Subgroups — C₃×C₅×#1999 #14275033

Order 1920.

992 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#121	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₅×#102	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#340	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1999	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₅×D₄	—	2	2	no	—
8	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×D₈	—	2	4	no	—
11	C₂×C₃×C₅×D₈	—	2	2	no	—
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₃×C₅×#121	—	2	4	no	—
15	C₃×C₅×#121	—	2	4	no	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
18	C₃×C₅×#102	—	2	4	no	—
19	C₃×C₅×C₂²⋊C₈	—	2	2	no	—
20	C₃×#1999	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂²×C₅×D₈	C₂×C₃	1	1	yes	characteristic, complemented
22	C₂×C₅×#121	C₂×C₃	1	2	yes	complemented
23	C₂×C₅×#102	C₂×C₃	1	2	yes	complemented
24	C₂×C₅×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
25	C₅×#340	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂⁴×C₃×C₅	—	2	2	no	—
27	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
28	C₂×C₃×C₅×D₄	—	2	8	no	—
29	C₂×C₃×C₅×D₄	—	2	2	no	—
30	C₂×C₃×C₅×D₄	—	2	2	no	—
31	C₂×C₃×C₅×D₄	—	2	2	no	—
32	C₂×C₃×C₅×D₄	—	2	2	no	—
33	C₂×C₃×C₅×D₄	—	2	2	no	—
34	C₂×C₃×C₅×D₄	—	4	4	no	—
35	C₂×C₃×C₅×D₄	—	4	4	no	—
36	C₂×C₃×C₅×D₄	D₄	1	4	yes	complemented
37	C₂²×C₃×C₄×C₅	—	2	2	no	—
38	C₂²×C₃×C₄×C₅	—	2	2	no	—
39	C₂²×C₃×C₄×C₅	—	2	2	no	—
40	C₂²×C₃×C₄×C₅	—	2	1	no	—
41	C₂²×C₃×C₄×C₅	—	2	1	no	—
42	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₃×C₅×D₈	—	2	8	no	—
45	C₂×C₃×C₅×C₈	—	2	2	no	—
46	C₂×C₃×C₅×C₈	—	2	1	no	—
47	C₂×C₃×C₅×C₈	—	2	2	no	—
48	C₂×C₃×C₅×C₈	D₄	1	2	yes	complemented
49	C₃×C₅×C₄⋊C₄	—	2	2	no	—
50	C₃×C₅×C₄⋊C₄	D₄	1	4	yes	complemented
51	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
52	C₂²×C₃×D₈	C₂×C₅	1	1	yes	characteristic, complemented
53	C₂×C₃×#121	C₂×C₅	1	2	yes	complemented
54	C₂×C₃×#102	C₂×C₅	1	2	yes	complemented
55	C₂×C₃×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
56	C₃×#340	C₂×C₅	1	1	yes	characteristic, complemented
57	C₂²×C₅×D₄	—	2	2	no	—
58	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
59	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
60	C₂×C₅×D₈	—	2	4	no	—
61	C₂×C₅×D₈	—	2	2	no	—
62	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
63	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
64	C₅×#121	—	2	4	no	—
65	C₅×#121	—	2	4	no	—
66	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
