Subgroups — C₄×C₅×#875 #14321938

Order 1920.

1304 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#875	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄³×C₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4940	C₂	1	4	yes	maximal, complemented
6	C₅×#4939	C₂	1	1	yes	maximal, characteristic
7	C₄×C₅×(C₂×D₃)⋊C₄	C₂	1	4	yes	maximal, complemented
8	C₅×#4936	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4929	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₅×#124	—	3	1	no	maximal, Hall
11	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
12	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
13	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
16	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
20	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
21	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
22	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
23	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
24	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
25	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
26	C₅×#875	C₄	1	8	yes	direct product factor
27	C₄×C₅×D₁₂	—	2	4	no	—
28	C₄×C₅×Dic₆	—	2	4	no	—
29	C₅×C₃⋊#95	C₂²	1	4	yes	—
30	C₅×C₃⋊#95	C₂²	1	4	yes	—
31	C₄×#875	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂×C₅×#124	—	3	1	no	—
33	C₂×C₄×C₅×Q₈	—	3	1	no	—
34	C₂×C₄×C₅×D₄	—	3	1	no	—
35	C₅×#391	—	3	1	no	—
36	C₅×#390	—	3	1	no	—
37	C₅×#388	—	3	4	no	—
38	C₅×#382	—	3	1	no	—
39	C₄×C₅×C₂²⋊C₄	—	3	4	no	—
40	C₄³×C₅	D₃	1	1	yes	characteristic, complemented
41	C₂³×C₅×D₃	C₂³	1	2	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
48	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
49	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
50	C₂×C₅×D₁₂	—	2	2	no	—
51	C₂×C₅×D₁₂	—	2	2	no	—
52	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	—
53	C₂×C₄×C₅×D₃	—	2	4	no	—
54	C₂×C₄×C₅×D₃	—	2	8	no	—
55	C₂×C₅×Dic₆	—	2	2	no	—
56	C₂×C₅×Dic₆	—	2	2	no	—
57	C₂×C₅×Dic₆	C₂×C₄	1	4	yes	complemented
58	C₃×C₄²×C₅	—	2	4	no	—
59	C₃×C₄²×C₅	—	2	2	no	—
60	C₃×C₄²×C₅	—	2	4	no	—
61	C₃×C₄²×C₅	C₂×C₄	1	4	yes	complemented
62	C₃×C₄²×C₅	D₄	1	4	yes	—
63	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
64	C₅×(C₂×D₃)⋊C₄	—	2	8	no	—
65	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	16	yes	complemented
66	C₅×C₄⋊Dic₃	—	2	2	no	—
67	C₅×C₄⋊Dic₃	—	2	2	no	—
68	C₅×Dic₃⋊C₄	—	2	4	no	—
69	C₄×C₅×Dic₃	—	2	4	no	—
70	C₂×#875	C₂×C₅	1	1	yes	characteristic
71	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic
72	C₂×C₄×Dic₆	C₂×C₅	1	1	yes	characteristic, complemented
73	C₃×C₄³	C₂×C₅	1	1	yes	characteristic, complemented
74	#4940	C₂×C₅	1	4	yes	complemented
75	#4939	C₂×C₅	1	1	yes	characteristic
76	C₄×(C₂×D₃)⋊C₄	C₂×C₅	1	4	yes	complemented
77	#4936	C₂×C₅	1	1	yes	characteristic, complemented
78	#4929	C₂×C₅	1	1	yes	characteristic, complemented
79	C₂²×C₅×Q₈	—	3	1	no	—
80	C₂²×C₅×D₄	—	3	1	no	—
81	C₂³×C₄×C₅	—	3	2	no	—
82	C₅×#124	—	3	8	no	—
83	C₄×C₅×Q₈	—	6	4	no	—
84	C₄×C₅×D₄	—	6	4	no	—
85	C₂×C₅×C₄⋊C₄	—	3	1	no	—
86	C₂×C₅×C₄⋊C₄	—	3	1	no	—
87	C₂×C₅×C₄⋊C₄	—	3	2	no	—
88	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
89	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
90	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
91	C₂×C₄²×C₅	—	3	2	no	—
92	C₂×C₄²×C₅	C₂×D₃	1	2	yes	—
