Subgroups — C₅×#70527 #14297550

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#423	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#823	C₂	1	2	yes	maximal
4	C₅×#4924	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4554	C₂	1	2	yes	maximal, complemented
6	C₅×#1800	—	3	1	no	maximal, Hall
7	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
8	C₂²×C₄×C₅×D₃	C₄	1	2	yes	—
9	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
10	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
11	C₂×C₅×(C₂×D₃)⋊C₄	C₄	1	2	yes	—
12	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
13	C₂×C₅×#208	C₂²	1	2	yes	—
14	C₄×C₅×D₁₂	—	2	1	no	—
15	C₄×C₅×D₁₂	—	2	1	no	—
16	C₄×C₅×D₁₂	—	2	1	no	—
17	C₄×C₅×D₁₂	—	2	1	no	—
18	C₃×C₅×C₄⋊C₈	—	2	1	no	—
19	C₃×C₅×C₄⋊C₈	—	2	1	no	—
20	C₅×#823	—	2	4	no	—
21	C₅×C₄⋊(C₃⋊C₈)	—	2	1	no	—
22	C₅×C₄⋊(C₃⋊C₈)	—	2	1	no	—
23	#70527	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂×C₄×C₅×D₄	—	3	1	no	—
25	C₅×#423	—	3	1	no	—
26	C₅×#423	D₃	1	1	yes	characteristic, complemented
27	C₂×C₅×#100	—	3	2	no	—
28	C₅×#343	—	3	2	no	—
29	C₂³×C₅×D₃	C₂×C₄	1	2	yes	—
30	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
33	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
34	C₂×C₅×D₁₂	—	2	1	no	—
35	C₂×C₅×D₁₂	—	2	1	no	—
36	C₂×C₅×D₁₂	—	2	1	no	—
37	C₂×C₅×D₁₂	—	2	1	no	—
38	C₂×C₅×D₁₂	D₄	1	2	yes	—
39	C₂×C₅×D₁₂	Q₈	1	2	yes	—
40	C₂×C₄×C₅×D₃	—	2	2	no	—
41	C₂×C₄×C₅×D₃	—	2	2	no	—
42	C₂×C₄×C₅×D₃	—	4	4	no	—
43	C₃×C₅×M₁₆	—	2	2	no	—
44	C₃×C₅×M₁₆	—	2	2	no	—
45	C₂×C₃×C₅×C₈	—	2	2	no	—
46	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
47	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
48	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
49	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
50	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
51	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
52	C₅×C₄⋊Dic₃	—	2	1	no	—
53	C₅×C₄⋊Dic₃	—	2	1	no	—
54	C₅×#208	—	2	2	no	—
55	C₅×#208	—	2	2	no	—
56	C₂×C₅×C₃⋊C₈	—	2	2	no	—
57	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic
58	C₃×#423	C₂×C₅	1	1	yes	characteristic, complemented
59	C₂×#823	C₂×C₅	1	2	yes	—
60	#4924	C₂×C₅	1	1	yes	characteristic, complemented
61	#4554	C₂×C₅	1	2	yes	complemented
62	C₂²×C₅×D₄	—	3	1	no	—
63	C₂³×C₄×C₅	—	3	2	no	—
64	C₂×C₅×M₁₆	—	3	2	no	—
65	C₂×C₅×M₁₆	C₂×D₃	1	2	yes	—
66	C₄×C₅×D₄	—	6	1	no	—
67	C₄×C₅×D₄	—	6	1	no	—
68	C₄×C₅×D₄	—	6	1	no	—
69	C₄×C₅×D₄	—	6	1	no	—
70	C₂×C₅×C₄⋊C₄	—	3	1	no	—
71	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
72	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
73	C₅×C₄⋊C₈	—	2	1	no	—
74	C₅×C₄⋊C₈	—	2	1	no	—
75	C₅×C₄⋊C₈	—	6	1	no	—
76	C₅×C₄⋊C₈	—	6	1	no	—
77	C₅×#100	—	6	4	no	—
78	#1800	—	3	1	no	Sylow
79	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₅×D₃	—	2	2	no	—
