Subgroups — C₅×D₃×#423 #14412994

Order 1920.

1152 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×M₁₆	C₂	1	2	yes	maximal
2	C₂×C₄²×C₅×D₃	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#423	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5118	C₂	1	2	yes	maximal, complemented
5	C₅×#4924	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4837	C₂	1	4	yes	maximal, complemented
7	C₅×D₃×C₄⋊C₈	C₂	1	4	yes	maximal, complemented
8	C₂×C₅×#423	—	3	1	no	maximal, Hall
9	C₂²×C₄×C₅×D₃	C₄	1	2	yes	—
10	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₅×Dic₃	C₄	1	2	yes	—
14	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
15	C₂×C₅×#208	C₂²	1	2	yes	—
16	C₅×D₃×M₁₆	—	2	8	no	—
17	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	4	yes	—
18	C₂×C₅×D₃×C₈	C₂²	1	4	yes	—
19	C₄²×C₅×D₃	C₄	1	1	yes	characteristic
20	C₄²×C₅×D₃	C₄	1	1	yes	characteristic
21	C₄²×C₅×D₃	C₄	1	1	yes	characteristic
22	C₄²×C₅×D₃	C₄	1	1	yes	characteristic
23	C₄²×C₅×D₃	C₂²	1	2	yes	—
24	C₄²×C₅×D₃	C₂²	1	2	yes	—
25	C₃×C₅×C₄⋊C₈	C₂²	1	4	yes	complemented
26	C₅×Dic₃⋊C₈	C₂²	1	8	yes	complemented
27	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	complemented
28	D₃×#423	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂²×C₅×M₁₆	—	3	2	no	—
30	C₂²×C₄²×C₅	—	3	1	no	—
31	C₅×#423	—	3	4	no	—
32	C₅×#423	—	3	2	no	—
33	C₅×#423	—	3	1	no	—
34	C₅×#423	D₃	1	1	yes	characteristic, direct product factor
35	C₂×C₅×C₄⋊C₈	—	3	4	no	—
36	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
38	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
39	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
40	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄×C₅×D₃	—	2	8	no	—
42	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
43	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
44	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
45	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
48	C₂×C₄×C₅×D₃	D₄	1	4	yes	—
49	C₂×C₄×C₅×D₃	Q₈	1	4	yes	—
50	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
51	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
52	C₃×C₅×M₁₆	—	2	4	no	—
53	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
54	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
55	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
56	C₃×C₄²×C₅	C₂³	1	2	yes	—
57	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
58	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
59	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
60	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
61	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
62	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
63	C₄×C₅×Dic₃	C₂³	1	2	yes	—
64	C₅×#208	—	2	4	no	—
65	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
66	C₅×ΓL(1,𝔽₂₅)	—	2	8	no	—
67	C₅×D₃×C₈	—	2	8	no	—
68	C₂×D₃×M₁₆	C₂×C₅	1	2	yes	—