93	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
94	C₂×C₄²×C₅	C₂×D₃	1	2	yes	—
95	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
96	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
97	C₅×#95	—	3	4	no	—
98	C₅×#95	—	3	4	no	—
99	C₄×#124	—	3	1	no	Sylow
100	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
101	C₂²×C₅×D₃	—	2	2	no	—
102	C₂²×C₅×D₃	—	2	4	no	—
103	C₂²×C₅×D₃	—	2	4	no	—
104	C₂²×C₅×D₃	—	2	2	no	—
105	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
112	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
113	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
114	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
115	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
116	C₂×C₃×C₄×C₅	#41	1	4	yes	—
117	C₂×C₃×C₄×C₅	#41	1	2	yes	—
118	C₂×C₃×C₄×C₅	#41	1	4	yes	—
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	—	2	2	no	—
123	C₂×C₅×Dic₃	—	2	4	no	—
124	C₂×C₅×Dic₃	—	2	4	no	—
125	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
126	C₅×D₁₂	—	2	8	no	—
127	C₄×C₅×D₃	—	4	8	no	—
128	C₅×Dic₆	—	2	8	no	—
129	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
130	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
131	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
132	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
133	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
134	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
135	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
136	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
137	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
138	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
139	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
140	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
141	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
142	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
143	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
144	#875	C₄×C₅	1	8	yes	direct product factor
145	C₄×D₁₂	—	2	4	no	—
146	C₄×Dic₆	—	2	4	no	—
147	C₃⋊#95	C₂²×C₅	1	4	yes	—
148	C₃⋊#95	C₂²×C₅	1	4	yes	—
149	C₂⁴×C₅	—	3	2	no	—
150	C₂×C₅×Q₈	—	3	4	no	—
151	C₂×C₅×Q₈	—	6	2	no	—
152	C₂×C₅×Q₈	—	6	2	no	—
153	C₂×C₅×D₄	—	3	4	no	—
154	C₂×C₅×D₄	—	6	2	no	—
155	C₂×C₅×D₄	—	6	2	no	—
156	C₂²×C₄×C₅	—	3	2	no	—
157	C₂²×C₄×C₅	—	3	2	no	—
158	C₂²×C₄×C₅	—	3	2	no	—
159	C₂²×C₄×C₅	—	6	4	no	—
160	C₂²×C₄×C₅	—	6	8	no	—
161	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
162	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
163	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
164	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
165	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
166	C₅×C₄⋊C₄	—	6	2	no	—
167	C₅×C₄⋊C₄	—	6	4	no	—
168	C₅×C₄⋊C₄	—	6	2	no	—
169	C₅×C₂²⋊C₄	—	3	16	no	—
170	C₅×C₂²⋊C₄	—	6	4	no	—
171	C₅×C₂²⋊C₄	—	6	8	no	—
172	C₄²×C₅	—	2	4	no	—
173	C₄²×C₅	—	2	2	no	—
174	C₄²×C₅	—	2	4	no	—
175	C₄²×C₅	—	6	4	no	—
176	C₄²×C₅	C₄×D₃	1	4	yes	complemented
177	C₄²×C₅	D₁₂	1	4	yes	—
178	C₂×#124	—	3	1	no	—
179	C₂×C₄×Q₈	—	3	1	no	—
180	C₂×C₄×D₄	—	3	1	no	—
181	#391	—	3	1	no	—
182	#390	—	3	1	no	—
183	#388	—	3	4	no	—
184	#382	—	3	1	no	—
185	C₄×C₂²⋊C₄	—	3	4	no	—
186	C₄³	C₅×D₃	1	1	yes	characteristic, complemented
187	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
188	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
