Subgroups — C₃×C₅×#2006 #14275040

Order 1920.

812 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#537	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#104	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#343	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2006	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
8	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
9	C₃×C₅×AGL(1,ℤ/8)	—	2	4	no	—
10	C₃×C₅×AGL(1,ℤ/8)	—	2	4	no	—
11	C₂×C₃×C₅×SD₁₆	—	2	2	no	—
12	C₂×C₃×C₅×D₈	—	2	2	no	—
13	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
14	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
15	C₃×C₅×#121	—	2	2	no	—
16	C₃×C₅×#121	—	2	2	no	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
19	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
20	C₃×C₅×#104	—	2	4	no	—
21	C₃×#2006	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	1	2	yes	complemented
23	C₅×#537	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂×C₅×#104	C₂×C₃	1	2	yes	complemented
25	C₅×#390	C₂×C₃	1	1	yes	characteristic, complemented
26	C₅×#343	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂⁴×C₃×C₅	—	2	1	no	—
28	C₃×C₅×#41	—	2	2	no	—
29	C₃×C₅×#41	—	2	2	no	—
30	C₃×C₅×#41	—	2	2	no	—
31	C₃×C₅×#41	—	2	2	no	—
32	C₂×C₃×C₅×Q₈	D₄	1	2	yes	—
33	C₂×C₃×C₅×D₄	—	2	2	no	—
34	C₂×C₃×C₅×D₄	—	2	2	no	—
35	C₂×C₃×C₅×D₄	—	2	2	no	—
36	C₂×C₃×C₅×D₄	—	2	2	no	—
37	C₂×C₃×C₅×D₄	—	2	1	no	—
38	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
39	C₂×C₃×C₅×D₄	D₄	1	2	yes	complemented
40	C₂²×C₃×C₄×C₅	—	2	1	no	—
41	C₂²×C₃×C₄×C₅	—	2	2	no	—
42	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₃×C₅×SD₁₆	—	2	8	no	—
45	C₃×C₅×D₈	—	2	8	no	—
46	C₃×C₅×M₁₆	—	2	2	no	—
47	C₃×C₅×M₁₆	D₄	1	4	yes	complemented
48	C₂×C₃×C₅×C₈	—	2	2	no	—
49	C₃×C₅×C₄⋊C₄	—	2	2	no	—
50	C₃×C₅×C₄⋊C₄	—	2	2	no	—
51	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
52	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
53	C₃×C₄²×C₅	—	2	2	no	—
54	C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	1	2	yes	complemented
55	C₃×#537	C₂×C₅	1	1	yes	characteristic, complemented
56	C₂×C₃×#104	C₂×C₅	1	2	yes	complemented
57	C₃×#390	C₂×C₅	1	1	yes	characteristic, complemented
58	C₃×#343	C₂×C₅	1	1	yes	characteristic, complemented
59	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
60	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
61	C₅×AGL(1,ℤ/8)	—	2	4	no	—
62	C₅×AGL(1,ℤ/8)	—	2	4	no	—
63	C₂×C₅×SD₁₆	—	2	2	no	—
64	C₂×C₅×D₈	—	2	2	no	—
65	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
66	C₅×C₂²⋊Q₈	—	2	2	no	—
67	C₅×#121	—	2	2	no	—
68	C₅×#121	—	2	2	no	—
69	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
70	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
72	C₅×#104	—	2	4	no	—