69	C₂×C₄²×D₃	C₂×C₅	1	1	yes	characteristic
70	C₃×#423	C₂×C₅	1	1	yes	characteristic, complemented
71	#5118	C₂×C₅	1	2	yes	complemented
72	#4924	C₂×C₅	1	1	yes	characteristic, complemented
73	#4837	C₂×C₅	1	4	yes	complemented
74	D₃×C₄⋊C₈	C₂×C₅	1	4	yes	complemented
75	C₂³×C₄×C₅	—	3	1	no	—
76	C₂³×C₄×C₅	—	3	2	no	—
77	C₂×C₅×M₁₆	—	3	2	no	—
78	C₂×C₅×M₁₆	—	3	4	no	—
79	C₂×C₅×M₁₆	—	6	8	no	—
80	C₂×C₅×M₁₆	C₂×D₃	1	2	yes	—
81	C₂²×C₅×C₈	—	3	4	no	—
82	C₂×C₄²×C₅	—	3	2	no	—
83	C₂×C₄²×C₅	—	3	1	no	—
84	C₂×C₄²×C₅	—	3	1	no	—
85	C₂×C₄²×C₅	—	3	1	no	—
86	C₂×C₄²×C₅	—	3	1	no	—
87	C₂×C₄²×C₅	—	3	1	no	—
88	C₂×C₄²×C₅	—	3	2	no	—
89	C₂×C₄²×C₅	—	3	2	no	—
90	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
91	C₅×C₄⋊C₈	—	3	8	no	—
92	C₅×C₄⋊C₈	—	3	4	no	—
93	C₅×C₄⋊C₈	C₂×D₃	1	4	yes	complemented
94	C₂×#423	—	3	1	no	Sylow
95	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₅×D₃	—	2	4	no	—
97	C₂²×C₅×D₃	C₄⋊C₄	1	4	yes	—
98	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	—	2	4	no	—
101	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
102	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
104	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
105	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
106	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
107	C₂×C₅×Dic₃	—	2	4	no	—
108	C₂×C₅×Dic₃	C₄⋊C₄	1	4	yes	—
109	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
110	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
113	C₄×C₅×D₃	—	2	4	no	—
114	C₄×C₅×D₃	—	2	4	no	—
115	C₄×C₅×D₃	—	2	4	no	—
116	C₄×C₅×D₃	C₄⋊C₄	1	4	yes	—
117	C₄×C₅×D₃	C₄⋊C₄	1	4	yes	—
118	C₄×C₅×D₃	M₁₆	1	8	yes	complemented
119	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
120	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
121	C₄×C₅×D₃	C₂×Q₈	1	2	yes	—
122	C₄×C₅×D₃	C₂×Q₈	1	2	yes	—
123	C₃×C₅×C₈	—	2	4	no	—
124	C₅×C₃⋊C₈	—	2	4	no	—
125	C₂²×C₄×D₃	C₄×C₅	1	2	yes	—
126	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
127	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
128	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
129	C₂×C₄×Dic₃	C₄×C₅	1	2	yes	—
130	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
131	C₂×#208	C₂²×C₅	1	2	yes	—
132	D₃×M₁₆	—	2	8	no	—
133	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	4	yes	—
134	C₂×D₃×C₈	C₂²×C₅	1	4	yes	—
135	C₄²×D₃	C₄×C₅	1	1	yes	characteristic
136	C₄²×D₃	C₄×C₅	1	1	yes	characteristic
137	C₄²×D₃	C₄×C₅	1	1	yes	characteristic
138	C₄²×D₃	C₄×C₅	1	1	yes	characteristic
139	C₄²×D₃	C₂²×C₅	1	2	yes	—
140	C₄²×D₃	C₂²×C₅	1	2	yes	—
141	C₃×C₄⋊C₈	C₂²×C₅	1	4	yes	complemented
142	Dic₃⋊C₈	C₂²×C₅	1	8	yes	complemented
143	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	4	yes	complemented
144	C₂⁴×C₅	—	3	1	no	—
145	C₂²×C₄×C₅	—	3	1	no	—
146	C₂²×C₄×C₅	—	3	1	no	—
147	C₂²×C₄×C₅	—	3	1	no	—
148	C₂²×C₄×C₅	—	3	2	no	—
149	C₂²×C₄×C₅	—	3	4	no	—
150	C₂²×C₄×C₅	—	3	4	no	—
151	C₂²×C₄×C₅	—	3	1	no	—
152	C₂²×C₄×C₅	—	3	1	no	—