81	C₂²×C₅×D₃	—	2	2	no	—
82	C₂²×C₅×D₃	—	4	2	no	—
83	C₂²×C₅×D₃	—	4	2	no	—
84	C₂²×C₅×D₃	C₄⋊C₄	1	4	yes	—
85	C₂×C₃×C₄×C₅	—	2	2	no	—
86	C₂×C₃×C₄×C₅	—	4	1	no	—
87	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
97	C₂×C₅×Dic₃	—	2	2	no	—
98	C₂×C₅×Dic₃	—	4	2	no	—
99	C₅×D₁₂	—	2	2	no	—
100	C₅×D₁₂	—	2	2	no	—
101	C₅×D₁₂	—	2	2	no	—
102	C₅×D₁₂	—	2	2	no	—
103	C₄×C₅×D₃	—	4	4	no	—
104	C₄×C₅×D₃	—	4	4	no	—
105	C₃×C₅×C₈	—	4	2	no	—
106	C₅×C₃⋊C₈	—	4	2	no	—
107	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
108	C₂²×C₄×D₃	C₄×C₅	1	2	yes	—
109	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
110	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
111	C₂×(C₂×D₃)⋊C₄	C₄×C₅	1	2	yes	—
112	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
113	C₂×#208	C₂²×C₅	1	2	yes	—
114	C₄×D₁₂	—	2	1	no	—
115	C₄×D₁₂	—	2	1	no	—
116	C₄×D₁₂	—	2	1	no	—
117	C₄×D₁₂	—	2	1	no	—
118	C₃×C₄⋊C₈	—	2	1	no	—
119	C₃×C₄⋊C₈	—	2	1	no	—
120	#823	—	2	4	no	—
121	C₄⋊(C₃⋊C₈)	—	2	1	no	—
122	C₄⋊(C₃⋊C₈)	—	2	1	no	—
123	C₂⁴×C₅	—	3	2	no	—
124	C₂×C₅×D₄	—	3	2	no	—
125	C₂×C₅×D₄	—	3	2	no	—
126	C₂×C₅×D₄	—	6	1	no	—
127	C₂×C₅×D₄	—	6	1	no	—
128	C₂×C₅×D₄	—	6	1	no	—
129	C₂×C₅×D₄	—	6	1	no	—
130	C₂²×C₄×C₅	—	3	2	no	—
131	C₂²×C₄×C₅	—	6	2	no	—
132	C₂²×C₄×C₅	—	6	2	no	—
133	C₂²×C₄×C₅	—	12	4	no	—
134	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
135	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
137	C₅×M₁₆	—	2	2	no	—
138	C₅×M₁₆	—	2	2	no	—
139	C₅×M₁₆	—	6	2	no	—
140	C₅×M₁₆	—	6	2	no	—
141	C₂×C₅×C₈	—	2	2	no	—
142	C₂×C₅×C₈	—	6	2	no	—
143	C₅×C₄⋊C₄	—	6	1	no	—
144	C₅×C₄⋊C₄	—	6	1	no	—
145	C₅×C₂²⋊C₄	—	6	2	no	—
146	C₅×C₂²⋊C₄	—	6	2	no	—
147	C₄²×C₅	D₁₂	1	1	yes	characteristic
148	C₄²×C₅	D₁₂	1	1	yes	characteristic
149	C₄²×C₅	#67	1	1	yes	characteristic
150	C₄²×C₅	#67	1	1	yes	characteristic
151	C₂×C₄×D₄	—	3	1	no	—
152	#423	—	3	1	no	—
153	#423	C₅×D₃	1	1	yes	characteristic, complemented
154	C₂×#100	—	3	2	no	—
155	#343	—	3	2	no	—
156	C₂²×C₃×C₅	—	2	1	no	—
157	C₂²×C₃×C₅	—	2	1	no	—
158	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂²×C₃×C₅	#117	1	1	yes	characteristic
161	C₂×C₅×D₃	—	2	4	no	—
162	C₂×C₅×D₃	—	4	4	no	—
163	C₂×C₅×D₃	—	4	2	no	—
164	C₂×C₅×D₃	—	4	2	no	—
165	C₂×C₅×D₃	—	4	4	no	—
166	C₃×C₄×C₅	—	2	1	no	—
167	C₃×C₄×C₅	—	2	1	no	—
168	C₃×C₄×C₅	—	2	1	no	—
169	C₃×C₄×C₅	#100	1	2	yes	complemented
170	C₃×C₄×C₅	#121	1	1	yes	characteristic
171	C₃×C₄×C₅	#121	1	1	yes	characteristic
172	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
173	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
174	C₅×Dic₃	—	4	2	no	—
175	C₂³×D₃	C₂×C₄×C₅	1	2	yes	—
176	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
177	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
178	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
