Subgroups — C₂×C₅×#5164 #14416323

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 444 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
2	C₂×C₅×Q₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₄×Dic₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#835	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#832	C₂	1	1	yes	maximal, characteristic
6	C₅×#5164	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₅×#818	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#815	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#440	—	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	C₂³×C₅×Dic₃	—	2	1	no	—
13	C₂×C₃×C₅×SD₁₆	C₄	1	8	yes	complemented
14	C₂×C₃×C₅×SD₁₆	C₂²	1	4	yes	—
15	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₂×C₅×#217	—	2	1	no	—
17	C₅×Q₈×Dic₃	—	2	2	no	—
18	C₅×Q₈×Dic₃	C₂²	1	4	yes	complemented
19	C₅×D₄×Dic₃	—	2	2	no	—
20	C₅×D₄×Dic₃	C₂²	1	4	yes	—
21	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
22	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
23	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₅×Dic₃	—	2	1	no	—
25	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
26	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
27	C₅×#835	C₂²	1	4	yes	complemented
28	C₅×#832	C₂²	1	4	yes	—
29	C₅×#818	C₂²	1	4	yes	complemented
30	C₅×#815	C₂²	1	4	yes	complemented
31	C₂×#5164	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂²×C₅×SD₁₆	D₃	1	1	yes	characteristic
33	C₂×C₄×C₅×Q₈	—	3	1	no	—
34	C₂×C₄×C₅×D₄	—	3	1	no	—
35	C₅×#440	—	3	8	no	—
36	C₂×C₅×#107	—	3	1	no	—
37	C₂×C₅×#103	—	3	1	no	—
38	C₂×C₅×#102	—	3	1	no	—
39	C₂×C₅×#97	—	3	1	no	—
40	C₂⁴×C₃×C₅	—	2	1	no	—
41	C₂×C₃×C₅×Q₈	—	2	1	no	—
42	C₂×C₃×C₅×Q₈	—	2	2	no	—
43	C₂×C₃×C₅×Q₈	C₂×C₄	1	4	yes	complemented
44	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
45	C₂×C₃×C₅×D₄	—	2	1	no	—
46	C₂×C₃×C₅×D₄	—	2	2	no	—
47	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
48	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
49	C₂²×C₃×C₄×C₅	—	2	1	no	—
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂²×C₅×Dic₃	—	2	1	no	—
52	C₂²×C₅×Dic₃	—	2	1	no	—
53	C₂²×C₅×Dic₃	—	2	4	no	—
54	C₂²×C₅×Dic₃	—	4	4	no	—
55	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
56	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
57	C₃×C₅×SD₁₆	C₂×C₄	1	16	yes	complemented
58	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
59	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
60	C₅×#217	—	2	4	no	—
61	C₅×C₄⋊Dic₃	—	2	1	no	—
62	C₅×C₄⋊Dic₃	—	2	1	no	—
63	C₅×C₄⋊Dic₃	—	2	4	no	—
64	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
65	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
66	C₄×C₅×Dic₃	—	2	4	no	—
67	C₄×C₅×Dic₃	D₄	1	2	yes	—
68	C₄×C₅×Dic₃	C₂³	1	2	yes	—
69	C₂×C₅×C₃⋊C₈	—	2	2	no	—
70	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
71	C₂²×C₃×SD₁₆	C₂×C₅	1	1	yes	characteristic
