	no	—
58	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
59	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
60	C₂×C₅×D₁₂	—	2	2	no	—
61	C₂×C₅×D₁₂	—	2	2	no	—
62	C₂×C₅×D₁₂	—	2	1	no	—
63	C₂×C₅×D₁₂	C₂³	1	2	yes	—
64	C₃×C₅×SD₁₆	—	2	8	no	—
65	C₂×C₃×C₅×C₈	—	2	2	no	—
66	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
67	C₅×#215	—	2	8	no	—
68	C₅×C₄⋊Dic₃	—	2	1	no	—
69	C₅×C₄⋊Dic₃	—	2	4	no	—
70	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
71	C₄×C₅×Dic₃	—	2	4	no	—
72	C₄×C₅×Dic₃	D₄	1	2	yes	—
73	C₄×C₅×Dic₃	C₂³	1	2	yes	—
74	C₂×C₅×C₃⋊C₈	—	2	2	no	—
75	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
76	C₂²×C₃×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
77	C₂×Q₈×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
78	C₂²×#215	C₂×C₅	1	1	yes	characteristic, complemented
79	C₂×#940	C₂×C₅	1	1	yes	characteristic
80	C₂×#832	C₂×C₅	1	1	yes	characteristic, complemented
81	#5163	C₂×C₅	1	8	yes	direct product factor
82	C₂×#821	C₂×C₅	1	1	yes	characteristic, complemented
83	C₂×Dic₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
84	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
85	C₂²×C₅×D₄	—	3	1	no	—
86	C₂²×C₅×D₄	—	6	1	no	—
87	C₂²×C₅×D₄	—	6	1	no	—
88	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
89	C₂×C₅×SD₁₆	—	2	4	no	—
90	C₂×C₅×SD₁₆	—	3	4	no	—
91	C₂×C₅×SD₁₆	—	6	4	no	—
92	C₂×C₅×SD₁₆	C₂×D₃	1	4	yes	complemented
93	C₂²×C₅×C₈	—	3	1	no	—
94	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
95	C₅×#127	—	3	4	no	—
96	C₅×#127	—	6	2	no	—
97	C₄×C₅×Q₈	—	3	4	no	—
98	C₄×C₅×Q₈	—	6	2	no	—
99	C₂×C₅×C₄⋊C₄	—	3	1	no	—
100	C₂×C₅×C₄⋊C₄	—	6	1	no	—
101	C₂×C₄²×C₅	—	3	1	no	—
102	C₂×C₄²×C₅	—	6	1	no	—
103	C₅×C₄⋊C₈	—	3	4	no	—
104	C₅×#102	—	3	4	no	—
105	C₅×#102	—	3	4	no	—
106	C₂×#460	—	3	1	no	Sylow
107	C₂³×C₃×C₅	—	2	2	no	—
108	C₂³×C₃×C₅	—	4	2	no	—
109	C₂³×C₃×C₅	—	4	2	no	—
110	C₂³×C₃×C₅	—	4	2	no	—
111	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₅×D₃	—	2	2	no	—
113	C₂²×C₅×D₃	—	4	2	no	—
114	C₂²×C₅×D₃	—	4	2	no	—
115	C₂²×C₅×D₃	—	4	2	no	—
116	C₃×C₅×Q₈	—	2	4	no	—
117	C₃×C₅×Q₈	—	2	2	no	—
118	C₃×C₅×Q₈	C₂×D₄	1	4	yes	complemented
119	C₃×C₅×D₄	—	2	2	no	—
120	C₃×C₅×D₄	—	2	2	no	—
121	C₃×C₅×D₄	—	4	2	no	—
122	C₂×C₃×C₄×C₅	—	2	4	no	—
123	C₂×C₃×C₄×C₅	—	2	2	no	—
124	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
125	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
126	C₂×C₃×C₄×C₅	#41	1	2	yes	—
127	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
128	C₅×#67	—	4	8	no	—
129	C₅×#67	—	4	8	no	—
130	C₂×C₅×Dic₃	—	2	2	no	—
131	C₂×C₅×Dic₃	—	2	2	no	—
132	C₂×C₅×Dic₃	—	4	2	no	—
133	C₂×C₅×Dic₃	SD₁₆	1	4	yes	complemented
134	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