189	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
190	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
191	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
192	C₂×C₅×D₃	—	2	4	no	—
193	C₂×C₅×D₃	—	2	8	no	—
194	C₂×C₅×D₃	—	4	2	no	—
195	C₂×C₅×D₃	—	4	4	no	—
196	C₂×C₅×D₃	—	4	2	no	—
197	C₃×C₄×C₅	—	2	4	no	—
198	C₃×C₄×C₅	—	2	4	no	—
199	C₃×C₄×C₅	—	2	2	no	—
200	C₃×C₄×C₅	C₄×D₄	1	4	yes	—
201	C₃×C₄×C₅	#124	1	4	yes	complemented
202	C₅×Dic₃	—	2	4	no	—
203	C₅×Dic₃	—	4	2	no	—
204	C₅×Dic₃	—	4	2	no	—
205	C₂³×D₃	C₂³×C₅	1	2	yes	—
206	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
207	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
208	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
209	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
210	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
211	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
212	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
213	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
214	C₂×D₁₂	—	2	2	no	—
215	C₂×D₁₂	—	2	2	no	—
216	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	—
217	C₂×C₄×D₃	—	2	4	no	—
218	C₂×C₄×D₃	—	2	8	no	—
219	C₂×Dic₆	—	2	2	no	—
220	C₂×Dic₆	—	2	2	no	—
221	C₂×Dic₆	C₂×C₄×C₅	1	4	yes	complemented
222	C₃×C₄²	—	2	4	no	—
223	C₃×C₄²	—	2	2	no	—
224	C₃×C₄²	—	2	4	no	—
225	C₃×C₄²	C₂×C₄×C₅	1	4	yes	complemented
226	C₃×C₄²	C₅×D₄	1	4	yes	—
227	(C₂×D₃)⋊C₄	—	2	4	no	—
228	(C₂×D₃)⋊C₄	—	2	8	no	—
229	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	16	yes	complemented
230	C₄⋊Dic₃	—	2	2	no	—
231	C₄⋊Dic₃	—	2	2	no	—
232	Dic₃⋊C₄	—	2	4	no	—
233	C₄×Dic₃	—	2	4	no	—
234	C₂³×C₅	—	3	4	no	—
235	C₂³×C₅	—	6	2	no	—
236	C₂³×C₅	—	6	4	no	—
237	C₂³×C₅	—	6	4	no	—
238	C₂³×C₅	—	6	2	no	—
239	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
240	C₅×Q₈	—	6	8	no	—
241	C₅×D₄	—	6	8	no	—
242	C₂×C₄×C₅	—	2	2	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	3	4	no	—
248	C₂×C₄×C₅	—	6	2	no	—
249	C₂×C₄×C₅	—	6	2	no	—
250	C₂×C₄×C₅	—	6	2	no	—
251	C₂×C₄×C₅	—	6	2	no	—
252	C₂×C₄×C₅	—	6	4	no	—
253	C₂×C₄×C₅	—	6	4	no	—
254	C₂×C₄×C₅	—	12	8	no	—
255	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
256	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
257	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
258	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
259	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
260	C₂×C₄×C₅	#235	1	4	yes	—
261	C₂×C₄×C₅	#235	1	2	yes	—
262	C₂×C₄×C₅	#235	1	4	yes	—
263	C₂²×Q₈	—	3	1	no	—
264	C₂²×D₄	—	3	1	no	—
265	C₂³×C₄	—	3	2	no	—
266	#124	—	3	8	no	—
267	C₄×Q₈	—	6	4	no	—
268	C₄×D₄	—	6	4	no	—
269	C₂×C₄⋊C₄	—	3	1	no	—
270	C₂×C₄⋊C₄	—	3	1	no	—
271	C₂×C₄⋊C₄	—	3	2	no	—
272	C₂×C₂²⋊C₄	—	3	4	no	—
273	C₂×C₂²⋊C₄	—	3	2	no	—
274	C₂×C₂²⋊C₄	—	3	4	no	—
275	C₂×C₄²	—	3	2	no	—
276	C₂×C₄²	C₂×C₅×D₃	1	2	yes	—
277	C₂×C₄²	C₂×C₅×D₃	1	2	yes	—
278	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
279	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
280	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
281	#95	—	3	4	no	—
282	#95	—	3	4	no	—
283	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
284	C₂×C₃×C₅	C₄×#41	1	2	yes	—
285	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
286	C₂×C₃×C₅	#529	1	2	yes	—
287	C₂×C₃×C₅	#532	1	1	yes	characteristic
288	C₅×D₃	—	4	4	no	—