73	#2006	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
74	C₂³×C₃×C₅	—	2	2	no	—
75	C₂³×C₃×C₅	—	2	2	no	—
76	C₂³×C₃×C₅	—	4	2	no	—
77	C₂³×C₃×C₅	—	4	2	no	—
78	C₂³×C₃×C₅	—	4	1	no	—
79	C₂³×C₃×C₅	—	4	1	no	—
80	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
81	C₃×C₅×Q₈	—	2	2	no	—
82	C₃×C₅×Q₈	—	2	2	no	—
83	C₃×C₅×D₄	—	2	2	no	—
84	C₃×C₅×D₄	—	2	4	no	—
85	C₃×C₅×D₄	—	2	2	no	—
86	C₃×C₅×D₄	—	4	2	no	—
87	C₃×C₅×D₄	—	4	2	no	—
88	C₃×C₅×D₄	—	4	2	no	—
89	C₃×C₅×D₄	—	8	2	no	—
90	C₂×C₃×C₄×C₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	—	2	2	no	—
92	C₂×C₃×C₄×C₅	—	2	2	no	—
93	C₂×C₃×C₄×C₅	—	4	1	no	—
94	C₂×C₃×C₄×C₅	—	4	1	no	—
95	C₂×C₃×C₄×C₅	—	4	2	no	—
96	C₂×C₃×C₄×C₅	—	4	2	no	—
97	C₂×C₃×C₄×C₅	—	4	2	no	—
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	C₂×D₄	1	2	yes	—
101	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
102	C₃×C₅×C₈	—	2	4	no	—
103	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
104	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
105	C₃×AGL(1,ℤ/8)	—	2	4	no	—
106	C₃×AGL(1,ℤ/8)	—	2	4	no	—
107	C₂×C₃×SD₁₆	—	2	2	no	—
108	C₂×C₃×D₈	—	2	2	no	—
109	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
110	C₃×C₂²⋊Q₈	—	2	2	no	—
111	C₃×#121	—	2	2	no	—
112	C₃×#121	—	2	2	no	—
113	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
114	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
115	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
116	C₃×#104	—	2	4	no	—
117	C₂⁴×C₅	—	2	1	no	—
118	C₅×#41	—	2	2	no	—
119	C₅×#41	—	2	2	no	—
120	C₅×#41	—	2	2	no	—
121	C₅×#41	—	2	2	no	—
122	C₂×C₅×Q₈	C₃×D₄	1	2	yes	—
123	C₂×C₅×D₄	—	2	2	no	—
124	C₂×C₅×D₄	—	2	2	no	—
125	C₂×C₅×D₄	—	2	2	no	—
126	C₂×C₅×D₄	—	2	2	no	—
127	C₂×C₅×D₄	—	2	1	no	—
128	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
129	C₂×C₅×D₄	C₃×D₄	1	2	yes	complemented
130	C₂²×C₄×C₅	—	2	1	no	—
131	C₂²×C₄×C₅	—	2	2	no	—
132	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
133	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
134	C₅×SD₁₆	—	2	8	no	—
135	C₅×D₈	—	2	8	no	—
136	C₅×M₁₆	—	2	2	no	—
137	C₅×M₁₆	C₃×D₄	1	4	yes	complemented
138	C₂×C₅×C₈	—	2	2	no	—
139	C₅×C₄⋊C₄	—	2	2	no	—
140	C₅×C₄⋊C₄	—	2	2	no	—
141	C₅×C₂²⋊C₄	—	2	4	no	—
142	C₅×C₂²⋊C₄	—	4	4	no	—
143	C₄²×C₅	—	2	2	no	—
144	C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	1	2	yes	complemented
145	#537	C₂×C₃×C₅	1	1	yes	characteristic, complemented
146	C₂×#104	C₂×C₃×C₅	1	2	yes	complemented
147	#390	C₂×C₃×C₅	1	1	yes	characteristic, complemented
148	#343	C₂×C₃×C₅	1	1	yes	characteristic, complemented
149	C₂²×C₃×C₅	—	2	1	no	—
150	C₂²×C₃×C₅	—	2	1	no	—
151	C₂²×C₃×C₅	—	4	4	no	—
152	C₂²×C₃×C₅	—	4	2	no	—
153	C₂²×C₃×C₅	—	4	2	no	—
154	C₂²×C₃×C₅	—	4	2	no	—
155	C₂²×C₃×C₅	—	4	2	no	—
156	C₂²×C₃×C₅	—	8	2	no	—