67	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
68	C₅×#102	—	2	4	no	—
69	C₅×C₂²⋊C₈	—	2	2	no	—
70	#1999	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
71	C₂³×C₃×C₅	—	2	2	no	—
72	C₂³×C₃×C₅	—	2	1	no	—
73	C₂³×C₃×C₅	—	2	1	no	—
74	C₂³×C₃×C₅	—	2	2	no	—
75	C₂³×C₃×C₅	—	2	4	no	—
76	C₂³×C₃×C₅	—	4	2	no	—
77	C₂³×C₃×C₅	—	4	2	no	—
78	C₂³×C₃×C₅	—	4	2	no	—
79	C₂³×C₃×C₅	—	4	2	no	—
80	C₂³×C₃×C₅	—	4	2	no	—
81	C₂³×C₃×C₅	—	4	2	no	—
82	C₂³×C₃×C₅	D₈	1	2	yes	complemented
83	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
84	C₃×C₅×D₄	—	2	4	no	—
85	C₃×C₅×D₄	—	2	4	no	—
86	C₃×C₅×D₄	—	4	16	no	—
87	C₃×C₅×D₄	—	4	2	no	—
88	C₃×C₅×D₄	—	4	2	no	—
89	C₂×C₃×C₄×C₅	—	2	2	no	—
90	C₂×C₃×C₄×C₅	—	2	4	no	—
91	C₂×C₃×C₄×C₅	—	2	1	no	—
92	C₂×C₃×C₄×C₅	—	4	2	no	—
93	C₂×C₃×C₄×C₅	—	4	2	no	—
94	C₂×C₃×C₄×C₅	—	4	1	no	—
95	C₂×C₃×C₄×C₅	—	4	2	no	—
96	C₂×C₃×C₄×C₅	—	4	1	no	—
97	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
100	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
101	C₃×C₅×C₈	—	2	2	no	—
102	C₃×C₅×C₈	—	4	1	no	—
103	C₂²×C₃×D₄	—	2	2	no	—
104	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
105	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
106	C₂×C₃×D₈	—	2	4	no	—
107	C₂×C₃×D₈	—	2	2	no	—
108	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
109	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
110	C₃×#121	—	2	4	no	—
111	C₃×#121	—	2	4	no	—
112	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
113	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
114	C₃×#102	—	2	4	no	—
115	C₃×C₂²⋊C₈	—	2	2	no	—
116	C₂⁴×C₅	—	2	2	no	—
117	C₂⁴×C₅	C₃×D₄	1	1	yes	characteristic
118	C₂×C₅×D₄	—	2	8	no	—
119	C₂×C₅×D₄	—	2	2	no	—
120	C₂×C₅×D₄	—	2	2	no	—
121	C₂×C₅×D₄	—	2	2	no	—
122	C₂×C₅×D₄	—	2	2	no	—
123	C₂×C₅×D₄	—	2	2	no	—
124	C₂×C₅×D₄	—	4	4	no	—
125	C₂×C₅×D₄	—	4	4	no	—
126	C₂×C₅×D₄	C₃×D₄	1	4	yes	complemented
127	C₂²×C₄×C₅	—	2	2	no	—
128	C₂²×C₄×C₅	—	2	2	no	—
129	C₂²×C₄×C₅	—	2	2	no	—
130	C₂²×C₄×C₅	—	2	1	no	—
131	C₂²×C₄×C₅	—	2	1	no	—
132	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
134	C₅×D₈	—	2	8	no	—
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	—	2	1	no	—
137	C₂×C₅×C₈	—	2	2	no	—
138	C₂×C₅×C₈	C₃×D₄	1	2	yes	complemented
139	C₅×C₄⋊C₄	—	2	2	no	—
140	C₅×C₄⋊C₄	C₃×D₄	1	4	yes	complemented
141	C₅×C₂²⋊C₄	—	2	8	no	—
142	C₂²×D₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
143	C₂×#121	C₂×C₃×C₅	1	2	yes	complemented