135	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
136	C₅×D₁₂	—	2	2	no	—
137	C₅×D₁₂	—	2	2	no	—
138	C₅×D₁₂	—	4	2	no	—
139	C₃×C₅×C₈	—	2	2	no	—
140	C₅×C₃⋊C₈	—	2	2	no	—
141	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
142	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
143	C₂²×#67	—	2	1	no	—
144	C₂²×#67	—	2	1	no	—
145	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
146	C₂×C₃×SD₁₆	—	2	4	no	—
147	C₂×C₃×SD₁₆	C₂²×C₅	1	4	yes	complemented
148	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
149	Q₈×Dic₃	—	2	2	no	—
150	Q₈×Dic₃	C₂²×C₅	1	4	yes	complemented
151	C₂×#215	—	2	4	no	—
152	C₂×#215	C₂²×C₅	1	4	yes	complemented
153	#940	—	2	2	no	—
154	#940	C₂²×C₅	1	4	yes	—
155	C₂×C₄⋊Dic₃	—	2	1	no	—
156	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
157	C₂×C₄×Dic₃	—	2	1	no	—
158	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
159	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
160	#832	C₂²×C₅	1	4	yes	complemented
161	#821	C₂²×C₅	1	4	yes	complemented
162	Dic₃⋊C₈	C₂²×C₅	1	4	yes	complemented
163	C₂⁴×C₅	—	2	1	no	—
164	C₂⁴×C₅	—	6	1	no	—
165	C₂×C₅×Q₈	—	2	1	no	—
166	C₂×C₅×Q₈	—	2	2	no	—
167	C₂×C₅×Q₈	#67	1	4	yes	complemented
168	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
169	C₂×C₅×D₄	—	2	1	no	—
170	C₂×C₅×D₄	—	2	2	no	—
171	C₂×C₅×D₄	—	2	2	no	—
172	C₂×C₅×D₄	—	3	2	no	—
173	C₂×C₅×D₄	—	6	4	no	—
174	C₂×C₅×D₄	—	6	4	no	—
175	C₂×C₅×D₄	—	6	1	no	—
176	C₂×C₅×D₄	—	6	2	no	—
177	C₂×C₅×D₄	—	6	2	no	—
178	C₂×C₅×D₄	—	12	4	no	—
179	C₂×C₅×D₄	—	12	4	no	—
180	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
181	C₂²×C₄×C₅	—	2	1	no	—
182	C₂²×C₄×C₅	—	3	1	no	—
183	C₂²×C₄×C₅	—	3	1	no	—
184	C₂²×C₄×C₅	—	6	1	no	—
185	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
186	C₅×SD₁₆	—	2	8	no	—
187	C₅×SD₁₆	—	6	8	no	—
188	C₂×C₅×C₈	—	2	2	no	—
189	C₂×C₅×C₈	—	3	2	no	—
190	C₂×C₅×C₈	—	6	2	no	—
191	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
192	C₅×C₄⋊C₄	—	3	2	no	—
193	C₅×C₄⋊C₄	—	6	4	no	—
194	C₅×C₄⋊C₄	—	6	1	no	—
195	C₄²×C₅	—	3	2	no	—
196	C₄²×C₅	—	3	2	no	—
197	C₄²×C₅	—	6	4	no	—
198	C₂²×SD₁₆	—	3	1	no	—
199	C₂²×SD₁₆	C₅×D₃	1	1	yes	characteristic, complemented
200	C₂×#127	—	3	1	no	—
201	C₂×C₄×Q₈	—	3	1	no	—
202	#460	—	3	8	no	—
203	C₂×C₄⋊C₈	—	3	1	no	—
204	C₂×#102	—	3	1	no	—
205	C₂×#102	—	3	1	no	—
206	C₂²×C₃×C₅	—	4	2	no	—
207	C₂²×C₃×C₅	—	4	2	no	—
208	C₂²×C₃×C₅	—	4	2	no	—
209	C₂²×C₃×C₅	—	8	4	no	—
210	C₂²×C₃×C₅	#121	1	2	yes	—
211	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
212	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
213	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₅×D₃	—	4	2	no	—
215	C₂×C₅×D₃	—	4	2	no	—