157	C₂²×C₃×C₅	—	8	1	no	—
158	C₂²×C₃×C₅	—	8	1	no	—
159	C₂²×C₃×C₅	#120	1	1	yes	characteristic
160	C₂²×C₃×C₅	#121	1	1	yes	characteristic
161	C₂²×C₃×C₅	#127	1	1	yes	characteristic
162	C₃×C₄×C₅	—	4	2	no	—
163	C₃×C₄×C₅	—	4	2	no	—
164	C₃×C₄×C₅	—	4	2	no	—
165	C₃×C₄×C₅	#120	1	2	yes	—
166	C₃×C₄×C₅	#121	1	2	yes	—
167	C₂⁴×C₃	—	2	1	no	—
168	C₃×#41	—	2	2	no	—
169	C₃×#41	—	2	2	no	—
170	C₃×#41	—	2	2	no	—
171	C₃×#41	—	2	2	no	—
172	C₂×C₃×Q₈	C₅×D₄	1	2	yes	—
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	—	2	1	no	—
178	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
179	C₂×C₃×D₄	C₅×D₄	1	2	yes	complemented
180	C₂²×C₃×C₄	—	2	1	no	—
181	C₂²×C₃×C₄	—	2	2	no	—
182	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
183	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
184	C₃×SD₁₆	—	2	8	no	—
185	C₃×D₈	—	2	8	no	—
186	C₃×M₁₆	—	2	2	no	—
187	C₃×M₁₆	C₅×D₄	1	4	yes	complemented
188	C₂×C₃×C₈	—	2	2	no	—
189	C₃×C₄⋊C₄	—	2	2	no	—
190	C₃×C₄⋊C₄	—	2	2	no	—
191	C₃×C₂²⋊C₄	—	2	4	no	—
192	C₃×C₂²⋊C₄	—	4	4	no	—
193	C₃×C₄²	—	2	2	no	—
194	C₂³×C₅	—	2	2	no	—
195	C₂³×C₅	—	2	2	no	—
196	C₂³×C₅	—	4	2	no	—
197	C₂³×C₅	—	4	2	no	—
198	C₂³×C₅	—	4	1	no	—
199	C₂³×C₅	—	4	1	no	—
200	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
201	C₅×Q₈	—	2	2	no	—
202	C₅×Q₈	—	2	2	no	—
203	C₅×D₄	—	2	2	no	—
204	C₅×D₄	—	2	4	no	—
205	C₅×D₄	—	2	2	no	—
206	C₅×D₄	—	4	2	no	—
207	C₅×D₄	—	4	2	no	—
208	C₅×D₄	—	4	2	no	—
209	C₅×D₄	—	8	2	no	—
210	C₂×C₄×C₅	—	2	2	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	2	2	no	—
213	C₂×C₄×C₅	—	4	1	no	—
214	C₂×C₄×C₅	—	4	1	no	—
215	C₂×C₄×C₅	—	4	2	no	—
216	C₂×C₄×C₅	—	4	2	no	—
217	C₂×C₄×C₅	—	4	2	no	—
218	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
220	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
221	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
222	C₅×C₈	—	2	4	no	—
223	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
224	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
225	AGL(1,ℤ/8)	—	2	4	no	—
226	AGL(1,ℤ/8)	—	2	4	no	—
227	C₂×SD₁₆	—	2	2	no	—
228	C₂×D₈	—	2	2	no	—
229	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
230	C₂²⋊Q₈	—	2	2	no	—
231	#121	—	2	2	no	—
232	#121	—	2	2	no	—
233	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
234	C₂×C₂²⋊C₄	—	2	2	no	—
235	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
236	#104	—	2	4	no	—
237	C₂×C₃×C₅	—	2	1	no	—
238	C₂×C₃×C₅	—	2	1	no	—
239	C₂×C₃×C₅	—	8	2	no	—
240	C₂×C₃×C₅	—	8	2	no	—
241	C₂×C₃×C₅	#392	1	1	yes	characteristic
242	C₂×C₃×C₅	#453	1	1	yes	characteristic
243	C₂×C₃×C₅	#454	1	1	yes	characteristic
244	C₂³×C₃	—	2	2	no	—
245	C₂³×C₃	—	2	2	no	—
246	C₂³×C₃	—	4	2	no	—
247	C₂³×C₃	—	4	2	no	—
248	C₂³×C₃	—	4	1	no	—
249	C₂³×C₃	—	4	1	no	—
250	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
