Subgroups — C₅×#69908 #14297420

Order 1920.

800 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#830	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×Dic₃⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₅×#4550	C₂	1	2	yes	maximal, complemented
6	C₅×#1797	—	3	1	no	maximal, Hall
7	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₂³×C₅×Dic₃	C₄	1	1	yes	characteristic
9	C₂³×C₅×Dic₃	C₄	1	1	yes	characteristic
10	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
11	C₂×C₄×C₅×Dic₃	—	2	4	no	—
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	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
16	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
17	C₃×C₅×C₂²⋊C₈	—	2	2	no	—
18	C₅×#830	—	2	2	no	—
19	C₅×Dic₃⋊C₈	—	2	4	no	—
20	#69908	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂²×C₄²×C₅	—	3	1	no	—
22	C₂×C₅×C₄⋊C₈	—	3	2	no	—
23	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
24	C₂×C₅×C₂²⋊C₈	D₃	1	1	yes	characteristic
25	C₅×#336	—	3	2	no	—
26	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₃×C₄×C₅	—	2	2	no	—
28	C₂²×C₃×C₄×C₅	—	2	2	no	—
29	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
31	C₂²×C₃×C₄×C₅	Q₈	1	2	yes	—
32	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
33	C₂²×C₅×Dic₃	—	2	2	no	—
34	C₂²×C₅×Dic₃	—	2	2	no	—
35	C₂²×C₅×Dic₃	—	2	2	no	—
36	C₂²×C₅×Dic₃	—	2	2	no	—
37	C₂²×C₅×Dic₃	—	2	2	no	—
38	C₂²×C₅×Dic₃	C₈	1	4	yes	complemented
39	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃×C₅×C₈	—	2	2	no	—
44	C₂×C₃×C₅×C₈	—	2	2	no	—
45	C₂×C₃×C₅×C₈	—	2	2	no	—
46	C₄×C₅×Dic₃	—	2	2	no	—
47	C₄×C₅×Dic₃	—	2	2	no	—
48	C₄×C₅×Dic₃	—	2	2	no	—
49	C₄×C₅×Dic₃	D₄	1	4	yes	—
50	C₂×C₅×C₃⋊C₈	—	2	2	no	—
51	C₂×C₅×C₃⋊C₈	—	2	2	no	—
52	C₂×C₅×C₃⋊C₈	—	2	2	no	—
53	C₂²×C₄×Dic₃	C₂×C₅	1	1	yes	characteristic
54	C₂×C₃×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic
55	C₂×#830	C₂×C₅	1	1	yes	characteristic
56	C₂×Dic₃⋊C₈	C₂×C₅	1	2	yes	complemented
57	#4550	C₂×C₅	1	2	yes	complemented
58	C₂³×C₄×C₅	—	3	1	no	—
59	C₂³×C₄×C₅	—	3	1	no	—
60	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
61	C₂²×C₅×C₈	—	3	2	no	—
62	C₂²×C₅×C₈	C₂×D₃	1	2	yes	—
63	C₂×C₄²×C₅	—	3	1	no	—
64	C₂×C₄²×C₅	—	3	1	no	—
65	C₂×C₄²×C₅	—	3	1	no	—
66	C₂×C₄²×C₅	—	3	1	no	—
67	C₂×C₄²×C₅	—	6	4	no	—
68	C₅×C₄⋊C₈	—	6	4	no	—
69	C₅×C₂²⋊C₈	—	2	2	no	—
70	C₅×C₂²⋊C₈	—	6	2	no	—
71	#1797	—	3	1	no	Sylow
72	C₂³×C₃×C₅	—	2	1	no	—
73	C₂³×C₃×C₅	—	2	1	no	—
74	C₂³×C₃×C₅	—	2	1	no	—
