Subgroups — C₅×#68662 #14297423

Order 1920.

800 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₅×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×(C₂×D₃)⋊C₈	C₂	1	2	yes	maximal
3	C₂×C₅×Dic₃⋊C₈	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#336	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4524	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1797	—	3	1	no	maximal, Hall
7	C₂²×C₄×C₅×D₃	C₄	1	1	yes	characteristic
8	C₂²×C₄×C₅×D₃	C₄	1	1	yes	characteristic
9	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₅×Dic₃	C₄	1	1	yes	characteristic
13	C₂×C₄×C₅×Dic₃	C₄	1	1	yes	characteristic
14	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
15	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
16	C₄²×C₅×D₃	—	2	4	no	—
17	C₅×(C₂×D₃)⋊C₈	—	2	4	no	—
18	C₅×Dic₃⋊C₈	—	2	4	no	—
19	#68662	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂²×C₄²×C₅	—	3	1	no	—
21	C₂×C₅×C₄⋊C₈	—	3	2	no	—
22	C₂×C₅×C₂²⋊C₈	—	3	2	no	—
23	C₅×#336	—	3	1	no	—
24	C₅×#336	D₃	1	1	yes	characteristic, complemented
25	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
29	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄×C₅×D₃	—	2	2	no	—
33	C₂×C₄×C₅×D₃	—	2	2	no	—
34	C₂×C₄×C₅×D₃	—	2	2	no	—
35	C₂×C₄×C₅×D₃	—	2	2	no	—
36	C₂×C₄×C₅×D₃	—	2	2	no	—
37	C₂×C₄×C₅×D₃	—	2	2	no	—
38	C₂×C₄×C₅×D₃	—	2	2	no	—
39	C₂×C₄×C₅×D₃	C₈	1	4	yes	complemented
40	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
41	C₂×C₄×C₅×D₃	Q₈	1	2	yes	—
42	C₂×C₃×C₅×C₈	—	2	2	no	—
43	C₂×C₃×C₅×C₈	—	2	2	no	—
44	C₂×C₃×C₅×C₈	—	2	2	no	—
45	C₃×C₄²×C₅	—	2	2	no	—
46	C₄×C₅×Dic₃	—	2	2	no	—
47	C₄×C₅×Dic₃	—	2	2	no	—
48	C₄×C₅×Dic₃	D₄	1	4	yes	—
49	C₂×C₅×C₃⋊C₈	—	2	2	no	—
50	C₂×C₅×C₃⋊C₈	—	2	2	no	—
51	C₂×C₅×C₃⋊C₈	—	2	2	no	—
52	C₂×C₄²×D₃	C₂×C₅	1	1	yes	characteristic
53	C₂×(C₂×D₃)⋊C₈	C₂×C₅	1	2	yes	—
54	C₂×Dic₃⋊C₈	C₂×C₅	1	2	yes	complemented
55	C₃×#336	C₂×C₅	1	1	yes	characteristic, complemented
56	#4524	C₂×C₅	1	1	yes	characteristic, complemented
57	C₂³×C₄×C₅	—	3	1	no	—
58	C₂³×C₄×C₅	—	3	1	no	—
59	C₂³×C₄×C₅	—	3	1	no	—
60	C₂²×C₅×C₈	—	3	2	no	—
61	C₂²×C₅×C₈	C₂×D₃	1	2	yes	—
62	C₂×C₄²×C₅	—	3	1	no	—
63	C₂×C₄²×C₅	—	3	1	no	—
64	C₂×C₄²×C₅	—	3	1	no	—
65	C₂×C₄²×C₅	—	6	4	no	—
66	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
67	C₅×C₄⋊C₈	—	6	4	no	—
68	C₅×C₂²⋊C₈	—	6	4	no	—
69	#1797	—	3	1	no	Sylow
70	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₅×D₃	—	2	1	no	—
72	C₂²×C₅×D₃	—	2	1	no	—
73	C₂²×C₅×D₃	—	2	1	no	—
74	C₂²×C₅×D₃	—	2	1	no	—