216	C₂×C₅×D₃	—	4	2	no	—
217	C₂×C₅×D₃	—	8	4	no	—
218	C₃×C₄×C₅	—	2	4	no	—
219	C₃×C₄×C₅	#121	1	2	yes	—
220	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
221	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
222	C₅×Dic₃	—	2	2	no	—
223	C₅×Dic₃	—	4	2	no	—
224	C₅×Dic₃	C₂×SD₁₆	1	4	yes	complemented
225	C₂⁴×C₃	—	2	1	no	—
226	C₂³×D₃	—	2	1	no	—
227	C₂×C₃×Q₈	—	2	1	no	—
228	C₂×C₃×Q₈	—	2	2	no	—
229	C₂×C₃×Q₈	C₅×D₄	1	4	yes	complemented
230	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
231	C₂×C₃×D₄	—	2	2	no	—
232	C₂×C₃×D₄	—	2	1	no	—
233	C₂×C₃×D₄	—	2	2	no	—
234	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
235	C₂²×C₃×C₄	—	2	1	no	—
236	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
237	C₂×#67	—	2	4	no	—
238	C₂×#67	—	2	4	no	—
239	C₂×#67	—	4	4	no	—
240	C₂×#67	—	4	4	no	—
241	C₂²×Dic₃	—	2	1	no	—
242	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
243	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
244	C₂×D₁₂	—	2	2	no	—
245	C₂×D₁₂	—	2	2	no	—
246	C₂×D₁₂	—	2	1	no	—
247	C₂×D₁₂	C₂³×C₅	1	2	yes	—
248	C₃×SD₁₆	—	2	8	no	—
249	C₂×C₃×C₈	—	2	2	no	—
250	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
251	#215	—	2	8	no	—
252	C₄⋊Dic₃	—	2	1	no	—
253	C₄⋊Dic₃	—	2	4	no	—
254	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
255	C₄×Dic₃	—	2	4	no	—
256	C₄×Dic₃	C₅×D₄	1	2	yes	—
257	C₄×Dic₃	C₂³×C₅	1	2	yes	—
258	C₂×C₃⋊C₈	—	2	2	no	—
259	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
260	C₂³×C₅	—	2	2	no	—
261	C₂³×C₅	—	4	2	no	—
262	C₂³×C₅	—	4	2	no	—
263	C₂³×C₅	—	4	2	no	—
264	C₂³×C₅	—	6	2	no	—
265	C₂³×C₅	—	12	2	no	—
266	C₂³×C₅	—	12	2	no	—
267	C₂³×C₅	—	12	2	no	—
268	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
269	C₅×Q₈	—	2	4	no	—
270	C₅×Q₈	—	2	2	no	—
271	C₅×Q₈	C₂×#67	1	4	yes	complemented
272	C₅×D₄	—	2	2	no	—
273	C₅×D₄	—	2	2	no	—
274	C₅×D₄	—	4	2	no	—
275	C₅×D₄	—	6	2	no	—
276	C₅×D₄	—	6	2	no	—
277	C₅×D₄	—	12	8	no	—
278	C₅×D₄	—	12	8	no	—
279	C₅×D₄	—	12	2	no	—
280	C₂×C₄×C₅	—	2	4	no	—
281	C₂×C₄×C₅	—	2	2	no	—
282	C₂×C₄×C₅	—	3	4	no	—
283	C₂×C₄×C₅	—	3	2	no	—
284	C₂×C₄×C₅	—	3	2	no	—
285	C₂×C₄×C₅	—	6	2	no	—
286	C₂×C₄×C₅	—	6	2	no	—
287	C₂×C₄×C₅	—	12	2	no	—
288	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
289	C₂×C₄×C₅	#237	1	2	yes	—
290	C₂×C₄×C₅	C₂×#67	1	2	yes	—
291	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
292	C₅×C₈	—	2	2	no	—
293	C₅×C₈	—	6	2	no	—
294	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
295	C₂²×D₄	—	3	1	no	—
296	C₂²×D₄	—	6	1	no	—
297	C₂²×D₄	—	6	1	no	—
298	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
299	C₂×SD₁₆	—	2	4	no	—
300	C₂×SD₁₆	—	3	4	no	—
301	C₂×SD₁₆	—	6	4	no	—
302	C₂×SD₁₆	C₂×C₅×D₃	1	4	yes	complemented