75	C₂³×C₃×C₅	—	2	1	no	—
76	C₂³×C₃×C₅	C₄⋊C₄	1	2	yes	—
77	C₂³×C₃×C₅	C₂×C₈	1	2	yes	—
78	C₂³×C₃×C₅	M₁₆	1	2	yes	—
79	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
80	C₂×C₃×C₄×C₅	—	2	1	no	—
81	C₂×C₃×C₄×C₅	—	2	1	no	—
82	C₂×C₃×C₄×C₅	—	2	4	no	—
83	C₂×C₃×C₄×C₅	—	2	4	no	—
84	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
85	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
86	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
87	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	#41	1	2	yes	—
89	C₂×C₅×Dic₃	—	2	8	no	—
90	C₂×C₅×Dic₃	—	2	1	no	—
91	C₂×C₅×Dic₃	—	2	1	no	—
92	C₂×C₅×Dic₃	—	2	1	no	—
93	C₂×C₅×Dic₃	—	2	1	no	—
94	C₂×C₅×Dic₃	—	2	1	no	—
95	C₂×C₅×Dic₃	—	2	1	no	—
96	C₂×C₅×Dic₃	—	2	8	no	—
97	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
98	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
99	C₂×C₅×Dic₃	C₂×C₈	1	2	yes	—
100	C₂×C₅×Dic₃	C₂×C₈	1	2	yes	—
101	C₂×C₅×Dic₃	M₁₆	1	2	yes	—
102	C₂×C₅×Dic₃	M₁₆	1	2	yes	—
103	C₃×C₅×C₈	—	4	2	no	—
104	C₅×C₃⋊C₈	—	4	2	no	—
105	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
106	C₂³×Dic₃	C₄×C₅	1	1	yes	characteristic
107	C₂³×Dic₃	C₄×C₅	1	1	yes	characteristic
108	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
109	C₂×C₄×Dic₃	—	2	4	no	—
110	C₂×C₄×Dic₃	C₄×C₅	1	1	yes	characteristic
111	C₂×C₄×Dic₃	C₄×C₅	1	1	yes	characteristic
112	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
113	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
114	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
115	C₃×C₂²⋊C₈	—	2	2	no	—
116	#830	—	2	2	no	—
117	Dic₃⋊C₈	—	2	4	no	—
118	C₂⁴×C₅	C₄×D₃	1	1	yes	characteristic
119	C₂²×C₄×C₅	—	2	2	no	—
120	C₂²×C₄×C₅	—	2	2	no	—
121	C₂²×C₄×C₅	—	3	1	no	—
122	C₂²×C₄×C₅	—	3	4	no	—
123	C₂²×C₄×C₅	—	3	1	no	—
124	C₂²×C₄×C₅	—	3	1	no	—
125	C₂²×C₄×C₅	—	3	1	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	—	6	2	no	—
130	C₂²×C₄×C₅	—	6	2	no	—
131	C₂²×C₄×C₅	Dic₆	1	2	yes	—
132	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
133	C₂²×C₄×C₅	#67	1	2	yes	—
134	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	—	2	2	no	—
137	C₂×C₅×C₈	—	2	2	no	—
138	C₂×C₅×C₈	—	6	2	no	—
139	C₂×C₅×C₈	—	6	2	no	—
140	C₂×C₅×C₈	—	6	2	no	—
141	C₄²×C₅	—	3	4	no	—
142	C₄²×C₅	—	6	2	no	—
143	C₄²×C₅	—	6	2	no	—
144	C₄²×C₅	—	6	2	no	—
145	C₂²×C₄²	—	3	1	no	—
146	C₂×C₄⋊C₈	—	3	2	no	—
147	C₂×C₂²⋊C₈	—	3	1	no	—
148	C₂×C₂²⋊C₈	C₅×D₃	1	1	yes	characteristic
149	#336	—	3	2	no	—
150	C₂²×C₃×C₅	—	2	2	no	—