153	C₂²×C₄×C₅	—	3	2	no	—
154	C₂²×C₄×C₅	—	3	2	no	—
155	C₂²×C₄×C₅	—	3	2	no	—
156	C₂²×C₄×C₅	—	3	2	no	—
157	C₂²×C₄×C₅	—	6	8	no	—
158	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
159	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
160	C₅×M₁₆	—	2	4	no	—
161	C₅×M₁₆	—	6	8	no	—
162	C₅×M₁₆	—	6	4	no	—
163	C₂×C₅×C₈	—	3	4	no	—
164	C₂×C₅×C₈	—	6	8	no	—
165	C₂×C₅×C₈	C₂²×D₃	1	4	yes	—
166	C₄²×C₅	—	3	2	no	—
167	C₄²×C₅	—	3	1	no	—
168	C₄²×C₅	—	3	2	no	—
169	C₄²×C₅	—	3	2	no	—
170	C₄²×C₅	—	3	2	no	—
171	C₄²×C₅	—	3	1	no	—
172	C₄²×C₅	—	3	2	no	—
173	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
174	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
175	C₄²×C₅	C₂²×D₃	1	2	yes	—
176	C₂²×M₁₆	—	3	2	no	—
177	C₂²×C₄²	—	3	1	no	—
178	#423	—	3	2	no	—
179	#423	—	3	1	no	—
180	#423	—	3	4	no	—
181	#423	C₅×D₃	1	1	yes	characteristic, direct product factor
182	C₂×C₄⋊C₈	—	3	4	no	—
183	C₂²×C₃×C₅	—	2	2	no	—
184	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	2	yes	—
185	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₅×D₃	—	2	2	no	—
187	C₂×C₅×D₃	—	2	8	no	—
188	C₂×C₅×D₃	C₂×C₄⋊C₄	1	2	yes	—
189	C₂×C₅×D₃	C₂×C₄⋊C₄	1	2	yes	—
190	C₂×C₅×D₃	C₂×M₁₆	1	4	yes	—
191	C₃×C₄×C₅	—	2	2	no	—
192	C₃×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
193	C₃×C₄×C₅	C₂×M₁₆	1	4	yes	complemented
194	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
195	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
196	C₅×Dic₃	—	2	2	no	—
197	C₅×Dic₃	C₂×C₄⋊C₄	1	2	yes	—
198	C₅×Dic₃	C₂×C₄⋊C₄	1	2	yes	—
199	C₅×Dic₃	C₂×M₁₆	1	4	yes	complemented
200	C₂³×D₃	C₂×C₄×C₅	1	1	yes	characteristic
201	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
202	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
203	C₂²×Dic₃	C₂×C₄×C₅	1	2	yes	—
204	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
205	C₂×C₄×D₃	—	2	8	no	—
206	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
207	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
208	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
209	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
210	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
211	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
212	C₂×C₄×D₃	C₅×D₄	1	4	yes	—
213	C₂×C₄×D₃	C₅×Q₈	1	4	yes	—
214	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
215	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
216	C₃×M₁₆	—	2	4	no	—
217	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
218	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
219	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
220	C₃×C₄²	C₂³×C₅	1	2	yes	—
221	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
222	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
223	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
224	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
225	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