72	C₂×Q₈×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
73	C₂×D₄×Dic₃	C₂×C₅	1	1	yes	characteristic
74	C₂×#835	C₂×C₅	1	1	yes	characteristic, complemented
75	C₂×#832	C₂×C₅	1	1	yes	characteristic
76	#5164	C₂×C₅	1	8	yes	direct product factor
77	C₂×#818	C₂×C₅	1	1	yes	characteristic, complemented
78	C₂×#815	C₂×C₅	1	1	yes	characteristic, complemented
79	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
80	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
81	C₂³×C₄×C₅	—	6	1	no	—
82	C₂×C₅×SD₁₆	Dic₃	1	8	yes	complemented
83	C₂×C₅×SD₁₆	C₂×D₃	1	4	yes	—
84	C₂²×C₅×C₈	—	3	1	no	—
85	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
86	C₄×C₅×Q₈	—	3	4	no	—
87	C₄×C₅×Q₈	—	6	2	no	—
88	C₄×C₅×D₄	—	3	4	no	—
89	C₄×C₅×D₄	—	6	2	no	—
90	C₂×C₅×C₄⋊C₄	—	3	1	no	—
91	C₂×C₅×C₄⋊C₄	—	3	1	no	—
92	C₂×C₅×C₄⋊C₄	—	6	1	no	—
93	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
94	C₂×C₄²×C₅	—	3	1	no	—
95	C₂×C₄²×C₅	—	6	1	no	—
96	C₅×#107	—	3	4	no	—
97	C₅×#103	—	3	4	no	—
98	C₅×#102	—	3	4	no	—
99	C₅×#97	—	3	4	no	—
100	C₂×#440	—	3	1	no	Sylow
101	C₂³×C₃×C₅	—	2	4	no	—
102	C₂³×C₃×C₅	—	2	2	no	—
103	C₂³×C₃×C₅	—	4	2	no	—
104	C₂³×C₃×C₅	—	4	2	no	—
105	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
106	C₃×C₅×Q₈	—	2	4	no	—
107	C₃×C₅×Q₈	—	2	2	no	—
108	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	complemented
109	C₃×C₅×D₄	—	2	4	no	—
110	C₃×C₅×D₄	—	2	2	no	—
111	C₃×C₅×D₄	C₂²×C₄	1	4	yes	—
112	C₂×C₃×C₄×C₅	—	2	4	no	—
113	C₂×C₃×C₄×C₅	—	2	2	no	—
114	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
115	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
116	C₂×C₃×C₄×C₅	#41	1	2	yes	—
117	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
118	C₂×C₅×Dic₃	—	2	2	no	—
119	C₂×C₅×Dic₃	—	2	2	no	—
120	C₂×C₅×Dic₃	—	2	2	no	—
121	C₂×C₅×Dic₃	—	2	2	no	—
122	C₂×C₅×Dic₃	—	4	8	no	—
123	C₂×C₅×Dic₃	—	4	2	no	—
124	C₂×C₅×Dic₃	—	4	2	no	—
125	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
126	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
127	C₃×C₅×C₈	C₂²×C₄	1	4	yes	complemented
128	C₅×C₃⋊C₈	—	2	2	no	—
129	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
130	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
131	C₂³×Dic₃	—	2	1	no	—
132	C₂×C₃×SD₁₆	C₄×C₅	1	8	yes	complemented
133	C₂×C₃×SD₁₆	C₂²×C₅	1	4	yes	—
134	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
135	C₂×#217	—	2	1	no	—
136	Q₈×Dic₃	—	2	2	no	—
137	Q₈×Dic₃	C₂²×C₅	1	4	yes	complemented
138	D₄×Dic₃	—	2	2	no	—
139	D₄×Dic₃	C₂²×C₅	1	4	yes	—
140	C₂×C₄⋊Dic₃	—	2	1	no	—
141	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
142	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
143	C₂×C₄×Dic₃	—	2	1	no	—
144	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
145	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
146	#835	C₂²×C₅	1	4	yes	complemented
147	#832	C₂²×C₅	1	4	yes	—
148	#818	C₂²×C₅	1	4	yes	complemented
149	#815	C₂²×C₅	1	4	yes	complemented