151	C₂²×C₃×C₅	—	2	2	no	—
152	C₂²×C₃×C₅	—	2	2	no	—
153	C₂²×C₃×C₅	—	2	2	no	—
154	C₂²×C₃×C₅	—	2	2	no	—
155	C₂²×C₃×C₅	—	2	2	no	—
156	C₂²×C₃×C₅	C₄⋊C₈	1	4	yes	complemented
157	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂²×C₃×C₅	#117	1	1	yes	characteristic
160	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
161	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
162	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
163	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
164	C₃×C₄×C₅	—	2	2	no	—
165	C₃×C₄×C₅	#121	1	2	yes	—
166	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
167	C₅×Dic₃	—	2	2	no	—
168	C₅×Dic₃	—	2	2	no	—
169	C₅×Dic₃	—	2	2	no	—
170	C₅×Dic₃	C₂²⋊C₈	1	4	yes	complemented
171	C₂⁴×C₃	C₂×C₄×C₅	1	1	yes	characteristic
172	C₂²×C₃×C₄	—	2	2	no	—
173	C₂²×C₃×C₄	—	2	2	no	—
174	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
175	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
176	C₂²×C₃×C₄	C₅×Q₈	1	2	yes	—
177	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
178	C₂²×Dic₃	—	2	2	no	—
179	C₂²×Dic₃	—	2	2	no	—
180	C₂²×Dic₃	—	2	2	no	—
181	C₂²×Dic₃	—	2	2	no	—
182	C₂²×Dic₃	—	2	2	no	—
183	C₂²×Dic₃	C₅×C₈	1	4	yes	complemented
184	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
185	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
186	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
187	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
188	C₂×C₃×C₈	—	2	2	no	—
189	C₂×C₃×C₈	—	2	2	no	—
190	C₂×C₃×C₈	—	2	2	no	—
191	C₄×Dic₃	—	2	2	no	—
192	C₄×Dic₃	—	2	2	no	—
193	C₄×Dic₃	—	2	2	no	—
194	C₄×Dic₃	C₅×D₄	1	4	yes	—
195	C₂×C₃⋊C₈	—	2	2	no	—
196	C₂×C₃⋊C₈	—	2	2	no	—
197	C₂×C₃⋊C₈	—	2	2	no	—
198	C₂³×C₅	—	2	1	no	—
199	C₂³×C₅	—	2	1	no	—
200	C₂³×C₅	—	2	1	no	—
201	C₂³×C₅	—	2	1	no	—
202	C₂³×C₅	D₃×C₈	1	2	yes	—
203	C₂³×C₅	ΓL(1,𝔽₂₅)	1	2	yes	—
204	C₂³×C₅	Dic₃⋊C₄	1	2	yes	—
205	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
206	C₂×C₄×C₅	—	2	1	no	—
207	C₂×C₄×C₅	—	2	1	no	—
208	C₂×C₄×C₅	—	2	4	no	—
209	C₂×C₄×C₅	—	2	4	no	—
210	C₂×C₄×C₅	—	3	2	no	—
211	C₂×C₄×C₅	—	3	2	no	—
212	C₂×C₄×C₅	—	3	2	no	—
213	C₂×C₄×C₅	—	3	2	no	—
214	C₂×C₄×C₅	—	3	2	no	—
215	C₂×C₄×C₅	—	3	2	no	—
216	C₂×C₄×C₅	—	6	8	no	—
217	C₂×C₄×C₅	—	6	8	no	—
218	C₂×C₄×C₅	—	6	1	no	—
219	C₂×C₄×C₅	—	6	1	no	—
220	C₂×C₄×C₅	—	6	1	no	—
221	C₂×C₄×C₅	—	6	1	no	—
222	C₂×C₄×C₅	—	6	1	no	—
223	C₂×C₄×C₅	—	6	1	no	—
224	C₂×C₄×C₅	Dic₃⋊C₄	1	2	yes	—
225	C₂×C₄×C₅	C₂×Dic₆	1	1	yes	characteristic