303	C₂²×C₈	—	3	1	no	—
304	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
305	#127	—	3	4	no	—
306	#127	—	6	2	no	—
307	C₄×Q₈	—	3	4	no	—
308	C₄×Q₈	—	6	2	no	—
309	C₂×C₄⋊C₄	—	3	1	no	—
310	C₂×C₄⋊C₄	—	6	1	no	—
311	C₂×C₄²	—	3	1	no	—
312	C₂×C₄²	—	6	1	no	—
313	C₄⋊C₈	—	3	4	no	—
314	#102	—	3	4	no	—
315	#102	—	3	4	no	—
316	C₂×C₃×C₅	—	8	2	no	—
317	C₂×C₃×C₅	#460	1	4	yes	complemented
318	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
319	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
320	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
321	C₅×D₃	—	8	2	no	—
322	C₂³×C₃	—	2	2	no	—
323	C₂³×C₃	—	4	2	no	—
324	C₂³×C₃	—	4	2	no	—
325	C₂³×C₃	—	4	2	no	—
326	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
327	C₂²×D₃	—	2	2	no	—
328	C₂²×D₃	—	4	2	no	—
329	C₂²×D₃	—	4	2	no	—
330	C₂²×D₃	—	4	2	no	—
331	C₃×Q₈	—	2	4	no	—
332	C₃×Q₈	—	2	2	no	—
333	C₃×Q₈	C₂×C₅×D₄	1	4	yes	complemented
334	C₃×D₄	—	2	2	no	—
335	C₃×D₄	—	2	2	no	—
336	C₃×D₄	—	4	2	no	—
337	C₂×C₃×C₄	—	2	4	no	—
338	C₂×C₃×C₄	—	2	2	no	—
339	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
340	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
341	C₂×C₃×C₄	C₅×#41	1	2	yes	—
342	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
343	#67	—	4	8	no	—
344	#67	—	4	8	no	—
345	C₂×Dic₃	—	2	2	no	—
346	C₂×Dic₃	—	2	2	no	—
347	C₂×Dic₃	—	4	2	no	—
348	C₂×Dic₃	C₅×SD₁₆	1	4	yes	complemented
349	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
350	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
351	D₁₂	—	2	2	no	—
352	D₁₂	—	2	2	no	—
353	D₁₂	—	4	2	no	—
354	C₃×C₈	—	2	2	no	—
355	C₃⋊C₈	—	2	2	no	—
356	C₂²×C₅	—	4	2	no	—
357	C₂²×C₅	—	4	2	no	—
358	C₂²×C₅	—	4	2	no	—
359	C₂²×C₅	—	8	4	no	—
360	C₂²×C₅	—	12	2	no	—
361	C₂²×C₅	—	12	2	no	—
362	C₂²×C₅	—	12	2	no	—
363	C₂²×C₅	—	24	4	no	—
364	C₂²×C₅	D₃×SD₁₆	1	2	yes	—
365	C₂²×C₅	#914	1	2	yes	—
366	C₂²×C₅	#939	1	2	yes	—
367	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
368	C₄×C₅	—	2	4	no	—
369	C₄×C₅	—	3	4	no	—
370	C₄×C₅	—	6	2	no	—
371	C₄×C₅	—	12	2	no	—
372	C₄×C₅	#939	1	2	yes	—
373	C₄×C₅	C₂×#237	1	1	yes	characteristic
374	C₄×C₅	C₂²×#67	1	1	yes	characteristic
375	C₂⁴	—	2	1	no	—
376	C₂⁴	—	6	1	no	—
377	C₂×Q₈	—	2	1	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	C₅×#67	1	4	yes	complemented
380	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	3	2	no	—
385	C₂×D₄	—	6	4	no	—
386	C₂×D₄	—	6	4	no	—
387	C₂×D₄	—	6	1	no	—
388	C₂×D₄	—	6	2	no	—
389	C₂×D₄	—	6	2	no	—
390	C₂×D₄	—	12	4	no	—
391	C₂×D₄	—	12	4	no	—
392	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	3	1	no	—
395	C₂²×C₄	—	3	1	no	—
396	C₂²×C₄	—	6	1	no	—
397	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