150	C₂⁴×C₅	—	2	1	no	—
151	C₂×C₅×Q₈	—	2	1	no	—
152	C₂×C₅×Q₈	—	2	2	no	—
153	C₂×C₅×Q₈	C₂×Dic₃	1	4	yes	complemented
154	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
155	C₂×C₅×D₄	—	2	1	no	—
156	C₂×C₅×D₄	—	2	2	no	—
157	C₂×C₅×D₄	C₂×Dic₃	1	4	yes	—
158	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
159	C₂²×C₄×C₅	—	2	1	no	—
160	C₂²×C₄×C₅	—	3	1	no	—
161	C₂²×C₄×C₅	—	3	1	no	—
162	C₂²×C₄×C₅	—	6	4	no	—
163	C₂²×C₄×C₅	—	6	1	no	—
164	C₂²×C₄×C₅	—	6	1	no	—
165	C₂²×C₄×C₅	—	12	4	no	—
166	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
167	C₅×SD₁₆	C₂×Dic₃	1	16	yes	complemented
168	C₂×C₅×C₈	—	3	2	no	—
169	C₂×C₅×C₈	—	6	2	no	—
170	C₂×C₅×C₈	C₂×Dic₃	1	4	yes	complemented
171	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
172	C₅×C₄⋊C₄	—	3	2	no	—
173	C₅×C₄⋊C₄	—	3	2	no	—
174	C₅×C₄⋊C₄	—	6	4	no	—
175	C₅×C₄⋊C₄	—	6	1	no	—
176	C₅×C₄⋊C₄	—	6	1	no	—
177	C₅×C₂²⋊C₄	—	6	4	no	—
178	C₄²×C₅	—	3	2	no	—
179	C₄²×C₅	—	3	2	no	—
180	C₄²×C₅	—	6	4	no	—
181	C₂²×SD₁₆	C₅×D₃	1	1	yes	characteristic
182	C₂×C₄×Q₈	—	3	1	no	—
183	C₂×C₄×D₄	—	3	1	no	—
184	#440	—	3	8	no	—
185	C₂×#107	—	3	1	no	—
186	C₂×#103	—	3	1	no	—
187	C₂×#102	—	3	1	no	—
188	C₂×#97	—	3	1	no	—
189	C₂²×C₃×C₅	—	2	4	no	—
190	C₂²×C₃×C₅	—	4	2	no	—
191	C₂²×C₃×C₅	—	4	2	no	—
192	C₂²×C₃×C₅	—	4	8	no	—
193	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
194	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
195	C₂²×C₃×C₅	#137	1	2	yes	—
196	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
197	C₃×C₄×C₅	—	2	4	no	—
198	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
199	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
200	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
201	C₅×Dic₃	—	2	2	no	—
202	C₅×Dic₃	—	2	2	no	—
203	C₅×Dic₃	—	4	2	no	—
204	C₅×Dic₃	—	4	2	no	—
205	C₂⁴×C₃	—	2	1	no	—
206	C₂×C₃×Q₈	—	2	1	no	—
207	C₂×C₃×Q₈	—	2	2	no	—
208	C₂×C₃×Q₈	C₂×C₄×C₅	1	4	yes	complemented
209	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
210	C₂×C₃×D₄	—	2	1	no	—
211	C₂×C₃×D₄	—	2	2	no	—
212	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	—
213	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
214	C₂²×C₃×C₄	—	2	1	no	—
215	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
216	C₂²×Dic₃	—	2	1	no	—
217	C₂²×Dic₃	—	2	1	no	—
218	C₂²×Dic₃	—	2	4	no	—
219	C₂²×Dic₃	—	4	4	no	—
220	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
221	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
222	C₃×SD₁₆	C₂×C₄×C₅	1	16	yes	complemented
223	C₂×C₃×C₈	C₂×C₄×C₅	1	4	yes	complemented
224	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
225	#217	—	2	4	no	—
226	C₄⋊Dic₃	—	2	1	no	—
227	C₄⋊Dic₃	—	2	1	no	—
228	C₄⋊Dic₃	—	2	4	no	—
229	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
230	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
231	C₄×Dic₃	—	2	4	no	—
232	C₄×Dic₃	C₅×D₄	1	2	yes	—
233	C₄×Dic₃	C₂³×C₅	1	2	yes	—
234	C₂×C₃⋊C₈	—	2	2	no	—