226	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
227	C₄×Dic₃	C₂³×C₅	1	2	yes	—
228	#208	—	2	4	no	—
229	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	—
230	ΓL(1,𝔽₂₅)	—	2	8	no	—
231	D₃×C₈	—	2	8	no	—
232	C₂³×C₅	—	3	1	no	—
233	C₂³×C₅	—	3	4	no	—
234	C₂³×C₅	—	3	1	no	—
235	C₂³×C₅	—	6	4	no	—
236	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
237	C₂×C₄×C₅	—	2	4	no	—
238	C₂×C₄×C₅	—	3	4	no	—
239	C₂×C₄×C₅	—	3	2	no	—
240	C₂×C₄×C₅	—	3	1	no	—
241	C₂×C₄×C₅	—	3	1	no	—
242	C₂×C₄×C₅	—	3	4	no	—
243	C₂×C₄×C₅	—	3	4	no	—
244	C₂×C₄×C₅	—	3	8	no	—
245	C₂×C₄×C₅	—	3	2	no	—
246	C₂×C₄×C₅	—	3	2	no	—
247	C₂×C₄×C₅	—	3	2	no	—
248	C₂×C₄×C₅	—	3	2	no	—
249	C₂×C₄×C₅	—	3	2	no	—
250	C₂×C₄×C₅	—	6	4	no	—
251	C₂×C₄×C₅	—	6	4	no	—
252	C₂×C₄×C₅	—	6	4	no	—
253	C₂×C₄×C₅	—	6	4	no	—
254	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
255	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
256	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
257	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
258	C₂×C₄×C₅	D₃×Q₈	1	2	yes	—
259	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
260	C₅×C₈	—	2	4	no	—
261	C₅×C₈	—	6	4	no	—
262	C₂³×C₄	—	3	1	no	—
263	C₂³×C₄	—	3	2	no	—
264	C₂×M₁₆	—	3	2	no	—
265	C₂×M₁₆	—	3	4	no	—
266	C₂×M₁₆	—	6	8	no	—
267	C₂×M₁₆	C₂×C₅×D₃	1	2	yes	—
268	C₂²×C₈	—	3	4	no	—
269	C₂×C₄²	—	3	2	no	—
270	C₂×C₄²	—	3	1	no	—
271	C₂×C₄²	—	3	1	no	—
272	C₂×C₄²	—	3	1	no	—
273	C₂×C₄²	—	3	1	no	—
274	C₂×C₄²	—	3	1	no	—
275	C₂×C₄²	—	3	2	no	—
276	C₂×C₄²	—	3	2	no	—
277	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
278	C₄⋊C₈	—	3	8	no	—
279	C₄⋊C₈	—	3	4	no	—
280	C₄⋊C₈	C₂×C₅×D₃	1	4	yes	complemented
281	C₂×C₃×C₅	—	2	2	no	—
282	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
283	C₂×C₃×C₅	C₂²×M₁₆	1	2	yes	—
284	C₅×D₃	—	2	2	no	—
285	C₅×D₃	#423	1	4	yes	direct product factor
286	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
287	C₂²×D₃	—	2	4	no	—
288	C₂²×D₃	C₅×C₄⋊C₄	1	4	yes	—
289	C₂²×D₃	C₂²×C₄×C₅	1	1	yes	characteristic
290	C₂²×D₃	C₂²×C₄×C₅	1	1	yes	characteristic
291	C₂×C₃×C₄	—	2	4	no	—
292	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
293	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
295	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
296	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
297	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
298	C₂×Dic₃	—	2	4	no	—
299	C₂×Dic₃	C₅×C₄⋊C₄	1	4	yes	—
300	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
301	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
302	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
303	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
304	C₄×D₃	—	2	4	no	—
305	C₄×D₃	—	2	4	no	—
306	C₄×D₃	—	2	4	no	—
307	C₄×D₃	C₅×C₄⋊C₄	1	4	yes	—
308	C₄×D₃	C₅×C₄⋊C₄	1	4	yes	—
309	C₄×D₃	C₅×M₁₆	1	8	yes	complemented
310	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