226	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
227	C₂×C₄×C₅	#237	1	2	yes	—
228	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
229	C₅×C₈	—	4	2	no	—
230	C₅×C₈	—	12	2	no	—
231	C₂³×C₄	—	3	1	no	—
232	C₂³×C₄	—	3	1	no	—
233	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
234	C₂²×C₈	—	3	2	no	—
235	C₂²×C₈	C₂×C₅×D₃	1	2	yes	—
236	C₂×C₄²	—	3	1	no	—
237	C₂×C₄²	—	3	1	no	—
238	C₂×C₄²	—	3	1	no	—
239	C₂×C₄²	—	3	1	no	—
240	C₂×C₄²	—	6	4	no	—
241	C₄⋊C₈	—	6	4	no	—
242	C₂²⋊C₈	—	2	2	no	—
243	C₂²⋊C₈	—	6	2	no	—
244	C₂×C₃×C₅	—	2	4	no	—
245	C₂×C₃×C₅	#380	1	1	yes	characteristic
246	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
247	C₂×C₃×C₅	#407	1	1	yes	characteristic
248	C₂×C₃×C₅	C₂×C₄⋊C₈	1	1	yes	characteristic
249	C₂×C₃×C₅	#423	1	1	yes	characteristic
250	C₂×C₃×C₅	#431	1	1	yes	characteristic
251	C₂×C₃×C₅	#432	1	1	yes	characteristic
252	C₂³×C₃	—	2	1	no	—
253	C₂³×C₃	—	2	1	no	—
254	C₂³×C₃	—	2	1	no	—
255	C₂³×C₃	—	2	1	no	—
256	C₂³×C₃	C₅×C₄⋊C₄	1	2	yes	—
257	C₂³×C₃	C₂×C₅×C₈	1	2	yes	—
258	C₂³×C₃	C₅×M₁₆	1	2	yes	—
259	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
260	C₂×C₃×C₄	—	2	1	no	—
261	C₂×C₃×C₄	—	2	1	no	—
262	C₂×C₃×C₄	—	2	4	no	—
263	C₂×C₃×C₄	—	2	4	no	—
264	C₂×C₃×C₄	C₅×C₄⋊C₄	1	2	yes	—
265	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
266	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
268	C₂×C₃×C₄	C₅×#41	1	2	yes	—
269	C₂×Dic₃	—	2	8	no	—
270	C₂×Dic₃	—	2	1	no	—
271	C₂×Dic₃	—	2	1	no	—
272	C₂×Dic₃	—	2	1	no	—
273	C₂×Dic₃	—	2	1	no	—
274	C₂×Dic₃	—	2	1	no	—
275	C₂×Dic₃	—	2	1	no	—
276	C₂×Dic₃	—	2	8	no	—
277	C₂×Dic₃	C₅×C₂²⋊C₄	1	2	yes	—
278	C₂×Dic₃	C₅×C₂²⋊C₄	1	2	yes	—
279	C₂×Dic₃	C₂×C₅×C₈	1	2	yes	—
280	C₂×Dic₃	C₂×C₅×C₈	1	2	yes	—
281	C₂×Dic₃	C₅×M₁₆	1	2	yes	—
282	C₂×Dic₃	C₅×M₁₆	1	2	yes	—
283	C₃×C₈	—	4	2	no	—
284	C₃⋊C₈	—	4	2	no	—
285	C₂²×C₅	—	2	2	no	—
286	C₂²×C₅	—	2	2	no	—
287	C₂²×C₅	—	2	2	no	—
288	C₂²×C₅	—	2	2	no	—
289	C₂²×C₅	—	2	2	no	—
290	C₂²×C₅	—	2	2	no	—
291	C₂²×C₅	Dic₃⋊C₈	1	4	yes	complemented
292	C₂²×C₅	#877	1	1	yes	characteristic
293	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
294	C₂²×C₅	C₂×D₃×C₈	1	1	yes	characteristic
295	C₂²×C₅	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
296	C₂²×C₅	D₃×M₁₆	1	1	yes	characteristic
297	C₂²×C₅	D₃×M₁₆	1	1	yes	characteristic
298	C₂²×C₅	C₂×Dic₃⋊C₄	1	1	yes	characteristic
299	C₄×C₅	—	2	2	no	—
300	C₄×C₅	—	3	4	no	—
301	C₄×C₅	—	6	2	no	—
302	C₄×C₅	—	6	2	no	—
303	C₄×C₅	—	6	2	no	—
304	C₄×C₅	#878	1	2	yes	—