398	SD₁₆	—	2	8	no	—
399	SD₁₆	—	6	8	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	3	2	no	—
402	C₂×C₈	—	6	2	no	—
403	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
404	C₄⋊C₄	—	3	2	no	—
405	C₄⋊C₄	—	6	4	no	—
406	C₄⋊C₄	—	6	1	no	—
407	C₄²	—	3	2	no	—
408	C₄²	—	3	2	no	—
409	C₄²	—	6	4	no	—
410	C₃×C₅	C₂×#460	1	1	yes	characteristic, complemented, Hall
411	C₂²×C₃	—	4	2	no	—
412	C₂²×C₃	—	4	2	no	—
413	C₂²×C₃	—	4	2	no	—
414	C₂²×C₃	—	8	4	no	—
415	C₂²×C₃	C₅×#121	1	2	yes	—
416	C₂²×C₃	C₂×C₅×SD₁₆	1	2	yes	—
417	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
418	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
419	C₂×D₃	—	4	2	no	—
420	C₂×D₃	—	4	2	no	—
421	C₂×D₃	—	4	2	no	—
422	C₂×D₃	—	8	4	no	—
423	C₃×C₄	—	2	4	no	—
424	C₃×C₄	C₅×#121	1	2	yes	—
425	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
426	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
427	Dic₃	—	2	2	no	—
428	Dic₃	—	4	2	no	—
429	Dic₃	C₂×C₅×SD₁₆	1	4	yes	complemented
430	C₂×C₅	—	8	2	no	—
431	C₂×C₅	—	24	2	no	—
432	C₂×C₅	#5163	1	4	yes	direct product factor
433	C₂×C₅	C₂×D₃×SD₁₆	1	1	yes	characteristic
434	C₂×C₅	C₂×#914	1	1	yes	characteristic
435	C₂×C₅	C₂×#939	1	1	yes	characteristic
436	C₂³	—	2	2	no	—
437	C₂³	—	4	2	no	—
438	C₂³	—	4	2	no	—
439	C₂³	—	4	2	no	—
440	C₂³	—	6	2	no	—
441	C₂³	—	12	2	no	—
442	C₂³	—	12	2	no	—
443	C₂³	—	12	2	no	—
444	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
445	Q₈	—	2	4	no	—
446	Q₈	—	2	2	no	—
447	Q₈	C₂×C₅×#67	1	4	yes	complemented
448	D₄	—	2	2	no	—
449	D₄	—	2	2	no	—
450	D₄	—	4	2	no	—
451	D₄	—	6	2	no	—
452	D₄	—	6	2	no	—
453	D₄	—	12	8	no	—
454	D₄	—	12	8	no	—
455	D₄	—	12	2	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	3	4	no	—
459	C₂×C₄	—	3	2	no	—
460	C₂×C₄	—	3	2	no	—
461	C₂×C₄	—	6	2	no	—
462	C₂×C₄	—	6	2	no	—
463	C₂×C₄	—	12	2	no	—
464	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
465	C₂×C₄	C₅×#237	1	2	yes	—
466	C₂×C₄	C₂×C₅×#67	1	2	yes	—
467	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
468	C₈	—	2	2	no	—
469	C₈	—	6	2	no	—
470	C₂×C₃	—	8	2	no	—
471	C₂×C₃	C₅×#460	1	4	yes	complemented
472	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
473	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
474	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
475	D₃	—	8	2	no	—
476	C₅	C₂×#5163	1	1	yes	characteristic, direct product factor, Sylow
477	C₂²	—	4	2	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	8	4	no	—
481	C₂²	—	12	2	no	—
482	C₂²	—	12	2	no	—
483	C₂²	—	12	2	no	—
484	C₂²	—	24	4	no	—
485	C₂²	C₅×D₃×SD₁₆	1	2	yes	—
486	C₂²	C₅×#914	1	2	yes	—
487	C₂²	C₅×#939	1	2	yes	—
488	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