144	C₂×#102	C₂×C₃×C₅	1	2	yes	complemented
145	C₂×C₂²⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
146	#340	C₂×C₃×C₅	1	1	yes	characteristic, complemented
147	C₂²×C₃×C₅	—	2	4	no	—
148	C₂²×C₃×C₅	—	2	2	no	—
149	C₂²×C₃×C₅	—	4	1	no	—
150	C₂²×C₃×C₅	—	4	2	no	—
151	C₂²×C₃×C₅	—	4	1	no	—
152	C₂²×C₃×C₅	—	4	4	no	—
153	C₂²×C₃×C₅	—	4	4	no	—
154	C₂²×C₃×C₅	—	4	4	no	—
155	C₂²×C₃×C₅	—	8	2	no	—
156	C₂²×C₃×C₅	—	8	2	no	—
157	C₂²×C₃×C₅	—	8	2	no	—
158	C₂²×C₃×C₅	—	8	2	no	—
159	C₂²×C₃×C₅	#120	1	2	yes	—
160	C₂²×C₃×C₅	#121	1	1	yes	characteristic
161	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
162	C₂²×C₃×C₅	#135	1	1	yes	characteristic
163	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
164	C₃×C₄×C₅	—	4	1	no	—
165	C₃×C₄×C₅	—	4	4	no	—
166	C₃×C₄×C₅	#120	1	1	yes	characteristic
167	C₃×C₄×C₅	#121	1	2	yes	—
168	C₃×C₄×C₅	#127	1	1	yes	characteristic
169	C₂⁴×C₃	—	2	2	no	—
170	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
171	C₂×C₃×D₄	—	2	8	no	—
172	C₂×C₃×D₄	—	2	2	no	—
173	C₂×C₃×D₄	—	2	2	no	—
174	C₂×C₃×D₄	—	2	2	no	—
175	C₂×C₃×D₄	—	2	2	no	—
176	C₂×C₃×D₄	—	2	2	no	—
177	C₂×C₃×D₄	—	4	4	no	—
178	C₂×C₃×D₄	—	4	4	no	—
179	C₂×C₃×D₄	C₅×D₄	1	4	yes	complemented
180	C₂²×C₃×C₄	—	2	2	no	—
181	C₂²×C₃×C₄	—	2	1	no	—
182	C₂²×C₃×C₄	—	2	2	no	—
183	C₂²×C₃×C₄	—	2	2	no	—
184	C₂²×C₃×C₄	—	2	1	no	—
185	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
186	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
187	C₃×D₈	—	2	8	no	—
188	C₂×C₃×C₈	—	2	2	no	—
189	C₂×C₃×C₈	—	2	1	no	—
190	C₂×C₃×C₈	—	2	2	no	—
191	C₂×C₃×C₈	C₅×D₄	1	2	yes	complemented
192	C₃×C₄⋊C₄	—	2	2	no	—
193	C₃×C₄⋊C₄	C₅×D₄	1	4	yes	complemented
194	C₃×C₂²⋊C₄	—	2	8	no	—
195	C₂³×C₅	—	2	2	no	—
196	C₂³×C₅	—	2	1	no	—
197	C₂³×C₅	—	2	1	no	—
198	C₂³×C₅	—	2	2	no	—
199	C₂³×C₅	—	2	4	no	—
200	C₂³×C₅	—	4	2	no	—
201	C₂³×C₅	—	4	2	no	—
202	C₂³×C₅	—	4	2	no	—
203	C₂³×C₅	—	4	2	no	—
204	C₂³×C₅	—	4	2	no	—
205	C₂³×C₅	—	4	2	no	—
206	C₂³×C₅	C₃×D₈	1	2	yes	complemented
207	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
208	C₅×D₄	—	2	4	no	—
209	C₅×D₄	—	2	4	no	—
210	C₅×D₄	—	4	16	no	—
211	C₅×D₄	—	4	2	no	—
212	C₅×D₄	—	4	2	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	2	4	no	—
215	C₂×C₄×C₅	—	2	1	no	—
216	C₂×C₄×C₅	—	4	2	no	—
217	C₂×C₄×C₅	—	4	2	no	—
218	C₂×C₄×C₅	—	4	1	no	—
219	C₂×C₄×C₅	—	4	2	no	—
220	C₂×C₄×C₅	—	4	1	no	—
221	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
222	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