305	C₄×C₅	#939	1	2	yes	—
306	C₂⁴	C₄×C₅×D₃	1	1	yes	characteristic
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	3	1	no	—
310	C₂²×C₄	—	3	4	no	—
311	C₂²×C₄	—	3	1	no	—
312	C₂²×C₄	—	3	1	no	—
313	C₂²×C₄	—	3	1	no	—
314	C₂²×C₄	—	6	2	no	—
315	C₂²×C₄	—	6	2	no	—
316	C₂²×C₄	—	6	2	no	—
317	C₂²×C₄	—	6	2	no	—
318	C₂²×C₄	—	6	2	no	—
319	C₂²×C₄	C₅×Dic₆	1	2	yes	—
320	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
321	C₂²×C₄	C₅×#67	1	2	yes	—
322	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	6	2	no	—
327	C₂×C₈	—	6	2	no	—
328	C₂×C₈	—	6	2	no	—
329	C₄²	—	3	4	no	—
330	C₄²	—	6	2	no	—
331	C₄²	—	6	2	no	—
332	C₄²	—	6	2	no	—
333	C₃×C₅	#1797	1	1	yes	characteristic, complemented, Hall
334	C₂²×C₃	—	2	2	no	—
335	C₂²×C₃	—	2	2	no	—
336	C₂²×C₃	—	2	2	no	—
337	C₂²×C₃	—	2	2	no	—
338	C₂²×C₃	—	2	2	no	—
339	C₂²×C₃	—	2	2	no	—
340	C₂²×C₃	C₅×C₄⋊C₈	1	4	yes	complemented
341	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
342	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
343	C₂²×C₃	C₅×#117	1	1	yes	characteristic
344	C₂²×C₃	C₂²×C₅×C₈	1	1	yes	characteristic
345	C₂²×C₃	C₂×C₅×M₁₆	1	1	yes	characteristic
346	C₂²×C₃	C₂×C₅×M₁₆	1	1	yes	characteristic
347	C₂²×C₃	C₂×C₅×M₁₆	1	1	yes	characteristic
348	C₃×C₄	—	2	2	no	—
349	C₃×C₄	C₅×#121	1	2	yes	—
350	C₃×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
351	Dic₃	—	2	2	no	—
352	Dic₃	—	2	2	no	—
353	Dic₃	—	2	2	no	—
354	Dic₃	C₅×C₂²⋊C₈	1	4	yes	complemented
355	C₂×C₅	—	2	4	no	—
356	C₂×C₅	#4718	1	1	yes	characteristic
357	C₂×C₅	#4719	1	1	yes	characteristic
358	C₂×C₅	D₃×C₂²⋊C₈	1	1	yes	characteristic
359	C₂×C₅	#4726	1	1	yes	characteristic
360	C₂×C₅	#4942	1	1	yes	characteristic
361	C₂×C₅	C₂×Dic₃⋊C₈	1	1	yes	characteristic
362	C₂×C₅	#5118	1	1	yes	characteristic
363	C₂³	—	2	1	no	—
364	C₂³	—	2	1	no	—
365	C₂³	—	2	1	no	—
366	C₂³	—	2	1	no	—
367	C₂³	C₅×D₃×C₈	1	2	yes	—
368	C₂³	C₅×ΓL(1,𝔽₂₅)	1	2	yes	—
369	C₂³	C₅×Dic₃⋊C₄	1	2	yes	—
370	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	3	2	no	—
376	C₂×C₄	—	3	2	no	—
377	C₂×C₄	—	3	2	no	—
378	C₂×C₄	—	3	2	no	—
379	C₂×C₄	—	3	2	no	—
380	C₂×C₄	—	3	2	no	—
381	C₂×C₄	—	6	8	no	—
382	C₂×C₄	—	6	8	no	—
383	C₂×C₄	—	6	1	no	—
384	C₂×C₄	—	6	1	no	—
385	C₂×C₄	—	6	1	no	—
386	C₂×C₄	—	6	1	no	—
387	C₂×C₄	—	6	1	no	—
388	C₂×C₄	—	6	1	no	—
389	C₂×C₄	C₅×Dic₃⋊C₄	1	2	yes	—
390	C₂×C₄	C₂×C₅×Dic₆	1	1	yes	characteristic
391	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
392	C₂×C₄	C₅×#237	1	2	yes	—