289	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
290	C₂²×D₃	—	2	2	no	—
291	C₂²×D₃	—	2	4	no	—
292	C₂²×D₃	—	2	4	no	—
293	C₂²×D₃	—	2	2	no	—
294	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
295	C₂×C₃×C₄	—	2	2	no	—
296	C₂×C₃×C₄	—	2	2	no	—
297	C₂×C₃×C₄	—	2	2	no	—
298	C₂×C₃×C₄	—	2	2	no	—
299	C₂×C₃×C₄	—	2	2	no	—
300	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
301	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
302	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
303	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
304	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
305	C₂×C₃×C₄	C₅×#41	1	4	yes	—
306	C₂×C₃×C₄	C₅×#41	1	2	yes	—
307	C₂×C₃×C₄	C₅×#41	1	4	yes	—
308	C₂×Dic₃	—	2	2	no	—
309	C₂×Dic₃	—	2	2	no	—
310	C₂×Dic₃	—	2	2	no	—
311	C₂×Dic₃	—	2	2	no	—
312	C₂×Dic₃	—	2	4	no	—
313	C₂×Dic₃	—	2	4	no	—
314	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
315	D₁₂	—	2	8	no	—
316	C₄×D₃	—	4	8	no	—
317	Dic₆	—	2	8	no	—
318	C₂²×C₅	—	6	4	no	—
319	C₂²×C₅	—	6	8	no	—
320	C₂²×C₅	—	12	2	no	—
321	C₂²×C₅	—	12	2	no	—
322	C₂²×C₅	—	12	4	no	—
323	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
324	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
325	C₂²×C₅	C₂×#235	1	1	yes	characteristic
326	C₂²×C₅	C₂×#235	1	2	yes	—
327	C₂²×C₅	C₂×#235	1	2	yes	—
328	C₄×C₅	—	2	4	no	—
329	C₄×C₅	—	2	2	no	—
330	C₄×C₅	—	2	4	no	—
331	C₄×C₅	—	6	4	no	—
332	C₄×C₅	—	12	2	no	—
333	C₄×C₅	—	12	2	no	—
334	C₄×C₅	C₄×D₁₂	1	4	yes	—
335	C₄×C₅	#875	1	4	yes	direct product factor
336	C₂⁴	—	3	2	no	—
337	C₂×Q₈	—	3	4	no	—
338	C₂×Q₈	—	6	2	no	—
339	C₂×Q₈	—	6	2	no	—
340	C₂×D₄	—	3	4	no	—
341	C₂×D₄	—	6	2	no	—
342	C₂×D₄	—	6	2	no	—
343	C₂²×C₄	—	3	2	no	—
344	C₂²×C₄	—	3	2	no	—
345	C₂²×C₄	—	3	2	no	—
346	C₂²×C₄	—	6	4	no	—
347	C₂²×C₄	—	6	8	no	—
348	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
349	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
350	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
351	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
352	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
353	C₄⋊C₄	—	6	2	no	—
354	C₄⋊C₄	—	6	4	no	—
355	C₄⋊C₄	—	6	2	no	—
356	C₂²⋊C₄	—	3	16	no	—
357	C₂²⋊C₄	—	6	4	no	—
358	C₂²⋊C₄	—	6	8	no	—
359	C₄²	—	2	4	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	4	no	—
362	C₄²	—	6	4	no	—
363	C₄²	C₄×C₅×D₃	1	4	yes	complemented
364	C₄²	C₅×D₁₂	1	4	yes	—
365	C₃×C₅	C₄×#124	1	1	yes	characteristic, complemented, Hall
366	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
367	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
368	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
369	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
370	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
371	C₂×D₃	—	2	4	no	—
372	C₂×D₃	—	2	8	no	—
373	C₂×D₃	—	4	2	no	—
374	C₂×D₃	—	4	4	no	—
375	C₂×D₃	—	4	2	no	—
376	C₃×C₄	—	2	4	no	—
377	C₃×C₄	—	2	4	no	—
378	C₃×C₄	—	2	2	no	—
379	C₃×C₄	C₄×C₅×D₄	1	4	yes	—
380	C₃×C₄	C₅×#124	1	4	yes	complemented
381	Dic₃	—	2	4	no	—
382	Dic₃	—	4	2	no	—
383	Dic₃	—	4	2	no	—
384	C₂×C₅	—	12	4	no	—
385	C₂×C₅	C₂×C₄×D₁₂	1	1	yes	characteristic
386	C₂×C₅	C₄×#235	1	2	yes	—
387	C₂×C₅	C₂×#875	1	1	yes	characteristic
388	C₂×C₅	#5477	1	1	yes	characteristic
389	C₂×C₅	#5479	1	2	yes	—
390	C₂³	—	3	4	no	—
391	C₂³	—	6	2	no	—
392	C₂³	—	6	4	no	—
393	C₂³	—	6	4	no	—
394	C₂³	—	6	2	no	—
395	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