75	C₂²×C₅×D₃	C₄⋊C₄	1	2	yes	—
76	C₂²×C₅×D₃	C₂×C₈	1	2	yes	—
77	C₂²×C₅×D₃	M₁₆	1	2	yes	—
78	C₂×C₃×C₄×C₅	—	2	1	no	—
79	C₂×C₃×C₄×C₅	—	2	1	no	—
80	C₂×C₃×C₄×C₅	—	2	1	no	—
81	C₂×C₃×C₄×C₅	—	2	1	no	—
82	C₂×C₃×C₄×C₅	C₂×C₈	1	2	yes	—
83	C₂×C₃×C₄×C₅	M₁₆	1	2	yes	—
84	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
85	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
86	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
87	C₂×C₃×C₄×C₅	#41	1	2	yes	—
88	C₂×C₅×Dic₃	—	2	1	no	—
89	C₂×C₅×Dic₃	—	2	1	no	—
90	C₂×C₅×Dic₃	—	2	1	no	—
91	C₂×C₅×Dic₃	—	2	1	no	—
92	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
93	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
94	C₂×C₅×Dic₃	C₄⋊C₄	1	2	yes	—
95	C₂×C₅×Dic₃	C₂×C₈	1	2	yes	—
96	C₂×C₅×Dic₃	M₁₆	1	2	yes	—
97	C₄×C₅×D₃	—	2	8	no	—
98	C₄×C₅×D₃	—	2	4	no	—
99	C₄×C₅×D₃	—	2	4	no	—
100	C₄×C₅×D₃	—	2	8	no	—
101	C₃×C₅×C₈	—	4	2	no	—
102	C₅×C₃⋊C₈	—	4	2	no	—
103	C₂²×C₄×D₃	C₄×C₅	1	1	yes	characteristic
104	C₂²×C₄×D₃	C₄×C₅	1	1	yes	characteristic
105	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
106	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
107	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
108	C₂×C₄×Dic₃	C₄×C₅	1	1	yes	characteristic
109	C₂×C₄×Dic₃	C₄×C₅	1	1	yes	characteristic
110	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
111	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
112	C₄²×D₃	—	2	4	no	—
113	(C₂×D₃)⋊C₈	—	2	4	no	—
114	Dic₃⋊C₈	—	2	4	no	—
115	C₂⁴×C₅	—	3	1	no	—
116	C₂²×C₄×C₅	—	3	1	no	—
117	C₂²×C₄×C₅	—	3	1	no	—
118	C₂²×C₄×C₅	—	3	1	no	—
119	C₂²×C₄×C₅	—	3	4	no	—
120	C₂²×C₄×C₅	—	3	2	no	—
121	C₂²×C₄×C₅	—	3	2	no	—
122	C₂²×C₄×C₅	—	6	2	no	—
123	C₂²×C₄×C₅	—	6	2	no	—
124	C₂²×C₄×C₅	—	6	2	no	—
125	C₂²×C₄×C₅	—	6	2	no	—
126	C₂²×C₄×C₅	—	6	2	no	—
127	C₂²×C₄×C₅	—	6	2	no	—
128	C₂²×C₄×C₅	—	6	2	no	—
129	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
130	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
132	C₂×C₅×C₈	—	2	2	no	—
133	C₂×C₅×C₈	—	2	2	no	—
134	C₂×C₅×C₈	—	2	2	no	—
135	C₂×C₅×C₈	—	6	2	no	—
136	C₂×C₅×C₈	—	6	2	no	—
137	C₂×C₅×C₈	—	6	2	no	—
138	C₄²×C₅	—	2	2	no	—
139	C₄²×C₅	—	3	4	no	—
140	C₄²×C₅	—	6	2	no	—
141	C₄²×C₅	—	6	2	no	—
142	C₂²×C₄²	—	3	1	no	—
143	C₂×C₄⋊C₈	—	3	2	no	—
144	C₂×C₂²⋊C₈	—	3	2	no	—
145	#336	—	3	1	no	—
146	#336	C₅×D₃	1	1	yes	characteristic, complemented
147	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂²×C₃×C₅	#117	1	1	yes	characteristic
150	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