393	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
394	C₈	—	4	2	no	—
395	C₈	—	12	2	no	—
396	C₂×C₃	—	2	4	no	—
397	C₂×C₃	C₅×#380	1	1	yes	characteristic
398	C₂×C₃	C₂×C₅×C₂²⋊C₈	1	1	yes	characteristic
399	C₂×C₃	C₅×#407	1	1	yes	characteristic
400	C₂×C₃	C₂×C₅×C₄⋊C₈	1	1	yes	characteristic
401	C₂×C₃	C₅×#423	1	1	yes	characteristic
402	C₂×C₃	C₅×#431	1	1	yes	characteristic
403	C₂×C₃	C₅×#432	1	1	yes	characteristic
404	C₅	#69908	1	1	yes	characteristic, direct product factor, Sylow
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	2	2	no	—
411	C₂²	C₅×Dic₃⋊C₈	1	4	yes	complemented
412	C₂²	C₅×#877	1	1	yes	characteristic
413	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
414	C₂²	C₂×C₅×D₃×C₈	1	1	yes	characteristic
415	C₂²	C₂×C₅×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
416	C₂²	C₅×D₃×M₁₆	1	1	yes	characteristic
417	C₂²	C₅×D₃×M₁₆	1	1	yes	characteristic
418	C₂²	C₂×C₅×Dic₃⋊C₄	1	1	yes	characteristic
419	C₄	—	2	2	no	—
420	C₄	—	3	4	no	—
421	C₄	—	6	2	no	—
422	C₄	—	6	2	no	—
423	C₄	—	6	2	no	—
424	C₄	C₅×#878	1	2	yes	—
425	C₄	C₅×#939	1	2	yes	—
426	C₃	C₅×#1797	1	1	yes	characteristic, complemented, Sylow
427	C₂	—	2	4	no	—
428	C₂	C₅×#4718	1	1	yes	characteristic
429	C₂	C₅×#4719	1	1	yes	characteristic
430	C₂	C₅×D₃×C₂²⋊C₈	1	1	yes	characteristic
431	C₂	C₅×#4726	1	1	yes	characteristic
432	C₂	C₅×#4942	1	1	yes	characteristic
433	C₂	C₂×C₅×Dic₃⋊C₈	1	1	yes	characteristic
434	C₂	C₅×#5118	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	C₂×C₃×C₅×C₂²⋊C₈	C₂
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂⁴×C₃×C₅	C₂×C₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂×C₅×C₂²⋊C₈	D₃
hypocenter	C₃	C₅×#1797
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
4. C₂×C₅×Dic₃⋊C₈	C₂	semidirect
5. C₅×#4550	C₂	semidirect
20. #69908	C₅	direct (N × H)
38. C₂²×C₅×Dic₃	C₈	semidirect
56. C₂×Dic₃⋊C₈	C₂×C₅	semidirect
57. #4550	C₂×C₅	semidirect
156. C₂²×C₃×C₅	C₄⋊C₈	semidirect
170. C₅×Dic₃	C₂²⋊C₈	semidirect
183. C₂²×Dic₃	C₅×C₈	semidirect
291. C₂²×C₅	Dic₃⋊C₈	semidirect
333. C₃×C₅	#1797	semidirect
340. C₂²×C₃	C₅×C₄⋊C₈	semidirect
354. Dic₃	C₅×C₂²⋊C₈	semidirect
404. C₅	#69908	direct (N × H)
411. C₂²	C₅×Dic₃⋊C₈	semidirect
426. 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
C₂²×C₄×C₅×Dic₃	2
C₂×C₃×C₅×C₂²⋊C₈	2
C₂×C₅×#830	2
C₂×C₅×Dic₃⋊C₈	2
C₅×#4550	2
C₅×#1797	3
#69908	5

Subgroups — C5×#69908 #14297420

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#69908 #14297420