311	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
312	C₄×D₃	C₂×C₅×Q₈	1	2	yes	—
313	C₄×D₃	C₂×C₅×Q₈	1	2	yes	—
314	C₃×C₈	—	2	4	no	—
315	C₃⋊C₈	—	2	4	no	—
316	C₂²×C₅	—	2	2	no	—
317	C₂²×C₅	—	3	4	no	—
318	C₂²×C₅	—	3	2	no	—
319	C₂²×C₅	—	3	2	no	—
320	C₂²×C₅	—	6	8	no	—
321	C₂²×C₅	—	6	2	no	—
322	C₂²×C₅	D₃×C₄⋊C₄	1	2	yes	—
323	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
324	C₄×C₅	—	2	2	no	—
325	C₄×C₅	—	3	4	no	—
326	C₄×C₅	—	3	2	no	—
327	C₄×C₅	—	3	2	no	—
328	C₄×C₅	—	6	2	no	—
329	C₄×C₅	D₃×C₄⋊C₄	1	2	yes	—
330	C₄×C₅	D₃×M₁₆	1	4	yes	complemented
331	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
332	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
333	C₂⁴	—	3	1	no	—
334	C₂²×C₄	—	3	1	no	—
335	C₂²×C₄	—	3	1	no	—
336	C₂²×C₄	—	3	1	no	—
337	C₂²×C₄	—	3	2	no	—
338	C₂²×C₄	—	3	4	no	—
339	C₂²×C₄	—	3	4	no	—
340	C₂²×C₄	—	3	1	no	—
341	C₂²×C₄	—	3	1	no	—
342	C₂²×C₄	—	3	2	no	—
343	C₂²×C₄	—	3	2	no	—
344	C₂²×C₄	—	3	2	no	—
345	C₂²×C₄	—	3	2	no	—
346	C₂²×C₄	—	6	8	no	—
347	C₂²×C₄	C₄×C₅×D₃	1	2	yes	—
348	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
349	M₁₆	—	2	4	no	—
350	M₁₆	—	6	8	no	—
351	M₁₆	—	6	4	no	—
352	C₂×C₈	—	3	4	no	—
353	C₂×C₈	—	6	8	no	—
354	C₂×C₈	C₂²×C₅×D₃	1	4	yes	—
355	C₄²	—	3	2	no	—
356	C₄²	—	3	1	no	—
357	C₄²	—	3	2	no	—
358	C₄²	—	3	2	no	—
359	C₄²	—	3	2	no	—
360	C₄²	—	3	1	no	—
361	C₄²	—	3	2	no	—
362	C₄²	C₄×C₅×D₃	1	1	yes	characteristic
363	C₄²	C₄×C₅×D₃	1	1	yes	characteristic
364	C₄²	C₂²×C₅×D₃	1	2	yes	—
365	C₃×C₅	C₂×#423	1	1	yes	characteristic, complemented, Hall
366	C₂²×C₃	—	2	2	no	—
367	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	2	yes	—
368	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
369	C₂×D₃	—	2	2	no	—
370	C₂×D₃	—	2	8	no	—
371	C₂×D₃	C₂×C₅×C₄⋊C₄	1	2	yes	—
372	C₂×D₃	C₂×C₅×C₄⋊C₄	1	2	yes	—
373	C₂×D₃	C₂×C₅×M₁₆	1	4	yes	—
374	C₃×C₄	—	2	2	no	—
375	C₃×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
376	C₃×C₄	C₂×C₅×M₁₆	1	4	yes	complemented
377	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
378	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
379	Dic₃	—	2	2	no	—
380	Dic₃	C₂×C₅×C₄⋊C₄	1	2	yes	—
381	Dic₃	C₂×C₅×C₄⋊C₄	1	2	yes	—
382	Dic₃	C₂×C₅×M₁₆	1	4	yes	complemented
383	C₂×C₅	—	2	2	no	—
384	C₂×C₅	—	3	4	no	—
385	C₂×C₅	—	6	2	no	—
386	C₂×C₅	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
387	C₂×C₅	C₂×D₃×M₁₆	1	2	yes	—
388	C₂³	—	3	1	no	—
389	C₂³	—	3	4	no	—
390	C₂³	—	3	1	no	—
391	C₂³	—	6	4	no	—
392	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	3	4	no	—
395	C₂×C₄	—	3	2	no	—
396	C₂×C₄	—	3	1	no	—
397	C₂×C₄	—	3	1	no	—
398	C₂×C₄	—	3	4	no	—
399	C₂×C₄	—	3	4	no	—
400	C₂×C₄	—	3	8	no	—
401	C₂×C₄	—	3	2	no	—
402	C₂×C₄	—	3	2	no	—
403	C₂×C₄	—	3	2	no	—
404	C₂×C₄	—	3	2	no	—
405	C₂×C₄	—	3	2	no	—
406	C₂×C₄	—	6	4	no	—
407	C₂×C₄	—	6	4	no	—
408	C₂×C₄	—	6	4	no	—
409	C₂×C₄	—	6	4	no	—
410	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