151	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
152	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
153	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
154	C₂×C₅×D₃	—	2	2	no	—
155	C₂×C₅×D₃	—	2	2	no	—
156	C₂×C₅×D₃	—	2	2	no	—
157	C₂×C₅×D₃	—	2	2	no	—
158	C₂×C₅×D₃	—	2	2	no	—
159	C₂×C₅×D₃	—	2	2	no	—
160	C₂×C₅×D₃	C₄⋊C₈	1	4	yes	complemented
161	C₃×C₄×C₅	—	2	2	no	—
162	C₃×C₄×C₅	—	2	2	no	—
163	C₃×C₄×C₅	#121	1	2	yes	—
164	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
165	C₅×Dic₃	—	2	2	no	—
166	C₅×Dic₃	—	2	2	no	—
167	C₅×Dic₃	C₂²⋊C₈	1	4	yes	complemented
168	C₂³×D₃	C₂×C₄×C₅	1	1	yes	characteristic
169	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
170	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
171	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
172	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
173	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
174	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
175	C₂×C₄×D₃	—	2	2	no	—
176	C₂×C₄×D₃	—	2	2	no	—
177	C₂×C₄×D₃	—	2	2	no	—
178	C₂×C₄×D₃	—	2	2	no	—
179	C₂×C₄×D₃	—	2	2	no	—
180	C₂×C₄×D₃	—	2	2	no	—
181	C₂×C₄×D₃	—	2	2	no	—
182	C₂×C₄×D₃	C₅×C₈	1	4	yes	complemented
183	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
184	C₂×C₄×D₃	C₅×Q₈	1	2	yes	—
185	C₂×C₃×C₈	—	2	2	no	—
186	C₂×C₃×C₈	—	2	2	no	—
187	C₂×C₃×C₈	—	2	2	no	—
188	C₃×C₄²	—	2	2	no	—
189	C₄×Dic₃	—	2	2	no	—
190	C₄×Dic₃	—	2	2	no	—
191	C₄×Dic₃	C₅×D₄	1	4	yes	—
192	C₂×C₃⋊C₈	—	2	2	no	—
193	C₂×C₃⋊C₈	—	2	2	no	—
194	C₂×C₃⋊C₈	—	2	2	no	—
195	C₂³×C₅	—	3	2	no	—
196	C₂³×C₅	—	3	2	no	—
197	C₂³×C₅	—	3	2	no	—
198	C₂³×C₅	—	6	1	no	—
199	C₂³×C₅	—	6	1	no	—
200	C₂³×C₅	—	6	1	no	—
201	C₂³×C₅	—	6	1	no	—
202	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
203	C₂×C₄×C₅	—	2	1	no	—
204	C₂×C₄×C₅	—	2	1	no	—
205	C₂×C₄×C₅	—	2	1	no	—
206	C₂×C₄×C₅	—	2	1	no	—
207	C₂×C₄×C₅	—	3	2	no	—
208	C₂×C₄×C₅	—	3	2	no	—
209	C₂×C₄×C₅	—	3	2	no	—
210	C₂×C₄×C₅	—	3	2	no	—
211	C₂×C₄×C₅	—	3	2	no	—
212	C₂×C₄×C₅	—	6	8	no	—
213	C₂×C₄×C₅	—	6	8	no	—
214	C₂×C₄×C₅	—	6	1	no	—
215	C₂×C₄×C₅	—	6	1	no	—
216	C₂×C₄×C₅	—	6	1	no	—
217	C₂×C₄×C₅	—	6	1	no	—
218	C₂×C₄×C₅	—	6	4	no	—
219	C₂×C₄×C₅	—	6	4	no	—
220	C₂×C₄×C₅	D₃×C₈	1	2	yes	—
221	C₂×C₄×C₅	ΓL(1,𝔽₂₅)	1	2	yes	—
222	C₂×C₄×C₅	#235	1	2	yes	—
223	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
224	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
225	C₂×C₄×C₅	D₃×Q₈	1	1	yes	characteristic
226	C₅×C₈	—	4	2	no	—