251	C₃×Q₈	—	2	2	no	—
252	C₃×Q₈	—	2	2	no	—
253	C₃×D₄	—	2	2	no	—
254	C₃×D₄	—	2	4	no	—
255	C₃×D₄	—	2	2	no	—
256	C₃×D₄	—	4	2	no	—
257	C₃×D₄	—	4	2	no	—
258	C₃×D₄	—	4	2	no	—
259	C₃×D₄	—	8	2	no	—
260	C₂×C₃×C₄	—	2	2	no	—
261	C₂×C₃×C₄	—	2	2	no	—
262	C₂×C₃×C₄	—	2	2	no	—
263	C₂×C₃×C₄	—	4	1	no	—
264	C₂×C₃×C₄	—	4	1	no	—
265	C₂×C₃×C₄	—	4	2	no	—
266	C₂×C₃×C₄	—	4	2	no	—
267	C₂×C₃×C₄	—	4	2	no	—
268	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
269	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
270	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
271	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
272	C₃×C₈	—	2	4	no	—
273	C₂²×C₅	—	2	1	no	—
274	C₂²×C₅	—	2	1	no	—
275	C₂²×C₅	—	4	4	no	—
276	C₂²×C₅	—	4	2	no	—
277	C₂²×C₅	—	4	2	no	—
278	C₂²×C₅	—	4	2	no	—
279	C₂²×C₅	—	4	2	no	—
280	C₂²×C₅	—	8	2	no	—
281	C₂²×C₅	—	8	1	no	—
282	C₂²×C₅	—	8	1	no	—
283	C₂²×C₅	C₃×#120	1	1	yes	characteristic
284	C₂²×C₅	C₃×#121	1	1	yes	characteristic
285	C₂²×C₅	C₃×#127	1	1	yes	characteristic
286	C₄×C₅	—	4	2	no	—
287	C₄×C₅	—	4	2	no	—
288	C₄×C₅	—	4	2	no	—
289	C₄×C₅	C₃×#120	1	2	yes	—
290	C₄×C₅	C₃×#121	1	2	yes	—
291	C₂⁴	—	2	1	no	—
292	#41	—	2	2	no	—
293	#41	—	2	2	no	—
294	#41	—	2	2	no	—
295	#41	—	2	2	no	—
296	C₂×Q₈	C₃×C₅×D₄	1	2	yes	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	C₃×C₅×D₄	1	2	yes	—
303	C₂×D₄	C₃×C₅×D₄	1	2	yes	complemented
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
307	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
308	SD₁₆	—	2	8	no	—
309	D₈	—	2	8	no	—
310	M₁₆	—	2	2	no	—
311	M₁₆	C₃×C₅×D₄	1	4	yes	complemented
312	C₂×C₈	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₂²⋊C₄	—	2	4	no	—
316	C₂²⋊C₄	—	4	4	no	—
317	C₄²	—	2	2	no	—
318	C₃×C₅	#2006	1	1	yes	characteristic, direct product factor, Hall
319	C₂²×C₃	—	2	1	no	—
320	C₂²×C₃	—	2	1	no	—
321	C₂²×C₃	—	4	4	no	—
322	C₂²×C₃	—	4	2	no	—
323	C₂²×C₃	—	4	2	no	—
324	C₂²×C₃	—	4	2	no	—
325	C₂²×C₃	—	4	2	no	—
326	C₂²×C₃	—	8	2	no	—
327	C₂²×C₃	—	8	1	no	—
328	C₂²×C₃	—	8	1	no	—
329	C₂²×C₃	C₅×#120	1	1	yes	characteristic
330	C₂²×C₃	C₅×#121	1	1	yes	characteristic
331	C₂²×C₃	C₅×#127	1	1	yes	characteristic
332	C₃×C₄	—	4	2	no	—
333	C₃×C₄	—	4	2	no	—
334	C₃×C₄	—	4	2	no	—
335	C₃×C₄	C₅×#120	1	2	yes	—
336	C₃×C₄	C₅×#121	1	2	yes	—
337	C₂×C₅	—	2	1	no	—
338	C₂×C₅	—	2	1	no	—
339	C₂×C₅	—	8	2	no	—
340	C₂×C₅	—	8	2	no	—
341	C₂×C₅	C₃×#392	1	1	yes	characteristic
342	C₂×C₅	C₃×#453	1	1	yes	characteristic
343	C₂×C₅	C₃×#454	1	1	yes	characteristic
344	C₂³	—	2	2	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	4	1	no	—
349	C₂³	—	4	1	no	—
350	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
351	Q₈	—	2	2	no	—
352	Q₈	—	2	2	no	—
353	D₄	—	2	2	no	—
354	D₄	—	2	4	no	—
355	D₄	—	2	2	no	—
356	D₄	—	4	2	no	—