411	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
412	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
413	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
414	C₂×C₄	C₅×D₃×Q₈	1	2	yes	—
415	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
416	C₈	—	2	4	no	—
417	C₈	—	6	4	no	—
418	C₂×C₃	—	2	2	no	—
419	C₂×C₃	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
420	C₂×C₃	C₂²×C₅×M₁₆	1	2	yes	—
421	D₃	—	2	2	no	—
422	D₃	C₅×#423	1	4	yes	direct product factor
423	C₅	D₃×#423	1	1	yes	characteristic, direct product factor, Sylow
424	C₂²	—	2	2	no	—
425	C₂²	—	3	4	no	—
426	C₂²	—	3	2	no	—
427	C₂²	—	3	2	no	—
428	C₂²	—	6	8	no	—
429	C₂²	—	6	2	no	—
430	C₂²	C₅×D₃×C₄⋊C₄	1	2	yes	—
431	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
432	C₄	—	2	2	no	—
433	C₄	—	3	4	no	—
434	C₄	—	3	2	no	—
435	C₄	—	3	2	no	—
436	C₄	—	6	2	no	—
437	C₄	C₅×D₃×C₄⋊C₄	1	2	yes	—
438	C₄	C₅×D₃×M₁₆	1	4	yes	complemented
439	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
440	C₄	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
441	C₃	C₂×C₅×#423	1	1	yes	characteristic, complemented, Sylow
442	C₂	—	2	2	no	—
443	C₂	—	3	4	no	—
444	C₂	—	6	2	no	—
445	C₂	C₂×C₅×D₃×C₄⋊C₄	1	1	yes	characteristic
446	C₂	C₂×C₅×D₃×M₁₆	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#423	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂³×C₅×D₃	C₂×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#423	D₃
hypocenter	C₃	C₂×C₅×#423
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#423

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×#423	C₂	semidirect
4. C₅×#5118	C₂	semidirect
5. C₅×#4924	C₂	semidirect
6. C₅×#4837	C₂	semidirect
7. C₅×D₃×C₄⋊C₈	C₂	semidirect
25. C₃×C₅×C₄⋊C₈	C₂²	semidirect
26. C₅×Dic₃⋊C₈	C₂²	semidirect
27. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
28. D₃×#423	C₅	direct (N × H)
34. C₅×#423	D₃	direct (N × H)
70. C₃×#423	C₂×C₅	semidirect
71. #5118	C₂×C₅	semidirect
72. #4924	C₂×C₅	semidirect
73. #4837	C₂×C₅	semidirect
74. D₃×C₄⋊C₈	C₂×C₅	semidirect
93. C₅×C₄⋊C₈	C₂×D₃	semidirect
118. C₄×C₅×D₃	M₁₆	semidirect
141. C₃×C₄⋊C₈	C₂²×C₅	semidirect
142. Dic₃⋊C₈	C₂²×C₅	semidirect
143. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
181. #423	C₅×D₃	direct (N × H)
193. C₃×C₄×C₅	C₂×M₁₆	semidirect
199. C₅×Dic₃	C₂×M₁₆	semidirect
280. C₄⋊C₈	C₂×C₅×D₃	semidirect
285. C₅×D₃	#423	direct (N × H)
309. C₄×D₃	C₅×M₁₆	semidirect
330. C₄×C₅	D₃×M₁₆	semidirect
365. C₃×C₅	C₂×#423	semidirect
376. C₃×C₄	C₂×C₅×M₁₆	semidirect
382. Dic₃	C₂×C₅×M₁₆	semidirect
422. D₃	C₅×#423	direct (N × H)
423. C₅	D₃×#423	direct (N × H)
438. C₄	C₅×D₃×M₁₆	semidirect
441. C₃	C₂×C₅×#423	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×M₁₆	2
C₂×C₄²×C₅×D₃	2
C₃×C₅×#423	2
C₅×#5118	2
C₅×#4924	2
C₅×#4837	2
C₅×D₃×C₄⋊C₈	2
C₂×C₅×#423	3
D₃×#423	5

Subgroups — C5×D3×#423 #14412994

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#423 #14412994