227	C₅×C₈	—	12	2	no	—
228	C₂³×C₄	—	3	1	no	—
229	C₂³×C₄	—	3	1	no	—
230	C₂³×C₄	—	3	1	no	—
231	C₂²×C₈	—	3	2	no	—
232	C₂²×C₈	C₂×C₅×D₃	1	2	yes	—
233	C₂×C₄²	—	3	1	no	—
234	C₂×C₄²	—	3	1	no	—
235	C₂×C₄²	—	3	1	no	—
236	C₂×C₄²	—	6	4	no	—
237	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
238	C₄⋊C₈	—	6	4	no	—
239	C₂²⋊C₈	—	6	4	no	—
240	C₂×C₃×C₅	#380	1	1	yes	characteristic
241	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
242	C₂×C₃×C₅	#407	1	1	yes	characteristic
243	C₂×C₃×C₅	C₂×C₄⋊C₈	1	1	yes	characteristic
244	C₂×C₃×C₅	#423	1	1	yes	characteristic
245	C₂×C₃×C₅	#431	1	1	yes	characteristic
246	C₂×C₃×C₅	#432	1	1	yes	characteristic
247	C₅×D₃	—	2	4	no	—
248	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
249	C₂²×D₃	—	2	1	no	—
250	C₂²×D₃	—	2	1	no	—
251	C₂²×D₃	—	2	1	no	—
252	C₂²×D₃	—	2	1	no	—
253	C₂²×D₃	C₅×C₄⋊C₄	1	2	yes	—
254	C₂²×D₃	C₂×C₅×C₈	1	2	yes	—
255	C₂²×D₃	C₅×M₁₆	1	2	yes	—
256	C₂×C₃×C₄	—	2	1	no	—
257	C₂×C₃×C₄	—	2	1	no	—
258	C₂×C₃×C₄	—	2	1	no	—
259	C₂×C₃×C₄	—	2	1	no	—
260	C₂×C₃×C₄	C₂×C₅×C₈	1	2	yes	—
261	C₂×C₃×C₄	C₅×M₁₆	1	2	yes	—
262	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
264	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
265	C₂×C₃×C₄	C₅×#41	1	2	yes	—
266	C₂×Dic₃	—	2	1	no	—
267	C₂×Dic₃	—	2	1	no	—
268	C₂×Dic₃	—	2	1	no	—
269	C₂×Dic₃	—	2	1	no	—
270	C₂×Dic₃	C₅×C₂²⋊C₄	1	2	yes	—
271	C₂×Dic₃	C₅×C₂²⋊C₄	1	2	yes	—
272	C₂×Dic₃	C₅×C₄⋊C₄	1	2	yes	—
273	C₂×Dic₃	C₂×C₅×C₈	1	2	yes	—
274	C₂×Dic₃	C₅×M₁₆	1	2	yes	—
275	C₄×D₃	—	2	8	no	—
276	C₄×D₃	—	2	4	no	—
277	C₄×D₃	—	2	4	no	—
278	C₄×D₃	—	2	8	no	—
279	C₃×C₈	—	4	2	no	—
280	C₃⋊C₈	—	4	2	no	—
281	C₂²×C₅	—	3	4	no	—
282	C₂²×C₅	—	6	2	no	—
283	C₂²×C₅	—	6	2	no	—
284	C₂²×C₅	—	6	2	no	—
285	C₂²×C₅	—	6	2	no	—
286	C₂²×C₅	—	6	2	no	—
287	C₂²×C₅	—	6	2	no	—
288	C₂²×C₅	#872	1	1	yes	characteristic
289	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
290	C₂²×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
291	C₂²×C₅	C₂×D₃×C₈	1	1	yes	characteristic
292	C₂²×C₅	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
293	C₂²×C₅	D₃×M₁₆	1	1	yes	characteristic
294	C₂²×C₅	D₃×M₁₆	1	1	yes	characteristic
295	C₄×C₅	—	2	2	no	—
296	C₄×C₅	—	2	2	no	—
297	C₄×C₅	—	3	4	no	—
298	C₄×C₅	—	6	2	no	—
299	C₄×C₅	—	6	2	no	—
300	C₄×C₅	#884	1	2	yes	—
301	C₄×C₅	#896	1	2	yes	—
302	C₂⁴	—	3	1	no	—
303	C₂²×C₄	—	3	1	no	—
304	C₂²×C₄	—	3	1	no	—
305	C₂²×C₄	—	3	1	no	—
306	C₂²×C₄	—	3	4	no	—
307	C₂²×C₄	—	3	2	no	—
308	C₂²×C₄	—	3	2	no	—
309	C₂²×C₄	—	6	2	no	—