357	D₄	—	4	2	no	—
358	D₄	—	4	2	no	—
359	D₄	—	8	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
369	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
370	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
371	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
372	C₈	—	2	4	no	—
373	C₂×C₃	—	2	1	no	—
374	C₂×C₃	—	2	1	no	—
375	C₂×C₃	—	8	2	no	—
376	C₂×C₃	—	8	2	no	—
377	C₂×C₃	C₅×#392	1	1	yes	characteristic
378	C₂×C₃	C₅×#453	1	1	yes	characteristic
379	C₂×C₃	C₅×#454	1	1	yes	characteristic
380	C₅	C₃×#2006	1	1	yes	characteristic, direct product factor, Sylow
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	4	2	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	8	1	no	—
390	C₂²	—	8	1	no	—
391	C₂²	C₃×C₅×#120	1	1	yes	characteristic
392	C₂²	C₃×C₅×#121	1	1	yes	characteristic
393	C₂²	C₃×C₅×#127	1	1	yes	characteristic
394	C₄	—	4	2	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	2	no	—
397	C₄	C₃×C₅×#120	1	2	yes	—
398	C₄	C₃×C₅×#121	1	2	yes	—
399	C₃	C₅×#2006	1	1	yes	characteristic, direct product factor, Sylow
400	C₂	—	2	1	no	—
401	C₂	—	2	1	no	—
402	C₂	—	8	2	no	—
403	C₂	—	8	2	no	—
404	C₂	C₃×C₅×#392	1	1	yes	characteristic
405	C₂	C₃×C₅×#453	1	1	yes	characteristic
406	C₂	C₃×C₅×#454	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂²×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	semidirect
2. C₃×C₅×#537	C₂	semidirect
3. C₂×C₃×C₅×#104	C₂	semidirect
4. C₃×C₅×#390	C₂	semidirect
5. C₃×C₅×#343	C₂	semidirect
6. C₅×#2006	C₃	direct (N × H)
21. C₃×#2006	C₅	direct (N × H)
22. C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	semidirect
23. C₅×#537	C₂×C₃	semidirect
24. C₂×C₅×#104	C₂×C₃	semidirect
25. C₅×#390	C₂×C₃	semidirect
26. C₅×#343	C₂×C₃	semidirect
39. C₂×C₃×C₅×D₄	D₄	semidirect
47. C₃×C₅×M₁₆	D₄	semidirect
54. C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	semidirect
55. C₃×#537	C₂×C₅	semidirect
56. C₂×C₃×#104	C₂×C₅	semidirect
57. C₃×#390	C₂×C₅	semidirect
58. C₃×#343	C₂×C₅	semidirect
73. #2006	C₃×C₅	direct (N × H)
129. C₂×C₅×D₄	C₃×D₄	semidirect
137. C₅×M₁₆	C₃×D₄	semidirect
144. C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	semidirect
145. #537	C₂×C₃×C₅	semidirect
146. C₂×#104	C₂×C₃×C₅	semidirect
147. #390	C₂×C₃×C₅	semidirect
148. #343	C₂×C₃×C₅	semidirect
179. C₂×C₃×D₄	C₅×D₄	semidirect
187. C₃×M₁₆	C₅×D₄	semidirect
303. C₂×D₄	C₃×C₅×D₄	semidirect
311. M₁₆	C₃×C₅×D₄	semidirect
318. C₃×C₅	#2006	direct (N × H)
380. C₅	C₃×#2006	direct (N × H)
399. C₃	C₅×#2006	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×AGL(1,ℤ/8)	2
C₃×C₅×#537	2
C₂×C₃×C₅×#104	2
C₃×C₅×#390	2
C₃×C₅×#343	2
C₅×#2006	3
C₃×#2006	5

Subgroups — C3×C5×#2006 #14275040

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2006 #14275040