235	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
236	C₂³×C₅	—	2	4	no	—
237	C₂³×C₅	—	2	2	no	—
238	C₂³×C₅	—	4	2	no	—
239	C₂³×C₅	—	4	2	no	—
240	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
241	C₅×Q₈	—	2	4	no	—
242	C₅×Q₈	—	2	2	no	—
243	C₅×Q₈	C₂²×Dic₃	1	4	yes	complemented
244	C₅×D₄	—	2	4	no	—
245	C₅×D₄	—	2	2	no	—
246	C₅×D₄	C₂²×Dic₃	1	4	yes	—
247	C₂×C₄×C₅	—	2	4	no	—
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	3	2	no	—
250	C₂×C₄×C₅	—	3	2	no	—
251	C₂×C₄×C₅	—	6	2	no	—
252	C₂×C₄×C₅	—	6	2	no	—
253	C₂×C₄×C₅	—	6	2	no	—
254	C₂×C₄×C₅	—	6	2	no	—
255	C₂×C₄×C₅	—	12	8	no	—
256	C₂×C₄×C₅	—	12	2	no	—
257	C₂×C₄×C₅	—	12	2	no	—
258	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
259	C₂×C₄×C₅	#237	1	2	yes	—
260	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
261	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
262	C₅×C₈	—	6	2	no	—
263	C₅×C₈	C₂²×Dic₃	1	4	yes	complemented
264	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
265	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
266	C₂³×C₄	—	6	1	no	—
267	C₂×SD₁₆	C₅×Dic₃	1	8	yes	complemented
268	C₂×SD₁₆	C₂×C₅×D₃	1	4	yes	—
269	C₂²×C₈	—	3	1	no	—
270	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
271	C₄×Q₈	—	3	4	no	—
272	C₄×Q₈	—	6	2	no	—
273	C₄×D₄	—	3	4	no	—
274	C₄×D₄	—	6	2	no	—
275	C₂×C₄⋊C₄	—	3	1	no	—
276	C₂×C₄⋊C₄	—	3	1	no	—
277	C₂×C₄⋊C₄	—	6	1	no	—
278	C₂×C₂²⋊C₄	—	6	1	no	—
279	C₂×C₄²	—	3	1	no	—
280	C₂×C₄²	—	6	1	no	—
281	#107	—	3	4	no	—
282	#103	—	3	4	no	—
283	#102	—	3	4	no	—
284	#97	—	3	4	no	—
285	C₂×C₃×C₅	—	4	4	no	—
286	C₂×C₃×C₅	#440	1	4	yes	complemented
287	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
288	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
289	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
290	C₂³×C₃	—	2	4	no	—
291	C₂³×C₃	—	2	2	no	—
292	C₂³×C₃	—	4	2	no	—
293	C₂³×C₃	—	4	2	no	—
294	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
295	C₃×Q₈	—	2	4	no	—
296	C₃×Q₈	—	2	2	no	—
297	C₃×Q₈	C₂²×C₄×C₅	1	4	yes	complemented
298	C₃×D₄	—	2	4	no	—
299	C₃×D₄	—	2	2	no	—
300	C₃×D₄	C₂²×C₄×C₅	1	4	yes	—
301	C₂×C₃×C₄	—	2	4	no	—
302	C₂×C₃×C₄	—	2	2	no	—
303	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
304	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
305	C₂×C₃×C₄	C₅×#41	1	2	yes	—
306	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
307	C₂×Dic₃	—	2	2	no	—
308	C₂×Dic₃	—	2	2	no	—
309	C₂×Dic₃	—	2	2	no	—
310	C₂×Dic₃	—	2	2	no	—
311	C₂×Dic₃	—	4	8	no	—
312	C₂×Dic₃	—	4	2	no	—
313	C₂×Dic₃	—	4	2	no	—
314	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
315	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
316	C₃×C₈	C₂²×C₄×C₅	1	4	yes	complemented
317	C₃⋊C₈	—	2	2	no	—
318	C₂²×C₅	—	2	4	no	—
319	C₂²×C₅	—	4	8	no	—
320	C₂²×C₅	—	4	2	no	—
321	C₂²×C₅	—	4	2	no	—
322	C₂²×C₅	#914	1	2	yes	—
323	C₂²×C₅	#915	1	2	yes	—
324	C₂²×C₅	D₄×Dic₃	1	2	yes	—
325	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