396	Q₈	—	6	8	no	—
397	D₄	—	6	8	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	3	4	no	—
404	C₂×C₄	—	6	2	no	—
405	C₂×C₄	—	6	2	no	—
406	C₂×C₄	—	6	2	no	—
407	C₂×C₄	—	6	2	no	—
408	C₂×C₄	—	6	4	no	—
409	C₂×C₄	—	6	4	no	—
410	C₂×C₄	—	12	8	no	—
411	C₂×C₄	C₂×C₄×C₅×D₃	1	4	yes	—
412	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
413	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
414	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
415	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
416	C₂×C₄	C₅×#235	1	4	yes	—
417	C₂×C₄	C₅×#235	1	2	yes	—
418	C₂×C₄	C₅×#235	1	4	yes	—
419	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
420	C₂×C₃	C₄×C₅×#41	1	2	yes	—
421	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
422	C₂×C₃	C₅×#529	1	2	yes	—
423	C₂×C₃	C₅×#532	1	1	yes	characteristic
424	D₃	—	4	4	no	—
425	C₅	C₄×#875	1	1	yes	characteristic, direct product factor, Sylow
426	C₂²	—	6	4	no	—
427	C₂²	—	6	8	no	—
428	C₂²	—	12	2	no	—
429	C₂²	—	12	2	no	—
430	C₂²	—	12	4	no	—
431	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
432	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
433	C₂²	C₂×C₅×#235	1	1	yes	characteristic
434	C₂²	C₂×C₅×#235	1	2	yes	—
435	C₂²	C₂×C₅×#235	1	2	yes	—
436	C₄	—	2	4	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	4	no	—
439	C₄	—	6	4	no	—
440	C₄	—	12	2	no	—
441	C₄	—	12	2	no	—
442	C₄	C₄×C₅×D₁₂	1	4	yes	—
443	C₄	C₅×#875	1	4	yes	direct product factor
444	C₃	C₄×C₅×#124	1	1	yes	characteristic, complemented, Sylow
445	C₂	—	12	4	no	—
446	C₂	C₂×C₄×C₅×D₁₂	1	1	yes	characteristic
447	C₂	C₄×C₅×#235	1	2	yes	—
448	C₂	C₂×C₅×#875	1	1	yes	characteristic
449	C₂	C₅×#5477	1	1	yes	characteristic
450	C₂	C₅×#5479	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₄³×C₅	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₅×D₁₂	C₂²
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₄³×C₅	D₃
hypocenter	C₃	C₄×C₅×#124
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₄³×C₅

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×C₅×Dic₆	C₂	semidirect
4. C₃×C₄³×C₅	C₂	semidirect
5. C₅×#4940	C₂	semidirect
7. C₄×C₅×(C₂×D₃)⋊C₄	C₂	semidirect
8. C₅×#4936	C₂	semidirect
9. C₅×#4929	C₂	semidirect
26. C₅×#875	C₄	direct (N × H)
31. C₄×#875	C₅	direct (N × H)
40. C₄³×C₅	D₃	semidirect
57. C₂×C₅×Dic₆	C₂×C₄	semidirect
61. C₃×C₄²×C₅	C₂×C₄	semidirect
65. C₅×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
72. C₂×C₄×Dic₆	C₂×C₅	semidirect
73. C₃×C₄³	C₂×C₅	semidirect
74. #4940	C₂×C₅	semidirect
76. C₄×(C₂×D₃)⋊C₄	C₂×C₅	semidirect
77. #4936	C₂×C₅	semidirect
78. #4929	C₂×C₅	semidirect
144. #875	C₄×C₅	direct (N × H)
176. C₄²×C₅	C₄×D₃	semidirect
186. C₄³	C₅×D₃	semidirect
201. C₃×C₄×C₅	#124	semidirect
221. C₂×Dic₆	C₂×C₄×C₅	semidirect
225. C₃×C₄²	C₂×C₄×C₅	semidirect
229. (C₂×D₃)⋊C₄	C₂×C₄×C₅	semidirect
335. C₄×C₅	#875	direct (N × H)
363. C₄²	C₄×C₅×D₃	semidirect
365. C₃×C₅	C₄×#124	semidirect
380. C₃×C₄	C₅×#124	semidirect
425. C₅	C₄×#875	direct (N × H)
443. C₄	C₅×#875	direct (N × H)
444. C₃	C₄×C₅×#124	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#875	2
C₂×C₄×C₅×D₁₂	2
C₂×C₄×C₅×Dic₆	2
C₃×C₄³×C₅	2
C₅×#4940	2
C₅×#4939	2
C₄×C₅×(C₂×D₃)⋊C₄	2
C₅×#4936	2
C₅×#4929	2
C₄×C₅×#124	3
C₄×#875	5

Subgroups — C4×C5×#875 #14321938

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×#875 #14321938