179	C₂²×Dic₃	C₂×C₄×C₅	1	2	yes	—
180	C₂×D₁₂	—	2	1	no	—
181	C₂×D₁₂	—	2	1	no	—
182	C₂×D₁₂	—	2	1	no	—
183	C₂×D₁₂	—	2	1	no	—
184	C₂×D₁₂	C₅×D₄	1	2	yes	—
185	C₂×D₁₂	C₅×Q₈	1	2	yes	—
186	C₂×C₄×D₃	—	2	2	no	—
187	C₂×C₄×D₃	—	2	2	no	—
188	C₂×C₄×D₃	—	4	4	no	—
189	C₃×M₁₆	—	2	2	no	—
190	C₃×M₁₆	—	2	2	no	—
191	C₂×C₃×C₈	—	2	2	no	—
192	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
193	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
194	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
195	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
196	(C₂×D₃)⋊C₄	—	2	2	no	—
197	(C₂×D₃)⋊C₄	—	2	2	no	—
198	C₄⋊Dic₃	—	2	1	no	—
199	C₄⋊Dic₃	—	2	1	no	—
200	#208	—	2	2	no	—
201	#208	—	2	2	no	—
202	C₂×C₃⋊C₈	—	2	2	no	—
203	C₂³×C₅	—	3	4	no	—
204	C₂³×C₅	—	6	2	no	—
205	C₂³×C₅	—	6	2	no	—
206	C₂³×C₅	—	12	2	no	—
207	C₂³×C₅	—	12	2	no	—
208	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
209	C₅×D₄	—	6	2	no	—
210	C₅×D₄	—	6	2	no	—
211	C₅×D₄	—	6	2	no	—
212	C₅×D₄	—	6	2	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	4	1	no	—
215	C₂×C₄×C₅	—	6	2	no	—
216	C₂×C₄×C₅	—	12	4	no	—
217	C₂×C₄×C₅	—	12	4	no	—
218	C₂×C₄×C₅	—	12	2	no	—
219	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
223	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
224	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
225	C₂×C₄×C₅	#237	1	1	yes	characteristic
226	C₂×C₄×C₅	D₃×Q₈	1	1	yes	characteristic
227	C₂×C₄×C₅	#239	1	1	yes	characteristic
228	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
229	C₅×C₈	—	4	2	no	—
230	C₅×C₈	—	12	2	no	—
231	C₂²×D₄	—	3	1	no	—
232	C₂³×C₄	—	3	2	no	—
233	C₂×M₁₆	—	3	2	no	—
234	C₂×M₁₆	C₂×C₅×D₃	1	2	yes	—
235	C₄×D₄	—	6	1	no	—
236	C₄×D₄	—	6	1	no	—
237	C₄×D₄	—	6	1	no	—
238	C₄×D₄	—	6	1	no	—
239	C₂×C₄⋊C₄	—	3	1	no	—
240	C₂×C₂²⋊C₄	—	3	2	no	—
241	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
242	C₄⋊C₈	—	2	1	no	—
243	C₄⋊C₈	—	2	1	no	—
244	C₄⋊C₈	—	6	1	no	—
245	C₄⋊C₈	—	6	1	no	—
246	#100	—	6	4	no	—
247	C₂×C₃×C₅	—	2	1	no	—
248	C₂×C₃×C₅	—	2	1	no	—
249	C₂×C₃×C₅	#380	1	1	yes	characteristic
250	C₂×C₃×C₅	C₂×#100	1	1	yes	characteristic
251	C₂×C₃×C₅	#413	1	1	yes	characteristic
252	C₅×D₃	—	4	4	no	—
253	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
254	C₂²×D₃	—	2	2	no	—
255	C₂²×D₃	—	2	2	no	—
256	C₂²×D₃	—	4	2	no	—
257	C₂²×D₃	—	4	2	no	—
258	C₂²×D₃	C₅×C₄⋊C₄	1	4	yes	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	4	1	no	—
261	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
262	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
263	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
266	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
269	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
270	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