326	C₄×C₅	—	2	4	no	—
327	C₄×C₅	—	6	2	no	—
328	C₄×C₅	—	6	2	no	—
329	C₄×C₅	—	12	2	no	—
330	C₄×C₅	—	12	2	no	—
331	C₄×C₅	D₄×Dic₃	1	2	yes	—
332	C₄×C₅	C₂×#237	1	1	yes	characteristic
333	C₄×C₅	C₂³×Dic₃	1	1	yes	characteristic
334	C₂⁴	—	2	1	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	C₂×C₅×Dic₃	1	4	yes	complemented
338	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	C₂×C₅×Dic₃	1	4	yes	—
342	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	3	1	no	—
345	C₂²×C₄	—	3	1	no	—
346	C₂²×C₄	—	6	4	no	—
347	C₂²×C₄	—	6	1	no	—
348	C₂²×C₄	—	6	1	no	—
349	C₂²×C₄	—	12	4	no	—
350	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
351	SD₁₆	C₂×C₅×Dic₃	1	16	yes	complemented
352	C₂×C₈	—	3	2	no	—
353	C₂×C₈	—	6	2	no	—
354	C₂×C₈	C₂×C₅×Dic₃	1	4	yes	complemented
355	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
356	C₄⋊C₄	—	3	2	no	—
357	C₄⋊C₄	—	3	2	no	—
358	C₄⋊C₄	—	6	4	no	—
359	C₄⋊C₄	—	6	1	no	—
360	C₄⋊C₄	—	6	1	no	—
361	C₂²⋊C₄	—	6	4	no	—
362	C₄²	—	3	2	no	—
363	C₄²	—	3	2	no	—
364	C₄²	—	6	4	no	—
365	C₃×C₅	C₂×#440	1	1	yes	characteristic, complemented, Hall
366	C₂²×C₃	—	2	4	no	—
367	C₂²×C₃	—	4	8	no	—
368	C₂²×C₃	—	4	2	no	—
369	C₂²×C₃	—	4	2	no	—
370	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
371	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
372	C₂²×C₃	C₅×#137	1	2	yes	—
373	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
374	C₃×C₄	—	2	4	no	—
375	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
376	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
377	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
378	Dic₃	—	2	2	no	—
379	Dic₃	—	2	2	no	—
380	Dic₃	—	4	2	no	—
381	Dic₃	—	4	2	no	—
382	C₂×C₅	—	4	4	no	—
383	C₂×C₅	#5164	1	4	yes	direct product factor
384	C₂×C₅	C₂×#914	1	1	yes	characteristic
385	C₂×C₅	C₂×#915	1	1	yes	characteristic
386	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
387	C₂³	—	2	4	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	4	2	no	—
391	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
392	Q₈	—	2	4	no	—
393	Q₈	—	2	2	no	—
394	Q₈	C₂²×C₅×Dic₃	1	4	yes	complemented
395	D₄	—	2	4	no	—
396	D₄	—	2	2	no	—
397	D₄	C₂²×C₅×Dic₃	1	4	yes	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	3	2	no	—
401	C₂×C₄	—	3	2	no	—
402	C₂×C₄	—	6	2	no	—
403	C₂×C₄	—	6	2	no	—
404	C₂×C₄	—	6	2	no	—
405	C₂×C₄	—	6	2	no	—
406	C₂×C₄	—	12	8	no	—
407	C₂×C₄	—	12	2	no	—
408	C₂×C₄	—	12	2	no	—
409	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
410	C₂×C₄	C₅×#237	1	2	yes	—
411	C₂×C₄	C₂²×C₅×Dic₃	1	2	yes	—
412	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
413	C₈	—	6	2	no	—
414	C₈	C₂²×C₅×Dic₃	1	4	yes	complemented
415	C₂×C₃	—	4	4	no	—
416	C₂×C₃	C₅×#440	1	4	yes	complemented
417	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
418	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
419	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