223	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
224	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
225	C₅×C₈	—	2	2	no	—
226	C₅×C₈	—	4	1	no	—
227	C₂²×D₄	—	2	2	no	—
228	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
229	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
230	C₂×D₈	—	2	4	no	—
231	C₂×D₈	—	2	2	no	—
232	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
233	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
234	#121	—	2	4	no	—
235	#121	—	2	4	no	—
236	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
237	C₂×C₂²⋊C₄	—	2	2	no	—
238	#102	—	2	4	no	—
239	C₂²⋊C₈	—	2	2	no	—
240	C₂×C₃×C₅	—	4	2	no	—
241	C₂×C₃×C₅	—	8	4	no	—
242	C₂×C₃×C₅	#392	1	1	yes	characteristic
243	C₂×C₃×C₅	#447	1	2	yes	—
244	C₂×C₃×C₅	#449	1	2	yes	—
245	C₂×C₃×C₅	#466	1	1	yes	characteristic
246	C₂×C₃×C₅	#469	1	1	yes	characteristic
247	C₂³×C₃	—	2	2	no	—
248	C₂³×C₃	—	2	1	no	—
249	C₂³×C₃	—	2	1	no	—
250	C₂³×C₃	—	2	2	no	—
251	C₂³×C₃	—	2	4	no	—
252	C₂³×C₃	—	4	2	no	—
253	C₂³×C₃	—	4	2	no	—
254	C₂³×C₃	—	4	2	no	—
255	C₂³×C₃	—	4	2	no	—
256	C₂³×C₃	—	4	2	no	—
257	C₂³×C₃	—	4	2	no	—
258	C₂³×C₃	C₅×D₈	1	2	yes	complemented
259	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
260	C₃×D₄	—	2	4	no	—
261	C₃×D₄	—	2	4	no	—
262	C₃×D₄	—	4	16	no	—
263	C₃×D₄	—	4	2	no	—
264	C₃×D₄	—	4	2	no	—
265	C₂×C₃×C₄	—	2	2	no	—
266	C₂×C₃×C₄	—	2	4	no	—
267	C₂×C₃×C₄	—	2	1	no	—
268	C₂×C₃×C₄	—	4	2	no	—
269	C₂×C₃×C₄	—	4	2	no	—
270	C₂×C₃×C₄	—	4	1	no	—
271	C₂×C₃×C₄	—	4	2	no	—
272	C₂×C₃×C₄	—	4	1	no	—
273	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
274	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
275	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
276	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
277	C₃×C₈	—	2	2	no	—
278	C₃×C₈	—	4	1	no	—
279	C₂²×C₅	—	2	4	no	—
280	C₂²×C₅	—	2	2	no	—
281	C₂²×C₅	—	4	1	no	—
282	C₂²×C₅	—	4	2	no	—
283	C₂²×C₅	—	4	1	no	—
284	C₂²×C₅	—	4	4	no	—
285	C₂²×C₅	—	4	4	no	—
286	C₂²×C₅	—	4	4	no	—
287	C₂²×C₅	—	8	2	no	—
288	C₂²×C₅	—	8	2	no	—
289	C₂²×C₅	—	8	2	no	—
290	C₂²×C₅	—	8	2	no	—
291	C₂²×C₅	C₃×#120	1	2	yes	—
292	C₂²×C₅	C₃×#121	1	1	yes	characteristic
293	C₂²×C₅	C₂×C₃×D₈	1	1	yes	characteristic
294	C₂²×C₅	C₃×#135	1	1	yes	characteristic
295	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
296	C₄×C₅	—	4	1	no	—
297	C₄×C₅	—	4	4	no	—
298	C₄×C₅	C₃×#120	1	1	yes	characteristic
299	C₄×C₅	C₃×#121	1	2	yes	—
300	C₄×C₅	C₃×#127	1	1	yes	characteristic
301	C₂⁴	—	2	2	no	—