271	C₂×Dic₃	—	2	2	no	—
272	C₂×Dic₃	—	4	2	no	—
273	D₁₂	—	2	2	no	—
274	D₁₂	—	2	2	no	—
275	D₁₂	—	2	2	no	—
276	D₁₂	—	2	2	no	—
277	C₄×D₃	—	4	4	no	—
278	C₄×D₃	—	4	4	no	—
279	C₃×C₈	—	4	2	no	—
280	C₃⋊C₈	—	4	2	no	—
281	C₂²×C₅	—	2	1	no	—
282	C₂²×C₅	—	2	1	no	—
283	C₂²×C₅	—	6	4	no	—
284	C₂²×C₅	—	12	4	no	—
285	C₂²×C₅	—	12	4	no	—
286	C₂²×C₅	—	12	2	no	—
287	C₂²×C₅	—	12	2	no	—
288	C₂²×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
289	C₂²×C₅	#892	1	1	yes	characteristic
290	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
291	C₄×C₅	—	2	1	no	—
292	C₄×C₅	—	2	1	no	—
293	C₄×C₅	—	2	1	no	—
294	C₄×C₅	—	12	2	no	—
295	C₄×C₅	#823	1	2	yes	complemented
296	C₄×C₅	#895	1	1	yes	characteristic
297	C₄×C₅	#897	1	1	yes	characteristic
298	C₄×C₅	#938	1	1	yes	characteristic
299	C₄×C₅	#946	1	1	yes	characteristic
300	C₂⁴	—	3	2	no	—
301	C₂×D₄	—	3	2	no	—
302	C₂×D₄	—	3	2	no	—
303	C₂×D₄	—	6	1	no	—
304	C₂×D₄	—	6	1	no	—
305	C₂×D₄	—	6	1	no	—
306	C₂×D₄	—	6	1	no	—
307	C₂²×C₄	—	3	2	no	—
308	C₂²×C₄	—	6	2	no	—
309	C₂²×C₄	—	6	2	no	—
310	C₂²×C₄	—	12	4	no	—
311	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
312	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
313	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
314	M₁₆	—	2	2	no	—
315	M₁₆	—	2	2	no	—
316	M₁₆	—	6	2	no	—
317	M₁₆	—	6	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	6	2	no	—
320	C₄⋊C₄	—	6	1	no	—
321	C₄⋊C₄	—	6	1	no	—
322	C₂²⋊C₄	—	6	2	no	—
323	C₂²⋊C₄	—	6	2	no	—
324	C₄²	C₅×D₁₂	1	1	yes	characteristic
325	C₄²	C₅×D₁₂	1	1	yes	characteristic
326	C₄²	C₅×#67	1	1	yes	characteristic
327	C₄²	C₅×#67	1	1	yes	characteristic
328	C₃×C₅	#1800	1	1	yes	characteristic, complemented, Hall
329	C₂²×C₃	—	2	1	no	—
330	C₂²×C₃	—	2	1	no	—
331	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
332	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
333	C₂²×C₃	C₅×#117	1	1	yes	characteristic
334	C₂×D₃	—	2	4	no	—
335	C₂×D₃	—	4	4	no	—
336	C₂×D₃	—	4	2	no	—
337	C₂×D₃	—	4	2	no	—
338	C₂×D₃	—	4	4	no	—
339	C₃×C₄	—	2	1	no	—
340	C₃×C₄	—	2	1	no	—
341	C₃×C₄	—	2	1	no	—
342	C₃×C₄	C₅×#100	1	2	yes	complemented
343	C₃×C₄	C₅×#121	1	1	yes	characteristic
344	C₃×C₄	C₅×#121	1	1	yes	characteristic
345	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
346	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
347	Dic₃	—	4	2	no	—
348	C₂×C₅	—	2	1	no	—
349	C₂×C₅	—	2	1	no	—
350	C₂×C₅	—	12	4	no	—
351	C₂×C₅	#4987	1	1	yes	characteristic
352	C₂×C₅	C₂×#823	1	1	yes	characteristic
353	C₂×C₅	#5132	1	1	yes	characteristic
354	C₂³	—	3	4	no	—
355	C₂³	—	6	2	no	—
356	C₂³	—	6	2	no	—
357	C₂³	—	12	2	no	—
358	C₂³	—	12	2	no	—
359	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
360	D₄	—	6	2	no	—
361	D₄	—	6	2	no	—
362	D₄	—	6	2	no	—