420	C₅	C₂×#5164	1	1	yes	characteristic, direct product factor, Sylow
421	C₂²	—	2	4	no	—
422	C₂²	—	4	8	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	4	2	no	—
425	C₂²	C₅×#914	1	2	yes	—
426	C₂²	C₅×#915	1	2	yes	—
427	C₂²	C₅×D₄×Dic₃	1	2	yes	—
428	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
429	C₄	—	2	4	no	—
430	C₄	—	6	2	no	—
431	C₄	—	6	2	no	—
432	C₄	—	12	2	no	—
433	C₄	—	12	2	no	—
434	C₄	C₅×D₄×Dic₃	1	2	yes	—
435	C₄	C₂×C₅×#237	1	1	yes	characteristic
436	C₄	C₂³×C₅×Dic₃	1	1	yes	characteristic
437	C₃	C₂×C₅×#440	1	1	yes	characteristic, complemented, Sylow
438	C₂	—	4	4	no	—
439	C₂	C₅×#5164	1	4	yes	direct product factor
440	C₂	C₂×C₅×#914	1	1	yes	characteristic
441	C₂	C₂×C₅×#915	1	1	yes	characteristic
442	C₂	C₂×C₅×D₄×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂²×C₃×C₅×SD₁₆	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₃×C₅×D₄	C₂²
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂²×C₅×SD₁₆	D₃
hypocenter	C₃	C₂×C₅×#440
LCS	G ▷ 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
2. C₂×C₅×Q₈×Dic₃	C₂	semidirect
4. C₂×C₅×#835	C₂	semidirect
6. C₅×#5164	C₂	direct (N × H)
7. C₂×C₅×#818	C₂	semidirect
8. C₂×C₅×#815	C₂	semidirect
13. C₂×C₃×C₅×SD₁₆	C₄	semidirect
18. C₅×Q₈×Dic₃	C₂²	semidirect
27. C₅×#835	C₂²	semidirect
29. C₅×#818	C₂²	semidirect
30. C₅×#815	C₂²	semidirect
31. C₂×#5164	C₅	direct (N × H)
43. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
57. C₃×C₅×SD₁₆	C₂×C₄	semidirect
58. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
72. C₂×Q₈×Dic₃	C₂×C₅	semidirect
74. C₂×#835	C₂×C₅	semidirect
76. #5164	C₂×C₅	direct (N × H)
77. C₂×#818	C₂×C₅	semidirect
78. C₂×#815	C₂×C₅	semidirect
82. C₂×C₅×SD₁₆	Dic₃	semidirect
108. C₃×C₅×Q₈	C₂²×C₄	semidirect
127. C₃×C₅×C₈	C₂²×C₄	semidirect
132. C₂×C₃×SD₁₆	C₄×C₅	semidirect
137. Q₈×Dic₃	C₂²×C₅	semidirect
146. #835	C₂²×C₅	semidirect
148. #818	C₂²×C₅	semidirect
149. #815	C₂²×C₅	semidirect
153. C₂×C₅×Q₈	C₂×Dic₃	semidirect
167. C₅×SD₁₆	C₂×Dic₃	semidirect
170. C₂×C₅×C₈	C₂×Dic₃	semidirect
208. C₂×C₃×Q₈	C₂×C₄×C₅	semidirect
222. C₃×SD₁₆	C₂×C₄×C₅	semidirect
223. C₂×C₃×C₈	C₂×C₄×C₅	semidirect
243. C₅×Q₈	C₂²×Dic₃	semidirect
263. C₅×C₈	C₂²×Dic₃	semidirect
267. C₂×SD₁₆	C₅×Dic₃	semidirect
286. C₂×C₃×C₅	#440	semidirect
297. C₃×Q₈	C₂²×C₄×C₅	semidirect
316. C₃×C₈	C₂²×C₄×C₅	semidirect
337. C₂×Q₈	C₂×C₅×Dic₃	semidirect
351. SD₁₆	C₂×C₅×Dic₃	semidirect
354. C₂×C₈	C₂×C₅×Dic₃	semidirect
365. C₃×C₅	C₂×#440	semidirect
383. C₂×C₅	#5164	direct (N × H)
394. Q₈	C₂²×C₅×Dic₃	semidirect
414. C₈	C₂²×C₅×Dic₃	semidirect
416. C₂×C₃	C₅×#440	semidirect
420. C₅	C₂×#5164	direct (N × H)
437. C₃	C₂×C₅×#440	semidirect
439. C₂	C₅×#5164	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
C₂×C₅×D₄×Dic₃	2
C₂×C₅×#835	2
C₂×C₅×#832	2
C₅×#5164	2
C₂×C₅×#818	2
C₂×C₅×#815	2
C₂×C₅×#440	3
C₂×#5164	5

Subgroups — C2×C5×#5164 #14416323

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5164 #14416323