302	C₂⁴	C₃×C₅×D₄	1	1	yes	characteristic
303	C₂×D₄	—	2	8	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	4	4	no	—
310	C₂×D₄	—	4	4	no	—
311	C₂×D₄	C₃×C₅×D₄	1	4	yes	complemented
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
318	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
319	D₈	—	2	8	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	C₃×C₅×D₄	1	2	yes	complemented
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	C₃×C₅×D₄	1	4	yes	complemented
326	C₂²⋊C₄	—	2	8	no	—
327	C₃×C₅	#1999	1	1	yes	characteristic, direct product factor, Hall
328	C₂²×C₃	—	2	4	no	—
329	C₂²×C₃	—	2	2	no	—
330	C₂²×C₃	—	4	1	no	—
331	C₂²×C₃	—	4	2	no	—
332	C₂²×C₃	—	4	1	no	—
333	C₂²×C₃	—	4	4	no	—
334	C₂²×C₃	—	4	4	no	—
335	C₂²×C₃	—	4	4	no	—
336	C₂²×C₃	—	8	2	no	—
337	C₂²×C₃	—	8	2	no	—
338	C₂²×C₃	—	8	2	no	—
339	C₂²×C₃	—	8	2	no	—
340	C₂²×C₃	C₅×#120	1	2	yes	—
341	C₂²×C₃	C₅×#121	1	1	yes	characteristic
342	C₂²×C₃	C₂×C₅×D₈	1	1	yes	characteristic
343	C₂²×C₃	C₅×#135	1	1	yes	characteristic
344	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
345	C₃×C₄	—	4	1	no	—
346	C₃×C₄	—	4	4	no	—
347	C₃×C₄	C₅×#120	1	1	yes	characteristic
348	C₃×C₄	C₅×#121	1	2	yes	—
349	C₃×C₄	C₅×#127	1	1	yes	characteristic
350	C₂×C₅	—	4	2	no	—
351	C₂×C₅	—	8	4	no	—
352	C₂×C₅	C₃×#392	1	1	yes	characteristic
353	C₂×C₅	C₃×#447	1	2	yes	—
354	C₂×C₅	C₃×#449	1	2	yes	—
355	C₂×C₅	C₃×#466	1	1	yes	characteristic
356	C₂×C₅	C₃×#469	1	1	yes	characteristic
357	C₂³	—	2	2	no	—
358	C₂³	—	2	1	no	—
359	C₂³	—	2	1	no	—
360	C₂³	—	2	2	no	—
361	C₂³	—	2	4	no	—
362	C₂³	—	4	2	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	2	no	—
367	C₂³	—	4	2	no	—
368	C₂³	C₃×C₅×D₈	1	2	yes	complemented
369	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
370	D₄	—	2	4	no	—
371	D₄	—	2	4	no	—
372	D₄	—	4	16	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
384	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
385	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
386	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
387	C₈	—	2	2	no	—
388	C₈	—	4	1	no	—
389	C₂×C₃	—	4	2	no	—
390	C₂×C₃	—	8	4	no	—
391	C₂×C₃	C₅×#392	1	1	yes	characteristic
392	C₂×C₃	C₅×#447	1	2	yes	—
393	C₂×C₃	C₅×#449	1	2	yes	—
394	C₂×C₃	C₅×#466	1	1	yes	characteristic
395	C₂×C₃	C₅×#469	1	1	yes	characteristic
396	C₅	C₃×#1999	1	1	yes	characteristic, direct product factor, Sylow
397	C₂²	—	2	2	no	—
398	C₂²	—	2	4	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	4	no	—