310	C₂²×C₄	—	6	2	no	—
311	C₂²×C₄	—	6	2	no	—
312	C₂²×C₄	—	6	2	no	—
313	C₂²×C₄	—	6	2	no	—
314	C₂²×C₄	—	6	2	no	—
315	C₂²×C₄	—	6	2	no	—
316	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
317	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
318	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	6	2	no	—
323	C₂×C₈	—	6	2	no	—
324	C₂×C₈	—	6	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	3	4	no	—
327	C₄²	—	6	2	no	—
328	C₄²	—	6	2	no	—
329	C₃×C₅	#1797	1	1	yes	characteristic, complemented, Hall
330	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
331	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
332	C₂²×C₃	C₅×#117	1	1	yes	characteristic
333	C₂²×C₃	C₂²×C₅×C₈	1	1	yes	characteristic
334	C₂²×C₃	C₂×C₅×M₁₆	1	1	yes	characteristic
335	C₂²×C₃	C₂×C₅×M₁₆	1	1	yes	characteristic
336	C₂²×C₃	C₂×C₅×M₁₆	1	1	yes	characteristic
337	C₂×D₃	—	2	2	no	—
338	C₂×D₃	—	2	2	no	—
339	C₂×D₃	—	2	2	no	—
340	C₂×D₃	—	2	2	no	—
341	C₂×D₃	—	2	2	no	—
342	C₂×D₃	—	2	2	no	—
343	C₂×D₃	C₅×C₄⋊C₈	1	4	yes	complemented
344	C₃×C₄	—	2	2	no	—
345	C₃×C₄	—	2	2	no	—
346	C₃×C₄	C₅×#121	1	2	yes	—
347	C₃×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
348	Dic₃	—	2	2	no	—
349	Dic₃	—	2	2	no	—
350	Dic₃	C₅×C₂²⋊C₈	1	4	yes	complemented
351	C₂×C₅	—	6	4	no	—
352	C₂×C₅	#4667	1	1	yes	characteristic
353	C₂×C₅	#4685	1	1	yes	characteristic
354	C₂×C₅	#4705	1	1	yes	characteristic
355	C₂×C₅	D₃×C₂²⋊C₈	1	1	yes	characteristic
356	C₂×C₅	#4726	1	1	yes	characteristic
357	C₂×C₅	D₃×C₄⋊C₈	1	1	yes	characteristic
358	C₂×C₅	#4837	1	1	yes	characteristic
359	C₂³	—	3	2	no	—
360	C₂³	—	3	2	no	—
361	C₂³	—	3	2	no	—
362	C₂³	—	6	1	no	—
363	C₂³	—	6	1	no	—
364	C₂³	—	6	1	no	—
365	C₂³	—	6	1	no	—
366	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	3	2	no	—
372	C₂×C₄	—	3	2	no	—
373	C₂×C₄	—	3	2	no	—
374	C₂×C₄	—	3	2	no	—
375	C₂×C₄	—	3	2	no	—
376	C₂×C₄	—	6	8	no	—
377	C₂×C₄	—	6	8	no	—
378	C₂×C₄	—	6	1	no	—
379	C₂×C₄	—	6	1	no	—
380	C₂×C₄	—	6	1	no	—
381	C₂×C₄	—	6	1	no	—
382	C₂×C₄	—	6	4	no	—
383	C₂×C₄	—	6	4	no	—
384	C₂×C₄	C₅×D₃×C₈	1	2	yes	—
385	C₂×C₄	C₅×ΓL(1,𝔽₂₅)	1	2	yes	—
386	C₂×C₄	C₅×#235	1	2	yes	—
387	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
388	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
389	C₂×C₄	C₅×D₃×Q₈	1	1	yes	characteristic
390	C₈	—	4	2	no	—
391	C₈	—	12	2	no	—
392	C₂×C₃	C₅×#380	1	1	yes	characteristic
393	C₂×C₃	C₂×C₅×C₂²⋊C₈	1	1	yes	characteristic
394	C₂×C₃	C₅×#407	1	1	yes	characteristic