489	C₄	—	2	4	no	—
490	C₄	—	3	4	no	—
491	C₄	—	6	2	no	—
492	C₄	—	12	2	no	—
493	C₄	C₅×#939	1	2	yes	—
494	C₄	C₂×C₅×#237	1	1	yes	characteristic
495	C₄	C₂²×C₅×#67	1	1	yes	characteristic
496	C₃	C₂×C₅×#460	1	1	yes	characteristic, complemented, Sylow
497	C₂	—	8	2	no	—
498	C₂	—	24	2	no	—
499	C₂	C₅×#5163	1	4	yes	direct product factor
500	C₂	C₂×C₅×D₃×SD₁₆	1	1	yes	characteristic
501	C₂	C₂×C₅×#914	1	1	yes	characteristic
502	C₂	C₂×C₅×#939	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂²×C₃×C₅×SD₁₆	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂×C₅×#940	C₂
hypercenter	C₂²×C₅×SD₁₆	D₃
hypocenter	C₃	C₂×C₅×#460
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅ ◁ C₂²×C₅×SD₁₆

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×SD₁₆	C₂	semidirect
2. C₂×C₅×Q₈×Dic₃	C₂	semidirect
3. C₂²×C₅×#215	C₂	semidirect
5. C₂×C₅×#832	C₂	semidirect
6. C₅×#5163	C₂	direct (N × H)
7. C₂×C₅×#821	C₂	semidirect
8. C₂×C₅×Dic₃⋊C₈	C₂	semidirect
16. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
19. C₅×Q₈×Dic₃	C₂²	semidirect
21. C₂×C₅×#215	C₂²	semidirect
29. C₅×#832	C₂²	semidirect
30. C₅×#821	C₂²	semidirect
31. C₅×Dic₃⋊C₈	C₂²	semidirect
32. C₂×#5163	C₅	direct (N × H)
34. C₂²×C₅×SD₁₆	D₃	semidirect
45. C₂×C₃×C₅×Q₈	D₄	semidirect
76. C₂²×C₃×SD₁₆	C₂×C₅	semidirect
77. C₂×Q₈×Dic₃	C₂×C₅	semidirect
78. C₂²×#215	C₂×C₅	semidirect
80. C₂×#832	C₂×C₅	semidirect
81. #5163	C₂×C₅	direct (N × H)
82. C₂×#821	C₂×C₅	semidirect
83. C₂×Dic₃⋊C₈	C₂×C₅	semidirect
92. C₂×C₅×SD₁₆	C₂×D₃	semidirect
118. C₃×C₅×Q₈	C₂×D₄	semidirect
133. C₂×C₅×Dic₃	SD₁₆	semidirect
147. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
150. Q₈×Dic₃	C₂²×C₅	semidirect
152. C₂×#215	C₂²×C₅	semidirect
160. #832	C₂²×C₅	semidirect
161. #821	C₂²×C₅	semidirect
162. Dic₃⋊C₈	C₂²×C₅	semidirect
167. C₂×C₅×Q₈	#67	semidirect
199. C₂²×SD₁₆	C₅×D₃	semidirect
224. C₅×Dic₃	C₂×SD₁₆	semidirect
229. C₂×C₃×Q₈	C₅×D₄	semidirect
271. C₅×Q₈	C₂×#67	semidirect
302. C₂×SD₁₆	C₂×C₅×D₃	semidirect
317. C₂×C₃×C₅	#460	semidirect
333. C₃×Q₈	C₂×C₅×D₄	semidirect
348. C₂×Dic₃	C₅×SD₁₆	semidirect
379. C₂×Q₈	C₅×#67	semidirect
410. C₃×C₅	C₂×#460	semidirect
429. Dic₃	C₂×C₅×SD₁₆	semidirect
432. C₂×C₅	#5163	direct (N × H)
447. Q₈	C₂×C₅×#67	semidirect
471. C₂×C₃	C₅×#460	semidirect
476. C₅	C₂×#5163	direct (N × H)
496. C₃	C₂×C₅×#460	semidirect
499. C₂	C₅×#5163	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×C₃×C₅×SD₁₆	2
C₂×C₅×Q₈×Dic₃	2
C₂²×C₅×#215	2
C₂×C₅×#940	2
C₂×C₅×#832	2
C₅×#5163	2
C₂×C₅×#821	2
C₂×C₅×Dic₃⋊C₈	2
C₂×C₅×#460	3
C₂×#5163	5

Subgroups — C2×C5×#5163 #14426010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5163 #14426010