363	D₄	—	6	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	6	2	no	—
367	C₂×C₄	—	12	4	no	—
368	C₂×C₄	—	12	4	no	—
369	C₂×C₄	—	12	2	no	—
370	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
371	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
372	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
373	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
374	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
375	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
376	C₂×C₄	C₅×#237	1	1	yes	characteristic
377	C₂×C₄	C₅×D₃×Q₈	1	1	yes	characteristic
378	C₂×C₄	C₅×#239	1	1	yes	characteristic
379	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
380	C₈	—	4	2	no	—
381	C₈	—	12	2	no	—
382	C₂×C₃	—	2	1	no	—
383	C₂×C₃	—	2	1	no	—
384	C₂×C₃	C₅×#380	1	1	yes	characteristic
385	C₂×C₃	C₂×C₅×#100	1	1	yes	characteristic
386	C₂×C₃	C₅×#413	1	1	yes	characteristic
387	D₃	—	4	4	no	—
388	C₅	#70527	1	1	yes	characteristic, direct product factor, Sylow
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	6	4	no	—
392	C₂²	—	12	4	no	—
393	C₂²	—	12	4	no	—
394	C₂²	—	12	2	no	—
395	C₂²	—	12	2	no	—
396	C₂²	C₅×D₃×C₄⋊C₄	1	1	yes	characteristic
397	C₂²	C₅×#892	1	1	yes	characteristic
398	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	12	2	no	—
403	C₄	C₅×#823	1	2	yes	complemented
404	C₄	C₅×#895	1	1	yes	characteristic
405	C₄	C₅×#897	1	1	yes	characteristic
406	C₄	C₅×#938	1	1	yes	characteristic
407	C₄	C₅×#946	1	1	yes	characteristic
408	C₃	C₅×#1800	1	1	yes	characteristic, complemented, Sylow
409	C₂	—	2	1	no	—
410	C₂	—	2	1	no	—
411	C₂	—	12	4	no	—
412	C₂	C₅×#4987	1	1	yes	characteristic
413	C₂	C₂×C₅×#823	1	1	yes	characteristic
414	C₂	C₅×#5132	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×(C₂×D₃)⋊C₄
commutator	C₂³×C₃	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#423	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂²×C₅×D₁₂	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#423	D₃
hypocenter	C₃	C₅×#1800
LCS	G ▷ C₂³×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ C₅×#423

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#423	C₂	semidirect
4. C₅×#4924	C₂	semidirect
5. C₅×#4554	C₂	semidirect
23. #70527	C₅	direct (N × H)
26. C₅×#423	D₃	semidirect
58. C₃×#423	C₂×C₅	semidirect
60. #4924	C₂×C₅	semidirect
61. #4554	C₂×C₅	semidirect
153. #423	C₅×D₃	semidirect
169. C₃×C₄×C₅	#100	semidirect
295. C₄×C₅	#823	semidirect
328. C₃×C₅	#1800	semidirect
342. C₃×C₄	C₅×#100	semidirect
388. C₅	#70527	direct (N × H)
403. C₄	C₅×#823	semidirect
408. C₃	C₅×#1800	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×D₁₂	2
C₃×C₅×#423	2
C₂×C₅×#823	2
C₅×#4924	2
C₅×#4554	2
C₅×#1800	3
#70527	5

Subgroups — C5×#70527 #14297550

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#70527 #14297550