395	C₂×C₃	C₂×C₅×C₄⋊C₈	1	1	yes	characteristic
396	C₂×C₃	C₅×#423	1	1	yes	characteristic
397	C₂×C₃	C₅×#431	1	1	yes	characteristic
398	C₂×C₃	C₅×#432	1	1	yes	characteristic
399	D₃	—	2	4	no	—
400	C₅	#68662	1	1	yes	characteristic, direct product factor, Sylow
401	C₂²	—	3	4	no	—
402	C₂²	—	6	2	no	—
403	C₂²	—	6	2	no	—
404	C₂²	—	6	2	no	—
405	C₂²	—	6	2	no	—
406	C₂²	—	6	2	no	—
407	C₂²	—	6	2	no	—
408	C₂²	C₅×#872	1	1	yes	characteristic
409	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
410	C₂²	C₅×D₃×C₄⋊C₄	1	1	yes	characteristic
411	C₂²	C₂×C₅×D₃×C₈	1	1	yes	characteristic
412	C₂²	C₂×C₅×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
413	C₂²	C₅×D₃×M₁₆	1	1	yes	characteristic
414	C₂²	C₅×D₃×M₁₆	1	1	yes	characteristic
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	3	4	no	—
418	C₄	—	6	2	no	—
419	C₄	—	6	2	no	—
420	C₄	C₅×#884	1	2	yes	—
421	C₄	C₅×#896	1	2	yes	—
422	C₃	C₅×#1797	1	1	yes	characteristic, complemented, Sylow
423	C₂	—	6	4	no	—
424	C₂	C₅×#4667	1	1	yes	characteristic
425	C₂	C₅×#4685	1	1	yes	characteristic
426	C₂	C₅×#4705	1	1	yes	characteristic
427	C₂	C₅×D₃×C₂²⋊C₈	1	1	yes	characteristic
428	C₂	C₅×#4726	1	1	yes	characteristic
429	C₂	C₅×D₃×C₄⋊C₈	1	1	yes	characteristic
430	C₂	C₅×#4837	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²×D₃
commutator	C₂²×C₃	C₂²×C₅×C₈
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#336	C₂
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂³×C₅×D₃	C₂×C₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#336	D₃
hypocenter	C₃	C₅×#1797
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₅×#336

Complements

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

N	H ≅ G/N	type
3. C₂×C₅×Dic₃⋊C₈	C₂	semidirect
4. C₃×C₅×#336	C₂	semidirect
5. C₅×#4524	C₂	semidirect
19. #68662	C₅	direct (N × H)
24. C₅×#336	D₃	semidirect
39. C₂×C₄×C₅×D₃	C₈	semidirect
54. C₂×Dic₃⋊C₈	C₂×C₅	semidirect
55. C₃×#336	C₂×C₅	semidirect
56. #4524	C₂×C₅	semidirect
146. #336	C₅×D₃	semidirect
160. C₂×C₅×D₃	C₄⋊C₈	semidirect
167. C₅×Dic₃	C₂²⋊C₈	semidirect
182. C₂×C₄×D₃	C₅×C₈	semidirect
329. C₃×C₅	#1797	semidirect
343. C₂×D₃	C₅×C₄⋊C₈	semidirect
350. Dic₃	C₅×C₂²⋊C₈	semidirect
400. C₅	#68662	direct (N × H)
422. C₃	C₅×#1797	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄²×C₅×D₃	2
C₂×C₅×(C₂×D₃)⋊C₈	2
C₂×C₅×Dic₃⋊C₈	2
C₃×C₅×#336	2
C₅×#4524	2
C₅×#1797	3
#68662	5

Subgroups — C5×#68662 #14297423

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68662 #14297423