403	C₂²	—	4	4	no	—
404	C₂²	—	4	4	no	—
405	C₂²	—	8	2	no	—
406	C₂²	—	8	2	no	—
407	C₂²	—	8	2	no	—
408	C₂²	—	8	2	no	—
409	C₂²	C₃×C₅×#120	1	2	yes	—
410	C₂²	C₃×C₅×#121	1	1	yes	characteristic
411	C₂²	C₂×C₃×C₅×D₈	1	1	yes	characteristic
412	C₂²	C₃×C₅×#135	1	1	yes	characteristic
413	C₂²	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
414	C₄	—	4	1	no	—
415	C₄	—	4	4	no	—
416	C₄	C₃×C₅×#120	1	1	yes	characteristic
417	C₄	C₃×C₅×#121	1	2	yes	—
418	C₄	C₃×C₅×#127	1	1	yes	characteristic
419	C₃	C₅×#1999	1	1	yes	characteristic, direct product factor, Sylow
420	C₂	—	4	2	no	—
421	C₂	—	8	4	no	—
422	C₂	C₃×C₅×#392	1	1	yes	characteristic
423	C₂	C₃×C₅×#447	1	2	yes	—
424	C₂	C₃×C₅×#449	1	2	yes	—
425	C₂	C₃×C₅×#466	1	1	yes	characteristic
426	C₂	C₃×C₅×#469	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ C₂³×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×D₈	C₂	semidirect
2. C₂×C₃×C₅×#121	C₂	semidirect
3. C₂×C₃×C₅×#102	C₂	semidirect
4. C₂×C₃×C₅×C₂²⋊C₈	C₂	semidirect
5. C₃×C₅×#340	C₂	semidirect
6. C₅×#1999	C₃	direct (N × H)
20. C₃×#1999	C₅	direct (N × H)
21. C₂²×C₅×D₈	C₂×C₃	semidirect
22. C₂×C₅×#121	C₂×C₃	semidirect
23. C₂×C₅×#102	C₂×C₃	semidirect
24. C₂×C₅×C₂²⋊C₈	C₂×C₃	semidirect
25. C₅×#340	C₂×C₃	semidirect
36. C₂×C₃×C₅×D₄	D₄	semidirect
48. C₂×C₃×C₅×C₈	D₄	semidirect
50. C₃×C₅×C₄⋊C₄	D₄	semidirect
52. C₂²×C₃×D₈	C₂×C₅	semidirect
53. C₂×C₃×#121	C₂×C₅	semidirect
54. C₂×C₃×#102	C₂×C₅	semidirect
55. C₂×C₃×C₂²⋊C₈	C₂×C₅	semidirect
56. C₃×#340	C₂×C₅	semidirect
70. #1999	C₃×C₅	direct (N × H)
82. C₂³×C₃×C₅	D₈	semidirect
126. C₂×C₅×D₄	C₃×D₄	semidirect
138. C₂×C₅×C₈	C₃×D₄	semidirect
140. C₅×C₄⋊C₄	C₃×D₄	semidirect
142. C₂²×D₈	C₂×C₃×C₅	semidirect
143. C₂×#121	C₂×C₃×C₅	semidirect
144. C₂×#102	C₂×C₃×C₅	semidirect
145. C₂×C₂²⋊C₈	C₂×C₃×C₅	semidirect
146. #340	C₂×C₃×C₅	semidirect
179. C₂×C₃×D₄	C₅×D₄	semidirect
191. C₂×C₃×C₈	C₅×D₄	semidirect
193. C₃×C₄⋊C₄	C₅×D₄	semidirect
206. C₂³×C₅	C₃×D₈	semidirect
258. C₂³×C₃	C₅×D₈	semidirect
311. C₂×D₄	C₃×C₅×D₄	semidirect
323. C₂×C₈	C₃×C₅×D₄	semidirect
325. C₄⋊C₄	C₃×C₅×D₄	semidirect
327. C₃×C₅	#1999	direct (N × H)
368. C₂³	C₃×C₅×D₈	semidirect
396. C₅	C₃×#1999	direct (N × H)
419. C₃	C₅×#1999	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₅×D₈	2
C₂×C₃×C₅×#121	2
C₂×C₃×C₅×#102	2
C₂×C₃×C₅×C₂²⋊C₈	2
C₃×C₅×#340	2
C₅×#1999	3
C₃×#1999	5

Subgroups — C3×C5×#1999 #14275033

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1999 #14275033